Finite Group Databasebeta

← C2×#13082401 #15662188

Subgroups — C2×#13082401 #15662188

Order 2816.

11126 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67043C212yesmaximal, complemented
2#13082401C2132yesmaximal, direct product factor
3C2×Q8×D44C214yesmaximal, complemented
4C2×#10623086C2112yesmaximal, complemented
5C2×#10623057C216yesmaximal, complemented
6C2×#10623008C213yesmaximal, complemented
7C22×#66922C213yesmaximal, complemented
8C2×C4×C11×#41C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C2×#67043—232no—
11C2×#67043C22132yescomplemented
12C22×Q8×D11C2214yes—
13C22×#4341C22112yes—
14C22×#4339C2216yes—
15C23×Dic22C2216yes—
16C4×C11×#41C22116yescomplemented
17C2×C4×Q8×C11C2212yes—
18C2×C4×D4×C11C2216yes—
19C2×C11×#117C2213yes—
20C22×C42×C11C2213yes—
21C2×#66983C22112yes—
22C22×C4⋊Dic11C22112yes—
23Q8×D44C22164yescomplemented
24#10623086C221192yescomplemented
25#10623057C22196yescomplemented
26C2×#66950C22124yes—
27C2×#66939C22124yes—
28#10623008C22148yescomplemented
29C2×#66928C2216yes—
30C2×#66927C2211yescharacteristic
31C2×C4×D44C22112yes—
32C2×#66922C2213yes—
33C2×#66922C2216yes—
34C2×#66922C22112yes—
35C2×#66922C22148yescomplemented
36C2×C11×#41D4116yescomplemented
37C2×C11×#41C2318yes—
38C22×Q8×C11C2311yescharacteristic
39C22×D4×C11C2313yes—
40C23×C4×C11C2316yes—
41C23×C4×C11C2313yes—
42C22×C22⋊D11C23112yes—
43C23×Dic11C23112yes—
44#67043—2256no—
45C2×Q8×D11—232no—
46C2×Q8×D11C23132yes—
47C2×#4341—296no—
48C2×#4341C23196yes—
49C2×#4339—248no—
50C2×#4339C23148yes—
51C22×D44C2314yes—
52C22×D44C2312yes—
53C22×C4×D11C23112yes—
54C22×Dic22—248no—
55C22×Dic22C2316yes—
56C22×Dic22C23112yes—
57C22×Dic22C23148yes—
58C4×Q8×C11C23116yes—
59C4×D4×C11C23148yes—
60C11×#117C23124yes—
61C2×C11×C4⋊C4C2316yes—
62C2×C11×C22⋊C4C2316yes—
63C2×C42×C11C2311yescharacteristic
64C2×C42×C11C2316yes—
65C2×C42×C11C2313yes—
66C2×C42×C11C23124yes—
67#66983C23196yes—
68C2×(C2×D11)⋊C4C23124yes—
69C2×C4⋊Dic11C23112yes—
70C2×C4⋊Dic11C23124yes—
71C2×C4⋊Dic11C23196yes—
72#66950C231192yes—
73#66939C231192yes—
74#66928C23148yes—
75#66927C2318yes—
76C4×D44C23196yes—
77#66922C23124yes—
78#66922C23148yes—
79#66922C23196yes—
80C2×#3499—111nomaximal, Sylow
81C24×C11C2413yes—
82C23×D11C2414yes—
83C11×#41C2×D4164yescomplemented
84C2×Q8×C11C2×D418yes—
85C2×Q8×C11C2414yes—
86C2×D4×C11C2×D4124yes—
87C2×D4×C11C24112yes—
88C22×C4×C11—224no—
89C22×C4×C11C2×D4124yes—
90C22×C4×C11C2416yes—
91C22×C4×C11C24124yes—
92C22×C4×C11C2411yescharacteristic
93C22×C4×C11C2413yes—
94C22×C4×C11C24112yes—
95C22×C4×C11C2412yes—
96C2×C22⋊D11—248no—
97C2×C22⋊D11C24148yes—
98C22×Dic11—248no—
99C22×Dic11C24148yes—
100C22×Dic11C24112yes—
101Q8×D11—2128no—
102#4341—2384no—
103#4339—2192no—
104C2×D44—28no—
105C2×D44—216no—
106C2×D44C24116yes—
107C2×D44C2418yes—
108C2×C4×D11—248no—
109C2×C4×D11C24148yes—
110C2×Dic22—224no—
111C2×Dic22—248no—
112C2×Dic22—2192no—
113C2×Dic22C24124yes—
114C2×Dic22C24148yes—
115C11×C4⋊C4C24124yes—
116C11×C22⋊C4C24124yes—
117C42×C11C2414yes—
118C42×C11C24124yes—
119C42×C11C24112yes—
120(C2×D11)⋊C4C24196yes—
121C4⋊Dic11C24148yes—
122C4⋊Dic11C24196yes—
123C22×2−1+4—112no—
124#3499—1132no—
125C2×D4×Q8—114no—
126C2×#547—1112no—
127C2×#536—116no—
128C2×#532—113no—
129C22×C4⋊Q8—113no—
130C2×C4×#41D1111yescharacteristic, complemented
131C23×C11—212no—
132C23×C11C22×D4112yes—
133C23×C11C2516yes—
134C23×C11C2511yescharacteristic
135C22×D11—28no—
136C22×D11—216no—
137C22×D11C2518yes—
138Q8×C11C22×D4116yes—
139D4×C11C22×D4148yes—
140C2×C4×C11—212no—
141C2×C4×C11—248no—
142C2×C4×C11C22×D414yes—
143C2×C4×C11C22×D4112yes—
144C2×C4×C11C22×D4148yes—
145C2×C4×C112−1+418yescomplemented
146C2×C4×C11C25112yes—
147C2×C4×C11C2512yes—
148C2×C4×C11C2516yes—
149C2×C4×C11C2514yes—
150C22⋊D11—296no—
151C2×Dic11—224no—
152C2×Dic11—296no—
153C2×Dic11C25124yes—
154D44—216no—
155D44—232no—
156C4×D11—296no—
157Dic22—248no—
158Dic22—296no—
159C2×2−1+4—1132no—
160C2×2−1+4—2232no—
161C22×#41—1112no—
162C22×#41—116no—
163C22×#41C2×D1111yescharacteristic
164C23×Q8—114no—
165C23×Q8—116no—
166D4×Q8—1164no—
167#547—11192no—
168#536—1196no—
169#532—1148no—
170C2×C4⋊Q8—113no—
171C2×C4⋊Q8—116no—
172C2×C4⋊Q8—1112no—
173C2×C4⋊Q8—1148no—
174C2×#127—111no—
175C2×#124—116no—
176C2×#123—1124no—
177C2×C22⋊Q8—1124no—
178C2×#121—1112no—
179C4×#41C2×D11116yescomplemented
180C2×C4×Q8C2×D1112yes—
181C2×C4×D4—1112no—
182C2×C4×D4C2×D1116yes—
183C2×#117C2×D1113yes—
184C22×C4⋊C4—1112no—
185C22×C42C2×D1113yes—
186C22×C11—212no—
187C22×C11—224no—
188C22×C11C23×D4112yes—
189C22×C11C23×D412yes—
190C22×C11C2×2−1+414yes—
191C22×C11C2611yescharacteristic
192C2×D11—28no—
193C2×D11—216no—
194C2×D11—416no—
195C4×C11—212no—
196C4×C11C23×D414yes—
197C4×C11C23×D4112yes—
198C4×C11C2×2−1+418yescomplemented
199Dic11—224no—
2002−1+4—22256no—
201C2×#41—1196no—
202C2×#41—1148no—
203C2×#41—2296no—
204C2×#41—2248no—
205C2×#41D44116yescomplemented
206C2×#41C22×D1118yes—
207C22×Q8—1132no—
208C22×Q8—1112no—
209C22×Q8—116no—
210C22×Q8—1148no—
211C22×Q8—2232no—
212C22×Q8—2248no—
213C22×Q8C22×D1111yescharacteristic
214C22×D4—1112no—
215C22×D4—114no—
216C22×D4—112no—
217C22×D4C22×D1113yes—
218C23×C4—1112no—
219C23×C4—1112no—
220C23×C4C22×D1116yes—
221C23×C4C22×D1113yes—
222C4⋊Q8—1124no—
223C4⋊Q8—1148no—
224C4⋊Q8—1196no—
225#127—118no—
226#124—1148no—
227#123—11192no—
228C22⋊Q8—11192no—
229#121—1196no—
230C4×Q8C22×D11116yes—
231C4×D4—1196no—
232C4×D4C22×D11148yes—
233#117C22×D11124yes—
234C2×C4⋊C4—1112no—
235C2×C4⋊C4—1124no—
236C2×C4⋊C4—1196no—
237C2×C4⋊C4C22×D1116yes—
238C2×C22⋊C4—1124no—
239C2×C22⋊C4C22×D1116yes—
240C2×C42C22×D1113yes—
241C2×C42C22×D1116yes—
242C2×C42C22×D11124yes—
243C2×C42C22×D1111yescharacteristic
244C2×C11—212no—
245C2×C11#349914yescomplemented
246C2×C11C24×D411yescharacteristic
247C2×C11C22×2−1+412yes—
248D11—48no—
249C24—114no—
250C24C23×D1113yes—
251#41—22384no—
252#41—22192no—
253#41C2×D44164yescomplemented
254C2×Q8—1148no—
255C2×Q8—1124no—
256C2×Q8—22128no—
257C2×Q8—2248no—
258C2×Q8—2224no—
259C2×Q8—22192no—
260C2×Q8C2×D4418yes—
261C2×Q8C23×D1114yes—
262C2×D4—1148no—
263C2×D4—1116no—
264C2×D4—118no—
265C2×D4—2248no—
266C2×D4—228no—
267C2×D4—2216no—
268C2×D4C2×D44124yes—
269C2×D4C23×D11112yes—
270C22×C4—224no—
271C22×C4—1148no—
272C22×C4—1112no—
273C22×C4—1148no—
274C22×C4—2248no—
275C22×C4—2248no—
276C22×C4C2×D44124yes—
277C22×C4C23×D11124yes—
278C22×C4C23×D1116yes—
279C22×C4C23×D11112yes—
280C22×C4C23×D1111yescharacteristic
281C22×C4C23×D1113yes—
282C22×C4C23×D1112yes—
283C4⋊C4—1148no—
284C4⋊C4—1196no—
285C4⋊C4C23×D11124yes—
286C22⋊C4—1196no—
287C22⋊C4C23×D11124yes—
288C42C23×D1114yes—
289C42C23×D11112yes—
290C42C23×D11124yes—
291C11C2×#349911yescharacteristic, complemented, Sylow
292C23—212no—
293C23—118no—
294C23—228no—
295C23—2216no—
296C23C22×D44112yes—
297C23C24×D1116yes—
298C23C24×D1111yescharacteristic
299Q8—2296no—
300Q8—2248no—
301Q8C22×D44116yes—
302D4—2296no—
303D4—2216no—
304D4—2232no—
305D4C22×D44148yes—
306C2×C4—212no—
307C2×C4—248no—
308C2×C4—1124no—
309C2×C4—2224no—
310C2×C4—2296no—
311C2×C4—2296no—
312C2×C4C22×D44112yes—
313C2×C4C22×D4414yes—
314C2×C4C22×D44148yes—
315C2×C4#6704318yescomplemented
316C2×C4C24×D11112yes—
317C2×C4C24×D1112yes—
318C2×C4C24×D1116yes—
319C2×C4C24×D1114yes—
320C22—212no—
321C22—224no—
322C22—228no—
323C22—2216no—
324C22—4416no—
325C22C23×D44112yes—
326C22C23×D4412yes—
327C22C2×#6704314yes—
328C22C25×D1111yescharacteristic
329C4—212no—
330C4—2224no—
331C4C23×D44112yes—
332C4C23×D4414yes—
333C4C2×#6704318yescomplemented
334C2—212no—
335C2—448no—
336C2#1308240114yesdirect product factor
337C2C24×D4411yescharacteristic
338C2C22×#6704312yes—
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C4×C11×#41C2
socleC23×C11C25
hypercenterC2×C4×#41D11
hypocenterC11C2×#3499
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. C22×#67043C2semidirect
2. #13082401C2direct (N × H)
3. C2×Q8×D44C2semidirect
4. C2×#10623086C2semidirect
5. C2×#10623057C2semidirect
6. C2×#10623008C2semidirect
7. C22×#66922C2semidirect
8. C2×C4×C11×#41C2semidirect
11. C2×#67043C22semidirect
16. C4×C11×#41C22semidirect
23. Q8×D44C22semidirect
24. #10623086C22semidirect
25. #10623057C22semidirect
28. #10623008C22semidirect
35. C2×#66922C22semidirect
36. C2×C11×#41D4semidirect
83. C11×#41C2×D4semidirect
130. C2×C4×#41D11semidirect
145. C2×C4×C112−1+4semidirect
179. C4×#41C2×D11semidirect
198. C4×C11C2×2−1+4semidirect
205. C2×#41D44semidirect
245. C2×C11#3499semidirect
253. #41C2×D44semidirect
291. C11C2×#3499semidirect
315. C2×C4#67043semidirect
333. C4C2×#67043semidirect
336. C2#13082401direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670432
#130824012
C2×Q8×D442
C2×#106230862
C2×#106230572
C2×#106230082
C22×#669222
C2×C4×C11×#412
C2×#349911