Finite Group Databasebeta

← #14672133

Subgroups — #14672133

Order 2816.

432 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 99 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#13078271C211yesmaximal, characteristic
2#13070310C212yesmaximal
3#13070269C212yesmaximal
4#13068666C211yesmaximal, characteristic
5C11×#1757C211yesmaximal, characteristic
6C2×C11×#131C2211yescharacteristic
7#10623356C2212yes—
8C22×Dic44C411yescharacteristic, complemented
9C11×#413C2211yescharacteristic
10C11×#410C2211yescharacteristic
11C11×#405—21no—
12#10622850C2212yes—
13#10622750—21no—
14#10622750—21no—
15#10622733C412yescomplemented
16#10622729—21no—
17#10622729—21no—
18C2×#66883—21no—
19#10622719C411yescharacteristic, complemented
20C11×#344—21no—
21C11⋊#338—21no—
22#10622116—24no—
23#10622110—24no—
24C2×C11×#41C2311yescharacteristic
25C22×Dic22C2×C412yes—
26C11×#131—41no—
27C11×#131—41no—
28C2×C11×M16—21no—
29C2×C11×M16C2×C411yescharacteristic
30C2×C11×M16D411yescharacteristic
31C2×C11×M16D411yescharacteristic
32C22×C8×C11C2×C411yescharacteristic
33C22×C8×C11D411yescharacteristic
34C22×C8×C11D411yescharacteristic
35C11×#117—21no—
36#66997—22no—
37#66989—22no—
38#66988—22no—
39#66988—22no—
40#66979C2×C412yes—
41#66977—22no—
42#66977—22no—
43C2×#4318—22no—
44C2×Dic44—21no—
45C2×Dic44—21no—
46C2×Dic44—41no—
47C2×Dic44—41no—
48C11×#101D412yes—
49C11×#100—21no—
50C11×#99—21no—
51C11×#99D412yes—
52C11×#97—41no—
53C4×C8×C11—41no—
54#66900—22no—
55#66897—22no—
56#66883—41no—
57#66883—41no—
58#66882—21no—
59#66881—21no—
60#66880—22no—
61#66880—22no—
62#13233—111nomaximal, Sylow
63C11×#41—41no—
64C11×#41—41no—
65C2×Q8×C11C2×D411yescharacteristic
66C2×D4×C11C2×D411yescharacteristic
67C2×D4×C11#4111yescharacteristic
68C2×D4×C11#4111yescharacteristic
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—22no—
73C2×Dic22—22no—
74C2×Dic22—22no—
75C2×Dic22—42no—
76C2×Dic22—42no—
77C11×M16—22no—
78C11×M16—41no—
79C11×M16—41no—
80C11×M16—41no—
81C11×M16—41no—
82C2×C8×C11—21no—
83C2×C8×C11—21no—
84C2×C8×C11—21no—
85C2×C8×C11—21no—
86C2×C8×C11—21no—
87C2×C8×C11—21no—
88C2×C8×C11—41no—
89C2×C8×C11C22⋊C411yescharacteristic
90C2×C8×C11C22⋊C411yescharacteristic
91C2×C8×C11C22⋊C411yescharacteristic
92C2×C8×C11C22⋊C411yescharacteristic
93C11×C4⋊C4—41no—
94C11×C22⋊C4—22no—
95C42×C11—41no—
96C22⋊Dic11—22no—
97C22⋊Dic11—42no—
98C22⋊Dic11—42no—
99C4⋊Dic11—22no—
100Dic11⋊C4—42no—
101Dic11⋊C4—42no—
102C4×Dic11—22no—
103#4318—42no—
104#4318—42no—
105C2×C11⋊C8—42no—
106Dic44—42no—
107Dic44—41no—
108Dic44—41no—
109#3059—111no—
110#2135—112no—
111#2123—112no—
112#1813—111no—
113#1757D1111yescharacteristic
114C23×C11C4×D411yescharacteristic
115C23×C11#12111yescharacteristic
116C23×C11#12411yescharacteristic
117Q8×C11—41no—
118D4×C11—41no—
119D4×C11—41no—
120D4×C11—41no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—42no—
128C2×C4×C11C2×C22⋊C411yescharacteristic
129C2×C4×C11C4×D411yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12711yescharacteristic
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—82no—
135Dic22—42no—
136Dic22—42no—
137Dic22—82no—
138C8×C11—21no—
139C8×C11—21no—
140C8×C11—21no—
141C8×C11—42no—
142C8×C11#9911yescharacteristic
143C8×C11#9911yescharacteristic
144C11⋊C8—82no—
145C22×Q16—111no—
146C2×#131C2×D1111yescharacteristic
147#536—112no—
148#470—221no—
149#470—221no—
150#467—221no—
151#467—221no—
152C2×#108—221no—
153#427—111no—
154#419—112no—
155#413—112no—
156#413C2×D1111yescharacteristic
157#410C2×D1111yescharacteristic
158#405—21no—
159#356—224no—
160#352—224no—
161#344—21no—
162#338—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×C11C2×#9911yescharacteristic
175C4×C11#41011yescharacteristic
176Dic11—82no—
177Dic11—82no—
178C2×#41C22×D1111yescharacteristic
179C22×Q8—112no—
180C2×Q16—221no—
181C2×Q16—221no—
182C2×Q16—441no—
183C2×Q16—441no—
184#131—41no—
185#131—41no—
186C2×M16—21no—
187C2×M16—222no—
188C2×M16C4×D1111yescharacteristic
189C2×M16D4411yescharacteristic
190C2×M16C22⋊D1111yescharacteristic
191C22×C8C4×D1111yescharacteristic
192C22×C8D4411yescharacteristic
193C22×C8C22⋊D1111yescharacteristic
194C4⋊Q8—222no—
195#124—222no—
196#123—222no—
197#123—222no—
198C22⋊Q8—222no—
199C22⋊Q8—222no—
200#117—21no—
201#117—112no—
202#108—441no—
203#108—441no—
204#107—221no—
205#106—221no—
206#103—222no—
207#103—222no—
208#101—222no—
209#101D4412yes—
210#100—21no—
211#100—222no—
212#99—21no—
213#99D4412yes—
214#97—41no—
215C4×C8—41no—
216C2×C11—21no—
217C2×C11—41no—
218C2×C11—41no—
219C2×C11—41no—
220C2×C11#196411yescharacteristic
221#41—41no—
222#41—41no—
223C2×Q8—222no—
224C2×Q8—222no—
225C2×Q8—442no—
226C2×Q8—442no—
227C2×Q8C2×D4411yescharacteristic
228C2×D4C2×D4411yescharacteristic
229C2×D4#433911yescharacteristic
230C2×D4#433911yescharacteristic
231C22×C4—222no—
232C22×C4C2×C4×D1111yescharacteristic
233C22×C4C2×D4411yescharacteristic
234C22×C4C2×C22⋊D1111yescharacteristic
235Q16—442no—
236Q16—441no—
237Q16—441no—
238M16—22no—
239M16—41no—
240M16—41no—
241M16—41no—
242M16—41no—
243M16—442no—
244M16—442no—
245C2×C8—21no—
246C2×C8—21no—
247C2×C8—21no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—41no—
252C2×C8—442no—
253C2×C8(C2×D11)⋊C411yescharacteristic
254C2×C8(C2×D11)⋊C411yescharacteristic
255C2×C8(C2×D11)⋊C411yescharacteristic
256C2×C8(C2×D11)⋊C411yescharacteristic
257C4⋊C4—41no—
258C4⋊C4—222no—
259C4⋊C4—442no—
260C4⋊C4—442no—
261C22⋊C4—22no—
262C22⋊C4—222no—
263C22⋊C4—442no—
264C22⋊C4—442no—
265C42—41no—
266C42—222no—
267C11#1323311yescharacteristic, complemented, Sylow
268C23C4×D4411yescharacteristic
269C23#6692811yescharacteristic
270C23#6698311yescharacteristic
271Q8—41no—
272Q8—442no—
273Q8—442no—
274Q8—882no—
275D4—41no—
276D4—41no—
277D4—41no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—42no—
285C2×C4—442no—
286C2×C4—442no—
287C2×C4—882no—
288C2×C4C4×D4411yescharacteristic
289C2×C4#6692711yescharacteristic
290C2×C4C2×(C2×D11)⋊C411yescharacteristic
291C2×C4#6698311yescharacteristic
292C8—21no—
293C8—21no—
294C8—21no—
295C8—42no—
296C8—882no—
297C8#6687011yescharacteristic
298C8#6687011yescharacteristic
299C22—21no—
300C22—21no—
301C22—21no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22#1062255211yescharacteristic
306C4—21no—
307C4—21no—
308C4—21no—
309C4—82no—
310C4—882no—
311C4—882no—
312C4C2×#6687011yescharacteristic
313C4#1062261911yescharacteristic
314C2—21no—
315C2—41no—
316C2—41no—
317C2—41no—
318C2#1306945211yescharacteristic
subgroupG/H
centerC2#13069452
commutatorC22×C4×C11C22×C4
FrattiniC2×#41C22×D11
FittingC11×#1757C2
socleC2×C11#1964
prime radical, cosocleC2×C11×#41C23
hypercenter#1757D11
hypocenterC11#13233
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#131 ◁ #1757

Complements

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

NH ≅ G/Ntype
8. C22×Dic44C4semidirect
15. #10622733C4semidirect
19. #10622719C4semidirect
267. C11#13233semidirect

Maximal subgroups

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

subgroupindex
#130782712
#130703102
#130702692
#130686662
C11×#17572
#1323311