Finite Group Databasebeta

← #15622287

Subgroups — #15622287

Order 2816.

2074 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623065C211yesmaximal, characteristic, complemented
2#13078893C214yesmaximal, complemented
3#13078878C214yesmaximal, complemented
4#13078845C214yesmaximal, complemented
5#13078800C214yesmaximal, complemented
6#13078564C211yesmaximal, characteristic, complemented
7#13078556C211yesmaximal, characteristic, complemented
8#13078431C212yesmaximal, complemented
9#13078110C212yesmaximal, complemented
10#13077876C211yesmaximal, characteristic, complemented
11#13077868C211yesmaximal, characteristic
12C4×#67004C212yesmaximal, complemented
13C4×#67002C212yesmaximal, complemented
14#13077254C211yesmaximal, characteristic, complemented
15C11×#3428C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C11×#520—21no—
18C11×#520—21no—
19C11×#520C2212yescomplemented
20C11×#520C2212yescomplemented
21C11×#519C2212yescomplemented
22C11×#518—21no—
23C11×#518—21no—
24C11×#518C2212yescomplemented
25C4×C11×#41—22no—
26C4×C11×#41C2212yes—
27C4×C11×#41C2212yes—
28C2×C11×#117—22no—
29C2×C11×#117C2211yescharacteristic
30C2×C11×#117C2211yescharacteristic
31C2×#67004C2212yes—
32C2×#67002C2212yes—
33C2×#66983C2211yescharacteristic
34C2×#66977C2211yescharacteristic
35#10623065—22no—
36#10623065—22no—
37#10623065C2214yes—
38#10623065C2214yescomplemented
39C2×#66951—21no—
40C2×#66949—21no—
41C2×#66938—21no—
42C2×#66936—21no—
43C2×#66928C2211yescharacteristic, complemented
44C2×C4×D44C2211yescharacteristic, complemented
45C2×#66922C2211yescharacteristic, complemented
46C2×C4×Dic22C2211yescharacteristic, complemented
47#10622852C2214yescomplemented
48#10622851C2214yes—
49#10622845C2212yes—
50#10622845C2212yes—
51#10622841C2212yescomplemented
52#10622840C2212yes—
53#10622831C2212yescomplemented
54#10622830C2212yes—
55#10622820C2211yescharacteristic
56#10622820C2211yescharacteristic
57#10622643C2214yescomplemented
58C4×#4326C2214yescomplemented
59#10622641C2214yescomplemented
60#10622641C2214yescomplemented
61#10622639C2214yescomplemented
62C4×#4325C2214yescomplemented
63#10622634C2214yescomplemented
64#10622633C2214yescomplemented
65#10622631C2214yescomplemented
66C4×#4324C2214yescomplemented
67#10622629C2214yescomplemented
68#10622629C2214yescomplemented
69#10622627C2214yescomplemented
70C4×#4323C2214yescomplemented
71#10622621C2214yescomplemented
72#10622620C2214yescomplemented
73#10622617C2212yescomplemented
74#10622616C2214yes—
75#10622614C2212yescomplemented
76#10622613C2214yescomplemented
77#10622613C2214yescomplemented
78#10622609C2214yescomplemented
79#10622608C2212yescomplemented
80#10622608C2212yescomplemented
81#10622584C2212yescomplemented
82#10622583C2212yescomplemented
83#10622581C2212yescomplemented
84#10622580C2212yescomplemented
85#10622537C2212yescomplemented
86C4×#4318C2212yescomplemented
87C2×C11×#41—28no—
88C2×C11×#41—21no—
89C2×C11×#41—21no—
90C2×C11×#41C2312yes—
91C2×C11×#41C2312yes—
92C22×Q8×C11C2311yescharacteristic
93C22×D4×C11—21no—
94C22×D4×C11C2311yescharacteristic
95C23×C4×C11—21no—
96C23×C4×C11C2311yescharacteristic
97C22×C22⋊D11—21no—
98C22×D44C2311yescharacteristic
99C22×C4×D11—21no—
100C22×Dic22—21no—
101C22×Dic22C2311yescharacteristic
102C4×Q8×C11—22no—
103C4×Q8×C11—22no—
104C4×Q8×C11C2312yes—
105C4×Q8×C11C2312yes—
106C4×Q8×C11C2312yes—
107C4×Q8×C11C2312yes—
108C4×D4×C11—22no—
109C4×D4×C11—22no—
110C4×D4×C11—22no—
111C4×D4×C11—22no—
112C4×D4×C11—22no—
113C4×D4×C11—22no—
114C4×D4×C11—22no—
115C4×D4×C11—22no—
116C4×D4×C11—22no—
117C4×D4×C11—22no—
118C4×D4×C11C2312yes—
119C4×D4×C11C2312yes—
120C4×D4×C11C2312yes—
121C4×D4×C11C2312yes—
122C11×#117—21no—
123C11×#117—21no—
124C11×#117—22no—
125C11×#117—22no—
126C11×#117—22no—
127C11×#117—22no—
128C11×#117—22no—
129C11×#117—22no—
130C11×#117D412yes—
131C11×#117D412yes—
132C11×#117C2312yes—
133C11×#117C2312yes—
134C11×#117C2312yes—
135C11×#117C2312yes—
136C2×C11×C4⋊C4—22no—
137C2×C11×C4⋊C4—22no—
138C2×C11×C4⋊C4D411yescharacteristic
139C2×C11×C4⋊C4D411yescharacteristic
140C2×C11×C4⋊C4C2311yescharacteristic
141C2×C11×C4⋊C4C2311yescharacteristic
142C2×C11×C22⋊C4—21no—
143C2×C11×C22⋊C4—22no—
144C2×C11×C22⋊C4—22no—
145C2×C11×C22⋊C4D411yescharacteristic
146C2×C11×C22⋊C4D411yescharacteristic
147C2×C42×C11—21no—
148C2×C42×C11—22no—
149C2×C42×C11—22no—
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C2311yescharacteristic
152C2×C22⋊Dic11—21no—
153#67004—28no—
154#67002—28no—
155C2×#4326C2314yes—
156C2×#4325C2314yes—
157C2×#4324C2314yes—
158C2×#4323C2314yes—
159#66983—21no—
160#66983—21no—
161#66983C2312yes—
162#66983C2312yes—
163C2×(C2×D11)⋊C4—21no—
164C2×(C2×D11)⋊C4—21no—
165C2×(C2×D11)⋊C4—21no—
166C2×(C2×D11)⋊C4—21no—
167C2×C4⋊Dic11—21no—
168C2×C4⋊Dic11C2311yescharacteristic
169C2×C4⋊Dic11C2311yescharacteristic
170#66977—21no—
171#66977—21no—
172#66977C2312yes—
173#66977C2312yes—
174C2×Dic11⋊C4—21no—
175C2×Dic11⋊C4—21no—
176C2×C4×Dic11—21no—
177C2×#4318C2312yes—
178C2×#4318C2312yes—
179#66951—24no—
180#66951—24no—
181#66949—24no—
182#66949—24no—
183#66938—24no—
184#66938—24no—
185#66936—24no—
186#66936—24no—
187#66928—22no—
188#66928C2314yes—
189C4×D44—22no—
190C4×D44C2314yes—
191#66922—22no—
192#66922C2314yes—
193C4×Dic22—22no—
194C4×Dic22C2314yes—
195#66899C2314yes—
196#66899C2314yes—
197#66896C2314yes—
198#66896C2314yes—
199C22⋊(C11⋊C8)C2312yes—
200C22⋊(C11⋊C8)C2312yes—
201C22⋊(C11⋊C8)C2312yes—
202C22⋊(C11⋊C8)C2312yes—
203#66874C2314yes—
204#66874C2314yes—
205#66873C2314yes—
206#66873C2314yes—
207#66872C2314yes—
208#66872C2314yes—
209#66871C2314yes—
210#66871C2314yes—
211C4⋊(C11⋊C8)C2314yes—
212C4⋊(C11⋊C8)C2314yes—
213#66867C2314yes—
214C4×C11⋊C8C2314yes—
215#60567—111nomaximal, Sylow
216C24×C11—21no—
217C24×C11C2×D411yescharacteristic
218C23×D11—21no—
219C11×#41—28no—
220C11×#41—28no—
221C11×#41—24no—
222C11×#41—24no—
223C11×#41—24no—
224C11×#41#4118yes—
225C2×Q8×C11—24no—
226C2×Q8×C11—21no—
227C2×Q8×C11C2412yes—
228C2×D4×C11—28no—
229C2×D4×C11—22no—
230C2×D4×C11—22no—
231C2×D4×C11—24no—
232C2×D4×C11—21no—
233C2×D4×C11C2412yes—
234C22×C4×C11—28no—
235C22×C4×C11—21no—
236C22×C4×C11—22no—
237C22×C4×C11—22no—
238C22×C4×C11—24no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—22no—
242C22×C4×C11—22no—
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2411yescharacteristic
254C22×C4×C11C2411yescharacteristic
255C2×C22⋊D11—22no—
256C2×C22⋊D11—22no—
257C2×C22⋊D11—82no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C2×D44—21no—
262C2×D44—24no—
263C2×D44C2412yes—
264C2×C4×D11—24no—
265C2×C4×D11—82no—
266C2×Dic22—21no—
267C2×Dic22—24no—
268C2×Dic22—24no—
269C2×Dic22—82no—
270C2×Dic22C2412yes—
271C11×C4⋊C4—21no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4—22no—
274C11×C4⋊C4—22no—
275C11×C4⋊C4—22no—
276C11×C4⋊C4—22no—
277C11×C4⋊C4C2×D412yes—
278C11×C4⋊C4C2×D412yes—
279C11×C4⋊C4C2×D412yes—
280C11×C4⋊C4C2×D412yes—
281C11×C4⋊C4C2412yes—
282C11×C4⋊C4C2412yes—
283C11×C22⋊C4—22no—
284C11×C22⋊C4—22no—
285C11×C22⋊C4—22no—
286C11×C22⋊C4—22no—
287C11×C22⋊C4—22no—
288C11×C22⋊C4—22no—
289C11×C22⋊C4C2×D412yes—
290C11×C22⋊C4C2×D412yes—
291C11×C22⋊C4C2×D412yes—
292C11×C22⋊C4C2×D412yes—
293C42×C11—22no—
294C42×C11—22no—
295C42×C11—22no—
296C42×C11—22no—
297C42×C11—22no—
298C42×C11—22no—
299C42×C11C2×D412yes—
300C42×C11C2×D412yes—
301C42×C11C2412yes—
302C42×C11C2412yes—
303C22⋊Dic11—22no—
304C22⋊Dic11—22no—
305#4326—28no—
306#4325—28no—
307#4324—28no—
308#4323—28no—
309(C2×D11)⋊C4—24no—
310(C2×D11)⋊C4—24no—
311(C2×D11)⋊C4—24no—
312(C2×D11)⋊C4—22no—
313(C2×D11)⋊C4—22no—
314C4⋊Dic11—21no—
315C4⋊Dic11—21no—
316C4⋊Dic11—24no—
317C4⋊Dic11C2412yes—
318C4⋊Dic11C2412yes—
319Dic11⋊C4—24no—
320Dic11⋊C4—22no—
321Dic11⋊C4—22no—
322C4×Dic11—24no—
323#4318—24no—
324#4318—24no—
325C2×C11⋊C8C2414yes—
326C2×C11⋊C8C2414yes—
327C2×#542—111no—
328#3428D1111yescharacteristic, complemented
329#3125—114no—
330#3124—114no—
331#3121—114no—
332#3118—114no—
333#3095—111no—
334#3094—111no—
335#3079—112no—
336#3040—112no—
337#3007—111no—
338#3006—111no—
339C4×#137—112no—
340C4×AGL(1,ℤ/8)—112no—
341#2921—111no—
342C23×C11—24no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—81no—
348C23×C11—81no—
349C23×C11C22×D411yescharacteristic
350C23×C11C22×D411yescharacteristic
351C23×C11C22×D411yescharacteristic
352C22×D11—22no—
353C22×D11—42no—
354C22×D11—42no—
355C22×D11—42no—
356Q8×C11—24no—
357Q8×C11—22no—
358Q8×C11C2×#4114yes—
359D4×C11—28no—
360D4×C11—24no—
361D4×C11—28no—
362D4×C11—22no—
363D4×C11C2×#4114yes—
364C2×C4×C11—24no—
365C2×C4×C11—28no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—28no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—82no—
380C2×C4×C11—82no—
381C2×C4×C11—82no—
382C2×C4×C11—82no—
383C2×C4×C11—81no—
384C2×C4×C11—81no—
385C2×C4×C11C22×D412yes—
386C2×C4×C11C22×D411yescharacteristic
387C2×C4×C11C22×D411yescharacteristic
388C2×C4×C11C22×D412yes—
389C2×C4×C11C22×D412yes—
390C2×C4×C11C22×D412yes—
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C2×#4114yes—
393C2×C4×C11C2511yescharacteristic
394C22⋊D11—82no—
395C22⋊D11—82no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—42no—
400C2×Dic11—42no—
401C2×Dic11—42no—
402D44—24no—
403D44—42no—
404C4×D11—84no—
405Dic22—24no—
406Dic22—42no—
407Dic22—84no—
408C11⋊C8—24no—
409C11⋊C8—24no—
410C22×#41C2×D1111yescharacteristic
411C2×#137—112no—
412C2×AGL(1,ℤ/8)—112no—
413#542—114no—
414#542—114no—
415#542—222no—
416#542—222no—
417C2×C4⋊Q8—111no—
418C2×#126—221no—
419C2×#124—111no—
420C2×#124—221no—
421C2×#123—221no—
422C2×C22⋊Q8—111no—
423C2×C22⋊Q8—221no—
424C2×#121—111no—
425#520—21no—
426#520—21no—
427#520C2×D1112yescomplemented
428#520C2×D1112yescomplemented
429#519C2×D1112yescomplemented
430#518—21no—
431#518—21no—
432#518C2×D1112yescomplemented
433C4×#41—22no—
434C4×#41C2×D1112yes—
435C4×#41C2×D1112yes—
436C2×C4×Q8—111no—
437C2×C4×D4—111no—
438C2×#117—22no—
439C2×#117C2×D1111yescharacteristic
440C2×#117C2×D1111yescharacteristic
441#485—114no—
442#484—112no—
443#483—112no—
444#482—114no—
445#481—112no—
446#480—112no—
447#477—114no—
448#476—114no—
449#475—114no—
450#474—114no—
451#464—114no—
452#464—114no—
453#463—114no—
454#463—114no—
455#452—114no—
456#451—112no—
457#450—112no—
458#449—114no—
459#448—112no—
460#447—112no—
461#442—114no—
462#441—114no—
463#440—114no—
464#440—114no—
465C4×Q16—114no—
466C4×SD16—114no—
467C4×SD16—114no—
468C4×D8—114no—
469#433—114no—
470#433—114no—
471#428—112no—
472#428—112no—
473#423—112no—
474#419—112no—
475#418—112no—
476#417—112no—
477#417—112no—
478#407—111no—
479#407—111no—
480C4×M16—112no—
481C22×C11—21no—
482C22×C11—21no—
483C22×C11—21no—
484C22×C11—21no—
485C22×C11—21no—
486C22×C11—21no—
487C22×C11—21no—
488C22×C11—21no—
489C22×C11—24no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—82no—
493C22×C11—84no—
494C22×C11#52512yes—
495C22×C11C23×D411yescharacteristic
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—84no—
500C4×C11—22no—
501C4×C11—22no—
502C4×C11—22no—
503C4×C11—22no—
504C4×C11—21no—
505C4×C11—24no—
506C4×C11—21no—
507C4×C11—42no—
508C4×C11—42no—
509C4×C11#52512yes—
510C4×C11C22×#4112yes—
511Dic11—42no—
512Dic11—42no—
513Dic11—42no—
514C2×#41—28no—
515C2×#41—21no—
516C2×#41—21no—
517C2×#41C22×D1112yes—
518C2×#41C22×D1112yes—
519C22×Q8—111no—
520C22×Q8—221no—
521C22×Q8C22×D1111yescharacteristic
522C22×D4—21no—
523C22×D4—111no—
524C22×D4—221no—
525C22×D4C22×D1111yescharacteristic
526C23×C4—21no—
527C23×C4—221no—
528C23×C4C22×D1111yescharacteristic
529#137—228no—
530AGL(1,ℤ/8)—228no—
531C2×Q16—114no—
532C2×SD16—114no—
533C2×SD16—114no—
534C2×D8—114no—
535C2×M16—112no—
536C2×M16—112no—
537C4⋊Q8—114no—
538C4⋊Q8—222no—
539#126—224no—
540#126—224no—
541#124—114no—
542#124—224no—
543#124—224no—
544#124—222no—
545#123—224no—
546#123—224no—
547C22⋊Q8—112no—
548C22⋊Q8—112no—
549C22⋊Q8—221no—
550C22⋊Q8—221no—
551C22⋊Q8—224no—
552C22⋊Q8—224no—
553#121—112no—
554#121—112no—
555#121—221no—
556#121—221no—
557C4×Q8—22no—
558C4×Q8—22no—
559C4×Q8—114no—
560C4×Q8—222no—
561C4×Q8C22×D1112yes—
562C4×Q8C22×D1112yes—
563C4×Q8C22×D1112yes—
564C4×Q8C22×D1112yes—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—114no—
576C4×D4—222no—
577C4×D4C22×D1112yes—
578C4×D4C22×D1112yes—
579C4×D4C22×D1112yes—
580C4×D4C22×D1112yes—
581#117—21no—
582#117—21no—
583#117—22no—
584#117—22no—
585#117—22no—
586#117—22no—
587#117—22no—
588#117—22no—
589#117C22⋊D1112yes—
590#117C22⋊D1112yes—
591#117C22×D1112yes—
592#117C22×D1112yes—
593#117C22×D1112yes—
594#117C22×D1112yes—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—111no—
598C2×C4⋊C4—111no—
599C2×C4⋊C4—221no—
600C2×C4⋊C4—221no—
601C2×C4⋊C4—221no—
602C2×C4⋊C4C22⋊D1111yescharacteristic
603C2×C4⋊C4C22⋊D1111yescharacteristic
604C2×C4⋊C4C22×D1111yescharacteristic
605C2×C4⋊C4C22×D1111yescharacteristic
606C2×C22⋊C4—21no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—221no—
610C2×C22⋊C4—221no—
611C2×C22⋊C4—221no—
612C2×C22⋊C4—221no—
613C2×C22⋊C4—221no—
614C2×C22⋊C4C22⋊D1111yescharacteristic
615C2×C22⋊C4C22⋊D1111yescharacteristic
616C2×C42—21no—
617C2×C42—22no—
618C2×C42—22no—
619C2×C42—221no—
620C2×C42C22×D1111yescharacteristic
621C2×C42C22×D1111yescharacteristic
622#107—114no—
623#107—114no—
624#106—114no—
625#106—114no—
626C4⋊C8—114no—
627C4⋊C8—114no—
628#103—114no—
629#103—114no—
630#103—114no—
631#103—114no—
632#102—114no—
633#102—114no—
634#102—114no—
635#102—114no—
636C22⋊C8—112no—
637C22⋊C8—112no—
638C22⋊C8—112no—
639C22⋊C8—112no—
640#97—114no—
641C4×C8—114no—
642C2×C11—22no—
643C2×C11—41no—
644C2×C11—41no—
645C2×C11—44no—
646C2×C11C2×#52511yescharacteristic
647C2×C11#358511yescharacteristic
648C2×C11#358611yescharacteristic
649D11—82no—
650C24—21no—
651C24—221no—
652C24C2×C22⋊D1111yescharacteristic
653#41—28no—
654#41—28no—
655#41—24no—
656#41—24no—
657#41—24no—
658#41#433918yes—
659C2×Q8—24no—
660C2×Q8—21no—
661C2×Q8—112no—
662C2×Q8—221no—
663C2×Q8—224no—
664C2×Q8—224no—
665C2×Q8—882no—
666C2×Q8C23×D1112yes—
667C2×D4—28no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—21no—
672C2×D4—112no—
673C2×D4—222no—
674C2×D4—222no—
675C2×D4—224no—
676C2×D4—221no—
677C2×D4—882no—
678C2×D4C23×D1112yes—
679C22×C4—28no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—221no—
691C22×C4—221no—
692C22×C4—221no—
693C22×C4—224no—
694C22×C4—882no—
695C22×C4C2×C22⋊D1111yescharacteristic
696C22×C4C2×C22⋊D1111yescharacteristic
697C22×C4C2×C22⋊D1111yescharacteristic
698C22×C4C2×C22⋊D1111yescharacteristic
699C22×C4C2×C22⋊D1111yescharacteristic
700C22×C4C2×C22⋊D1111yescharacteristic
701C22×C4C2×C22⋊D1111yescharacteristic
702C22×C4C23×D1111yescharacteristic
703C22×C4C23×D1111yescharacteristic
704C22×C4C23×D1111yescharacteristic
705Q16—228no—
706SD16—228no—
707SD16—228no—
708D8—228no—
709M16—224no—
710M16—224no—
711C2×C8—114no—
712C2×C8—114no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—22no—
716C4⋊C4—22no—
717C4⋊C4—22no—
718C4⋊C4—22no—
719C4⋊C4—112no—
720C4⋊C4—112no—
721C4⋊C4—221no—
722C4⋊C4—221no—
723C4⋊C4—224no—
724C4⋊C4—222no—
725C4⋊C4—222no—
726C4⋊C4—224no—
727C4⋊C4C2×C22⋊D1112yes—
728C4⋊C4C2×C22⋊D1112yes—
729C4⋊C4C2×C22⋊D1112yes—
730C4⋊C4C2×C22⋊D1112yes—
731C4⋊C4C23×D1112yes—
732C4⋊C4C23×D1112yes—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—222no—
740C22⋊C4—222no—
741C22⋊C4—224no—
742C22⋊C4—222no—
743C22⋊C4—222no—
744C22⋊C4—224no—
745C22⋊C4—224no—
746C22⋊C4C2×C22⋊D1112yes—
747C22⋊C4C2×C22⋊D1112yes—
748C22⋊C4C2×C22⋊D1112yes—
749C22⋊C4C2×C22⋊D1112yes—
750C42—22no—
751C42—22no—
752C42—22no—
753C42—22no—
754C42—22no—
755C42—22no—
756C42—224no—
757C42C2×C22⋊D1112yes—
758C42C2×C22⋊D1112yes—
759C42C23×D1112yes—
760C42C23×D1112yes—
761C11#6056711yescharacteristic, complemented, Sylow
762C23—24no—
763C23—22no—
764C23—22no—
765C23—41no—
766C23—41no—
767C23—81no—
768C23—81no—
769C23—222no—
770C23—442no—
771C23—442no—
772C23—442no—
773C23C22×C22⋊D1111yescharacteristic
774C23C22×C22⋊D1111yescharacteristic
775C23C22×C22⋊D1111yescharacteristic
776Q8—24no—
777Q8—22no—
778Q8—224no—
779Q8—442no—
780Q8—884no—
781Q8C2×#433914yes—
782D4—28no—
783D4—24no—
784D4—28no—
785D4—22no—
786D4—224no—
787D4—442no—
788D4—882no—
789D4—882no—
790D4C2×#433914yes—
791C2×C4—24no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—28no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—82no—
807C2×C4—82no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4—81no—
811C2×C4—81no—
812C2×C4—222no—
813C2×C4—222no—
814C2×C4—222no—
815C2×C4—442no—
816C2×C4—442no—
817C2×C4—442no—
818C2×C4—884no—
819C2×C4C2×#433914yes—
820C2×C4C22×C22⋊D1111yescharacteristic
821C2×C4C22×C22⋊D1112yes—
822C2×C4C22×C22⋊D1112yes—
823C2×C4C22×C22⋊D1112yes—
824C2×C4C22×C22⋊D1112yes—
825C2×C4C22×C22⋊D1111yescharacteristic
826C2×C4C22×C22⋊D1111yescharacteristic
827C2×C4C24×D1111yescharacteristic
828C8—224no—
829C8—224no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—24no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—42no—
840C22—42no—
841C22—82no—
842C22—84no—
843C22—442no—
844C22—442no—
845C22—442no—
846C22—884no—
847C22#1062332212yes—
848C22C23×C22⋊D1111yescharacteristic
849C4—21no—
850C4—24no—
851C4—21no—
852C4—22no—
853C4—22no—
854C4—22no—
855C4—22no—
856C4—42no—
857C4—42no—
858C4—442no—
859C4—442no—
860C4—442no—
861C4#1062332212yes—
862C4C22×#433912yes—
863C2—22no—
864C2—41no—
865C2—41no—
866C2—44no—
867C2—882no—
868C2C2×#1062332211yescharacteristic
869C2#1308339511yescharacteristic
870C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3428C2
socleC22×C11C23×D4
prime radical#13077868C2
hypercenter#3428D11
hypocenterC11#60567
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3428

Complements

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

NH ≅ G/Ntype
1. C2×#10623065C2semidirect
2. #13078893C2semidirect
3. #13078878C2semidirect
4. #13078845C2semidirect
5. #13078800C2semidirect
6. #13078564C2semidirect
7. #13078556C2semidirect
8. #13078431C2semidirect
9. #13078110C2semidirect
10. #13077876C2semidirect
12. C4×#67004C2semidirect
13. C4×#67002C2semidirect
14. #13077254C2semidirect
15. C11×#3428C2semidirect
19. C11×#520C22semidirect
20. C11×#520C22semidirect
21. C11×#519C22semidirect
24. C11×#518C22semidirect
38. #10623065C22semidirect
43. C2×#66928C22semidirect
44. C2×C4×D44C22semidirect
45. C2×#66922C22semidirect
46. C2×C4×Dic22C22semidirect
47. #10622852C22semidirect
51. #10622841C22semidirect
53. #10622831C22semidirect
57. #10622643C22semidirect
58. C4×#4326C22semidirect
59. #10622641C22semidirect
60. #10622641C22semidirect
61. #10622639C22semidirect
62. C4×#4325C22semidirect
63. #10622634C22semidirect
64. #10622633C22semidirect
65. #10622631C22semidirect
66. C4×#4324C22semidirect
67. #10622629C22semidirect
68. #10622629C22semidirect
69. #10622627C22semidirect
70. C4×#4323C22semidirect
71. #10622621C22semidirect
72. #10622620C22semidirect
73. #10622617C22semidirect
75. #10622614C22semidirect
76. #10622613C22semidirect
77. #10622613C22semidirect
78. #10622609C22semidirect
79. #10622608C22semidirect
80. #10622608C22semidirect
81. #10622584C22semidirect
82. #10622583C22semidirect
83. #10622581C22semidirect
84. #10622580C22semidirect
85. #10622537C22semidirect
86. C4×#4318C22semidirect
328. #3428D11semidirect
427. #520C2×D11semidirect
428. #520C2×D11semidirect
429. #519C2×D11semidirect
432. #518C2×D11semidirect
761. C11#60567semidirect

Maximal subgroups

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

subgroupindex
C2×#106230652
#130788932
#130788782
#130788452
#130788002
#130785642
#130785562
#130784312
#130781102
#130778762
#130778682
C4×#670042
C4×#670022
#130772542
C11×#34282
#6056711