Finite Group Databasebeta

← #14909703

Subgroups — #14909703

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079044C211yesmaximal, characteristic
2#13070873C211yesmaximal, characteristic, complemented
3#13070868C211yesmaximal, characteristic, complemented
4#13070845C211yesmaximal, characteristic, complemented
5#13070841C211yesmaximal, characteristic, complemented
6#13070678C214yesmaximal, complemented
7#13070554C214yesmaximal, complemented
8#13070415C211yesmaximal, characteristic, complemented
9C11×#3170C211yesmaximal, characteristic, complemented
10C11×#533—21no—
11C2×#66957—21no—
12C2×#66957C2212yes—
13#10623008—21no—
14C11×#500C2211yescharacteristic
15C11×#494C2211yescharacteristic
16C11×#487—21no—
17C11×#467—21no—
18C11×#467C2212yes—
19C4×C11×Q16—21no—
20C4×C11×Q16C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22C2×#66893C2214yes—
23C2×#66892C2214yes—
24#10622312C2211yescharacteristic
25#10622309—21no—
26#10622309C2212yes—
27#10622308C2211yescharacteristic
28#10622306—21no—
29C22⋊(C11⋊C16)C2212yes—
30#10622130C2214yes—
31#10622129C2214yes—
32C4⋊(C11⋊C16)C2212yes—
33C4×C11⋊C16C2211yescharacteristic
34C4×C11⋊C16C2211yescharacteristic
35C2×#4339—22no—
36C2×C11×Q16—21no—
37C2×C11×Q16C2312yes—
38C22×C8×C11D411yescharacteristic
39C22×C8×C11C2311yescharacteristic
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×#125—41no—
43C11×C22⋊Q8—22no—
44C11×C22⋊Q8—41no—
45C4×Q8×C11—22no—
46C4×Q8×C11—41no—
47C11×#117—41no—
48C2×C42×C11D411yescharacteristic
49#66983—41no—
50#66983—41no—
51C2×Dic44—21no—
52C2×Dic44C2312yes—
53#66957—44no—
54#66957—44no—
55C2×D88—21no—
56C2×D88C2312yes—
57C2×#4314—22no—
58C2×#4314—22no—
59#66928—22no—
60#66927—21no—
61C4×D44—41no—
62C4×D44—41no—
63#66922—21no—
64C11×#107—21no—
65C11×#107C2312yes—
66C11×#103—22no—
67C11×#103—22no—
68C4×C8×C11D411yescharacteristic
69C4×C8×C11D411yescharacteristic
70C4×C8×C11C2311yescharacteristic
71C4×C8×C11C2311yescharacteristic
72#66893—44no—
73#66892—44no—
74C2×C11⋊C16C2312yes—
75C2×C11⋊C16C2312yes—
76#33776—111nomaximal, Sylow
77C2×Q8×C11—22no—
78C2×Q8×C11—41no—
79C22×C4×C11D811yescharacteristic
80C22×C4×C11D811yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C2×C22⋊D11—42no—
83#4339—44no—
84#4339—44no—
85C2×D44—22no—
86C2×D44—41no—
87C2×D44—41no—
88C2×C4×D11—42no—
89C2×Dic22—22no—
90C11×Q16—24no—
91C11×Q16—42no—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2411yescharacteristic
98C11×C4⋊C4—22no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—42no—
102C11×C4⋊C4—42no—
103C11×C4⋊C4—41no—
104C11×C22⋊C4—42no—
105C42×C11—42no—
106C42×C11D811yescharacteristic
107C42×C11D811yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110(C2×D11)⋊C4—42no—
111(C2×D11)⋊C4—42no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114Dic44—24no—
115Dic44—42no—
116D88—24no—
117D88—42no—
118#4314—44no—
119#4314—44no—
120C11⋊C16—22no—
121C11⋊C16—22no—
122#3170D1111yescharacteristic, complemented
123#3147—111no—
124#2248—111no—
125#2247—111no—
126#2241—111no—
127#2240—111no—
128#2211—114no—
129#2189—114no—
130#2162—111no—
131C23×C11C2×D811yescharacteristic
132C22×D11—42no—
133Q8×C11—42no—
134Q8×C11—42no—
135Q8×C11—82no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C2×D811yescharacteristic
145C2×C4×C11C2×D811yescharacteristic
146C2×C4×C11C2×D811yescharacteristic
147C2×C4×C11C22×D411yescharacteristic
148C22⋊D11—84no—
149C2×Dic11—42no—
150D44—42no—
151D44—42no—
152D44—82no—
153D44—82no—
154C4×D11—84no—
155Dic22—42no—
156Dic22—42no—
157C8×C11—21no—
158C8×C11—21no—
159C8×C11AGL(1,ℤ/8)12yes—
160C8×C11H(5,𝔽2)12yes—
161C2×#135—112no—
162C2×#135—221no—
163#533—21no—
164#532—221no—
165C2×Q32—114no—
166C2×SD32—114no—
167#500C2×D1111yescharacteristic
168#495—112no—
169#495—221no—
170#494—111no—
171#494C2×D1111yescharacteristic
172#493—111no—
173#492—221no—
174#487—21no—
175#467—21no—
176#467C2×D1112yes—
177C4×Q16—21no—
178C4×Q16C2×D1112yes—
179C2×C4×C8C2×D1111yescharacteristic
180C4⋊C16—112no—
181#358—114no—
182#357—114no—
183C22⋊C16—112no—
184C4×C16—111no—
185C4×C16—111no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11C22×D811yescharacteristic
190C2×D11—82no—
191C2×D11—82no—
192C2×D11—82no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—82no—
197C4×C11—82no—
198C4×C11#50812yes—
199C4×C11#51012yes—
200C4×C11#53511yescharacteristic
201C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
202Dic11—82no—
203C2×#41—222no—
204#135—444no—
205#135—444no—
206C2×Q16—21no—
207C2×Q16—112no—
208C2×Q16—221no—
209C2×Q16C22×D1112yes—
210C2×SD16—222no—
211C2×SD16—222no—
212C2×D8—112no—
213C2×D8—221no—
214C22×C8C22⋊D1111yescharacteristic
215C22×C8C22×D1111yescharacteristic
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—221no—
219#127—221no—
220#125—41no—
221#124—222no—
222C22⋊Q8—22no—
223C22⋊Q8—41no—
224#121—441no—
225#121—441no—
226C4×Q8—22no—
227C4×Q8—41no—
228C4×D4—441no—
229C4×D4—441no—
230#117—41no—
231C2×C42C22⋊D1111yescharacteristic
232Q32—444no—
233SD32—444no—
234C2×C16—112no—
235C2×C16—112no—
236#107—21no—
237#107C22×D1112yes—
238#103—22no—
239#103—22no—
240C4×C8C22⋊D1111yescharacteristic
241C4×C8C22⋊D1111yescharacteristic
242C4×C8C22×D1111yescharacteristic
243C4×C8C22×D1111yescharacteristic
244C2×C11—41no—
245C2×C11#320511yescharacteristic
246C2×C11C2×#50811yescharacteristic
247C2×C11C2×#51011yescharacteristic
248D11—162no—
249#41—444no—
250#41—444no—
251C2×Q8—22no—
252C2×Q8—41no—
253C2×Q8—222no—
254C2×D4—222no—
255C2×D4—442no—
256C2×D4—441no—
257C2×D4—441no—
258C22×C4—442no—
259C22×C4#432311yescharacteristic
260C22×C4#432311yescharacteristic
261C22×C4C2×C22⋊D1111yescharacteristic
262Q16—24no—
263Q16—42no—
264Q16—224no—
265Q16—442no—
266SD16—444no—
267SD16—444no—
268D8—224no—
269D8—442no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8C2×C22⋊D1111yescharacteristic
273C2×C8C2×C22⋊D1111yescharacteristic
274C2×C8C2×C22⋊D1111yescharacteristic
275C2×C8C23×D1111yescharacteristic
276C4⋊C4—22no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—41no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C22⋊C4—42no—
285C22⋊C4—442no—
286C22⋊C4—442no—
287C42—42no—
288C42#432311yescharacteristic
289C42#432311yescharacteristic
290C42C2×C22⋊D1111yescharacteristic
291C42C2×C22⋊D1111yescharacteristic
292C16—222no—
293C16—222no—
294C11#3377611yescharacteristic, complemented, Sylow
295C23—442no—
296C23C2×#432311yescharacteristic
297Q8—42no—
298Q8—42no—
299Q8—82no—
300Q8—442no—
301Q8—442no—
302D4—442no—
303D4—442no—
304D4—884no—
305D4—882no—
306D4—882no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—442no—
314C2×C4—884no—
315C2×C4C2×#432311yescharacteristic
316C2×C4C2×#432311yescharacteristic
317C2×C4C2×#432311yescharacteristic
318C2×C4C2×#432311yescharacteristic
319C2×C4C2×#432311yescharacteristic
320C2×C4C22×C22⋊D1111yescharacteristic
321C8—21no—
322C8—21no—
323C8#6700212yes—
324C8#6704212yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—882no—
329C22—882no—
330C22—882no—
331C22C22×#432311yescharacteristic
332C4—21no—
333C4—21no—
334C4—21no—
335C4—82no—
336C4—82no—
337C4—882no—
338C4#1062279212yes—
339C4#1062280712yes—
340C4C2×#6700211yescharacteristic
341C4#1062336111yescharacteristic
342C2—41no—
343C2—1762no—
344C2#1307953111yescharacteristic
345C2C2×#1062280711yescharacteristic
346C2C2×#1062279211yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3170C2
socleC22×C11C22×D8
prime radical#13079044C2
hypercenter#3170D11
hypocenterC11#33776
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3170

Complements

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

NH ≅ G/Ntype
2. #13070873C2semidirect
3. #13070868C2semidirect
4. #13070845C2semidirect
5. #13070841C2semidirect
6. #13070678C2semidirect
7. #13070554C2semidirect
8. #13070415C2semidirect
9. C11×#3170C2semidirect
122. #3170D11semidirect
294. C11#33776semidirect

Maximal subgroups

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

subgroupindex
#130790442
#130708732
#130708682
#130708452
#130708412
#130706782
#130705542
#130704152
C11×#31702
#3377611