Finite Group Databasebeta

← #14913967

Subgroups — #14913967

Order 2816.

2250 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071581C216yesmaximal, complemented
2#13071537C212yesmaximal, complemented
3#13071493C216yesmaximal
4Q8×C22⋊Dic11C212yesmaximal
5#13071267C216yesmaximal, complemented
6#13071014C213yesmaximal
7#13071014C213yesmaximal
8#13070981C212yesmaximal, complemented
9C22×C4×Q8×C11C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C2×C4×Q8×C11C4116yescomplemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×C4×Q8×C11C2213yes—
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×Q8×C11C2213yes—
16C22×C11×C4⋊C4C2213yes—
17C22×C42×C11C2213yes—
18C2×Q8×Dic11C2214yes—
19#10622843C22112yes—
20#10622825C2216yes—
21#10622825C2216yes—
22#10622824C2211yescharacteristic
23#10622824C2213yes—
24C4×C22⋊Dic11C2216yes—
25C4×C22⋊Dic11C2216yes—
26#10622598C22112yes—
27#10622594C22124yes—
28C4⋊C4×Dic11C22112yes—
29#10622550C2216yes—
30#10622550C2216yes—
31#10622549C2216yes—
32#10622549C2216yes—
33C4×C4⋊Dic11C2216yes—
34C4×C4⋊Dic11C2216yes—
35#10622545C2216yes—
36#10622545C2216yes—
37C22×Q8×C11—28no—
38C22×Q8×C11C2×C418yes—
39C22×Q8×C11C2313yes—
40C22×Q8×C11C2311yescharacteristic
41C23×C4×C11C2313yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2313yes—
44C4×Q8×C11C2×C4124yes—
45C4×Q8×C11C2×C4124yes—
46C4×Q8×C11C2×C418yes—
47C4×Q8×C11C2×C418yes—
48C2×C11×C4⋊C4C2×C4124yes—
49C2×C11×C4⋊C4C2313yes—
50C2×C11×C4⋊C4C2316yes—
51C2×C11×C4⋊C4C2313yes—
52C2×C42×C11C2×C4124yes—
53C2×C42×C11C2313yes—
54C2×C42×C11C2313yes—
55C2×C42×C11C2313yes—
56C2×C42×C11C2313yes—
57C2×C22⋊Dic11C2312yes—
58C2×C22⋊Dic11C2316yes—
59Q8×Dic11—216no—
60C2×C4⋊Dic11C23112yes—
61C2×C4⋊Dic11C23112yes—
62C2×C4×Dic11C23112yes—
63C2×C4×Dic11C23112yes—
64C11⋊#95C2312yes—
65C11⋊#95C2316yes—
66C11⋊#95C2316yes—
67C11⋊#95C23112yes—
68C11⋊#95C23112yes—
69C11⋊#95C2312yes—
70C11⋊#95C23112yes—
71C11⋊#95C23112yes—
72#34192—111nomaximal, Sylow
73C24×C11C2411yescharacteristic
74C2×Q8×C11—232no—
75C2×Q8×C11—212no—
76C2×Q8×C11C22×C4112yes—
77C2×Q8×C11C22×C414yes—
78C2×Q8×C11#4118yes—
79C22×C4×C11—24no—
80C22×C4×C11—212no—
81C22×C4×C11—46no—
82C22×C4×C11C22×C414yes—
83C22×C4×C11C22×C4112yes—
84C22×C4×C11C22×C4112yes—
85C22×C4×C11C2411yescharacteristic
86C22×C4×C11C2411yescharacteristic
87C22×C4×C11C2413yes—
88C22×C4×C11C2413yes—
89C22×C4×C11C2413yes—
90C22×C4×C11C2413yes—
91C22×Dic11C2414yes—
92C22×Dic11C24112yes—
93C11×C4⋊C4C22×C4124yes—
94C11×C4⋊C4C22×C4112yes—
95C11×C4⋊C4C22×C4112yes—
96C42×C11C22×C4112yes—
97C42×C11C22×C4112yes—
98C42×C11C22×C4112yes—
99C42×C11C22×C4112yes—
100C22⋊Dic11—24no—
101C22⋊Dic11—212no—
102C4⋊Dic11—224no—
103C4⋊Dic11—412no—
104C4×Dic11—224no—
105C4×Dic11—412no—
106C22×C4×Q8D1111yescharacteristic
107#2356—116no—
108#2351—112no—
109#2345—116no—
110Q8×C22⋊C4—112no—
111#2320—116no—
112#2283—113no—
113#2283—113no—
114#2276—112no—
115C23×C11—22no—
116C23×C11—22no—
117C23×C11C23×C412yes—
118C23×C112−1+414yes—
119C23×C11C2511yescharacteristic
120Q8×C11—224no—
121Q8×C11#117116yes—
122C2×C4×C11—28no—
123C2×C4×C11—26no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—26no—
127C2×C4×C11—26no—
128C2×C4×C11—224no—
129C2×C4×C11—412no—
130C2×C4×C11C23×C412yes—
131C2×C4×C11C23×C412yes—
132C2×C4×C11C23×C416yes—
133C2×C4×C11C23×C416yes—
134C2×C4×C11C23×C416yes—
135C2×C4×C11C23×C416yes—
136C2×C4×C11C2×#41112yes—
137C2×Dic11—24no—
138C2×Dic11—212no—
139C2×Dic11—24no—
140C2×Dic11—212no—
141C2×Dic11—212no—
142C2×Dic11—24no—
143C23×Q8C2×D1111yescharacteristic
144C2×C4×Q8—114no—
145C2×C4×Q8Dic11116yescomplemented
146C2×C4×Q8C2×D1113yes—
147C2×C4×Q8C2×D1111yescharacteristic
148C2×C4×Q8C2×D1113yes—
149C2×C4×Q8C2×D1111yescharacteristic
150C22×C4⋊C4C2×D1113yes—
151C22×C42C2×D1113yes—
152#391—1112no—
153#389—1112no—
154#387—1124no—
155#383—116no—
156#383—116no—
157#382—116no—
158#382—116no—
159#381—111no—
160#381—113no—
161#380—116no—
162#380—116no—
163C4×C4⋊C4—1112no—
164C4×C4⋊C4—116no—
165C4×C4⋊C4—116no—
166C4×C22⋊C4—116no—
167C4×C22⋊C4—116no—
168#376—116no—
169#376—116no—
170C22×C11—22no—
171C22×C11—22no—
172C22×C11—28no—
173C22×C11#51914yes—
174C22×C11C24×C411yescharacteristic
175C22×C11C22×#4112yes—
176C22×C11C2×2−1+412yes—
177C22×C11#58512yes—
178C4×C11—26no—
179C4×C11—22no—
180C4×C11—22no—
181C4×C11—26no—
182C4×C11—26no—
183C4×C11C2×#117112yes—
184Dic11—44no—
185Dic11—412no—
186C22×Q8—28no—
187C22×Q8C2×Dic1118yes—
188C22×Q8C22×D1113yes—
189C22×Q8C22×D1111yescharacteristic
190C23×C4C22×D1113yes—
191C23×C4C22×D1111yescharacteristic
192C23×C4C22×D1113yes—
193C4×Q8—2216no—
194C4×Q8C2×Dic11124yes—
195C4×Q8C2×Dic11124yes—
196C4×Q8C2×Dic1118yes—
197C4×Q8C2×Dic1118yes—
198C2×C4⋊C4—1112no—
199C2×C4⋊C4—1112no—
200C2×C4⋊C4C2×Dic11124yes—
201C2×C4⋊C4C22×D1113yes—
202C2×C4⋊C4C22×D1116yes—
203C2×C4⋊C4C22×D1113yes—
204C2×C22⋊C4—112no—
205C2×C22⋊C4—116no—
206C2×C42—1112no—
207C2×C42—1112no—
208C2×C42C2×Dic11124yes—
209C2×C42C22×D1113yes—
210C2×C42C22×D1113yes—
211C2×C42C22×D1113yes—
212C2×C42C22×D1113yes—
213#95—112no—
214#95—116no—
215#95—1112no—
216#95—116no—
217#95—1112no—
218#95—1112no—
219#95—1112no—
220#95—112no—
221C2×C11—24no—
222C2×C11C22×#11711yescharacteristic
223C2×C11C2×#51911yescharacteristic
224C2×C11#342811yescharacteristic
225C2×C11#351614yes—
226C24C23×D1111yescharacteristic
227C2×Q8—232no—
228C2×Q8—212no—
229C2×Q8#433918yes—
230C2×Q8C22×Dic11112yes—
231C2×Q8C22×Dic1114yes—
232C22×C4—24no—
233C22×C4—212no—
234C22×C4—46no—
235C22×C4—114no—
236C22×C4—1112no—
237C22×C4C22×Dic1114yes—
238C22×C4C22×Dic11112yes—
239C22×C4C22×Dic11112yes—
240C22×C4C23×D1111yescharacteristic
241C22×C4C23×D1111yescharacteristic
242C22×C4C23×D1113yes—
243C22×C4C23×D1113yes—
244C22×C4C23×D1113yes—
245C22×C4C23×D1113yes—
246C4⋊C4—2224no—
247C4⋊C4—4412no—
248C4⋊C4C22×Dic11124yes—
249C4⋊C4C22×Dic11112yes—
250C4⋊C4C22×Dic11112yes—
251C22⋊C4—224no—
252C22⋊C4—2212no—
253C42—2224no—
254C42—4412no—
255C42C22×Dic11112yes—
256C42C22×Dic11112yes—
257C42C22×Dic11112yes—
258C42C22×Dic11112yes—
259C11#3419211yescharacteristic, complemented, Sylow
260C23—22no—
261C23—22no—
262C23#6704014yes—
263C23C23×Dic1112yes—
264C23C24×D1111yescharacteristic
265Q8—224no—
266Q8#66979116yes—
267C2×C4—28no—
268C2×C4—26no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—26no—
272C2×C4—26no—
273C2×C4—224no—
274C2×C4—412no—
275C2×C4—224no—
276C2×C4—2212no—
277C2×C4—224no—
278C2×C4—2212no—
279C2×C4—2212no—
280C2×C4—224no—
281C2×C4C2×#4339112yes—
282C2×C4C23×Dic1112yes—
283C2×C4C23×Dic1112yes—
284C2×C4C23×Dic1116yes—
285C2×C4C23×Dic1116yes—
286C2×C4C23×Dic1116yes—
287C2×C4C23×Dic1116yes—
288C22—22no—
289C22—22no—
290C22—28no—
291C22#1062334314yes—
292C22C22×#433912yes—
293C22C2×#6704012yes—
294C22#1062345312yes—
295C22C24×Dic1111yescharacteristic
296C4—26no—
297C4—22no—
298C4—22no—
299C4—26no—
300C4—26no—
301C4—444no—
302C4—4412no—
303C4C2×#66979112yes—
304C2—24no—
305C2C22×#6697911yescharacteristic
306C2C2×#1062334311yescharacteristic
307C2#1308181911yescharacteristic
308C2#1308260914yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC22×C4×Q8×C11C2
socle, cosocleC23×C11C25
prime radicalC24×C11C24
hypercenterC22×C4×Q8D11
hypocenterC11#34192
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #13071581C2semidirect
2. #13071537C2semidirect
5. #13071267C2semidirect
8. #13070981C2semidirect
11. C2×C4×Q8×C11C4semidirect
145. C2×C4×Q8Dic11semidirect
259. C11#34192semidirect

Maximal subgroups

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

subgroupindex
#130715812
#130715372
#130714932
Q8×C22⋊Dic112
#130712672
#130710142
#130709812
C22×C4×Q8×C112
#3419211