Finite Group Databasebeta

← #14908428

Subgroups — #14908428

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079130C211yesmaximal, characteristic, complemented
2#13070773C214yesmaximal, complemented
3#13070763C212yesmaximal, complemented
4#13070753C212yesmaximal, complemented
5#13070402C212yesmaximal, complemented
6#13070372C211yesmaximal, characteristic, complemented
7#13070332C212yesmaximal
8C2×C4×C11×D8C211yesmaximal, characteristic
9C22×C11×D8C2211yescharacteristic
10C2×C4×D4×C11—21no—
11#10623001—21no—
12C4×C11×D8—21no—
13C4×C11×D8—21no—
14C4×C11×D8C2212yes—
15C4×C11×D8C2212yes—
16C2×C11×#107C2211yescharacteristic
17C2×C11×#102—21no—
18C2×C4×C8×C11C2211yescharacteristic
19#10622719—21no—
20#10622719C2212yes—
21C2×#66876C2212yes—
22#10622296—21no—
23#10622296C2212yescomplemented
24#10622295C2211yescharacteristic, complemented
25#10622295C2211yescharacteristic, complemented
26#10622293—21no—
27#10622200C2214yes—
28#10622200C2214yes—
29#10622128C2214yescomplemented
30#10622127C2214yescomplemented
31C4⋊(C11⋊C16)C2212yescomplemented
32C4⋊(C11⋊C16)C2212yescomplemented
33C22×D4×C11—21no—
34C23×C4×C11—41no—
35C2×C11×D8—21no—
36C2×C11×D8—22no—
37C2×C11×D8Q814yescomplemented
38C2×C11×D8C2312yes—
39C22×C8×C11D411yescharacteristic
40C22×C8×C11C2311yescharacteristic
41C4×D4×C11—22no—
42C4×D4×C11—22no—
43C4×D4×C11—41no—
44C4×D4×C11—41no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C22⋊C4—41no—
47C2×C42×C11D411yescharacteristic
48#66979—22no—
49#66977—41no—
50#66977—41no—
51#66923—22no—
52#66922—21no—
53#66922—21no—
54C4×Dic22—41no—
55C4×Dic22—41no—
56C11×#107—21no—
57C11×#107C2312yes—
58C11×#102—22no—
59C11×#102—22no—
60C4×C8×C11D411yescharacteristic
61C4×C8×C11D411yescharacteristic
62C4×C8×C11C2311yescharacteristic
63C4×C8×C11C2311yescharacteristic
64#66882—21no—
65#66882—21no—
66#66882C2312yes—
67#66882C2312yes—
68#66881—22no—
69#66881—22no—
70#66876—24no—
71C2×C11⋊C16C2314yes—
72#33627—111nomaximal, Sylow
73C24×C11—41no—
74C2×D4×C11—24no—
75C2×D4×C11—22no—
76C2×D4×C11—41no—
77C2×D4×C11—42no—
78C22×C4×C11—41no—
79C22×C4×C11—42no—
80C22×C4×C11—42no—
81C22×C4×C11—84no—
82C22×C4×C11D811yescharacteristic
83C22×C4×C11D811yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C2×Dic22—41no—
86C2×Dic22—41no—
87C11×D8—24no—
88C11×D8—22no—
89C11×D8C2×Q814yes—
90C2×C8×C11—22no—
91C2×C8×C11C2×D411yescharacteristic
92C2×C8×C11C2×D411yescharacteristic
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11C2×Q812yes—
95C2×C8×C11#4112yes—
96C2×C8×C11C2411yescharacteristic
97C11×C4⋊C4—22no—
98C11×C4⋊C4—41no—
99C11×C22⋊C4—42no—
100C11×C22⋊C4—42no—
101C42×C11D811yescharacteristic
102C42×C11D811yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C22⋊Dic11—42no—
106C4⋊Dic11—22no—
107C4⋊Dic11—22no—
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110Dic11⋊C4—42no—
111Dic11⋊C4—42no—
112C4×Dic11—42no—
113C11⋊C16—24no—
114#3160—111no—
115C2×C4×D8D1111yescharacteristic
116#2228—114no—
117#2226—112no—
118#2224—112no—
119#2159—112no—
120#2150—111no—
121#2140—112no—
122C23×C11—42no—
123C23×C11—44no—
124C23×C11—82no—
125C23×C11—82no—
126C23×C11C2×D811yescharacteristic
127D4×C11—24no—
128D4×C11—42no—
129D4×C11—44no—
130C2×C4×C11—22no—
131C2×C4×C11—41no—
132C2×C4×C11—42no—
133C2×C4×C11—84no—
134C2×C4×C11—82no—
135C2×C4×C11—84no—
136C2×C4×C11C22⋊Q812yes—
137C2×C4×C11C2×D811yescharacteristic
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11C2×D811yescharacteristic
140C2×C4×C11C2×D811yescharacteristic
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11#13712yes—
143C2×C4×C11C22×D411yescharacteristic
144C2×Dic11—42no—
145C2×Dic11—42no—
146Dic22—82no—
147Dic22—82no—
148C8×C11—21no—
149C8×C11—21no—
150C8×C11C22⋊Q812yes—
151C8×C11C22×Q811yescharacteristic
152C8×C11C2×#4111yescharacteristic
153C22×D8C2×D1111yescharacteristic
154#533—221no—
155C2×C4×D4—21no—
156C2×M32—112no—
157#500—111no—
158#500—111no—
159#499—112no—
160#499—221no—
161#498—221no—
162C4×D8—21no—
163C4×D8—21no—
164C4×D8C2×D1112yes—
165C4×D8C2×D1112yes—
166#427—112no—
167#427—221no—
168C2×#107C2×D1111yescharacteristic
169C2×#102—21no—
170C2×C4×C8C2×D1111yescharacteristic
171#367—114no—
172#366—114no—
173C4⋊C16—112no—
174C4⋊C16—112no—
175#357—114no—
176#357—114no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—44no—
180C22×C11—88no—
181C22×C11—82no—
182C22×C11—82no—
183C22×C11#47412yes—
184C22×C11C22×D811yescharacteristic
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—82no—
189C4×C11#47412yes—
190C4×C11#50912yes—
191C4×C11C2×C22⋊Q811yescharacteristic
192C4×C11C2×#13711yescharacteristic
193Dic11—82no—
194Dic11—82no—
195C22×D4—21no—
196C23×C4—41no—
197C2×D8—22no—
198C2×D8—21no—
199C2×D8Dic2214yescomplemented
200C2×D8C22×D1112yes—
201C22×C8C22⋊D1111yescharacteristic
202C22×C8C22×D1111yescharacteristic
203C4⋊Q8—221no—
204C4⋊Q8—221no—
205#125—222no—
206C22⋊Q8—441no—
207C22⋊Q8—441no—
208C4×Q8—441no—
209C4×Q8—441no—
210C4×D4—22no—
211C4×D4—22no—
212C4×D4—41no—
213C4×D4—41no—
214#117—222no—
215C2×C4⋊C4—21no—
216C2×C22⋊C4—41no—
217C2×C42C22⋊D1111yescharacteristic
218M32—224no—
219C2×C16—114no—
220#107—21no—
221#107—112no—
222#107—112no—
223#107—221no—
224#107—221no—
225#107C22×D1112yes—
226#106—222no—
227#106—222no—
228#102—22no—
229#102—22no—
230C4×C8C22⋊D1111yescharacteristic
231C4×C8C22⋊D1111yescharacteristic
232C4×C8C22×D1111yescharacteristic
233C4×C8C22×D1111yescharacteristic
234C2×C11—22no—
235C2×C11—84no—
236C2×C11C2×#47411yescharacteristic
237C2×C11C2×#50911yescharacteristic
238C2×C11#341411yescharacteristic
239C24—41no—
240C2×Q8—441no—
241C2×Q8—441no—
242C2×D4—24no—
243C2×D4—22no—
244C2×D4—41no—
245C2×D4—42no—
246C22×C4—41no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—84no—
250C22×C4#432311yescharacteristic
251C22×C4#432311yescharacteristic
252C22×C4C2×C22⋊D1111yescharacteristic
253D8—24no—
254D8—22no—
255D8C2×Dic2214yes—
256C2×C8—22no—
257C2×C8C2×Dic2212yes—
258C2×C8#433912yes—
259C2×C8C2×C22⋊D1111yescharacteristic
260C2×C8C2×C22⋊D1111yescharacteristic
261C2×C8C2×C22⋊D1111yescharacteristic
262C2×C8C23×D1111yescharacteristic
263C4⋊C4—22no—
264C4⋊C4—41no—
265C4⋊C4—222no—
266C4⋊C4—222no—
267C4⋊C4—442no—
268C4⋊C4—442no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—442no—
274C42—442no—
275C42#432311yescharacteristic
276C42#432311yescharacteristic
277C42C2×C22⋊D1111yescharacteristic
278C42C2×C22⋊D1111yescharacteristic
279C16—224no—
280C11#3362711yescharacteristic, complemented, Sylow
281C23—42no—
282C23—44no—
283C23—82no—
284C23—82no—
285C23C2×#432311yescharacteristic
286Q8—882no—
287Q8—882no—
288D4—24no—
289D4—42no—
290D4—44no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—84no—
295C2×C4—82no—
296C2×C4—84no—
297C2×C4—442no—
298C2×C4—442no—
299C2×C4#6697712yes—
300C2×C4C2×#432311yescharacteristic
301C2×C4C2×#432311yescharacteristic
302C2×C4C2×#432311yescharacteristic
303C2×C4C2×#432311yescharacteristic
304C2×C4C2×#432311yescharacteristic
305C2×C4#6700412yes—
306C2×C4C22×C22⋊D1111yescharacteristic
307C8—21no—
308C8—21no—
309C8#6697712yes—
310C8C22×Dic2211yescharacteristic
311C8C2×#433911yescharacteristic
312C22—21no—
313C22—21no—
314C22—44no—
315C22—88no—
316C22—82no—
317C22—82no—
318C22#1062262012yes—
319C22C22×#432311yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—82no—
324C4—882no—
325C4—882no—
326C4#1062262012yes—
327C4#1062276012yes—
328C4C2×#6697711yescharacteristic
329C4C2×#6700411yescharacteristic
330C2—22no—
331C2—84no—
332C2C2×#1062262011yescharacteristic
333C2C2×#1062276011yescharacteristic
334C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C4×C11×D8C2
socleC22×C11C22×D8
prime radicalC22×C11×D8C22
hypercenterC2×C4×D8D11
hypocenterC11#33627
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. #13079130C2semidirect
2. #13070773C2semidirect
3. #13070763C2semidirect
4. #13070753C2semidirect
5. #13070402C2semidirect
6. #13070372C2semidirect
23. #10622296C22semidirect
24. #10622295C22semidirect
25. #10622295C22semidirect
29. #10622128C22semidirect
30. #10622127C22semidirect
31. C4⋊(C11⋊C16)C22semidirect
32. C4⋊(C11⋊C16)C22semidirect
37. C2×C11×D8Q8semidirect
199. C2×D8Dic22semidirect
280. C11#33627semidirect

Maximal subgroups

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

subgroupindex
#130791302
#130707732
#130707632
#130707532
#130704022
#130703722
#130703322
C2×C4×C11×D82
#3362711