Finite Group Databasebeta

← #15631746

Subgroups — #15631746

Order 2816.

2116 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082378C211yesmaximal, characteristic, complemented
2#13080826C212yesmaximal, complemented
3#13080811C212yesmaximal, complemented
4#13080751C212yesmaximal, complemented
5#13080706C212yesmaximal, complemented
6#13080631C212yesmaximal, complemented
7#13080586C212yesmaximal, complemented
8#13080460C212yesmaximal, complemented
9#13080445C212yesmaximal, complemented
10#13079019C211yesmaximal, characteristic, complemented
11#13078605C211yesmaximal, characteristic, complemented
12#13078594C211yesmaximal, characteristic, complemented
13C2×#10622679C211yesmaximal, characteristic, complemented
14#13078283C211yesmaximal, characteristic, complemented
15#13078275C211yesmaximal, characteristic, complemented
16#13078071C211yesmaximal, characteristic, complemented
17#13077917C211yesmaximal, characteristic, complemented
18#13077917C211yesmaximal, characteristic, complemented
19C4×#67002C211yesmaximal, characteristic, complemented
20#13077360C211yesmaximal, characteristic, complemented
21#13077139C211yesmaximal, characteristic, complemented
22#13077139C211yesmaximal, characteristic, complemented
23C11×#3512C211yesmaximal, characteristic, complemented
24C2×#67042C2211yescharacteristic
25C2×#67042C2211yescharacteristic
26C11×#553—22no—
27C11×#553—22no—
28C11×#553C2212yescomplemented
29C11×#553C2212yescomplemented
30C11×#552C2212yescomplemented
31C11×#552C2212yescomplemented
32C11×#541—21no—
33C11×#540—21no—
34C11×#537C2211yescharacteristic, complemented
35C11×#537C2211yescharacteristic, complemented
36C11×#532C2211yescharacteristic
37C11×#529—21no—
38C11×#529—21no—
39C2×C11×#125C2211yescharacteristic, complemented
40C11×#520C2211yescharacteristic, complemented
41C11×#520C2211yescharacteristic, complemented
42C4×C11×#41C2211yescharacteristic, complemented
43#10623364C2211yescharacteristic
44#10623364C2211yescharacteristic
45C2×#67003C2211yescharacteristic, complemented
46C2×#67003C2211yescharacteristic, complemented
47C2×#67002C2211yescharacteristic
48C2×#67001C2211yescharacteristic, complemented
49C2×#67001C2211yescharacteristic, complemented
50#10623257—21no—
51#10623248—21no—
52#10623207—21no—
53#10623207—21no—
54#10623136—22no—
55D11×#121—22no—
56#10623082C2212yes—
57#10623081C2212yes—
58#10623081C2212yes—
59D4×D44C2212yes—
60#10623008C2211yescharacteristic
61C2×C4×D44C2211yescharacteristic
62#10622847C2211yescharacteristic, complemented
63#10622847C2211yescharacteristic, complemented
64#10622845C2211yescharacteristic, complemented
65#10622682C2212yescomplemented
66#10622681C2212yescomplemented
67#10622681C2212yescomplemented
68#10622680C2212yescomplemented
69#10622679C2212yescomplemented
70#10622679C2212yescomplemented
71#10622679C2212yescomplemented
72#10622679C2212yescomplemented
73#10622665C2212yescomplemented
74#10622664C2212yescomplemented
75#10622662C2212yescomplemented
76#10622661C2212yescomplemented
77#10622660C2212yescomplemented
78#10622660C2212yescomplemented
79#10622659C2212yescomplemented
80#10622659C2212yescomplemented
81#10622655C2212yescomplemented
82#10622654C2212yescomplemented
83#10622652C2212yescomplemented
84#10622651C2212yescomplemented
85#10622650C2212yescomplemented
86#10622650C2212yescomplemented
87#10622649C2212yescomplemented
88#10622649C2212yescomplemented
89#10622644C2211yescharacteristic, complemented
90#10622641C2211yescharacteristic, complemented
91#10622641C2211yescharacteristic, complemented
92#10622640C2211yescharacteristic, complemented
93#10622639C2212yescomplemented
94C4×#4325C2212yescomplemented
95#10622632C2211yescharacteristic, complemented
96#10622629C2211yescharacteristic, complemented
97#10622629C2211yescharacteristic, complemented
98#10622628C2211yescharacteristic, complemented
99#10622627C2212yescomplemented
100C4×#4323C2212yescomplemented
101#10622625C2212yescomplemented
102#10622624C2212yescomplemented
103#10622624C2212yescomplemented
104D4×C11⋊C8C2212yescomplemented
105#10622616C2212yescomplemented
106#10622616C2212yescomplemented
107#10622615C2212yescomplemented
108#10622615C2211yescharacteristic, complemented
109#10622615C2211yescharacteristic, complemented
110#10622615C2212yescomplemented
111#10622614C2211yescharacteristic
112#10622614C2212yescomplemented
113#10622614C2212yescomplemented
114#10622609C2212yescomplemented
115#10622609C2212yescomplemented
116#10622608C2211yescharacteristic, complemented
117#10622584C2212yescomplemented
118#10622583C2212yescomplemented
119#10622581C2212yescomplemented
120#10622580C2212yescomplemented
121#10622579C2211yescharacteristic, complemented
122#10622579C2212yescomplemented
123#10622579C2211yescharacteristic, complemented
124#10622579C2211yescharacteristic, complemented
125#10622579C2211yescharacteristic, complemented
126#10622579C2212yescomplemented
127C2×#66873C2211yescharacteristic
128C2×#66873C2211yescharacteristic
129C2×#66873C2212yescomplemented
130C2×#66873C2212yescomplemented
131C2×#66872C2211yescharacteristic, complemented
132C2×#66871C2211yescharacteristic, complemented
133C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
134C4×#4318C2211yescharacteristic, complemented
135C2×C11×#41C2311yescharacteristic
136C2×C11×#41C2311yescharacteristic
137C2×C11×#41C2311yescharacteristic
138#67042—24no—
139#67042—24no—
140#67042—42no—
141#67042—42no—
142C2×#4343—21no—
143C2×#4343—21no—
144C2×D4×D11—21no—
145C2×D4×D11—21no—
146C2×D4×D11—22no—
147C2×D4×D11—22no—
148C2×D4×D11—22no—
149C2×#4339C2311yescharacteristic
150C2×#4339C2311yescharacteristic
151C2×#4339C2312yes—
152C2×#4339C2312yes—
153C22×D44C2312yes—
154C22×D44C2312yes—
155C22×D44C2311yescharacteristic
156C22×C4×D11—21no—
157C11×C4⋊Q8D411yescharacteristic
158C11×#127D411yescharacteristic
159C11×#126—22no—
160C11×#126—22no—
161C11×#126—22no—
162C11×#126—22no—
163C11×#125—22no—
164C11×#125—22no—
165C11×#125—21no—
166C11×#125—21no—
167C11×#125C2312yes—
168C11×#125C2312yes—
169C11×#124D411yescharacteristic
170C11×#124D411yescharacteristic
171C11×#123—22no—
172C11×#123—22no—
173C11×#123—22no—
174C11×#123—22no—
175C11×C22⋊Q8—21no—
176C11×C22⋊Q8—21no—
177C11×C22⋊Q8C2312yes—
178C11×C22⋊Q8C2312yes—
179C11×#121—21no—
180C11×#121—21no—
181C11×#121—22no—
182C11×#121—22no—
183C11×#121—22no—
184C11×#121—22no—
185C11×#121D412yes—
186C11×#121D412yes—
187C11×#121C2312yes—
188C11×#121C2312yes—
189C4×Q8×C11—21no—
190C4×Q8×C11—21no—
191C4×Q8×C11C2311yescharacteristic
192C4×Q8×C11C2311yescharacteristic
193C4×D4×C11—21no—
194C4×D4×C11—21no—
195C4×D4×C11—22no—
196C4×D4×C11—22no—
197C4×D4×C11—21no—
198C4×D4×C11—21no—
199C4×D4×C11—22no—
200C4×D4×C11—22no—
201C4×D4×C11C2311yescharacteristic
202C4×D4×C11C2311yescharacteristic
203C4×D4×C11C2312yes—
204C4×D4×C11C2312yes—
205C11×#117—22no—
206C11×#117—22no—
207C11×#117—21no—
208C11×#117C2311yescharacteristic
209C11×#117C2312yes—
210C11×#117C2312yes—
211C2×C11×C4⋊C4—21no—
212C2×C11×C4⋊C4—21no—
213C2×C11×C4⋊C4C2311yescharacteristic
214C2×C11×C4⋊C4C2311yescharacteristic
215C2×C11×C4⋊C4C2312yes—
216C2×C11×C4⋊C4C2312yes—
217C2×C42×C11—21no—
218C2×C42×C11C2311yescharacteristic
219#67003—42no—
220#67003—42no—
221#67002—24no—
222#67001—42no—
223#67001—42no—
224#66999—21no—
225#66999—21no—
226C2×#4326C2311yescharacteristic
227C2×#4326C2311yescharacteristic
228C2×#4325C2312yes—
229C2×#4325C2311yescharacteristic
230C2×#4325C2311yescharacteristic
231#66992—22no—
232#66992—22no—
233#66991—22no—
234#66991—21no—
235#66991—21no—
236#66990—22no—
237#66990—22no—
238C2×#4324C2311yescharacteristic
239C2×#4324C2311yescharacteristic
240C2×#4323C2312yes—
241C2×#4323C2311yescharacteristic
242C2×#4323C2311yescharacteristic
243#66983—21no—
244#66983—21no—
245#66983C2312yes—
246#66983C2312yes—
247C2×(C2×D11)⋊C4—21no—
248C2×C4⋊Dic11C2311yescharacteristic
249#66977C2312yes—
250#66977C2312yes—
251C2×#4318C2311yescharacteristic
252C2×#4318C2311yescharacteristic
253C2×#4318C2312yes—
254C2×#4318C2312yes—
255C22×C11⋊C8C2311yescharacteristic
256C22×C11⋊C8C2311yescharacteristic
257C22×C11⋊C8C2312yes—
258C22×C11⋊C8C2312yes—
259#66948—22no—
260#66947—22no—
261#66947—22no—
262C4⋊C4×D11—22no—
263#66937—22no—
264#66937—22no—
265#66936—22no—
266#66936—22no—
267#66935—22no—
268#66935—22no—
269C22⋊C4×D11—22no—
270C22⋊C4×D11—22no—
271#66928C2311yescharacteristic
272#66928C2311yescharacteristic
273#66927C2311yescharacteristic
274C4×D44—21no—
275C4×D44—21no—
276C4×D44—21no—
277C4×D44—21no—
278C4×D44C2312yes—
279C4×D44C2312yes—
280#66922C2311yescharacteristic
281#66899C2312yes—
282#66896C2312yes—
283C22⋊(C11⋊C8)C2312yes—
284C22⋊(C11⋊C8)C2312yes—
285C22⋊(C11⋊C8)C2312yes—
286C22⋊(C11⋊C8)C2312yes—
287#66874C2311yescharacteristic
288#66874C2311yescharacteristic
289#66874C2312yes—
290#66874C2312yes—
291#66874C2312yes—
292#66874C2312yes—
293#66874C2311yescharacteristic
294#66874C2311yescharacteristic
295#66873C2312yes—
296#66873C2312yes—
297#66873C2312yes—
298#66873C2312yes—
299#66873C2311yescharacteristic
300#66873C2311yescharacteristic
301#66873C2312yes—
302#66873C2312yes—
303#66873C2312yes—
304#66873C2312yes—
305#66873C2312yes—
306#66873C2312yes—
307#66873C2311yescharacteristic
308#66873C2311yescharacteristic
309#66872C2312yes—
310#66872C2312yes—
311#66872C2312yes—
312#66871C2312yes—
313#66871C2312yes—
314#66871C2312yes—
315C4⋊(C11⋊C8)C2311yescharacteristic
316C4⋊(C11⋊C8)C2311yescharacteristic
317C4⋊(C11⋊C8)C2311yescharacteristic
318C4⋊(C11⋊C8)C2311yescharacteristic
319#66867C2312yes—
320C4×C11⋊C8C2312yes—
321#61201—111nomaximal, Sylow
322C23×D11—21no—
323C23×D11—22no—
324C23×D11—22no—
325C11×#41—22no—
326C11×#41—22no—
327C11×#41—22no—
328C11×#41—22no—
329C11×#41—22no—
330C11×#41—22no—
331C2×Q8×C11C2×D411yescharacteristic
332C2×Q8×C11C2×D411yescharacteristic
333C2×Q8×C11C2411yescharacteristic
334C2×D4×C11—21no—
335C2×D4×C11—22no—
336C2×D4×C11—22no—
337C2×D4×C11C2×D411yescharacteristic
338C2×D4×C11C2×D411yescharacteristic
339C2×D4×C11C2×D412yes—
340C2×D4×C11C2×D412yes—
341C2×D4×C11C2×D412yes—
342C2×D4×C11C2×D412yes—
343C2×D4×C11C2411yescharacteristic
344C22×C4×C11—21no—
345C22×C4×C11—21no—
346C22×C4×C11—22no—
347C22×C4×C11—22no—
348C22×C4×C11—21no—
349C22×C4×C11—21no—
350C22×C4×C11—21no—
351C22×C4×C11C2×D411yescharacteristic
352C22×C4×C11C2×D411yescharacteristic
353C22×C4×C11C2412yes—
354C22×C4×C11C2412yes—
355C22×C4×C11C2411yescharacteristic
356C2×C22⋊D11—22no—
357C2×C22⋊D11—22no—
358C2×C22⋊D11—21no—
359C2×C22⋊D11—21no—
360C2×C22⋊D11—22no—
361C2×C22⋊D11—22no—
362C22×Dic11—21no—
363#4343—44no—
364#4343—44no—
365D4×D11—48no—
366D4×D11—48no—
367D4×D11—44no—
368D4×D11—44no—
369D4×D11—84no—
370#4339—24no—
371#4339—24no—
372#4339—22no—
373#4339—22no—
374#4339—22no—
375#4339—22no—
376#4339—42no—
377#4339—42no—
378C2×D44—24no—
379C2×D44—24no—
380C2×D44—21no—
381C2×D44—21no—
382C2×D44—22no—
383C2×D44—22no—
384C2×D44—21no—
385C2×D44—22no—
386C2×D44—42no—
387C2×D44—42no—
388C2×D44#4114yes—
389C2×D44C2411yescharacteristic
390C2×D44C2411yescharacteristic
391C2×D44C2412yes—
392C2×C4×D11—21no—
393C2×C4×D11—21no—
394C2×C4×D11—22no—
395C2×C4×D11—22no—
396C2×C4×D11—22no—
397C2×C4×D11—22no—
398C2×C4×D11—82no—
399C2×Dic22C2411yescharacteristic
400C2×Dic22C2411yescharacteristic
401C11×C4⋊C4—22no—
402C11×C4⋊C4—22no—
403C11×C4⋊C4—22no—
404C11×C4⋊C4—22no—
405C11×C4⋊C4—21no—
406C11×C4⋊C4—21no—
407C11×C4⋊C4—22no—
408C11×C4⋊C4—22no—
409C11×C4⋊C4—21no—
410C11×C4⋊C4—21no—
411C11×C4⋊C4—22no—
412C11×C4⋊C4—22no—
413C11×C4⋊C4C2×D412yes—
414C11×C4⋊C4C2×D412yes—
415C11×C4⋊C4C2411yescharacteristic
416C11×C4⋊C4C2412yes—
417C11×C4⋊C4C2411yescharacteristic
418C11×C4⋊C4C2412yes—
419C11×C22⋊C4—22no—
420C11×C22⋊C4—22no—
421C11×C22⋊C4—21no—
422C11×C22⋊C4—22no—
423C11×C22⋊C4—22no—
424C11×C22⋊C4—21no—
425C11×C22⋊C4—21no—
426C11×C22⋊C4—22no—
427C11×C22⋊C4—22no—
428C11×C22⋊C4C2×D412yes—
429C11×C22⋊C4C2×D412yes—
430C11×C22⋊C4C2×D412yes—
431C11×C22⋊C4C2×D412yes—
432C42×C11—21no—
433C42×C11—21no—
434C42×C11—21no—
435C42×C11—22no—
436C42×C11—22no—
437C42×C11C2×D411yescharacteristic
438C42×C11C2×D411yescharacteristic
439C42×C11C2411yescharacteristic
440C42×C11C2411yescharacteristic
441C22⋊Dic11—22no—
442C22⋊Dic11—22no—
443#4326—41no—
444#4326—41no—
445#4325—24no—
446#4325—41no—
447#4325—41no—
448#4324—41no—
449#4324—41no—
450#4323—24no—
451#4323—41no—
452#4323—41no—
453(C2×D11)⋊C4—22no—
454(C2×D11)⋊C4—22no—
455(C2×D11)⋊C4—21no—
456(C2×D11)⋊C4—21no—
457(C2×D11)⋊C4—21no—
458(C2×D11)⋊C4—21no—
459(C2×D11)⋊C4—22no—
460(C2×D11)⋊C4—22no—
461C4⋊Dic11—21no—
462C4⋊Dic11—21no—
463C4⋊Dic11—21no—
464C4⋊Dic11C2412yes—
465Dic11⋊C4—22no—
466Dic11⋊C4—22no—
467#4318—22no—
468#4318—22no—
469#4318—42no—
470#4318—42no—
471C2×C11⋊C8—22no—
472C2×C11⋊C8—22no—
473C2×C11⋊C8—42no—
474C2×C11⋊C8—42no—
475C2×C11⋊C8C2412yes—
476C2×C11⋊C8C2412yes—
477C2×C11⋊C8C2411yescharacteristic
478C2×C11⋊C8C2411yescharacteristic
479C2×C11⋊C8C2411yescharacteristic
480C2×C11⋊C8C2411yescharacteristic
481#3512D1111yescharacteristic, complemented
482#3496—111no—
483#3323—112no—
484#3322—112no—
485#3318—112no—
486#3315—112no—
487#3310—112no—
488#3307—112no—
489#3297—112no—
490#3296—112no—
491#3142—111no—
492#3099—111no—
493#3098—111no—
494C2×#478—111no—
495#3061—111no—
496#3060—111no—
497#3035—111no—
498#3012—111no—
499#3012—111no—
500C4×AGL(1,ℤ/8)—111no—
501#2935—111no—
502#2897—111no—
503#2897—111no—
504C23×C11—21no—
505C23×C11C22×D412yes—
506C23×C11C22×D412yes—
507C23×C11C22×D411yescharacteristic
508C22×D11—22no—
509C22×D11—24no—
510C22×D11—21no—
511C22×D11—21no—
512C22×D11—44no—
513C22×D11—44no—
514C22×D11—81no—
515C22×D11—81no—
516C22×D11—82no—
517C22×D11—82no—
518C22×D11—82no—
519C22×D11—82no—
520Q8×C11—22no—
521Q8×C11—22no—
522Q8×C11—21no—
523Q8×C11—21no—
524D4×C11—24no—
525D4×C11—24no—
526D4×C11—22no—
527D4×C11—22no—
528D4×C11—21no—
529D4×C11—21no—
530D4×C11—42no—
531D4×C11—42no—
532D4×C11—42no—
533D4×C11—82no—
534D4×C11—82no—
535C2×C4×C11—22no—
536C2×C4×C11—22no—
537C2×C4×C11—22no—
538C2×C4×C11—22no—
539C2×C4×C11—21no—
540C2×C4×C11—21no—
541C2×C4×C11—21no—
542C2×C4×C11—22no—
543C2×C4×C11—22no—
544C2×C4×C11—41no—
545C2×C4×C11—41no—
546C2×C4×C11—42no—
547C2×C4×C11—81no—
548C2×C4×C11—81no—
549C2×C4×C11—82no—
550C2×C4×C11—81no—
551C2×C4×C11—82no—
552C2×C4×C11—81no—
553C2×C4×C11C22×D412yes—
554C2×C4×C11C22×D412yes—
555C2×C4×C11C22×D411yescharacteristic
556C2×C4×C11C22×D411yescharacteristic
557C2×C4×C11C22×D411yescharacteristic
558C2×C4×C11C22×D411yescharacteristic
559C2×C4×C11C22×D411yescharacteristic
560C2×C4×C11C2×#4112yes—
561C2×C4×C11H(5,𝔽2)12yes—
562C2×C4×C11C2511yescharacteristic
563C22⋊D11—44no—
564C22⋊D11—44no—
565C22⋊D11—42no—
566C22⋊D11—42no—
567C22⋊D11—82no—
568C22⋊D11—82no—
569C2×Dic11—21no—
570C2×Dic11—21no—
571C2×Dic11—22no—
572C2×Dic11—81no—
573D44—24no—
574D44—21no—
575D44—21no—
576D44—22no—
577D44—21no—
578D44—21no—
579D44—44no—
580D44—44no—
581D44—42no—
582D44—81no—
583D44C2×#4114yes—
584C4×D11—44no—
585C4×D11—44no—
586C4×D11—44no—
587C4×D11—42no—
588C4×D11—42no—
589C4×D11—82no—
590Dic22—21no—
591Dic22—21no—
592Dic22—21no—
593Dic22—21no—
594C11⋊C8—22no—
595C11⋊C8—21no—
596C11⋊C8—21no—
597C11⋊C8—21no—
598C11⋊C8—21no—
599C11⋊C8—22no—
600C2×H(5,𝔽2)—111no—
601C2×H(5,𝔽2)—111no—
602C2×AGL(1,ℤ/8)—111no—
603C2×#135—111no—
604C2×#135—111no—
605C2×#131—111no—
606C2×#131—111no—
607#553—22no—
608#553—22no—
609#553C2×D1112yescomplemented
610#553C2×D1112yescomplemented
611#552C2×D1112yescomplemented
612#552C2×D1112yescomplemented
613#547—112no—
614#547—221no—
615#546—112no—
616#546—112no—
617#546—221no—
618#546—221no—
619D42—112no—
620D42—221no—
621#541—21no—
622#540—21no—
623#537—111no—
624#537—111no—
625#537C2×D1111yescharacteristic, complemented
626#537C2×D1111yescharacteristic, complemented
627#534—222no—
628#532—111no—
629#532C2×D1111yescharacteristic
630#529—21no—
631#529—21no—
632C2×#125C2×D1111yescharacteristic, complemented
633C2×#121—222no—
634#520C2×D1111yescharacteristic, complemented
635#520C2×D1111yescharacteristic, complemented
636C4×#41C2×D1111yescharacteristic, complemented
637C2×C4×D4—111no—
638#491—112no—
639#490—112no—
640#488—112no—
641#488—112no—
642#485—112no—
643#485—112no—
644#484—112no—
645#483—112no—
646#482—112no—
647#482—112no—
648#481—112no—
649#480—112no—
650#478—112no—
651#478—112no—
652#478—112no—
653#478—112no—
654#470—112no—
655#469—112no—
656#468—112no—
657#468—112no—
658#467—112no—
659#466—112no—
660#465—112no—
661#465—112no—
662#464—111no—
663#464—111no—
664#463—111no—
665#463—111no—
666#462—111no—
667#461—111no—
668#460—111no—
669#459—111no—
670#452—112no—
671#452—112no—
672#450—112no—
673#450—112no—
674#449—112no—
675#449—112no—
676#447—112no—
677#447—112no—
678#442—112no—
679#440—112no—
680C4×SD16—112no—
681C4×D8—112no—
682#436—112no—
683#435—112no—
684#435—112no—
685C8×D4—112no—
686#428—111no—
687C2×#107—111no—
688C2×#106—111no—
689C2×C4⋊C8—111no—
690#418—111no—
691#418—112no—
692#418—112no—
693#417—111no—
694#417—111no—
695#417—111no—
696#417—111no—
697#417—111no—
698#417—112no—
699#417—112no—
700#416—111no—
701#416—111no—
702#416—112no—
703#416—112no—
704C2×#102—111no—
705C2×#102—111no—
706C2×#102—112no—
707C2×#102—112no—
708#408—111no—
709#408—111no—
710C4×M16—111no—
711C22×C11—21no—
712C22×C11—21no—
713C22×C11—22no—
714C22×C11—22no—
715C22×C11—22no—
716C22×C11—22no—
717C22×C11—22no—
718C22×C11—22no—
719C22×C11—41no—
720C22×C11—41no—
721C22×C11—41no—
722C22×C11#54612yes—
723C22×C11C23×D411yescharacteristic
724C2×D11—24no—
725C2×D11—42no—
726C2×D11—42no—
727C2×D11—41no—
728C2×D11—41no—
729C2×D11—41no—
730C2×D11—41no—
731C2×D11—41no—
732C2×D11—41no—
733C2×D11—84no—
734C2×D11—164no—
735C2×D11—164no—
736C4×C11—21no—
737C4×C11—21no—
738C4×C11—21no—
739C4×C11—21no—
740C4×C11—22no—
741C4×C11—22no—
742C4×C11—41no—
743C4×C11—42no—
744C4×C11—41no—
745C4×C11—42no—
746C4×C11—41no—
747C4×C11#54612yes—
748C4×C11C22×#4111yescharacteristic
749C4×C11C2×H(5,𝔽2)11yescharacteristic
750Dic11—42no—
751Dic11—41no—
752Dic11—41no—
753H(5,𝔽2)—224no—
754H(5,𝔽2)—224no—
755H(5,𝔽2)—442no—
756H(5,𝔽2)—442no—
757C2×#41—111no—
758C2×#41—111no—
759C2×#41—112no—
760C2×#41—112no—
761C2×#41—221no—
762C2×#41—221no—
763C2×#41C22×D1111yescharacteristic
764C2×#41C22×D1111yescharacteristic
765C2×#41C22×D1111yescharacteristic
766C22×D4—111no—
767C22×D4—112no—
768C22×D4—112no—
769C22×D4—222no—
770C22×D4—222no—
771C22×D4—221no—
772C22×D4—221no—
773C22×D4—222no—
774C23×C4—221no—
775AGL(1,ℤ/8)—224no—
776#135—442no—
777#135—442no—
778C2×Q16—111no—
779C2×Q16—111no—
780C2×SD16—112no—
781C2×SD16—111no—
782C2×SD16—111no—
783C2×SD16—111no—
784C2×SD16—111no—
785C2×D8—112no—
786C2×D8—111no—
787C2×D8—111no—
788#131—442no—
789#131—442no—
790C2×M16—111no—
791C2×M16—111no—
792C2×M16—112no—
793C2×M16—112no—
794C22×C8—111no—
795C22×C8—111no—
796C22×C8—112no—
797C22×C8—112no—
798C4⋊Q8—111no—
799C4⋊Q8C22⋊D1111yescharacteristic
800#127—111no—
801#127C22⋊D1111yescharacteristic
802#126—22no—
803#126—22no—
804#126—22no—
805#126—22no—
806#125—22no—
807#125—22no—
808#125—21no—
809#125—21no—
810#125C22×D1112yes—
811#125C22×D1112yes—
812#124—111no—
813#124—111no—
814#124C22⋊D1111yescharacteristic
815#124C22⋊D1111yescharacteristic
816#123—22no—
817#123—22no—
818#123—22no—
819#123—22no—
820#123—222no—
821#123—222no—
822#123—222no—
823#123—222no—
824C22⋊Q8—21no—
825C22⋊Q8—21no—
826C22⋊Q8—112no—
827C22⋊Q8—112no—
828C22⋊Q8—221no—
829C22⋊Q8—221no—
830C22⋊Q8C22×D1112yes—
831C22⋊Q8C22×D1112yes—
832#121—21no—
833#121—21no—
834#121—22no—
835#121—22no—
836#121—22no—
837#121—22no—
838#121—112no—
839#121—112no—
840#121—222no—
841#121—222no—
842#121—222no—
843#121—221no—
844#121—221no—
845#121—221no—
846#121—221no—
847#121—222no—
848#121—222no—
849#121—222no—
850#121C22⋊D1112yes—
851#121C22⋊D1112yes—
852#121C22×D1112yes—
853#121C22×D1112yes—
854#120—222no—
855#120—222no—
856#120—222no—
857#120—222no—
858C4×Q8—21no—
859C4×Q8—21no—
860C4×Q8C22×D1111yescharacteristic
861C4×Q8C22×D1111yescharacteristic
862C4×D4—21no—
863C4×D4—21no—
864C4×D4—22no—
865C4×D4—22no—
866C4×D4—21no—
867C4×D4—21no—
868C4×D4—22no—
869C4×D4—22no—
870C4×D4—112no—
871C4×D4—112no—
872C4×D4—221no—
873C4×D4—221no—
874C4×D4—221no—
875C4×D4—221no—
876C4×D4C22×D1111yescharacteristic
877C4×D4C22×D1111yescharacteristic
878C4×D4C22×D1112yes—
879C4×D4C22×D1112yes—
880#117—22no—
881#117—22no—
882#117—21no—
883#117C22×D1111yescharacteristic
884#117C22×D1112yes—
885#117C22×D1112yes—
886C2×C4⋊C4—21no—
887C2×C4⋊C4—21no—
888C2×C4⋊C4—111no—
889C2×C4⋊C4—222no—
890C2×C4⋊C4C22×D1111yescharacteristic
891C2×C4⋊C4C22×D1111yescharacteristic
892C2×C4⋊C4C22×D1112yes—
893C2×C4⋊C4C22×D1112yes—
894C2×C22⋊C4—221no—
895C2×C22⋊C4—222no—
896C2×C22⋊C4—222no—
897C2×C42—21no—
898C2×C42C22×D1111yescharacteristic
899#107—112no—
900#107—112no—
901#107—112no—
902#106—112no—
903#106—112no—
904#106—112no—
905C4⋊C8—111no—
906C4⋊C8—111no—
907C4⋊C8—111no—
908C4⋊C8—111no—
909#103—112no—
910#103—111no—
911#103—111no—
912#103—111no—
913#103—111no—
914#103—112no—
915#103—112no—
916#103—112no—
917#103—112no—
918#102—112no—
919#102—112no—
920#102—112no—
921#102—111no—
922#102—111no—
923#102—112no—
924#102—112no—
925#102—112no—
926#102—112no—
927#102—112no—
928#102—112no—
929#102—111no—
930#102—111no—
931#102—112no—
932#102—112no—
933C22⋊C8—112no—
934C22⋊C8—112no—
935C22⋊C8—112no—
936C22⋊C8—112no—
937#97—112no—
938C4×C8—112no—
939C2×C11—22no—
940C2×C11—42no—
941C2×C11—42no—
942C2×C11—81no—
943C2×C11C2×#54611yescharacteristic
944C2×C11#358411yescharacteristic
945C2×C11#358511yescharacteristic
946D11—44no—
947D11—81no—
948D11—81no—
949C24—221no—
950C24—222no—
951C24—222no—
952#41—22no—
953#41—22no—
954#41—22no—
955#41—22no—
956#41—22no—
957#41—22no—
958#41—224no—
959#41—224no—
960#41—222no—
961#41—222no—
962#41—222no—
963#41—222no—
964#41—442no—
965#41—442no—
966#41—444no—
967#41—444no—
968C2×Q8—111no—
969C2×Q8—111no—
970C2×Q8C2×C22⋊D1111yescharacteristic
971C2×Q8C2×C22⋊D1111yescharacteristic
972C2×Q8C23×D1111yescharacteristic
973C2×D4—21no—
974C2×D4—22no—
975C2×D4—22no—
976C2×D4—114no—
977C2×D4—112no—
978C2×D4—111no—
979C2×D4—111no—
980C2×D4—224no—
981C2×D4—224no—
982C2×D4—222no—
983C2×D4—222no—
984C2×D4—221no—
985C2×D4—221no—
986C2×D4—222no—
987C2×D4—222no—
988C2×D4—222no—
989C2×D4—221no—
990C2×D4—221no—
991C2×D4—222no—
992C2×D4—222no—
993C2×D4—221no—
994C2×D4—442no—
995C2×D4—442no—
996C2×D4—444no—
997C2×D4—444no—
998C2×D4—448no—
999C2×D4—448no—
1000C2×D4—884no—
1001C2×D4C2×C22⋊D1112yes—
1002C2×D4C2×C22⋊D1112yes—
1003C2×D4C2×C22⋊D1111yescharacteristic
1004C2×D4C2×C22⋊D1111yescharacteristic
1005C2×D4C2×C22⋊D1112yes—
1006C2×D4C2×C22⋊D1112yes—
1007C2×D4C23×D1111yescharacteristic
1008C22×C4—21no—
1009C22×C4—21no—
1010C22×C4—22no—
1011C22×C4—22no—
1012C22×C4—21no—
1013C22×C4—21no—
1014C22×C4—21no—
1015C22×C4—221no—
1016C22×C4—222no—
1017C22×C4—222no—
1018C22×C4—222no—
1019C22×C4—221no—
1020C22×C4—221no—
1021C22×C4—222no—
1022C22×C4—882no—
1023C22×C4C2×C22⋊D1111yescharacteristic
1024C22×C4C2×C22⋊D1111yescharacteristic
1025C22×C4C23×D1112yes—
1026C22×C4C23×D1112yes—
1027C22×C4C23×D1111yescharacteristic
1028Q16—441no—
1029Q16—441no—
1030SD16—224no—
1031SD16—441no—
1032SD16—441no—
1033SD16—441no—
1034SD16—441no—
1035D8—224no—
1036D8—441no—
1037D8—441no—
1038M16—222no—
1039M16—222no—
1040M16—442no—
1041M16—442no—
1042C2×C8—112no—
1043C2×C8—112no—
1044C2×C8—111no—
1045C2×C8—111no—
1046C2×C8—111no—
1047C2×C8—111no—
1048C2×C8—222no—
1049C2×C8—222no—
1050C2×C8—442no—
1051C2×C8—442no—
1052C4⋊C4—22no—
1053C4⋊C4—22no—
1054C4⋊C4—22no—
1055C4⋊C4—22no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—22no—
1059C4⋊C4—22no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—22no—
1063C4⋊C4—22no—
1064C4⋊C4—112no—
1065C4⋊C4—221no—
1066C4⋊C4—221no—
1067C4⋊C4—222no—
1068C4⋊C4—222no—
1069C4⋊C4—221no—
1070C4⋊C4C2×C22⋊D1112yes—
1071C4⋊C4C2×C22⋊D1112yes—
1072C4⋊C4C23×D1111yescharacteristic
1073C4⋊C4C23×D1112yes—
1074C4⋊C4C23×D1111yescharacteristic
1075C4⋊C4C23×D1112yes—
1076C22⋊C4—22no—
1077C22⋊C4—22no—
1078C22⋊C4—21no—
1079C22⋊C4—22no—
1080C22⋊C4—22no—
1081C22⋊C4—21no—
1082C22⋊C4—21no—
1083C22⋊C4—22no—
1084C22⋊C4—22no—
1085C22⋊C4—222no—
1086C22⋊C4—222no—
1087C22⋊C4—221no—
1088C22⋊C4—221no—
1089C22⋊C4—222no—
1090C22⋊C4—222no—
1091C22⋊C4—222no—
1092C22⋊C4—222no—
1093C22⋊C4—221no—
1094C22⋊C4—221no—
1095C22⋊C4C2×C22⋊D1112yes—
1096C22⋊C4C2×C22⋊D1112yes—
1097C22⋊C4C2×C22⋊D1112yes—
1098C22⋊C4C2×C22⋊D1112yes—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—22no—
1103C42—22no—
1104C42C2×C22⋊D1111yescharacteristic
1105C42C2×C22⋊D1111yescharacteristic
1106C42C23×D1111yescharacteristic
1107C42C23×D1111yescharacteristic
1108C11#6120111yescharacteristic, complemented, Sylow
1109C23—21no—
1110C23—222no—
1111C23—224no—
1112C23—221no—
1113C23—221no—
1114C23—444no—
1115C23—444no—
1116C23—881no—
1117C23—881no—
1118C23—882no—
1119C23—882no—
1120C23—882no—
1121C23—882no—
1122C23C22×C22⋊D1112yes—
1123C23C22×C22⋊D1112yes—
1124C23C22×C22⋊D1111yescharacteristic
1125Q8—22no—
1126Q8—22no—
1127Q8—21no—
1128Q8—21no—
1129Q8—221no—
1130Q8—221no—
1131Q8—221no—
1132Q8—221no—
1133D4—24no—
1134D4—24no—
1135D4—22no—
1136D4—22no—
1137D4—21no—
1138D4—21no—
1139D4—42no—
1140D4—42no—
1141D4—42no—
1142D4—82no—
1143D4—82no—
1144D4—114no—
1145D4—224no—
1146D4—221no—
1147D4—221no—
1148D4—222no—
1149D4—221no—
1150D4—221no—
1151D4—444no—
1152D4—444no—
1153D4—442no—
1154D4—444no—
1155D4—444no—
1156D4—442no—
1157D4—442no—
1158D4—881no—
1159D4—882no—
1160D4—882no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—42no—
1173C2×C4—81no—
1174C2×C4—81no—
1175C2×C4—82no—
1176C2×C4—81no—
1177C2×C4—82no—
1178C2×C4—81no—
1179C2×C4—222no—
1180C2×C4—221no—
1181C2×C4—221no—
1182C2×C4—444no—
1183C2×C4—444no—
1184C2×C4—444no—
1185C2×C4—442no—
1186C2×C4—442no—
1187C2×C4—882no—
1188C2×C4—881no—
1189C2×C4#41×D1112yes—
1190C2×C4#6704212yes—
1191C2×C4C22×C22⋊D1111yescharacteristic
1192C2×C4C22×C22⋊D1111yescharacteristic
1193C2×C4C22×C22⋊D1112yes—
1194C2×C4C22×C22⋊D1112yes—
1195C2×C4C22×C22⋊D1111yescharacteristic
1196C2×C4C22×C22⋊D1111yescharacteristic
1197C2×C4C22×C22⋊D1111yescharacteristic
1198C2×C4C24×D1111yescharacteristic
1199C8—222no—
1200C8—221no—
1201C8—221no—
1202C8—221no—
1203C8—221no—
1204C8—222no—
1205C22—21no—
1206C22—21no—
1207C22—22no—
1208C22—22no—
1209C22—22no—
1210C22—22no—
1211C22—22no—
1212C22—22no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—224no—
1217C22—442no—
1218C22—442no—
1219C22—441no—
1220C22—441no—
1221C22—441no—
1222C22—441no—
1223C22—441no—
1224C22—441no—
1225C22—884no—
1226C22—1764no—
1227C22—1764no—
1228C22#1062336012yes—
1229C22C23×C22⋊D1111yescharacteristic
1230C4—21no—
1231C4—21no—
1232C4—22no—
1233C4—22no—
1234C4—21no—
1235C4—21no—
1236C4—41no—
1237C4—42no—
1238C4—41no—
1239C4—41no—
1240C4—42no—
1241C4—442no—
1242C4—441no—
1243C4—441no—
1244C4#1062336012yes—
1245C4C2×#41×D1111yescharacteristic
1246C4C2×#6704211yescharacteristic
1247C2—22no—
1248C2—42no—
1249C2—42no—
1250C2—81no—
1251C2—444no—
1252C2—881no—
1253C2—881no—
1254C2C2×#1062336011yescharacteristic
1255C2#1308338711yescharacteristic
1256C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3512C2
socleC22×C11C23×D4
hypercenter#3512D11
hypocenterC11#61201
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #532 ◁ #3512

Complements

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

NH ≅ G/Ntype
1. #13082378C2semidirect
2. #13080826C2semidirect
3. #13080811C2semidirect
4. #13080751C2semidirect
5. #13080706C2semidirect
6. #13080631C2semidirect
7. #13080586C2semidirect
8. #13080460C2semidirect
9. #13080445C2semidirect
10. #13079019C2semidirect
11. #13078605C2semidirect
12. #13078594C2semidirect
13. C2×#10622679C2semidirect
14. #13078283C2semidirect
15. #13078275C2semidirect
16. #13078071C2semidirect
17. #13077917C2semidirect
18. #13077917C2semidirect
19. C4×#67002C2semidirect
20. #13077360C2semidirect
21. #13077139C2semidirect
22. #13077139C2semidirect
23. C11×#3512C2semidirect
28. C11×#553C22semidirect
29. C11×#553C22semidirect
30. C11×#552C22semidirect
31. C11×#552C22semidirect
34. C11×#537C22semidirect
35. C11×#537C22semidirect
39. C2×C11×#125C22semidirect
40. C11×#520C22semidirect
41. C11×#520C22semidirect
42. C4×C11×#41C22semidirect
45. C2×#67003C22semidirect
46. C2×#67003C22semidirect
48. C2×#67001C22semidirect
49. C2×#67001C22semidirect
62. #10622847C22semidirect
63. #10622847C22semidirect
64. #10622845C22semidirect
65. #10622682C22semidirect
66. #10622681C22semidirect
67. #10622681C22semidirect
68. #10622680C22semidirect
69. #10622679C22semidirect
70. #10622679C22semidirect
71. #10622679C22semidirect
72. #10622679C22semidirect
73. #10622665C22semidirect
74. #10622664C22semidirect
75. #10622662C22semidirect
76. #10622661C22semidirect
77. #10622660C22semidirect
78. #10622660C22semidirect
79. #10622659C22semidirect
80. #10622659C22semidirect
81. #10622655C22semidirect
82. #10622654C22semidirect
83. #10622652C22semidirect
84. #10622651C22semidirect
85. #10622650C22semidirect
86. #10622650C22semidirect
87. #10622649C22semidirect
88. #10622649C22semidirect
89. #10622644C22semidirect
90. #10622641C22semidirect
91. #10622641C22semidirect
92. #10622640C22semidirect
93. #10622639C22semidirect
94. C4×#4325C22semidirect
95. #10622632C22semidirect
96. #10622629C22semidirect
97. #10622629C22semidirect
98. #10622628C22semidirect
99. #10622627C22semidirect
100. C4×#4323C22semidirect
101. #10622625C22semidirect
102. #10622624C22semidirect
103. #10622624C22semidirect
104. D4×C11⋊C8C22semidirect
105. #10622616C22semidirect
106. #10622616C22semidirect
107. #10622615C22semidirect
108. #10622615C22semidirect
109. #10622615C22semidirect
110. #10622615C22semidirect
112. #10622614C22semidirect
113. #10622614C22semidirect
114. #10622609C22semidirect
115. #10622609C22semidirect
116. #10622608C22semidirect
117. #10622584C22semidirect
118. #10622583C22semidirect
119. #10622581C22semidirect
120. #10622580C22semidirect
121. #10622579C22semidirect
122. #10622579C22semidirect
123. #10622579C22semidirect
124. #10622579C22semidirect
125. #10622579C22semidirect
126. #10622579C22semidirect
129. C2×#66873C22semidirect
130. C2×#66873C22semidirect
131. C2×#66872C22semidirect
132. C2×#66871C22semidirect
133. C2×C4⋊(C11⋊C8)C22semidirect
134. C4×#4318C22semidirect
481. #3512D11semidirect
609. #553C2×D11semidirect
610. #553C2×D11semidirect
611. #552C2×D11semidirect
612. #552C2×D11semidirect
625. #537C2×D11semidirect
626. #537C2×D11semidirect
632. C2×#125C2×D11semidirect
634. #520C2×D11semidirect
635. #520C2×D11semidirect
636. C4×#41C2×D11semidirect
1108. C11#61201semidirect

Maximal subgroups

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

subgroupindex
#130823782
#130808262
#130808112
#130807512
#130807062
#130806312
#130805862
#130804602
#130804452
#130790192
#130786052
#130785942
C2×#106226792
#130782832
#130782752
#130780712
#130779172
C4×#670022
#130773602
#130771392
C11×#35122
#6120111