Finite Group Databasebeta

← #15622757

Subgroups — #15622757

Order 2816.

2074 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082502C211yesmaximal, characteristic, complemented
2#13078868C214yesmaximal, complemented
3#13078830C214yesmaximal, complemented
4#13078778C212yesmaximal, complemented
5#13078715C212yesmaximal, complemented
6#13078687C212yesmaximal, complemented
7#13078624C212yesmaximal, complemented
8#13078585C212yesmaximal, complemented
9#13078413C211yesmaximal, characteristic, complemented
10#13078404C211yesmaximal, characteristic, complemented
11#13078103C211yesmaximal, characteristic, complemented
12C2×#10622632C211yesmaximal, characteristic, complemented
13#13077893C212yesmaximal
14#13077473C212yesmaximal, complemented
15#13077455C212yesmaximal, complemented
16#13077282C211yesmaximal, characteristic, complemented
17C4×C11×H(5,𝔽2)C211yesmaximal, characteristic
18C2×C11×H(5,𝔽2)C2211yescharacteristic
19C11×#520—21no—
20C11×#520C2212yes—
21C11×#520C2211yescharacteristic
22C11×#520C2211yescharacteristic
23C11×#518—22no—
24C11×#518—21no—
25C11×#518C2212yes—
26C11×#518C2211yescharacteristic
27C4×C11×#41—21no—
28C4×C11×#41C2211yescharacteristic
29C4×C11×#41C2212yes—
30C4×C11×#41C2211yescharacteristic
31C2×C4×D4×C11—22no—
32C2×C4×D4×C11—21no—
33C2×C4×D4×C11C2211yescharacteristic
34C2×C4×D4×C11C2212yes—
35#10623356C2212yes—
36C2×#67004C2212yes—
37C22×#4324C2212yes—
38#10623098—21no—
39#10623098—21no—
40#10623073—21no—
41#10623073—21no—
42#10623072—22no—
43#10623072—22no—
44#10623049C2214yescomplemented
45#10623047C2212yescomplemented
46#10623001C2211yescharacteristic, complemented
47#10623001C2212yescomplemented
48#10623001C2212yescomplemented
49C2×#66922C2211yescharacteristic, complemented
50#10622852C2214yes—
51#10622852C2214yes—
52#10622847C2212yes—
53#10622846C2212yes—
54#10622831C2214yes—
55#10622831C2214yes—
56#10622828C2212yes—
57#10622644C2212yescomplemented
58#10622644C2212yescomplemented
59#10622643C2214yescomplemented
60C4×#4326C2214yescomplemented
61#10622635C2212yescomplemented
62#10622634C2211yescharacteristic, complemented
63#10622633C2211yescharacteristic, complemented
64#10622632C2214yescomplemented
65#10622632C2212yescomplemented
66#10622632C2212yescomplemented
67#10622632C2212yescomplemented
68#10622632C2212yescomplemented
69#10622631C2214yescomplemented
70#10622631C2214yescomplemented
71#10622631C2214yescomplemented
72C4×#4324C2214yescomplemented
73C4×#4324C2214yescomplemented
74C4×#4324C2214yescomplemented
75#10622622C2214yescomplemented
76#10622622C2212yescomplemented
77#10622621C2211yescharacteristic, complemented
78#10622621C2212yescomplemented
79#10622620C2211yescharacteristic, complemented
80#10622620C2212yescomplemented
81#10622617C2212yescomplemented
82#10622613C2214yescomplemented
83#10622611C2212yescomplemented
84#10622610C2212yescomplemented
85#10622609C2214yescomplemented
86#10622609C2214yescomplemented
87#10622584C2214yescomplemented
88#10622583C2214yescomplemented
89C2×#66874C2212yescomplemented
90#10622577C2212yescomplemented
91#10622539C2212yescomplemented
92#10622538C2212yescomplemented
93#10622537C2211yescharacteristic, complemented
94C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
95C11×H(5,𝔽2)—24no—
96C11×H(5,𝔽2)—24no—
97C2×C11×#41—21no—
98C2×C11×#41C2312yes—
99C2×C11×#41C2311yescharacteristic
100C2×C11×#41C2311yescharacteristic
101C22×D4×C11—22no—
102C22×D4×C11—21no—
103C22×D4×C11C2312yes—
104C22×D4×C11C2311yescharacteristic
105C23×C4×C11—21no—
106C23×C4×C11—22no—
107C22×Dic22C2312yes—
108C4×Q8×C11—21no—
109C4×Q8×C11D411yescharacteristic
110C4×Q8×C11D411yescharacteristic
111C4×Q8×C11C2311yescharacteristic
112C4×Q8×C11C2311yescharacteristic
113C4×Q8×C11C2312yes—
114C4×D4×C11—22no—
115C4×D4×C11—21no—
116C4×D4×C11—21no—
117C4×D4×C11—22no—
118C4×D4×C11—21no—
119C4×D4×C11—22no—
120C4×D4×C11—21no—
121C4×D4×C11—22no—
122C4×D4×C11—21no—
123C4×D4×C11—22no—
124C4×D4×C11—22no—
125C4×D4×C11—22no—
126C4×D4×C11—22no—
127C4×D4×C11—21no—
128C4×D4×C11—22no—
129C4×D4×C11—21no—
130C4×D4×C11—22no—
131C4×D4×C11D412yes—
132C4×D4×C11D412yes—
133C4×D4×C11D411yescharacteristic
134C4×D4×C11D411yescharacteristic
135C4×D4×C11C2312yes—
136C4×D4×C11C2311yescharacteristic
137C4×D4×C11C2312yes—
138C4×D4×C11C2312yes—
139C4×D4×C11C2312yes—
140C4×D4×C11C2311yescharacteristic
141C4×D4×C11C2312yes—
142C11×#117—21no—
143C11×#117—22no—
144C11×#117—21no—
145C11×#117—22no—
146C11×#117C2312yes—
147C11×#117C2311yescharacteristic
148C11×#117C2311yescharacteristic
149C11×#117C2312yes—
150C2×C11×C4⋊C4—21no—
151C2×C11×C4⋊C4—22no—
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2312yes—
154C2×C11×C22⋊C4—21no—
155C2×C11×C22⋊C4—22no—
156C2×C11×C22⋊C4—22no—
157C2×C11×C22⋊C4—22no—
158C2×C11×C22⋊C4—22no—
159C2×C42×C11—21no—
160C2×C42×C11—22no—
161C2×C42×C11C2311yescharacteristic
162C2×C42×C11C2312yes—
163#67004—28no—
164#66997—22no—
165C2×#4326C2314yes—
166#66989—22no—
167#66988—24no—
168C2×#4324—28no—
169C2×#4324C2314yes—
170C2×#4324C2314yes—
171C2×#4324C2314yes—
172#66979—22no—
173#66979—22no—
174#66979C2312yes—
175C2×C4⋊Dic11—21no—
176C2×C4⋊Dic11—21no—
177#66977—21no—
178#66977—21no—
179#66977—22no—
180#66977—22no—
181#66977C2314yes—
182#66977C2314yes—
183C2×#4318C2312yes—
184C22×C11⋊C8C2312yes—
185#66942—24no—
186#66942—24no—
187#66940—22no—
188#66940—22no—
189#66932—24no—
190#66932—24no—
191#66930—24no—
192#66923—22no—
193#66923—22no—
194#66923C2312yes—
195#66922—21no—
196#66922—21no—
197#66922C2312yes—
198#66922C2312yes—
199#66922C2311yescharacteristic
200#66922C2311yescharacteristic
201C4×Dic22—22no—
202C4×Dic22—22no—
203C4×Dic22—21no—
204C4×Dic22—21no—
205C4×Dic22C2314yes—
206C4×Dic22C2314yes—
207#66899C2312yes—
208#66899C2312yes—
209#66896C2314yes—
210#66896C2314yes—
211#66896C2312yes—
212#66896C2312yes—
213C22⋊(C11⋊C8)C2314yes—
214C22⋊(C11⋊C8)C2314yes—
215#66874C2314yes—
216#66874C2314yes—
217#66874C2314yes—
218#66874C2314yes—
219#66872C2314yes—
220#66872C2312yes—
221#66872C2312yes—
222#66871C2314yes—
223#66871C2312yes—
224#66871C2312yes—
225C4⋊(C11⋊C8)C2311yescharacteristic
226C4⋊(C11⋊C8)C2311yescharacteristic
227C4⋊(C11⋊C8)C2312yes—
228C4⋊(C11⋊C8)C2312yes—
229C4⋊(C11⋊C8)C2312yes—
230#66867C2314yes—
231C4×C11⋊C8C2314yes—
232#60591—111nomaximal, Sylow
233C24×C11—22no—
234C24×C11—21no—
235C11×#41—28no—
236C11×#41—24no—
237C11×#41—24no—
238C11×#41—22no—
239C11×#41—22no—
240C11×#41—22no—
241C11×#41#4114yes—
242C2×Q8×C11C2×D411yescharacteristic
243C2×Q8×C11C2411yescharacteristic
244C2×D4×C11—216no—
245C2×D4×C11—28no—
246C2×D4×C11—22no—
247C2×D4×C11—21no—
248C2×D4×C11—24no—
249C2×D4×C11—24no—
250C2×D4×C11—22no—
251C2×D4×C11—21no—
252C2×D4×C11—22no—
253C2×D4×C11C2×D412yes—
254C2×D4×C11C2×D411yescharacteristic
255C2×D4×C11#4114yes—
256C2×D4×C11C2411yescharacteristic
257C2×D4×C11C2412yes—
258C22×C4×C11—22no—
259C22×C4×C11—21no—
260C22×C4×C11—22no—
261C22×C4×C11—21no—
262C22×C4×C11—21no—
263C22×C4×C11—22no—
264C22×C4×C11—22no—
265C22×C4×C11—21no—
266C22×C4×C11—22no—
267C22×C4×C11—22no—
268C22×C4×C11—22no—
269C22×C4×C11—82no—
270C22×C4×C11—84no—
271C22×C4×C11C2×D411yescharacteristic
272C22×C4×C11C2×D412yes—
273C22×C4×C11C2×D411yescharacteristic
274C22×C4×C11C2×D412yes—
275C22×C4×C11C2412yes—
276C22×C4×C11C2411yescharacteristic
277C22×Dic11—22no—
278C2×Dic22—21no—
279C2×Dic22—21no—
280C2×Dic22—22no—
281C2×Dic22—24no—
282C2×Dic22—24no—
283C2×Dic22C2414yes—
284C11×C4⋊C4—22no—
285C11×C4⋊C4—21no—
286C11×C4⋊C4—22no—
287C11×C4⋊C4—21no—
288C11×C4⋊C4—21no—
289C11×C4⋊C4C2×D411yescharacteristic
290C11×C4⋊C4C2×D411yescharacteristic
291C11×C4⋊C4C2×D412yes—
292C11×C4⋊C4C2×D412yes—
293C11×C4⋊C4C2412yes—
294C11×C4⋊C4C2411yescharacteristic
295C11×C4⋊C4C2411yescharacteristic
296C11×C22⋊C4—22no—
297C11×C22⋊C4—21no—
298C11×C22⋊C4—22no—
299C11×C22⋊C4—21no—
300C11×C22⋊C4—22no—
301C11×C22⋊C4—22no—
302C11×C22⋊C4—22no—
303C11×C22⋊C4—22no—
304C11×C22⋊C4—21no—
305C11×C22⋊C4C2×D412yes—
306C11×C22⋊C4C2×D412yes—
307C11×C22⋊C4C2×D412yes—
308C42×C11—21no—
309C42×C11—22no—
310C42×C11—21no—
311C42×C11—22no—
312C42×C11—21no—
313C42×C11C2×D411yescharacteristic
314C42×C11C2×D411yescharacteristic
315C42×C11C2×D412yes—
316C42×C11C2×D412yes—
317C42×C11C2412yes—
318C42×C11C2411yescharacteristic
319C42×C11C2411yescharacteristic
320C22⋊Dic11—22no—
321C22⋊Dic11—24no—
322C22⋊Dic11—24no—
323#4326—28no—
324#4324—28no—
325#4324—28no—
326#4324—28no—
327C4⋊Dic11—22no—
328C4⋊Dic11—22no—
329C4⋊Dic11—21no—
330C4⋊Dic11—21no—
331C4⋊Dic11—22no—
332C4⋊Dic11—22no—
333C4⋊Dic11C2412yes—
334C4⋊Dic11C2412yes—
335Dic11⋊C4—24no—
336Dic11⋊C4—24no—
337Dic11⋊C4—22no—
338Dic11⋊C4—22no—
339Dic11⋊C4—24no—
340Dic11⋊C4—24no—
341C4×Dic11—22no—
342C4×Dic11—24no—
343C4×Dic11—24no—
344#4318—24no—
345C2×C11⋊C8—24no—
346C2×C11⋊C8C2412yes—
347C2×C11⋊C8C2414yes—
348C2×C11⋊C8C2412yes—
349#3509—111no—
350C4×H(5,𝔽2)D1111yescharacteristic
351#3123—114no—
352#3120—114no—
353#3116—112no—
354#3110—112no—
355#3107—112no—
356#3101—112no—
357#3097—112no—
358#3077—111no—
359#3076—111no—
360#3039—111no—
361C2×#461—111no—
362#3009—112no—
363#2949—112no—
364#2947—112no—
365#2925—111no—
366C23×C11—28no—
367C23×C11—22no—
368C23×C11—21no—
369C23×C11—24no—
370C23×C11—81no—
371C23×C11—82no—
372C23×C11—81no—
373C23×C11—82no—
374C23×C11C22×D412yes—
375C23×C11C22×D411yescharacteristic
376Q8×C11—22no—
377Q8×C11—21no—
378Q8×C11C2×#4112yes—
379D4×C11—28no—
380D4×C11—28no—
381D4×C11—24no—
382D4×C11—24no—
383D4×C11—22no—
384D4×C11—24no—
385D4×C11—22no—
386D4×C11—21no—
387D4×C11C2×#4112yes—
388D4×C11C2×#4114yes—
389C2×C4×C11—28no—
390C2×C4×C11—21no—
391C2×C4×C11—24no—
392C2×C4×C11—22no—
393C2×C4×C11—24no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—21no—
397C2×C4×C11—22no—
398C2×C4×C11—21no—
399C2×C4×C11—41no—
400C2×C4×C11—42no—
401C2×C4×C11—44no—
402C2×C4×C11—42no—
403C2×C4×C11—82no—
404C2×C4×C11—81no—
405C2×C4×C11—82no—
406C2×C4×C11—82no—
407C2×C4×C11—82no—
408C2×C4×C11—81no—
409C2×C4×C11—82no—
410C2×C4×C11C22×D412yes—
411C2×C4×C11C22×D412yes—
412C2×C4×C11C22×D412yes—
413C2×C4×C11C22×D411yescharacteristic
414C2×C4×C11C22×D411yescharacteristic
415C2×C4×C11C22×D411yescharacteristic
416C2×C4×C11C22×D411yescharacteristic
417C2×C4×C11C22×D411yescharacteristic
418C2×C4×C11C2×#4112yes—
419C2×C4×C11C2×#4112yes—
420C2×C4×C11C2511yescharacteristic
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—24no—
424C2×Dic11—44no—
425Dic22—24no—
426Dic22—24no—
427Dic22—42no—
428Dic22—44no—
429Dic22—42no—
430C11⋊C8—22no—
431C11⋊C8—22no—
432C11⋊C8—24no—
433C2×H(5,𝔽2)C2×D1111yescharacteristic
434C2×#137—112no—
435C22×SD16—112no—
436#557—221no—
437#557—221no—
438#556—221no—
439#556—221no—
440#552—222no—
441#552—222no—
442#541—114no—
443#536—112no—
444#533—111no—
445#533—112no—
446#533—112no—
447C2×C4⋊Q8—111no—
448#520—21no—
449#520C2×D1112yes—
450#520C2×D1111yescharacteristic
451#520C2×D1111yescharacteristic
452#519—112no—
453#518—22no—
454#518—21no—
455#518C2×D1112yes—
456#518C2×D1111yescharacteristic
457C4×#41—21no—
458C4×#41C2×D1111yescharacteristic
459C4×#41C2×D1112yes—
460C4×#41C2×D1111yescharacteristic
461C2×C4×D4—22no—
462C2×C4×D4—21no—
463C2×C4×D4C2×D1111yescharacteristic
464C2×C4×D4C2×D1112yes—
465#485—114no—
466#485—114no—
467#484—114no—
468#483—114no—
469#479—112no—
470#478—112no—
471#478—114no—
472#477—111no—
473#476—111no—
474#476—112no—
475#475—111no—
476#474—111no—
477#474—112no—
478#462—112no—
479#462—112no—
480#461—112no—
481#461—112no—
482#461—112no—
483#461—114no—
484#461—112no—
485#452—114no—
486#452—114no—
487#450—114no—
488#450—114no—
489#441—114no—
490#440—114no—
491#440—114no—
492#440—114no—
493C4×Q16—114no—
494C4×SD16—114no—
495C4×SD16—114no—
496C4×SD16—114no—
497#433—114no—
498#432—112no—
499#431—112no—
500#428—112no—
501#427—112no—
502#423—111no—
503C2×C4⋊C8—111no—
504#419—112no—
505#418—112no—
506#416—112no—
507C2×#103—112no—
508#408—112no—
509#405—112no—
510C22×C11—21no—
511C22×C11—21no—
512C22×C11—22no—
513C22×C11—22no—
514C22×C11—24no—
515C22×C11—22no—
516C22×C11—22no—
517C22×C11—42no—
518C22×C11—41no—
519C22×C11—42no—
520C22×C11—41no—
521C22×C11—84no—
522C22×C11—88no—
523C22×C11#52512yes—
524C22×C11C23×D411yescharacteristic
525C4×C11—21no—
526C4×C11—22no—
527C4×C11—21no—
528C4×C11—22no—
529C4×C11—22no—
530C4×C11—22no—
531C4×C11—21no—
532C4×C11—41no—
533C4×C11—42no—
534C4×C11—41no—
535C4×C11#52512yes—
536C4×C11#57712yes—
537C4×C11C22×#4111yescharacteristic
538C4×C11C22×#4111yescharacteristic
539Dic11—42no—
540Dic11—44no—
541Dic11—42no—
542H(5,𝔽2)—24no—
543H(5,𝔽2)—24no—
544C2×#41—21no—
545C2×#41C22×D1112yes—
546C2×#41C22×D1111yescharacteristic
547C2×#41C22×D1111yescharacteristic
548C22×Q8—112no—
549C22×D4—22no—
550C22×D4—21no—
551C22×D4C22×D1112yes—
552C22×D4C22×D1111yescharacteristic
553C23×C4—21no—
554C23×C4—22no—
555#137—228no—
556C2×Q16—114no—
557C2×SD16—114no—
558C2×SD16—114no—
559C2×SD16—114no—
560C2×SD16—228no—
561C2×M16—112no—
562C22×C8—112no—
563C4⋊Q8—111no—
564C4⋊Q8—111no—
565C4⋊Q8—112no—
566C4⋊Q8—112no—
567C4⋊Q8—222no—
568C4⋊Q8—221no—
569C4⋊Q8—221no—
570#126—224no—
571#126—224no—
572#125—112no—
573#125—224no—
574#125—224no—
575#125—222no—
576#125—222no—
577#124—222no—
578#123—224no—
579C22⋊Q8—114no—
580C22⋊Q8—114no—
581C22⋊Q8—221no—
582C22⋊Q8—221no—
583C22⋊Q8—222no—
584C22⋊Q8—222no—
585C4×Q8—21no—
586C4×Q8—114no—
587C4×Q8—114no—
588C4×Q8—222no—
589C4×Q8—222no—
590C4×Q8—222no—
591C4×Q8—222no—
592C4×Q8—221no—
593C4×Q8—221no—
594C4×Q8C22⋊D1111yescharacteristic
595C4×Q8C22⋊D1111yescharacteristic
596C4×Q8C22×D1111yescharacteristic
597C4×Q8C22×D1112yes—
598C4×Q8C22×D1111yescharacteristic
599C4×D4—22no—
600C4×D4—21no—
601C4×D4—21no—
602C4×D4—22no—
603C4×D4—21no—
604C4×D4—22no—
605C4×D4—21no—
606C4×D4—22no—
607C4×D4—21no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—21no—
614C4×D4—22no—
615C4×D4—21no—
616C4×D4C22⋊D1112yes—
617C4×D4C22⋊D1111yescharacteristic
618C4×D4C22⋊D1112yes—
619C4×D4C22⋊D1111yescharacteristic
620C4×D4C22×D1112yes—
621C4×D4C22×D1111yescharacteristic
622C4×D4C22×D1112yes—
623C4×D4C22×D1112yes—
624C4×D4C22×D1112yes—
625C4×D4C22×D1112yes—
626C4×D4C22×D1111yescharacteristic
627#117—21no—
628#117—22no—
629#117—22no—
630#117—21no—
631#117—112no—
632#117—222no—
633#117—222no—
634#117—224no—
635#117C22×D1111yescharacteristic
636#117C22×D1112yes—
637#117C22×D1111yescharacteristic
638#117C22×D1112yes—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—221no—
642C2×C4⋊C4—221no—
643C2×C4⋊C4C22×D1111yescharacteristic
644C2×C4⋊C4C22×D1112yes—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—22no—
650C2×C42—22no—
651C2×C42—21no—
652C2×C42C22×D1111yescharacteristic
653C2×C42C22×D1112yes—
654#107—112no—
655#107—112no—
656#107—114no—
657#106—112no—
658#106—112no—
659#106—114no—
660C4⋊C8—111no—
661C4⋊C8—111no—
662C4⋊C8—112no—
663C4⋊C8—112no—
664C4⋊C8—112no—
665#103—112no—
666#103—112no—
667#103—114no—
668#103—114no—
669#103—114no—
670#103—114no—
671#102—112no—
672#102—112no—
673#102—114no—
674#102—114no—
675C22⋊C8—114no—
676C22⋊C8—114no—
677#97—114no—
678C4×C8—114no—
679C2×C11—22no—
680C2×C11—42no—
681C2×C11—44no—
682C2×C11—42no—
683C2×C11C2×#52511yescharacteristic
684C2×C11C2×#57711yescharacteristic
685C2×C11#358611yescharacteristic
686C24—22no—
687C24—21no—
688#41—28no—
689#41—24no—
690#41—24no—
691#41—22no—
692#41—22no—
693#41—22no—
694#41#433914yes—
695C2×Q8—114no—
696C2×Q8—221no—
697C2×Q8—221no—
698C2×Q8—222no—
699C2×Q8—224no—
700C2×Q8—224no—
701C2×Q8C2×C22⋊D1111yescharacteristic
702C2×Q8C23×D1111yescharacteristic
703C2×D4—216no—
704C2×D4—28no—
705C2×D4—22no—
706C2×D4—21no—
707C2×D4—24no—
708C2×D4—24no—
709C2×D4—22no—
710C2×D4—22no—
711C2×D4—21no—
712C2×D4#433914yes—
713C2×D4C2×C22⋊D1112yes—
714C2×D4C2×C22⋊D1111yescharacteristic
715C2×D4C23×D1111yescharacteristic
716C2×D4C23×D1112yes—
717C22×C4—22no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—21no—
721C22×C4—22no—
722C22×C4—21no—
723C22×C4—22no—
724C22×C4—21no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—82no—
729C22×C4—84no—
730C22×C4—222no—
731C22×C4C2×C22⋊D1111yescharacteristic
732C22×C4C2×C22⋊D1112yes—
733C22×C4C2×C22⋊D1111yescharacteristic
734C22×C4C2×C22⋊D1112yes—
735C22×C4C23×D1112yes—
736C22×C4C23×D1111yescharacteristic
737Q16—228no—
738SD16—228no—
739SD16—228no—
740SD16—228no—
741M16—224no—
742C2×C8—112no—
743C2×C8—114no—
744C2×C8—112no—
745C2×C8—224no—
746C4⋊C4—22no—
747C4⋊C4—21no—
748C4⋊C4—22no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—112no—
752C4⋊C4—112no—
753C4⋊C4—222no—
754C4⋊C4—222no—
755C4⋊C4—222no—
756C4⋊C4—222no—
757C4⋊C4—221no—
758C4⋊C4—221no—
759C4⋊C4—224no—
760C4⋊C4—224no—
761C4⋊C4—224no—
762C4⋊C4—224no—
763C4⋊C4—222no—
764C4⋊C4—222no—
765C4⋊C4C2×C22⋊D1111yescharacteristic
766C4⋊C4C2×C22⋊D1112yes—
767C4⋊C4C2×C22⋊D1111yescharacteristic
768C4⋊C4C2×C22⋊D1112yes—
769C4⋊C4C23×D1112yes—
770C4⋊C4C23×D1111yescharacteristic
771C4⋊C4C23×D1111yescharacteristic
772C22⋊C4—22no—
773C22⋊C4—21no—
774C22⋊C4—22no—
775C22⋊C4—21no—
776C22⋊C4—22no—
777C22⋊C4—22no—
778C22⋊C4—22no—
779C22⋊C4—22no—
780C22⋊C4—21no—
781C22⋊C4—222no—
782C22⋊C4—224no—
783C22⋊C4—224no—
784C22⋊C4C2×C22⋊D1112yes—
785C22⋊C4C2×C22⋊D1112yes—
786C22⋊C4C2×C22⋊D1112yes—
787C42—21no—
788C42—22no—
789C42—21no—
790C42—22no—
791C42—21no—
792C42—222no—
793C42—224no—
794C42—224no—
795C42C2×C22⋊D1112yes—
796C42C2×C22⋊D1111yescharacteristic
797C42C2×C22⋊D1112yes—
798C42C2×C22⋊D1111yescharacteristic
799C42C23×D1112yes—
800C42C23×D1111yescharacteristic
801C42C23×D1111yescharacteristic
802C11#6059111yescharacteristic, complemented, Sylow
803C23—28no—
804C23—22no—
805C23—21no—
806C23—24no—
807C23—81no—
808C23—82no—
809C23—81no—
810C23—82no—
811C23C22×C22⋊D1112yes—
812C23C22×C22⋊D1111yescharacteristic
813Q8—22no—
814Q8—21no—
815Q8—224no—
816Q8—224no—
817Q8—442no—
818Q8—444no—
819Q8—442no—
820Q8C2×#433912yes—
821D4—28no—
822D4—28no—
823D4—24no—
824D4—24no—
825D4—24no—
826D4—22no—
827D4—22no—
828D4—21no—
829D4C2×#433912yes—
830D4C2×#433914yes—
831C2×C4—28no—
832C2×C4—21no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—24no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—41no—
842C2×C4—42no—
843C2×C4—44no—
844C2×C4—42no—
845C2×C4—82no—
846C2×C4—81no—
847C2×C4—82no—
848C2×C4—82no—
849C2×C4—82no—
850C2×C4—81no—
851C2×C4—82no—
852C2×C4—222no—
853C2×C4—222no—
854C2×C4—224no—
855C2×C4—444no—
856C2×C4C2×#433912yes—
857C2×C4C2×#433912yes—
858C2×C4C22×C22⋊D1112yes—
859C2×C4C22×C22⋊D1112yes—
860C2×C4C22×C22⋊D1111yescharacteristic
861C2×C4C22×C22⋊D1112yes—
862C2×C4C22×C22⋊D1111yescharacteristic
863C2×C4C22×C22⋊D1111yescharacteristic
864C2×C4C22×C22⋊D1111yescharacteristic
865C2×C4C22×C22⋊D1111yescharacteristic
866C2×C4C24×D1111yescharacteristic
867C8—222no—
868C8—222no—
869C8—224no—
870C22—21no—
871C22—21no—
872C22—22no—
873C22—24no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—42no—
878C22—41no—
879C22—42no—
880C22—41no—
881C22—84no—
882C22—88no—
883C22#1062332212yes—
884C22C23×C22⋊D1111yescharacteristic
885C4—22no—
886C4—22no—
887C4—21no—
888C4—22no—
889C4—21no—
890C4—22no—
891C4—21no—
892C4—41no—
893C4—42no—
894C4—41no—
895C4—444no—
896C4—442no—
897C4—442no—
898C4#1062332212yes—
899C4#1062336712yes—
900C4C22×#433911yescharacteristic
901C4C22×#433911yescharacteristic
902C2—22no—
903C2—42no—
904C2—44no—
905C2—42no—
906C2C2×#1062332211yescharacteristic
907C2C2×#1062336711yescharacteristic
908C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC4×C11×H(5,𝔽2)C2
socleC22×C11C23×D4
prime radicalC2×C11×H(5,𝔽2)C22
hypercenterC4×H(5,𝔽2)D11
hypocenterC11#60591
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ C4×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #13082502C2semidirect
2. #13078868C2semidirect
3. #13078830C2semidirect
4. #13078778C2semidirect
5. #13078715C2semidirect
6. #13078687C2semidirect
7. #13078624C2semidirect
8. #13078585C2semidirect
9. #13078413C2semidirect
10. #13078404C2semidirect
11. #13078103C2semidirect
12. C2×#10622632C2semidirect
14. #13077473C2semidirect
15. #13077455C2semidirect
16. #13077282C2semidirect
44. #10623049C22semidirect
45. #10623047C22semidirect
46. #10623001C22semidirect
47. #10623001C22semidirect
48. #10623001C22semidirect
49. C2×#66922C22semidirect
57. #10622644C22semidirect
58. #10622644C22semidirect
59. #10622643C22semidirect
60. C4×#4326C22semidirect
61. #10622635C22semidirect
62. #10622634C22semidirect
63. #10622633C22semidirect
64. #10622632C22semidirect
65. #10622632C22semidirect
66. #10622632C22semidirect
67. #10622632C22semidirect
68. #10622632C22semidirect
69. #10622631C22semidirect
70. #10622631C22semidirect
71. #10622631C22semidirect
72. C4×#4324C22semidirect
73. C4×#4324C22semidirect
74. C4×#4324C22semidirect
75. #10622622C22semidirect
76. #10622622C22semidirect
77. #10622621C22semidirect
78. #10622621C22semidirect
79. #10622620C22semidirect
80. #10622620C22semidirect
81. #10622617C22semidirect
82. #10622613C22semidirect
83. #10622611C22semidirect
84. #10622610C22semidirect
85. #10622609C22semidirect
86. #10622609C22semidirect
87. #10622584C22semidirect
88. #10622583C22semidirect
89. C2×#66874C22semidirect
90. #10622577C22semidirect
91. #10622539C22semidirect
92. #10622538C22semidirect
93. #10622537C22semidirect
94. C2×C4⋊(C11⋊C8)C22semidirect
802. C11#60591semidirect

Maximal subgroups

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

subgroupindex
#130825022
#130788682
#130788302
#130787782
#130787152
#130786872
#130786242
#130785852
#130784132
#130784042
#130781032
C2×#106226322
#130778932
#130774732
#130774552
#130772822
C4×C11×H(5,𝔽2)2
#6059111