Finite Group Databasebeta

← #14911379

Subgroups — #14911379

Order 2816.

514 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#13081039C211yesmaximal, characteristic, complemented
2#13080964C211yesmaximal, characteristic, complemented
3#13070898C211yesmaximal, characteristic, complemented
4#13070808C212yesmaximal, complemented
5#13070802C212yesmaximal, complemented
6#13070764C211yesmaximal, characteristic, complemented
7#13070754C211yesmaximal, characteristic, complemented
8#13070719C212yesmaximal, complemented
9C4×D176C211yesmaximal, characteristic, complemented
10#13070404C212yesmaximal, complemented
11C11×#2169C211yesmaximal, characteristic, complemented
12#10623094—21no—
13#10623086—21no—
14C2×C11×M32C2212yes—
15C8×D4×C11C2211yescharacteristic
16#10622728C2212yes—
17#10622728C2212yes—
18#10622719C2212yes—
19C2×#66882C2212yes—
20C2×D176C2211yescharacteristic
21#10622459—21no—
22#10622455—21no—
23#10622350—22no—
24#10622349—22no—
25C4×D88C2211yescharacteristic
26C4×D88C2211yescharacteristic
27#10622295C2211yescharacteristic
28#10622295C2211yescharacteristic
29C11×C4⋊C16C2211yescharacteristic
30C11×C22⋊C16C2212yes—
31C4×C11×C16C2211yescharacteristic
32#10622147C2212yes—
33#10622147C2212yes—
34#10622147C2211yescharacteristic
35#10622147C2211yescharacteristic
36#10622143C2212yes—
37#10622143C2212yes—
38#10622143C2212yes—
39#10622142C2211yescharacteristic
40#10622142C2212yes—
41C2×#4341—41no—
42C22×C8×C11C2312yes—
43C4×D4×C11D411yescharacteristic
44#66991—41no—
45#66983—22no—
46#66983—22no—
47#66979—22no—
48C2×C4⋊Dic11—22no—
49C2×D88C2311yescharacteristic
50C2×D88C2311yescharacteristic
51#66950—41no—
52#66945—41no—
53#66939—42no—
54#66938—42no—
55C4×D44—21no—
56C4×D44—21no—
57#66922—21no—
58#66922—21no—
59C11×M32—24no—
60C2×C11×C16C2312yes—
61C2×C11×C16C2311yescharacteristic
62C2×C11×C16C2311yescharacteristic
63C11×C4⋊C8D411yescharacteristic
64C11×C22⋊C8D412yes—
65C4×C8×C11C2311yescharacteristic
66#66885—22no—
67#66885—22no—
68#66885—21no—
69#66885—21no—
70#66882—21no—
71#66882—21no—
72#66882—22no—
73#66882C2312yes—
74#66882C2312yes—
75#66882C2311yescharacteristic
76#66882C2311yescharacteristic
77#66881—22no—
78D176—22no—
79#33921—111nomaximal, Sylow
80C2×D4×C11D811yescharacteristic
81C22×C4×C11C2×D412yes—
82C2×C22⋊D11—42no—
83C2×C22⋊D11—42no—
84C22×Dic11—42no—
85#4341—84no—
86C2×D44—21no—
87C2×D44—21no—
88C2×C4×D11—41no—
89C2×C4×D11—41no—
90C2×Dic22—41no—
91C2×Dic22—41no—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11C2×D412yes—
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2411yescharacteristic
97C11×C4⋊C4D811yescharacteristic
98C11×C22⋊C4D812yes—
99C42×C11C2×D411yescharacteristic
100C22⋊Dic11—42no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4—42no—
105C4⋊Dic11—21no—
106C4⋊Dic11—22no—
107C4⋊Dic11—22no—
108C4⋊Dic11—21no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111C4⋊Dic11—42no—
112C4×Dic11—42no—
113D88—21no—
114D88—21no—
115D88—21no—
116D88—21no—
117C11×C16—22no—
118C11×C16—21no—
119C11×C16#4112yescomplemented
120#3341—111no—
121#3334—111no—
122#2254—111no—
123#2234—112no—
124#2233—112no—
125#2226—111no—
126#2224—111no—
127#2218—112no—
128C4×D16—111no—
129#2169D1111yescharacteristic, complemented
130#2159—112no—
131C23×C11C2×D812yes—
132C22×D11—41no—
133C22×D11—41no—
134D4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11C2×D812yes—
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11C2×D811yescharacteristic
140C2×C4×C11C22×D411yescharacteristic
141C22⋊D11—84no—
142C22⋊D11—162no—
143C2×Dic11—41no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11—41no—
147C2×Dic11—84no—
148D44—41no—
149D44—41no—
150D44—41no—
151D44—41no—
152C4×D11—82no—
153C4×D11—82no—
154Dic22—82no—
155Dic22—161no—
156C8×C11—22no—
157C8×C11—21no—
158C8×C11C2×#4111yescharacteristic
159C8×C112−1+411yescharacteristic
160#555—221no—
161#547—221no—
162C2×D16—111no—
163C2×M32C2×D1112yes—
164#500—111no—
165#500—111no—
166#482—222no—
167#480—222no—
168#476—221no—
169#474—221no—
170#466—112no—
171#466—112no—
172C4×D8—111no—
173C4×D8—111no—
174C8×D4C2×D1111yescharacteristic
175#427—112no—
176C2×#107—112no—
177#367—112no—
178#367—112no—
179#367—112no—
180#366—111no—
181#366—112no—
182C4⋊C16C2×D1111yescharacteristic
183#357—111no—
184#357—111no—
185#357—112no—
186#357—112no—
187C22⋊C16C2×D1112yes—
188C4×C16C2×D1111yescharacteristic
189C22×C11—22no—
190C22×C11—22no—
191C22×C11—22no—
192C22×C11C22×D811yescharacteristic
193C2×D11—81no—
194C2×D11—81no—
195C2×D11—81no—
196C2×D11—81no—
197C2×D11—81no—
198C2×D11—81no—
199C4×C11—22no—
200C4×C11—21no—
201C4×C11#50912yes—
202C4×C11#54711yescharacteristic
203C4×C11#57811yescharacteristic
204Dic11—82no—
205Dic11—81no—
206Dic11—81no—
207Dic11—82no—
208C2×#41—441no—
209C2×D8—111no—
210C2×D8—111no—
211C22×C8C22×D1112yes—
212C4⋊Q8—221no—
213C4⋊Q8—221no—
214#124—442no—
215#123—442no—
216C22⋊Q8—441no—
217#121—222no—
218#121—222no—
219#121—441no—
220C4×D4—221no—
221C4×D4—221no—
222C4×D4D4411yescharacteristic
223#117—222no—
224#117—441no—
225C2×C4⋊C4—222no—
226D16—222no—
227M32—24no—
228C2×C16C22×D1111yescharacteristic
229C2×C16C22×D1112yes—
230C2×C16C22×D1111yescharacteristic
231#107—111no—
232#107—111no—
233#107—112no—
234#107—112no—
235#107—222no—
236#107—221no—
237#107—221no—
238#106—222no—
239C4⋊C8D4411yescharacteristic
240#102—221no—
241#102—221no—
242#102—222no—
243#102—222no—
244C22⋊C8D4412yes—
245C4×C8C22×D1111yescharacteristic
246C2×C11—42no—
247C2×C11#333411yescharacteristic
248C2×C11C2×#50911yescharacteristic
249C2×C11#341611yescharacteristic
250D11—161no—
251D11—161no—
252#41—884no—
253C2×Q8—441no—
254C2×Q8—441no—
255C2×D4—221no—
256C2×D4—221no—
257C2×D4—442no—
258C2×D4—442no—
259C2×D4D8811yescharacteristic
260C22×C4—442no—
261C22×C4—441no—
262C22×C4—441no—
263C22×C4C2×D4412yes—
264D8—221no—
265D8—221no—
266D8—221no—
267D8—221no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8C2×D4411yescharacteristic
271C2×C8C2×D4412yes—
272C2×C8C23×D1111yescharacteristic
273C4⋊C4—221no—
274C4⋊C4—222no—
275C4⋊C4—221no—
276C4⋊C4—222no—
277C4⋊C4—442no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4D8811yescharacteristic
281C22⋊C4—442no—
282C22⋊C4—442no—
283C22⋊C4—441no—
284C22⋊C4—441no—
285C22⋊C4—442no—
286C22⋊C4D8812yes—
287C42—442no—
288C42C2×D4411yescharacteristic
289C16—22no—
290C16—21no—
291C16#434112yescomplemented
292C11#3392111yescharacteristic, complemented, Sylow
293C23—441no—
294C23—441no—
295C23C2×D8812yes—
296Q8—882no—
297Q8—1761no—
298D4—22no—
299D4—441no—
300D4—441no—
301D4—441no—
302D4—441no—
303D4—884no—
304D4—1762no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—441no—
308C2×C4—442no—
309C2×C4—441no—
310C2×C4—442no—
311C2×C4—884no—
312C2×C4—882no—
313C2×C4—882no—
314C2×C4C2×D8812yes—
315C2×C4C2×D8811yescharacteristic
316C2×C4C2×D8811yescharacteristic
317C2×C4C22×D4411yescharacteristic
318C8—21no—
319C8—22no—
320C8C2×#434111yescharacteristic
321C8#6704311yescharacteristic
322C22—22no—
323C22—22no—
324C22—22no—
325C22—881no—
326C22—881no—
327C22—881no—
328C22—881no—
329C22—881no—
330C22—881no—
331C22C22×D8811yescharacteristic
332C4—22no—
333C4—21no—
334C4—881no—
335C4—882no—
336C4—881no—
337C4—882no—
338C4#1062252112yes—
339C4#1062308611yescharacteristic
340C4#1062328411yescharacteristic
341C2—42no—
342C2—1761no—
343C2—1761no—
344C2#1308096411yescharacteristic
345C2C2×#1062252111yescharacteristic
346C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2169C2
socleC22×C11C22×D8
hypercenter#2169D11
hypocenterC11#33921
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #2169

Complements

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

NH ≅ G/Ntype
1. #13081039C2semidirect
2. #13080964C2semidirect
3. #13070898C2semidirect
4. #13070808C2semidirect
5. #13070802C2semidirect
6. #13070764C2semidirect
7. #13070754C2semidirect
8. #13070719C2semidirect
9. C4×D176C2semidirect
10. #13070404C2semidirect
11. C11×#2169C2semidirect
119. C11×C16#41semidirect
129. #2169D11semidirect
291. C16#4341semidirect
292. C11#33921semidirect

Maximal subgroups

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

subgroupindex
#130810392
#130809642
#130708982
#130708082
#130708022
#130707642
#130707542
#130707192
C4×D1762
#130704042
C11×#21692
#3392111