Finite Group Databasebeta

← #14911413

Subgroups — #14911413

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#13081589C211yesmaximal, characteristic, complemented
2D8×Dic22C211yesmaximal, characteristic, complemented
3#13070839C211yesmaximal, characteristic, complemented
4#13070838C212yesmaximal, complemented
5#13070754C211yesmaximal, characteristic, complemented
6#13070751C212yesmaximal, complemented
7#13070649C212yesmaximal, complemented
8#13070518C211yesmaximal, characteristic, complemented
9D16×Dic11C212yesmaximal, complemented
10C4×#66890C211yesmaximal, characteristic, complemented
11C11×#2206C211yesmaximal, characteristic, complemented
12#10623249—21no—
13D4×Dic22—21no—
14C2×C11×D16C2212yes—
15C11×#493C2211yescharacteristic
16C4×C11×D8C2211yescharacteristic
17#10622764C2212yes—
18#10622763—22no—
19D8×Dic11C2212yes—
20D8×Dic11C2212yes—
21C2×#66890C2211yescharacteristic
22#10622685—21no—
23#10622620—21no—
24#10622487C2212yes—
25#10622372—22no—
26C4×D88C2211yescharacteristic
27#10622295C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×C4⋊C16C2211yescharacteristic
30C11×#357C2212yes—
31#10622200C2212yes—
32#10622200C2211yescharacteristic
33#10622200C2212yes—
34#10622147C2212yes—
35#10622142C2212yes—
36Dic11⋊C16C2212yes—
37C16×Dic11C2212yes—
38#10622129C2211yescharacteristic
39#10622127C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×#4341—41no—
42C22×Dic22—41no—
43C2×C11×D8—21no—
44C2×C11×D8C2312yes—
45C2×C11×D8C2311yescharacteristic
46C11×#127—21no—
47C4×D4×C11—21no—
48#66993—22no—
49#66992—42no—
50#66991—41no—
51D4×Dic11—22no—
52D4×Dic11—22no—
53C2×#4323—22no—
54#66977—41no—
55C2×D88C2311yescharacteristic
56#66941—22no—
57#66931—42no—
58C4×D44—21no—
59#66922—21no—
60C4×Dic22D411yescharacteristic
61C11×D16—24no—
62C2×C11×C16C2312yes—
63C11×#107C2311yescharacteristic
64C11×#102—21no—
65C4×C8×C11C2311yescharacteristic
66#66896—22no—
67#66896—22no—
68#66890—22no—
69#66885—21no—
70#66882—21no—
71#66882C2312yes—
72#66882C2311yescharacteristic
73Dic11⋊C8D412yes—
74C8×Dic11C2312yes—
75C2×C11⋊C16C2311yescharacteristic
76C2×C11⋊C16C2311yescharacteristic
77#66871—22no—
78C4⋊(C11⋊C8)D411yescharacteristic
79#33925—111nomaximal, Sylow
80C2×D4×C11—21no—
81C2×D4×C11—22no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C22×C4×C11—41no—
85C2×C22⋊D11—42no—
86C2×C22⋊D11—42no—
87C22×Dic11—42no—
88C22×Dic11—42no—
89#4341—84no—
90C2×D44—21no—
91C2×C4×D11—41no—
92C2×Dic22—42no—
93C2×Dic22—41no—
94C2×Dic22—84no—
95C2×Dic22D811yescharacteristic
96C11×D8—21no—
97C11×D8—22no—
98C11×D8—22no—
99C11×D8—81no—
100C11×D8#4112yescomplemented
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2411yescharacteristic
103C11×C4⋊C4—21no—
104C11×C22⋊C4—41no—
105C42×C11C2×D411yescharacteristic
106C22⋊Dic11—42no—
107C22⋊Dic11—42no—
108#4323—82no—
109(C2×D11)⋊C4—41no—
110C4⋊Dic11—22no—
111C4⋊Dic11—21no—
112C4⋊Dic11—41no—
113C4⋊Dic11D811yescharacteristic
114Dic11⋊C4—42no—
115Dic11⋊C4D812yes—
116C4×Dic11C2×D412yes—
117C2×C11⋊C8C2×D412yes—
118D88—21no—
119D88—21no—
120C11×C16—22no—
121C11⋊C16—21no—
122C11⋊C16—21no—
123#3391—111no—
124Q8×D8—111no—
125#2240—111no—
126#2240—112no—
127#2224—111no—
128#2224—112no—
129#2206—112no—
130#2206D1111yescharacteristic, complemented
131Q8×C16—111no—
132C4×D16—112no—
133C4×D16—111no—
134C23×C11—41no—
135C23×C11—42no—
136C22×D11—41no—
137D4×C11—22no—
138D4×C11—42no—
139D4×C11—41no—
140D4×C11—42no—
141D4×C11—82no—
142D4×C11—161no—
143C2×C4×C11—41no—
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—41no—
152C2×Dic11—84no—
153C2×Dic11—84no—
154C2×Dic11C2×D812yes—
155C2×Dic11C2×D812yes—
156D44—41no—
157D44—41no—
158C4×D11—82no—
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—111no—
169C2×D16C2×D1112yes—
170#500—112no—
171#500—111no—
172#493—112no—
173#493C2×D1111yescharacteristic
174#474—222no—
175#474—221no—
176#459—221no—
177#459—222no—
178C8×Q8—111no—
179C4×D8—112no—
180C4×D8—112no—
181C4×D8—111no—
182C4×D8C2×D1111yescharacteristic
183#366—112no—
184#366—111no—
185C4⋊C16—112no—
186C4⋊C16C2×D1111yescharacteristic
187#357—111no—
188#357—112no—
189#357—112no—
190#357—112no—
191#357—111no—
192#357C2×D1112yes—
193C4×C16—112no—
194C4×C16—111no—
195C22×C11—42no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11—82no—
199C22×C11—82no—
200C22×C11—82no—
201C22×C11C22×D811yescharacteristic
202C2×D11—81no—
203C2×D11—81no—
204C2×D11—81no—
205C4×C11—21no—
206C4×C11—81no—
207C4×C11C2×D1612yes—
208C4×C11#54811yescharacteristic
209C4×C11#57711yescharacteristic
210Dic11—22no—
211Dic11—82no—
212Dic11—81no—
213Dic11C2×D1614yes—
214C2×#41—441no—
215C22×Q8—441no—
216C2×D8—21no—
217C2×D8—111no—
218C2×D8—222no—
219C2×D8C22×D1112yes—
220C2×D8C22×D1111yescharacteristic
221C4⋊Q8—222no—
222C4⋊Q8—221no—
223#127—21no—
224#127—222no—
225C22⋊Q8—442no—
226C22⋊Q8—441no—
227#121—441no—
228#121—442no—
229C4×Q8—111no—
230C4×D4—21no—
231C4×D4—222no—
232C4×D4—222no—
233C4×D4—221no—
234D16—24no—
235D16—222no—
236C2×C16—111no—
237C2×C16—111no—
238C2×C16C22×D1112yes—
239#107—112no—
240#107—111no—
241#107—222no—
242#107—221no—
243#107C22×D1111yescharacteristic
244C4⋊C8—112no—
245C4⋊C8—111no—
246#102—21no—
247#102—222no—
248#102—222no—
249#102—221no—
250C4×C8—112no—
251C4×C8C22×D1111yescharacteristic
252C2×C11—82no—
253C2×C11—162no—
254C2×C11#335811yescharacteristic
255C2×C11C22×D1611yescharacteristic
256C2×C11#341611yescharacteristic
257D11—161no—
258#41—884no—
259C2×Q8—111no—
260C2×Q8—442no—
261C2×Q8—441no—
262C2×Q8—884no—
263C2×D4—21no—
264C2×D4—22no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—221no—
268C2×D4—442no—
269C2×D4—442no—
270C22×C4—41no—
271C22×C4—442no—
272C22×C4—442no—
273C22×C4—441no—
274D8—22no—
275D8—21no—
276D8—22no—
277D8—81no—
278D8—221no—
279D8—221no—
280D8—882no—
281D8#434112yescomplemented
282C2×C8—112no—
283C2×C8D4×D1111yescharacteristic
284C2×C8C23×D1111yescharacteristic
285C4⋊C4—21no—
286C4⋊C4—112no—
287C4⋊C4—111no—
288C4⋊C4—221no—
289C4⋊C4—222no—
290C4⋊C4—442no—
291C4⋊C4—441no—
292C22⋊C4—41no—
293C22⋊C4—442no—
294C22⋊C4—442no—
295C22⋊C4—441no—
296C42—112no—
297C42D4×D1111yescharacteristic
298C16—22no—
299C16—221no—
300C16—221no—
301C11#3392511yescharacteristic, complemented, Sylow
302C23—41no—
303C23—42no—
304C23—441no—
305Q8—114no—
306Q8—884no—
307Q8—882no—
308D4—22no—
309D4—41no—
310D4—42no—
311D4—42no—
312D4—82no—
313D4—161no—
314D4—441no—
315D4—441no—
316D4—884no—
317D4—1762no—
318C2×C4—41no—
319C2×C4—82no—
320C2×C4—112no—
321C2×C4—112no—
322C2×C4—441no—
323C2×C4—442no—
324C2×C4—884no—
325C2×C4—884no—
326C2×C4—882no—
327C2×C4D8×D1111yescharacteristic
328C2×C4D8×D1111yescharacteristic
329C2×C4C2×D4×D1111yescharacteristic
330C8—21no—
331C8—222no—
332C8C2×#434111yescharacteristic
333C8#6704311yescharacteristic
334C22—42no—
335C22—81no—
336C22—81no—
337C22—82no—
338C22—82no—
339C22—82no—
340C22—881no—
341C22—881no—
342C22—881no—
343C22C2×D8×D1111yescharacteristic
344C4—21no—
345C4—81no—
346C4—114no—
347C4—222no—
348C4—881no—
349C4—882no—
350C4D11×D1612yes—
351C4#1062312911yescharacteristic
352C4#1062330611yescharacteristic
353C2—82no—
354C2—162no—
355C2—1761no—
356C2#1308124611yescharacteristic
357C2C2×D11×D1611yescharacteristic
358C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2206C2
socleC22×C11C22×D8
hypercenter#2206D11
hypocenterC11#33925
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2206

Complements

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

NH ≅ G/Ntype
1. #13081589C2semidirect
2. D8×Dic22C2semidirect
3. #13070839C2semidirect
4. #13070838C2semidirect
5. #13070754C2semidirect
6. #13070751C2semidirect
7. #13070649C2semidirect
8. #13070518C2semidirect
9. D16×Dic11C2semidirect
10. C4×#66890C2semidirect
11. C11×#2206C2semidirect
100. C11×D8#41semidirect
130. #2206D11semidirect
161. Dic22D16semidirect
281. D8#4341semidirect
301. C11#33925semidirect

Maximal subgroups

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

subgroupindex
#130815892
D8×Dic222
#130708392
#130708382
#130707542
#130707512
#130706492
#130705182
D16×Dic112
C4×#668902
C11×#22062
#3392511