Finite Group Databasebeta

← C2×#13079453 #15624399

Subgroups — C2×#13079453 #15624399

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×#10623322C211yesmaximal, characteristic, complemented
2#13079453C2116yesmaximal, direct product factor
3C2×#10622609C211yesmaximal, characteristic, complemented
4C2×#10622658C211yesmaximal, characteristic, complemented
5C2×#10622616C211yesmaximal, characteristic, complemented
6C2×#10622648C211yesmaximal, characteristic, complemented
7C2×#10622665C211yesmaximal, characteristic, complemented
8C2×#10622652C211yesmaximal, characteristic, complemented
9C2×#10622662C211yesmaximal, characteristic, complemented
10C2×#10622655C211yesmaximal, characteristic, complemented
11C2×#10622852C211yesmaximal, characteristic, complemented
12C2×#10622660C211yesmaximal, characteristic, complemented
13C2×#10622851C211yesmaximal, characteristic, complemented
14C2×#10622650C211yesmaximal, characteristic, complemented
15C2×#10622820C211yesmaximal, characteristic, complemented
16C2×C11×#525C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C11×#525—24no—
21C11×#525C2218yescomplemented
22C2×C11×#123—21no—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C11×#120—21no—
28C2×C4×D4×C11—21no—
29C2×C4×D4×C11—21no—
30C2×C11×#117C2211yescharacteristic
31C2×#67006—21no—
32C22×#4326C2211yescharacteristic, complemented
33C22×#4325C2211yescharacteristic, complemented
34C22×#4324C2211yescharacteristic, complemented
35C22×#4323C2211yescharacteristic, complemented
36#10623322—24no—
37#10623322C2218yescomplemented
38C2×#66983C2211yescharacteristic
39C2×#66983C2211yescharacteristic
40C2×#66982—21no—
41C2×C4×C22⋊D11—21no—
42C2×C4×C22⋊D11—21no—
43C2×#66979C2211yescharacteristic
44C2×#66977C2211yescharacteristic
45C2×#66977C2211yescharacteristic
46C22×#4318C2211yescharacteristic
47C22×#4318C2211yescharacteristic
48#10622852C2218yescomplemented
49#10622851C2218yescomplemented
50C2×#66899C2211yescharacteristic, complemented
51C2×#66899C2211yescharacteristic, complemented
52C2×#66896C2211yescharacteristic, complemented
53C2×#66896C2211yescharacteristic, complemented
54#10622820C2218yescomplemented
55C2×C22⋊(C11⋊C8)C2211yescharacteristic
56C2×C22⋊(C11⋊C8)C2211yescharacteristic
57C2×C22⋊(C11⋊C8)C2211yescharacteristic
58C2×C22⋊(C11⋊C8)C2211yescharacteristic
59#10622665C2218yescomplemented
60#10622662C2218yescomplemented
61#10622660C2218yescomplemented
62#10622658C2218yescomplemented
63#10622655C2218yescomplemented
64#10622652C2218yescomplemented
65#10622650C2218yescomplemented
66#10622648C2218yescomplemented
67#10622616C2218yescomplemented
68#10622609C2218yescomplemented
69C2×#66874C2211yescharacteristic, complemented
70C2×#66874C2211yescharacteristic, complemented
71C2×#66873C2211yescharacteristic, complemented
72C2×#66873C2211yescharacteristic, complemented
73C2×#66872C2211yescharacteristic, complemented
74C2×#66872C2211yescharacteristic, complemented
75C2×#66871C2211yescharacteristic, complemented
76C2×#66871C2211yescharacteristic, complemented
77C25×C11D411yescharacteristic
78C2×C11×#41—22no—
79C2×C11×#41—42no—
80C2×C11×#41—42no—
81C2×C11×#41C2314yes—
82C22×Q8×C11C2311yescharacteristic
83C22×D4×C11—21no—
84C22×D4×C11—21no—
85C22×D4×C11—21no—
86C22×D4×C11C2311yescharacteristic
87C23×C4×C11—21no—
88C23×C4×C11—42no—
89C23×C4×C11—42no—
90C23×C4×C11D411yescharacteristic
91C23×C4×C11D411yescharacteristic
92C23×C4×C11D411yescharacteristic
93C23×C4×C11D414yes—
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C23×C4×C11C2314yes—
98C22×C22⋊D11—21no—
99C22×C22⋊D11—21no—
100C22×C22⋊D11—21no—
101C2×#4339—22no—
102C2×#4339—42no—
103C2×#4339—42no—
104C2×#4339C2314yes—
105C22×D44C2311yescharacteristic
106C22×C4×D11—21no—
107C22×Dic22C2311yescharacteristic
108C11×#123—28no—
109C11×C22⋊Q8—22no—
110C11×C22⋊Q8—22no—
111C11×C22⋊Q8C2314yes—
112C11×C22⋊Q8C2314yes—
113C11×#121—22no—
114C11×#121—22no—
115C11×#121C2314yes—
116C11×#121C2314yes—
117C11×#120—28no—
118C4×D4×C11—28no—
119C4×D4×C11—28no—
120C11×#117—22no—
121C11×#117C2314yes—
122C2×C11×C4⋊C4—21no—
123C2×C11×C4⋊C4—21no—
124C2×C11×C4⋊C4C2311yescharacteristic
125C2×C11×C4⋊C4C2311yescharacteristic
126C2×C11×C22⋊C4—21no—
127C2×C11×C22⋊C4—21no—
128C2×C11×C22⋊C4—21no—
129C2×C11×C22⋊C4—21no—
130C2×C11×C22⋊C4—21no—
131C2×C42×C11—21no—
132#67006—28no—
133C2×C22⋊Dic11—21no—
134C2×C22⋊Dic11—21no—
135C2×C22⋊Dic11—21no—
136C2×#4326—42no—
137C2×#4326C2314yescomplemented
138C2×#4325—42no—
139C2×#4325C2314yescomplemented
140C2×#4324—42no—
141C2×#4324C2314yescomplemented
142C2×#4323—42no—
143C2×#4323C2314yescomplemented
144#66983—22no—
145#66983—22no—
146#66983C2314yes—
147#66983C2314yes—
148#66982—28no—
149C4×C22⋊D11—28no—
150C4×C22⋊D11—28no—
151C2×(C2×D11)⋊C4—21no—
152C2×(C2×D11)⋊C4—21no—
153#66979—22no—
154#66979C2314yes—
155C2×C4⋊Dic11C2311yescharacteristic
156C2×C4⋊Dic11C2311yescharacteristic
157#66977—22no—
158#66977—22no—
159#66977C2314yes—
160#66977C2314yes—
161C2×Dic11⋊C4—21no—
162C2×Dic11⋊C4—21no—
163C2×C4×Dic11—21no—
164C2×#4318—42no—
165C2×#4318—42no—
166C2×#4318C2314yes—
167C2×#4318C2314yes—
168C22×C11⋊C8C2311yescharacteristic
169C22×C11⋊C8C2311yescharacteristic
170C22×C11⋊C8C2311yescharacteristic
171C22×C11⋊C8C2311yescharacteristic
172#66899C2314yescomplemented
173#66899C2314yescomplemented
174#66896C2314yescomplemented
175#66896C2314yescomplemented
176C22⋊(C11⋊C8)C2314yes—
177C22⋊(C11⋊C8)C2314yes—
178C22⋊(C11⋊C8)C2314yes—
179C22⋊(C11⋊C8)C2314yes—
180#66874C2314yescomplemented
181#66874C2314yescomplemented
182#66873C2314yescomplemented
183#66873C2314yescomplemented
184#66872C2314yescomplemented
185#66872C2314yescomplemented
186#66871C2314yescomplemented
187#66871C2314yescomplemented
188C2×#3197—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11—42no—
191C24×C11—42no—
192C24×C11—42no—
193C24×C11C2×D411yescharacteristic
194C24×C11C2×D411yescharacteristic
195C24×C11C2×D411yescharacteristic
196C24×C11C2×D414yes—
197C23×D11—21no—
198C11×#41—44no—
199C11×#41—44no—
200C11×#41—48no—
201C2×Q8×C11—21no—
202C2×Q8×C11—22no—
203C2×Q8×C11—22no—
204C2×Q8×C11C2412yes—
205C2×D4×C11—24no—
206C2×D4×C11—24no—
207C2×D4×C11—24no—
208C2×D4×C11—21no—
209C2×D4×C11—22no—
210C2×D4×C11—22no—
211C2×D4×C11—44no—
212C2×D4×C11—44no—
213C2×D4×C11—44no—
214C2×D4×C11C2412yes—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—22no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—22no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—24no—
225C22×C4×C11—48no—
226C22×C4×C11—44no—
227C22×C4×C11—44no—
228C22×C4×C11—42no—
229C22×C4×C11—42no—
230C22×C4×C11—42no—
231C22×C4×C11—44no—
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D412yes—
236C22×C4×C11C2×D412yes—
237C22×C4×C11C2×D412yes—
238C22×C4×C11C2×D414yes—
239C22×C4×C11C2×D414yes—
240C22×C4×C11C2×D414yes—
241C22×C4×C11C2412yes—
242C22×C4×C11C2412yes—
243C22×C4×C11C2412yes—
244C22×C4×C11C2411yescharacteristic
245C2×C22⋊D11—24no—
246C2×C22⋊D11—24no—
247C2×C22⋊D11—24no—
248C2×C22⋊D11—44no—
249C2×C22⋊D11—44no—
250C2×C22⋊D11—44no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254#4339—44no—
255#4339—44no—
256#4339—48no—
257C2×D44—21no—
258C2×D44—22no—
259C2×D44—22no—
260C2×D44C2412yes—
261C2×C4×D11—24no—
262C2×C4×D11—44no—
263C2×Dic22—21no—
264C2×Dic22—22no—
265C2×Dic22—22no—
266C2×Dic22C2412yes—
267C11×C4⋊C4—24no—
268C11×C4⋊C4—24no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4C2412yes—
272C11×C4⋊C4C2412yes—
273C11×C22⋊C4—24no—
274C11×C22⋊C4—24no—
275C11×C22⋊C4—24no—
276C11×C22⋊C4—24no—
277C11×C22⋊C4—24no—
278C42×C11—24no—
279C22⋊Dic11—24no—
280C22⋊Dic11—24no—
281C22⋊Dic11—24no—
282#4326—44no—
283#4325—44no—
284#4324—44no—
285#4323—44no—
286(C2×D11)⋊C4—24no—
287(C2×D11)⋊C4—24no—
288C4⋊Dic11—21no—
289C4⋊Dic11—21no—
290C4⋊Dic11C2412yes—
291C4⋊Dic11C2412yes—
292Dic11⋊C4—24no—
293Dic11⋊C4—24no—
294C4×Dic11—24no—
295#4318—44no—
296#4318—44no—
297C2×C11⋊C8—22no—
298C2×C11⋊C8—22no—
299C2×C11⋊C8—22no—
300C2×C11⋊C8—22no—
301C2×C11⋊C8C2412yes—
302C2×C11⋊C8C2412yes—
303C2×C11⋊C8C2412yes—
304C2×C11⋊C8C2412yes—
305C2×#525—111no—
306C2×#525D1111yescharacteristic, complemented
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×#468—111no—
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—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—44no—
332C23×C11—44no—
333C23×C11—44no—
334C23×C11—416no—
335C23×C11—42no—
336C23×C11—42no—
337C23×C11—42no—
338C23×C11C22×D412yes—
339C23×C11C22×D412yes—
340C23×C11C22×D412yes—
341C23×C11C22×D411yescharacteristic
342C22×D11—22no—
343C22×D11—42no—
344C22×D11—42no—
345C22×D11—42no—
346Q8×C11—22no—
347Q8×C11—22no—
348Q8×C11—42no—
349D4×C11—22no—
350D4×C11—22no—
351D4×C11—48no—
352D4×C11—48no—
353D4×C11—48no—
354D4×C11—42no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—24no—
359C2×C4×C11—24no—
360C2×C4×C11—24no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—44no—
371C2×C4×C11—44no—
372C2×C4×C11—44no—
373C2×C4×C11—48no—
374C2×C4×C11—42no—
375C2×C4×C11—42no—
376C2×C4×C11—42no—
377C2×C4×C11C22×D412yes—
378C2×C4×C11C22×D412yes—
379C2×C4×C11C22×D412yes—
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11H(5,𝔽2)12yes—
382C2×C4×C11H(5,𝔽2)12yes—
383C2×C4×C11C2511yescharacteristic
384C22⋊D11—48no—
385C22⋊D11—48no—
386C22⋊D11—48no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—42no—
391C2×Dic11—42no—
392C2×Dic11—42no—
393D44—22no—
394D44—22no—
395D44—42no—
396C4×D11—48no—
397Dic22—22no—
398Dic22—22no—
399Dic22—42no—
400C11⋊C8—22no—
401C11⋊C8—22no—
402C11⋊C8—22no—
403C11⋊C8—22no—
404C22×#41—111no—
405C22×#41C2×D1111yescharacteristic
406C24×C4C2×D1111yescharacteristic
407C22×Q16—111no—
408C22×SD16—111no—
409C22×SD16—111no—
410C22×D8—111no—
411C22×M16—111no—
412C22×M16—111no—
413#525—24no—
414#525—118no—
415#525—224no—
416#525C2×D1118yescomplemented
417C2×#123—21no—
418C2×#123—221no—
419C2×C22⋊Q8—111no—
420C2×C22⋊Q8—111no—
421C2×C22⋊Q8C2×D1111yescharacteristic
422C2×C22⋊Q8C2×D1111yescharacteristic
423C2×#121—111no—
424C2×#121—111no—
425C2×#121C2×D1111yescharacteristic
426C2×#121C2×D1111yescharacteristic
427C2×#120—21no—
428C2×#120—221no—
429C2×C4×D4—21no—
430C2×C4×D4—21no—
431C2×C4×D4—221no—
432C2×C4×D4—221no—
433C2×#117—111no—
434C2×#117C2×D1111yescharacteristic
435#485—118no—
436#485—118no—
437#482—118no—
438#482—118no—
439#470—118no—
440#469—118no—
441#468—118no—
442#468—118no—
443#452—118no—
444#452—118no—
445#449—118no—
446#449—118no—
447C2×#107—111no—
448C2×#107—111no—
449C2×#106—111no—
450C2×#106—111no—
451C2×#103—111no—
452C2×#103—111no—
453C2×#103—111no—
454C2×#103—111no—
455C2×#102—111no—
456C2×#102—111no—
457C2×#102—111no—
458C2×#102—111no—
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—22no—
468C22×C11—22no—
469C22×C11—22no—
470C22×C11—22no—
471C22×C11—22no—
472C22×C11—22no—
473C22×C11—416no—
474C22×C11—44no—
475C22×C11—44no—
476C22×C11—44no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—84no—
481C22×C11#53412yes—
482C22×C11#57512yes—
483C22×C11#57512yes—
484C22×C11C23×D411yescharacteristic
485C2×D11—42no—
486C2×D11—42no—
487C2×D11—42no—
488C2×D11—84no—
489C4×C11—22no—
490C4×C11—22no—
491C4×C11—22no—
492C4×C11—42no—
493C4×C11—42no—
494C4×C11—42no—
495C4×C11#53412yes—
496C4×C11C2×H(5,𝔽2)11yescharacteristic
497C4×C11C2×H(5,𝔽2)11yescharacteristic
498Dic11—42no—
499Dic11—42no—
500Dic11—42no—
501C25C22⋊D1111yescharacteristic
502C2×#41—22no—
503C2×#41—42no—
504C2×#41—42no—
505C2×#41—114no—
506C2×#41—222no—
507C2×#41—442no—
508C2×#41—442no—
509C2×#41C22×D1114yes—
510C22×Q8—111no—
511C22×Q8C22×D1111yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—111no—
516C22×D4—221no—
517C22×D4—221no—
518C22×D4—221no—
519C22×D4C22×D1111yescharacteristic
520C23×C4—21no—
521C23×C4—42no—
522C23×C4—42no—
523C23×C4—221no—
524C23×C4C22⋊D1111yescharacteristic
525C23×C4C22⋊D1111yescharacteristic
526C23×C4C22⋊D1111yescharacteristic
527C23×C4C22⋊D1114yes—
528C23×C4C22×D1111yescharacteristic
529C23×C4C22×D1111yescharacteristic
530C23×C4C22×D1111yescharacteristic
531C23×C4C22×D1114yes—
532C2×Q16—114no—
533C2×Q16—442no—
534C2×SD16—114no—
535C2×SD16—114no—
536C2×SD16—442no—
537C2×SD16—442no—
538C2×D8—114no—
539C2×D8—442no—
540C2×M16—114no—
541C2×M16—114no—
542C2×M16—442no—
543C2×M16—442no—
544C22×C8—111no—
545C22×C8—111no—
546C22×C8—111no—
547C22×C8—111no—
548#123—28no—
549#123—228no—
550C22⋊Q8—22no—
551C22⋊Q8—22no—
552C22⋊Q8—114no—
553C22⋊Q8—114no—
554C22⋊Q8—222no—
555C22⋊Q8—222no—
556C22⋊Q8C22×D1114yes—
557C22⋊Q8C22×D1114yes—
558#121—22no—
559#121—22no—
560#121—114no—
561#121—114no—
562#121—222no—
563#121—222no—
564#121C22×D1114yes—
565#121C22×D1114yes—
566#120—28no—
567#120—228no—
568C4×D4—28no—
569C4×D4—28no—
570C4×D4—228no—
571C4×D4—228no—
572#117—22no—
573#117—114no—
574#117—222no—
575#117C22×D1114yes—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—111no—
579C2×C4⋊C4—111no—
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—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—221no—
590C2×C22⋊C4—221no—
591C2×C22⋊C4—221no—
592C2×C22⋊C4—221no—
593C2×C22⋊C4—221no—
594C2×C42—21no—
595C2×C42—221no—
596#107—114no—
597#107—114no—
598#106—114no—
599#106—114no—
600#103—114no—
601#103—114no—
602#103—114no—
603#103—114no—
604#102—114no—
605#102—114no—
606#102—114no—
607#102—114no—
608C22⋊C8—114no—
609C22⋊C8—114no—
610C22⋊C8—114no—
611C22⋊C8—114no—
612C2×C11—42no—
613C2×C11—42no—
614C2×C11—42no—
615C2×C11—82no—
616C2×C11#319714yescomplemented
617C2×C11C2×#53411yescharacteristic
618C2×C11C2×#57511yescharacteristic
619C2×C11C2×#57511yescharacteristic
620D11—82no—
621C24—21no—
622C24—42no—
623C24—42no—
624C24—42no—
625C24—221no—
626C24C2×C22⋊D1111yescharacteristic
627C24C2×C22⋊D1111yescharacteristic
628C24C2×C22⋊D1111yescharacteristic
629C24C2×C22⋊D1114yes—
630#41—44no—
631#41—44no—
632#41—48no—
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—24no—
646C2×D4—24no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—21no—
650C2×D4—44no—
651C2×D4—44no—
652C2×D4—44no—
653C2×D4—112no—
654C2×D4—224no—
655C2×D4—224no—
656C2×D4—224no—
657C2×D4—222no—
658C2×D4—222no—
659C2×D4—221no—
660C2×D4—444no—
661C2×D4—444no—
662C2×D4—444no—
663C2×D4C23×D1112yes—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—24no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—48no—
677C22×C4—42no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—44no—
681C22×C4—221no—
682C22×C4—221no—
683C22×C4—221no—
684C22×C4—224no—
685C22×C4—444no—
686C22×C4C2×C22⋊D1112yes—
687C22×C4C2×C22⋊D1112yes—
688C22×C4C2×C22⋊D1112yes—
689C22×C4C2×C22⋊D1111yescharacteristic
690C22×C4C2×C22⋊D1111yescharacteristic
691C22×C4C2×C22⋊D1111yescharacteristic
692C22×C4C2×C22⋊D1114yes—
693C22×C4C2×C22⋊D1114yes—
694C22×C4C2×C22⋊D1114yes—
695C22×C4C23×D1112yes—
696C22×C4C23×D1112yes—
697C22×C4C23×D1112yes—
698C22×C4C23×D1111yescharacteristic
699Q16—444no—
700SD16—444no—
701SD16—444no—
702D8—444no—
703M16—444no—
704M16—444no—
705C2×C8—112no—
706C2×C8—112no—
707C2×C8—112no—
708C2×C8—112no—
709C2×C8—222no—
710C2×C8—222no—
711C2×C8—222no—
712C2×C8—222no—
713C4⋊C4—24no—
714C4⋊C4—24no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—112no—
718C4⋊C4—112no—
719C4⋊C4—221no—
720C4⋊C4—221no—
721C4⋊C4—224no—
722C4⋊C4—224no—
723C4⋊C4C23×D1112yes—
724C4⋊C4C23×D1112yes—
725C22⋊C4—24no—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—224no—
731C22⋊C4—224no—
732C22⋊C4—224no—
733C22⋊C4—224no—
734C22⋊C4—224no—
735C42—24no—
736C42—224no—
737C11C2×#319711yescharacteristic, complemented, Sylow
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—416no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—222no—
756C23—442no—
757C23—442no—
758C23—442no—
759C23C22×C22⋊D1112yes—
760C23C22×C22⋊D1112yes—
761C23C22×C22⋊D1112yes—
762C23C22×C22⋊D1111yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—42no—
766Q8—222no—
767Q8—222no—
768Q8—442no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—48no—
773D4—48no—
774D4—42no—
775D4—222no—
776D4—222no—
777D4—448no—
778D4—448no—
779D4—448no—
780D4—442no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—48no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—448no—
807C2×C4—442no—
808C2×C4—442no—
809C2×C4—442no—
810C2×C4#6703712yes—
811C2×C4#6703712yes—
812C2×C4C22×C22⋊D1112yes—
813C2×C4C22×C22⋊D1112yes—
814C2×C4C22×C22⋊D1112yes—
815C2×C4C22×C22⋊D1111yescharacteristic
816C2×C4C24×D1111yescharacteristic
817C8—222no—
818C8—222no—
819C8—222no—
820C8—222no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—416no—
831C22—44no—
832C22—44no—
833C22—44no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—84no—
838C22—442no—
839C22—442no—
840C22—442no—
841C22—884no—
842C22#1062333512yes—
843C22#1062335312yes—
844C22#1062335312yes—
845C22C23×C22⋊D1111yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—442no—
853C4—442no—
854C4—442no—
855C4#1062333512yes—
856C4C2×#6703711yescharacteristic
857C4C2×#6703711yescharacteristic
858C2—42no—
859C2—42no—
860C2—42no—
861C2—82no—
862C2—882no—
863C2#1307945314yesdirect product factor
864C2C2×#1062333511yescharacteristic
865C2C2×#1062335311yescharacteristic
866C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#525C2
socleC23×C11C22×D4
hypercenterC2×#525D11
hypocenterC11C2×#3197
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#10623322C2semidirect
2. #13079453C2direct (N × H)
3. C2×#10622609C2semidirect
4. C2×#10622658C2semidirect
5. C2×#10622616C2semidirect
6. C2×#10622648C2semidirect
7. C2×#10622665C2semidirect
8. C2×#10622652C2semidirect
9. C2×#10622662C2semidirect
10. C2×#10622655C2semidirect
11. C2×#10622852C2semidirect
12. C2×#10622660C2semidirect
13. C2×#10622851C2semidirect
14. C2×#10622650C2semidirect
15. C2×#10622820C2semidirect
16. C2×C11×#525C2semidirect
21. C11×#525C22semidirect
32. C22×#4326C22semidirect
33. C22×#4325C22semidirect
34. C22×#4324C22semidirect
35. C22×#4323C22semidirect
37. #10623322C22semidirect
48. #10622852C22semidirect
49. #10622851C22semidirect
50. C2×#66899C22semidirect
51. C2×#66899C22semidirect
52. C2×#66896C22semidirect
53. C2×#66896C22semidirect
54. #10622820C22semidirect
59. #10622665C22semidirect
60. #10622662C22semidirect
61. #10622660C22semidirect
62. #10622658C22semidirect
63. #10622655C22semidirect
64. #10622652C22semidirect
65. #10622650C22semidirect
66. #10622648C22semidirect
67. #10622616C22semidirect
68. #10622609C22semidirect
69. C2×#66874C22semidirect
70. C2×#66874C22semidirect
71. C2×#66873C22semidirect
72. C2×#66873C22semidirect
73. C2×#66872C22semidirect
74. C2×#66872C22semidirect
75. C2×#66871C22semidirect
76. C2×#66871C22semidirect
137. C2×#4326C23semidirect
139. C2×#4325C23semidirect
141. C2×#4324C23semidirect
143. C2×#4323C23semidirect
172. #66899C23semidirect
173. #66899C23semidirect
174. #66896C23semidirect
175. #66896C23semidirect
180. #66874C23semidirect
181. #66874C23semidirect
182. #66873C23semidirect
183. #66873C23semidirect
184. #66872C23semidirect
185. #66872C23semidirect
186. #66871C23semidirect
187. #66871C23semidirect
306. C2×#525D11semidirect
416. #525C2×D11semidirect
616. C2×C11#3197semidirect
737. C11C2×#3197semidirect
863. C2#13079453direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233222
#130794532
C2×#106226092
C2×#106226582
C2×#106226162
C2×#106226482
C2×#106226652
C2×#106226522
C2×#106226622
C2×#106226552
C2×#106228522
C2×#106226602
C2×#106228512
C2×#106226502
C2×#106228202
C2×C11×#5252
C2×#319711