Finite Group Databasebeta

← #15631114

Subgroups — #15631114

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#13082288C211yesmaximal, characteristic
2#13080706C212yesmaximal, complemented
3#13080691C212yesmaximal, complemented
4#13080676C212yesmaximal, complemented
5#13080661C212yesmaximal, complemented
6#13080527C212yesmaximal, complemented
7#13080497C212yesmaximal, complemented
8#13080486C212yesmaximal, complemented
9#13080445C212yesmaximal, complemented
10#13078986C211yesmaximal, characteristic, complemented
11#13078594C211yesmaximal, characteristic, complemented
12#13078564C211yesmaximal, characteristic, complemented
13#13078463C211yesmaximal, characteristic, complemented
14#13078303C211yesmaximal, characteristic, complemented
15C2×#10622664C211yesmaximal, characteristic, complemented
16#13078146C211yesmaximal, characteristic, complemented
17#13077909C211yesmaximal, characteristic, complemented
18#13077874C211yesmaximal, characteristic, complemented
19#13077459C211yesmaximal, characteristic, complemented
20#13077311C211yesmaximal, characteristic, complemented
21#13077146C211yesmaximal, characteristic, complemented
22C2×#10622615C211yesmaximal, characteristic, complemented
23C11×#3495C211yesmaximal, characteristic, complemented
24C2×#67043C2211yescharacteristic
25C22×#4339C2211yescharacteristic
26C11×#556C2212yescomplemented
27C11×#554C2212yes—
28C11×#552—22no—
29C11×#552C2212yes—
30C11×#552C2212yescomplemented
31C11×#551—22no—
32C11×#544C2211yescharacteristic, complemented
33C11×#542—21no—
34C11×#541—21no—
35C11×#536C2211yescharacteristic, complemented
36C11×#533—21no—
37C11×#529—21no—
38C11×#525C2211yescharacteristic
39C2×C11×C22⋊Q8C2211yescharacteristic
40C11×#520C2211yescharacteristic, complemented
41C11×#519C2211yescharacteristic, complemented
42C2×C11×#117C2211yescharacteristic
43#10623364C2211yescharacteristic
44C2×#67001C2211yescharacteristic, complemented
45C22×#4326C2211yescharacteristic, complemented
46C2×#66995C2211yescharacteristic
47C2×#66995C2211yescharacteristic
48C2×#66977C2211yescharacteristic
49C23×C11⋊C8C2211yescharacteristic
50#10623186—22no—
51#10623159—21no—
52D11×C22⋊Q8—21no—
53#10623139—21no—
54#10623137—21no—
55#10623122—22no—
56#10623083C2212yes—
57#10623082C2212yes—
58#10623081C2212yes—
59D4×Dic22C2212yes—
60#10623057C2211yescharacteristic
61#10623054C2211yescharacteristic
62#10622847C2211yescharacteristic, complemented
63C2×#66899C2211yescharacteristic, complemented
64#10622820C2211yescharacteristic
65#10622706C2212yescomplemented
66#10622704C2212yescomplemented
67#10622702C2212yescomplemented
68#10622700C2212yescomplemented
69#10622682C2212yescomplemented
70#10622681C2212yescomplemented
71#10622679C2212yescomplemented
72#10622676C2212yescomplemented
73#10622665C2212yescomplemented
74#10622664C2212yes—
75#10622664C2212yes—
76#10622664C2212yescomplemented
77#10622664C2212yescomplemented
78#10622664C2212yescomplemented
79#10622663C2212yes—
80#10622663C2212yescomplemented
81#10622663C2212yescomplemented
82#10622662C2212yescomplemented
83#10622661C2212yescomplemented
84#10622660C2212yes—
85#10622660C2212yes—
86#10622660C2212yescomplemented
87#10622660C2212yescomplemented
88#10622659C2212yes—
89#10622644C2212yescomplemented
90#10622644C2212yescomplemented
91#10622643C2212yescomplemented
92C4×#4326C2212yescomplemented
93#10622641C2212yescomplemented
94#10622641C2212yescomplemented
95#10622639C2212yescomplemented
96C4×#4325C2212yescomplemented
97#10622624C2212yes—
98#10622624C2212yescomplemented
99D4×C11⋊C8C2212yes—
100D4×C11⋊C8C2212yescomplemented
101#10622617C2211yescharacteristic, complemented
102#10622617C2211yescharacteristic, complemented
103#10622617C2212yescomplemented
104#10622616C2212yescomplemented
105#10622615C2211yescharacteristic
106#10622615C2211yescharacteristic
107#10622615C2211yescharacteristic
108#10622615C2211yescharacteristic
109#10622615C2211yescharacteristic
110#10622615C2211yescharacteristic
111#10622615C2211yescharacteristic
112#10622615C2211yescharacteristic
113#10622615C2212yescomplemented
114#10622612C2211yescharacteristic, complemented
115#10622610C2211yescharacteristic, complemented
116#10622609C2212yescomplemented
117#10622609C2212yescomplemented
118#10622609C2212yescomplemented
119#10622608C2211yescharacteristic, complemented
120#10622608C2211yescharacteristic, complemented
121#10622584C2212yes—
122#10622583C2212yes—
123#10622583C2212yescomplemented
124C2×#66874C2211yescharacteristic
125C2×#66874C2211yescharacteristic
126C2×#66874C2212yescomplemented
127C2×#66874C2211yescharacteristic, complemented
128#10622580C2212yescomplemented
129#10622579C2211yescharacteristic
130#10622579C2211yescharacteristic
131#10622579C2212yescomplemented
132C2×#66873C2211yescharacteristic
133C2×#66873C2211yescharacteristic
134C2×#66871C2211yescharacteristic, complemented
135C2×C11×#41C2311yescharacteristic
136C22×Q8×C11C2311yescharacteristic
137C23×C4×C11C2311yescharacteristic
138C22×C22⋊D11—21no—
139#67043—24no—
140#67043—42no—
141C2×Q8×D11—21no—
142C2×#4341—22no—
143C2×#4341—21no—
144C2×#4339—21no—
145C2×#4339—21no—
146C2×#4339—24no—
147C2×#4339—42no—
148C2×#4339C2311yescharacteristic
149C2×#4339C2312yes—
150C2×#4339C2311yescharacteristic
151C2×#4339C2311yescharacteristic
152C2×#4339C2311yescharacteristic
153C22×D44C2311yescharacteristic
154C22×C4×D11—21no—
155C22×Dic22C2311yescharacteristic
156C22×Dic22C2311yescharacteristic
157C22×Dic22C2312yes—
158C11×C4⋊Q8—21no—
159C11×C4⋊Q8—21no—
160C11×C4⋊Q8C2312yes—
161C11×#126—22no—
162C11×#126—22no—
163C11×#126—22no—
164C11×#126—22no—
165C11×#125—21no—
166C11×#125—22no—
167C11×#125—22no—
168C11×#125—22no—
169C11×#125C2312yes—
170C11×#124—21no—
171C11×#124—22no—
172C11×#123—22no—
173C11×#123—22no—
174C11×#123—22no—
175C11×#123D412yes—
176C11×C22⋊Q8—21no—
177C11×C22⋊Q8—21no—
178C11×C22⋊Q8—22no—
179C11×C22⋊Q8—22no—
180C11×C22⋊Q8—22no—
181C11×C22⋊Q8D411yescharacteristic
182C11×C22⋊Q8D411yescharacteristic
183C11×C22⋊Q8C2312yes—
184C11×C22⋊Q8C2312yes—
185C11×C22⋊Q8C2312yes—
186C11×C22⋊Q8C2312yes—
187C11×#121D411yescharacteristic
188C11×#121D411yescharacteristic
189C11×#120D412yes—
190C4×Q8×C11—21no—
191C4×Q8×C11—21no—
192C4×Q8×C11—21no—
193C4×Q8×C11—22no—
194C4×Q8×C11C2312yes—
195C4×Q8×C11C2312yes—
196C4×D4×C11—21no—
197C4×D4×C11—22no—
198C4×D4×C11—22no—
199C4×D4×C11C2312yes—
200C4×D4×C11C2312yes—
201C11×#117—21no—
202C11×#117—21no—
203C11×#117—22no—
204C11×#117—22no—
205C11×#117—22no—
206C11×#117C2311yescharacteristic
207C11×#117C2311yescharacteristic
208C11×#117C2311yescharacteristic
209C11×#117C2311yescharacteristic
210C11×#117C2312yes—
211C11×#117C2311yescharacteristic
212C2×C11×C4⋊C4—21no—
213C2×C11×C4⋊C4C2311yescharacteristic
214C2×C11×C4⋊C4C2311yescharacteristic
215C2×C11×C4⋊C4C2311yescharacteristic
216C2×C11×C4⋊C4C2312yes—
217C2×C11×C22⋊C4—21no—
218C2×C11×C22⋊C4—21no—
219C2×C42×C11—21no—
220C2×C22⋊Dic11—21no—
221#67001—42no—
222#66999—21no—
223C2×#4326—42no—
224C2×#4326C2312yes—
225C2×#4326C2312yes—
226C2×#4326C2312yes—
227C2×#4326C2312yes—
228#66995—24no—
229#66995—42no—
230C2×#4325C2312yes—
231C2×#4325C2312yes—
232#66992—22no—
233#66992—22no—
234#66991—22no—
235#66991—21no—
236#66990—22no—
237D4×Dic11—22no—
238#66983C2312yes—
239C2×C4⋊Dic11C2311yescharacteristic
240#66977—21no—
241#66977—21no—
242#66977C2312yes—
243#66977C2312yes—
244#66977C2312yes—
245C2×Dic11⋊C4—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#66950—21no—
258#66950—21no—
259#66949—22no—
260#66947—22no—
261#66945—21no—
262C4⋊C4×D11—21no—
263C4⋊C4×D11—22no—
264#66941—22no—
265#66939—22no—
266#66938—22no—
267#66937—22no—
268#66936—22no—
269#66936—22no—
270(C22⋊D11)⋊C4—22no—
271(C22⋊D11)⋊C4—22no—
272C22⋊C4×D11—22no—
273#66931—22no—
274#66931—22no—
275#66928C2312yes—
276C4×D44C2312yes—
277#66922C2312yes—
278C4×Dic22C2312yes—
279#66899C2312yes—
280#66899C2312yes—
281C22⋊(C11⋊C8)C2312yes—
282C22⋊(C11⋊C8)C2312yes—
283C22⋊(C11⋊C8)C2312yes—
284C22⋊(C11⋊C8)C2312yes—
285#66874C2312yes—
286#66874C2312yes—
287#66874C2312yes—
288#66874C2312yes—
289#66874C2311yescharacteristic
290#66874C2311yescharacteristic
291#66874C2311yescharacteristic
292#66874C2311yescharacteristic
293#66874C2311yescharacteristic
294#66874C2311yescharacteristic
295#66874C2311yescharacteristic
296#66874C2311yescharacteristic
297#66874C2312yes—
298#66874C2312yes—
299#66874C2312yes—
300#66874C2312yes—
301#66873C2311yescharacteristic
302#66873C2311yescharacteristic
303#66873C2311yescharacteristic
304#66873C2311yescharacteristic
305#66873C2311yescharacteristic
306#66873C2311yescharacteristic
307#66873C2311yescharacteristic
308#66873C2311yescharacteristic
309#66873C2312yes—
310#66873C2312yes—
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×C11C2×D411yescharacteristic
323C23×D11—21no—
324C11×#41—22no—
325C11×#41—22no—
326C2×Q8×C11—21no—
327C2×Q8×C11—22no—
328C2×Q8×C11—22no—
329C2×Q8×C11—22no—
330C2×Q8×C11C2×D411yescharacteristic
331C2×Q8×C11C2412yes—
332C2×D4×C11C2×D412yes—
333C2×D4×C11C2×D411yescharacteristic
334C2×D4×C11C2×D412yes—
335C2×D4×C11C2×D412yes—
336C22×C4×C11—22no—
337C22×C4×C11—22no—
338C22×C4×C11—21no—
339C22×C4×C11—21no—
340C22×C4×C11—21no—
341C22×C4×C11—21no—
342C22×C4×C11—22no—
343C22×C4×C11C2×D411yescharacteristic
344C22×C4×C11C2×D411yescharacteristic
345C22×C4×C11C2×D411yescharacteristic
346C22×C4×C11C2411yescharacteristic
347C22×C4×C11C2411yescharacteristic
348C22×C4×C11C2412yes—
349C22×C4×C11C2411yescharacteristic
350C2×C22⋊D11—21no—
351C2×C22⋊D11—21no—
352C2×C22⋊D11—22no—
353C2×C22⋊D11—21no—
354C2×C22⋊D11—21no—
355C2×C22⋊D11—22no—
356C2×C22⋊D11—44no—
357C22×Dic11—21no—
358C22×Dic11—22no—
359C22×Dic11—21no—
360C22×Dic11—21no—
361Q8×D11—44no—
362#4341—44no—
363#4341—48no—
364#4339—22no—
365#4339—24no—
366#4339—22no—
367#4339—22no—
368#4339—22no—
369#4339—22no—
370#4339—41no—
371#4339—41no—
372#4339—42no—
373#4339—44no—
374#4339—44no—
375#4339#4114yes—
376C2×D44—22no—
377C2×D44—21no—
378C2×D44—41no—
379C2×D44C2411yescharacteristic
380C2×D44C2411yescharacteristic
381C2×C4×D11—21no—
382C2×C4×D11—22no—
383C2×C4×D11—21no—
384C2×C4×D11—21no—
385C2×C4×D11—21no—
386C2×C4×D11—22no—
387C2×C4×D11—44no—
388C2×Dic22—22no—
389C2×Dic22—24no—
390C2×Dic22—21no—
391C2×Dic22—22no—
392C2×Dic22—21no—
393C2×Dic22—22no—
394C2×Dic22—22no—
395C2×Dic22—41no—
396C2×Dic22—42no—
397C2×Dic22C2411yescharacteristic
398C2×Dic22C2412yes—
399C2×Dic22C2411yescharacteristic
400C11×C4⋊C4—22no—
401C11×C4⋊C4—22no—
402C11×C4⋊C4—21no—
403C11×C4⋊C4—21no—
404C11×C4⋊C4—21no—
405C11×C4⋊C4—22no—
406C11×C4⋊C4—22no—
407C11×C4⋊C4—22no—
408C11×C4⋊C4—22no—
409C11×C4⋊C4—22no—
410C11×C4⋊C4—22no—
411C11×C4⋊C4—22no—
412C11×C4⋊C4—22no—
413C11×C4⋊C4C2×D412yes—
414C11×C4⋊C4C2×D412yes—
415C11×C4⋊C4C2×D411yescharacteristic
416C11×C4⋊C4C2×D411yescharacteristic
417C11×C4⋊C4C2411yescharacteristic
418C11×C4⋊C4C2412yes—
419C11×C4⋊C4C2411yescharacteristic
420C11×C4⋊C4C2411yescharacteristic
421C11×C4⋊C4C2411yescharacteristic
422C11×C22⋊C4—21no—
423C11×C22⋊C4—21no—
424C11×C22⋊C4—21no—
425C11×C22⋊C4—21no—
426C11×C22⋊C4—22no—
427C11×C22⋊C4—22no—
428C11×C22⋊C4—22no—
429C11×C22⋊C4—22no—
430C11×C22⋊C4—22no—
431C11×C22⋊C4C2×D412yes—
432C11×C22⋊C4C2×D412yes—
433C11×C22⋊C4C2×D412yes—
434C11×C22⋊C4C2×D412yes—
435C11×C22⋊C4C2×D412yes—
436C42×C11—21no—
437C42×C11—21no—
438C42×C11—21no—
439C42×C11—21no—
440C42×C11—22no—
441C42×C11—22no—
442C42×C11—22no—
443C42×C11C2412yes—
444C22⋊Dic11—22no—
445C22⋊Dic11—22no—
446C22⋊Dic11—22no—
447#4326—24no—
448#4326—42no—
449#4326—42no—
450#4326—42no—
451#4325—24no—
452#4325—42no—
453(C2×D11)⋊C4—22no—
454(C2×D11)⋊C4—22no—
455(C2×D11)⋊C4—22no—
456(C2×D11)⋊C4—22no—
457C4⋊Dic11—22no—
458C4⋊Dic11—22no—
459C4⋊Dic11—21no—
460C4⋊Dic11C2412yes—
461Dic11⋊C4—22no—
462Dic11⋊C4—22no—
463Dic11⋊C4—22no—
464Dic11⋊C4—22no—
465C4×Dic11—22no—
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#3495D1111yescharacteristic, complemented
483#3489—111no—
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—41no—
508C23×C11C22×D411yescharacteristic
509C23×C11C22×D412yes—
510C23×C11C22×D411yescharacteristic
511C23×C11C22×D411yescharacteristic
512C22×D11—21no—
513C22×D11—21no—
514C22×D11—42no—
515C22×D11—42no—
516C22×D11—81no—
517Q8×C11—22no—
518Q8×C11—22no—
519Q8×C11—22no—
520Q8×C11—42no—
521Q8×C11—82no—
522D4×C11—24no—
523D4×C11—24no—
524D4×C11—22no—
525D4×C11—42no—
526C2×C4×C11—22no—
527C2×C4×C11—22no—
528C2×C4×C11—22no—
529C2×C4×C11—21no—
530C2×C4×C11—22no—
531C2×C4×C11—21no—
532C2×C4×C11—21no—
533C2×C4×C11—21no—
534C2×C4×C11—22no—
535C2×C4×C11—21no—
536C2×C4×C11—21no—
537C2×C4×C11—21no—
538C2×C4×C11—22no—
539C2×C4×C11—21no—
540C2×C4×C11—22no—
541C2×C4×C11—42no—
542C2×C4×C11—42no—
543C2×C4×C11—82no—
544C2×C4×C11—81no—
545C2×C4×C11—81no—
546C2×C4×C11C22×D412yes—
547C2×C4×C11C22×D411yescharacteristic
548C2×C4×C11C22×D411yescharacteristic
549C2×C4×C11C22×D412yes—
550C2×C4×C11C22×D412yes—
551C2×C4×C11C22×D411yescharacteristic
552C2×C4×C11C2×#4112yes—
553C2×C4×C11H(5,𝔽2)12yes—
554C2×C4×C11C2511yescharacteristic
555C22⋊D11—24no—
556C22⋊D11—42no—
557C22⋊D11—42no—
558C22⋊D11—44no—
559C22⋊D11—42no—
560C22⋊D11—82no—
561C2×Dic11—21no—
562C2×Dic11—22no—
563C2×Dic11—21no—
564C2×Dic11—22no—
565C2×Dic11—42no—
566C2×Dic11—44no—
567C2×Dic11—42no—
568C2×Dic11—81no—
569D44—21no—
570D44—21no—
571D44—21no—
572D44—42no—
573D44C2×#4112yes—
574C4×D11—24no—
575C4×D11—42no—
576C4×D11—42no—
577C4×D11—44no—
578C4×D11—42no—
579C4×D11—82no—
580Dic22—21no—
581Dic22—22no—
582Dic22—21no—
583Dic22—22no—
584Dic22—21no—
585Dic22—42no—
586Dic22—44no—
587Dic22—42no—
588Dic22C2×#4112yes—
589C11⋊C8—22no—
590C11⋊C8—21no—
591C11⋊C8—21no—
592C11⋊C8—21no—
593C11⋊C8—21no—
594C11⋊C8—22no—
595C2×2−1+4—111no—
596C22×#41—111no—
597C2×#137—111no—
598C2×#137—111no—
599C22×Q16—111no—
600C2×#131—111no—
601C23×C8—111no—
602#556C2×D1112yescomplemented
603#554C2×D1112yes—
604#552—22no—
605#552C2×D1112yes—
606#552C2×D1112yescomplemented
607#551—22no—
608D4×Q8—112no—
609#548—112no—
610#547—112no—
611#547—222no—
612#546—112no—
613#546—222no—
614#544C2×D1111yescharacteristic, complemented
615#542—21no—
616#541—21no—
617#537—111no—
618#537—221no—
619#536—111no—
620#536—221no—
621#536C2×D1111yescharacteristic, complemented
622#533—21no—
623#529—21no—
624#525—221no—
625#525C2×D1111yescharacteristic
626C2×C22⋊Q8—111no—
627C2×C22⋊Q8—221no—
628C2×C22⋊Q8C2×D1111yescharacteristic
629#520—111no—
630#520C2×D1111yescharacteristic, complemented
631#519C2×D1111yescharacteristic, complemented
632C2×#117C2×D1111yescharacteristic
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—111no—
700C2×#103—112no—
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—22no—
711C22×C11—21no—
712C22×C11—21no—
713C22×C11—22no—
714C22×C11—22no—
715C22×C11—21no—
716C22×C11—44no—
717C22×C11#54612yes—
718C22×C11#57812yes—
719C22×C11C23×D411yescharacteristic
720C2×D11—22no—
721C2×D11—41no—
722C2×D11—41no—
723C2×D11—41no—
724C2×D11—41no—
725C2×D11—41no—
726C2×D11—84no—
727C4×C11—22no—
728C4×C11—21no—
729C4×C11—21no—
730C4×C11—22no—
731C4×C11—22no—
732C4×C11—41no—
733C4×C11—42no—
734C4×C11—41no—
735C4×C11—42no—
736C4×C11—41no—
737C4×C11—41no—
738C4×C11#54612yes—
739C4×C11C22×#4111yescharacteristic
740C4×C11C2×H(5,𝔽2)11yescharacteristic
741Dic11—22no—
742Dic11—42no—
743Dic11—42no—
744Dic11—41no—
7452−1+4—224no—
7462−1+4—442no—
747C2×#41—111no—
748C2×#41—111no—
749C2×#41—112no—
750C2×#41—111no—
751C2×#41—111no—
752C2×#41—224no—
753C2×#41—221no—
754C2×#41—222no—
755C2×#41—221no—
756C2×#41—221no—
757C2×#41—442no—
758C2×#41C22×D1111yescharacteristic
759C22×Q8—111no—
760C22×Q8—112no—
761C22×Q8—111no—
762C22×Q8—221no—
763C22×Q8C22×D1111yescharacteristic
764C22×D4—111no—
765C22×D4—221no—
766C23×C4—221no—
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—21no—
790C4⋊Q8—21no—
791C4⋊Q8—112no—
792C4⋊Q8—222no—
793C4⋊Q8C22×D1112yes—
794#126—22no—
795#126—22no—
796#126—22no—
797#126—22no—
798#125—21no—
799#125—22no—
800#125—22no—
801#125—22no—
802#125C22×D1112yes—
803#124—21no—
804#124—22no—
805#124—112no—
806#124—222no—
807#123—22no—
808#123—22no—
809#123—22no—
810#123—222no—
811#123—222no—
812#123—222no—
813#123—222no—
814#123C22⋊D1112yes—
815C22⋊Q8—21no—
816C22⋊Q8—21no—
817C22⋊Q8—22no—
818C22⋊Q8—22no—
819C22⋊Q8—22no—
820C22⋊Q8—112no—
821C22⋊Q8—112no—
822C22⋊Q8—112no—
823C22⋊Q8—221no—
824C22⋊Q8—221no—
825C22⋊Q8—221no—
826C22⋊Q8—221no—
827C22⋊Q8—222no—
828C22⋊Q8—221no—
829C22⋊Q8—222no—
830C22⋊Q8—222no—
831C22⋊Q8C22⋊D1111yescharacteristic
832C22⋊Q8C22⋊D1111yescharacteristic
833C22⋊Q8C22×D1112yes—
834C22⋊Q8C22×D1112yes—
835C22⋊Q8C22×D1112yes—
836C22⋊Q8C22×D1112yes—
837#121—112no—
838#121—221no—
839#121—222no—
840#121—222no—
841#121—222no—
842#121—222no—
843#121C22⋊D1111yescharacteristic
844#121C22⋊D1111yescharacteristic
845#120—222no—
846#120C22⋊D1112yes—
847C4×Q8—21no—
848C4×Q8—21no—
849C4×Q8—21no—
850C4×Q8—22no—
851C4×Q8—112no—
852C4×Q8C22×D1112yes—
853C4×Q8C22×D1112yes—
854C4×D4—21no—
855C4×D4—22no—
856C4×D4—22no—
857C4×D4—112no—
858C4×D4—222no—
859C4×D4—222no—
860C4×D4—222no—
861C4×D4C22×D1112yes—
862C4×D4C22×D1112yes—
863#117—21no—
864#117—21no—
865#117—22no—
866#117—22no—
867#117—22no—
868#117—221no—
869#117C22×D1111yescharacteristic
870#117C22×D1111yescharacteristic
871#117C22×D1111yescharacteristic
872#117C22×D1111yescharacteristic
873#117C22×D1112yes—
874#117C22×D1111yescharacteristic
875C2×C4⋊C4—21no—
876C2×C4⋊C4—111no—
877C2×C4⋊C4—221no—
878C2×C4⋊C4—221no—
879C2×C4⋊C4—222no—
880C2×C4⋊C4C22×D1111yescharacteristic
881C2×C4⋊C4C22×D1111yescharacteristic
882C2×C4⋊C4C22×D1111yescharacteristic
883C2×C4⋊C4C22×D1112yes—
884C2×C22⋊C4—21no—
885C2×C22⋊C4—21no—
886C2×C22⋊C4—221no—
887C2×C22⋊C4—222no—
888C2×C42—21no—
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—112no—
898#103—112no—
899#103—111no—
900#103—112no—
901#103—111no—
902#103—111no—
903#103—111no—
904#103—111no—
905#103—111no—
906#103—111no—
907#103—111no—
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×C11C2×#54611yescharacteristic
936C2×C11C2×#57811yescharacteristic
937C2×C11#358411yescharacteristic
938D11—42no—
939D11—81no—
940C24—221no—
941C24C2×C22⋊D1111yescharacteristic
942#41—22no—
943#41—22no—
944#41—114no—
945#41—222no—
946#41—224no—
947#41—222no—
948#41—222no—
949#41—222no—
950#41—222no—
951#41—444no—
952#41—441no—
953#41—441no—
954#41—442no—
955#41—444no—
956#41—444no—
957#41—448no—
958C2×Q8—21no—
959C2×Q8—22no—
960C2×Q8—22no—
961C2×Q8—22no—
962C2×Q8—111no—
963C2×Q8—112no—
964C2×Q8—111no—
965C2×Q8—222no—
966C2×Q8—224no—
967C2×Q8—221no—
968C2×Q8—222no—
969C2×Q8—221no—
970C2×Q8—222no—
971C2×Q8—222no—
972C2×Q8—441no—
973C2×Q8—442no—
974C2×Q8—444no—
975C2×Q8C2×C22⋊D1111yescharacteristic
976C2×Q8C23×D1112yes—
977C2×D4—111no—
978C2×D4—111no—
979C2×D4—222no—
980C2×D4—221no—
981C2×D4—222no—
982C2×D4—221no—
983C2×D4—221no—
984C2×D4—221no—
985C2×D4—222no—
986C2×D4—221no—
987C2×D4—441no—
988C2×D4—444no—
989C2×D4C2×C22⋊D1112yes—
990C2×D4C2×C22⋊D1112yes—
991C2×D4C2×C22⋊D1111yescharacteristic
992C2×D4C2×C22⋊D1112yes—
993C22×C4—22no—
994C22×C4—22no—
995C22×C4—21no—
996C22×C4—21no—
997C22×C4—21no—
998C22×C4—21no—
999C22×C4—22no—
1000C22×C4—221no—
1001C22×C4—221no—
1002C22×C4—222no—
1003C22×C4—221no—
1004C22×C4—221no—
1005C22×C4—222no—
1006C22×C4—221no—
1007C22×C4—221no—
1008C22×C4—221no—
1009C22×C4—222no—
1010C22×C4—444no—
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—22no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—22no—
1046C4⋊C4—22no—
1047C4⋊C4—22no—
1048C4⋊C4—22no—
1049C4⋊C4—22no—
1050C4⋊C4—22no—
1051C4⋊C4—22no—
1052C4⋊C4—22no—
1053C4⋊C4—112no—
1054C4⋊C4—221no—
1055C4⋊C4—222no—
1056C4⋊C4—222no—
1057C4⋊C4—222no—
1058C4⋊C4—222no—
1059C4⋊C4—222no—
1060C4⋊C4—222no—
1061C4⋊C4C2×C22⋊D1111yescharacteristic
1062C4⋊C4C2×C22⋊D1112yes—
1063C4⋊C4C2×C22⋊D1111yescharacteristic
1064C4⋊C4C2×C22⋊D1112yes—
1065C4⋊C4C23×D1111yescharacteristic
1066C4⋊C4C23×D1111yescharacteristic
1067C4⋊C4C23×D1111yescharacteristic
1068C4⋊C4C23×D1112yes—
1069C4⋊C4C23×D1111yescharacteristic
1070C22⋊C4—21no—
1071C22⋊C4—21no—
1072C22⋊C4—21no—
1073C22⋊C4—21no—
1074C22⋊C4—22no—
1075C22⋊C4—22no—
1076C22⋊C4—22no—
1077C22⋊C4—22no—
1078C22⋊C4—22no—
1079C22⋊C4—222no—
1080C22⋊C4—222no—
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—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—22no—
1096C42—22no—
1097C42—22no—
1098C42—222no—
1099C42C23×D1112yes—
1100C11#6117311yescharacteristic, complemented, Sylow
1101C23—22no—
1102C23—22no—
1103C23—41no—
1104C23—221no—
1105C23—221no—
1106C23—442no—
1107C23—442no—
1108C23—881no—
1109C23C22×C22⋊D1111yescharacteristic
1110C23C22×C22⋊D1112yes—
1111C23C22×C22⋊D1111yescharacteristic
1112C23C22×C22⋊D1111yescharacteristic
1113Q8—22no—
1114Q8—22no—
1115Q8—22no—
1116Q8—42no—
1117Q8—82no—
1118Q8—112no—
1119Q8—221no—
1120Q8—222no—
1121Q8—221no—
1122Q8—222no—
1123Q8—221no—
1124Q8—444no—
1125Q8—442no—
1126Q8—442no—
1127D4—24no—
1128D4—24no—
1129D4—22no—
1130D4—42no—
1131D4—112no—
1132D4—224no—
1133D4—221no—
1134D4—221no—
1135D4—221no—
1136D4—442no—
1137D4—442no—
1138D4—442no—
1139D4—444no—
1140D4—442no—
1141D4—882no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—22no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—22no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—22no—
1155C2×C4—21no—
1156C2×C4—22no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—82no—
1160C2×C4—81no—
1161C2×C4—81no—
1162C2×C4—221no—
1163C2×C4—224no—
1164C2×C4—222no—
1165C2×C4—222no—
1166C2×C4—221no—
1167C2×C4—442no—
1168C2×C4—442no—
1169C2×C4—444no—
1170C2×C4—442no—
1171C2×C4—444no—
1172C2×C4—442no—
1173C2×C4—442no—
1174C2×C4—882no—
1175C2×C4—881no—
1176C2×C4#41×D1112yes—
1177C2×C4#6704212yes—
1178C2×C4C22×C22⋊D1111yescharacteristic
1179C2×C4C22×C22⋊D1112yes—
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—21no—
1199C22—22no—
1200C22—21no—
1201C22—44no—
1202C22—222no—
1203C22—441no—
1204C22—441no—
1205C22—441no—
1206C22—441no—
1207C22—441no—
1208C22—884no—
1209C22#1062336012yes—
1210C22#1062336912yes—
1211C22C23×C22⋊D1111yescharacteristic
1212C4—21no—
1213C4—21no—
1214C4—22no—
1215C4—22no—
1216C4—22no—
1217C4—42no—
1218C4—41no—
1219C4—41no—
1220C4—41no—
1221C4—42no—
1222C4—41no—
1223C4—222no—
1224C4—441no—
1225C4—442no—
1226C4—442no—
1227C4#1062336012yes—
1228C4C2×#41×D1111yescharacteristic
1229C4C2×#6704211yescharacteristic
1230C2—22no—
1231C2—22no—
1232C2—41no—
1233C2—42no—
1234C2—442no—
1235C2—881no—
1236C2C2×#1062336011yescharacteristic
1237C2C2×#1062336911yescharacteristic
1238C2#1308338711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3495C2
socleC22×C11C23×D4
prime radical#13082288C2
hypercenter#3495D11
hypocenterC11#61173
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #525 ◁ #3495

Complements

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

NH ≅ G/Ntype
2. #13080706C2semidirect
3. #13080691C2semidirect
4. #13080676C2semidirect
5. #13080661C2semidirect
6. #13080527C2semidirect
7. #13080497C2semidirect
8. #13080486C2semidirect
9. #13080445C2semidirect
10. #13078986C2semidirect
11. #13078594C2semidirect
12. #13078564C2semidirect
13. #13078463C2semidirect
14. #13078303C2semidirect
15. C2×#10622664C2semidirect
16. #13078146C2semidirect
17. #13077909C2semidirect
18. #13077874C2semidirect
19. #13077459C2semidirect
20. #13077311C2semidirect
21. #13077146C2semidirect
22. C2×#10622615C2semidirect
23. C11×#3495C2semidirect
26. C11×#556C22semidirect
30. C11×#552C22semidirect
32. C11×#544C22semidirect
35. C11×#536C22semidirect
40. C11×#520C22semidirect
41. C11×#519C22semidirect
44. C2×#67001C22semidirect
45. C22×#4326C22semidirect
62. #10622847C22semidirect
63. C2×#66899C22semidirect
65. #10622706C22semidirect
66. #10622704C22semidirect
67. #10622702C22semidirect
68. #10622700C22semidirect
69. #10622682C22semidirect
70. #10622681C22semidirect
71. #10622679C22semidirect
72. #10622676C22semidirect
73. #10622665C22semidirect
76. #10622664C22semidirect
77. #10622664C22semidirect
78. #10622664C22semidirect
80. #10622663C22semidirect
81. #10622663C22semidirect
82. #10622662C22semidirect
83. #10622661C22semidirect
86. #10622660C22semidirect
87. #10622660C22semidirect
89. #10622644C22semidirect
90. #10622644C22semidirect
91. #10622643C22semidirect
92. C4×#4326C22semidirect
93. #10622641C22semidirect
94. #10622641C22semidirect
95. #10622639C22semidirect
96. C4×#4325C22semidirect
98. #10622624C22semidirect
100. D4×C11⋊C8C22semidirect
101. #10622617C22semidirect
102. #10622617C22semidirect
103. #10622617C22semidirect
104. #10622616C22semidirect
113. #10622615C22semidirect
114. #10622612C22semidirect
115. #10622610C22semidirect
116. #10622609C22semidirect
117. #10622609C22semidirect
118. #10622609C22semidirect
119. #10622608C22semidirect
120. #10622608C22semidirect
123. #10622583C22semidirect
126. C2×#66874C22semidirect
127. C2×#66874C22semidirect
128. #10622580C22semidirect
131. #10622579C22semidirect
134. C2×#66871C22semidirect
482. #3495D11semidirect
602. #556C2×D11semidirect
606. #552C2×D11semidirect
614. #544C2×D11semidirect
621. #536C2×D11semidirect
630. #520C2×D11semidirect
631. #519C2×D11semidirect
1100. C11#61173semidirect

Maximal subgroups

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

subgroupindex
#130822882
#130807062
#130806912
#130806762
#130806612
#130805272
#130804972
#130804862
#130804452
#130789862
#130785942
#130785642
#130784632
#130783032
C2×#106226642
#130781462
#130779092
#130778742
#130774592
#130773112
#130771462
C2×#106226152
C11×#34952
#6117311