Finite Group Databasebeta

← #14911497

Subgroups — #14911497

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
1Q8×D88C211yesmaximal, characteristic, complemented
2#13070852C212yesmaximal, complemented
3#13070843C211yesmaximal, characteristic, complemented
4#13070768C212yesmaximal, complemented
5#13070753C211yesmaximal, characteristic, complemented
6#13070668C212yesmaximal
7#13070658C211yesmaximal, characteristic, complemented
8#13070525C211yesmaximal, characteristic, complemented
9#13070478C212yesmaximal, complemented
10C4×#66890C211yesmaximal, characteristic
11C11×#3393C211yesmaximal, characteristic, complemented
12C11×#556—21no—
13Q8×D44—21no—
14C11×#495C2212yes—
15C11×#494C2211yescharacteristic
16C11×#464—22no—
17C11×#461—21no—
18C8×Q8×C11C2211yescharacteristic
19C4×C11×Q16C2212yes—
20C4×C11×D8C2211yescharacteristic
21C2×#66892C2212yes—
22C2×#66890C2211yescharacteristic
23#10622459—21no—
24#10622459—22no—
25C4×D88C2211yescharacteristic
26C4×D88C2212yes—
27#10622295C2212yes—
28#10622295C2211yescharacteristic
29#10622202C2212yes—
30#10622202C2212yes—
31#10622202C2212yes—
32#10622200C2211yescharacteristic
33#10622200C2212yes—
34#10622129C2211yescharacteristic
35#10622127C2211yescharacteristic
36#10622127C2212yes—
37C4⋊(C11⋊C16)C2211yescharacteristic
38C4⋊(C11⋊C16)C2212yes—
39#10622099C2212yes—
40C4×C11⋊C16C2211yescharacteristic
41C2×Q8×D11—41no—
42C2×C11×Q16—21no—
43C2×C11×Q16C2312yes—
44C2×C11×SD16—22no—
45C2×C11×D8C2311yescharacteristic
46C11×C4⋊Q8—21no—
47C11×#126—42no—
48C11×#124—22no—
49C11×C22⋊Q8—41no—
50C4×Q8×C11—22no—
51C4×Q8×C11D411yescharacteristic
52C4×D4×C11—21no—
53C11×#117—41no—
54C2×D88C2311yescharacteristic
55#66950—41no—
56#66950—42no—
57C4×D44—21no—
58C4×D44—22no—
59#66922—21no—
60#66922—22no—
61C11×#107C2311yescharacteristic
62C11×C4⋊C8D411yescharacteristic
63C11×C4⋊C8D412yes—
64C11×#103—22no—
65C11×#102—21no—
66C4×C8×C11C2311yescharacteristic
67C4×C8×C11C2312yes—
68#66892—24no—
69#66890—22no—
70#66885—21no—
71#66885—22no—
72#66882—21no—
73#66882—22no—
74#66882C2311yescharacteristic
75#66882C2312yes—
76C2×C11⋊C16C2311yescharacteristic
77C2×C11⋊C16C2312yes—
78C2×C11⋊C16C2311yescharacteristic
79#33934—111nomaximal, Sylow
80C2×Q8×C11—22no—
81C2×Q8×C11D811yescharacteristic
82C2×D4×C11—21no—
83C22×C4×C11—41no—
84Q8×D11—84no—
85C2×D44—21no—
86C2×C4×D11—42no—
87C2×C4×D11—41no—
88C2×Dic22—42no—
89C2×Dic22—41no—
90C11×Q16—22no—
91C11×Q16—22no—
92C11×Q16—81no—
93C11×SD16—82no—
94C11×D8—21no—
95C11×D8—21no—
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D412yes—
98C2×C8×C11C2411yescharacteristic
99C11×C4⋊C4—21no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—42no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4D811yescharacteristic
104C11×C4⋊C4D812yes—
105C11×C22⋊C4—42no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—42no—
108C42×C11—42no—
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D412yes—
111(C2×D11)⋊C4—42no—
112(C2×D11)⋊C4—41no—
113C4⋊Dic11—22no—
114C4⋊Dic11—21no—
115C4⋊Dic11—42no—
116C4⋊Dic11—41no—
117D88—21no—
118D88#4112yes—
119C11⋊C16—21no—
120C11⋊C16—22no—
121C11⋊C16—21no—
122#3393D1111yescharacteristic, complemented
123Q8×D8—111no—
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—42no—
137Q8×C11—42no—
138D4×C11—41no—
139D4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—82no—
143C2×C4×C11C2×D812yes—
144C2×C4×C11C2×D811yescharacteristic
145C2×C4×C11C2×D812yes—
146C2×C4×C11C2×D811yescharacteristic
147C2×C4×C11C22×D411yescharacteristic
148C2×Dic11—41no—
149C2×Dic11—42no—
150D44—22no—
151D44—41no—
152C4×D11—84no—
153C4×D11—82no—
154Dic22—84no—
155Dic22—82no—
156C8×C11—22no—
157C8×C11—21no—
158C8×C11C2×#4111yescharacteristic
159C8×C112−1+411yescharacteristic
160#556—21no—
161D4×Q8—221no—
162C2×SD32—112no—
163C2×D16—111no—
164#500—111no—
165#500—112no—
166#495C2×D1112yes—
167#494C2×D1111yescharacteristic
168#474—221no—
169#474—222no—
170#464—22no—
171#461—21no—
172C8×Q8C2×D1111yescharacteristic
173C4×Q16C2×D1112yes—
174C4×D8—111no—
175C4×D8—112no—
176C4×D8C2×D1111yescharacteristic
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—112no—
186#357—111no—
187#346—112no—
188C4×C16—111no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11C22×D811yescharacteristic
193C2×D11—42no—
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—81no—
205Dic11—82no—
206C22×Q8—441no—
207C2×Q16—21no—
208C2×Q16C22×D1112yes—
209C2×SD16—22no—
210C2×D8—111no—
211C2×D8C22×D1111yescharacteristic
212C4⋊Q8—21no—
213C4⋊Q8—221no—
214C4⋊Q8—222no—
215#126—42no—
216#124—22no—
217C22⋊Q8—41no—
218C22⋊Q8—441no—
219C22⋊Q8—442no—
220C4×Q8—22no—
221C4×Q8C22⋊D1111yescharacteristic
222C4×D4—21no—
223C4×D4—221no—
224C4×D4—222no—
225#117—41no—
226SD32—224no—
227D16—222no—
228C2×C16—111no—
229C2×C16—111no—
230C2×C16—112no—
231#107—111no—
232#107—112no—
233#107—221no—
234#107—222no—
235#107C22×D1111yescharacteristic
236C4⋊C8C22⋊D1111yescharacteristic
237C4⋊C8C22⋊D1112yes—
238#103—22no—
239#102—21no—
240#102—221no—
241#102—222no—
242C4×C8C22×D1111yescharacteristic
243C4×C8C22×D1112yes—
244C2×C11—161no—
245C2×C11#335811yescharacteristic
246C2×C11C2×#50911yescharacteristic
247C2×C11#341711yescharacteristic
248D11—82no—
249C2×Q8—22no—
250C2×Q8—442no—
251C2×Q8—441no—
252C2×Q8—884no—
253C2×Q8#432311yescharacteristic
254C2×D4—21no—
255C2×D4—221no—
256C22×C4—41no—
257C22×C4—442no—
258C22×C4—441no—
259Q16—22no—
260Q16—22no—
261Q16—81no—
262SD16—82no—
263D8—21no—
264D8—21no—
265D8—112no—
266D8—221no—
267C2×C8C2×C22⋊D1111yescharacteristic
268C2×C8C2×C22⋊D1112yes—
269C2×C8C23×D1111yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—41no—
272C4⋊C4—42no—
273C4⋊C4—41no—
274C4⋊C4—221no—
275C4⋊C4—222no—
276C4⋊C4—442no—
277C4⋊C4—441no—
278C4⋊C4#432311yescharacteristic
279C4⋊C4#432312yes—
280C22⋊C4—42no—
281C22⋊C4—41no—
282C22⋊C4—42no—
283C22⋊C4—442no—
284C22⋊C4—441no—
285C42—42no—
286C42C2×C22⋊D1111yescharacteristic
287C42C2×C22⋊D1112yes—
288C16—221no—
289C16—222no—
290C16—221no—
291C11#3393411yescharacteristic, complemented, Sylow
292C23—41no—
293C23—441no—
294Q8—22no—
295Q8—42no—
296Q8—42no—
297Q8—884no—
298Q8—882no—
299D4—41no—
300D4—41no—
301D4—222no—
302D4—441no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—82no—
306C2×C4—442no—
307C2×C4—441no—
308C2×C4—884no—
309C2×C4—882no—
310C2×C4C2×#432312yes—
311C2×C4C2×#432311yescharacteristic
312C2×C4C2×#432312yes—
313C2×C4C2×#432311yescharacteristic
314C2×C4C22×C22⋊D1111yescharacteristic
315C8—22no—
316C8—21no—
317C8#41×D1111yescharacteristic
318C8#6704311yescharacteristic
319C22—81no—
320C22—81no—
321C22—81no—
322C22—442no—
323C22—881no—
324C22—881no—
325C22C22×#432311yescharacteristic
326C4—22no—
327C4—22no—
328C4—21no—
329C4—81no—
330C4—82no—
331C4—882no—
332C4—881no—
333C4#1062280612yes—
334C4#1062336211yescharacteristic
335C4#1062336711yescharacteristic
336C2—161no—
337C2—882no—
338C2#1308124711yescharacteristic
339C2C2×#1062280611yescharacteristic
340C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3393C2
socleC22×C11C22×D8
prime radicalC2×#66890C22
hypercenter#3393D11
hypocenterC11#33934
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3393

Complements

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

NH ≅ G/Ntype
1. Q8×D88C2semidirect
2. #13070852C2semidirect
3. #13070843C2semidirect
4. #13070768C2semidirect
5. #13070753C2semidirect
7. #13070658C2semidirect
8. #13070525C2semidirect
9. #13070478C2semidirect
11. C11×#3393C2semidirect
122. #3393D11semidirect
291. C11#33934semidirect

Maximal subgroups

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

subgroupindex
Q8×D882
#130708522
#130708432
#130707682
#130707532
#130706682
#130706582
#130705252
#130704782
C4×#668902
C11×#33932
#3393411