Finite Group Databasebeta

← #14911381

Subgroups — #14911381

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#13081040C211yesmaximal, characteristic, complemented
2#13080963C211yesmaximal, characteristic, complemented
3#13070896C211yesmaximal, characteristic, complemented
4#13070810C212yesmaximal, complemented
5#13070800C212yesmaximal, complemented
6#13070764C211yesmaximal, characteristic, complemented
7#13070718C212yesmaximal, complemented
8C4×#66890C211yesmaximal, characteristic, complemented
9#13070447C211yesmaximal, characteristic, complemented
10#13070401C212yesmaximal, complemented
11C11×#2224C211yesmaximal, characteristic, complemented
12#10623257—21no—
13#10623094—21no—
14C11×#500C2211yescharacteristic
15C4×C11×D8C2211yescharacteristic
16#10622770C2212yes—
17C2×#66890C2211yescharacteristic
18#10622700—21no—
19#10622621—21no—
20C2×#66862C2212yes—
21#10622496C2212yes—
22#10622495—22no—
23#10622493C2212yes—
24D11×#107C2212yes—
25#10622397—22no—
26C4×D88C2211yescharacteristic
27C8×D44C2211yescharacteristic
28#10622295C2211yescharacteristic
29C11×#366C2212yes—
30C11×C4⋊C16C2211yescharacteristic
31C11×#357C2212yes—
32#10622200C2211yescharacteristic
33#10622147C2212yes—
34(C2×D11)⋊C16C2212yes—
35#10622143C2212yes—
36#10622129C2211yescharacteristic
37#10622128C2212yes—
38#10622128C2212yes—
39#10622127C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×#4343—41no—
42C2×C11×D8C2311yescharacteristic
43C11×C4⋊Q8—21no—
44C4×D4×C11—21no—
45#66999—41no—
46#66991—22no—
47#66983—41no—
48#66979—41no—
49C2×D88C2311yescharacteristic
50C2×C8×D11C2312yes—
51#66948—22no—
52#66947—42no—
53#66945—22no—
54C4⋊C4×D11—22no—
55#66938—42no—
56C4×D44—21no—
57C4×D44D411yescharacteristic
58#66922—21no—
59C2×C11×C16C2312yes—
60C11×#107—21no—
61C11×#107C2312yes—
62C11×#107C2311yescharacteristic
63C11×#102—21no—
64C4×C8×C11C2311yescharacteristic
65#66896—22no—
66#66890—22no—
67#66885—21no—
68(C2×D11)⋊C8D412yes—
69#66882—21no—
70#66882C2311yescharacteristic
71#66882C2312yes—
72C2×C11⋊C16C2311yescharacteristic
73C2×C11⋊C16C2311yescharacteristic
74#66873—22no—
75#66872—22no—
76#66871—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78#66862—24no—
79#33921—111nomaximal, Sylow
80C2×Q8×C11—41no—
81C2×D4×C11—21no—
82C22×C4×C11—41no—
83C2×C22⋊D11—42no—
84#4343—84no—
85C2×D44—21no—
86C2×D44—42no—
87C2×D44D811yescharacteristic
88C2×C4×D11—42no—
89C2×C4×D11—41no—
90C2×C4×D11C2×D412yes—
91C2×Dic22—41no—
92C11×D8—21no—
93C11×D8—21no—
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2411yescharacteristic
96C11×C4⋊C4—22no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C22⋊C4—41no—
100C42×C11C2×D411yescharacteristic
101C22⋊Dic11—42no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4D812yes—
106C4⋊Dic11—21no—
107C4⋊Dic11—22no—
108C4⋊Dic11—41no—
109C4⋊Dic11D811yescharacteristic
110Dic11⋊C4—42no—
111C4×Dic11—42no—
112C2×C11⋊C8C2×D412yes—
113D88—21no—
114D88—21no—
115C8×D11—22no—
116C8×D11—22no—
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#2224D1111yescharacteristic, complemented
127#2218—112no—
128C4×D16—111no—
129#2169—111no—
130#2159—112no—
131C23×C11—41no—
132C22×D11—41no—
133C22×D11C2×D812yes—
134Q8×C11—82no—
135D4×C11—41no—
136D4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—42no—
139C2×C4×C11—82no—
140C2×C4×C11C2×D811yescharacteristic
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11C22×D411yescharacteristic
143C22⋊D11—162no—
144C2×Dic11—42no—
145C2×Dic11—41no—
146C2×Dic11C2×D812yes—
147D44—22no—
148D44—41no—
149D44—41no—
150D44—84no—
151C4×D11—22no—
152C4×D11—22no—
153C4×D11—84no—
154C4×D11—82no—
155Dic22—161no—
156C8×C11—21no—
157C8×C11C2×#4111yescharacteristic
158C8×C112−1+411yescharacteristic
159C11⋊C8—22no—
160#555—221no—
161#547—221no—
162C2×D16—111no—
163C2×M32—112no—
164#500—111no—
165#500C2×D1111yescharacteristic
166#482—222no—
167#480—222no—
168#476—221no—
169#474—221no—
170#466—112no—
171#466—112no—
172C4×D8—111no—
173C4×D8C2×D1111yescharacteristic
174C8×D4—111no—
175#427—112no—
176C2×#107—112no—
177#367—112no—
178#367—112no—
179#367—112no—
180#366—111no—
181#366C2×D1112yes—
182C4⋊C16C2×D1111yescharacteristic
183#357—111no—
184#357—112no—
185#357—111no—
186#357C2×D1112yes—
187C22⋊C16—112no—
188C4×C16—111no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11C22×D811yescharacteristic
193C2×D11—22no—
194C2×D11—22no—
195C2×D11—22no—
196C2×D11—81no—
197C2×D11—81no—
198C2×D11—81no—
199C4×C11—21no—
200C4×C11—81no—
201C4×C11—82no—
202C4×C11#50912yes—
203C4×C11#54711yescharacteristic
204C4×C11#57811yescharacteristic
205Dic11—22no—
206Dic11—81no—
207Dic11—82no—
208C2×#41—441no—
209C2×D8—111no—
210C2×D8C22×D1111yescharacteristic
211C22×C8—112no—
212C4⋊Q8—21no—
213C4⋊Q8—221no—
214#124—442no—
215#123—442no—
216C22⋊Q8—441no—
217#121—222no—
218#121—222no—
219#121—441no—
220C4×D4—21no—
221C4×D4—111no—
222C4×D4—221no—
223#117—222no—
224#117—441no—
225C2×C4⋊C4—222no—
226D16—222no—
227M32—224no—
228C2×C16—111no—
229C2×C16—111no—
230C2×C16C22×D1112yes—
231#107—21no—
232#107—111no—
233#107—112no—
234#107—222no—
235#107—221no—
236#107C22×D1111yescharacteristic
237#107C22×D1112yes—
238#106—222no—
239C4⋊C8—111no—
240#102—21no—
241#102—222no—
242#102—222no—
243#102—221no—
244C22⋊C8—112no—
245C4×C8C22×D1111yescharacteristic
246C2×C11—161no—
247C2×C11#333411yescharacteristic
248C2×C11C2×#50911yescharacteristic
249C2×C11#341611yescharacteristic
250D11—42no—
251D11—161no—
252#41—884no—
253C2×Q8—41no—
254C2×Q8—441no—
255C2×D4—21no—
256C2×D4—111no—
257C2×D4—221no—
258C2×D4—442no—
259C2×D4—442no—
260C22×C4—41no—
261C22×C4—112no—
262C22×C4—442no—
263C22×C4—441no—
264D8—21no—
265D8—21no—
266D8—221no—
267D8—221no—
268C2×C8—112no—
269C2×C8—222no—
270C2×C8—222no—
271C2×C8D4×D1111yescharacteristic
272C2×C8C23×D1111yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—22no—
275C4⋊C4—41no—
276C4⋊C4—111no—
277C4⋊C4—222no—
278C4⋊C4—221no—
279C4⋊C4—442no—
280C4⋊C4—441no—
281C22⋊C4—41no—
282C22⋊C4—112no—
283C22⋊C4—442no—
284C22⋊C4—442no—
285C22⋊C4—442no—
286C22⋊C4—441no—
287C42—442no—
288C42D4×D1111yescharacteristic
289C16—22no—
290C16—112no—
291C16—221no—
292C11#3392111yescharacteristic, complemented, Sylow
293C23—41no—
294C23—112no—
295C23—441no—
296Q8—82no—
297Q8—1761no—
298D4—41no—
299D4—41no—
300D4—222no—
301D4—441no—
302D4—441no—
303D4—884no—
304D4—1762no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—82no—
308C2×C4—112no—
309C2×C4—222no—
310C2×C4—222no—
311C2×C4—442no—
312C2×C4—441no—
313C2×C4—884no—
314C2×C4—882no—
315C2×C4D8×D1111yescharacteristic
316C2×C4D8×D1111yescharacteristic
317C2×C4C2×D4×D1111yescharacteristic
318C8—21no—
319C8—222no—
320C8#6704011yescharacteristic
321C8#41×D1111yescharacteristic
322C22—81no—
323C22—81no—
324C22—81no—
325C22—222no—
326C22—222no—
327C22—222no—
328C22—881no—
329C22—881no—
330C22—881no—
331C22C2×D8×D1111yescharacteristic
332C4—21no—
333C4—81no—
334C4—82no—
335C4—222no—
336C4—881no—
337C4—882no—
338C4#1062252412yes—
339C4#1062316211yescharacteristic
340C4#1062331011yescharacteristic
341C2—161no—
342C2—442no—
343C2—1761no—
344C2#1308096211yescharacteristic
345C2C2×#1062252411yescharacteristic
346C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2224C2
socleC22×C11C22×D8
hypercenter#2224D11
hypocenterC11#33921
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2224

Complements

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

NH ≅ G/Ntype
1. #13081040C2semidirect
2. #13080963C2semidirect
3. #13070896C2semidirect
4. #13070810C2semidirect
5. #13070800C2semidirect
6. #13070764C2semidirect
7. #13070718C2semidirect
8. C4×#66890C2semidirect
9. #13070447C2semidirect
10. #13070401C2semidirect
11. C11×#2224C2semidirect
119. C11⋊C16#41semidirect
126. #2224D11semidirect
292. C11#33921semidirect

Maximal subgroups

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

subgroupindex
#130810402
#130809632
#130708962
#130708102
#130708002
#130707642
#130707182
C4×#668902
#130704472
#130704012
C11×#22242
#3392111