Finite Group Databasebeta

← #15632585

Subgroups — #15632585

Order 2816.

1872 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623074C211yesmaximal, characteristic, complemented
2#13081236C212yesmaximal, complemented
3#13081225C212yesmaximal, complemented
4#13081101C214yesmaximal, complemented
5#13081071C214yesmaximal, complemented
6#13081004C212yesmaximal, complemented
7#13080973C212yesmaximal, complemented
8#13079163C211yesmaximal, characteristic, complemented
9#13078564C212yesmaximal, complemented
10#13078536C212yesmaximal, complemented
11#13078431C211yesmaximal, characteristic, complemented
12#13078417C211yesmaximal, characteristic, complemented
13#13078248C212yesmaximal, complemented
14C4×#67004C211yesmaximal, characteristic, complemented
15D4×#4318C211yesmaximal, characteristic, complemented
16C2×#10622608C212yesmaximal, complemented
17C11×#3475C211yesmaximal, characteristic
18C11×#556C2211yescharacteristic
19C11×#555C2211yescharacteristic
20C11×#554C2211yescharacteristic
21C11×#553C2212yes—
22C11×#552—21no—
23C11×#552C2212yes—
24C11×#551—22no—
25C11×#547C2211yescharacteristic
26C11×#546—21no—
27C11×#533C2211yescharacteristic
28C11×#529—22no—
29C11×#529—21no—
30C11×#525C2212yes—
31C4×C11×#41—21no—
32C4×C11×#41C2211yescharacteristic
33C2×C4×D4×C11C2211yescharacteristic
34C2×C11×#117C2212yes—
35C2×#67004C2211yescharacteristic
36C2×D4×Dic11—21no—
37C22×C4⋊Dic11C2212yes—
38C2×#66977C2212yes—
39C22×#4318C2212yes—
40#10623074—21no—
41#10623074—21no—
42#10623074—22no—
43#10623074C2214yes—
44#10623074C2212yes—
45#10623074C2212yes—
46C2×#66943—21no—
47C2×#66931—22no—
48C2×#66922C2211yescharacteristic
49C2×C4×Dic22C2211yescharacteristic
50#10622845C2211yescharacteristic
51#10622845C2212yes—
52#10622820C2212yes—
53#10622707C2212yescomplemented
54#10622704C2212yescomplemented
55#10622692C2212yescomplemented
56#10622691C2212yescomplemented
57#10622678C2214yescomplemented
58#10622676C2214yescomplemented
59#10622665C2214yescomplemented
60#10622664C2214yescomplemented
61#10622657C2214yescomplemented
62#10622656C2214yescomplemented
63#10622655C2214yescomplemented
64#10622654C2214yescomplemented
65#10622647C2214yescomplemented
66#10622646C2214yescomplemented
67#10622643C2212yescomplemented
68C4×#4326C2212yescomplemented
69#10622634C2212yescomplemented
70#10622633C2212yescomplemented
71#10622631C2212yescomplemented
72C4×#4324C2212yescomplemented
73#10622625C2212yes—
74#10622624C2214yes—
75D4×C11⋊C8C2212yes—
76#10622621C2212yescomplemented
77#10622620C2212yescomplemented
78#10622617C2211yescharacteristic
79#10622617C2212yes—
80#10622609C2214yescomplemented
81#10622609C2214yescomplemented
82#10622608C2212yes—
83#10622608C2212yes—
84#10622608C2212yes—
85#10622608C2212yes—
86#10622608C2211yescharacteristic
87#10622608C2214yescomplemented
88#10622608C2214yescomplemented
89#10622584C2214yescomplemented
90#10622583C2214yescomplemented
91C2×#66872C2214yescomplemented
92C2×#66871C2214yescomplemented
93#10622537C2211yescharacteristic
94C4×#4318C2211yescharacteristic
95C2×C11×#41—21no—
96C2×C11×#41C2311yescharacteristic
97C22×D4×C11D411yescharacteristic
98C23×C4×C11C2312yes—
99C23×Dic11—22no—
100C22×Dic22—21no—
101C22×Dic22C2311yescharacteristic
102C11×C4⋊Q8C2311yescharacteristic
103C11×C4⋊Q8C2311yescharacteristic
104C11×#126—22no—
105C11×#126—22no—
106C11×#126—22no—
107C11×#125—22no—
108C11×#125—21no—
109C11×#125C2312yes—
110C11×#124—21no—
111C11×#124—22no—
112C11×#123—22no—
113C11×#123—22no—
114C11×#123—22no—
115C11×#123—22no—
116C11×C22⋊Q8—21no—
117C11×C22⋊Q8—21no—
118C11×C22⋊Q8—21no—
119C11×C22⋊Q8—22no—
120C11×C22⋊Q8C2312yes—
121C11×C22⋊Q8C2312yes—
122C11×#121—22no—
123C11×#121—21no—
124C11×#121C2312yes—
125C11×#121C2312yes—
126C11×#120—22no—
127C4×Q8×C11—21no—
128C4×Q8×C11—21no—
129C4×Q8×C11—21no—
130C4×Q8×C11C2311yescharacteristic
131C4×Q8×C11C2311yescharacteristic
132C4×D4×C11—21no—
133C4×D4×C11—22no—
134C4×D4×C11—21no—
135C4×D4×C11—21no—
136C4×D4×C11—22no—
137C4×D4×C11—22no—
138C4×D4×C11D411yescharacteristic
139C4×D4×C11D411yescharacteristic
140C4×D4×C11D412yes—
141C4×D4×C11C2311yescharacteristic
142C4×D4×C11C2311yescharacteristic
143C4×D4×C11C2311yescharacteristic
144C4×D4×C11C2312yes—
145C4×D4×C11C2311yescharacteristic
146C11×#117—22no—
147C11×#117—22no—
148C11×#117—21no—
149C11×#117—22no—
150C11×#117—21no—
151C11×#117C2311yescharacteristic
152C11×#117C2312yes—
153C11×#117C2312yes—
154C11×#117C2312yes—
155C2×C11×C4⋊C4D411yescharacteristic
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C22⋊C4—22no—
159C2×C11×C22⋊C4D412yes—
160C2×C42×C11—22no—
161C2×C42×C11—21no—
162C2×C42×C11C2311yescharacteristic
163C2×C22⋊Dic11—22no—
164#67004—24no—
165C2×#4326C2312yes—
166D4×Dic11—24no—
167D4×Dic11—22no—
168D4×Dic11—22no—
169C2×#4324C2312yes—
170C2×C4⋊Dic11—21no—
171C2×C4⋊Dic11—22no—
172C2×C4⋊Dic11—22no—
173C2×C4⋊Dic11—22no—
174C2×C4⋊Dic11C2311yescharacteristic
175C2×C4⋊Dic11C2312yes—
176C2×C4⋊Dic11C2314yes—
177C2×C4⋊Dic11C2314yes—
178#66977—22no—
179#66977—22no—
180#66977C2314yes—
181#66977C2314yes—
182C2×Dic11⋊C4—21no—
183C2×Dic11⋊C4—22no—
184C2×C4×Dic11—21no—
185C2×#4318—28no—
186C2×#4318C2311yescharacteristic
187C2×#4318C2312yes—
188C2×#4318C2314yes—
189C2×#4318C2311yescharacteristic
190C22×C11⋊C8C2314yes—
191#66943—22no—
192#66943—22no—
193#66943—24no—
194#66931—24no—
195#66931—24no—
196#66931—24no—
197#66931—24no—
198#66922—21no—
199#66922—21no—
200#66922C2312yes—
201#66922C2312yes—
202C4×Dic22—21no—
203C4×Dic22—21no—
204C4×Dic22C2312yes—
205C4×Dic22C2312yes—
206#66899C2314yes—
207#66899C2312yes—
208#66896C2314yes—
209#66896C2312yes—
210C22⋊(C11⋊C8)C2314yes—
211C22⋊(C11⋊C8)C2314yes—
212#66874C2312yes—
213#66874C2314yes—
214#66874C2312yes—
215#66874C2314yes—
216#66872C2312yes—
217#66872C2314yes—
218#66872C2314yes—
219#66872C2314yes—
220#66872C2314yes—
221#66871C2312yes—
222#66871C2314yes—
223#66871C2314yes—
224#66871C2314yes—
225#66871C2314yes—
226C4⋊(C11⋊C8)C2312yes—
227C4⋊(C11⋊C8)C2312yes—
228#66867C2312yes—
229C4×C11⋊C8C2312yes—
230#61254—111nomaximal, Sylow
231C24×C11C2×D412yes—
232C11×#41—22no—
233C11×#41—22no—
234C11×#41—44no—
235C2×Q8×C11—21no—
236C2×Q8×C11—21no—
237C2×Q8×C11C2411yescharacteristic
238C2×D4×C11—24no—
239C2×D4×C11—21no—
240C2×D4×C11—22no—
241C2×D4×C11—22no—
242C2×D4×C11C2×D412yes—
243C2×D4×C11C2×D411yescharacteristic
244C2×D4×C11C2×D411yescharacteristic
245C2×D4×C11C2411yescharacteristic
246C22×C4×C11—24no—
247C22×C4×C11—24no—
248C22×C4×C11—22no—
249C22×C4×C11—22no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D412yes—
255C22×C4×C11C2×D412yes—
256C22×C4×C11C2×D412yes—
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2412yes—
259C22×C4×C11C2412yes—
260C22×C4×C11C2411yescharacteristic
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—22no—
264C22×Dic11—24no—
265C22×Dic11—24no—
266C22×Dic11—84no—
267C2×Dic22—21no—
268C2×Dic22—22no—
269C2×Dic22—22no—
270C2×Dic22—22no—
271C2×Dic22—22no—
272C2×Dic22—82no—
273C2×Dic22C2412yes—
274C11×C4⋊C4—22no—
275C11×C4⋊C4—22no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—22no—
278C11×C4⋊C4—22no—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—21no—
281C11×C4⋊C4—22no—
282C11×C4⋊C4—22no—
283C11×C4⋊C4—21no—
284C11×C4⋊C4C2×D411yescharacteristic
285C11×C4⋊C4C2×D411yescharacteristic
286C11×C4⋊C4C2×D412yes—
287C11×C4⋊C4C2411yescharacteristic
288C11×C4⋊C4C2412yes—
289C11×C4⋊C4C2411yescharacteristic
290C11×C4⋊C4C2412yes—
291C11×C22⋊C4—21no—
292C11×C22⋊C4—22no—
293C11×C22⋊C4—22no—
294C11×C22⋊C4—22no—
295C11×C22⋊C4—22no—
296C11×C22⋊C4—22no—
297C11×C22⋊C4—22no—
298C11×C22⋊C4—21no—
299C11×C22⋊C4—21no—
300C11×C22⋊C4—22no—
301C11×C22⋊C4C2×D412yes—
302C11×C22⋊C4C2×D412yes—
303C11×C22⋊C4C2×D412yes—
304C11×C22⋊C4C2×D412yes—
305C42×C11—21no—
306C42×C11—22no—
307C42×C11—21no—
308C42×C11—22no—
309C42×C11—22no—
310C42×C11—21no—
311C42×C11C2×D411yescharacteristic
312C42×C11C2×D411yescharacteristic
313C42×C11C2411yescharacteristic
314C42×C11C2411yescharacteristic
315C22⋊Dic11—24no—
316C22⋊Dic11—24no—
317#4326—24no—
318#4324—24no—
319C4⋊Dic11—21no—
320C4⋊Dic11—22no—
321C4⋊Dic11—22no—
322C4⋊Dic11—22no—
323C4⋊Dic11—24no—
324C4⋊Dic11—24no—
325C4⋊Dic11C2412yes—
326C4⋊Dic11C2414yes—
327Dic11⋊C4—22no—
328Dic11⋊C4—22no—
329Dic11⋊C4—24no—
330Dic11⋊C4—24no—
331C4×Dic11—22no—
332C4×Dic11—22no—
333#4318—28no—
334#4318—24no—
335#4318—22no—
336#4318#4114yescomplemented
337C2×C11⋊C8—28no—
338C2×C11⋊C8C2412yes—
339C2×C11⋊C8C2414yes—
340C2×C11⋊C8C2412yes—
341#3475D1111yescharacteristic
342C2×#554—111no—
343#3357—112no—
344#3356—112no—
345#3346—114no—
346#3344—114no—
347#3338—112no—
348#3335—112no—
349#3165—111no—
350#3095—112no—
351#3092—112no—
352#3079—111no—
353#3078—111no—
354#3056—112no—
355C4×#137—111no—
356D4×M16—111no—
357C2×#428—112no—
358C23×C11—24no—
359C23×C11—24no—
360C23×C11—21no—
361C23×C11—42no—
362C23×C11C22×D412yes—
363C23×C11C22×D411yescharacteristic
364C23×C11C22×D412yes—
365Q8×C11—21no—
366Q8×C11—21no—
367Q8×C11—42no—
368Q8×C11—81no—
369D4×C11—24no—
370D4×C11—22no—
371D4×C11—21no—
372D4×C11—21no—
373D4×C11—42no—
374D4×C11—44no—
375D4×C11—82no—
376D4×C11#13714yescomplemented
377C2×C4×C11—24no—
378C2×C4×C11—24no—
379C2×C4×C11—24no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—21no—
386C2×C4×C11—21no—
387C2×C4×C11—21no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—41no—
391C2×C4×C11—44no—
392C2×C4×C11—42no—
393C2×C4×C11—42no—
394C2×C4×C11—81no—
395C2×C4×C11—82no—
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D412yes—
398C2×C4×C11C22×D412yes—
399C2×C4×C11C22×D411yescharacteristic
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11C22×D411yescharacteristic
402C2×C4×C11C22×D411yescharacteristic
403C2×C4×C11C2×#4112yes—
404C2×C4×C112−1+412yes—
405C2×C4×C11C2511yescharacteristic
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—24no—
409C2×Dic11—44no—
410C2×Dic11—42no—
411C2×Dic11—42no—
412C2×Dic11—84no—
413C2×Dic11—84no—
414Dic22—22no—
415Dic22—22no—
416Dic22—42no—
417Dic22—82no—
418Dic22—82no—
419C11⋊C8—24no—
420C11⋊C8—22no—
421C11⋊C8C2×#4114yes—
422C2×#137—111no—
423C22×M16—112no—
424#556C2×D1111yescharacteristic
425#555C2×D1111yescharacteristic
426#554—112no—
427#554—114no—
428#554—112no—
429#554—221no—
430#554—222no—
431#554—221no—
432#554C2×D1111yescharacteristic
433#553C2×D1112yes—
434#552—21no—
435#552C2×D1112yes—
436#551—22no—
437#547C2×D1111yescharacteristic
438#546—21no—
439#533C2×D1111yescharacteristic
440C2×C4⋊Q8—111no—
441#529—22no—
442#529—21no—
443C2×#125—221no—
444#525C2×D1112yes—
445C2×C22⋊Q8—112no—
446C2×C22⋊Q8—222no—
447C4×#41—21no—
448C4×#41C2×D1111yescharacteristic
449C2×C4×Q8—111no—
450C2×C4×D4—221no—
451C2×C4×D4C2×D1111yescharacteristic
452C2×#117C2×D1112yes—
453C22×C4⋊C4—112no—
454#501—114no—
455#500—112no—
456#498—112no—
457#485—114no—
458#485—114no—
459#484—114no—
460#484—114no—
461#483—114no—
462#483—114no—
463#481—114no—
464#480—114no—
465#479—114no—
466#477—112no—
467#477—112no—
468#476—112no—
469#475—112no—
470#475—112no—
471#474—112no—
472#470—114no—
473#468—114no—
474#467—114no—
475#465—114no—
476#441—112no—
477#440—112no—
478C4×Q16—112no—
479C4×SD16—112no—
480#436—112no—
481#435—114no—
482C8×D4—112no—
483#428—112no—
484#428—112no—
485#428—114no—
486#428—114no—
487#428—112no—
488#428—112no—
489#428—111no—
490C2×#107—114no—
491C2×#106—114no—
492#423—111no—
493#419—112no—
494#419—111no—
495#417—112no—
496#417—111no—
497#407—112no—
498C4×M16—111no—
499C22×C11—21no—
500C22×C11—22no—
501C22×C11—22no—
502C22×C11—21no—
503C22×C11—22no—
504C22×C11—22no—
505C22×C11—22no—
506C22×C11—48no—
507C22×C11—41no—
508C22×C11—41no—
509C22×C11—41no—
510C22×C11#54712yes—
511C22×C11C2×#13714yes—
512C22×C11C23×D411yescharacteristic
513C4×C11—21no—
514C4×C11—21no—
515C4×C11—22no—
516C4×C11—22no—
517C4×C11—21no—
518C4×C11—41no—
519C4×C11—42no—
520C4×C11—41no—
521C4×C11—41no—
522C4×C11—42no—
523C4×C11#54712yes—
524C4×C11C2×#13712yes—
525C4×C11C22×#4111yescharacteristic
526C4×C11C2×2−1+411yescharacteristic
527Dic11—44no—
528Dic11—42no—
529Dic11—42no—
530C2×#41—21no—
531C2×#41C22×D1111yescharacteristic
532C22×Q8—111no—
533C22×Q8—221no—
534C22×D4C22⋊D1111yescharacteristic
535C23×C4—222no—
536C23×C4C22×D1112yes—
537#137—224no—
538C2×Q16—112no—
539C2×SD16—112no—
540C2×M16—111no—
541C2×M16—112no—
542C2×M16—114no—
543C2×M16—111no—
544C2×M16—228no—
545C22×C8—114no—
546C4⋊Q8—112no—
547C4⋊Q8—112no—
548C4⋊Q8—221no—
549C4⋊Q8—221no—
550C4⋊Q8C22×D1111yescharacteristic
551C4⋊Q8C22×D1111yescharacteristic
552#126—22no—
553#126—22no—
554#126—22no—
555#125—22no—
556#125—21no—
557#125—222no—
558#125—222no—
559#125—224no—
560#125C22×D1112yes—
561#124—21no—
562#124—22no—
563#123—22no—
564#123—22no—
565#123—22no—
566#123—22no—
567C22⋊Q8—21no—
568C22⋊Q8—21no—
569C22⋊Q8—21no—
570C22⋊Q8—22no—
571C22⋊Q8—114no—
572C22⋊Q8—114no—
573C22⋊Q8—222no—
574C22⋊Q8—222no—
575C22⋊Q8—224no—
576C22⋊Q8—224no—
577C22⋊Q8—224no—
578C22⋊Q8—224no—
579C22⋊Q8C22×D1112yes—
580C22⋊Q8C22×D1112yes—
581#121—22no—
582#121—21no—
583#121C22×D1112yes—
584#121C22×D1112yes—
585#120—22no—
586C4×Q8—21no—
587C4×Q8—21no—
588C4×Q8—21no—
589C4×Q8—112no—
590C4×Q8—112no—
591C4×Q8—221no—
592C4×Q8—221no—
593C4×Q8C22×D1111yescharacteristic
594C4×Q8C22×D1111yescharacteristic
595C4×D4—21no—
596C4×D4—22no—
597C4×D4—21no—
598C4×D4—21no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—224no—
602C4×D4—222no—
603C4×D4—222no—
604C4×D4C22⋊D1111yescharacteristic
605C4×D4C22⋊D1111yescharacteristic
606C4×D4C22⋊D1112yes—
607C4×D4C22×D1111yescharacteristic
608C4×D4C22×D1111yescharacteristic
609C4×D4C22×D1111yescharacteristic
610C4×D4C22×D1112yes—
611C4×D4C22×D1111yescharacteristic
612#117—22no—
613#117—22no—
614#117—21no—
615#117—22no—
616#117—21no—
617#117C22×D1111yescharacteristic
618#117C22×D1112yes—
619#117C22×D1112yes—
620#117C22×D1112yes—
621C2×C4⋊C4—111no—
622C2×C4⋊C4—112no—
623C2×C4⋊C4—114no—
624C2×C4⋊C4—114no—
625C2×C4⋊C4—222no—
626C2×C4⋊C4—222no—
627C2×C4⋊C4—222no—
628C2×C4⋊C4—221no—
629C2×C4⋊C4—221no—
630C2×C4⋊C4—222no—
631C2×C4⋊C4C22⋊D1111yescharacteristic
632C2×C4⋊C4C22×D1112yes—
633C2×C4⋊C4C22×D1112yes—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—222no—
636C2×C22⋊C4C22⋊D1112yes—
637C2×C42—22no—
638C2×C42—21no—
639C2×C42—221no—
640C2×C42C22×D1111yescharacteristic
641#107—112no—
642#107—114no—
643#107—114no—
644#107—114no—
645#107—114no—
646#106—112no—
647#106—114no—
648#106—114no—
649#106—114no—
650#106—114no—
651C4⋊C8—112no—
652C4⋊C8—112no—
653#103—112no—
654#103—114no—
655#103—112no—
656#103—112no—
657#103—114no—
658#103—114no—
659#102—112no—
660#102—114no—
661C22⋊C8—114no—
662C22⋊C8—114no—
663#97—112no—
664C4×C8—112no—
665C2×C11—22no—
666C2×C11—24no—
667C2×C11—42no—
668C2×C11—81no—
669C2×C11C2×#54711yescharacteristic
670C2×C11C22×#13711yescharacteristic
671C2×C11#358511yescharacteristic
672C24C2×C22⋊D1112yes—
673#41—22no—
674#41—22no—
675#41—44no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—112no—
679C2×Q8—221no—
680C2×Q8—222no—
681C2×Q8—222no—
682C2×Q8—222no—
683C2×Q8—222no—
684C2×Q8—882no—
685C2×Q8C23×D1111yescharacteristic
686C2×D4—24no—
687C2×D4—21no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4C2×C22⋊D1112yes—
691C2×D4C2×C22⋊D1111yescharacteristic
692C2×D4C2×C22⋊D1111yescharacteristic
693C2×D4C23×D1111yescharacteristic
694C22×C4—24no—
695C22×C4—24no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—221no—
702C22×C4—221no—
703C22×C4—222no—
704C22×C4—224no—
705C22×C4—224no—
706C22×C4—884no—
707C22×C4C2×C22⋊D1112yes—
708C22×C4C2×C22⋊D1111yescharacteristic
709C22×C4C2×C22⋊D1112yes—
710C22×C4C2×C22⋊D1112yes—
711C22×C4C2×C22⋊D1111yescharacteristic
712C22×C4C23×D1112yes—
713C22×C4C23×D1112yes—
714C22×C4C23×D1111yescharacteristic
715Q16—224no—
716SD16—224no—
717M16—114no—
718M16—228no—
719M16—224no—
720M16—222no—
721C2×C8—112no—
722C2×C8—112no—
723C2×C8—114no—
724C2×C8—228no—
725C4⋊C4—22no—
726C4⋊C4—22no—
727C4⋊C4—21no—
728C4⋊C4—22no—
729C4⋊C4—22no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—22no—
733C4⋊C4—22no—
734C4⋊C4—21no—
735C4⋊C4—112no—
736C4⋊C4—114no—
737C4⋊C4—221no—
738C4⋊C4—224no—
739C4⋊C4—224no—
740C4⋊C4—222no—
741C4⋊C4—222no—
742C4⋊C4—222no—
743C4⋊C4—222no—
744C4⋊C4—222no—
745C4⋊C4—224no—
746C4⋊C4—224no—
747C4⋊C4C2×C22⋊D1111yescharacteristic
748C4⋊C4C2×C22⋊D1111yescharacteristic
749C4⋊C4C2×C22⋊D1112yes—
750C4⋊C4C23×D1111yescharacteristic
751C4⋊C4C23×D1112yes—
752C4⋊C4C23×D1111yescharacteristic
753C4⋊C4C23×D1112yes—
754C22⋊C4—21no—
755C22⋊C4—22no—
756C22⋊C4—22no—
757C22⋊C4—22no—
758C22⋊C4—22no—
759C22⋊C4—22no—
760C22⋊C4—22no—
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—22no—
764C22⋊C4—224no—
765C22⋊C4—224no—
766C22⋊C4C2×C22⋊D1112yes—
767C22⋊C4C2×C22⋊D1112yes—
768C22⋊C4C2×C22⋊D1112yes—
769C22⋊C4C2×C22⋊D1112yes—
770C42—21no—
771C42—22no—
772C42—21no—
773C42—22no—
774C42—22no—
775C42—21no—
776C42—222no—
777C42—222no—
778C42C2×C22⋊D1111yescharacteristic
779C42C2×C22⋊D1111yescharacteristic
780C42C23×D1111yescharacteristic
781C42C23×D1111yescharacteristic
782C11#6125411yescharacteristic, complemented, Sylow
783C23—24no—
784C23—24no—
785C23—21no—
786C23—42no—
787C23C22×C22⋊D1112yes—
788C23C22×C22⋊D1112yes—
789C23C22×C22⋊D1111yescharacteristic
790Q8—21no—
791Q8—21no—
792Q8—42no—
793Q8—81no—
794Q8—222no—
795Q8—222no—
796Q8—442no—
797Q8—882no—
798Q8—882no—
799D4—24no—
800D4—22no—
801D4—21no—
802D4—21no—
803D4—44no—
804D4—42no—
805D4—82no—
806D4#6700414yescomplemented
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—41no—
821C2×C4—44no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—81no—
825C2×C4—82no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—224no—
829C2×C4—442no—
830C2×C4—444no—
831C2×C4—442no—
832C2×C4—884no—
833C2×C4—884no—
834C2×C4#41×D1112yes—
835C2×C4#6704312yes—
836C2×C4C22×C22⋊D1112yes—
837C2×C4C22×C22⋊D1111yescharacteristic
838C2×C4C22×C22⋊D1111yescharacteristic
839C2×C4C22×C22⋊D1111yescharacteristic
840C2×C4C22×C22⋊D1112yes—
841C2×C4C22×C22⋊D1111yescharacteristic
842C2×C4C22×C22⋊D1111yescharacteristic
843C2×C4C24×D1111yescharacteristic
844C8—114no—
845C8—224no—
846C8—222no—
847C22—21no—
848C22—22no—
849C22—22no—
850C22—21no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—48no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22C2×#6700414yes—
859C22#1062335512yes—
860C22C23×C22⋊D1111yescharacteristic
861C4—21no—
862C4—21no—
863C4—22no—
864C4—22no—
865C4—21no—
866C4—41no—
867C4—42no—
868C4—41no—
869C4—41no—
870C4—42no—
871C4—442no—
872C4—444no—
873C4—442no—
874C4C2×#6700412yes—
875C4#1062335512yes—
876C4C2×#41×D1111yescharacteristic
877C4C2×#6704311yescharacteristic
878C2—22no—
879C2—24no—
880C2—42no—
881C2—81no—
882C2C2×#1062335511yescharacteristic
883C2C22×#6700411yescharacteristic
884C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC11×#3475C2
socleC22×C11C23×D4
hypercenter#3475D11
hypocenterC11#61254
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3475

Complements

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

NH ≅ G/Ntype
1. C2×#10623074C2semidirect
2. #13081236C2semidirect
3. #13081225C2semidirect
4. #13081101C2semidirect
5. #13081071C2semidirect
6. #13081004C2semidirect
7. #13080973C2semidirect
8. #13079163C2semidirect
9. #13078564C2semidirect
10. #13078536C2semidirect
11. #13078431C2semidirect
12. #13078417C2semidirect
13. #13078248C2semidirect
14. C4×#67004C2semidirect
15. D4×#4318C2semidirect
16. C2×#10622608C2semidirect
53. #10622707C22semidirect
54. #10622704C22semidirect
55. #10622692C22semidirect
56. #10622691C22semidirect
57. #10622678C22semidirect
58. #10622676C22semidirect
59. #10622665C22semidirect
60. #10622664C22semidirect
61. #10622657C22semidirect
62. #10622656C22semidirect
63. #10622655C22semidirect
64. #10622654C22semidirect
65. #10622647C22semidirect
66. #10622646C22semidirect
67. #10622643C22semidirect
68. C4×#4326C22semidirect
69. #10622634C22semidirect
70. #10622633C22semidirect
71. #10622631C22semidirect
72. C4×#4324C22semidirect
76. #10622621C22semidirect
77. #10622620C22semidirect
80. #10622609C22semidirect
81. #10622609C22semidirect
87. #10622608C22semidirect
88. #10622608C22semidirect
89. #10622584C22semidirect
90. #10622583C22semidirect
91. C2×#66872C22semidirect
92. C2×#66871C22semidirect
336. #4318#41semidirect
376. D4×C11#137semidirect
782. C11#61254semidirect
806. D4#67004semidirect

Maximal subgroups

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

subgroupindex
C2×#106230742
#130812362
#130812252
#130811012
#130810712
#130810042
#130809732
#130791632
#130785642
#130785362
#130784312
#130784172
#130782482
C4×#670042
D4×#43182
C2×#106226082
C11×#34752
#6125411