Finite Group Databasebeta

← C2×#13081283 #15633365

Subgroups — C2×#13081283 #15633365

Order 2816.

2174 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×Q8×Dic22C211yesmaximal, characteristic, complemented
2#13081283C2116yesmaximal, direct product factor
3C2×#10622683C213yesmaximal, complemented
4C2×#10622621C213yesmaximal, complemented
5C2×#10622688C213yesmaximal, 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—
18Q8×Dic22—24no—
19Q8×Dic22C2218yescomplemented
20C2×#66941—23no—
21C2×#66922C2213yes—
22C2×C4×Dic22C2213yes—
23C2×#66896C2216yes—
24C2×#66896C2213yes—
25#10622688C22124yescomplemented
26#10622683C22124yescomplemented
27Q8×C11⋊C8C2218yescomplemented
28C4×#4324C22124yescomplemented
29#10622621C22124yescomplemented
30C2×#66874C2211yescharacteristic
31C2×#66872C2213yes—
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×Dic22—23no—
42C22×Dic22C2311yescharacteristic
43C11×#127—26no—
44C11×#127C23112yes—
45C11×#121—224no—
46C4×Q8×C11D414yes—
47C4×Q8×C11C2314yes—
48C4×D4×C11—26no—
49C4×D4×C11C23112yes—
50C2×C11×C4⋊C4D413yes—
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C22⋊C4—23no—
53C2×C42×C11C2313yes—
54Q8×Dic11—28no—
55C2×#4324—212no—
56C2×#4324C23112yes—
57C2×C4⋊Dic11—23no—
58C2×C4⋊Dic11C2313yes—
59C2×Dic11⋊C4—23no—
60C2×C4×Dic11—23no—
61C22×C11⋊C8C2311yescharacteristic
62C22×C11⋊C8C2313yes—
63#66941—224no—
64#66922—26no—
65#66922C23112yes—
66C4×Dic22—26no—
67C4×Dic22C23112yes—
68#66896C23124yes—
69#66896C23112yes—
70#66874C2314yes—
71#66872C23112yes—
72C4⋊(C11⋊C8)C23112yes—
73C4×C11⋊C8C23112yes—
74C2×#3362—111nomaximal, Sylow
75C24×C11—23no—
76C11×#41—432no—
77C2×Q8×C11SD1618yescomplemented
78C2×Q8×C11C2×D414yes—
79C2×D4×C11—23no—
80C2×D4×C11—212no—
81C2×D4×C11—212no—
82C2×D4×C11—26no—
83C2×D4×C11—26no—
84C2×D4×C11—412no—
85C2×D4×C11—86no—
86C2×D4×C11C2416yes—
87C22×C4×C11—21no—
88C22×C4×C11—212no—
89C22×C4×C11—412no—
90C22×C4×C11C2×D413yes—
91C22×C4×C11C2×D413yes—
92C22×C4×C11C2411yescharacteristic
93C22×Dic11—21no—
94C22×Dic11—23no—
95C2×Dic22—21no—
96C2×Dic22—212no—
97C2×Dic22—22no—
98C2×Dic22—86no—
99C2×Dic22#4114yescomplemented
100C2×Dic22C2412yes—
101C11×C4⋊C4—21no—
102C11×C4⋊C4C2×D4112yes—
103C11×C4⋊C4C2412yes—
104C11×C22⋊C4—212no—
105C42×C11C2×D416yes—
106C42×C11C2416yes—
107#4324—224no—
108C4⋊Dic11—23no—
109C4⋊Dic11—212no—
110C4⋊Dic11C2416yes—
111Dic11⋊C4—212no—
112C4×Dic11—212no—
113C2×C11⋊C8—26no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8C2412yes—
116C2×C11⋊C8C2416yes—
117C2×Q82—111no—
118C2×#550D1111yescharacteristic
119#3362—1116no—
120C2×#486—113no—
121C2×#476—113no—
122C2×#460—113no—
123C2×C8×Q8—111no—
124C2×C4×SD16—113no—
125C23×C11—26no—
126C23×C11—46no—
127C23×C11—46no—
128C23×C11—46no—
129C23×C11C22×D411yescharacteristic
130Q8×C11C2×SD16116yescomplemented
131D4×C11—26no—
132D4×C11—26no—
133D4×C11—46no—
134D4×C11—424no—
135D4×C11—812no—
136C2×C4×C11—26no—
137C2×C4×C11—22no—
138C2×C4×C11—42no—
139C2×C4×C11—424no—
140C2×C4×C11C2×SD16112yes—
141C2×C4×C11C22×D416yes—
142C2×C4×C11C22×D411yescharacteristic
143C2×C4×C11C22×D416yes—
144C2×C4×C11C2×#4112yes—
145C2×C4×C112−1+412yes—
146C2×C4×C11C2511yescharacteristic
147C2×Dic11—24no—
148C2×Dic11—22no—
149C2×Dic11—26no—
150C2×Dic11—46no—
151Dic22—24no—
152Dic22—22no—
153Dic22—812no—
154Dic22C2×#4114yescomplemented
155C11⋊C8—26no—
156C11⋊C8—22no—
157C22×#41—21no—
158C22×SD16—113no—
159Q82—118no—
160Q82—224no—
161#550—24no—
162#550C2×D1118yes—
163C2×C4⋊Q8—113no—
164C2×C4⋊Q8—223no—
165C2×#127C2×D1113yes—
166C2×#121—23no—
167C2×C4×Q8—113no—
168C2×C4×Q8—221no—
169C2×C4×Q8C2×D1111yescharacteristic
170C2×C4×D4C2×D1113yes—
171#486—1124no—
172#476—1124no—
173#460—1124no—
174C8×Q8—118no—
175C4×SD16—1124no—
176C2×#106—113no—
177C2×C4⋊C8—113no—
178C2×#103—111no—
179C2×#102—113no—
180C2×#102—116no—
181C2×C4×C8—113no—
182C22×C11—46no—
183C22×C11—46no—
184C22×C11—46no—
185C22×C11—812no—
186C22×C11#54812yes—
187C22×C11C22×SD1612yes—
188C22×C11#57612yes—
189C22×C11C23×D411yescharacteristic
190C4×C11—26no—
191C4×C11—42no—
192C4×C11#54812yes—
193C4×C11C22×SD16112yes—
194C4×C11C22×#4111yescharacteristic
195C4×C11C2×2−1+411yescharacteristic
196Dic11—24no—
197Dic11—46no—
198C2×#41—28no—
199C2×#41—48no—
200C22×Q8—111no—
201C22×Q8—223no—
202C22×Q8C22⋊D1111yescharacteristic
203C22×D4—23no—
204C22×D4—23no—
205C22×D4C22×D1113yes—
206C23×C4—23no—
207C2×SD16—1112no—
208C2×SD16—2212no—
209C22×C8—113no—
210C22×C8—111no—
211C4⋊Q8—1112no—
212C4⋊Q8—2224no—
213C4⋊Q8—226no—
214#127—26no—
215#127C22×D11112yes—
216#121—224no—
217C4×Q8—1112no—
218C4×Q8—228no—
219C4×Q8—226no—
220C4×Q8C22⋊D1114yes—
221C4×Q8C22×D1114yes—
222C4×D4—26no—
223C4×D4C22×D11112yes—
224C2×C4⋊C4—113no—
225C2×C4⋊C4—223no—
226C2×C4⋊C4—223no—
227C2×C4⋊C4C22⋊D1113yes—
228C2×C4⋊C4C22×D1111yescharacteristic
229C2×C22⋊C4—23no—
230C2×C42—223no—
231C2×C42C22×D1113yes—
232#106—1112no—
233C4⋊C8—1112no—
234#103—114no—
235#102—1112no—
236#102—1124no—
237C4×C8—1112no—
238C2×C11—86no—
239C2×C11#336214yescomplemented
240C2×C11C2×#54811yescharacteristic
241C2×C11C23×SD1611yescharacteristic
242C2×C11C2×#57611yescharacteristic
243C24—23no—
244#41—432no—
245C2×Q8—114no—
246C2×Q8—112no—
247C2×Q8—222no—
248C2×Q8—221no—
249C2×Q8—2212no—
250C2×Q8—886no—
251C2×Q8#432418yescomplemented
252C2×Q8C2×C22⋊D1114yes—
253C2×D4—26no—
254C2×D4—26no—
255C2×D4—23no—
256C2×D4—212no—
257C2×D4—212no—
258C2×D4—412no—
259C2×D4—86no—
260C2×D4C23×D1116yes—
261C22×C4—21no—
262C22×C4—212no—
263C22×C4—412no—
264C22×C4—221no—
265C22×C4—223no—
266C22×C4C2×C22⋊D1113yes—
267C22×C4C2×C22⋊D1113yes—
268C22×C4C23×D1111yescharacteristic
269SD16—2224no—
270C2×C8—112no—
271C2×C8—116no—
272C2×C8—226no—
273C2×C8—222no—
274C4⋊C4—21no—
275C4⋊C4—116no—
276C4⋊C4—223no—
277C4⋊C4—2212no—
278C4⋊C4—2212no—
279C4⋊C4C2×C22⋊D11112yes—
280C4⋊C4C23×D1112yes—
281C22⋊C4—212no—
282C42—2212no—
283C42C2×C22⋊D1116yes—
284C42C23×D1116yes—
285C11C2×#336211yescharacteristic, complemented, Sylow
286C23—26no—
287C23—46no—
288C23—46no—
289C23—46no—
290C23C22×C22⋊D1111yescharacteristic
291Q8—114no—
292Q8—224no—
293Q8—222no—
294Q8—8812no—
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—224no—
306C2×C4—222no—
307C2×C4—226no—
308C2×C4—446no—
309C2×C4C2×#4324112yes—
310C2×C4#41×D1112yes—
311C2×C4#6704312yes—
312C2×C4C22×C22⋊D1116yes—
313C2×C4C22×C22⋊D1116yes—
314C2×C4C22×C22⋊D1111yescharacteristic
315C2×C4C24×D1111yescharacteristic
316C8—226no—
317C8—222no—
318C22—46no—
319C22—46no—
320C22—46no—
321C22—812no—
322C22C22×#432412yes—
323C22#1062336212yes—
324C22#1062336612yes—
325C22C23×C22⋊D1111yescharacteristic
326C4—26no—
327C4—42no—
328C4—224no—
329C4—446no—
330C4C22×#4324112yes—
331C4#1062336212yes—
332C4C2×#41×D1111yescharacteristic
333C4C2×#6704311yescharacteristic
334C2—86no—
335C2#1308128314yesdirect product factor
336C2C2×#1062336211yescharacteristic
337C2C23×#432411yescharacteristic
338C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#550C2
socleC23×C11C22×D4
hypercenterC2×#550D11
hypocenterC11C2×#3362
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×Q8×Dic22C2semidirect
2. #13081283C2direct (N × H)
3. C2×#10622683C2semidirect
4. C2×#10622621C2semidirect
5. C2×#10622688C2semidirect
6. C2×Q8×C11⋊C8C2semidirect
7. C2×C4×#4324C2semidirect
19. Q8×Dic22C22semidirect
25. #10622688C22semidirect
26. #10622683C22semidirect
27. Q8×C11⋊C8C22semidirect
28. C4×#4324C22semidirect
29. #10622621C22semidirect
77. C2×Q8×C11SD16semidirect
99. C2×Dic22#41semidirect
130. Q8×C11C2×SD16semidirect
154. Dic22C2×#41semidirect
239. C2×C11#3362semidirect
251. C2×Q8#4324semidirect
285. C11C2×#3362semidirect
295. Q8C2×#4324semidirect
335. C2#13081283direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×Dic222
#130812832
C2×#106226832
C2×#106226212
C2×#106226882
C2×Q8×C11⋊C82
C2×C4×#43242
C2×C11×#5502
C2×#336211