Finite Group Databasebeta

← #14737639

Subgroups — #14737639

Order 2816.

650 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#13078734C212yesmaximal, complemented
2C2×C8×Dic22C211yesmaximal, characteristic, complemented
3#13068029C214yesmaximal, complemented
4#13068017C212yesmaximal, complemented
5#13067973C212yesmaximal, complemented
6#13067379C211yesmaximal, characteristic, complemented
7#13067311C212yesmaximal, complemented
8C11×#3169C211yesmaximal, characteristic
9C11×#532C2212yes—
10C2×C4×Dic22C2211yescharacteristic
11C11×#500C2211yescharacteristic
12C11×#493C2211yescharacteristic
13C11×#486C2212yes—
14C11×#466—21no—
15C11×#466—21no—
16C4×C11×D8—21no—
17C4×C11×D8—21no—
18C2×C4×C8×C11C2211yescharacteristic
19C2×Dic11⋊C8—21no—
20C2×C8×Dic11—21no—
21#10622704C2214yes—
22#10622688C2214yes—
23#10622653—22no—
24#10622646—22no—
25#10622631—24no—
26#10622539C2212yes—
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28C8×Dic22—21no—
29C8×Dic22—21no—
30C8×Dic22C2212yes—
31C8×Dic22C2212yes—
32#10622184C2214yes—
33#10622182C2214yes—
34#10622096C2212yes—
35#10622095C2212yes—
36C2×C11×#41—22no—
37C22×Dic22D411yescharacteristic
38C2×C11×D8—21no—
39C2×C11×D8—21no—
40C22×C8×C11D411yescharacteristic
41C22×C8×C11D411yescharacteristic
42C11×C4⋊Q8C2312yes—
43C11×#127C2312yes—
44C11×#124—22no—
45C11×#121—22no—
46C11×#121—22no—
47C4×D4×C11—22no—
48C4×D4×C11—22no—
49C2×C42×C11C2311yescharacteristic
50C2×#4324—24no—
51C2×C4⋊Dic11D411yescharacteristic
52C2×Dic11⋊C4—21no—
53C2×C4×Dic11—21no—
54C22×C11⋊C8—21no—
55C4×Dic22—21no—
56C4×Dic22—21no—
57C4×Dic22D412yes—
58C4×Dic22C2312yes—
59C11×#107—21no—
60C11×#107—21no—
61C11×#102—22no—
62C11×#102—22no—
63C4×C8×C11D411yescharacteristic
64C4×C8×C11D411yescharacteristic
65C4×C8×C11C2311yescharacteristic
66C4×C8×C11C2311yescharacteristic
67#66896—24no—
68C22⋊(C11⋊C8)—22no—
69Dic11⋊C8—22no—
70Dic11⋊C8—22no—
71C8×Dic11—22no—
72C8×Dic11—22no—
73#66874—24no—
74#66871—24no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)C2312yes—
77C4⋊(C11⋊C8)C2314yes—
78#66867—22no—
79#19264—111nomaximal, Sylow
80C11×#41—84no—
81C2×Q8×C11—22no—
82C2×D4×C11—22no—
83C2×D4×C11—22no—
84C2×D4×C11—22no—
85C2×D4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×Dic11—21no—
91C22×Dic11—21no—
92C2×Dic22—24no—
93C2×Dic22—21no—
94C2×Dic22C2×D412yes—
95C11×D8—42no—
96C11×D8—42no—
97C2×C8×C11—22no—
98C2×C8×C11—41no—
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2×D411yescharacteristic
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C22⋊C4—42no—
106C11×C22⋊C4—42no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11#4111yescharacteristic
110C42×C11C2411yescharacteristic
111#4324—48no—
112C4⋊Dic11—21no—
113C4⋊Dic11C2×D412yes—
114Dic11⋊C4—22no—
115Dic11⋊C4—22no—
116C4×Dic11—22no—
117C4×Dic11—22no—
118C2×C11⋊C8—24no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—42no—
121#3169D1111yescharacteristic
122#3112—112no—
123C2×C8×Q8—111no—
124#1678—114no—
125#1676—112no—
126#1668—112no—
127#1568—111no—
128#1551—112no—
129C23×C11—42no—
130C23×C11#12111yescharacteristic
131Q8×C11—82no—
132D4×C11—44no—
133D4×C11—42no—
134D4×C11—42no—
135D4×C11—82no—
136D4×C11—84no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—42no—
142C2×C4×C11—84no—
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C2×C4×C11C22×D411yescharacteristic
148C2×C4×C11C2×#4111yescharacteristic
149C2×Dic11—24no—
150C2×Dic11—22no—
151C2×Dic11—22no—
152C2×Dic11—42no—
153Dic22—24no—
154Dic22—22no—
155Dic22#13514yes—
156C8×C11—21no—
157C8×C11—21no—
158C8×C11—21no—
159C8×C11#13712yes—
160C11⋊C8—44no—
161C11⋊C8—42no—
162#532C2×D1112yes—
163C2×C4×Q8—111no—
164#500C2×D1111yescharacteristic
165#493C2×D1111yescharacteristic
166#486C2×D1112yes—
167#480—222no—
168#477—114no—
169#466—21no—
170#466—21no—
171#460—114no—
172#448—222no—
173C8×Q8—112no—
174C8×Q8—112no—
175C8×Q8—221no—
176C8×Q8—221no—
177#440—224no—
178C4×D8—21no—
179C4×D8—21no—
180#432—112no—
181C2×C4⋊C8—111no—
182C2×C4⋊C8—221no—
183C2×C4×C8—221no—
184C2×C4×C8C2×D1111yescharacteristic
185#335—112no—
186#334—112no—
187#333—114no—
188#331—114no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—82no—
192C22×C11—82no—
193C22×C11—82no—
194C22×C11#47212yes—
195C22×C11C2×#12111yescharacteristic
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—82no—
201C4×C11C2×#13512yes—
202C4×C11C2×#13711yescharacteristic
203C4×C11#57511yescharacteristic
204Dic11—24no—
205Dic11—42no—
206C2×#41—22no—
207C22×Q8—111no—
208C2×SD16—224no—
209C2×D8—21no—
210C2×D8—21no—
211C22×C8—221no—
212C22×C8C22⋊D1111yescharacteristic
213C22×C8C22⋊D1111yescharacteristic
214C4⋊Q8C22×D1112yes—
215#127C22×D1112yes—
216#124—22no—
217#121—22no—
218#121—22no—
219C4×Q8—112no—
220C4×Q8—112no—
221C4×Q8—221no—
222C4×Q8—221no—
223C4×D4—22no—
224C4×D4—22no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—221no—
227C2×C42—221no—
228C2×C42C22×D1111yescharacteristic
229#107—21no—
230#107—21no—
231#107—224no—
232C4⋊C8—112no—
233C4⋊C8—114no—
234C4⋊C8—222no—
235C4⋊C8—222no—
236C4⋊C8—221no—
237#103—224no—
238#102—22no—
239#102—22no—
240#102—224no—
241C22⋊C8—222no—
242#97—222no—
243C4×C8—222no—
244C4×C8—222no—
245C4×C8C22⋊D1111yescharacteristic
246C4×C8C22⋊D1111yescharacteristic
247C4×C8C22×D1111yescharacteristic
248C4×C8C22×D1111yescharacteristic
249C2×C11—22no—
250C2×C11—162no—
251C2×C11#303711yescharacteristic
252C2×C11#305011yescharacteristic
253C2×C11C2×#47211yescharacteristic
254#41—84no—
255C2×Q8—22no—
256C2×Q8—112no—
257C2×Q8—224no—
258C2×Q8—221no—
259C2×D4—22no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—42no—
263C22×C4—42no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4D4×D1111yescharacteristic
267C22×C4#434111yescharacteristic
268C22×C4C2×C22⋊D1111yescharacteristic
269SD16—448no—
270D8—42no—
271D8—42no—
272C2×C8—22no—
273C2×C8—41no—
274C2×C8—224no—
275C2×C8—222no—
276C2×C8—442no—
277C2×C8C2×C22⋊D1111yescharacteristic
278C2×C8C2×C22⋊D1111yescharacteristic
279C2×C8C2×C22⋊D1111yescharacteristic
280C2×C8C2×C22⋊D1111yescharacteristic
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—112no—
284C4⋊C4—221no—
285C4⋊C4—222no—
286C4⋊C4—222no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C42—222no—
290C42—222no—
291C42D4×D1111yescharacteristic
292C42#434111yescharacteristic
293C42C2×C22⋊D1111yescharacteristic
294C42C23×D1111yescharacteristic
295C11#1926411yescharacteristic, complemented, Sylow
296C23—42no—
297C23#6699111yescharacteristic
298Q8—82no—
299Q8—114no—
300Q8—224no—
301Q8—222no—
302D4—44no—
303D4—42no—
304D4—42no—
305D4—82no—
306D4—84no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—84no—
313C2×C4—224no—
314C2×C4—222no—
315C2×C4—222no—
316C2×C4—442no—
317C2×C4#6699111yescharacteristic
318C2×C4#6699111yescharacteristic
319C2×C4#6699111yescharacteristic
320C2×C4C2×D4×D1111yescharacteristic
321C2×C4C2×#434111yescharacteristic
322C2×C4C22×C22⋊D1111yescharacteristic
323C8—21no—
324C8—21no—
325C8—21no—
326C8—444no—
327C8—442no—
328C8#6700412yes—
329C22—21no—
330C22—21no—
331C22—82no—
332C22—82no—
333C22—82no—
334C22#1062277312yes—
335C22C2×#6699111yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—82no—
341C4—224no—
342C4—442no—
343C4D11×#13512yes—
344C4#1062335311yescharacteristic
345C4C2×#6700411yescharacteristic
346C2—22no—
347C2—162no—
348C2#1307808411yescharacteristic
349C2#1307819311yescharacteristic
350C2C2×#1062277311yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3169C2
socleC22×C11C2×#121
hypercenter#3169D11
hypocenterC11#19264
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #13078734C2semidirect
2. C2×C8×Dic22C2semidirect
3. #13068029C2semidirect
4. #13068017C2semidirect
5. #13067973C2semidirect
6. #13067379C2semidirect
7. #13067311C2semidirect
295. C11#19264semidirect

Maximal subgroups

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

subgroupindex
#130787342
C2×C8×Dic222
#130680292
#130680172
#130679732
#130673792
#130673112
C11×#31692
#1926411