Finite Group Databasebeta

← C2×#13077726 #15618819

Subgroups — C2×#13077726 #15618819

Order 2816.

2434 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4343C211yesmaximal, characteristic
2#13077726C2116yesmaximal, direct product factor
3C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
4C2×C8×D44C213yesmaximal, complemented
5C2×#10622447C213yesmaximal, complemented
6C2×#10622298C213yesmaximal, complemented
7C2×D11×C4⋊C8C213yesmaximal, complemented
8C2×C8×Q8×C11C211yesmaximal, characteristic, complemented
9C22×#4343C411yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C2×Q8×Dic11C411yescharacteristic
12C22×C8×D11C2216yes—
13C4×#4343C418yes—
14C4×#4343C2218yes—
15C2×#66946C413yes—
16C2×#66945C413yes—
17C2×C4×D44C2213yes—
18C2×C42×D11C2213yes—
19C8×Q8×C11C2218yescomplemented
20C2×C11×C4⋊C8C2213yes—
21C2×C4×C8×C11C2213yes—
22C2×(C2×D11)⋊C8C2213yes—
23C2×(C2×D11)⋊C8C2213yes—
24C2×Dic11⋊C8C2213yes—
25C2×Dic11⋊C8C2211yescharacteristic
26Q8×C11⋊C8C2218yescomplemented
27C2×C4⋊(C11⋊C8)C2213yes—
28C2×C4×C11⋊C8C2213yes—
29#10622447C22124yescomplemented
30D11×C4⋊C8C22124yescomplemented
31C8×D44C22124yescomplemented
32#10622298C22124yescomplemented
33C22×Q8×C11C2×C411yescharacteristic
34C2×#4343C8116yescomplemented
35C2×#4343C2×C418yes—
36C22×D44C2×C413yes—
37C22×C4×D11C2×C413yes—
38C22×C4×D11C2×C413yes—
39C22×C4×D11C2313yes—
40C22×C8×C11C2311yescharacteristic
41C22×C8×C11C2313yes—
42C4×Q8×C11C2×C414yes—
43C4×Q8×C11C2314yes—
44C2×C11×C4⋊C4C2×C413yes—
45C2×C42×C11C2313yes—
46Q8×Dic11C2×C418yes—
47C2×(C2×D11)⋊C4C2×C416yes—
48C2×C4⋊Dic11C2×C413yes—
49C2×C4×Dic11C2×C413yes—
50C2×C4×Dic11C2×C413yes—
51C2×C4×Dic11C2311yescharacteristic
52C22×C11⋊C8C2311yescharacteristic
53C22×C11⋊C8C2313yes—
54C2×C8×D11—412no—
55C2×C8×D11C23124yes—
56#66946C2×C4124yes—
57#66945C2×C4124yes—
58C4×D44C2×C4112yes—
59C4×D44C23112yes—
60C42×D11C2×C4112yes—
61C42×D11C23112yes—
62C11×C4⋊C8C23112yes—
63C4×C8×C11C23112yes—
64(C2×D11)⋊C8C23112yes—
65(C2×D11)⋊C8C23112yes—
66Dic11⋊C8C2314yes—
67Dic11⋊C8C23112yes—
68C4⋊(C11⋊C8)C23112yes—
69C4×C11⋊C8C23112yes—
70C2×#2988—111nomaximal, Sylow
71C23×D11C22×C413yes—
72C2×Q8×C11C2×C818yescomplemented
73C2×Q8×C11C22×C414yes—
74C22×C4×C11C22×C413yes—
75C22×C4×C11C22×C413yes—
76C22×C4×C11C2411yescharacteristic
77C22×Dic11C22×C411yescharacteristic
78C22×Dic11C22×C413yes—
79C22×Dic11C22×C411yescharacteristic
80#4343C2×C8164yescomplemented
81C2×D44C2×C8124yescomplemented
82C2×D44C22×C4112yes—
83C2×C4×D11—26no—
84C2×C4×D11—26no—
85C2×C4×D11—46no—
86C2×C4×D11C2×C8124yescomplemented
87C2×C4×D11C22×C416yes—
88C2×C4×D11C22×C4112yes—
89C2×C4×D11C22×C4112yes—
90C2×C4×D11C2416yes—
91C2×C8×C11—26no—
92C2×C8×C11—22no—
93C2×C8×C11C2412yes—
94C2×C8×C11C2416yes—
95C11×C4⋊C4C22×C4112yes—
96C42×C11C22×C416yes—
97C42×C11C2416yes—
98(C2×D11)⋊C4C22×C4124yes—
99C4⋊Dic11C22×C4112yes—
100C4×Dic11C22×C412yes—
101C4×Dic11C22×C4112yes—
102C4×Dic11C22×C4112yes—
103C4×Dic11C2412yes—
104C2×C11⋊C8—26no—
105C2×C11⋊C8—22no—
106C2×C11⋊C8C2412yes—
107C2×C11⋊C8C2416yes—
108C8×D11—424no—
109C2×C4×#41—111no—
110#2988—1116no—
111C2×C8×Q8—111no—
112C2×C8×Q8D1111yescharacteristic, complemented
113C2×C8×D4—113no—
114C2×C8×D4—113no—
115C2×#431—113no—
116C22×C4⋊C8—113no—
117C23×C11C23×C411yescharacteristic
118C22×D11—26no—
119C22×D11—26no—
120C22×D11C22×C8112yes—
121C22×D11C23×C416yes—
122Q8×C11C22×C8116yescomplemented
123C2×C4×C11—26no—
124C2×C4×C11C22×C8112yes—
125C2×C4×C11C23×C416yes—
126C2×C4×C11C23×C411yescharacteristic
127C2×C4×C11C23×C416yes—
128C2×C4×C11H(5,𝔽2)12yes—
129C2×C4×C112−1+412yes—
130C2×C4×C11C2511yescharacteristic
131C2×Dic11—26no—
132C2×Dic11—22no—
133C2×Dic11C22×C814yes—
134C2×Dic11C23×C412yes—
135C2×Dic11C23×C416yes—
136C2×Dic11C23×C412yes—
137D44C22×C8148yescomplemented
138C4×D11—212no—
139C4×D11—26no—
140C4×D11—26no—
141C4×D11—412no—
142C4×D11C22×C8148yescomplemented
143C8×C11—26no—
144C8×C11—22no—
145C11⋊C8—26no—
146C11⋊C8—22no—
147C22×#41—111no—
148C23×C8—116no—
149C4×#41—118no—
150C4×#41—118no—
151C2×C4×Q8—111no—
152C2×C4×Q8C2×D1111yescharacteristic
153C2×C4×D4—113no—
154C2×C4×D4—113no—
155C2×#117—113no—
156C22×C42—113no—
157C8×Q8—118no—
158C8×Q8C2×D1118yescomplemented
159C8×D4—1124no—
160C8×D4—1124no—
161#431—1124no—
162C2×C4⋊C8—113no—
163C2×C4⋊C8—111no—
164C2×C4⋊C8—113no—
165C2×C4⋊C8—1124no—
166C2×C4⋊C8C2×D1113yes—
167C2×C22⋊C8—113no—
168C2×C22⋊C8—113no—
169C2×C4×C8—113no—
170C2×C4×C8C2×D1113yes—
171C22×C11#52012yes—
172C22×C11C23×C812yes—
173C22×C11#56812yes—
174C22×C11C24×C411yescharacteristic
175C2×D11—26no—
176C2×D11—224no—
177C2×D11—26no—
178C2×D11C23×C8112yes—
179C4×C11—26no—
180C4×C11#52012yes—
181C4×C11C23×C8112yes—
182C4×C11C2×H(5,𝔽2)11yescharacteristic
183C4×C11C2×2−1+411yescharacteristic
184Dic11—26no—
185Dic11—22no—
186Dic11C23×C814yes—
187C2×#41—1116no—
188C2×#41—118no—
189C22×Q8C4×D1111yescharacteristic
190C22×D4—113no—
191C23×C4—113no—
192C23×C4—113no—
193C23×C4—113no—
194C22×C8—113no—
195C22×C8—111no—
196C22×C8—1124no—
197C22×C8—4412no—
198C22×C8C22×D1113yes—
199C22×C8C22×D1111yescharacteristic
200C4×Q8—118no—
201C4×Q8C4×D1114yes—
202C4×Q8C22×D1114yes—
203C4×D4—1124no—
204C4×D4—1112no—
205C4×D4—1112no—
206#117—1124no—
207C2×C4⋊C4—113no—
208C2×C4⋊C4C4×D1113yes—
209C2×C22⋊C4—116no—
210C2×C42—113no—
211C2×C42—113no—
212C2×C42—111no—
213C2×C42—1112no—
214C2×C42—1112no—
215C2×C42C22×D1113yes—
216C4⋊C8—1112no—
217C4⋊C8—114no—
218C4⋊C8—1112no—
219C4⋊C8C22×D11112yes—
220C22⋊C8—1112no—
221C22⋊C8—1112no—
222C4×C8—1112no—
223C4×C8C22×D11112yes—
224C2×C11#298814yescomplemented
225C2×C11C2×#52011yescharacteristic
226C2×C11C24×C811yescharacteristic
227C2×C11C2×#56811yescharacteristic
228D11—212no—
229C24—113no—
230#41—1164no—
231C2×Q8C8×D1118yescomplemented
232C2×Q8C2×C4×D1114yes—
233C2×D4—1124no—
234C2×D4—1112no—
235C22×C4—111no—
236C22×C4—1124no—
237C22×C4—1112no—
238C22×C4—111no—
239C22×C4—113no—
240C22×C4—116no—
241C22×C4—116no—
242C22×C4—1112no—
243C22×C4—226no—
244C22×C4—226no—
245C22×C4—446no—
246C22×C4C2×C4×D1113yes—
247C22×C4C2×C4×D1113yes—
248C22×C4C23×D1111yescharacteristic
249C2×C8—22no—
250C2×C8—26no—
251C2×C8—112no—
252C2×C8—116no—
253C2×C8—222no—
254C2×C8—226no—
255C2×C8—4424no—
256C2×C8C23×D1112yes—
257C2×C8C23×D1116yes—
258C4⋊C4—1112no—
259C4⋊C4C2×C4×D11112yes—
260C22⋊C4—1124no—
261C42—112no—
262C42—1112no—
263C42—1112no—
264C42—112no—
265C42C2×C4×D1116yes—
266C42C23×D1116yes—
267C11C2×#298811yescharacteristic, complemented, Sylow
268C23—1112no—
269C23—116no—
270C23—226no—
271C23—226no—
272C23C22×C4×D1111yescharacteristic
273Q8C2×C8×D11116yescomplemented
274D4—1148no—
275C2×C4—26no—
276C2×C4—114no—
277C2×C4—112no—
278C2×C4—1148no—
279C2×C4—112no—
280C2×C4—116no—
281C2×C4—222no—
282C2×C4—226no—
283C2×C4—2212no—
284C2×C4—226no—
285C2×C4—226no—
286C2×C4—4412no—
287C2×C4C2×C8×D11112yes—
288C2×C4C22×C4×D1116yes—
289C2×C4C22×C4×D1116yes—
290C2×C4C22×C4×D1111yescharacteristic
291C2×C4#6704012yes—
292C2×C4#6704212yes—
293C2×C4C24×D1111yescharacteristic
294C8—22no—
295C8—26no—
296C8—222no—
297C8—226no—
298C22—1112no—
299C22—226no—
300C22—226no—
301C22—2224no—
302C22#1062310512yes—
303C22C22×C8×D1112yes—
304C22#1062328112yes—
305C22C23×C4×D1111yescharacteristic
306C4—26no—
307C4—114no—
308C4—222no—
309C4—226no—
310C4#1062310512yes—
311C4C22×C8×D11112yes—
312C4C2×#6704011yescharacteristic
313C4C2×#6704211yescharacteristic
314C2—2212no—
315C2#1307772614yesdirect product factor
316C2C2×#1062310511yescharacteristic
317C2C23×C8×D1111yescharacteristic
318C2C2×#1062328111yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutatorC2×C11C24×C8
FrattiniC2×C4C24×D11
FittingC2×C8×Q8×C11C2
socleC23×C11C23×C4
prime radicalC22×#4343C4
cosocleC2×C4×C11C25
hypercenterC2×C8×Q8D11
hypocenterC11C2×#2988
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
2. #13077726C2direct (N × H)
3. C2×Q8×C11⋊C8C2semidirect
4. C2×C8×D44C2semidirect
5. C2×#10622447C2semidirect
6. C2×#10622298C2semidirect
7. C2×D11×C4⋊C8C2semidirect
8. C2×C8×Q8×C11C2semidirect
19. C8×Q8×C11C22semidirect
26. Q8×C11⋊C8C22semidirect
29. #10622447C22semidirect
30. D11×C4⋊C8C22semidirect
31. C8×D44C22semidirect
32. #10622298C22semidirect
34. C2×#4343C8semidirect
72. C2×Q8×C11C2×C8semidirect
80. #4343C2×C8semidirect
81. C2×D44C2×C8semidirect
86. C2×C4×D11C2×C8semidirect
112. C2×C8×Q8D11semidirect
122. Q8×C11C22×C8semidirect
137. D44C22×C8semidirect
142. C4×D11C22×C8semidirect
158. C8×Q8C2×D11semidirect
224. C2×C11#2988semidirect
231. C2×Q8C8×D11semidirect
267. C11C2×#2988semidirect
273. Q8C2×C8×D11semidirect
315. C2#13077726direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#43432
#130777262
C2×Q8×C11⋊C82
C2×C8×D442
C2×#106224472
C2×#106222982
C2×D11×C4⋊C82
C2×C8×Q8×C112
C2×#298811