Finite Group Databasebeta

← #14725242

Subgroups — #14725242

Order 2816.

652 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077636C212yesmaximal, complemented
2#13067501C212yesmaximal, complemented
3#13067460C214yesmaximal, complemented
4Q16×C11⋊C8C212yesmaximal, complemented
5#13067379C211yesmaximal, characteristic, complemented
6#13067050C212yesmaximal, complemented
7C8×#4318C211yesmaximal, characteristic, complemented
8C4×C11×#135C211yesmaximal, characteristic
9C2×C11×#135C411yescharacteristic
10C4×C11×#41C2212yes—
11C4×C11×Q16C411yescharacteristic
12C4×C11×Q16C2211yescharacteristic
13C4×C11×SD16C412yes—
14C4×C11×SD16C2212yes—
15C4×C11×D8C411yescharacteristic
16C4×C11×D8C2211yescharacteristic
17C11×#427C411yescharacteristic
18C11×#416C412yes—
19C2×C4×C8×C11C2211yescharacteristic
20Q8×C11⋊C8C2214yes—
21#10622625—24no—
22#10622625C2214yes—
23#10622539—22no—
24#10622539C2212yes—
25#10622538C2211yescharacteristic
26C4×#4318—22no—
27C4×#4318C2211yescharacteristic
28Q8⋊(C11⋊C8)C2214yes—
29D4⋊(C11⋊C8)C2214yes—
30#10622096C2212yes—
31#10622095C2212yes—
32#10622092C2212yes—
33C8×C11⋊C8C2212yes—
34C2×C11×#41C2×C412yes—
35C11×#135—24no—
36C2×C11×Q16C2×C411yescharacteristic
37C2×C11×SD16C2×C412yes—
38C2×C11×D8C2×C411yescharacteristic
39C22×C8×C11C2×C411yescharacteristic
40C22×C8×C11C2×C411yescharacteristic
41C4×Q8×C11C2×C412yes—
42C4×Q8×C11C2312yes—
43C4×D4×C11—22no—
44C4×D4×C11—22no—
45C4×D4×C11C2×C412yes—
46C4×D4×C11C2312yes—
47C11×#117—22no—
48C11×#117C2×C412yes—
49C2×C42×C11—22no—
50C2×C42×C11C2311yescharacteristic
51C2×#4318—24no—
52C2×#4318D412yes—
53C11×#107C2×C411yescharacteristic
54C11×#107C2×C411yescharacteristic
55C11×#106C2×C412yes—
56C11×#103C2×C412yes—
57C11×#103C2×C412yes—
58C11×#102C2×C412yes—
59C11×#102C2×C412yes—
60C4×C8×C11C2×C411yescharacteristic
61C4×C8×C11C2×C411yescharacteristic
62C4×C8×C11C2311yescharacteristic
63C4×C8×C11C2311yescharacteristic
64C22⋊(C11⋊C8)—22no—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—24no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—24no—
69C4⋊(C11⋊C8)C2314yes—
70#66867—22no—
71#66867D411yescharacteristic
72#66867D411yescharacteristic
73C4×C11⋊C8—24no—
74C4×C11⋊C8C2312yes—
75C4×C11⋊C8C2312yes—
76#18039—111nomaximal, Sylow
77C11×#41—24no—
78C11×#41—42no—
79C2×Q8×C11C22×C412yes—
80C2×D4×C11—22no—
81C2×D4×C11C22×C412yes—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11C22×C411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C11×Q16M1614yescomplemented
89C11×SD16—24no—
90C11×D8—22no—
91C2×C8×C11—22no—
92C2×C8×C11—41no—
93C2×C8×C11C22×C411yescharacteristic
94C2×C8×C11C22×C411yescharacteristic
95C2×C8×C11C22×C411yescharacteristic
96C2×C8×C11C22×C411yescharacteristic
97C11×C4⋊C4—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4C22×C412yes—
100C11×C4⋊C4C22×C412yes—
101C11×C22⋊C4—22no—
102C11×C22⋊C4—22no—
103C11×C22⋊C4—22no—
104C42×C11—22no—
105C42×C11—22no—
106C42×C11—22no—
107C42×C11C22×C411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11#4111yescharacteristic
110C42×C11C2411yescharacteristic
111#4318—24no—
112#4318—48no—
113C2×C11⋊C8—24no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8C2×D412yes—
116C2×C11⋊C8C2×D412yes—
117#2971—112no—
118C4×#135D1111yescharacteristic
119#1589—112no—
120#1583—114no—
121C8×Q16—112no—
122#1568—111no—
123#1488—112no—
124C8×M16—111no—
125C23×C11—22no—
126C23×C11C4×D411yescharacteristic
127Q8×C11—22no—
128Q8×C11C2×M1614yes—
129D4×C11—22no—
130D4×C11—22no—
131D4×C11—44no—
132C2×C4×C11—22no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11—44no—
140C2×C4×C11—44no—
141C2×C4×C11—82no—
142C2×C4×C11C4×D411yescharacteristic
143C2×C4×C11C4×D411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11C23×C411yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C2×C4×C11C2×#4111yescharacteristic
148C8×C11—21no—
149C8×C11—21no—
150C8×C11—21no—
151C8×C11C2×M1612yes—
152C11⋊C8—22no—
153C11⋊C8—42no—
154C11⋊C8—44no—
155C11⋊C8#13514yescomplemented
156C2×#135Dic1111yescharacteristic
157C4×#41C2×D1112yes—
158C8×Q8—114no—
159C4×Q16Dic1111yescharacteristic
160C4×Q16C2×D1111yescharacteristic
161C4×SD16Dic1112yes—
162C4×SD16C2×D1112yes—
163C4×D8Dic1111yescharacteristic
164C4×D8C2×D1111yescharacteristic
165#436—114no—
166#436—224no—
167#432—112no—
168#432—222no—
169#431—111no—
170#427Dic1111yescharacteristic
171#416Dic1112yes—
172C4×M16—111no—
173C4×M16—222no—
174C2×C4×C8C2×D1111yescharacteristic
175#335—112no—
176#334—112no—
177Q8⋊C8—114no—
178D4⋊C8—114no—
179#322—112no—
180C82—112no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—42no—
185C22×C11—42no—
186C22×C11—42no—
187C22×C11C2×C4×D411yescharacteristic
188C4×C11—21no—
189C4×C11—24no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—42no—
194C4×C11—42no—
195C4×C11C22×M1611yescharacteristic
196C4×C11#56811yescharacteristic
197C4×C11C2×#13512yes—
198C2×#41C2×Dic1112yes—
199#135—24no—
200C2×Q16C2×Dic1111yescharacteristic
201C2×SD16C2×Dic1112yes—
202C2×D8C2×Dic1111yescharacteristic
203C2×M16—112no—
204C2×M16—224no—
205C22×C8C2×Dic1111yescharacteristic
206C22×C8C2×Dic1111yescharacteristic
207C4×Q8C2×Dic1112yes—
208C4×Q8C22×D1112yes—
209C4×D4—22no—
210C4×D4—22no—
211C4×D4C2×Dic1112yes—
212C4×D4C22×D1112yes—
213#117—22no—
214#117C2×Dic1112yes—
215C2×C42—22no—
216C2×C42C22×D1111yescharacteristic
217#107C2×Dic1111yescharacteristic
218#107C2×Dic1111yescharacteristic
219#106C2×Dic1112yes—
220C4⋊C8—114no—
221C4⋊C8—224no—
222C4⋊C8—221no—
223#103C2×Dic1112yes—
224#103C2×Dic1112yes—
225#102C2×Dic1112yes—
226#102C2×Dic1112yes—
227C22⋊C8—224no—
228C22⋊C8—222no—
229C22⋊C8—221no—
230#97—111no—
231#97—111no—
232#97—222no—
233C4×C8—112no—
234C4×C8—112no—
235C4×C8—224no—
236C4×C8C2×Dic1111yescharacteristic
237C4×C8C2×Dic1111yescharacteristic
238C4×C8C22×D1111yescharacteristic
239C4×C8C22×D1111yescharacteristic
240C2×C11—41no—
241C2×C11—82no—
242C2×C11D4×M1611yescharacteristic
243C2×C11C4×#13511yescharacteristic
244C2×C11#295711yescharacteristic
245#41—24no—
246#41—42no—
247C2×Q8C22×Dic1112yes—
248C2×D4—22no—
249C2×D4C22×Dic1112yes—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4D4×D1111yescharacteristic
254C22×C4#434111yescharacteristic
255C22×C4C22×Dic1111yescharacteristic
256Q16#431814yescomplemented
257SD16—24no—
258D8—22no—
259M16—224no—
260M16—448no—
261C2×C8—22no—
262C2×C8—41no—
263C2×C8—112no—
264C2×C8—112no—
265C2×C8—224no—
266C2×C8—222no—
267C2×C8C22×Dic1111yescharacteristic
268C2×C8C22×Dic1111yescharacteristic
269C2×C8C22×Dic1111yescharacteristic
270C2×C8C22×Dic1111yescharacteristic
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4C22×Dic1112yes—
274C4⋊C4C22×Dic1112yes—
275C22⋊C4—22no—
276C22⋊C4—22no—
277C22⋊C4—22no—
278C42—22no—
279C42—22no—
280C42—22no—
281C42D4×D1111yescharacteristic
282C42#434111yescharacteristic
283C42C22×Dic1111yescharacteristic
284C42C23×D1111yescharacteristic
285C11#1803911yescharacteristic, complemented, Sylow
286C23—22no—
287C23D4×Dic1111yescharacteristic
288Q8—22no—
289Q8C2×#431814yes—
290D4—22no—
291D4—22no—
292D4—44no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—44no—
301C2×C4—44no—
302C2×C4—82no—
303C2×C4D4×Dic1111yescharacteristic
304C2×C4D4×Dic1111yescharacteristic
305C2×C4D4×Dic1111yescharacteristic
306C2×C4C2×D4×D1111yescharacteristic
307C2×C4C2×#434111yescharacteristic
308C2×C4C23×Dic1111yescharacteristic
309C8—21no—
310C8—21no—
311C8—21no—
312C8—114no—
313C8—222no—
314C8—442no—
315C8—444no—
316C8C2×#431812yes—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—42no—
321C22—42no—
322C22—42no—
323C22C2×D4×Dic1111yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—24no—
328C4—21no—
329C4—42no—
330C4—42no—
331C4D11×#13512yes—
332C4C22×#431811yescharacteristic
333C4#1062335011yescharacteristic
334C2—41no—
335C2—82no—
336C2D4×#431811yescharacteristic
337C2#135×Dic1111yescharacteristic
338C2#1307753311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC4×C11×#135C2
socleC22×C11C2×C4×D4
prime radicalC2×C11×#135C4
cosocleC42×C11C24
hypercenterC4×#135D11
hypocenterC11#18039
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
1. #13077636C2semidirect
2. #13067501C2semidirect
3. #13067460C2semidirect
4. Q16×C11⋊C8C2semidirect
5. #13067379C2semidirect
6. #13067050C2semidirect
7. C8×#4318C2semidirect
88. C11×Q16M16semidirect
155. C11⋊C8#135semidirect
256. Q16#4318semidirect
285. C11#18039semidirect

Maximal subgroups

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

subgroupindex
#130776362
#130675012
#130674602
Q16×C11⋊C82
#130673792
#130670502
C8×#43182
C4×C11×#1352
#1803911