Finite Group Databasebeta

← #14646760

Subgroups — #14646760

Order 2816.

456 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068654C211yesmaximal, characteristic, complemented
2#13068641C211yesmaximal, characteristic, complemented
3#13067159C212yesmaximal
4#13066521C212yesmaximal, complemented
5C11×#2929C211yesmaximal, characteristic
6C2×C11×#131C411yescharacteristic, complemented
7C23×C8×C11C2211yescharacteristic
8C11×#525C2211yescharacteristic
9C11×#435—21no—
10C11×#435—21no—
11C8×D4×C11—21no—
12C8×D4×C11—21no—
13C11×#424C411yescharacteristic, complemented
14C11×#408C411yescharacteristic, complemented
15C11×#407C2211yescharacteristic
16C11×#405C411yescharacteristic, complemented
17#10622825C2212yes—
18#10622820C2212yes—
19C2×#66883—21no—
20C2×#66881—21no—
21#10622190—21no—
22#10622189—21no—
23#10622176—22no—
24#10622175—22no—
25C2×C11×#41C2×C411yescharacteristic
26C23×C4×C11C2311yescharacteristic
27C11×#131—42no—
28C2×C11×M16—21no—
29C2×C11×M16C2×C411yescharacteristic
30C2×C11×M16C2×C411yescharacteristic
31C22×C8×C11—21no—
32C22×C8×C11—42no—
33C22×C8×C11C2×C411yescharacteristic
34C22×C8×C11C2×C411yescharacteristic
35C22×C8×C11D411yescharacteristic
36C22×C8×C11D411yescharacteristic
37C22×C8×C11D411yescharacteristic
38C22×C8×C11D411yescharacteristic
39C11×#123—21no—
40C11×C22⋊Q8D411yescharacteristic
41C11×C22⋊Q8Q811yescharacteristic
42C11×#121D411yescharacteristic
43C11×#121Q811yescharacteristic
44C11×#120—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C11×#117C2×C411yescharacteristic
48C2×C22⋊Dic11—22no—
49C2×C4⋊Dic11—22no—
50C2×#4318—22no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C22⋊C8—21no—
54C11×C22⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×C22⋊C8—21no—
57C11×#97—21no—
58C4×C8×C11—21no—
59C11⋊#95—22no—
60C22⋊(C11⋊C8)—22no—
61C22⋊(C11⋊C8)—22no—
62#66883—42no—
63#66881—42no—
64#8629—111nomaximal, Sylow
65C24×C11#4111yescharacteristic
66C11×#41—41no—
67C11×#41—41no—
68C2×Q8×C11C4⋊C411yescharacteristic
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11C4⋊C411yescharacteristic
73C22×C4×C11—21no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×Q811yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C22×Dic11—42no—
83C11×M16—41no—
84C11×M16—41no—
85C11×M16—42no—
86C2×C8×C11—22no—
87C2×C8×C11—22no—
88C2×C8×C11—22no—
89C2×C8×C11—21no—
90C2×C8×C11—21no—
91C2×C8×C11—41no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C2×C8×C11—42no—
95C2×C8×C11C22⋊C411yescharacteristic
96C2×C8×C11C22⋊C411yescharacteristic
97C2×C8×C11C22⋊C411yescharacteristic
98C2×C8×C11C22⋊C411yescharacteristic
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4C4⋊C411yescharacteristic
102C11×C4⋊C4C4⋊C411yescharacteristic
103C11×C22⋊C4—21no—
104C11×C22⋊C4—21no—
105C11×C22⋊C4—21no—
106C11×C22⋊C4—21no—
107C11×C22⋊C4—21no—
108C42×C11—21no—
109C22⋊Dic11—82no—
110C4⋊Dic11—42no—
111C4⋊Dic11—42no—
112#4318—42no—
113#4318—42no—
114C2×C11⋊C8—42no—
115#2929D1111yescharacteristic
116#1810—111no—
117#1807—111no—
118#1513—112no—
119#1305—112no—
120C23×C11—22no—
121C23×C11—21no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11#11711yescharacteristic
125C23×C11#12111yescharacteristic
126C23×C11C22⋊Q811yescharacteristic
127Q8×C11—41no—
128D4×C11—41no—
129D4×C11—42no—
130D4×C11—42no—
131D4×C11—42no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11C2×C22⋊C411yescharacteristic
147C2×C4×C11C2×C4⋊C411yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11C22⋊Q811yescharacteristic
150C2×Dic11—82no—
151C2×Dic11—82no—
152C2×Dic11—82no—
153C8×C11—21no—
154C8×C11—21no—
155C8×C11—21no—
156C8×C11—41no—
157C8×C11—41no—
158C8×C11#9912yes—
159C11⋊C8—82no—
160C2×#131Dic1111yescharacteristic, complemented
161C23×C8C2×D1111yescharacteristic
162#525C2×D1111yescharacteristic
163#435—21no—
164#435—21no—
165C8×D4—21no—
166C8×D4—21no—
167C2×#108—221no—
168C2×#106—221no—
169#424Dic1111yescharacteristic, complemented
170#408Dic1111yescharacteristic, complemented
171#407—112no—
172#407C2×D1111yescharacteristic
173#405Dic1111yescharacteristic, complemented
174#380—112no—
175#341—221no—
176#340—221no—
177#328—222no—
178#327—222no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—44no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11#38011yescharacteristic
192C22×C11#47112yes—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11—41no—
199C4×C11C2×#9911yescharacteristic
200C4×C11#41011yescharacteristic
201Dic11—162no—
202C2×#41C2×Dic1111yescharacteristic
203C23×C4C22×D1111yescharacteristic
204#131—42no—
205C2×M16—21no—
206C2×M16—222no—
207C2×M16C2×Dic1111yescharacteristic
208C2×M16C2×Dic1111yescharacteristic
209C22×C8—21no—
210C22×C8—42no—
211C22×C8C2×Dic1111yescharacteristic
212C22×C8C2×Dic1111yescharacteristic
213C22×C8C22⋊D1111yescharacteristic
214C22×C8C22⋊D1111yescharacteristic
215C22×C8C22⋊D1111yescharacteristic
216C22×C8C22⋊D1111yescharacteristic
217#123—21no—
218C22⋊Q8Dic2211yescharacteristic
219C22⋊Q8D4411yescharacteristic
220#121Dic2211yescharacteristic
221#121D4411yescharacteristic
222#120—21no—
223C4×D4—21no—
224C4×D4—21no—
225#117C2×Dic1111yescharacteristic
226C2×C4⋊C4—222no—
227C2×C22⋊C4—222no—
228#108—442no—
229#106—442no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C22⋊C8—21no—
233C22⋊C8—21no—
234C22⋊C8—21no—
235C22⋊C8—21no—
236C22⋊C8—222no—
237C22⋊C8—222no—
238#97—21no—
239C4×C8—21no—
240#95—222no—
241C2×C11—22no—
242C2×C11—41no—
243C2×C11—41no—
244C2×C11—81no—
245C2×C11#179911yescharacteristic
246C2×C11#181411yescharacteristic
247C2×C11#181511yescharacteristic
248C24#433911yescharacteristic
249#41—41no—
250#41—41no—
251C2×Q8C4⋊Dic1111yescharacteristic
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4C4⋊Dic1111yescharacteristic
256C22×C4—21no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—442no—
260C22×C4C2×Dic2211yescharacteristic
261C22×C4C2×D4411yescharacteristic
262C22×C4#433911yescharacteristic
263C22×C4C22×Dic1111yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265C22×C4C2×C22⋊D1111yescharacteristic
266M16—42no—
267M16—41no—
268M16—41no—
269M16—442no—
270M16—442no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—42no—
280C2×C8—442no—
281C2×C8C22⋊Dic1111yescharacteristic
282C2×C8C22⋊Dic1111yescharacteristic
283C2×C8C22⋊Dic1111yescharacteristic
284C2×C8C22⋊Dic1111yescharacteristic
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—442no—
288C4⋊C4—442no—
289C4⋊C4C4⋊Dic1111yescharacteristic
290C4⋊C4C4⋊Dic1111yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—21no—
296C22⋊C4—882no—
297C42—21no—
298C11#862911yescharacteristic, complemented, Sylow
299C23—22no—
300C23—21no—
301C23—41no—
302C23—41no—
303C23#6697711yescharacteristic
304C23#6697911yescharacteristic
305C23#6698311yescharacteristic
306Q8—41no—
307D4—41no—
308D4—42no—
309D4—42no—
310D4—42no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—882no—
326C2×C4—882no—
327C2×C4—882no—
328C2×C4#6697711yescharacteristic
329C2×C4C2×C4⋊Dic1111yescharacteristic
330C2×C4#6698311yescharacteristic
331C2×C4C2×C22⋊Dic1111yescharacteristic
332C8—21no—
333C8—21no—
334C8—21no—
335C8—41no—
336C8—41no—
337C8—882no—
338C8#6689812yes—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—44no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22#1062275412yes—
352C22#1062282511yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—1762no—
360C4C2×#6689811yescharacteristic
361C4#1062285311yescharacteristic
362C2—22no—
363C2—41no—
364C2—41no—
365C2—81no—
366C2#1306860411yescharacteristic
367C2#1306867011yescharacteristic
368C2#1306867511yescharacteristic
subgroupG/H
centerC22#10622825
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2929C2
socleC22×C11#380
prime radicalC11×#525C22
cosocleC23×C4×C11C23
hypercenter#2929D11
hypocenterC11#8629
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2929

Complements

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

NH ≅ G/Ntype
1. #13068654C2semidirect
2. #13068641C2semidirect
4. #13066521C2semidirect
6. C2×C11×#131C4semidirect
13. C11×#424C4semidirect
14. C11×#408C4semidirect
16. C11×#405C4semidirect
160. C2×#131Dic11semidirect
169. #424Dic11semidirect
170. #408Dic11semidirect
173. #405Dic11semidirect
298. C11#8629semidirect

Maximal subgroups

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

subgroupindex
#130686542
#130686412
#130671592
#130665212
C11×#29292
#862911