Finite Group Databasebeta

← C2×#13077268 #15617520

Subgroups — C2×#13077268 #15617520

Order 2816.

2134 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
1C2×C4×#4339C211yesmaximal, characteristic
2#13077268C2116yesmaximal, direct product factor
3C2×#10622303C214yesmaximal, complemented
4C2×#10622318C214yesmaximal, complemented
5C2×#10622732C212yesmaximal, complemented
6C2×#10622742C212yesmaximal
7C22×#66867C211yesmaximal, characteristic, complemented
8C2×C4×C11×M16C211yesmaximal, characteristic, complemented
9C22×#4339C2211yescharacteristic
10C22×C11×M16C2212yes—
11C22×C42×C11C2211yescharacteristic
12C2×C4×C22⋊D11C414yes—
13C2×#66979C2211yescharacteristic
14C23×C11⋊C8C2212yes—
15C4×#4339C418yes—
16C4×#4339C2218yes—
17C2×C4×D44C412yes—
18C2×#66925C2212yes—
19C2×C42×D11C2212yes—
20C2×C4×Dic22C412yes—
21C4×C11×M16C2218yescomplemented
22C2×C11×#97C2212yes—
23C2×C4×C8×C11C2212yes—
24#10622742C22116yes—
25#10622732C22116yescomplemented
26C2×(C2×D11)⋊C8C2218yes—
27C2×Dic11⋊C8C2218yes—
28C2×#66867C2212yes—
29C2×#66867C2212yes—
30C2×#66867C2218yescomplemented
31#10622318C22132yescomplemented
32#10622303C22132yescomplemented
33C23×C4×C11C2×C412yes—
34C23×C4×C11C2311yescharacteristic
35C22×C22⋊D11C2×C412yes—
36C2×#4339—28no—
37C2×#4339C2×C414yes—
38C2×#4339C2314yes—
39C22×D44C2×C411yescharacteristic
40C22×C4×D11C2×C414yes—
41C22×C4×D11C2312yes—
42C22×Dic22C2×C411yescharacteristic
43C2×C11×M16—28no—
44C2×C11×M16C2318yes—
45C22×C8×C11C2314yes—
46C2×C42×C11C2×C412yes—
47C2×C42×C11C2×C414yes—
48C2×C42×C11C2311yescharacteristic
49C2×C42×C11C2311yescharacteristic
50C2×C42×C11C2314yes—
51C2×C22⋊Dic11C2×C412yes—
52C4×C22⋊D11C2×C4132yes—
53C2×(C2×D11)⋊C4C2×C414yes—
54#66979C2×C414yes—
55#66979C2314yes—
56C2×C4⋊Dic11C2×C412yes—
57C2×Dic11⋊C4C2×C414yes—
58C2×C4×Dic11C2×C414yes—
59C2×C4×Dic11C2312yes—
60C22×C11⋊C8—28no—
61C22×C11⋊C8C2314yes—
62C22×C11⋊C8C2318yes—
63C4×D44C2×C4116yes—
64#66925C2×C418yes—
65#66925C2318yes—
66C42×D11C2×C418yes—
67C42×D11C2318yes—
68C4×Dic22C2×C4116yes—
69C11×#97C2318yes—
70C4×C8×C11C2318yes—
71(C2×D11)⋊C8C23132yes—
72Dic11⋊C8C23132yes—
73#66867C2318yes—
74#66867C2318yes—
75C2×#2923—111nomaximal, Sylow
76C24×C11C22×C411yescharacteristic
77C23×D11C22×C412yes—
78C22×C4×C11—44no—
79C22×C4×C11C22×C412yes—
80C22×C4×C11C22×C412yes—
81C22×C4×C11C22×C418yes—
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C22×C412yes—
84C22×C4×C11#4118yes—
85C22×C4×C11C2412yes—
86C22×C4×C11C2411yescharacteristic
87C2×C22⋊D11—28no—
88C2×C22⋊D11C22×C418yes—
89C22×Dic11C22×C412yes—
90C22×Dic11C22×C414yes—
91#4339—216no—
92#4339—216no—
93C2×D44—24no—
94C2×D44C22×C414yes—
95C2×C4×D11—28no—
96C2×C4×D11—48no—
97C2×C4×D11C22×C414yes—
98C2×C4×D11C22×C4116yes—
99C2×C4×D11C2414yes—
100C2×Dic22—24no—
101C2×Dic22C22×C414yes—
102C11×M16—216no—
103C2×C8×C11—28no—
104C2×C8×C11C2418yes—
105C42×C11C22×C418yes—
106C42×C11C22×C412yes—
107C42×C11C22×C412yes—
108C42×C11C2412yes—
109C42×C11C2412yes—
110C22⋊Dic11C22×C418yes—
111(C2×D11)⋊C4C22×C4116yes—
112C4⋊Dic11C22×C418yes—
113Dic11⋊C4C22×C4116yes—
114C4×Dic11C22×C4116yes—
115C4×Dic11C22×C414yes—
116C4×Dic11C2414yes—
117C2×C11⋊C8—28no—
118C2×C11⋊C8—216no—
119C2×C11⋊C8C2418yes—
120C2×C4×#41—111no—
121#2923—1116no—
122C2×#433—114no—
123C2×#432—114no—
124C2×#424—112no—
125C2×#408—112no—
126C2×C4×M16D1111yescharacteristic, complemented
127C22×#97—111no—
128C23×C11—24no—
129C23×C11#11714yes—
130C23×C11C23×C412yes—
131C23×C11C23×C411yescharacteristic
132C22×D11—24no—
133C22×D11—28no—
134C22×D11C23×C414yes—
135C2×C4×C11—24no—
136C2×C4×C11—24no—
137C2×C4×C11—48no—
138C2×C4×C11#11714yes—
139C2×C4×C11#11718yes—
140C2×C4×C11C23×C414yes—
141C2×C4×C11C23×C414yes—
142C2×C4×C11C23×C411yescharacteristic
143C2×C4×C11C23×C412yes—
144C2×C4×C11C2×#4114yes—
145C2×C4×C11C2×#4118yes—
146C2×C4×C11C2511yescharacteristic
147C22⋊D11—216no—
148C2×Dic11—24no—
149C2×Dic11—28no—
150C2×Dic11C23×C414yes—
151C2×Dic11C23×C418yes—
152D44—28no—
153C4×D11—28no—
154C4×D11—28no—
155C4×D11—416no—
156Dic22—28no—
157C8×C11—28no—
158C11⋊C8—28no—
159C22×#41—111no—
160C22×M16C2×D1112yes—
161C23×C8—112no—
162C4×#41—118no—
163C4×#41—118no—
164C2×C4×Q8—112no—
165C2×C4×D4—114no—
166C2×C4×D4—112no—
167C2×#117—111no—
168C2×#117—112no—
169C22×C42—112no—
170C22×C42C2×D1111yescharacteristic
171#433—1132no—
172#432—1132no—
173#424—1116no—
174C2×C4⋊C8—118no—
175#408—1116no—
176C2×C22⋊C8—118no—
177C4×M16C2×D1118yescomplemented
178C2×#97—112no—
179C2×#97—112no—
180C2×#97—118no—
181C2×#97C2×D1112yes—
182C2×C4×C8C2×D1112yes—
183C22×C11—28no—
184C22×C11—24no—
185C22×C11C2×#11714yes—
186C22×C11C2×#11712yes—
187C22×C11#56814yes—
188C22×C11C24×C411yescharacteristic
189C2×D11—24no—
190C2×D11—28no—
191C2×D11—48no—
192C4×C11—24no—
193C4×C11—24no—
194C4×C11C2×#11714yes—
195C4×C11C2×#11712yes—
196C4×C11C22×#4112yes—
197Dic11—24no—
198Dic11—28no—
199C2×#41—114no—
200C2×#41—114no—
201C2×#41—228no—
202C22×Q8—111no—
203C22×D4—112no—
204C22×D4—111no—
205C23×C4—112no—
206C23×C4—114no—
207C23×C4C4×D1112yes—
208C23×C4C22×D1111yescharacteristic
209C2×M16—28no—
210C2×M16C22×D1118yes—
211C22×C8—118no—
212C22×C8—114no—
213C22×C8—228no—
214C22×C8C22×D1114yes—
215C4×Q8—1116no—
216C4×D4—1132no—
217C4×D4—1116no—
218#117—114no—
219#117—114no—
220#117—118no—
221#117—118no—
222C2×C4⋊C4—114no—
223C2×C4⋊C4—112no—
224C2×C22⋊C4—112no—
225C2×C22⋊C4—114no—
226C2×C42—114no—
227C2×C42—112no—
228C2×C42—118no—
229C2×C42—118no—
230C2×C42C4×D1112yes—
231C2×C42C4×D1114yes—
232C2×C42C22×D1114yes—
233C2×C42C22×D1111yescharacteristic
234C2×C42C22×D1111yescharacteristic
235C4⋊C8—1132no—
236C22⋊C8—1132no—
237#97—118no—
238#97—118no—
239#97C22×D1118yes—
240C4×C8C22×D1118yes—
241C2×C11—24no—
242C2×C11#292314yescomplemented
243C2×C11C22×#11711yescharacteristic
244C2×C11C2×#56812yes—
245D11—44no—
246C24—112no—
247C24C2×C4×D1111yescharacteristic
248#41—2216no—
249#41—2216no—
250C2×Q8—114no—
251C2×Q8—224no—
252C2×D4—118no—
253C2×D4—114no—
254C2×D4—228no—
255C2×D4—224no—
256C22×C4—44no—
257C22×C4—114no—
258C22×C4—112no—
259C22×C4—114no—
260C22×C4—114no—
261C22×C4—1116no—
262C22×C4—228no—
263C22×C4—448no—
264C22×C4C2×C4×D1112yes—
265C22×C4C2×C4×D1112yes—
266C22×C4C2×C4×D1118yes—
267C22×C4C2×C4×D1111yescharacteristic
268C22×C4C2×C4×D1112yes—
269C22×C4#433918yes—
270C22×C4C23×D1112yes—
271C22×C4C23×D1111yescharacteristic
272M16—216no—
273C2×C8—28no—
274C2×C8—118no—
275C2×C8—228no—
276C2×C8—2216no—
277C2×C8C23×D1118yes—
278C4⋊C4—1116no—
279C4⋊C4—118no—
280C22⋊C4—118no—
281C22⋊C4—1116no—
282C42—114no—
283C42—1116no—
284C42—114no—
285C42C2×C4×D1112yes—
286C42C2×C4×D1112yes—
287C42C2×C4×D1118yes—
288C42C23×D1112yes—
289C42C23×D1112yes—
290C11C2×#292311yescharacteristic, complemented, Sylow
291C23—24no—
292C23—114no—
293C23—224no—
294C23—228no—
295C23#6692514yes—
296C23C22×C4×D1112yes—
297C23C22×C4×D1111yescharacteristic
298Q8—228no—
299D4—2216no—
300D4—228no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—48no—
304C2×C4—118no—
305C2×C4—114no—
306C2×C4—224no—
307C2×C4—228no—
308C2×C4—228no—
309C2×C4—228no—
310C2×C4—4416no—
311C2×C4#6692514yes—
312C2×C4#6692518yes—
313C2×C4C22×C4×D1114yes—
314C2×C4C22×C4×D1114yes—
315C2×C4C22×C4×D1111yescharacteristic
316C2×C4C22×C4×D1112yes—
317C2×C4C2×#433914yes—
318C2×C4C2×#433918yes—
319C2×C4C24×D1111yescharacteristic
320C8—28no—
321C8—228no—
322C22—28no—
323C22—24no—
324C22—224no—
325C22—228no—
326C22—448no—
327C22C2×#6692514yes—
328C22C2×#6692512yes—
329C22#1062327614yes—
330C22C23×C4×D1111yescharacteristic
331C4—24no—
332C4—24no—
333C4—224no—
334C4—228no—
335C4C2×#6692512yes—
336C4C2×#6692514yes—
337C4C22×#433912yes—
338C2—24no—
339C2—444no—
340C2#1307726814yesdirect product factor
341C2C22×#6692511yescharacteristic
342C2C2×#1062327612yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C4×C11×M16C2
socleC23×C11C23×C4
prime radicalC22×#4339C22
cosocleC2×C4×C11C25
hypercenterC2×C4×M16D11
hypocenterC11C2×#2923
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C4×M16

Complements

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

NH ≅ G/Ntype
2. #13077268C2direct (N × H)
3. C2×#10622303C2semidirect
4. C2×#10622318C2semidirect
5. C2×#10622732C2semidirect
7. C22×#66867C2semidirect
8. C2×C4×C11×M16C2semidirect
21. C4×C11×M16C22semidirect
25. #10622732C22semidirect
30. C2×#66867C22semidirect
31. #10622318C22semidirect
32. #10622303C22semidirect
126. C2×C4×M16D11semidirect
177. C4×M16C2×D11semidirect
242. C2×C11#2923semidirect
290. C11C2×#2923semidirect
340. C2#13077268direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#43392
#130772682
C2×#106223032
C2×#106223182
C2×#106227322
C2×#106227422
C22×#668672
C2×C4×C11×M162
C2×#292311