Finite Group Databasebeta

← #15622814

Subgroups — #15622814

Order 2816.

1990 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082502C211yesmaximal, characteristic, complemented
2#13078916C214yesmaximal, complemented
3#13078830C214yesmaximal, complemented
4#13078778C212yesmaximal, complemented
5#13078746C212yesmaximal, complemented
6#13078687C212yesmaximal, complemented
7#13078655C212yesmaximal, complemented
8#13078585C212yesmaximal, complemented
9#13078421C211yesmaximal, characteristic, complemented
10#13078404C211yesmaximal, characteristic, complemented
11#13078103C211yesmaximal, characteristic, complemented
12C2×#10622644C211yesmaximal, characteristic, complemented
13#13077911C212yesmaximal
14#13077482C212yesmaximal, complemented
15#13077455C212yesmaximal, complemented
16#13077282C211yesmaximal, characteristic, complemented
17C4×C11×2−1+4C211yesmaximal, characteristic
18C2×C11×2−1+4C2211yescharacteristic
19C11×#520—22no—
20C11×#520—21no—
21C11×#520C2212yes—
22C11×#520C2211yescharacteristic
23C11×#520C2211yescharacteristic
24C11×#519—21no—
25C11×#519C2212yes—
26C11×#519C2211yescharacteristic
27C4×C11×#41—22no—
28C4×C11×#41—21no—
29C4×C11×#41C2211yescharacteristic
30C4×C11×#41C2212yes—
31C4×C11×#41C2211yescharacteristic
32C2×C4×Q8×C11—21no—
33C2×C4×Q8×C11C2211yescharacteristic
34C2×C4×Q8×C11C2212yes—
35#10623356C2212yes—
36C2×#67004C2212yes—
37C22×#4326C2212yes—
38#10623098—21no—
39#10623098—21no—
40#10623073—21no—
41#10623073—21no—
42#10623072—22no—
43#10623072—22no—
44#10623049C2214yes—
45#10623047C2212yes—
46#10623001C2211yescharacteristic
47#10623001C2212yes—
48#10623001C2212yes—
49C2×#66922C2211yescharacteristic
50#10622852C2214yes—
51#10622852C2214yes—
52#10622847C2212yes—
53#10622846C2212yes—
54#10622841C2214yes—
55#10622841C2214yes—
56#10622838C2212yes—
57#10622644C2214yes—
58#10622644C2212yes—
59#10622644C2212yes—
60#10622644C2212yes—
61#10622644C2212yes—
62#10622643C2214yes—
63#10622643C2214yes—
64#10622643C2214yes—
65C4×#4326C2214yes—
66C4×#4326C2214yes—
67C4×#4326C2214yes—
68#10622635C2214yes—
69#10622635C2212yes—
70#10622634C2211yescharacteristic
71#10622634C2212yes—
72#10622633C2211yescharacteristic
73#10622633C2212yes—
74#10622632C2212yes—
75#10622632C2212yes—
76#10622631C2214yes—
77C4×#4324C2214yes—
78#10622622C2212yes—
79#10622621C2211yescharacteristic
80#10622620C2211yescharacteristic
81#10622617C2212yes—
82#10622613C2214yes—
83#10622611C2212yes—
84#10622610C2212yes—
85#10622609C2214yes—
86#10622609C2214yes—
87#10622584C2214yes—
88#10622583C2214yes—
89C2×#66874C2212yes—
90#10622577C2212yes—
91#10622539C2212yes—
92#10622538C2212yes—
93#10622537C2211yescharacteristic
94C2×C4⋊(C11⋊C8)C2211yescharacteristic
95C11×2−1+4—24no—
96C11×2−1+4—24no—
97C2×C11×#41—22no—
98C2×C11×#41—21no—
99C2×C11×#41C2312yes—
100C2×C11×#41C2311yescharacteristic
101C2×C11×#41C2311yescharacteristic
102C22×Q8×C11—21no—
103C22×Q8×C11C2312yes—
104C22×Q8×C11C2311yescharacteristic
105C22×Dic22C2312yes—
106C4×Q8×C11—21no—
107C4×Q8×C11—21no—
108C4×Q8×C11—22no—
109C4×Q8×C11—21no—
110C4×Q8×C11—22no—
111C4×Q8×C11—21no—
112C4×Q8×C11—22no—
113C4×Q8×C11—21no—
114C4×Q8×C11—22no—
115C4×Q8×C11D411yescharacteristic
116C4×Q8×C11D411yescharacteristic
117C4×Q8×C11C2312yes—
118C4×Q8×C11C2311yescharacteristic
119C4×Q8×C11C2312yes—
120C4×Q8×C11C2312yes—
121C4×Q8×C11C2312yes—
122C4×Q8×C11C2311yescharacteristic
123C4×Q8×C11C2312yes—
124C4×D4×C11—22no—
125C4×D4×C11—21no—
126C4×D4×C11—21no—
127C4×D4×C11—22no—
128C4×D4×C11—21no—
129C4×D4×C11—22no—
130C4×D4×C11—22no—
131C4×D4×C11—22no—
132C4×D4×C11—22no—
133C4×D4×C11D412yes—
134C4×D4×C11D412yes—
135C4×D4×C11D411yescharacteristic
136C4×D4×C11D411yescharacteristic
137C4×D4×C11C2311yescharacteristic
138C4×D4×C11C2311yescharacteristic
139C4×D4×C11C2312yes—
140C11×#117—21no—
141C11×#117—22no—
142C11×#117—22no—
143C11×#117—22no—
144C11×#117—22no—
145C11×#117—21no—
146C11×#117—22no—
147C11×#117C2312yes—
148C11×#117C2311yescharacteristic
149C11×#117C2311yescharacteristic
150C11×#117C2312yes—
151C2×C11×C4⋊C4—21no—
152C2×C11×C4⋊C4—22no—
153C2×C11×C4⋊C4—21no—
154C2×C11×C4⋊C4—22no—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2312yes—
157C2×C42×C11—21no—
158C2×C42×C11—22no—
159C2×C42×C11—21no—
160C2×C42×C11—22no—
161C2×C42×C11C2311yescharacteristic
162C2×C42×C11C2312yes—
163#67004—28no—
164#66997—22no—
165C2×#4326—28no—
166C2×#4326C2314yes—
167C2×#4326C2314yes—
168C2×#4326C2314yes—
169#66989—22no—
170#66988—24no—
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#66899C2314yes—
208#66899C2314yes—
209#66899C2312yes—
210#66899C2312yes—
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#60594—111nomaximal, Sylow
233C11×#41—216no—
234C11×#41—28no—
235C11×#41—24no—
236C11×#41—24no—
237C11×#41—22no—
238C11×#41—22no—
239C11×#41—22no—
240C11×#41#4114yes—
241C2×Q8×C11—28no—
242C2×Q8×C11—24no—
243C2×Q8×C11—24no—
244C2×Q8×C11—22no—
245C2×Q8×C11—21no—
246C2×Q8×C11—22no—
247C2×Q8×C11C2×D411yescharacteristic
248C2×Q8×C11#4114yes—
249C2×Q8×C11C2411yescharacteristic
250C2×Q8×C11C2412yes—
251C2×D4×C11—22no—
252C2×D4×C11—21no—
253C2×D4×C11C2×D412yes—
254C2×D4×C11C2×D411yescharacteristic
255C2×D4×C11C2411yescharacteristic
256C22×C4×C11—22no—
257C22×C4×C11—21no—
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—21no—
265C22×C4×C11C2×D411yescharacteristic
266C22×C4×C11C2×D412yes—
267C22×C4×C11C2×D411yescharacteristic
268C22×C4×C11C2×D412yes—
269C22×C4×C11C2412yes—
270C22×C4×C11C2411yescharacteristic
271C22×Dic11—22no—
272C2×Dic22—21no—
273C2×Dic22—21no—
274C2×Dic22—22no—
275C2×Dic22—24no—
276C2×Dic22—24no—
277C2×Dic22C2414yes—
278C11×C4⋊C4—22no—
279C11×C4⋊C4—22no—
280C11×C4⋊C4—22no—
281C11×C4⋊C4—22no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4—22no—
284C11×C4⋊C4—21no—
285C11×C4⋊C4—22no—
286C11×C4⋊C4—21no—
287C11×C4⋊C4C2×D411yescharacteristic
288C11×C4⋊C4C2×D411yescharacteristic
289C11×C4⋊C4C2×D412yes—
290C11×C4⋊C4C2×D412yes—
291C11×C4⋊C4C2412yes—
292C11×C4⋊C4C2411yescharacteristic
293C11×C4⋊C4C2411yescharacteristic
294C11×C22⋊C4—22no—
295C11×C22⋊C4—21no—
296C11×C22⋊C4—21no—
297C11×C22⋊C4—22no—
298C11×C22⋊C4—21no—
299C11×C22⋊C4C2×D412yes—
300C11×C22⋊C4C2×D412yes—
301C11×C22⋊C4C2×D412yes—
302C42×C11—22no—
303C42×C11—21no—
304C42×C11—22no—
305C42×C11—21no—
306C42×C11—22no—
307C42×C11—22no—
308C42×C11—22no—
309C42×C11—22no—
310C42×C11—21no—
311C42×C11C2×D411yescharacteristic
312C42×C11C2×D411yescharacteristic
313C42×C11C2×D412yes—
314C42×C11C2×D412yes—
315C42×C11C2412yes—
316C42×C11C2411yescharacteristic
317C42×C11C2411yescharacteristic
318C22⋊Dic11—22no—
319C22⋊Dic11—24no—
320C22⋊Dic11—24no—
321#4326—28no—
322#4326—28no—
323#4326—28no—
324#4324—28no—
325C4⋊Dic11—22no—
326C4⋊Dic11—22no—
327C4⋊Dic11—21no—
328C4⋊Dic11—21no—
329C4⋊Dic11—22no—
330C4⋊Dic11—22no—
331C4⋊Dic11C2412yes—
332C4⋊Dic11C2412yes—
333Dic11⋊C4—24no—
334Dic11⋊C4—24no—
335Dic11⋊C4—22no—
336Dic11⋊C4—22no—
337Dic11⋊C4—24no—
338Dic11⋊C4—24no—
339C4×Dic11—22no—
340C4×Dic11—24no—
341C4×Dic11—24no—
342#4318—24no—
343C2×C11⋊C8—24no—
344C2×C11⋊C8C2412yes—
345C2×C11⋊C8C2414yes—
346C2×C11⋊C8C2412yes—
347#3509—111no—
348C4×2−1+4D1111yescharacteristic
349#3127—114no—
350#3120—114no—
351#3116—112no—
352#3113—112no—
353#3107—112no—
354#3104—112no—
355#3097—112no—
356#3078—111no—
357#3076—111no—
358#3039—111no—
359C2×#462—111no—
360#3011—112no—
361#2950—112no—
362#2947—112no—
363#2925—111no—
364C23×C11—21no—
365C23×C11C22×D412yes—
366C23×C11C22×D411yescharacteristic
367Q8×C11—28no—
368Q8×C11—22no—
369Q8×C11—24no—
370Q8×C11—21no—
371Q8×C11—22no—
372Q8×C11C2×#4112yes—
373Q8×C11C2×#4114yes—
374D4×C11—28no—
375D4×C11—24no—
376D4×C11—24no—
377D4×C11—22no—
378D4×C11—21no—
379D4×C11C2×#4112yes—
380C2×C4×C11—28no—
381C2×C4×C11—28no—
382C2×C4×C11—24no—
383C2×C4×C11—22no—
384C2×C4×C11—21no—
385C2×C4×C11—24no—
386C2×C4×C11—22no—
387C2×C4×C11—24no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—21no—
391C2×C4×C11—21no—
392C2×C4×C11—22no—
393C2×C4×C11—41no—
394C2×C4×C11—42no—
395C2×C4×C11—42no—
396C2×C4×C11—82no—
397C2×C4×C11—81no—
398C2×C4×C11—81no—
399C2×C4×C11—82no—
400C2×C4×C11C22×D412yes—
401C2×C4×C11C22×D412yes—
402C2×C4×C11C22×D412yes—
403C2×C4×C11C22×D411yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D411yescharacteristic
406C2×C4×C11C22×D411yescharacteristic
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11C2×#4112yes—
409C2×C4×C11C2×#4112yes—
410C2×C4×C11C2511yescharacteristic
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—24no—
414C2×Dic11—44no—
415Dic22—24no—
416Dic22—24no—
417Dic22—42no—
418Dic22—44no—
419Dic22—42no—
420C11⋊C8—22no—
421C11⋊C8—22no—
422C11⋊C8—24no—
423C2×2−1+4C2×D1111yescharacteristic
424C2×#137—112no—
425C22×Q16—112no—
426#557—221no—
427#557—221no—
428#556—221no—
429#556—221no—
430#552—222no—
431#552—222no—
432#541—114no—
433#536—112no—
434#533—111no—
435#533—112no—
436#533—112no—
437C2×C4⋊Q8—111no—
438#520—22no—
439#520—21no—
440#520C2×D1112yes—
441#520C2×D1111yescharacteristic
442#520C2×D1111yescharacteristic
443#519—21no—
444#519—112no—
445#519C2×D1112yes—
446#519C2×D1111yescharacteristic
447C4×#41—22no—
448C4×#41—21no—
449C4×#41C2×D1111yescharacteristic
450C4×#41C2×D1112yes—
451C4×#41C2×D1111yescharacteristic
452C2×C4×Q8—21no—
453C2×C4×Q8C2×D1111yescharacteristic
454C2×C4×Q8C2×D1112yes—
455#485—114no—
456#485—114no—
457#484—114no—
458#483—114no—
459#479—112no—
460#479—114no—
461#478—112no—
462#477—111no—
463#477—112no—
464#476—111no—
465#475—111no—
466#475—112no—
467#474—111no—
468#462—112no—
469#462—112no—
470#462—112no—
471#462—114no—
472#462—112no—
473#461—112no—
474#461—112no—
475#452—114no—
476#452—114no—
477#451—114no—
478#451—114no—
479#441—114no—
480#441—114no—
481#441—114no—
482#440—114no—
483C4×Q16—114no—
484C4×Q16—114no—
485C4×Q16—114no—
486C4×SD16—114no—
487#433—114no—
488#432—112no—
489#431—112no—
490#428—112no—
491#427—112no—
492#423—111no—
493C2×C4⋊C8—111no—
494#419—112no—
495#419—112no—
496#416—112no—
497C2×#103—112no—
498#408—112no—
499#405—112no—
500C22×C11—21no—
501C22×C11—21no—
502C22×C11—22no—
503C22×C11—22no—
504C22×C11—22no—
505C22×C11—22no—
506C22×C11—41no—
507C22×C11—41no—
508C22×C11#52512yes—
509C22×C11C23×D411yescharacteristic
510C4×C11—21no—
511C4×C11—22no—
512C4×C11—21no—
513C4×C11—24no—
514C4×C11—22no—
515C4×C11—22no—
516C4×C11—22no—
517C4×C11—21no—
518C4×C11—42no—
519C4×C11—41no—
520C4×C11—41no—
521C4×C11#52512yes—
522C4×C11#57812yes—
523C4×C11C22×#4111yescharacteristic
524C4×C11C22×#4111yescharacteristic
525Dic11—42no—
526Dic11—44no—
527Dic11—42no—
5282−1+4—24no—
5292−1+4—24no—
530C2×#41—22no—
531C2×#41—21no—
532C2×#41C22×D1112yes—
533C2×#41C22×D1111yescharacteristic
534C2×#41C22×D1111yescharacteristic
535C22×Q8—21no—
536C22×Q8—112no—
537C22×Q8C22×D1112yes—
538C22×Q8C22×D1111yescharacteristic
539#137—228no—
540C2×Q16—114no—
541C2×Q16—114no—
542C2×Q16—114no—
543C2×Q16—228no—
544C2×SD16—114no—
545C2×M16—112no—
546C22×C8—112no—
547C4⋊Q8—111no—
548C4⋊Q8—111no—
549C4⋊Q8—112no—
550C4⋊Q8—112no—
551C4⋊Q8—222no—
552C4⋊Q8—221no—
553C4⋊Q8—221no—
554#126—224no—
555#126—224no—
556#125—112no—
557#125—224no—
558#125—224no—
559#125—222no—
560#125—222no—
561#124—222no—
562#123—224no—
563C22⋊Q8—114no—
564C22⋊Q8—114no—
565C22⋊Q8—221no—
566C22⋊Q8—221no—
567C22⋊Q8—222no—
568C22⋊Q8—222no—
569C4×Q8—21no—
570C4×Q8—21no—
571C4×Q8—22no—
572C4×Q8—21no—
573C4×Q8—22no—
574C4×Q8—22no—
575C4×Q8—21no—
576C4×Q8—22no—
577C4×Q8—21no—
578C4×Q8—114no—
579C4×Q8—114no—
580C4×Q8—222no—
581C4×Q8—222no—
582C4×Q8—222no—
583C4×Q8—222no—
584C4×Q8—221no—
585C4×Q8—221no—
586C4×Q8C22⋊D1111yescharacteristic
587C4×Q8C22⋊D1111yescharacteristic
588C4×Q8C22×D1112yes—
589C4×Q8C22×D1111yescharacteristic
590C4×Q8C22×D1112yes—
591C4×Q8C22×D1112yes—
592C4×Q8C22×D1112yes—
593C4×Q8C22×D1112yes—
594C4×Q8C22×D1111yescharacteristic
595C4×D4—22no—
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—22no—
599C4×D4—21no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4C22⋊D1112yes—
605C4×D4C22⋊D1111yescharacteristic
606C4×D4C22⋊D1112yes—
607C4×D4C22⋊D1111yescharacteristic
608C4×D4C22×D1111yescharacteristic
609C4×D4C22×D1112yes—
610C4×D4C22×D1111yescharacteristic
611#117—21no—
612#117—22no—
613#117—22no—
614#117—22no—
615#117—22no—
616#117—22no—
617#117—21no—
618#117—112no—
619#117—222no—
620#117—222no—
621#117—224no—
622#117C22×D1111yescharacteristic
623#117C22×D1112yes—
624#117C22×D1111yescharacteristic
625#117C22×D1112yes—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4—221no—
631C2×C4⋊C4—221no—
632C2×C4⋊C4C22×D1111yescharacteristic
633C2×C4⋊C4C22×D1112yes—
634C2×C42—21no—
635C2×C42—22no—
636C2×C42—22no—
637C2×C42—21no—
638C2×C42C22×D1111yescharacteristic
639C2×C42C22×D1112yes—
640#107—112no—
641#107—112no—
642#107—114no—
643#106—112no—
644#106—112no—
645#106—114no—
646C4⋊C8—111no—
647C4⋊C8—111no—
648C4⋊C8—112no—
649C4⋊C8—112no—
650C4⋊C8—112no—
651#103—112no—
652#103—112no—
653#103—114no—
654#103—114no—
655#103—114no—
656#103—114no—
657#103—114no—
658#103—114no—
659#102—112no—
660#102—112no—
661C22⋊C8—114no—
662C22⋊C8—114no—
663#97—114no—
664C4×C8—114no—
665C2×C11—22no—
666C2×C11—42no—
667C2×C11—42no—
668C2×C11C2×#52511yescharacteristic
669C2×C11C2×#57811yescharacteristic
670C2×C11#358611yescharacteristic
671#41—216no—
672#41—28no—
673#41—24no—
674#41—24no—
675#41—22no—
676#41—22no—
677#41—22no—
678#41#433914yes—
679C2×Q8—28no—
680C2×Q8—24no—
681C2×Q8—24no—
682C2×Q8—22no—
683C2×Q8—22no—
684C2×Q8—21no—
685C2×Q8—114no—
686C2×Q8—221no—
687C2×Q8—221no—
688C2×Q8—222no—
689C2×Q8—224no—
690C2×Q8—224no—
691C2×Q8#433914yes—
692C2×Q8C2×C22⋊D1111yescharacteristic
693C2×Q8C23×D1111yescharacteristic
694C2×Q8C23×D1112yes—
695C2×D4—22no—
696C2×D4—21no—
697C2×D4C2×C22⋊D1112yes—
698C2×D4C2×C22⋊D1111yescharacteristic
699C2×D4C23×D1111yescharacteristic
700C22×C4—22no—
701C22×C4—21no—
702C22×C4—22no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—22no—
708C22×C4—21no—
709C22×C4—222no—
710C22×C4C2×C22⋊D1111yescharacteristic
711C22×C4C2×C22⋊D1112yes—
712C22×C4C2×C22⋊D1111yescharacteristic
713C22×C4C2×C22⋊D1112yes—
714C22×C4C23×D1112yes—
715C22×C4C23×D1111yescharacteristic
716Q16—228no—
717Q16—228no—
718Q16—228no—
719SD16—228no—
720M16—224no—
721C2×C8—112no—
722C2×C8—114no—
723C2×C8—112no—
724C2×C8—224no—
725C4⋊C4—22no—
726C4⋊C4—22no—
727C4⋊C4—22no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—22no—
731C4⋊C4—21no—
732C4⋊C4—22no—
733C4⋊C4—21no—
734C4⋊C4—112no—
735C4⋊C4—112no—
736C4⋊C4—222no—
737C4⋊C4—222no—
738C4⋊C4—222no—
739C4⋊C4—222no—
740C4⋊C4—221no—
741C4⋊C4—221no—
742C4⋊C4—224no—
743C4⋊C4—224no—
744C4⋊C4—224no—
745C4⋊C4—224no—
746C4⋊C4—222no—
747C4⋊C4—222no—
748C4⋊C4C2×C22⋊D1111yescharacteristic
749C4⋊C4C2×C22⋊D1112yes—
750C4⋊C4C2×C22⋊D1111yescharacteristic
751C4⋊C4C2×C22⋊D1112yes—
752C4⋊C4C23×D1112yes—
753C4⋊C4C23×D1111yescharacteristic
754C4⋊C4C23×D1111yescharacteristic
755C22⋊C4—22no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—22no—
759C22⋊C4—21no—
760C22⋊C4—222no—
761C22⋊C4—224no—
762C22⋊C4—224no—
763C22⋊C4C2×C22⋊D1112yes—
764C22⋊C4C2×C22⋊D1112yes—
765C22⋊C4C2×C22⋊D1112yes—
766C42—22no—
767C42—21no—
768C42—22no—
769C42—21no—
770C42—22no—
771C42—22no—
772C42—22no—
773C42—22no—
774C42—21no—
775C42—222no—
776C42—224no—
777C42—224no—
778C42C2×C22⋊D1112yes—
779C42C2×C22⋊D1111yescharacteristic
780C42C2×C22⋊D1112yes—
781C42C2×C22⋊D1111yescharacteristic
782C42C23×D1112yes—
783C42C23×D1111yescharacteristic
784C42C23×D1111yescharacteristic
785C11#6059411yescharacteristic, complemented, Sylow
786C23—21no—
787C23C22×C22⋊D1112yes—
788C23C22×C22⋊D1111yescharacteristic
789Q8—28no—
790Q8—24no—
791Q8—22no—
792Q8—21no—
793Q8—22no—
794Q8—224no—
795Q8—224no—
796Q8—442no—
797Q8—444no—
798Q8—442no—
799Q8C2×#433912yes—
800Q8C2×#433914yes—
801D4—28no—
802D4—24no—
803D4—24no—
804D4—22no—
805D4—21no—
806D4C2×#433912yes—
807C2×C4—28no—
808C2×C4—28no—
809C2×C4—24no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—24no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—22no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—82no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—82no—
827C2×C4—222no—
828C2×C4—222no—
829C2×C4—224no—
830C2×C4—444no—
831C2×C4C2×#433912yes—
832C2×C4C2×#433912yes—
833C2×C4C22×C22⋊D1112yes—
834C2×C4C22×C22⋊D1111yescharacteristic
835C2×C4C22×C22⋊D1112yes—
836C2×C4C22×C22⋊D1112yes—
837C2×C4C22×C22⋊D1111yescharacteristic
838C2×C4C22×C22⋊D1111yescharacteristic
839C2×C4C22×C22⋊D1111yescharacteristic
840C2×C4C22×C22⋊D1111yescharacteristic
841C2×C4C24×D1111yescharacteristic
842C8—222no—
843C8—222no—
844C8—224no—
845C22—21no—
846C22—21no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22#1062332212yes—
854C22C23×C22⋊D1111yescharacteristic
855C4—24no—
856C4—22no—
857C4—22no—
858C4—21no—
859C4—22no—
860C4—21no—
861C4—22no—
862C4—21no—
863C4—42no—
864C4—41no—
865C4—41no—
866C4—444no—
867C4—442no—
868C4—442no—
869C4#1062332212yes—
870C4#1062336912yes—
871C4C22×#433911yescharacteristic
872C4C22×#433911yescharacteristic
873C2—22no—
874C2—42no—
875C2—42no—
876C2C2×#1062332211yescharacteristic
877C2C2×#1062336911yescharacteristic
878C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC4×C11×2−1+4C2
socleC22×C11C23×D4
prime radicalC2×C11×2−1+4C22
hypercenterC4×2−1+4D11
hypocenterC11#60594
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
1. #13082502C2semidirect
2. #13078916C2semidirect
3. #13078830C2semidirect
4. #13078778C2semidirect
5. #13078746C2semidirect
6. #13078687C2semidirect
7. #13078655C2semidirect
8. #13078585C2semidirect
9. #13078421C2semidirect
10. #13078404C2semidirect
11. #13078103C2semidirect
12. C2×#10622644C2semidirect
14. #13077482C2semidirect
15. #13077455C2semidirect
16. #13077282C2semidirect
785. C11#60594semidirect

Maximal subgroups

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

subgroupindex
#130825022
#130789162
#130788302
#130787782
#130787462
#130786872
#130786552
#130785852
#130784212
#130784042
#130781032
C2×#106226442
#130779112
#130774822
#130774552
#130772822
C4×C11×2−1+42
#6059411