Finite Group Databasebeta

← Q8×C11×#124 #14613741

Subgroups — Q8×C11×#124 #14613741

Order 2816.

2326 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q82×C11C211yesmaximal, characteristic, complemented
2C2×D4×Q8×C11C211yesmaximal, characteristic
3C11×#2862C213yesmaximal, complemented
4C11×#2568C213yesmaximal, complemented
5C11×#2563C213yesmaximal
6C11×#2492C2112yesmaximal, complemented
7Q8×C11×C22⋊C4C214yesmaximal, complemented
8C4×C11×#124C213yesmaximal
9C42×Q8×C11C211yesmaximal, characteristic, complemented
10C23×Q8×C11C2212yes—
11Q82×C11—28no—
12D4×Q8×C11—28no—
13C2×C11×C4⋊Q8C2213yes—
14C2×C11×C4⋊Q8C2216yes—
15C2×C11×C4⋊Q8C2213yes—
16C2×C11×#124C2211yescharacteristic
17C2×C11×C22⋊Q8C2216yes—
18C2×C4×Q8×C11C2213yes—
19C2×C4×Q8×C11C2212yes—
20C2×C4×Q8×C11C2212yes—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11C2213yes—
23C11×#400C22112yes—
24C11×#393C22112yes—
25C11×#391C22112yes—
26C11×#391C22112yes—
27C11×#391C22112yes—
28C11×#391C2213yes—
29C11×#390C2213yes—
30C11×#388C22112yes—
31C11×#382C2213yes—
32C11×#382C2216yes—
33C11×#380C22112yes—
34C4×C11×C4⋊C4C2216yes—
35C4×C11×C4⋊C4C2213yes—
36C4×C11×C22⋊C4C22112yes—
37C43×C11C2213yes—
38C22×Q8×C11—28no—
39C22×Q8×C11—216no—
40C22×Q8×C11C2316yes—
41C22×Q8×C11C2311yescharacteristic
42C22×Q8×C11C2316yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11C2316yes—
46C11×C4⋊Q8—224no—
47C11×C4⋊Q8—212no—
48C11×C4⋊Q8—212no—
49C11×#124Q818yesdirect product factor
50C11×C22⋊Q8—224no—
51C4×Q8×C11—28no—
52C4×Q8×C11—28no—
53C4×Q8×C11—212no—
54C4×Q8×C11D418yes—
55C4×D4×C11—212no—
56C2×C11×C4⋊C4C2313yes—
57C2×C11×C4⋊C4C2316yes—
58C2×C11×C4⋊C4C2316yes—
59C2×C11×C4⋊C4C2313yes—
60C2×C11×C4⋊C4C2316yes—
61C2×C11×C4⋊C4C2316yes—
62C2×C11×C4⋊C4C2313yes—
63C2×C11×C22⋊C4C2316yes—
64C2×C11×C22⋊C4C23112yes—
65C2×C11×C22⋊C4C2314yes—
66C2×C42×C11C2316yes—
67C2×C42×C11C2313yes—
68C2×C42×C11C2316yes—
69C2×C42×C11C2316yes—
70C2×C42×C11C2313yes—
71C2×C42×C11C2311yescharacteristic
72C11×#95C23112yes—
73C11×#95C23112yes—
74C11×#95C2316yes—
75C11×#95C23124yes—
76Q8×#124C1111yesmaximal, characteristic, direct product factor, Sylow
77C24×C11C2412yes—
78C2×Q8×C11—22no—
79C2×Q8×C11—212no—
80C2×Q8×C11—212no—
81C2×Q8×C11—224no—
82C2×Q8×C11—22no—
83C2×Q8×C11—412no—
84C2×Q8×C11—432no—
85C2×Q8×C11C2×D414yes—
86C2×Q8×C11C2×Q814yescomplemented
87C2×Q8×C11#4118yes—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11C2×Q814yes—
91C22×C4×C11—212no—
92C22×C4×C11—224no—
93C22×C4×C11C2416yes—
94C22×C4×C11C2416yes—
95C22×C4×C11C2416yes—
96C22×C4×C11C2413yes—
97C22×C4×C11C2412yes—
98C22×C4×C11C2412yes—
99C22×C4×C11C2411yescharacteristic
100C22×C4×C11C2413yes—
101C11×C4⋊C4—26no—
102C11×C4⋊C4—212no—
103C11×C4⋊C4—212no—
104C11×C4⋊C4—26no—
105C11×C4⋊C4—212no—
106C11×C4⋊C4—212no—
107C11×C4⋊C4C2×D4112yes—
108C11×C22⋊C4—212no—
109C11×C22⋊C4—412no—
110C11×C22⋊C4C2×Q8116yescomplemented
111C42×C11—212no—
112C42×C11—212no—
113C42×C11—26no—
114C42×C11—46no—
115C42×C11C2×D4112yes—
116C42×C11C2×Q814yescomplemented
117C2×Q82C2×C1111yescharacteristic, complemented
118C2×D4×Q8C2×C1111yescharacteristic
119#2862C2×C1113yescomplemented
120#2568C2×C1113yescomplemented
121#2563C2×C1113yes—
122#2492C2×C11112yescomplemented
123Q8×C22⋊C4C2×C1114yescomplemented
124C4×#124C2×C1113yes—
125C42×Q8C2×C1111yescharacteristic, complemented
126C23×C11—22no—
127C23×C11—24no—
128C23×C11—22no—
129C23×C11—24no—
130C23×C11C22×Q814yes—
131C23×C11C2511yescharacteristic
132Q8×C11—28no—
133Q8×C11—424no—
134Q8×C11—812no—
135Q8×C11#124116yesdirect product factor
136D4×C11—28no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—26no—
142C2×C4×C11—26no—
143C2×C4×C11—26no—
144C2×C4×C11—26no—
145C2×C4×C11—212no—
146C2×C4×C11—26no—
147C2×C4×C11—26no—
148C2×C4×C11—212no—
149C2×C4×C11—424no—
150C2×C4×C11C22×D416yes—
151C2×C4×C11C22×D416yes—
152C2×C4×C11C22×D412yes—
153C2×C4×C11C22×Q814yes—
154C2×C4×C11C22×Q814yes—
155C2×C4×C11C22×Q812yes—
156C2×C4×C11C2×#41112yes—
157C2×C4×C112−1+412yes—
158C23×Q8C22×C1112yes—
159Q82—28no—
160D4×Q8—28no—
161C2×C4⋊Q8C22×C1113yes—
162C2×C4⋊Q8C22×C1113yes—
163C2×C4⋊Q8C22×C1116yes—
164C2×#124C22×C1111yescharacteristic
165C2×C22⋊Q8C22×C1116yes—
166C2×C4×Q8C22×C1113yes—
167C2×C4×Q8C22×C1112yes—
168C2×C4×Q8C22×C1112yes—
169C2×C4×Q8C22×C1111yescharacteristic
170C2×C4×D4C22×C1113yes—
171#400C22×C11112yes—
172#393C22×C11112yes—
173#391C22×C1113yes—
174#391C22×C11112yes—
175#391C22×C11112yes—
176#391C22×C11112yes—
177#390C22×C1113yes—
178#388C22×C11112yes—
179#382C22×C1116yes—
180#382C22×C1113yes—
181#380C22×C11112yes—
182C4×C4⋊C4C22×C1113yes—
183C4×C4⋊C4C22×C1116yes—
184C4×C22⋊C4C22×C11112yes—
185C43C22×C1113yes—
186C22×C11—24no—
187C22×C11—28no—
188C22×C11—42no—
189C22×C11—42no—
190C22×C11—44no—
191C22×C11C23×D411yescharacteristic
192C22×C11C23×Q811yescharacteristic
193C22×C11C22×#4112yes—
194C22×C11C2×2−1+411yescharacteristic
195C22×C11#58512yes—
196C4×C11—24no—
197C4×C11—24no—
198C4×C11—26no—
199C4×C11—46no—
200C4×C11—46no—
201C4×C11—46no—
202C4×C11C2×#124112yes—
203C4×C11D4×Q814yes—
204C22×Q8—28no—
205C22×Q8—216no—
206C22×Q8C23×C1116yes—
207C22×Q8C23×C1111yescharacteristic
208C22×Q8C23×C1116yes—
209C22×Q8C23×C1111yescharacteristic
210C22×D4C23×C1111yescharacteristic
211C23×C4C23×C1116yes—
212C4⋊Q8—224no—
213C4⋊Q8—212no—
214C4⋊Q8—212no—
215#124Q8×C1118yesdirect product factor
216C22⋊Q8—224no—
217C4×Q8—28no—
218C4×Q8—28no—
219C4×Q8—212no—
220C4×Q8D4×C1118yes—
221C4×D4—212no—
222C2×C4⋊C4C23×C1113yes—
223C2×C4⋊C4C23×C1116yes—
224C2×C4⋊C4C23×C1113yes—
225C2×C4⋊C4C23×C1116yes—
226C2×C4⋊C4C23×C1116yes—
227C2×C4⋊C4C23×C1116yes—
228C2×C4⋊C4C23×C1113yes—
229C2×C22⋊C4C23×C1116yes—
230C2×C22⋊C4C23×C11112yes—
231C2×C22⋊C4C23×C1114yes—
232C2×C42C23×C1116yes—
233C2×C42C23×C1116yes—
234C2×C42C23×C1113yes—
235C2×C42C23×C1116yes—
236C2×C42C23×C1113yes—
237C2×C42C23×C1111yescharacteristic
238#95C23×C11112yes—
239#95C23×C11112yes—
240#95C23×C1116yes—
241#95C23×C11124yes—
242C2×C11—44no—
243C2×C11C22×#12411yescharacteristic
244C2×C11C2×D4×Q811yescharacteristic
245C2×C11Q8×#4112yes—
246C2×C11#350011yescharacteristic
247C2×C11#351812yes—
248C24C24×C1112yes—
249C2×Q8—22no—
250C2×Q8—212no—
251C2×Q8—212no—
252C2×Q8—224no—
253C2×Q8—22no—
254C2×Q8—412no—
255C2×Q8—432no—
256C2×Q8C2×D4×C1114yes—
257C2×Q8C2×Q8×C1114yescomplemented
258C2×Q8C11×#4118yes—
259C2×D4—22no—
260C2×D4—22no—
261C2×D4C2×Q8×C1114yes—
262C22×C4—212no—
263C22×C4—224no—
264C22×C4C24×C1116yes—
265C22×C4C24×C1116yes—
266C22×C4C24×C1116yes—
267C22×C4C24×C1113yes—
268C22×C4C24×C1112yes—
269C22×C4C24×C1112yes—
270C22×C4C24×C1111yescharacteristic
271C22×C4C24×C1113yes—
272C4⋊C4—26no—
273C4⋊C4—212no—
274C4⋊C4—212no—
275C4⋊C4—26no—
276C4⋊C4—212no—
277C4⋊C4—212no—
278C4⋊C4C2×D4×C11112yes—
279C22⋊C4—212no—
280C22⋊C4—412no—
281C22⋊C4C2×Q8×C11116yescomplemented
282C42—212no—
283C42—212no—
284C42—26no—
285C42—46no—
286C42C2×D4×C11112yes—
287C42C2×Q8×C1114yescomplemented
288C11Q8×#12411yescharacteristic, direct product factor, Sylow
289C23—22no—
290C23—24no—
291C23—22no—
292C23—24no—
293C23C22×Q8×C1114yes—
294C23C25×C1111yescharacteristic
295Q8—28no—
296Q8—424no—
297Q8—812no—
298Q8C11×#124116yesdirect product factor
299D4—28no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—26no—
305C2×C4—26no—
306C2×C4—26no—
307C2×C4—26no—
308C2×C4—212no—
309C2×C4—26no—
310C2×C4—26no—
311C2×C4—212no—
312C2×C4—424no—
313C2×C4C22×D4×C1116yes—
314C2×C4C22×D4×C1116yes—
315C2×C4C22×D4×C1112yes—
316C2×C4C22×Q8×C1114yes—
317C2×C4C22×Q8×C1114yes—
318C2×C4C22×Q8×C1112yes—
319C2×C4C2×C11×#41112yes—
320C2×C4C11×2−1+412yes—
321C22—24no—
322C22—28no—
323C22—42no—
324C22—42no—
325C22—44no—
326C22C23×D4×C1111yescharacteristic
327C22C23×Q8×C1111yescharacteristic
328C22C22×C11×#4112yes—
329C22C2×C11×2−1+411yescharacteristic
330C22C11×#58512yes—
331C4—24no—
332C4—24no—
333C4—26no—
334C4—46no—
335C4—46no—
336C4—46no—
337C4C2×C11×#124112yes—
338C4D4×Q8×C1114yes—
339C2—44no—
340C2C22×C11×#12411yescharacteristic
341C2C2×D4×Q8×C1111yescharacteristic
342C2Q8×C11×#4112yes—
343C2C11×#350011yescharacteristic
344C2C11×#351812yes—
subgroupG/H
center, socleC23×C11C25
commutator, Frattini, cosocleC23C25×C11
prime radicalC22×D4×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×Q82×C11C2semidirect
3. C11×#2862C2semidirect
4. C11×#2568C2semidirect
6. C11×#2492C2semidirect
7. Q8×C11×C22⋊C4C2semidirect
9. C42×Q8×C11C2semidirect
49. C11×#124Q8direct (N × H)
76. Q8×#124C11direct (N × H)
86. C2×Q8×C11C2×Q8semidirect
110. C11×C22⋊C4C2×Q8semidirect
116. C42×C11C2×Q8semidirect
117. C2×Q82C2×C11semidirect
119. #2862C2×C11semidirect
120. #2568C2×C11semidirect
122. #2492C2×C11semidirect
123. Q8×C22⋊C4C2×C11semidirect
125. C42×Q8C2×C11semidirect
135. Q8×C11#124direct (N × H)
215. #124Q8×C11direct (N × H)
257. C2×Q8C2×Q8×C11semidirect
281. C22⋊C4C2×Q8×C11semidirect
287. C42C2×Q8×C11semidirect
288. C11Q8×#124direct (N × H)
298. Q8C11×#124direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q82×C112
C2×D4×Q8×C112
C11×#28622
C11×#25682
C11×#25632
C11×#24922
Q8×C11×C22⋊C42
C4×C11×#1242
C42×Q8×C112
Q8×#12411