Finite Group Databasebeta

← C2×#13080335 #15629014

Subgroups — C2×#13080335 #15629014

Order 2816.

2806 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66972C211yesmaximal, characteristic, complemented
2C22×#66957C211yesmaximal, characteristic, complemented
3C2×#10623162C212yesmaximal, complemented
4#13080335C2116yesmaximal, direct product factor
5C2×#10622794C211yesmaximal, characteristic, complemented
6C2×#10622500C211yesmaximal, characteristic, complemented
7C2×#10622431C212yesmaximal, complemented
8C2×#10622423C212yesmaximal, complemented
9C2×#10622660C212yesmaximal, complemented
10C2×#10622485C211yesmaximal, characteristic, complemented
11C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
12C2×C11×#467C211yesmaximal, characteristic, complemented
13C22×#4343C2212yes—
14C22×#4339C2212yes—
15C22×C11×Q16C2211yescharacteristic
16C23×C8×C11C2211yescharacteristic
17C2×C11×C22⋊Q8C2212yes—
18C2×#66997C2212yes—
19C22×#4326C2212yes—
20C22×#4325C2212yes—
21C2×C4×C22⋊D11C2211yescharacteristic
22C2×#66972—28no—
23C2×#66972C2218yescomplemented
24C22×Dic44C2211yescharacteristic
25C2×#66957—28no—
26C2×#66957C2218yescomplemented
27C22×D88C2211yescharacteristic
28C22×#4314C2212yes—
29C22×C8×D11C2211yescharacteristic
30#10623162—28no—
31#10623162C22116yescomplemented
32C2×#66950C2212yes—
33C2×#66947—22no—
34C2×#66946C2212yes—
35C2×C4⋊C4×D11—22no—
36C2×#66937—22no—
37C2×#66936—22no—
38C11×#467C2218yescomplemented
39C2×C11×#107C2211yescharacteristic
40C2×C11×#103C2212yes—
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42#10622794C2218yescomplemented
43C8×C22⋊D11C2218yescomplemented
44C2×(C2×D11)⋊C8C2211yescharacteristic
45C2×Dic11⋊C8C2211yescharacteristic
46C2×C8×Dic11C2211yescharacteristic
47#10622660C22116yescomplemented
48C2×#66874C2212yes—
49C2×#66873C2212yes—
50#10622500C2218yescomplemented
51#10622485C2218yescomplemented
52#10622431C22116yescomplemented
53#10622423C22116yescomplemented
54C22×Q8×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11—22no—
57C22×C22⋊D11D411yescharacteristic
58C2×#4343—24no—
59C2×#4343—28no—
60C2×#4343—44no—
61C2×#4343C2318yes—
62C2×#4339—24no—
63C2×#4339—28no—
64C2×#4339—44no—
65C2×#4339C2318yes—
66C22×D44—22no—
67C22×D44C2312yes—
68C22×C4×D11—22no—
69C22×C4×D11—22no—
70C22×C4×D11—22no—
71C22×C4×D11C2311yescharacteristic
72C22×Dic22C2312yes—
73C2×C11×Q16—24no—
74C2×C11×Q16C2314yes—
75C22×C8×C11—24no—
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2314yes—
78C22×C8×C11C2311yescharacteristic
79C11×C22⋊Q8—24no—
80C11×C22⋊Q8C2318yes—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C22⋊C4—22no—
84C2×C22⋊Dic11D411yescharacteristic
85#66997—24no—
86#66997C2318yes—
87C2×#4326—44no—
88C2×#4326C2318yes—
89C2×#4325—28no—
90C2×#4325C2318yes—
91C4×C22⋊D11D414yes—
92C4×C22⋊D11C2314yes—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4D411yescharacteristic
96C2×C4⋊Dic11—22no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4D411yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66972—232no—
104C2×Dic44—24no—
105C2×Dic44C2314yes—
106#66957—232no—
107C2×D88D418yescomplemented
108C2×D88C2314yes—
109C2×#4314—28no—
110C2×#4314C2318yes—
111C2×C8×D11—24no—
112C2×C8×D11C2314yes—
113#66950—24no—
114#66950C2318yes—
115#66947—216no—
116#66946—24no—
117#66946C2318yes—
118C4⋊C4×D11—216no—
119#66937—216no—
120#66936—216no—
121C11×#107C2314yes—
122C11×#103C2318yes—
123C22⋊(C11⋊C8)C2314yes—
124(C2×D11)⋊C8C2314yes—
125Dic11⋊C8C2314yes—
126C8×Dic11C2314yes—
127#66874C2318yes—
128#66873C2318yes—
129C2×#3283—111nomaximal, Sylow
130C24×C11C2×D411yescharacteristic
131C23×D11—22no—
132C23×D11C2×D411yescharacteristic
133C2×Q8×C11—22no—
134C2×Q8×C11—24no—
135C2×Q8×C11—24no—
136C2×Q8×C11C2414yes—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2411yescharacteristic
145C2×C22⋊D11—24no—
146C2×C22⋊D11—28no—
147C2×C22⋊D11—48no—
148C2×C22⋊D11C2×D414yes—
149C22×Dic11—22no—
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153#4343—216no—
154#4343—48no—
155#4343—416no—
156#4339—216no—
157#4339—48no—
158#4339—416no—
159C2×D44—28no—
160C2×D44—22no—
161C2×D44—24no—
162C2×D44—48no—
163C2×D44C2×D418yes—
164C2×D44C2414yes—
165C2×C4×D11—28no—
166C2×C4×D11—28no—
167C2×C4×D11—22no—
168C2×C4×D11—28no—
169C2×C4×D11—22no—
170C2×C4×D11—48no—
171C2×C4×D11—48no—
172C2×C4×D11—48no—
173C2×C4×D11C2×D412yes—
174C2×C4×D11C2412yes—
175C2×Dic22—24no—
176C2×Dic22—22no—
177C2×Dic22—24no—
178C2×Dic22C2414yes—
179C11×Q16—28no—
180C2×C8×C11—28no—
181C2×C8×C11—22no—
182C2×C8×C11C2×D414yes—
183C2×C8×C11C2412yes—
184C2×C8×C11C2412yes—
185C11×C4⋊C4—28no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4C2414yes—
188C11×C22⋊C4—28no—
189C22⋊Dic11C2×D414yes—
190#4326—48no—
191#4325—216no—
192(C2×D11)⋊C4—28no—
193(C2×D11)⋊C4—28no—
194(C2×D11)⋊C4C2×D414yes—
195C4⋊Dic11—28no—
196Dic11⋊C4—28no—
197Dic11⋊C4—28no—
198Dic11⋊C4C2×D414yes—
199C4×Dic11C2×D412yes—
200C4×Dic11C2412yes—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8C2412yes—
204C2×C11⋊C8C2412yes—
205Dic44—28no—
206D88C2×D4116yescomplemented
207#4314—216no—
208C8×D11—28no—
209C22×#135—111no—
210C22×#135—111no—
211C2×#547—112no—
212#3283—1116no—
213C2×#494—111no—
214C2×#467—111no—
215C2×#467D1111yescharacteristic, complemented
216C2×#461—112no—
217C2×#452—112no—
218C2×#452—112no—
219C2×C4×D8—111no—
220C2×C8×D4—111no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11C22×D412yes—
225C23×C11C22×D411yescharacteristic
226C22×D11—22no—
227C22×D11—28no—
228C22×D11—22no—
229C22×D11—22no—
230C22×D11—24no—
231C22×D11—44no—
232C22×D11—44no—
233C22×D11C22×D412yes—
234Q8×C11—24no—
235Q8×C11—24no—
236Q8×C11—44no—
237C2×C4×C11—22no—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—44no—
244C2×C4×C11—44no—
245C2×C4×C11C22×D412yes—
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D412yes—
248C2×C4×C11H(5,𝔽2)12yes—
249C2×C4×C11C2511yescharacteristic
250C22⋊D11—28no—
251C22⋊D11—416no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—24no—
255C2×Dic11—44no—
256C2×Dic11#13514yescomplemented
257C2×Dic11C22×D412yes—
258C2×Dic11C22×D412yes—
259C2×Dic11C22×D412yes—
260D44—28no—
261D44—24no—
262D44—416no—
263D44C22×D418yes—
264C4×D11—24no—
265C4×D11—22no—
266C4×D11—22no—
267C4×D11—416no—
268C4×D11—416no—
269C4×D11—416no—
270Dic22—24no—
271Dic22—24no—
272Dic22—44no—
273C8×C11—22no—
274C8×C11C22×D414yes—
275C11⋊C8—22no—
276C11⋊C8—22no—
277C22×#41—112no—
278C22×#41—112no—
279C2×#135—118no—
280C2×#135—118no—
281C2×#135—228no—
282C2×#135—228no—
283C22×Q16—112no—
284C22×Q16—111no—
285C22×Q16C2×D1111yescharacteristic
286C22×SD16—112no—
287C22×SD16—112no—
288C22×D8—111no—
289C23×C8—111no—
290C23×C8C2×D1111yescharacteristic
291#547—1116no—
292#547—228no—
293C2×C4⋊Q8—112no—
294C2×#123—222no—
295C2×#123—222no—
296C2×C22⋊Q8—112no—
297C2×C22⋊Q8C2×D1112yes—
298C2×#121—222no—
299C2×C4×D4—111no—
300C2×C4×D4—112no—
301C22×C4⋊C4—222no—
302#494—118no—
303#467—118no—
304#467C2×D1118yescomplemented
305#461—1116no—
306#452—1116no—
307#452—1116no—
308C4×D8—118no—
309C8×D4—118no—
310C2×#107C2×D1111yescharacteristic
311C2×C4⋊C8—111no—
312C2×#103—112no—
313C2×#103C2×D1112yes—
314C2×#102—112no—
315C2×C22⋊C8—111no—
316C2×C22⋊C8—111no—
317C2×C4×C8—111no—
318C22×C11—22no—
319C22×C11—22no—
320C22×C11—22no—
321C22×C11—44no—
322C22×C11D4212yes—
323C22×C11C2×#13512yes—
324C22×C11#57812yes—
325C22×C11C23×D411yescharacteristic
326C2×D11—28no—
327C2×D11—22no—
328C2×D11—22no—
329C2×D11—22no—
330C2×D11—44no—
331C2×D11—416no—
332C2×D11—44no—
333C2×D11—44no—
334C4×C11—22no—
335C4×C11—44no—
336C4×C11—44no—
337C4×C11D4212yes—
338C4×C11C23×D411yescharacteristic
339C4×C11C2×H(5,𝔽2)11yescharacteristic
340Dic11—22no—
341Dic11—22no—
342Dic11—44no—
343Dic11C2×#13514yescomplemented
344C2×#41—118no—
345C2×#41—118no—
346C2×#41—228no—
347C2×#41—224no—
348C2×#41—224no—
349C2×#41—228no—
350C2×#41—444no—
351C2×#41—444no—
352C22×Q8—112no—
353C22×Q8C22×D1112yes—
354C22×D4—111no—
355C22×D4—112no—
356C22×D4—222no—
357C22×D4—222no—
358C23×C4—111no—
359C23×C4—222no—
360C23×C4—222no—
361C23×C4—222no—
362C23×C4C22×D1111yescharacteristic
363#135—2232no—
364#135—2232no—
365C2×Q16—24no—
366C2×Q16—118no—
367C2×Q16—114no—
368C2×Q16—224no—
369C2×Q16—444no—
370C2×Q16C22×D1114yes—
371C2×SD16—118no—
372C2×SD16—118no—
373C2×SD16—228no—
374C2×SD16—228no—
375C2×D8—118no—
376C2×D8—114no—
377C22×C8—24no—
378C22×C8—111no—
379C22×C8—111no—
380C22×C8—114no—
381C22×C8—224no—
382C22×C8C22×D1111yescharacteristic
383C22×C8C22×D1114yes—
384C22×C8C22×D1111yescharacteristic
385C4⋊Q8—118no—
386C4⋊Q8—224no—
387#123—2216no—
388#123—2216no—
389C22⋊Q8—24no—
390C22⋊Q8—118no—
391C22⋊Q8—224no—
392C22⋊Q8C22×D1118yes—
393#121—2216no—
394C4×D4—114no—
395C4×D4—114no—
396C4×D4—118no—
397C4×D4—224no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—2216no—
401C2×C4⋊C4—222no—
402C2×C4⋊C4—222no—
403C2×C4⋊C4—222no—
404C2×C4⋊C4C22×D1112yes—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—111no—
407C2×C22⋊C4—111no—
408C2×C22⋊C4—222no—
409C2×C22⋊C4—222no—
410C2×C42—111no—
411#107C22×D1114yes—
412C4⋊C8—114no—
413#103—118no—
414#103C22×D1118yes—
415#102—118no—
416C22⋊C8—114no—
417C22⋊C8—114no—
418C4×C8—114no—
419C2×C11—42no—
420C2×C11#328314yescomplemented
421C2×C11C2×D4211yescharacteristic
422C2×C11C22×#13511yescharacteristic
423C2×C11C2×#57811yescharacteristic
424D11—42no—
425D11—48no—
426C24—111no—
427C24—222no—
428C24D4×D1111yescharacteristic
429#41—2216no—
430#41—2216no—
431#41—448no—
432#41—4416no—
433#41—448no—
434#41—4416no—
435C2×Q8—22no—
436C2×Q8—24no—
437C2×Q8—24no—
438C2×Q8—114no—
439C2×Q8—222no—
440C2×Q8—224no—
441C2×Q8—224no—
442C2×Q8C23×D1114yes—
443C2×D4—114no—
444C2×D4—118no—
445C2×D4—114no—
446C2×D4—228no—
447C2×D4—224no—
448C2×D4—228no—
449C2×D4—222no—
450C2×D4—224no—
451C2×D4—448no—
452C2×D4—448no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—111no—
460C22×C4—112no—
461C22×C4—112no—
462C22×C4—228no—
463C22×C4—228no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—228no—
468C22×C4—448no—
469C22×C4—448no—
470C22×C4—448no—
471C22×C4D4×D1112yes—
472C22×C4D4×D1111yescharacteristic
473C22×C4C23×D1112yes—
474C22×C4C23×D1111yescharacteristic
475Q16—28no—
476Q16—228no—
477Q16—448no—
478SD16—2216no—
479SD16—2216no—
480D8—1116no—
481C2×C8—22no—
482C2×C8—28no—
483C2×C8—112no—
484C2×C8—112no—
485C2×C8—222no—
486C2×C8—222no—
487C2×C8—228no—
488C2×C8D4×D1114yes—
489C2×C8C23×D1112yes—
490C2×C8C23×D1112yes—
491C4⋊C4—28no—
492C4⋊C4—22no—
493C4⋊C4—114no—
494C4⋊C4—228no—
495C4⋊C4—228no—
496C4⋊C4—228no—
497C4⋊C4C23×D1114yes—
498C22⋊C4—28no—
499C22⋊C4—114no—
500C22⋊C4—114no—
501C22⋊C4—228no—
502C22⋊C4—228no—
503C42—112no—
504C42—112no—
505C11C2×#328311yescharacteristic, complemented, Sylow
506C23—22no—
507C23—22no—
508C23—22no—
509C23—112no—
510C23—222no—
511C23—222no—
512C23—222no—
513C23—228no—
514C23—224no—
515C23—444no—
516C23—444no—
517C23C2×D4×D1112yes—
518C23C2×D4×D1111yescharacteristic
519Q8—24no—
520Q8—24no—
521Q8—44no—
522Q8—224no—
523Q8—224no—
524Q8—444no—
525D4—118no—
526D4—228no—
527D4—228no—
528D4—224no—
529D4—4416no—
530D4—4416no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—44no—
538C2×C4—44no—
539C2×C4—114no—
540C2×C4—112no—
541C2×C4—112no—
542C2×C4—112no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—224no—
546C2×C4—222no—
547C2×C4—222no—
548C2×C4—224no—
549C2×C4—4416no—
550C2×C4—4416no—
551C2×C4—4416no—
552C2×C4—444no—
553C2×C4C2×D4×D1112yes—
554C2×C4C2×D4×D1111yescharacteristic
555C2×C4C2×D4×D1112yes—
556C2×C4#6704212yes—
557C2×C4C24×D1111yescharacteristic
558C8—22no—
559C8—222no—
560C8—222no—
561C8C2×D4×D1114yes—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—44no—
566C22—222no—
567C22—228no—
568C22—222no—
569C22—222no—
570C22—444no—
571C22—4416no—
572C22—444no—
573C22—444no—
574C22#1062314012yes—
575C22#1062329712yes—
576C22D11×#13512yes—
577C22C22×D4×D1111yescharacteristic
578C4—22no—
579C4—44no—
580C4—44no—
581C4—114no—
582C4—222no—
583C4—222no—
584C4—444no—
585C4#1062314012yes—
586C4C22×D4×D1111yescharacteristic
587C4C2×#6704211yescharacteristic
588C2—42no—
589C2—442no—
590C2—448no—
591C2#1308033514yesdirect product factor
592C2C2×#1062314011yescharacteristic
593C2C2×D11×#13511yescharacteristic
594C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#467C2
socleC23×C11C22×D4
hypercenterC2×#467D11
hypocenterC11C2×#3283
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C22×#66972C2semidirect
2. C22×#66957C2semidirect
3. C2×#10623162C2semidirect
4. #13080335C2direct (N × H)
5. C2×#10622794C2semidirect
6. C2×#10622500C2semidirect
7. C2×#10622431C2semidirect
8. C2×#10622423C2semidirect
9. C2×#10622660C2semidirect
10. C2×#10622485C2semidirect
11. C2×C8×C22⋊D11C2semidirect
12. C2×C11×#467C2semidirect
23. C2×#66972C22semidirect
26. C2×#66957C22semidirect
31. #10623162C22semidirect
38. C11×#467C22semidirect
42. #10622794C22semidirect
43. C8×C22⋊D11C22semidirect
47. #10622660C22semidirect
50. #10622500C22semidirect
51. #10622485C22semidirect
52. #10622431C22semidirect
53. #10622423C22semidirect
107. C2×D88D4semidirect
206. D88C2×D4semidirect
215. C2×#467D11semidirect
256. C2×Dic11#135semidirect
304. #467C2×D11semidirect
343. Dic11C2×#135semidirect
420. C2×C11#3283semidirect
505. C11C2×#3283semidirect
591. C2#13080335direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669722
C22×#669572
C2×#106231622
#130803352
C2×#106227942
C2×#106225002
C2×#106224312
C2×#106224232
C2×#106226602
C2×#106224852
C2×C8×C22⋊D112
C2×C11×#4672
C2×#328311