Finite Group Databasebeta

← #14723634

Subgroups — #14723634

Order 2816.

646 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#13077733C212yesmaximal, complemented
2#13067530C212yesmaximal, complemented
3#13067525C212yesmaximal, complemented
4#13067507C214yesmaximal, complemented
5C2×#10622095C211yesmaximal, characteristic, complemented
6#13067003C212yesmaximal, complemented
7#13066899C211yesmaximal, 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
20#10622637C2214yes—
21#10622625C2214yes—
22#10622624—24no—
23#10622539—22no—
24#10622538C2211yescharacteristic
25#10622538C2211yescharacteristic
26#10622537—22no—
27C2×C4⋊(C11⋊C8)C2212yes—
28Q8⋊(C11⋊C8)C2214yes—
29D4⋊(C11⋊C8)C2214yes—
30#10622095C2212yes—
31#10622095C2212yes—
32#10622093C2212yes—
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—
52C22×C11⋊C8—22no—
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)—21no—
65C22⋊(C11⋊C8)—24no—
66C22⋊(C11⋊C8)D412yes—
67C4⋊(C11⋊C8)—22no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—24no—
70C4⋊(C11⋊C8)D412yes—
71C4⋊(C11⋊C8)C2314yes—
72#66867—24no—
73C4×C11⋊C8C2312yes—
74C4×C11⋊C8C2312yes—
75#17899—111nomaximal, Sylow
76C11×#41—24no—
77C11×#41—24no—
78C2×Q8×C11C22×C412yes—
79C2×D4×C11—22no—
80C2×D4×C11C22×C412yes—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C11×Q16—22no—
88C11×SD16—24no—
89C11×D8—22no—
90C2×C8×C11—22no—
91C2×C8×C11M1614yescomplemented
92C2×C8×C11C22×C411yescharacteristic
93C2×C8×C11C22×C411yescharacteristic
94C2×C8×C11C22×C411yescharacteristic
95C2×C8×C11C22×C411yescharacteristic
96C11×C4⋊C4—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4C22×C412yes—
99C11×C4⋊C4C22×C412yes—
100C11×C22⋊C4—22no—
101C11×C22⋊C4—22no—
102C11×C22⋊C4—22no—
103C42×C11—22no—
104C42×C11—22no—
105C42×C11—22no—
106C42×C11C22×C411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11#4111yescharacteristic
109C42×C11C2411yescharacteristic
110#4318—84no—
111C2×C11⋊C8—24no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—82no—
114C2×C11⋊C8C2×D414yes—
115#2989—112no—
116C4×#135D1111yescharacteristic
117#1594—112no—
118#1593—112no—
119#1590—114no—
120C2×#334—111no—
121#1477—112no—
122#1450—111no—
123C23×C11—22no—
124C23×C11C4×D411yescharacteristic
125Q8×C11—22no—
126Q8×C11—22no—
127D4×C11—22no—
128D4×C11—22no—
129D4×C11—44no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—44no—
138C2×C4×C11—82no—
139C2×C4×C11C4×D411yescharacteristic
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11C2×M1612yes—
143C2×C4×C11#13112yes—
144C2×C4×C11C23×C411yescharacteristic
145C2×C4×C11C22×D411yescharacteristic
146C2×C4×C11C2×#4111yescharacteristic
147C8×C11—21no—
148C8×C11—21no—
149C8×C11C2×M1612yes—
150C8×C11C2×M1612yes—
151C11⋊C8—24no—
152C11⋊C8—42no—
153C11⋊C8—44no—
154C2×#135Dic1111yescharacteristic
155C4×#41C2×D1112yes—
156#446—114no—
157C4×Q16Dic1111yescharacteristic
158C4×Q16C2×D1111yescharacteristic
159C4×SD16Dic1112yes—
160C4×SD16C2×D1112yes—
161C4×D8Dic1111yescharacteristic
162C4×D8C2×D1111yescharacteristic
163#436—114no—
164#435—224no—
165#432—222no—
166#431—111no—
167#431—111no—
168#427Dic1111yescharacteristic
169#423—222no—
170C2×C4⋊C8—112no—
171#416Dic1112yes—
172C2×C4×C8C2×D1111yescharacteristic
173#334—112no—
174#334—112no—
175Q8⋊C8—114no—
176D4⋊C8—114no—
177#322—112no—
178C82—112no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—42no—
182C22×C11—42no—
183C22×C11—42no—
184C22×C11#43612yes—
185C22×C11C2×C4×D411yescharacteristic
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—42no—
190C4×C11—42no—
191C4×C11—42no—
192C4×C11#43612yes—
193C4×C11C22×M1611yescharacteristic
194C4×C11C2×#13111yescharacteristic
195C4×C11#57712yes—
196C2×#41C2×Dic1112yes—
197#135—24no—
198C2×Q16C2×Dic1111yescharacteristic
199C2×SD16C2×Dic1112yes—
200C2×D8C2×Dic1111yescharacteristic
201C2×M16—224no—
202C22×C8—222no—
203C22×C8C2×Dic1111yescharacteristic
204C22×C8C2×Dic1111yescharacteristic
205C4×Q8C2×Dic1112yes—
206C4×Q8C22×D1112yes—
207C4×D4—22no—
208C4×D4—22no—
209C4×D4C2×Dic1112yes—
210C4×D4C22×D1112yes—
211#117—22no—
212#117C2×Dic1112yes—
213C2×C42—22no—
214C2×C42C22×D1111yescharacteristic
215#107C2×Dic1111yescharacteristic
216#107C2×Dic1111yescharacteristic
217#106C2×Dic1112yes—
218C4⋊C8—112no—
219C4⋊C8—114no—
220C4⋊C8—224no—
221C4⋊C8—222no—
222C4⋊C8—221no—
223#103C2×Dic1112yes—
224#103C2×Dic1112yes—
225#102C2×Dic1112yes—
226#102C2×Dic1112yes—
227C22⋊C8—112no—
228C22⋊C8—224no—
229C22⋊C8—221no—
230#97—224no—
231C4×C8—112no—
232C4×C8—112no—
233C4×C8C2×Dic1111yescharacteristic
234C4×C8C2×Dic1111yescharacteristic
235C4×C8C22×D1111yescharacteristic
236C4×C8C22×D1111yescharacteristic
237C2×C11—22no—
238C2×C11—82no—
239C2×C11C2×#43611yescharacteristic
240C2×C11#295211yescharacteristic
241C2×C11#295711yescharacteristic
242#41—24no—
243#41—24no—
244C2×Q8C22×Dic1112yes—
245C2×D4—22no—
246C2×D4C22×Dic1112yes—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4D4×D1111yescharacteristic
251C22×C4#434111yescharacteristic
252C22×C4C22×Dic1111yescharacteristic
253Q16—22no—
254SD16—24no—
255D8—22no—
256M16—884no—
257C2×C8—22no—
258C2×C8—114no—
259C2×C8—224no—
260C2×C8—222no—
261C2×C8—882no—
262C2×C8#431814yescomplemented
263C2×C8C22×Dic1111yescharacteristic
264C2×C8C22×Dic1111yescharacteristic
265C2×C8C22×Dic1111yescharacteristic
266C2×C8C22×Dic1111yescharacteristic
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4C22×Dic1112yes—
270C4⋊C4C22×Dic1112yes—
271C22⋊C4—22no—
272C22⋊C4—22no—
273C22⋊C4—22no—
274C42—22no—
275C42—22no—
276C42—22no—
277C42D4×D1111yescharacteristic
278C42#434111yescharacteristic
279C42C22×Dic1111yescharacteristic
280C42C23×D1111yescharacteristic
281C11#1789911yescharacteristic, complemented, Sylow
282C23—22no—
283C23D4×Dic1111yescharacteristic
284Q8—22no—
285Q8—22no—
286D4—22no—
287D4—22no—
288D4—44no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—44no—
297C2×C4—82no—
298C2×C4C2×#431812yes—
299C2×C4D4×Dic1111yescharacteristic
300C2×C4D4×Dic1111yescharacteristic
301C2×C4D4×Dic1111yescharacteristic
302C2×C4#6700112yes—
303C2×C4C2×D4×D1111yescharacteristic
304C2×C4C2×#434111yescharacteristic
305C2×C4C23×Dic1111yescharacteristic
306C8—21no—
307C8—21no—
308C8—224no—
309C8—442no—
310C8—444no—
311C8C2×#431812yes—
312C8C2×#431812yes—
313C22—21no—
314C22—21no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22#1062262512yes—
319C22C2×D4×Dic1111yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—42no—
324C4—42no—
325C4—42no—
326C4#1062262512yes—
327C4#1062330112yes—
328C4C22×#431811yescharacteristic
329C4C2×#6700111yescharacteristic
330C2—22no—
331C2—82no—
332C2C2×#1062262511yescharacteristic
333C2#1307750011yescharacteristic
334C2#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#17899
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. #13077733C2semidirect
2. #13067530C2semidirect
3. #13067525C2semidirect
4. #13067507C2semidirect
5. C2×#10622095C2semidirect
6. #13067003C2semidirect
7. #13066899C2semidirect
91. C2×C8×C11M16semidirect
262. C2×C8#4318semidirect
281. C11#17899semidirect

Maximal subgroups

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

subgroupindex
#130777332
#130675302
#130675252
#130675072
C2×#106220952
#130670032
#130668992
C4×C11×#1352
#1789911