Finite Group Databasebeta

← #14736893

Subgroups — #14736893

Order 2816.

638 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#13079928C212yesmaximal
2#13077329C211yesmaximal, characteristic
3#13068136C212yesmaximal, complemented
4#13068126C212yesmaximal, complemented
5#13067988C214yesmaximal, complemented
6C2×#10622095C211yesmaximal, characteristic, complemented
7#13067306C212yesmaximal, complemented
8C11×#3160C211yesmaximal, characteristic, complemented
9C11×#533C2212yes—
10C2×#66954—21no—
11#10623008C2211yescharacteristic
12C11×#500C2211yescharacteristic
13C11×#500C2211yescharacteristic
14C11×#499—21no—
15C11×#499—21no—
16C11×#498C2212yes—
17C11×#427—21no—
18C11×#427—21no—
19C2×C4×C8×C11C2211yescharacteristic
20#10622723—21no—
21#10622697C2214yes—
22#10622696C2214yes—
23#10622661—24no—
24#10622640—22no—
25#10622633—22no—
26#10622537C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2212yes—
28#10622301—21no—
29#10622301C2212yes—
30C8×D44—21no—
31C8×D44C2212yes—
32#10622185C2214yes—
33#10622184C2214yes—
34#10622095C2212yes—
35#10622095C2212yes—
36C2×#4339—21no—
37C22×C8×C11D411yescharacteristic
38C22×C8×C11D411yescharacteristic
39C11×C4⋊Q8C2312yes—
40C11×C4⋊Q8C2312yes—
41C11×#125—22no—
42C11×C22⋊Q8—22no—
43C11×C22⋊Q8—22no—
44C4×Q8×C11—22no—
45C4×Q8×C11—22no—
46C11×#117—22no—
47C2×C42×C11C2311yescharacteristic
48C2×#4325—24no—
49#66983—21no—
50#66983D412yes—
51C2×#4318—21no—
52C22×C11⋊C8—22no—
53#66954—44no—
54C2×#4313—22no—
55C2×C8×D11—22no—
56#66928—21no—
57#66927D411yescharacteristic
58C4×D44—21no—
59C4×D44C2312yes—
60#66922D411yescharacteristic
61C11×#107—21no—
62C11×#107—21no—
63C11×#107—21no—
64C11×#107—21no—
65C11×#106—22no—
66C11×#106—22no—
67C4×C8×C11D411yescharacteristic
68C4×C8×C11D411yescharacteristic
69C4×C8×C11C2311yescharacteristic
70C4×C8×C11C2311yescharacteristic
71#66899—24no—
72(C2×D11)⋊C8—22no—
73(C2×D11)⋊C8—22no—
74#66873—24no—
75#66872—24no—
76C4⋊(C11⋊C8)—22no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)C2314yes—
79C4⋊(C11⋊C8)C2312yes—
80#19194—111nomaximal, Sylow
81C2×Q8×C11—22no—
82C2×Q8×C11—22no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C2×C22⋊D11—22no—
87#4339—42no—
88#4339—42no—
89C2×D44—21no—
90C2×D44—21no—
91C2×D44C2×D412yes—
92C2×C4×D11—22no—
93C2×Dic22—21no—
94C2×C8×C11—22no—
95C2×C8×C11SD1614yescomplemented
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2×D411yescharacteristic
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—42no—
105C11×C4⋊C4—42no—
106C11×C22⋊C4—42no—
107C42×C11—42no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111C42×C11C2411yescharacteristic
112#4325—84no—
113(C2×D11)⋊C4—22no—
114(C2×D11)⋊C4—22no—
115C4⋊Dic11—21no—
116C4⋊Dic11C2×D412yes—
117#4318—42no—
118C2×C11⋊C8—24no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—82no—
121#4313—44no—
122C8×D11—44no—
123#3246—112no—
124#3160D1111yescharacteristic, complemented
125#2931—111no—
126#1695—112no—
127#1693—112no—
128#1671—114no—
129C2×#334—111no—
130#1550—112no—
131C23×C11#12111yescharacteristic
132C22×D11—22no—
133Q8×C11—42no—
134Q8×C11—42no—
135Q8×C11—82no—
136C2×C4×C11—22no—
137C2×C4×C11—41no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11C2×SD1612yes—
144C2×C4×C11#13712yes—
145C2×C4×C11C22×D411yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C2×C4×C11C2×#4111yescharacteristic
148C22⋊D11—44no—
149C2×Dic11—22no—
150D44—24no—
151D44—42no—
152D44—42no—
153C4×D11—42no—
154C4×D11—42no—
155Dic22—42no—
156C8×C11—21no—
157C8×C11—21no—
158C8×C11C2×SD1612yes—
159C8×C11C2×SD1612yes—
160C11⋊C8—42no—
161C11⋊C8—44no—
162C2×#131—221no—
163#533C2×D1112yes—
164#532—111no—
165#500C2×D1111yescharacteristic
166#500C2×D1111yescharacteristic
167#499—21no—
168#499—21no—
169#498C2×D1112yes—
170#476—114no—
171#475—222no—
172#465—224no—
173#461—114no—
174#460—222no—
175#436—112no—
176#436—221no—
177C8×D4—112no—
178C8×D4—221no—
179#427—21no—
180#427—21no—
181#423—111no—
182C2×C4⋊C8—112no—
183#408—221no—
184C2×C4×C8C2×D1111yescharacteristic
185#334—112no—
186#334—112no—
187#333—114no—
188#332—114no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11#46112yes—
192C22×C11C2×#12111yescharacteristic
193C2×D11—42no—
194C2×D11—42no—
195C2×D11—42no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—82no—
200C4×C11—82no—
201C4×C11#46112yes—
202C4×C11C22×SD1611yescharacteristic
203C4×C11C2×#13711yescharacteristic
204C4×C11#57712yes—
205Dic11—42no—
206C2×#41—221no—
207C2×SD16—224no—
208#131—444no—
209C2×M16—221no—
210C2×M16—222no—
211C22×C8—222no—
212C22×C8—222no—
213C22×C8C22⋊D1111yescharacteristic
214C22×C8C22⋊D1111yescharacteristic
215C4⋊Q8—111no—
216C4⋊Q8C22×D1112yes—
217C4⋊Q8C22×D1112yes—
218#127—111no—
219#125—22no—
220#124—221no—
221C22⋊Q8—22no—
222C22⋊Q8—22no—
223#121—112no—
224#121—221no—
225C4×Q8—22no—
226C4×Q8—22no—
227C4×D4—112no—
228C4×D4—221no—
229#117—22no—
230C2×C42C22×D1111yescharacteristic
231#107—21no—
232#107—21no—
233#107—21no—
234#107—21no—
235#106—22no—
236#106—22no—
237#106—224no—
238C4⋊C8—112no—
239C4⋊C8—114no—
240C4⋊C8—222no—
241C4⋊C8—221no—
242#103—224no—
243#102—224no—
244C22⋊C8—222no—
245C22⋊C8—222no—
246C4×C8C22⋊D1111yescharacteristic
247C4×C8C22⋊D1111yescharacteristic
248C4×C8C22×D1111yescharacteristic
249C4×C8C22×D1111yescharacteristic
250C2×C11—22no—
251C2×C11C2×#46111yescharacteristic
252C2×C11#306011yescharacteristic
253C2×C11#306711yescharacteristic
254D11—82no—
255#41—442no—
256#41—442no—
257C2×Q8—22no—
258C2×Q8—22no—
259C2×Q8—221no—
260C2×D4—112no—
261C2×D4—222no—
262C2×D4—221no—
263C2×D4—221no—
264C22×C4—222no—
265C22×C4D4×D1111yescharacteristic
266C22×C4#434111yescharacteristic
267C22×C4C2×C22⋊D1111yescharacteristic
268SD16—884no—
269M16—442no—
270M16—444no—
271C2×C8—22no—
272C2×C8—224no—
273C2×C8—222no—
274C2×C8—444no—
275C2×C8—882no—
276C2×C8#432514yescomplemented
277C2×C8C2×C22⋊D1111yescharacteristic
278C2×C8C2×C22⋊D1111yescharacteristic
279C2×C8C2×C22⋊D1111yescharacteristic
280C2×C8C2×C22⋊D1111yescharacteristic
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—42no—
286C4⋊C4—42no—
287C4⋊C4—112no—
288C4⋊C4—221no—
289C22⋊C4—42no—
290C22⋊C4—222no—
291C22⋊C4—222no—
292C42—42no—
293C42D4×D1111yescharacteristic
294C42#434111yescharacteristic
295C42C2×C22⋊D1111yescharacteristic
296C42C23×D1111yescharacteristic
297C11#1919411yescharacteristic, complemented, Sylow
298C23—222no—
299C23#6699111yescharacteristic
300Q8—42no—
301Q8—42no—
302Q8—82no—
303Q8—442no—
304D4—224no—
305D4—442no—
306D4—444no—
307D4—442no—
308C2×C4—22no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—222no—
313C2×C4—442no—
314C2×C4—442no—
315C2×C4#6699111yescharacteristic
316C2×C4#6699111yescharacteristic
317C2×C4#6699111yescharacteristic
318C2×C4C2×#432512yes—
319C2×C4#6699512yes—
320C2×C4C2×D4×D1111yescharacteristic
321C2×C4C2×#434111yescharacteristic
322C2×C4C22×C22⋊D1111yescharacteristic
323C8—21no—
324C8—21no—
325C8—444no—
326C8—442no—
327C8C2×#432512yes—
328C8C2×#432512yes—
329C22—21no—
330C22—21no—
331C22—442no—
332C22—442no—
333C22—442no—
334C22#1062269612yes—
335C22C2×#6699111yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—82no—
340C4—82no—
341C4—442no—
342C4#1062269612yes—
343C4#1062330112yes—
344C4C22×#432511yescharacteristic
345C4C2×#6699511yescharacteristic
346C2—22no—
347C2—882no—
348C2C2×#1062269611yescharacteristic
349C2#1307827411yescharacteristic
350C2#1307833211yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3160C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#3160D11
hypocenterC11#19194
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3160

Complements

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

NH ≅ G/Ntype
3. #13068136C2semidirect
4. #13068126C2semidirect
5. #13067988C2semidirect
6. C2×#10622095C2semidirect
7. #13067306C2semidirect
8. C11×#3160C2semidirect
95. C2×C8×C11SD16semidirect
124. #3160D11semidirect
276. C2×C8#4325semidirect
297. C11#19194semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130773292
#130681362
#130681262
#130679882
C2×#106220952
#130673062
C11×#31602
#1919411