Finite Group Databasebeta

← #14909070

Subgroups — #14909070

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079127C211yesmaximal, characteristic, complemented
2#13079043C211yesmaximal, characteristic
3#13070846C214yesmaximal, complemented
4#13070845C211yesmaximal, characteristic, complemented
5#13070844C211yesmaximal, characteristic, complemented
6#13070839C211yesmaximal, characteristic, complemented
7#13070320C214yesmaximal, complemented
8C4×C16×D11C211yesmaximal, characteristic, complemented
9C11×#2240C211yesmaximal, characteristic, complemented
10C2×#66965—21no—
11C2×#66965C2212yes—
12#10623259—21no—
13#10623247—21no—
14C11×#500C2211yescharacteristic
15C11×#493C2211yescharacteristic
16#10622768—21no—
17#10622768C2212yes—
18#10622692—21no—
19#10622689—21no—
20C2×C16×D11C2212yes—
21#10622493—21no—
22#10622493C2212yes—
23#10622491—21no—
24#10622491C2212yes—
25#10622312C2211yescharacteristic
26C4×C8×D11C2211yescharacteristic
27#10622295C2211yescharacteristic
28C11×#357C2214yes—
29C4×C11×C16C2211yescharacteristic
30#10622200C2214yes—
31#10622141C2214yes—
32C16×Dic11C2212yes—
33#10622130C2214yes—
34C4×C11⋊C16C2211yescharacteristic
35C2×#4341—22no—
36C2×C11×D8—21no—
37C2×C11×D8C2312yes—
38C11×C4⋊Q8—21no—
39C11×#127—21no—
40#66999—41no—
41Q8×Dic11—41no—
42#66991—41no—
43#66991—41no—
44#66989—22no—
45D4×Dic11—41no—
46D4×Dic11—41no—
47C2×#4324—22no—
48C2×#4324—22no—
49#66965—28no—
50#66965—44no—
51C2×Dic44—21no—
52C2×Dic44C2312yes—
53C2×C8×D11D411yescharacteristic
54C2×C8×D11C2311yescharacteristic
55#66950—41no—
56#66945—22no—
57#66943—22no—
58#66940—41no—
59C42×D11D411yescharacteristic
60#66922—21no—
61#66922—21no—
62C2×C11×C16C2312yes—
63C11×#107—21no—
64C11×#107C2312yes—
65C4×C8×C11C2311yescharacteristic
66#66882—21no—
67#66882C2312yes—
68C8×Dic11D411yescharacteristic
69C8×Dic11C2311yescharacteristic
70C2×C11⋊C16C2312yes—
71#66872—22no—
72#66872—22no—
73C4×C11⋊C8D411yescharacteristic
74C16×D11—24no—
75#33697—111nomaximal, Sylow
76C2×Q8×C11—41no—
77C2×D4×C11—22no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×C22⋊D11—42no—
81C22×Dic11—42no—
82#4341—44no—
83#4341—44no—
84C2×C4×D11D811yescharacteristic
85C2×C4×D11D811yescharacteristic
86C2×C4×D11C2×D411yescharacteristic
87C2×Dic22—22no—
88C2×Dic22—41no—
89C11×D8—24no—
90C11×D8—42no—
91C2×C8×C11C2×D411yescharacteristic
92C2×C8×C11C2411yescharacteristic
93C11×C4⋊C4—22no—
94C11×C4⋊C4—41no—
95C42×C11C2×D411yescharacteristic
96C22⋊Dic11—42no—
97C22⋊Dic11—42no—
98#4324—44no—
99#4324—44no—
100(C2×D11)⋊C4—42no—
101C4⋊Dic11—22no—
102C4⋊Dic11—42no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106Dic11⋊C4—42no—
107C4×Dic11—42no—
108C4×Dic11D811yescharacteristic
109C4×Dic11D811yescharacteristic
110C4×Dic11C2×D411yescharacteristic
111C2×C11⋊C8C2×D411yescharacteristic
112C2×C11⋊C8C2×D411yescharacteristic
113Dic44—24no—
114Dic44—42no—
115C8×D11SD1614yes—
116C8×D11#4114yes—
117C11×C16—22no—
118C11⋊C16—22no—
119#3160—111no—
120#3147—111no—
121#2242—114no—
122#2241—111no—
123#2241—111no—
124#2240—111no—
125#2240D1111yescharacteristic, complemented
126#2138—114no—
127C2×C4×C16—111no—
128C23×C11—42no—
129C22×D11C2×D811yescharacteristic
130Q8×C11—82no—
131D4×C11—42no—
132D4×C11—42no—
133D4×C11—82no—
134D4×C11—82no—
135C2×C4×C11—42no—
136C2×C4×C11C2×D811yescharacteristic
137C2×C4×C11C2×D811yescharacteristic
138C2×C4×C11C22×D411yescharacteristic
139C22⋊D11—84no—
140C2×Dic11—42no—
141C2×Dic11—42no—
142C2×Dic11—84no—
143C2×Dic11C2×D811yescharacteristic
144C2×Dic11C2×D811yescharacteristic
145C2×Dic11C2×D811yescharacteristic
146C4×D11—22no—
147C4×D11—22no—
148C4×D11#12412yes—
149C4×D11C2×SD1612yes—
150Dic22—42no—
151Dic22—42no—
152Dic22—82no—
153C8×C11C2×SD1612yes—
154C8×C11C2×#4112yes—
155C11⋊C8#12412yes—
156C11⋊C8C2×SD1612yes—
157C2×#135—112no—
158C2×#135—221no—
159#533—221no—
160#532—221no—
161C22×C16—112no—
162#500—111no—
163#500C2×D1111yescharacteristic
164#499—112no—
165#499—221no—
166#498—221no—
167#495—112no—
168#495—221no—
169#494—111no—
170#493C2×D1111yescharacteristic
171#492—221no—
172#427—112no—
173#427—221no—
174C2×C4×C8—111no—
175#358—114no—
176#358—114no—
177#357—114no—
178#357C2×D1114yes—
179C4×C16—112no—
180C4×C16—111no—
181C4×C16C2×D1111yescharacteristic
182C22×C11—82no—
183C22×C11—82no—
184C22×C11—82no—
185C22×C11C22×D811yescharacteristic
186C2×D11—21no—
187C2×D11—21no—
188C2×D11#48612yes—
189C4×C11—82no—
190C4×C11#50812yes—
191C4×C11#50812yes—
192C4×C11C2×#12411yescharacteristic
193C4×C11C22×SD1611yescharacteristic
194Dic11—21no—
195Dic11—21no—
196Dic11—82no—
197Dic11—82no—
198Dic11#48612yes—
199C2×#41—222no—
200#135—228no—
201#135—444no—
202C2×Q16—112no—
203C2×Q16—221no—
204C2×SD16—222no—
205C2×SD16—222no—
206C2×D8—21no—
207C2×D8C22×D1112yes—
208C22×C8—111no—
209C22×C8—111no—
210C4⋊Q8—21no—
211C4⋊Q8—221no—
212C4⋊Q8—221no—
213#127—21no—
214#125—222no—
215#124—222no—
216C22⋊Q8—441no—
217C22⋊Q8—441no—
218#121—441no—
219#121—441no—
220C4×Q8—441no—
221C4×Q8—441no—
222C4×D4—441no—
223C4×D4—441no—
224#117—222no—
225C2×C42—111no—
226C2×C16—112no—
227C2×C16—224no—
228C2×C16C22×D1112yes—
229#107—21no—
230#107—112no—
231#107—221no—
232#107C22×D1112yes—
233#106—222no—
234#106—222no—
235C4×C8—111no—
236C4×C8—111no—
237C4×C8—111no—
238C4×C8C22×D1111yescharacteristic
239C2×C11—162no—
240C2×C11C2×#48611yescharacteristic
241C2×C11C2×#50811yescharacteristic
242C2×C11C2×#50811yescharacteristic
243D11—22no—
244#41—444no—
245#41—444no—
246C2×Q8—41no—
247C2×Q8—222no—
248C2×Q8—441no—
249C2×D4—22no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—442no—
253C22×C4—111no—
254C22×C4—111no—
255C22×C4—111no—
256C22×C4—442no—
257Q16—224no—
258Q16—442no—
259SD16—444no—
260SD16—444no—
261D8—24no—
262D8—42no—
263C2×C8—111no—
264C2×C8—111no—
265C2×C8—114no—
266C2×C8—114no—
267C2×C8D4×D1111yescharacteristic
268C2×C8C23×D1111yescharacteristic
269C4⋊C4—22no—
270C4⋊C4—41no—
271C4⋊C4—222no—
272C4⋊C4—442no—
273C4⋊C4—442no—
274C4⋊C4—441no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C22⋊C4—442no—
278C22⋊C4—442no—
279C22⋊C4—442no—
280C42—111no—
281C42—111no—
282C42—111no—
283C42—442no—
284C42D4×D1111yescharacteristic
285C16—22no—
286C16—222no—
287C11#3369711yescharacteristic, complemented, Sylow
288C23—42no—
289C23—111no—
290Q8—82no—
291Q8—442no—
292Q8—442no—
293Q8—882no—
294D4—42no—
295D4—42no—
296D4—82no—
297D4—82no—
298D4—884no—
299C2×C4—42no—
300C2×C4—111no—
301C2×C4—112no—
302C2×C4—112no—
303C2×C4—111no—
304C2×C4—111no—
305C2×C4—222no—
306C2×C4—222no—
307C2×C4—442no—
308C2×C4—442no—
309C2×C4—884no—
310C2×C4D8×D1111yescharacteristic
311C2×C4D8×D1111yescharacteristic
312C2×C4C2×D4×D1111yescharacteristic
313C8—112no—
314C8—112no—
315C8SD16×D1112yes—
316C8#41×D1112yes—
317C22—82no—
318C22—82no—
319C22—82no—
320C22—112no—
321C22—221no—
322C22—221no—
323C22C2×D8×D1111yescharacteristic
324C4—82no—
325C4—112no—
326C4—221no—
327C4—221no—
328C4—882no—
329C4—882no—
330C4#1062252512yes—
331C4#1062252912yes—
332C4D11×#12411yescharacteristic
333C4C2×SD16×D1111yescharacteristic
334C2—162no—
335C2—222no—
336C2D11×#48611yescharacteristic
337C2C2×#1062252511yescharacteristic
338C2C2×#1062252911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2240C2
socleC22×C11C22×D8
prime radical#13079043C2
hypercenter#2240D11
hypocenterC11#33697
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2240

Complements

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

NH ≅ G/Ntype
1. #13079127C2semidirect
3. #13070846C2semidirect
4. #13070845C2semidirect
5. #13070844C2semidirect
6. #13070839C2semidirect
7. #13070320C2semidirect
8. C4×C16×D11C2semidirect
9. C11×#2240C2semidirect
125. #2240D11semidirect
287. C11#33697semidirect

Maximal subgroups

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

subgroupindex
#130791272
#130790432
#130708462
#130708452
#130708442
#130708392
#130703202
C4×C16×D112
C11×#22402
#3369711