Finite Group Databasebeta

← #14911197

Subgroups — #14911197

Order 2816.

480 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081047C211yesmaximal, characteristic, complemented
2#13081039C211yesmaximal, characteristic
3#13070898C211yesmaximal, characteristic, complemented
4#13070825C212yesmaximal, complemented
5#13070808C212yesmaximal, complemented
6#13070769C211yesmaximal, characteristic, complemented
7#13070754C211yesmaximal, characteristic, complemented
8#13070712C212yesmaximal, complemented
9C4×#66864C211yesmaximal, characteristic, complemented
10#13070400C212yesmaximal, complemented
11D4×C11×C16C211yesmaximal, characteristic, complemented
12#10623094—21no—
13#10623073—21no—
14C22×C11×C16C2212yes—
15C8×D4×C11C2211yescharacteristic
16#10622729C2212yes—
17#10622728C2212yes—
18#10622719C2212yes—
19#10622719C2212yes—
20C2×#66864C2211yescharacteristic
21#10622464—21no—
22#10622455—21no—
23#10622350—22no—
24#10622336—22no—
25C4×Dic44C2211yescharacteristic
26C4×D88C2211yescharacteristic
27#10622295C2211yescharacteristic
28#10622295C2211yescharacteristic
29C11×C4⋊C16C2211yescharacteristic
30C11×C22⋊C16C2212yes—
31C4×C11×C16C2211yescharacteristic
32#10622147C2212yes—
33#10622147C2211yescharacteristic
34#10622143C2212yes—
35#10622143C2212yes—
36#10622143C2211yescharacteristic
37#10622142C2212yes—
38#10622142C2212yes—
39#10622141C2212yes—
40#10622141C2211yescharacteristic
41C22×C8×C11C2312yes—
42C4×D4×C11D411yescharacteristic
43#66991—41no—
44#66989—41no—
45#66983—22no—
46#66979—22no—
47#66979—22no—
48#66977—22no—
49C2×Dic44C2311yescharacteristic
50C2×D88C2311yescharacteristic
51#66945—41no—
52#66940—41no—
53#66938—42no—
54#66932—42no—
55C4×D44—21no—
56#66922—21no—
57#66922—21no—
58C4×Dic22—21no—
59C2×C11×C16—24no—
60C2×C11×C16C2312yes—
61C2×C11×C16C2311yescharacteristic
62C2×C11×C16C2311yescharacteristic
63C11×C4⋊C8D411yescharacteristic
64C11×C22⋊C8D412yes—
65C4×C8×C11C2311yescharacteristic
66#66885—22no—
67#66885—21no—
68#66882—21no—
69#66882—21no—
70#66882C2312yes—
71#66882C2312yes—
72#66882C2311yescharacteristic
73#66882C2311yescharacteristic
74#66881—22no—
75#66881—22no—
76#66880—22no—
77#66880—21no—
78#66864—22no—
79#33907—111nomaximal, Sylow
80C2×D4×C11D811yescharacteristic
81C22×C4×C11C2×D412yes—
82C2×C22⋊D11—42no—
83C2×D44—21no—
84C2×C4×D11—41no—
85C2×Dic22—21no—
86C2×Dic22—41no—
87C2×Dic22—41no—
88C2×C8×C11—22no—
89C2×C8×C11—22no—
90C2×C8×C11C2×D412yes—
91C2×C8×C11C2×D411yescharacteristic
92C2×C8×C11C2411yescharacteristic
93C11×C4⋊C4D811yescharacteristic
94C11×C22⋊C4D812yes—
95C42×C11C2×D411yescharacteristic
96C22⋊Dic11—42no—
97C22⋊Dic11—42no—
98C22⋊Dic11—42no—
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—42no—
101C4⋊Dic11—21no—
102C4⋊Dic11—22no—
103C4⋊Dic11—21no—
104C4⋊Dic11—22no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107Dic11⋊C4—41no—
108Dic11⋊C4—42no—
109C4×Dic11—41no—
110C4×Dic11—42no—
111C4×Dic11—42no—
112Dic44—21no—
113Dic44—21no—
114D88—21no—
115D88—21no—
116C11×C16—22no—
117C11×C16—21no—
118C11×C16#4112yes—
119#3342—111no—
120#3341—111no—
121#2254—111no—
122#2237—112no—
123#2234—112no—
124#2227—111no—
125#2224—111no—
126#2217—112no—
127C4×SD32—111no—
128D4×C16D1111yescharacteristic, complemented
129#2158—112no—
130C23×C11C2×D812yes—
131C22×D11—41no—
132D4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11C2×D812yes—
136C2×C4×C11C2×D811yescharacteristic
137C2×C4×C11C2×D811yescharacteristic
138C2×C4×C11C22×D411yescharacteristic
139C22⋊D11—162no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145D44—41no—
146D44—41no—
147C4×D11—82no—
148Dic22—41no—
149Dic22—41no—
150Dic22—82no—
151Dic22—161no—
152C8×C11—22no—
153C8×C11—21no—
154C8×C11C2×#4111yescharacteristic
155C8×C112−1+411yescharacteristic
156#556—221no—
157#555—221no—
158C2×SD32—111no—
159C22×C16C2×D1112yes—
160#500—111no—
161#500—111no—
162#485—222no—
163#482—222no—
164#476—221no—
165#475—221no—
166#467—112no—
167#466—112no—
168C4×Q16—111no—
169C4×D8—111no—
170C8×D4C2×D1111yescharacteristic
171#427—112no—
172#427—112no—
173#367—111no—
174#367—112no—
175#367—112no—
176#366—112no—
177#366—112no—
178C4⋊C16C2×D1111yescharacteristic
179#358—111no—
180#358—112no—
181#357—111no—
182#357—112no—
183C22⋊C16C2×D1112yes—
184C4×C16C2×D1111yescharacteristic
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—22no—
188C22×C11C22×D811yescharacteristic
189C2×D11—81no—
190C2×D11—81no—
191C2×D11—81no—
192C4×C11—22no—
193C4×C11—21no—
194C4×C11#50812yes—
195C4×C11#54711yescharacteristic
196C4×C11#57811yescharacteristic
197Dic11—81no—
198Dic11—82no—
199Dic11—81no—
200Dic11—82no—
201Dic11—81no—
202C2×Q16—111no—
203C2×D8—111no—
204C22×C8C22×D1112yes—
205C4⋊Q8—221no—
206C4⋊Q8—221no—
207#126—442no—
208#124—441no—
209#124—442no—
210C22⋊Q8—222no—
211#121—222no—
212#121—441no—
213C4×Q8—221no—
214C4×Q8—441no—
215C4×D4—221no—
216C4×D4D4411yescharacteristic
217#117—222no—
218#117—222no—
219#117—441no—
220SD32—222no—
221C2×C16—24no—
222C2×C16C22×D1111yescharacteristic
223C2×C16C22×D1112yes—
224C2×C16C22×D1111yescharacteristic
225#107—111no—
226#107—112no—
227#107—111no—
228#107—112no—
229#107—221no—
230#107—221no—
231#106—222no—
232#106—222no—
233C4⋊C8D4411yescharacteristic
234#103—221no—
235#103—222no—
236#102—221no—
237#102—222no—
238C22⋊C8D4412yes—
239C4×C8C22×D1111yescharacteristic
240C2×C11—42no—
241C2×C11#333411yescharacteristic
242C2×C11C2×#50811yescharacteristic
243C2×C11#341611yescharacteristic
244D11—161no—
245C2×Q8—221no—
246C2×Q8—441no—
247C2×Q8—441no—
248C2×D4—221no—
249C2×D4—442no—
250C2×D4D8811yescharacteristic
251C22×C4—441no—
252C22×C4C2×D4412yes—
253Q16—221no—
254Q16—221no—
255D8—221no—
256D8—221no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8C2×D4411yescharacteristic
260C2×C8C2×D4412yes—
261C2×C8C23×D1111yescharacteristic
262C4⋊C4—221no—
263C4⋊C4—222no—
264C4⋊C4—221no—
265C4⋊C4—222no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C4⋊C4—442no—
269C4⋊C4—441no—
270C4⋊C4D8811yescharacteristic
271C22⋊C4—442no—
272C22⋊C4—442no—
273C22⋊C4—442no—
274C22⋊C4—442no—
275C22⋊C4—441no—
276C22⋊C4D8812yes—
277C42—442no—
278C42—442no—
279C42—441no—
280C42C2×D4411yescharacteristic
281C16—22no—
282C16—21no—
283C16#434112yes—
284C11#3390711yescharacteristic, complemented, Sylow
285C23—441no—
286C23C2×D8812yes—
287Q8—441no—
288Q8—441no—
289Q8—882no—
290Q8—1761no—
291D4—22no—
292D4—441no—
293D4—441no—
294D4—1762no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—441no—
298C2×C4—441no—
299C2×C4—442no—
300C2×C4—442no—
301C2×C4—441no—
302C2×C4—882no—
303C2×C4C2×D8812yes—
304C2×C4C2×D8811yescharacteristic
305C2×C4C2×D8811yescharacteristic
306C2×C4C22×D4411yescharacteristic
307C8—21no—
308C8—22no—
309C8C2×#434111yescharacteristic
310C8#6704311yescharacteristic
311C22—22no—
312C22—22no—
313C22—22no—
314C22—881no—
315C22—881no—
316C22—881no—
317C22C22×D8811yescharacteristic
318C4—22no—
319C4—21no—
320C4—881no—
321C4—881no—
322C4—882no—
323C4—882no—
324C4—881no—
325C4#1062251712yes—
326C4#1062308611yescharacteristic
327C4#1062328411yescharacteristic
328C2—42no—
329C2—1761no—
330C2#1308096411yescharacteristic
331C2C2×#1062251711yescharacteristic
332C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingD4×C11×C16C2
socleC22×C11C22×D8
prime radical#13081039C2
hypercenterD4×C16D11
hypocenterC11#33907
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×C16

Complements

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

NH ≅ G/Ntype
1. #13081047C2semidirect
3. #13070898C2semidirect
4. #13070825C2semidirect
5. #13070808C2semidirect
6. #13070769C2semidirect
7. #13070754C2semidirect
8. #13070712C2semidirect
9. C4×#66864C2semidirect
10. #13070400C2semidirect
11. D4×C11×C16C2semidirect
128. D4×C16D11semidirect
284. C11#33907semidirect

Maximal subgroups

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

subgroupindex
#130810472
#130810392
#130708982
#130708252
#130708082
#130707692
#130707542
#130707122
C4×#668642
#130704002
D4×C11×C162
#3390711