Finite Group Databasebeta

← C2×#13079825 #15625920

Subgroups — C2×#13079825 #15625920

Order 2816.

1758 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623219C211yesmaximal, characteristic
2C2×#10623259C211yesmaximal, characteristic
3#13079825C2116yesmaximal, direct product factor
4C2×#10622678C211yesmaximal, characteristic, complemented
5C2×#10622315C211yesmaximal, characteristic, complemented
6C2×#10622695C211yesmaximal, characteristic, complemented
7C2×#10622427C212yesmaximal
8C2×#10622428C212yesmaximal
9C2×#10622407C212yesmaximal, complemented
10C2×#10622404C212yesmaximal, complemented
11C2×#10622318C211yesmaximal, characteristic
12C2×C11×#491C211yesmaximal, characteristic, complemented
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×#125C2211yescharacteristic
15C2×#66999C2212yes—
16C2×Q8×Dic11C2212yes—
17#10623259—24no—
18#10623259C2218yes—
19#10623219—24no—
20#10623219C2218yes—
21C2×#66950—21no—
22C2×#66949—21no—
23C2×#66949—21no—
24C2×#66945—21no—
25C2×#66945C2211yescharacteristic
26C2×#66945C2211yescharacteristic
27C2×#66943—21no—
28C2×#66941C2211yescharacteristic
29C2×#66941C2211yescharacteristic
30C2×#66940—21no—
31C2×#66940—21no—
32C2×#66940—21no—
33C2×C42×D11C2211yescharacteristic
34C2×#66923C2211yescharacteristic
35C2×#66922C2211yescharacteristic
36C11×#491C2218yescomplemented
37C2×C11×#103C2212yes—
38C2×C11×#103C2212yes—
39C2×C11×#97C2211yescharacteristic
40C2×#66899C2212yes—
41C2×#66899C2212yes—
42C2×(C2×D11)⋊C8C2212yes—
43C2×#66882C2212yes—
44C2×#66881C2212yes—
45C2×Dic11⋊C8C2212yes—
46#10622695C2218yescomplemented
47#10622678C2218yescomplemented
48C2×#66872C2212yes—
49C2×#66871C2212yes—
50C2×#66867C2211yescharacteristic
51#10622428C22116yes—
52#10622427C22116yes—
53#10622407C22116yescomplemented
54#10622404C22116yescomplemented
55#10622318C2218yes—
56#10622315C2218yescomplemented
57C22×Q8×C11C2312yes—
58C22×C4×D11D411yescharacteristic
59C22×C4×D11D411yescharacteristic
60C22×C4×D11C2311yescharacteristic
61C22×Dic22—21no—
62C22×Dic22—21no—
63C22×Dic22—21no—
64C22×C8×C11C2312yes—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8C2314yes—
67C11×#125—22no—
68C11×#125C2314yes—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76#66999—24no—
77#66999C2318yes—
78Q8×Dic11—24no—
79Q8×Dic11C2318yes—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11C2312yes—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—22no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—22no—
96C2×C4×Dic11D411yescharacteristic
97C2×C4×Dic11D411yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2312yes—
100#66950—28no—
101#66949—28no—
102#66949—28no—
103#66945—28no—
104#66945—22no—
105#66945—22no—
106#66945C2314yes—
107#66945C2314yes—
108#66943—28no—
109#66941—22no—
110#66941—22no—
111#66941C2314yes—
112#66941C2314yes—
113#66940—28no—
114#66940—28no—
115#66940—28no—
116C42×D11D414yes—
117C42×D11C2314yes—
118#66923—22no—
119#66923C2314yes—
120#66922—22no—
121#66922C2314yes—
122C11×#103C2318yes—
123C11×#103C2318yes—
124C11×#97C2314yes—
125#66899C2318yes—
126#66899C2318yes—
127(C2×D11)⋊C8C2318yes—
128#66882C2318yes—
129#66881C2318yes—
130Dic11⋊C8C2318yes—
131#66872C2318yes—
132#66871C2318yes—
133#66867C2314yes—
134C2×#3237—111nomaximal, Sylow
135C23×D11C2×D411yescharacteristic
136C2×Q8×C11—22no—
137C2×Q8×C11—28no—
138C2×Q8×C11C2414yes—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—22no—
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C2×C4×D11—24no—
152C2×C4×D11—24no—
153C2×C4×D11—42no—
154C2×C4×D11C2×D412yes—
155C2×C4×D11C2×D414yes—
156C2×C4×D11C2×D414yes—
157C2×C4×D11C2412yes—
158C2×Dic22—24no—
159C2×Dic22—24no—
160C2×Dic22—24no—
161C2×Dic22—44no—
162C2×Dic22—44no—
163C2×Dic22—44no—
164C2×C8×C11—24no—
165C2×C8×C11C2414yes—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4C2412yes—
173C11×C4⋊C4C2412yes—
174C42×C11C2×D412yes—
175C42×C11C2412yes—
176(C2×D11)⋊C4—28no—
177(C2×D11)⋊C4—24no—
178(C2×D11)⋊C4—24no—
179C4⋊Dic11—28no—
180C4⋊Dic11—22no—
181C4⋊Dic11—24no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11C2414yes—
185C4⋊Dic11C2412yes—
186C4⋊Dic11C2412yes—
187Dic11⋊C4—24no—
188Dic11⋊C4—24no—
189Dic11⋊C4—28no—
190Dic11⋊C4—24no—
191Dic11⋊C4—24no—
192C4×Dic11—24no—
193C4×Dic11—24no—
194C4×Dic11—28no—
195C4×Dic11C2×D412yes—
196C4×Dic11C2×D414yes—
197C4×Dic11C2×D414yes—
198C4×Dic11C2412yes—
199C2×C11⋊C8—24no—
200C2×C11⋊C8C2414yes—
201C2×#533—111no—
202C2×#533—111no—
203#3237—1116no—
204C2×#501—111no—
205C2×#501—111no—
206C2×#491—111no—
207C2×#491D1111yescharacteristic, complemented
208C2×#485—112no—
209C2×#485—112no—
210C2×#477—112no—
211C2×#475—112no—
212C2×#432—111no—
213C23×C11C22×D411yescharacteristic
214C22×D11—22no—
215C22×D11—22no—
216C22×D11—22no—
217C22×D11C22×D412yes—
218Q8×C11—28no—
219Q8×C11—44no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—44no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11C22×D412yes—
229C2×C4×C11C22×D412yes—
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C112−1+414yes—
232C2×C4×C11C2511yescharacteristic
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—24no—
238C2×Dic11—42no—
239C2×Dic11—44no—
240C2×Dic11—42no—
241C2×Dic11#13714yes—
242C2×Dic11C22×D412yes—
243C2×Dic11C22×D412yes—
244C2×Dic11C22×D412yes—
245C4×D11—24no—
246C4×D11—24no—
247C4×D11—28no—
248C4×D11—44no—
249Dic22—48no—
250Dic22—48no—
251Dic22—48no—
252C8×C11—24no—
253C11⋊C8—24no—
254#533—118no—
255#533—118no—
256#533—224no—
257#533—224no—
258C2×C4⋊Q8—111no—
259C2×C4⋊Q8—111no—
260C2×C4⋊Q8—111no—
261C2×C4⋊Q8C2×D1111yescharacteristic
262C2×#125—111no—
263C2×#125—221no—
264C2×#125C2×D1111yescharacteristic
265C2×C22⋊Q8—112no—
266C2×C22⋊Q8—221no—
267C2×C22⋊Q8—221no—
268C2×C22⋊Q8—221no—
269C2×C4×Q8—112no—
270C2×C4×Q8—221no—
271C2×C4×Q8—221no—
272C2×C4×Q8—221no—
273C2×#117—111no—
274C2×#117—111no—
275C2×#117—221no—
276C22×C42—111no—
277#501—118no—
278#501—118no—
279#491—118no—
280#491C2×D1118yescomplemented
281#485—1116no—
282#485—1116no—
283#477—1116no—
284#475—1116no—
285#432—118no—
286C2×#107—112no—
287C2×#107—112no—
288C2×#106—112no—
289C2×#106—112no—
290C2×C4⋊C8—112no—
291C2×#103—112no—
292C2×#103—112no—
293C2×#103C2×D1112yes—
294C2×#103C2×D1112yes—
295C2×C22⋊C8—112no—
296C2×#97—111no—
297C2×#97C2×D1111yescharacteristic
298C22×C11#53612yes—
299C22×C11C2×#13712yes—
300C22×C11#57512yes—
301C22×C11C23×D411yescharacteristic
302C2×D11—22no—
303C2×D11—22no—
304C2×D11—22no—
305C2×D11—44no—
306C4×C11—22no—
307C4×C11—22no—
308C4×C11—44no—
309C4×C11—42no—
310C4×C11—42no—
311C4×C11#53612yes—
312C4×C11C2×2−1+412yes—
313Dic11—22no—
314Dic11—22no—
315Dic11—42no—
316Dic11—42no—
317Dic11—44no—
318Dic11C2×#13714yes—
319C22×Q8—221no—
320C22×Q8—221no—
321C22×Q8—221no—
322C22×Q8C22×D1112yes—
323C23×C4—111no—
324C23×C4—111no—
325C23×C4—111no—
326C22×C8—112no—
327C22×C8C22×D1112yes—
328C4⋊Q8—22no—
329C4⋊Q8—114no—
330C4⋊Q8—114no—
331C4⋊Q8—114no—
332C4⋊Q8—222no—
333C4⋊Q8—222no—
334C4⋊Q8—222no—
335C4⋊Q8C22×D1114yes—
336#125—22no—
337#125—114no—
338#125—228no—
339#125—222no—
340#125C22×D1114yes—
341C22⋊Q8—118no—
342C22⋊Q8—228no—
343C22⋊Q8—228no—
344C22⋊Q8—228no—
345C22⋊Q8—224no—
346C4×Q8—118no—
347C4×Q8—228no—
348C4×Q8—228no—
349C4×Q8—228no—
350C4×Q8—224no—
351#117—114no—
352#117—114no—
353#117—222no—
354#117—222no—
355#117—228no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—112no—
363C2×C4⋊C4—222no—
364C2×C4⋊C4—222no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—222no—
375C2×C42—111no—
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—114no—
379C2×C42—114no—
380C2×C42—221no—
381C2×C42—221no—
382C2×C42—222no—
383C2×C42C22×D1111yescharacteristic
384#107—118no—
385#107—118no—
386#106—118no—
387#106—118no—
388C4⋊C8—118no—
389#103—118no—
390#103—118no—
391#103C22×D1118yes—
392#103C22×D1118yes—
393C22⋊C8—118no—
394#97—114no—
395#97C22×D1114yes—
396C2×C11#323714yescomplemented
397C2×C11C2×#53611yescharacteristic
398C2×C11C22×#13711yescharacteristic
399C2×C11C2×#57511yescharacteristic
400D11—42no—
401C24—111no—
402C2×Q8—22no—
403C2×Q8—28no—
404C2×Q8—224no—
405C2×Q8—224no—
406C2×Q8—224no—
407C2×Q8—444no—
408C2×Q8—444no—
409C2×Q8—444no—
410C2×Q8C23×D1114yes—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—111no—
415C22×C4—111no—
416C22×C4—111no—
417C22×C4—114no—
418C22×C4—112no—
419C22×C4—112no—
420C22×C4—114no—
421C22×C4—224no—
422C22×C4—224no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—222no—
426C22×C4—442no—
427C22×C4D4×D1111yescharacteristic
428C22×C4D4×D1111yescharacteristic
429C22×C4C23×D1111yescharacteristic
430C2×C8—24no—
431C2×C8—114no—
432C2×C8—224no—
433C2×C8C23×D1114yes—
434C4⋊C4—24no—
435C4⋊C4—24no—
436C4⋊C4—24no—
437C4⋊C4—24no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—112no—
441C4⋊C4—112no—
442C4⋊C4—114no—
443C4⋊C4—228no—
444C4⋊C4—228no—
445C4⋊C4—224no—
446C4⋊C4—224no—
447C4⋊C4—221no—
448C4⋊C4—221no—
449C4⋊C4—222no—
450C4⋊C4—224no—
451C4⋊C4—224no—
452C4⋊C4—224no—
453C4⋊C4C23×D1112yes—
454C4⋊C4C23×D1112yes—
455C22⋊C4—224no—
456C22⋊C4—224no—
457C22⋊C4—228no—
458C42—114no—
459C42—114no—
460C42—112no—
461C42—112no—
462C42—224no—
463C42—224no—
464C42—228no—
465C42D4×D1112yes—
466C42C23×D1112yes—
467C11C2×#323711yescharacteristic, complemented, Sylow
468C23—112no—
469C23—222no—
470C23—222no—
471C23—222no—
472C23C2×D4×D1111yescharacteristic
473Q8—28no—
474Q8—44no—
475Q8—448no—
476Q8—448no—
477Q8—448no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—24no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—44no—
486C2×C4—114no—
487C2×C4—112no—
488C2×C4—112no—
489C2×C4—112no—
490C2×C4—228no—
491C2×C4—222no—
492C2×C4—222no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—224no—
498C2×C4—444no—
499C2×C4—442no—
500C2×C4—444no—
501C2×C4—442no—
502C2×C4C2×D4×D1112yes—
503C2×C4C2×D4×D1112yes—
504C2×C4C2×D4×D1111yescharacteristic
505C2×C4#6704314yes—
506C2×C4C24×D1111yescharacteristic
507C8—24no—
508C8—224no—
509C22—222no—
510C22—222no—
511C22—222no—
512C22—444no—
513C22#1062320612yes—
514C22D11×#13712yes—
515C22#1062330812yes—
516C22C22×D4×D1111yescharacteristic
517C4—22no—
518C4—22no—
519C4—44no—
520C4—42no—
521C4—42no—
522C4—114no—
523C4—222no—
524C4—222no—
525C4—442no—
526C4—444no—
527C4—442no—
528C4#1062320612yes—
529C4C2×#6704312yes—
530C2—442no—
531C2#1307982514yesdirect product factor
532C2C2×#1062320611yescharacteristic
533C2C2×D11×#13711yescharacteristic
534C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#491C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#491D11
hypocenterC11C2×#3237
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
3. #13079825C2direct (N × H)
4. C2×#10622678C2semidirect
5. C2×#10622315C2semidirect
6. C2×#10622695C2semidirect
9. C2×#10622407C2semidirect
10. C2×#10622404C2semidirect
12. C2×C11×#491C2semidirect
36. C11×#491C22semidirect
46. #10622695C22semidirect
47. #10622678C22semidirect
53. #10622407C22semidirect
54. #10622404C22semidirect
56. #10622315C22semidirect
207. C2×#491D11semidirect
280. #491C2×D11semidirect
396. C2×C11#3237semidirect
467. C11C2×#3237semidirect
531. C2#13079825direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232192
C2×#106232592
#130798252
C2×#106226782
C2×#106223152
C2×#106226952
C2×#106224272
C2×#106224282
C2×#106224072
C2×#106224042
C2×#106223182
C2×C11×#4912
C2×#323711