Finite Group Databasebeta

← C2×#13079795 #15625851

Subgroups — C2×#13079795 #15625851

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×#10623010C211yesmaximal, characteristic
2#13079795C2116yesmaximal, direct product factor
3C2×#10622677C212yesmaximal, complemented
4C2×#10622681C212yesmaximal, complemented
5C2×#10622609C212yesmaximal, complemented
6C2×#10622616C212yesmaximal
7C2×#10622704C211yesmaximal, characteristic, complemented
8C2×#10622707C211yesmaximal, characteristic, complemented
9C2×#10622697C211yesmaximal, characteristic, complemented
10C2×#10622700C211yesmaximal, characteristic, complemented
11C2×#10622538C211yesmaximal, characteristic, complemented
12C2×C11×#533C211yesmaximal, characteristic, complemented
13C11×#533—24no—
14C11×#533C2218yescomplemented
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#125C2212yes—
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8—21no—
20C2×C4×Q8×C11—21no—
21C2×C4×Q8×C11—21no—
22C2×C11×#117C2212yes—
23C22×C42×C11C2211yescharacteristic
24C2×#66983C2211yescharacteristic
25C2×#66982—21no—
26C2×C4×C22⋊D11—21no—
27C2×#66977C2211yescharacteristic
28#10623010—24no—
29#10623010C2218yes—
30C2×#66929—21no—
31C2×#66928C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C2×#66925—21no—
34C2×#66923C2211yescharacteristic
35C2×C4×Dic22C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622707C2218yescomplemented
38#10622704C2218yescomplemented
39#10622700C2218yescomplemented
40#10622697C2218yescomplemented
41#10622681C22116yescomplemented
42#10622677C22116yescomplemented
43#10622616C22116yes—
44#10622609C22116yescomplemented
45C2×#66874C2212yes—
46C2×#66874C2212yes—
47C2×#66873C2212yes—
48C2×#66873C2212yes—
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×C11—21no—
58C22×Q8×C11—21no—
59C23×C4×C11D411yescharacteristic
60C23×C4×C11D411yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×Dic22C2311yescharacteristic
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8C2314yes—
69C11×C4⋊Q8C2314yes—
70C11×#125—24no—
71C11×#125C2318yes—
72C11×C22⋊Q8—28no—
73C11×C22⋊Q8—28no—
74C4×Q8×C11—28no—
75C4×Q8×C11—28no—
76C11×#117—24no—
77C11×#117C2318yes—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C22⋊C4—22no—
85C2×C42×C11—22no—
86C2×C42×C11D411yescharacteristic
87C2×C42×C11D411yescharacteristic
88C2×C42×C11D414yes—
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2314yes—
92C2×C22⋊Dic11—21no—
93#66983—22no—
94#66983C2314yes—
95#66982—28no—
96C4×C22⋊D11—28no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103#66977—22no—
104#66977C2314yes—
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4—21no—
109C2×C4×Dic11—21no—
110C22×C11⋊C8C2312yes—
111C22×C11⋊C8C2312yes—
112#66929—28no—
113#66928—22no—
114#66928C2314yes—
115C4×D44—22no—
116C4×D44C2314yes—
117#66925—28no—
118#66923—22no—
119#66923C2314yes—
120C4×Dic22—22no—
121C4×Dic22C2314yes—
122C22⋊(C11⋊C8)C2318yes—
123#66874C2318yes—
124#66874C2318yes—
125#66873C2318yes—
126#66873C2318yes—
127#66872C2318yes—
128#66872C2318yes—
129#66871C2318yes—
130#66871C2318yes—
131C4⋊(C11⋊C8)C2314yes—
132C4⋊(C11⋊C8)C2314yes—
133C4×C11⋊C8C2318yes—
134C2×#3233—111nomaximal, Sylow
135C24×C11C2×D411yescharacteristic
136C23×D11—21no—
137C2×Q8×C11—24no—
138C2×Q8×C11—24no—
139C2×Q8×C11—44no—
140C2×Q8×C11—44no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—42no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2×D414yes—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2412yes—
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—24no—
158C2×C22⋊D11—44no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C2×D44—21no—
163C2×D44—22no—
164C2×D44—22no—
165C2×D44C2412yes—
166C2×C4×D11—24no—
167C2×C4×D11—44no—
168C2×Dic22—21no—
169C2×Dic22—22no—
170C2×Dic22—22no—
171C2×Dic22C2412yes—
172C11×C4⋊C4—28no—
173C11×C4⋊C4—28no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4C2414yes—
179C11×C4⋊C4C2414yes—
180C11×C22⋊C4—28no—
181C42×C11—28no—
182C42×C11C2×D412yes—
183C42×C11C2×D412yes—
184C42×C11C2×D414yes—
185C42×C11C2×D414yes—
186C42×C11C2412yes—
187C42×C11C2412yes—
188C22⋊Dic11—24no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—24no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11C2412yes—
196C4⋊Dic11C2412yes—
197Dic11⋊C4—24no—
198Dic11⋊C4—24no—
199Dic11⋊C4—24no—
200Dic11⋊C4—24no—
201C4×Dic11—24no—
202C2×C11⋊C8—24no—
203C2×C11⋊C8—24no—
204C2×C11⋊C8C2414yes—
205C2×C11⋊C8C2414yes—
206C2×#533D1111yescharacteristic, complemented
207C2×#529—111no—
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×C11C22×D412yes—
222C23×C11C22×D411yescharacteristic
223C22×D11—22no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—42no—
227Q8×C11—48no—
228Q8×C11—48no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—28no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—44no—
240C2×C4×C11—44no—
241C2×C4×C11—44no—
242C2×C4×C11#13514yes—
243C2×C4×C11C22×D412yes—
244C2×C4×C11C22×D412yes—
245C2×C4×C11C22×D412yes—
246C2×C4×C11C22×D412yes—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D412yes—
249C2×C4×C112−1+412yes—
250C2×C4×C112−1+412yes—
251C2×C4×C11C2511yescharacteristic
252C22⋊D11—48no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259D44—22no—
260D44—22no—
261D44—42no—
262C4×D11—48no—
263Dic22—22no—
264Dic22—22no—
265Dic22—42no—
266C11⋊C8—24no—
267C11⋊C8—24no—
268#533—24no—
269#533C2×D1118yescomplemented
270C2×C4⋊Q8C2×D1111yescharacteristic
271C2×C4⋊Q8C2×D1111yescharacteristic
272#529—118no—
273#529—224no—
274C2×#126—221no—
275C2×#125—111no—
276C2×#125C2×D1112yes—
277C2×#124—111no—
278C2×#123—221no—
279C2×C22⋊Q8—21no—
280C2×C22⋊Q8—21no—
281C2×C22⋊Q8—111no—
282C2×#121—111no—
283C2×C4×Q8—21no—
284C2×C4×Q8—21no—
285C2×C4×Q8—111no—
286C2×C4×D4—111no—
287C2×C4×D4—221no—
288C2×#117—221no—
289C2×#117C2×D1112yes—
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#53612yes—
317C22×C11C2×#13512yes—
318C22×C11#57512yes—
319C22×C11C23×D411yescharacteristic
320C2×D11—42no—
321C2×D11—42no—
322C2×D11—42no—
323C2×D11—84no—
324C4×C11—22no—
325C4×C11—22no—
326C4×C11—22no—
327C4×C11—22no—
328C4×C11—44no—
329C4×C11—44no—
330C4×C11#53612yes—
331C4×C11C2×#13514yes—
332C4×C11C2×2−1+411yescharacteristic
333C4×C11C2×2−1+411yescharacteristic
334Dic11—42no—
335Dic11—42no—
336Dic11—42no—
337C22×Q8—21no—
338C22×Q8—21no—
339C22×Q8—111no—
340C22×D4—111no—
341C22×D4—221no—
342C23×C4—221no—
343C23×C4C22⋊D1111yescharacteristic
344C23×C4C22⋊D1111yescharacteristic
345C23×C4C22×D1111yescharacteristic
346C22×C8—112no—
347C22×C8—112no—
348C4⋊Q8—22no—
349C4⋊Q8—22no—
350C4⋊Q8C22×D1114yes—
351C4⋊Q8C22×D1114yes—
352#126—228no—
353#125—24no—
354#125—114no—
355#125—222no—
356#125C22×D1118yes—
357#124—114no—
358#124—222no—
359#123—228no—
360C22⋊Q8—28no—
361C22⋊Q8—28no—
362C22⋊Q8—114no—
363C22⋊Q8—222no—
364#121—114no—
365#121—222no—
366C4×Q8—28no—
367C4×Q8—28no—
368C4×Q8—114no—
369C4×Q8—222no—
370C4×D4—114no—
371C4×D4—228no—
372C4×D4—222no—
373#117—24no—
374#117—228no—
375#117C22×D1118yes—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4C22×D1112yes—
387C2×C4⋊C4C22×D1112yes—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C42—22no—
395C2×C42—221no—
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#323314yescomplemented
416C2×C11C2×#53611yescharacteristic
417C2×C11C22×#13511yescharacteristic
418C2×C11C2×#57511yescharacteristic
419D11—82no—
420C24—221no—
421C24C2×C22⋊D1111yescharacteristic
422C2×Q8—24no—
423C2×Q8—24no—
424C2×Q8—44no—
425C2×Q8—44no—
426C2×Q8—112no—
427C2×Q8—221no—
428C2×Q8—222no—
429C2×Q8—222no—
430C2×D4—112no—
431C2×D4—224no—
432C2×D4—222no—
433C2×D4—222no—
434C2×D4—221no—
435C2×D4—444no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—42no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—224no—
446C22×C4—444no—
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—28no—
462C4⋊C4—28no—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—112no—
468C4⋊C4—112no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—224no—
472C4⋊C4—224no—
473C4⋊C4—224no—
474C4⋊C4—224no—
475C4⋊C4C23×D1114yes—
476C4⋊C4C23×D1114yes—
477C22⋊C4—28no—
478C22⋊C4—224no—
479C22⋊C4—224no—
480C22⋊C4—224no—
481C22⋊C4—224no—
482C22⋊C4—224no—
483C42—28no—
484C42—224no—
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—222no—
496C23—442no—
497C23—442no—
498C23—442no—
499C23C22×C22⋊D1112yes—
500C23C22×C22⋊D1111yescharacteristic
501Q8—48no—
502Q8—48no—
503Q8—222no—
504Q8—222no—
505Q8—442no—
506D4—222no—
507D4—222no—
508D4—448no—
509D4—442no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—28no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—44no—
521C2×C4—44no—
522C2×C4—44no—
523C2×C4—222no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4—442no—
529C2×C4—448no—
530C2×C4#6700314yes—
531C2×C4#6704012yes—
532C2×C4#6704012yes—
533C2×C4C22×C22⋊D1112yes—
534C2×C4C22×C22⋊D1112yes—
535C2×C4C22×C22⋊D1112yes—
536C2×C4C22×C22⋊D1112yes—
537C2×C4C22×C22⋊D1111yescharacteristic
538C2×C4C22×C22⋊D1112yes—
539C2×C4C24×D1111yescharacteristic
540C8—224no—
541C8—224no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—44no—
546C22—442no—
547C22—442no—
548C22—442no—
549C22—884no—
550C22#1062334712yes—
551C22C2×#6700312yes—
552C22#1062335312yes—
553C22C23×C22⋊D1111yescharacteristic
554C4—22no—
555C4—22no—
556C4—22no—
557C4—22no—
558C4—44no—
559C4—44no—
560C4—442no—
561C4—442no—
562C4—442no—
563C4#1062334712yes—
564C4C2×#6700314yes—
565C4C2×#6704011yescharacteristic
566C4C2×#6704011yescharacteristic
567C2—42no—
568C2—882no—
569C2#1307979514yesdirect product factor
570C2C2×#1062334711yescharacteristic
571C2C22×#6700311yescharacteristic
572C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#533C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#533D11
hypocenterC11C2×#3233
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
2. #13079795C2direct (N × H)
3. C2×#10622677C2semidirect
4. C2×#10622681C2semidirect
5. C2×#10622609C2semidirect
7. C2×#10622704C2semidirect
8. C2×#10622707C2semidirect
9. C2×#10622697C2semidirect
10. C2×#10622700C2semidirect
11. C2×#10622538C2semidirect
12. C2×C11×#533C2semidirect
14. C11×#533C22semidirect
37. #10622707C22semidirect
38. #10622704C22semidirect
39. #10622700C22semidirect
40. #10622697C22semidirect
41. #10622681C22semidirect
42. #10622677C22semidirect
44. #10622609C22semidirect
53. #10622538C22semidirect
206. C2×#533D11semidirect
269. #533C2×D11semidirect
415. C2×C11#3233semidirect
491. C11C2×#3233semidirect
569. C2#13079795direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230102
#130797952
C2×#106226772
C2×#106226812
C2×#106226092
C2×#106226162
C2×#106227042
C2×#106227072
C2×#106226972
C2×#106227002
C2×#106225382
C2×C11×#5332
C2×#323311