Finite Group Databasebeta

← #14672114

Subgroups — #14672114

Order 2816.

436 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 95 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#13070290C212yesmaximal
3#13070269C212yesmaximal
4#13068416C211yesmaximal, characteristic
5C11×#1812C211yesmaximal, characteristic
6C2×C11×#131C2211yescharacteristic
7#10623356C2212yes—
8C22×Dic44C411yescharacteristic, complemented
9C11×#427—21no—
10C11×#410C2212yes—
11#10622853C2211yescharacteristic
12#10622850C2211yescharacteristic
13#10622750—21no—
14#10622750—21no—
15#10622733C412yescomplemented
16#10622729—21no—
17#10622729—21no—
18#10622719C411yescharacteristic, complemented
19#10622714—21no—
20C11×H(3,ℤ/4)—21no—
21#10622194—21no—
22#10622111—24no—
23#10622110—24no—
24C2×C11×#41C2311yescharacteristic
25C22×Dic22C2×C412yes—
26C11×#131—41no—
27C11×#131—41no—
28C2×C11×M16C2×C411yescharacteristic
29C2×C11×M16D411yescharacteristic
30C2×C11×M16D411yescharacteristic
31C22×C8×C11C2×C411yescharacteristic
32C22×C8×C11D411yescharacteristic
33C22×C8×C11D411yescharacteristic
34C11×#117—22no—
35#66997—22no—
36#66989—22no—
37#66988—22no—
38#66988—22no—
39#66979—21no—
40#66979C2×C412yes—
41#66977—22no—
42#66977—22no—
43C2×#4318—21no—
44C2×Dic44—21no—
45C2×Dic44—21no—
46C2×Dic44—41no—
47C2×Dic44—41no—
48C11×#107—41no—
49C11×#106—41no—
50C11×#99—22no—
51C11×#99—22no—
52#66900—21no—
53#66898—21no—
54#66898D412yes—
55#66897D412yes—
56#66882—21no—
57#66881—21no—
58#66880—22no—
59#66880—22no—
60#66879—41no—
61C8×Dic11—41no—
62#13230—111nomaximal, Sylow
63C11×#41—41no—
64C11×#41—41no—
65C2×Q8×C11#4111yescharacteristic
66C2×D4×C11C2×D411yescharacteristic
67C2×D4×C11C2×D411yescharacteristic
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—41no—
78C11×M16—41no—
79C11×M16—41no—
80C2×C8×C11—21no—
81C2×C8×C11—21no—
82C2×C8×C11—21no—
83C2×C8×C11—21no—
84C2×C8×C11—21no—
85C2×C8×C11—21no—
86C2×C8×C11C22⋊C411yescharacteristic
87C2×C8×C11C22⋊C411yescharacteristic
88C2×C8×C11C22⋊C411yescharacteristic
89C2×C8×C11C22⋊C411yescharacteristic
90C11×C4⋊C4—42no—
91C11×C22⋊C4—42no—
92C42×C11—42no—
93C22⋊Dic11—22no—
94C22⋊Dic11—22no—
95C22⋊Dic11—42no—
96C22⋊Dic11—42no—
97C4⋊Dic11—22no—
98C4⋊Dic11—41no—
99Dic11⋊C4—42no—
100Dic11⋊C4—42no—
101C4×Dic11—22no—
102C4×Dic11—41no—
103#4318—22no—
104#4318—41no—
105C2×C11⋊C8—41no—
106Dic44—42no—
107Dic44—41no—
108Dic44—41no—
109#3059—111no—
110#2129—112no—
111#2123—112no—
112#1812D1111yescharacteristic
113#1757—111no—
114C23×C11C4×D411yescharacteristic
115C23×C11#12111yescharacteristic
116C23×C11#12711yescharacteristic
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—82no—
128C2×C4×C11C2×C22⋊C411yescharacteristic
129C2×C4×C11C4×D411yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12411yescharacteristic
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—42no—
135C2×Dic11—82no—
136Dic22—42no—
137Dic22—42no—
138Dic22—82no—
139C8×C11—21no—
140C8×C11—21no—
141C8×C11—21no—
142C8×C11#9911yescharacteristic
143C8×C11#9911yescharacteristic
144C11⋊C8—42no—
145C22×Q16—111no—
146C2×#131C2×D1111yescharacteristic
147#536—112no—
148#470—221no—
149#470—221no—
150#467—221no—
151#467—221no—
152#427—21no—
153#427—111no—
154#419—112no—
155#413—111no—
156#410—111no—
157#410C2×D1112yes—
158#405—221no—
159#354—224no—
160#352—224no—
161#344—221no—
162H(3,ℤ/4)—21no—
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—162no—
174C4×C11C2×#9911yescharacteristic
175C4×C11#41011yescharacteristic
176Dic11—82no—
177Dic11—82no—
178Dic11—82no—
179C2×#41C22×D1111yescharacteristic
180C22×Q8—112no—
181C2×Q16—221no—
182C2×Q16—221no—
183C2×Q16—441no—
184C2×Q16—441no—
185#131—41no—
186#131—41no—
187C2×M16—221no—
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—22no—
201#117—112no—
202#117—221no—
203#107—41no—
204#107—221no—
205#106—41no—
206#106—221no—
207#103—222no—
208#103—222no—
209#101—221no—
210#100—112no—
211#99—22no—
212#99—22no—
213#99—112no—
214#99—221no—
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—222no—
225C2×Q8—222no—
226C2×Q8—442no—
227C2×Q8—442no—
228C2×Q8#434311yescharacteristic
229C2×D4D4×D1111yescharacteristic
230C2×D4D4×D1111yescharacteristic
231C2×D4#434311yescharacteristic
232C22×C4—222no—
233C22×C4C2×C4×D1111yescharacteristic
234C22×C4C2×D4411yescharacteristic
235C22×C4C2×C22⋊D1111yescharacteristic
236Q16—442no—
237Q16—441no—
238Q16—441no—
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×C8(C2×D11)⋊C411yescharacteristic
252C2×C8(C2×D11)⋊C411yescharacteristic
253C2×C8(C2×D11)⋊C411yescharacteristic
254C2×C8(C2×D11)⋊C411yescharacteristic
255C4⋊C4—42no—
256C4⋊C4—222no—
257C4⋊C4—441no—
258C4⋊C4—442no—
259C4⋊C4—442no—
260C22⋊C4—42no—
261C22⋊C4—222no—
262C22⋊C4—222no—
263C22⋊C4—442no—
264C22⋊C4—442no—
265C42—42no—
266C42—222no—
267C42—441no—
268C11#1323011yescharacteristic, complemented, Sylow
269C23#6694611yescharacteristic
270C23#6694811yescharacteristic
271C23#6699311yescharacteristic
272Q8—41no—
273Q8—442no—
274Q8—442no—
275Q8—882no—
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—82no—
286C2×C4—442no—
287C2×C4—442no—
288C2×C4—442no—
289C2×C4—882no—
290C2×C4#6694611yescharacteristic
291C2×C4#6694811yescharacteristic
292C2×C4C2×(C2×D11)⋊C411yescharacteristic
293C2×C4#6700011yescharacteristic
294C8—21no—
295C8—21no—
296C8—21no—
297C8—442no—
298C8#6687011yescharacteristic
299C8#6687011yescharacteristic
300C22—21no—
301C22—21no—
302C22—21no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22#1062260111yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—162no—
311C4—882no—
312C4—882no—
313C4—882no—
314C4C2×#6687011yescharacteristic
315C4#1062261911yescharacteristic
316C2—21no—
317C2—41no—
318C2—41no—
319C2—41no—
320C2#1306945111yescharacteristic
subgroupG/H
centerC2#13069451
commutatorC22×C4×C11C22×C4
FrattiniC2×#41C22×D11
FittingC11×#1812C2
socleC2×C11#1964
prime radical, cosocleC2×C11×#41C23
hypercenter#1812D11
hypocenterC11#13230
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#131 ◁ #1812

Complements

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

NH ≅ G/Ntype
8. C22×Dic44C4semidirect
15. #10622733C4semidirect
18. #10622719C4semidirect
268. C11#13230semidirect

Maximal subgroups

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

subgroupindex
#130782712
#130702902
#130702692
#130684162
C11×#18122
#1323011