Finite Group Databasebeta

← #14736901

Subgroups — #14736901

Order 2816.

638 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079928C212yesmaximal
2#13077329C211yesmaximal, characteristic
3#13068112C214yesmaximal, complemented
4#13068012C212yesmaximal, complemented
5#13068002C212yesmaximal, complemented
6C2×#10622096C211yesmaximal, 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#10622096C2212yes—
35#10622096C2212yes—
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#19195—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#1691—114no—
127#1675—112no—
128#1673—112no—
129C2×#335—111no—
130#1550—112no—
131C23×C11#12111yescharacteristic
132C22×D11—22no—
133Q8×C11—42no—
134Q8×C11—42no—
135Q8×C11—82no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11C2×SD1612yes—
145C2×C4×C11#13712yes—
146C2×C4×C11C22×D411yescharacteristic
147C2×C4×C11C22×D411yescharacteristic
148C2×C4×C11C2×#4111yescharacteristic
149C22⋊D11—44no—
150C2×Dic11—22no—
151D44—22no—
152D44—22no—
153D44—42no—
154D44—42no—
155C4×D11—42no—
156C4×D11—42no—
157Dic22—42no—
158C8×C11—21no—
159C8×C11—21no—
160C8×C11C2×SD1612yes—
161C8×C11C2×SD1612yes—
162C11⋊C8—42no—
163C11⋊C8—44no—
164C2×#131—221no—
165#533C2×D1112yes—
166#532—111no—
167#500C2×D1111yescharacteristic
168#500C2×D1111yescharacteristic
169#499—21no—
170#499—21no—
171#498C2×D1112yes—
172#476—114no—
173#475—222no—
174#465—224no—
175#461—114no—
176#460—222no—
177#436—112no—
178#436—221no—
179C8×D4—112no—
180C8×D4—221no—
181#427—21no—
182#427—21no—
183#423—111no—
184C2×C4⋊C8—112no—
185#408—221no—
186C2×C4×C8C2×D1111yescharacteristic
187#335—112no—
188#335—112no—
189#333—114no—
190#332—114no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11#46112yes—
194C22×C11C2×#12111yescharacteristic
195C2×D11—42no—
196C2×D11—42no—
197C2×D11—42no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—82no—
202C4×C11—82no—
203C4×C11#46112yes—
204C4×C11C22×SD1611yescharacteristic
205C4×C11C2×#13711yescharacteristic
206C4×C11#57611yescharacteristic
207C4×C11#57811yescharacteristic
208Dic11—42no—
209C2×#41—221no—
210C2×SD16—224no—
211#131—444no—
212C2×M16—221no—
213C2×M16—222no—
214C22×C8—222no—
215C22×C8—222no—
216C22×C8C22⋊D1111yescharacteristic
217C22×C8C22⋊D1111yescharacteristic
218C4⋊Q8—111no—
219C4⋊Q8C22×D1112yes—
220C4⋊Q8C22×D1112yes—
221#127—111no—
222#125—22no—
223#124—221no—
224C22⋊Q8—22no—
225C22⋊Q8—22no—
226#121—112no—
227#121—221no—
228C4×Q8—22no—
229C4×Q8—22no—
230C4×D4—112no—
231C4×D4—221no—
232#117—22no—
233C2×C42C22×D1111yescharacteristic
234#107—21no—
235#107—21no—
236#107—21no—
237#107—21no—
238#106—22no—
239#106—22no—
240#106—224no—
241C4⋊C8—112no—
242C4⋊C8—114no—
243C4⋊C8—222no—
244C4⋊C8—221no—
245#103—224no—
246#102—224no—
247C22⋊C8—222no—
248C22⋊C8—222no—
249C4×C8C22⋊D1111yescharacteristic
250C4×C8C22⋊D1111yescharacteristic
251C4×C8C22×D1111yescharacteristic
252C4×C8C22×D1111yescharacteristic
253C2×C11—22no—
254C2×C11C2×#46111yescharacteristic
255C2×C11#306111yescharacteristic
256C2×C11#306711yescharacteristic
257D11—82no—
258#41—442no—
259#41—442no—
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—221no—
263C2×D4—112no—
264C2×D4—222no—
265C2×D4—221no—
266C2×D4—221no—
267C22×C4—222no—
268C22×C4D4×D1111yescharacteristic
269C22×C4#434111yescharacteristic
270C22×C4C2×C22⋊D1111yescharacteristic
271SD16—884no—
272M16—442no—
273M16—444no—
274C2×C8—22no—
275C2×C8—224no—
276C2×C8—222no—
277C2×C8—444no—
278C2×C8—882no—
279C2×C8#432514yescomplemented
280C2×C8C2×C22⋊D1111yescharacteristic
281C2×C8C2×C22⋊D1111yescharacteristic
282C2×C8C2×C22⋊D1111yescharacteristic
283C2×C8C2×C22⋊D1111yescharacteristic
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C4⋊C4—112no—
291C4⋊C4—221no—
292C22⋊C4—42no—
293C22⋊C4—222no—
294C22⋊C4—222no—
295C42—42no—
296C42D4×D1111yescharacteristic
297C42#434111yescharacteristic
298C42C2×C22⋊D1111yescharacteristic
299C42C23×D1111yescharacteristic
300C11#1919511yescharacteristic, complemented, Sylow
301C23—222no—
302C23#6699111yescharacteristic
303Q8—42no—
304Q8—42no—
305Q8—82no—
306Q8—442no—
307D4—222no—
308D4—222no—
309D4—442no—
310D4—444no—
311D4—442no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—222no—
318C2×C4—442no—
319C2×C4—442no—
320C2×C4#6699111yescharacteristic
321C2×C4#6699111yescharacteristic
322C2×C4#6699111yescharacteristic
323C2×C4C2×#432512yes—
324C2×C4#6699512yes—
325C2×C4C2×D4×D1111yescharacteristic
326C2×C4C2×#434111yescharacteristic
327C2×C4C22×C22⋊D1111yescharacteristic
328C8—21no—
329C8—21no—
330C8—444no—
331C8—442no—
332C8C2×#432512yes—
333C8C2×#432512yes—
334C22—21no—
335C22—21no—
336C22—442no—
337C22—442no—
338C22—442no—
339C22#1062269612yes—
340C22C2×#6699111yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—82no—
345C4—82no—
346C4—442no—
347C4#1062269612yes—
348C4#1062330011yescharacteristic
349C4#1062330211yescharacteristic
350C4C22×#432511yescharacteristic
351C4C2×#6699511yescharacteristic
352C2—22no—
353C2—882no—
354C2C2×#1062269611yescharacteristic
355C2#1307828211yescharacteristic
356C2#1307833211yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3160C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#3160D11
hypocenterC11#19195
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. #13068112C2semidirect
4. #13068012C2semidirect
5. #13068002C2semidirect
6. C2×#10622096C2semidirect
7. #13067306C2semidirect
8. C11×#3160C2semidirect
95. C2×C8×C11SD16semidirect
124. #3160D11semidirect
279. C2×C8#4325semidirect
300. C11#19195semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130773292
#130681122
#130680122
#130680022
C2×#106220962
#130673062
C11×#31602
#1919511