Finite Group Databasebeta

← C2×#13079319 #15623690

Subgroups — C2×#13079319 #15623690

Order 2816.

1998 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623010C211yesmaximal, characteristic
2#13079319C2116yesmaximal, direct product factor
3C2×#10622693C211yesmaximal, characteristic, complemented
4C2×#10622699C211yesmaximal, characteristic, complemented
5C2×#10622695C211yesmaximal, characteristic, complemented
6C2×#10622702C211yesmaximal, characteristic, complemented
7C2×#10622664C212yesmaximal, complemented
8C2×#10622661C212yesmaximal
9C2×#10622643C212yesmaximal, complemented
10C2×#10622639C212yesmaximal, complemented
11C22×#66867C211yesmaximal, characteristic, complemented
12C2×C11×#533C211yesmaximal, characteristic, complemented
13C11×#533—24no—
14C11×#533C2218yescomplemented
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#125—21no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8C2212yes—
20C2×C4×Q8×C11—21no—
21C2×C4×Q8×C11C2212yes—
22C2×C11×#117—21no—
23C22×C42×C11C2211yescharacteristic
24C22×#4326C2212yes—
25C22×#4325C2212yes—
26C2×#66983C2211yescharacteristic
27C2×#66982—21no—
28C2×C4×C22⋊D11—21no—
29C2×#66977C2211yescharacteristic
30C23×C11⋊C8C2212yes—
31#10623010—24no—
32#10623010C2218yes—
33C2×#66929—21no—
34C2×#66928C2211yescharacteristic
35C2×C4×D44C2211yescharacteristic
36C2×#66925—21no—
37C2×#66923C2211yescharacteristic
38C2×C4×Dic22C2211yescharacteristic
39C2×#66899C2212yes—
40C2×#66899C2212yes—
41#10622702C2218yescomplemented
42#10622699C2218yescomplemented
43#10622695C2218yescomplemented
44#10622693C2218yescomplemented
45#10622664C22116yescomplemented
46#10622661C22116yes—
47#10622643C22116yescomplemented
48#10622639C22116yescomplemented
49C2×#66874C2212yes—
50C2×#66873C2212yes—
51C2×#66872C2212yes—
52C2×#66871C2212yes—
53C2×#66867C2211yescharacteristic
54C2×#66867C2212yes—
55C2×#66867C2211yescharacteristic
56C2×#66867C2218yescomplemented
57C22×Q8×C11—21no—
58C22×Q8×C11C2312yes—
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—28no—
71C11×C22⋊Q8—28no—
72C11×C22⋊Q8—24no—
73C11×C22⋊Q8C2318yes—
74C4×Q8×C11—28no—
75C4×Q8×C11—24no—
76C4×Q8×C11C2318yes—
77C11×#117—28no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
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—
93C2×#4326—28no—
94C2×#4326C2318yes—
95C2×#4325—28no—
96C2×#4325C2318yes—
97#66983—22no—
98#66983C2314yes—
99#66982—28no—
100C4×C22⋊D11—28no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107#66977—22no—
108#66977C2314yes—
109C2×Dic11⋊C4—21no—
110C2×Dic11⋊C4—21no—
111C2×Dic11⋊C4—21no—
112C2×Dic11⋊C4—21no—
113C2×C4×Dic11—21no—
114C22×C11⋊C8—28no—
115C22×C11⋊C8C2312yes—
116C22×C11⋊C8C2318yes—
117C22×C11⋊C8C2312yes—
118#66929—28no—
119#66928—22no—
120#66928C2314yes—
121C4×D44—22no—
122C4×D44C2314yes—
123#66925—28no—
124#66923—22no—
125#66923C2314yes—
126C4×Dic22—22no—
127C4×Dic22C2314yes—
128#66899C2318yes—
129#66899C2318yes—
130#66874C2318yes—
131#66873C2318yes—
132#66872C2318yes—
133#66871C2318yes—
134#66867C2318yes—
135#66867C2314yes—
136#66867C2314yes—
137C2×#3181—111nomaximal, Sylow
138C24×C11C2×D411yescharacteristic
139C23×D11—21no—
140C2×Q8×C11—22no—
141C2×Q8×C11—24no—
142C2×Q8×C11—24no—
143C2×Q8×C11—24no—
144C2×Q8×C11—44no—
145C2×Q8×C11C2414yes—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—42no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D414yes—
158C22×C4×C11C2×D414yes—
159C22×C4×C11C2412yes—
160C22×C4×C11C2411yescharacteristic
161C2×C22⋊D11—24no—
162C2×C22⋊D11—44no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C2×D44—21no—
167C2×D44—24no—
168C2×D44C2412yes—
169C2×C4×D11—24no—
170C2×C4×D11—44no—
171C2×Dic22—21no—
172C2×Dic22—24no—
173C2×Dic22C2412yes—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—28no—
178C11×C4⋊C4—28no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4C2414yes—
181C11×C22⋊C4—28no—
182C42×C11—28no—
183C42×C11C2×D412yes—
184C42×C11C2×D412yes—
185C42×C11C2×D414yes—
186C42×C11C2×D414yes—
187C42×C11C2412yes—
188C42×C11C2412yes—
189C22⋊Dic11—24no—
190#4326—216no—
191#4325—216no—
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4—24no—
194(C2×D11)⋊C4—24no—
195(C2×D11)⋊C4—24no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11C2412yes—
199C4⋊Dic11C2412yes—
200Dic11⋊C4—24no—
201Dic11⋊C4—24no—
202Dic11⋊C4—24no—
203Dic11⋊C4—24no—
204C4×Dic11—24no—
205C2×C11⋊C8—216no—
206C2×C11⋊C8—24no—
207C2×C11⋊C8#4118yes—
208C2×C11⋊C8C2414yes—
209C2×C11⋊C8C2414yes—
210C2×#533D1111yescharacteristic, complemented
211C2×#529—111no—
212#3181—1116no—
213C2×#501—111no—
214C2×#497—111no—
215C2×#491—111no—
216C2×#489—111no—
217C2×#467—112no—
218C2×#465—112no—
219C2×#441—112no—
220C2×#440—112no—
221C22×#97—111no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11#13714yes—
225C23×C11C22×D412yes—
226C23×C11C22×D411yescharacteristic
227C22×D11—22no—
228C22×D11—42no—
229C22×D11—42no—
230C22×D11—42no—
231Q8×C11—24no—
232Q8×C11—24no—
233Q8×C11—48no—
234Q8×C11—44no—
235C2×C4×C11—22no—
236C2×C4×C11—28no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—44no—
246C2×C4×C11—44no—
247C2×C4×C11—44no—
248C2×C4×C11C22×D412yes—
249C2×C4×C11C22×D412yes—
250C2×C4×C11C22×D412yes—
251C2×C4×C11C22×D412yes—
252C2×C4×C11C22×D412yes—
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C2×#4114yes—
255C2×C4×C11C2511yescharacteristic
256C22⋊D11—48no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263D44—24no—
264D44—42no—
265C4×D11—48no—
266Dic22—24no—
267Dic22—42no—
268C11⋊C8—24no—
269C11⋊C8C2×#4118yes—
270C22×Q16—112no—
271C22×SD16—112no—
272C23×C8—112no—
273#533—24no—
274#533C2×D1118yescomplemented
275C2×C4⋊Q8C2×D1111yescharacteristic
276C2×C4⋊Q8C2×D1111yescharacteristic
277#529—118no—
278#529—224no—
279C2×#126—221no—
280C2×#125—21no—
281C2×#125—111no—
282C2×#124—111no—
283C2×#123—221no—
284C2×C22⋊Q8—21no—
285C2×C22⋊Q8—111no—
286C2×C22⋊Q8C2×D1112yes—
287C2×#121—111no—
288C2×C4×Q8—21no—
289C2×C4×Q8—111no—
290C2×C4×Q8C2×D1112yes—
291C2×C4×D4—111no—
292C2×C4×D4—221no—
293C2×#117—21no—
294C2×#117—221no—
295C22×C42C2×D1111yescharacteristic
296#501—118no—
297#497—118no—
298#491—118no—
299#489—118no—
300#467—1116no—
301#465—1116no—
302#441—1116no—
303#440—1116no—
304C2×#107—112no—
305C2×#106—112no—
306C2×#103—112no—
307C2×#103—112no—
308C2×#103—112no—
309C2×#102—112no—
310C2×#97—111no—
311C2×#97—111no—
312C2×#97—112no—
313C2×#97—118no—
314C22×C11—28no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11#53212yes—
318C22×C11C2×#13714yes—
319C22×C11C2×#13712yes—
320C22×C11#57512yes—
321C22×C11C23×D411yescharacteristic
322C2×D11—42no—
323C2×D11—42no—
324C2×D11—42no—
325C2×D11—84no—
326C4×C11—22no—
327C4×C11—22no—
328C4×C11—22no—
329C4×C11—22no—
330C4×C11—22no—
331C4×C11—44no—
332C4×C11—44no—
333C4×C11#53212yes—
334C4×C11C22×#4112yes—
335Dic11—42no—
336Dic11—42no—
337Dic11—42no—
338C22×Q8—21no—
339C22×Q8—111no—
340C22×Q8C22×D1112yes—
341C22×D4—111no—
342C22×D4—221no—
343C23×C4—221no—
344C23×C4C22⋊D1111yescharacteristic
345C23×C4C22⋊D1111yescharacteristic
346C23×C4C22×D1111yescharacteristic
347C2×Q16—118no—
348C2×Q16—228no—
349C2×SD16—118no—
350C2×SD16—228no—
351C22×C8—112no—
352C22×C8—112no—
353C22×C8—118no—
354C22×C8—228no—
355C4⋊Q8—22no—
356C4⋊Q8—22no—
357C4⋊Q8C22×D1114yes—
358C4⋊Q8C22×D1114yes—
359#126—228no—
360#125—28no—
361#125—114no—
362#125—222no—
363#124—114no—
364#124—222no—
365#123—228no—
366C22⋊Q8—28no—
367C22⋊Q8—24no—
368C22⋊Q8—114no—
369C22⋊Q8—222no—
370C22⋊Q8C22×D1118yes—
371#121—114no—
372#121—222no—
373C4×Q8—28no—
374C4×Q8—24no—
375C4×Q8—114no—
376C4×Q8—222no—
377C4×Q8C22×D1118yes—
378C4×D4—114no—
379C4×D4—228no—
380C4×D4—222no—
381#117—28no—
382#117—228no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4C22×D1112yes—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4—221no—
398C2×C22⋊C4—221no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C42—22no—
402C2×C42—221no—
403C2×C42C22⋊D1111yescharacteristic
404C2×C42C22⋊D1111yescharacteristic
405C2×C42C22⋊D1114yes—
406C2×C42C22×D1111yescharacteristic
407C2×C42C22×D1111yescharacteristic
408C2×C42C22×D1114yes—
409#107—118no—
410#106—118no—
411#103—118no—
412#103—118no—
413#103—118no—
414#102—118no—
415#97—118no—
416#97—114no—
417#97—114no—
418C2×C11—24no—
419C2×C11#318114yescomplemented
420C2×C11C2×#53211yescharacteristic
421C2×C11C22×#13711yescharacteristic
422C2×C11C2×#57511yescharacteristic
423D11—82no—
424C24—221no—
425C24C2×C22⋊D1111yescharacteristic
426C2×Q8—22no—
427C2×Q8—24no—
428C2×Q8—24no—
429C2×Q8—24no—
430C2×Q8—44no—
431C2×Q8—112no—
432C2×Q8—221no—
433C2×Q8—224no—
434C2×Q8C23×D1114yes—
435C2×D4—112no—
436C2×D4—224no—
437C2×D4—224no—
438C2×D4—221no—
439C2×D4—444no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—42no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—224no—
449C22×C4—444no—
450C22×C4C2×C22⋊D1114yes—
451C22×C4C2×C22⋊D1112yes—
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C2×C22⋊D1111yescharacteristic
457C22×C4C2×C22⋊D1114yes—
458C22×C4C23×D1112yes—
459C22×C4C23×D1111yescharacteristic
460Q16—2216no—
461SD16—2216no—
462C2×C8—118no—
463C2×C8—114no—
464C2×C8—114no—
465C2×C8—2216no—
466C2×C8—224no—
467C4⋊C4—24no—
468C4⋊C4—24no—
469C4⋊C4—24no—
470C4⋊C4—28no—
471C4⋊C4—28no—
472C4⋊C4—22no—
473C4⋊C4—112no—
474C4⋊C4—112no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—224no—
478C4⋊C4—224no—
479C4⋊C4—224no—
480C4⋊C4—224no—
481C4⋊C4C23×D1114yes—
482C22⋊C4—28no—
483C22⋊C4—224no—
484C22⋊C4—224no—
485C22⋊C4—224no—
486C22⋊C4—224no—
487C22⋊C4—224no—
488C42—28no—
489C42—224no—
490C42C2×C22⋊D1114yes—
491C42C2×C22⋊D1112yes—
492C42C2×C22⋊D1114yes—
493C42C2×C22⋊D1112yes—
494C42C23×D1112yes—
495C42C23×D1112yes—
496C11C2×#318111yescharacteristic, complemented, Sylow
497C23—22no—
498C23—22no—
499C23—222no—
500C23—442no—
501C23—442no—
502C23—442no—
503C23#6699514yes—
504C23C22×C22⋊D1112yes—
505C23C22×C22⋊D1111yescharacteristic
506Q8—24no—
507Q8—24no—
508Q8—48no—
509Q8—44no—
510Q8—224no—
511Q8—442no—
512D4—224no—
513D4—448no—
514D4—442no—
515C2×C4—28no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—44no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—222no—
529C2×C4—222no—
530C2×C4—222no—
531C2×C4—448no—
532C2×C4—442no—
533C2×C4—442no—
534C2×C4—442no—
535C2×C4#41×D1114yes—
536C2×C4C22×C22⋊D1112yes—
537C2×C4C22×C22⋊D1112yes—
538C2×C4C22×C22⋊D1112yes—
539C2×C4C22×C22⋊D1112yes—
540C2×C4C22×C22⋊D1112yes—
541C2×C4C22×C22⋊D1111yescharacteristic
542C2×C4C24×D1111yescharacteristic
543C8—118no—
544C8—224no—
545C22—28no—
546C22—22no—
547C22—22no—
548C22—442no—
549C22—442no—
550C22—442no—
551C22—884no—
552C22C2×#6699514yes—
553C22C2×#6699512yes—
554C22#1062335312yes—
555C22#1062336312yes—
556C22C23×C22⋊D1111yescharacteristic
557C4—22no—
558C4—22no—
559C4—22no—
560C4—22no—
561C4—22no—
562C4—44no—
563C4—44no—
564C4—442no—
565C4—442no—
566C4—442no—
567C4#1062336312yes—
568C4C2×#41×D1112yes—
569C2—24no—
570C2—882no—
571C2#1307931914yesdirect product factor
572C2C2×#1062336311yescharacteristic
573C2C22×#6699511yescharacteristic
574C2C2×#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×#3181
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. #13079319C2direct (N × H)
3. C2×#10622693C2semidirect
4. C2×#10622699C2semidirect
5. C2×#10622695C2semidirect
6. C2×#10622702C2semidirect
7. C2×#10622664C2semidirect
9. C2×#10622643C2semidirect
10. C2×#10622639C2semidirect
11. C22×#66867C2semidirect
12. C2×C11×#533C2semidirect
14. C11×#533C22semidirect
41. #10622702C22semidirect
42. #10622699C22semidirect
43. #10622695C22semidirect
44. #10622693C22semidirect
45. #10622664C22semidirect
47. #10622643C22semidirect
48. #10622639C22semidirect
56. C2×#66867C22semidirect
210. C2×#533D11semidirect
274. #533C2×D11semidirect
419. C2×C11#3181semidirect
496. C11C2×#3181semidirect
571. C2#13079319direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230102
#130793192
C2×#106226932
C2×#106226992
C2×#106226952
C2×#106227022
C2×#106226642
C2×#106226612
C2×#106226432
C2×#106226392
C22×#668672
C2×C11×#5332
C2×#318111