Finite Group Databasebeta

← #14764185

Subgroups — #14764185

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
1#13071225C212yesmaximal
2#13069386C212yesmaximal, complemented
3#13069386C212yesmaximal, complemented
4#13069380C212yesmaximal, complemented
5#13069375C212yesmaximal, complemented
6#13068649C212yesmaximal
7#13068645C211yesmaximal, characteristic
8#13068641C211yesmaximal, characteristic
9C2×C11×#424C211yesmaximal, characteristic
10C22×C11×M16C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C11×#424C418yescomplemented
14C2×C11×C4⋊C8C2212yes—
15C2×C11×C4⋊C8C2212yes—
16#10622825C2212yes—
17#10622825C2212yes—
18C2×#66882C2212yes—
19C2×#66882C2212yes—
20C2×#66881C2212yes—
21C2×#66881C2212yes—
22#10622594—22no—
23#10622594—22no—
24#10622564—22no—
25#10622564—22no—
26#10622549C2212yes—
27#10622548C2212yes—
28C4×C4⋊Dic11C2212yes—
29C4×C4⋊Dic11C2212yes—
30#10622189C2211yescharacteristic
31#10622189C2212yes—
32#10622189C2211yescharacteristic
33#10622189C2211yescharacteristic
34#10622189C2211yescharacteristic
35#10622189C2212yes—
36C23×C4×C11C2311yescharacteristic
37C2×C11×M16—42no—
38C2×C11×M16C2×C414yes—
39C22×C8×C11—42no—
40C22×C8×C11C2×C414yes—
41C22×C8×C11C2311yescharacteristic
42C22×C8×C11C2311yescharacteristic
43C22×C8×C11C2312yes—
44C11×#117C2×C414yes—
45C11×#117Q814yes—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C22⋊C4D412yes—
49C2×C42×C11C2312yes—
50C2×C22⋊Dic11—22no—
51C2×C22⋊Dic11—22no—
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11—22no—
54C2×C4⋊Dic11C2312yes—
55C2×C4⋊Dic11C2312yes—
56C2×C4⋊Dic11C2312yes—
57C2×C4⋊Dic11C2312yes—
58C2×C4×Dic11—22no—
59C2×C4×Dic11—22no—
60C11×C4⋊C8C2×C418yes—
61C11×C4⋊C8C2×C418yes—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C11⋊#95—22no—
65C11⋊#95—22no—
66C11⋊#95—22no—
67C11⋊#95—22no—
68#66882—42no—
69#66882—42no—
70#66881—42no—
71#66881—42no—
72#21966—111nomaximal, Sylow
73C24×C11C2×D411yescharacteristic
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11C22×C412yes—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D412yes—
79C22×C4×C11C2×D412yes—
80C22×C4×C11C2×Q812yes—
81C22×C4×C11C2411yescharacteristic
82C22×Dic11—22no—
83C22×Dic11—22no—
84C22×Dic11—22no—
85C22×Dic11—22no—
86C11×M16—44no—
87C2×C8×C11—22no—
88C2×C8×C11—22no—
89C2×C8×C11—22no—
90C2×C8×C11—22no—
91C2×C8×C11—44no—
92C2×C8×C11C22×C412yes—
93C2×C8×C11C22×C412yes—
94C2×C8×C11C22×C414yes—
95C11×C4⋊C4C4⋊C414yes—
96C11×C4⋊C4C4⋊C414yes—
97C11×C22⋊C4C4⋊C418yes—
98C42×C11C22×C414yes—
99C42×C11C2×Q814yes—
100C22⋊Dic11—82no—
101C22⋊Dic11—82no—
102C4⋊Dic11—22no—
103C4⋊Dic11—22no—
104C4⋊Dic11—22no—
105C4⋊Dic11—22no—
106C4⋊Dic11—22no—
107C4⋊Dic11—22no—
108C4⋊Dic11—22no—
109C4⋊Dic11—22no—
110C4⋊Dic11—82no—
111C4⋊Dic11—82no—
112C4×Dic11—82no—
113C4×Dic11—82no—
114C2×#424D1111yescharacteristic
115#2314—112no—
116#1949—112no—
117#1949—112no—
118#1948—112no—
119#1947—112no—
120#1809—112no—
121#1808—111no—
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—22no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—24no—
137C2×C4×C11C2×C4⋊C414yes—
138C2×C4×C11C2×C4⋊C414yes—
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—42no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—42no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155C2×Dic11—42no—
156C8×C11—22no—
157C8×C11—22no—
158C8×C11—24no—
159C22×M16C2×D1111yescharacteristic
160C23×C8C2×D1111yescharacteristic
161C2×#117C2×D1111yescharacteristic
162C2×#107—112no—
163C2×#107—112no—
164C2×#106—112no—
165C2×#106—112no—
166#424Dic1118yescomplemented
167C2×C4⋊C8C2×D1112yes—
168C2×C4⋊C8C2×D1112yes—
169#388—222no—
170#388—222no—
171#387—222no—
172#387—222no—
173#384—112no—
174#382—112no—
175#380—112no—
176#380—112no—
177C4×C4⋊C4—112no—
178C4×C4⋊C4—112no—
179#340—111no—
180#340—111no—
181#340—111no—
182#340—111no—
183#340—112no—
184#340—112no—
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—24no—
197C4×C11—24no—
198C4×C11#51811yescharacteristic
199C4×C11#51911yescharacteristic
200C4×C11#54412yes—
201Dic11—82no—
202Dic11—82no—
203Dic11—82no—
204Dic11—82no—
205C23×C4C22×D1111yescharacteristic
206C2×M16—42no—
207C2×M16C2×Dic1114yes—
208C22×C8—42no—
209C22×C8C2×Dic1114yes—
210C22×C8C22×D1111yescharacteristic
211C22×C8C22×D1111yescharacteristic
212C22×C8C22×D1112yes—
213#117Dic2214yes—
214#117C2×Dic1114yes—
215C2×C4⋊C4—112no—
216C2×C4⋊C4—112no—
217C2×C4⋊C4—112no—
218C2×C4⋊C4—112no—
219C2×C4⋊C4—222no—
220C2×C4⋊C4—222no—
221C2×C4⋊C4D4411yescharacteristic
222C2×C4⋊C4D4411yescharacteristic
223C2×C22⋊C4—222no—
224C2×C22⋊C4—222no—
225C2×C22⋊C4D4412yes—
226C2×C42—222no—
227C2×C42—222no—
228C2×C42C22×D1112yes—
229#107—442no—
230#107—442no—
231#106—442no—
232#106—442no—
233C4⋊C8C2×Dic1118yes—
234C4⋊C8C2×Dic1118yes—
235#95—222no—
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—
247C24C2×D4411yescharacteristic
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—222no—
251C22×C4—222no—
252C22×C4—222no—
253C22×C4—222no—
254C22×C4C2×Dic2212yes—
255C22×C4C2×D4411yescharacteristic
256C22×C4C2×D4412yes—
257C22×C4C2×D4412yes—
258C22×C4C22×Dic1112yes—
259C22×C4C23×D1111yescharacteristic
260M16—44no—
261C2×C8—22no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—44no—
266C2×C8C22×Dic1112yes—
267C2×C8C22×Dic1112yes—
268C2×C8C22×Dic1114yes—
269C4⋊C4—222no—
270C4⋊C4—222no—
271C4⋊C4—222no—
272C4⋊C4—222no—
273C4⋊C4—222no—
274C4⋊C4—222no—
275C4⋊C4—222no—
276C4⋊C4—222no—
277C4⋊C4—882no—
278C4⋊C4—882no—
279C4⋊C4C4⋊Dic1114yes—
280C4⋊C4C4⋊Dic1114yes—
281C22⋊C4—882no—
282C22⋊C4—882no—
283C22⋊C4C4⋊Dic1118yes—
284C42—882no—
285C42—882no—
286C42C2×Dic2214yes—
287C42C22×Dic1114yes—
288C11#2196611yescharacteristic, complemented, Sylow
289C23—22no—
290C23—21no—
291C23—21no—
292C23—22no—
293C23C2×C4⋊Dic1112yes—
294C23C22×D4411yescharacteristic
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—24no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—442no—
304C2×C4—442no—
305C2×C4—442no—
306C2×C4—442no—
307C2×C4—442no—
308C2×C4—442no—
309C2×C4—442no—
310C2×C4—442no—
311C2×C4—442no—
312C2×C4—442no—
313C2×C4—442no—
314C2×C4—442no—
315C2×C4C2×C4⋊Dic1114yes—
316C2×C4C2×C4⋊Dic1114yes—
317C2×C4C2×C4⋊Dic1112yes—
318C2×C4C22×Dic2211yescharacteristic
319C2×C4#6703712yes—
320C2×C4#6704012yes—
321C2×C4C23×Dic1111yescharacteristic
322C8—22no—
323C8—22no—
324C8—24no—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—42no—
329C22—42no—
330C22#1062304112yes—
331C22#1062328212yes—
332C22#1062328311yescharacteristic
333C22#1062328411yescharacteristic
334C22C22×C4⋊Dic1111yescharacteristic
335C4—22no—
336C4—24no—
337C4—24no—
338C4—882no—
339C4—882no—
340C4—882no—
341C4—882no—
342C4#1062303112yes—
343C4#1062332911yescharacteristic
344C4#1062334311yescharacteristic
345C2—42no—
346C2#1307123411yescharacteristic
347C2#1307721111yescharacteristic
348C2#1307721611yescharacteristic
349C2#1308002912yes—
350C2#1308004412yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#424C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#424D11
hypocenterC11#21966
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
2. #13069386C2semidirect
3. #13069386C2semidirect
4. #13069380C2semidirect
5. #13069375C2semidirect
13. C11×#424C4semidirect
166. #424Dic11semidirect
288. C11#21966semidirect

Maximal subgroups

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

subgroupindex
#130712252
#130693862
#130693802
#130693752
#130686492
#130686452
#130686412
C2×C11×#4242
#2196611