Finite Group Databasebeta

← C2×#13077178 #15617393

Subgroups — C2×#13077178 #15617393

Order 2816.

2830 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D11C212yesmaximal
2C22×#66925C211yesmaximal, characteristic
3#13077178C2116yesmaximal, direct product factor
4C2×#10622452C218yesmaximal, complemented
5C2×#10622537C211yesmaximal, characteristic, complemented
6C2×#10622731C212yesmaximal, complemented
7C2×C11×#423C211yesmaximal, characteristic, complemented
8C23×C4×D11C2211yescharacteristic
9C22×C11×M16C2212yes—
10C22×C42×C11C2211yescharacteristic
11C22×(C2×D11)⋊C4C412yes—
12C22×Dic11⋊C4C412yes—
13C22×C4×Dic11C2211yescharacteristic
14C22×#4318C2212yes—
15C2×M16×D11—216no—
16C2×M16×D11C22116yes—
17C22×#4313C2214yes—
18C22×C8×D11C2214yes—
19C2×#66925C418yes—
20C2×#66925C414yes—
21C2×#66925C2214yes—
22C2×#66925C2218yes—
23C11×#423C2218yescomplemented
24C2×C11×C4⋊C8C2214yescomplemented
25#10622731C22116yescomplemented
26C2×Dic11⋊C8C2218yescomplemented
27#10622537C2218yescomplemented
28C2×C4⋊(C11⋊C8)C2214yescomplemented
29#10622452C22164yescomplemented
30C24×D11C2×C411yescharacteristic
31C23×C4×C11C2×C412yes—
32C23×C4×C11C2311yescharacteristic
33C23×Dic11C2×C412yes—
34C23×Dic11C2×C411yescharacteristic
35C22×C4×D11C2×C412yes—
36C22×C4×D11C2×C414yes—
37C22×C4×D11D418yes—
38C22×C4×D11Q818yes—
39C22×C4×D11C2312yes—
40C22×C4×D11C2314yes—
41C2×C11×M16—28no—
42C2×C11×M16C2318yes—
43C22×C8×C11C2314yes—
44C2×C42×C11C2×C412yes—
45C2×C42×C11C2×C414yes—
46C2×C42×C11C2312yes—
47C2×C42×C11C2314yes—
48C2×(C2×D11)⋊C4C2×C418yes—
49C2×(C2×D11)⋊C4C2×C4116yes—
50C2×Dic11⋊C4C2×C418yes—
51C2×Dic11⋊C4C2×C4116yes—
52C2×C4×Dic11C2×C412yes—
53C2×C4×Dic11C2×C414yes—
54C2×C4×Dic11C2314yes—
55C2×C4×Dic11C2312yes—
56C2×#4318—28no—
57C2×#4318C2318yes—
58C22×C11⋊C8C2314yes—
59M16×D11—264no—
60C2×#4313—216no—
61C2×#4313C23116yes—
62C2×C8×D11—216no—
63C2×C8×D11C23116yes—
64#66925C2×C4116yes—
65#66925C2×C4132yes—
66#66925C23116yes—
67C11×C4⋊C8C23116yescomplemented
68Dic11⋊C8C23132yescomplemented
69C4⋊(C11⋊C8)C23116yescomplemented
70C2×#2905—111nomaximal, Sylow
71C24×C11C22×C411yescharacteristic
72C23×D11—44no—
73C23×D11C4⋊C418yes—
74C23×D11C22×C412yes—
75C23×D11C22×C414yes—
76C22×C4×C11—44no—
77C22×C4×C11C22×C414yes—
78C22×C4×C11C22×C418yes—
79C22×C4×C11C22×C412yes—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D414yes—
82C22×C4×C11C2×Q814yes—
83C22×C4×C11C2412yes—
84C22×C4×C11C2411yescharacteristic
85C22×Dic11—44no—
86C22×Dic11C4⋊C418yes—
87C22×Dic11C22×C414yes—
88C22×Dic11C22×C418yes—
89C22×Dic11C22×C414yes—
90C22×Dic11C22×C412yes—
91C2×C4×D11C4⋊C4116yes—
92C2×C4×D11C4⋊C4132yes—
93C2×C4×D11C22×C414yes—
94C2×C4×D11C22×C418yes—
95C2×C4×D11C2×D418yes—
96C2×C4×D11C2×D4116yes—
97C2×C4×D11C2×Q818yes—
98C2×C4×D11C2×Q8116yes—
99C2×C4×D11C2414yes—
100C11×M16—216no—
101C2×C8×C11—28no—
102C2×C8×C11C2418yes—
103C42×C11C22×C414yes—
104C42×C11C22×C418yes—
105C42×C11C2414yes—
106(C2×D11)⋊C4C22×C4132yes—
107Dic11⋊C4C22×C4132yes—
108C4×Dic11C22×C418yes—
109C4×Dic11C22×C414yes—
110C4×Dic11C2414yes—
111#4318—216no—
112C2×C11⋊C8—28no—
113C2×C11⋊C8C2418yes—
114#4313—232no—
115C8×D11—232no—
116C23×M16—112no—
117C22×#117—111no—
118#2905—1116no—
119C2×#424—118no—
120C2×#423—111no—
121C2×#423—112no—
122C2×#423D1111yescharacteristic, complemented
123C23×C11—24no—
124C23×C11C2×C4⋊C414yes—
125C23×C11C23×C412yes—
126C23×C11C23×C411yescharacteristic
127C22×D11—28no—
128C22×D11—416no—
129C22×D11—48no—
130C22×D11C2×C4⋊C418yes—
131C22×D11C2×C4⋊C4116yes—
132C22×D11C23×C414yes—
133C2×C4×C11—28no—
134C2×C4×C11—48no—
135C2×C4×C11C2×C4⋊C418yes—
136C2×C4×C11C2×C4⋊C414yes—
137C2×C4×C11C23×C418yes—
138C2×C4×C11C23×C412yes—
139C2×C4×C11C23×C411yescharacteristic
140C2×C4×C11C22×D412yes—
141C2×C4×C11C22×D414yes—
142C2×C4×C11C22×Q814yes—
143C2×C4×C11C22×Q812yes—
144C2×C4×C11C2511yescharacteristic
145C2×Dic11—28no—
146C2×Dic11—48no—
147C2×Dic11C2×C4⋊C4116yes—
148C2×Dic11C2×C4⋊C418yes—
149C2×Dic11C23×C418yes—
150C2×Dic11C23×C414yes—
151C4×D11C2×C4⋊C4116yes—
152C4×D11C2×C4⋊C4132yes—
153C4×D11C22×D418yes—
154C4×D11C22×Q818yes—
155C8×C11—28no—
156C11⋊C8—28no—
157C24×C4—111no—
158C22×M16—112no—
159C22×M16—1116no—
160C22×M16—114no—
161C22×M16—2216no—
162C22×M16C2×D1112yes—
163C23×C8—114no—
164C2×#117—114no—
165C2×#117—118no—
166C2×#117—114no—
167C2×#117—118no—
168C22×C4⋊C4—112no—
169C22×C22⋊C4—112no—
170C22×C42—111no—
171C22×C42C2×D1111yescharacteristic
172#424—1164no—
173#423—1116no—
174#423—118no—
175#423C2×D1118yescomplemented
176C2×C4⋊C8—118no—
177C2×C4⋊C8—114no—
178C2×C4⋊C8C2×D1114yescomplemented
179C22×C11—28no—
180C22×C11—24no—
181C22×C11C22×C4⋊C414yes—
182C22×C11C22×C4⋊C412yes—
183C22×C11#56814yes—
184C22×C11C24×C411yescharacteristic
185C2×D11—216no—
186C2×D11—28no—
187C2×D11—416no—
188C2×D11C22×C4⋊C418yes—
189C4×C11—28no—
190C4×C11C22×C4⋊C412yes—
191C4×C11C22×C4⋊C414yes—
192C4×C11C23×D411yescharacteristic
193C4×C11C23×Q811yescharacteristic
194Dic11—28no—
195Dic11C22×C4⋊C418yes—
196C25—111no—
197C23×C4—111no—
198C23×C4—112no—
199C23×C4—114no—
200C23×C4—118no—
201C23×C4—118no—
202C23×C4—114no—
203C23×C4—112no—
204C23×C4—112no—
205C23×C4C4×D1112yes—
206C23×C4C22×D1111yescharacteristic
207C2×M16—28no—
208C2×M16—118no—
209C2×M16—1116no—
210C2×M16—2216no—
211C2×M16—2264no—
212C2×M16—228no—
213C2×M16C22×D1118yes—
214C22×C8—114no—
215C22×C8—1116no—
216C22×C8—2216no—
217C22×C8C22×D1114yes—
218#117—1116no—
219#117—1132no—
220#117—1116no—
221C2×C4⋊C4—118no—
222C2×C4⋊C4—1116no—
223C2×C22⋊C4—118no—
224C2×C22⋊C4—1116no—
225C2×C42—112no—
226C2×C42—114no—
227C2×C42—114no—
228C2×C42—112no—
229C2×C42C4×D1112yes—
230C2×C42C4×D1114yes—
231C2×C42C22×D1114yes—
232C2×C42C22×D1112yes—
233C4⋊C8—1132no—
234C4⋊C8—1116no—
235C4⋊C8C22×D11116yescomplemented
236C2×C11—24no—
237C2×C11#290514yescomplemented
238C2×C11C23×C4⋊C411yescharacteristic
239C2×C11C2×#56812yes—
240D11—28no—
241C24—112no—
242C24—118no—
243C24—114no—
244C24—444no—
245C24C2×C4×D1111yescharacteristic
246C22×C4—44no—
247C22×C4—118no—
248C22×C4—114no—
249C22×C4—112no—
250C22×C4—1116no—
251C22×C4—1132no—
252C22×C4—118no—
253C22×C4—114no—
254C22×C4—118no—
255C22×C4—1116no—
256C22×C4—1116no—
257C22×C4—118no—
258C22×C4—114no—
259C22×C4—114no—
260C22×C4—118no—
261C22×C4—444no—
262C22×C4C2×C4×D1114yes—
263C22×C4C2×C4×D1118yes—
264C22×C4C2×C4×D1111yescharacteristic
265C22×C4C2×C4×D1112yes—
266C22×C4D4×D1114yes—
267C22×C4Q8×D1114yes—
268C22×C4C23×D1112yes—
269C22×C4C23×D1111yescharacteristic
270M16—216no—
271M16—2232no—
272M16—2216no—
273C2×C8—28no—
274C2×C8—118no—
275C2×C8—2232no—
276C2×C8—228no—
277C2×C8C23×D1118yes—
278C4⋊C4—1132no—
279C22⋊C4—1132no—
280C42—118no—
281C42—114no—
282C42—114no—
283C42C2×C4×D1118yes—
284C42C2×C4×D1114yes—
285C42C23×D1114yes—
286C11C2×#290511yescharacteristic, complemented, Sylow
287C23—24no—
288C23—118no—
289C23—114no—
290C23—1116no—
291C23—228no—
292C23—4416no—
293C23—448no—
294C23C4⋊C4×D1114yes—
295C23C22×C4×D1112yes—
296C23C22×C4×D1111yescharacteristic
297C2×C4—28no—
298C2×C4—48no—
299C2×C4—1116no—
300C2×C4—118no—
301C2×C4—114no—
302C2×C4—1116no—
303C2×C4—1132no—
304C2×C4—118no—
305C2×C4—118no—
306C2×C4—118no—
307C2×C4—228no—
308C2×C4—448no—
309C2×C4C4⋊C4×D1118yes—
310C2×C4C4⋊C4×D1114yes—
311C2×C4C22×C4×D1118yes—
312C2×C4C22×C4×D1112yes—
313C2×C4C22×C4×D1111yescharacteristic
314C2×C4C2×D4×D1112yes—
315C2×C4C2×D4×D1114yes—
316C2×C4C2×Q8×D1114yes—
317C2×C4C2×Q8×D1112yes—
318C2×C4C24×D1111yescharacteristic
319C8—28no—
320C8—228no—
321C22—28no—
322C22—24no—
323C22—118no—
324C22—2216no—
325C22—228no—
326C22—4416no—
327C22C2×C4⋊C4×D1114yes—
328C22C2×C4⋊C4×D1112yes—
329C22#1062327614yes—
330C22C23×C4×D1111yescharacteristic
331C4—28no—
332C4—118no—
333C4—228no—
334C4C2×C4⋊C4×D1114yes—
335C4C2×C4⋊C4×D1112yes—
336C4C22×D4×D1111yescharacteristic
337C4C22×Q8×D1111yescharacteristic
338C2—24no—
339C2—228no—
340C2#1307717814yesdirect product factor
341C2C22×C4⋊C4×D1111yescharacteristic
342C2C2×#1062327612yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#423C2
socleC23×C11C23×C4
prime radicalC24×D11C2×C4
cosocleC2×C4×C11C25
hypercenterC2×#423D11
hypocenterC11C2×#2905
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
3. #13077178C2direct (N × H)
4. C2×#10622452C2semidirect
5. C2×#10622537C2semidirect
6. C2×#10622731C2semidirect
7. C2×C11×#423C2semidirect
23. C11×#423C22semidirect
24. C2×C11×C4⋊C8C22semidirect
25. #10622731C22semidirect
26. C2×Dic11⋊C8C22semidirect
27. #10622537C22semidirect
28. C2×C4⋊(C11⋊C8)C22semidirect
29. #10622452C22semidirect
67. C11×C4⋊C8C23semidirect
68. Dic11⋊C8C23semidirect
69. C4⋊(C11⋊C8)C23semidirect
122. C2×#423D11semidirect
175. #423C2×D11semidirect
178. C2×C4⋊C8C2×D11semidirect
235. C4⋊C8C22×D11semidirect
237. C2×C11#2905semidirect
286. C11C2×#2905semidirect
340. C2#13077178direct (N × H)

Maximal subgroups

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

subgroupindex
C22×M16×D112
C22×#669252
#130771782
C2×#106224522
C2×#106225372
C2×#106227312
C2×C11×#4232
C2×#290511