Finite Group Databasebeta

← #15629365

Subgroups — #15629365

Order 2816.

3230 conjugacy classes of subgroups.

The subgroup lattice has 1674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66961C211yesmaximal, characteristic, complemented
2C2×D11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
3#13082099C211yesmaximal, characteristic, complemented
4C2×#10623140C211yesmaximal, characteristic, complemented
5#13080309C212yesmaximal, complemented
6#13080290C212yesmaximal, complemented
7#13080233C212yesmaximal, complemented
8#13080213C212yesmaximal, complemented
9#13080118C212yesmaximal, complemented
10#13080108C212yesmaximal, complemented
11#13080103C212yesmaximal, complemented
12#13080093C212yesmaximal, complemented
13#13079064C211yesmaximal, characteristic, complemented
14#13078236C211yesmaximal, characteristic, complemented
15#13078095C211yesmaximal, characteristic, complemented
16#13078079C211yesmaximal, characteristic, complemented
17#13077869C211yesmaximal, characteristic, complemented
18#13077866C211yesmaximal, characteristic, complemented
19#13077845C211yesmaximal, characteristic, complemented
20#13077842C211yesmaximal, characteristic, complemented
21#13077423C211yesmaximal, characteristic, complemented
22M16×C22⋊D11C211yesmaximal, characteristic, complemented
23C11×#3055C211yesmaximal, characteristic, complemented
24C2×#41×D11C2211yescharacteristic, complemented
25C22×D4×D11—21no—
26C22×D4×D11C2211yescharacteristic, complemented
27C22×#4339C2211yescharacteristic, complemented
28C23×D44C2211yescharacteristic, complemented
29C2×C11×AGL(1,ℤ/8)C2211yescharacteristic, complemented
30C22×C11×M16C2211yescharacteristic, complemented
31C11×#525C2211yescharacteristic, complemented
32C2×C11×#121C2211yescharacteristic, complemented
33#10623363C2211yescharacteristic, complemented
34C2×#67002C2211yescharacteristic, complemented
35C2×#67002C2211yescharacteristic, complemented
36C2×#66993C2211yescharacteristic, complemented
37C2×#66990—21no—
38C2×#66985C2211yescharacteristic, complemented
39C2×#66985C2211yescharacteristic, complemented
40C2×C4×C22⋊D11C2211yescharacteristic
41D11×AGL(1,ℤ/8)—28no—
42C2×#66967C2212yescomplemented
43C2×SD16×D11C2212yescomplemented
44C2×#66964C2212yescomplemented
45C2×D8×D11C2212yescomplemented
46C2×#66961—28no—
47C2×#66961C2211yescharacteristic
48C2×#66961C2211yescharacteristic, complemented
49C2×#66961C2212yescomplemented
50C2×#66961C2212yescomplemented
51C2×#66961C2211yescharacteristic, complemented
52C2×#66961C2211yescharacteristic, complemented
53C2×M16×D11C2211yescharacteristic, complemented
54C22×D88C2212yescomplemented
55C22×#4314C2212yescomplemented
56#10623186—21no—
57#10623185—21no—
58#10623164C2211yescharacteristic, complemented
59#10623163C2211yescharacteristic, complemented
60#10623162C2211yescharacteristic, complemented
61#10623161C2211yescharacteristic, complemented
62#10623143C2211yescharacteristic, complemented
63#10623140—21no—
64#10623140—21no—
65#10623140—21no—
66#10623140—21no—
67#10623140C2212yes—
68#10623140C2212yescomplemented
69#10623140C2212yescomplemented
70#10623140C2212yescomplemented
71#10623140C2211yescharacteristic, complemented
72#10623130C2211yescharacteristic, complemented
73#10623129C2211yescharacteristic, complemented
74#10623122—21no—
75#10623121—21no—
76#10623079—21no—
77#10623078—21no—
78#10623078—21no—
79C4×D4×D11—21no—
80#10623055C2211yescharacteristic, complemented
81#10623053C2211yescharacteristic, complemented
82C2×#66948C2211yescharacteristic, complemented
83C2×#66946C2211yescharacteristic, complemented
84C2×#66937—21no—
85C2×#66935—21no—
86C11×#469C2212yescomplemented
87C11×#468C2212yescomplemented
88C11×#466C2212yescomplemented
89C11×#465C2212yescomplemented
90C11×#428C2211yescharacteristic, complemented
91C11×#418C2211yescharacteristic, complemented
92C11×#417C2211yescharacteristic, complemented
93#10622820C2211yescharacteristic, complemented
94#10622789C2212yescomplemented
95#10622788C2212yescomplemented
96#10622767C2212yescomplemented
97#10622764C2212yescomplemented
98#10622741C2212yescomplemented
99#10622740C2212yescomplemented
100#10622739C2211yescharacteristic, complemented
101#10622731C2211yescharacteristic, complemented
102M16×Dic11C2211yescharacteristic, complemented
103#10622724C2212yescomplemented
104C8×C22⋊D11C2212yescomplemented
105#10622659C2212yescomplemented
106#10622659C2212yescomplemented
107#10622653C2212yescomplemented
108#10622650C2212yescomplemented
109#10622650C2212yescomplemented
110#10622649C2212yescomplemented
111#10622649C2212yescomplemented
112#10622649C2212yescomplemented
113#10622614C2211yescharacteristic, complemented
114#10622614C2211yescharacteristic, complemented
115#10622579C2211yescharacteristic, complemented
116#10622579C2211yescharacteristic, complemented
117#10622502C2212yescomplemented
118#10622499C2212yescomplemented
119#10622496C2212yescomplemented
120#10622485C2212yescomplemented
121#10622482C2212yescomplemented
122#10622478C2212yescomplemented
123#10622477C2212yescomplemented
124#10622465C2212yescomplemented
125#10622432C2212yescomplemented
126#10622431C2212yescomplemented
127#10622424C2212yescomplemented
128#10622419C2212yescomplemented
129#10622400C2212yescomplemented
130#10622399C2212yescomplemented
131#10622399C2212yescomplemented
132#10622399C2212yescomplemented
133#10622394C2212yescomplemented
134#10622389C2212yescomplemented
135#10622389C2212yescomplemented
136#10622386C2212yescomplemented
137#10622386C2212yescomplemented
138#10622386C2212yescomplemented
139#10622375C2212yescomplemented
140#10622375C2212yescomplemented
141C24×D11—21no—
142C24×D11—21no—
143C2×C11×#41C2311yescharacteristic
144C22×D4×C11—21no—
145C22×D4×C11C2311yescharacteristic
146C23×C4×C11C2311yescharacteristic
147C22×C22⋊D11—21no—
148C22×C22⋊D11—21no—
149C22×C22⋊D11—21no—
150C22×C22⋊D11—21no—
151C22×C22⋊D11D411yescharacteristic
152#41×D11—24no—
153#41×D11—42no—
154C2×#4343C2311yescharacteristic, complemented
155C2×Q8×D11C2311yescharacteristic, complemented
156C2×#4341—21no—
157C2×#4341C2311yescharacteristic, complemented
158C2×D4×D11—21no—
159C2×D4×D11—21no—
160C2×D4×D11—22no—
161C2×D4×D11—22no—
162C2×D4×D11—22no—
163C2×D4×D11—22no—
164C2×D4×D11—24no—
165C2×D4×D11—21no—
166C2×D4×D11—21no—
167C2×D4×D11—42no—
168C2×D4×D11—48no—
169C2×D4×D11C2312yes—
170C2×D4×D11C2312yes—
171C2×D4×D11C2311yescharacteristic, complemented
172C2×#4339—21no—
173C2×#4339—21no—
174C2×#4339—21no—
175C2×#4339—24no—
176C2×#4339—42no—
177C2×#4339C2311yescharacteristic
178C2×#4339C2311yescharacteristic
179C2×#4339C2311yescharacteristic, complemented
180C2×#4339C2311yescharacteristic, complemented
181C22×D44—24no—
182C22×D44—21no—
183C22×D44—21no—
184C22×D44—21no—
185C22×D44—21no—
186C22×D44—42no—
187C22×D44C2311yescharacteristic
188C22×D44C2312yes—
189C22×D44C2312yes—
190C22×D44C2311yescharacteristic
191C22×D44C2311yescharacteristic, complemented
192C22×C4×D11—21no—
193C22×C4×D11—21no—
194C22×C4×D11—21no—
195C22×C4×D11C2311yescharacteristic
196C22×Dic22C2311yescharacteristic, complemented
197C11×AGL(1,ℤ/8)—24no—
198C2×C11×SD16C2312yescomplemented
199C2×C11×D8C2312yescomplemented
200C2×C11×M16—24no—
201C2×C11×M16C2311yescharacteristic
202C2×C11×M16C2311yescharacteristic
203C2×C11×M16C2312yescomplemented
204C22×C8×C11C2312yescomplemented
205C11×#123—21no—
206C11×C22⋊Q8C2311yescharacteristic, complemented
207C11×C22⋊Q8C2311yescharacteristic, complemented
208C11×#121—21no—
209C11×#121—21no—
210C11×#121C2312yes—
211C11×#121C2312yes—
212C11×#121C2311yescharacteristic, complemented
213C11×#121C2311yescharacteristic, complemented
214C11×#120—21no—
215C4×D4×C11—21no—
216C4×D4×C11—21no—
217C11×#117C2311yescharacteristic
218C2×C11×C4⋊C4C2311yescharacteristic
219C2×C11×C22⋊C4—21no—
220C2×C22⋊Dic11D411yescharacteristic
221#67002—24no—
222#67002—42no—
223#67000C2311yescharacteristic, complemented
224#66997C2311yescharacteristic, complemented
225C2×#4325C2312yes—
226C2×#4325C2312yescomplemented
227#66993—21no—
228#66993—21no—
229#66993—21no—
230#66993C2312yes—
231#66993C2312yes—
232#66993C2311yescharacteristic, complemented
233#66992—21no—
234#66992—21no—
235#66992—21no—
236#66992—21no—
237#66991—21no—
238#66990—21no—
239#66990—22no—
240#66990—22no—
241#66990—22no—
242#66990—22no—
243#66990—21no—
244#66989C2311yescharacteristic, complemented
245D4×Dic11—21no—
246C2×#4324C2312yescomplemented
247C2×#4324C2312yescomplemented
248#66985—24no—
249#66985—42no—
250C2×#4323C2312yes—
251C2×#4323C2312yescomplemented
252C2×#4323C2312yescomplemented
253C2×#4323C2312yescomplemented
254C4×C22⋊D11—21no—
255C4×C22⋊D11—21no—
256C4×C22⋊D11D411yescharacteristic
257C4×C22⋊D11D411yescharacteristic
258C4×C22⋊D11D411yescharacteristic
259C4×C22⋊D11D411yescharacteristic
260C4×C22⋊D11C2311yescharacteristic
261C4×C22⋊D11C2311yescharacteristic
262C4×C22⋊D11C2311yescharacteristic
263C4×C22⋊D11C2311yescharacteristic
264C2×(C2×D11)⋊C4—21no—
265C2×(C2×D11)⋊C4—21no—
266C2×(C2×D11)⋊C4D411yescharacteristic
267C2×Dic11⋊C4D411yescharacteristic
268C2×C4×Dic11C2311yescharacteristic
269C2×#4318C2311yescharacteristic
270C2×#4318C2311yescharacteristic
271#66967—28no—
272SD16×D11—28no—
273#66964—28no—
274D8×D11—28no—
275#66961—24no—
276#66961—24no—
277#66961—24no—
278#66961—28no—
279#66961—28no—
280#66961D418yescomplemented
281M16×D11—24no—
282C2×D88—28no—
283C2×D88C2312yes—
284C2×D88C2312yes—
285C2×D88C2312yescomplemented
286C2×D88C2312yescomplemented
287C2×#4314—28no—
288C2×#4314C2312yes—
289C2×#4314C2312yes—
290C2×#4314C2312yescomplemented
291C2×#4314C2312yescomplemented
292C2×#4313C2312yescomplemented
293C2×C8×D11C2312yescomplemented
294#66950C2311yescharacteristic, complemented
295#66950C2311yescharacteristic, complemented
296#66949—21no—
297#66949—21no—
298#66948—21no—
299#66948—21no—
300#66948—21no—
301#66948C2312yes—
302#66948C2312yes—
303#66948C2311yescharacteristic, complemented
304#66948C2311yescharacteristic, complemented
305#66947—21no—
306#66947—21no—
307#66946—21no—
308#66946—21no—
309#66946—21no—
310#66946C2312yes—
311#66946C2312yes—
312#66946C2311yescharacteristic, complemented
313#66946C2311yescharacteristic, complemented
314C4⋊C4×D11—21no—
315#66941—21no—
316#66940C2311yescharacteristic, complemented
317#66940C2311yescharacteristic, complemented
318#66939—21no—
319#66938—21no—
320#66938—21no—
321#66937—21no—
322#66937—21no—
323#66937—21no—
324#66937—22no—
325#66937—22no—
326#66937—22no—
327#66937—22no—
328#66937—21no—
329#66936—21no—
330#66936—21no—
331#66935—21no—
332#66935—21no—
333#66935—22no—
334#66935—22no—
335#66935—22no—
336#66935—22no—
337#66935—21no—
338(C22⋊D11)⋊C4—21no—
339(C22⋊D11)⋊C4—21no—
340(C22⋊D11)⋊C4—21no—
341(C22⋊D11)⋊C4—21no—
342C22⋊C4×D11—21no—
343C22⋊C4×D11—21no—
344#66931—21no—
345#66931—21no—
346C4×D44—21no—
347C4×D44—21no—
348#66925—21no—
349C42×D11—21no—
350C11×#107C2312yescomplemented
351C11×#106C2312yescomplemented
352C11×#103C2312yescomplemented
353C11×#102C2312yescomplemented
354C11×#102C2312yescomplemented
355C11×#102C2312yescomplemented
356C22⋊(C11⋊C8)C2312yescomplemented
357C22⋊(C11⋊C8)C2312yescomplemented
358(C2×D11)⋊C8C2312yescomplemented
359(C2×D11)⋊C8C2312yescomplemented
360#66879C2312yescomplemented
361Dic11⋊C8C2312yescomplemented
362Dic11⋊C8C2312yescomplemented
363C8×Dic11C2312yescomplemented
364#66874C2312yescomplemented
365#66874C2312yescomplemented
366#66873C2312yes—
367#66873C2312yes—
368#66873C2312yescomplemented
369#66873C2312yescomplemented
370#66873C2312yescomplemented
371#66873C2312yescomplemented
372D4×AGL(1,ℤ/8)—111nomaximal, Sylow
373C24×C11—21no—
374C24×C11C2×D411yescharacteristic
375C23×D11—21no—
376C23×D11—21no—
377C23×D11—21no—
378C23×D11—22no—
379C23×D11—22no—
380C23×D11—21no—
381C23×D11—22no—
382C23×D11—22no—
383C23×D11—44no—
384C23×D11—44no—
385C23×D11—44no—
386C23×D11—44no—
387C23×D11—82no—
388C23×D11—82no—
389C23×D11C2×D411yescharacteristic
390C11×#41—22no—
391C11×#41—22no—
392C2×Q8×C11C2411yescharacteristic
393C2×D4×C11—21no—
394C2×D4×C11—22no—
395C2×D4×C11—22no—
396C2×D4×C11—21no—
397C2×D4×C11—21no—
398C2×D4×C11—22no—
399C2×D4×C11—21no—
400C2×D4×C11—22no—
401C2×D4×C11—44no—
402C2×D4×C11C2411yescharacteristic
403C2×D4×C11C2412yes—
404C22×C4×C11—22no—
405C22×C4×C11—22no—
406C22×C4×C11—21no—
407C22×C4×C11—21no—
408C22×C4×C11C2×D411yescharacteristic
409C22×C4×C11C2×D411yescharacteristic
410C22×C4×C11C2×D411yescharacteristic
411C22×C4×C11C2411yescharacteristic
412C22×C4×C11C2411yescharacteristic
413C22×C4×C11C2411yescharacteristic
414C2×C22⋊D11—24no—
415C2×C22⋊D11—21no—
416C2×C22⋊D11—21no—
417C2×C22⋊D11—22no—
418C2×C22⋊D11—22no—
419C2×C22⋊D11—22no—
420C2×C22⋊D11—22no—
421C2×C22⋊D11—22no—
422C2×C22⋊D11—22no—
423C2×C22⋊D11—21no—
424C2×C22⋊D11—21no—
425C2×C22⋊D11—21no—
426C2×C22⋊D11—21no—
427C2×C22⋊D11—21no—
428C2×C22⋊D11—21no—
429C2×C22⋊D11—44no—
430C2×C22⋊D11—44no—
431C2×C22⋊D11—44no—
432C2×C22⋊D11—82no—
433C2×C22⋊D11C2×D411yescharacteristic
434C2×C22⋊D11C2×D411yescharacteristic
435C2×C22⋊D11C2×D411yescharacteristic
436C2×C22⋊D11C2×D411yescharacteristic
437C22×Dic11—21no—
438C22×Dic11—21no—
439C22×Dic11C2×D411yescharacteristic
440C22×Dic11C2×D411yescharacteristic
441C22×Dic11C2×D411yescharacteristic
442#4343—22no—
443#4343—41no—
444Q8×D11—22no—
445Q8×D11—41no—
446#4341—22no—
447#4341—41no—
448#4341—44no—
449D4×D11—24no—
450D4×D11—24no—
451D4×D11—22no—
452D4×D11—42no—
453D4×D11—42no—
454D4×D11—41no—
455D4×D11—44no—
456D4×D11—44no—
457D4×D11—44no—
458D4×D11—48no—
459D4×D11—48no—
460D4×D11—48no—
461D4×D11—44no—
462D4×D11—48no—
463#4339—22no—
464#4339—22no—
465#4339—22no—
466#4339—22no—
467#4339—22no—
468#4339—41no—
469#4339—41no—
470#4339—44no—
471#4339—44no—
472#4339—44no—
473#4339C2×D414yescomplemented
474C2×D44—21no—
475C2×D44—22no—
476C2×D44—22no—
477C2×D44—21no—
478C2×D44—21no—
479C2×D44—24no—
480C2×D44—24no—
481C2×D44—22no—
482C2×D44—21no—
483C2×D44—22no—
484C2×D44—22no—
485C2×D44—21no—
486C2×D44—21no—
487C2×D44—22no—
488C2×D44—22no—
489C2×D44—22no—
490C2×D44—44no—
491C2×D44—42no—
492C2×D44—42no—
493C2×D44—41no—
494C2×D44—44no—
495C2×D44—44no—
496C2×D44—44no—
497C2×D44C2×D414yescomplemented
498C2×D44C2412yes—
499C2×D44C2411yescharacteristic
500C2×D44C2412yes—
501C2×D44C2411yescharacteristic
502C2×C4×D11—21no—
503C2×C4×D11—21no—
504C2×C4×D11—22no—
505C2×C4×D11—22no—
506C2×C4×D11—21no—
507C2×C4×D11—21no—
508C2×C4×D11—21no—
509C2×C4×D11—22no—
510C2×C4×D11—21no—
511C2×C4×D11—21no—
512C2×C4×D11—21no—
513C2×C4×D11—22no—
514C2×C4×D11—44no—
515C2×C4×D11—44no—
516C2×C4×D11—44no—
517C2×C4×D11C2×D411yescharacteristic
518C2×C4×D11C2×D411yescharacteristic
519C2×C4×D11C2411yescharacteristic
520C2×C4×D11C2411yescharacteristic
521C2×Dic22—22no—
522C2×Dic22—21no—
523C2×Dic22—21no—
524C2×Dic22—41no—
525C2×Dic22C2411yescharacteristic
526C2×Dic22C2411yescharacteristic
527C11×SD16—24no—
528C11×D8—24no—
529C11×M16—24no—
530C11×M16—22no—
531C11×M16C2×D414yescomplemented
532C2×C8×C11—24no—
533C2×C8×C11C2412yes—
534C2×C8×C11C2412yes—
535C11×C4⋊C4—21no—
536C11×C4⋊C4—21no—
537C11×C4⋊C4—21no—
538C11×C4⋊C4C2411yescharacteristic
539C11×C4⋊C4C2411yescharacteristic
540C11×C4⋊C4C2412yes—
541C11×C22⋊C4—21no—
542C11×C22⋊C4—21no—
543C11×C22⋊C4—21no—
544C11×C22⋊C4—21no—
545C11×C22⋊C4—21no—
546C11×C22⋊C4—22no—
547C11×C22⋊C4—22no—
548C42×C11—21no—
549C22⋊Dic11—21no—
550C22⋊Dic11—21no—
551C22⋊Dic11C2×D411yescharacteristic
552C22⋊Dic11C2×D411yescharacteristic
553C22⋊Dic11C2×D411yescharacteristic
554C22⋊Dic11C2×D411yescharacteristic
555#4325—24no—
556#4325—42no—
557#4324—24no—
558#4324—42no—
559#4323—24no—
560#4323—24no—
561#4323—42no—
562#4323—42no—
563(C2×D11)⋊C4—21no—
564(C2×D11)⋊C4—21no—
565(C2×D11)⋊C4—21no—
566(C2×D11)⋊C4—21no—
567(C2×D11)⋊C4—21no—
568(C2×D11)⋊C4—22no—
569(C2×D11)⋊C4—22no—
570(C2×D11)⋊C4—21no—
571(C2×D11)⋊C4—22no—
572(C2×D11)⋊C4—22no—
573(C2×D11)⋊C4—21no—
574(C2×D11)⋊C4—21no—
575(C2×D11)⋊C4C2×D411yescharacteristic
576(C2×D11)⋊C4C2×D411yescharacteristic
577(C2×D11)⋊C4C2×D411yescharacteristic
578(C2×D11)⋊C4C2×D411yescharacteristic
579C4⋊Dic11—21no—
580C4⋊Dic11—21no—
581Dic11⋊C4—21no—
582Dic11⋊C4—21no—
583Dic11⋊C4—21no—
584Dic11⋊C4—21no—
585Dic11⋊C4C2×D411yescharacteristic
586Dic11⋊C4C2×D411yescharacteristic
587Dic11⋊C4C2×D411yescharacteristic
588Dic11⋊C4C2×D411yescharacteristic
589C4×Dic11—21no—
590C4×Dic11—21no—
591C4×Dic11C2×D411yescharacteristic
592C4×Dic11C2×D411yescharacteristic
593C4×Dic11C2411yescharacteristic
594C4×Dic11C2411yescharacteristic
595#4318—22no—
596#4318—22no—
597C2×C11⋊C8C2412yes—
598C2×C11⋊C8C2412yes—
599D88—24no—
600D88—24no—
601D88—24no—
602D88C2×D418yescomplemented
603#4314—24no—
604#4314—24no—
605#4314—24no—
606#4314C2×D418yescomplemented
607#4313—24no—
608C8×D11—24no—
609C22×AGL(1,ℤ/8)—111no—
610C22×AGL(1,ℤ/8)—111no—
611D4×#41—111no—
612C2×D42—111no—
613D4×SD16—112no—
614D4×D8—112no—
615#3274—112no—
616#3272—112no—
617#3265—112no—
618#3265—112no—
619#3264—112no—
620#3264—112no—
621#3151—111no—
622#3055—111no—
623#3055D1111yescharacteristic, complemented
624#3038—111no—
625#3036—111no—
626#3006—111no—
627#3006—111no—
628#3003—111no—
629#3003—111no—
630C4×AGL(1,ℤ/8)—111no—
631D4×M16—111no—
632C23×C11—22no—
633C23×C11—22no—
634C23×C11—21no—
635C23×C11—22no—
636C23×C11—41no—
637C23×C11—42no—
638C23×C11—42no—
639C23×C11—42no—
640C23×C11C22×D411yescharacteristic
641C23×C11C22×D411yescharacteristic
642C23×C11C22×D411yescharacteristic
643C22×D11—22no—
644C22×D11—24no—
645C22×D11—21no—
646C22×D11—22no—
647C22×D11—22no—
648C22×D11—21no—
649C22×D11—22no—
650C22×D11—41no—
651C22×D11—42no—
652C22×D11—44no—
653C22×D11—44no—
654C22×D11—42no—
655C22×D11—44no—
656C22×D11—44no—
657C22×D11—44no—
658C22×D11—42no—
659C22×D11—42no—
660C22×D11—42no—
661C22×D11—44no—
662C22×D11—42no—
663C22×D11—42no—
664C22×D11—44no—
665C22×D11—42no—
666C22×D11—44no—
667C22×D11—42no—
668C22×D11—81no—
669C22×D11—82no—
670C22×D11—82no—
671C22×D11—81no—
672C22×D11—82no—
673C22×D11—82no—
674C22×D11—816no—
675C22×D11—816no—
676C22×D11C22×D411yescharacteristic
677C22×D11C22×D411yescharacteristic
678Q8×C11—21no—
679Q8×C11—21no—
680D4×C11—21no—
681D4×C11—22no—
682D4×C11—21no—
683D4×C11—22no—
684D4×C11—44no—
685D4×C11—42no—
686D4×C11—44no—
687D4×C11—42no—
688D4×C11—42no—
689D4×C11—81no—
690C2×C4×C11—22no—
691C2×C4×C11—22no—
692C2×C4×C11—22no—
693C2×C4×C11—21no—
694C2×C4×C11—21no—
695C2×C4×C11—21no—
696C2×C4×C11—21no—
697C2×C4×C11—21no—
698C2×C4×C11—21no—
699C2×C4×C11—21no—
700C2×C4×C11—22no—
701C2×C4×C11—42no—
702C2×C4×C11—42no—
703C2×C4×C11C22×D411yescharacteristic
704C2×C4×C11C22×D411yescharacteristic
705C2×C4×C11C22×D411yescharacteristic
706C2×C4×C11C22×D412yes—
707C2×C4×C11H(5,𝔽2)12yes—
708C2×C4×C11C2511yescharacteristic
709C22⋊D11—24no—
710C22⋊D11—22no—
711C22⋊D11—22no—
712C22⋊D11—22no—
713C22⋊D11—42no—
714C22⋊D11—42no—
715C22⋊D11—44no—
716C22⋊D11—44no—
717C22⋊D11—42no—
718C22⋊D11—44no—
719C22⋊D11—42no—
720C22⋊D11—42no—
721C22⋊D11—44no—
722C22⋊D11—42no—
723C22⋊D11—81no—
724C22⋊D11—82no—
725C22⋊D11—82no—
726C22⋊D11AGL(1,ℤ/8)14yescomplemented
727C2×Dic11—22no—
728C2×Dic11—21no—
729C2×Dic11—22no—
730C2×Dic11—21no—
731C2×Dic11—41no—
732C2×Dic11—42no—
733C2×Dic11—42no—
734C2×Dic11C22×D411yescharacteristic
735C2×Dic11C22×D411yescharacteristic
736C2×Dic11C22×D411yescharacteristic
737C2×Dic11C22×D411yescharacteristic
738C2×Dic11C22×D411yescharacteristic
739C2×Dic11C22×D411yescharacteristic
740D44—24no—
741D44—22no—
742D44—21no—
743D44—22no—
744D44—21no—
745D44—21no—
746D44—22no—
747D44—44no—
748D44—44no—
749D44—42no—
750D44—42no—
751D44—44no—
752D44—44no—
753D44—42no—
754D44—42no—
755D44—81no—
756D44C22×D414yes—
757D44C22×D412yescomplemented
758C4×D11—22no—
759C4×D11—22no—
760C4×D11—24no—
761C4×D11—21no—
762C4×D11—21no—
763C4×D11—21no—
764C4×D11—21no—
765C4×D11—42no—
766C4×D11—42no—
767C4×D11—42no—
768C4×D11—44no—
769C4×D11—42no—
770C4×D11—42no—
771C4×D11—44no—
772C4×D11—42no—
773C4×D11—81no—
774Dic22—21no—
775Dic22—21no—
776Dic22—21no—
777Dic22—42no—
778Dic22—42no—
779Dic22C22×D412yescomplemented
780C8×C11—22no—
781C8×C11C22×D414yescomplemented
782C11⋊C8—22no—
783C11⋊C8—22no—
784C22×#41—111no—
785C22×#41—111no—
786C23×D4—111no—
787C23×D4—111no—
788C23×D4—221no—
789C2×AGL(1,ℤ/8)—111no—
790C2×AGL(1,ℤ/8)—111no—
791C2×AGL(1,ℤ/8)—111no—
792C2×AGL(1,ℤ/8)—111no—
793C2×AGL(1,ℤ/8)—112no—
794C2×AGL(1,ℤ/8)—112no—
795C2×AGL(1,ℤ/8)—111no—
796C2×AGL(1,ℤ/8)—111no—
797C2×AGL(1,ℤ/8)—111no—
798C2×AGL(1,ℤ/8)—111no—
799C2×AGL(1,ℤ/8)—112no—
800C2×AGL(1,ℤ/8)—112no—
801C2×AGL(1,ℤ/8)—228no—
802C2×AGL(1,ℤ/8)—228no—
803C2×AGL(1,ℤ/8)C2×D1111yescharacteristic, complemented
804C22×SD16—112no—
805C22×SD16—112no—
806C22×D8—112no—
807C22×D8—112no—
808C22×M16—111no—
809C22×M16C2×D1111yescharacteristic, complemented
810#550—111no—
811D4×Q8—111no—
812#548—111no—
813#548—111no—
814#547—111no—
815#547—221no—
816#546—111no—
817#546—111no—
818#546—221no—
819#546—221no—
820D42—112no—
821D42—112no—
822D42—112no—
823D42—112no—
824D42—111no—
825D42—221no—
826D42—221no—
827D42—221no—
828D42—221no—
829D42—221no—
830#532—111no—
831#532—221no—
832C2×#127—111no—
833#525—111no—
834#525—221no—
835#525—221no—
836#525C2×D1111yescharacteristic, complemented
837C2×#121—111no—
838C2×#121—221no—
839C2×#121C2×D1111yescharacteristic, complemented
840C2×#120—221no—
841C2×#120—221no—
842C4×#41—111no—
843C2×C4×D4—111no—
844C2×C4×D4—111no—
845C2×C4×D4—221no—
846#496—112no—
847#496—112no—
848#493—112no—
849#492—112no—
850#469—112no—
851#469C2×D1112yescomplemented
852#468—112no—
853#468C2×D1112yescomplemented
854#466—112no—
855#466C2×D1112yescomplemented
856#465—112no—
857#465C2×D1112yescomplemented
858#463—112no—
859#463—112no—
860#461—112no—
861#460—112no—
862#460—112no—
863#459—112no—
864#459—112no—
865#459—112no—
866#450—112no—
867#450—112no—
868#450—112no—
869#450—112no—
870#449—112no—
871#449—112no—
872#449—112no—
873#449—112no—
874#448—112no—
875#448—112no—
876#447—112no—
877#447—112no—
878#447—112no—
879#447—112no—
880#447—112no—
881#447—112no—
882#442—112no—
883#440—112no—
884C4×SD16—112no—
885C4×D8—112no—
886#436—112no—
887#435—112no—
888#435—112no—
889C8×D4—112no—
890#428C2×D1111yescharacteristic, complemented
891#423—111no—
892#418—111no—
893#418—111no—
894#418C2×D1111yescharacteristic, complemented
895#417—111no—
896#417—111no—
897#417C2×D1111yescharacteristic, complemented
898#407—111no—
899#407—111no—
900C4×M16—111no—
901C22×C11—21no—
902C22×C11—21no—
903C22×C11—21no—
904C22×C11—21no—
905C22×C11—21no—
906C22×C11—21no—
907C22×C11—21no—
908C22×C11—44no—
909C22×C11—41no—
910C22×C11—42no—
911C22×C11—41no—
912C22×C11—42no—
913C22×C11—42no—
914C22×C11—41no—
915C22×C11—84no—
916C22×C11D4212yes—
917C22×C11C2×AGL(1,ℤ/8)12yescomplemented
918C22×C11C23×D411yescharacteristic
919C2×D11—21no—
920C2×D11—21no—
921C2×D11—21no—
922C2×D11—24no—
923C2×D11—21no—
924C2×D11—22no—
925C2×D11—21no—
926C2×D11—44no—
927C2×D11—48no—
928C2×D11—42no—
929C2×D11—41no—
930C2×D11—42no—
931C2×D11—41no—
932C2×D11—42no—
933C2×D11—41no—
934C2×D11—42no—
935C2×D11—41no—
936C2×D11—42no—
937C2×D11—41no—
938C2×D11—84no—
939C2×D11—88no—
940C2×D11—88no—
941C2×D11—84no—
942C2×D11—88no—
943C2×D11—88no—
944C2×D11—84no—
945C2×D11C2×AGL(1,ℤ/8)12yescomplemented
946C4×C11—21no—
947C4×C11—21no—
948C4×C11—41no—
949C4×C11—41no—
950C4×C11—42no—
951C4×C11—41no—
952C4×C11D4212yes—
953C4×C11C23×D411yescharacteristic
954C4×C11C2×H(5,𝔽2)11yescharacteristic
955Dic11—21no—
956Dic11—21no—
957Dic11—22no—
958Dic11—21no—
959Dic11—21no—
960Dic11—21no—
961Dic11—41no—
962Dic11C2×AGL(1,ℤ/8)12yescomplemented
963C25—221no—
964C25—221no—
965C2×#41—111no—
966C2×#41—111no—
967C2×#41—111no—
968C2×#41—111no—
969C2×#41—111no—
970C2×#41—111no—
971C2×#41—221no—
972C2×#41—224no—
973C2×#41—221no—
974C2×#41—221no—
975C2×#41—221no—
976C2×#41—224no—
977C2×#41—442no—
978C2×#41—442no—
979C2×#41C22×D1111yescharacteristic
980C22×Q8—111no—
981C22×Q8—111no—
982C22×D4—21no—
983C22×D4—111no—
984C22×D4—112no—
985C22×D4—112no—
986C22×D4—111no—
987C22×D4—111no—
988C22×D4—111no—
989C22×D4—112no—
990C22×D4—112no—
991C22×D4—111no—
992C22×D4—224no—
993C22×D4—221no—
994C22×D4—221no—
995C22×D4—221no—
996C22×D4—221no—
997C22×D4—221no—
998C22×D4—221no—
999C22×D4—224no—
1000C22×D4—221no—
1001C22×D4—222no—
1002C22×D4—222no—
1003C22×D4—222no—
1004C22×D4—222no—
1005C22×D4—221no—
1006C22×D4—221no—
1007C22×D4—221no—
1008C22×D4—221no—
1009C22×D4—221no—
1010C22×D4—442no—
1011C22×D4—442no—
1012C22×D4—448no—
1013C22×D4C22×D1111yescharacteristic
1014C23×C4—111no—
1015C23×C4—221no—
1016C23×C4—221no—
1017C23×C4—221no—
1018C23×C4C22×D1111yescharacteristic
1019AGL(1,ℤ/8)—24no—
1020AGL(1,ℤ/8)—118no—
1021AGL(1,ℤ/8)—228no—
1022AGL(1,ℤ/8)—228no—
1023AGL(1,ℤ/8)—224no—
1024AGL(1,ℤ/8)—224no—
1025AGL(1,ℤ/8)—228no—
1026AGL(1,ℤ/8)—228no—
1027AGL(1,ℤ/8)—224no—
1028AGL(1,ℤ/8)—224no—
1029AGL(1,ℤ/8)—224no—
1030AGL(1,ℤ/8)—442no—
1031AGL(1,ℤ/8)—442no—
1032C2×SD16—112no—
1033C2×SD16—112no—
1034C2×SD16—112no—
1035C2×SD16—112no—
1036C2×SD16—112no—
1037C2×SD16—112no—
1038C2×SD16—112no—
1039C2×SD16—112no—
1040C2×SD16—228no—
1041C2×SD16—228no—
1042C2×SD16C22×D1112yescomplemented
1043C2×D8—112no—
1044C2×D8—112no—
1045C2×D8—112no—
1046C2×D8—112no—
1047C2×D8—112no—
1048C2×D8—112no—
1049C2×D8—112no—
1050C2×D8—112no—
1051C2×D8—228no—
1052C2×D8—228no—
1053C2×D8C22×D1112yescomplemented
1054C2×M16—24no—
1055C2×M16—111no—
1056C2×M16—111no—
1057C2×M16—112no—
1058C2×M16—224no—
1059C2×M16C22×D1111yescharacteristic
1060C2×M16C22×D1111yescharacteristic
1061C2×M16C22×D1112yescomplemented
1062C22×C8—112no—
1063C22×C8C22×D1112yescomplemented
1064C4⋊Q8—111no—
1065C4⋊Q8—221no—
1066#127—112no—
1067#127—112no—
1068#127—111no—
1069#127—221no—
1070#127—221no—
1071#127—221no—
1072#124—111no—
1073#124—111no—
1074#124—221no—
1075#124—221no—
1076#123—21no—
1077#123—221no—
1078#123—221no—
1079#123—221no—
1080#123—221no—
1081#123—221no—
1082C22⋊Q8—111no—
1083C22⋊Q8—111no—
1084C22⋊Q8—221no—
1085C22⋊Q8—221no—
1086C22⋊Q8—221no—
1087C22⋊Q8—221no—
1088C22⋊Q8C22×D1111yescharacteristic, complemented
1089C22⋊Q8C22×D1111yescharacteristic, complemented
1090#121—21no—
1091#121—21no—
1092#121—112no—
1093#121—112no—
1094#121—111no—
1095#121—111no—
1096#121—221no—
1097#121—222no—
1098#121—222no—
1099#121—222no—
1100#121—222no—
1101#121—221no—
1102#121—221no—
1103#121—221no—
1104#121—221no—
1105#121—221no—
1106#121—221no—
1107#121—221no—
1108#121—221no—
1109#121—221no—
1110#121—221no—
1111#121—221no—
1112#121C22×D1112yes—
1113#121C22×D1112yes—
1114#121C22×D1111yescharacteristic, complemented
1115#121C22×D1111yescharacteristic, complemented
1116#120—21no—
1117#120—222no—
1118#120—222no—
1119#120—222no—
1120#120—222no—
1121#120—221no—
1122#120—221no—
1123#120—221no—
1124#120—222no—
1125#120—222no—
1126#120—222no—
1127#120—222no—
1128#120—221no—
1129#120—221no—
1130C4×Q8—111no—
1131C4×Q8—111no—
1132C4×D4—21no—
1133C4×D4—21no—
1134C4×D4—111no—
1135C4×D4—111no—
1136C4×D4—111no—
1137C4×D4—111no—
1138C4×D4—111no—
1139C4×D4—111no—
1140C4×D4—111no—
1141C4×D4—111no—
1142C4×D4—112no—
1143C4×D4—112no—
1144C4×D4—111no—
1145C4×D4—111no—
1146C4×D4—221no—
1147C4×D4—221no—
1148C4×D4—221no—
1149C4×D4—221no—
1150C4×D4—221no—
1151C4×D4—221no—
1152C4×D4—221no—
1153C4×D4—221no—
1154C4×D4—221no—
1155C4×D4—221no—
1156C4×D4—221no—
1157C4×D4—221no—
1158#117—221no—
1159#117C22×D1111yescharacteristic
1160C2×C4⋊C4—111no—
1161C2×C4⋊C4—221no—
1162C2×C4⋊C4C22×D1111yescharacteristic
1163C2×C22⋊C4—21no—
1164C2×C22⋊C4—111no—
1165C2×C22⋊C4—111no—
1166C2×C22⋊C4—221no—
1167C2×C22⋊C4—221no—
1168C2×C22⋊C4—221no—
1169C2×C22⋊C4—221no—
1170C2×C42—111no—
1171C2×C42—221no—
1172#107C22×D1112yescomplemented
1173#106C22×D1112yescomplemented
1174C4⋊C8—112no—
1175C4⋊C8—112no—
1176#103—112no—
1177#103—112no—
1178#103C22×D1112yescomplemented
1179#102—112no—
1180#102—112no—
1181#102—112no—
1182#102—112no—
1183#102—112no—
1184#102—112no—
1185#102C22×D1112yescomplemented
1186#102C22×D1112yescomplemented
1187#102C22×D1112yescomplemented
1188C22⋊C8—112no—
1189C22⋊C8—112no—
1190C22⋊C8—112no—
1191C22⋊C8—112no—
1192#97—112no—
1193C4×C8—112no—
1194C2×C11—22no—
1195C2×C11—22no—
1196C2×C11—41no—
1197C2×C11—82no—
1198C2×C11—81no—
1199C2×C11C2×D4211yescharacteristic
1200C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
1201C2×C11#358511yescharacteristic
1202D11—22no—
1203D11—41no—
1204D11—44no—
1205D11—42no—
1206D11—81no—
1207D11—82no—
1208C24—21no—
1209C24—111no—
1210C24—221no—
1211C24—222no—
1212C24—222no—
1213C24—221no—
1214C24—221no—
1215C24—221no—
1216C24—222no—
1217C24—222no—
1218C24—444no—
1219C24—444no—
1220C24—444no—
1221C24—444no—
1222C24—882no—
1223C24—882no—
1224C24D4×D1111yescharacteristic
1225#41—22no—
1226#41—22no—
1227#41—114no—
1228#41—222no—
1229#41—222no—
1230#41—222no—
1231#41—222no—
1232#41—222no—
1233#41—222no—
1234#41—222no—
1235#41—444no—
1236#41—441no—
1237#41—441no—
1238#41—444no—
1239#41—444no—
1240#41—441no—
1241#41—444no—
1242#41—441no—
1243C2×Q8—111no—
1244C2×Q8—111no—
1245C2×Q8—221no—
1246C2×Q8—222no—
1247C2×Q8—221no—
1248C2×Q8—222no—
1249C2×Q8—441no—
1250C2×Q8—441no—
1251C2×Q8C23×D1111yescharacteristic
1252C2×D4—21no—
1253C2×D4—21no—
1254C2×D4—22no—
1255C2×D4—22no—
1256C2×D4—21no—
1257C2×D4—22no—
1258C2×D4—21no—
1259C2×D4—22no—
1260C2×D4—44no—
1261C2×D4—111no—
1262C2×D4—111no—
1263C2×D4—111no—
1264C2×D4—111no—
1265C2×D4—114no—
1266C2×D4—111no—
1267C2×D4—112no—
1268C2×D4—111no—
1269C2×D4—112no—
1270C2×D4—222no—
1271C2×D4—224no—
1272C2×D4—224no—
1273C2×D4—221no—
1274C2×D4—222no—
1275C2×D4—222no—
1276C2×D4—221no—
1277C2×D4—221no—
1278C2×D4—221no—
1279C2×D4—222no—
1280C2×D4—222no—
1281C2×D4—221no—
1282C2×D4—222no—
1283C2×D4—222no—
1284C2×D4—221no—
1285C2×D4—222no—
1286C2×D4—222no—
1287C2×D4—222no—
1288C2×D4—224no—
1289C2×D4—224no—
1290C2×D4—224no—
1291C2×D4—221no—
1292C2×D4—221no—
1293C2×D4—221no—
1294C2×D4—221no—
1295C2×D4—221no—
1296C2×D4—221no—
1297C2×D4—222no—
1298C2×D4—222no—
1299C2×D4—222no—
1300C2×D4—221no—
1301C2×D4—221no—
1302C2×D4—222no—
1303C2×D4—222no—
1304C2×D4—442no—
1305C2×D4—442no—
1306C2×D4—441no—
1307C2×D4—444no—
1308C2×D4—444no—
1309C2×D4—444no—
1310C2×D4—444no—
1311C2×D4—442no—
1312C2×D4—442no—
1313C2×D4—441no—
1314C2×D4—444no—
1315C2×D4—444no—
1316C2×D4—444no—
1317C2×D4—444no—
1318C2×D4—448no—
1319C2×D4—444no—
1320C2×D4—444no—
1321C2×D4—448no—
1322C2×D4—448no—
1323C2×D4—448no—
1324C2×D4—444no—
1325C2×D4—882no—
1326C2×D4C23×D1112yes—
1327C2×D4C23×D1111yescharacteristic
1328C22×C4—22no—
1329C22×C4—22no—
1330C22×C4—21no—
1331C22×C4—21no—
1332C22×C4—111no—
1333C22×C4—111no—
1334C22×C4—111no—
1335C22×C4—111no—
1336C22×C4—111no—
1337C22×C4—111no—
1338C22×C4—111no—
1339C22×C4—221no—
1340C22×C4—221no—
1341C22×C4—222no—
1342C22×C4—222no—
1343C22×C4—221no—
1344C22×C4—221no—
1345C22×C4—221no—
1346C22×C4—221no—
1347C22×C4—222no—
1348C22×C4—222no—
1349C22×C4—221no—
1350C22×C4—221no—
1351C22×C4—221no—
1352C22×C4—221no—
1353C22×C4—444no—
1354C22×C4—444no—
1355C22×C4—444no—
1356C22×C4D4×D1111yescharacteristic
1357C22×C4D4×D1111yescharacteristic
1358C22×C4D4×D1111yescharacteristic
1359C22×C4C23×D1111yescharacteristic
1360C22×C4C23×D1111yescharacteristic
1361C22×C4C23×D1111yescharacteristic
1362SD16—24no—
1363SD16—118no—
1364SD16—224no—
1365SD16—224no—
1366SD16—224no—
1367SD16—224no—
1368SD16—224no—
1369SD16—442no—
1370SD16—442no—
1371D8—24no—
1372D8—118no—
1373D8—224no—
1374D8—224no—
1375D8—224no—
1376D8—224no—
1377D8—224no—
1378D8—442no—
1379D8—442no—
1380M16—22no—
1381M16—24no—
1382M16—222no—
1383M16—222no—
1384M16—224no—
1385M16D4×D1114yescomplemented
1386C2×C8—24no—
1387C2×C8—112no—
1388C2×C8—112no—
1389C2×C8—224no—
1390C2×C8C23×D1112yes—
1391C2×C8C23×D1112yes—
1392C4⋊C4—21no—
1393C4⋊C4—21no—
1394C4⋊C4—21no—
1395C4⋊C4—111no—
1396C4⋊C4—111no—
1397C4⋊C4—111no—
1398C4⋊C4—111no—
1399C4⋊C4—221no—
1400C4⋊C4—221no—
1401C4⋊C4—221no—
1402C4⋊C4—221no—
1403C4⋊C4—221no—
1404C4⋊C4—221no—
1405C4⋊C4C23×D1111yescharacteristic
1406C4⋊C4C23×D1111yescharacteristic
1407C4⋊C4C23×D1112yes—
1408C22⋊C4—21no—
1409C22⋊C4—21no—
1410C22⋊C4—21no—
1411C22⋊C4—22no—
1412C22⋊C4—22no—
1413C22⋊C4—21no—
1414C22⋊C4—21no—
1415C22⋊C4—111no—
1416C22⋊C4—111no—
1417C22⋊C4—111no—
1418C22⋊C4—111no—
1419C22⋊C4—111no—
1420C22⋊C4—111no—
1421C22⋊C4—111no—
1422C22⋊C4—111no—
1423C22⋊C4—222no—
1424C22⋊C4—222no—
1425C22⋊C4—221no—
1426C22⋊C4—221no—
1427C22⋊C4—222no—
1428C22⋊C4—222no—
1429C22⋊C4—221no—
1430C22⋊C4—221no—
1431C22⋊C4—221no—
1432C22⋊C4—221no—
1433C22⋊C4—221no—
1434C22⋊C4—221no—
1435C22⋊C4—221no—
1436C22⋊C4—221no—
1437C42—21no—
1438C42—111no—
1439C42—111no—
1440C42—111no—
1441C42—111no—
1442C42—221no—
1443C42—221no—
1444C11D4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
1445C23—22no—
1446C23—22no—
1447C23—21no—
1448C23—22no—
1449C23—41no—
1450C23—42no—
1451C23—42no—
1452C23—42no—
1453C23—111no—
1454C23—111no—
1455C23—222no—
1456C23—222no—
1457C23—224no—
1458C23—221no—
1459C23—222no—
1460C23—221no—
1461C23—222no—
1462C23—441no—
1463C23—442no—
1464C23—444no—
1465C23—444no—
1466C23—442no—
1467C23—442no—
1468C23—442no—
1469C23—444no—
1470C23—442no—
1471C23—444no—
1472C23—442no—
1473C23—442no—
1474C23—444no—
1475C23—444no—
1476C23—444no—
1477C23—444no—
1478C23—442no—
1479C23—442no—
1480C23—881no—
1481C23—882no—
1482C23—882no—
1483C23—881no—
1484C23—882no—
1485C23—882no—
1486C23—8816no—
1487C23—8816no—
1488C23C2×D4×D1111yescharacteristic
1489C23C2×D4×D1111yescharacteristic
1490C23C2×D4×D1111yescharacteristic
1491Q8—21no—
1492Q8—21no—
1493Q8—112no—
1494Q8—221no—
1495Q8—221no—
1496Q8—221no—
1497Q8—442no—
1498Q8—442no—
1499D4—21no—
1500D4—22no—
1501D4—21no—
1502D4—22no—
1503D4—44no—
1504D4—44no—
1505D4—42no—
1506D4—42no—
1507D4—42no—
1508D4—81no—
1509D4—114no—
1510D4—112no—
1511D4—114no—
1512D4—222no—
1513D4—222no—
1514D4—222no—
1515D4—224no—
1516D4—224no—
1517D4—221no—
1518D4—222no—
1519D4—222no—
1520D4—221no—
1521D4—221no—
1522D4—222no—
1523D4—444no—
1524D4—444no—
1525D4—442no—
1526D4—444no—
1527D4—442no—
1528D4—442no—
1529D4—444no—
1530D4—444no—
1531D4—442no—
1532D4—442no—
1533D4—444no—
1534D4—444no—
1535D4—442no—
1536D4—442no—
1537D4—444no—
1538D4—442no—
1539D4—442no—
1540D4—442no—
1541D4—881no—
1542D4—882no—
1543D4—882no—
1544D4—881no—
1545C2×C4—22no—
1546C2×C4—22no—
1547C2×C4—22no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—22no—
1555C2×C4—21no—
1556C2×C4—42no—
1557C2×C4—42no—
1558C2×C4—111no—
1559C2×C4—111no—
1560C2×C4—111no—
1561C2×C4—111no—
1562C2×C4—111no—
1563C2×C4—111no—
1564C2×C4—222no—
1565C2×C4—222no—
1566C2×C4—221no—
1567C2×C4—222no—
1568C2×C4—222no—
1569C2×C4—224no—
1570C2×C4—221no—
1571C2×C4—221no—
1572C2×C4—221no—
1573C2×C4—221no—
1574C2×C4—221no—
1575C2×C4—442no—
1576C2×C4—442no—
1577C2×C4—444no—
1578C2×C4—442no—
1579C2×C4—442no—
1580C2×C4—442no—
1581C2×C4—444no—
1582C2×C4—441no—
1583C2×C4—442no—
1584C2×C4—442no—
1585C2×C4—442no—
1586C2×C4—881no—
1587C2×C4C2×D4×D1111yescharacteristic
1588C2×C4C2×D4×D1111yescharacteristic
1589C2×C4C2×D4×D1111yescharacteristic
1590C2×C4C2×D4×D1112yes—
1591C2×C4#6704212yes—
1592C2×C4C24×D1111yescharacteristic
1593C8—22no—
1594C8—222no—
1595C8—222no—
1596C8C2×D4×D1114yescomplemented
1597C22—21no—
1598C22—21no—
1599C22—21no—
1600C22—21no—
1601C22—21no—
1602C22—21no—
1603C22—21no—
1604C22—44no—
1605C22—41no—
1606C22—42no—
1607C22—41no—
1608C22—42no—
1609C22—42no—
1610C22—41no—
1611C22—84no—
1612C22—112no—
1613C22—221no—
1614C22—221no—
1615C22—221no—
1616C22—221no—
1617C22—222no—
1618C22—224no—
1619C22—221no—
1620C22—444no—
1621C22—448no—
1622C22—441no—
1623C22—442no—
1624C22—442no—
1625C22—441no—
1626C22—442no—
1627C22—441no—
1628C22—441no—
1629C22—442no—
1630C22—442no—
1631C22—441no—
1632C22—888no—
1633C22—884no—
1634C22—884no—
1635C22—888no—
1636C22—888no—
1637C22—884no—
1638C22—888no—
1639C22#1062314012yes—
1640C22D11×AGL(1,ℤ/8)12yescomplemented
1641C22C22×D4×D1111yescharacteristic
1642C4—21no—
1643C4—21no—
1644C4—41no—
1645C4—41no—
1646C4—42no—
1647C4—41no—
1648C4—112no—
1649C4—221no—
1650C4—221no—
1651C4—221no—
1652C4—221no—
1653C4—222no—
1654C4—221no—
1655C4—441no—
1656C4#1062314012yes—
1657C4C22×D4×D1111yescharacteristic
1658C4C2×#6704211yescharacteristic
1659C2—22no—
1660C2—22no—
1661C2—41no—
1662C2—82no—
1663C2—81no—
1664C2—222no—
1665C2—441no—
1666C2—444no—
1667C2—442no—
1668C2—882no—
1669C2—881no—
1670C2C2×#1062314011yescharacteristic
1671C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
1672C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3055C2
socleC22×C11C23×D4
hypercenter#3055D11
hypocenterC11D4×AGL(1,ℤ/8)
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3055

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#66961C2semidirect
2. C2×D11×AGL(1,ℤ/8)C2semidirect
3. #13082099C2semidirect
4. C2×#10623140C2semidirect
5. #13080309C2semidirect
6. #13080290C2semidirect
7. #13080233C2semidirect
8. #13080213C2semidirect
9. #13080118C2semidirect
10. #13080108C2semidirect
11. #13080103C2semidirect
12. #13080093C2semidirect
13. #13079064C2semidirect
14. #13078236C2semidirect
15. #13078095C2semidirect
16. #13078079C2semidirect
17. #13077869C2semidirect
18. #13077866C2semidirect
19. #13077845C2semidirect
20. #13077842C2semidirect
21. #13077423C2semidirect
22. M16×C22⋊D11C2semidirect
23. C11×#3055C2semidirect
24. C2×#41×D11C22semidirect
26. C22×D4×D11C22semidirect
27. C22×#4339C22semidirect
28. C23×D44C22semidirect
29. C2×C11×AGL(1,ℤ/8)C22semidirect
30. C22×C11×M16C22semidirect
31. C11×#525C22semidirect
32. C2×C11×#121C22semidirect
33. #10623363C22semidirect
34. C2×#67002C22semidirect
35. C2×#67002C22semidirect
36. C2×#66993C22semidirect
38. C2×#66985C22semidirect
39. C2×#66985C22semidirect
42. C2×#66967C22semidirect
43. C2×SD16×D11C22semidirect
44. C2×#66964C22semidirect
45. C2×D8×D11C22semidirect
48. C2×#66961C22semidirect
49. C2×#66961C22semidirect
50. C2×#66961C22semidirect
51. C2×#66961C22semidirect
52. C2×#66961C22semidirect
53. C2×M16×D11C22semidirect
54. C22×D88C22semidirect
55. C22×#4314C22semidirect
58. #10623164C22semidirect
59. #10623163C22semidirect
60. #10623162C22semidirect
61. #10623161C22semidirect
62. #10623143C22semidirect
68. #10623140C22semidirect
69. #10623140C22semidirect
70. #10623140C22semidirect
71. #10623140C22semidirect
72. #10623130C22semidirect
73. #10623129C22semidirect
80. #10623055C22semidirect
81. #10623053C22semidirect
82. C2×#66948C22semidirect
83. C2×#66946C22semidirect
86. C11×#469C22semidirect
87. C11×#468C22semidirect
88. C11×#466C22semidirect
89. C11×#465C22semidirect
90. C11×#428C22semidirect
91. C11×#418C22semidirect
92. C11×#417C22semidirect
93. #10622820C22semidirect
94. #10622789C22semidirect
95. #10622788C22semidirect
96. #10622767C22semidirect
97. #10622764C22semidirect
98. #10622741C22semidirect
99. #10622740C22semidirect
100. #10622739C22semidirect
101. #10622731C22semidirect
102. M16×Dic11C22semidirect
103. #10622724C22semidirect
104. C8×C22⋊D11C22semidirect
105. #10622659C22semidirect
106. #10622659C22semidirect
107. #10622653C22semidirect
108. #10622650C22semidirect
109. #10622650C22semidirect
110. #10622649C22semidirect
111. #10622649C22semidirect
112. #10622649C22semidirect
113. #10622614C22semidirect
114. #10622614C22semidirect
115. #10622579C22semidirect
116. #10622579C22semidirect
117. #10622502C22semidirect
118. #10622499C22semidirect
119. #10622496C22semidirect
120. #10622485C22semidirect
121. #10622482C22semidirect
122. #10622478C22semidirect
123. #10622477C22semidirect
124. #10622465C22semidirect
125. #10622432C22semidirect
126. #10622431C22semidirect
127. #10622424C22semidirect
128. #10622419C22semidirect
129. #10622400C22semidirect
130. #10622399C22semidirect
131. #10622399C22semidirect
132. #10622399C22semidirect
133. #10622394C22semidirect
134. #10622389C22semidirect
135. #10622389C22semidirect
136. #10622386C22semidirect
137. #10622386C22semidirect
138. #10622386C22semidirect
139. #10622375C22semidirect
140. #10622375C22semidirect
154. C2×#4343C23semidirect
155. C2×Q8×D11C23semidirect
157. C2×#4341C23semidirect
171. C2×D4×D11C23semidirect
179. C2×#4339C23semidirect
180. C2×#4339C23semidirect
191. C22×D44C23semidirect
196. C22×Dic22C23semidirect
198. C2×C11×SD16C23semidirect
199. C2×C11×D8C23semidirect
203. C2×C11×M16C23semidirect
204. C22×C8×C11C23semidirect
206. C11×C22⋊Q8C23semidirect
207. C11×C22⋊Q8C23semidirect
212. C11×#121C23semidirect
213. C11×#121C23semidirect
223. #67000C23semidirect
224. #66997C23semidirect
226. C2×#4325C23semidirect
232. #66993C23semidirect
244. #66989C23semidirect
246. C2×#4324C23semidirect
247. C2×#4324C23semidirect
251. C2×#4323C23semidirect
252. C2×#4323C23semidirect
253. C2×#4323C23semidirect
280. #66961D4semidirect
285. C2×D88C23semidirect
286. C2×D88C23semidirect
290. C2×#4314C23semidirect
291. C2×#4314C23semidirect
292. C2×#4313C23semidirect
293. C2×C8×D11C23semidirect
294. #66950C23semidirect
295. #66950C23semidirect
303. #66948C23semidirect
304. #66948C23semidirect
312. #66946C23semidirect
313. #66946C23semidirect
316. #66940C23semidirect
317. #66940C23semidirect
350. C11×#107C23semidirect
351. C11×#106C23semidirect
352. C11×#103C23semidirect
353. C11×#102C23semidirect
354. C11×#102C23semidirect
355. C11×#102C23semidirect
356. C22⋊(C11⋊C8)C23semidirect
357. C22⋊(C11⋊C8)C23semidirect
358. (C2×D11)⋊C8C23semidirect
359. (C2×D11)⋊C8C23semidirect
360. #66879C23semidirect
361. Dic11⋊C8C23semidirect
362. Dic11⋊C8C23semidirect
363. C8×Dic11C23semidirect
364. #66874C23semidirect
365. #66874C23semidirect
368. #66873C23semidirect
369. #66873C23semidirect
370. #66873C23semidirect
371. #66873C23semidirect
473. #4339C2×D4semidirect
497. C2×D44C2×D4semidirect
531. C11×M16C2×D4semidirect
602. D88C2×D4semidirect
606. #4314C2×D4semidirect
623. #3055D11semidirect
726. C22⋊D11AGL(1,ℤ/8)semidirect
757. D44C22×D4semidirect
779. Dic22C22×D4semidirect
781. C8×C11C22×D4semidirect
803. C2×AGL(1,ℤ/8)C2×D11semidirect
809. C22×M16C2×D11semidirect
836. #525C2×D11semidirect
839. C2×#121C2×D11semidirect
851. #469C2×D11semidirect
853. #468C2×D11semidirect
855. #466C2×D11semidirect
857. #465C2×D11semidirect
890. #428C2×D11semidirect
894. #418C2×D11semidirect
897. #417C2×D11semidirect
917. C22×C11C2×AGL(1,ℤ/8)semidirect
945. C2×D11C2×AGL(1,ℤ/8)semidirect
962. Dic11C2×AGL(1,ℤ/8)semidirect
1042. C2×SD16C22×D11semidirect
1053. C2×D8C22×D11semidirect
1061. C2×M16C22×D11semidirect
1063. C22×C8C22×D11semidirect
1088. C22⋊Q8C22×D11semidirect
1089. C22⋊Q8C22×D11semidirect
1114. #121C22×D11semidirect
1115. #121C22×D11semidirect
1172. #107C22×D11semidirect
1173. #106C22×D11semidirect
1178. #103C22×D11semidirect
1185. #102C22×D11semidirect
1186. #102C22×D11semidirect
1187. #102C22×D11semidirect
1385. M16D4×D11semidirect
1444. C11D4×AGL(1,ℤ/8)semidirect
1596. C8C2×D4×D11semidirect
1640. C22D11×AGL(1,ℤ/8)semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#669612
C2×D11×AGL(1,ℤ/8)2
#130820992
C2×#106231402
#130803092
#130802902
#130802332
#130802132
#130801182
#130801082
#130801032
#130800932
#130790642
#130782362
#130780952
#130780792
#130778692
#130778662
#130778452
#130778422
#130774232
M16×C22⋊D112
C11×#30552
D4×AGL(1,ℤ/8)11