Finite Group Databasebeta

← C2×#13079454 #15624400

Subgroups — C2×#13079454 #15624400

Order 2816.

2362 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623158C211yesmaximal, characteristic, complemented
2C2×#10623137C211yesmaximal, characteristic, complemented
3#13079454C2116yesmaximal, direct product factor
4C2×#10622501C211yesmaximal, characteristic, complemented
5C2×#10622427C211yesmaximal, characteristic, complemented
6C2×#10622498C211yesmaximal, characteristic, complemented
7C2×#10622397C211yesmaximal, characteristic, complemented
8C2×#10622665C211yesmaximal, characteristic, complemented
9C2×#10622652C211yesmaximal, characteristic, complemented
10C2×#10622747C211yesmaximal, characteristic, complemented
11C2×#10622423C211yesmaximal, characteristic, complemented
12C2×#10622786C211yesmaximal, characteristic, complemented
13C2×#10622394C211yesmaximal, characteristic, complemented
14C2×#10622785C211yesmaximal, characteristic, complemented
15C2×#10622739C211yesmaximal, characteristic, complemented
16C2×C11×#468C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic, complemented
21C22×C11×M16C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×#66999C2211yescharacteristic
25C22×#4326C2211yescharacteristic, complemented
26C2×#66991C2211yescharacteristic
27C2×#66990—21no—
28C2×D4×Dic11—21no—
29C22×#4323C2211yescharacteristic, complemented
30C2×#66983C2211yescharacteristic
31C2×#66977C2211yescharacteristic
32C22×#4318C2211yescharacteristic
33C22×#4314C2211yescharacteristic, complemented
34#10623158—24no—
35#10623158C2218yescomplemented
36#10623137—24no—
37#10623137C2218yescomplemented
38C2×#66950C2211yescharacteristic
39C2×#66948C2211yescharacteristic
40C2×#66947—21no—
41C2×#66946—21no—
42C2×#66945C2211yescharacteristic
43C2×#66945C2211yescharacteristic
44C2×#66936—21no—
45C2×#66935—21no—
46C2×(C22⋊D11)⋊C4—21no—
47C2×(C22⋊D11)⋊C4—21no—
48C11×#468C2218yescomplemented
49C2×C11×#107C2211yescharacteristic, complemented
50C2×C11×#103C2211yescharacteristic, complemented
51C2×C11×#102C2211yescharacteristic, complemented
52C2×#66899C2211yescharacteristic, complemented
53C2×#66896C2211yescharacteristic, complemented
54#10622786C2218yescomplemented
55#10622785C2218yescomplemented
56#10622747C2218yescomplemented
57#10622739C2218yescomplemented
58C2×#66885C2211yescharacteristic, complemented
59C2×(C2×D11)⋊C8C2211yescharacteristic
60C2×(C2×D11)⋊C8C2211yescharacteristic
61C2×(C2×D11)⋊C8C2211yescharacteristic
62C2×(C2×D11)⋊C8C2211yescharacteristic
63C2×#66882C2211yescharacteristic, complemented
64C2×#66880C2211yescharacteristic, complemented
65#10622665C2218yescomplemented
66#10622652C2218yescomplemented
67C2×#66874C2211yescharacteristic, complemented
68C2×#66873C2211yescharacteristic, complemented
69C2×#66872C2211yescharacteristic, complemented
70C2×#66872C2211yescharacteristic, complemented
71#10622501C2218yescomplemented
72#10622498C2218yescomplemented
73#10622427C2218yescomplemented
74#10622423C2218yescomplemented
75#10622397C2218yescomplemented
76#10622394C2218yescomplemented
77C24×D11D411yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11—21no—
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C23×Dic11—21no—
86C23×Dic11D411yescharacteristic
87C2×#4343—22no—
88C2×#4343—42no—
89C2×#4343—42no—
90C2×#4343C2314yes—
91C2×#4341—22no—
92C2×#4341—42no—
93C2×#4341—42no—
94C2×#4341C2314yes—
95C22×D44—21no—
96C22×D44—21no—
97C22×D44C2311yescharacteristic
98C22×C4×D11—21no—
99C22×C4×D11—42no—
100C22×C4×D11—42no—
101C22×C4×D11D411yescharacteristic
102C22×C4×D11D411yescharacteristic
103C22×C4×D11D414yes—
104C22×C4×D11C2311yescharacteristic
105C22×C4×D11C2311yescharacteristic
106C22×C4×D11C2314yes—
107C22×Dic22C2311yescharacteristic
108C2×C11×SD16—42no—
109C2×C11×SD16C2314yescomplemented
110C2×C11×M16—42no—
111C2×C11×M16C2314yes—
112C22×C8×C11C2311yescharacteristic
113C22×C8×C11C2311yescharacteristic
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8C2314yes—
116C11×#121—22no—
117C11×#121C2314yes—
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C22⋊Dic11—21no—
124C2×C22⋊Dic11—21no—
125#66999—22no—
126#66999C2314yes—
127C2×#4326—42no—
128C2×#4326C2314yescomplemented
129#66991—22no—
130#66991C2314yes—
131#66990—28no—
132D4×Dic11—28no—
133C2×#4323—42no—
134C2×#4323C2314yescomplemented
135#66983—22no—
136#66983C2314yes—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4—21no—
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—21no—
143C2×C4⋊Dic11—21no—
144C2×C4⋊Dic11C2311yescharacteristic
145C2×C4⋊Dic11C2311yescharacteristic
146#66977—22no—
147#66977C2314yes—
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4—21no—
150C2×C4×Dic11—21no—
151C2×C4×Dic11—21no—
152C2×#4318—42no—
153C2×#4318C2314yes—
154C22×C11⋊C8C2311yescharacteristic
155C22×C11⋊C8C2311yescharacteristic
156C2×#4314—42no—
157C2×#4314C2314yescomplemented
158#66950—22no—
159#66950C2314yes—
160#66948—22no—
161#66948C2314yes—
162#66947—28no—
163#66946—28no—
164#66945—22no—
165#66945—22no—
166#66945C2314yes—
167#66945C2314yes—
168#66936—28no—
169#66935—28no—
170(C22⋊D11)⋊C4—28no—
171(C22⋊D11)⋊C4—28no—
172C11×#107C2314yescomplemented
173C11×#103C2314yescomplemented
174C11×#102C2314yescomplemented
175#66899C2314yescomplemented
176#66896C2314yescomplemented
177#66885C2314yescomplemented
178(C2×D11)⋊C8C2314yes—
179(C2×D11)⋊C8C2314yes—
180(C2×D11)⋊C8C2314yes—
181(C2×D11)⋊C8C2314yes—
182#66882C2314yescomplemented
183#66880C2314yescomplemented
184#66874C2314yescomplemented
185#66873C2314yescomplemented
186#66872C2314yescomplemented
187#66872C2314yescomplemented
188C2×#3197—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11C2×D411yescharacteristic
191C23×D11—21no—
192C23×D11—42no—
193C23×D11—42no—
194C23×D11—42no—
195C23×D11C2×D411yescharacteristic
196C23×D11C2×D411yescharacteristic
197C23×D11C2×D414yes—
198C2×Q8×C11—21no—
199C2×Q8×C11—22no—
200C2×Q8×C11—22no—
201C2×Q8×C11C2412yes—
202C2×D4×C11—24no—
203C2×D4×C11—21no—
204C2×D4×C11—22no—
205C2×D4×C11—22no—
206C2×D4×C11—44no—
207C2×D4×C11C2412yes—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D412yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2411yescharacteristic
217C2×C22⋊D11—24no—
218C2×C22⋊D11—24no—
219C2×C22⋊D11—24no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11—44no—
223C22×Dic11—24no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—42no—
228C22×Dic11—44no—
229C22×Dic11C2×D411yescharacteristic
230C22×Dic11C2×D411yescharacteristic
231C22×Dic11C2×D414yes—
232#4343—44no—
233#4343—44no—
234#4343—48no—
235#4341—44no—
236#4341—44no—
237#4341—48no—
238C2×D44—24no—
239C2×D44—24no—
240C2×D44—21no—
241C2×D44—22no—
242C2×D44—22no—
243C2×D44—44no—
244C2×D44—44no—
245C2×D44C2412yes—
246C2×C4×D11—24no—
247C2×C4×D11—22no—
248C2×C4×D11—22no—
249C2×C4×D11—22no—
250C2×C4×D11—22no—
251C2×C4×D11—42no—
252C2×C4×D11—42no—
253C2×C4×D11—48no—
254C2×C4×D11—44no—
255C2×C4×D11—44no—
256C2×C4×D11—44no—
257C2×C4×D11C2×D412yes—
258C2×C4×D11C2×D412yes—
259C2×C4×D11C2×D414yes—
260C2×C4×D11C2×D414yes—
261C2×C4×D11C2412yes—
262C2×C4×D11C2412yes—
263C2×Dic22—21no—
264C2×Dic22—22no—
265C2×Dic22—22no—
266C2×Dic22C2412yes—
267C11×SD16—44no—
268C11×M16—44no—
269C2×C8×C11—22no—
270C2×C8×C11—22no—
271C2×C8×C11C2412yes—
272C2×C8×C11C2412yes—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—24no—
276C11×C4⋊C4C2412yes—
277C11×C4⋊C4C2412yes—
278C11×C22⋊C4—24no—
279C11×C22⋊C4—24no—
280C22⋊Dic11—24no—
281C22⋊Dic11—24no—
282#4326—44no—
283#4323—44no—
284(C2×D11)⋊C4—24no—
285(C2×D11)⋊C4—24no—
286(C2×D11)⋊C4—24no—
287(C2×D11)⋊C4—24no—
288(C2×D11)⋊C4—24no—
289(C2×D11)⋊C4—24no—
290C4⋊Dic11—24no—
291C4⋊Dic11—21no—
292C4⋊Dic11—21no—
293C4⋊Dic11C2412yes—
294C4⋊Dic11C2412yes—
295Dic11⋊C4—24no—
296Dic11⋊C4—24no—
297C4×Dic11—24no—
298C4×Dic11—24no—
299#4318—44no—
300C2×C11⋊C8—22no—
301C2×C11⋊C8—22no—
302C2×C11⋊C8C2412yes—
303C2×C11⋊C8C2412yes—
304#4314—44no—
305C2×#525—111no—
306C2×#525—111no—
307#3197—1116no—
308C2×#485—111no—
309C2×#485—111no—
310C2×#482—111no—
311C2×#482—111no—
312C2×#470—111no—
313C2×#469—111no—
314C2×#468—111no—
315C2×#468D1111yescharacteristic, complemented
316C2×#452—111no—
317C2×#452—111no—
318C2×#449—111no—
319C2×#449—111no—
320C2×#407—111no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—42no—
326C23×C11—42no—
327C23×C11—42no—
328C23×C11C22×D412yes—
329C23×C11C22×D411yescharacteristic
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—44no—
338C22×D11—44no—
339C22×D11—44no—
340C22×D11—416no—
341C22×D11—42no—
342C22×D11—42no—
343C22×D11—42no—
344C22×D11C22×D412yes—
345C22×D11C22×D412yes—
346Q8×C11—22no—
347Q8×C11—22no—
348Q8×C11—42no—
349D4×C11—22no—
350D4×C11—22no—
351D4×C11—48no—
352D4×C11—42no—
353C2×C4×C11—22no—
354C2×C4×C11—24no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—42no—
361C2×C4×C11—42no—
362C2×C4×C11—42no—
363C2×C4×C11C22×D412yes—
364C2×C4×C11C22×D411yescharacteristic
365C2×C4×C11H(5,𝔽2)12yes—
366C2×C4×C11H(5,𝔽2)12yes—
367C2×C4×C11C2511yescharacteristic
368C22⋊D11—48no—
369C22⋊D11—48no—
370C22⋊D11—48no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—44no—
377C2×Dic11—48no—
378C2×Dic11—42no—
379C2×Dic11—42no—
380C2×Dic11—42no—
381C2×Dic11C22×D412yes—
382C2×Dic11C22×D412yes—
383D44—22no—
384D44—22no—
385D44—48no—
386D44—48no—
387D44—42no—
388C4×D11—24no—
389C4×D11—24no—
390C4×D11—22no—
391C4×D11—22no—
392C4×D11—22no—
393C4×D11—22no—
394C4×D11—44no—
395C4×D11—44no—
396C4×D11—48no—
397Dic22—22no—
398Dic22—22no—
399Dic22—42no—
400C8×C11—22no—
401C8×C11—22no—
402C11⋊C8—22no—
403C11⋊C8—22no—
404C22×#41—111no—
405C22×#41—111no—
406C24×C4—111no—
407C22×Q16—111no—
408C22×SD16—111no—
409C22×SD16C2×D1111yescharacteristic, complemented
410C22×D8—111no—
411C22×M16—111no—
412C22×M16C2×D1111yescharacteristic
413#525—118no—
414#525—118no—
415#525—224no—
416#525—224no—
417C2×#123—221no—
418C2×#123—221no—
419C2×C22⋊Q8—111no—
420C2×C22⋊Q8—111no—
421C2×C22⋊Q8—111no—
422C2×C22⋊Q8C2×D1111yescharacteristic
423C2×#121—111no—
424C2×#121—111no—
425C2×#121—111no—
426C2×#121C2×D1111yescharacteristic
427C2×#120—221no—
428C2×#120—221no—
429C2×C4×D4—221no—
430C2×C4×D4—221no—
431C2×C4×D4—221no—
432C2×C4×D4—221no—
433C2×#117—111no—
434C2×#117—111no—
435#485—118no—
436#485—118no—
437#482—118no—
438#482—118no—
439#470—118no—
440#469—118no—
441#468—118no—
442#468C2×D1118yescomplemented
443#452—118no—
444#452—118no—
445#449—118no—
446#449—118no—
447C2×#107—111no—
448C2×#107C2×D1111yescharacteristic, complemented
449C2×#106—111no—
450C2×#106—111no—
451C2×#103—111no—
452C2×#103—111no—
453C2×#103—111no—
454C2×#103C2×D1111yescharacteristic, complemented
455C2×#102—111no—
456C2×#102—111no—
457C2×#102—111no—
458C2×#102C2×D1111yescharacteristic, complemented
459#407—118no—
460C2×C22⋊C8—111no—
461C2×C22⋊C8—111no—
462C2×C22⋊C8—111no—
463C2×C22⋊C8—111no—
464C22×C11—22no—
465C22×C11—22no—
466C22×C11—22no—
467C22×C11—44no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—84no—
472C22×C11#53412yes—
473C22×C11#57512yes—
474C22×C11#57512yes—
475C22×C11C23×D411yescharacteristic
476C2×D11—22no—
477C2×D11—22no—
478C2×D11—22no—
479C2×D11—22no—
480C2×D11—22no—
481C2×D11—22no—
482C2×D11—416no—
483C2×D11—44no—
484C2×D11—44no—
485C2×D11—42no—
486C2×D11—42no—
487C2×D11—42no—
488C2×D11—84no—
489C4×C11—22no—
490C4×C11—42no—
491C4×C11—42no—
492C4×C11—42no—
493C4×C11#53412yes—
494C4×C11C2×H(5,𝔽2)11yescharacteristic
495C4×C11C2×H(5,𝔽2)11yescharacteristic
496Dic11—22no—
497Dic11—22no—
498Dic11—42no—
499Dic11—42no—
500Dic11—42no—
501C25—111no—
502C2×#41—114no—
503C2×#41—114no—
504C2×#41—222no—
505C2×#41—222no—
506C2×#41—442no—
507C2×#41—442no—
508C2×#41—442no—
509C2×#41—442no—
510C22×Q8—111no—
511C22×Q8C22×D1111yescharacteristic
512C22×D4—21no—
513C22×D4—111no—
514C22×D4—221no—
515C22×D4—221no—
516C22×D4—221no—
517C22×D4—221no—
518C22×D4—221no—
519C22×D4C22×D1111yescharacteristic
520C23×C4—111no—
521C23×C4—111no—
522C23×C4—111no—
523C23×C4—111no—
524C23×C4—111no—
525C23×C4—114no—
526C23×C4—114no—
527C23×C4—221no—
528C23×C4—221no—
529C23×C4—442no—
530C23×C4—442no—
531C23×C4C22×D1111yescharacteristic
532C2×Q16—114no—
533C2×Q16—442no—
534C2×SD16—42no—
535C2×SD16—114no—
536C2×SD16—442no—
537C2×SD16C22×D1114yescomplemented
538C2×D8—114no—
539C2×D8—442no—
540C2×M16—42no—
541C2×M16—114no—
542C2×M16—442no—
543C2×M16C22×D1114yes—
544C22×C8—111no—
545C22×C8—111no—
546C22×C8C22×D1111yescharacteristic
547C22×C8C22×D1111yescharacteristic
548#123—228no—
549#123—228no—
550C22⋊Q8—22no—
551C22⋊Q8—114no—
552C22⋊Q8—114no—
553C22⋊Q8—114no—
554C22⋊Q8—222no—
555C22⋊Q8—222no—
556C22⋊Q8—222no—
557C22⋊Q8C22×D1114yes—
558#121—22no—
559#121—114no—
560#121—114no—
561#121—114no—
562#121—222no—
563#121—222no—
564#121—222no—
565#121C22×D1114yes—
566#120—228no—
567#120—228no—
568C4×D4—228no—
569C4×D4—228no—
570C4×D4—228no—
571C4×D4—228no—
572#117—114no—
573#117—114no—
574#117—222no—
575#117—222no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—111no—
578C2×C4⋊C4—111no—
579C2×C4⋊C4—221no—
580C2×C4⋊C4—221no—
581C2×C4⋊C4—221no—
582C2×C4⋊C4C22×D1111yescharacteristic
583C2×C4⋊C4C22×D1111yescharacteristic
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—221no—
587C2×C22⋊C4—221no—
588C2×C22⋊C4—221no—
589C2×C22⋊C4—221no—
590C2×C22⋊C4—221no—
591C2×C22⋊C4—221no—
592C2×C22⋊C4—221no—
593C2×C22⋊C4—221no—
594C2×C42—221no—
595C2×C42—221no—
596#107—114no—
597#107C22×D1114yescomplemented
598#106—114no—
599#106—114no—
600#103—114no—
601#103—114no—
602#103—114no—
603#103C22×D1114yescomplemented
604#102—114no—
605#102—114no—
606#102—114no—
607#102C22×D1114yescomplemented
608C22⋊C8—114no—
609C22⋊C8—114no—
610C22⋊C8—114no—
611C22⋊C8—114no—
612C2×C11—42no—
613C2×C11—82no—
614C2×C11#319714yescomplemented
615C2×C11C2×#53411yescharacteristic
616C2×C11C2×#57511yescharacteristic
617C2×C11C2×#57511yescharacteristic
618D11—42no—
619D11—42no—
620D11—82no—
621C24—21no—
622C24—111no—
623C24—111no—
624C24—114no—
625C24—221no—
626C24—442no—
627C24—442no—
628C24—442no—
629C24D4×D1111yescharacteristic
630#41—444no—
631#41—444no—
632#41—448no—
633#41—444no—
634#41—444no—
635#41—448no—
636C2×Q8—21no—
637C2×Q8—22no—
638C2×Q8—22no—
639C2×Q8—112no—
640C2×Q8—221no—
641C2×Q8—222no—
642C2×Q8—222no—
643C2×Q8C23×D1112yes—
644C2×D4—24no—
645C2×D4—21no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—44no—
649C2×D4—112no—
650C2×D4—224no—
651C2×D4—224no—
652C2×D4—224no—
653C2×D4—224no—
654C2×D4—224no—
655C2×D4—221no—
656C2×D4—222no—
657C2×D4—222no—
658C2×D4—444no—
659C2×D4—444no—
660C2×D4—444no—
661C2×D4—444no—
662C2×D4—444no—
663C2×D4C23×D1112yes—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—111no—
670C22×C4—111no—
671C22×C4—114no—
672C22×C4—112no—
673C22×C4—112no—
674C22×C4—112no—
675C22×C4—112no—
676C22×C4—114no—
677C22×C4—114no—
678C22×C4—224no—
679C22×C4—224no—
680C22×C4—222no—
681C22×C4—222no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—221no—
685C22×C4—221no—
686C22×C4—221no—
687C22×C4—448no—
688C22×C4—444no—
689C22×C4—444no—
690C22×C4—442no—
691C22×C4—442no—
692C22×C4—444no—
693C22×C4—442no—
694C22×C4—444no—
695C22×C4D4×D1112yes—
696C22×C4D4×D1111yescharacteristic
697C22×C4C23×D1112yes—
698C22×C4C23×D1111yescharacteristic
699Q16—444no—
700SD16—44no—
701SD16—444no—
702D8—444no—
703M16—44no—
704M16—444no—
705C2×C8—22no—
706C2×C8—22no—
707C2×C8—112no—
708C2×C8—112no—
709C2×C8—222no—
710C2×C8—222no—
711C2×C8C23×D1112yes—
712C2×C8C23×D1112yes—
713C4⋊C4—24no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—112no—
717C4⋊C4—112no—
718C4⋊C4—224no—
719C4⋊C4—224no—
720C4⋊C4—221no—
721C4⋊C4—221no—
722C4⋊C4—224no—
723C4⋊C4C23×D1112yes—
724C4⋊C4C23×D1112yes—
725C22⋊C4—24no—
726C22⋊C4—24no—
727C22⋊C4—224no—
728C22⋊C4—224no—
729C22⋊C4—224no—
730C22⋊C4—224no—
731C22⋊C4—224no—
732C22⋊C4—224no—
733C22⋊C4—224no—
734C22⋊C4—224no—
735C42—224no—
736C42—224no—
737C11C2×#319711yescharacteristic, complemented, Sylow
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—112no—
746C23—112no—
747C23—222no—
748C23—222no—
749C23—222no—
750C23—222no—
751C23—222no—
752C23—222no—
753C23—222no—
754C23—444no—
755C23—444no—
756C23—444no—
757C23—4416no—
758C23—442no—
759C23—442no—
760C23—442no—
761C23C2×D4×D1112yes—
762C23C2×D4×D1111yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—42no—
766Q8—222no—
767Q8—222no—
768Q8—442no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—42no—
773D4—222no—
774D4—222no—
775D4—448no—
776D4—448no—
777D4—448no—
778D4—448no—
779D4—448no—
780D4—442no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—112no—
792C2×C4—112no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—224no—
796C2×C4—224no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—444no—
805C2×C4—444no—
806C2×C4—448no—
807C2×C4—444no—
808C2×C4—448no—
809C2×C4—442no—
810C2×C4—442no—
811C2×C4—442no—
812C2×C4C2×D4×D1112yes—
813C2×C4C2×D4×D1111yescharacteristic
814C2×C4#6703712yes—
815C2×C4#6704212yes—
816C2×C4C24×D1111yescharacteristic
817C8—22no—
818C8—22no—
819C8—222no—
820C8—222no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—44no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—84no—
829C22—222no—
830C22—222no—
831C22—222no—
832C22—222no—
833C22—222no—
834C22—222no—
835C22—4416no—
836C22—444no—
837C22—444no—
838C22—442no—
839C22—442no—
840C22—442no—
841C22—884no—
842C22#1062313612yes—
843C22#1062330412yes—
844C22#1062330812yes—
845C22C22×D4×D1111yescharacteristic
846C4—22no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—222no—
851C4—222no—
852C4—442no—
853C4—442no—
854C4—442no—
855C4#1062313612yes—
856C4C2×#6703711yescharacteristic
857C4C2×#6704211yescharacteristic
858C2—42no—
859C2—82no—
860C2—442no—
861C2—442no—
862C2—882no—
863C2#1307945414yesdirect product factor
864C2C2×#1062313611yescharacteristic
865C2C2×#1062330411yescharacteristic
866C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#468C2
socleC23×C11C22×D4
hypercenterC2×#468D11
hypocenterC11C2×#3197
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#10623158C2semidirect
2. C2×#10623137C2semidirect
3. #13079454C2direct (N × H)
4. C2×#10622501C2semidirect
5. C2×#10622427C2semidirect
6. C2×#10622498C2semidirect
7. C2×#10622397C2semidirect
8. C2×#10622665C2semidirect
9. C2×#10622652C2semidirect
10. C2×#10622747C2semidirect
11. C2×#10622423C2semidirect
12. C2×#10622786C2semidirect
13. C2×#10622394C2semidirect
14. C2×#10622785C2semidirect
15. C2×#10622739C2semidirect
16. C2×C11×#468C2semidirect
20. C22×C11×SD16C22semidirect
25. C22×#4326C22semidirect
29. C22×#4323C22semidirect
33. C22×#4314C22semidirect
35. #10623158C22semidirect
37. #10623137C22semidirect
48. C11×#468C22semidirect
49. C2×C11×#107C22semidirect
50. C2×C11×#103C22semidirect
51. C2×C11×#102C22semidirect
52. C2×#66899C22semidirect
53. C2×#66896C22semidirect
54. #10622786C22semidirect
55. #10622785C22semidirect
56. #10622747C22semidirect
57. #10622739C22semidirect
58. C2×#66885C22semidirect
63. C2×#66882C22semidirect
64. C2×#66880C22semidirect
65. #10622665C22semidirect
66. #10622652C22semidirect
67. C2×#66874C22semidirect
68. C2×#66873C22semidirect
69. C2×#66872C22semidirect
70. C2×#66872C22semidirect
71. #10622501C22semidirect
72. #10622498C22semidirect
73. #10622427C22semidirect
74. #10622423C22semidirect
75. #10622397C22semidirect
76. #10622394C22semidirect
109. C2×C11×SD16C23semidirect
128. C2×#4326C23semidirect
134. C2×#4323C23semidirect
157. C2×#4314C23semidirect
172. C11×#107C23semidirect
173. C11×#103C23semidirect
174. C11×#102C23semidirect
175. #66899C23semidirect
176. #66896C23semidirect
177. #66885C23semidirect
182. #66882C23semidirect
183. #66880C23semidirect
184. #66874C23semidirect
185. #66873C23semidirect
186. #66872C23semidirect
187. #66872C23semidirect
315. C2×#468D11semidirect
409. C22×SD16C2×D11semidirect
442. #468C2×D11semidirect
448. C2×#107C2×D11semidirect
454. C2×#103C2×D11semidirect
458. C2×#102C2×D11semidirect
537. C2×SD16C22×D11semidirect
597. #107C22×D11semidirect
603. #103C22×D11semidirect
607. #102C22×D11semidirect
614. C2×C11#3197semidirect
737. C11C2×#3197semidirect
863. C2#13079454direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231582
C2×#106231372
#130794542
C2×#106225012
C2×#106224272
C2×#106224982
C2×#106223972
C2×#106226652
C2×#106226522
C2×#106227472
C2×#106224232
C2×#106227862
C2×#106223942
C2×#106227852
C2×#106227392
C2×C11×#4682
C2×#319711