Finite Group Databasebeta

← #15631089

Subgroups — #15631089

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#13082365C211yesmaximal, characteristic, complemented
2#13082278C211yesmaximal, characteristic
3#13080735C212yesmaximal, complemented
4#13080720C212yesmaximal, complemented
5#13080645C212yesmaximal, complemented
6#13080630C212yesmaximal, complemented
7#13080548C212yesmaximal, complemented
8#13080496C212yesmaximal, complemented
9#13080455C212yesmaximal, complemented
10#13080433C212yesmaximal, complemented
11#13078966C211yesmaximal, characteristic, complemented
12#13078607C211yesmaximal, characteristic, complemented
13#13078554C211yesmaximal, characteristic, complemented
14#13078476C211yesmaximal, characteristic, complemented
15#13078303C211yesmaximal, characteristic, complemented
16C2×#10622784C211yesmaximal, characteristic, complemented
17#13078134C211yesmaximal, characteristic, complemented
18#13077872C211yesmaximal, characteristic, complemented
19#13077460C211yesmaximal, characteristic, complemented
20#13077313C211yesmaximal, characteristic, complemented
21#13077142C211yesmaximal, characteristic, complemented
22D11×#416C211yesmaximal, characteristic, complemented
23C11×#3009C211yesmaximal, characteristic, complemented
24C2×C11×H(5,𝔽2)C2211yescharacteristic
25C2×#41×D11C2211yescharacteristic
26C2×C11×#137C2211yescharacteristic
27C22×C11×SD16C2211yescharacteristic, complemented
28C11×#536C2211yescharacteristic, complemented
29#10623365C2212yes—
30#10623364—21no—
31#10623364C2211yescharacteristic
32#10623362C2212yes—
33#10623359—21no—
34#10623359C2211yescharacteristic
35#10623358C2211yescharacteristic
36#10623358C2211yescharacteristic, complemented
37C2×#67001C2211yescharacteristic, complemented
38C2×#66999C2211yescharacteristic, complemented
39#10623343C2211yescharacteristic, complemented
40C2×#66995C2211yescharacteristic, complemented
41#10623337—22no—
42#10623337C2212yes—
43#10623336—21no—
44#10623336C2211yescharacteristic
45D4×C22⋊D11—22no—
46D4×C22⋊D11C2212yes—
47C2×#66991—21no—
48C2×#66991C2211yescharacteristic
49C22×C8×D11C2211yescharacteristic, complemented
50#10623262—21no—
51#10623259—21no—
52#10623213—21no—
53#10623211—21no—
54#10623189—22no—
55#10623181—22no—
56#10623173C2212yescomplemented
57#10623172C2212yescomplemented
58#10623170C2212yescomplemented
59#10623166C2212yescomplemented
60D11×#117C2211yescharacteristic, complemented
61#10623050C2211yescharacteristic, complemented
62C11×#452C2212yescomplemented
63C11×#452C2212yescomplemented
64C11×#450C2212yescomplemented
65C11×#450C2212yescomplemented
66C11×#418C2211yescharacteristic, complemented
67C11×#416C2211yescharacteristic
68C11×#408C2211yescharacteristic, complemented
69#10622846C2211yescharacteristic
70#10622846C2212yescomplemented
71#10622845C2211yescharacteristic
72#10622845C2212yescomplemented
73C2×#66899C2211yescharacteristic, complemented
74#10622828C2211yescharacteristic, complemented
75#10622828C2212yescomplemented
76C2×#66896C2212yescomplemented
77C2×#66896C2211yescharacteristic, complemented
78#10622800C2212yescomplemented
79#10622799C2212yescomplemented
80#10622797C2212yescomplemented
81Q16×Dic11C2212yescomplemented
82#10622786C2212yescomplemented
83#10622784C2212yescomplemented
84#10622784C2212yescomplemented
85#10622784C2212yescomplemented
86#10622784C2212yescomplemented
87#10622782C2212yescomplemented
88#10622779C2212yescomplemented
89#10622779C2212yescomplemented
90#10622777C2212yescomplemented
91#10622776C2212yescomplemented
92#10622776C2212yescomplemented
93SD16×Dic11C2212yescomplemented
94#10622746C2211yescharacteristic, complemented
95#10622739C2211yescharacteristic, complemented
96#10622735C2211yescharacteristic, complemented
97#10622734C2211yescharacteristic, complemented
98#10622726C2211yescharacteristic, complemented
99C2×#66881C2211yescharacteristic, complemented
100#10622715C2211yescharacteristic, complemented
101#10622665C2212yescomplemented
102#10622664C2212yescomplemented
103#10622662C2212yescomplemented
104#10622661C2212yescomplemented
105#10622615C2211yescharacteristic, complemented
106#10622608C2211yescharacteristic, complemented
107#10622417C2211yescharacteristic, complemented
108#10622417C2211yescharacteristic, complemented
109D11×#103C2211yescharacteristic, complemented
110D11×#103C2211yescharacteristic, complemented
111#10622412C2212yescomplemented
112#10622404C2212yescomplemented
113#10622397C2212yescomplemented
114#10622392C2212yescomplemented
115#10622390C2212yescomplemented
116#10622387C2212yescomplemented
117#10622385C2211yescharacteristic, complemented
118#10622385C2211yescharacteristic, complemented
119D11×#102C2211yescharacteristic, complemented
120D11×#102C2211yescharacteristic, complemented
121#10622381C2212yescomplemented
122#10622378C2212yescomplemented
123#10622377C2212yescomplemented
124#10622376C2212yescomplemented
125#10622374C2212yescomplemented
126#10622373C2212yescomplemented
127#10622350C2212yescomplemented
128#10622348C2212yescomplemented
129#10622341C2212yescomplemented
130#10622341C2212yescomplemented
131(C22⋊D11)⋊C8C2212yescomplemented
132(C22⋊D11)⋊C8C2212yescomplemented
133#10622336C2212yescomplemented
134#10622334C2212yescomplemented
135C11×H(5,𝔽2)—24no—
136C11×H(5,𝔽2)—42no—
137C2×C11×#41—21no—
138C2×C11×#41C2312yes—
139C2×C11×#41C2311yescharacteristic
140C2×C11×#41C2311yescharacteristic
141C22×Q8×C11C2311yescharacteristic
142C22×D4×C11—21no—
143C22×D4×C11—22no—
144C22×D4×C11C2311yescharacteristic
145C22×D4×C11C2312yes—
146C22×C22⋊D11—21no—
147C22×C22⋊D11—22no—
148#41×D11—24no—
149#41×D11—42no—
150C2×#4343C2311yescharacteristic
151C2×Q8×D11C2311yescharacteristic
152C2×#4341—21no—
153C2×#4341C2311yescharacteristic
154C2×D4×D11—21no—
155C2×D4×D11C2311yescharacteristic
156C2×#4339—21no—
157C2×#4339C2311yescharacteristic
158C22×C4×D11—21no—
159C22×C4×D11C2311yescharacteristic
160C11×#137—24no—
161C2×C11×Q16C2312yes—
162C2×C11×SD16—42no—
163C2×C11×SD16C2312yes—
164C2×C11×SD16C2312yes—
165C2×C11×SD16C2312yes—
166C2×C11×M16C2311yescharacteristic
167C22×C8×C11C2311yescharacteristic
168C11×C4⋊Q8—21no—
169C11×#124—21no—
170C11×#123—22no—
171C11×C22⋊Q8C2312yes—
172C11×C22⋊Q8C2312yes—
173C11×#117C2311yescharacteristic
174#67006—22no—
175#67006—22no—
176#67006—22no—
177C2×C22⋊Dic11—21no—
178C2×C22⋊Dic11—22no—
179#67001—42no—
180#66999—21no—
181#66999—21no—
182#66999—21no—
183#66999D411yescharacteristic
184#66999D411yescharacteristic
185#66999C2312yes—
186#66999C2312yes—
187Q8×Dic11—21no—
188Q8×Dic11—21no—
189Q8×Dic11—21no—
190Q8×Dic11C2312yes—
191Q8×Dic11C2312yes—
192Q8×Dic11C2312yes—
193C2×#4326C2312yes—
194#66995—42no—
195C2×#4325C2312yes—
196#66993—22no—
197#66993C2312yes—
198#66992—22no—
199#66992—22no—
200#66992—22no—
201#66991—21no—
202#66991—22no—
203#66991—21no—
204#66991—21no—
205#66991—22no—
206#66991—21no—
207#66991—21no—
208#66991D411yescharacteristic
209#66991D411yescharacteristic
210#66991C2312yes—
211#66991C2312yes—
212#66990—22no—
213#66990D412yes—
214#66989—22no—
215#66989C2312yes—
216#66988—22no—
217#66988D412yes—
218D4×Dic11—22no—
219D4×Dic11—21no—
220D4×Dic11—22no—
221D4×Dic11C2312yes—
222#66983—22no—
223#66983C2312yes—
224C4×C22⋊D11—22no—
225C4×C22⋊D11—22no—
226C4×C22⋊D11C2312yes—
227C4×C22⋊D11C2312yes—
228C2×(C2×D11)⋊C4—21no—
229#66979—22no—
230#66979—21no—
231#66979C2311yescharacteristic
232#66979C2312yes—
233#66979C2311yescharacteristic
234C2×C4⋊Dic11—21no—
235C2×C4⋊Dic11C2311yescharacteristic
236C2×C4⋊Dic11C2311yescharacteristic
237C2×C4⋊Dic11C2312yes—
238#66977—22no—
239#66977C2312yes—
240C2×Dic11⋊C4—21no—
241C2×#4318C2311yescharacteristic
242C2×#4318C2312yes—
243C22×C11⋊C8C2311yescharacteristic
244C22×C11⋊C8C2312yes—
245C2×C8×D11—42no—
246C2×C8×D11C2311yescharacteristic
247C2×C8×D11C2311yescharacteristic
248C2×C8×D11C2311yescharacteristic
249C2×C8×D11C2311yescharacteristic
250#66951—22no—
251#66951—22no—
252#66950—22no—
253#66945—22no—
254#66945C2311yescharacteristic
255#66945C2311yescharacteristic
256C4⋊C4×D11C2311yescharacteristic
257C4⋊C4×D11C2311yescharacteristic
258#66943—22no—
259#66943C2312yes—
260#66942—22no—
261#66942—22no—
262#66941C2312yes—
263#66940—22no—
264#66939—22no—
265#66938—22no—
266#66936—22no—
267(C22⋊D11)⋊C4—22no—
268C22⋊C4×D11—21no—
269#66932—22no—
270#66932—22no—
271#66931—22no—
272#66931—22no—
273#66930—21no—
274#66930—22no—
275#66925—21no—
276C42×D11—21no—
277#66923—21no—
278#66922—21no—
279C11×#103C2311yescharacteristic
280C11×#103C2311yescharacteristic
281C11×#102C2312yes—
282C11×#102C2311yescharacteristic
283C11×#102C2311yescharacteristic
284C11×#102C2312yes—
285C11×C22⋊C8C2312yes—
286C11×C22⋊C8C2312yes—
287#66899C2312yes—
288#66899C2312yes—
289#66899C2311yescharacteristic
290#66899C2311yescharacteristic
291#66899C2312yes—
292#66896C2311yescharacteristic
293#66896C2312yes—
294#66896C2312yes—
295#66896C2311yescharacteristic
296#66896C2312yes—
297#66896C2312yes—
298#66896C2312yes—
299#66885C2311yescharacteristic
300#66885C2311yescharacteristic
301#66885C2312yes—
302(C2×D11)⋊C8C2312yes—
303(C2×D11)⋊C8C2312yes—
304#66882C2312yes—
305#66881C2312yes—
306#66881C2312yes—
307#66881C2312yes—
308#66880C2311yescharacteristic
309#66880C2311yescharacteristic
310#66880C2312yes—
311#66879C2312yes—
312Dic11⋊C8C2312yes—
313Dic11⋊C8C2312yes—
314C8×Dic11C2312yes—
315#66874C2311yescharacteristic
316#66874C2311yescharacteristic
317#66873C2311yescharacteristic
318#66873C2311yescharacteristic
319#66872C2312yes—
320#66871C2312yes—
321#61172—111nomaximal, Sylow
322C24×C11—22no—
323C24×C11—21no—
324C23×D11—21no—
325C23×D11C2×D411yescharacteristic
326C11×#41—22no—
327C11×#41—22no—
328C11×#41—22no—
329C11×#41—24no—
330C11×#41—42no—
331C11×#41—44no—
332C11×#41#4114yes—
333C2×Q8×C11—21no—
334C2×Q8×C11—22no—
335C2×Q8×C11—22no—
336C2×Q8×C11C2×D411yescharacteristic
337C2×Q8×C11C2412yes—
338C2×Q8×C11C2411yescharacteristic
339C2×D4×C11—21no—
340C2×D4×C11—24no—
341C2×D4×C11—22no—
342C2×D4×C11—22no—
343C2×D4×C11—21no—
344C2×D4×C11—22no—
345C2×D4×C11—22no—
346C2×D4×C11—42no—
347C2×D4×C11—44no—
348C2×D4×C11—48no—
349C2×D4×C11C2×D412yes—
350C2×D4×C11C2×D411yescharacteristic
351C2×D4×C11C2412yes—
352C2×D4×C11C2411yescharacteristic
353C22×C4×C11—21no—
354C22×C4×C11—21no—
355C22×C4×C11—22no—
356C22×C4×C11C2412yes—
357C22×C4×C11C2411yescharacteristic
358C2×C22⋊D11—21no—
359C2×C22⋊D11—22no—
360C2×C22⋊D11—22no—
361C2×C22⋊D11—21no—
362C2×C22⋊D11—22no—
363C2×C22⋊D11—22no—
364C2×C22⋊D11—21no—
365C2×C22⋊D11—22no—
366C2×C22⋊D11—82no—
367C2×C22⋊D11—84no—
368C2×C22⋊D11C2×D412yes—
369C2×C22⋊D11C2×D412yes—
370C22×Dic11—21no—
371C22×Dic11—22no—
372C22×Dic11—22no—
373C22×Dic11—21no—
374C22×Dic11—21no—
375C22×Dic11C2×D411yescharacteristic
376#4343—22no—
377#4343—41no—
378Q8×D11—22no—
379Q8×D11—41no—
380#4341—22no—
381#4341—41no—
382#4341—44no—
383D4×D11—22no—
384D4×D11—44no—
385D4×D11—41no—
386#4339—22no—
387#4339—22no—
388#4339—44no—
389C2×D44—21no—
390C2×D44C2411yescharacteristic
391C2×C4×D11—21no—
392C2×C4×D11—21no—
393C2×C4×D11—21no—
394C2×C4×D11—21no—
395C2×C4×D11—21no—
396C2×C4×D11—22no—
397C2×C4×D11—22no—
398C2×C4×D11—44no—
399C2×C4×D11C2×D411yescharacteristic
400C2×C4×D11C2×D411yescharacteristic
401C2×C4×D11C2411yescharacteristic
402C2×C4×D11C2411yescharacteristic
403C2×Dic22—21no—
404C2×Dic22—22no—
405C2×Dic22C2411yescharacteristic
406C11×Q16—24no—
407C11×SD16—24no—
408C11×SD16—42no—
409C11×SD16—42no—
410C11×M16—22no—
411C2×C8×C11—22no—
412C2×C8×C11C2412yes—
413C2×C8×C11C2411yescharacteristic
414C2×C8×C11C2411yescharacteristic
415C11×C4⋊C4—22no—
416C11×C4⋊C4—22no—
417C11×C4⋊C4C2411yescharacteristic
418C11×C4⋊C4C2411yescharacteristic
419C11×C22⋊C4—21no—
420C11×C22⋊C4—22no—
421C11×C22⋊C4—22no—
422C42×C11—21no—
423C22⋊Dic11—22no—
424C22⋊Dic11—22no—
425C22⋊Dic11—22no—
426C22⋊Dic11—22no—
427C22⋊Dic11—22no—
428C22⋊Dic11—21no—
429C22⋊Dic11—22no—
430C22⋊Dic11—22no—
431C22⋊Dic11C2×D412yes—
432C22⋊Dic11C2×D412yes—
433C22⋊Dic11C2×D412yes—
434#4326—42no—
435#4325—42no—
436(C2×D11)⋊C4—21no—
437(C2×D11)⋊C4—21no—
438(C2×D11)⋊C4—22no—
439(C2×D11)⋊C4—22no—
440(C2×D11)⋊C4—22no—
441(C2×D11)⋊C4C2×D412yes—
442(C2×D11)⋊C4C2×D412yes—
443C4⋊Dic11—22no—
444C4⋊Dic11—22no—
445C4⋊Dic11—22no—
446C4⋊Dic11—22no—
447C4⋊Dic11—21no—
448C4⋊Dic11—22no—
449C4⋊Dic11—21no—
450C4⋊Dic11C2×D411yescharacteristic
451C4⋊Dic11C2×D411yescharacteristic
452C4⋊Dic11C2412yes—
453C4⋊Dic11C2412yes—
454C4⋊Dic11C2411yescharacteristic
455C4⋊Dic11C2411yescharacteristic
456Dic11⋊C4—22no—
457Dic11⋊C4—22no—
458Dic11⋊C4—21no—
459Dic11⋊C4—21no—
460Dic11⋊C4—22no—
461Dic11⋊C4—22no—
462Dic11⋊C4—22no—
463Dic11⋊C4C2×D412yes—
464Dic11⋊C4C2×D412yes—
465C4×Dic11—21no—
466C4×Dic11—21no—
467C4×Dic11—22no—
468C4×Dic11—22no—
469C4×Dic11—22no—
470C4×Dic11—21no—
471C4×Dic11—22no—
472C4×Dic11C2412yes—
473#4318—22no—
474#4318—42no—
475C2×C11⋊C8—22no—
476C2×C11⋊C8—42no—
477C2×C11⋊C8C2412yes—
478C2×C11⋊C8C2411yescharacteristic
479C2×C11⋊C8C2411yescharacteristic
480C8×D11—41no—
481C8×D11—41no—
482C8×D11—41no—
483C8×D11—41no—
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#3009D1111yescharacteristic, complemented
502#3007—111no—
503#2947—111no—
504#2929—111no—
505#2897—111no—
506C2×#416—111no—
507C23×C11—21no—
508C23×C11—22no—
509C23×C11—44no—
510C23×C11—42no—
511C23×C11—81no—
512C23×C11—82no—
513C23×C11—81no—
514C23×C11—82no—
515C23×C11C22×D412yes—
516C23×C11C22×D411yescharacteristic
517C22×D11—22no—
518C22×D11—22no—
519C22×D11—21no—
520C22×D11—41no—
521C22×D11—42no—
522C22×D11—42no—
523C22×D11—81no—
524C22×D11C22×D411yescharacteristic
525C22×D11C22×D411yescharacteristic
526Q8×C11—22no—
527Q8×C11—21no—
528Q8×C11—22no—
529Q8×C11—22no—
530Q8×C11—42no—
531Q8×C11C2×#4112yes—
532D4×C11—24no—
533D4×C11—24no—
534D4×C11—22no—
535D4×C11—22no—
536D4×C11—21no—
537D4×C11—22no—
538D4×C11—44no—
539D4×C11—44no—
540D4×C11—42no—
541D4×C11C2×#4112yes—
542C2×C4×C11—21no—
543C2×C4×C11—24no—
544C2×C4×C11—22no—
545C2×C4×C11—22no—
546C2×C4×C11—22no—
547C2×C4×C11—21no—
548C2×C4×C11—21no—
549C2×C4×C11—44no—
550C2×C4×C11—42no—
551C2×C4×C11C22×D412yes—
552C2×C4×C11C22×D411yescharacteristic
553C2×C4×C11C2×#4112yes—
554C2×C4×C11H(5,𝔽2)12yes—
555C2×C4×C11C2511yescharacteristic
556C22⋊D11—24no—
557C22⋊D11—42no—
558C22⋊D11—42no—
559C22⋊D11—42no—
560C22⋊D11—42no—
561C22⋊D11—44no—
562C22⋊D11—82no—
563C22⋊D11—82no—
564C22⋊D11—82no—
565C22⋊D11—82no—
566C2×Dic11—22no—
567C2×Dic11—21no—
568C2×Dic11—21no—
569C2×Dic11—22no—
570C2×Dic11—22no—
571C2×Dic11—21no—
572C2×Dic11—42no—
573C2×Dic11—82no—
574C2×Dic11—81no—
575C2×Dic11—82no—
576C2×Dic11—81no—
577C2×Dic11C22×D412yes—
578C2×Dic11C22×D411yescharacteristic
579C2×Dic11C22×D412yes—
580C2×Dic11C22×D411yescharacteristic
581D44—21no—
582D44—21no—
583D44—42no—
584C4×D11—22no—
585C4×D11—22no—
586C4×D11—21no—
587C4×D11—21no—
588C4×D11—21no—
589C4×D11—21no—
590C4×D11—42no—
591C4×D11—42no—
592C4×D11—42no—
593C4×D11—42no—
594C4×D11—81no—
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)C2×D1111yescharacteristic
606C22×#41—111no—
607C2×#137—111no—
608C2×#137C2×D1111yescharacteristic
609C22×SD16C2×D1111yescharacteristic, complemented
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#536C2×D1111yescharacteristic, complemented
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#520—111no—
641#519—111no—
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#452C2×D1112yescomplemented
674#452C2×D1112yescomplemented
675#451—112no—
676#450—112no—
677#450C2×D1112yescomplemented
678#450C2×D1112yescomplemented
679#441—112no—
680#440—112no—
681C4×Q16—112no—
682C4×SD16—112no—
683#435—112no—
684#435—112no—
685C8×D4—112no—
686C8×D4—112no—
687#428—111no—
688#428—111no—
689C2×#106—111no—
690#424—111no—
691#418—111no—
692#418—112no—
693#418C2×D1111yescharacteristic, complemented
694#417—111no—
695#417—112no—
696#417—111no—
697#416—111no—
698#416—112no—
699#416—111no—
700#416—111no—
701#416—111no—
702#416—111no—
703#416—111no—
704#416—111no—
705#416C2×D1111yescharacteristic
706C2×#103—111no—
707C2×#103—111no—
708C2×#103—111no—
709C2×#102—111no—
710C2×#102—112no—
711C2×#102—111no—
712C2×#102—111no—
713#408C2×D1111yescharacteristic, complemented
714#407—111no—
715#405—111no—
716C22×C11—21no—
717C22×C11—21no—
718C22×C11—22no—
719C22×C11—22no—
720C22×C11—22no—
721C22×C11—22no—
722C22×C11—41no—
723C22×C11—41no—
724C22×C11—42no—
725C22×C11—42no—
726C22×C11—42no—
727C22×C11—162no—
728C22×C11—164no—
729C22×C11#54612yes—
730C22×C11C23×D411yescharacteristic
731C2×D11—21no—
732C2×D11—21no—
733C2×D11—21no—
734C2×D11—21no—
735C2×D11—21no—
736C2×D11—44no—
737C2×D11—41no—
738C2×D11—41no—
739C2×D11—41no—
740C2×D11—84no—
741C2×D11#57712yes—
742C4×C11—22no—
743C4×C11—22no—
744C4×C11—41no—
745C4×C11—42no—
746C4×C11—41no—
747C4×C11#54612yes—
748C4×C11C22×#4111yescharacteristic
749C4×C11C2×H(5,𝔽2)11yescharacteristic
750Dic11—22no—
751Dic11—21no—
752Dic11—21no—
753Dic11—22no—
754Dic11—42no—
755Dic11—41no—
756Dic11—41no—
757Dic11—41no—
758Dic11—42no—
759H(5,𝔽2)—24no—
760H(5,𝔽2)—42no—
761C2×#41—21no—
762C2×#41—111no—
763C2×#41—111no—
764C2×#41—111no—
765C2×#41—221no—
766C2×#41—221no—
767C2×#41—224no—
768C2×#41—442no—
769C2×#41C22×D1112yes—
770C2×#41C22×D1111yescharacteristic
771C2×#41C22×D1111yescharacteristic
772C22×Q8—111no—
773C22×Q8C22×D1111yescharacteristic
774C22×D4—21no—
775C22×D4—22no—
776C22×D4—111no—
777C22×D4—221no—
778C22×D4—222no—
779C22×D4—221no—
780C22×D4C22×D1111yescharacteristic
781C22×D4C22×D1112yes—
782C23×C4—111no—
783C23×C4—221no—
784#137—24no—
785#137—442no—
786C2×Q16—112no—
787C2×Q16C22×D1112yes—
788C2×SD16—42no—
789C2×SD16—112no—
790C2×SD16C22×D1112yes—
791C2×SD16C22×D1112yes—
792C2×SD16C22×D1112yes—
793#131—442no—
794C2×M16—111no—
795C2×M16—112no—
796C2×M16C22×D1111yescharacteristic
797C22×C8—111no—
798C22×C8—112no—
799C22×C8—111no—
800C22×C8—111no—
801C22×C8—111no—
802C22×C8—111no—
803C22×C8—442no—
804C22×C8C22×D1111yescharacteristic
805C4⋊Q8—21no—
806C4⋊Q8—112no—
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—221no—
816#125—222no—
817#125—222no—
818#125—222no—
819#124—21no—
820#124—112no—
821#124—222no—
822#124—222no—
823#123—22no—
824#123—112no—
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—222no—
834C22⋊Q8—222no—
835C22⋊Q8—222no—
836C22⋊Q8—222no—
837C22⋊Q8—221no—
838C22⋊Q8—221no—
839C22⋊Q8—221no—
840C22⋊Q8C22×D1112yes—
841C22⋊Q8C22×D1112yes—
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—222no—
853#121—221no—
854#121—221no—
855#121—222no—
856#121—221no—
857#121—222no—
858#120—112no—
859#120—222no—
860#120—222no—
861#120—222no—
862#120—222no—
863C4×Q8—112no—
864C4×Q8—112no—
865C4×Q8—112no—
866C4×Q8—222no—
867C4×Q8—221no—
868C4×Q8—221no—
869C4×Q8—221no—
870C4×D4—112no—
871C4×D4—112no—
872C4×D4—112no—
873C4×D4—222no—
874C4×D4—222no—
875C4×D4—222no—
876C4×D4—222no—
877C4×D4—221no—
878C4×D4—222no—
879#117—111no—
880#117—111no—
881#117—112no—
882#117—111no—
883#117—111no—
884#117—221no—
885#117—222no—
886#117—221no—
887#117—222no—
888#117—222no—
889#117—221no—
890#117C22×D1111yescharacteristic
891C2×C4⋊C4—111no—
892C2×C4⋊C4—111no—
893C2×C4⋊C4—112no—
894C2×C4⋊C4—111no—
895C2×C4⋊C4—111no—
896C2×C4⋊C4—221no—
897C2×C4⋊C4—221no—
898C2×C22⋊C4—221no—
899C2×C22⋊C4—222no—
900C2×C22⋊C4—221no—
901C2×C22⋊C4—221no—
902C2×C42—221no—
903#107—112no—
904#107—112no—
905#106—112no—
906#106—112no—
907#106—112no—
908#106—112no—
909C4⋊C8—112no—
910C4⋊C8—112no—
911#103—111no—
912#103—111no—
913#103—112no—
914#103—112no—
915#103—112no—
916#103—111no—
917#103—111no—
918#103—112no—
919#103—111no—
920#103—111no—
921#103C22×D1111yescharacteristic
922#103C22×D1111yescharacteristic
923#102—111no—
924#102—112no—
925#102—111no—
926#102—112no—
927#102—112no—
928#102—112no—
929#102—112no—
930#102—111no—
931#102—111no—
932#102—112no—
933#102—111no—
934#102—111no—
935#102C22×D1111yescharacteristic
936#102C22×D1111yescharacteristic
937#102C22×D1112yes—
938#102C22×D1112yes—
939C22⋊C8—112no—
940C22⋊C8—112no—
941C22⋊C8C22×D1112yes—
942C22⋊C8C22×D1112yes—
943#97—112no—
944C4×C8—112no—
945C2×C11—22no—
946C2×C11—42no—
947C2×C11—42no—
948C2×C11—82no—
949C2×C11C2×#54611yescharacteristic
950C2×C11C2×#57711yescharacteristic
951C2×C11#358411yescharacteristic
952D11—22no—
953D11—41no—
954D11—81no—
955C24—22no—
956C24—21no—
957C24—111no—
958C24—221no—
959#41—22no—
960#41—22no—
961#41—22no—
962#41—24no—
963#41—42no—
964#41—44no—
965#41—222no—
966#41—222no—
967#41—222no—
968#41—222no—
969#41—444no—
970#41—441no—
971#41—444no—
972#41—441no—
973#41#434114yes—
974C2×Q8—21no—
975C2×Q8—22no—
976C2×Q8—22no—
977C2×Q8—111no—
978C2×Q8—221no—
979C2×Q8—222no—
980C2×Q8—222no—
981C2×Q8—441no—
982C2×Q8D4×D1111yescharacteristic
983C2×Q8C23×D1112yes—
984C2×Q8C23×D1111yescharacteristic
985C2×D4—21no—
986C2×D4—24no—
987C2×D4—22no—
988C2×D4—22no—
989C2×D4—21no—
990C2×D4—22no—
991C2×D4—22no—
992C2×D4—42no—
993C2×D4—44no—
994C2×D4—48no—
995C2×D4—112no—
996C2×D4—112no—
997C2×D4—111no—
998C2×D4—221no—
999C2×D4—221no—
1000C2×D4—222no—
1001C2×D4—222no—
1002C2×D4—222no—
1003C2×D4—222no—
1004C2×D4—221no—
1005C2×D4—221no—
1006C2×D4—222no—
1007C2×D4—222no—
1008C2×D4—441no—
1009C2×D4—444no—
1010C2×D4—884no—
1011C2×D4—882no—
1012C2×D4D4×D1112yes—
1013C2×D4D4×D1111yescharacteristic
1014C2×D4C23×D1112yes—
1015C2×D4C23×D1111yescharacteristic
1016C22×C4—21no—
1017C22×C4—21no—
1018C22×C4—22no—
1019C22×C4—111no—
1020C22×C4—111no—
1021C22×C4—111no—
1022C22×C4—111no—
1023C22×C4—111no—
1024C22×C4—221no—
1025C22×C4—221no—
1026C22×C4—221no—
1027C22×C4—221no—
1028C22×C4—221no—
1029C22×C4—222no—
1030C22×C4—222no—
1031C22×C4—222no—
1032C22×C4—221no—
1033C22×C4—221no—
1034C22×C4—222no—
1035C22×C4—221no—
1036C22×C4—444no—
1037C22×C4C23×D1112yes—
1038C22×C4C23×D1111yescharacteristic
1039Q16—24no—
1040Q16—442no—
1041SD16—24no—
1042SD16—42no—
1043SD16—42no—
1044SD16—442no—
1045M16—22no—
1046M16—222no—
1047M16—442no—
1048C2×C8—22no—
1049C2×C8—111no—
1050C2×C8—111no—
1051C2×C8—112no—
1052C2×C8—222no—
1053C2×C8—441no—
1054C2×C8—441no—
1055C2×C8—441no—
1056C2×C8—441no—
1057C2×C8—442no—
1058C2×C8C23×D1112yes—
1059C2×C8C23×D1111yescharacteristic
1060C2×C8C23×D1111yescharacteristic
1061C4⋊C4—22no—
1062C4⋊C4—22no—
1063C4⋊C4—111no—
1064C4⋊C4—111no—
1065C4⋊C4—112no—
1066C4⋊C4—112no—
1067C4⋊C4—111no—
1068C4⋊C4—112no—
1069C4⋊C4—111no—
1070C4⋊C4—112no—
1071C4⋊C4—221no—
1072C4⋊C4—221no—
1073C4⋊C4—222no—
1074C4⋊C4—222no—
1075C4⋊C4—222no—
1076C4⋊C4—222no—
1077C4⋊C4—222no—
1078C4⋊C4—222no—
1079C4⋊C4—222no—
1080C4⋊C4—222no—
1081C4⋊C4—221no—
1082C4⋊C4—221no—
1083C4⋊C4—222no—
1084C4⋊C4—222no—
1085C4⋊C4C23×D1111yescharacteristic
1086C4⋊C4C23×D1111yescharacteristic
1087C22⋊C4—21no—
1088C22⋊C4—22no—
1089C22⋊C4—22no—
1090C22⋊C4—112no—
1091C22⋊C4—112no—
1092C22⋊C4—112no—
1093C22⋊C4—112no—
1094C22⋊C4—112no—
1095C22⋊C4—221no—
1096C22⋊C4—221no—
1097C22⋊C4—222no—
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⋊C4—222no—
1108C42—21no—
1109C42—112no—
1110C42—221no—
1111C42—221no—
1112C42—222no—
1113C42—222no—
1114C42—222no—
1115C42—221no—
1116C42—222no—
1117C11#6117211yescharacteristic, complemented, Sylow
1118C23—21no—
1119C23—22no—
1120C23—44no—
1121C23—42no—
1122C23—81no—
1123C23—82no—
1124C23—81no—
1125C23—82no—
1126C23—111no—
1127C23—111no—
1128C23—222no—
1129C23—222no—
1130C23—221no—
1131C23—441no—
1132C23—442no—
1133C23—442no—
1134C23—881no—
1135C23C2×D4×D1112yes—
1136C23C2×D4×D1111yescharacteristic
1137Q8—22no—
1138Q8—21no—
1139Q8—22no—
1140Q8—22no—
1141Q8—42no—
1142Q8—221no—
1143Q8—221no—
1144Q8—442no—
1145Q8—882no—
1146Q8C2×#434112yes—
1147D4—24no—
1148D4—24no—
1149D4—22no—
1150D4—22no—
1151D4—21no—
1152D4—22no—
1153D4—44no—
1154D4—44no—
1155D4—42no—
1156D4—224no—
1157D4—221no—
1158D4—221no—
1159D4—442no—
1160D4—442no—
1161D4—442no—
1162D4—442no—
1163D4—444no—
1164D4—442no—
1165D4—882no—
1166D4—882no—
1167D4—882no—
1168D4—882no—
1169D4C2×#434112yes—
1170C2×C4—21no—
1171C2×C4—24no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—22no—
1177C2×C4—44no—
1178C2×C4—42no—
1179C2×C4—112no—
1180C2×C4—112no—
1181C2×C4—111no—
1182C2×C4—111no—
1183C2×C4—222no—
1184C2×C4—222no—
1185C2×C4—222no—
1186C2×C4—221no—
1187C2×C4—221no—
1188C2×C4—221no—
1189C2×C4—221no—
1190C2×C4—221no—
1191C2×C4—221no—
1192C2×C4—222no—
1193C2×C4—222no—
1194C2×C4—221no—
1195C2×C4—442no—
1196C2×C4—442no—
1197C2×C4—442no—
1198C2×C4—442no—
1199C2×C4—442no—
1200C2×C4—881no—
1201C2×C4—882no—
1202C2×C4—881no—
1203C2×C4—882no—
1204C2×C4—881no—
1205C2×C4C2×D4×D1112yes—
1206C2×C4C2×D4×D1111yescharacteristic
1207C2×C4C2×#434112yes—
1208C2×C4#6703712yes—
1209C2×C4C24×D1111yescharacteristic
1210C8—22no—
1211C8—21no—
1212C8—21no—
1213C8—221no—
1214C8—221no—
1215C8—222no—
1216C22—21no—
1217C22—21no—
1218C22—22no—
1219C22—22no—
1220C22—22no—
1221C22—22no—
1222C22—41no—
1223C22—41no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—112no—
1228C22—162no—
1229C22—164no—
1230C22—221no—
1231C22—221no—
1232C22—221no—
1233C22—221no—
1234C22—221no—
1235C22—444no—
1236C22—441no—
1237C22—441no—
1238C22—441no—
1239C22—884no—
1240C22#1062312212yes—
1241C22C22×D4×D1111yescharacteristic
1242C4—22no—
1243C4—22no—
1244C4—42no—
1245C4—41no—
1246C4—41no—
1247C4—221no—
1248C4—221no—
1249C4—222no—
1250C4—222no—
1251C4—441no—
1252C4—441no—
1253C4—442no—
1254C4—441no—
1255C4—442no—
1256C4#1062312212yes—
1257C4C22×#434111yescharacteristic
1258C4C2×#6703711yescharacteristic
1259C2—22no—
1260C2—42no—
1261C2—42no—
1262C2—82no—
1263C2—222no—
1264C2—441no—
1265C2—881no—
1266C2C2×#1062312211yescharacteristic
1267C2D11×#57711yescharacteristic
1268C2#1308338811yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3009C2
socleC22×C11C23×D4
prime radical#13082278C2
hypercenter#3009D11
hypocenterC11#61172
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3009

Complements

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

NH ≅ G/Ntype
1. #13082365C2semidirect
3. #13080735C2semidirect
4. #13080720C2semidirect
5. #13080645C2semidirect
6. #13080630C2semidirect
7. #13080548C2semidirect
8. #13080496C2semidirect
9. #13080455C2semidirect
10. #13080433C2semidirect
11. #13078966C2semidirect
12. #13078607C2semidirect
13. #13078554C2semidirect
14. #13078476C2semidirect
15. #13078303C2semidirect
16. C2×#10622784C2semidirect
17. #13078134C2semidirect
18. #13077872C2semidirect
19. #13077460C2semidirect
20. #13077313C2semidirect
21. #13077142C2semidirect
22. D11×#416C2semidirect
23. C11×#3009C2semidirect
27. C22×C11×SD16C22semidirect
28. C11×#536C22semidirect
36. #10623358C22semidirect
37. C2×#67001C22semidirect
38. C2×#66999C22semidirect
39. #10623343C22semidirect
40. C2×#66995C22semidirect
49. C22×C8×D11C22semidirect
56. #10623173C22semidirect
57. #10623172C22semidirect
58. #10623170C22semidirect
59. #10623166C22semidirect
60. D11×#117C22semidirect
61. #10623050C22semidirect
62. C11×#452C22semidirect
63. C11×#452C22semidirect
64. C11×#450C22semidirect
65. C11×#450C22semidirect
66. C11×#418C22semidirect
68. C11×#408C22semidirect
70. #10622846C22semidirect
72. #10622845C22semidirect
73. C2×#66899C22semidirect
74. #10622828C22semidirect
75. #10622828C22semidirect
76. C2×#66896C22semidirect
77. C2×#66896C22semidirect
78. #10622800C22semidirect
79. #10622799C22semidirect
80. #10622797C22semidirect
81. Q16×Dic11C22semidirect
82. #10622786C22semidirect
83. #10622784C22semidirect
84. #10622784C22semidirect
85. #10622784C22semidirect
86. #10622784C22semidirect
87. #10622782C22semidirect
88. #10622779C22semidirect
89. #10622779C22semidirect
90. #10622777C22semidirect
91. #10622776C22semidirect
92. #10622776C22semidirect
93. SD16×Dic11C22semidirect
94. #10622746C22semidirect
95. #10622739C22semidirect
96. #10622735C22semidirect
97. #10622734C22semidirect
98. #10622726C22semidirect
99. C2×#66881C22semidirect
100. #10622715C22semidirect
101. #10622665C22semidirect
102. #10622664C22semidirect
103. #10622662C22semidirect
104. #10622661C22semidirect
105. #10622615C22semidirect
106. #10622608C22semidirect
107. #10622417C22semidirect
108. #10622417C22semidirect
109. D11×#103C22semidirect
110. D11×#103C22semidirect
111. #10622412C22semidirect
112. #10622404C22semidirect
113. #10622397C22semidirect
114. #10622392C22semidirect
115. #10622390C22semidirect
116. #10622387C22semidirect
117. #10622385C22semidirect
118. #10622385C22semidirect
119. D11×#102C22semidirect
120. D11×#102C22semidirect
121. #10622381C22semidirect
122. #10622378C22semidirect
123. #10622377C22semidirect
124. #10622376C22semidirect
125. #10622374C22semidirect
126. #10622373C22semidirect
127. #10622350C22semidirect
128. #10622348C22semidirect
129. #10622341C22semidirect
130. #10622341C22semidirect
131. (C22⋊D11)⋊C8C22semidirect
132. (C22⋊D11)⋊C8C22semidirect
133. #10622336C22semidirect
134. #10622334C22semidirect
501. #3009D11semidirect
609. C22×SD16C2×D11semidirect
629. #536C2×D11semidirect
673. #452C2×D11semidirect
674. #452C2×D11semidirect
677. #450C2×D11semidirect
678. #450C2×D11semidirect
693. #418C2×D11semidirect
713. #408C2×D11semidirect
1117. C11#61172semidirect

Maximal subgroups

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

subgroupindex
#130823652
#130822782
#130807352
#130807202
#130806452
#130806302
#130805482
#130804962
#130804552
#130804332
#130789662
#130786072
#130785542
#130784762
#130783032
C2×#106227842
#130781342
#130778722
#130774602
#130773132
#130771422
D11×#4162
C11×#30092
#6117211