Finite Group Databasebeta

← C2×#13081598 #15634675

Subgroups — C2×#13081598 #15634675

Order 2816.

2238 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
1C2×#10623101C211yesmaximal, characteristic, complemented
2C2×#10623108C211yesmaximal, characteristic
3#13081598C2116yesmaximal, direct product factor
4C2×#10622306C213yesmaximal, complemented
5C2×#10622461C213yesmaximal, complemented
6C2×#10622454C213yesmaximal, complemented
7C2×C4×#4314C213yesmaximal, complemented
8C2×C8×Q8×C11C211yesmaximal, characteristic, complemented
9C22×#4343—21no—
10C2×C4×Q8×C11C2211yescharacteristic
11C2×Q8×Dic11—21no—
12C22×#4314C2213yes—
13C22×#4314C2216yes—
14#10623108—24no—
15#10623108C2218yes—
16#10623101—24no—
17#10623101C2218yescomplemented
18C2×#66948—23no—
19C2×#66943—23no—
20C2×#66927C2213yes—
21C2×C4×D44C2213yes—
22C2×#66922C2213yes—
23C2×C4×Dic22C2213yes—
24C8×Q8×C11C2218yescomplemented
25C2×C11×C4⋊C8C2213yes—
26C2×C4×C8×C11C2213yes—
27C2×#66885C2213yes—
28C2×#66881C2211yescharacteristic
29C2×#66880C2213yes—
30#10622461C22124yescomplemented
31#10622454C22124yescomplemented
32#10622306C22124yescomplemented
33C4×#4314C22124yescomplemented
34C22×Q8×C11D411yescharacteristic
35C2×#4343—28no—
36C2×#4343—48no—
37C22×D44—23no—
38C22×D44—23no—
39C22×D44C2313yes—
40C22×C4×D11—23no—
41C22×Dic22C2313yes—
42C22×C8×C11C2313yes—
43C22×C8×C11C2311yescharacteristic
44C4×Q8×C11D414yes—
45C4×Q8×C11C2314yes—
46C2×C11×C4⋊C4D413yes—
47C2×C42×C11C2313yes—
48Q8×Dic11—28no—
49C2×(C2×D11)⋊C4—23no—
50C2×C4⋊Dic11—23no—
51C2×C4⋊Dic11—23no—
52C2×C4⋊Dic11C2311yescharacteristic
53C2×C4⋊Dic11C2311yescharacteristic
54C2×Dic11⋊C4—23no—
55C2×C4×Dic11—23no—
56C2×#4314—212no—
57C2×#4314—412no—
58C2×#4314C23112yes—
59C2×#4314C23124yes—
60#66948—224no—
61#66943—224no—
62#66927—26no—
63#66927C23112yes—
64C4×D44—26no—
65C4×D44C23112yes—
66#66922—26no—
67#66922C23112yes—
68C4×Dic22—26no—
69C4×Dic22C23112yes—
70C11×C4⋊C8C23112yes—
71C4×C8×C11C23112yes—
72#66885C23112yes—
73#66881C2314yes—
74#66880C23112yes—
75C2×#3392—111nomaximal, Sylow
76C23×D11—23no—
77C2×Q8×C11SD1618yescomplemented
78C2×Q8×C11C2×D414yes—
79C22×C4×C11C2×D413yes—
80C22×C4×C11C2×D413yes—
81C22×C4×C11C2411yescharacteristic
82C22×Dic11—21no—
83C22×Dic11—23no—
84C22×Dic11—21no—
85#4343—432no—
86C2×D44—23no—
87C2×D44—212no—
88C2×D44—212no—
89C2×D44—26no—
90C2×D44—26no—
91C2×D44—412no—
92C2×D44—86no—
93C2×D44C2416yes—
94C2×C4×D11—212no—
95C2×C4×D11—412no—
96C2×Dic22—23no—
97C2×Dic22—26no—
98C2×Dic22—26no—
99C2×Dic22C2416yes—
100C2×C8×C11—26no—
101C2×C8×C11#4114yescomplemented
102C2×C8×C11C2416yes—
103C2×C8×C11C2412yes—
104C11×C4⋊C4C2×D4112yes—
105C42×C11C2×D416yes—
106C42×C11C2416yes—
107(C2×D11)⋊C4—212no—
108C4⋊Dic11—21no—
109C4⋊Dic11—212no—
110C4⋊Dic11—212no—
111C4⋊Dic11—21no—
112C4⋊Dic11C2412yes—
113C4⋊Dic11C2412yes—
114Dic11⋊C4—212no—
115C4×Dic11—212no—
116#4314—224no—
117#4314—424no—
118C2×#557—111no—
119C2×#550—111no—
120#3392—1116no—
121C2×#492—113no—
122C2×#460—113no—
123C2×#461—113no—
124C2×C8×Q8D1111yescharacteristic, complemented
125C2×C4×SD16—113no—
126C23×C11C22×D411yescharacteristic
127C22×D11—26no—
128C22×D11—46no—
129C22×D11—46no—
130C22×D11—46no—
131Q8×C11C2×SD16116yescomplemented
132C2×C4×C11—26no—
133C2×C4×C11C2×SD16112yes—
134C2×C4×C11C22×D416yes—
135C2×C4×C11C22×D411yescharacteristic
136C2×C4×C11C22×D416yes—
137C2×C4×C11C2×#4112yes—
138C2×C4×C11H(5,𝔽2)12yes—
139C2×C4×C11C2511yescharacteristic
140C2×Dic11—22no—
141C2×Dic11—26no—
142C2×Dic11—22no—
143C2×Dic11—46no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146D44—26no—
147D44—26no—
148D44—46no—
149D44—424no—
150D44—812no—
151C4×D11—424no—
152Dic22—26no—
153Dic22—26no—
154Dic22—46no—
155C8×C11—26no—
156C8×C11C2×#4114yescomplemented
157C22×#41—221no—
158C22×SD16—113no—
159C22×SD16—116no—
160#557—118no—
161#557—224no—
162#550—118no—
163#550—224no—
164C2×C4⋊Q8—113no—
165C2×#127—113no—
166C2×#125—223no—
167C2×#121—223no—
168C2×C4×Q8—113no—
169C2×C4×Q8—221no—
170C2×C4×Q8C2×D1111yescharacteristic
171C2×C4×D4—113no—
172#492—1124no—
173#461—1124no—
174#460—1124no—
175C8×Q8C2×D1118yescomplemented
176C4×SD16—1124no—
177C2×#106—111no—
178C2×C4⋊C8C2×D1113yes—
179C2×#103—113no—
180C2×#102—113no—
181C2×C4×C8C2×D1113yes—
182C22×C11#55012yes—
183C22×C11C22×SD1612yes—
184C22×C11#57712yes—
185C22×C11C23×D411yescharacteristic
186C2×D11—46no—
187C2×D11—46no—
188C2×D11—46no—
189C2×D11—812no—
190C4×C11—26no—
191C4×C11#55012yes—
192C4×C11C22×SD16112yes—
193C4×C11C22×#4111yescharacteristic
194C4×C11C2×H(5,𝔽2)11yescharacteristic
195Dic11—46no—
196Dic11—42no—
197Dic11—42no—
198C2×#41—228no—
199C2×#41—448no—
200C22×Q8—113no—
201C22×Q8D4411yescharacteristic
202C22×D4—113no—
203C22×D4—223no—
204C22×D4—223no—
205C23×C4—223no—
206C2×SD16—1112no—
207C2×SD16—1124no—
208C2×SD16—2212no—
209C2×SD16—4412no—
210C22×C8C22×D1113yes—
211C22×C8C22×D1111yescharacteristic
212C4⋊Q8—1112no—
213C4⋊Q8—226no—
214#127—1112no—
215#127—226no—
216#125—2224no—
217#121—2224no—
218C4×Q8—1112no—
219C4×Q8—228no—
220C4×Q8—226no—
221C4×Q8D4414yes—
222C4×Q8C22×D1114yes—
223C4×D4—1112no—
224C4×D4—226no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—111no—
227C2×C4⋊C4—223no—
228C2×C4⋊C4—223no—
229C2×C4⋊C4—223no—
230C2×C4⋊C4D4413yes—
231C2×C22⋊C4—223no—
232C2×C42—223no—
233C2×C42C22×D1113yes—
234#106—114no—
235C4⋊C8C22×D11112yes—
236#103—1112no—
237#102—1112no—
238C4×C8C22×D11112yes—
239C2×C11#339214yescomplemented
240C2×C11C2×#55011yescharacteristic
241C2×C11C23×SD1611yescharacteristic
242C2×C11C2×#57711yescharacteristic
243D11—86no—
244C24—223no—
245#41—4432no—
246C2×Q8—116no—
247C2×Q8—223no—
248C2×Q8—226no—
249C2×Q8—226no—
250C2×Q8#431418yescomplemented
251C2×Q8C2×D4414yes—
252C2×D4—116no—
253C2×D4—223no—
254C2×D4—2212no—
255C2×D4—2212no—
256C2×D4—226no—
257C2×D4—226no—
258C2×D4—4412no—
259C2×D4—886no—
260C22×C4—221no—
261C22×C4—223no—
262C22×C4—221no—
263C22×C4—2212no—
264C22×C4—4412no—
265C22×C4C2×D4413yes—
266C22×C4C2×D4413yes—
267C22×C4C23×D1111yescharacteristic
268SD16—2224no—
269SD16—4424no—
270C2×C8—26no—
271C2×C8#434314yescomplemented
272C2×C8C23×D1116yes—
273C2×C8C23×D1112yes—
274C4⋊C4—112no—
275C4⋊C4—112no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—2212no—
279C4⋊C4—2212no—
280C4⋊C4—2212no—
281C4⋊C4C2×D44112yes—
282C22⋊C4—2212no—
283C42—2212no—
284C42C2×D4416yes—
285C42C23×D1116yes—
286C11C2×#339211yescharacteristic, complemented, Sylow
287C23—226no—
288C23—446no—
289C23—446no—
290C23—446no—
291C23C22×D4411yescharacteristic
292Q8—226no—
293Q8—226no—
294Q8—446no—
295Q8C2×#4314116yescomplemented
296D4—226no—
297D4—226no—
298D4—4424no—
299D4—446no—
300D4—8812no—
301C2×C4—26no—
302C2×C4—222no—
303C2×C4—226no—
304C2×C4—222no—
305C2×C4—442no—
306C2×C4—442no—
307C2×C4—446no—
308C2×C4—4424no—
309C2×C4C2×#4314112yes—
310C2×C4C22×D4416yes—
311C2×C4C22×D4416yes—
312C2×C4C22×D4411yescharacteristic
313C2×C4C2×#434312yes—
314C2×C4#6704212yes—
315C2×C4C24×D1111yescharacteristic
316C8—26no—
317C8C2×#434314yescomplemented
318C22—446no—
319C22—446no—
320C22—446no—
321C22—8812no—
322C22#1062310812yes—
323C22C22×#431412yes—
324C22#1062328212yes—
325C22C23×D4411yescharacteristic
326C4—26no—
327C4—442no—
328C4—446no—
329C4—442no—
330C4#1062310812yes—
331C4C22×#4314112yes—
332C4C22×#434311yescharacteristic
333C4C2×#6704211yescharacteristic
334C2—886no—
335C2#1308159814yesdirect product factor
336C2C2×#1062310811yescharacteristic
337C2C23×#431411yescharacteristic
338C2C2×#1062328211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C8×Q8×C11C2
socleC23×C11C22×D4
prime radicalC2×#10623108C2
hypercenterC2×C8×Q8D11
hypocenterC11C2×#3392
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#10623101C2semidirect
3. #13081598C2direct (N × H)
4. C2×#10622306C2semidirect
5. C2×#10622461C2semidirect
6. C2×#10622454C2semidirect
7. C2×C4×#4314C2semidirect
8. C2×C8×Q8×C11C2semidirect
17. #10623101C22semidirect
24. C8×Q8×C11C22semidirect
30. #10622461C22semidirect
31. #10622454C22semidirect
32. #10622306C22semidirect
33. C4×#4314C22semidirect
77. C2×Q8×C11SD16semidirect
101. C2×C8×C11#41semidirect
124. C2×C8×Q8D11semidirect
131. Q8×C11C2×SD16semidirect
156. C8×C11C2×#41semidirect
175. C8×Q8C2×D11semidirect
239. C2×C11#3392semidirect
250. C2×Q8#4314semidirect
271. C2×C8#4343semidirect
286. C11C2×#3392semidirect
295. Q8C2×#4314semidirect
317. C8C2×#4343semidirect
335. C2#13081598direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231012
C2×#106231082
#130815982
C2×#106223062
C2×#106224612
C2×#106224542
C2×C4×#43142
C2×C8×Q8×C112
C2×#339211