Finite Group Databasebeta

← C2×#13079791 #15625847

Subgroups — C2×#13079791 #15625847

Order 2816.

1810 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic, complemented
2#13079791C2116yesmaximal, direct product factor
3C2×#10622677C212yesmaximal, complemented
4C2×#10622669C212yesmaximal, complemented
5C2×#10622658C212yesmaximal, complemented
6C2×#10622648C212yesmaximal
7C2×#10622634C211yesmaximal, characteristic, complemented
8C2×#10622633C211yesmaximal, characteristic, complemented
9C2×#10622621C211yesmaximal, characteristic, complemented
10C2×#10622620C211yesmaximal, characteristic, complemented
11C2×#10622538C211yesmaximal, characteristic, complemented
12C2×C11×#529C211yesmaximal, characteristic
13C11×#529—24no—
14C11×#529C2218yes—
15C2×C11×#126—21no—
16C2×C11×#125C2211yescharacteristic
17C2×C11×#124C2211yescharacteristic
18C2×C11×#123—21no—
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C2×C11×#117—21no—
25C22×C42×C11C2211yescharacteristic
26C2×#66979C2212yes—
27C2×#66977—21no—
28C2×#66977—21no—
29#10623001—24no—
30#10623001C2218yescomplemented
31C2×#66923C2212yes—
32C2×#66922C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C2×C4×Dic22—21no—
35C2×C4×Dic22—21no—
36C2×#66899C2212yes—
37C2×#66899C2212yes—
38C2×#66896C2212yes—
39C2×#66896C2212yes—
40C2×C22⋊(C11⋊C8)C2212yes—
41#10622677C22116yescomplemented
42#10622669C22116yescomplemented
43#10622658C22116yescomplemented
44#10622648C22116yes—
45#10622634C2218yescomplemented
46#10622633C2218yescomplemented
47#10622621C2218yescomplemented
48#10622620C2218yescomplemented
49C2×#66872C2212yes—
50C2×#66872C2212yes—
51C2×#66871C2212yes—
52C2×#66871C2212yes—
53#10622538C2218yescomplemented
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4×C11⋊C8C2212yes—
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11D411yescharacteristic
62C23×C4×C11D411yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×Dic22—21no—
65C22×Dic22—21no—
66C11×#126—28no—
67C11×#125—22no—
68C11×#125C2314yes—
69C11×#124—22no—
70C11×#124C2314yes—
71C11×#123—28no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8C2314yes—
74C11×#121—22no—
75C11×#121C2314yes—
76C4×Q8×C11—22no—
77C4×Q8×C11C2314yes—
78C4×D4×C11—28no—
79C4×D4×C11—22no—
80C4×D4×C11C2314yes—
81C11×#117—28no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C42×C11—21no—
94C2×C42×C11D411yescharacteristic
95C2×C42×C11D411yescharacteristic
96C2×C42×C11D414yes—
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2314yes—
100C2×C22⋊Dic11—22no—
101#66979—24no—
102#66979C2318yes—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11C2312yes—
106C2×C4⋊Dic11C2312yes—
107#66977—28no—
108#66977—28no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—22no—
111C2×C4×Dic11—22no—
112C22×C11⋊C8C2312yes—
113C22×C11⋊C8C2312yes—
114#66923—24no—
115#66923C2318yes—
116#66922—22no—
117#66922—22no—
118#66922C2314yes—
119#66922C2314yes—
120C4×Dic22—28no—
121C4×Dic22—28no—
122#66899C2318yes—
123#66899C2318yes—
124#66896C2318yes—
125#66896C2318yes—
126C22⋊(C11⋊C8)C2318yes—
127#66872C2318yes—
128#66872C2318yes—
129#66871C2318yes—
130#66871C2318yes—
131C4⋊(C11⋊C8)C2314yes—
132C4⋊(C11⋊C8)C2314yes—
133C4×C11⋊C8C2318yes—
134C2×#3233—111nomaximal, Sylow
135C24×C11—21no—
136C24×C11C2×D411yescharacteristic
137C2×Q8×C11—21no—
138C2×Q8×C11—22no—
139C2×Q8×C11—22no—
140C2×Q8×C11C2412yes—
141C2×D4×C11—24no—
142C2×D4×C11—21no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—44no—
146C2×D4×C11C2412yes—
147C22×C4×C11—24no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—24no—
154C22×C4×C11—42no—
155C22×C4×C11—44no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D414yes—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D414yes—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2412yes—
165C22×C4×C11C2411yescharacteristic
166C22×Dic11—22no—
167C22×Dic11—22no—
168C2×Dic22—24no—
169C2×Dic22—24no—
170C2×Dic22—44no—
171C2×Dic22—44no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C2412yes—
179C11×C4⋊C4C2412yes—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—24no—
185C42×C11—24no—
186C42×C11C2×D414yes—
187C42×C11C2×D414yes—
188C42×C11C2×D412yes—
189C42×C11C2×D412yes—
190C42×C11C2412yes—
191C42×C11C2412yes—
192C22⋊Dic11—28no—
193C4⋊Dic11—24no—
194C4⋊Dic11—24no—
195C4⋊Dic11—22no—
196C4⋊Dic11—22no—
197C4⋊Dic11C2414yes—
198C4⋊Dic11C2414yes—
199Dic11⋊C4—28no—
200Dic11⋊C4—28no—
201C4×Dic11—28no—
202C2×C11⋊C8—24no—
203C2×C11⋊C8—24no—
204C2×C11⋊C8C2414yes—
205C2×C11⋊C8C2414yes—
206C2×#533—111no—
207C2×#529D1111yescharacteristic
208#3233—1116no—
209C2×#499—112no—
210C2×#488—112no—
211C2×#485—112no—
212C2×#482—112no—
213C2×#477—111no—
214C2×#475—111no—
215C2×#476—111no—
216C2×#474—111no—
217C2×#431—111no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11C22×D412yes—
226C23×C11C22×D411yescharacteristic
227Q8×C11—22no—
228Q8×C11—22no—
229Q8×C11—42no—
230D4×C11—22no—
231D4×C11—22no—
232D4×C11—48no—
233D4×C11—42no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—24no—
239C2×C4×C11—28no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—44no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—48no—
250C2×C4×C11#13514yes—
251C2×C4×C11C22×D412yes—
252C2×C4×C11C22×D412yes—
253C2×C4×C11C22×D412yes—
254C2×C4×C11C22×D412yes—
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D412yes—
257C2×C4×C112−1+412yes—
258C2×C4×C112−1+412yes—
259C2×C4×C11C2511yescharacteristic
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—44no—
263C2×Dic11—44no—
264Dic22—48no—
265Dic22—48no—
266C11⋊C8—24no—
267C11⋊C8—24no—
268#533—118no—
269#533—224no—
270C2×C4⋊Q8—111no—
271C2×C4⋊Q8—111no—
272#529—24no—
273#529C2×D1118yes—
274C2×#126—21no—
275C2×#125—112no—
276C2×#125C2×D1111yescharacteristic
277C2×#124C2×D1111yescharacteristic
278C2×#123—21no—
279C2×C22⋊Q8—221no—
280C2×C22⋊Q8—221no—
281C2×C22⋊Q8C2×D1111yescharacteristic
282C2×#121C2×D1111yescharacteristic
283C2×C4×Q8—221no—
284C2×C4×Q8—221no—
285C2×C4×Q8C2×D1111yescharacteristic
286C2×C4×D4—21no—
287C2×C4×D4C2×D1111yescharacteristic
288C2×#117—21no—
289C2×#117—112no—
290C22×C42C2×D1111yescharacteristic
291#499—1116no—
292#488—1116no—
293#485—1116no—
294#482—1116no—
295#477—118no—
296#476—118no—
297#475—118no—
298#474—118no—
299#431—118no—
300C2×#107—112no—
301C2×#107—112no—
302C2×#106—112no—
303C2×#106—112no—
304C2×C4⋊C8—111no—
305C2×C4⋊C8—111no—
306C2×#103—112no—
307C2×#103—112no—
308C2×#102—112no—
309C2×#102—112no—
310C2×C22⋊C8—112no—
311C2×C4×C8—112no—
312C22×C11—22no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—44no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—84no—
320C22×C11#53612yes—
321C22×C11C2×#13512yes—
322C22×C11#57512yes—
323C22×C11C23×D411yescharacteristic
324C4×C11—22no—
325C4×C11—22no—
326C4×C11—22no—
327C4×C11—22no—
328C4×C11—42no—
329C4×C11—42no—
330C4×C11—42no—
331C4×C11#53612yes—
332C4×C11C2×#13514yes—
333C4×C11C2×2−1+411yescharacteristic
334C4×C11C2×2−1+411yescharacteristic
335Dic11—44no—
336Dic11—44no—
337C22×Q8—221no—
338C22×Q8—221no—
339C22×Q8C22×D1111yescharacteristic
340C22×D4—21no—
341C22×D4C22×D1111yescharacteristic
342C23×C4—21no—
343C23×C4C22⋊D1111yescharacteristic
344C23×C4C22⋊D1111yescharacteristic
345C23×C4C22×D1111yescharacteristic
346C22×C8—112no—
347C22×C8—112no—
348C4⋊Q8—114no—
349C4⋊Q8—114no—
350C4⋊Q8—222no—
351C4⋊Q8—222no—
352#126—28no—
353#125—22no—
354#125—118no—
355#125—224no—
356#125C22×D1114yes—
357#124—22no—
358#124C22×D1114yes—
359#123—28no—
360C22⋊Q8—22no—
361C22⋊Q8—228no—
362C22⋊Q8—228no—
363C22⋊Q8C22×D1114yes—
364#121—22no—
365#121C22×D1114yes—
366C4×Q8—22no—
367C4×Q8—228no—
368C4×Q8—228no—
369C4×Q8C22×D1114yes—
370C4×D4—28no—
371C4×D4—22no—
372C4×D4C22×D1114yes—
373#117—28no—
374#117—118no—
375#117—224no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—112no—
381C2×C4⋊C4—112no—
382C2×C4⋊C4—222no—
383C2×C4⋊C4—222no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—222no—
394C2×C42—21no—
395C2×C42—222no—
396C2×C42C22⋊D1111yescharacteristic
397C2×C42C22⋊D1111yescharacteristic
398C2×C42C22⋊D1114yes—
399C2×C42C22×D1111yescharacteristic
400C2×C42C22×D1111yescharacteristic
401C2×C42C22×D1114yes—
402#107—118no—
403#107—118no—
404#106—118no—
405#106—118no—
406C4⋊C8—114no—
407C4⋊C8—114no—
408#103—118no—
409#103—118no—
410#102—118no—
411#102—118no—
412C22⋊C8—118no—
413C4×C8—118no—
414C2×C11—42no—
415C2×C11—82no—
416C2×C11#323314yescomplemented
417C2×C11C2×#53611yescharacteristic
418C2×C11C22×#13511yescharacteristic
419C2×C11C2×#57511yescharacteristic
420C24—21no—
421C24C2×C22⋊D1111yescharacteristic
422C2×Q8—21no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—224no—
426C2×Q8—224no—
427C2×Q8—444no—
428C2×Q8—444no—
429C2×Q8C23×D1112yes—
430C2×D4—24no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—21no—
434C2×D4—44no—
435C2×D4C23×D1112yes—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—24no—
443C22×C4—42no—
444C22×C4—44no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4C2×C22⋊D1114yes—
448C22×C4C2×C22⋊D1112yes—
449C22×C4C2×C22⋊D1111yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451C22×C4C2×C22⋊D1111yescharacteristic
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C2×C22⋊D1114yes—
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C23×D1112yes—
456C22×C4C23×D1111yescharacteristic
457C2×C8—114no—
458C2×C8—114no—
459C2×C8—224no—
460C2×C8—224no—
461C4⋊C4—24no—
462C4⋊C4—24no—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—114no—
468C4⋊C4—114no—
469C4⋊C4—222no—
470C4⋊C4—222no—
471C4⋊C4—228no—
472C4⋊C4—228no—
473C4⋊C4—224no—
474C4⋊C4—224no—
475C4⋊C4C23×D1112yes—
476C4⋊C4C23×D1112yes—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—228no—
483C42—24no—
484C42—228no—
485C42C2×C22⋊D1114yes—
486C42C2×C22⋊D1112yes—
487C42C2×C22⋊D1114yes—
488C42C2×C22⋊D1112yes—
489C42C23×D1112yes—
490C42C23×D1112yes—
491C11C2×#323311yescharacteristic, complemented, Sylow
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23C22×C22⋊D1112yes—
500C23C22×C22⋊D1111yescharacteristic
501Q8—22no—
502Q8—22no—
503Q8—42no—
504Q8—448no—
505Q8—448no—
506D4—22no—
507D4—22no—
508D4—48no—
509D4—42no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—28no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—44no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—48no—
526C2×C4—224no—
527C2×C4—224no—
528C2×C4—444no—
529C2×C4—444no—
530C2×C4#6700314yes—
531C2×C4#6704312yes—
532C2×C4#6704312yes—
533C2×C4C22×C22⋊D1112yes—
534C2×C4C22×C22⋊D1112yes—
535C2×C4C22×C22⋊D1112yes—
536C2×C4C22×C22⋊D1112yes—
537C2×C4C22×C22⋊D1112yes—
538C2×C4C22×C22⋊D1111yescharacteristic
539C2×C4C24×D1111yescharacteristic
540C8—224no—
541C8—224no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—44no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—84no—
550C22C2×#6700312yes—
551C22#1062335312yes—
552C22#1062335612yes—
553C22C23×C22⋊D1111yescharacteristic
554C4—22no—
555C4—22no—
556C4—22no—
557C4—22no—
558C4—42no—
559C4—42no—
560C4—42no—
561C4—444no—
562C4—444no—
563C4C2×#6700314yes—
564C4#1062335612yes—
565C4C2×#6704311yescharacteristic
566C4C2×#6704311yescharacteristic
567C2—42no—
568C2—82no—
569C2#1307979114yesdirect product factor
570C2C2×#1062335611yescharacteristic
571C2C22×#6700311yescharacteristic
572C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#529C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenterC2×#529D11
hypocenterC11C2×#3233
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#10623001C2semidirect
2. #13079791C2direct (N × H)
3. C2×#10622677C2semidirect
4. C2×#10622669C2semidirect
5. C2×#10622658C2semidirect
7. C2×#10622634C2semidirect
8. C2×#10622633C2semidirect
9. C2×#10622621C2semidirect
10. C2×#10622620C2semidirect
11. C2×#10622538C2semidirect
30. #10623001C22semidirect
41. #10622677C22semidirect
42. #10622669C22semidirect
43. #10622658C22semidirect
45. #10622634C22semidirect
46. #10622633C22semidirect
47. #10622621C22semidirect
48. #10622620C22semidirect
53. #10622538C22semidirect
416. C2×C11#3233semidirect
491. C11C2×#3233semidirect
569. C2#13079791direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230012
#130797912
C2×#106226772
C2×#106226692
C2×#106226582
C2×#106226482
C2×#106226342
C2×#106226332
C2×#106226212
C2×#106226202
C2×#106225382
C2×C11×#5292
C2×#323311