Finite Group Databasebeta

← C2×#13082756 #15660666

Subgroups — C2×#13082756 #15660666

Order 2816.

7418 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082756C2132yesmaximal, direct product factor
2C2×#10623203C213yesmaximal, complemented
3C2×#10623215C216yesmaximal, complemented
4C2×#10623126C216yesmaximal, complemented
5C2×#10623199C213yesmaximal, complemented
6C2×#10623211C216yesmaximal, complemented
7C2×#10623117C216yesmaximal, complemented
8C2×C11×H(3,𝔽4)C211yesmaximal, characteristic, complemented
9C24×Dic11C2212yescomplemented
10C22×#4343C2211yescharacteristic, complemented
11C22×#4341C2213yes—
12C11×H(3,𝔽4)C22116yescomplemented
13C2×C11×#124C2216yes—
14C2×C11×#124C2213yes—
15C2×C11×#120C2216yes—
16C2×#67006C2216yescomplemented
17C2×#66999C2216yescomplemented
18C2×Q8×Dic11C2212yescomplemented
19C2×#66997C2213yescomplemented
20C2×#66993C2213yes—
21C2×#66992C22112yes—
22C2×#66991C2216yes—
23C2×#66988C2216yes—
24C2×D4×Dic11C2216yes—
25#10623215C22196yescomplemented
26#10623211C22196yescomplemented
27#10623203C22148yescomplemented
28#10623199C22148yescomplemented
29#10623126C22196yescomplemented
30#10623117C22196yescomplemented
31C2×#66939C2216yescomplemented
32C2×#66937C22112yescomplemented
33C2×#66936C22112yescomplemented
34C2×(C22⋊D11)⋊C4C22112yescomplemented
35C2×#66932C22112yescomplemented
36C2×#66931C22112yescomplemented
37C2×#66930C2216yescomplemented
38C2×#66928C2213yescomplemented
39C2×C42×D11C2213yescomplemented
40C2×#66923C2216yescomplemented
41C25×C11C2312yes—
42C22×Q8×C11C2311yescharacteristic
43C22×Q8×C11C2312yes—
44C22×D4×C11C2316yes—
45C22×D4×C11C2313yes—
46C22×C22⋊D11C23112yes—
47C22×C22⋊D11C2316yes—
48C23×Dic11—48no—
49C23×Dic11C2316yes—
50C23×Dic11C2316yes—
51C23×Dic11C23116yescomplemented
52C2×#4343—44no—
53C2×#4343C2318yescomplemented
54C2×#4341—412no—
55C2×#4341C23124yes—
56C22×D44C2313yes—
57C22×C4×D11C2313yes—
58C22×C4×D11C2316yes—
59C22×Dic22C2313yes—
60C11×#124C23124yes—
61C11×#124C23148yes—
62C11×#120C23148yes—
63C2×C11×C22⋊C4C2316yes—
64C2×C11×C22⋊C4C23112yes—
65C2×C42×C11C2313yes—
66#67006C23148yescomplemented
67C2×C22⋊Dic11C2316yes—
68C2×C22⋊Dic11C23112yes—
69#66999C23148yescomplemented
70Q8×Dic11C23116yescomplemented
71#66997C23124yescomplemented
72#66993C23124yes—
73#66992C23196yes—
74#66991C23148yes—
75#66988C23148yes—
76D4×Dic11C23148yes—
77C2×(C2×D11)⋊C4C23112yes—
78C2×C4⋊Dic11C2316yes—
79C2×C4⋊Dic11C2316yes—
80C2×Dic11⋊C4C23112yes—
81C2×Dic11⋊C4C23112yes—
82C2×C4×Dic11C2316yes—
83C2×C4×Dic11C2313yes—
84#66939C23148yescomplemented
85#66937C23196yescomplemented
86#66936C23196yescomplemented
87(C22⋊D11)⋊C4C23196yescomplemented
88#66932C23196yescomplemented
89#66931C23196yescomplemented
90#66930C23148yescomplemented
91#66928C23124yescomplemented
92C42×D11C23124yescomplemented
93#66923C23148yescomplemented
94C2×#3529—111nomaximal, Sylow
95C24×C11—44no—
96C24×C11—48no—
97C24×C11C2416yes—
98C24×C11C2418yes—
99C23×D11C2413yes—
100C2×Q8×C11—42no—
101C2×Q8×C11—44no—
102C2×Q8×C11C2414yes—
103C2×Q8×C11C2418yes—
104C2×D4×C11—46no—
105C2×D4×C11—412no—
106C2×D4×C11C24124yes—
107C2×D4×C11C24112yes—
108C22×C4×C11C2413yes—
109C22×C4×C11C2416yes—
110C2×C22⋊D11—412no—
111C2×C22⋊D11—424no—
112C2×C22⋊D11C24148yes—
113C2×C22⋊D11C24124yes—
114C22×Dic11—224no—
115C22×Dic11—412no—
116C22×Dic11—432no—
117C22×Dic11C24124yes—
118C22×Dic11C2416yes—
119C22×Dic11C2416yes—
120C22×Dic11C24124yes—
121C22×Dic11C2411yescharacteristic
122#4343—416no—
123#4341—448no—
124C2×D44—46no—
125C2×D44C24112yes—
126C2×C4×D11—212no—
127C2×C4×D11—412no—
128C2×C4×D11C24112yes—
129C2×C4×D11C24124yes—
130C2×Dic22—46no—
131C2×Dic22C24112yes—
132C11×C22⋊C4C24124yes—
133C11×C22⋊C4C24148yes—
134C42×C11C24112yes—
135C22⋊Dic11C24124yes—
136C22⋊Dic11C24148yes—
137(C2×D11)⋊C4C24148yes—
138C4⋊Dic11C24124yes—
139C4⋊Dic11C24124yes—
140Dic11⋊C4C24148yes—
141Dic11⋊C4C24148yes—
142C4×Dic11C24124yes—
143C4×Dic11C24112yes—
144#3529—1132no—
145C2×#563—113no—
146C2×#562—116no—
147C2×H(3,𝔽4)D1111yescharacteristic, complemented
148C2×#560—116no—
149C2×#532—113no—
150C2×#529—116no—
151C2×#525—116no—
152C23×C11—212no—
153C23×C11—224no—
154C23×C11—48no—
155C23×C11—416no—
156C23×C11—432no—
157C23×C11C25112yes—
158C23×C11C2511yescharacteristic
159C22×D11—26no—
160C22×D11—212no—
161C22×D11C2516yes—
162Q8×C11—44no—
163Q8×C11—48no—
164D4×C11—412no—
165D4×C11—424no—
166C2×C4×C11—26no—
167C2×C4×C11—212no—
168C2×C4×C11C2516yes—
169C2×C4×C11C25112yes—
170C22⋊D11—424no—
171C22⋊D11—448no—
172C2×Dic11—212no—
173C2×Dic11—212no—
174C2×Dic11—248no—
175C2×Dic11—424no—
176C2×Dic11H(5,𝔽2)14yes—
177C2×Dic11C25112yes—
178C2×Dic11C25112yes—
179C2×Dic11C2512yes—
180D44—412no—
181C4×D11—224no—
182C4×D11—424no—
183Dic22—412no—
184C22×#41—111no—
185C22×#41—113no—
186C24×C4—112no—
187#563—1148no—
188#562—1196no—
189H(3,𝔽4)C2×D11116yescomplemented
190#560—1196no—
191#532—1148no—
192C2×C4⋊Q8—113no—
193C2×#127—113no—
194#529—1196no—
195C2×#126—1112no—
196C2×#125—116no—
197C2×#124—113no—
198C2×#124C2×D1116yes—
199C2×#124C2×D1113yes—
200#525—1196no—
201C2×#123—116no—
202C2×#123—1112no—
203C2×#123—116no—
204C2×C22⋊Q8—116no—
205C2×C22⋊Q8—1112no—
206C2×#121—116no—
207C2×#121—1112no—
208C2×#121—1112no—
209C2×#120—116no—
210C2×#120C2×D1116yes—
211C2×C4×Q8—112no—
212C2×C4×D4—116no—
213C2×C4×D4—1112no—
214C2×#117—116no—
215C22×C42—113no—
216C22×C11—212no—
217C22×C11—224no—
218C22×C11—432no—
219C22×C11—424no—
220C22×C11C2×H(5,𝔽2)12yes—
221C22×C11#58514yes—
222C22×C11C2611yescharacteristic
223C2×D11—26no—
224C2×D11—212no—
225C2×D11—412no—
226C4×C11—26no—
227C4×C11—212no—
228Dic11—212no—
229Dic11—212no—
230Dic11C2×H(5,𝔽2)14yes—
231C25C22×D1112yes—
232C2×#41—118no—
233C2×#41—1124no—
234C2×#41—4412no—
235C2×#41—444no—
236C22×Q8—113no—
237C22×Q8C22×D1112yes—
238C22×Q8C22×D1111yescharacteristic
239C22×D4—1112no—
240C22×D4—116no—
241C22×D4—113no—
242C22×D4C22×D1116yes—
243C22×D4C22×D1113yes—
244C23×C4—116no—
245C23×C4—116no—
246C23×C4—1116no—
247C23×C4—113no—
248C23×C4—116no—
249C23×C4—448no—
250C4⋊Q8—1124no—
251#127—1124no—
252#126—1196no—
253#125—1148no—
254#124—1124no—
255#124C22×D11148yes—
256#124C22×D11124yes—
257#123—1148no—
258#123—1148no—
259#123—1196no—
260C22⋊Q8—1148no—
261C22⋊Q8—1196no—
262#121—1196no—
263#121—1148no—
264#121—1196no—
265#120—1148no—
266#120C22×D11148yes—
267C4×Q8—1116no—
268C4×D4—1148no—
269C4×D4—1196no—
270#117—1148no—
271C2×C4⋊C4—1112no—
272C2×C4⋊C4—1112no—
273C2×C4⋊C4—116no—
274C2×C4⋊C4—116no—
275C2×C22⋊C4—116no—
276C2×C22⋊C4—1112no—
277C2×C22⋊C4—1112no—
278C2×C22⋊C4C22×D1116yes—
279C2×C22⋊C4C22×D11112yes—
280C2×C42—116no—
281C2×C42—113no—
282C2×C42—1124no—
283C2×C42C22×D1113yes—
284C2×C11—412no—
285C2×C11#352914yescomplemented
286C2×C11C22×H(5,𝔽2)11yescharacteristic
287C2×C11C2×#58512yes—
288D11—46no—
289C24—44no—
290C24—48no—
291C24—113no—
292C24C23×D1116yes—
293C24C23×D1118yes—
294#41—4448no—
295#41—4416no—
296C2×Q8—42no—
297C2×Q8—44no—
298C2×Q8—1112no—
299C2×Q8—446no—
300C2×Q8C23×D1118yes—
301C2×Q8C23×D1114yes—
302C2×D4—46no—
303C2×D4—412no—
304C2×D4—1148no—
305C2×D4—1124no—
306C2×D4—1112no—
307C2×D4—446no—
308C2×D4—4412no—
309C2×D4—4424no—
310C2×D4C23×D11124yes—
311C2×D4C23×D11112yes—
312C22×C4—111no—
313C22×C4—1124no—
314C22×C4—116no—
315C22×C4—116no—
316C22×C4—1124no—
317C22×C4—1112no—
318C22×C4—1124no—
319C22×C4—2212no—
320C22×C4—2224no—
321C22×C4—4412no—
322C22×C4—4432no—
323C22×C4—4412no—
324C22×C4C23×D1116yes—
325C22×C4C23×D1113yes—
326C4⋊C4—1148no—
327C4⋊C4—1148no—
328C4⋊C4—1124no—
329C4⋊C4—1124no—
330C22⋊C4—1124no—
331C22⋊C4—1148no—
332C22⋊C4—1148no—
333C22⋊C4C23×D11124yes—
334C22⋊C4C23×D11148yes—
335C42—1124no—
336C42—1112no—
337C42C23×D11112yes—
338C11C2×#352911yescharacteristic, complemented, Sylow
339C23—212no—
340C23—224no—
341C23—48no—
342C23—416no—
343C23—432no—
344C23—116no—
345C23—226no—
346C23—2212no—
347C23C24×D11112yes—
348C23C24×D1111yescharacteristic
349Q8—48no—
350Q8—44no—
351Q8—4412no—
352D4—424no—
353D4—412no—
354D4—4412no—
355D4—4424no—
356D4—4448no—
357C2×C4—26no—
358C2×C4—212no—
359C2×C4—114no—
360C2×C4—112no—
361C2×C4—1112no—
362C2×C4—1112no—
363C2×C4—2224no—
364C2×C4—2248no—
365C2×C4—2212no—
366C2×C4—2212no—
367C2×C4—4424no—
368C2×C4—4424no—
369C2×C4C24×D11112yes—
370C2×C4C24×D1116yes—
371C22—212no—
372C22—224no—
373C22—432no—
374C22—424no—
375C22—226no—
376C22—2212no—
377C22—4412no—
378C22D11×H(5,𝔽2)12yes—
379C22#1062345514yes—
380C22C25×D1111yescharacteristic
381C4—26no—
382C4—212no—
383C4—114no—
384C4—2212no—
385C4—2212no—
386C2—412no—
387C2—446no—
388C2#1308275614yesdirect product factor
389C2C2×D11×H(5,𝔽2)11yescharacteristic
390C2C2×#1062345512yes—
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×H(3,𝔽4)C2
socleC23×C11C25
hypercenterC2×H(3,𝔽4)D11
hypocenterC11C2×#3529
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #13082756C2direct (N × H)
2. C2×#10623203C2semidirect
3. C2×#10623215C2semidirect
4. C2×#10623126C2semidirect
5. C2×#10623199C2semidirect
6. C2×#10623211C2semidirect
7. C2×#10623117C2semidirect
8. C2×C11×H(3,𝔽4)C2semidirect
9. C24×Dic11C22semidirect
10. C22×#4343C22semidirect
12. C11×H(3,𝔽4)C22semidirect
16. C2×#67006C22semidirect
17. C2×#66999C22semidirect
18. C2×Q8×Dic11C22semidirect
19. C2×#66997C22semidirect
25. #10623215C22semidirect
26. #10623211C22semidirect
27. #10623203C22semidirect
28. #10623199C22semidirect
29. #10623126C22semidirect
30. #10623117C22semidirect
31. C2×#66939C22semidirect
32. C2×#66937C22semidirect
33. C2×#66936C22semidirect
34. C2×(C22⋊D11)⋊C4C22semidirect
35. C2×#66932C22semidirect
36. C2×#66931C22semidirect
37. C2×#66930C22semidirect
38. C2×#66928C22semidirect
39. C2×C42×D11C22semidirect
40. C2×#66923C22semidirect
51. C23×Dic11C23semidirect
53. C2×#4343C23semidirect
66. #67006C23semidirect
69. #66999C23semidirect
70. Q8×Dic11C23semidirect
71. #66997C23semidirect
84. #66939C23semidirect
85. #66937C23semidirect
86. #66936C23semidirect
87. (C22⋊D11)⋊C4C23semidirect
88. #66932C23semidirect
89. #66931C23semidirect
90. #66930C23semidirect
91. #66928C23semidirect
92. C42×D11C23semidirect
93. #66923C23semidirect
147. C2×H(3,𝔽4)D11semidirect
189. H(3,𝔽4)C2×D11semidirect
285. C2×C11#3529semidirect
338. C11C2×#3529semidirect
388. C2#13082756direct (N × H)

Maximal subgroups

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

subgroupindex
#130827562
C2×#106232032
C2×#106232152
C2×#106231262
C2×#106231992
C2×#106232112
C2×#106231172
C2×C11×H(3,𝔽4)2
C2×#352911