Finite Group Databasebeta

← #14764320

Subgroups — #14764320

Order 2816.

806 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071023C211yesmaximal, characteristic
2#13071014C211yesmaximal, characteristic
3#13069380C212yesmaximal, complemented
4#13069375C212yesmaximal, complemented
5#13068817C214yesmaximal
6#13068780C212yesmaximal, complemented
7#13068747C212yesmaximal, complemented
8C2×C11×#431C211yesmaximal, characteristic
9C22×C42×C11C2211yescharacteristic
10C2×#66979C2212yes—
11C11×#431C418yescomplemented
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×C22⋊C8C2212yes—
15C2×C4×C8×C11C2212yes—
16#10622825—21no—
17#10622825—21no—
18#10622825C2212yes—
19#10622824—21no—
20C4×C22⋊Dic11—21no—
21C2×#66882C2214yes—
22C2×#66881C2214yes—
23#10622550—21no—
24#10622549C2211yescharacteristic
25#10622549C2211yescharacteristic
26#10622549C2212yes—
27#10622548C2212yes—
28C4×C4⋊Dic11—21no—
29C4×C4⋊Dic11—21no—
30C4×C4⋊Dic11C2212yes—
31#10622545—21no—
32#10622189C2214yes—
33#10622189C2214yes—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C22×C8×C11C2312yes—
38C22×C8×C11C2312yes—
39C2×C42×C11C2×C414yes—
40C2×C42×C11D411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×C42×C11Q814yes—
43C2×C42×C11C2311yescharacteristic
44C2×C42×C11C2311yescharacteristic
45C2×C22⋊Dic11—22no—
46C2×C22⋊Dic11—22no—
47#66979—42no—
48#66979—42no—
49C2×C4⋊Dic11—22no—
50C2×C4⋊Dic11—22no—
51C2×C4⋊Dic11C2312yes—
52C2×C4⋊Dic11C2312yes—
53C2×C4⋊Dic11C2314yes—
54C2×C4×Dic11—22no—
55C2×C4×Dic11—22no—
56C11×C4⋊C8C2×C414yes—
57C11×C4⋊C8C2×C414yes—
58C11×C22⋊C8C2×C418yes—
59C4×C8×C11C2×C418yes—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C11⋊#95—22no—
65C11⋊#95—22no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68#66882—44no—
69#66881—44no—
70#21985—111nomaximal, Sylow
71C24×C11C2×D411yescharacteristic
72C22×C4×C11—24no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—42no—
78C22×C4×C11C4⋊C414yes—
79C22×C4×C11C4⋊C414yes—
80C22×C4×C11C22×C412yes—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×Q812yes—
87C22×C4×C11C2411yescharacteristic
88C22×Dic11—22no—
89C22×Dic11—22no—
90C22×Dic11—24no—
91C2×C8×C11—22no—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11C22×C414yes—
96C2×C8×C11C22×C414yes—
97C42×C11C4⋊C414yes—
98C42×C11C4⋊C414yes—
99C42×C11C22×C412yes—
100C42×C11C22×C412yes—
101C42×C11C2×Q812yes—
102C42×C11C2×Q812yes—
103C22⋊Dic11—44no—
104C22⋊Dic11—44no—
105C4⋊Dic11—22no—
106C4⋊Dic11—24no—
107C4⋊Dic11—22no—
108C4⋊Dic11—24no—
109C4⋊Dic11—22no—
110C4⋊Dic11—22no—
111C4⋊Dic11—44no—
112C4⋊Dic11—44no—
113C4×Dic11—44no—
114C4×Dic11—44no—
115C2×#431D1111yescharacteristic
116#2285—111no—
117#2283—111no—
118#1948—112no—
119#1947—112no—
120#1854—114no—
121#1846—112no—
122#1835—112no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—22no—
126C23×C11—22no—
127C23×C11C2×C4⋊C412yes—
128C23×C11C22×D411yescharacteristic
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—28no—
139C2×C4×C11—44no—
140C2×C4×C11C2×C4⋊C412yes—
141C2×C4×C11C2×C4⋊C412yes—
142C2×C4×C11C2×C4⋊C412yes—
143C2×C4×C11C2×C4⋊C412yes—
144C2×C4×C11C2×C4⋊C412yes—
145C2×C4×C11#13514yes—
146C2×C4×C11C23×C411yescharacteristic
147C2×C4×C11C22×Q811yescharacteristic
148C2×C4×C11H(5,𝔽2)11yescharacteristic
149C2×C4×C11H(5,𝔽2)11yescharacteristic
150C2×C4×C112−1+411yescharacteristic
151C2×C4×C112−1+411yescharacteristic
152C2×Dic11—44no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155C2×Dic11—42no—
156C2×Dic11—42no—
157C2×Dic11—44no—
158C2×Dic11—44no—
159C2×Dic11—42no—
160C2×Dic11—42no—
161C8×C11—24no—
162C8×C11—24no—
163C2×#117—112no—
164C22×C42C2×D1111yescharacteristic
165#431Dic1118yescomplemented
166C2×#107—114no—
167C2×#106—114no—
168C2×C4⋊C8C2×D1111yescharacteristic
169C2×C4⋊C8C2×D1111yescharacteristic
170C2×C22⋊C8C2×D1112yes—
171C2×C4×C8C2×D1112yes—
172#384—112no—
173#383—221no—
174#382—111no—
175#382—112no—
176#382—111no—
177#381—221no—
178#380—112no—
179#380—221no—
180#380—221no—
181C4×C4⋊C4—112no—
182C4×C4⋊C4—221no—
183C4×C4⋊C4—221no—
184C4×C22⋊C4—221no—
185#376—221no—
186#340—114no—
187#340—114no—
188C22×C11—22no—
189C22×C11—22no—
190C22×C11—22no—
191C22×C11—42no—
192C22×C11—42no—
193C22×C11C22×C4⋊C411yescharacteristic
194C22×C11#53511yescharacteristic
195C22×C11#53611yescharacteristic
196C22×C11C2×#13512yes—
197C22×C11#57512yes—
198C4×C11—22no—
199C4×C11—22no—
200C4×C11—22no—
201C4×C11—22no—
202C4×C11#42714yes—
203C4×C11#52011yescharacteristic
204C4×C11#52011yescharacteristic
205C4×C11#54411yescharacteristic
206C4×C11#54411yescharacteristic
207Dic11—84no—
208Dic11—82no—
209Dic11—82no—
210C23×C4D4411yescharacteristic
211C23×C4D4411yescharacteristic
212C23×C4C22×D1111yescharacteristic
213C22×C8C22×D1112yes—
214C22×C8C22×D1112yes—
215#117—442no—
216#117—442no—
217C2×C4⋊C4—114no—
218C2×C4⋊C4—112no—
219C2×C4⋊C4—112no—
220C2×C4⋊C4—222no—
221C2×C4⋊C4—222no—
222C2×C22⋊C4—222no—
223C2×C22⋊C4—222no—
224C2×C42—222no—
225C2×C42—222no—
226C2×C42Dic2214yes—
227C2×C42D4411yescharacteristic
228C2×C42D4411yescharacteristic
229C2×C42C2×Dic1114yes—
230C2×C42C22×D1111yescharacteristic
231C2×C42C22×D1111yescharacteristic
232#107—444no—
233#106—444no—
234C4⋊C8C2×Dic1114yes—
235C4⋊C8C2×Dic1114yes—
236C22⋊C8C2×Dic1118yes—
237C4×C8C2×Dic1118yes—
238#95—222no—
239#95—221no—
240#95—221no—
241#95—221no—
242#95—221no—
243#95—222no—
244#95—222no—
245#95—222no—
246C2×C11—42no—
247C2×C11#231711yescharacteristic
248C2×C11C2×#42711yescharacteristic
249C2×C11#291111yescharacteristic
250C2×C11#321212yes—
251C2×C11#323312yes—
252C24C2×D4411yescharacteristic
253C22×C4—24no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—42no—
259C22×C4—222no—
260C22×C4—222no—
261C22×C4—224no—
262C22×C4C4⋊Dic1114yes—
263C22×C4C4⋊Dic1114yes—
264C22×C4C2×Dic2212yes—
265C22×C4C2×D4411yescharacteristic
266C22×C4C2×D4411yescharacteristic
267C22×C4C2×D4411yescharacteristic
268C22×C4C2×D4411yescharacteristic
269C22×C4C2×D4411yescharacteristic
270C22×C4C22×Dic1112yes—
271C22×C4C23×D1111yescharacteristic
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8C22×Dic1114yes—
277C2×C8C22×Dic1114yes—
278C4⋊C4—222no—
279C4⋊C4—224no—
280C4⋊C4—222no—
281C4⋊C4—224no—
282C4⋊C4—222no—
283C4⋊C4—222no—
284C4⋊C4—444no—
285C4⋊C4—444no—
286C22⋊C4—444no—
287C22⋊C4—444no—
288C42—444no—
289C42—444no—
290C42C4⋊Dic1114yes—
291C42C4⋊Dic1114yes—
292C42C2×Dic2212yes—
293C42C2×Dic2212yes—
294C42C22×Dic1112yes—
295C42C22×Dic1112yes—
296C11#2198511yescharacteristic, complemented, Sylow
297C23—22no—
298C23—22no—
299C23—21no—
300C23—21no—
301C23C2×C4⋊Dic1112yes—
302C23C22×D4411yescharacteristic
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—28no—
313C2×C4—44no—
314C2×C4—442no—
315C2×C4—442no—
316C2×C4—444no—
317C2×C4—442no—
318C2×C4—442no—
319C2×C4—444no—
320C2×C4—444no—
321C2×C4—442no—
322C2×C4—442no—
323C2×C4#6695714yes—
324C2×C4C2×C4⋊Dic1112yes—
325C2×C4C2×C4⋊Dic1112yes—
326C2×C4C2×C4⋊Dic1112yes—
327C2×C4C2×C4⋊Dic1112yes—
328C2×C4C2×C4⋊Dic1112yes—
329C2×C4C22×Dic2211yescharacteristic
330C2×C4#6704211yescharacteristic
331C2×C4#6704211yescharacteristic
332C2×C4#6704311yescharacteristic
333C2×C4#6704311yescharacteristic
334C2×C4C23×Dic1111yescharacteristic
335C8—24no—
336C8—24no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—42no—
341C22—42no—
342C22#1062305611yescharacteristic
343C22#1062305711yescharacteristic
344C22C2×#6695712yes—
345C22#1062327912yes—
346C22C22×C4⋊Dic1111yescharacteristic
347C4—22no—
348C4—22no—
349C4—22no—
350C4—22no—
351C4—882no—
352C4—884no—
353C4—882no—
354C4#1062271914yes—
355C4#1062305011yescharacteristic
356C4#1062305011yescharacteristic
357C4#1062335811yescharacteristic
358C4#1062335811yescharacteristic
359C2—42no—
360C2#1307123911yescharacteristic
361C2C2×#1062271911yescharacteristic
362C2#1307720611yescharacteristic
363C2#1307959412yes—
364C2#1307979712yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#431C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#431D11
hypocenterC11#21985
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
3. #13069380C2semidirect
4. #13069375C2semidirect
6. #13068780C2semidirect
7. #13068747C2semidirect
11. C11×#431C4semidirect
165. #431Dic11semidirect
296. C11#21985semidirect

Maximal subgroups

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

subgroupindex
#130710232
#130710142
#130693802
#130693752
#130688172
#130687802
#130687472
C2×C11×#4312
#2198511