Finite Group Databasebeta

← #15639644

Subgroups — #15639644

Order 2816.

2156 conjugacy classes of subgroups.

The subgroup lattice has 1226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082855C211yesmaximal, characteristic, complemented
2#13080869C212yesmaximal, complemented
3#13080787C212yesmaximal, complemented
4#13080592C212yesmaximal, complemented
5#13080466C212yesmaximal, complemented
6D4×#4325C212yesmaximal, complemented
7#13080216C212yesmaximal, complemented
8#13080112C212yesmaximal, complemented
9#13080097C212yesmaximal, complemented
10#13079677C212yesmaximal, complemented
11#13079462C212yesmaximal, complemented
12#13079418C211yesmaximal, characteristic, complemented
13#13079369C211yesmaximal, characteristic, complemented
14#13078815C212yesmaximal, complemented
15#13077902C212yesmaximal, complemented
16#13077868C211yesmaximal, characteristic, complemented
17C2×#10622851C211yesmaximal, characteristic, complemented
18#13077664C211yesmaximal, characteristic, complemented
19C11×#3489C211yesmaximal, characteristic, complemented
20C2×C11×2−1+4C2211yescharacteristic, complemented
21C22×C11×#41C2211yescharacteristic, complemented
22D4×Q8×C11C2212yescomplemented
23C11×#548C2212yescomplemented
24C11×#547—22no—
25C11×#547C2212yescomplemented
26C11×#546—22no—
27C11×#546C2212yescomplemented
28C11×#537—21no—
29C11×#537C2211yescharacteristic, complemented
30C11×#536—21no—
31C11×#536C2211yescharacteristic, complemented
32C11×#525—21no—
33C11×#525C2211yescharacteristic
34C2×C11×C22⋊Q8—21no—
35C2×C11×C22⋊Q8C2211yescharacteristic, complemented
36C11×#520C2211yescharacteristic, complemented
37#10623361C2212yescomplemented
38C2×#67002C2212yescomplemented
39C2×#67002C2211yescharacteristic, complemented
40C2×#67002C2211yescharacteristic, complemented
41C22×#4325C2212yescomplemented
42C22×#4325C2211yescharacteristic, complemented
43C22×#4323C2211yescharacteristic, complemented
44C2×#66983C2211yescharacteristic
45C2×#66983C2211yescharacteristic
46#10623197—22no—
47#10623175—21no—
48#10623175—21no—
49#10623136—21no—
50#10623136—21no—
51#10623121—22no—
52#10623096C2212yes—
53#10623096C2212yescomplemented
54D4×D44C2212yes—
55D4×D44C2212yescomplemented
56#10623066C2212yescomplemented
57#10622851C2212yescomplemented
58#10622851C2212yescomplemented
59#10622851C2212yescomplemented
60#10622851C2212yescomplemented
61#10622851C2212yescomplemented
62#10622851C2212yescomplemented
63#10622851C2212yescomplemented
64#10622851C2212yescomplemented
65#10622847C2212yescomplemented
66#10622846C2212yescomplemented
67#10622845C2211yescharacteristic, complemented
68#10622845C2211yescharacteristic, complemented
69#10622840C2212yescomplemented
70#10622840C2212yescomplemented
71#10622840C2212yescomplemented
72#10622840C2212yescomplemented
73#10622840C2212yescomplemented
74#10622838C2212yescomplemented
75C2×#66899C2211yescharacteristic, complemented
76#10622830C2212yescomplemented
77C2×#66896C2211yescharacteristic, complemented
78#10622820C2211yescharacteristic, complemented
79C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
80#10622698C2212yescomplemented
81#10622696C2212yescomplemented
82#10622696C2212yescomplemented
83#10622695C2212yescomplemented
84#10622671C2212yescomplemented
85#10622670C2212yescomplemented
86#10622670C2212yescomplemented
87#10622669C2212yescomplemented
88#10622662C2212yescomplemented
89#10622662C2212yescomplemented
90#10622662C2212yescomplemented
91#10622661C2212yescomplemented
92#10622661C2212yescomplemented
93#10622661C2212yescomplemented
94#10622659C2212yescomplemented
95#10622659C2212yescomplemented
96#10622659C2212yescomplemented
97#10622658C2212yescomplemented
98#10622657C2212yescomplemented
99#10622656C2212yescomplemented
100#10622652C2212yescomplemented
101#10622651C2212yescomplemented
102#10622649C2212yescomplemented
103#10622648C2212yescomplemented
104#10622640C2212yescomplemented
105#10622639C2212yescomplemented
106C4×#4325C2212yescomplemented
107#10622635C2212yescomplemented
108#10622628C2212yescomplemented
109#10622627C2212yescomplemented
110C4×#4323C2212yescomplemented
111#10622625C2212yescomplemented
112#10622624C2212yescomplemented
113#10622624C2212yescomplemented
114D4×C11⋊C8C2212yescomplemented
115#10622622C2212yescomplemented
116#10622613C2212yescomplemented
117#10622581C2212yescomplemented
118#10622580C2212yescomplemented
119C11×2−1+4—42no—
120C11×2−1+4—42no—
121C2×C11×#41—21no—
122C2×C11×#41—22no—
123C2×C11×#41—21no—
124C2×C11×#41—21no—
125C2×C11×#41—42no—
126C2×C11×#41—42no—
127C2×C11×#41C2311yescharacteristic
128C2×C11×#41C2311yescharacteristic
129C2×C11×#41C2311yescharacteristic
130C2×C11×#41C2312yes—
131C2×C11×#41C2311yescharacteristic
132C2×C11×#41C2311yescharacteristic
133C22×Q8×C11—21no—
134C22×Q8×C11C2311yescharacteristic
135C22×Q8×C11C2312yes—
136C22×Q8×C11C2311yescharacteristic
137C22×D4×C11—21no—
138C22×D4×C11C2311yescharacteristic
139C23×C4×C11—21no—
140C23×C4×C11C2311yescharacteristic
141C22×C22⋊D11—21no—
142C22×C22⋊D11—21no—
143C2×D4×D11—22no—
144C2×D4×D11—22no—
145C22×D44C2311yescharacteristic
146C22×D44C2311yescharacteristic
147C22×D44C2312yes—
148C11×C4⋊Q8—22no—
149C11×C4⋊Q8C2312yes—
150C11×#124—22no—
151C11×#124C2312yes—
152C11×#123—22no—
153C11×#123—22no—
154C11×#123—22no—
155C11×#123—22no—
156C11×#123D412yes—
157C11×C22⋊Q8—21no—
158C11×C22⋊Q8—21no—
159C11×C22⋊Q8—21no—
160C11×C22⋊Q8—21no—
161C11×C22⋊Q8—22no—
162C11×C22⋊Q8—21no—
163C11×C22⋊Q8—22no—
164C11×C22⋊Q8—22no—
165C11×C22⋊Q8D411yescharacteristic
166C11×C22⋊Q8D411yescharacteristic
167C11×C22⋊Q8C2312yes—
168C11×C22⋊Q8C2312yes—
169C11×C22⋊Q8C2312yes—
170C11×#121—21no—
171C11×#121—22no—
172C11×#121—22no—
173C11×#121—22no—
174C11×#121—22no—
175C11×#121D411yescharacteristic
176C11×#121D411yescharacteristic
177C11×#121C2312yes—
178C11×#120—22no—
179C11×#120D412yes—
180C4×Q8×C11C2312yes—
181C4×D4×C11—22no—
182C4×D4×C11—22no—
183C4×D4×C11—22no—
184C4×D4×C11C2312yes—
185C4×D4×C11C2312yes—
186C4×D4×C11C2312yes—
187C11×#117—21no—
188C11×#117C2311yescharacteristic
189C2×C11×C4⋊C4—21no—
190C2×C11×C4⋊C4—21no—
191C2×C11×C4⋊C4—22no—
192C2×C11×C4⋊C4C2311yescharacteristic
193C2×C11×C22⋊C4—21no—
194C2×C11×C22⋊C4—22no—
195#67002—44no—
196#67002—42no—
197#67002—42no—
198#67000—22no—
199C2×#4325—42no—
200C2×#4325—44no—
201C2×#4325C2312yes—
202C2×#4325C2312yes—
203C2×#4325C2312yes—
204C2×#4325C2312yes—
205C2×#4325C2312yes—
206C2×#4325C2312yes—
207C2×#4325C2312yes—
208C2×#4325C2312yes—
209#66993—22no—
210#66992—22no—
211#66992—22no—
212#66990—22no—
213#66990—22no—
214C2×#4323—42no—
215C2×#4323C2312yes—
216C2×#4323C2312yes—
217C2×#4323C2312yes—
218C2×#4323C2312yes—
219#66983—21no—
220#66983—21no—
221#66983—21no—
222#66983—21no—
223#66983C2312yes—
224#66983C2312yes—
225#66983C2312yes—
226#66983C2312yes—
227#66983C2312yes—
228#66983C2312yes—
229C2×(C2×D11)⋊C4—21no—
230C2×(C2×D11)⋊C4—21no—
231#66979C2312yes—
232C2×C4⋊Dic11C2311yescharacteristic
233C2×C4⋊Dic11C2311yescharacteristic
234C2×#4318C2311yescharacteristic
235C2×#4318C2311yescharacteristic
236C2×#4318C2312yes—
237C22×C11⋊C8C2311yescharacteristic
238C22×C11⋊C8C2311yescharacteristic
239C22×C11⋊C8C2312yes—
240#66951—22no—
241#66951—22no—
242#66948—22no—
243#66948—22no—
244#66947—22no—
245#66947—22no—
246#66937—22no—
247#66937—22no—
248#66936—22no—
249#66936—22no—
250#66935—22no—
251#66935—22no—
252#66935—22no—
253#66935—22no—
254(C22⋊D11)⋊C4—22no—
255(C22⋊D11)⋊C4—22no—
256#66927C2312yes—
257C4×D44C2312yes—
258C4×D44C2312yes—
259#66923C2312yes—
260#66899C2312yes—
261#66899C2312yes—
262#66899C2312yes—
263#66899C2312yes—
264#66899C2312yes—
265#66899C2312yes—
266#66899C2312yes—
267#66899C2312yes—
268#66896C2312yes—
269#66896C2312yes—
270#66896C2312yes—
271#66896C2312yes—
272C22⋊(C11⋊C8)C2312yes—
273C22⋊(C11⋊C8)C2312yes—
274C22⋊(C11⋊C8)C2312yes—
275C22⋊(C11⋊C8)C2312yes—
276C22⋊(C11⋊C8)C2312yes—
277C22⋊(C11⋊C8)C2312yes—
278#66873C2312yes—
279#66873C2312yes—
280#66873C2312yes—
281#66873C2312yes—
282#66872C2312yes—
283#66872C2312yes—
284#66871C2312yes—
285#66871C2312yes—
286C4⋊(C11⋊C8)C2312yes—
287C4⋊(C11⋊C8)C2312yes—
288#66867C2312yes—
289C4×C11⋊C8C2312yes—
290#61621—111nomaximal, Sylow
291C24×C11—21no—
292C24×C11C2×D411yescharacteristic
293C23×D11—21no—
294C23×D11—21no—
295C23×D11—22no—
296C11×#41—22no—
297C11×#41—22no—
298C11×#41—22no—
299C11×#41—22no—
300C11×#41—24no—
301C11×#41—41no—
302C11×#41—41no—
303C11×#41—41no—
304C11×#41—41no—
305C11×#41—41no—
306C11×#41—41no—
307C11×#41—42no—
308C11×#41—44no—
309C11×#41—44no—
310C11×#41—44no—
311C11×#41—48no—
312C2×Q8×C11—21no—
313C2×Q8×C11—22no—
314C2×Q8×C11—21no—
315C2×Q8×C11—22no—
316C2×Q8×C11—24no—
317C2×Q8×C11—41no—
318C2×Q8×C11—42no—
319C2×Q8×C11—41no—
320C2×Q8×C11—41no—
321C2×Q8×C11—44no—
322C2×Q8×C11C2×D411yescharacteristic
323C2×Q8×C11C2412yes—
324C2×Q8×C11C2411yescharacteristic
325C2×Q8×C11C2411yescharacteristic
326C2×D4×C11—21no—
327C2×D4×C11—22no—
328C2×D4×C11—22no—
329C2×D4×C11—21no—
330C2×D4×C11—21no—
331C2×D4×C11—21no—
332C2×D4×C11—22no—
333C2×D4×C11—21no—
334C2×D4×C11—41no—
335C2×D4×C11—44no—
336C2×D4×C11C2×D412yes—
337C2×D4×C11C2×D411yescharacteristic
338C2×D4×C11C2×D412yes—
339C2×D4×C11C2×D412yes—
340C2×D4×C11C2411yescharacteristic
341C2×D4×C11C2411yescharacteristic
342C22×C4×C11—21no—
343C22×C4×C11—21no—
344C22×C4×C11—22no—
345C22×C4×C11—21no—
346C22×C4×C11—21no—
347C22×C4×C11—22no—
348C22×C4×C11—21no—
349C22×C4×C11—21no—
350C22×C4×C11—21no—
351C22×C4×C11—22no—
352C22×C4×C11—41no—
353C22×C4×C11—41no—
354C22×C4×C11—44no—
355C22×C4×C11C2×D411yescharacteristic
356C22×C4×C11C2×D411yescharacteristic
357C22×C4×C11C2×D411yescharacteristic
358C22×C4×C11C2411yescharacteristic
359C22×C4×C11C2411yescharacteristic
360C22×C4×C11C2412yes—
361C22×C4×C11C2411yescharacteristic
362C2×C22⋊D11—22no—
363C2×C22⋊D11—22no—
364C2×C22⋊D11—22no—
365C2×C22⋊D11—22no—
366C2×C22⋊D11—22no—
367C2×C22⋊D11—22no—
368C2×C22⋊D11—82no—
369C2×C22⋊D11—82no—
370C22×Dic11—21no—
371C22×Dic11—21no—
372D4×D11—84no—
373D4×D11—84no—
374C2×D44—22no—
375C2×D44—22no—
376C2×D44—21no—
377C2×D44—21no—
378C2×D44—22no—
379C2×D44—41no—
380C2×D44—41no—
381C2×D44—42no—
382C2×D44—41no—
383C2×D44—41no—
384C2×D44—42no—
385C2×D44C2412yes—
386C2×D44C2412yes—
387C2×C4×D11—22no—
388C2×C4×D11—22no—
389C11×C4⋊C4—22no—
390C11×C4⋊C4—21no—
391C11×C4⋊C4—22no—
392C11×C4⋊C4—22no—
393C11×C4⋊C4—22no—
394C11×C4⋊C4—22no—
395C11×C4⋊C4—22no—
396C11×C4⋊C4C2×D411yescharacteristic
397C11×C4⋊C4C2×D411yescharacteristic
398C11×C4⋊C4C2×D412yes—
399C11×C4⋊C4C2×D412yes—
400C11×C4⋊C4C2412yes—
401C11×C22⋊C4—22no—
402C11×C22⋊C4—22no—
403C11×C22⋊C4—22no—
404C11×C22⋊C4—22no—
405C11×C22⋊C4—22no—
406C11×C22⋊C4—22no—
407C11×C22⋊C4—22no—
408C11×C22⋊C4C2×D412yes—
409C11×C22⋊C4C2×D412yes—
410C11×C22⋊C4C2×D412yes—
411C11×C22⋊C4C2×D412yes—
412C11×C22⋊C4C2×D412yes—
413C42×C11—22no—
414C42×C11C2412yes—
415C22⋊Dic11—22no—
416#4325—24no—
417#4325—24no—
418#4325—42no—
419#4325—42no—
420#4325—42no—
421#4325—42no—
422#4325—42no—
423#4325—42no—
424#4323—24no—
425#4323—24no—
426#4323—42no—
427#4323—42no—
428(C2×D11)⋊C4—22no—
429(C2×D11)⋊C4—22no—
430(C2×D11)⋊C4—22no—
431(C2×D11)⋊C4—22no—
432(C2×D11)⋊C4—22no—
433(C2×D11)⋊C4—22no—
434(C2×D11)⋊C4—22no—
435(C2×D11)⋊C4—22no—
436C4⋊Dic11—21no—
437C4⋊Dic11—21no—
438C4⋊Dic11C2412yes—
439C4⋊Dic11C2412yes—
440Dic11⋊C4—22no—
441Dic11⋊C4—22no—
442C4×Dic11—22no—
443#4318—41no—
444#4318—41no—
445#4318—42no—
446C2×C11⋊C8—41no—
447C2×C11⋊C8—41no—
448C2×C11⋊C8—42no—
449C2×C11⋊C8C2412yes—
450C2×C11⋊C8C2412yes—
451C2×C11⋊C8C2412yes—
452C2×C11⋊C8C2412yes—
453#3537—111no—
454#3489D1111yescharacteristic, complemented
455#3326—112no—
456#3320—112no—
457#3307—112no—
458#3297—112no—
459D4×SD16—112no—
460#3272—112no—
461#3265—112no—
462#3264—112no—
463#3221—112no—
464#3198—112no—
465#3193—111no—
466#3187—111no—
467#3119—112no—
468#3010—112no—
469#3006—111no—
470C2×#449—111no—
471#2976—111no—
472C23×C11—21no—
473C23×C11—22no—
474C23×C11—21no—
475C23×C11—41no—
476C23×C11—41no—
477C23×C11—42no—
478C23×C11—42no—
479C23×C11—81no—
480C23×C11C22×D412yes—
481C23×C11C22×D411yescharacteristic
482C23×C11C22×D411yescharacteristic
483C23×C11C22×D411yescharacteristic
484C22×D11—22no—
485C22×D11—22no—
486C22×D11—42no—
487C22×D11—42no—
488C22×D11—81no—
489C22×D11—81no—
490C22×D11—82no—
491C22×D11—82no—
492C22×D11—82no—
493C22×D11—81no—
494C22×D11—81no—
495Q8×C11—21no—
496Q8×C11—22no—
497Q8×C11—21no—
498Q8×C11—22no—
499Q8×C11—21no—
500Q8×C11—41no—
501Q8×C11—44no—
502Q8×C11—42no—
503Q8×C11—42no—
504Q8×C11H(5,𝔽2)12yes—
505D4×C11—24no—
506D4×C11—24no—
507D4×C11—21no—
508D4×C11—21no—
509D4×C11—21no—
510D4×C11—42no—
511D4×C11—41no—
512D4×C11—42no—
513D4×C11—42no—
514D4×C11—42no—
515D4×C11—42no—
516D4×C11—44no—
517D4×C11—42no—
518D4×C11—82no—
519D4×C11H(5,𝔽2)12yes—
520C2×C4×C11—24no—
521C2×C4×C11—21no—
522C2×C4×C11—21no—
523C2×C4×C11—21no—
524C2×C4×C11—22no—
525C2×C4×C11—21no—
526C2×C4×C11—21no—
527C2×C4×C11—22no—
528C2×C4×C11—21no—
529C2×C4×C11—21no—
530C2×C4×C11—22no—
531C2×C4×C11—22no—
532C2×C4×C11—21no—
533C2×C4×C11—41no—
534C2×C4×C11—41no—
535C2×C4×C11—41no—
536C2×C4×C11—42no—
537C2×C4×C11—42no—
538C2×C4×C11—42no—
539C2×C4×C11—44no—
540C2×C4×C11—44no—
541C2×C4×C11—42no—
542C2×C4×C11—42no—
543C2×C4×C11—82no—
544C2×C4×C11—81no—
545C2×C4×C11C22×D412yes—
546C2×C4×C11C22×D412yes—
547C2×C4×C11C22×D412yes—
548C2×C4×C11C22×D411yescharacteristic
549C2×C4×C11C22×D411yescharacteristic
550C2×C4×C11C22×D411yescharacteristic
551C2×C4×C11C2511yescharacteristic
552C22⋊D11—44no—
553C22⋊D11—44no—
554C22⋊D11—82no—
555C22⋊D11—82no—
556C22⋊D11—82no—
557C22⋊D11—82no—
558C2×Dic11—22no—
559C2×Dic11—22no—
560C2×Dic11—81no—
561C2×Dic11—81no—
562D44—22no—
563D44—22no—
564D44—22no—
565D44—22no—
566D44—81no—
567D44—81no—
568D44—82no—
569D44—82no—
570D44—82no—
571C4×D11—82no—
572C4×D11—82no—
573C11⋊C8—22no—
574C11⋊C8—22no—
575C11⋊C8—22no—
576C11⋊C8—22no—
577C2×2−1+4C2×D1111yescharacteristic, complemented
578C22×#41C2×D1111yescharacteristic, complemented
579C2×AGL(1,ℤ/8)—111no—
580C2×AGL(1,ℤ/8)—111no—
581C2×AGL(1,ℤ/8)—112no—
582C22×SD16—111no—
583C22×SD16—112no—
584C22×D8—111no—
585#560—222no—
586#553—112no—
587#553—112no—
588D4×Q8C2×D1112yescomplemented
589#548C2×D1112yescomplemented
590#547—22no—
591#547C2×D1112yescomplemented
592#546—22no—
593#546C2×D1112yescomplemented
594D42—112no—
595D42—112no—
596D42—222no—
597#540—112no—
598#538—221no—
599#538—221no—
600#537—21no—
601#537C2×D1111yescharacteristic, complemented
602#536—21no—
603#536C2×D1111yescharacteristic, complemented
604#535—112no—
605#534—221no—
606#534—221no—
607#525—21no—
608#525C2×D1111yescharacteristic
609C2×C22⋊Q8—21no—
610C2×C22⋊Q8C2×D1111yescharacteristic, complemented
611C2×#121—111no—
612C2×#121—111no—
613#520C2×D1111yescharacteristic, complemented
614#496—112no—
615#492—112no—
616#491—112no—
617#488—112no—
618#485—112no—
619#484—112no—
620#483—112no—
621#482—112no—
622#481—112no—
623#480—112no—
624#479—112no—
625#478—112no—
626#469—112no—
627#468—112no—
628#468—112no—
629#468—112no—
630#466—112no—
631#465—112no—
632#465—112no—
633#465—112no—
634#463—112no—
635#463—112no—
636#461—112no—
637#461—112no—
638#460—112no—
639#459—112no—
640#450—112no—
641#450—112no—
642#450—112no—
643#449—112no—
644#449—112no—
645#449—112no—
646#449—112no—
647#449—112no—
648#449—112no—
649#449—112no—
650#449—112no—
651#448—112no—
652#448—112no—
653#448—112no—
654#448—112no—
655#448—112no—
656#447—112no—
657#447—112no—
658#442—112no—
659#440—112no—
660C4×SD16—112no—
661C4×D8—112no—
662#436—112no—
663#435—112no—
664#435—112no—
665C8×D4—112no—
666#433—112no—
667#419—112no—
668#417—111no—
669#417—111no—
670#416—112no—
671C2×#103—111no—
672C2×#102—111no—
673#408—112no—
674#407—111no—
675C2×C22⋊C8—111no—
676C22×C11—21no—
677C22×C11—21no—
678C22×C11—21no—
679C22×C11—21no—
680C22×C11—22no—
681C22×C11—21no—
682C22×C11—22no—
683C22×C11—22no—
684C22×C11—21no—
685C22×C11—22no—
686C22×C11—21no—
687C22×C11—21no—
688C22×C11—41no—
689C22×C11—41no—
690C22×C11—41no—
691C22×C11—41no—
692C22×C11—41no—
693C22×C11—82no—
694C22×C11—84no—
695C22×C11#57712yes—
696C22×C11C23×D411yescharacteristic
697C2×D11—42no—
698C2×D11—42no—
699C2×D11—42no—
700C2×D11—42no—
701C2×D11—42no—
702C2×D11—42no—
703C2×D11—162no—
704C2×D11—162no—
705C2×D11—164no—
706C4×C11—22no—
707C4×C11—21no—
708C4×C11—22no—
709C4×C11—21no—
710C4×C11—21no—
711C4×C11—22no—
712C4×C11—22no—
713C4×C11—42no—
714C4×C11—41no—
715C4×C11—42no—
716C4×C11C2×H(5,𝔽2)11yescharacteristic
717C4×C11C2×H(5,𝔽2)11yescharacteristic
718Dic11—42no—
719Dic11—42no—
7202−1+4—42no—
7212−1+4—42no—
722C2×#41—21no—
723C2×#41—22no—
724C2×#41—21no—
725C2×#41—21no—
726C2×#41—42no—
727C2×#41—42no—
728C2×#41C22×D1111yescharacteristic
729C2×#41C22×D1112yes—
730C2×#41C22×D1111yescharacteristic
731C2×#41C22×D1111yescharacteristic
732C2×#41C22×D1111yescharacteristic
733C2×#41C22×D1111yescharacteristic
734C22×Q8—21no—
735C22×Q8C22×D1112yes—
736C22×Q8C22×D1111yescharacteristic
737C22×Q8C22×D1111yescharacteristic
738C22×D4—21no—
739C22×D4—111no—
740C22×D4—111no—
741C22×D4—112no—
742C22×D4—221no—
743C22×D4—221no—
744C22×D4—222no—
745C22×D4—222no—
746C22×D4C22×D1111yescharacteristic
747C23×C4—21no—
748C23×C4C22×D1111yescharacteristic
749AGL(1,ℤ/8)—444no—
750AGL(1,ℤ/8)—442no—
751AGL(1,ℤ/8)—442no—
752C2×SD16—112no—
753C2×SD16—112no—
754C2×SD16—112no—
755C2×SD16—112no—
756C2×SD16—112no—
757C2×SD16—112no—
758C2×SD16—112no—
759C2×SD16—112no—
760C2×SD16—442no—
761C2×SD16—444no—
762C2×D8—112no—
763C2×D8—112no—
764C2×D8—112no—
765C2×D8—112no—
766C2×D8—442no—
767C2×M16—111no—
768C2×M16—111no—
769C2×M16—112no—
770C22×C8—111no—
771C22×C8—111no—
772C22×C8—112no—
773C4⋊Q8—22no—
774C4⋊Q8C22×D1112yes—
775#127—112no—
776#127—222no—
777#126—222no—
778#126—222no—
779#125—112no—
780#124—22no—
781#124—222no—
782#124C22×D1112yes—
783#123—22no—
784#123—22no—
785#123—22no—
786#123—22no—
787#123—222no—
788#123—222no—
789#123—222no—
790#123—222no—
791#123C22⋊D1112yes—
792C22⋊Q8—21no—
793C22⋊Q8—21no—
794C22⋊Q8—21no—
795C22⋊Q8—21no—
796C22⋊Q8—22no—
797C22⋊Q8—21no—
798C22⋊Q8—22no—
799C22⋊Q8—22no—
800C22⋊Q8C22⋊D1111yescharacteristic
801C22⋊Q8C22⋊D1111yescharacteristic
802C22⋊Q8C22×D1112yes—
803C22⋊Q8C22×D1112yes—
804C22⋊Q8C22×D1112yes—
805#121—21no—
806#121—22no—
807#121—22no—
808#121—22no—
809#121—22no—
810#121—112no—
811#121—112no—
812#121—112no—
813#121—112no—
814#121—112no—
815#121—112no—
816#121—222no—
817#121—222no—
818#121—221no—
819#121—221no—
820#121—221no—
821#121—221no—
822#121—222no—
823#121—222no—
824#121—222no—
825#121—222no—
826#121C22⋊D1111yescharacteristic
827#121C22⋊D1111yescharacteristic
828#121C22×D1112yes—
829#120—22no—
830#120—222no—
831#120—222no—
832#120—222no—
833#120—222no—
834#120—222no—
835#120—222no—
836#120C22⋊D1112yes—
837C4×Q8C22×D1112yes—
838C4×D4—22no—
839C4×D4—22no—
840C4×D4—22no—
841C4×D4—112no—
842C4×D4—112no—
843C4×D4—222no—
844C4×D4—222no—
845C4×D4C22×D1112yes—
846C4×D4C22×D1112yes—
847C4×D4C22×D1112yes—
848#117—21no—
849#117—112no—
850#117C22×D1111yescharacteristic
851C2×C4⋊C4—21no—
852C2×C4⋊C4—21no—
853C2×C4⋊C4—22no—
854C2×C4⋊C4—111no—
855C2×C4⋊C4—111no—
856C2×C4⋊C4C22×D1111yescharacteristic
857C2×C22⋊C4—21no—
858C2×C22⋊C4—22no—
859C2×C22⋊C4—221no—
860C2×C22⋊C4—221no—
861#107—112no—
862#107—112no—
863#106—112no—
864#106—112no—
865C4⋊C8—112no—
866C4⋊C8—112no—
867#103—112no—
868#103—112no—
869#103—112no—
870#103—112no—
871#103—112no—
872#103—112no—
873#103—112no—
874#103—112no—
875#102—112no—
876#102—112no—
877#102—112no—
878#102—112no—
879#102—112no—
880#102—112no—
881#102—112no—
882#102—112no—
883C22⋊C8—112no—
884C22⋊C8—112no—
885C22⋊C8—112no—
886C22⋊C8—112no—
887C22⋊C8—112no—
888C22⋊C8—112no—
889#97—112no—
890C4×C8—112no—
891C2×C11—22no—
892C2×C11—42no—
893C2×C11—41no—
894C2×C11—41no—
895C2×C11—42no—
896C2×C11—81no—
897C2×C11#348411yescharacteristic
898C2×C11C2×#57711yescharacteristic
899C2×C11#358511yescharacteristic
900D11—82no—
901D11—82no—
902C24—21no—
903C24—221no—
904C24—221no—
905C24—222no—
906C24C2×C22⋊D1111yescharacteristic
907#41—22no—
908#41—22no—
909#41—22no—
910#41—22no—
911#41—24no—
912#41—41no—
913#41—41no—
914#41—41no—
915#41—41no—
916#41—41no—
917#41—41no—
918#41—42no—
919#41—44no—
920#41—44no—
921#41—44no—
922#41—48no—
923C2×Q8—21no—
924C2×Q8—22no—
925C2×Q8—21no—
926C2×Q8—22no—
927C2×Q8—24no—
928C2×Q8—41no—
929C2×Q8—42no—
930C2×Q8—41no—
931C2×Q8—41no—
932C2×Q8—44no—
933C2×Q8C2×C22⋊D1111yescharacteristic
934C2×Q8C23×D1112yes—
935C2×Q8C23×D1111yescharacteristic
936C2×Q8C23×D1111yescharacteristic
937C2×D4—21no—
938C2×D4—22no—
939C2×D4—22no—
940C2×D4—21no—
941C2×D4—21no—
942C2×D4—21no—
943C2×D4—22no—
944C2×D4—21no—
945C2×D4—41no—
946C2×D4—44no—
947C2×D4—112no—
948C2×D4—112no—
949C2×D4—222no—
950C2×D4—222no—
951C2×D4—222no—
952C2×D4—222no—
953C2×D4—222no—
954C2×D4—222no—
955C2×D4—221no—
956C2×D4—221no—
957C2×D4—222no—
958C2×D4—222no—
959C2×D4—222no—
960C2×D4—441no—
961C2×D4—441no—
962C2×D4—442no—
963C2×D4—441no—
964C2×D4—441no—
965C2×D4—442no—
966C2×D4—884no—
967C2×D4—884no—
968C2×D4—882no—
969C2×D4—882no—
970C2×D4C2×C22⋊D1112yes—
971C2×D4C2×C22⋊D1112yes—
972C2×D4C2×C22⋊D1111yescharacteristic
973C2×D4C2×C22⋊D1112yes—
974C2×D4C23×D1111yescharacteristic
975C2×D4C23×D1111yescharacteristic
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—22no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—22no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—22no—
986C22×C4—41no—
987C22×C4—41no—
988C22×C4—44no—
989C22×C4—221no—
990C22×C4—221no—
991C22×C4—222no—
992C22×C4—222no—
993C22×C4C2×C22⋊D1111yescharacteristic
994C22×C4C2×C22⋊D1111yescharacteristic
995C22×C4C2×C22⋊D1111yescharacteristic
996C22×C4C23×D1111yescharacteristic
997C22×C4C23×D1111yescharacteristic
998C22×C4C23×D1111yescharacteristic
999C22×C4C23×D1112yes—
1000SD16—224no—
1001SD16—224no—
1002SD16—442no—
1003SD16—442no—
1004SD16—442no—
1005SD16—442no—
1006SD16—442no—
1007SD16—442no—
1008D8—224no—
1009D8—224no—
1010D8—442no—
1011D8—442no—
1012M16—442no—
1013M16—441no—
1014M16—441no—
1015C2×C8—112no—
1016C2×C8—112no—
1017C2×C8—112no—
1018C2×C8—112no—
1019C2×C8—441no—
1020C2×C8—441no—
1021C2×C8—442no—
1022C4⋊C4—22no—
1023C4⋊C4—21no—
1024C4⋊C4—22no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—22no—
1028C4⋊C4—22no—
1029C4⋊C4—112no—
1030C4⋊C4—112no—
1031C4⋊C4—221no—
1032C4⋊C4—221no—
1033C4⋊C4—222no—
1034C4⋊C4—222no—
1035C4⋊C4C2×C22⋊D1111yescharacteristic
1036C4⋊C4C2×C22⋊D1112yes—
1037C4⋊C4C2×C22⋊D1111yescharacteristic
1038C4⋊C4C2×C22⋊D1112yes—
1039C4⋊C4C23×D1112yes—
1040C22⋊C4—22no—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—22no—
1044C22⋊C4—22no—
1045C22⋊C4—22no—
1046C22⋊C4—22no—
1047C22⋊C4—222no—
1048C22⋊C4—222no—
1049C22⋊C4—222no—
1050C22⋊C4—222no—
1051C22⋊C4—222no—
1052C22⋊C4—222no—
1053C22⋊C4—222no—
1054C22⋊C4—222no—
1055C22⋊C4—222no—
1056C22⋊C4C2×C22⋊D1112yes—
1057C22⋊C4C2×C22⋊D1112yes—
1058C22⋊C4C2×C22⋊D1112yes—
1059C22⋊C4C2×C22⋊D1112yes—
1060C22⋊C4C2×C22⋊D1112yes—
1061C42—22no—
1062C42—222no—
1063C42C23×D1112yes—
1064C11#6162111yescharacteristic, complemented, Sylow
1065C23—21no—
1066C23—22no—
1067C23—21no—
1068C23—41no—
1069C23—41no—
1070C23—42no—
1071C23—42no—
1072C23—81no—
1073C23—222no—
1074C23—222no—
1075C23—442no—
1076C23—442no—
1077C23—881no—
1078C23—882no—
1079C23—881no—
1080C23—881no—
1081C23—882no—
1082C23—881no—
1083C23—882no—
1084C23C22×C22⋊D1111yescharacteristic
1085C23C22×C22⋊D1112yes—
1086C23C22×C22⋊D1111yescharacteristic
1087C23C22×C22⋊D1111yescharacteristic
1088Q8—21no—
1089Q8—22no—
1090Q8—21no—
1091Q8—22no—
1092Q8—21no—
1093Q8—41no—
1094Q8—44no—
1095Q8—42no—
1096Q8—42no—
1097Q8#6703712yes—
1098D4—24no—
1099D4—24no—
1100D4—21no—
1101D4—21no—
1102D4—21no—
1103D4—42no—
1104D4—41no—
1105D4—42no—
1106D4—42no—
1107D4—42no—
1108D4—42no—
1109D4—44no—
1110D4—42no—
1111D4—82no—
1112D4—222no—
1113D4—222no—
1114D4—222no—
1115D4—222no—
1116D4—444no—
1117D4—444no—
1118D4—881no—
1119D4—881no—
1120D4—882no—
1121D4—882no—
1122D4—882no—
1123D4—882no—
1124D4—882no—
1125D4—882no—
1126D4—882no—
1127D4#6703712yes—
1128C2×C4—24no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—22no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—22no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—21no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—44no—
1148C2×C4—44no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—82no—
1152C2×C4—81no—
1153C2×C4—222no—
1154C2×C4—222no—
1155C2×C4—882no—
1156C2×C4—882no—
1157C2×C4—881no—
1158C2×C4—881no—
1159C2×C4C22×C22⋊D1112yes—
1160C2×C4C22×C22⋊D1112yes—
1161C2×C4C22×C22⋊D1112yes—
1162C2×C4C22×C22⋊D1111yescharacteristic
1163C2×C4C22×C22⋊D1111yescharacteristic
1164C2×C4C22×C22⋊D1111yescharacteristic
1165C2×C4C24×D1111yescharacteristic
1166C8—222no—
1167C8—222no—
1168C8—222no—
1169C8—222no—
1170C22—21no—
1171C22—21no—
1172C22—21no—
1173C22—21no—
1174C22—22no—
1175C22—21no—
1176C22—22no—
1177C22—22no—
1178C22—21no—
1179C22—21no—
1180C22—22no—
1181C22—21no—
1182C22—41no—
1183C22—41no—
1184C22—41no—
1185C22—41no—
1186C22—41no—
1187C22—82no—
1188C22—84no—
1189C22—442no—
1190C22—442no—
1191C22—442no—
1192C22—442no—
1193C22—442no—
1194C22—442no—
1195C22—1762no—
1196C22—1762no—
1197C22—1764no—
1198C22#1062336812yes—
1199C22C23×C22⋊D1111yescharacteristic
1200C4—22no—
1201C4—21no—
1202C4—22no—
1203C4—21no—
1204C4—21no—
1205C4—22no—
1206C4—22no—
1207C4—42no—
1208C4—41no—
1209C4—42no—
1210C4—442no—
1211C4—442no—
1212C4C2×#6703711yescharacteristic
1213C4C2×#6703711yescharacteristic
1214C2—22no—
1215C2—41no—
1216C2—41no—
1217C2—42no—
1218C2—42no—
1219C2—81no—
1220C2—882no—
1221C2—882no—
1222C2#1308225111yescharacteristic
1223C2C2×#1062336811yescharacteristic
1224C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3489C2
socleC22×C11C23×D4
hypercenter#3489D11
hypocenterC11#61621
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #525 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. #13082855C2semidirect
2. #13080869C2semidirect
3. #13080787C2semidirect
4. #13080592C2semidirect
5. #13080466C2semidirect
6. D4×#4325C2semidirect
7. #13080216C2semidirect
8. #13080112C2semidirect
9. #13080097C2semidirect
10. #13079677C2semidirect
11. #13079462C2semidirect
12. #13079418C2semidirect
13. #13079369C2semidirect
14. #13078815C2semidirect
15. #13077902C2semidirect
16. #13077868C2semidirect
17. C2×#10622851C2semidirect
18. #13077664C2semidirect
19. C11×#3489C2semidirect
20. C2×C11×2−1+4C22semidirect
21. C22×C11×#41C22semidirect
22. D4×Q8×C11C22semidirect
23. C11×#548C22semidirect
25. C11×#547C22semidirect
27. C11×#546C22semidirect
29. C11×#537C22semidirect
31. C11×#536C22semidirect
35. C2×C11×C22⋊Q8C22semidirect
36. C11×#520C22semidirect
37. #10623361C22semidirect
38. C2×#67002C22semidirect
39. C2×#67002C22semidirect
40. C2×#67002C22semidirect
41. C22×#4325C22semidirect
42. C22×#4325C22semidirect
43. C22×#4323C22semidirect
53. #10623096C22semidirect
55. D4×D44C22semidirect
56. #10623066C22semidirect
57. #10622851C22semidirect
58. #10622851C22semidirect
59. #10622851C22semidirect
60. #10622851C22semidirect
61. #10622851C22semidirect
62. #10622851C22semidirect
63. #10622851C22semidirect
64. #10622851C22semidirect
65. #10622847C22semidirect
66. #10622846C22semidirect
67. #10622845C22semidirect
68. #10622845C22semidirect
69. #10622840C22semidirect
70. #10622840C22semidirect
71. #10622840C22semidirect
72. #10622840C22semidirect
73. #10622840C22semidirect
74. #10622838C22semidirect
75. C2×#66899C22semidirect
76. #10622830C22semidirect
77. C2×#66896C22semidirect
78. #10622820C22semidirect
79. C2×C22⋊(C11⋊C8)C22semidirect
80. #10622698C22semidirect
81. #10622696C22semidirect
82. #10622696C22semidirect
83. #10622695C22semidirect
84. #10622671C22semidirect
85. #10622670C22semidirect
86. #10622670C22semidirect
87. #10622669C22semidirect
88. #10622662C22semidirect
89. #10622662C22semidirect
90. #10622662C22semidirect
91. #10622661C22semidirect
92. #10622661C22semidirect
93. #10622661C22semidirect
94. #10622659C22semidirect
95. #10622659C22semidirect
96. #10622659C22semidirect
97. #10622658C22semidirect
98. #10622657C22semidirect
99. #10622656C22semidirect
100. #10622652C22semidirect
101. #10622651C22semidirect
102. #10622649C22semidirect
103. #10622648C22semidirect
104. #10622640C22semidirect
105. #10622639C22semidirect
106. C4×#4325C22semidirect
107. #10622635C22semidirect
108. #10622628C22semidirect
109. #10622627C22semidirect
110. C4×#4323C22semidirect
111. #10622625C22semidirect
112. #10622624C22semidirect
113. #10622624C22semidirect
114. D4×C11⋊C8C22semidirect
115. #10622622C22semidirect
116. #10622613C22semidirect
117. #10622581C22semidirect
118. #10622580C22semidirect
454. #3489D11semidirect
577. C2×2−1+4C2×D11semidirect
578. C22×#41C2×D11semidirect
588. D4×Q8C2×D11semidirect
589. #548C2×D11semidirect
591. #547C2×D11semidirect
593. #546C2×D11semidirect
601. #537C2×D11semidirect
603. #536C2×D11semidirect
610. C2×C22⋊Q8C2×D11semidirect
613. #520C2×D11semidirect
1064. C11#61621semidirect

Maximal subgroups

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

subgroupindex
#130828552
#130808692
#130807872
#130805922
#130804662
D4×#43252
#130802162
#130801122
#130800972
#130796772
#130794622
#130794182
#130793692
#130788152
#130779022
#130778682
C2×#106228512
#130776642
C11×#34892
#6162111