Finite Group Databasebeta

← #15624577

Subgroups — #15624577

Order 2816.

2194 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623364C211yesmaximal, characteristic, complemented
2#13079522C214yesmaximal, complemented
3#13079513C214yesmaximal, complemented
4#13079498C214yesmaximal, complemented
5#13079468C214yesmaximal, complemented
6#13078564C211yesmaximal, characteristic, complemented
7#13078556C211yesmaximal, characteristic, complemented
8#13078536C212yesmaximal, complemented
9#13078248C212yesmaximal, complemented
10#13078237C212yesmaximal, complemented
11#13077876C211yesmaximal, characteristic, complemented
12#13077868C211yesmaximal, characteristic, complemented
13#13077856C212yesmaximal, complemented
14#13077061C211yesmaximal, characteristic, complemented
15C11×#3449C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C22×#4339C2211yescharacteristic, complemented
19C11×#537C2212yescomplemented
20C11×#537C2212yescomplemented
21C11×#536—21no—
22C11×#536C2212yescomplemented
23C11×#535—21no—
24C11×#535C2212yescomplemented
25C11×#534—21no—
26C11×#534—21no—
27C11×#532—22no—
28C11×#525—22no—
29C11×#525C2212yes—
30C11×#525C2212yes—
31C2×C11×#117C2211yescharacteristic
32#10623364—22no—
33#10623364—22no—
34#10623364C2214yes—
35#10623364C2214yescomplemented
36C2×#67004C2212yes—
37C2×#67002C2212yes—
38C2×#66999—21no—
39C2×#66992—21no—
40C2×#66992—21no—
41C2×#66991—21no—
42C2×#66983C2211yescharacteristic
43C2×#66983C2211yescharacteristic, complemented
44C22×C4⋊Dic11C2211yescharacteristic, complemented
45C2×#66977C2211yescharacteristic
46C2×#66977C2211yescharacteristic, complemented
47C22×#4318C2212yescomplemented
48#10622852C2214yescomplemented
49#10622851C2214yescomplemented
50#10622847C2214yescomplemented
51#10622847C2214yescomplemented
52#10622845C2212yes—
53#10622845C2212yes—
54#10622841C2212yescomplemented
55#10622840C2212yescomplemented
56#10622831C2212yescomplemented
57#10622830C2212yescomplemented
58#10622820C2211yescharacteristic
59#10622820C2211yescharacteristic
60#10622820C2212yescomplemented
61#10622665C2214yescomplemented
62#10622664C2214yescomplemented
63#10622662C2214yescomplemented
64#10622661C2214yescomplemented
65#10622660C2214yescomplemented
66#10622660C2214yescomplemented
67#10622657C2214yescomplemented
68#10622656C2214yescomplemented
69#10622655C2214yescomplemented
70#10622654C2214yescomplemented
71#10622652C2214yescomplemented
72#10622651C2214yescomplemented
73#10622650C2214yescomplemented
74#10622650C2214yescomplemented
75#10622647C2214yescomplemented
76#10622646C2214yescomplemented
77#10622617C2212yescomplemented
78#10622616C2214yescomplemented
79#10622614C2212yescomplemented
80#10622609C2214yescomplemented
81#10622608C2212yescomplemented
82#10622608C2212yescomplemented
83#10622584C2212yescomplemented
84#10622583C2212yescomplemented
85#10622581C2212yescomplemented
86#10622580C2212yescomplemented
87C2×C11×#41—21no—
88C2×C11×#41—21no—
89C2×C11×#41—44no—
90C2×C11×#41—44no—
91C2×C11×#41D412yes—
92C2×C11×#41D412yes—
93C2×C11×#41C2312yes—
94C2×C11×#41C2312yes—
95C2×C11×#41C2312yes—
96C2×C11×#41C2312yes—
97C22×Q8×C11D411yescharacteristic
98C22×Q8×C11C2311yescharacteristic
99C22×D4×C11—21no—
100C22×D4×C11D411yescharacteristic
101C22×D4×C11D411yescharacteristic
102C22×D4×C11D411yescharacteristic
103C22×D4×C11C2311yescharacteristic
104C23×C4×C11—21no—
105C23×C4×C11C2311yescharacteristic
106C23×C4×C11C2311yescharacteristic
107C23×C4×C11C2311yescharacteristic
108C22×C22⋊D11—21no—
109C22×C22⋊D11—21no—
110C22×C22⋊D11—21no—
111C23×Dic11—21no—
112C2×#4339—22no—
113C2×#4339—44no—
114C2×#4339C2314yes—
115C22×D44C2311yescharacteristic
116C22×C4×D11—21no—
117C22×Dic22C2311yescharacteristic
118C11×C4⋊Q8—22no—
119C11×#127—22no—
120C11×#124—22no—
121C11×#124—22no—
122C11×#123—22no—
123C11×#123—22no—
124C11×#123—22no—
125C11×#123—22no—
126C11×C22⋊Q8—22no—
127C11×C22⋊Q8—22no—
128C11×C22⋊Q8C2312yes—
129C11×C22⋊Q8C2312yes—
130C11×C22⋊Q8C2312yes—
131C11×C22⋊Q8C2312yes—
132C11×#121—22no—
133C11×#121—22no—
134C11×#121—22no—
135C11×#121—22no—
136C11×#121—22no—
137C11×#121—22no—
138C11×#121C2312yes—
139C11×#121C2312yes—
140C11×#121C2312yes—
141C11×#121C2312yes—
142C11×#120—22no—
143C11×#120—22no—
144C11×#120—22no—
145C11×#120—22no—
146C4×D4×C11—22no—
147C4×D4×C11—22no—
148C4×D4×C11—22no—
149C4×D4×C11—22no—
150C11×#117—21no—
151C11×#117—21no—
152C11×#117C2312yes—
153C11×#117C2312yes—
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C22⋊C4—21no—
157C2×C42×C11—21no—
158C2×C22⋊Dic11—21no—
159C2×C22⋊Dic11—21no—
160#67004—44no—
161#67002—44no—
162#66999—24no—
163#66999—24no—
164C2×#4326C2314yes—
165C2×#4325C2314yes—
166#66992—24no—
167#66992—24no—
168#66992—24no—
169#66992—24no—
170#66991—24no—
171#66991—24no—
172C2×#4324C2314yes—
173C2×#4323C2314yes—
174#66983—21no—
175#66983—21no—
176#66983—22no—
177#66983C2312yes—
178#66983C2312yes—
179#66983C2314yes—
180C2×(C2×D11)⋊C4—21no—
181C2×(C2×D11)⋊C4—21no—
182C2×C4⋊Dic11—21no—
183C2×C4⋊Dic11—22no—
184C2×C4⋊Dic11C2311yescharacteristic
185C2×C4⋊Dic11C2311yescharacteristic
186C2×C4⋊Dic11C2314yes—
187#66977—21no—
188#66977—21no—
189#66977—22no—
190#66977C2312yes—
191#66977C2312yes—
192#66977C2314yes—
193C2×Dic11⋊C4—21no—
194C2×Dic11⋊C4—21no—
195C2×#4318—44no—
196C2×#4318C2312yes—
197C2×#4318C2312yes—
198C2×#4318C2314yes—
199C22×C11⋊C8C2314yes—
200#66899C2314yes—
201#66899C2314yes—
202#66896C2314yes—
203#66896C2314yes—
204C22⋊(C11⋊C8)C2312yes—
205C22⋊(C11⋊C8)C2312yes—
206C22⋊(C11⋊C8)C2312yes—
207C22⋊(C11⋊C8)C2312yes—
208C22⋊(C11⋊C8)C2314yes—
209C22⋊(C11⋊C8)C2314yes—
210#66874C2314yes—
211#66874C2314yes—
212#66873C2314yes—
213#66873C2314yes—
214#66872C2314yes—
215#66872C2314yes—
216#66871C2314yes—
217#66871C2314yes—
218#60755—111nomaximal, Sylow
219C24×C11—21no—
220C24×C11C2×D411yescharacteristic
221C24×C11C2×D411yescharacteristic
222C24×C11C2×D411yescharacteristic
223C23×D11—21no—
224C11×#41—24no—
225C11×#41—24no—
226C11×#41—44no—
227C11×#41—44no—
228C11×#41—42no—
229C11×#41—42no—
230C11×#41—42no—
231C11×#41—42no—
232C11×#41—42no—
233C11×#41—42no—
234C11×#41—44no—
235C11×#41—44no—
236C2×Q8×C11—21no—
237C2×Q8×C11—42no—
238C2×Q8×C11—42no—
239C2×Q8×C11C2×D412yes—
240C2×Q8×C11C2×D412yes—
241C2×Q8×C11C2412yes—
242C2×D4×C11—22no—
243C2×D4×C11—22no—
244C2×D4×C11—22no—
245C2×D4×C11—22no—
246C2×D4×C11—22no—
247C2×D4×C11—22no—
248C2×D4×C11—21no—
249C2×D4×C11—42no—
250C2×D4×C11—42no—
251C2×D4×C11—42no—
252C2×D4×C11—42no—
253C2×D4×C11—44no—
254C2×D4×C11C2×D412yes—
255C2×D4×C11C2×D412yes—
256C2×D4×C11C2×D412yes—
257C2×D4×C11C2×D412yes—
258C2×D4×C11C2×D412yes—
259C2×D4×C11C2×D412yes—
260C2×D4×C11C2412yes—
261C22×C4×C11—24no—
262C22×C4×C11—24no—
263C22×C4×C11—24no—
264C22×C4×C11—21no—
265C22×C4×C11—21no—
266C22×C4×C11—21no—
267C22×C4×C11—22no—
268C22×C4×C11—22no—
269C22×C4×C11—44no—
270C22×C4×C11C2×D411yescharacteristic
271C22×C4×C11C2×D411yescharacteristic
272C22×C4×C11C2×D411yescharacteristic
273C22×C4×C11C2×D411yescharacteristic
274C22×C4×C11C2×D412yes—
275C22×C4×C11C2×D412yes—
276C22×C4×C11C2×D411yescharacteristic
277C22×C4×C11C2411yescharacteristic
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2412yes—
280C22×C4×C11C2412yes—
281C22×C4×C11C2411yescharacteristic
282C2×C22⋊D11—24no—
283C2×C22⋊D11—22no—
284C2×C22⋊D11—24no—
285C2×C22⋊D11—22no—
286C2×C22⋊D11—44no—
287C2×C22⋊D11—82no—
288C2×C22⋊D11—82no—
289C22×Dic11—21no—
290C22×Dic11—21no—
291C22×Dic11—21no—
292C22×Dic11—24no—
293C22×Dic11—82no—
294#4339—44no—
295#4339—44no—
296#4339—48no—
297C2×D44—21no—
298C2×D44—24no—
299C2×D44C2412yes—
300C2×C4×D11—24no—
301C2×C4×D11—44no—
302C2×Dic22—21no—
303C2×Dic22—24no—
304C2×Dic22C2412yes—
305C11×C4⋊C4—21no—
306C11×C4⋊C4—21no—
307C11×C4⋊C4—22no—
308C11×C4⋊C4—22no—
309C11×C4⋊C4—22no—
310C11×C4⋊C4—22no—
311C11×C4⋊C4C2412yes—
312C11×C4⋊C4C2412yes—
313C11×C22⋊C4—22no—
314C11×C22⋊C4—22no—
315C11×C22⋊C4—22no—
316C11×C22⋊C4—22no—
317C11×C22⋊C4—22no—
318C11×C22⋊C4—22no—
319C11×C22⋊C4—22no—
320C11×C22⋊C4—22no—
321C11×C22⋊C4—22no—
322C11×C22⋊C4—22no—
323C42×C11—22no—
324C42×C11—22no—
325C22⋊Dic11—22no—
326C22⋊Dic11—24no—
327C22⋊Dic11—22no—
328#4326—44no—
329#4325—44no—
330#4324—44no—
331#4323—44no—
332(C2×D11)⋊C4—22no—
333(C2×D11)⋊C4—24no—
334(C2×D11)⋊C4—22no—
335C4⋊Dic11—21no—
336C4⋊Dic11—21no—
337C4⋊Dic11—24no—
338C4⋊Dic11C2412yes—
339C4⋊Dic11C2412yes—
340Dic11⋊C4—22no—
341Dic11⋊C4—24no—
342Dic11⋊C4—22no—
343#4318—24no—
344#4318—24no—
345#4318—44no—
346C2×C11⋊C8—44no—
347C2×C11⋊C8C2414yes—
348C2×C11⋊C8C2414yes—
349#3449D1111yescharacteristic, complemented
350C2×#537—111no—
351#3204—114no—
352#3203—114no—
353#3201—114no—
354#3198—114no—
355#3095—111no—
356#3094—111no—
357#3092—112no—
358#3056—112no—
359#3055—112no—
360#3007—111no—
361#3006—111no—
362#3005—112no—
363#2879—111no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11—42no—
375C23×C11—81no—
376C23×C11—81no—
377C23×C11C22×D411yescharacteristic
378C23×C11C22×D412yes—
379C23×C11C22×D411yescharacteristic
380C23×C11C22×D412yes—
381C23×C11C22×D411yescharacteristic
382C22×D11—22no—
383C22×D11—42no—
384C22×D11—42no—
385C22×D11—42no—
386Q8×C11—22no—
387Q8×C11—22no—
388Q8×C11—42no—
389Q8×C11—42no—
390Q8×C11—42no—
391D4×C11—22no—
392D4×C11—22no—
393D4×C11—42no—
394D4×C11—42no—
395D4×C11—42no—
396D4×C11—42no—
397D4×C11—42no—
398D4×C11—42no—
399D4×C11—42no—
400D4×C11—44no—
401D4×C11—44no—
402D4×C11—82no—
403D4×C11—82no—
404D4×C11—82no—
405D4×C11—82no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—24no—
410C2×C4×C11—22no—
411C2×C4×C11—24no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—44no—
423C2×C4×C11—42no—
424C2×C4×C11—44no—
425C2×C4×C11—81no—
426C2×C4×C11—81no—
427C2×C4×C11C22×D411yescharacteristic
428C2×C4×C11C22×D412yes—
429C2×C4×C11C22×D411yescharacteristic
430C2×C4×C11C22×D412yes—
431C2×C4×C11C22×D411yescharacteristic
432C2×C4×C11H(5,𝔽2)14yes—
433C2×C4×C11C2511yescharacteristic
434C22⋊D11—48no—
435C22⋊D11—82no—
436C22⋊D11—84no—
437C22⋊D11—82no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—42no—
442C2×Dic11—42no—
443C2×Dic11—42no—
444C2×Dic11—84no—
445D44—24no—
446D44—42no—
447C4×D11—48no—
448Dic22—24no—
449Dic22—42no—
450C11⋊C8—24no—
451C11⋊C8—24no—
452C22×#41—111no—
453C22×#41C2×D1111yescharacteristic
454C22×#41C2×D1111yescharacteristic
455C2×#137—112no—
456C2×AGL(1,ℤ/8)—112no—
457C22×M16—112no—
458#537—114no—
459#537—114no—
460#537—222no—
461#537—222no—
462#537C2×D1112yescomplemented
463#537C2×D1112yescomplemented
464#536—21no—
465#536C2×D1112yescomplemented
466#535—21no—
467#535C2×D1112yescomplemented
468#534—21no—
469#534—21no—
470#532—22no—
471#525—22no—
472#525C2×D1112yes—
473#525C2×D1112yes—
474C2×C22⋊Q8—111no—
475C2×C22⋊Q8—111no—
476C2×C22⋊Q8—221no—
477C2×#121—111no—
478C2×#121—111no—
479C2×#121—221no—
480C2×#121—221no—
481C2×#121—221no—
482C2×#117C2×D1111yescharacteristic
483C22×C4⋊C4—111no—
484#485—114no—
485#484—114no—
486#484—112no—
487#483—114no—
488#483—112no—
489#482—114no—
490#481—114no—
491#481—112no—
492#480—114no—
493#480—112no—
494#470—114no—
495#469—114no—
496#468—114no—
497#468—114no—
498#467—114no—
499#466—114no—
500#465—114no—
501#465—114no—
502#452—114no—
503#452—114no—
504#452—114no—
505#451—112no—
506#450—112no—
507#449—114no—
508#449—114no—
509#449—114no—
510#448—112no—
511#447—112no—
512#428—112no—
513#428—112no—
514#419—112no—
515#418—112no—
516#417—112no—
517#417—112no—
518#408—114no—
519#408—114no—
520#407—112no—
521#407—111no—
522#407—111no—
523C22×C11—21no—
524C22×C11—21no—
525C22×C11—21no—
526C22×C11—22no—
527C22×C11—22no—
528C22×C11—21no—
529C22×C11—21no—
530C22×C11—22no—
531C22×C11—22no—
532C22×C11—21no—
533C22×C11—21no—
534C22×C11—21no—
535C22×C11—22no—
536C22×C11—22no—
537C22×C11—44no—
538C22×C11—42no—
539C22×C11—42no—
540C22×C11—42no—
541C22×C11—82no—
542C22×C11—82no—
543C22×C11—84no—
544C22×C11#53412yes—
545C22×C11C23×D411yescharacteristic
546C2×D11—42no—
547C2×D11—42no—
548C2×D11—42no—
549C2×D11—84no—
550C4×C11—21no—
551C4×C11—21no—
552C4×C11—22no—
553C4×C11—22no—
554C4×C11—42no—
555C4×C11—42no—
556C4×C11—42no—
557C4×C11#53412yes—
558C4×C11C2×H(5,𝔽2)12yes—
559Dic11—42no—
560Dic11—42no—
561Dic11—42no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—44no—
565C2×#41—44no—
566C2×#41—114no—
567C2×#41—222no—
568C2×#41—444no—
569C2×#41C22⋊D1112yes—
570C2×#41C22⋊D1112yes—
571C2×#41C22×D1112yes—
572C2×#41C22×D1112yes—
573C2×#41C22×D1112yes—
574C2×#41C22×D1112yes—
575C22×Q8—111no—
576C22×Q8C22⋊D1111yescharacteristic
577C22×Q8C22×D1111yescharacteristic
578C22×D4—21no—
579C22×D4—111no—
580C22×D4—221no—
581C22×D4—221no—
582C22×D4—221no—
583C22×D4C22⋊D1111yescharacteristic
584C22×D4C22⋊D1111yescharacteristic
585C22×D4C22⋊D1111yescharacteristic
586C22×D4C22×D1111yescharacteristic
587C23×C4—21no—
588C23×C4—221no—
589C23×C4—221no—
590C23×C4C22×D1111yescharacteristic
591C23×C4C22×D1111yescharacteristic
592C23×C4C22×D1111yescharacteristic
593#137—444no—
594AGL(1,ℤ/8)—444no—
595C2×Q16—114no—
596C2×SD16—114no—
597C2×SD16—114no—
598C2×D8—114no—
599C2×M16—112no—
600C2×M16—112no—
601C2×M16—114no—
602C2×M16—444no—
603C22×C8—114no—
604C4⋊Q8—22no—
605#127—22no—
606#124—22no—
607#124—22no—
608#123—22no—
609#123—22no—
610#123—22no—
611#123—22no—
612C22⋊Q8—22no—
613C22⋊Q8—22no—
614C22⋊Q8—112no—
615C22⋊Q8—112no—
616C22⋊Q8—114no—
617C22⋊Q8—224no—
618C22⋊Q8—224no—
619C22⋊Q8—221no—
620C22⋊Q8—221no—
621C22⋊Q8—222no—
622C22⋊Q8C22×D1112yes—
623C22⋊Q8C22×D1112yes—
624C22⋊Q8C22×D1112yes—
625C22⋊Q8C22×D1112yes—
626#121—22no—
627#121—22no—
628#121—22no—
629#121—22no—
630#121—22no—
631#121—22no—
632#121—112no—
633#121—112no—
634#121—114no—
635#121—224no—
636#121—224no—
637#121—224no—
638#121—224no—
639#121—224no—
640#121—224no—
641#121—221no—
642#121—221no—
643#121—222no—
644#121C22×D1112yes—
645#121C22×D1112yes—
646#121C22×D1112yes—
647#121C22×D1112yes—
648#120—22no—
649#120—22no—
650#120—22no—
651#120—22no—
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—22no—
655C4×D4—22no—
656#117—21no—
657#117—21no—
658#117C22×D1112yes—
659#117C22×D1112yes—
660C2×C4⋊C4—111no—
661C2×C4⋊C4—111no—
662C2×C4⋊C4—114no—
663C2×C4⋊C4—221no—
664C2×C4⋊C4—222no—
665C2×C4⋊C4—221no—
666C2×C4⋊C4—221no—
667C2×C4⋊C4C22×D1111yescharacteristic
668C2×C4⋊C4C22×D1111yescharacteristic
669C2×C22⋊C4—21no—
670C2×C22⋊C4—221no—
671C2×C22⋊C4—221no—
672C2×C22⋊C4—221no—
673C2×C22⋊C4—221no—
674C2×C42—21no—
675#107—114no—
676#107—114no—
677#106—114no—
678#106—114no—
679#103—114no—
680#103—114no—
681#103—114no—
682#103—114no—
683#102—114no—
684#102—114no—
685#102—114no—
686#102—114no—
687C22⋊C8—112no—
688C22⋊C8—112no—
689C22⋊C8—114no—
690C22⋊C8—114no—
691C22⋊C8—112no—
692C22⋊C8—112no—
693C2×C11—22no—
694C2×C11—42no—
695C2×C11—41no—
696C2×C11—42no—
697C2×C11—41no—
698C2×C11—82no—
699C2×C11C2×#53411yescharacteristic
700C2×C11#358511yescharacteristic
701C2×C11#358611yescharacteristic
702D11—82no—
703C24—21no—
704C24—221no—
705C24C2×C22⋊D1111yescharacteristic
706C24C2×C22⋊D1111yescharacteristic
707C24C2×C22⋊D1111yescharacteristic
708#41—24no—
709#41—24no—
710#41—42no—
711#41—42no—
712#41—42no—
713#41—42no—
714#41—44no—
715#41—44no—
716#41—42no—
717#41—42no—
718#41—44no—
719#41—44no—
720#41—444no—
721#41—444no—
722#41—448no—
723C2×Q8—21no—
724C2×Q8—42no—
725C2×Q8—42no—
726C2×Q8—112no—
727C2×Q8—221no—
728C2×Q8—224no—
729C2×Q8C2×C22⋊D1112yes—
730C2×Q8C2×C22⋊D1112yes—
731C2×Q8C23×D1112yes—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—21no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—44no—
744C2×D4—112no—
745C2×D4—224no—
746C2×D4—222no—
747C2×D4—224no—
748C2×D4—222no—
749C2×D4—224no—
750C2×D4—221no—
751C2×D4—444no—
752C2×D4—882no—
753C2×D4—882no—
754C2×D4C2×C22⋊D1112yes—
755C2×D4C2×C22⋊D1112yes—
756C2×D4C2×C22⋊D1112yes—
757C2×D4C2×C22⋊D1112yes—
758C2×D4C2×C22⋊D1112yes—
759C2×D4C2×C22⋊D1112yes—
760C2×D4C23×D1112yes—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—44no—
770C22×C4—221no—
771C22×C4—221no—
772C22×C4—221no—
773C22×C4—224no—
774C22×C4—224no—
775C22×C4—444no—
776C22×C4—882no—
777C22×C4C2×C22⋊D1111yescharacteristic
778C22×C4C2×C22⋊D1111yescharacteristic
779C22×C4C2×C22⋊D1111yescharacteristic
780C22×C4C2×C22⋊D1112yes—
781C22×C4C2×C22⋊D1111yescharacteristic
782C22×C4C2×C22⋊D1111yescharacteristic
783C22×C4C2×C22⋊D1112yes—
784C22×C4C23×D1112yes—
785C22×C4C23×D1111yescharacteristic
786C22×C4C23×D1111yescharacteristic
787C22×C4C23×D1112yes—
788C22×C4C23×D1111yescharacteristic
789Q16—444no—
790SD16—444no—
791SD16—444no—
792D8—444no—
793M16—224no—
794M16—224no—
795M16—444no—
796C2×C8—114no—
797C2×C8—114no—
798C2×C8—444no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—22no—
802C4⋊C4—22no—
803C4⋊C4—22no—
804C4⋊C4—22no—
805C4⋊C4—112no—
806C4⋊C4—112no—
807C4⋊C4—224no—
808C4⋊C4—221no—
809C4⋊C4—221no—
810C4⋊C4—222no—
811C4⋊C4—224no—
812C4⋊C4—222no—
813C4⋊C4C23×D1112yes—
814C4⋊C4C23×D1112yes—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—22no—
818C22⋊C4—22no—
819C22⋊C4—22no—
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—222no—
826C22⋊C4—224no—
827C22⋊C4—222no—
828C22⋊C4—222no—
829C22⋊C4—224no—
830C22⋊C4—222no—
831C42—22no—
832C42—22no—
833C11#6075511yescharacteristic, complemented, Sylow
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—42no—
845C23—81no—
846C23—81no—
847C23—222no—
848C23—442no—
849C23—442no—
850C23—442no—
851C23C22×C22⋊D1111yescharacteristic
852C23C22×C22⋊D1112yes—
853C23C22×C22⋊D1112yes—
854C23C22×C22⋊D1111yescharacteristic
855C23C22×C22⋊D1111yescharacteristic
856Q8—22no—
857Q8—22no—
858Q8—42no—
859Q8—42no—
860Q8—42no—
861Q8—224no—
862Q8—442no—
863D4—22no—
864D4—22no—
865D4—42no—
866D4—42no—
867D4—42no—
868D4—42no—
869D4—42no—
870D4—42no—
871D4—42no—
872D4—44no—
873D4—44no—
874D4—82no—
875D4—82no—
876D4—82no—
877D4—82no—
878D4—224no—
879D4—448no—
880D4—442no—
881D4—882no—
882D4—884no—
883D4—882no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—24no—
889C2×C4—22no—
890C2×C4—24no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—44no—
901C2×C4—42no—
902C2×C4—44no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—448no—
909C2×C4—442no—
910C2×C4—442no—
911C2×C4—442no—
912C2×C4—884no—
913C2×C4#6703714yes—
914C2×C4C22×C22⋊D1111yescharacteristic
915C2×C4C22×C22⋊D1112yes—
916C2×C4C22×C22⋊D1112yes—
917C2×C4C22×C22⋊D1111yescharacteristic
918C2×C4C22×C22⋊D1111yescharacteristic
919C2×C4C24×D1111yescharacteristic
920C8—224no—
921C8—224no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—22no—
926C22—22no—
927C22—21no—
928C22—21no—
929C22—22no—
930C22—22no—
931C22—21no—
932C22—21no—
933C22—21no—
934C22—22no—
935C22—22no—
936C22—44no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—82no—
941C22—82no—
942C22—84no—
943C22—442no—
944C22—442no—
945C22—442no—
946C22—884no—
947C22#1062333512yes—
948C22C23×C22⋊D1111yescharacteristic
949C4—21no—
950C4—22no—
951C4—21no—
952C4—22no—
953C4—42no—
954C4—42no—
955C4—42no—
956C4—442no—
957C4—442no—
958C4—442no—
959C4#1062333512yes—
960C4C2×#6703712yes—
961C2—22no—
962C2—42no—
963C2—41no—
964C2—41no—
965C2—42no—
966C2—82no—
967C2—882no—
968C2C2×#1062333511yescharacteristic
969C2#1308339511yescharacteristic
970C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3449C2
socleC22×C11C23×D4
hypercenter#3449D11
hypocenterC11#60755
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×#41 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#10623364C2semidirect
2. #13079522C2semidirect
3. #13079513C2semidirect
4. #13079498C2semidirect
5. #13079468C2semidirect
6. #13078564C2semidirect
7. #13078556C2semidirect
8. #13078536C2semidirect
9. #13078248C2semidirect
10. #13078237C2semidirect
11. #13077876C2semidirect
12. #13077868C2semidirect
13. #13077856C2semidirect
14. #13077061C2semidirect
15. C11×#3449C2semidirect
18. C22×#4339C22semidirect
19. C11×#537C22semidirect
20. C11×#537C22semidirect
22. C11×#536C22semidirect
24. C11×#535C22semidirect
35. #10623364C22semidirect
43. C2×#66983C22semidirect
44. C22×C4⋊Dic11C22semidirect
46. C2×#66977C22semidirect
47. C22×#4318C22semidirect
48. #10622852C22semidirect
49. #10622851C22semidirect
50. #10622847C22semidirect
51. #10622847C22semidirect
54. #10622841C22semidirect
55. #10622840C22semidirect
56. #10622831C22semidirect
57. #10622830C22semidirect
60. #10622820C22semidirect
61. #10622665C22semidirect
62. #10622664C22semidirect
63. #10622662C22semidirect
64. #10622661C22semidirect
65. #10622660C22semidirect
66. #10622660C22semidirect
67. #10622657C22semidirect
68. #10622656C22semidirect
69. #10622655C22semidirect
70. #10622654C22semidirect
71. #10622652C22semidirect
72. #10622651C22semidirect
73. #10622650C22semidirect
74. #10622650C22semidirect
75. #10622647C22semidirect
76. #10622646C22semidirect
77. #10622617C22semidirect
78. #10622616C22semidirect
79. #10622614C22semidirect
80. #10622609C22semidirect
81. #10622608C22semidirect
82. #10622608C22semidirect
83. #10622584C22semidirect
84. #10622583C22semidirect
85. #10622581C22semidirect
86. #10622580C22semidirect
349. #3449D11semidirect
462. #537C2×D11semidirect
463. #537C2×D11semidirect
465. #536C2×D11semidirect
467. #535C2×D11semidirect
833. C11#60755semidirect

Maximal subgroups

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

subgroupindex
C2×#106233642
#130795222
#130795132
#130794982
#130794682
#130785642
#130785562
#130785362
#130782482
#130782372
#130778762
#130778682
#130778562
#130770612
C11×#34492
#6075511