Finite Group Databasebeta

← #14672117

Subgroups — #14672117

Order 2816.

436 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 103 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#13070291C212yesmaximal
2#13070270C212yesmaximal
3#13068662C211yesmaximal, characteristic
4#13068416C211yesmaximal, characteristic
5C11×#3059C211yesmaximal, characteristic
6C22×C11×Q16C411yescharacteristic, complemented
7C2×C11×#131C2211yescharacteristic
8C11×#536C2212yes—
9C11×#470—21no—
10C11×#470—21no—
11C11×#467—21no—
12C11×#467—21no—
13C11×#427C411yescharacteristic, complemented
14C11×#419C412yescomplemented
15#10622853C2212yes—
16#10622853C2211yescharacteristic
17#10622850C2211yescharacteristic
18#10622719—21no—
19#10622714—21no—
20#10622195—21no—
21#10622194—21no—
22#10622179—24no—
23#10622177—24no—
24C2×C11×#41C2311yescharacteristic
25C22×Q8×C11C2×C412yes—
26C2×C11×Q16—21no—
27C2×C11×Q16—21no—
28C2×C11×Q16—41no—
29C2×C11×Q16—41no—
30C11×#131—41no—
31C11×#131—41no—
32C2×C11×M16C2×C411yescharacteristic
33C2×C11×M16D411yescharacteristic
34C2×C11×M16D411yescharacteristic
35C22×C8×C11C2×C411yescharacteristic
36C22×C8×C11D411yescharacteristic
37C22×C8×C11D411yescharacteristic
38C11×C4⋊Q8—22no—
39C11×#124—22no—
40C11×#123—22no—
41C11×#123—22no—
42C11×C22⋊Q8—22no—
43C11×C22⋊Q8—22no—
44C11×#117C2×C412yes—
45#66979—21no—
46#66979—22no—
47C2×#4318—21no—
48C11×#107—21no—
49C11×#106—21no—
50C11×#103—22no—
51C11×#103—22no—
52#66900—21no—
53#66898—21no—
54#66898—22no—
55#66898—22no—
56#66898D412yes—
57#66897D412yes—
58#66882—41no—
59#66881—41no—
60#66879—41no—
61C8×Dic11—41no—
62#13230—111nomaximal, Sylow
63C11×#41—41no—
64C11×#41—41no—
65C2×Q8×C11—22no—
66C2×Q8×C11—22no—
67C2×Q8×C11—42no—
68C2×Q8×C11—42no—
69C2×Q8×C11#4111yescharacteristic
70C2×D4×C11C2×D411yescharacteristic
71C2×D4×C11C2×D411yescharacteristic
72C2×D4×C11#4111yescharacteristic
73C22×C4×C11—22no—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C11×Q16—42no—
78C11×Q16—41no—
79C11×Q16—41no—
80C11×M16—41no—
81C11×M16—41no—
82C11×M16—41no—
83C2×C8×C11—21no—
84C2×C8×C11—21no—
85C2×C8×C11—21no—
86C2×C8×C11—21no—
87C2×C8×C11—21no—
88C2×C8×C11—21no—
89C2×C8×C11C22⋊C411yescharacteristic
90C2×C8×C11C22⋊C411yescharacteristic
91C2×C8×C11C22⋊C411yescharacteristic
92C2×C8×C11C22⋊C411yescharacteristic
93C11×C4⋊C4—22no—
94C11×C4⋊C4—42no—
95C11×C4⋊C4—42no—
96C11×C22⋊C4—22no—
97C11×C22⋊C4—42no—
98C11×C22⋊C4—42no—
99C42×C11—22no—
100C22⋊Dic11—22no—
101C22⋊Dic11—42no—
102C4⋊Dic11—41no—
103C4⋊Dic11—42no—
104C4×Dic11—41no—
105C4×Dic11—42no—
106#4318—22no—
107#4318—41no—
108C2×C11⋊C8—41no—
109#3059D1111yescharacteristic
110#2129—112no—
111#2123—112no—
112#1812—111no—
113#1757—111no—
114C23×C11C4×D411yescharacteristic
115C23×C11#12111yescharacteristic
116C23×C11#12711yescharacteristic
117Q8×C11—41no—
118Q8×C11—42no—
119Q8×C11—42no—
120Q8×C11—82no—
121D4×C11—41no—
122D4×C11—41no—
123D4×C11—41no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—82no—
133C2×C4×C11C2×C22⋊C411yescharacteristic
134C2×C4×C11C4×D411yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12411yescharacteristic
137C2×Dic11—42no—
138C2×Dic11—82no—
139C8×C11—21no—
140C8×C11—21no—
141C8×C11—21no—
142C8×C11#9911yescharacteristic
143C8×C11#9911yescharacteristic
144C11⋊C8—42no—
145C22×Q16Dic1111yescharacteristic, complemented
146C2×#131C2×D1111yescharacteristic
147#536C2×D1112yes—
148#470—21no—
149#470—21no—
150#467—21no—
151#467—21no—
152#427—221no—
153#427Dic1111yescharacteristic, complemented
154#419Dic1112yescomplemented
155#413—111no—
156#410—111no—
157#410—112no—
158#405—221no—
159#354—224no—
160#352—224no—
161#344—221no—
162H(3,ℤ/4)—221no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11#39011yescharacteristic
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—82no—
174C4×C11—82no—
175C4×C11C2×#9911yescharacteristic
176C4×C11#41011yescharacteristic
177Dic11—82no—
178Dic11—162no—
179C2×#41C22×D1111yescharacteristic
180C22×Q8C2×Dic1112yes—
181C2×Q16—21no—
182C2×Q16—21no—
183C2×Q16—41no—
184C2×Q16—41no—
185#131—41no—
186#131—41no—
187C2×M16—221no—
188C2×M16C2×Dic1111yescharacteristic
189C2×M16C22⋊D1111yescharacteristic
190C2×M16C22⋊D1111yescharacteristic
191C22×C8C2×Dic1111yescharacteristic
192C22×C8C22⋊D1111yescharacteristic
193C22×C8C22⋊D1111yescharacteristic
194C4⋊Q8—22no—
195#124—22no—
196#123—22no—
197#123—22no—
198C22⋊Q8—22no—
199C22⋊Q8—22no—
200#117—221no—
201#117—222no—
202#117C2×Dic1112yes—
203#107—21no—
204#107—441no—
205#106—21no—
206#106—441no—
207#103—22no—
208#103—22no—
209#101—221no—
210#100—112no—
211#99—112no—
212#99—221no—
213#99—222no—
214#99—222no—
215#97—441no—
216C4×C8—441no—
217C2×C11—21no—
218C2×C11—41no—
219C2×C11—41no—
220C2×C11—41no—
221C2×C11#196411yescharacteristic
222#41—41no—
223#41—41no—
224C2×Q8—22no—
225C2×Q8—22no—
226C2×Q8—42no—
227C2×Q8—42no—
228C2×Q8#434111yescharacteristic
229C2×D4D4×D1111yescharacteristic
230C2×D4D4×D1111yescharacteristic
231C2×D4#434111yescharacteristic
232C22×C4—22no—
233C22×C4C22×Dic1111yescharacteristic
234C22×C4C2×C22⋊D1111yescharacteristic
235C22×C4C2×C22⋊D1111yescharacteristic
236Q16—42no—
237Q16—41no—
238Q16—41no—
239M16—41no—
240M16—41no—
241M16—41no—
242M16—222no—
243M16—441no—
244C2×C8—21no—
245C2×C8—21no—
246C2×C8—21no—
247C2×C8—21no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—441no—
251C2×C8C22⋊Dic1111yescharacteristic
252C2×C8C22⋊Dic1111yescharacteristic
253C2×C8C22⋊Dic1111yescharacteristic
254C2×C8C22⋊Dic1111yescharacteristic
255C4⋊C4—22no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C4⋊C4—441no—
259C4⋊C4—442no—
260C22⋊C4—22no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C22⋊C4—222no—
264C22⋊C4—442no—
265C42—22no—
266C42—441no—
267C42—442no—
268C11#1323011yescharacteristic, complemented, Sylow
269C23D4×Dic1111yescharacteristic
270C23#6699111yescharacteristic
271C23#6699311yescharacteristic
272Q8—41no—
273Q8—42no—
274Q8—42no—
275Q8—82no—
276D4—41no—
277D4—41no—
278D4—41no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—82no—
288C2×C4—442no—
289C2×C4—882no—
290C2×C4D4×Dic1111yescharacteristic
291C2×C4#6698911yescharacteristic
292C2×C4#6699111yescharacteristic
293C2×C4C2×C22⋊Dic1111yescharacteristic
294C8—21no—
295C8—21no—
296C8—21no—
297C8—442no—
298C8#6689811yescharacteristic
299C8#6689811yescharacteristic
300C22—21no—
301C22—21no—
302C22—21no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22#1062283411yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—82no—
311C4—82no—
312C4—882no—
313C4—1762no—
314C4C2×#6689811yescharacteristic
315C4#1062285311yescharacteristic
316C2—21no—
317C2—41no—
318C2—41no—
319C2—41no—
320C2#1306945311yescharacteristic
subgroupG/H
centerC2#13069453
commutatorC22×C4×C11C22×C4
FrattiniC2×#41C22×D11
FittingC11×#3059C2
socleC2×C11#1964
prime radical, cosocleC2×C11×#41C23
hypercenter#3059D11
hypocenterC11#13230
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#131 ◁ #3059

Complements

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

NH ≅ G/Ntype
6. C22×C11×Q16C4semidirect
13. C11×#427C4semidirect
14. C11×#419C4semidirect
145. C22×Q16Dic11semidirect
153. #427Dic11semidirect
154. #419Dic11semidirect
268. C11#13230semidirect

Maximal subgroups

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

subgroupindex
#130702912
#130702702
#130686622
#130684162
C11×#30592
#1323011