Finite Group Databasebeta

← C2×Q8×#4325 #15634191

Subgroups — C2×Q8×#4325 #15634191

Order 2816.

2058 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×D44C211yesmaximal, characteristic
2Q8×#4325C2116yesmaximal, direct product factor
3C2×#10622692C213yesmaximal, complemented
4C2×#10622633C213yesmaximal, complemented
5C2×#10622697C213yesmaximal
6C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
7C2×C4×#4325C213yesmaximal
8C2×Q82×C11C211yesmaximal, characteristic, complemented
9C22×Q8×D11—21no—
10Q82×C11—24no—
11Q82×C11C2218yescomplemented
12C2×C11×C4⋊Q8—23no—
13C2×C11×C4⋊Q8C2213yes—
14C2×C4×Q8×C11—21no—
15C2×C4×Q8×C11C2213yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C22×#4325C2211yescharacteristic
18Q8×D44—24no—
19Q8×D44C2218yes—
20C2×#66950—23no—
21C2×C4×D44C2213yes—
22C2×#66922C2213yes—
23C2×#66899C2213yes—
24#10622697C22124yes—
25#10622692C22124yescomplemented
26C4×#4325C22124yes—
27Q8×C11⋊C8C2218yescomplemented
28#10622633C22124yescomplemented
29C2×#66873C2213yes—
30C2×#66872C2213yes—
31C2×#66872C2216yes—
32C2×C4⋊(C11⋊C8)C2213yes—
33C2×C4×C11⋊C8C2213yes—
34C22×Q8×C11—23no—
35C22×Q8×C11D411yescharacteristic
36C22×Q8×C11C2311yescharacteristic
37C2×Q8×D11—28no—
38C2×Q8×D11—48no—
39C22×D44C2311yescharacteristic
40C22×C4×D11—23no—
41C22×Dic22—23no—
42C11×C4⋊Q8—224no—
43C11×C4⋊Q8—26no—
44C11×C4⋊Q8C23112yes—
45C4×Q8×C11—28no—
46C4×Q8×C11—26no—
47C4×Q8×C11D414yes—
48C4×Q8×C11C23112yes—
49C4×Q8×C11C2314yes—
50C2×C11×C4⋊C4—23no—
51C2×C11×C4⋊C4—23no—
52C2×C11×C4⋊C4D413yes—
53C2×C11×C4⋊C4C2313yes—
54C2×C42×C11—23no—
55C2×C42×C11C2313yes—
56C2×#4325Q818yesdirect product factor
57C2×#4325C2314yes—
58C2×(C2×D11)⋊C4—23no—
59C2×C4⋊Dic11—23no—
60C2×C4⋊Dic11C2313yes—
61C22×C11⋊C8C2313yes—
62C22×C11⋊C8C2311yescharacteristic
63#66950—224no—
64C4×D44—26no—
65C4×D44C23112yes—
66#66922—26no—
67#66922C23112yes—
68#66899C23112yes—
69#66873C23112yes—
70#66872C23124yes—
71#66872C23112yes—
72C4⋊(C11⋊C8)C23112yes—
73C4×C11⋊C8C23112yes—
74C2×Q8×SD16—111nomaximal, Sylow
75C23×D11—21no—
76C2×Q8×C11—21no—
77C2×Q8×C11—212no—
78C2×Q8×C11—22no—
79C2×Q8×C11—86no—
80C2×Q8×C11SD1618yescomplemented
81C2×Q8×C11C2×D414yes—
82C2×Q8×C11C2×Q814yescomplemented
83C2×Q8×C11C2412yes—
84C22×C4×C11—21no—
85C22×C4×C11—23no—
86C22×C4×C11C2×D413yes—
87C22×C4×C11C2×D413yes—
88C22×C4×C11C2411yescharacteristic
89C22×Dic11—23no—
90Q8×D11—432no—
91C2×D44—21no—
92C2×D44—22no—
93C2×D44C2×Q814yes—
94C2×D44C2412yes—
95C2×C4×D11—212no—
96C2×C4×D11—412no—
97C2×Dic22—212no—
98C2×Dic22—412no—
99C11×C4⋊C4—212no—
100C11×C4⋊C4—212no—
101C11×C4⋊C4—23no—
102C11×C4⋊C4C2×D4112yes—
103C11×C4⋊C4C2416yes—
104C42×C11—212no—
105C42×C11C2×D416yes—
106C42×C11C2416yes—
107#4325C2×Q8116yesdirect product factor
108(C2×D11)⋊C4—212no—
109C4⋊Dic11—23no—
110C4⋊Dic11—212no—
111C4⋊Dic11C2416yes—
112C2×C11⋊C8—26no—
113C2×C11⋊C8C2×Q814yescomplemented
114C2×C11⋊C8C2416yes—
115C2×C11⋊C8C2412yes—
116C2×Q82D1111yescharacteristic, complemented
117C2×D4×Q8—111no—
118Q8×SD16—1116no—
119C2×#498—113no—
120C2×#475—113no—
121C2×#476—113no—
122C2×C8×Q8—111no—
123C2×C4×SD16—113no—
124C23×C11C22×D411yescharacteristic
125C22×D11—24no—
126C22×D11—22no—
127C22×D11—42no—
128C22×D11—42no—
129Q8×C11—24no—
130Q8×C11—22no—
131Q8×C11—812no—
132Q8×C11C2×SD16116yescomplemented
133Q8×C11C22×Q814yescomplemented
134C2×C4×C11—24no—
135C2×C4×C11—26no—
136C2×C4×C11—22no—
137C2×C4×C11—26no—
138C2×C4×C11—46no—
139C2×C4×C11C2×SD16112yes—
140C2×C4×C11C22×D416yes—
141C2×C4×C11C22×D411yescharacteristic
142C2×C4×C11C22×D416yes—
143C2×C4×C11C22×Q812yes—
144C2×C4×C112−1+412yes—
145C2×C4×C11C2511yescharacteristic
146C2×Dic11—26no—
147C2×Dic11—46no—
148D44—24no—
149D44—22no—
150D44C22×Q814yes—
151C4×D11—424no—
152Dic22—424no—
153C11⋊C8—26no—
154C11⋊C8C22×Q814yescomplemented
155C23×Q8—221no—
156C22×SD16—111no—
157Q82—24no—
158Q82C2×D1118yescomplemented
159D4×Q8—118no—
160D4×Q8—224no—
161C2×C4⋊Q8—23no—
162C2×C4⋊Q8—113no—
163C2×C4⋊Q8C2×D1113yes—
164C2×C22⋊Q8—223no—
165C2×C4×Q8—21no—
166C2×C4×Q8C2×D1113yes—
167C2×C4×Q8C2×D1111yescharacteristic
168C2×C4×D4—113no—
169#498—1124no—
170#476—1124no—
171#475—1124no—
172C8×Q8—118no—
173C4×SD16—1124no—
174C2×#106—116no—
175C2×#106—113no—
176C2×C4⋊C8—113no—
177C2×#103—113no—
178C2×#102—113no—
179C2×C4×C8—113no—
180C22×C11D4×Q812yes—
181C22×C11C22×SD1612yes—
182C22×C11#57712yes—
183C22×C11C23×D411yescharacteristic
184C2×D11—24no—
185C2×D11—48no—
186C2×D11—42no—
187C2×D11—42no—
188C4×C11—24no—
189C4×C11—26no—
190C4×C11—46no—
191C4×C11D4×Q812yes—
192C4×C11C22×SD16112yes—
193C4×C11C23×Q811yescharacteristic
194C4×C11C2×2−1+411yescharacteristic
195Dic11—46no—
196C22×Q8—23no—
197C22×Q8—228no—
198C22×Q8—223no—
199C22×Q8—448no—
200C22×Q8C22⋊D1111yescharacteristic
201C22×Q8C22×D1111yescharacteristic
202C22×D4—111no—
203C23×C4—223no—
204C2×SD16—118no—
205C2×SD16—114no—
206C22×C8—111no—
207C22×C8—113no—
208C4⋊Q8—224no—
209C4⋊Q8—26no—
210C4⋊Q8—1112no—
211C4⋊Q8—226no—
212C4⋊Q8C22×D11112yes—
213C22⋊Q8—2224no—
214C4×Q8—28no—
215C4×Q8—26no—
216C4×Q8C22⋊D1114yes—
217C4×Q8C22×D11112yes—
218C4×Q8C22×D1114yes—
219C4×D4—1112no—
220C4×D4—226no—
221C2×C4⋊C4—23no—
222C2×C4⋊C4—23no—
223C2×C4⋊C4—113no—
224C2×C4⋊C4—223no—
225C2×C4⋊C4C22⋊D1113yes—
226C2×C4⋊C4C22×D1113yes—
227C2×C22⋊C4—223no—
228C2×C42—23no—
229C2×C42C22×D1113yes—
230#106—1112no—
231#106—1124no—
232C4⋊C8—1112no—
233#103—1112no—
234#102—1112no—
235C4×C8—1112no—
236C2×C11Q8×SD1614yescomplemented
237C2×C11C2×D4×Q811yescharacteristic
238C2×C11C23×SD1611yescharacteristic
239C2×C11C2×#57711yescharacteristic
240D11—44no—
241C24—221no—
242C2×Q8—22no—
243C2×Q8—21no—
244C2×Q8—212no—
245C2×Q8—86no—
246C2×Q8—2212no—
247C2×Q8—4432no—
248C2×Q8—4412no—
249C2×Q8#432518yesdirect product factor
250C2×Q8Q8×D1114yescomplemented
251C2×Q8C2×C22⋊D1114yes—
252C2×Q8C23×D1112yes—
253C2×D4—114no—
254C2×D4—112no—
255C2×D4—222no—
256C2×D4—221no—
257C22×C4—21no—
258C22×C4—23no—
259C22×C4—223no—
260C22×C4—2212no—
261C22×C4—4412no—
262C22×C4C2×C22⋊D1113yes—
263C22×C4C2×C22⋊D1113yes—
264C22×C4C23×D1111yescharacteristic
265SD16—1116no—
266C2×C8—114no—
267C2×C8—112no—
268C2×C8—116no—
269C2×C8—226no—
270C4⋊C4—212no—
271C4⋊C4—212no—
272C4⋊C4—23no—
273C4⋊C4—116no—
274C4⋊C4—223no—
275C4⋊C4—2212no—
276C4⋊C4C2×C22⋊D11112yes—
277C4⋊C4C23×D1116yes—
278C22⋊C4—2212no—
279C42—212no—
280C42C2×C22⋊D1116yes—
281C42C23×D1116yes—
282C11C2×Q8×SD1611yescharacteristic, complemented, Sylow
283C23—224no—
284C23—222no—
285C23—442no—
286C23—442no—
287C23C22×C22⋊D1111yescharacteristic
288Q8—24no—
289Q8—22no—
290Q8—812no—
291Q8—4424no—
292Q8C2×#4325116yesdirect product factor
293Q8C2×Q8×D1114yescomplemented
294D4—114no—
295D4—224no—
296D4—222no—
297C2×C4—24no—
298C2×C4—26no—
299C2×C4—22no—
300C2×C4—26no—
301C2×C4—46no—
302C2×C4—226no—
303C2×C4—446no—
304C2×C4—4424no—
305C2×C4C2×#4325112yes—
306C2×C4C2×Q8×D1112yes—
307C2×C4#6704012yes—
308C2×C4C22×C22⋊D1116yes—
309C2×C4C22×C22⋊D1116yes—
310C2×C4C22×C22⋊D1111yescharacteristic
311C2×C4C24×D1111yescharacteristic
312C8—114no—
313C8—226no—
314C22—224no—
315C22—448no—
316C22—442no—
317C22—442no—
318C22C22×#432512yes—
319C22Q8×C22⋊D1112yes—
320C22#1062336712yes—
321C22C23×C22⋊D1111yescharacteristic
322C4—24no—
323C4—26no—
324C4—46no—
325C4—446no—
326C4C22×#4325112yes—
327C4Q8×C22⋊D1112yes—
328C4C22×Q8×D1111yescharacteristic
329C4C2×#6704011yescharacteristic
330C2—444no—
331C2Q8×#432514yesdirect product factor
332C2C2×Q8×C22⋊D1111yescharacteristic
333C2C23×#432511yescharacteristic
334C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×Q82×C11C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×Q82D11
hypocenterC11C2×Q8×SD16
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×Q82

Complements

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

NH ≅ G/Ntype
2. Q8×#4325C2direct (N × H)
3. C2×#10622692C2semidirect
4. C2×#10622633C2semidirect
6. C2×Q8×C11⋊C8C2semidirect
8. C2×Q82×C11C2semidirect
11. Q82×C11C22semidirect
25. #10622692C22semidirect
27. Q8×C11⋊C8C22semidirect
28. #10622633C22semidirect
56. C2×#4325Q8direct (N × H)
80. C2×Q8×C11SD16semidirect
82. C2×Q8×C11C2×Q8semidirect
107. #4325C2×Q8direct (N × H)
113. C2×C11⋊C8C2×Q8semidirect
116. C2×Q82D11semidirect
132. Q8×C11C2×SD16semidirect
133. Q8×C11C22×Q8semidirect
154. C11⋊C8C22×Q8semidirect
158. Q82C2×D11semidirect
236. C2×C11Q8×SD16semidirect
249. C2×Q8#4325direct (N × H)
250. C2×Q8Q8×D11semidirect
282. C11C2×Q8×SD16semidirect
292. Q8C2×#4325direct (N × H)
293. Q8C2×Q8×D11semidirect
331. C2Q8×#4325direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×D442
Q8×#43252
C2×#106226922
C2×#106226332
C2×#106226972
C2×Q8×C11⋊C82
C2×C4×#43252
C2×Q82×C112
C2×Q8×SD1611