Finite Group Databasebeta

← #14909700

Subgroups — #14909700

Order 2816.

582 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079203C211yesmaximal, characteristic
2D11×#494C211yesmaximal, characteristic
3#13070869C211yesmaximal, characteristic, complemented
4#13070868C211yesmaximal, characteristic, complemented
5#13070845C211yesmaximal, characteristic, complemented
6#13070665C214yesmaximal, complemented
7#13070551C214yesmaximal
8#13070413C211yesmaximal, characteristic
9C11×#2241C211yesmaximal, characteristic, complemented
10C2×Q16×D11—21no—
11C2×Q16×D11C2212yes—
12#10623259—21no—
13D11×C4⋊Q8—21no—
14C11×#500C2211yescharacteristic
15C11×#494C2211yescharacteristic
16#10622794—21no—
17#10622794C2212yes—
18C2×#66893C2214yes—
19#10622706—21no—
20#10622705—21no—
21C2×Dic88C2214yes—
22#10622500—21no—
23#10622500C2212yes—
24#10622486—21no—
25#10622486C2212yes—
26#10622312C2211yescharacteristic
27#10622312C2211yescharacteristic
28C4×C8×D11C2211yescharacteristic
29C11×#358C2214yes—
30C4×C11×C16C2211yescharacteristic
31(C2×D11)⋊C16C2212yes—
32Dic11⋊C16C2212yes—
33#10622130C2214yes—
34C4×C11⋊C16C2211yescharacteristic
35C2×Q8×D11—22no—
36C2×C11×Q16—21no—
37C2×C11×Q16C2312yes—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40#66999—41no—
41Q8×Dic11—41no—
42#66997—22no—
43C2×#4326—22no—
44C2×#4326—22no—
45Q16×D11—44no—
46Q16×D11—44no—
47C2×Dic44—21no—
48C2×Dic44—21no—
49C2×Dic44C2312yes—
50C2×Dic44C2312yes—
51C2×C8×D11D411yescharacteristic
52C2×C8×D11C2311yescharacteristic
53#66950—22no—
54#66945—41no—
55C4⋊C4×D11—41no—
56C4⋊C4×D11—41no—
57#66943—41no—
58#66941—41no—
59#66941—41no—
60#66940—22no—
61C42×D11D411yescharacteristic
62#66922—21no—
63#66922—21no—
64C2×C11×C16C2312yes—
65C11×#107—21no—
66C11×#107C2312yes—
67C4×C8×C11C2311yescharacteristic
68#66893—44no—
69C8×Dic11D411yescharacteristic
70C8×Dic11C2311yescharacteristic
71C2×C11⋊C16C2312yes—
72#66874—22no—
73#66874—22no—
74C4×C11⋊C8D411yescharacteristic
75Dic88—44no—
76#33775—111nomaximal, Sylow
77C2×Q8×C11—22no—
78C2×Q8×C11—41no—
79Q8×D11—44no—
80Q8×D11—44no—
81C2×C4×D11—42no—
82C2×C4×D11D811yescharacteristic
83C2×C4×D11D811yescharacteristic
84C2×C4×D11C2×D411yescharacteristic
85C2×Dic22—22no—
86C2×Dic22—22no—
87C2×Dic22—42no—
88C11×Q16—24no—
89C11×Q16—42no—
90C2×C8×C11C2×D411yescharacteristic
91C2×C8×C11C2411yescharacteristic
92C11×C4⋊C4—22no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C42×C11C2×D411yescharacteristic
97#4326—44no—
98#4326—44no—
99(C2×D11)⋊C4—42no—
100C4⋊Dic11—42no—
101C4⋊Dic11—41no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105Dic11⋊C4—42no—
106Dic11⋊C4—42no—
107Dic11⋊C4—42no—
108C4×Dic11—42no—
109C4×Dic11D811yescharacteristic
110C4×Dic11D811yescharacteristic
111C4×Dic11C2×D411yescharacteristic
112C2×C11⋊C8C2×D411yescharacteristic
113C2×C11⋊C8C2×D411yescharacteristic
114Dic44—24no—
115Dic44—24no—
116Dic44—42no—
117Dic44—42no—
118C8×D11—22no—
119C8×D11—22no—
120C11×C16—22no—
121C11⋊C16—22no—
122#3170—111no—
123C2×#494—111no—
124#2247—111no—
125#2247—111no—
126#2241—111no—
127#2241D1111yescharacteristic, complemented
128#2209—114no—
129#2188—114no—
130#2162—111no—
131C22×D11C2×D811yescharacteristic
132Q8×C11—42no—
133Q8×C11—42no—
134Q8×C11—82no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11C2×D811yescharacteristic
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11C22×D411yescharacteristic
140C2×Dic11—42no—
141C2×Dic11—42no—
142C2×Dic11C2×D811yescharacteristic
143C2×Dic11C2×D811yescharacteristic
144C2×Dic11C2×D811yescharacteristic
145C4×D11—21no—
146C4×D11—21no—
147C4×D11—22no—
148C4×D11—84no—
149C4×D11Q3214yescomplemented
150Dic22—42no—
151Dic22—42no—
152Dic22—42no—
153Dic22—42no—
154Dic22—84no—
155C8×C11AGL(1,ℤ/8)12yes—
156C8×C11H(5,𝔽2)12yes—
157C11⋊C8—21no—
158C11⋊C8—21no—
159C22×Q16—112no—
160C22×Q16—221no—
161#533—221no—
162C2×C4⋊Q8—221no—
163C2×Q32—114no—
164C2×Q32—114no—
165#500C2×D1111yescharacteristic
166#494—112no—
167#494—111no—
168#494—111no—
169#494—221no—
170#494—221no—
171#494C2×D1111yescharacteristic
172#487—221no—
173#467—112no—
174#467—221no—
175C4×Q16—112no—
176C4×Q16—221no—
177C2×C4×C8—111no—
178C4⋊C16—112no—
179#358—114no—
180#358C2×D1114yes—
181C22⋊C16—112no—
182C4×C16—111no—
183C4×C16C2×D1111yescharacteristic
184C22×C11C22×D811yescharacteristic
185C2×D11—21no—
186C2×D11—21no—
187C2×D11C2×Q3212yes—
188C4×C11—82no—
189C4×C11—82no—
190C4×C11C2×Q3212yes—
191C4×C11#51012yes—
192C4×C11#53511yescharacteristic
193C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
194Dic11—21no—
195Dic11—21no—
196Dic11—82no—
197Dic11—82no—
198Dic11C2×Q3212yes—
199C22×Q8—222no—
200C2×Q16—21no—
201C2×Q16—112no—
202C2×Q16—112no—
203C2×Q16—222no—
204C2×Q16—222no—
205C2×Q16—221no—
206C2×Q16—221no—
207C2×Q16—444no—
208C2×Q16—444no—
209C2×Q16C22×D1112yes—
210C22×C8—111no—
211C22×C8—111no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—222no—
215C4⋊Q8—221no—
216C4⋊Q8—221no—
217C4⋊Q8—441no—
218C4⋊Q8—441no—
219#125—441no—
220C22⋊Q8—222no—
221C22⋊Q8—441no—
222C4×Q8—222no—
223C4×Q8—441no—
224#117—441no—
225C2×C4⋊C4—441no—
226C2×C4⋊C4—441no—
227C2×C42—111no—
228Q32—444no—
229Q32—444no—
230C2×C16—112no—
231C2×C16C22×D1112yes—
232#107—21no—
233#107C22×D1112yes—
234#103—222no—
235#103—222no—
236C4×C8—111no—
237C4×C8—111no—
238C4×C8—111no—
239C4×C8C22×D1111yescharacteristic
240C2×C11#320511yescharacteristic
241C2×C11C22×Q3211yescharacteristic
242C2×C11C2×#51011yescharacteristic
243D11—22no—
244C2×Q8—22no—
245C2×Q8—41no—
246C2×Q8—222no—
247C2×Q8—222no—
248C2×Q8—442no—
249C2×Q8—444no—
250C2×Q8—444no—
251C22×C4—111no—
252C22×C4—111no—
253C22×C4—111no—
254C22×C4—442no—
255Q16—24no—
256Q16—42no—
257Q16—224no—
258Q16—224no—
259Q16—444no—
260Q16—444no—
261Q16—442no—
262Q16—442no—
263C2×C8—111no—
264C2×C8—111no—
265C2×C8—222no—
266C2×C8—222no—
267C2×C8D4×D1111yescharacteristic
268C2×C8C23×D1111yescharacteristic
269C4⋊C4—22no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—442no—
274C4⋊C4—442no—
275C4⋊C4—442no—
276C4⋊C4—442no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C22⋊C4—442no—
282C42—111no—
283C42—111no—
284C42—111no—
285C42—442no—
286C42D4×D1111yescharacteristic
287C16—22no—
288C16—222no—
289C11#3377511yescharacteristic, complemented, Sylow
290C23—111no—
291Q8—42no—
292Q8—42no—
293Q8—82no—
294Q8—442no—
295Q8—442no—
296Q8—442no—
297Q8—442no—
298Q8—884no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—111no—
302C2×C4—114no—
303C2×C4—111no—
304C2×C4—111no—
305C2×C4—221no—
306C2×C4—222no—
307C2×C4—221no—
308C2×C4—442no—
309C2×C4—442no—
310C2×C4—884no—
311C2×C4D8×D1111yescharacteristic
312C2×C4D8×D1111yescharacteristic
313C2×C4C2×D4×D1111yescharacteristic
314C8—221no—
315C8—221no—
316C8#6696712yes—
317C8#6704212yes—
318C22—112no—
319C22—221no—
320C22—221no—
321C22C2×D8×D1111yescharacteristic
322C4—82no—
323C4—82no—
324C4—112no—
325C4—221no—
326C4—221no—
327C4—882no—
328C4—882no—
329C4#1062252812yes—
330C4D11×Q3212yes—
331C4#1062320511yescharacteristic
332C4C2×#6696711yescharacteristic
333C2—222no—
334C2#1307953511yescharacteristic
335C2C2×D11×Q3211yescharacteristic
336C2C2×#1062252811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2241C2
socleC22×C11C22×D8
prime radicalC22×D11C2×D8
hypercenter#2241D11
hypocenterC11#33775
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2241

Complements

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

NH ≅ G/Ntype
3. #13070869C2semidirect
4. #13070868C2semidirect
5. #13070845C2semidirect
6. #13070665C2semidirect
9. C11×#2241C2semidirect
127. #2241D11semidirect
149. C4×D11Q32semidirect
289. C11#33775semidirect

Maximal subgroups

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

subgroupindex
#130792032
D11×#4942
#130708692
#130708682
#130708452
#130706652
#130705512
#130704132
C11×#22412
#3377511