Finite Group Databasebeta

← #14911452

Subgroups — #14911452

Order 2816.

528 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#13081590C211yesmaximal, characteristic
2Q16×Dic22C211yesmaximal, characteristic, complemented
3#13070840C211yesmaximal, characteristic, complemented
4#13070838C212yesmaximal, complemented
5#13070763C211yesmaximal, characteristic, complemented
6#13070762C212yesmaximal, complemented
7#13070656C211yesmaximal, characteristic, complemented
8#13070654C212yesmaximal, complemented
9C16×Dic22C211yesmaximal, characteristic, complemented
10#13070465C212yesmaximal, complemented
11C4×C11×SD32C211yesmaximal, characteristic, complemented
12Q8×Dic22—21no—
13#10623084—21no—
14C2×C11×SD32C2211yescharacteristic
15C4×C11×Q16C2211yescharacteristic
16C4×C11×D8C2211yescharacteristic
17Q16×Dic11C2212yes—
18C2×#66892C2212yes—
19#10622764C2212yes—
20#10622634—21no—
21#10622628—21no—
22#10622487C2212yes—
23#10622485C2212yes—
24#10622407—22no—
25#10622399—22no—
26#10622308C2211yescharacteristic
27#10622295C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×#367C2211yescharacteristic
30C11×#358C2211yescharacteristic
31C11×#357C2211yescharacteristic
32C4×C11×C16C2211yescharacteristic
33#10622200C2212yes—
34#10622147C2212yes—
35#10622147C2212yes—
36Dic11⋊C16C2212yes—
37C16×Dic11C2212yes—
38#10622129C2212yes—
39#10622128C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×#4339—41no—
42C2×C11×Q16C2311yescharacteristic
43C2×C11×D8C2311yescharacteristic
44C4×Q8×C11—21no—
45C4×D4×C11—21no—
46Q8×Dic11—22no—
47#66993—22no—
48C2×#4323—22no—
49#66983—41no—
50C2×D88—21no—
51C2×D88C2312yes—
52#66946—22no—
53#66941—22no—
54#66941—42no—
55#66937—42no—
56#66927—21no—
57#66922—21no—
58#66922—41no—
59C4×Dic22—41no—
60C4×Dic22D411yescharacteristic
61C11×SD32—22no—
62C2×C11×C16C2311yescharacteristic
63C2×C11×C16C2311yescharacteristic
64C11×#107C2311yescharacteristic
65C11×#107C2311yescharacteristic
66C11×#103—21no—
67C11×#102—21no—
68C4×C8×C11C2311yescharacteristic
69#66899—22no—
70#66892—24no—
71#66882—21no—
72#66882C2312yes—
73Dic11⋊C8D412yes—
74C8×Dic11C2312yes—
75C2×C11⋊C16C2312yes—
76#66873—22no—
77#66871—22no—
78C4⋊(C11⋊C8)D411yescharacteristic
79#33929—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×D4×C11—21no—
82C22×C4×C11—41no—
83C2×C22⋊D11—42no—
84C2×C22⋊D11—42no—
85#4339—84no—
86C2×D44—22no—
87C2×D44—41no—
88C2×D44—41no—
89C2×C4×D11—42no—
90C2×Dic22—42no—
91C2×Dic22—41no—
92C2×Dic22D811yescharacteristic
93C11×Q16—21no—
94C11×Q16#4112yescomplemented
95C11×D8—21no—
96C11×D8—21no—
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11C2411yescharacteristic
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—41no—
102C11×C22⋊C4—41no—
103C42×C11—41no—
104C42×C11C2×D411yescharacteristic
105#4323—82no—
106(C2×D11)⋊C4—42no—
107C4⋊Dic11—22no—
108C4⋊Dic11—42no—
109C4⋊Dic11—41no—
110C4⋊Dic11D811yescharacteristic
111Dic11⋊C4—42no—
112Dic11⋊C4D812yes—
113C4×Dic11—42no—
114C4×Dic11C2×D412yes—
115C2×C11⋊C8C2×D412yes—
116D88—22no—
117D88—22no—
118D88—81no—
119C11×C16—21no—
120C11×C16—21no—
121C11⋊C16—22no—
122#3391—111no—
123Q8×Q16—111no—
124#2240—112no—
125#2240—111no—
126#2226—111no—
127#2226—112no—
128#2207—112no—
129#2207—111no—
130Q8×C16—111no—
131C4×SD32—112no—
132C4×SD32D1111yescharacteristic, complemented
133C23×C11—41no—
134C22×D11—42no—
135Q8×C11—22no—
136Q8×C11—41no—
137D4×C11—41no—
138D4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—82no—
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C2×D811yescharacteristic
145C2×C4×C11C22×D411yescharacteristic
146C22⋊D11—84no—
147C22⋊D11—162no—
148C2×Dic11—42no—
149C2×Dic11C2×D812yes—
150C2×Dic11C2×D812yes—
151D44—42no—
152D44—42no—
153D44—82no—
154D44—161no—
155C4×D11—84no—
156Dic22—162no—
157Dic22—161no—
158Dic22SD3214yescomplemented
159C8×C11—21no—
160C8×C11C2×#4111yescharacteristic
161C8×C112−1+411yescharacteristic
162C11⋊C8—22no—
163Q82—221no—
164#550—221no—
165C2×SD32—112no—
166C2×SD32C2×D1111yescharacteristic
167#500—112no—
168#500—111no—
169#493—112no—
170#493—111no—
171#477—222no—
172#477—221no—
173#459—222no—
174#459—221no—
175C8×Q8—111no—
176C4×Q16—112no—
177C4×Q16C2×D1111yescharacteristic
178C4×D8—112no—
179C4×D8C2×D1111yescharacteristic
180#367—112no—
181#367C2×D1111yescharacteristic
182C4⋊C16—112no—
183C4⋊C16—111no—
184#358C2×D1111yescharacteristic
185#357—112no—
186#357—112no—
187#357—112no—
188#357—112no—
189#357C2×D1111yescharacteristic
190C4×C16—112no—
191C4×C16C2×D1111yescharacteristic
192C22×C11—81no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11C22×D811yescharacteristic
196C2×D11—82no—
197C2×D11—82no—
198C2×D11—82no—
199C4×C11—21no—
200C4×C11—42no—
201C4×C11—81no—
202C4×C11—81no—
203C4×C11C2×SD3212yes—
204C4×C11#54811yescharacteristic
205C4×C11#57711yescharacteristic
206Dic11—22no—
207Dic11—82no—
208Dic11C2×SD3214yes—
209C2×#41—441no—
210C2×Q16C22×D1111yescharacteristic
211C2×D8—112no—
212C2×D8—222no—
213C2×D8—221no—
214C2×D8C22×D1111yescharacteristic
215C4⋊Q8—222no—
216C4⋊Q8—221no—
217C4⋊Q8—441no—
218C4⋊Q8—442no—
219#127—222no—
220#127—221no—
221#121—442no—
222#121—441no—
223C4×Q8—21no—
224C4×Q8—111no—
225C4×Q8—222no—
226C4×Q8—441no—
227C4×D4—21no—
228C4×D4—222no—
229SD32—22no—
230SD32—224no—
231C2×C16—112no—
232C2×C16C22×D1111yescharacteristic
233C2×C16C22×D1111yescharacteristic
234#107—112no—
235#107—222no—
236#107—221no—
237#107C22×D1111yescharacteristic
238#107C22×D1111yescharacteristic
239C4⋊C8—112no—
240C4⋊C8—111no—
241#103—21no—
242#103—222no—
243#102—21no—
244#102—222no—
245C4×C8—112no—
246C4×C8C22×D1111yescharacteristic
247C2×C11—161no—
248C2×C11#335811yescharacteristic
249C2×C11C22×SD3211yescharacteristic
250C2×C11#341511yescharacteristic
251D11—162no—
252#41—884no—
253C2×Q8—21no—
254C2×Q8—111no—
255C2×Q8—442no—
256C2×Q8—441no—
257C2×D4—21no—
258C2×D4—222no—
259C2×D4—442no—
260C2×D4—442no—
261C2×D4—441no—
262C2×D4—441no—
263C22×C4—41no—
264C22×C4—442no—
265Q16—21no—
266Q16#433912yescomplemented
267D8—21no—
268D8—21no—
269D8—222no—
270D8—222no—
271D8—881no—
272D8—882no—
273C2×C8—112no—
274C2×C8D4×D1111yescharacteristic
275C2×C8C23×D1111yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—41no—
279C4⋊C4—112no—
280C4⋊C4—111no—
281C4⋊C4—222no—
282C4⋊C4—442no—
283C4⋊C4—442no—
284C4⋊C4—441no—
285C22⋊C4—41no—
286C22⋊C4—442no—
287C42—41no—
288C42—112no—
289C42—442no—
290C42D4×D1111yescharacteristic
291C16—21no—
292C16—21no—
293C16—222no—
294C11#3392911yescharacteristic, complemented, Sylow
295C23—41no—
296C23—442no—
297Q8—22no—
298Q8—41no—
299Q8—114no—
300Q8—1761no—
301Q8—1762no—
302D4—41no—
303D4—41no—
304D4—442no—
305D4—442no—
306D4—884no—
307D4—882no—
308D4—1761no—
309D4—1762no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—82no—
314C2×C4—112no—
315C2×C4—112no—
316C2×C4—442no—
317C2×C4—884no—
318C2×C4D8×D1111yescharacteristic
319C2×C4D8×D1111yescharacteristic
320C2×C4C2×D4×D1111yescharacteristic
321C8—21no—
322C8—222no—
323C8C2×#433911yescharacteristic
324C8#6704311yescharacteristic
325C22—81no—
326C22—81no—
327C22—81no—
328C22—882no—
329C22—882no—
330C22—882no—
331C22C2×D8×D1111yescharacteristic
332C4—21no—
333C4—42no—
334C4—81no—
335C4—81no—
336C4—114no—
337C4—222no—
338C4—882no—
339C4D11×SD3212yes—
340C4#1062308311yescharacteristic
341C4#1062330111yescharacteristic
342C2—161no—
343C2—1762no—
344C2#1308124911yescharacteristic
345C2C2×D11×SD3211yescharacteristic
346C2#1308175411yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×SD32C2
socleC22×C11C22×D8
prime radical#13081590C2
hypercenterC4×SD32D11
hypocenterC11#33929
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
2. Q16×Dic22C2semidirect
3. #13070840C2semidirect
4. #13070838C2semidirect
5. #13070763C2semidirect
6. #13070762C2semidirect
7. #13070656C2semidirect
8. #13070654C2semidirect
9. C16×Dic22C2semidirect
10. #13070465C2semidirect
11. C4×C11×SD32C2semidirect
94. C11×Q16#41semidirect
132. C4×SD32D11semidirect
158. Dic22SD32semidirect
266. Q16#4339semidirect
294. C11#33929semidirect

Maximal subgroups

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

subgroupindex
#130815902
Q16×Dic222
#130708402
#130708382
#130707632
#130707622
#130706562
#130706542
C16×Dic222
#130704652
C4×C11×SD322
#3392911