Finite Group Databasebeta

← #14913257

Subgroups — #14913257

Order 2816.

2610 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
1#13071565C216yesmaximal, complemented
2Q8×C4⋊Dic11C212yesmaximal, complemented
3#13071501C216yesmaximal, complemented
4#13071457C212yesmaximal
5#13071081C216yesmaximal, complemented
6#13071023C213yesmaximal, complemented
7C4×Q8×Dic11C212yesmaximal, complemented
8C4×#66979C213yesmaximal, complemented
9C2×C4×C11×#41C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C4×C11×#41C4116yescomplemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2213yes—
15C2×C4×D4×C11C2213yes—
16C2×C11×#117C2213yes—
17C22×C42×C11C2213yes—
18C2×Q8×Dic11C2214yes—
19C2×#66979C2216yes—
20C2×#66979C2216yes—
21#10622834C22112yes—
22#10622825C2216yes—
23#10622825C2216yes—
24C4×C22⋊Dic11C2216yes—
25C4×C22⋊Dic11C2216yes—
26#10622598C22112yes—
27C4⋊C4×Dic11C22112yes—
28#10622564C22124yes—
29#10622549C2216yes—
30#10622548C2216yes—
31C4×C4⋊Dic11C2211yescharacteristic
32C4×C4⋊Dic11C2216yes—
33C4×C4⋊Dic11C2213yes—
34C4×C4⋊Dic11C2216yes—
35#10622545C2216yes—
36C42×Dic11C2216yes—
37C2×C11×#41—28no—
38C2×C11×#41C2×C418yes—
39C22×Q8×C11C2311yescharacteristic
40C22×D4×C11C2313yes—
41C23×C4×C11C2313yes—
42C23×C4×C11C2313yes—
43C23×C4×C11C2313yes—
44C4×Q8×C11C2×C418yes—
45C4×Q8×C11C2×C418yes—
46C4×D4×C11C2×C4124yes—
47C4×D4×C11C2×C4124yes—
48C11×#117C2×C4124yes—
49C2×C11×C4⋊C4C2313yes—
50C2×C11×C4⋊C4C2313yes—
51C2×C11×C22⋊C4C2316yes—
52C2×C42×C11C2×C4124yes—
53C2×C42×C11C2313yes—
54C2×C42×C11C2313yes—
55C2×C42×C11C2311yescharacteristic
56C2×C42×C11C2313yes—
57C2×C22⋊Dic11C23112yes—
58C2×C22⋊Dic11C23112yes—
59Q8×Dic11—216no—
60#66979—224no—
61#66979—412no—
62C2×C4⋊Dic11C2316yes—
63C2×C4⋊Dic11C23112yes—
64C2×C4⋊Dic11C23112yes—
65C2×C4⋊Dic11C2312yes—
66C2×C4×Dic11C2312yes—
67C2×C4×Dic11C23112yes—
68C2×C4×Dic11C2316yes—
69C2×C4×Dic11C23112yes—
70C11⋊#95C2312yes—
71C11⋊#95C2316yes—
72C11⋊#95C23112yes—
73C11⋊#95C23112yes—
74#34129—111nomaximal, Sylow
75C24×C11C2413yes—
76C11×#41—232no—
77C2×Q8×C11C22×C414yes—
78C2×Q8×C11#4118yes—
79C2×D4×C11—212no—
80C2×D4×C11C22×C4112yes—
81C22×C4×C11—212no—
82C22×C4×C11—212no—
83C22×C4×C11—26no—
84C22×C4×C11—26no—
85C22×C4×C11C22×C4112yes—
86C22×C4×C11C22×C4112yes—
87C22×C4×C11C22×C4112yes—
88C22×C4×C11C2411yescharacteristic
89C22×C4×C11C2413yes—
90C22×C4×C11C2413yes—
91C22×C4×C11C2413yes—
92C22×C4×C11C2411yescharacteristic
93C22×C4×C11C2411yescharacteristic
94C22×Dic11C24112yes—
95C22×Dic11C2414yes—
96C11×C4⋊C4C22×C4112yes—
97C11×C4⋊C4C22×C4112yes—
98C11×C22⋊C4C22×C4124yes—
99C42×C11C22×C414yes—
100C42×C11C22×C4112yes—
101C42×C11C22×C4112yes—
102C42×C11C22×C4112yes—
103C22⋊Dic11—224no—
104C22⋊Dic11—412no—
105C4⋊Dic11—212no—
106C4⋊Dic11—224no—
107C4⋊Dic11—412no—
108C4⋊Dic11#4118yescomplemented
109C4×Dic11—224no—
110C4×Dic11—224no—
111C4×Dic11—212no—
112C4×Dic11—24no—
113C2×C4×#41D1111yescharacteristic
114#2354—116no—
115Q8×C4⋊C4—112no—
116#2346—116no—
117#2341—112no—
118#2293—116no—
119#2285—113no—
120C42×Q8—112no—
121C4×#117—113no—
122C23×C11—26no—
123C23×C11—26no—
124C23×C11—23no—
125C23×C11—23no—
126C23×C11C23×C416yes—
127C23×C11C2511yescharacteristic
128Q8×C11#117116yescomplemented
129D4×C11—224no—
130C2×C4×C11—26no—
131C2×C4×C11—22no—
132C2×C4×C11—23no—
133C2×C4×C11—23no—
134C2×C4×C11—224no—
135C2×C4×C11—224no—
136C2×C4×C11—224no—
137C2×C4×C11C23×C412yes—
138C2×C4×C11C23×C416yes—
139C2×C4×C11C23×C416yes—
140C2×C4×C11C23×C416yes—
141C2×C4×C11C23×C412yes—
142C2×C4×C11C23×C412yes—
143C2×C4×C11C2×#41112yes—
144C2×C4×C11C2×#4114yes—
145C2×C4×C11H(5,𝔽2)12yes—
146C2×C4×C112−1+412yes—
147C2×Dic11—24no—
148C2×Dic11—24no—
149C2×Dic11—212no—
150C2×Dic11—212no—
151C2×Dic11—212no—
152C2×Dic11C2×#4118yes—
153C22×#41C2×D1111yescharacteristic
154C4×#41Dic11116yescomplemented
155C2×C4×Q8—114no—
156C2×C4×Q8C2×D1111yescharacteristic
157C2×C4×Q8C2×D1111yescharacteristic
158C2×C4×D4C2×D1113yes—
159C2×C4×D4C2×D1113yes—
160C2×#117—116no—
161C2×#117—116no—
162C2×#117C2×D1113yes—
163C22×C42C2×D1113yes—
164#390—1112no—
165#389—1112no—
166#388—1124no—
167#384—116no—
168#382—116no—
169#380—116no—
170#380—116no—
171C4×C4⋊C4—1112no—
172C4×C4⋊C4—116no—
173C4×C4⋊C4—111no—
174C4×C4⋊C4—113no—
175C4×C4⋊C4—116no—
176C4×C22⋊C4—116no—
177C4×C22⋊C4—116no—
178#376—116no—
179C43—116no—
180C22×C11—26no—
181C22×C11—26no—
182C22×C11—26no—
183C22×C11—46no—
184C22×C11—46no—
185C22×C11C24×C411yescharacteristic
186C22×C11C22×#4112yes—
187C22×C11C22×#4112yes—
188C22×C11C2×H(5,𝔽2)11yescharacteristic
189C22×C11C2×2−1+411yescharacteristic
190C4×C11—22no—
191C4×C11—26no—
192C4×C11—26no—
193C4×C11C2×#117112yes—
194C4×C11C4×#4114yes—
195C4×C11#52014yes—
196Dic11—28no—
197Dic11—412no—
198C2×#41—28no—
199C2×#41C2×Dic1118yes—
200C22×Q8C22×D1111yescharacteristic
201C22×D4C22×D1113yes—
202C23×C4C22×D1113yes—
203C23×C4C22×D1113yes—
204C23×C4C22×D1113yes—
205C4×Q8—2216no—
206C4×Q8C2×Dic1118yes—
207C4×Q8C2×Dic1118yes—
208C4×D4C2×Dic11124yes—
209C4×D4C2×Dic11124yes—
210#117—2224no—
211#117—4412no—
212#117C2×Dic11124yes—
213C2×C4⋊C4—112no—
214C2×C4⋊C4—116no—
215C2×C4⋊C4—1112no—
216C2×C4⋊C4—1112no—
217C2×C4⋊C4C22×D1113yes—
218C2×C4⋊C4C22×D1113yes—
219C2×C22⋊C4—1112no—
220C2×C22⋊C4—1112no—
221C2×C22⋊C4C22×D1116yes—
222C2×C42—1112no—
223C2×C42—1112no—
224C2×C42—116no—
225C2×C42—112no—
226C2×C42C2×Dic11124yes—
227C2×C42C22×D1113yes—
228C2×C42C22×D1113yes—
229C2×C42C22×D1113yes—
230C2×C42C22×D1111yescharacteristic
231#95—112no—
232#95—116no—
233#95—1112no—
234#95—1112no—
235C2×C11—46no—
236C2×C11C22×#11711yescharacteristic
237C2×C11C2×C4×#4111yescharacteristic
238C2×C11C2×#52011yescharacteristic
239C2×C11#348212yes—
240C2×C11#348312yes—
241C24C23×D1113yes—
242#41—232no—
243C2×Q8#433918yes—
244C2×Q8C22×Dic1114yes—
245C2×D4—212no—
246C2×D4C22×Dic11112yes—
247C22×C4—212no—
248C22×C4—212no—
249C22×C4—26no—
250C22×C4—26no—
251C22×C4—114no—
252C22×C4—1112no—
253C22×C4C22×Dic11112yes—
254C22×C4C22×Dic11112yes—
255C22×C4C22×Dic11112yes—
256C22×C4C23×D1111yescharacteristic
257C22×C4C23×D1113yes—
258C22×C4C23×D1113yes—
259C22×C4C23×D1113yes—
260C22×C4C23×D1111yescharacteristic
261C22×C4C23×D1111yescharacteristic
262C4⋊C4—118no—
263C4⋊C4—2224no—
264C4⋊C4—2212no—
265C4⋊C4—4412no—
266C4⋊C4C22×Dic11112yes—
267C4⋊C4C22×Dic11112yes—
268C22⋊C4—2224no—
269C22⋊C4—4412no—
270C22⋊C4C22×Dic11124yes—
271C42—2224no—
272C42—2224no—
273C42—2212no—
274C42—224no—
275C42C22×Dic1114yes—
276C42C22×Dic11112yes—
277C42C22×Dic11112yes—
278C42C22×Dic11112yes—
279C11#3412911yescharacteristic, complemented, Sylow
280C23—26no—
281C23—26no—
282C23—23no—
283C23—23no—
284C23C23×Dic1116yes—
285C23C24×D1111yescharacteristic
286Q8#66979116yescomplemented
287D4—224no—
288C2×C4—22no—
289C2×C4—26no—
290C2×C4—23no—
291C2×C4—23no—
292C2×C4—224no—
293C2×C4—224no—
294C2×C4—224no—
295C2×C4—118no—
296C2×C4—224no—
297C2×C4—224no—
298C2×C4—2212no—
299C2×C4—2212no—
300C2×C4—2212no—
301C2×C4C2×#4339112yes—
302C2×C4#41×D1114yes—
303C2×C4#6704212yes—
304C2×C4#6704312yes—
305C2×C4C23×Dic1112yes—
306C2×C4C23×Dic1116yes—
307C2×C4C23×Dic1116yes—
308C2×C4C23×Dic1116yes—
309C2×C4C23×Dic1112yes—
310C2×C4C23×Dic1112yes—
311C22—26no—
312C22—26no—
313C22—26no—
314C22—46no—
315C22—46no—
316C22C22×#433912yes—
317C22C2×#41×D1112yes—
318C22C2×#6704211yescharacteristic
319C22C2×#6704311yescharacteristic
320C22C24×Dic1111yescharacteristic
321C4—22no—
322C4—26no—
323C4—26no—
324C4—228no—
325C4—4412no—
326C4C2×#66979112yes—
327C4#41×Dic1114yes—
328C4#1062335814yes—
329C2—46no—
330C2C22×#6697911yescharacteristic
331C2C2×#41×Dic1111yescharacteristic
332C2C2×#1062335811yescharacteristic
333C2#1308223812yes—
334C2#1308224212yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C4×C11×#41C2
socle, cosocleC23×C11C25
prime radicalC22×C11×#41C22
hypercenterC2×C4×#41D11
hypocenterC11#34129
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #13071565C2semidirect
2. Q8×C4⋊Dic11C2semidirect
3. #13071501C2semidirect
5. #13071081C2semidirect
6. #13071023C2semidirect
7. C4×Q8×Dic11C2semidirect
8. C4×#66979C2semidirect
11. C4×C11×#41C4semidirect
108. C4⋊Dic11#41semidirect
128. Q8×C11#117semidirect
154. C4×#41Dic11semidirect
279. C11#34129semidirect
286. Q8#66979semidirect

Maximal subgroups

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

subgroupindex
#130715652
Q8×C4⋊Dic112
#130715012
#130714572
#130710812
#130710232
C4×Q8×Dic112
C4×#669792
C2×C4×C11×#412
#3412911