Finite Group Databasebeta

← C2×Q8×#4324 #15634195

Subgroups — C2×Q8×#4324 #15634195

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×Dic22C211yesmaximal, characteristic, complemented
2Q8×#4324C2116yesmaximal, direct product factor
3C2×#10622692C213yesmaximal, complemented
4C2×#10622707C213yesmaximal, complemented
5C2×#10622621C213yesmaximal
6C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
7C2×C4×#4324C213yesmaximal
8C2×D4×Q8×C11C211yesmaximal, characteristic
9C23×Q8×C11—21no—
10D4×Q8×C11—24no—
11D4×Q8×C11C2218yes—
12C2×C11×C4⋊Q8C2213yes—
13C2×C11×C22⋊Q8—23no—
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2213yes—
16C2×Q8×Dic11—21no—
17C22×#4324C2211yescharacteristic
18Q8×Dic22—24no—
19Q8×Dic22C2218yescomplemented
20C2×#66941—23no—
21C2×#66922C2213yes—
22C2×C4×Dic22C2213yes—
23C2×#66896C2213yes—
24#10622707C22124yescomplemented
25#10622692C22124yescomplemented
26Q8×C11⋊C8C2218yescomplemented
27C4×#4324C22124yes—
28#10622621C22124yes—
29C2×#66874C2213yes—
30C2×#66872C2213yes—
31C2×#66872C2216yes—
32C2×C4⋊(C11⋊C8)C2213yes—
33C2×C4×C11⋊C8C2213yes—
34C22×Q8×C11—28no—
35C22×Q8×C11—23no—
36C22×Q8×C11—48no—
37C22×Q8×C11D411yescharacteristic
38C22×D4×C11C2311yescharacteristic
39C23×C4×C11—23no—
40C22×Dic22—23no—
41C22×Dic22C2311yescharacteristic
42C11×C4⋊Q8—26no—
43C11×C4⋊Q8C23112yes—
44C11×C22⋊Q8—224no—
45C4×Q8×C11D414yes—
46C4×Q8×C11C2314yes—
47C4×D4×C11—26no—
48C4×D4×C11C23112yes—
49C2×C11×C4⋊C4—23no—
50C2×C11×C4⋊C4D413yes—
51C2×C11×C4⋊C4C2313yes—
52C2×C11×C22⋊C4—23no—
53C2×C42×C11C2313yes—
54Q8×Dic11—28no—
55C2×#4324Q818yesdirect product factor
56C2×#4324C2314yes—
57C2×C4⋊Dic11—23no—
58C2×C4⋊Dic11C2313yes—
59C2×Dic11⋊C4—23no—
60C2×C4×Dic11—23no—
61C22×C11⋊C8C2313yes—
62C22×C11⋊C8C2311yescharacteristic
63#66941—224no—
64#66922—26no—
65#66922C23112yes—
66C4×Dic22—26no—
67C4×Dic22C23112yes—
68#66896C23112yes—
69#66874C23112yes—
70#66872C23124yes—
71#66872C23112yes—
72C4⋊(C11⋊C8)C23112yes—
73C4×C11⋊C8C23112yes—
74C2×Q8×SD16—111nomaximal, Sylow
75C24×C11—21no—
76C2×Q8×C11—212no—
77C2×Q8×C11—432no—
78C2×Q8×C11—412no—
79C2×Q8×C11SD1618yescomplemented
80C2×Q8×C11C2×D414yes—
81C2×D4×C11—21no—
82C2×D4×C11—22no—
83C2×D4×C11C2×Q814yes—
84C2×D4×C11C2412yes—
85C22×C4×C11—23no—
86C22×C4×C11—212no—
87C22×C4×C11—412no—
88C22×C4×C11C2×D413yes—
89C22×C4×C11C2×D413yes—
90C22×C4×C11C2411yescharacteristic
91C22×Dic11—21no—
92C22×Dic11—23no—
93C2×Dic22—21no—
94C2×Dic22—212no—
95C2×Dic22—22no—
96C2×Dic22—86no—
97C2×Dic22C2×Q814yescomplemented
98C2×Dic22C2412yes—
99C11×C4⋊C4—212no—
100C11×C4⋊C4—23no—
101C11×C4⋊C4C2×D4112yes—
102C11×C4⋊C4C2416yes—
103C11×C22⋊C4—212no—
104C42×C11C2×D416yes—
105C42×C11C2416yes—
106#4324C2×Q8116yesdirect product factor
107C4⋊Dic11—23no—
108C4⋊Dic11—212no—
109C4⋊Dic11C2416yes—
110Dic11⋊C4—212no—
111C4×Dic11—212no—
112C2×C11⋊C8—26no—
113C2×C11⋊C8C2×Q814yescomplemented
114C2×C11⋊C8C2416yes—
115C2×C11⋊C8C2412yes—
116C2×Q82—111no—
117C2×D4×Q8D1111yescharacteristic
118Q8×SD16—1116no—
119C2×#498—113no—
120C2×#475—113no—
121C2×#476—113no—
122C2×C8×Q8—111no—
123C2×C4×SD16—113no—
124C23×C11—24no—
125C23×C11—22no—
126C23×C11—42no—
127C23×C11—42no—
128C23×C11C22×D411yescharacteristic
129Q8×C11—424no—
130Q8×C11C2×SD16116yescomplemented
131D4×C11—24no—
132D4×C11—22no—
133D4×C11C22×Q814yes—
134C2×C4×C11—26no—
135C2×C4×C11—26no—
136C2×C4×C11—46no—
137C2×C4×C11—424no—
138C2×C4×C11C2×SD16112yes—
139C2×C4×C11C22×D416yes—
140C2×C4×C11C22×D411yescharacteristic
141C2×C4×C11C22×D416yes—
142C2×C4×C11C22×Q812yes—
143C2×C4×C112−1+412yes—
144C2×C4×C11C2511yescharacteristic
145C2×Dic11—24no—
146C2×Dic11—22no—
147C2×Dic11—26no—
148C2×Dic11—46no—
149Dic22—24no—
150Dic22—22no—
151Dic22—812no—
152Dic22C22×Q814yescomplemented
153C11⋊C8—26no—
154C11⋊C8C22×Q814yescomplemented
155C23×Q8—21no—
156C22×SD16—111no—
157Q82—118no—
158Q82—224no—
159D4×Q8—24no—
160D4×Q8C2×D1118yes—
161C2×C4⋊Q8—113no—
162C2×C4⋊Q8—223no—
163C2×C4⋊Q8C2×D1113yes—
164C2×C22⋊Q8—23no—
165C2×C4×Q8—113no—
166C2×C4×Q8—221no—
167C2×C4×Q8C2×D1111yescharacteristic
168C2×C4×D4C2×D1113yes—
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×C11—24no—
181C22×C11—48no—
182C22×C11—42no—
183C22×C11—42no—
184C22×C11D4×Q812yes—
185C22×C11C22×SD1612yes—
186C22×C11#57712yes—
187C22×C11C23×D411yescharacteristic
188C4×C11—26no—
189C4×C11—46no—
190C4×C11D4×Q812yes—
191C4×C11C22×SD16112yes—
192C4×C11C23×Q811yescharacteristic
193C4×C11C2×2−1+411yescharacteristic
194Dic11—24no—
195Dic11—46no—
196C22×Q8—28no—
197C22×Q8—23no—
198C22×Q8—48no—
199C22×Q8—111no—
200C22×Q8—223no—
201C22×Q8C22⋊D1111yescharacteristic
202C22×D4C22×D1111yescharacteristic
203C23×C4—23no—
204C2×SD16—118no—
205C2×SD16—114no—
206C22×C8—111no—
207C22×C8—113no—
208C4⋊Q8—26no—
209C4⋊Q8—1112no—
210C4⋊Q8—2224no—
211C4⋊Q8—226no—
212C4⋊Q8C22×D11112yes—
213C22⋊Q8—224no—
214C4×Q8—1112no—
215C4×Q8—228no—
216C4×Q8—226no—
217C4×Q8C22⋊D1114yes—
218C4×Q8C22×D1114yes—
219C4×D4—26no—
220C4×D4C22×D11112yes—
221C2×C4⋊C4—23no—
222C2×C4⋊C4—113no—
223C2×C4⋊C4—223no—
224C2×C4⋊C4—223no—
225C2×C4⋊C4C22⋊D1113yes—
226C2×C4⋊C4C22×D1113yes—
227C2×C22⋊C4—23no—
228C2×C42—223no—
229C2×C42C22×D1113yes—
230#106—1112no—
231#106—1124no—
232C4⋊C8—1112no—
233#103—1112no—
234#102—1112no—
235C4×C8—1112no—
236C2×C11—44no—
237C2×C11Q8×SD1614yescomplemented
238C2×C11C2×D4×Q811yescharacteristic
239C2×C11C23×SD1611yescharacteristic
240C2×C11C2×#57711yescharacteristic
241C24—21no—
242C2×Q8—212no—
243C2×Q8—432no—
244C2×Q8—412no—
245C2×Q8—114no—
246C2×Q8—112no—
247C2×Q8—222no—
248C2×Q8—221no—
249C2×Q8—2212no—
250C2×Q8—886no—
251C2×Q8#432418yesdirect product factor
252C2×Q8C2×C22⋊D1114yes—
253C2×D4—22no—
254C2×D4—21no—
255C2×D4Q8×D1114yes—
256C2×D4C23×D1112yes—
257C22×C4—23no—
258C22×C4—212no—
259C22×C4—412no—
260C22×C4—221no—
261C22×C4—223no—
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—23no—
272C4⋊C4—116no—
273C4⋊C4—223no—
274C4⋊C4—2212no—
275C4⋊C4—2212no—
276C4⋊C4C2×C22⋊D11112yes—
277C4⋊C4C23×D1116yes—
278C22⋊C4—212no—
279C42—2212no—
280C42C2×C22⋊D1116yes—
281C42C23×D1116yes—
282C11C2×Q8×SD1611yescharacteristic, complemented, Sylow
283C23—24no—
284C23—22no—
285C23—42no—
286C23—42no—
287C23C22×C22⋊D1111yescharacteristic
288Q8—424no—
289Q8—114no—
290Q8—224no—
291Q8—222no—
292Q8—8812no—
293Q8C2×#4324116yesdirect product factor
294D4—24no—
295D4—22no—
296D4C2×Q8×D1114yes—
297C2×C4—26no—
298C2×C4—26no—
299C2×C4—46no—
300C2×C4—424no—
301C2×C4—224no—
302C2×C4—222no—
303C2×C4—226no—
304C2×C4—446no—
305C2×C4C2×#4324112yes—
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—24no—
315C22—48no—
316C22—42no—
317C22—42no—
318C22C22×#432412yes—
319C22Q8×C22⋊D1112yes—
320C22#1062336812yes—
321C22C23×C22⋊D1111yescharacteristic
322C4—26no—
323C4—46no—
324C4—224no—
325C4—446no—
326C4C22×#4324112yes—
327C4Q8×C22⋊D1112yes—
328C4C22×Q8×D1111yescharacteristic
329C4C2×#6704011yescharacteristic
330C2—44no—
331C2Q8×#432414yesdirect product factor
332C2C2×Q8×C22⋊D1111yescharacteristic
333C2C23×#432411yescharacteristic
334C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×D4×Q8×C11C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×D4×Q8D11
hypocenterC11C2×Q8×SD16
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic22C2semidirect
2. Q8×#4324C2direct (N × H)
3. C2×#10622692C2semidirect
4. C2×#10622707C2semidirect
6. C2×Q8×C11⋊C8C2semidirect
19. Q8×Dic22C22semidirect
24. #10622707C22semidirect
25. #10622692C22semidirect
26. Q8×C11⋊C8C22semidirect
55. C2×#4324Q8direct (N × H)
79. C2×Q8×C11SD16semidirect
97. C2×Dic22C2×Q8semidirect
106. #4324C2×Q8direct (N × H)
113. C2×C11⋊C8C2×Q8semidirect
130. Q8×C11C2×SD16semidirect
152. Dic22C22×Q8semidirect
154. C11⋊C8C22×Q8semidirect
237. C2×C11Q8×SD16semidirect
251. C2×Q8#4324direct (N × H)
282. C11C2×Q8×SD16semidirect
293. Q8C2×#4324direct (N × H)
331. C2Q8×#4324direct (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
Q8×#43242
C2×#106226922
C2×#106227072
C2×#106226212
C2×Q8×C11⋊C82
C2×C4×#43242
C2×D4×Q8×C112
C2×Q8×SD1611