Finite Group Databasebeta

← Q8×C11×#99 #14599705

Subgroups — Q8×C11×#99 #14599705

Order 2816.

1354 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C11C211yesmaximal, characteristic
2Q8×C11×C22⋊C4C212yesmaximal, complemented
3C11×#1996C216yesmaximal, complemented
4C11×#1799C213yesmaximal
5C4×C11×#99C213yesmaximal
6C23×Q8×C11C411yescharacteristic, complemented
7C23×Q8×C11C2211yescharacteristic
8D4×Q8×C11—22no—
9D4×Q8×C11—26no—
10C2×C11×C4⋊Q8C413yescomplemented
11C2×C11×C22⋊Q8C413yescomplemented
12C2×C11×C22⋊Q8C2213yes—
13C2×C4×Q8×C11—22no—
14C2×C4×Q8×C11C411yescharacteristic, complemented
15C2×C4×D4×C11C2213yes—
16C2×C11×#99C2213yes—
17C2×C11×#99C2211yescharacteristic
18C11×#391—26no—
19C11×#380C2216yes—
20C4×C11×C22⋊C4C2216yes—
21C11×#342C2216yes—
22C11×#342C2216yes—
23C22×Q8×C11—23no—
24C22×Q8×C11—21no—
25C22×Q8×C11—44no—
26C22×Q8×C11—44no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×Q8×C11C2×C413yes—
29C22×Q8×C11C2×C413yes—
30C22×Q8×C11D412yes—
31C22×Q8×C11D416yes—
32C22×D4×C11C2311yescharacteristic
33C23×C4×C11C2×C413yes—
34C23×C4×C11C2313yes—
35C11×C4⋊Q8—26no—
36C11×C4⋊Q8—26no—
37C11×C22⋊Q8—26no—
38C11×C22⋊Q8—26no—
39C11×C22⋊Q8—26no—
40C11×C22⋊Q8—26no—
41C4×Q8×C11—23no—
42C4×Q8×C11—21no—
43C4×Q8×C11—48no—
44C4×D4×C11—26no—
45C4×D4×C11—26no—
46C2×C11×C4⋊C4—26no—
47C2×C11×C4⋊C4C2×C413yes—
48C2×C11×C4⋊C4C2×C413yes—
49C2×C11×C4⋊C4C2×C416yes—
50C2×C11×C22⋊C4C2×C413yes—
51C2×C11×C22⋊C4C2316yes—
52C2×C11×C22⋊C4C2313yes—
53C2×C11×C22⋊C4C2312yes—
54C2×C42×C11—26no—
55C2×C42×C11C2×C413yes—
56C11×#99—26no—
57C11×#99Q814yesdirect product factor
58C11×#95—26no—
59C11×#95—26no—
60Q8×#99C1111yesmaximal, characteristic, direct product factor, Sylow
61C24×C11C22×C411yescharacteristic
62C24×C11C2411yescharacteristic
63C2×Q8×C11—28no—
64C2×Q8×C11—24no—
65C2×Q8×C11—23no—
66C2×Q8×C11—23no—
67C2×Q8×C11—46no—
68C2×Q8×C11—412no—
69C2×Q8×C11—46no—
70C2×Q8×C11—412no—
71C2×Q8×C11—44no—
72C2×Q8×C11C22⋊C413yes—
73C2×Q8×C11C22⋊C416yes—
74C2×Q8×C11C22⋊C416yes—
75C2×Q8×C11C22⋊C411yescharacteristic
76C2×D4×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11C2×Q812yes—
79C2×D4×C11#4112yes—
80C22×C4×C11—22no—
81C22×C4×C11—23no—
82C22×C4×C11—23no—
83C22×C4×C11—26no—
84C22×C4×C11—46no—
85C22×C4×C11—46no—
86C22×C4×C11C22×C413yes—
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C22×C413yes—
89C22×C4×C11C22×C413yes—
90C22×C4×C11C22×C413yes—
91C22×C4×C11C2×D416yes—
92C22×C4×C11C2×D416yes—
93C11×C4⋊C4—26no—
94C11×C4⋊C4—23no—
95C11×C4⋊C4—23no—
96C11×C4⋊C4—212no—
97C11×C4⋊C4—412no—
98C11×C22⋊C4—26no—
99C11×C22⋊C4—22no—
100C11×C22⋊C4—26no—
101C11×C22⋊C4—26no—
102C11×C22⋊C4—26no—
103C11×C22⋊C4C2×Q814yescomplemented
104C42×C11—23no—
105C42×C11—23no—
106C42×C11—412no—
107C2×D4×Q8C2×C1111yescharacteristic
108Q8×C22⋊C4C2×C1112yescomplemented
109#1996C2×C1116yescomplemented
110#1799C2×C1113yes—
111C4×#99C2×C1113yes—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—41no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11C4×Q812yescomplemented
119C23×C11C23×C411yescharacteristic
120C23×C11C22×D412yes—
121C23×C11C22×Q811yescharacteristic
122C23×C11C2×#4111yescharacteristic
123C23×C112−1+412yes—
124Q8×C11—26no—
125Q8×C11—212no—
126Q8×C11—46no—
127Q8×C11—46no—
128Q8×C11—46no—
129Q8×C11#9914yesdirect product factor
130D4×C11—24no—
131D4×C11—24no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—212no—
135C2×C4×C11—26no—
136C2×C4×C11—23no—
137C2×C4×C11—23no—
138C2×C4×C11—24no—
139C2×C4×C11—43no—
140C2×C4×C11—46no—
141C2×C4×C11—46no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—46no—
145C2×C4×C11—43no—
146C2×C4×C11—43no—
147C2×C4×C11—46no—
148C2×C4×C11—46no—
149C2×C4×C11—46no—
150C2×C4×C11C2×C22⋊C413yes—
151C2×C4×C11C2×C22⋊C416yes—
152C2×C4×C11C2×C22⋊C413yes—
153C2×C4×C11C4×Q812yescomplemented
154C23×Q8C4×C1111yescharacteristic, complemented
155C23×Q8C22×C1111yescharacteristic
156D4×Q8—22no—
157D4×Q8—26no—
158C2×C4⋊Q8C4×C1113yescomplemented
159C2×C22⋊Q8C4×C1113yescomplemented
160C2×C22⋊Q8C22×C1113yes—
161C2×C4×Q8—22no—
162C2×C4×Q8C4×C1111yescharacteristic, complemented
163C2×C4×D4C22×C1113yes—
164C2×#99C22×C1113yes—
165C2×#99C22×C1111yescharacteristic
166#391—26no—
167#380C22×C1116yes—
168C4×C22⋊C4C22×C1116yes—
169#342C22×C1116yes—
170#342C22×C1116yes—
171C22×C11—22no—
172C22×C11—21no—
173C22×C11—22no—
174C22×C11—21no—
175C22×C11—22no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—42no—
179C22×C11—42no—
180C22×C11—42no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11C22×C22⋊C411yescharacteristic
184C22×C11C2×C4×Q811yescharacteristic
185C22×C11#51911yescharacteristic
186C22×C11#54812yes—
187C22×C11D4×Q812yes—
188C4×C11—22no—
189C4×C11—23no—
190C4×C11—26no—
191C4×C11—44no—
192C4×C11—43no—
193C4×C11—43no—
194C4×C11—86no—
195C4×C11C2×#9916yes—
196C22×Q8—23no—
197C22×Q8—21no—
198C22×Q8—44no—
199C22×Q8—44no—
200C22×Q8C2×C4×C1111yescharacteristic
201C22×Q8C2×C4×C1113yes—
202C22×Q8C2×C4×C1113yes—
203C22×Q8D4×C1112yes—
204C22×Q8D4×C1116yes—
205C22×D4C23×C1111yescharacteristic
206C23×C4C2×C4×C1113yes—
207C23×C4C23×C1113yes—
208C4⋊Q8—26no—
209C4⋊Q8—26no—
210C22⋊Q8—26no—
211C22⋊Q8—26no—
212C22⋊Q8—26no—
213C22⋊Q8—26no—
214C4×Q8—23no—
215C4×Q8—21no—
216C4×Q8—48no—
217C4×D4—26no—
218C4×D4—26no—
219C2×C4⋊C4—26no—
220C2×C4⋊C4C2×C4×C1113yes—
221C2×C4⋊C4C2×C4×C1113yes—
222C2×C4⋊C4C2×C4×C1116yes—
223C2×C22⋊C4C2×C4×C1113yes—
224C2×C22⋊C4C23×C1116yes—
225C2×C22⋊C4C23×C1113yes—
226C2×C22⋊C4C23×C1112yes—
227C2×C42—26no—
228C2×C42C2×C4×C1113yes—
229#99—26no—
230#99Q8×C1114yesdirect product factor
231#95—26no—
232#95—26no—
233C2×C11—22no—
234C2×C11—22no—
235C2×C11—21no—
236C2×C11—21no—
237C2×C11—42no—
238C2×C11Q8×C22⋊C411yescharacteristic
239C2×C11C22×#9911yescharacteristic
240C2×C11#288411yescharacteristic
241C24C22×C4×C1111yescharacteristic
242C24C24×C1111yescharacteristic
243C2×Q8—28no—
244C2×Q8—24no—
245C2×Q8—23no—
246C2×Q8—23no—
247C2×Q8—46no—
248C2×Q8—412no—
249C2×Q8—46no—
250C2×Q8—412no—
251C2×Q8—44no—
252C2×Q8C11×C22⋊C413yes—
253C2×Q8C11×C22⋊C416yes—
254C2×Q8C11×C22⋊C416yes—
255C2×Q8C11×C22⋊C411yescharacteristic
256C2×D4—22no—
257C2×D4—22no—
258C2×D4C2×Q8×C1112yes—
259C2×D4C11×#4112yes—
260C22×C4—22no—
261C22×C4—23no—
262C22×C4—23no—
263C22×C4—26no—
264C22×C4—46no—
265C22×C4—46no—
266C22×C4C22×C4×C1113yes—
267C22×C4C22×C4×C1111yescharacteristic
268C22×C4C22×C4×C1113yes—
269C22×C4C22×C4×C1113yes—
270C22×C4C22×C4×C1113yes—
271C22×C4C2×D4×C1116yes—
272C22×C4C2×D4×C1116yes—
273C4⋊C4—26no—
274C4⋊C4—23no—
275C4⋊C4—23no—
276C4⋊C4—212no—
277C4⋊C4—412no—
278C22⋊C4—26no—
279C22⋊C4—22no—
280C22⋊C4—26no—
281C22⋊C4—26no—
282C22⋊C4—26no—
283C22⋊C4C2×Q8×C1114yescomplemented
284C42—23no—
285C42—23no—
286C42—412no—
287C11Q8×#9911yescharacteristic, direct product factor, Sylow
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23C4×Q8×C1112yescomplemented
295C23C23×C4×C1111yescharacteristic
296C23C22×D4×C1112yes—
297C23C22×Q8×C1111yescharacteristic
298C23C2×C11×#4111yescharacteristic
299C23C11×2−1+412yes—
300Q8—26no—
301Q8—212no—
302Q8—46no—
303Q8—46no—
304Q8—46no—
305Q8C11×#9914yesdirect product factor
306D4—24no—
307D4—24no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—212no—
311C2×C4—26no—
312C2×C4—23no—
313C2×C4—23no—
314C2×C4—24no—
315C2×C4—43no—
316C2×C4—46no—
317C2×C4—46no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—46no—
321C2×C4—43no—
322C2×C4—43no—
323C2×C4—46no—
324C2×C4—46no—
325C2×C4—46no—
326C2×C4C2×C11×C22⋊C413yes—
327C2×C4C2×C11×C22⋊C416yes—
328C2×C4C2×C11×C22⋊C413yes—
329C2×C4C4×Q8×C1112yescomplemented
330C22—22no—
331C22—21no—
332C22—22no—
333C22—21no—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—42no—
338C22—42no—
339C22—42no—
340C22—41no—
341C22—41no—
342C22C22×C11×C22⋊C411yescharacteristic
343C22C2×C4×Q8×C1111yescharacteristic
344C22C11×#51911yescharacteristic
345C22C11×#54812yes—
346C22D4×Q8×C1112yes—
347C4—22no—
348C4—23no—
349C4—26no—
350C4—44no—
351C4—43no—
352C4—43no—
353C4—86no—
354C4C2×C11×#9916yes—
355C2—22no—
356C2—22no—
357C2—21no—
358C2—21no—
359C2—42no—
360C2Q8×C11×C22⋊C411yescharacteristic
361C2C22×C11×#9911yescharacteristic
362C2C11×#288411yescharacteristic
subgroupG/H
center, socleC22×C11C22×C22⋊C4
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. Q8×C11×C22⋊C4C2semidirect
3. C11×#1996C2semidirect
6. C23×Q8×C11C4semidirect
10. C2×C11×C4⋊Q8C4semidirect
11. C2×C11×C22⋊Q8C4semidirect
14. C2×C4×Q8×C11C4semidirect
57. C11×#99Q8direct (N × H)
60. Q8×#99C11direct (N × H)
103. C11×C22⋊C4C2×Q8semidirect
108. Q8×C22⋊C4C2×C11semidirect
109. #1996C2×C11semidirect
118. C23×C11C4×Q8semidirect
129. Q8×C11#99direct (N × H)
153. C2×C4×C11C4×Q8semidirect
154. C23×Q8C4×C11semidirect
158. C2×C4⋊Q8C4×C11semidirect
159. C2×C22⋊Q8C4×C11semidirect
162. C2×C4×Q8C4×C11semidirect
230. #99Q8×C11direct (N × H)
283. C22⋊C4C2×Q8×C11semidirect
287. C11Q8×#99direct (N × H)
294. C23C4×Q8×C11semidirect
305. Q8C11×#99direct (N × H)
329. C2×C4C4×Q8×C11semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C112
Q8×C11×C22⋊C42
C11×#19962
C11×#17992
C4×C11×#992
Q8×#9911