Finite Group Databasebeta

← C2×#13078784 #15621918

Subgroups — C2×#13078784 #15621918

Order 2816.

2150 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623131C211yesmaximal, characteristic
2C22×#66940C211yesmaximal, characteristic, complemented
3#13078784C2116yesmaximal, direct product factor
4C2×#10622583C211yesmaximal, characteristic, complemented
5C2×#10622470C212yesmaximal, complemented
6C2×#10622380C212yesmaximal, complemented
7C2×#10622352C211yesmaximal, characteristic, complemented
8C2×#10622653C211yesmaximal, characteristic
9C2×#10622466C212yesmaximal, complemented
10C2×#10622370C212yesmaximal, complemented
11C2×#10622332C211yesmaximal, characteristic, complemented
12C2×C11×#481C211yesmaximal, characteristic
13C23×Dic22C2211yescharacteristic
14C2×C11×#121C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C2×#66989C2211yescharacteristic
17C2×#66988—21no—
18C2×D4×Dic11—21no—
19C2×D4×Dic11C2211yescharacteristic
20C22×#4324C2212yes—
21C2×#66977C2211yescharacteristic
22C22×Dic11⋊C4—21no—
23C22×C4×Dic11—21no—
24C22×C4×Dic11C2211yescharacteristic
25C22×Dic44C2212yes—
26#10623131—24no—
27#10623131C2218yes—
28C2×#66943C2211yescharacteristic
29C2×#66940—24no—
30C2×#66940—21no—
31C2×#66940—21no—
32C2×#66940C2211yescharacteristic
33C2×#66940C2212yes—
34C2×#66940C2212yes—
35C2×#66940C2218yescomplemented
36C2×#66932—21no—
37C2×#66930—21no—
38C11×#481C2218yes—
39C2×C11×#106C2212yes—
40C2×C11×#102C2212yes—
41C2×C11×C22⋊C8C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×#66880C2212yes—
44C2×#66879C2212yes—
45C2×Dic11⋊C8C2212yes—
46#10622653C2218yes—
47#10622583C2218yescomplemented
48C2×#66874C2212yes—
49C2×#66874C2212yes—
50C2×#66871C2212yes—
51#10622470C22116yescomplemented
52#10622466C22116yescomplemented
53#10622380C22116yescomplemented
54#10622370C22116yescomplemented
55#10622352C2218yescomplemented
56#10622332C2218yescomplemented
57C22×D4×C11—21no—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C23×Dic11—21no—
62C23×Dic11—21no—
63C23×Dic11D411yescharacteristic
64C23×Dic11D411yescharacteristic
65C22×Dic22—21no—
66C22×Dic22—22no—
67C22×Dic22—28no—
68C22×Dic22C2311yescharacteristic
69C22×Dic22C2314yes—
70C22×Dic22C2312yes—
71C22×C8×C11C2312yes—
72C11×#121—22no—
73C11×#121C2314yes—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C22⋊C4—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84#66989—22no—
85#66989C2314yes—
86#66988—28no—
87D4×Dic11—28no—
88D4×Dic11—22no—
89D4×Dic11C2314yes—
90C2×#4324—28no—
91C2×#4324C2318yes—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2311yescharacteristic
94#66977—22no—
95#66977C2314yes—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4—28no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—22no—
104C2×C4×Dic11—22no—
105C2×C4×Dic11—28no—
106C2×C4×Dic11D411yescharacteristic
107C2×C4×Dic11D411yescharacteristic
108C2×C4×Dic11D414yes—
109C2×C4×Dic11C2311yescharacteristic
110C2×C4×Dic11C2311yescharacteristic
111C2×C4×Dic11C2314yes—
112C22×C11⋊C8C2312yes—
113C2×Dic44—28no—
114C2×Dic44C2318yes—
115#66943—22no—
116#66943C2314yes—
117#66940—24no—
118#66940—24no—
119#66940—28no—
120#66940—28no—
121#66940—22no—
122#66940C2314yes—
123#66940C2318yes—
124#66940C2318yes—
125#66932—28no—
126#66930—28no—
127C11×#106C2318yes—
128C11×#102C2318yes—
129C11×C22⋊C8C2314yes—
130C22⋊(C11⋊C8)C2314yes—
131#66880C2318yes—
132#66879C2318yes—
133Dic11⋊C8C2318yes—
134#66874C2318yes—
135#66874C2318yes—
136#66871C2318yes—
137C2×#3117—111nomaximal, Sylow
138C24×C11—21no—
139C24×C11C2×D411yescharacteristic
140C2×D4×C11—24no—
141C2×D4×C11—21no—
142C2×D4×C11—24no—
143C2×D4×C11—44no—
144C2×D4×C11C2412yes—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—22no—
148C22×C4×C11—21no—
149C22×C4×C11—44no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2412yes—
153C22×C4×C11C2411yescharacteristic
154C22×Dic11—28no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—22no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—42no—
162C22×Dic11—44no—
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D414yes—
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D414yes—
169C2×Dic22—28no—
170C2×Dic22—216no—
171C2×Dic22—216no—
172C2×Dic22—24no—
173C2×Dic22—22no—
174C2×Dic22—21no—
175C2×Dic22—24no—
176C2×Dic22—24no—
177C2×Dic22#4118yes—
178C2×Dic22C2412yes—
179C2×Dic22C2414yes—
180C2×C8×C11—24no—
181C2×C8×C11C2414yes—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4C2414yes—
186C11×C4⋊C4C2412yes—
187C11×C22⋊C4—24no—
188C22⋊Dic11—24no—
189C22⋊Dic11—24no—
190C22⋊Dic11—24no—
191C22⋊Dic11—24no—
192#4324—216no—
193C4⋊Dic11—24no—
194C4⋊Dic11—21no—
195C4⋊Dic11C2412yes—
196Dic11⋊C4—24no—
197Dic11⋊C4—24no—
198Dic11⋊C4—28no—
199Dic11⋊C4—28no—
200Dic11⋊C4—24no—
201C4×Dic11—24no—
202C4×Dic11—28no—
203C4×Dic11—28no—
204C4×Dic11C2×D414yes—
205C4×Dic11C2×D414yes—
206C4×Dic11C2×D412yes—
207C4×Dic11C2×D412yes—
208C4×Dic11C2412yes—
209C4×Dic11C2412yes—
210C2×C11⋊C8—24no—
211C2×C11⋊C8C2414yes—
212Dic44—216no—
213C2×#529—111no—
214C22×C4×Q8—111no—
215#3117—1116no—
216C2×#484—111no—
217C2×#481D1111yescharacteristic
218C2×#479—112no—
219C2×#464—112no—
220C2×#451—111no—
221C2×#448—111no—
222C2×#441—112no—
223C2×#440—112no—
224C2×#432—111no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11#13714yes—
232C23×C11C22×D412yes—
233C23×C11C22×D411yescharacteristic
234D4×C11—24no—
235D4×C11—48no—
236D4×C11—42no—
237C2×C4×C11—22no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—22no—
242C2×C4×C11—48no—
243C2×C4×C11—42no—
244C2×C4×C11—44no—
245C2×C4×C11C22×D412yes—
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4114yes—
248C2×C4×C11C2511yescharacteristic
249C2×Dic11—216no—
250C2×Dic11—28no—
251C2×Dic11—28no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—24no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—44no—
260C2×Dic11—48no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11C22×D412yes—
264C2×Dic11C22×D412yes—
265C2×Dic11C22×D412yes—
266C2×Dic11C22×D412yes—
267Dic22—216no—
268Dic22—28no—
269Dic22—24no—
270Dic22—24no—
271Dic22—42no—
272Dic22C2×#4118yes—
273C8×C11—24no—
274C11⋊C8—24no—
275C23×Q8—111no—
276C22×Q16—112no—
277C22×SD16—112no—
278#529—118no—
279#529—224no—
280C2×#126—221no—
281C2×#125—111no—
282C2×#124—111no—
283C2×#123—221no—
284C2×C22⋊Q8—111no—
285C2×#121C2×D1111yescharacteristic
286C2×C4×Q8—112no—
287C2×C4×Q8—118no—
288C2×C4×Q8—112no—
289C2×C4×Q8—111no—
290C2×C4×Q8—221no—
291C2×C4×Q8—221no—
292C2×C4×Q8—224no—
293C2×C4×D4—111no—
294C2×C4×D4—221no—
295C2×#117—221no—
296C22×C4⋊C4—221no—
297C22×C4⋊C4C2×D1111yescharacteristic
298C22×C42—111no—
299C22×C42—221no—
300#484—118no—
301#481C2×D1118yes—
302#479—1116no—
303#464—1116no—
304#451—118no—
305#448—118no—
306#441—1116no—
307#440—1116no—
308#432—118no—
309C2×#107—112no—
310C2×#106C2×D1112yes—
311C2×C4⋊C8—112no—
312C2×#103—112no—
313C2×#103—112no—
314C2×#103—112no—
315C2×#102C2×D1112yes—
316C2×C22⋊C8—111no—
317C2×C22⋊C8C2×D1111yescharacteristic
318C2×#97—112no—
319C22×C11—28no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—84no—
326C22×C11#52512yes—
327C22×C11C2×#13714yes—
328C22×C11C2×#13712yes—
329C22×C11#57512yes—
330C22×C11C23×D411yescharacteristic
331C4×C11—22no—
332C4×C11—42no—
333C4×C11—44no—
334C4×C11#52512yes—
335C4×C11C22×#4112yes—
336Dic11—28no—
337Dic11—22no—
338Dic11—22no—
339Dic11—22no—
340Dic11—22no—
341Dic11—42no—
342Dic11—42no—
343C22×Q8—112no—
344C22×Q8—114no—
345C22×Q8—111no—
346C22×Q8—228no—
347C22×Q8—222no—
348C22×Q8—221no—
349C22×D4—21no—
350C22×D4C22×D1111yescharacteristic
351C23×C4—21no—
352C23×C4—111no—
353C23×C4—111no—
354C23×C4—221no—
355C23×C4—221no—
356C23×C4C22×D1111yescharacteristic
357C2×Q16—118no—
358C2×Q16—228no—
359C2×SD16—118no—
360C2×SD16—228no—
361C22×C8—112no—
362C22×C8C22×D1112yes—
363#126—228no—
364#125—114no—
365#125—222no—
366#124—114no—
367#124—222no—
368#123—228no—
369C22⋊Q8—114no—
370C22⋊Q8—222no—
371#121—22no—
372#121C22×D1114yes—
373C4×Q8—118no—
374C4×Q8—118no—
375C4×Q8—114no—
376C4×Q8—228no—
377C4×Q8—224no—
378C4×Q8—224no—
379C4×Q8—228no—
380C4×Q8—222no—
381C4×D4—114no—
382C4×D4—222no—
383C4×D4—228no—
384#117—228no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—228no—
389C2×C4⋊C4—222no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4C22×D1112yes—
396C2×C4⋊C4C22×D1114yes—
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4—221no—
403C2×C42—111no—
404C2×C42—111no—
405C2×C42—114no—
406C2×C42—111no—
407C2×C42—111no—
408C2×C42—114no—
409C2×C42—221no—
410C2×C42—228no—
411C2×C42—222no—
412C2×C42—222no—
413#107—118no—
414#106C22×D1118yes—
415C4⋊C8—118no—
416#103—118no—
417#103—118no—
418#103—118no—
419#102C22×D1118yes—
420C22⋊C8—114no—
421C22⋊C8C22×D1114yes—
422#97—118no—
423C2×C11—24no—
424C2×C11—82no—
425C2×C11#311714yescomplemented
426C2×C11C2×#52511yescharacteristic
427C2×C11C22×#13711yescharacteristic
428C2×C11C2×#57511yescharacteristic
429C24—21no—
430C24D4×D1111yescharacteristic
431C2×Q8—118no—
432C2×Q8—114no—
433C2×Q8—112no—
434C2×Q8—2216no—
435C2×Q8—228no—
436C2×Q8—2216no—
437C2×Q8—224no—
438C2×Q8—222no—
439C2×Q8—221no—
440C2×Q8—224no—
441C2×Q8—224no—
442C2×D4—24no—
443C2×D4—21no—
444C2×D4—24no—
445C2×D4—44no—
446C2×D4C23×D1112yes—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—44no—
452C22×C4—114no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—114no—
458C22×C4—224no—
459C22×C4—228no—
460C22×C4—224no—
461C22×C4—224no—
462C22×C4—222no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—442no—
466C22×C4—444no—
467C22×C4D4×D1112yes—
468C22×C4D4×D1111yescharacteristic
469C22×C4C23×D1112yes—
470C22×C4C23×D1111yescharacteristic
471Q16—2216no—
472SD16—2216no—
473C2×C8—24no—
474C2×C8—114no—
475C2×C8—224no—
476C2×C8C23×D1114yes—
477C4⋊C4—24no—
478C4⋊C4—22no—
479C4⋊C4—21no—
480C4⋊C4—112no—
481C4⋊C4—228no—
482C4⋊C4—228no—
483C4⋊C4—224no—
484C4⋊C4—224no—
485C4⋊C4—224no—
486C4⋊C4—221no—
487C4⋊C4—224no—
488C4⋊C4C23×D1114yes—
489C4⋊C4C23×D1112yes—
490C22⋊C4—24no—
491C22⋊C4—224no—
492C22⋊C4—224no—
493C22⋊C4—224no—
494C22⋊C4—224no—
495C42—114no—
496C42—112no—
497C42—112no—
498C42—114no—
499C42—112no—
500C42—112no—
501C42—228no—
502C42—228no—
503C42—224no—
504C11C2×#311711yescharacteristic, complemented, Sylow
505C23—22no—
506C23—22no—
507C23—22no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23#6696814yes—
512C23C2×D4×D1112yes—
513C23C2×D4×D1111yescharacteristic
514Q8—118no—
515Q8—2216no—
516Q8—228no—
517Q8—224no—
518Q8—224no—
519Q8—442no—
520D4—24no—
521D4—48no—
522D4—42no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—22no—
528C2×C4—48no—
529C2×C4—42no—
530C2×C4—44no—
531C2×C4—112no—
532C2×C4—112no—
533C2×C4—112no—
534C2×C4—112no—
535C2×C4—2216no—
536C2×C4—228no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—222no—
541C2×C4—228no—
542C2×C4—224no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—444no—
546C2×C4—448no—
547C2×C4—442no—
548C2×C4—442no—
549C2×C4C2×D4×D1112yes—
550C2×C4C2×D4×D1111yescharacteristic
551C2×C4#41×D1114yes—
552C2×C4C24×D1111yescharacteristic
553C8—24no—
554C8—224no—
555C22—28no—
556C22—22no—
557C22—22no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—84no—
562C22#1062318712yes—
563C22C2×#6696814yes—
564C22C2×#6696812yes—
565C22#1062330412yes—
566C22C22×D4×D1111yescharacteristic
567C4—22no—
568C4—42no—
569C4—44no—
570C4—222no—
571C4—222no—
572C4—222no—
573C4—222no—
574C4—228no—
575C4—442no—
576C4—442no—
577C4#1062318712yes—
578C4C2×#41×D1112yes—
579C2—24no—
580C2—82no—
581C2#1307878414yesdirect product factor
582C2C2×#1062318711yescharacteristic
583C2C22×#6696811yescharacteristic
584C2C2×#1062330411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#481C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenterC2×#481D11
hypocenterC11C2×#3117
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
2. C22×#66940C2semidirect
3. #13078784C2direct (N × H)
4. C2×#10622583C2semidirect
5. C2×#10622470C2semidirect
6. C2×#10622380C2semidirect
7. C2×#10622352C2semidirect
9. C2×#10622466C2semidirect
10. C2×#10622370C2semidirect
11. C2×#10622332C2semidirect
35. C2×#66940C22semidirect
47. #10622583C22semidirect
51. #10622470C22semidirect
52. #10622466C22semidirect
53. #10622380C22semidirect
54. #10622370C22semidirect
55. #10622352C22semidirect
56. #10622332C22semidirect
425. C2×C11#3117semidirect
504. C11C2×#3117semidirect
581. C2#13078784direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231312
C22×#669402
#130787842
C2×#106225832
C2×#106224702
C2×#106223802
C2×#106223522
C2×#106226532
C2×#106224662
C2×#106223702
C2×#106223322
C2×C11×#4812
C2×#311711