Finite Group Databasebeta

← #14911129

Subgroups — #14911129

Order 2816.

548 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#13080965C211yesmaximal, characteristic, complemented
2#13080963C211yesmaximal, characteristic, complemented
3#13070889C211yesmaximal, characteristic, complemented
4#13070798C212yesmaximal, complemented
5#13070795C212yesmaximal, complemented
6#13070754C211yesmaximal, characteristic, complemented
7#13070701C212yesmaximal, complemented
8C4×#66890C211yesmaximal, characteristic, complemented
9#13070435C211yesmaximal, characteristic, complemented
10D11×#366C212yesmaximal, complemented
11C11×#2224C211yesmaximal, characteristic, complemented
12#10623257—21no—
13#10623082—21no—
14C11×#500C2211yescharacteristic
15C4×C11×D8C2211yescharacteristic
16#10622770C2212yes—
17C2×#66890C2211yescharacteristic
18#10622700—21no—
19#10622620—21no—
20C2×C16×D11C2212yes—
21#10622496C2212yes—
22#10622495—22no—
23D11×#107C2212yes—
24D11×#107C2212yes—
25#10622387—22no—
26C4×D88C2211yescharacteristic
27C8×D44C2211yescharacteristic
28#10622295C2211yescharacteristic
29C11×#366C2212yes—
30C11×C4⋊C16C2211yescharacteristic
31C11×#357C2212yes—
32#10622200C2211yescharacteristic
33#10622147C2212yes—
34(C2×D11)⋊C16C2212yes—
35#10622142C2212yes—
36#10622129C2211yescharacteristic
37#10622127C2212yes—
38#10622127C2212yes—
39#10622127C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×#4343—41no—
42C2×#4339—41no—
43C2×C11×D8C2311yescharacteristic
44C11×C4⋊Q8—21no—
45C4×D4×C11—21no—
46#66999—41no—
47#66991—22no—
48#66977—41no—
49C2×D88C2311yescharacteristic
50C2×C8×D11C2312yes—
51#66948—22no—
52#66947—42no—
53C4⋊C4×D11—22no—
54C4⋊C4×D11—22no—
55#66936—42no—
56C4×D44—21no—
57C4×D44D411yescharacteristic
58#66922—21no—
59C2×C11×C16C2312yes—
60C11×#107—21no—
61C11×#107C2312yes—
62C11×#107C2311yescharacteristic
63C11×#102—21no—
64C4×C8×C11C2311yescharacteristic
65#66896—22no—
66#66890—22no—
67#66885—21no—
68(C2×D11)⋊C8D412yes—
69#66882—21no—
70#66882C2311yescharacteristic
71#66882C2312yes—
72C2×C11⋊C16C2311yescharacteristic
73C2×C11⋊C16C2311yescharacteristic
74#66873—22no—
75#66871—22no—
76#66871—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78C16×D11—24no—
79#33901—111nomaximal, Sylow
80C2×Q8×C11—41no—
81C2×D4×C11—21no—
82C22×C4×C11—41no—
83C2×C22⋊D11—42no—
84#4343—84no—
85#4339—84no—
86C2×D44—21no—
87C2×D44—42no—
88C2×D44D811yescharacteristic
89C2×C4×D11—42no—
90C2×C4×D11—42no—
91C2×C4×D11—41no—
92C2×C4×D11C2×D412yes—
93C2×Dic22—41no—
94C11×D8—21no—
95C11×D8—21no—
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2411yescharacteristic
98C11×C4⋊C4—21no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—41no—
101C11×C22⋊C4—41no—
102C42×C11C2×D411yescharacteristic
103C22⋊Dic11—42no—
104(C2×D11)⋊C4—42no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4D812yes—
107C4⋊Dic11—21no—
108C4⋊Dic11—22no—
109C4⋊Dic11—41no—
110C4⋊Dic11D811yescharacteristic
111Dic11⋊C4—42no—
112Dic11⋊C4—42no—
113C2×C11⋊C8C2×D412yes—
114D88—21no—
115D88—21no—
116C8×D11—22no—
117C8×D11—22no—
118C11×C16—22no—
119C11⋊C16—21no—
120C11⋊C16#4112yescomplemented
121#3334—111no—
122#3334—111no—
123#2252—111no—
124#2232—112no—
125#2232—112no—
126#2224—111no—
127#2224D1111yescharacteristic, complemented
128#2215—112no—
129C4×D16—111no—
130D4×C16—111no—
131C2×#366—112no—
132C23×C11—41no—
133C22×D11—41no—
134C22×D11C2×D812yes—
135Q8×C11—82no—
136D4×C11—41no—
137D4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—82no—
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11C22×D411yescharacteristic
144C22⋊D11—84no—
145C2×Dic11—41no—
146C2×Dic11—42no—
147C2×Dic11C2×D812yes—
148D44—41no—
149D44—41no—
150D44—84no—
151D44D1614yescomplemented
152C4×D11—22no—
153C4×D11—22no—
154C4×D11—84no—
155C4×D11—84no—
156C4×D11—82no—
157Dic22—82no—
158C8×C11—21no—
159C8×C11C2×#4111yescharacteristic
160C8×C112−1+411yescharacteristic
161C11⋊C8—22no—
162#547—221no—
163#547—221no—
164C2×D16—111no—
165C22×C16—112no—
166#500—111no—
167#500C2×D1111yescharacteristic
168#480—222no—
169#480—222no—
170#474—221no—
171#474—221no—
172#466—112no—
173#466—112no—
174C4×D8—111no—
175C4×D8C2×D1111yescharacteristic
176C8×D4—111no—
177C2×#107—112no—
178C2×#107—112no—
179#366—112no—
180#366—111no—
181#366—112no—
182#366—112no—
183#366C2×D1112yes—
184C4⋊C16C2×D1111yescharacteristic
185#357—111no—
186#357—112no—
187#357—111no—
188#357C2×D1112yes—
189C22⋊C16—112no—
190C4×C16—111no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11C22×D811yescharacteristic
195C2×D11—22no—
196C2×D11—22no—
197C2×D11—81no—
198C2×D11—81no—
199C2×D11—81no—
200C2×D11C2×D1614yes—
201C4×C11—21no—
202C4×C11—81no—
203C4×C11—82no—
204C4×C11C2×D1612yes—
205C4×C11#54711yescharacteristic
206C4×C11#57811yescharacteristic
207Dic11—22no—
208Dic11—82no—
209Dic11—81no—
210C2×#41—441no—
211C2×#41—441no—
212C2×D8—111no—
213C2×D8C22×D1111yescharacteristic
214C22×C8—112no—
215C4⋊Q8—21no—
216C4⋊Q8—221no—
217#123—442no—
218#123—442no—
219C22⋊Q8—441no—
220C22⋊Q8—441no—
221#121—222no—
222#121—222no—
223C4×D4—21no—
224C4×D4—111no—
225C4×D4—221no—
226C2×C4⋊C4—222no—
227C2×C4⋊C4—222no—
228D16—222no—
229C2×C16—111no—
230C2×C16—111no—
231C2×C16—224no—
232C2×C16C22×D1112yes—
233#107—21no—
234#107—111no—
235#107—112no—
236#107—222no—
237#107—222no—
238#107—221no—
239#107C22×D1111yescharacteristic
240#107C22×D1112yes—
241C4⋊C8—111no—
242#102—21no—
243#102—222no—
244#102—222no—
245#102—221no—
246C22⋊C8—112no—
247C4×C8C22×D1111yescharacteristic
248C2×C11—161no—
249C2×C11#333411yescharacteristic
250C2×C11C22×D1611yescharacteristic
251C2×C11#341711yescharacteristic
252D11—24no—
253D11—161no—
254#41—884no—
255#41—884no—
256C2×Q8—41no—
257C2×Q8—441no—
258C2×D4—21no—
259C2×D4—111no—
260C2×D4—221no—
261C2×D4—442no—
262C2×D4—442no—
263C22×C4—41no—
264C22×C4—112no—
265C22×C4—442no—
266C22×C4—442no—
267C22×C4—441no—
268D8—21no—
269D8—21no—
270D8—221no—
271D8—221no—
272C2×C8—112no—
273C2×C8—222no—
274C2×C8—222no—
275C2×C8D4×D1111yescharacteristic
276C2×C8C23×D1111yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—22no—
279C4⋊C4—41no—
280C4⋊C4—111no—
281C4⋊C4—221no—
282C4⋊C4—222no—
283C4⋊C4—442no—
284C4⋊C4—442no—
285C4⋊C4—441no—
286C22⋊C4—41no—
287C22⋊C4—112no—
288C22⋊C4—442no—
289C22⋊C4—442no—
290C22⋊C4—441no—
291C42D4×D1111yescharacteristic
292C16—22no—
293C16—112no—
294C16—221no—
295C11#3390111yescharacteristic, complemented, Sylow
296C23—41no—
297C23—112no—
298C23—441no—
299Q8—82no—
300Q8—882no—
301D4—41no—
302D4—41no—
303D4—114no—
304D4—441no—
305D4—441no—
306D4—884no—
307D4—884no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—82no—
311C2×C4—112no—
312C2×C4—222no—
313C2×C4—222no—
314C2×C4—441no—
315C2×C4—442no—
316C2×C4—884no—
317C2×C4—884no—
318C2×C4—882no—
319C2×C4D8×D1111yescharacteristic
320C2×C4D8×D1111yescharacteristic
321C2×C4C2×D4×D1111yescharacteristic
322C8—21no—
323C8—222no—
324C8#6704011yescharacteristic
325C8#41×D1111yescharacteristic
326C22—81no—
327C22—81no—
328C22—81no—
329C22—114no—
330C22—222no—
331C22—222no—
332C22—881no—
333C22—881no—
334C22—881no—
335C22C2×D8×D1111yescharacteristic
336C4—21no—
337C4—81no—
338C4—82no—
339C4—222no—
340C4—881no—
341C4—882no—
342C4D11×D1612yes—
343C4#1062316211yescharacteristic
344C4#1062331011yescharacteristic
345C2—161no—
346C2—224no—
347C2—1761no—
348C2#1308096211yescharacteristic
349C2C2×D11×D1611yescharacteristic
350C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2224C2
socleC22×C11C22×D8
hypercenter#2224D11
hypocenterC11#33901
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2224

Complements

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

NH ≅ G/Ntype
1. #13080965C2semidirect
2. #13080963C2semidirect
3. #13070889C2semidirect
4. #13070798C2semidirect
5. #13070795C2semidirect
6. #13070754C2semidirect
7. #13070701C2semidirect
8. C4×#66890C2semidirect
9. #13070435C2semidirect
10. D11×#366C2semidirect
11. C11×#2224C2semidirect
120. C11⋊C16#41semidirect
127. #2224D11semidirect
151. D44D16semidirect
295. C11#33901semidirect

Maximal subgroups

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

subgroupindex
#130809652
#130809632
#130708892
#130707982
#130707952
#130707542
#130707012
C4×#668902
#130704352
D11×#3662
C11×#22242
#3390111