Finite Group Databasebeta

← C2×#13080533 #15630212

Subgroups — C2×#13080533 #15630212

Order 2816.

2146 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623073C211yesmaximal, characteristic, complemented
2#13080533C2116yesmaximal, direct product factor
3C2×#10622694C211yesmaximal, characteristic, complemented
4C2×#10622658C212yesmaximal, complemented
5C2×#10622620C211yesmaximal, characteristic, complemented
6C2×#10622664C212yesmaximal, complemented
7C2×#10622703C211yesmaximal, characteristic, complemented
8C2×#10622852C212yesmaximal, complemented
9C2×C4×#4324C211yesmaximal, characteristic, complemented
10C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
11C2×#10622846C212yesmaximal, complemented
12C2×C11×#547C211yesmaximal, characteristic
13C22×C11×#41C2212yes—
14C11×#547—24no—
15C11×#547C2218yes—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#123—22no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C11×#121—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C22×C11×C4⋊C4—21no—
23C22×#4326C2212yes—
24C2×#66989—21no—
25C22×#4324C2211yescharacteristic
26C2×#66979C2212yes—
27C2×#66977C2212yes—
28C23×C11⋊C8C2212yes—
29#10623073—24no—
30#10623073C2218yescomplemented
31C2×#66940—21no—
32C2×#66932—22no—
33C2×#66922C2211yescharacteristic
34C2×C4×Dic22C2211yescharacteristic
35#10622852C22116yescomplemented
36#10622846C22116yescomplemented
37C2×#66899C2212yes—
38C2×#66899C2212yes—
39C2×#66899C2212yes—
40C2×#66896C2212yes—
41C2×#66896C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2212yes—
43#10622703C2218yescomplemented
44#10622694C2218yescomplemented
45#10622664C22116yescomplemented
46#10622658C22116yescomplemented
47C4×#4324C2218yescomplemented
48D4×C11⋊C8C2218yescomplemented
49#10622620C2218yescomplemented
50C2×#66874C2211yescharacteristic
51C2×#66872C2211yescharacteristic
52C2×#66871C2212yes—
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C2×C11×#41—24no—
56C2×C11×#41—28no—
57C2×C11×#41—44no—
58C2×C11×#41C2318yes—
59C22×Q8×C11C2312yes—
60C22×D4×C11—22no—
61C22×D4×C11D411yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—22no—
65C23×C4×C11C2312yes—
66C22×Dic22—21no—
67C22×Dic22C2311yescharacteristic
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8C2314yes—
70C11×#123—216no—
71C11×C22⋊Q8—24no—
72C11×C22⋊Q8C2318yes—
73C11×#121—28no—
74C4×D4×C11—22no—
75C4×D4×C11D414yes—
76C4×D4×C11C2314yes—
77C4×D4×C11C2314yes—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—28no—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4D412yes—
87C2×C42×C11C2311yescharacteristic
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—22no—
90C2×#4326—44no—
91C2×#4326C2318yes—
92#66989—28no—
93C2×#4324—24no—
94C2×#4324C2314yes—
95#66979—24no—
96#66979C2318yes—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2312yes—
100#66977—24no—
101#66977C2318yes—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—22no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—22no—
106C22×C11⋊C8—44no—
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2312yes—
110C22×C11⋊C8C2318yes—
111#66940—28no—
112#66932—216no—
113#66922—22no—
114#66922C2314yes—
115C4×Dic22—22no—
116C4×Dic22C2314yes—
117#66899C2318yes—
118#66899C2318yes—
119#66899C2318yes—
120#66896C2314yes—
121#66896C2318yes—
122C22⋊(C11⋊C8)C2318yes—
123#66874C2314yes—
124#66872C2314yes—
125#66871C2318yes—
126C4⋊(C11⋊C8)C2314yes—
127C4×C11⋊C8C2314yes—
128C2×#3302—111nomaximal, Sylow
129C24×C11—21no—
130C24×C11C2×D412yes—
131C11×#41—216no—
132C11×#41—48no—
133C11×#41—416no—
134C2×Q8×C11—22no—
135C2×Q8×C11—24no—
136C2×Q8×C11—24no—
137C2×Q8×C11C2414yes—
138C2×D4×C11—28no—
139C2×D4×C11—24no—
140C2×D4×C11—21no—
141C2×D4×C11—22no—
142C2×D4×C11—48no—
143C2×D4×C11C2×D414yes—
144C2×D4×C11#4114yes—
145C2×D4×C11C2412yes—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—24no—
151C22×C4×C11—28no—
152C22×C4×C11—48no—
153C22×C4×C11—44no—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D414yes—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2414yes—
159C22×C4×C11C2411yescharacteristic
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—22no—
163C2×Dic22—21no—
164C2×Dic22—24no—
165C2×Dic22—22no—
166C2×Dic22—22no—
167C2×Dic22—44no—
168C2×Dic22C2412yes—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—28no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4C2×D414yes—
174C11×C4⋊C4C2412yes—
175C11×C22⋊C4—28no—
176C11×C22⋊C4—24no—
177C11×C22⋊C4C2×D418yes—
178C42×C11C2×D412yes—
179C42×C11C2412yes—
180C22⋊Dic11—28no—
181C22⋊Dic11—28no—
182#4326—48no—
183#4324—28no—
184C4⋊Dic11—21no—
185C4⋊Dic11—22no—
186C4⋊Dic11—24no—
187C4⋊Dic11C2414yes—
188C4⋊Dic11C2412yes—
189Dic11⋊C4—24no—
190Dic11⋊C4—28no—
191C4×Dic11—24no—
192C4×Dic11—28no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—24no—
196C2×C11⋊C8—48no—
197C2×C11⋊C8C2412yes—
198C2×C11⋊C8C2412yes—
199C2×C11⋊C8C2414yes—
200C2×#556—111no—
201C2×#547D1111yescharacteristic
202#3302—1116no—
203C2×#487—111no—
204C2×#485—112no—
205C2×#474—111no—
206C2×#467—112no—
207C2×#462—111no—
208C2×#452—112no—
209C2×C4×SD16—111no—
210C2×C8×D4—111no—
211C2×#416—112no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11—24no—
215C23×C11—24no—
216C23×C11—22no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11C22×D414yes—
220C23×C11C22×D411yescharacteristic
221Q8×C11—24no—
222Q8×C11—24no—
223Q8×C11—44no—
224D4×C11—24no—
225D4×C11—28no—
226D4×C11—22no—
227D4×C11—416no—
228D4×C11C2×#4114yes—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—28no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—416no—
237C2×C4×C11—44no—
238C2×C4×C11—42no—
239C2×C4×C11—48no—
240C2×C4×C11#13514yes—
241C2×C4×C11C22×D414yes—
242C2×C4×C11C22×D412yes—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D412yes—
245C2×C4×C11C2×#4112yes—
246C2×C4×C11H(5,𝔽2)12yes—
247C2×C4×C11C2511yescharacteristic
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—24no—
251C2×Dic11—42no—
252C2×Dic11—44no—
253C2×Dic11—42no—
254Dic22—22no—
255Dic22—22no—
256Dic22—42no—
257Dic22—48no—
258C11⋊C8—22no—
259C11⋊C8—22no—
260C11⋊C8—24no—
261C22×#41C2×D1112yes—
262C22×Q16—112no—
263C22×SD16—111no—
264C23×C8—112no—
265#556—118no—
266#556—224no—
267#547—24no—
268#547C2×D1118yes—
269C2×C4⋊Q8—111no—
270C2×C4⋊Q8C2×D1111yescharacteristic
271C2×#126—222no—
272C2×#124—221no—
273C2×#123—22no—
274C2×C22⋊Q8—112no—
275C2×C22⋊Q8C2×D1112yes—
276C2×#121—21no—
277C2×C4×Q8—111no—
278C2×C4×Q8—221no—
279C2×C4×D4C2×D1111yescharacteristic
280C2×C4×D4C2×D1111yescharacteristic
281C2×#117—112no—
282C22×C4⋊C4—21no—
283#487—118no—
284#485—1116no—
285#474—118no—
286#467—1116no—
287#462—118no—
288#452—1116no—
289C4×SD16—118no—
290C8×D4—118no—
291C2×#107—112no—
292C2×#106—111no—
293C2×C4⋊C8—111no—
294#416—1116no—
295C2×#103—112no—
296C2×#103—112no—
297C2×#103—112no—
298C2×#103—111no—
299C2×#102—111no—
300C2×#102—112no—
301C2×C22⋊C8—112no—
302C2×C4×C8—111no—
303C22×C11—24no—
304C22×C11—24no—
305C22×C11—24no—
306C22×C11—24no—
307C22×C11—48no—
308C22×C11—48no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11#54612yes—
312C22×C11C2×#13512yes—
313C22×C11#57812yes—
314C22×C11C23×D411yescharacteristic
315C4×C11—24no—
316C4×C11—22no—
317C4×C11—44no—
318C4×C11—42no—
319C4×C11#54612yes—
320C4×C11C2×#13514yes—
321C4×C11C22×#4111yescharacteristic
322C4×C11C2×H(5,𝔽2)11yescharacteristic
323Dic11—42no—
324Dic11—44no—
325Dic11—42no—
326C2×#41—24no—
327C2×#41—28no—
328C2×#41—44no—
329C2×#41C22×D1118yes—
330C22×Q8—111no—
331C22×Q8—221no—
332C22×Q8C22×D1112yes—
333C22×D4—22no—
334C22×D4C22⋊D1111yescharacteristic
335C22×D4C22×D1111yescharacteristic
336C23×C4—21no—
337C23×C4—22no—
338C23×C4C22×D1112yes—
339C2×Q16—118no—
340C2×Q16—444no—
341C2×SD16—114no—
342C2×SD16—224no—
343C22×C8—111no—
344C22×C8—112no—
345C22×C8—111no—
346C22×C8—118no—
347C22×C8—444no—
348C4⋊Q8—22no—
349C4⋊Q8—114no—
350C4⋊Q8—222no—
351C4⋊Q8C22×D1114yes—
352#126—2216no—
353#124—228no—
354#123—216no—
355C22⋊Q8—24no—
356C22⋊Q8—118no—
357C22⋊Q8—224no—
358C22⋊Q8C22×D1118yes—
359#121—28no—
360C4×Q8—114no—
361C4×Q8—228no—
362C4×Q8—222no—
363C4×D4—22no—
364C4×D4C22⋊D1114yes—
365C4×D4C22×D1114yes—
366C4×D4C22×D1114yes—
367#117—118no—
368#117—224no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—28no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—112no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4C22⋊D1111yescharacteristic
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C22⋊C4—22no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4C22⋊D1112yes—
385C2×C42—222no—
386C2×C42—221no—
387C2×C42C22×D1111yescharacteristic
388#107—118no—
389#106—114no—
390C4⋊C8—114no—
391#103—118no—
392#103—118no—
393#103—118no—
394#103—114no—
395#102—114no—
396#102—118no—
397C22⋊C8—118no—
398C4×C8—114no—
399C2×C11—44no—
400C2×C11—44no—
401C2×C11#330214yescomplemented
402C2×C11C2×#54611yescharacteristic
403C2×C11C22×#13511yescharacteristic
404C2×C11C2×#57811yescharacteristic
405C24—21no—
406C24C2×C22⋊D1112yes—
407#41—216no—
408#41—48no—
409#41—416no—
410C2×Q8—22no—
411C2×Q8—24no—
412C2×Q8—24no—
413C2×Q8—112no—
414C2×Q8—221no—
415C2×Q8—224no—
416C2×Q8—222no—
417C2×Q8—222no—
418C2×Q8—444no—
419C2×Q8C23×D1114yes—
420C2×D4—28no—
421C2×D4—24no—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—48no—
425C2×D4#434114yes—
426C2×D4C2×C22⋊D1114yes—
427C2×D4C23×D1112yes—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—28no—
434C22×C4—48no—
435C22×C4—44no—
436C22×C4—221no—
437C22×C4—222no—
438C22×C4—221no—
439C22×C4C2×C22⋊D1114yes—
440C22×C4C2×C22⋊D1112yes—
441C22×C4C2×C22⋊D1111yescharacteristic
442C22×C4C2×C22⋊D1111yescharacteristic
443C22×C4C23×D1114yes—
444C22×C4C23×D1111yescharacteristic
445Q16—448no—
446SD16—228no—
447C2×C8—112no—
448C2×C8—112no—
449C2×C8—114no—
450C2×C8—222no—
451C2×C8—222no—
452C2×C8—224no—
453C2×C8—448no—
454C4⋊C4—24no—
455C4⋊C4—28no—
456C4⋊C4—24no—
457C4⋊C4—21no—
458C4⋊C4—112no—
459C4⋊C4—114no—
460C4⋊C4—221no—
461C4⋊C4—222no—
462C4⋊C4—224no—
463C4⋊C4—228no—
464C4⋊C4—224no—
465C4⋊C4C2×C22⋊D1114yes—
466C4⋊C4C23×D1112yes—
467C22⋊C4—28no—
468C22⋊C4—24no—
469C22⋊C4—228no—
470C22⋊C4—228no—
471C22⋊C4C2×C22⋊D1118yes—
472C42—228no—
473C42—224no—
474C42C2×C22⋊D1112yes—
475C42C23×D1112yes—
476C11C2×#330211yescharacteristic, complemented, Sylow
477C23—24no—
478C23—24no—
479C23—24no—
480C23—24no—
481C23—22no—
482C23—42no—
483C23—42no—
484C23C22×C22⋊D1114yes—
485C23C22×C22⋊D1111yescharacteristic
486Q8—24no—
487Q8—24no—
488Q8—44no—
489Q8—222no—
490Q8—222no—
491Q8—442no—
492Q8—448no—
493D4—24no—
494D4—28no—
495D4—22no—
496D4—416no—
497D4C2×#434114yes—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—28no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—416no—
506C2×C4—44no—
507C2×C4—42no—
508C2×C4—48no—
509C2×C4—222no—
510C2×C4—224no—
511C2×C4—222no—
512C2×C4—442no—
513C2×C4—444no—
514C2×C4—442no—
515C2×C4#6700314yes—
516C2×C4C2×#434112yes—
517C2×C4#6703712yes—
518C2×C4C22×C22⋊D1114yes—
519C2×C4C22×C22⋊D1112yes—
520C2×C4C22×C22⋊D1111yescharacteristic
521C2×C4C22×C22⋊D1112yes—
522C2×C4C24×D1111yescharacteristic
523C8—222no—
524C8—222no—
525C8—224no—
526C22—24no—
527C22—24no—
528C22—24no—
529C22—24no—
530C22—42no—
531C22—48no—
532C22—48no—
533C22—42no—
534C22#1062333712yes—
535C22C2×#6700312yes—
536C22#1062336912yes—
537C22C23×C22⋊D1111yescharacteristic
538C4—24no—
539C4—22no—
540C4—42no—
541C4—44no—
542C4—444no—
543C4—442no—
544C4—442no—
545C4#1062333712yes—
546C4C2×#6700314yes—
547C4C22×#434111yescharacteristic
548C4C2×#6703711yescharacteristic
549C2—44no—
550C2—44no—
551C2#1308053314yesdirect product factor
552C2C2×#1062333711yescharacteristic
553C2C22×#6700311yescharacteristic
554C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#547C2
socleC23×C11C22×D4
hypercenterC2×#547D11
hypocenterC11C2×#3302
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#10623073C2semidirect
2. #13080533C2direct (N × H)
3. C2×#10622694C2semidirect
4. C2×#10622658C2semidirect
5. C2×#10622620C2semidirect
6. C2×#10622664C2semidirect
7. C2×#10622703C2semidirect
8. C2×#10622852C2semidirect
9. C2×C4×#4324C2semidirect
10. C2×D4×C11⋊C8C2semidirect
11. C2×#10622846C2semidirect
30. #10623073C22semidirect
35. #10622852C22semidirect
36. #10622846C22semidirect
43. #10622703C22semidirect
44. #10622694C22semidirect
45. #10622664C22semidirect
46. #10622658C22semidirect
47. C4×#4324C22semidirect
48. D4×C11⋊C8C22semidirect
49. #10622620C22semidirect
401. C2×C11#3302semidirect
476. C11C2×#3302semidirect
551. C2#13080533direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230732
#130805332
C2×#106226942
C2×#106226582
C2×#106226202
C2×#106226642
C2×#106227032
C2×#106228522
C2×C4×#43242
C2×D4×C11⋊C82
C2×#106228462
C2×C11×#5472
C2×#330211