Finite Group Databasebeta

← #14911571

Subgroups — #14911571

Order 2816.

520 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×D88C211yesmaximal, characteristic, complemented
2#13070852C212yesmaximal, complemented
3#13070839C211yesmaximal, characteristic, complemented
4#13070763C212yesmaximal, complemented
5#13070758C211yesmaximal, characteristic, complemented
6#13070668C212yesmaximal, complemented
7#13070648C211yesmaximal, characteristic
8#13070525C211yesmaximal, characteristic, complemented
9#13070490C212yesmaximal, complemented
10C4×#66892C211yesmaximal, characteristic, complemented
11C11×#3396C211yesmaximal, characteristic, complemented
12C11×#559—21no—
13Q8×D44—21no—
14C11×#495C2212yes—
15C11×#493C2211yescharacteristic
16C11×#463—22no—
17C11×#460—21no—
18C8×Q8×C11C2211yescharacteristic
19C4×C11×Q16C2211yescharacteristic
20C4×C11×D8C2212yes—
21C2×#66892C2211yescharacteristic
22C2×#66890C2212yes—
23#10622459—21no—
24#10622459—22no—
25C4×D88C2211yescharacteristic
26C4×D88C2212yes—
27#10622295C2212yes—
28#10622295C2211yescharacteristic
29#10622202C2211yescharacteristic
30#10622202C2212yes—
31#10622200C2212yes—
32#10622200C2212yes—
33#10622200C2212yes—
34#10622129C2211yescharacteristic
35#10622128C2211yescharacteristic
36#10622128C2212yes—
37C4⋊(C11⋊C16)C2211yescharacteristic
38C4⋊(C11⋊C16)C2212yes—
39#10622099C2212yes—
40C4×C11⋊C16C2211yescharacteristic
41C2×Q8×D11—41no—
42C2×C11×Q16C2311yescharacteristic
43C2×C11×SD16—22no—
44C2×C11×D8—21no—
45C2×C11×D8C2312yes—
46C11×#127—21no—
47C11×#124—22no—
48C11×#124—41no—
49C11×#123—42no—
50C4×Q8×C11—21no—
51C4×Q8×C11D411yescharacteristic
52C4×D4×C11—22no—
53C4×D4×C11—41no—
54C2×D88C2311yescharacteristic
55#66950—41no—
56#66950—42no—
57C4×D44—22no—
58C4×D44—21no—
59#66922—22no—
60#66922—21no—
61C11×#107C2311yescharacteristic
62C11×C4⋊C8D411yescharacteristic
63C11×C4⋊C8D412yes—
64C11×#103—21no—
65C11×#102—22no—
66C4×C8×C11C2311yescharacteristic
67C4×C8×C11C2312yes—
68#66892—22no—
69#66890—24no—
70#66885—22no—
71#66885—21no—
72#66882—22no—
73#66882—21no—
74#66882C2311yescharacteristic
75#66882C2312yes—
76C2×C11⋊C16C2312yes—
77C2×C11⋊C16C2311yescharacteristic
78C2×C11⋊C16C2311yescharacteristic
79#33940—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11D811yescharacteristic
82C2×D4×C11—22no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C22×C4×C11—42no—
86Q8×D11—84no—
87C2×D44—21no—
88C2×C4×D11—42no—
89C2×C4×D11—41no—
90C2×Dic22—42no—
91C2×Dic22—41no—
92C11×Q16—21no—
93C11×Q16—21no—
94C11×SD16—82no—
95C11×D8—22no—
96C11×D8—22no—
97C11×D8—81no—
98C2×C8×C11C2×D412yes—
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2411yescharacteristic
101C11×C4⋊C4—21no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4D811yescharacteristic
104C11×C4⋊C4D812yes—
105C11×C22⋊C4—42no—
106C11×C22⋊C4—42no—
107C11×C22⋊C4—42no—
108C42×C11—41no—
109C42×C11C2×D412yes—
110C42×C11C2×D411yescharacteristic
111(C2×D11)⋊C4—42no—
112(C2×D11)⋊C4—41no—
113C4⋊Dic11—21no—
114C4⋊Dic11—22no—
115C4⋊Dic11—42no—
116C4⋊Dic11—41no—
117D88—21no—
118D88#4112yes—
119C11⋊C16—22no—
120C11⋊C16—21no—
121C11⋊C16—21no—
122#3396D1111yescharacteristic, complemented
123Q8×D8—111no—
124#2243—112no—
125#2240—111no—
126#2226—112no—
127#2225—111no—
128#2210—112no—
129#2206—111no—
130#2183—111no—
131#2177—112no—
132C4×SD32—111no—
133C23×C11—42no—
134C22×D11—41no—
135Q8×C11—22no—
136Q8×C11—41no—
137Q8×C11—41no—
138D4×C11—42no—
139D4×C11—42no—
140D4×C11—82no—
141D4×C11—161no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—162no—
145C2×C4×C11C2×D812yes—
146C2×C4×C11C2×D811yescharacteristic
147C2×C4×C11C2×D812yes—
148C2×C4×C11C2×D811yescharacteristic
149C2×C4×C11C22×D411yescharacteristic
150C2×Dic11—41no—
151C2×Dic11—42no—
152D44—22no—
153D44—41no—
154C4×D11—84no—
155C4×D11—82no—
156Dic22—84no—
157Dic22—82no—
158C8×C11—21no—
159C8×C11—22no—
160C8×C11C2×#4111yescharacteristic
161C8×C112−1+411yescharacteristic
162#559—21no—
163D4×Q8—221no—
164C2×SD32—111no—
165C2×D16—112no—
166#500—111no—
167#500—112no—
168#495C2×D1112yes—
169#493C2×D1111yescharacteristic
170#474—221no—
171#474—222no—
172#463—22no—
173#460—21no—
174C8×Q8C2×D1111yescharacteristic
175C4×Q16C2×D1111yescharacteristic
176C4×D8—111no—
177C4×D8—112no—
178C4×D8C2×D1112yes—
179#367—111no—
180#367—112no—
181C4⋊C16—111no—
182C4⋊C16—112no—
183#358—111no—
184#358—112no—
185#357—112no—
186#357—112no—
187#357—112no—
188#357—111no—
189#346—112no—
190C4×C16—111no—
191C22×C11—82no—
192C22×C11—82no—
193C22×C11—82no—
194C22×C11C22×D811yescharacteristic
195C2×D11—42no—
196C2×D11—81no—
197C2×D11—81no—
198C4×C11—22no—
199C4×C11—22no—
200C4×C11—21no—
201C4×C11—81no—
202C4×C11—81no—
203C4×C11#50912yes—
204C4×C11#54811yescharacteristic
205C4×C11#57711yescharacteristic
206Dic11—81no—
207Dic11—82no—
208C22×Q8—441no—
209C2×Q16C22×D1111yescharacteristic
210C2×SD16—22no—
211C2×D8—21no—
212C2×D8—111no—
213C2×D8C22×D1112yes—
214C4⋊Q8—222no—
215C4⋊Q8—221no—
216#127—21no—
217#124—22no—
218#124—41no—
219#123—42no—
220C22⋊Q8—441no—
221C22⋊Q8—442no—
222C4×Q8—21no—
223C4×Q8C22⋊D1111yescharacteristic
224C4×D4—22no—
225C4×D4—41no—
226C4×D4—222no—
227C4×D4—221no—
228SD32—222no—
229D16—224no—
230C2×C16—111no—
231C2×C16—111no—
232C2×C16—112no—
233#107—112no—
234#107—111no—
235#107—222no—
236#107—221no—
237#107C22×D1111yescharacteristic
238C4⋊C8C22⋊D1111yescharacteristic
239C4⋊C8C22⋊D1112yes—
240#103—21no—
241#102—22no—
242#102—222no—
243#102—221no—
244C4×C8C22×D1111yescharacteristic
245C4×C8C22×D1112yes—
246C2×C11—162no—
247C2×C11#335811yescharacteristic
248C2×C11C2×#50911yescharacteristic
249C2×C11#341611yescharacteristic
250D11—82no—
251C2×Q8—21no—
252C2×Q8—442no—
253C2×Q8—441no—
254C2×Q8—884no—
255C2×Q8#432311yescharacteristic
256C2×D4—22no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—221no—
260C22×C4—42no—
261C22×C4—442no—
262C22×C4—441no—
263Q16—21no—
264Q16—21no—
265SD16—82no—
266D8—22no—
267D8—22no—
268D8—81no—
269D8—112no—
270D8—221no—
271C2×C8C2×C22⋊D1112yes—
272C2×C8C2×C22⋊D1111yescharacteristic
273C2×C8C23×D1111yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—41no—
276C4⋊C4—222no—
277C4⋊C4—221no—
278C4⋊C4—442no—
279C4⋊C4—441no—
280C4⋊C4#432311yescharacteristic
281C4⋊C4#432312yes—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—442no—
286C22⋊C4—441no—
287C42—41no—
288C42C2×C22⋊D1112yes—
289C42C2×C22⋊D1111yescharacteristic
290C16—222no—
291C16—221no—
292C16—221no—
293C11#3394011yescharacteristic, complemented, Sylow
294C23—42no—
295C23—441no—
296Q8—22no—
297Q8—41no—
298Q8—41no—
299Q8—884no—
300Q8—882no—
301D4—42no—
302D4—42no—
303D4—82no—
304D4—161no—
305D4—222no—
306D4—441no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—162no—
310C2×C4—442no—
311C2×C4—441no—
312C2×C4—884no—
313C2×C4—882no—
314C2×C4C2×#432312yes—
315C2×C4C2×#432312yes—
316C2×C4C2×#432311yescharacteristic
317C2×C4C2×#432311yescharacteristic
318C2×C4C22×C22⋊D1111yescharacteristic
319C8—21no—
320C8—22no—
321C8#41×D1111yescharacteristic
322C8#6704311yescharacteristic
323C22—82no—
324C22—82no—
325C22—82no—
326C22—442no—
327C22—881no—
328C22—881no—
329C22C22×#432311yescharacteristic
330C4—22no—
331C4—22no—
332C4—21no—
333C4—81no—
334C4—81no—
335C4—882no—
336C4—881no—
337C4#1062280612yes—
338C4#1062336211yescharacteristic
339C4#1062336711yescharacteristic
340C2—162no—
341C2—882no—
342C2#1308124711yescharacteristic
343C2C2×#1062280611yescharacteristic
344C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3396C2
socleC22×C11C22×D8
prime radical#13070648C2
hypercenter#3396D11
hypocenterC11#33940
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3396

Complements

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

NH ≅ G/Ntype
1. Q8×D88C2semidirect
2. #13070852C2semidirect
3. #13070839C2semidirect
4. #13070763C2semidirect
5. #13070758C2semidirect
6. #13070668C2semidirect
8. #13070525C2semidirect
9. #13070490C2semidirect
10. C4×#66892C2semidirect
11. C11×#3396C2semidirect
122. #3396D11semidirect
293. C11#33940semidirect

Maximal subgroups

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

subgroupindex
Q8×D882
#130708522
#130708392
#130707632
#130707582
#130706682
#130706482
#130705252
#130704902
C4×#668922
C11×#33962
#3394011