Finite Group Databasebeta

← #14911416

Subgroups — #14911416

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081590C211yesmaximal, characteristic, complemented
2D8×Dic22C211yesmaximal, characteristic, complemented
3#13070840C211yesmaximal, characteristic, complemented
4#13070838C212yesmaximal, complemented
5#13070753C211yesmaximal, characteristic, complemented
6#13070752C212yesmaximal, complemented
7#13070651C211yesmaximal, characteristic, complemented
8#13070649C212yesmaximal, complemented
9C16×Dic22C211yesmaximal, characteristic, complemented
10#13070460C212yesmaximal, complemented
11C4×C11×D16C211yesmaximal, characteristic, complemented
12#10623084—21no—
13D4×Dic22—21no—
14C2×C11×D16C2211yescharacteristic
15C4×C11×D8C2211yescharacteristic
16C4×C11×D8C2211yescharacteristic
17#10622764C2212yes—
18D8×Dic11C2212yes—
19C2×#66890C2212yes—
20#10622628—21no—
21#10622620—21no—
22#10622487C2212yes—
23#10622485C2212yes—
24#10622399—22no—
25#10622372—22no—
26#10622308C2211yescharacteristic
27#10622295C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×#366C2211yescharacteristic
30C11×#357C2211yescharacteristic
31C11×#357C2211yescharacteristic
32C4×C11×C16C2211yescharacteristic
33#10622200C2212yes—
34#10622147C2212yes—
35#10622147C2212yes—
36Dic11⋊C16C2212yes—
37C16×Dic11C2212yes—
38#10622129C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×#4339—41no—
42C22×Dic22—41no—
43C2×C11×D8C2311yescharacteristic
44C2×C11×D8C2311yescharacteristic
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47#66993—22no—
48D4×Dic11—22no—
49C2×#4323—22no—
50#66983—41no—
51#66977—41no—
52C2×D88—21no—
53C2×D88C2312yes—
54#66946—22no—
55#66941—22no—
56#66937—42no—
57#66931—42no—
58#66927—21no—
59#66922—21no—
60C4×Dic22D411yescharacteristic
61C11×D16—22no—
62C2×C11×C16C2311yescharacteristic
63C2×C11×C16C2311yescharacteristic
64C11×#107C2311yescharacteristic
65C11×#107C2311yescharacteristic
66C11×#102—21no—
67C11×#102—21no—
68C4×C8×C11C2311yescharacteristic
69#66896—22no—
70#66890—24no—
71#66882—21no—
72#66882C2312yes—
73Dic11⋊C8D412yes—
74C8×Dic11C2312yes—
75C2×C11⋊C16C2312yes—
76#66873—22no—
77#66871—22no—
78C4⋊(C11⋊C8)D411yescharacteristic
79#33925—111nomaximal, Sylow
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C2×C22⋊D11—42no—
85C2×C22⋊D11—42no—
86C22×Dic11—42no—
87#4339—84no—
88C2×D44—22no—
89C2×D44—41no—
90C2×D44—41no—
91C2×C4×D11—42no—
92C2×Dic22—42no—
93C2×Dic22—41no—
94C2×Dic22—84no—
95C2×Dic22D811yescharacteristic
96C11×D8—21no—
97C11×D8—21no—
98C11×D8—21no—
99C11×D8#4112yescomplemented
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2411yescharacteristic
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C42×C11C2×D411yescharacteristic
107C22⋊Dic11—42no—
108#4323—82no—
109(C2×D11)⋊C4—42no—
110C4⋊Dic11—22no—
111C4⋊Dic11—41no—
112C4⋊Dic11D811yescharacteristic
113Dic11⋊C4—42no—
114Dic11⋊C4D812yes—
115C4×Dic11C2×D412yes—
116C2×C11⋊C8C2×D412yes—
117D88—22no—
118D88—22no—
119D88—81no—
120C11×C16—21no—
121C11×C16—21no—
122C11⋊C16—22no—
123#3391—111no—
124Q8×D8—111no—
125#2240—112no—
126#2240—111no—
127#2224—111no—
128#2224—112no—
129#2206—112no—
130#2206—111no—
131Q8×C16—111no—
132C4×D16—112no—
133C4×D16D1111yescharacteristic, complemented
134C23×C11—41no—
135C23×C11—41no—
136C22×D11—42no—
137D4×C11—22no—
138D4×C11—41no—
139D4×C11—41no—
140D4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—82no—
144C2×C4×C11—82no—
145C2×C4×C11C2×D811yescharacteristic
146C2×C4×C11C2×D811yescharacteristic
147C2×C4×C11C22×D411yescharacteristic
148C22⋊D11—84no—
149C22⋊D11—162no—
150C2×Dic11—42no—
151C2×Dic11—84no—
152C2×Dic11C2×D812yes—
153C2×Dic11C2×D812yes—
154D44—42no—
155D44—42no—
156D44—82no—
157D44—161no—
158C4×D11—84no—
159Dic22—82no—
160Dic22—84no—
161Dic22D1614yescomplemented
162C8×C11—21no—
163C8×C11C2×#4111yescharacteristic
164C8×C112−1+411yescharacteristic
165C11⋊C8—22no—
166#550—221no—
167D4×Q8—221no—
168C2×D16—112no—
169C2×D16C2×D1111yescharacteristic
170#500—112no—
171#500—111no—
172#493—112no—
173#493—111no—
174#474—222no—
175#474—221no—
176#459—222no—
177#459—221no—
178C8×Q8—111no—
179C4×D8—112no—
180C4×D8—112no—
181C4×D8C2×D1111yescharacteristic
182C4×D8C2×D1111yescharacteristic
183#366—112no—
184#366C2×D1111yescharacteristic
185C4⋊C16—112no—
186C4⋊C16—111no—
187#357—112no—
188#357—112no—
189#357—112no—
190#357—112no—
191#357C2×D1111yescharacteristic
192#357C2×D1111yescharacteristic
193C4×C16—112no—
194C4×C16C2×D1111yescharacteristic
195C22×C11—42no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11C22×D811yescharacteristic
202C2×D11—82no—
203C2×D11—82no—
204C2×D11—82no—
205C4×C11—21no—
206C4×C11—81no—
207C4×C11—81no—
208C4×C11C2×D1612yes—
209C4×C11#54811yescharacteristic
210C4×C11#57711yescharacteristic
211Dic11—22no—
212Dic11—82no—
213Dic11C2×D1614yes—
214C2×#41—441no—
215C22×Q8—441no—
216C2×D8—112no—
217C2×D8—222no—
218C2×D8—221no—
219C2×D8C22×D1111yescharacteristic
220C2×D8C22×D1111yescharacteristic
221C4⋊Q8—222no—
222C4⋊Q8—221no—
223#127—222no—
224#127—221no—
225C22⋊Q8—442no—
226C22⋊Q8—441no—
227#121—442no—
228#121—441no—
229C4×Q8—111no—
230C4×D4—21no—
231C4×D4—21no—
232C4×D4—222no—
233C4×D4—222no—
234D16—22no—
235D16—224no—
236C2×C16—112no—
237C2×C16C22×D1111yescharacteristic
238C2×C16C22×D1111yescharacteristic
239#107—112no—
240#107—222no—
241#107—221no—
242#107C22×D1111yescharacteristic
243#107C22×D1111yescharacteristic
244C4⋊C8—112no—
245C4⋊C8—111no—
246#102—21no—
247#102—21no—
248#102—222no—
249#102—222no—
250C4×C8—112no—
251C4×C8C22×D1111yescharacteristic
252C2×C11—82no—
253C2×C11—161no—
254C2×C11#335811yescharacteristic
255C2×C11C22×D1611yescharacteristic
256C2×C11#341611yescharacteristic
257D11—162no—
258#41—884no—
259C2×Q8—111no—
260C2×Q8—442no—
261C2×Q8—441no—
262C2×Q8—884no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—222no—
266C2×D4—442no—
267C2×D4—442no—
268C2×D4—441no—
269C2×D4—441no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—442no—
273C22×C4—442no—
274D8—21no—
275D8—21no—
276D8—21no—
277D8—222no—
278D8—222no—
279D8—881no—
280D8—882no—
281D8#433912yescomplemented
282C2×C8—112no—
283C2×C8D4×D1111yescharacteristic
284C2×C8C23×D1111yescharacteristic
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—112no—
288C4⋊C4—111no—
289C4⋊C4—222no—
290C4⋊C4—442no—
291C4⋊C4—441no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—442no—
295C22⋊C4—442no—
296C42—112no—
297C42D4×D1111yescharacteristic
298C16—21no—
299C16—21no—
300C16—222no—
301C11#3392511yescharacteristic, complemented, Sylow
302C23—41no—
303C23—41no—
304C23—442no—
305Q8—114no—
306Q8—884no—
307Q8—882no—
308D4—22no—
309D4—41no—
310D4—41no—
311D4—41no—
312D4—442no—
313D4—442no—
314D4—884no—
315D4—882no—
316D4—1761no—
317D4—1762no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—82no—
321C2×C4—82no—
322C2×C4—112no—
323C2×C4—112no—
324C2×C4—442no—
325C2×C4—884no—
326C2×C4—884no—
327C2×C4D8×D1111yescharacteristic
328C2×C4D8×D1111yescharacteristic
329C2×C4C2×D4×D1111yescharacteristic
330C8—21no—
331C8—222no—
332C8C2×#433911yescharacteristic
333C8#6704311yescharacteristic
334C22—42no—
335C22—81no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22—882no—
341C22—882no—
342C22—882no—
343C22C2×D8×D1111yescharacteristic
344C4—21no—
345C4—81no—
346C4—81no—
347C4—114no—
348C4—222no—
349C4—882no—
350C4D11×D1612yes—
351C4#1062308311yescharacteristic
352C4#1062330111yescharacteristic
353C2—82no—
354C2—161no—
355C2—1762no—
356C2#1308124911yescharacteristic
357C2C2×D11×D1611yescharacteristic
358C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×D16C2
socleC22×C11C22×D8
hypercenterC4×D16D11
hypocenterC11#33925
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×D16

Complements

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

NH ≅ G/Ntype
1. #13081590C2semidirect
2. D8×Dic22C2semidirect
3. #13070840C2semidirect
4. #13070838C2semidirect
5. #13070753C2semidirect
6. #13070752C2semidirect
7. #13070651C2semidirect
8. #13070649C2semidirect
9. C16×Dic22C2semidirect
10. #13070460C2semidirect
11. C4×C11×D16C2semidirect
99. C11×D8#41semidirect
133. C4×D16D11semidirect
161. Dic22D16semidirect
281. D8#4339semidirect
301. C11#33925semidirect

Maximal subgroups

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

subgroupindex
#130815902
D8×Dic222
#130708402
#130708382
#130707532
#130707522
#130706512
#130706492
C16×Dic222
#130704602
C4×C11×D162
#3392511