Finite Group Databasebeta

← C2×#13082237 #15660862

Subgroups — C2×#13082237 #15660862

Order 2816.

7706 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082237C2132yesmaximal, direct product factor
2C2×#10623101C211yesmaximal, characteristic, complemented
3C2×#10623263C213yesmaximal, complemented
4C2×#10623173C216yesmaximal, complemented
5C2×#10623348C212yesmaximal, complemented
6C2×#10623086C213yesmaximal, complemented
7C2×#10623259C213yesmaximal, complemented
8C2×#10623155C216yesmaximal, complemented
9C2×C4×#4343C211yesmaximal, characteristic, complemented
10C2×C4×#4341C213yesmaximal, complemented
11C22×Q8×Dic11C212yesmaximal, complemented
12C2×D4×Q8×C11C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2212yes—
14C22×#4343C2211yescharacteristic
15C22×#4341C2213yes—
16D4×Q8×C11C22116yescomplemented
17C2×C11×C4⋊Q8C2213yes—
18C2×C11×C22⋊Q8C2216yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2213yes—
21#10623348C22132yescomplemented
22C2×#67000C2216yes—
23C2×#66999C2216yes—
24C2×Q8×Dic11C2216yes—
25C2×Q8×Dic11C2216yes—
26C2×Q8×Dic11C2212yes—
27C2×Q8×Dic11C2211yescharacteristic
28C2×Q8×Dic11C22132yescomplemented
29C2×D4×Dic11C2211yescharacteristic
30C2×#66983C2216yes—
31C2×C4×C22⋊D11C2216yes—
32C22×C4⋊Dic11C2216yes—
33C22×C4×Dic11C2216yes—
34#10623263C22148yescomplemented
35#10623259C22148yescomplemented
36#10623173C22196yescomplemented
37#10623155C22196yescomplemented
38C4×#4343C22116yescomplemented
39#10623101C22116yescomplemented
40#10623086C22148yescomplemented
41C4×#4341C22148yescomplemented
42C2×#66951C22112yes—
43C2×#66950C2216yes—
44C2×#66946C2213yes—
45C2×#66945C2213yes—
46C2×#66945C2216yes—
47C2×#66945C2213yes—
48C2×#66943C2216yes—
49C2×#66943C2216yes—
50C2×#66940C2213yes—
51C2×#66939C22112yes—
52C2×(C22⋊D11)⋊C4C2216yes—
53C2×#66930C2216yes—
54C2×C4×D44C2213yes—
55C2×C42×D11C2213yes—
56C2×#66922C2213yes—
57C2×C4×Dic22C2213yes—
58C22×Q8×C11—216no—
59C22×Q8×C11C2316yes—
60C22×Q8×C11C23116yes—
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11C2316yes—
64C22×C22⋊D11C2316yes—
65C23×Dic11C2316yes—
66C23×Dic11C2312yes—
67C2×#4343—28no—
68C2×#4343C2318yes—
69C2×#4341—224no—
70C2×#4341C23124yes—
71C22×D44C2313yes—
72C22×C4×D11C2313yes—
73C22×C4×D11C2313yes—
74C22×C4×D11C2313yes—
75C22×Dic22C2313yes—
76C11×C4⋊Q8C23124yes—
77C11×C22⋊Q8C23148yes—
78C4×Q8×C11C2318yes—
79C4×D4×C11C23124yes—
80C2×C11×C4⋊C4C2313yes—
81C2×C11×C4⋊C4C2313yes—
82C2×C11×C4⋊C4C2316yes—
83C2×C11×C22⋊C4C2316yes—
84C2×C42×C11C2313yes—
85C2×C22⋊Dic11C2312yes—
86#67000C23148yes—
87#66999C23148yes—
88Q8×Dic11C23148yes—
89Q8×Dic11C23148yes—
90Q8×Dic11C2318yes—
91Q8×Dic11C23116yes—
92D4×Dic11C2318yes—
93#66983C23148yes—
94C4×C22⋊D11C23148yes—
95C2×(C2×D11)⋊C4C2316yes—
96C2×(C2×D11)⋊C4C2316yes—
97C2×(C2×D11)⋊C4C23112yes—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2316yes—
100C2×C4⋊Dic11C2316yes—
101C2×C4⋊Dic11C2313yes—
102C2×C4⋊Dic11C23112yes—
103C2×C4⋊Dic11C23148yes—
104C2×Dic11⋊C4C2316yes—
105C2×Dic11⋊C4C2316yes—
106C2×C4×Dic11C2316yes—
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2313yes—
109C2×C4×Dic11C2313yes—
110C2×C4×Dic11C2316yes—
111C2×C4×Dic11C2316yes—
112C2×C4×Dic11C23148yes—
113#66951C23196yes—
114#66950C23148yes—
115#66946C23124yes—
116#66945C23148yes—
117#66945C23124yes—
118#66945C23124yes—
119#66943C23148yes—
120#66943C23148yes—
121#66940C23124yes—
122#66939C23196yes—
123(C22⋊D11)⋊C4C23148yes—
124#66930C23148yes—
125C4×D44C23124yes—
126C42×D11C23124yes—
127#66922C23124yes—
128C4×Dic22C23124yes—
129C2×#3482—111nomaximal, Sylow
130C24×C11C2412yes—
131C23×D11C2413yes—
132C2×Q8×C11—264no—
133C2×Q8×C11—224no—
134C2×Q8×C11#4118yescomplemented
135C2×Q8×C11C24124yes—
136C2×Q8×C11C2414yes—
137C2×D4×C11#4118yescomplemented
138C2×D4×C11C2414yes—
139C22×C4×C11—224no—
140C22×C4×C11C2416yes—
141C22×C4×C11C24124yes—
142C22×C4×C11C2413yes—
143C22×C4×C11C2413yes—
144C22×C4×C11C2411yescharacteristic
145C2×C22⋊D11—224no—
146C2×C22⋊D11C24124yes—
147C22×Dic11—28no—
148C22×Dic11—224no—
149C22×Dic11C24124yes—
150C22×Dic11C2418yes—
151C22×Dic11C2412yes—
152C22×Dic11C2411yescharacteristic
153C22×Dic11C2413yes—
154C22×Dic11C2416yes—
155C22×Dic11C2411yescharacteristic
156#4343—232no—
157#4341—296no—
158C2×D44—212no—
159C2×D44C24112yes—
160C2×C4×D11—212no—
161C2×C4×D11—212no—
162C2×C4×D11—212no—
163C2×C4×D11C24112yes—
164C2×C4×D11C24112yes—
165C2×C4×D11C24112yes—
166C2×Dic22—212no—
167C2×Dic22C24112yes—
168C11×C4⋊C4C24112yes—
169C11×C4⋊C4C24112yes—
170C11×C4⋊C4C24124yes—
171C11×C22⋊C4C24124yes—
172C42×C11C24112yes—
173C22⋊Dic11C2418yes—
174(C2×D11)⋊C4C24124yes—
175(C2×D11)⋊C4C24124yes—
176(C2×D11)⋊C4C24148yes—
177C4⋊Dic11C2414yes—
178C4⋊Dic11C24124yes—
179C4⋊Dic11C24124yes—
180C4⋊Dic11C24112yes—
181C4⋊Dic11C24148yes—
182Dic11⋊C4C24124yes—
183Dic11⋊C4C24124yes—
184C4×Dic11C24124yes—
185C4×Dic11C2414yes—
186C4×Dic11C24112yes—
187C4×Dic11C24112yes—
188C4×Dic11C24124yes—
189C4×Dic11C24124yes—
190#3482—1132no—
191C2×#557—111no—
192C2×#556—113no—
193C2×#552—116no—
194C2×D4×Q8D1111yescharacteristic, complemented
195C2×#548—112no—
196C2×#547—113no—
197C2×#533—113no—
198C2×#529—116no—
199C2×C4×#41—111no—
200C2×C4×#41—113no—
201C22×C4×Q8—112no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11C2×#4118yes—
205C23×C11C2514yes—
206C23×C11C2511yescharacteristic
207C22×D11—26no—
208C22×D11—26no—
209C22×D11—26no—
210C22×D11C2516yes—
211Q8×C11—248no—
212Q8×C11C2×#41116yescomplemented
213D4×C11C2×#41116yescomplemented
214C2×C4×C11—212no—
215C2×C4×C11—26no—
216C2×C4×C11—248no—
217C2×C4×C11C2×#41112yes—
218C2×C4×C11C2×#4114yes—
219C2×C4×C11C25112yes—
220C2×C4×C11C2516yes—
221C2×C4×C11C2516yes—
222C2×C4×C11C2512yes—
223C22⋊D11—248no—
224C2×Dic11—212no—
225C2×Dic11—22no—
226C2×Dic11—26no—
227C2×Dic11—248no—
228C2×Dic11—24no—
229C2×Dic11—216no—
230C2×Dic112−1+414yes—
231C2×Dic11C2514yes—
232C2×Dic11C2512yes—
233C2×Dic11C2516yes—
234C2×Dic11C25112yes—
235C2×Dic11C2512yes—
236D44—224no—
237C4×D11—224no—
238C4×D11—224no—
239C4×D11—224no—
240Dic22—224no—
241C22×#41—111no—
242C22×#41—113no—
243C23×Q8C2×D1112yes—
244#557—1116no—
245#556—1148no—
246#552—1196no—
247D4×Q8C2×D11116yescomplemented
248#548—1132no—
249#547—1148no—
250#533—1148no—
251C2×C4⋊Q8—113no—
252C2×C4⋊Q8C2×D1113yes—
253#529—1196no—
254C2×#126—1112no—
255C2×#125—116no—
256C2×#125—116no—
257C2×#124—116no—
258C2×#123—1112no—
259C2×C22⋊Q8—116no—
260C2×C22⋊Q8—116no—
261C2×C22⋊Q8C2×D1116yes—
262C2×#121—116no—
263C4×#41—1116no—
264C4×#41—1148no—
265C2×C4×Q8—111no—
266C2×C4×Q8—116no—
267C2×C4×Q8—112no—
268C2×C4×Q8—116no—
269C2×C4×Q8—1132no—
270C2×C4×Q8—113no—
271C2×C4×Q8—113no—
272C2×C4×Q8C2×D1111yescharacteristic
273C2×C4×D4—111no—
274C2×C4×D4—116no—
275C2×C4×D4—113no—
276C2×C4×D4—116no—
277C2×C4×D4—113no—
278C2×C4×D4C2×D1113yes—
279C2×#117—113no—
280C2×#117—113no—
281C2×#117—116no—
282C2×#117—116no—
283C22×C4⋊C4—116no—
284C22×C42—116no—
285C22×C42—113no—
286C22×C11—24no—
287C22×C11—24no—
288C22×C11—216no—
289C22×C11C22×#4112yes—
290C22×C11C22×#4118yes—
291C22×C11C22×#4112yes—
292C22×C11C2×2−1+412yes—
293C22×C11C2611yescharacteristic
294C2×D11—26no—
295C2×D11—26no—
296C2×D11—26no—
297C2×D11—412no—
298C4×C11—212no—
299C4×C11—26no—
300C4×C11C22×#41112yes—
301C4×C11C22×#4114yes—
302Dic11—212no—
303Dic11—22no—
304Dic11—26no—
305Dic11—24no—
306Dic11C2×2−1+414yes—
307C2×#41—118no—
308C2×#41—1124no—
309C2×#41—228no—
310C2×#41—2224no—
311C22×Q8—216no—
312C22×Q8—113no—
313C22×Q8C22×D1116yes—
314C22×Q8C22×D11116yes—
315C22×Q8C22×D1111yescharacteristic
316C22×D4—116no—
317C22×D4—113no—
318C22×D4C22×D1111yescharacteristic
319C23×C4—116no—
320C23×C4—112no—
321C23×C4—113no—
322C23×C4—113no—
323C23×C4—113no—
324C23×C4C22×D1116yes—
325C4⋊Q8—1124no—
326C4⋊Q8C22×D11124yes—
327#126—1196no—
328#125—1148no—
329#125—1148no—
330#124—1148no—
331#123—1196no—
332C22⋊Q8—1148no—
333C22⋊Q8—1148no—
334C22⋊Q8C22×D11148yes—
335#121—1148no—
336C4×Q8—118no—
337C4×Q8—1148no—
338C4×Q8—1116no—
339C4×Q8—1148no—
340C4×Q8—1124no—
341C4×Q8—1124no—
342C4×Q8C22×D1118yes—
343C4×D4—118no—
344C4×D4—1148no—
345C4×D4—1124no—
346C4×D4—1148no—
347C4×D4—1124no—
348C4×D4C22×D11124yes—
349#117—1124no—
350#117—1124no—
351#117—1148no—
352#117—1148no—
353C2×C4⋊C4—113no—
354C2×C4⋊C4—116no—
355C2×C4⋊C4—1112no—
356C2×C4⋊C4—1148no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—116no—
359C2×C4⋊C4—116no—
360C2×C4⋊C4—116no—
361C2×C4⋊C4C22×D1113yes—
362C2×C4⋊C4C22×D1113yes—
363C2×C4⋊C4C22×D1116yes—
364C2×C22⋊C4—112no—
365C2×C22⋊C4—116no—
366C2×C22⋊C4—116no—
367C2×C22⋊C4—1112no—
368C2×C22⋊C4C22×D1116yes—
369C2×C42—113no—
370C2×C42—116no—
371C2×C42—116no—
372C2×C42—116no—
373C2×C42—113no—
374C2×C42—111no—
375C2×C42—1148no—
376C2×C42—1124no—
377C2×C42C22×D1113yes—
378C2×C11—28no—
379C2×C11#348214yescomplemented
380C2×C11C23×#4111yescharacteristic
381C2×C11C23×#4111yescharacteristic
382C2×C11C22×2−1+411yescharacteristic
383D11—46no—
384C24—113no—
385C24C23×D1112yes—
386#41—2232no—
387#41—2296no—
388C2×Q8—264no—
389C2×Q8—224no—
390C2×Q8—1112no—
391C2×Q8—2212no—
392C2×Q8#434118yescomplemented
393C2×Q8C23×D11124yes—
394C2×Q8C23×D1114yes—
395C2×D4—1124no—
396C2×D4—1112no—
397C2×D4—2224no—
398C2×D4—2212no—
399C2×D4#434318yescomplemented
400C2×D4C23×D1114yes—
401C22×C4—224no—
402C22×C4—111no—
403C22×C4—118no—
404C22×C4—1124no—
405C22×C4—112no—
406C22×C4—111no—
407C22×C4—113no—
408C22×C4—116no—
409C22×C4—1112no—
410C22×C4—1112no—
411C22×C4—1112no—
412C22×C4—2212no—
413C22×C4—228no—
414C22×C4—2224no—
415C22×C4—2212no—
416C22×C4—2212no—
417C22×C4C23×D11124yes—
418C22×C4C23×D1116yes—
419C22×C4C23×D1113yes—
420C22×C4C23×D1113yes—
421C22×C4C23×D1111yescharacteristic
422C4⋊C4—1112no—
423C4⋊C4—1124no—
424C4⋊C4—1148no—
425C4⋊C4—114no—
426C4⋊C4—1124no—
427C4⋊C4—1124no—
428C4⋊C4—1124no—
429C4⋊C4C23×D11112yes—
430C4⋊C4C23×D11112yes—
431C4⋊C4C23×D11124yes—
432C22⋊C4—118no—
433C22⋊C4—1124no—
434C22⋊C4—1124no—
435C22⋊C4—1148no—
436C22⋊C4C23×D11124yes—
437C42—1112no—
438C42—114no—
439C42—1112no—
440C42—1124no—
441C42—1124no—
442C42—1124no—
443C42C23×D11112yes—
444C11C2×#348211yescharacteristic, complemented, Sylow
445C23—24no—
446C23—24no—
447C23—116no—
448C23—226no—
449C23—226no—
450C23—226no—
451C23C2×#434318yes—
452C23C24×D1114yes—
453C23C24×D1111yescharacteristic
454Q8—248no—
455Q8—2224no—
456Q8C2×#4341116yescomplemented
457D4—2248no—
458D4—2224no—
459D4C2×#4343116yescomplemented
460C2×C4—212no—
461C2×C4—26no—
462C2×C4—248no—
463C2×C4—114no—
464C2×C4—112no—
465C2×C4—114no—
466C2×C4—112no—
467C2×C4—116no—
468C2×C4—1112no—
469C2×C4—2224no—
470C2×C4—2216no—
471C2×C4—222no—
472C2×C4—226no—
473C2×C4—2212no—
474C2×C4—2248no—
475C2×C4—224no—
476C2×C4—2224no—
477C2×C4—2224no—
478C2×C4C2×#4341112yes—
479C2×C4C2×#434314yes—
480C2×C4C24×D11112yes—
481C2×C4C24×D1116yes—
482C2×C4C24×D1116yes—
483C2×C4C24×D1112yes—
484C22—24no—
485C22—24no—
486C22—216no—
487C22—226no—
488C22—226no—
489C22—226no—
490C22—4412no—
491C22C22×#434112yes—
492C22C22×#434318yes—
493C22C22×#434312yes—
494C22D11×2−1+412yes—
495C22C25×D1111yescharacteristic
496C4—212no—
497C4—26no—
498C4—114no—
499C4—222no—
500C4—226no—
501C4—2212no—
502C4—224no—
503C4C22×#4341112yes—
504C4C22×#434314yes—
505C2—28no—
506C2—446no—
507C2#1308223714yesdirect product factor
508C2C23×#434111yescharacteristic
509C2C23×#434311yescharacteristic
510C2C2×D11×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×D4×Q8×C11C2
socleC23×C11C25
hypercenterC2×D4×Q8D11
hypocenterC11C2×#3482
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #13082237C2direct (N × H)
2. C2×#10623101C2semidirect
3. C2×#10623263C2semidirect
4. C2×#10623173C2semidirect
5. C2×#10623348C2semidirect
6. C2×#10623086C2semidirect
7. C2×#10623259C2semidirect
8. C2×#10623155C2semidirect
9. C2×C4×#4343C2semidirect
10. C2×C4×#4341C2semidirect
11. C22×Q8×Dic11C2semidirect
12. C2×D4×Q8×C11C2semidirect
16. D4×Q8×C11C22semidirect
21. #10623348C22semidirect
28. C2×Q8×Dic11C22semidirect
34. #10623263C22semidirect
35. #10623259C22semidirect
36. #10623173C22semidirect
37. #10623155C22semidirect
38. C4×#4343C22semidirect
39. #10623101C22semidirect
40. #10623086C22semidirect
41. C4×#4341C22semidirect
134. C2×Q8×C11#41semidirect
137. C2×D4×C11#41semidirect
194. C2×D4×Q8D11semidirect
212. Q8×C11C2×#41semidirect
213. D4×C11C2×#41semidirect
247. D4×Q8C2×D11semidirect
379. C2×C11#3482semidirect
392. C2×Q8#4341semidirect
399. C2×D4#4343semidirect
444. C11C2×#3482semidirect
456. Q8C2×#4341semidirect
459. D4C2×#4343semidirect
507. C2#13082237direct (N × H)

Maximal subgroups

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

subgroupindex
#130822372
C2×#106231012
C2×#106232632
C2×#106231732
C2×#106233482
C2×#106230862
C2×#106232592
C2×#106231552
C2×C4×#43432
C2×C4×#43412
C22×Q8×Dic112
C2×D4×Q8×C112
C2×#348211