Finite Group Databasebeta

← C2×#13077041 #15617180

Subgroups — C2×#13077041 #15617180

Order 2816.

3278 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66954C212yesmaximal
2C2×C4×#4339C211yesmaximal, characteristic
3#13077041C2116yesmaximal, direct product factor
4C2×#10622321C214yesmaximal, complemented
5C2×#10622714C212yesmaximal, complemented
6C2×C4×#4318C211yesmaximal, characteristic, complemented
7C2×#10622320C212yesmaximal, complemented
8C2×D11×#97C212yesmaximal, complemented
9C22×C11×#97C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C23×C8×C11C2212yes—
12C22×C42×C11C2211yescharacteristic
13C2×C4×C22⋊D11C414yes—
14C2×#66979C2211yescharacteristic
15C22×#4318C2212yes—
16C2×#66954C4132yescomplemented
17C2×#66954C22116yes—
18C22×#4313C2214yes—
19C22×C8×D11C2214yes—
20C4×#4339C418yes—
21C4×#4339C2218yes—
22C2×C4×D44C412yes—
23C2×#66925C2212yes—
24C2×C42×D11C2212yes—
25C2×C4×Dic22C412yes—
26C2×C11×#97C2211yescharacteristic
27C2×C11×#97C2211yescharacteristic
28C2×C11×#97C2212yes—
29C2×C11×#97C2218yescomplemented
30#10622714C22116yescomplemented
31C2×#66879C2214yes—
32C2×C8×Dic11C2214yes—
33C4×#4318C2218yescomplemented
34C2×#66867C2212yes—
35C2×C4×C11⋊C8C2212yes—
36#10622321C22132yescomplemented
37#10622320C22116yescomplemented
38D11×#97C22116yescomplemented
39C23×C4×C11C2×C412yes—
40C23×C4×C11C2311yescharacteristic
41C22×C22⋊D11C2×C412yes—
42C2×#4339C2×C4116yes—
43C2×#4339C2×C414yes—
44C2×#4339C2314yes—
45C22×D44C2×C411yescharacteristic
46C22×C4×D11C2×C414yes—
47C22×C4×D11C2312yes—
48C22×Dic22C2×C411yescharacteristic
49C22×C8×C11C2×C4116yescomplemented
50C22×C8×C11C2312yes—
51C22×C8×C11C2312yes—
52C22×C8×C11C2318yes—
53C2×C42×C11C2×C412yes—
54C2×C42×C11C2×C414yes—
55C2×C42×C11C2311yescharacteristic
56C2×C42×C11C2311yescharacteristic
57C2×C42×C11C2314yes—
58C2×C22⋊Dic11C2×C412yes—
59C4×C22⋊D11C2×C4132yes—
60C2×(C2×D11)⋊C4C2×C414yes—
61#66979C2×C414yes—
62#66979C2314yes—
63C2×C4⋊Dic11C2×C412yes—
64C2×Dic11⋊C4C2×C414yes—
65C2×C4×Dic11C2×C414yes—
66C2×C4×Dic11C2312yes—
67C2×#4318C2×C4116yescomplemented
68C2×#4318C2318yes—
69C22×C11⋊C8C2314yes—
70#66954C2×C41128yescomplemented
71C2×#4313C2×C4132yescomplemented
72C2×#4313C23116yes—
73C2×C8×D11C2×C4132yescomplemented
74C2×C8×D11C23116yes—
75C4×D44C2×C4116yes—
76#66925C2×C418yes—
77#66925C2318yes—
78C42×D11C2×C418yes—
79C42×D11C2318yes—
80C4×Dic22C2×C4116yes—
81C11×#97C2314yes—
82C11×#97C2314yes—
83C11×#97C2318yes—
84#66879C23116yes—
85C8×Dic11C23116yes—
86#66867C2318yes—
87C4×C11⋊C8C2318yes—
88C2×#2875—111nomaximal, Sylow
89C24×C11C22×C411yescharacteristic
90C23×D11C22×C412yes—
91C22×C4×C11—44no—
92C22×C4×C11C22×C412yes—
93C22×C4×C11C22×C412yes—
94C22×C4×C11C22×C418yes—
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C22×C412yes—
97C22×C4×C11C22×C418yes—
98C22×C4×C11C2412yes—
99C22×C4×C11C2411yescharacteristic
100C2×C22⋊D11C42116yes—
101C2×C22⋊D11C22×C418yes—
102C22×Dic11C22×C414yes—
103C22×Dic11C22×C412yes—
104#4339C42132yes—
105#4339C22×C4132yes—
106C2×D44C4218yes—
107C2×D44C22×C414yes—
108C2×C4×D11—48no—
109C2×C4×D11C22×C4116yes—
110C2×C4×D11C22×C4116yes—
111C2×C4×D11C22×C414yes—
112C2×C4×D11C2414yes—
113C2×Dic22C4218yes—
114C2×Dic22C22×C414yes—
115C2×C8×C11C22×C418yes—
116C2×C8×C11C22×C418yes—
117C2×C8×C11C22×C4132yescomplemented
118C2×C8×C11C2414yes—
119C2×C8×C11C2414yes—
120C42×C11C22×C418yes—
121C42×C11C22×C412yes—
122C42×C11C22×C412yes—
123C42×C11C2412yes—
124C42×C11C2412yes—
125C22⋊Dic11C22×C418yes—
126(C2×D11)⋊C4C22×C4116yes—
127C4⋊Dic11C22×C418yes—
128Dic11⋊C4C22×C4116yes—
129C4×Dic11C22×C4116yes—
130C4×Dic11C22×C414yes—
131C4×Dic11C2414yes—
132#4318C22×C4132yescomplemented
133C2×C11⋊C8C22×C4116yes—
134C2×C11⋊C8C2418yes—
135#4313C22×C4164yescomplemented
136C8×D11C22×C4164yescomplemented
137C22×#131—112no—
138C2×C4×#41—111no—
139#2875—1116no—
140C2×#405—114no—
141C2×#405—112no—
142C2×C4×M16—111no—
143C2×C4×M16—112no—
144C22×#97—112no—
145C22×#97D1111yescharacteristic, complemented
146C23×C11—24no—
147C23×C11C2×C4214yes—
148C23×C11C23×C412yes—
149C23×C11C23×C411yescharacteristic
150C22×D11—28no—
151C22×D11C2×C4218yes—
152C22×D11C23×C414yes—
153C2×C4×C11—24no—
154C2×C4×C11—24no—
155C2×C4×C11—48no—
156C2×C4×C11C2×C4214yes—
157C2×C4×C11C2×C4218yes—
158C2×C4×C11C23×C414yes—
159C2×C4×C11C23×C414yes—
160C2×C4×C11C23×C414yes—
161C2×C4×C11C23×C418yes—
162C2×C4×C11C23×C411yescharacteristic
163C2×C4×C11C23×C412yes—
164C2×C4×C11C2511yescharacteristic
165C22⋊D11C2×C42132yes—
166C2×Dic11—28no—
167C2×Dic11C2×C4218yes—
168C2×Dic11C23×C418yes—
169C2×Dic11C23×C414yes—
170D44C2×C42116yes—
171C4×D11—416no—
172C4×D11C2×C42116yes—
173C4×D11C23×C4116yes—
174Dic22C2×C42116yes—
175C8×C11C23×C418yes—
176C8×C11C23×C418yes—
177C11⋊C8C23×C4116yes—
178C22×#41—111no—
179C2×#131—1116no—
180C2×#131—1132no—
181C22×M16—112no—
182C22×M16—114no—
183C23×C8—114no—
184C23×C8C2×D1112yes—
185C4×#41—118no—
186C4×#41—118no—
187C2×C4×Q8—112no—
188C2×C4×D4—114no—
189C2×C4×D4—112no—
190C2×#117—111no—
191C2×#117—112no—
192C22×C42—112no—
193C22×C42C2×D1111yescharacteristic
194#405—1116no—
195#405—1132no—
196C4×M16—118no—
197C4×M16—1116no—
198C2×#97—114no—
199C2×#97—112no—
200C2×#97—1116no—
201C2×#97C2×D1111yescharacteristic
202C2×#97C2×D1111yescharacteristic
203C2×#97C2×D1112yes—
204C2×#97C2×D1118yescomplemented
205C2×C4×C8—114no—
206C2×C4×C8—112no—
207C22×C11—28no—
208C22×C11—24no—
209C22×C11C22×C4214yes—
210C22×C11C22×C4212yes—
211C22×C11#56814yes—
212C22×C11C24×C411yescharacteristic
213C2×D11—216no—
214C2×D11—28no—
215C2×D11C22×C4218yes—
216C4×C11—24no—
217C4×C11—24no—
218C4×C11C22×C4214yes—
219C4×C11C22×C4212yes—
220C4×C11C24×C412yes—
221Dic11—28no—
222Dic11C22×C4218yes—
223C2×#41—114no—
224C2×#41—1116no—
225C2×#41—114no—
226C22×Q8—111no—
227C22×D4—112no—
228C22×D4—111no—
229C23×C4—112no—
230C23×C4—114no—
231C23×C4C4×D1112yes—
232C23×C4C22×D1111yescharacteristic
233#131—11128no—
234C2×M16—1116no—
235C2×M16—118no—
236C2×M16—1132no—
237C2×M16—1116no—
238C22×C8—114no—
239C22×C8—1132no—
240C22×C8—1116no—
241C22×C8C4×D11116yescomplemented
242C22×C8C22×D1112yes—
243C22×C8C22×D1112yes—
244C22×C8C22×D1118yes—
245C4×Q8—1116no—
246C4×D4—1132no—
247C4×D4—1116no—
248#117—114no—
249#117—114no—
250#117—118no—
251#117—118no—
252C2×C4⋊C4—114no—
253C2×C4⋊C4—112no—
254C2×C22⋊C4—112no—
255C2×C22⋊C4—114no—
256C2×C42—114no—
257C2×C42—112no—
258C2×C42—118no—
259C2×C42—118no—
260C2×C42C4×D1112yes—
261C2×C42C4×D1114yes—
262C2×C42C22×D1114yes—
263C2×C42C22×D1111yescharacteristic
264C2×C42C22×D1111yescharacteristic
265#97—1116no—
266#97—118no—
267#97C22×D1114yes—
268#97C22×D1114yes—
269#97C22×D1118yes—
270C4×C8—1116no—
271C4×C8—118no—
272C2×C11—24no—
273C2×C11#287514yescomplemented
274C2×C11C23×C4211yescharacteristic
275C2×C11C2×#56812yes—
276D11—28no—
277C24—112no—
278C24C2×C4×D1111yescharacteristic
279#41—1132no—
280#41—1132no—
281C2×Q8—118no—
282C2×Q8—114no—
283C2×D4—1116no—
284C2×D4—118no—
285C2×D4—118no—
286C2×D4—114no—
287C22×C4—44no—
288C22×C4—112no—
289C22×C4—114no—
290C22×C4—1116no—
291C22×C4—114no—
292C22×C4—114no—
293C22×C4—1116no—
294C22×C4—448no—
295C22×C4C2×C4×D1112yes—
296C22×C4C2×C4×D1112yes—
297C22×C4C2×C4×D1118yes—
298C22×C4C2×C4×D1111yescharacteristic
299C22×C4C2×C4×D1112yes—
300C22×C4C2×C4×D1118yes—
301C22×C4C23×D1112yes—
302C22×C4C23×D1111yescharacteristic
303M16—1132no—
304M16—1164no—
305C2×C8—1116no—
306C2×C8—118no—
307C2×C8—1164no—
308C2×C8C2×C4×D1118yes—
309C2×C8C2×C4×D1118yes—
310C2×C8C2×C4×D11132yescomplemented
311C2×C8C23×D1114yes—
312C2×C8C23×D1114yes—
313C4⋊C4—1116no—
314C4⋊C4—118no—
315C22⋊C4—118no—
316C22⋊C4—1116no—
317C42—114no—
318C42—1116no—
319C42—114no—
320C42C2×C4×D1112yes—
321C42C2×C4×D1112yes—
322C42C2×C4×D1118yes—
323C42C23×D1112yes—
324C42C23×D1112yes—
325C11C2×#287511yescharacteristic, complemented, Sylow
326C23—24no—
327C23—118no—
328C23—114no—
329C23—228no—
330C23C42×D1114yes—
331C23C22×C4×D1112yes—
332C23C22×C4×D1111yescharacteristic
333Q8—1116no—
334D4—1132no—
335D4—1116no—
336C2×C4—24no—
337C2×C4—24no—
338C2×C4—48no—
339C2×C4—118no—
340C2×C4—114no—
341C2×C4—1116no—
342C2×C4—1116no—
343C2×C4—118no—
344C2×C4—228no—
345C2×C4—4416no—
346C2×C4C42×D1114yes—
347C2×C4C42×D1118yes—
348C2×C4C22×C4×D1114yes—
349C2×C4C22×C4×D1114yes—
350C2×C4C22×C4×D1111yescharacteristic
351C2×C4C22×C4×D1112yes—
352C2×C4C22×C4×D1114yes—
353C2×C4C22×C4×D1118yes—
354C2×C4C24×D1111yescharacteristic
355C8—1116no—
356C8C22×C4×D1118yes—
357C8C22×C4×D1118yes—
358C22—28no—
359C22—24no—
360C22—118no—
361C22—2216no—
362C22—228no—
363C22C2×C42×D1114yes—
364C22C2×C42×D1112yes—
365C22#1062327614yes—
366C22C23×C4×D1111yescharacteristic
367C4—24no—
368C4—24no—
369C4—118no—
370C4—228no—
371C4C2×C42×D1112yes—
372C4C2×C42×D1114yes—
373C4C23×C4×D1112yes—
374C2—24no—
375C2—228no—
376C2#1307704114yesdirect product factor
377C2C22×C42×D1111yescharacteristic
378C2C2×#1062327612yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC2×C11C23×C42
FrattiniC2×C4C24×D11
FittingC22×C11×#97C2
socleC23×C11C23×C4
prime radicalC22×#4339C22
cosocleC2×C4×C11C25
hypercenterC22×#97D11
hypocenterC11C2×#2875
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×#97

Complements

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

NH ≅ G/Ntype
3. #13077041C2direct (N × H)
4. C2×#10622321C2semidirect
5. C2×#10622714C2semidirect
6. C2×C4×#4318C2semidirect
7. C2×#10622320C2semidirect
8. C2×D11×#97C2semidirect
9. C22×C11×#97C2semidirect
16. C2×#66954C4semidirect
29. C2×C11×#97C22semidirect
30. #10622714C22semidirect
33. C4×#4318C22semidirect
36. #10622321C22semidirect
37. #10622320C22semidirect
38. D11×#97C22semidirect
49. C22×C8×C11C2×C4semidirect
67. C2×#4318C2×C4semidirect
70. #66954C2×C4semidirect
71. C2×#4313C2×C4semidirect
73. C2×C8×D11C2×C4semidirect
117. C2×C8×C11C22×C4semidirect
132. #4318C22×C4semidirect
135. #4313C22×C4semidirect
136. C8×D11C22×C4semidirect
145. C22×#97D11semidirect
204. C2×#97C2×D11semidirect
241. C22×C8C4×D11semidirect
273. C2×C11#2875semidirect
310. C2×C8C2×C4×D11semidirect
325. C11C2×#2875semidirect
376. C2#13077041direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669542
C2×C4×#43392
#130770412
C2×#106223212
C2×#106227142
C2×C4×#43182
C2×#106223202
C2×D11×#972
C22×C11×#972
C2×#287511