Finite Group Databasebeta

← #14911377

Subgroups — #14911377

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#13081038C211yesmaximal, characteristic, complemented
2#13080963C211yesmaximal, characteristic, complemented
3#13070809C212yesmaximal, complemented
4#13070803C212yesmaximal, complemented
5#13070760C211yesmaximal, characteristic, complemented
6#13070750C211yesmaximal, characteristic, complemented
7#13070720C212yesmaximal, complemented
8C4×D176C211yesmaximal, characteristic, complemented
9#13070449C211yesmaximal, characteristic, complemented
10#13070403C212yesmaximal, complemented
11C11×#2254C211yesmaximal, characteristic, complemented
12#10623265—21no—
13#10623257—21no—
14C11×#500C2211yescharacteristic
15C11×#500C2211yescharacteristic
16#10622700—21no—
17#10622697—21no—
18C2×D176C2211yescharacteristic
19C2×#66862C2212yes—
20#10622498—22no—
21#10622496C2212yes—
22#10622496C2212yes—
23#10622495—22no—
24#10622493C2212yes—
25D11×#107C2212yes—
26C4×D88C2211yescharacteristic
27C4×D88C2211yescharacteristic
28C8×D44C2211yescharacteristic
29C11×#367C2212yes—
30C11×#367C2212yes—
31C4×C11×C16C2211yescharacteristic
32#10622147C2211yescharacteristic
33#10622147C2211yescharacteristic
34(C2×D11)⋊C16C2212yes—
35#10622142C2211yescharacteristic
36#10622129C2212yes—
37#10622129C2212yes—
38#10622128C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×#4343—41no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44#67000—42no—
45#66999—41no—
46C2×D88C2311yescharacteristic
47C2×D88C2311yescharacteristic
48C2×C8×D11C2312yes—
49#66948—22no—
50#66948—22no—
51#66948—41no—
52#66947—42no—
53#66945—22no—
54#66945—41no—
55C4⋊C4×D11—22no—
56C4×D44—21no—
57C4×D44—21no—
58C4×D44D411yescharacteristic
59C2×C11×C16C2311yescharacteristic
60C2×C11×C16C2311yescharacteristic
61C11×#107—21no—
62C11×#107—21no—
63C11×#107C2312yes—
64C11×#107C2312yes—
65C4×C8×C11C2311yescharacteristic
66#66885—21no—
67#66885—21no—
68(C2×D11)⋊C8D412yes—
69#66882C2311yescharacteristic
70#66882C2311yescharacteristic
71C2×C11⋊C16C2312yes—
72#66873—22no—
73#66873—22no—
74#66872—22no—
75#66871—22no—
76C4⋊(C11⋊C8)D411yescharacteristic
77D176—22no—
78#66862—24no—
79#33921—111nomaximal, Sylow
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82#4343—84no—
83C2×D44—21no—
84C2×D44—21no—
85C2×D44—42no—
86C2×D44—42no—
87C2×D44D811yescharacteristic
88C2×C4×D11—42no—
89C2×C4×D11—41no—
90C2×C4×D11—41no—
91C2×C4×D11C2×D412yes—
92C2×C8×C11C2×D411yescharacteristic
93C2×C8×C11C2411yescharacteristic
94C11×C4⋊C4—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C42×C11C2×D411yescharacteristic
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4D812yes—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107C4⋊Dic11D811yescharacteristic
108Dic11⋊C4—42no—
109C4×Dic11—42no—
110C2×C11⋊C8C2×D412yes—
111D88—21no—
112D88—21no—
113D88—21no—
114D88—21no—
115C8×D11—22no—
116C8×D11—22no—
117C11×C16—21no—
118C11×C16#4112yescomplemented
119C11⋊C16—22no—
120#3341—111no—
121#3334—111no—
122#2254D1111yescharacteristic, complemented
123#2234—112no—
124#2233—112no—
125#2226—111no—
126#2224—111no—
127#2218—112no—
128C4×D16—111no—
129#2169—111no—
130#2159—112no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11C2×D812yes—
134Q8×C11—82no—
135Q8×C11—161no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11C2×D811yescharacteristic
140C2×C4×C11C22×D411yescharacteristic
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11C2×D812yes—
144D44—22no—
145D44—41no—
146D44—41no—
147D44—41no—
148D44—41no—
149D44—84no—
150D44—162no—
151C4×D11—22no—
152C4×D11—22no—
153C4×D11—84no—
154C4×D11—82no—
155C4×D11—82no—
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#500C2×D1111yescharacteristic
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×D8—111no—
174C8×D4—111no—
175#427—112no—
176C2×#107—112no—
177#367—112no—
178#367C2×D1112yes—
179#367C2×D1112yes—
180#366—111no—
181#366—112no—
182C4⋊C16—111no—
183#357—111no—
184#357—111no—
185#357—112no—
186#357—112no—
187C22⋊C16—112no—
188C4×C16C2×D1111yescharacteristic
189C22×C11C22×D811yescharacteristic
190C2×D11—22no—
191C2×D11—22no—
192C2×D11—22no—
193C2×D11—81no—
194C2×D11—81no—
195C2×D11—81no—
196C2×D11—81no—
197C2×D11—81no—
198C2×D11—81no—
199C4×C11—21no—
200C4×C11—82no—
201C4×C11—82no—
202C4×C11#50912yes—
203C4×C11#54711yescharacteristic
204C4×C11#57811yescharacteristic
205Dic11—22no—
206Dic11—81no—
207Dic11—81no—
208C2×#41—441no—
209C2×D8—111no—
210C2×D8—111no—
211C22×C8—112no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214#124—442no—
215#123—442no—
216C22⋊Q8—441no—
217#121—222no—
218#121—222no—
219#121—441no—
220C4×D4—111no—
221C4×D4—221no—
222C4×D4—221no—
223#117—222no—
224#117—441no—
225C2×C4⋊C4—222no—
226D16—222no—
227M32—224no—
228C2×C16—112no—
229C2×C16C22×D1111yescharacteristic
230C2×C16C22×D1111yescharacteristic
231#107—21no—
232#107—21no—
233#107—111no—
234#107—111no—
235#107—222no—
236#107C22×D1112yes—
237#107C22×D1112yes—
238#106—222no—
239C4⋊C8—111no—
240#102—222no—
241#102—222no—
242#102—221no—
243#102—221no—
244C22⋊C8—112no—
245C4×C8C22×D1111yescharacteristic
246C2×C11#333411yescharacteristic
247C2×C11C2×#50911yescharacteristic
248C2×C11#341611yescharacteristic
249D11—42no—
250D11—161no—
251D11—161no—
252#41—884no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×D4—111no—
256C2×D4—221no—
257C2×D4—221no—
258C2×D4—442no—
259C2×D4—442no—
260C22×C4—112no—
261C22×C4—442no—
262C22×C4—441no—
263C22×C4—441no—
264D8—221no—
265D8—221no—
266D8—221no—
267D8—221no—
268C2×C8—112no—
269C2×C8—222no—
270C2×C8—222no—
271C2×C8D4×D1111yescharacteristic
272C2×C8C23×D1111yescharacteristic
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—111no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—442no—
281C22⋊C4—112no—
282C22⋊C4—442no—
283C22⋊C4—442no—
284C22⋊C4—442no—
285C22⋊C4—441no—
286C22⋊C4—441no—
287C42—442no—
288C42D4×D1111yescharacteristic
289C16—21no—
290C16—222no—
291C16#434312yescomplemented
292C11#3392111yescharacteristic, complemented, Sylow
293C23—112no—
294C23—441no—
295C23—441no—
296Q8—82no—
297Q8—161no—
298D4—222no—
299D4—441no—
300D4—441no—
301D4—441no—
302D4—441no—
303D4—884no—
304D4—1762no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—112no—
308C2×C4—222no—
309C2×C4—222no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—884no—
313C2×C4—882no—
314C2×C4—882no—
315C2×C4D8×D1111yescharacteristic
316C2×C4D8×D1111yescharacteristic
317C2×C4C2×D4×D1111yescharacteristic
318C8—21no—
319C8—222no—
320C8C2×#434311yescharacteristic
321C8#6704011yescharacteristic
322C22—222no—
323C22—222no—
324C22—222no—
325C22—881no—
326C22—881no—
327C22—881no—
328C22—881no—
329C22—881no—
330C22—881no—
331C22C2×D8×D1111yescharacteristic
332C4—21no—
333C4—82no—
334C4—82no—
335C4—222no—
336C4—881no—
337C4—881no—
338C4#1062252712yes—
339C4#1062325711yescharacteristic
340C4#1062329711yescharacteristic
341C2—442no—
342C2—1761no—
343C2—1761no—
344C2#1308096311yescharacteristic
345C2C2×#1062252711yescharacteristic
346C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2254C2
socleC22×C11C22×D8
hypercenter#2254D11
hypocenterC11#33921
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2254

Complements

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

NH ≅ G/Ntype
1. #13081038C2semidirect
2. #13080963C2semidirect
3. #13070809C2semidirect
4. #13070803C2semidirect
5. #13070760C2semidirect
6. #13070750C2semidirect
7. #13070720C2semidirect
8. C4×D176C2semidirect
9. #13070449C2semidirect
10. #13070403C2semidirect
11. C11×#2254C2semidirect
118. C11×C16#41semidirect
122. #2254D11semidirect
291. C16#4343semidirect
292. C11#33921semidirect

Maximal subgroups

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

subgroupindex
#130810382
#130809632
#130708092
#130708032
#130707602
#130707502
#130707202
C4×D1762
#130704492
#130704032
C11×#22542
#3392111