Finite Group Databasebeta

← #14911126

Subgroups — #14911126

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#13080964C211yesmaximal, characteristic, complemented
2#13070889C211yesmaximal, characteristic, complemented
3#13070796C212yesmaximal, complemented
4#13070794C212yesmaximal, complemented
5#13070753C211yesmaximal, characteristic, complemented
6#13070750C211yesmaximal, characteristic, complemented
7#13070700C212yesmaximal, complemented
8C4×#66890C211yesmaximal, characteristic, complemented
9D4×C11⋊C16C211yesmaximal, characteristic, complemented
10C2×#10622127C212yesmaximal, complemented
11C11×#3334C211yesmaximal, characteristic, complemented
12C11×#547—21no—
13#10623086—21no—
14C11×#500C2211yescharacteristic
15C11×#480—22no—
16C11×#474—21no—
17C11×#466C2212yes—
18C4×C11×D8C2211yescharacteristic
19C8×D4×C11C2211yescharacteristic
20C2×C11×#107C2212yes—
21C2×#66890C2211yescharacteristic
22#10622728C2212yes—
23C2×#66882C2212yes—
24C22×C11⋊C16C2212yes—
25#10622459—21no—
26#10622349—22no—
27C4×D88C2211yescharacteristic
28#10622295C2211yescharacteristic
29#10622200C2212yes—
30#10622200C2211yescharacteristic
31C22⋊(C11⋊C16)C2212yes—
32#10622129C2212yes—
33#10622129C2211yescharacteristic
34#10622127C2212yes—
35#10622127C2212yes—
36#10622127C2211yescharacteristic
37#10622127C2212yes—
38#10622127C2212yes—
39C4⋊(C11⋊C16)C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×#41—41no—
42C2×#4341—41no—
43C2×C11×D8C2311yescharacteristic
44C22×C8×C11C2312yes—
45C11×C4⋊Q8—21no—
46C11×#123—42no—
47C11×C22⋊Q8—41no—
48C11×#121—22no—
49C4×D4×C11—21no—
50C4×D4×C11D411yescharacteristic
51C2×C11×C4⋊C4—22no—
52#66983—22no—
53C2×C4⋊Dic11—22no—
54C2×D88C2311yescharacteristic
55#66950—41no—
56#66939—42no—
57C4×D44—21no—
58#66922—21no—
59C11×#107—21no—
60C11×#107—22no—
61C11×#107C2312yes—
62C11×#107C2311yescharacteristic
63C11×C4⋊C8D411yescharacteristic
64C11×#102—21no—
65C11×#102—22no—
66C11×C22⋊C8D412yes—
67C4×C8×C11C2311yescharacteristic
68#66890—22no—
69#66885—22no—
70#66885—21no—
71#66882—21no—
72#66882—22no—
73#66882C2312yes—
74#66882C2311yescharacteristic
75C2×C11⋊C16—24no—
76C2×C11⋊C16C2311yescharacteristic
77C2×C11⋊C16C2312yes—
78C2×C11⋊C16C2311yescharacteristic
79#33901—111nomaximal, Sylow
80C11×#41—84no—
81C2×Q8×C11—41no—
82C2×D4×C11—21no—
83C2×D4×C11—42no—
84C2×D4×C11D811yescharacteristic
85C22×C4×C11—42no—
86C22×C4×C11—41no—
87C22×C4×C11C2×D412yes—
88C2×C22⋊D11—42no—
89C22×Dic11—42no—
90#4341—84no—
91C2×D44—21no—
92C2×C4×D11—41no—
93C2×Dic22—41no—
94C11×D8—21no—
95C11×D8—21no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2×D412yes—
100C2×C8×C11C2411yescharacteristic
101C11×C4⋊C4—21no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—42no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4D811yescharacteristic
106C11×C22⋊C4—41no—
107C11×C22⋊C4—42no—
108C11×C22⋊C4D812yes—
109C42×C11C2×D411yescharacteristic
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—42no—
112C4⋊Dic11—22no—
113C4⋊Dic11—21no—
114C4⋊Dic11—41no—
115C4⋊Dic11—42no—
116D88—21no—
117D88—21no—
118C11⋊C16—22no—
119C11⋊C16—21no—
120C11⋊C16#4112yescomplemented
121#3334—111no—
122#3334D1111yescharacteristic, complemented
123#2252—111no—
124#2232—112no—
125#2232—112no—
126#2224—111no—
127#2224—111no—
128#2215—112no—
129C4×D16—111no—
130D4×C16—111no—
131C2×#366—112no—
132C23×C11—41no—
133C23×C11C2×D812yes—
134C22×D11—41no—
135Q8×C11—82no—
136D4×C11—41no—
137D4×C11—41no—
138D4×C11—84no—
139D4×C11D1614yescomplemented
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—84no—
145C2×C4×C11—82no—
146C2×C4×C11C2×D811yescharacteristic
147C2×C4×C11C2×D812yes—
148C2×C4×C11C2×D811yescharacteristic
149C2×C4×C11C22×D411yescharacteristic
150C22⋊D11—84no—
151C2×Dic11—42no—
152C2×Dic11—41no—
153C2×Dic11—84no—
154D44—41no—
155D44—41no—
156C4×D11—82no—
157Dic22—82no—
158C8×C11—22no—
159C8×C11—21no—
160C8×C11C2×#4111yescharacteristic
161C8×C112−1+411yescharacteristic
162#547—21no—
163#547—221no—
164C2×D16—111no—
165C22×C16—112no—
166#500—111no—
167#500C2×D1111yescharacteristic
168#480—22no—
169#480—222no—
170#474—21no—
171#474—221no—
172#466—112no—
173#466C2×D1112yes—
174C4×D8—111no—
175C4×D8C2×D1111yescharacteristic
176C8×D4C2×D1111yescharacteristic
177C2×#107—112no—
178C2×#107C2×D1112yes—
179#366—111no—
180#366—112no—
181#366—112no—
182#366—112no—
183#366—112no—
184C4⋊C16—111no—
185#357—111no—
186#357—112no—
187#357—111no—
188#357—112no—
189C22⋊C16—112no—
190C4×C16—111no—
191C22×C11—22no—
192C22×C11—22no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11C2×D1614yes—
197C22×C11C22×D811yescharacteristic
198C2×D11—81no—
199C2×D11—81no—
200C2×D11—81no—
201C4×C11—22no—
202C4×C11—21no—
203C4×C11—81no—
204C4×C11—82no—
205C4×C11C2×D1612yes—
206C4×C11#54711yescharacteristic
207C4×C11#57811yescharacteristic
208Dic11—82no—
209Dic11—81no—
210C2×#41—41no—
211C2×#41—441no—
212C2×D8—111no—
213C2×D8C22×D1111yescharacteristic
214C22×C8C22×D1112yes—
215C4⋊Q8—21no—
216C4⋊Q8—221no—
217#123—42no—
218#123—442no—
219C22⋊Q8—41no—
220C22⋊Q8—441no—
221#121—22no—
222#121—222no—
223C4×D4—21no—
224C4×D4—221no—
225C4×D4C22⋊D1111yescharacteristic
226C2×C4⋊C4—22no—
227C2×C4⋊C4—222no—
228D16—222no—
229C2×C16—111no—
230C2×C16—111no—
231C2×C16—112no—
232C2×C16—224no—
233#107—22no—
234#107—21no—
235#107—111no—
236#107—112no—
237#107—222no—
238#107—221no—
239#107C22×D1111yescharacteristic
240#107C22×D1112yes—
241C4⋊C8C22⋊D1111yescharacteristic
242#102—21no—
243#102—22no—
244#102—221no—
245#102—222no—
246C22⋊C8C22⋊D1112yes—
247C4×C8C22×D1111yescharacteristic
248C2×C11—24no—
249C2×C11—161no—
250C2×C11#333411yescharacteristic
251C2×C11C22×D1611yescharacteristic
252C2×C11#341711yescharacteristic
253D11—161no—
254#41—84no—
255#41—884no—
256C2×Q8—41no—
257C2×Q8—441no—
258C2×D4—21no—
259C2×D4—42no—
260C2×D4—221no—
261C2×D4—442no—
262C2×D4#432311yescharacteristic
263C22×C4—42no—
264C22×C4—41no—
265C22×C4—442no—
266C22×C4—441no—
267C22×C4C2×C22⋊D1112yes—
268D8—21no—
269D8—21no—
270D8—221no—
271D8—221no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8C2×C22⋊D1111yescharacteristic
275C2×C8C2×C22⋊D1112yes—
276C2×C8C23×D1111yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—22no—
279C4⋊C4—42no—
280C4⋊C4—41no—
281C4⋊C4—221no—
282C4⋊C4—222no—
283C4⋊C4—442no—
284C4⋊C4—441no—
285C4⋊C4#432311yescharacteristic
286C22⋊C4—41no—
287C22⋊C4—42no—
288C22⋊C4—441no—
289C22⋊C4—442no—
290C22⋊C4#432312yes—
291C42C2×C22⋊D1111yescharacteristic
292C16—112no—
293C16—222no—
294C16—221no—
295C11#3390111yescharacteristic, complemented, Sylow
296C23—41no—
297C23—441no—
298C23C2×#432312yes—
299Q8—82no—
300Q8—882no—
301D4—41no—
302D4—41no—
303D4—84no—
304D4—441no—
305D4—441no—
306D4—884no—
307D4#6689014yescomplemented
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—84no—
313C2×C4—82no—
314C2×C4—441no—
315C2×C4—442no—
316C2×C4—884no—
317C2×C4—882no—
318C2×C4C2×#432311yescharacteristic
319C2×C4C2×#432312yes—
320C2×C4C2×#432311yescharacteristic
321C2×C4C22×C22⋊D1111yescharacteristic
322C8—22no—
323C8—21no—
324C8#41×D1111yescharacteristic
325C8#6704311yescharacteristic
326C22—22no—
327C22—22no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—881no—
332C22—881no—
333C22—881no—
334C22C2×#6689014yes—
335C22C22×#432311yescharacteristic
336C4—22no—
337C4—21no—
338C4—81no—
339C4—82no—
340C4—881no—
341C4—882no—
342C4C2×#6689012yes—
343C4#1062335511yescharacteristic
344C4#1062336911yescharacteristic
345C2—24no—
346C2—161no—
347C2—1761no—
348C2#1308095911yescharacteristic
349C2C22×#6689011yescharacteristic
350C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3334C2
socleC22×C11C22×D8
hypercenter#3334D11
hypocenterC11#33901
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3334

Complements

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

NH ≅ G/Ntype
1. #13080964C2semidirect
2. #13070889C2semidirect
3. #13070796C2semidirect
4. #13070794C2semidirect
5. #13070753C2semidirect
6. #13070750C2semidirect
7. #13070700C2semidirect
8. C4×#66890C2semidirect
9. D4×C11⋊C16C2semidirect
10. C2×#10622127C2semidirect
11. C11×#3334C2semidirect
120. C11⋊C16#41semidirect
122. #3334D11semidirect
139. D4×C11D16semidirect
295. C11#33901semidirect
307. D4#66890semidirect

Maximal subgroups

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

subgroupindex
#130809642
#130708892
#130707962
#130707942
#130707532
#130707502
#130707002
C4×#668902
D4×C11⋊C162
C2×#106221272
C11×#33342
#3390111