Finite Group Databasebeta

← #14911501

Subgroups — #14911501

Order 2816.

508 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081605C211yesmaximal, characteristic, complemented
2#13070855C212yesmaximal, complemented
3#13070845C211yesmaximal, characteristic, complemented
4#13070765C212yesmaximal, complemented
5#13070750C211yesmaximal, characteristic, complemented
6#13070671C212yesmaximal
7#13070661C211yesmaximal, characteristic, complemented
8#13070525C211yesmaximal, characteristic, complemented
9#13070480C212yesmaximal, complemented
10C4×#66890C211yesmaximal, characteristic
11Q8×C11×D8C211yesmaximal, characteristic, complemented
12D4×Q8×C11—21no—
13#10623115—21no—
14C11×#500C2212yes—
15C11×#500C2211yescharacteristic
16C11×#474—21no—
17C11×#474—22no—
18C8×Q8×C11C2211yescharacteristic
19C4×C11×D8C2211yescharacteristic
20C4×C11×D8C2212yes—
21C2×#66891C2212yes—
22C2×#66890C2211yescharacteristic
23#10622458—22no—
24#10622454—21no—
25#10622312C2211yescharacteristic
26C4×Dic44C2212yes—
27#10622309C2212yes—
28C4×D88C2211yescharacteristic
29#10622200C2211yescharacteristic
30#10622130C2212yes—
31#10622130C2212yes—
32#10622130C2212yes—
33#10622129C2211yescharacteristic
34#10622129C2212yes—
35#10622127C2211yescharacteristic
36#10622127C2212yes—
37C4⋊(C11⋊C16)C2211yescharacteristic
38C4⋊(C11⋊C16)C2212yes—
39#10622099C2212yes—
40C4×C11⋊C16C2211yescharacteristic
41C22×Q8×C11—41no—
42C2×C11×D8C2311yescharacteristic
43C11×C4⋊Q8—22no—
44C11×C4⋊Q8—21no—
45C11×C22⋊Q8—41no—
46C11×C22⋊Q8—42no—
47C4×Q8×C11D411yescharacteristic
48C4×D4×C11—22no—
49C4×D4×C11—21no—
50#66999—41no—
51C2×Dic44—21no—
52C2×Dic44C2312yes—
53C2×D88C2311yescharacteristic
54C2×#4314—22no—
55#66951—42no—
56#66945—41no—
57#66928—22no—
58C4×D44—21no—
59#66922—21no—
60C4×Dic22—22no—
61C11×#107—22no—
62C11×#107—21no—
63C11×#107C2311yescharacteristic
64C11×#107C2312yes—
65C11×C4⋊C8D411yescharacteristic
66C11×C4⋊C8D412yes—
67C11×#102—22no—
68C11×#102—21no—
69C4×C8×C11C2311yescharacteristic
70C4×C8×C11C2312yes—
71#66891—24no—
72#66890—22no—
73#66885—21no—
74#66882C2311yescharacteristic
75#66880—22no—
76C2×C11⋊C16C2311yescharacteristic
77C2×C11⋊C16C2312yes—
78C2×C11⋊C16C2311yescharacteristic
79#33934—111nomaximal, Sylow
80C2×Q8×C11—42no—
81C2×Q8×C11—41no—
82C2×Q8×C11—84no—
83C2×Q8×C11D811yescharacteristic
84C2×D4×C11—21no—
85C22×C4×C11—42no—
86C22×C4×C11—41no—
87C2×D44—21no—
88C2×C4×D11—41no—
89C2×Dic22—22no—
90C11×D8—21no—
91C11×D8#4112yes—
92C2×C8×C11C2×D412yes—
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11C2411yescharacteristic
95C11×C4⋊C4—22no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—42no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4D811yescharacteristic
100C11×C4⋊C4D812yes—
101C11×C22⋊C4—42no—
102C11×C22⋊C4—41no—
103C42×C11C2×D412yes—
104C42×C11C2×D411yescharacteristic
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—42no—
107(C2×D11)⋊C4—42no—
108C4⋊Dic11—21no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111Dic11⋊C4—42no—
112C4×Dic11—42no—
113Dic44—22no—
114Dic44—22no—
115Dic44—81no—
116D88—21no—
117D88—21no—
118#4314—82no—
119C11⋊C16—21no—
120C11⋊C16—22no—
121C11⋊C16—21no—
122#3393—111no—
123Q8×D8D1111yescharacteristic, complemented
124#2243—112no—
125#2241—111no—
126#2227—112no—
127#2224—111no—
128#2210—112no—
129#2208—111no—
130#2183—111no—
131#2175—112no—
132C4×D16—111no—
133C23×C11—41no—
134C22×D11—41no—
135Q8×C11—22no—
136Q8×C11—84no—
137Q8×C11—82no—
138D4×C11—22no—
139D4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—41no—
142C2×C4×C11—84no—
143C2×C4×C11—82no—
144C2×C4×C11C2×D812yes—
145C2×C4×C11C2×D812yes—
146C2×C4×C11C2×D811yescharacteristic
147C2×C4×C11C2×D811yescharacteristic
148C2×C4×C11C22×D411yescharacteristic
149C2×Dic11—41no—
150C2×Dic11—42no—
151D44—41no—
152D44—41no—
153C4×D11—82no—
154Dic22—42no—
155Dic22—42no—
156C8×C11—22no—
157C8×C11—21no—
158C8×C11C2×#4111yescharacteristic
159C8×C112−1+411yescharacteristic
160#556—221no—
161D4×Q8—21no—
162C2×SD32—112no—
163C2×D16—111no—
164#500C2×D1111yescharacteristic
165#500C2×D1112yes—
166#495—112no—
167#494—111no—
168#474—21no—
169#474—22no—
170#464—222no—
171#461—221no—
172C8×Q8C2×D1111yescharacteristic
173C4×Q16—112no—
174C4×D8—111no—
175C4×D8C2×D1111yescharacteristic
176C4×D8C2×D1112yes—
177#366—111no—
178#366—112no—
179C4⋊C16—111no—
180C4⋊C16—112no—
181#358—112no—
182#358—112no—
183#358—112no—
184#357—111no—
185#357—111no—
186#357—112no—
187#346—112no—
188C4×C16—111no—
189C22×C11—42no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11C22×D811yescharacteristic
193C2×D11—81no—
194C2×D11—81no—
195C2×D11—81no—
196C4×C11—22no—
197C4×C11—22no—
198C4×C11—21no—
199C4×C11—82no—
200C4×C11—81no—
201C4×C11#50912yes—
202C4×C11#54811yescharacteristic
203C4×C11#57711yescharacteristic
204Dic11—82no—
205Dic11—81no—
206C22×Q8—41no—
207C2×Q16—112no—
208C2×Q16—221no—
209C2×SD16—222no—
210C2×D8—111no—
211C2×D8C22×D1111yescharacteristic
212C4⋊Q8—21no—
213C4⋊Q8—22no—
214C4⋊Q8—221no—
215#126—442no—
216#124—222no—
217C22⋊Q8—41no—
218C22⋊Q8—42no—
219C22⋊Q8—441no—
220C4×Q8—222no—
221C4×Q8C22⋊D1111yescharacteristic
222C4×D4—21no—
223C4×D4—22no—
224C4×D4—221no—
225#117—441no—
226SD32—224no—
227D16—222no—
228C2×C16—111no—
229C2×C16—111no—
230C2×C16—112no—
231#107—21no—
232#107—22no—
233#107—111no—
234#107C22×D1111yescharacteristic
235#107C22×D1112yes—
236C4⋊C8C22⋊D1111yescharacteristic
237C4⋊C8C22⋊D1112yes—
238#103—222no—
239#102—21no—
240#102—22no—
241#102—221no—
242C4×C8C22×D1111yescharacteristic
243C4×C8C22×D1112yes—
244C2×C11—82no—
245C2×C11#335811yescharacteristic
246C2×C11C2×#50911yescharacteristic
247C2×C11#341711yescharacteristic
248D11—161no—
249C2×Q8—42no—
250C2×Q8—41no—
251C2×Q8—84no—
252C2×Q8—222no—
253C2×Q8#432311yescharacteristic
254C2×D4—21no—
255C2×D4—221no—
256C22×C4—42no—
257C22×C4—41no—
258C22×C4—441no—
259Q16—222no—
260Q16—222no—
261Q16—881no—
262SD16—882no—
263D8—21no—
264D8—221no—
265D8—221no—
266D8#434312yes—
267C2×C8C2×C22⋊D1111yescharacteristic
268C2×C8C2×C22⋊D1112yes—
269C2×C8C23×D1111yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—22no—
272C4⋊C4—42no—
273C4⋊C4—41no—
274C4⋊C4—221no—
275C4⋊C4—441no—
276C4⋊C4—442no—
277C4⋊C4—441no—
278C4⋊C4#432311yescharacteristic
279C4⋊C4#432312yes—
280C22⋊C4—42no—
281C22⋊C4—41no—
282C22⋊C4—442no—
283C22⋊C4—441no—
284C22⋊C4—442no—
285C42—442no—
286C42C2×C22⋊D1111yescharacteristic
287C42C2×C22⋊D1112yes—
288C16—221no—
289C16—222no—
290C16—221no—
291C11#3393411yescharacteristic, complemented, Sylow
292C23—41no—
293C23—441no—
294Q8—22no—
295Q8—84no—
296Q8—82no—
297Q8—442no—
298Q8—442no—
299D4—22no—
300D4—41no—
301D4—441no—
302D4—441no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—84no—
306C2×C4—82no—
307C2×C4—441no—
308C2×C4—442no—
309C2×C4—882no—
310C2×C4C2×#432312yes—
311C2×C4C2×#432311yescharacteristic
312C2×C4C2×#432312yes—
313C2×C4C2×#432311yescharacteristic
314C2×C4C22×C22⋊D1111yescharacteristic
315C8—22no—
316C8—21no—
317C8C2×#434311yescharacteristic
318C8#6704011yescharacteristic
319C22—42no—
320C22—81no—
321C22—81no—
322C22—881no—
323C22—881no—
324C22—881no—
325C22C22×#432311yescharacteristic
326C4—22no—
327C4—22no—
328C4—21no—
329C4—82no—
330C4—81no—
331C4—881no—
332C4—882no—
333C4#1062276012yes—
334C4#1062334811yescharacteristic
335C4#1062336811yescharacteristic
336C2—82no—
337C2—1761no—
338C2#1308125111yescharacteristic
339C2C2×#1062276011yescharacteristic
340C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingQ8×C11×D8C2
socleC22×C11C22×D8
prime radicalC2×#66890C22
hypercenterQ8×D8D11
hypocenterC11#33934
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ Q8×D8

Complements

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

NH ≅ G/Ntype
1. #13081605C2semidirect
2. #13070855C2semidirect
3. #13070845C2semidirect
4. #13070765C2semidirect
5. #13070750C2semidirect
7. #13070661C2semidirect
8. #13070525C2semidirect
9. #13070480C2semidirect
11. Q8×C11×D8C2semidirect
123. Q8×D8D11semidirect
291. C11#33934semidirect

Maximal subgroups

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

subgroupindex
#130816052
#130708552
#130708452
#130707652
#130707502
#130706712
#130706612
#130705252
#130704802
C4×#668902
Q8×C11×D82
#3393411