Finite Group Databasebeta

← #15631122

Subgroups — #15631122

Order 2816.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082370C211yesmaximal, characteristic, complemented
2#13080712C212yesmaximal, complemented
3#13080697C212yesmaximal, complemented
4#13080682C212yesmaximal, complemented
5#13080667C212yesmaximal, complemented
6#13080533C212yesmaximal, complemented
7#13080503C212yesmaximal, complemented
8#13080492C212yesmaximal, complemented
9#13080451C212yesmaximal, complemented
10#13078981C211yesmaximal, characteristic, complemented
11#13078590C211yesmaximal, characteristic, complemented
12#13078560C211yesmaximal, characteristic, complemented
13#13078467C211yesmaximal, characteristic, complemented
14#13078309C211yesmaximal, characteristic, complemented
15C2×#10622664C211yesmaximal, characteristic, complemented
16#13078142C211yesmaximal, characteristic, complemented
17#13077911C211yesmaximal, characteristic, complemented
18#13077876C211yesmaximal, characteristic, complemented
19#13077455C211yesmaximal, characteristic, complemented
20#13077311C211yesmaximal, characteristic, complemented
21#13077149C211yesmaximal, characteristic, complemented
22C2×#10622846C211yesmaximal, characteristic, complemented
23C11×#3489C211yesmaximal, characteristic
24C2×C11×2−1+4C2211yescharacteristic
25C22×C11×#41C2211yescharacteristic
26D4×Q8×C11C2212yes—
27C11×#548C2212yes—
28C11×#547—22no—
29C11×#547C2212yes—
30C11×#546—22no—
31C11×#546C2212yes—
32C11×#537—21no—
33C11×#537C2211yescharacteristic
34C11×#536—21no—
35C11×#536C2211yescharacteristic
36C11×#525—21no—
37C11×#525C2211yescharacteristic
38C2×C11×C22⋊Q8—21no—
39C2×C11×C22⋊Q8C2211yescharacteristic
40C11×#520C2211yescharacteristic
41#10623358C2211yescharacteristic, complemented
42#10623356C2211yescharacteristic, complemented
43C2×#67004C2211yescharacteristic
44C2×#67004C2211yescharacteristic
45C2×#67001C2211yescharacteristic, complemented
46C22×#4326C2211yescharacteristic, complemented
47C2×#66979C2211yescharacteristic
48C2×#66977C2211yescharacteristic
49C23×C11⋊C8C2211yescharacteristic
50#10623181—22no—
51#10623156—21no—
52#10623153—21no—
53#10623134—21no—
54#10623131—21no—
55#10623118—22no—
56#10623074C2212yes—
57#10623073C2212yescomplemented
58#10623072C2212yes—
59#10623072C2212yescomplemented
60#10623050C2211yescharacteristic, complemented
61#10623047C2211yescharacteristic, complemented
62#10622852C2212yes—
63#10622852C2212yes—
64#10622852C2212yescomplemented
65#10622852C2212yescomplemented
66#10622847C2211yescharacteristic, complemented
67#10622846C2211yescharacteristic
68#10622846C2211yescharacteristic
69#10622846C2211yescharacteristic
70#10622846C2211yescharacteristic
71#10622846C2211yescharacteristic
72#10622846C2211yescharacteristic
73#10622846C2211yescharacteristic
74#10622846C2211yescharacteristic
75#10622846C2212yescomplemented
76#10622845C2211yescharacteristic
77#10622845C2211yescharacteristic
78#10622845C2212yescomplemented
79#10622841C2212yes—
80#10622841C2212yescomplemented
81#10622841C2212yescomplemented
82#10622838C2211yescharacteristic, complemented
83#10622838C2211yescharacteristic, complemented
84#10622838C2212yescomplemented
85C2×#66899C2211yescharacteristic
86C2×#66899C2211yescharacteristic
87C2×#66899C2211yescharacteristic, complemented
88C2×#66899C2212yescomplemented
89#10622831C2212yes—
90C2×#66896C2211yescharacteristic
91C2×#66896C2211yescharacteristic
92#10622820C2211yescharacteristic
93#10622703C2212yescomplemented
94#10622703C2212yescomplemented
95#10622695C2212yescomplemented
96#10622694C2212yescomplemented
97#10622669C2212yescomplemented
98#10622668C2212yescomplemented
99#10622667C2212yescomplemented
100#10622667C2212yescomplemented
101#10622665C2212yescomplemented
102#10622664C2212yes—
103#10622664C2212yes—
104#10622664C2212yescomplemented
105#10622664C2212yescomplemented
106#10622664C2212yescomplemented
107#10622658C2212yescomplemented
108#10622658C2212yescomplemented
109#10622658C2212yescomplemented
110#10622657C2212yes—
111#10622657C2212yescomplemented
112#10622656C2212yes—
113#10622655C2212yescomplemented
114#10622654C2212yescomplemented
115#10622648C2212yescomplemented
116#10622646C2212yescomplemented
117#10622643C2212yescomplemented
118C4×#4326C2212yescomplemented
119#10622635C2212yescomplemented
120#10622634C2212yescomplemented
121#10622631C2212yescomplemented
122C4×#4324C2212yescomplemented
123#10622624C2212yes—
124#10622624C2212yescomplemented
125D4×C11⋊C8C2212yes—
126D4×C11⋊C8C2212yescomplemented
127#10622622C2212yescomplemented
128#10622620C2212yescomplemented
129#10622612C2211yescharacteristic, complemented
130#10622610C2211yescharacteristic, complemented
131C2×#66874C2211yescharacteristic, complemented
132#10622577C2211yescharacteristic, complemented
133#10622577C2211yescharacteristic, complemented
134C2×#66871C2211yescharacteristic, complemented
135C11×2−1+4—24no—
136C11×2−1+4—42no—
137C2×C11×#41—21no—
138C2×C11×#41—22no—
139C2×C11×#41—21no—
140C2×C11×#41—21no—
141C2×C11×#41—24no—
142C2×C11×#41—42no—
143C2×C11×#41C2311yescharacteristic
144C2×C11×#41C2312yes—
145C2×C11×#41C2311yescharacteristic
146C2×C11×#41C2311yescharacteristic
147C2×C11×#41C2311yescharacteristic
148C2×C11×#41C2311yescharacteristic
149C22×Q8×C11—21no—
150C22×Q8×C11C2311yescharacteristic
151C22×Q8×C11C2311yescharacteristic
152C22×Q8×C11C2312yes—
153C22×D4×C11—21no—
154C22×D4×C11C2311yescharacteristic
155C23×C4×C11—21no—
156C23×C4×C11C2311yescharacteristic
157C22×Dic22C2311yescharacteristic
158C11×C4⋊Q8—22no—
159C11×C4⋊Q8C2312yes—
160C11×#124—22no—
161C11×#124C2312yes—
162C11×#123—22no—
163C11×#123—22no—
164C11×#123—22no—
165C11×#123—22no—
166C11×#123D412yes—
167C11×C22⋊Q8—21no—
168C11×C22⋊Q8—21no—
169C11×C22⋊Q8—21no—
170C11×C22⋊Q8—21no—
171C11×C22⋊Q8—22no—
172C11×C22⋊Q8—21no—
173C11×C22⋊Q8—22no—
174C11×C22⋊Q8—22no—
175C11×C22⋊Q8D411yescharacteristic
176C11×C22⋊Q8D411yescharacteristic
177C11×C22⋊Q8C2312yes—
178C11×C22⋊Q8C2312yes—
179C11×C22⋊Q8C2312yes—
180C11×#121—21no—
181C11×#121—22no—
182C11×#121—22no—
183C11×#121—22no—
184C11×#121—22no—
185C11×#121D411yescharacteristic
186C11×#121D411yescharacteristic
187C11×#121C2312yes—
188C11×#120—22no—
189C11×#120D412yes—
190C4×Q8×C11C2312yes—
191C4×D4×C11—22no—
192C4×D4×C11—22no—
193C4×D4×C11—22no—
194C4×D4×C11C2312yes—
195C4×D4×C11C2312yes—
196C4×D4×C11C2312yes—
197C11×#117—21no—
198C11×#117C2311yescharacteristic
199C2×C11×C4⋊C4—21no—
200C2×C11×C4⋊C4—21no—
201C2×C11×C4⋊C4—22no—
202C2×C11×C4⋊C4C2311yescharacteristic
203C2×C11×C22⋊C4—21no—
204C2×C11×C22⋊C4—22no—
205C2×C22⋊Dic11—21no—
206C2×C22⋊Dic11—21no—
207#67004—24no—
208#67004—42no—
209#67001—42no—
210Q8×Dic11—21no—
211#66997—21no—
212C2×#4326—42no—
213C2×#4326C2312yes—
214C2×#4326C2312yes—
215C2×#4326C2312yes—
216C2×#4326C2312yes—
217#66989—22no—
218#66989—21no—
219#66988—22no—
220#66988—22no—
221#66988—22no—
222D4×Dic11—22no—
223D4×Dic11—22no—
224D4×Dic11—21no—
225C2×#4324C2312yes—
226C2×#4324C2312yes—
227#66979—21no—
228#66979—21no—
229#66979C2311yescharacteristic
230#66979C2311yescharacteristic
231#66979C2311yescharacteristic
232#66979C2311yescharacteristic
233#66979C2312yes—
234C2×C4⋊Dic11C2311yescharacteristic
235C2×C4⋊Dic11C2311yescharacteristic
236C2×C4⋊Dic11C2311yescharacteristic
237C2×C4⋊Dic11C2312yes—
238#66977—21no—
239#66977—21no—
240#66977C2312yes—
241#66977C2312yes—
242#66977C2312yes—
243#66977C2312yes—
244C2×Dic11⋊C4—21no—
245C2×C4×Dic11—21no—
246C2×#4318C2311yescharacteristic
247C2×#4318C2311yescharacteristic
248C2×#4318C2312yes—
249C22×C11⋊C8—42no—
250C22×C11⋊C8C2311yescharacteristic
251C22×C11⋊C8C2311yescharacteristic
252C22×C11⋊C8C2311yescharacteristic
253C22×C11⋊C8C2311yescharacteristic
254C22×C11⋊C8C2311yescharacteristic
255C22×C11⋊C8C2311yescharacteristic
256C22×C11⋊C8C2312yes—
257#66943—21no—
258#66943—22no—
259#66942—22no—
260#66942—22no—
261#66941—21no—
262#66940—21no—
263#66940—21no—
264#66940—22no—
265#66932—22no—
266#66932—22no—
267#66932—22no—
268#66932—22no—
269#66931—22no—
270#66931—22no—
271#66931—22no—
272#66930—22no—
273#66930—22no—
274#66930—22no—
275#66923C2312yes—
276#66922C2312yes—
277C4×Dic22C2312yes—
278C4×Dic22C2312yes—
279#66899C2311yescharacteristic
280#66899C2311yescharacteristic
281#66899C2311yescharacteristic
282#66899C2311yescharacteristic
283#66899C2311yescharacteristic
284#66899C2311yescharacteristic
285#66899C2311yescharacteristic
286#66899C2311yescharacteristic
287#66899C2312yes—
288#66899C2312yes—
289#66899C2312yes—
290#66899C2312yes—
291#66899C2312yes—
292#66899C2312yes—
293#66899C2312yes—
294#66899C2312yes—
295#66896C2311yescharacteristic
296#66896C2311yescharacteristic
297#66896C2311yescharacteristic
298#66896C2311yescharacteristic
299#66896C2311yescharacteristic
300#66896C2311yescharacteristic
301#66896C2311yescharacteristic
302#66896C2311yescharacteristic
303#66896C2312yes—
304#66896C2312yes—
305C22⋊(C11⋊C8)C2312yes—
306C22⋊(C11⋊C8)C2312yes—
307C22⋊(C11⋊C8)C2312yes—
308C22⋊(C11⋊C8)C2312yes—
309#66874C2312yes—
310#66874C2312yes—
311#66872C2312yes—
312#66872C2312yes—
313#66871C2312yes—
314#66871C2312yes—
315#66871C2312yes—
316#66871C2312yes—
317C4⋊(C11⋊C8)C2312yes—
318C4⋊(C11⋊C8)C2312yes—
319#66867C2312yes—
320C4×C11⋊C8C2312yes—
321#61173—111nomaximal, Sylow
322C24×C11—21no—
323C24×C11C2×D411yescharacteristic
324C11×#41—22no—
325C11×#41—22no—
326C11×#41—22no—
327C11×#41—22no—
328C11×#41—22no—
329C11×#41—24no—
330C11×#41—22no—
331C11×#41—22no—
332C11×#41—44no—
333C11×#41—41no—
334C11×#41—41no—
335C11×#41—42no—
336C11×#41—44no—
337C11×#41—44no—
338C11×#41—48no—
339C11×#41#4114yes—
340C2×Q8×C11—21no—
341C2×Q8×C11—22no—
342C2×Q8×C11—21no—
343C2×Q8×C11—22no—
344C2×Q8×C11—24no—
345C2×Q8×C11—22no—
346C2×Q8×C11—22no—
347C2×Q8×C11—41no—
348C2×Q8×C11—42no—
349C2×Q8×C11—44no—
350C2×Q8×C11C2×D411yescharacteristic
351C2×Q8×C11C2412yes—
352C2×Q8×C11C2411yescharacteristic
353C2×Q8×C11C2411yescharacteristic
354C2×D4×C11—21no—
355C2×D4×C11—22no—
356C2×D4×C11—22no—
357C2×D4×C11—21no—
358C2×D4×C11—21no—
359C2×D4×C11—21no—
360C2×D4×C11—22no—
361C2×D4×C11—21no—
362C2×D4×C11—41no—
363C2×D4×C11—44no—
364C2×D4×C11C2×D412yes—
365C2×D4×C11C2×D412yes—
366C2×D4×C11C2×D411yescharacteristic
367C2×D4×C11C2×D412yes—
368C2×D4×C11C2411yescharacteristic
369C2×D4×C11C2411yescharacteristic
370C22×C4×C11—21no—
371C22×C4×C11—22no—
372C22×C4×C11—22no—
373C22×C4×C11—21no—
374C22×C4×C11—22no—
375C22×C4×C11—21no—
376C22×C4×C11—21no—
377C22×C4×C11—22no—
378C22×C4×C11—21no—
379C22×C4×C11—21no—
380C22×C4×C11—21no—
381C22×C4×C11—22no—
382C22×C4×C11—44no—
383C22×C4×C11C2×D411yescharacteristic
384C22×C4×C11C2×D411yescharacteristic
385C22×C4×C11C2×D411yescharacteristic
386C22×C4×C11C2411yescharacteristic
387C22×C4×C11C2411yescharacteristic
388C22×C4×C11C2412yes—
389C22×C4×C11C2411yescharacteristic
390C22×Dic11—21no—
391C22×Dic11—21no—
392C22×Dic11—22no—
393C22×Dic11—21no—
394C22×Dic11—21no—
395C2×Dic22—21no—
396C2×Dic22—22no—
397C2×Dic22—22no—
398C2×Dic22—22no—
399C2×Dic22C2412yes—
400C11×C4⋊C4—22no—
401C11×C4⋊C4—21no—
402C11×C4⋊C4—22no—
403C11×C4⋊C4—22no—
404C11×C4⋊C4—22no—
405C11×C4⋊C4—22no—
406C11×C4⋊C4—22no—
407C11×C4⋊C4C2×D411yescharacteristic
408C11×C4⋊C4C2×D412yes—
409C11×C4⋊C4C2×D411yescharacteristic
410C11×C4⋊C4C2×D412yes—
411C11×C4⋊C4C2412yes—
412C11×C22⋊C4—22no—
413C11×C22⋊C4—22no—
414C11×C22⋊C4—22no—
415C11×C22⋊C4—22no—
416C11×C22⋊C4—22no—
417C11×C22⋊C4—22no—
418C11×C22⋊C4—22no—
419C11×C22⋊C4C2×D412yes—
420C11×C22⋊C4C2×D412yes—
421C11×C22⋊C4C2×D412yes—
422C11×C22⋊C4C2×D412yes—
423C11×C22⋊C4C2×D412yes—
424C42×C11—22no—
425C42×C11C2412yes—
426C22⋊Dic11—21no—
427C22⋊Dic11—22no—
428C22⋊Dic11—22no—
429C22⋊Dic11—21no—
430C22⋊Dic11—22no—
431C22⋊Dic11—22no—
432C22⋊Dic11—21no—
433C22⋊Dic11—21no—
434C22⋊Dic11—22no—
435#4326—24no—
436#4326—42no—
437#4326—42no—
438#4326—42no—
439#4324—24no—
440#4324—42no—
441C4⋊Dic11—22no—
442C4⋊Dic11—21no—
443C4⋊Dic11—22no—
444C4⋊Dic11—21no—
445C4⋊Dic11—21no—
446C4⋊Dic11C2411yescharacteristic
447C4⋊Dic11C2411yescharacteristic
448C4⋊Dic11C2412yes—
449C4⋊Dic11C2411yescharacteristic
450C4⋊Dic11C2411yescharacteristic
451Dic11⋊C4—22no—
452Dic11⋊C4—22no—
453Dic11⋊C4—22no—
454Dic11⋊C4—22no—
455Dic11⋊C4—22no—
456Dic11⋊C4—22no—
457Dic11⋊C4—22no—
458Dic11⋊C4—22no—
459C4×Dic11—22no—
460C4×Dic11—22no—
461C4×Dic11—21no—
462C4×Dic11—22no—
463C4×Dic11—21no—
464C4×Dic11—21no—
465C4×Dic11—21no—
466#4318—22no—
467#4318—22no—
468#4318—42no—
469C2×C11⋊C8—22no—
470C2×C11⋊C8—22no—
471C2×C11⋊C8—41no—
472C2×C11⋊C8—41no—
473C2×C11⋊C8—41no—
474C2×C11⋊C8—41no—
475C2×C11⋊C8—42no—
476C2×C11⋊C8C2411yescharacteristic
477C2×C11⋊C8C2412yes—
478C2×C11⋊C8C2411yescharacteristic
479C2×C11⋊C8C2411yescharacteristic
480C2×C11⋊C8C2411yescharacteristic
481C2×C11⋊C8C2412yes—
482#3495—111no—
483#3489D1111yescharacteristic
484#3315—112no—
485#3314—112no—
486#3313—112no—
487#3312—112no—
488#3302—112no—
489#3300—112no—
490#3299—112no—
491#3296—112no—
492#3137—111no—
493#3098—111no—
494#3095—111no—
495#3083—111no—
496#3063—111no—
497C2×#467—111no—
498#3044—111no—
499#3011—111no—
500#3007—111no—
501#2947—111no—
502#2929—111no—
503#2898—111no—
504C2×#416—111no—
505C23×C11—22no—
506C23×C11—22no—
507C23×C11—21no—
508C23×C11—21no—
509C23×C11—41no—
510C23×C11—42no—
511C23×C11—42no—
512C23×C11—81no—
513C23×C11C22×D411yescharacteristic
514C23×C11C22×D412yes—
515C23×C11C22×D411yescharacteristic
516C23×C11C22×D411yescharacteristic
517Q8×C11—22no—
518Q8×C11—21no—
519Q8×C11—22no—
520Q8×C11—21no—
521Q8×C11—22no—
522Q8×C11—21no—
523Q8×C11—44no—
524Q8×C11—42no—
525Q8×C11—42no—
526Q8×C11C2×#4112yes—
527D4×C11—24no—
528D4×C11—24no—
529D4×C11—24no—
530D4×C11—22no—
531D4×C11—21no—
532D4×C11—21no—
533D4×C11—21no—
534D4×C11—42no—
535D4×C11—42no—
536D4×C11—42no—
537D4×C11—42no—
538D4×C11—44no—
539D4×C11—42no—
540D4×C11—82no—
541D4×C11C2×#4112yes—
542C2×C4×C11—22no—
543C2×C4×C11—21no—
544C2×C4×C11—22no—
545C2×C4×C11—22no—
546C2×C4×C11—24no—
547C2×C4×C11—21no—
548C2×C4×C11—21no—
549C2×C4×C11—22no—
550C2×C4×C11—21no—
551C2×C4×C11—21no—
552C2×C4×C11—22no—
553C2×C4×C11—22no—
554C2×C4×C11—22no—
555C2×C4×C11—21no—
556C2×C4×C11—42no—
557C2×C4×C11—42no—
558C2×C4×C11—42no—
559C2×C4×C11—44no—
560C2×C4×C11—44no—
561C2×C4×C11—42no—
562C2×C4×C11—42no—
563C2×C4×C11—82no—
564C2×C4×C11—81no—
565C2×C4×C11C22×D411yescharacteristic
566C2×C4×C11C22×D412yes—
567C2×C4×C11C22×D412yes—
568C2×C4×C11C22×D412yes—
569C2×C4×C11C22×D411yescharacteristic
570C2×C4×C11C22×D411yescharacteristic
571C2×C4×C11C2×#4112yes—
572C2×C4×C11H(5,𝔽2)12yes—
573C2×C4×C11C2511yescharacteristic
574C2×Dic11—21no—
575C2×Dic11—21no—
576C2×Dic11—21no—
577C2×Dic11—22no—
578C2×Dic11—21no—
579C2×Dic11—22no—
580C2×Dic11—42no—
581C2×Dic11—42no—
582C2×Dic11—81no—
583C2×Dic11—81no—
584C2×Dic11—82no—
585Dic22—22no—
586Dic22—22no—
587Dic22—42no—
588Dic22—82no—
589C11⋊C8—22no—
590C11⋊C8—21no—
591C11⋊C8—21no—
592C11⋊C8—21no—
593C11⋊C8—21no—
594C11⋊C8—22no—
595C2×2−1+4C2×D1111yescharacteristic
596C22×#41C2×D1111yescharacteristic
597C2×#137—111no—
598C2×#137—111no—
599C22×Q16—111no—
600C2×#131—111no—
601C23×C8—111no—
602#556—112no—
603#554—112no—
604#552—112no—
605#552—112no—
606#552—222no—
607#551—222no—
608D4×Q8C2×D1112yes—
609#548C2×D1112yes—
610#547—22no—
611#547C2×D1112yes—
612#546—22no—
613#546C2×D1112yes—
614#544—111no—
615#542—221no—
616#541—221no—
617#537—21no—
618#537C2×D1111yescharacteristic
619#536—21no—
620#536—111no—
621#536C2×D1111yescharacteristic
622#533—221no—
623#529—221no—
624#525—21no—
625#525C2×D1111yescharacteristic
626C2×C22⋊Q8—21no—
627C2×C22⋊Q8—111no—
628C2×C22⋊Q8C2×D1111yescharacteristic
629#520—111no—
630#520C2×D1111yescharacteristic
631#519—111no—
632C2×#117—111no—
633#491—112no—
634#489—112no—
635#488—112no—
636#487—112no—
637#485—112no—
638#485—112no—
639#485—112no—
640#484—112no—
641#484—112no—
642#483—112no—
643#482—112no—
644#480—112no—
645#479—112no—
646#478—112no—
647#477—112no—
648#474—112no—
649#470—112no—
650#468—112no—
651#467—112no—
652#467—112no—
653#467—112no—
654#467—112no—
655#467—112no—
656#465—112no—
657#464—112no—
658#464—112no—
659#462—112no—
660#462—112no—
661#452—112no—
662#452—112no—
663#452—112no—
664#452—112no—
665#451—112no—
666#451—112no—
667#451—112no—
668#450—112no—
669#441—112no—
670#440—112no—
671C4×Q16—112no—
672C4×SD16—112no—
673#435—112no—
674#435—112no—
675C8×D4—112no—
676C8×D4—112no—
677#428—111no—
678#428—111no—
679C2×#107—111no—
680#424—111no—
681#419—111no—
682#419—111no—
683#419—112no—
684#417—111no—
685#417—111no—
686#417—112no—
687#416—111no—
688#416—111no—
689#416—111no—
690#416—111no—
691#416—111no—
692#416—111no—
693#416—111no—
694#416—111no—
695#416—112no—
696C2×#103—111no—
697C2×#103—111no—
698C2×#103—111no—
699C2×#103—112no—
700C2×#103—111no—
701C2×#102—111no—
702C2×#102—111no—
703#408—111no—
704#407—111no—
705#405—111no—
706C22×C11—21no—
707C22×C11—21no—
708C22×C11—21no—
709C22×C11—21no—
710C22×C11—21no—
711C22×C11—22no—
712C22×C11—21no—
713C22×C11—22no—
714C22×C11—22no—
715C22×C11—22no—
716C22×C11—21no—
717C22×C11—44no—
718C22×C11—41no—
719C22×C11—41no—
720C22×C11—41no—
721C22×C11—41no—
722C22×C11—41no—
723C22×C11—84no—
724C22×C11#54612yes—
725C22×C11#57812yes—
726C22×C11C23×D411yescharacteristic
727C4×C11—22no—
728C4×C11—21no—
729C4×C11—21no—
730C4×C11—22no—
731C4×C11—22no—
732C4×C11—22no—
733C4×C11—42no—
734C4×C11—41no—
735C4×C11—42no—
736C4×C11#54612yes—
737C4×C11C22×#4111yescharacteristic
738C4×C11C2×H(5,𝔽2)11yescharacteristic
739Dic11—41no—
740Dic11—42no—
741Dic11—41no—
742Dic11—42no—
743Dic11—41no—
744Dic11—41no—
7452−1+4—24no—
7462−1+4—42no—
747C2×#41—21no—
748C2×#41—22no—
749C2×#41—21no—
750C2×#41—21no—
751C2×#41—24no—
752C2×#41—42no—
753C2×#41C22×D1111yescharacteristic
754C2×#41C22×D1112yes—
755C2×#41C22×D1111yescharacteristic
756C2×#41C22×D1111yescharacteristic
757C2×#41C22×D1111yescharacteristic
758C2×#41C22×D1111yescharacteristic
759C22×Q8—21no—
760C22×Q8—111no—
761C22×Q8C22×D1111yescharacteristic
762C22×Q8C22×D1112yes—
763C22×Q8C22×D1111yescharacteristic
764C22×D4—21no—
765C22×D4C22×D1111yescharacteristic
766C23×C4—21no—
767C23×C4C22×D1111yescharacteristic
768#137—224no—
769#137—442no—
770C2×Q16—112no—
771C2×Q16—112no—
772C2×Q16—112no—
773C2×Q16—112no—
774C2×Q16—442no—
775C2×SD16—112no—
776C2×SD16—112no—
777#131—442no—
778C2×M16—111no—
779C2×M16—111no—
780C2×M16—112no—
781C22×C8—111no—
782C22×C8—111no—
783C22×C8—111no—
784C22×C8—111no—
785C22×C8—111no—
786C22×C8—111no—
787C22×C8—112no—
788C22×C8—442no—
789C4⋊Q8—22no—
790C4⋊Q8—112no—
791C4⋊Q8—221no—
792C4⋊Q8—221no—
793C4⋊Q8C22×D1112yes—
794#126—222no—
795#126—222no—
796#126—222no—
797#126—222no—
798#125—112no—
799#125—221no—
800#125—222no—
801#125—222no—
802#125—222no—
803#124—22no—
804#124—221no—
805#124—222no—
806#124C22×D1112yes—
807#123—22no—
808#123—22no—
809#123—22no—
810#123—22no—
811#123—222no—
812#123—222no—
813#123—222no—
814#123C22⋊D1112yes—
815C22⋊Q8—21no—
816C22⋊Q8—21no—
817C22⋊Q8—21no—
818C22⋊Q8—21no—
819C22⋊Q8—22no—
820C22⋊Q8—21no—
821C22⋊Q8—22no—
822C22⋊Q8—22no—
823C22⋊Q8—112no—
824C22⋊Q8—112no—
825C22⋊Q8—112no—
826C22⋊Q8—112no—
827C22⋊Q8—221no—
828C22⋊Q8—221no—
829C22⋊Q8—222no—
830C22⋊Q8—222no—
831C22⋊Q8—222no—
832C22⋊Q8C22⋊D1111yescharacteristic
833C22⋊Q8C22⋊D1111yescharacteristic
834C22⋊Q8C22×D1112yes—
835C22⋊Q8C22×D1112yes—
836C22⋊Q8C22×D1112yes—
837#121—21no—
838#121—22no—
839#121—22no—
840#121—22no—
841#121—22no—
842#121C22⋊D1111yescharacteristic
843#121C22⋊D1111yescharacteristic
844#121C22×D1112yes—
845#120—22no—
846#120C22⋊D1112yes—
847C4×Q8—112no—
848C4×Q8—112no—
849C4×Q8—221no—
850C4×Q8—221no—
851C4×Q8—221no—
852C4×Q8—222no—
853C4×Q8C22×D1112yes—
854C4×D4—22no—
855C4×D4—22no—
856C4×D4—22no—
857C4×D4—221no—
858C4×D4—222no—
859C4×D4—222no—
860C4×D4C22×D1112yes—
861C4×D4C22×D1112yes—
862C4×D4C22×D1112yes—
863#117—21no—
864#117—111no—
865#117—111no—
866#117—111no—
867#117—111no—
868#117—112no—
869#117—221no—
870#117—221no—
871#117—222no—
872#117—222no—
873#117—222no—
874#117C22×D1111yescharacteristic
875C2×C4⋊C4—21no—
876C2×C4⋊C4—21no—
877C2×C4⋊C4—22no—
878C2×C4⋊C4—111no—
879C2×C4⋊C4—111no—
880C2×C4⋊C4—111no—
881C2×C4⋊C4—112no—
882C2×C4⋊C4—221no—
883C2×C4⋊C4C22×D1111yescharacteristic
884C2×C22⋊C4—21no—
885C2×C22⋊C4—22no—
886C2×C22⋊C4—221no—
887C2×C22⋊C4—221no—
888C2×C42—221no—
889#107—112no—
890#107—112no—
891#107—112no—
892#107—112no—
893#106—112no—
894#106—112no—
895C4⋊C8—112no—
896C4⋊C8—112no—
897#103—111no—
898#103—112no—
899#103—111no—
900#103—111no—
901#103—111no—
902#103—111no—
903#103—111no—
904#103—111no—
905#103—111no—
906#103—112no—
907#103—112no—
908#103—112no—
909#103—112no—
910#103—112no—
911#103—112no—
912#103—112no—
913#103—112no—
914#103—112no—
915#102—111no—
916#102—111no—
917#102—111no—
918#102—111no—
919#102—111no—
920#102—111no—
921#102—111no—
922#102—111no—
923#102—112no—
924#102—112no—
925C22⋊C8—112no—
926C22⋊C8—112no—
927C22⋊C8—112no—
928C22⋊C8—112no—
929#97—112no—
930C4×C8—112no—
931C2×C11—22no—
932C2×C11—22no—
933C2×C11—42no—
934C2×C11—41no—
935C2×C11—42no—
936C2×C11—81no—
937C2×C11C2×#54611yescharacteristic
938C2×C11C2×#57811yescharacteristic
939C2×C11#358411yescharacteristic
940C24—21no—
941C24C2×C22⋊D1111yescharacteristic
942#41—22no—
943#41—22no—
944#41—22no—
945#41—22no—
946#41—22no—
947#41—24no—
948#41—22no—
949#41—22no—
950#41—44no—
951#41—41no—
952#41—41no—
953#41—42no—
954#41—44no—
955#41—44no—
956#41—48no—
957#41#434114yes—
958C2×Q8—21no—
959C2×Q8—22no—
960C2×Q8—21no—
961C2×Q8—22no—
962C2×Q8—24no—
963C2×Q8—22no—
964C2×Q8—22no—
965C2×Q8—41no—
966C2×Q8—42no—
967C2×Q8—44no—
968C2×Q8—112no—
969C2×Q8—221no—
970C2×Q8—222no—
971C2×Q8—222no—
972C2×Q8—222no—
973C2×Q8C2×C22⋊D1111yescharacteristic
974C2×Q8C23×D1112yes—
975C2×Q8C23×D1111yescharacteristic
976C2×Q8C23×D1111yescharacteristic
977C2×D4—21no—
978C2×D4—22no—
979C2×D4—22no—
980C2×D4—21no—
981C2×D4—21no—
982C2×D4—21no—
983C2×D4—22no—
984C2×D4—21no—
985C2×D4—41no—
986C2×D4—44no—
987C2×D4C2×C22⋊D1112yes—
988C2×D4C2×C22⋊D1112yes—
989C2×D4C2×C22⋊D1111yescharacteristic
990C2×D4C2×C22⋊D1112yes—
991C2×D4C23×D1111yescharacteristic
992C2×D4C23×D1111yescharacteristic
993C22×C4—22no—
994C22×C4—22no—
995C22×C4—21no—
996C22×C4—21no—
997C22×C4—22no—
998C22×C4—21no—
999C22×C4—21no—
1000C22×C4—22no—
1001C22×C4—21no—
1002C22×C4—21no—
1003C22×C4—21no—
1004C22×C4—22no—
1005C22×C4—44no—
1006C22×C4—221no—
1007C22×C4—221no—
1008C22×C4—221no—
1009C22×C4—221no—
1010C22×C4—222no—
1011C22×C4C2×C22⋊D1111yescharacteristic
1012C22×C4C2×C22⋊D1111yescharacteristic
1013C22×C4C2×C22⋊D1111yescharacteristic
1014C22×C4C23×D1111yescharacteristic
1015C22×C4C23×D1112yes—
1016C22×C4C23×D1111yescharacteristic
1017C22×C4C23×D1111yescharacteristic
1018Q16—224no—
1019Q16—442no—
1020Q16—442no—
1021Q16—442no—
1022SD16—224no—
1023SD16—442no—
1024M16—222no—
1025M16—222no—
1026M16—442no—
1027C2×C8—111no—
1028C2×C8—112no—
1029C2×C8—111no—
1030C2×C8—111no—
1031C2×C8—111no—
1032C2×C8—112no—
1033C2×C8—222no—
1034C2×C8—222no—
1035C2×C8—441no—
1036C2×C8—441no—
1037C2×C8—441no—
1038C2×C8—441no—
1039C2×C8—442no—
1040C4⋊C4—22no—
1041C4⋊C4—21no—
1042C4⋊C4—22no—
1043C4⋊C4—22no—
1044C4⋊C4—22no—
1045C4⋊C4—22no—
1046C4⋊C4—22no—
1047C4⋊C4—111no—
1048C4⋊C4—111no—
1049C4⋊C4—111no—
1050C4⋊C4—112no—
1051C4⋊C4—111no—
1052C4⋊C4—221no—
1053C4⋊C4—221no—
1054C4⋊C4—221no—
1055C4⋊C4—222no—
1056C4⋊C4—222no—
1057C4⋊C4—222no—
1058C4⋊C4—222no—
1059C4⋊C4—222no—
1060C4⋊C4—222no—
1061C4⋊C4—222no—
1062C4⋊C4—222no—
1063C4⋊C4—222no—
1064C4⋊C4—222no—
1065C4⋊C4C2×C22⋊D1111yescharacteristic
1066C4⋊C4C2×C22⋊D1112yes—
1067C4⋊C4C2×C22⋊D1111yescharacteristic
1068C4⋊C4C2×C22⋊D1112yes—
1069C4⋊C4C23×D1112yes—
1070C22⋊C4—22no—
1071C22⋊C4—22no—
1072C22⋊C4—22no—
1073C22⋊C4—22no—
1074C22⋊C4—22no—
1075C22⋊C4—22no—
1076C22⋊C4—22no—
1077C22⋊C4—221no—
1078C22⋊C4—221no—
1079C22⋊C4—221no—
1080C22⋊C4—221no—
1081C22⋊C4—222no—
1082C22⋊C4—222no—
1083C22⋊C4—222no—
1084C22⋊C4—222no—
1085C22⋊C4—222no—
1086C22⋊C4C2×C22⋊D1112yes—
1087C22⋊C4C2×C22⋊D1112yes—
1088C22⋊C4C2×C22⋊D1112yes—
1089C22⋊C4C2×C22⋊D1112yes—
1090C22⋊C4C2×C22⋊D1112yes—
1091C42—22no—
1092C42—221no—
1093C42—221no—
1094C42—221no—
1095C42—221no—
1096C42—222no—
1097C42—222no—
1098C42—222no—
1099C42C23×D1112yes—
1100C11#6117311yescharacteristic, complemented, Sylow
1101C23—22no—
1102C23—22no—
1103C23—21no—
1104C23—21no—
1105C23—41no—
1106C23—42no—
1107C23—42no—
1108C23—81no—
1109C23C22×C22⋊D1111yescharacteristic
1110C23C22×C22⋊D1112yes—
1111C23C22×C22⋊D1111yescharacteristic
1112C23C22×C22⋊D1111yescharacteristic
1113Q8—22no—
1114Q8—21no—
1115Q8—22no—
1116Q8—21no—
1117Q8—22no—
1118Q8—21no—
1119Q8—44no—
1120Q8—42no—
1121Q8—42no—
1122Q8—222no—
1123Q8—222no—
1124Q8—442no—
1125Q8—882no—
1126Q8C2×#434112yes—
1127D4—24no—
1128D4—24no—
1129D4—24no—
1130D4—22no—
1131D4—21no—
1132D4—21no—
1133D4—21no—
1134D4—42no—
1135D4—42no—
1136D4—42no—
1137D4—42no—
1138D4—44no—
1139D4—42no—
1140D4—82no—
1141D4C2×#434112yes—
1142C2×C4—22no—
1143C2×C4—21no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—24no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—22no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—21no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—44no—
1160C2×C4—44no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—82no—
1164C2×C4—81no—
1165C2×C4—221no—
1166C2×C4—221no—
1167C2×C4—221no—
1168C2×C4—221no—
1169C2×C4—222no—
1170C2×C4—222no—
1171C2×C4—442no—
1172C2×C4—442no—
1173C2×C4—882no—
1174C2×C4—881no—
1175C2×C4—881no—
1176C2×C4C2×#434112yes—
1177C2×C4#6703712yes—
1178C2×C4C22×C22⋊D1112yes—
1179C2×C4C22×C22⋊D1111yescharacteristic
1180C2×C4C22×C22⋊D1112yes—
1181C2×C4C22×C22⋊D1112yes—
1182C2×C4C22×C22⋊D1111yescharacteristic
1183C2×C4C22×C22⋊D1111yescharacteristic
1184C2×C4C24×D1111yescharacteristic
1185C8—222no—
1186C8—221no—
1187C8—221no—
1188C8—221no—
1189C8—221no—
1190C8—222no—
1191C22—21no—
1192C22—21no—
1193C22—21no—
1194C22—21no—
1195C22—21no—
1196C22—22no—
1197C22—22no—
1198C22—22no—
1199C22—21no—
1200C22—22no—
1201C22—21no—
1202C22—44no—
1203C22—41no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—84no—
1209C22#1062333712yes—
1210C22#1062336912yes—
1211C22C23×C22⋊D1111yescharacteristic
1212C4—21no—
1213C4—21no—
1214C4—22no—
1215C4—22no—
1216C4—22no—
1217C4—22no—
1218C4—41no—
1219C4—42no—
1220C4—42no—
1221C4—442no—
1222C4—441no—
1223C4—441no—
1224C4—441no—
1225C4—442no—
1226C4—441no—
1227C4#1062333712yes—
1228C4C22×#434111yescharacteristic
1229C4C2×#6703711yescharacteristic
1230C2—22no—
1231C2—22no—
1232C2—41no—
1233C2—42no—
1234C2—42no—
1235C2—81no—
1236C2C2×#1062333711yescharacteristic
1237C2C2×#1062336911yescharacteristic
1238C2#1308338711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC11×#3489C2
socleC22×C11C23×D4
hypercenter#3489D11
hypocenterC11#61173
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. #13082370C2semidirect
2. #13080712C2semidirect
3. #13080697C2semidirect
4. #13080682C2semidirect
5. #13080667C2semidirect
6. #13080533C2semidirect
7. #13080503C2semidirect
8. #13080492C2semidirect
9. #13080451C2semidirect
10. #13078981C2semidirect
11. #13078590C2semidirect
12. #13078560C2semidirect
13. #13078467C2semidirect
14. #13078309C2semidirect
15. C2×#10622664C2semidirect
16. #13078142C2semidirect
17. #13077911C2semidirect
18. #13077876C2semidirect
19. #13077455C2semidirect
20. #13077311C2semidirect
21. #13077149C2semidirect
22. C2×#10622846C2semidirect
41. #10623358C22semidirect
42. #10623356C22semidirect
45. C2×#67001C22semidirect
46. C22×#4326C22semidirect
57. #10623073C22semidirect
59. #10623072C22semidirect
60. #10623050C22semidirect
61. #10623047C22semidirect
64. #10622852C22semidirect
65. #10622852C22semidirect
66. #10622847C22semidirect
75. #10622846C22semidirect
78. #10622845C22semidirect
80. #10622841C22semidirect
81. #10622841C22semidirect
82. #10622838C22semidirect
83. #10622838C22semidirect
84. #10622838C22semidirect
87. C2×#66899C22semidirect
88. C2×#66899C22semidirect
93. #10622703C22semidirect
94. #10622703C22semidirect
95. #10622695C22semidirect
96. #10622694C22semidirect
97. #10622669C22semidirect
98. #10622668C22semidirect
99. #10622667C22semidirect
100. #10622667C22semidirect
101. #10622665C22semidirect
104. #10622664C22semidirect
105. #10622664C22semidirect
106. #10622664C22semidirect
107. #10622658C22semidirect
108. #10622658C22semidirect
109. #10622658C22semidirect
111. #10622657C22semidirect
113. #10622655C22semidirect
114. #10622654C22semidirect
115. #10622648C22semidirect
116. #10622646C22semidirect
117. #10622643C22semidirect
118. C4×#4326C22semidirect
119. #10622635C22semidirect
120. #10622634C22semidirect
121. #10622631C22semidirect
122. C4×#4324C22semidirect
124. #10622624C22semidirect
126. D4×C11⋊C8C22semidirect
127. #10622622C22semidirect
128. #10622620C22semidirect
129. #10622612C22semidirect
130. #10622610C22semidirect
131. C2×#66874C22semidirect
132. #10622577C22semidirect
133. #10622577C22semidirect
134. C2×#66871C22semidirect
1100. C11#61173semidirect

Maximal subgroups

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

subgroupindex
#130823702
#130807122
#130806972
#130806822
#130806672
#130805332
#130805032
#130804922
#130804512
#130789812
#130785902
#130785602
#130784672
#130783092
C2×#106226642
#130781422
#130779112
#130778762
#130774552
#130773112
#130771492
C2×#106228462
C11×#34892
#6117311