Finite Group Databasebeta

← #14764187

Subgroups — #14764187

Order 2816.

754 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622715C211yesmaximal, characteristic
2#13071223C212yesmaximal
3#13069383C212yesmaximal, complemented
4#13069381C212yesmaximal, complemented
5#13069378C212yesmaximal, complemented
6#13069371C212yesmaximal, complemented
7#13068647C212yesmaximal
8#13068641C211yesmaximal, characteristic
9C11×#1808C211yesmaximal, characteristic
10C23×C8×C11C2211yescharacteristic
11C2×#66979C2211yescharacteristic
12C22×#4318C2211yescharacteristic
13C2×C11×#107C2212yes—
14C11×#380C2212yes—
15#10622825C2212yes—
16C2×#66881C2212yes—
17#10622715C418yescomplemented
18C2×Dic11⋊C8C2212yes—
19C2×Dic11⋊C8C2212yes—
20#10622590C2212yes—
21#10622589C2212yes—
22C4⋊C4×Dic11C2212yes—
23C4⋊C4×Dic11C2212yes—
24C2×#66872C2212yes—
25C2×#66871C2212yes—
26#10622558—22no—
27#10622557—22no—
28#10622267—22no—
29#10622266—22no—
30C11×#340C2211yescharacteristic
31C11×#340C2211yescharacteristic
32#10622189C2211yescharacteristic
33#10622189C2211yescharacteristic
34#10622167C2212yes—
35#10622167C2212yes—
36C23×C4×C11C2311yescharacteristic
37C22×C8×C11—42no—
38C22×C8×C11C2×C414yes—
39C22×C8×C11C2311yescharacteristic
40C22×C8×C11C2311yescharacteristic
41C2×C11×C4⋊C4C2312yes—
42C2×C11×C4⋊C4C2312yes—
43C2×C11×C22⋊C4—22no—
44C2×C22⋊Dic11—22no—
45C2×C22⋊Dic11D412yes—
46#66979C2×C414yes—
47#66979Q814yes—
48C2×C4⋊Dic11D411yescharacteristic
49C2×C4⋊Dic11D411yescharacteristic
50C2×C4⋊Dic11C2312yes—
51C2×C4⋊Dic11C2312yes—
52C2×Dic11⋊C4—22no—
53C2×Dic11⋊C4—22no—
54C2×C4×Dic11—22no—
55C2×C4×Dic11—22no—
56C2×C4×Dic11C2312yes—
57C2×#4318—42no—
58C2×#4318C2×C414yes—
59C22×C11⋊C8C2312yes—
60C11×#107—42no—
61C11×#95—22no—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C11⋊#95—22no—
65C11⋊#95—22no—
66C11⋊#95—22no—
67#66881—42no—
68Dic11⋊C8C2×C418yes—
69Dic11⋊C8C2×C418yes—
70#66872—42no—
71#66871—42no—
72#21966—111nomaximal, Sylow
73C24×C11C2×D411yescharacteristic
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11C22×C412yes—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×Q812yes—
81C22×C4×C11C2411yescharacteristic
82C22×Dic11—22no—
83C22×Dic11—22no—
84C22×Dic11C2×D412yes—
85C22×Dic11C2×D412yes—
86C2×C8×C11—22no—
87C2×C8×C11—22no—
88C2×C8×C11—44no—
89C2×C8×C11C22×C412yes—
90C2×C8×C11C22×C412yes—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—22no—
95C11×C22⋊C4—82no—
96C22⋊Dic11—82no—
97C22⋊Dic11C4⋊C418yes—
98C4⋊Dic11—22no—
99C4⋊Dic11—22no—
100C4⋊Dic11—22no—
101C4⋊Dic11—22no—
102C4⋊Dic11C4⋊C414yes—
103C4⋊Dic11C4⋊C414yes—
104Dic11⋊C4—82no—
105Dic11⋊C4—82no—
106C4×Dic11—82no—
107C4×Dic11—82no—
108C4×Dic11C22×C414yes—
109C4×Dic11C2×Q814yes—
110#4318—44no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8C22×C414yes—
114C2×#424—111no—
115#2314—112no—
116#1949—112no—
117#1949—112no—
118#1948—112no—
119#1947—112no—
120#1809—112no—
121#1808D1111yescharacteristic
122#1807—111no—
123C23×C11—22no—
124C23×C11—21no—
125C23×C11—22no—
126C23×C11—21no—
127C23×C11C2×C4⋊C412yes—
128C23×C11C22×D411yescharacteristic
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—24no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11C2×C4⋊C412yes—
140C2×C4×C11C23×C411yescharacteristic
141C2×C4×C11C22×Q811yescharacteristic
142C2×C4×C11H(5,𝔽2)12yes—
143C2×C4×C112−1+412yes—
144C2×Dic11—22no—
145C2×Dic11—22no—
146C2×Dic11—22no—
147C2×Dic11—22no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—42no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154C2×Dic11C2×C4⋊C414yes—
155C2×Dic11C2×C4⋊C414yes—
156C8×C11—22no—
157C8×C11—22no—
158C11⋊C8—24no—
159C22×M16—111no—
160C23×C8C2×D1111yescharacteristic
161C2×#117—111no—
162C2×#107—112no—
163C2×#107C2×D1112yes—
164C2×#106—112no—
165C2×#106—112no—
166#424—118no—
167C2×C4⋊C8—112no—
168C2×C4⋊C8—112no—
169#388—222no—
170#388—222no—
171#387—222no—
172#387—222no—
173#384—112no—
174#382—112no—
175#380—112no—
176#380C2×D1112yes—
177C4×C4⋊C4—112no—
178C4×C4⋊C4—112no—
179#340—111no—
180#340—111no—
181#340—112no—
182#340—112no—
183#340C2×D1111yescharacteristic
184#340C2×D1111yescharacteristic
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—22no—
188C22×C11—42no—
189C22×C11—42no—
190C22×C11C22×C4⋊C411yescharacteristic
191C22×C11#53712yes—
192C22×C11#57611yescharacteristic
193C22×C11#57712yes—
194C22×C11#57811yescharacteristic
195C4×C11—22no—
196C4×C11—82no—
197C4×C11—82no—
198C4×C11#51811yescharacteristic
199C4×C11#51911yescharacteristic
200C4×C11#54412yes—
201Dic11—24no—
202Dic11—24no—
203Dic11—82no—
204Dic11—82no—
205C23×C4C22×D1111yescharacteristic
206C2×M16—114no—
207C2×M16—442no—
208C22×C8—42no—
209C22×C8—112no—
210C22×C8C4×D1114yes—
211C22×C8C22×D1111yescharacteristic
212C22×C8C22×D1111yescharacteristic
213#117—114no—
214#117—114no—
215C2×C4⋊C4—111no—
216C2×C4⋊C4—111no—
217C2×C4⋊C4—112no—
218C2×C4⋊C4—112no—
219C2×C4⋊C4—222no—
220C2×C4⋊C4—222no—
221C2×C4⋊C4C22×D1112yes—
222C2×C4⋊C4C22×D1112yes—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—112no—
225C2×C22⋊C4—222no—
226C2×C42—112no—
227C2×C42—222no—
228C2×C42—222no—
229#107—42no—
230#107—442no—
231#106—442no—
232#106—442no—
233C4⋊C8—118no—
234C4⋊C8—118no—
235#95—22no—
236#95—222no—
237#95—222no—
238#95—222no—
239#95—222no—
240#95—222no—
241C2×C11—42no—
242C2×C11#231611yescharacteristic
243C2×C11#291211yescharacteristic
244C2×C11#291311yescharacteristic
245C2×C11#325712yes—
246C2×C11#325812yes—
247C24D4×D1111yescharacteristic
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—112no—
253C22×C4—112no—
254C22×C4—222no—
255C22×C4—222no—
256C22×C4C2×C4×D1112yes—
257C22×C4D4×D1111yescharacteristic
258C22×C4Q8×D1112yes—
259C22×C4C23×D1111yescharacteristic
260M16—444no—
261C2×C8—22no—
262C2×C8—22no—
263C2×C8—44no—
264C2×C8—114no—
265C2×C8—222no—
266C2×C8—222no—
267C2×C8C2×C4×D1112yes—
268C2×C8C2×C4×D1112yes—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—114no—
274C4⋊C4—114no—
275C4⋊C4—222no—
276C4⋊C4—222no—
277C4⋊C4—222no—
278C4⋊C4—222no—
279C4⋊C4—882no—
280C4⋊C4—882no—
281C22⋊C4—82no—
282C22⋊C4—118no—
283C22⋊C4—882no—
284C42—114no—
285C42—114no—
286C42—882no—
287C42—882no—
288C11#2196611yescharacteristic, complemented, Sylow
289C23—21no—
290C23—21no—
291C23—22no—
292C23—22no—
293C23C4⋊C4×D1112yes—
294C23C2×D4×D1111yescharacteristic
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—24no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—114no—
306C2×C4—114no—
307C2×C4—222no—
308C2×C4—222no—
309C2×C4—222no—
310C2×C4—222no—
311C2×C4—442no—
312C2×C4—442no—
313C2×C4—442no—
314C2×C4—442no—
315C2×C4—442no—
316C2×C4—442no—
317C2×C4C4⋊C4×D1112yes—
318C2×C4C22×C4×D1111yescharacteristic
319C2×C4#6703712yes—
320C2×C4C2×Q8×D1111yescharacteristic
321C2×C4#6704312yes—
322C8—22no—
323C8—22no—
324C8—224no—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—42no—
329C22—42no—
330C22C2×C4⋊C4×D1111yescharacteristic
331C22#1062312812yes—
332C22#1062328811yescharacteristic
333C22#1062329711yescharacteristic
334C22#1062330112yes—
335C4—22no—
336C4—82no—
337C4—82no—
338C4—224no—
339C4—224no—
340C4—882no—
341C4—882no—
342C4#1062301711yescharacteristic
343C4#1062304711yescharacteristic
344C4#1062315412yes—
345C2—42no—
346C2#1307123311yescharacteristic
347C2#1307720811yescharacteristic
348C2#1307721211yescharacteristic
349C2#1308002012yes—
350C2#1308004512yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1808C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1808D11
hypocenterC11#21966
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1808

Complements

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

NH ≅ G/Ntype
3. #13069383C2semidirect
4. #13069381C2semidirect
5. #13069378C2semidirect
6. #13069371C2semidirect
17. #10622715C4semidirect
288. C11#21966semidirect

Maximal subgroups

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

subgroupindex
C2×#106227152
#130712232
#130693832
#130693812
#130693782
#130693712
#130686472
#130686412
C11×#18082
#2196611