Finite Group Databasebeta

← #15631108

Subgroups — #15631108

Order 2816.

2114 conjugacy classes of subgroups.

The subgroup lattice has 1270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082358C211yesmaximal, characteristic, complemented
2#13082286C211yesmaximal, characteristic
3#13080747C212yesmaximal, complemented
4#13080732C212yesmaximal, complemented
5#13080657C212yesmaximal, complemented
6#13080642C212yesmaximal, complemented
7#13080557C212yesmaximal, complemented
8#13080508C212yesmaximal, complemented
9#13080456C212yesmaximal, complemented
10#13080442C212yesmaximal, complemented
11#13078972C211yesmaximal, characteristic, complemented
12#13078609C211yesmaximal, characteristic, complemented
13#13078558C211yesmaximal, characteristic, complemented
14#13078478C211yesmaximal, characteristic, complemented
15#13078305C211yesmaximal, characteristic, complemented
16C2×#10622420C211yesmaximal, characteristic, complemented
17#13078137C211yesmaximal, characteristic, complemented
18#13077892C211yesmaximal, characteristic, complemented
19#13077872C211yesmaximal, characteristic, complemented
20#13077312C211yesmaximal, characteristic, complemented
21#13077138C211yesmaximal, characteristic, complemented
22D11×#416C211yesmaximal, characteristic, complemented
23C11×#2947C211yesmaximal, characteristic, complemented
24C2×#67042C2211yescharacteristic
25C2×#41×D11C2211yescharacteristic
26C2×C11×#137C2211yescharacteristic
27C11×#520C2211yescharacteristic
28C11×#519C2211yescharacteristic, complemented
29#10623347C2211yescharacteristic, complemented
30C2×#66999C2211yescharacteristic, complemented
31C2×#66995C2211yescharacteristic, complemented
32C22×#4325C2211yescharacteristic, complemented
33C2×#66954C2211yescharacteristic, complemented
34C22×C8×D11C2211yescharacteristic, complemented
35#10623115C2212yescomplemented
36#10623114—21no—
37#10623113—21no—
38#10623112C2212yescomplemented
39#10623112C2212yescomplemented
40#10623111—21no—
41#10623110C2212yescomplemented
42#10623109—21no—
43#10623108C2212yes—
44#10623107C2212yes—
45#10623085—22no—
46#10623085C2212yes—
47D4×D44—22no—
48D4×D44C2212yes—
49#10623062—22no—
50#10623058—22no—
51#10623056—21no—
52#10623056C2211yescharacteristic
53#10623055—21no—
54#10623055C2211yescharacteristic
55#10623054C2211yescharacteristic, complemented
56D11×#117C2211yescharacteristic, complemented
57#10623050C2211yescharacteristic, complemented
58#10623041—21no—
59#10623041C2211yescharacteristic
60C2×#66948—21no—
61C2×#66948C2211yescharacteristic
62C11×#441C2212yescomplemented
63C11×#440C2212yescomplemented
64C4×C11×Q16C2212yescomplemented
65C4×C11×SD16C2212yescomplemented
66C11×#428C2211yescharacteristic, complemented
67C11×#416C2211yescharacteristic
68C2×C11×#103C2211yescharacteristic, complemented
69C11×#405C2211yescharacteristic, complemented
70#10622846C2211yescharacteristic
71#10622845C2211yescharacteristic
72#10622800C2212yescomplemented
73#10622800C2212yescomplemented
74#10622800C2212yescomplemented
75#10622799C2212yescomplemented
76#10622786C2212yescomplemented
77#10622782C2212yescomplemented
78#10622782C2212yescomplemented
79#10622782C2212yescomplemented
80#10622746C2211yescharacteristic, complemented
81#10622744C2211yescharacteristic, complemented
82#10622742C2211yescharacteristic, complemented
83#10622739C2211yescharacteristic, complemented
84#10622726C2211yescharacteristic, complemented
85C2×#66885C2211yescharacteristic, complemented
86#10622641C2212yescomplemented
87#10622641C2212yescomplemented
88#10622640C2212yescomplemented
89#10622640C2212yescomplemented
90#10622635C2212yescomplemented
91#10622633C2212yescomplemented
92#10622622C2212yescomplemented
93#10622621C2212yescomplemented
94#10622615C2211yescharacteristic, complemented
95#10622614C2211yescharacteristic, complemented
96#10622612C2211yescharacteristic, complemented
97#10622577C2211yescharacteristic, complemented
98C2×#66872C2211yescharacteristic, complemented
99#10622501C2212yescomplemented
100#10622498C2212yescomplemented
101#10622498C2212yescomplemented
102#10622495C2212yescomplemented
103#10622479C2212yescomplemented
104#10622476C2212yescomplemented
105#10622476C2212yescomplemented
106#10622475C2212yescomplemented
107#10622429C2212yescomplemented
108#10622426C2212yescomplemented
109#10622425C2212yescomplemented
110#10622420C2212yescomplemented
111#10622420C2212yescomplemented
112#10622420C2212yescomplemented
113#10622420C2212yescomplemented
114#10622420C2212yescomplemented
115#10622417C2211yescharacteristic, complemented
116#10622417C2211yescharacteristic, complemented
117#10622417C2212yescomplemented
118#10622416C2212yescomplemented
119D11×#103C2211yescharacteristic, complemented
120D11×#103C2211yescharacteristic, complemented
121#10622385C2211yescharacteristic, complemented
122#10622385C2211yescharacteristic, complemented
123#10622383C2212yescomplemented
124D11×#102C2211yescharacteristic, complemented
125D11×#102C2211yescharacteristic, complemented
126D11×#102C2212yescomplemented
127#10622327C2212yescomplemented
128#10622326C2212yescomplemented
129#10622319C2212yescomplemented
130#10622319C2212yescomplemented
131#10622310C2212yescomplemented
132#10622307C2212yescomplemented
133C8×D44C2212yescomplemented
134C8×D44C2212yescomplemented
135C2×C11×#41C2311yescharacteristic
136C22×Q8×C11C2311yescharacteristic
137#67042—24no—
138#67042—42no—
139#41×D11—24no—
140#41×D11—42no—
141C2×#4343C2312yes—
142C2×#4343C2311yescharacteristic
143C2×Q8×D11C2311yescharacteristic
144C2×#4341—21no—
145C2×#4341C2311yescharacteristic
146C2×D4×D11—21no—
147C2×D4×D11—22no—
148C2×D4×D11C2311yescharacteristic
149C2×D4×D11C2312yes—
150C2×#4339—21no—
151C2×#4339—21no—
152C2×#4339C2311yescharacteristic
153C2×#4339C2311yescharacteristic
154C22×D44—21no—
155C22×D44—21no—
156C22×D44—22no—
157C22×D44C2311yescharacteristic
158C22×C4×D11—21no—
159C22×C4×D11C2311yescharacteristic
160C11×#137—24no—
161C2×C11×Q16C2312yes—
162C2×C11×SD16C2312yes—
163C2×C11×M16C2311yescharacteristic
164C22×C8×C11C2311yescharacteristic
165C4×Q8×C11—21no—
166C4×Q8×C11—21no—
167C4×Q8×C11C2312yes—
168C4×Q8×C11C2312yes—
169C4×Q8×C11C2312yes—
170C4×D4×C11—22no—
171C4×D4×C11C2312yes—
172C11×#117—21no—
173C11×#117—22no—
174C11×#117C2311yescharacteristic
175C11×#117C2311yescharacteristic
176C2×C11×C4⋊C4—21no—
177C2×C11×C4⋊C4C2311yescharacteristic
178#67000—21no—
179#66999—21no—
180#66999—21no—
181#66999C2312yes—
182#66999C2312yes—
183#66999C2312yes—
184#66999C2312yes—
185#66997—21no—
186C2×#4326C2312yes—
187#66995—42no—
188C2×#4325—42no—
189C2×#4325C2312yes—
190C2×#4325C2312yes—
191C2×#4325C2312yes—
192#66983—22no—
193#66983—22no—
194#66983—22no—
195#66982—22no—
196C2×(C2×D11)⋊C4—21no—
197C2×(C2×D11)⋊C4—21no—
198C2×(C2×D11)⋊C4—22no—
199#66979C2311yescharacteristic
200C2×C4⋊Dic11C2311yescharacteristic
201C2×Dic11⋊C4—21no—
202C2×#4318C2311yescharacteristic
203C22×C11⋊C8C2311yescharacteristic
204#66954—42no—
205C2×#4313C2312yes—
206C2×C8×D11—42no—
207C2×C8×D11C2311yescharacteristic
208C2×C8×D11C2311yescharacteristic
209C2×C8×D11C2311yescharacteristic
210C2×C8×D11C2311yescharacteristic
211C2×C8×D11C2312yes—
212#66951—22no—
213#66951—22no—
214#66950—21no—
215#66950—22no—
216#66950D411yescharacteristic
217#66950D411yescharacteristic
218#66950C2312yes—
219#66949—22no—
220#66949—22no—
221#66948—21no—
222#66948—22no—
223#66948—21no—
224#66948—21no—
225#66948—21no—
226#66948—21no—
227#66948—22no—
228#66948—22no—
229#66948D411yescharacteristic
230#66948D411yescharacteristic
231#66948C2312yes—
232#66948C2312yes—
233#66948C2312yes—
234#66947—22no—
235#66947—22no—
236#66945C2311yescharacteristic
237#66945C2311yescharacteristic
238#66945C2312yes—
239C4⋊C4×D11C2312yes—
240C4⋊C4×D11C2311yescharacteristic
241C4⋊C4×D11C2311yescharacteristic
242#66943—21no—
243#66942—22no—
244#66942—22no—
245#66941—21no—
246#66939—22no—
247#66939D412yes—
248#66935—22no—
249#66935—22no—
250#66935—22no—
251#66935—22no—
252#66935D412yes—
253(C22⋊D11)⋊C4—22no—
254C22⋊C4×D11—21no—
255#66931—22no—
256#66930—21no—
257#66929—22no—
258#66929—22no—
259#66928—22no—
260#66928—22no—
261#66928C2312yes—
262#66927—22no—
263#66927C2312yes—
264C4×D44—21no—
265C4×D44—22no—
266C4×D44—22no—
267C4×D44—22no—
268C4×D44C2312yes—
269C4×D44C2312yes—
270#66925—21no—
271#66925—22no—
272#66925—22no—
273C42×D11—21no—
274#66923—22no—
275#66923C2312yes—
276#66922C2312yes—
277C4×Dic22—21no—
278C4×Dic22—22no—
279C11×#107C2312yes—
280C11×#106C2312yes—
281C11×#103C2312yes—
282C11×#103C2312yes—
283C11×#103C2311yescharacteristic
284C11×#103C2311yescharacteristic
285C11×#102C2311yescharacteristic
286C11×#102C2311yescharacteristic
287C11×#97C2312yes—
288C4×C8×C11C2312yes—
289#66899C2312yes—
290#66899C2311yescharacteristic
291#66899C2311yescharacteristic
292#66896C2311yescharacteristic
293#66896C2311yescharacteristic
294#66896C2312yes—
295#66885C2312yes—
296#66885C2312yes—
297#66885C2311yescharacteristic
298#66885C2311yescharacteristic
299#66885C2312yes—
300#66885C2312yes—
301#66885C2312yes—
302(C2×D11)⋊C8C2312yes—
303(C2×D11)⋊C8C2312yes—
304(C2×D11)⋊C8C2312yes—
305(C2×D11)⋊C8C2312yes—
306#66880C2311yescharacteristic
307#66880C2311yescharacteristic
308#66880C2312yes—
309#66874C2311yescharacteristic
310#66874C2311yescharacteristic
311#66873C2311yescharacteristic
312#66873C2312yes—
313#66873C2312yes—
314#66873C2311yescharacteristic
315#66872C2312yes—
316#66872C2312yes—
317#66872C2312yes—
318#66871C2312yes—
319C4⋊(C11⋊C8)C2312yes—
320C4⋊(C11⋊C8)C2312yes—
321#61172—111nomaximal, Sylow
322C23×D11—21no—
323C23×D11—21no—
324C23×D11—22no—
325C23×D11C2×D411yescharacteristic
326C11×#41—22no—
327C11×#41#4114yes—
328C2×Q8×C11—21no—
329C2×Q8×C11—22no—
330C2×Q8×C11—22no—
331C2×Q8×C11C2412yes—
332C2×Q8×C11C2411yescharacteristic
333C2×D4×C11—21no—
334C2×D4×C11C2411yescharacteristic
335C22×C4×C11—21no—
336C22×C4×C11—21no—
337C22×C4×C11—21no—
338C22×C4×C11—22no—
339C22×C4×C11C2411yescharacteristic
340C2×C22⋊D11—21no—
341C2×C22⋊D11—22no—
342C2×C22⋊D11—21no—
343C2×C22⋊D11—21no—
344C2×C22⋊D11C2×D412yes—
345C22×Dic11—21no—
346C22×Dic11—21no—
347C22×Dic11C2×D411yescharacteristic
348#4343—22no—
349#4343—24no—
350#4343—41no—
351#4343—42no—
352Q8×D11—22no—
353Q8×D11—41no—
354#4341—22no—
355#4341—41no—
356#4341—44no—
357D4×D11—22no—
358D4×D11—24no—
359D4×D11—44no—
360D4×D11—41no—
361D4×D11—42no—
362D4×D11—48no—
363#4339—22no—
364#4339—22no—
365#4339—22no—
366#4339—22no—
367#4339—44no—
368#4339—44no—
369C2×D44—22no—
370C2×D44—21no—
371C2×D44—22no—
372C2×D44—22no—
373C2×D44—22no—
374C2×D44—21no—
375C2×D44—22no—
376C2×D44—22no—
377C2×D44—22no—
378C2×D44—22no—
379C2×D44—44no—
380C2×D44—82no—
381C2×D44—84no—
382C2×D44C2×D412yes—
383C2×D44C2×D411yescharacteristic
384C2×D44C2×D412yes—
385C2×D44C2411yescharacteristic
386C2×D44C2412yes—
387C2×C4×D11—21no—
388C2×C4×D11—22no—
389C2×C4×D11—21no—
390C2×C4×D11—21no—
391C2×C4×D11—21no—
392C2×C4×D11—22no—
393C2×C4×D11—21no—
394C2×C4×D11—22no—
395C2×C4×D11—22no—
396C2×C4×D11—44no—
397C2×C4×D11C2×D411yescharacteristic
398C2×C4×D11C2×D411yescharacteristic
399C2×C4×D11C2411yescharacteristic
400C2×C4×D11C2412yes—
401C2×C4×D11C2411yescharacteristic
402C2×Dic22—21no—
403C2×Dic22—22no—
404C2×Dic22C2×D411yescharacteristic
405C2×Dic22C2411yescharacteristic
406C11×Q16—24no—
407C11×SD16—24no—
408C11×M16—22no—
409C2×C8×C11—22no—
410C2×C8×C11C2412yes—
411C2×C8×C11C2411yescharacteristic
412C2×C8×C11C2411yescharacteristic
413C11×C4⋊C4—22no—
414C11×C4⋊C4—22no—
415C11×C4⋊C4—21no—
416C11×C4⋊C4—22no—
417C11×C4⋊C4C2×D411yescharacteristic
418C11×C4⋊C4C2×D411yescharacteristic
419C11×C4⋊C4C2412yes—
420C11×C4⋊C4C2411yescharacteristic
421C11×C4⋊C4C2411yescharacteristic
422C11×C22⋊C4—21no—
423C11×C22⋊C4—22no—
424C11×C22⋊C4C2×D412yes—
425C42×C11—21no—
426C42×C11—22no—
427C42×C11—22no—
428C42×C11—22no—
429C42×C11C2412yes—
430C22⋊Dic11—21no—
431#4326—42no—
432#4325—42no—
433#4325—42no—
434#4325—42no—
435(C2×D11)⋊C4—22no—
436(C2×D11)⋊C4—22no—
437(C2×D11)⋊C4—22no—
438(C2×D11)⋊C4—22no—
439(C2×D11)⋊C4—21no—
440(C2×D11)⋊C4—21no—
441(C2×D11)⋊C4—22no—
442(C2×D11)⋊C4—22no—
443(C2×D11)⋊C4—22no—
444(C2×D11)⋊C4—22no—
445(C2×D11)⋊C4—22no—
446(C2×D11)⋊C4—22no—
447(C2×D11)⋊C4—22no—
448(C2×D11)⋊C4C2×D412yes—
449(C2×D11)⋊C4C2×D412yes—
450(C2×D11)⋊C4C2×D412yes—
451(C2×D11)⋊C4C2×D412yes—
452C4⋊Dic11—22no—
453C4⋊Dic11—21no—
454C4⋊Dic11—22no—
455C4⋊Dic11C2×D412yes—
456C4⋊Dic11C2×D412yes—
457C4⋊Dic11C2411yescharacteristic
458C4⋊Dic11C2411yescharacteristic
459C4⋊Dic11C2412yes—
460Dic11⋊C4—22no—
461Dic11⋊C4—22no—
462Dic11⋊C4—22no—
463Dic11⋊C4—21no—
464Dic11⋊C4—22no—
465Dic11⋊C4—21no—
466Dic11⋊C4—22no—
467Dic11⋊C4—22no—
468Dic11⋊C4—22no—
469C4×Dic11—21no—
470C4×Dic11—22no—
471C4×Dic11—21no—
472C4×Dic11—21no—
473#4318—22no—
474C2×C11⋊C8—22no—
475C2×C11⋊C8C2412yes—
476C2×C11⋊C8C2411yescharacteristic
477C2×C11⋊C8C2411yescharacteristic
478#4313—42no—
479C8×D11—41no—
480C8×D11—41no—
481C8×D11—41no—
482C8×D11—41no—
483C8×D11—42no—
484#3495—111no—
485#3488—111no—
486#3317—112no—
487#3316—112no—
488#3311—112no—
489#3310—112no—
490#3304—112no—
491#3300—112no—
492#3296—112no—
493#3295—112no—
494#3136—111no—
495#3099—111no—
496#3094—111no—
497#3084—111no—
498#3063—111no—
499C2×#465—111no—
500#3043—111no—
501#3009—111no—
502#3007—111no—
503#2947D1111yescharacteristic, complemented
504#2929—111no—
505#2897—111no—
506C2×#416—111no—
507C23×C11—21no—
508C23×C11C22×D411yescharacteristic
509C22×D11—22no—
510C22×D11—22no—
511C22×D11—22no—
512C22×D11—21no—
513C22×D11—41no—
514C22×D11—42no—
515C22×D11—44no—
516C22×D11—42no—
517C22×D11—42no—
518C22×D11—81no—
519C22×D11—82no—
520C22×D11—82no—
521C22×D11—81no—
522C22×D11—81no—
523C22×D11C22×D412yes—
524C22×D11C22×D411yescharacteristic
525C22×D11C22×D411yescharacteristic
526Q8×C11—21no—
527Q8×C11—22no—
528Q8×C11—22no—
529Q8×C11—42no—
530Q8×C11C2×#4112yes—
531D4×C11—24no—
532D4×C11—21no—
533D4×C11C2×#4112yes—
534C2×C4×C11—21no—
535C2×C4×C11—24no—
536C2×C4×C11—21no—
537C2×C4×C11—21no—
538C2×C4×C11—22no—
539C2×C4×C11—22no—
540C2×C4×C11—42no—
541C2×C4×C11—82no—
542C2×C4×C11—81no—
543C2×C4×C11C22×D412yes—
544C2×C4×C11C22×D412yes—
545C2×C4×C11C22×D411yescharacteristic
546C2×C4×C11C2×#4112yes—
547C2×C4×C11H(5,𝔽2)12yes—
548C2×C4×C11C2511yescharacteristic
549C22⋊D11—24no—
550C22⋊D11—44no—
551C22⋊D11—42no—
552C22⋊D11—42no—
553C22⋊D11—42no—
554C2×Dic11—22no—
555C2×Dic11—21no—
556C2×Dic11—21no—
557C2×Dic11—22no—
558C2×Dic11—21no—
559C2×Dic11—42no—
560C2×Dic11—81no—
561C2×Dic11C22×D411yescharacteristic
562C2×Dic11C22×D412yes—
563C2×Dic11C22×D411yescharacteristic
564D44—24no—
565D44—22no—
566D44—22no—
567D44—21no—
568D44—22no—
569D44—21no—
570D44—42no—
571D44—44no—
572D44—42no—
573D44—44no—
574D44—42no—
575D44—82no—
576D44—82no—
577D44—82no—
578D44—82no—
579C4×D11—22no—
580C4×D11—22no—
581C4×D11—21no—
582C4×D11—21no—
583C4×D11—22no—
584C4×D11—21no—
585C4×D11—21no—
586C4×D11—22no—
587C4×D11—42no—
588C4×D11—44no—
589C4×D11—42no—
590C4×D11—42no—
591C4×D11—42no—
592C4×D11—81no—
593C4×D11—82no—
594Dic22—22no—
595Dic22—21no—
596Dic22—21no—
597Dic22—42no—
598Dic22—82no—
599C8×C11—22no—
600C8×C11—21no—
601C8×C11—21no—
602C11⋊C8—21no—
603C11⋊C8—21no—
604C11⋊C8—22no—
605C2×H(5,𝔽2)—111no—
606C22×#41—111no—
607C2×#137—111no—
608C2×#137C2×D1111yescharacteristic
609C22×SD16—111no—
610C2×#131—111no—
611C23×C8—111no—
612#556—112no—
613#554—112no—
614#552—112no—
615#552—112no—
616#552—222no—
617#551—222no—
618#550—112no—
619#548—112no—
620#546—112no—
621#546—222no—
622D42—112no—
623D42—222no—
624#544—111no—
625#542—221no—
626#541—221no—
627#537—111no—
628#537—221no—
629#536—111no—
630#535—111no—
631#535—221no—
632#533—221no—
633#529—221no—
634#525—111no—
635#525—221no—
636C2×C22⋊Q8—111no—
637C2×#121—111no—
638C2×#121—221no—
639#520—111no—
640#520C2×D1111yescharacteristic
641#519C2×D1111yescharacteristic, complemented
642C2×#117—111no—
643#490—112no—
644#489—112no—
645#488—112no—
646#486—112no—
647#485—112no—
648#483—112no—
649#482—112no—
650#482—112no—
651#482—112no—
652#481—112no—
653#481—112no—
654#480—112no—
655#479—112no—
656#478—112no—
657#476—112no—
658#475—112no—
659#470—112no—
660#468—112no—
661#467—112no—
662#465—112no—
663#465—112no—
664#465—112no—
665#465—112no—
666#465—112no—
667#464—112no—
668#464—112no—
669#460—112no—
670#460—112no—
671#452—112no—
672#452—112no—
673#452—112no—
674#452—112no—
675#451—112no—
676#450—112no—
677#450—112no—
678#450—112no—
679#441C2×D1112yescomplemented
680#440C2×D1112yescomplemented
681C4×Q16C2×D1112yescomplemented
682C4×SD16C2×D1112yescomplemented
683#435—112no—
684#435—112no—
685C8×D4—112no—
686C8×D4—112no—
687#428—111no—
688#428C2×D1111yescharacteristic, complemented
689C2×#106—111no—
690#424—111no—
691#418—111no—
692#418—111no—
693#418—112no—
694#417—111no—
695#417—111no—
696#417—112no—
697#416—111no—
698#416—111no—
699#416—111no—
700#416—111no—
701#416—111no—
702#416—112no—
703#416—111no—
704#416—111no—
705#416C2×D1111yescharacteristic
706C2×#103—111no—
707C2×#103—111no—
708C2×#103C2×D1111yescharacteristic, complemented
709C2×#102—111no—
710C2×#102—111no—
711C2×#102—111no—
712C2×#102—112no—
713#408—111no—
714#407—111no—
715#405C2×D1111yescharacteristic, complemented
716C22×C11—21no—
717C22×C11—21no—
718C22×C11—22no—
719C22×C11—41no—
720C22×C11—41no—
721C22×C11#54612yes—
722C22×C11C23×D411yescharacteristic
723C2×D11—21no—
724C2×D11—21no—
725C2×D11—21no—
726C2×D11—22no—
727C2×D11—21no—
728C2×D11—22no—
729C2×D11—21no—
730C2×D11—22no—
731C2×D11—44no—
732C2×D11—42no—
733C2×D11—41no—
734C2×D11—42no—
735C2×D11—41no—
736C2×D11—41no—
737C2×D11—42no—
738C2×D11—84no—
739C2×D11—164no—
740C2×D11—162no—
741C2×D11#57712yes—
742C4×C11—22no—
743C4×C11—22no—
744C4×C11—22no—
745C4×C11—41no—
746C4×C11—42no—
747C4×C11—42no—
748C4×C11—41no—
749C4×C11#54612yes—
750C4×C11C22×#4111yescharacteristic
751C4×C11C2×H(5,𝔽2)11yescharacteristic
752Dic11—22no—
753Dic11—21no—
754Dic11—21no—
755Dic11—41no—
756Dic11—42no—
757Dic11—41no—
758Dic11—41no—
759H(5,𝔽2)—224no—
760H(5,𝔽2)—442no—
761C2×#41—111no—
762C2×#41—112no—
763C2×#41—111no—
764C2×#41—111no—
765C2×#41—111no—
766C2×#41—221no—
767C2×#41—221no—
768C2×#41—221no—
769C2×#41—224no—
770C2×#41—442no—
771C2×#41C22×D1111yescharacteristic
772C22×Q8—111no—
773C22×Q8C22×D1111yescharacteristic
774C22×D4—111no—
775C22×D4—112no—
776C22×D4—111no—
777C22×D4—221no—
778C22×D4—222no—
779C22×D4—221no—
780C22×D4—222no—
781C22×D4—221no—
782C23×C4—111no—
783C23×C4—221no—
784#137—24no—
785#137—442no—
786C2×Q16—112no—
787C2×Q16C22×D1112yes—
788C2×SD16—112no—
789C2×SD16—112no—
790C2×SD16—112no—
791C2×SD16—442no—
792C2×SD16C22×D1112yes—
793#131—442no—
794C2×M16—111no—
795C2×M16—112no—
796C2×M16C22×D1111yescharacteristic
797C22×C8—111no—
798C22×C8—111no—
799C22×C8—111no—
800C22×C8—111no—
801C22×C8—111no—
802C22×C8—112no—
803C22×C8—442no—
804C22×C8C22×D1111yescharacteristic
805C4⋊Q8—112no—
806C4⋊Q8—221no—
807C4⋊Q8—221no—
808#127—112no—
809#127—222no—
810#126—222no—
811#126—222no—
812#126—222no—
813#126—222no—
814#125—112no—
815#125—222no—
816#125—222no—
817#125—222no—
818#125—221no—
819#124—112no—
820#124—222no—
821#124—222no—
822#124—221no—
823#123—112no—
824#123—222no—
825#123—222no—
826#123—222no—
827#123—222no—
828C22⋊Q8—111no—
829C22⋊Q8—111no—
830C22⋊Q8—112no—
831C22⋊Q8—112no—
832C22⋊Q8—112no—
833C22⋊Q8—112no—
834C22⋊Q8—112no—
835C22⋊Q8—222no—
836C22⋊Q8—222no—
837C22⋊Q8—222no—
838C22⋊Q8—221no—
839C22⋊Q8—221no—
840C22⋊Q8—221no—
841C22⋊Q8—222no—
842#121—111no—
843#121—111no—
844#121—112no—
845#121—112no—
846#121—112no—
847#121—222no—
848#121—222no—
849#121—222no—
850#121—221no—
851#121—221no—
852#121—221no—
853#121—222no—
854#121—222no—
855#121—222no—
856#121—221no—
857#121—221no—
858#120—112no—
859#120—222no—
860#120—222no—
861#120—222no—
862#120—222no—
863C4×Q8—21no—
864C4×Q8—21no—
865C4×Q8—222no—
866C4×Q8—221no—
867C4×Q8C22×D1112yes—
868C4×Q8C22×D1112yes—
869C4×Q8C22×D1112yes—
870C4×D4—22no—
871C4×D4—112no—
872C4×D4—112no—
873C4×D4—222no—
874C4×D4—222no—
875C4×D4—221no—
876C4×D4—222no—
877C4×D4—222no—
878C4×D4C22×D1112yes—
879#117—21no—
880#117—22no—
881#117—111no—
882#117—111no—
883#117—111no—
884#117—112no—
885#117—222no—
886#117—222no—
887#117—221no—
888#117—221no—
889#117C22×D1111yescharacteristic
890#117C22×D1111yescharacteristic
891C2×C4⋊C4—21no—
892C2×C4⋊C4—111no—
893C2×C4⋊C4—111no—
894C2×C4⋊C4—111no—
895C2×C4⋊C4—112no—
896C2×C4⋊C4—221no—
897C2×C4⋊C4C22×D1111yescharacteristic
898C2×C22⋊C4—221no—
899C2×C22⋊C4—222no—
900C2×C22⋊C4—221no—
901C2×C22⋊C4—221no—
902C2×C42—221no—
903#107—112no—
904#107C22×D1112yes—
905#106—112no—
906#106—112no—
907#106—112no—
908#106C22×D1112yes—
909C4⋊C8—112no—
910C4⋊C8—112no—
911#103—111no—
912#103—111no—
913#103—112no—
914#103—111no—
915#103—111no—
916#103—112no—
917#103—111no—
918#103—111no—
919#103C22×D1111yescharacteristic
920#103C22×D1111yescharacteristic
921#103C22×D1112yes—
922#103C22×D1112yes—
923#102—111no—
924#102—111no—
925#102—112no—
926#102—112no—
927#102—111no—
928#102—111no—
929#102—112no—
930#102—112no—
931#102—112no—
932#102—112no—
933#102—111no—
934#102—111no—
935#102—112no—
936#102—112no—
937#102C22×D1111yescharacteristic
938#102C22×D1111yescharacteristic
939C22⋊C8—112no—
940C22⋊C8—112no—
941C22⋊C8—112no—
942C22⋊C8—112no—
943#97C22×D1112yes—
944C4×C8C22×D1112yes—
945C2×C11—22no—
946C2×C11—42no—
947C2×C11C2×#54611yescharacteristic
948C2×C11C2×#57711yescharacteristic
949C2×C11#358411yescharacteristic
950D11—22no—
951D11—41no—
952D11—42no—
953D11—81no—
954D11—82no—
955C24—111no—
956C24—221no—
957C24—222no—
958C24—221no—
959#41—22no—
960#41—222no—
961#41—222no—
962#41—222no—
963#41—224no—
964#41—222no—
965#41—222no—
966#41—222no—
967#41—444no—
968#41—444no—
969#41—441no—
970#41—444no—
971#41—441no—
972#41—442no—
973#41#433914yes—
974C2×Q8—21no—
975C2×Q8—22no—
976C2×Q8—22no—
977C2×Q8—111no—
978C2×Q8—111no—
979C2×Q8—221no—
980C2×Q8—222no—
981C2×Q8—222no—
982C2×Q8—441no—
983C2×Q8C23×D1112yes—
984C2×Q8C23×D1111yescharacteristic
985C2×D4—21no—
986C2×D4—112no—
987C2×D4—112no—
988C2×D4—111no—
989C2×D4—112no—
990C2×D4—112no—
991C2×D4—111no—
992C2×D4—222no—
993C2×D4—222no—
994C2×D4—221no—
995C2×D4—222no—
996C2×D4—222no—
997C2×D4—221no—
998C2×D4—222no—
999C2×D4—222no—
1000C2×D4—224no—
1001C2×D4—221no—
1002C2×D4—221no—
1003C2×D4—222no—
1004C2×D4—221no—
1005C2×D4—222no—
1006C2×D4—222no—
1007C2×D4—222no—
1008C2×D4—444no—
1009C2×D4—441no—
1010C2×D4—442no—
1011C2×D4—448no—
1012C2×D4—444no—
1013C2×D4—884no—
1014C2×D4—882no—
1015C2×D4C23×D1111yescharacteristic
1016C22×C4—21no—
1017C22×C4—21no—
1018C22×C4—21no—
1019C22×C4—22no—
1020C22×C4—111no—
1021C22×C4—111no—
1022C22×C4—111no—
1023C22×C4—111no—
1024C22×C4—112no—
1025C22×C4—111no—
1026C22×C4—221no—
1027C22×C4—222no—
1028C22×C4—221no—
1029C22×C4—221no—
1030C22×C4—221no—
1031C22×C4—222no—
1032C22×C4—221no—
1033C22×C4—222no—
1034C22×C4—222no—
1035C22×C4—221no—
1036C22×C4—221no—
1037C22×C4—444no—
1038C22×C4C23×D1111yescharacteristic
1039Q16—24no—
1040Q16—442no—
1041SD16—24no—
1042SD16—442no—
1043SD16—442no—
1044SD16—442no—
1045M16—22no—
1046M16—222no—
1047M16—442no—
1048C2×C8—22no—
1049C2×C8—112no—
1050C2×C8—111no—
1051C2×C8—111no—
1052C2×C8—222no—
1053C2×C8—441no—
1054C2×C8—441no—
1055C2×C8—441no—
1056C2×C8—441no—
1057C2×C8—442no—
1058C2×C8C23×D1111yescharacteristic
1059C2×C8C23×D1112yes—
1060C2×C8C23×D1111yescharacteristic
1061C4⋊C4—21no—
1062C4⋊C4—22no—
1063C4⋊C4—22no—
1064C4⋊C4—22no—
1065C4⋊C4—112no—
1066C4⋊C4—112no—
1067C4⋊C4—112no—
1068C4⋊C4—111no—
1069C4⋊C4—111no—
1070C4⋊C4—221no—
1071C4⋊C4—221no—
1072C4⋊C4—222no—
1073C4⋊C4—222no—
1074C4⋊C4—222no—
1075C4⋊C4—222no—
1076C4⋊C4—222no—
1077C4⋊C4—222no—
1078C4⋊C4—221no—
1079C4⋊C4—222no—
1080C4⋊C4—222no—
1081C4⋊C4—222no—
1082C4⋊C4D4×D1111yescharacteristic
1083C4⋊C4D4×D1111yescharacteristic
1084C4⋊C4C23×D1111yescharacteristic
1085C4⋊C4C23×D1111yescharacteristic
1086C4⋊C4C23×D1112yes—
1087C22⋊C4—21no—
1088C22⋊C4—22no—
1089C22⋊C4—112no—
1090C22⋊C4—112no—
1091C22⋊C4—112no—
1092C22⋊C4—112no—
1093C22⋊C4—222no—
1094C22⋊C4—222no—
1095C22⋊C4—222no—
1096C22⋊C4—221no—
1097C22⋊C4—221no—
1098C22⋊C4—222no—
1099C22⋊C4—222no—
1100C22⋊C4—222no—
1101C22⋊C4—222no—
1102C22⋊C4—222no—
1103C22⋊C4—222no—
1104C22⋊C4—221no—
1105C22⋊C4—222no—
1106C22⋊C4—222no—
1107C22⋊C4D4×D1112yes—
1108C42—21no—
1109C42—22no—
1110C42—22no—
1111C42—22no—
1112C42—221no—
1113C42—221no—
1114C42—222no—
1115C42—221no—
1116C42C23×D1112yes—
1117C11#6117211yescharacteristic, complemented, Sylow
1118C23—21no—
1119C23—111no—
1120C23—111no—
1121C23—112no—
1122C23—222no—
1123C23—222no—
1124C23—222no—
1125C23—221no—
1126C23—441no—
1127C23—442no—
1128C23—444no—
1129C23—442no—
1130C23—442no—
1131C23—881no—
1132C23—881no—
1133C23—881no—
1134C23—882no—
1135C23—882no—
1136C23C2×D4×D1111yescharacteristic
1137Q8—21no—
1138Q8—22no—
1139Q8—22no—
1140Q8—42no—
1141Q8—222no—
1142Q8—221no—
1143Q8—221no—
1144Q8—442no—
1145Q8—882no—
1146Q8C2×#433912yes—
1147D4—24no—
1148D4—21no—
1149D4—224no—
1150D4—224no—
1151D4—222no—
1152D4—222no—
1153D4—221no—
1154D4—222no—
1155D4—221no—
1156D4—442no—
1157D4—444no—
1158D4—442no—
1159D4—444no—
1160D4—444no—
1161D4—442no—
1162D4—442no—
1163D4—442no—
1164D4—442no—
1165D4—882no—
1166D4—882no—
1167D4—882no—
1168D4—882no—
1169D4C2×#433912yes—
1170C2×C4—21no—
1171C2×C4—24no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—42no—
1177C2×C4—82no—
1178C2×C4—81no—
1179C2×C4—111no—
1180C2×C4—112no—
1181C2×C4—111no—
1182C2×C4—222no—
1183C2×C4—222no—
1184C2×C4—222no—
1185C2×C4—221no—
1186C2×C4—221no—
1187C2×C4—222no—
1188C2×C4—221no—
1189C2×C4—221no—
1190C2×C4—222no—
1191C2×C4—221no—
1192C2×C4—221no—
1193C2×C4—222no—
1194C2×C4—221no—
1195C2×C4—442no—
1196C2×C4—444no—
1197C2×C4—442no—
1198C2×C4—442no—
1199C2×C4—442no—
1200C2×C4—442no—
1201C2×C4—882no—
1202C2×C4—881no—
1203C2×C4—881no—
1204C2×C4C2×#433912yes—
1205C2×C4C2×D4×D1112yes—
1206C2×C4C2×D4×D1112yes—
1207C2×C4C2×D4×D1111yescharacteristic
1208C2×C4#6704212yes—
1209C2×C4C24×D1111yescharacteristic
1210C8—22no—
1211C8—21no—
1212C8—21no—
1213C8—221no—
1214C8—221no—
1215C8—222no—
1216C22—21no—
1217C22—21no—
1218C22—22no—
1219C22—41no—
1220C22—41no—
1221C22—112no—
1222C22—221no—
1223C22—221no—
1224C22—221no—
1225C22—222no—
1226C22—222no—
1227C22—221no—
1228C22—222no—
1229C22—221no—
1230C22—444no—
1231C22—441no—
1232C22—442no—
1233C22—442no—
1234C22—441no—
1235C22—441no—
1236C22—442no—
1237C22—884no—
1238C22—1762no—
1239C22—1764no—
1240C22#1062308112yes—
1241C22C22×D4×D1111yescharacteristic
1242C4—22no—
1243C4—22no—
1244C4—22no—
1245C4—42no—
1246C4—42no—
1247C4—41no—
1248C4—41no—
1249C4—221no—
1250C4—221no—
1251C4—222no—
1252C4—441no—
1253C4—441no—
1254C4—442no—
1255C4—441no—
1256C4#1062308112yes—
1257C4C22×#433911yescharacteristic
1258C4C2×#6704211yescharacteristic
1259C2—22no—
1260C2—42no—
1261C2—222no—
1262C2—441no—
1263C2—442no—
1264C2—881no—
1265C2—882no—
1266C2C2×#1062308111yescharacteristic
1267C2D11×#57711yescharacteristic
1268C2#1308338611yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2947C2
socleC22×C11C23×D4
prime radical#13082286C2
hypercenter#2947D11
hypocenterC11#61172
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #2947

Complements

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

NH ≅ G/Ntype
1. #13082358C2semidirect
3. #13080747C2semidirect
4. #13080732C2semidirect
5. #13080657C2semidirect
6. #13080642C2semidirect
7. #13080557C2semidirect
8. #13080508C2semidirect
9. #13080456C2semidirect
10. #13080442C2semidirect
11. #13078972C2semidirect
12. #13078609C2semidirect
13. #13078558C2semidirect
14. #13078478C2semidirect
15. #13078305C2semidirect
16. C2×#10622420C2semidirect
17. #13078137C2semidirect
18. #13077892C2semidirect
19. #13077872C2semidirect
20. #13077312C2semidirect
21. #13077138C2semidirect
22. D11×#416C2semidirect
23. C11×#2947C2semidirect
28. C11×#519C22semidirect
29. #10623347C22semidirect
30. C2×#66999C22semidirect
31. C2×#66995C22semidirect
32. C22×#4325C22semidirect
33. C2×#66954C22semidirect
34. C22×C8×D11C22semidirect
35. #10623115C22semidirect
38. #10623112C22semidirect
39. #10623112C22semidirect
41. #10623110C22semidirect
55. #10623054C22semidirect
56. D11×#117C22semidirect
57. #10623050C22semidirect
62. C11×#441C22semidirect
63. C11×#440C22semidirect
64. C4×C11×Q16C22semidirect
65. C4×C11×SD16C22semidirect
66. C11×#428C22semidirect
68. C2×C11×#103C22semidirect
69. C11×#405C22semidirect
72. #10622800C22semidirect
73. #10622800C22semidirect
74. #10622800C22semidirect
75. #10622799C22semidirect
76. #10622786C22semidirect
77. #10622782C22semidirect
78. #10622782C22semidirect
79. #10622782C22semidirect
80. #10622746C22semidirect
81. #10622744C22semidirect
82. #10622742C22semidirect
83. #10622739C22semidirect
84. #10622726C22semidirect
85. C2×#66885C22semidirect
86. #10622641C22semidirect
87. #10622641C22semidirect
88. #10622640C22semidirect
89. #10622640C22semidirect
90. #10622635C22semidirect
91. #10622633C22semidirect
92. #10622622C22semidirect
93. #10622621C22semidirect
94. #10622615C22semidirect
95. #10622614C22semidirect
96. #10622612C22semidirect
97. #10622577C22semidirect
98. C2×#66872C22semidirect
99. #10622501C22semidirect
100. #10622498C22semidirect
101. #10622498C22semidirect
102. #10622495C22semidirect
103. #10622479C22semidirect
104. #10622476C22semidirect
105. #10622476C22semidirect
106. #10622475C22semidirect
107. #10622429C22semidirect
108. #10622426C22semidirect
109. #10622425C22semidirect
110. #10622420C22semidirect
111. #10622420C22semidirect
112. #10622420C22semidirect
113. #10622420C22semidirect
114. #10622420C22semidirect
115. #10622417C22semidirect
116. #10622417C22semidirect
117. #10622417C22semidirect
118. #10622416C22semidirect
119. D11×#103C22semidirect
120. D11×#103C22semidirect
121. #10622385C22semidirect
122. #10622385C22semidirect
123. #10622383C22semidirect
124. D11×#102C22semidirect
125. D11×#102C22semidirect
126. D11×#102C22semidirect
127. #10622327C22semidirect
128. #10622326C22semidirect
129. #10622319C22semidirect
130. #10622319C22semidirect
131. #10622310C22semidirect
132. #10622307C22semidirect
133. C8×D44C22semidirect
134. C8×D44C22semidirect
503. #2947D11semidirect
641. #519C2×D11semidirect
679. #441C2×D11semidirect
680. #440C2×D11semidirect
681. C4×Q16C2×D11semidirect
682. C4×SD16C2×D11semidirect
688. #428C2×D11semidirect
708. C2×#103C2×D11semidirect
715. #405C2×D11semidirect
1117. C11#61172semidirect

Maximal subgroups

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

subgroupindex
#130823582
#130822862
#130807472
#130807322
#130806572
#130806422
#130805572
#130805082
#130804562
#130804422
#130789722
#130786092
#130785582
#130784782
#130783052
C2×#106224202
#130781372
#130778922
#130778722
#130773122
#130771382
D11×#4162
C11×#29472
#6117211