Finite Group Databasebeta

← C2×#13081597 #15634674

Subgroups — C2×#13081597 #15634674

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
2#13081597C2116yesmaximal, direct product factor
3C2×#10622689C213yesmaximal, complemented
4C2×#10622688C213yesmaximal, complemented
5C2×#10622632C213yesmaximal, complemented
6C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
7C2×C4×#4324C213yesmaximal, complemented
8C2×C11×#550C211yesmaximal, characteristic
9C22×C11×#41—21no—
10C11×#550—24no—
11C11×#550C2218yes—
12C2×C11×#127C2213yes—
13C2×C11×#121—23no—
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2213yes—
16C2×Q8×Dic11—21no—
17C22×#4324C2213yes—
18C22×#4324C2216yes—
19#10623101—24no—
20#10623101C2218yescomplemented
21C2×#66943—23no—
22C2×#66922C2213yes—
23C2×C4×Dic22C2213yes—
24C2×#66896C2213yes—
25#10622689C22124yescomplemented
26#10622688C22124yescomplemented
27Q8×C11⋊C8C2218yescomplemented
28#10622632C22124yescomplemented
29C4×#4324C22124yescomplemented
30C2×#66874C2213yes—
31C2×#66872C2211yescharacteristic
32C2×C4⋊(C11⋊C8)C2213yes—
33C2×C4×C11⋊C8C2213yes—
34C2×C11×#41—28no—
35C2×C11×#41—48no—
36C22×Q8×C11D411yescharacteristic
37C22×D4×C11—23no—
38C22×D4×C11—23no—
39C22×D4×C11C2313yes—
40C23×C4×C11—23no—
41C22×Dic22C2313yes—
42C11×#127—26no—
43C11×#127C23112yes—
44C11×#121—224no—
45C4×Q8×C11D414yes—
46C4×Q8×C11C2314yes—
47C4×D4×C11—26no—
48C4×D4×C11C23112yes—
49C2×C11×C4⋊C4D413yes—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C22⋊C4—23no—
52C2×C42×C11C2313yes—
53Q8×Dic11—28no—
54C2×#4324—212no—
55C2×#4324—412no—
56C2×#4324C23112yes—
57C2×#4324C23124yes—
58C2×C4⋊Dic11—23no—
59C2×C4⋊Dic11—23no—
60C2×C4⋊Dic11C2311yescharacteristic
61C2×Dic11⋊C4—23no—
62C2×C4×Dic11—23no—
63C22×C11⋊C8C2313yes—
64C22×C11⋊C8C2311yescharacteristic
65#66943—224no—
66#66922—26no—
67#66922C23112yes—
68C4×Dic22—26no—
69C4×Dic22C23112yes—
70#66896C23112yes—
71#66874C23112yes—
72#66872C2314yes—
73C4⋊(C11⋊C8)C23112yes—
74C4×C11⋊C8C23112yes—
75C2×#3392—111nomaximal, Sylow
76C24×C11—23no—
77C11×#41—432no—
78C2×Q8×C11SD1618yescomplemented
79C2×Q8×C11C2×D414yes—
80C2×D4×C11—23no—
81C2×D4×C11—212no—
82C2×D4×C11—212no—
83C2×D4×C11—26no—
84C2×D4×C11—26no—
85C2×D4×C11—412no—
86C2×D4×C11—86no—
87C2×D4×C11C2416yes—
88C22×C4×C11—21no—
89C22×C4×C11—212no—
90C22×C4×C11—412no—
91C22×C4×C11C2×D413yes—
92C22×C4×C11C2×D413yes—
93C22×C4×C11C2411yescharacteristic
94C22×Dic11—21no—
95C22×Dic11—23no—
96C2×Dic22—23no—
97C2×Dic22—26no—
98C2×Dic22—26no—
99C2×Dic22C2416yes—
100C11×C4⋊C4—21no—
101C11×C4⋊C4C2×D4112yes—
102C11×C4⋊C4C2412yes—
103C11×C22⋊C4—212no—
104C42×C11C2×D416yes—
105C42×C11C2416yes—
106#4324—224no—
107#4324—424no—
108C4⋊Dic11—21no—
109C4⋊Dic11—212no—
110C4⋊Dic11—212no—
111C4⋊Dic11C2412yes—
112Dic11⋊C4—212no—
113C4×Dic11—212no—
114C2×C11⋊C8—26no—
115C2×C11⋊C8#4114yescomplemented
116C2×C11⋊C8C2416yes—
117C2×C11⋊C8C2412yes—
118C2×#557—111no—
119C2×#550D1111yescharacteristic
120#3392—1116no—
121C2×#492—113no—
122C2×#460—113no—
123C2×#461—113no—
124C2×C8×Q8—111no—
125C2×C4×SD16—113no—
126C23×C11—26no—
127C23×C11—46no—
128C23×C11—46no—
129C23×C11—46no—
130C23×C11C22×D411yescharacteristic
131Q8×C11C2×SD16116yescomplemented
132D4×C11—26no—
133D4×C11—26no—
134D4×C11—46no—
135D4×C11—424no—
136D4×C11—812no—
137C2×C4×C11—26no—
138C2×C4×C11—22no—
139C2×C4×C11—42no—
140C2×C4×C11—424no—
141C2×C4×C11C2×SD16112yes—
142C2×C4×C11C22×D416yes—
143C2×C4×C11C22×D411yescharacteristic
144C2×C4×C11C22×D416yes—
145C2×C4×C11C2×#4112yes—
146C2×C4×C11H(5,𝔽2)12yes—
147C2×C4×C11C2511yescharacteristic
148C2×Dic11—22no—
149C2×Dic11—26no—
150C2×Dic11—46no—
151C2×Dic11—42no—
152Dic22—26no—
153Dic22—26no—
154Dic22—46no—
155C11⋊C8—26no—
156C11⋊C8C2×#4114yescomplemented
157C22×#41—21no—
158C22×SD16—113no—
159C22×SD16—116no—
160#557—118no—
161#557—224no—
162#550—24no—
163#550C2×D1118yes—
164C2×C4⋊Q8—113no—
165C2×#127C2×D1113yes—
166C2×#125—223no—
167C2×#121—23no—
168C2×C4×Q8—113no—
169C2×C4×Q8—221no—
170C2×C4×Q8C2×D1111yescharacteristic
171C2×C4×D4C2×D1113yes—
172#492—1124no—
173#461—1124no—
174#460—1124no—
175C8×Q8—118no—
176C4×SD16—1124no—
177C2×#106—111no—
178C2×C4⋊C8—113no—
179C2×#103—113no—
180C2×#102—113no—
181C2×C4×C8—113no—
182C22×C11—46no—
183C22×C11—46no—
184C22×C11—46no—
185C22×C11—812no—
186C22×C11#55012yes—
187C22×C11C22×SD1612yes—
188C22×C11#57712yes—
189C22×C11C23×D411yescharacteristic
190C4×C11—26no—
191C4×C11—42no—
192C4×C11#55012yes—
193C4×C11C22×SD16112yes—
194C4×C11C22×#4111yescharacteristic
195C4×C11C2×H(5,𝔽2)11yescharacteristic
196Dic11—46no—
197Dic11—42no—
198C2×#41—28no—
199C2×#41—48no—
200C22×Q8—113no—
201C22×Q8C22⋊D1111yescharacteristic
202C22×D4—23no—
203C22×D4—23no—
204C22×D4C22×D1113yes—
205C23×C4—23no—
206C2×SD16—1112no—
207C2×SD16—1124no—
208C2×SD16—2212no—
209C2×SD16—4412no—
210C22×C8—111no—
211C22×C8—113no—
212C4⋊Q8—1112no—
213C4⋊Q8—226no—
214#127—26no—
215#127C22×D11112yes—
216#125—2224no—
217#121—224no—
218C4×Q8—1112no—
219C4×Q8—228no—
220C4×Q8—226no—
221C4×Q8C22⋊D1114yes—
222C4×Q8C22×D1114yes—
223C4×D4—26no—
224C4×D4C22×D11112yes—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—223no—
227C2×C4⋊C4—223no—
228C2×C4⋊C4—223no—
229C2×C4⋊C4C22⋊D1113yes—
230C2×C4⋊C4C22×D1111yescharacteristic
231C2×C22⋊C4—23no—
232C2×C42—223no—
233C2×C42C22×D1113yes—
234#106—114no—
235C4⋊C8—1112no—
236#103—1112no—
237#102—1112no—
238C4×C8—1112no—
239C2×C11—86no—
240C2×C11#339214yescomplemented
241C2×C11C2×#55011yescharacteristic
242C2×C11C23×SD1611yescharacteristic
243C2×C11C2×#57711yescharacteristic
244C24—23no—
245#41—432no—
246C2×Q8—116no—
247C2×Q8—223no—
248C2×Q8—226no—
249C2×Q8—226no—
250C2×Q8#432418yescomplemented
251C2×Q8C2×C22⋊D1114yes—
252C2×D4—26no—
253C2×D4—26no—
254C2×D4—23no—
255C2×D4—212no—
256C2×D4—212no—
257C2×D4—412no—
258C2×D4—86no—
259C2×D4C23×D1116yes—
260C22×C4—21no—
261C22×C4—212no—
262C22×C4—412no—
263C22×C4—221no—
264C22×C4—223no—
265C22×C4C2×C22⋊D1113yes—
266C22×C4C2×C22⋊D1113yes—
267C22×C4C23×D1111yescharacteristic
268SD16—2224no—
269SD16—4424no—
270C2×C8—114no—
271C2×C8—112no—
272C2×C8—116no—
273C2×C8—226no—
274C4⋊C4—21no—
275C4⋊C4—112no—
276C4⋊C4—221no—
277C4⋊C4—2212no—
278C4⋊C4—2212no—
279C4⋊C4—2212no—
280C4⋊C4C2×C22⋊D11112yes—
281C4⋊C4C23×D1112yes—
282C22⋊C4—212no—
283C42—2212no—
284C42C2×C22⋊D1116yes—
285C42C23×D1116yes—
286C11C2×#339211yescharacteristic, complemented, Sylow
287C23—26no—
288C23—46no—
289C23—46no—
290C23—46no—
291C23C22×C22⋊D1111yescharacteristic
292Q8—226no—
293Q8—226no—
294Q8—446no—
295Q8C2×#4324116yescomplemented
296D4—26no—
297D4—26no—
298D4—424no—
299D4—46no—
300D4—812no—
301C2×C4—26no—
302C2×C4—22no—
303C2×C4—42no—
304C2×C4—424no—
305C2×C4—222no—
306C2×C4—226no—
307C2×C4—446no—
308C2×C4—442no—
309C2×C4C2×#4324112yes—
310C2×C4#41×D1112yes—
311C2×C4#6704212yes—
312C2×C4C22×C22⋊D1116yes—
313C2×C4C22×C22⋊D1116yes—
314C2×C4C22×C22⋊D1111yescharacteristic
315C2×C4C24×D1111yescharacteristic
316C8—114no—
317C8—226no—
318C22—46no—
319C22—46no—
320C22—46no—
321C22—812no—
322C22C22×#432412yes—
323C22#1062336512yes—
324C22#1062336712yes—
325C22C23×C22⋊D1111yescharacteristic
326C4—26no—
327C4—42no—
328C4—446no—
329C4—442no—
330C4C22×#4324112yes—
331C4#1062336512yes—
332C4C2×#41×D1111yescharacteristic
333C4C2×#6704211yescharacteristic
334C2—86no—
335C2#1308159714yesdirect product factor
336C2C2×#1062336511yescharacteristic
337C2C23×#432411yescharacteristic
338C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#550C2
socleC23×C11C22×D4
hypercenterC2×#550D11
hypocenterC11C2×#3392
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#10623101C2semidirect
2. #13081597C2direct (N × H)
3. C2×#10622689C2semidirect
4. C2×#10622688C2semidirect
5. C2×#10622632C2semidirect
6. C2×Q8×C11⋊C8C2semidirect
7. C2×C4×#4324C2semidirect
20. #10623101C22semidirect
25. #10622689C22semidirect
26. #10622688C22semidirect
27. Q8×C11⋊C8C22semidirect
28. #10622632C22semidirect
29. C4×#4324C22semidirect
78. C2×Q8×C11SD16semidirect
115. C2×C11⋊C8#41semidirect
131. Q8×C11C2×SD16semidirect
156. C11⋊C8C2×#41semidirect
240. C2×C11#3392semidirect
250. C2×Q8#4324semidirect
286. C11C2×#3392semidirect
295. Q8C2×#4324semidirect
335. C2#13081597direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231012
#130815972
C2×#106226892
C2×#106226882
C2×#106226322
C2×Q8×C11⋊C82
C2×C4×#43242
C2×C11×#5502
C2×#339211