Finite Group Databasebeta

← #14911201

Subgroups — #14911201

Order 2816.

492 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081039C211yesmaximal, characteristic, complemented
2#13070889C211yesmaximal, characteristic, complemented
3#13070807C212yesmaximal, complemented
4#13070804C212yesmaximal, complemented
5#13070763C211yesmaximal, characteristic, complemented
6#13070760C211yesmaximal, characteristic, complemented
7#13070700C212yesmaximal, complemented
8C4×#66890C211yesmaximal, characteristic, complemented
9D4×C11⋊C16C211yesmaximal, characteristic, complemented
10#13070398C212yesmaximal, complemented
11C11×#3341C211yesmaximal, characteristic, complemented
12C11×#555—21no—
13#10623094—21no—
14C11×#500C2211yescharacteristic
15C11×#482—22no—
16C11×#476—21no—
17C11×#466C2212yes—
18C4×C11×D8C2211yescharacteristic
19C8×D4×C11C2211yescharacteristic
20C11×#427C2212yes—
21C2×#66890C2211yescharacteristic
22#10622728C2212yes—
23#10622719C2212yes—
24C22×C11⋊C16C2212yes—
25#10622455—21no—
26#10622350—22no—
27C4×D88C2211yescharacteristic
28#10622295C2211yescharacteristic
29#10622200C2212yes—
30#10622200C2211yescharacteristic
31C22⋊(C11⋊C16)C2212yes—
32#10622129C2212yes—
33#10622129C2211yescharacteristic
34#10622128C2212yes—
35#10622128C2212yes—
36#10622127C2212yes—
37#10622127C2212yes—
38#10622127C2211yescharacteristic
39C4⋊(C11⋊C16)C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×D8C2311yescharacteristic
42C22×C8×C11C2312yes—
43C11×C4⋊Q8—21no—
44C11×#124—42no—
45C11×#121—22no—
46C11×#121—41no—
47C4×D4×C11—21no—
48C4×D4×C11D411yescharacteristic
49C11×#117—22no—
50C11×#117—41no—
51#66991—41no—
52#66983—22no—
53#66979—22no—
54C2×D88C2311yescharacteristic
55#66945—41no—
56#66938—42no—
57C4×D44—21no—
58#66922—21no—
59C11×#107—21no—
60C11×#107C2312yes—
61C11×#107C2311yescharacteristic
62C11×#106—22no—
63C11×C4⋊C8D411yescharacteristic
64C11×#102—21no—
65C11×#102—22no—
66C11×C22⋊C8D412yes—
67C4×C8×C11C2311yescharacteristic
68#66890—22no—
69#66885—22no—
70#66885—21no—
71#66882—21no—
72#66882C2312yes—
73#66882C2311yescharacteristic
74#66881—22no—
75C2×C11⋊C16—24no—
76C2×C11⋊C16C2311yescharacteristic
77C2×C11⋊C16C2312yes—
78C2×C11⋊C16C2311yescharacteristic
79#33908—111nomaximal, Sylow
80C2×Q8×C11—41no—
81C2×D4×C11—21no—
82C2×D4×C11—42no—
83C2×D4×C11D811yescharacteristic
84C22×C4×C11—41no—
85C22×C4×C11C2×D412yes—
86C2×C22⋊D11—42no—
87C2×D44—21no—
88C2×C4×D11—41no—
89C2×Dic22—41no—
90C11×D8—21no—
91C11×D8—21no—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11C2×D412yes—
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2411yescharacteristic
97C11×C4⋊C4—21no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4D811yescharacteristic
101C11×C22⋊C4—42no—
102C11×C22⋊C4—42no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4D812yes—
105C42×C11—42no—
106C42×C11C2×D411yescharacteristic
107C22⋊Dic11—42no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—42no—
110C4⋊Dic11—21no—
111C4⋊Dic11—22no—
112C4⋊Dic11—41no—
113C4×Dic11—42no—
114D88—21no—
115D88—21no—
116C11⋊C16—22no—
117C11⋊C16—21no—
118C11⋊C16#4112yes—
119#3341—111no—
120#3341D1111yescharacteristic, complemented
121#2252—111no—
122#2234—112no—
123#2234—112no—
124#2226—111no—
125#2226—111no—
126#2215—112no—
127C4×D16—111no—
128D4×C16—111no—
129#2158—112no—
130C23×C11—41no—
131C23×C11C2×D812yes—
132C22×D11—41no—
133Q8×C11—161no—
134D4×C11—22no—
135D4×C11—41no—
136D4×C11—41no—
137D4×C11—162no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—82no—
143C2×C4×C11C2×D812yes—
144C2×C4×C11C2×D811yescharacteristic
145C2×C4×C11C2×D811yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C22⋊D11—162no—
148C2×Dic11—41no—
149C2×Dic11—42no—
150D44—41no—
151D44—41no—
152C4×D11—82no—
153Dic22—161no—
154C8×C11—22no—
155C8×C11—21no—
156C8×C11C2×#4111yescharacteristic
157C8×C112−1+411yescharacteristic
158#555—21no—
159#555—221no—
160C2×D16—111no—
161C22×C16—112no—
162#500—111no—
163#500C2×D1111yescharacteristic
164#482—22no—
165#482—222no—
166#476—21no—
167#476—221no—
168#466—112no—
169#466C2×D1112yes—
170C4×D8—111no—
171C4×D8C2×D1111yescharacteristic
172C8×D4C2×D1111yescharacteristic
173#427—112no—
174#427C2×D1112yes—
175#367—112no—
176#367—112no—
177#366—111no—
178#366—112no—
179#366—112no—
180C4⋊C16—111no—
181#357—111no—
182#357—112no—
183#357—111no—
184#357—112no—
185C22⋊C16—112no—
186C4×C16—111no—
187C22×C11—22no—
188C22×C11—22no—
189C22×C11—22no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11C22×D811yescharacteristic
194C2×D11—81no—
195C2×D11—81no—
196C2×D11—81no—
197C4×C11—22no—
198C4×C11—21no—
199C4×C11—81no—
200C4×C11—82no—
201C4×C11#50812yes—
202C4×C11#54711yescharacteristic
203C4×C11#57811yescharacteristic
204Dic11—81no—
205Dic11—82no—
206C2×D8—111no—
207C2×D8C22×D1111yescharacteristic
208C22×C8C22×D1112yes—
209C4⋊Q8—21no—
210C4⋊Q8—221no—
211#124—42no—
212#124—442no—
213#121—22no—
214#121—41no—
215#121—222no—
216#121—441no—
217C4×D4—21no—
218C4×D4—221no—
219C4×D4C22⋊D1111yescharacteristic
220#117—22no—
221#117—41no—
222#117—222no—
223#117—441no—
224D16—222no—
225C2×C16—111no—
226C2×C16—111no—
227C2×C16—112no—
228C2×C16—224no—
229#107—21no—
230#107—112no—
231#107—111no—
232#107—221no—
233#107C22×D1112yes—
234#107C22×D1111yescharacteristic
235#106—22no—
236#106—222no—
237C4⋊C8C22⋊D1111yescharacteristic
238#102—21no—
239#102—22no—
240#102—221no—
241#102—222no—
242C22⋊C8C22⋊D1112yes—
243C4×C8C22×D1111yescharacteristic
244C2×C11—42no—
245C2×C11—161no—
246C2×C11#333411yescharacteristic
247C2×C11C2×#50811yescharacteristic
248C2×C11#341511yescharacteristic
249D11—161no—
250C2×Q8—41no—
251C2×Q8—441no—
252C2×D4—21no—
253C2×D4—42no—
254C2×D4—221no—
255C2×D4—442no—
256C2×D4#432311yescharacteristic
257C22×C4—41no—
258C22×C4—441no—
259C22×C4C2×C22⋊D1112yes—
260D8—21no—
261D8—21no—
262D8—221no—
263D8—221no—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8C2×C22⋊D1111yescharacteristic
267C2×C8C2×C22⋊D1112yes—
268C2×C8C23×D1111yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—41no—
272C4⋊C4—221no—
273C4⋊C4—222no—
274C4⋊C4—441no—
275C4⋊C4#432311yescharacteristic
276C22⋊C4—42no—
277C22⋊C4—42no—
278C22⋊C4—41no—
279C22⋊C4—442no—
280C22⋊C4—442no—
281C22⋊C4—441no—
282C22⋊C4#432312yes—
283C42—42no—
284C42—442no—
285C42C2×C22⋊D1111yescharacteristic
286C16—112no—
287C16—222no—
288C16—221no—
289C11#3390811yescharacteristic, complemented, Sylow
290C23—41no—
291C23—441no—
292C23C2×#432312yes—
293Q8—161no—
294Q8—1761no—
295D4—22no—
296D4—41no—
297D4—41no—
298D4—162no—
299D4—441no—
300D4—441no—
301D4—1762no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—82no—
307C2×C4—441no—
308C2×C4—442no—
309C2×C4—882no—
310C2×C4C2×#432312yes—
311C2×C4C2×#432311yescharacteristic
312C2×C4C2×#432311yescharacteristic
313C2×C4C22×C22⋊D1111yescharacteristic
314C8—22no—
315C8—21no—
316C8#41×D1111yescharacteristic
317C8#6704311yescharacteristic
318C22—22no—
319C22—22no—
320C22—22no—
321C22—81no—
322C22—81no—
323C22—81no—
324C22—881no—
325C22—881no—
326C22—881no—
327C22C22×#432311yescharacteristic
328C4—22no—
329C4—21no—
330C4—81no—
331C4—82no—
332C4—881no—
333C4—882no—
334C4#1062280712yes—
335C4#1062335511yescharacteristic
336C4#1062336911yescharacteristic
337C2—42no—
338C2—161no—
339C2—1761no—
340C2#1308095911yescharacteristic
341C2C2×#1062280711yescharacteristic
342C2#1308175511yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3341C2
socleC22×C11C22×D8
hypercenter#3341D11
hypocenterC11#33908
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3341

Complements

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

NH ≅ G/Ntype
1. #13081039C2semidirect
2. #13070889C2semidirect
3. #13070807C2semidirect
4. #13070804C2semidirect
5. #13070763C2semidirect
6. #13070760C2semidirect
7. #13070700C2semidirect
8. C4×#66890C2semidirect
9. D4×C11⋊C16C2semidirect
10. #13070398C2semidirect
11. C11×#3341C2semidirect
120. #3341D11semidirect
289. C11#33908semidirect

Maximal subgroups

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

subgroupindex
#130810392
#130708892
#130708072
#130708042
#130707632
#130707602
#130707002
C4×#668902
D4×C11⋊C162
#130703982
C11×#33412
#3390811