Finite Group Databasebeta

← #15624718

Subgroups — #15624718

Order 2816.

2250 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082286C211yesmaximal, characteristic, complemented
2D11×#537C211yesmaximal, characteristic, complemented
3#13079520C212yesmaximal, complemented
4#13079516C212yesmaximal, complemented
5#13079474C212yesmaximal, complemented
6#13079466C212yesmaximal, complemented
7#13079434C212yesmaximal, complemented
8#13079421C212yesmaximal, complemented
9#13079401C212yesmaximal, complemented
10#13079366C212yesmaximal, complemented
11#13078594C211yesmaximal, characteristic, complemented
12#13078542C211yesmaximal, characteristic, complemented
13C2×#10622495C211yesmaximal, characteristic, complemented
14#13078299C211yesmaximal, characteristic, complemented
15#13078297C211yesmaximal, characteristic, complemented
16#13078288C211yesmaximal, characteristic, complemented
17#13078285C211yesmaximal, characteristic, complemented
18#13077923C211yesmaximal, characteristic, complemented
19#13077917C211yesmaximal, characteristic, complemented
20#13077869C211yesmaximal, characteristic, complemented
21#13077836C211yesmaximal, characteristic, complemented
22#13077064C211yesmaximal, characteristic, complemented
23C11×#3098C211yesmaximal, characteristic, complemented
24C2×#67042C2211yescharacteristic, complemented
25C2×#41×D11C2211yescharacteristic
26C2×#41×D11C2211yescharacteristic, complemented
27C11×#537C2211yescharacteristic
28C11×#520C2211yescharacteristic, complemented
29#10623364C2211yescharacteristic
30#10623364C2211yescharacteristic, complemented
31C2×#67003C2211yescharacteristic, complemented
32C2×#67002C2211yescharacteristic, complemented
33C2×#66961C2211yescharacteristic, complemented
34C2×#66960C2211yescharacteristic, complemented
35C2×#66957C2211yescharacteristic, complemented
36C2×#66954C2211yescharacteristic, complemented
37#10623160—21no—
38#10623160C2212yescomplemented
39D11×C22⋊Q8—21no—
40D11×C22⋊Q8C2212yescomplemented
41#10623139—21no—
42#10623139C2212yescomplemented
43D11×#121—21no—
44D11×#121—22no—
45D11×#121C2212yescomplemented
46#10623128—22no—
47#10623108—21no—
48#10623107—21no—
49#10623085—22no—
50#10623085—21no—
51D4×D44—21no—
52D4×D44—22no—
53#10623056C2211yescharacteristic, complemented
54#10623056C2212yescomplemented
55#10623055C2211yescharacteristic
56#10623055C2212yes—
57#10623041C2211yescharacteristic, complemented
58#10623041C2211yescharacteristic, complemented
59#10623041C2212yescomplemented
60C2×#66948C2212yes—
61C2×#66948C2211yescharacteristic
62C2×C4⋊C4×D11C2211yescharacteristic, complemented
63C11×#485C2212yescomplemented
64C11×#484C2212yescomplemented
65C11×#482C2212yescomplemented
66C11×#480C2212yescomplemented
67C11×#428C2211yescharacteristic, complemented
68C2×C11×#107C2211yescharacteristic, complemented
69C11×#417C2211yescharacteristic, complemented
70C11×#416C2211yescharacteristic, complemented
71C11×#408C2211yescharacteristic, complemented
72#10622847C2211yescharacteristic, complemented
73#10622746C2211yescharacteristic, complemented
74#10622739C2211yescharacteristic, complemented
75C2×#66885C2211yescharacteristic, complemented
76C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
77#10622660C2212yescomplemented
78#10622659C2212yescomplemented
79#10622650C2212yescomplemented
80#10622649C2212yescomplemented
81#10622616C2212yescomplemented
82#10622615C2211yescharacteristic, complemented
83#10622609C2212yescomplemented
84#10622608C2211yescharacteristic, complemented
85#10622583C2212yescomplemented
86#10622580C2212yescomplemented
87#10622579C2211yescharacteristic, complemented
88#10622579C2211yescharacteristic, complemented
89C2×#66873C2211yescharacteristic, complemented
90C2×#66871C2211yescharacteristic, complemented
91#10622500C2212yescomplemented
92#10622499C2212yescomplemented
93#10622499C2212yescomplemented
94#10622499C2212yescomplemented
95#10622497C2212yescomplemented
96#10622496C2212yescomplemented
97#10622496C2212yescomplemented
98#10622495C2212yescomplemented
99#10622495C2212yescomplemented
100#10622495C2212yescomplemented
101#10622495C2212yescomplemented
102#10622495C2212yescomplemented
103#10622478C2212yescomplemented
104#10622477C2212yescomplemented
105#10622476C2212yescomplemented
106#10622475C2212yescomplemented
107#10622426C2212yescomplemented
108#10622425C2212yescomplemented
109#10622425C2212yescomplemented
110#10622424C2211yescharacteristic, complemented
111#10622424C2212yescomplemented
112#10622423C2211yescharacteristic, complemented
113#10622421C2211yescharacteristic, complemented
114#10622420C2212yescomplemented
115#10622419C2211yescharacteristic, complemented
116#10622419C2212yescomplemented
117#10622396C2211yescharacteristic, complemented
118#10622395C2212yescomplemented
119#10622394C2211yescharacteristic, complemented
120#10622394C2212yescomplemented
121#10622393C2212yescomplemented
122#10622389C2211yescharacteristic, complemented
123#10622388C2212yescomplemented
124#10622388C2212yescomplemented
125#10622386C2211yescharacteristic, complemented
126#10622386C2212yescomplemented
127#10622347C2212yescomplemented
128#10622346C2212yescomplemented
129#10622345C2212yescomplemented
130#10622344C2212yescomplemented
131#10622340C2212yescomplemented
132#10622340C2212yescomplemented
133#10622339C2212yescomplemented
134D11×C22⋊C8C2212yescomplemented
135C2×C11×#41C2311yescharacteristic
136C2×C11×#41C2311yescharacteristic
137#67042—42no—
138#67042—42no—
139#41×D11—42no—
140#41×D11—42no—
141#41×D11—42no—
142#41×D11—42no—
143C2×#4343—21no—
144C2×#4343D411yescharacteristic
145C2×#4343C2311yescharacteristic
146C2×Q8×D11D411yescharacteristic
147C2×Q8×D11C2311yescharacteristic
148C2×#4341—21no—
149C2×#4341D412yes—
150C2×#4341D411yescharacteristic
151C2×#4341C2311yescharacteristic
152C2×D4×D11—21no—
153C2×D4×D11—21no—
154C2×D4×D11—22no—
155C2×D4×D11—22no—
156C2×D4×D11D411yescharacteristic
157C2×D4×D11D412yes—
158C2×D4×D11C2311yescharacteristic
159C2×#4339—21no—
160C2×#4339C2311yescharacteristic
161C2×#4339C2312yes—
162C2×#4339C2311yescharacteristic
163C2×#4339C2311yescharacteristic
164C2×#4339C2312yes—
165C22×D44—21no—
166C22×D44—22no—
167C22×D44C2311yescharacteristic
168C22×D44C2312yes—
169C22×C4×D11—21no—
170C22×C4×D11—21no—
171C22×C4×D11C2311yescharacteristic
172C22×C4×D11C2312yes—
173C2×C11×M16C2311yescharacteristic
174C22×C8×C11C2311yescharacteristic
175C11×C22⋊Q8—21no—
176C11×C22⋊Q8C2312yes—
177C11×#121—22no—
178C11×#121—21no—
179C11×#121C2312yes—
180C4×Q8×C11—21no—
181C4×D4×C11—21no—
182C4×D4×C11—22no—
183C11×#117C2311yescharacteristic
184C11×#117C2312yes—
185C2×C11×C4⋊C4C2311yescharacteristic
186C2×C11×C4⋊C4C2311yescharacteristic
187C2×C11×C4⋊C4C2312yes—
188#67003—42no—
189#67002—42no—
190#66999—21no—
191#66999C2312yes—
192C2×#4326C2311yescharacteristic
193C2×#4325C2312yes—
194C2×#4325C2311yescharacteristic
195#66992—22no—
196#66992—22no—
197#66992—22no—
198#66992—22no—
199#66991—21no—
200#66991—22no—
201#66991C2312yes—
202C2×#4324C2311yescharacteristic
203C2×#4323C2312yes—
204C2×#4323C2311yescharacteristic
205#66983—22no—
206#66983—22no—
207#66983—22no—
208#66983—22no—
209#66983—21no—
210#66983C2312yes—
211C2×(C2×D11)⋊C4—21no—
212C2×(C2×D11)⋊C4—22no—
213C2×C4⋊Dic11C2311yescharacteristic
214#66977—21no—
215#66977C2312yes—
216C2×Dic11⋊C4—21no—
217C2×#4318C2311yescharacteristic
218C22×C11⋊C8C2311yescharacteristic
219#66961—42no—
220#66960—42no—
221C2×Dic44C2311yescharacteristic
222#66957—42no—
223C2×D88C2312yes—
224C2×D88C2311yescharacteristic
225C2×#4314C2312yes—
226C2×#4314C2311yescharacteristic
227C2×#4314C2311yescharacteristic
228#66954—42no—
229C2×#4313C2312yes—
230C2×#4313C2312yes—
231C2×C8×D11C2312yes—
232C2×C8×D11C2312yes—
233#66950—21no—
234#66950—22no—
235#66950—21no—
236#66950C2311yescharacteristic
237#66950C2312yes—
238#66950C2311yescharacteristic
239#66950C2312yes—
240#66949—22no—
241#66949—22no—
242#66948—21no—
243#66948—22no—
244#66948—21no—
245#66948—22no—
246#66948—21no—
247#66948—22no—
248#66948—21no—
249#66948—22no—
250#66948C2311yescharacteristic
251#66948C2312yes—
252#66948C2312yes—
253#66948C2311yescharacteristic
254#66948C2312yes—
255#66948C2312yes—
256#66948C2312yes—
257#66948C2312yes—
258C4⋊C4×D11—21no—
259C4⋊C4×D11—21no—
260C4⋊C4×D11—22no—
261C4⋊C4×D11C2312yes—
262C4⋊C4×D11C2312yes—
263#66939—21no—
264#66939—22no—
265#66937—22no—
266#66937—22no—
267#66937—22no—
268#66937—22no—
269#66935—21no—
270#66935—22no—
271#66935—22no—
272#66935—22no—
273#66935—22no—
274C22⋊C4×D11—22no—
275C22⋊C4×D11—22no—
276#66931—22no—
277#66931—22no—
278#66928—21no—
279#66928—22no—
280#66927—21no—
281#66927—22no—
282C4×D44—21no—
283C4×D44—22no—
284C4×D44—21no—
285C4×D44—22no—
286C11×#107C2312yes—
287C11×#107C2312yes—
288C11×#107C2312yes—
289C11×#106C2312yes—
290C11×#103C2311yescharacteristic
291C11×#103C2311yescharacteristic
292C11×#103C2312yes—
293C11×#102C2311yescharacteristic
294C11×#102C2312yes—
295C11×#102C2311yescharacteristic
296C11×C22⋊C8C2312yes—
297C11×C22⋊C8C2312yes—
298C22⋊(C11⋊C8)C2312yes—
299C22⋊(C11⋊C8)C2312yes—
300#66885C2312yes—
301#66885C2312yes—
302#66885C2312yes—
303(C2×D11)⋊C8C2311yescharacteristic
304(C2×D11)⋊C8C2311yescharacteristic
305(C2×D11)⋊C8C2311yescharacteristic
306(C2×D11)⋊C8C2311yescharacteristic
307(C2×D11)⋊C8C2312yes—
308(C2×D11)⋊C8C2312yes—
309#66880C2312yes—
310#66874C2312yes—
311#66874C2311yescharacteristic
312#66874C2311yescharacteristic
313#66874C2312yes—
314#66873C2312yes—
315#66873C2312yes—
316#66873C2311yescharacteristic
317#66873C2312yes—
318#66873C2311yescharacteristic
319#66873C2312yes—
320#66872C2312yes—
321#66871C2312yes—
322#66871C2312yes—
323#66871C2312yes—
324#60762—111nomaximal, Sylow
325C23×D11—22no—
326C23×D11—21no—
327C23×D11—21no—
328C23×D11C2×D411yescharacteristic
329C23×D11C2×D412yes—
330C11×#41—22no—
331C11×#41—22no—
332C11×#41—22no—
333C11×#41—22no—
334C2×Q8×C11C2×D411yescharacteristic
335C2×Q8×C11C2411yescharacteristic
336C2×D4×C11—21no—
337C2×D4×C11—22no—
338C2×D4×C11C2×D411yescharacteristic
339C2×D4×C11C2×D412yes—
340C2×D4×C11C2411yescharacteristic
341C22×C4×C11—21no—
342C22×C4×C11—22no—
343C22×C4×C11—21no—
344C22×C4×C11—21no—
345C22×C4×C11C2412yes—
346C22×C4×C11C2411yescharacteristic
347C2×C22⋊D11—21no—
348C2×C22⋊D11—22no—
349C2×C22⋊D11—21no—
350C2×C22⋊D11—21no—
351C2×C22⋊D11—22no—
352C2×C22⋊D11—21no—
353C2×C22⋊D11—22no—
354C2×C22⋊D11C2×D412yes—
355C2×C22⋊D11C2×D412yes—
356C2×C22⋊D11C2×D412yes—
357C22×Dic11—21no—
358C22×Dic11—21no—
359C22×Dic11C2×D411yescharacteristic
360C22×Dic11C2×D412yes—
361#4343—42no—
362#4343—41no—
363#4343—41no—
364#4343—44no—
365Q8×D11—42no—
366Q8×D11—41no—
367Q8×D11—41no—
368#4341—42no—
369#4341—41no—
370#4341—41no—
371#4341—44no—
372#4341—44no—
373D4×D11—44no—
374D4×D11—42no—
375D4×D11—41no—
376D4×D11—41no—
377D4×D11—48no—
378D4×D11—44no—
379D4×D11—44no—
380D4×D11—84no—
381#4339—22no—
382#4339—22no—
383#4339—22no—
384#4339—22no—
385#4339—22no—
386#4339—22no—
387#4339—42no—
388#4339—42no—
389#4339—42no—
390#4339—42no—
391#4339—44no—
392C2×D44—21no—
393C2×D44—22no—
394C2×D44—21no—
395C2×D44—22no—
396C2×D44—21no—
397C2×D44—22no—
398C2×D44—22no—
399C2×D44—22no—
400C2×D44—22no—
401C2×D44—22no—
402C2×D44—21no—
403C2×D44—22no—
404C2×D44—22no—
405C2×D44—42no—
406C2×D44—42no—
407C2×D44—82no—
408C2×D44—84no—
409C2×D44C2×D411yescharacteristic
410C2×D44C2×D412yes—
411C2×D44C2411yescharacteristic
412C2×D44C2412yes—
413C2×D44C2411yescharacteristic
414C2×C4×D11—21no—
415C2×C4×D11—22no—
416C2×C4×D11—21no—
417C2×C4×D11—22no—
418C2×C4×D11—22no—
419C2×C4×D11—21no—
420C2×C4×D11—21no—
421C2×C4×D11—22no—
422C2×C4×D11—22no—
423C2×C4×D11—42no—
424C2×C4×D11—42no—
425C2×C4×D11—44no—
426C2×C4×D11—82no—
427C2×C4×D11C2×D411yescharacteristic
428C2×C4×D11C2×D411yescharacteristic
429C2×C4×D11C2×D412yes—
430C2×C4×D11C2×D412yes—
431C2×C4×D11C2411yescharacteristic
432C2×C4×D11C2411yescharacteristic
433C2×C4×D11C2412yes—
434C2×Dic22—21no—
435C2×Dic22C2×D411yescharacteristic
436C2×Dic22C2×D412yes—
437C2×Dic22C2411yescharacteristic
438C2×Dic22C2411yescharacteristic
439C11×M16—22no—
440C2×C8×C11—22no—
441C2×C8×C11C2412yes—
442C2×C8×C11C2411yescharacteristic
443C2×C8×C11C2411yescharacteristic
444C11×C4⋊C4—21no—
445C11×C4⋊C4—22no—
446C11×C4⋊C4—22no—
447C11×C4⋊C4—21no—
448C11×C4⋊C4C2412yes—
449C11×C4⋊C4C2411yescharacteristic
450C11×C4⋊C4C2411yescharacteristic
451C11×C4⋊C4C2412yes—
452C11×C22⋊C4—22no—
453C11×C22⋊C4—22no—
454C11×C22⋊C4—21no—
455C11×C22⋊C4—22no—
456C42×C11—22no—
457C42×C11—21no—
458C22⋊Dic11—22no—
459C22⋊Dic11—22no—
460#4326—41no—
461#4325—42no—
462#4325—41no—
463#4324—41no—
464#4323—42no—
465#4323—41no—
466(C2×D11)⋊C4—21no—
467(C2×D11)⋊C4—22no—
468(C2×D11)⋊C4—21no—
469(C2×D11)⋊C4—22no—
470(C2×D11)⋊C4—22no—
471(C2×D11)⋊C4—22no—
472(C2×D11)⋊C4—22no—
473(C2×D11)⋊C4—22no—
474(C2×D11)⋊C4—21no—
475(C2×D11)⋊C4—22no—
476(C2×D11)⋊C4—21no—
477(C2×D11)⋊C4—22no—
478(C2×D11)⋊C4—22no—
479(C2×D11)⋊C4—22no—
480C4⋊Dic11—21no—
481C4⋊Dic11—21no—
482C4⋊Dic11—22no—
483C4⋊Dic11—22no—
484C4⋊Dic11—21no—
485C4⋊Dic11C2412yes—
486Dic11⋊C4—22no—
487Dic11⋊C4—22no—
488Dic11⋊C4—22no—
489Dic11⋊C4—22no—
490#4318—22no—
491C2×C11⋊C8—22no—
492C2×C11⋊C8C2411yescharacteristic
493C2×C11⋊C8C2411yescharacteristic
494C2×C11⋊C8C2412yes—
495Dic44—41no—
496D88—41no—
497D88—42no—
498#4314—41no—
499#4314—41no—
500#4314—42no—
501#4313—42no—
502#4313—42no—
503C8×D11—42no—
504C8×D11—42no—
505#3488—111no—
506C2×#537—111no—
507#3203—112no—
508#3203—112no—
509#3198—112no—
510#3198—112no—
511#3194—112no—
512#3193—112no—
513#3190—112no—
514#3186—112no—
515#3098—111no—
516#3098D1111yescharacteristic, complemented
517#3092—111no—
518C2×#480—111no—
519#3062—111no—
520#3062—111no—
521#3061—111no—
522#3061—111no—
523#3012—111no—
524#3012—111no—
525#3006—111no—
526#3002—111no—
527#2880—111no—
528C23×C11—21no—
529C23×C11C22×D412yes—
530C23×C11C22×D411yescharacteristic
531C22×D11—22no—
532C22×D11—22no—
533C22×D11—24no—
534C22×D11—21no—
535C22×D11—21no—
536C22×D11—22no—
537C22×D11—41no—
538C22×D11—42no—
539C22×D11—42no—
540C22×D11—42no—
541C22×D11—42no—
542C22×D11—44no—
543C22×D11—42no—
544C22×D11—42no—
545C22×D11—81no—
546C22×D11—82no—
547C22×D11—81no—
548C22×D11—82no—
549C22×D11C22×D412yes—
550C22×D11C22×D411yescharacteristic
551C22×D11C22×D411yescharacteristic
552Q8×C11—22no—
553Q8×C11—21no—
554Q8×C11—21no—
555D4×C11—24no—
556D4×C11—22no—
557D4×C11—21no—
558D4×C11—21no—
559D4×C11—42no—
560D4×C11—82no—
561C2×C4×C11—22no—
562C2×C4×C11—22no—
563C2×C4×C11—22no—
564C2×C4×C11—21no—
565C2×C4×C11—21no—
566C2×C4×C11—21no—
567C2×C4×C11—22no—
568C2×C4×C11—42no—
569C2×C4×C11—81no—
570C2×C4×C11—81no—
571C2×C4×C11—82no—
572C2×C4×C11C22×D412yes—
573C2×C4×C11C22×D411yescharacteristic
574C2×C4×C11H(5,𝔽2)12yes—
575C2×C4×C11H(5,𝔽2)12yes—
576C2×C4×C11C2511yescharacteristic
577C22⋊D11—24no—
578C22⋊D11—42no—
579C22⋊D11—42no—
580C22⋊D11—42no—
581C22⋊D11—42no—
582C22⋊D11—44no—
583C22⋊D11—42no—
584C22⋊D11—42no—
585C22⋊D11—82no—
586C22⋊D11—82no—
587C2×Dic11—22no—
588C2×Dic11—22no—
589C2×Dic11—21no—
590C2×Dic11—21no—
591C2×Dic11—42no—
592C2×Dic11—42no—
593C2×Dic11—81no—
594C2×Dic11C22×D411yescharacteristic
595C2×Dic11C22×D411yescharacteristic
596C2×Dic11C22×D412yes—
597D44—22no—
598D44—22no—
599D44—21no—
600D44—21no—
601D44—21no—
602D44—22no—
603D44—21no—
604D44—42no—
605D44—44no—
606D44—42no—
607D44—44no—
608D44—42no—
609D44—42no—
610D44—81no—
611D44—82no—
612D44—82no—
613D44—82no—
614D44—82no—
615D44—82no—
616C4×D11—22no—
617C4×D11—22no—
618C4×D11—22no—
619C4×D11—22no—
620C4×D11—21no—
621C4×D11—21no—
622C4×D11—21no—
623C4×D11—21no—
624C4×D11—42no—
625C4×D11—42no—
626C4×D11—42no—
627C4×D11—44no—
628C4×D11—42no—
629C4×D11—44no—
630C4×D11—42no—
631C4×D11—42no—
632C4×D11—82no—
633Dic22—22no—
634Dic22—21no—
635Dic22—21no—
636Dic22—21no—
637Dic22—21no—
638Dic22—42no—
639Dic22—42no—
640C8×C11—21no—
641C8×C11—22no—
642C8×C11—21no—
643C11⋊C8—21no—
644C11⋊C8—22no—
645C11⋊C8—21no—
646C2×H(5,𝔽2)—111no—
647C22×#41—111no—
648C22×#41—111no—
649C2×AGL(1,ℤ/8)—111no—
650C2×AGL(1,ℤ/8)—111no—
651C2×#135—111no—
652C2×#135—111no—
653C2×#131—111no—
654C2×#131—111no—
655#550—221no—
656#548—221no—
657#546—222no—
658#546—221no—
659D42—221no—
660D42—222no—
661#537—111no—
662#537—111no—
663#537—112no—
664#537—112no—
665#537—111no—
666#537—112no—
667#537—111no—
668#537—222no—
669#537—221no—
670#537—221no—
671#537C2×D1111yescharacteristic
672#535—112no—
673#535—111no—
674#525—111no—
675#525—112no—
676C2×C22⋊Q8—112no—
677C2×C22⋊Q8—221no—
678C2×#121—112no—
679C2×#121—111no—
680C2×#121—112no—
681C2×#121—222no—
682C2×#121—221no—
683#520C2×D1111yescharacteristic, complemented
684C22×C4⋊C4—111no—
685#485—112no—
686#485C2×D1112yescomplemented
687#484—112no—
688#484—112no—
689#484C2×D1112yescomplemented
690#483—112no—
691#482—112no—
692#482C2×D1112yescomplemented
693#481—112no—
694#480—112no—
695#480—112no—
696#480—112no—
697#480—112no—
698#480—112no—
699#480—112no—
700#480C2×D1112yescomplemented
701#469—112no—
702#469—112no—
703#468—112no—
704#468—112no—
705#468—112no—
706#468—112no—
707#468—112no—
708#468—112no—
709#467—112no—
710#467—112no—
711#466—112no—
712#466—112no—
713#466—112no—
714#466—112no—
715#465—112no—
716#465—112no—
717#452—112no—
718#452—111no—
719#452—111no—
720#452—112no—
721#451—111no—
722#450—112no—
723#450—111no—
724#450—112no—
725#449—112no—
726#449—111no—
727#449—112no—
728#449—111no—
729#449—112no—
730#449—112no—
731#448—112no—
732#448—111no—
733#447—112no—
734#447—111no—
735#447—112no—
736#447—112no—
737#428—111no—
738#428C2×D1111yescharacteristic, complemented
739C2×#107—111no—
740C2×#107C2×D1111yescharacteristic, complemented
741#417—111no—
742#417—111no—
743#417—111no—
744#417C2×D1111yescharacteristic, complemented
745#416—111no—
746#416C2×D1111yescharacteristic, complemented
747C2×#102—111no—
748C2×#102—111no—
749#408—111no—
750#408—112no—
751#408—112no—
752#408C2×D1111yescharacteristic, complemented
753#407—111no—
754#407—112no—
755C2×C22⋊C8—111no—
756C2×C22⋊C8—112no—
757C22×C11—21no—
758C22×C11—21no—
759C22×C11—22no—
760C22×C11—22no—
761C22×C11—22no—
762C22×C11—41no—
763C22×C11—41no—
764C22×C11—41no—
765C22×C11#53412yes—
766C22×C11C23×D411yescharacteristic
767C2×D11—21no—
768C2×D11—21no—
769C2×D11—21no—
770C2×D11—22no—
771C2×D11—21no—
772C2×D11—22no—
773C2×D11—21no—
774C2×D11—22no—
775C2×D11—44no—
776C2×D11—41no—
777C2×D11—42no—
778C2×D11—41no—
779C2×D11—41no—
780C2×D11—42no—
781C2×D11—41no—
782C2×D11—41no—
783C2×D11—42no—
784C2×D11—41no—
785C2×D11—84no—
786C2×D11—84no—
787C2×D11—162no—
788C2×D11—164no—
789C2×D11#57612yes—
790C4×C11—22no—
791C4×C11—41no—
792C4×C11—41no—
793C4×C11—42no—
794C4×C11—41no—
795C4×C11—42no—
796C4×C11#53412yes—
797C4×C11C2×H(5,𝔽2)11yescharacteristic
798C4×C11C2×H(5,𝔽2)11yescharacteristic
799Dic11—22no—
800Dic11—21no—
801Dic11—21no—
802Dic11—41no—
803Dic11—41no—
804Dic11—42no—
805H(5,𝔽2)—442no—
806H(5,𝔽2)—442no—
807C2×#41—111no—
808C2×#41—112no—
809C2×#41—111no—
810C2×#41—111no—
811C2×#41—112no—
812C2×#41—111no—
813C2×#41—111no—
814C2×#41—111no—
815C2×#41—111no—
816C2×#41—112no—
817C2×#41—221no—
818C2×#41—221no—
819C2×#41—221no—
820C2×#41—442no—
821C2×#41—442no—
822C2×#41—442no—
823C2×#41—442no—
824C2×#41C22×D1111yescharacteristic
825C2×#41C22×D1111yescharacteristic
826C22×Q8—111no—
827C22×Q8—111no—
828C22×D4—111no—
829C22×D4—112no—
830C22×D4—111no—
831C22×D4—111no—
832C22×D4—112no—
833C22×D4—221no—
834C22×D4—222no—
835C22×D4—221no—
836C22×D4—222no—
837C22×D4—222no—
838C22×D4—221no—
839C23×C4—111no—
840C23×C4—112no—
841C23×C4—221no—
842C23×C4—221no—
843AGL(1,ℤ/8)—442no—
844AGL(1,ℤ/8)—442no—
845#135—442no—
846#135—442no—
847C2×Q16—111no—
848C2×Q16—111no—
849C2×SD16—111no—
850C2×SD16—112no—
851C2×SD16—111no—
852C2×SD16—111no—
853C2×SD16—111no—
854C2×SD16—112no—
855C2×D8—111no—
856C2×D8—112no—
857C2×D8—111no—
858C2×D8—112no—
859#131—442no—
860#131—442no—
861C2×M16—111no—
862C2×M16—112no—
863C2×M16—112no—
864C2×M16C22×D1111yescharacteristic
865C22×C8—111no—
866C22×C8—112no—
867C22×C8—112no—
868C22×C8C22×D1111yescharacteristic
869#127—221no—
870#127—222no—
871#124—221no—
872#124—222no—
873#123—221no—
874#123—222no—
875C22⋊Q8—21no—
876C22⋊Q8—112no—
877C22⋊Q8—112no—
878C22⋊Q8—112no—
879C22⋊Q8—111no—
880C22⋊Q8—111no—
881C22⋊Q8—112no—
882C22⋊Q8—222no—
883C22⋊Q8—222no—
884C22⋊Q8—222no—
885C22⋊Q8—222no—
886C22⋊Q8—221no—
887C22⋊Q8—221no—
888C22⋊Q8—222no—
889C22⋊Q8—221no—
890C22⋊Q8—221no—
891C22⋊Q8C22×D1112yes—
892#121—21no—
893#121—22no—
894#121—112no—
895#121—112no—
896#121—112no—
897#121—111no—
898#121—112no—
899#121—112no—
900#121—112no—
901#121—112no—
902#121—111no—
903#121—112no—
904#121—222no—
905#121—222no—
906#121—222no—
907#121—222no—
908#121—221no—
909#121—222no—
910#121—221no—
911#121—222no—
912#121—221no—
913#121—222no—
914#121—221no—
915#121—222no—
916#121—222no—
917#121—221no—
918#121—222no—
919#121—222no—
920#121—222no—
921#121—222no—
922#121—222no—
923#121—222no—
924#121—222no—
925#121—221no—
926#121—222no—
927#121C22×D1112yes—
928#120—222no—
929#120—222no—
930#120—222no—
931#120—221no—
932#120—222no—
933C4×Q8—21no—
934C4×D4—22no—
935C4×D4—21no—
936C4×D4—221no—
937C4×D4—222no—
938C4×D4—221no—
939C4×D4—222no—
940#117C22×D1111yescharacteristic
941#117C22×D1112yes—
942C2×C4⋊C4—111no—
943C2×C4⋊C4—112no—
944C2×C4⋊C4—112no—
945C2×C4⋊C4—221no—
946C2×C4⋊C4—221no—
947C2×C4⋊C4—222no—
948C2×C4⋊C4—221no—
949C2×C4⋊C4C22×D1111yescharacteristic
950C2×C4⋊C4C22×D1111yescharacteristic
951C2×C4⋊C4C22×D1112yes—
952C2×C22⋊C4—222no—
953C2×C22⋊C4—222no—
954C2×C22⋊C4—221no—
955C2×C22⋊C4—222no—
956#107—112no—
957#107—112no—
958#107—112no—
959#107C22×D1112yes—
960#107C22×D1112yes—
961#107C22×D1112yes—
962#106—112no—
963#106C22×D1112yes—
964#103—112no—
965#103—111no—
966#103—111no—
967#103—112no—
968#103—112no—
969#103C22×D1111yescharacteristic
970#103C22×D1111yescharacteristic
971#103C22×D1112yes—
972#102—112no—
973#102—112no—
974#102—112no—
975#102—112no—
976#102—112no—
977#102—111no—
978#102—111no—
979#102—112no—
980#102—112no—
981#102C22×D1111yescharacteristic
982#102C22×D1111yescharacteristic
983#102C22×D1112yes—
984C22⋊C8—112no—
985C22⋊C8—112no—
986C22⋊C8—111no—
987C22⋊C8—112no—
988C22⋊C8—111no—
989C22⋊C8—111no—
990C22⋊C8—111no—
991C22⋊C8—112no—
992C22⋊C8C22×D1112yes—
993C22⋊C8C22×D1112yes—
994C2×C11—22no—
995C2×C11—42no—
996C2×C11—81no—
997C2×C11C2×#53411yescharacteristic
998C2×C11C2×#57611yescharacteristic
999C2×C11#358611yescharacteristic
1000D11—22no—
1001D11—41no—
1002D11—42no—
1003D11—81no—
1004D11—82no—
1005D11—81no—
1006C24—111no—
1007C24—112no—
1008C24—221no—
1009C24—222no—
1010C24—221no—
1011#41—22no—
1012#41—22no—
1013#41—22no—
1014#41—22no—
1015#41—222no—
1016#41—222no—
1017#41—222no—
1018#41—222no—
1019#41—222no—
1020#41—222no—
1021#41—442no—
1022#41—442no—
1023#41—442no—
1024#41—442no—
1025#41—444no—
1026#41—444no—
1027#41—442no—
1028#41—441no—
1029#41—441no—
1030#41—444no—
1031#41—442no—
1032#41—441no—
1033#41—441no—
1034#41—444no—
1035C2×Q8—111no—
1036C2×Q8—112no—
1037C2×Q8—111no—
1038C2×Q8—111no—
1039C2×Q8—221no—
1040C2×Q8—442no—
1041C2×Q8—441no—
1042C2×Q8—441no—
1043C2×Q8D4×D1111yescharacteristic
1044C2×Q8C23×D1111yescharacteristic
1045C2×D4—21no—
1046C2×D4—22no—
1047C2×D4—112no—
1048C2×D4—112no—
1049C2×D4—112no—
1050C2×D4—111no—
1051C2×D4—112no—
1052C2×D4—111no—
1053C2×D4—112no—
1054C2×D4—111no—
1055C2×D4—221no—
1056C2×D4—222no—
1057C2×D4—221no—
1058C2×D4—222no—
1059C2×D4—221no—
1060C2×D4—222no—
1061C2×D4—222no—
1062C2×D4—222no—
1063C2×D4—222no—
1064C2×D4—221no—
1065C2×D4—221no—
1066C2×D4—222no—
1067C2×D4—221no—
1068C2×D4—221no—
1069C2×D4—222no—
1070C2×D4—222no—
1071C2×D4—222no—
1072C2×D4—221no—
1073C2×D4—222no—
1074C2×D4—222no—
1075C2×D4—442no—
1076C2×D4—442no—
1077C2×D4—442no—
1078C2×D4—441no—
1079C2×D4—441no—
1080C2×D4—444no—
1081C2×D4—448no—
1082C2×D4—444no—
1083C2×D4—444no—
1084C2×D4—882no—
1085C2×D4—884no—
1086C2×D4—884no—
1087C2×D4D4×D1112yes—
1088C2×D4D4×D1111yescharacteristic
1089C2×D4C23×D1111yescharacteristic
1090C22×C4—22no—
1091C22×C4—21no—
1092C22×C4—21no—
1093C22×C4—21no—
1094C22×C4—111no—
1095C22×C4—112no—
1096C22×C4—111no—
1097C22×C4—111no—
1098C22×C4—111no—
1099C22×C4—111no—
1100C22×C4—112no—
1101C22×C4—112no—
1102C22×C4—112no—
1103C22×C4—221no—
1104C22×C4—222no—
1105C22×C4—221no—
1106C22×C4—222no—
1107C22×C4—221no—
1108C22×C4—222no—
1109C22×C4—222no—
1110C22×C4—221no—
1111C22×C4—222no—
1112C22×C4—221no—
1113C22×C4—221no—
1114C22×C4—442no—
1115C22×C4—442no—
1116C22×C4—444no—
1117C22×C4—882no—
1118C22×C4C23×D1112yes—
1119C22×C4C23×D1111yescharacteristic
1120Q16—441no—
1121Q16—441no—
1122SD16—441no—
1123SD16—441no—
1124SD16—442no—
1125SD16—441no—
1126SD16—441no—
1127SD16—442no—
1128D8—441no—
1129D8—442no—
1130D8—441no—
1131D8—442no—
1132M16—22no—
1133M16—222no—
1134M16—442no—
1135M16—442no—
1136C2×C8—22no—
1137C2×C8—111no—
1138C2×C8—111no—
1139C2×C8—112no—
1140C2×C8—222no—
1141C2×C8—442no—
1142C2×C8—442no—
1143C2×C8C23×D1111yescharacteristic
1144C2×C8C23×D1111yescharacteristic
1145C2×C8C23×D1112yes—
1146C4⋊C4—21no—
1147C4⋊C4—22no—
1148C4⋊C4—22no—
1149C4⋊C4—21no—
1150C4⋊C4—112no—
1151C4⋊C4—222no—
1152C4⋊C4—222no—
1153C4⋊C4—222no—
1154C4⋊C4—222no—
1155C4⋊C4—221no—
1156C4⋊C4—222no—
1157C4⋊C4—221no—
1158C4⋊C4—221no—
1159C4⋊C4—222no—
1160C4⋊C4C23×D1112yes—
1161C4⋊C4C23×D1111yescharacteristic
1162C4⋊C4C23×D1111yescharacteristic
1163C4⋊C4C23×D1112yes—
1164C22⋊C4—22no—
1165C22⋊C4—22no—
1166C22⋊C4—21no—
1167C22⋊C4—22no—
1168C22⋊C4—222no—
1169C22⋊C4—221no—
1170C22⋊C4—222no—
1171C22⋊C4—222no—
1172C22⋊C4—222no—
1173C22⋊C4—222no—
1174C22⋊C4—222no—
1175C22⋊C4—221no—
1176C22⋊C4—222no—
1177C22⋊C4—222no—
1178C22⋊C4—221no—
1179C22⋊C4—222no—
1180C22⋊C4—221no—
1181C22⋊C4—222no—
1182C22⋊C4—222no—
1183C22⋊C4—222no—
1184C42—22no—
1185C42—21no—
1186C11#6076211yescharacteristic, complemented, Sylow
1187C23—21no—
1188C23—111no—
1189C23—112no—
1190C23—111no—
1191C23—222no—
1192C23—224no—
1193C23—222no—
1194C23—221no—
1195C23—222no—
1196C23—221no—
1197C23—441no—
1198C23—442no—
1199C23—442no—
1200C23—444no—
1201C23—442no—
1202C23—442no—
1203C23—442no—
1204C23—442no—
1205C23—881no—
1206C23—882no—
1207C23—881no—
1208C23—882no—
1209C23C2×D4×D1112yes—
1210C23C2×D4×D1111yescharacteristic
1211Q8—22no—
1212Q8—21no—
1213Q8—21no—
1214Q8—222no—
1215Q8—221no—
1216Q8—221no—
1217Q8—221no—
1218Q8—221no—
1219Q8—442no—
1220Q8—442no—
1221D4—24no—
1222D4—22no—
1223D4—21no—
1224D4—21no—
1225D4—42no—
1226D4—82no—
1227D4—224no—
1228D4—222no—
1229D4—221no—
1230D4—222no—
1231D4—222no—
1232D4—221no—
1233D4—221no—
1234D4—221no—
1235D4—442no—
1236D4—444no—
1237D4—444no—
1238D4—442no—
1239D4—442no—
1240D4—442no—
1241D4—442no—
1242D4—442no—
1243D4—444no—
1244D4—442no—
1245D4—442no—
1246D4—442no—
1247D4—442no—
1248D4—882no—
1249D4—882no—
1250D4—882no—
1251D4—882no—
1252D4—881no—
1253D4—882no—
1254D4—882no—
1255D4—882no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—21no—
1259C2×C4—22no—
1260C2×C4—21no—
1261C2×C4—22no—
1262C2×C4—21no—
1263C2×C4—42no—
1264C2×C4—81no—
1265C2×C4—81no—
1266C2×C4—82no—
1267C2×C4—112no—
1268C2×C4—111no—
1269C2×C4—111no—
1270C2×C4—222no—
1271C2×C4—222no—
1272C2×C4—222no—
1273C2×C4—222no—
1274C2×C4—222no—
1275C2×C4—221no—
1276C2×C4—221no—
1277C2×C4—221no—
1278C2×C4—221no—
1279C2×C4—222no—
1280C2×C4—221no—
1281C2×C4—221no—
1282C2×C4—442no—
1283C2×C4—442no—
1284C2×C4—444no—
1285C2×C4—442no—
1286C2×C4—444no—
1287C2×C4—442no—
1288C2×C4—442no—
1289C2×C4—442no—
1290C2×C4—442no—
1291C2×C4—442no—
1292C2×C4—882no—
1293C2×C4—881no—
1294C2×C4C2×D4×D1112yes—
1295C2×C4C2×D4×D1111yescharacteristic
1296C2×C4#6704212yes—
1297C2×C4#6704212yes—
1298C2×C4C24×D1111yescharacteristic
1299C8—21no—
1300C8—21no—
1301C8—22no—
1302C8—221no—
1303C8—221no—
1304C8—222no—
1305C22—21no—
1306C22—21no—
1307C22—22no—
1308C22—22no—
1309C22—22no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—112no—
1314C22—221no—
1315C22—221no—
1316C22—221no—
1317C22—222no—
1318C22—221no—
1319C22—222no—
1320C22—221no—
1321C22—222no—
1322C22—444no—
1323C22—442no—
1324C22—441no—
1325C22—441no—
1326C22—441no—
1327C22—442no—
1328C22—441no—
1329C22—442no—
1330C22—441no—
1331C22—441no—
1332C22—884no—
1333C22—884no—
1334C22—1762no—
1335C22—1764no—
1336C22#1062318412yes—
1337C22C22×D4×D1111yescharacteristic
1338C4—22no—
1339C4—41no—
1340C4—41no—
1341C4—42no—
1342C4—41no—
1343C4—42no—
1344C4—221no—
1345C4—221no—
1346C4—222no—
1347C4—441no—
1348C4—441no—
1349C4—442no—
1350C4#1062318412yes—
1351C4C2×#6704211yescharacteristic
1352C4C2×#6704211yescharacteristic
1353C2—22no—
1354C2—42no—
1355C2—81no—
1356C2—222no—
1357C2—441no—
1358C2—442no—
1359C2—881no—
1360C2—882no—
1361C2—881no—
1362C2C2×#1062318411yescharacteristic
1363C2D11×#57611yescharacteristic
1364C2#1308340111yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3098C2
socleC22×C11C23×D4
hypercenter#3098D11
hypocenterC11#60762
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3098

Complements

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

NH ≅ G/Ntype
1. #13082286C2semidirect
2. D11×#537C2semidirect
3. #13079520C2semidirect
4. #13079516C2semidirect
5. #13079474C2semidirect
6. #13079466C2semidirect
7. #13079434C2semidirect
8. #13079421C2semidirect
9. #13079401C2semidirect
10. #13079366C2semidirect
11. #13078594C2semidirect
12. #13078542C2semidirect
13. C2×#10622495C2semidirect
14. #13078299C2semidirect
15. #13078297C2semidirect
16. #13078288C2semidirect
17. #13078285C2semidirect
18. #13077923C2semidirect
19. #13077917C2semidirect
20. #13077869C2semidirect
21. #13077836C2semidirect
22. #13077064C2semidirect
23. C11×#3098C2semidirect
24. C2×#67042C22semidirect
26. C2×#41×D11C22semidirect
28. C11×#520C22semidirect
30. #10623364C22semidirect
31. C2×#67003C22semidirect
32. C2×#67002C22semidirect
33. C2×#66961C22semidirect
34. C2×#66960C22semidirect
35. C2×#66957C22semidirect
36. C2×#66954C22semidirect
38. #10623160C22semidirect
40. D11×C22⋊Q8C22semidirect
42. #10623139C22semidirect
45. D11×#121C22semidirect
53. #10623056C22semidirect
54. #10623056C22semidirect
57. #10623041C22semidirect
58. #10623041C22semidirect
59. #10623041C22semidirect
62. C2×C4⋊C4×D11C22semidirect
63. C11×#485C22semidirect
64. C11×#484C22semidirect
65. C11×#482C22semidirect
66. C11×#480C22semidirect
67. C11×#428C22semidirect
68. C2×C11×#107C22semidirect
69. C11×#417C22semidirect
70. C11×#416C22semidirect
71. C11×#408C22semidirect
72. #10622847C22semidirect
73. #10622746C22semidirect
74. #10622739C22semidirect
75. C2×#66885C22semidirect
76. C2×(C2×D11)⋊C8C22semidirect
77. #10622660C22semidirect
78. #10622659C22semidirect
79. #10622650C22semidirect
80. #10622649C22semidirect
81. #10622616C22semidirect
82. #10622615C22semidirect
83. #10622609C22semidirect
84. #10622608C22semidirect
85. #10622583C22semidirect
86. #10622580C22semidirect
87. #10622579C22semidirect
88. #10622579C22semidirect
89. C2×#66873C22semidirect
90. C2×#66871C22semidirect
91. #10622500C22semidirect
92. #10622499C22semidirect
93. #10622499C22semidirect
94. #10622499C22semidirect
95. #10622497C22semidirect
96. #10622496C22semidirect
97. #10622496C22semidirect
98. #10622495C22semidirect
99. #10622495C22semidirect
100. #10622495C22semidirect
101. #10622495C22semidirect
102. #10622495C22semidirect
103. #10622478C22semidirect
104. #10622477C22semidirect
105. #10622476C22semidirect
106. #10622475C22semidirect
107. #10622426C22semidirect
108. #10622425C22semidirect
109. #10622425C22semidirect
110. #10622424C22semidirect
111. #10622424C22semidirect
112. #10622423C22semidirect
113. #10622421C22semidirect
114. #10622420C22semidirect
115. #10622419C22semidirect
116. #10622419C22semidirect
117. #10622396C22semidirect
118. #10622395C22semidirect
119. #10622394C22semidirect
120. #10622394C22semidirect
121. #10622393C22semidirect
122. #10622389C22semidirect
123. #10622388C22semidirect
124. #10622388C22semidirect
125. #10622386C22semidirect
126. #10622386C22semidirect
127. #10622347C22semidirect
128. #10622346C22semidirect
129. #10622345C22semidirect
130. #10622344C22semidirect
131. #10622340C22semidirect
132. #10622340C22semidirect
133. #10622339C22semidirect
134. D11×C22⋊C8C22semidirect
516. #3098D11semidirect
683. #520C2×D11semidirect
686. #485C2×D11semidirect
689. #484C2×D11semidirect
692. #482C2×D11semidirect
700. #480C2×D11semidirect
738. #428C2×D11semidirect
740. C2×#107C2×D11semidirect
744. #417C2×D11semidirect
746. #416C2×D11semidirect
752. #408C2×D11semidirect
1186. C11#60762semidirect

Maximal subgroups

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

subgroupindex
#130822862
D11×#5372
#130795202
#130795162
#130794742
#130794662
#130794342
#130794212
#130794012
#130793662
#130785942
#130785422
C2×#106224952
#130782992
#130782972
#130782882
#130782852
#130779232
#130779172
#130778692
#130778362
#130770642
C11×#30982
#6076211