Finite Group Databasebeta

← #14911378

Subgroups — #14911378

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#13070896C211yesmaximal, characteristic, complemented
3#13070804C212yesmaximal, complemented
4#13070801C212yesmaximal, complemented
5#13070763C211yesmaximal, characteristic, complemented
6#13070750C211yesmaximal, characteristic, complemented
7#13070717C212yesmaximal, complemented
8C4×#66890C211yesmaximal, characteristic, complemented
9#13070448C211yesmaximal, characteristic, complemented
10#13070402C212yesmaximal, complemented
11C11×#3334C211yesmaximal, characteristic, complemented
12C11×#547—21no—
13#10623094—21no—
14C11×#500C2211yescharacteristic
15C11×#480—22no—
16C11×#474—21no—
17C11×#466C2212yes—
18C4×C11×D8C2211yescharacteristic
19C8×D4×C11C2211yescharacteristic
20C2×C11×#107C2212yes—
21C2×#66890C2211yescharacteristic
22#10622728C2212yes—
23#10622719C2212yes—
24C2×#66876C2212yes—
25#10622455—21no—
26#10622350—22no—
27C4×D88C2211yescharacteristic
28#10622295C2211yescharacteristic
29#10622200C2211yescharacteristic
30#10622200C2212yes—
31C22⋊(C11⋊C16)C2212yes—
32#10622129C2211yescharacteristic
33#10622129C2212yes—
34#10622128C2212yes—
35#10622128C2212yes—
36#10622128C2212yes—
37#10622127C2211yescharacteristic
38#10622127C2212yes—
39C4⋊(C11⋊C16)C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×#41—41no—
42C2×C11×D8C2311yescharacteristic
43C22×C8×C11C2312yes—
44C11×C4⋊Q8—21no—
45C11×#123—42no—
46C11×C22⋊Q8—41no—
47C11×#121—22no—
48C4×D4×C11—21no—
49C4×D4×C11D411yescharacteristic
50C2×C11×C4⋊C4—22no—
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×#107—22no—
61C11×#107C2312yes—
62C11×#107C2311yescharacteristic
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—
75#66876—24no—
76C2×C11⋊C16C2311yescharacteristic
77C2×C11⋊C16C2312yes—
78C2×C11⋊C16C2311yescharacteristic
79#33921—111nomaximal, Sylow
80C11×#41—84no—
81C2×Q8×C11—41no—
82C2×D4×C11—21no—
83C2×D4×C11—42no—
84C2×D4×C11D811yescharacteristic
85C22×C4×C11—42no—
86C22×C4×C11—41no—
87C22×C4×C11C2×D412yes—
88C2×C22⋊D11—42no—
89C2×D44—21no—
90C2×C4×D11—41no—
91C2×Dic22—41no—
92C11×D8—21no—
93C11×D8—21no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11C2×D412yes—
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11C2411yescharacteristic
99C11×C4⋊C4—21no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—42no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4D811yescharacteristic
104C11×C22⋊C4—41no—
105C11×C22⋊C4—42no—
106C11×C22⋊C4D812yes—
107C42×C11C2×D411yescharacteristic
108C22⋊Dic11—42no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—42no—
111C4⋊Dic11—21no—
112C4⋊Dic11—22no—
113C4⋊Dic11—41no—
114C4×Dic11—42no—
115D88—21no—
116D88—21no—
117C11⋊C16—22no—
118C11⋊C16—21no—
119C11⋊C16#4112yescomplemented
120#3341—111no—
121#3334D1111yescharacteristic, complemented
122#2254—111no—
123#2234—112no—
124#2233—112no—
125#2226—111no—
126#2224—111no—
127#2218—112no—
128C4×D16—111no—
129#2169—111no—
130#2159—112no—
131C23×C11—41no—
132C23×C11C2×D812yes—
133C22×D11—41no—
134Q8×C11—82no—
135D4×C11—22no—
136D4×C11—41no—
137D4×C11—41no—
138D4×C11—84no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—41no—
142C2×C4×C11—42no—
143C2×C4×C11—84no—
144C2×C4×C11—82no—
145C2×C4×C11C2×D812yes—
146C2×C4×C11C2×D811yescharacteristic
147C2×C4×C11C2×D811yescharacteristic
148C2×C4×C11C22×D411yescharacteristic
149C22⋊D11—162no—
150C2×Dic11—41no—
151C2×Dic11—42no—
152D44—41no—
153D44—41no—
154C4×D11—82no—
155Dic22—161no—
156C8×C11—22no—
157C8×C11—21no—
158C8×C11C2×#4111yescharacteristic
159C8×C112−1+411yescharacteristic
160#555—221no—
161#547—21no—
162C2×D16—111no—
163C2×M32—112no—
164#500—111no—
165#500C2×D1111yescharacteristic
166#482—222no—
167#480—22no—
168#476—221no—
169#474—21no—
170#466—112no—
171#466C2×D1112yes—
172C4×D8—111no—
173C4×D8C2×D1111yescharacteristic
174C8×D4C2×D1111yescharacteristic
175#427—112no—
176C2×#107C2×D1112yes—
177#367—112no—
178#367—112no—
179#367—112no—
180#366—111no—
181#366—112no—
182C4⋊C16—111no—
183#357—111no—
184#357—112no—
185#357—111no—
186#357—112no—
187C22⋊C16—112no—
188C4×C16—111no—
189C22×C11—22no—
190C22×C11—22no—
191C22×C11—22no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11C22×D811yescharacteristic
196C2×D11—81no—
197C2×D11—81no—
198C2×D11—81no—
199C4×C11—22no—
200C4×C11—21no—
201C4×C11—81no—
202C4×C11—82no—
203C4×C11#50912yes—
204C4×C11#54711yescharacteristic
205C4×C11#57811yescharacteristic
206Dic11—81no—
207Dic11—82no—
208C2×#41—41no—
209C2×D8—111no—
210C2×D8C22×D1111yescharacteristic
211C22×C8C22×D1112yes—
212C4⋊Q8—21no—
213C4⋊Q8—221no—
214#124—442no—
215#123—42no—
216C22⋊Q8—41no—
217#121—22no—
218#121—222no—
219#121—441no—
220C4×D4—21no—
221C4×D4—221no—
222C4×D4C22⋊D1111yescharacteristic
223#117—222no—
224#117—441no—
225C2×C4⋊C4—22no—
226D16—222no—
227M32—224no—
228C2×C16—111no—
229C2×C16—111no—
230C2×C16—112no—
231#107—22no—
232#107—21no—
233#107—111no—
234#107—112no—
235#107—221no—
236#107C22×D1111yescharacteristic
237#107C22×D1112yes—
238#106—222no—
239C4⋊C8C22⋊D1111yescharacteristic
240#102—21no—
241#102—22no—
242#102—221no—
243#102—222no—
244C22⋊C8C22⋊D1112yes—
245C4×C8C22×D1111yescharacteristic
246C2×C11—42no—
247C2×C11—161no—
248C2×C11#333411yescharacteristic
249C2×C11C2×#50911yescharacteristic
250C2×C11#341611yescharacteristic
251D11—161no—
252#41—84no—
253C2×Q8—41no—
254C2×Q8—441no—
255C2×D4—21no—
256C2×D4—42no—
257C2×D4—221no—
258C2×D4—442no—
259C2×D4#432311yescharacteristic
260C22×C4—42no—
261C22×C4—41no—
262C22×C4—441no—
263C22×C4C2×C22⋊D1112yes—
264D8—21no—
265D8—21no—
266D8—221no—
267D8—221no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8C2×C22⋊D1111yescharacteristic
271C2×C8C2×C22⋊D1112yes—
272C2×C8C23×D1111yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—22no—
275C4⋊C4—42no—
276C4⋊C4—41no—
277C4⋊C4—221no—
278C4⋊C4—222no—
279C4⋊C4—441no—
280C4⋊C4#432311yescharacteristic
281C22⋊C4—41no—
282C22⋊C4—42no—
283C22⋊C4—442no—
284C22⋊C4—442no—
285C22⋊C4—441no—
286C22⋊C4#432312yes—
287C42—442no—
288C42C2×C22⋊D1111yescharacteristic
289C16—112no—
290C16—222no—
291C16—221no—
292C11#3392111yescharacteristic, complemented, Sylow
293C23—41no—
294C23—441no—
295C23C2×#432312yes—
296Q8—82no—
297Q8—1761no—
298D4—22no—
299D4—41no—
300D4—41no—
301D4—84no—
302D4—441no—
303D4—441no—
304D4—1762no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—84no—
310C2×C4—82no—
311C2×C4—441no—
312C2×C4—442no—
313C2×C4—882no—
314C2×C4C2×#432312yes—
315C2×C4C2×#432311yescharacteristic
316C2×C4C2×#432311yescharacteristic
317C2×C4C22×C22⋊D1111yescharacteristic
318C8—22no—
319C8—21no—
320C8#41×D1111yescharacteristic
321C8#6704311yescharacteristic
322C22—22no—
323C22—22no—
324C22—22no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22—881no—
329C22—881no—
330C22—881no—
331C22C22×#432311yescharacteristic
332C4—22no—
333C4—21no—
334C4—81no—
335C4—82no—
336C4—881no—
337C4—882no—
338C4#1062276012yes—
339C4#1062335511yescharacteristic
340C4#1062336911yescharacteristic
341C2—42no—
342C2—161no—
343C2—1761no—
344C2#1308095911yescharacteristic
345C2C2×#1062276011yescharacteristic
346C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3334C2
socleC22×C11C22×D8
hypercenter#3334D11
hypocenterC11#33921
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3334

Complements

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

NH ≅ G/Ntype
1. #13081039C2semidirect
2. #13070896C2semidirect
3. #13070804C2semidirect
4. #13070801C2semidirect
5. #13070763C2semidirect
6. #13070750C2semidirect
7. #13070717C2semidirect
8. C4×#66890C2semidirect
9. #13070448C2semidirect
10. #13070402C2semidirect
11. C11×#3334C2semidirect
119. C11⋊C16#41semidirect
121. #3334D11semidirect
292. C11#33921semidirect

Maximal subgroups

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

subgroupindex
#130810392
#130708962
#130708042
#130708012
#130707632
#130707502
#130707172
C4×#668902
#130704482
#130704022
C11×#33342
#3392111