Finite Group Databasebeta

← #14664077

Subgroups — #14664077

Order 2816.

452 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 107 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#13071884C211yesmaximal, characteristic
2#13066930C211yesmaximal, characteristic
3#13066645C212yesmaximal, complemented
4#13066642C212yesmaximal, complemented
5C11×#1742C211yesmaximal, characteristic
6C22×C11×M16—21no—
7C2×C11×#117C2211yescharacteristic
8C2×C4×Dic22C411yescharacteristic
9C4×C22⋊Dic11—21no—
10#10622599C2211yescharacteristic
11#10622597—21no—
12#10622592C2211yescharacteristic
13#10622562C411yescharacteristic
14#10622561—21no—
15#10622560C411yescharacteristic
16C4×C4⋊Dic11C411yescharacteristic
17C4×Dic11⋊C4—21no—
18#10622538—21no—
19C11×#343—21no—
20C11×#343C2212yes—
21#10622166C2212yes—
22#10622163—21no—
23C23×C4×C11D411yescharacteristic
24C22×Dic22C2×C411yescharacteristic
25C2×C11×M16—24no—
26C2×C11×M16—22no—
27C2×C11×M16—41no—
28C2×C11×M16—42no—
29C22×C8×C11—41no—
30C11×#117—41no—
31C11×#117—41no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4C2311yescharacteristic
34C2×C11×C22⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4D411yescharacteristic
36C2×C42×C11C2×C411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11C2×C411yescharacteristic
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11—21no—
46C2×C4×Dic11—21no—
47C4×Dic22—41no—
48C4×Dic22—41no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95C2×C411yescharacteristic
54C11⋊#95C2×C411yescharacteristic
55C22⋊(C11⋊C8)—22no—
56C4⋊(C11⋊C8)—41no—
57C4×C11⋊C8—41no—
58#11721—111nomaximal, Sylow
59C24×C11C22⋊C411yescharacteristic
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—22no—
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11SD1612yes—
67C22×C4×C11Q1612yes—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C2×Dic22—41no—
76C2×Dic22—42no—
77C11×M16—24no—
78C11×M16—44no—
79C11×M16—42no—
80C2×C8×C11—42no—
81C2×C8×C11—44no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11—21no—
90C22⋊Dic11—42no—
91C22⋊Dic11—42no—
92C4⋊Dic11—41no—
93C4⋊Dic11—42no—
94Dic11⋊C4—42no—
95Dic11⋊C4—42no—
96Dic11⋊C4—42no—
97C4×Dic11—41no—
98C4×Dic11—41no—
99C4×Dic11—42no—
100C2×C11⋊C8—42no—
101#2396—111no—
102#1742D1111yescharacteristic
103#1458—111no—
104#1354—112no—
105#1353—112no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—41no—
109C23×C11—41no—
110C23×C11#10312yes—
111C23×C11C2×C22⋊C411yescharacteristic
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11#9911yescharacteristic
127C2×C4×C11#9911yescharacteristic
128C2×C4×C11#10312yes—
129C2×C4×C11#10412yes—
130C2×C4×C11C2×SD1611yescharacteristic
131C2×C4×C11C2×Q1611yescharacteristic
132C2×Dic11—22no—
133C2×Dic11—22no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144Dic22—42no—
145Dic22—42no—
146C8×C11—44no—
147C11⋊C8—82no—
148C22×M16—21no—
149C2×C4×Q8—111no—
150C2×#117C2×D1111yescharacteristic
151#431—221no—
152#400—111no—
153#399—111no—
154#398—221no—
155#396—221no—
156#395—111no—
157#393—111no—
158C4×C4⋊C4—111no—
159C4×C4⋊C4—221no—
160C4×C22⋊C4—221no—
161#343—21no—
162#343C2×D1112yes—
163#324—112no—
164#323—221no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—22no—
168C22×C11—42no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—81no—
172C22×C11C2×#9911yescharacteristic
173C22×C11C2×#10311yescharacteristic
174C22×C11C2×#10411yescharacteristic
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11#32812yes—
182C4×C11#32812yes—
183Dic11—42no—
184Dic11—42no—
185Dic11—81no—
186Dic11—81no—
187C22×Q8—111no—
188C23×C4C22⋊D1111yescharacteristic
189C2×M16—24no—
190C2×M16—22no—
191C2×M16—41no—
192C2×M16—42no—
193C22×C8—41no—
194C4×Q8—441no—
195C4×Q8—441no—
196#117—41no—
197#117—41no—
198C2×C4⋊C4—111no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4C22⋊D1111yescharacteristic
204C2×C4⋊C4C22×D1111yescharacteristic
205C2×C22⋊C4—221no—
206C2×C22⋊C4—221no—
207C2×C22⋊C4C4×D1111yescharacteristic
208C2×C22⋊C4D4411yescharacteristic
209C2×C42—221no—
210C2×C42—221no—
211C2×C42C4×D1111yescharacteristic
212C2×C42D4411yescharacteristic
213C4⋊C8—441no—
214C22⋊C8—222no—
215C4×C8—441no—
216#95—111no—
217#95—111no—
218#95—221no—
219#95—221no—
220#95—221no—
221#95—221no—
222C2×C11—21no—
223C2×C11—21no—
224C2×C11—42no—
225C2×C11C2×#32811yescharacteristic
226C2×C11#212011yescharacteristic
227C2×C11#213211yescharacteristic
228C24(C2×D11)⋊C411yescharacteristic
229C2×Q8—441no—
230C2×Q8—442no—
231C22×C4—22no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—221no—
235C22×C4—221no—
236C22×C4—221no—
237C22×C4—221no—
238C22×C4(C2×D11)⋊C411yescharacteristic
239C22×C4(C2×D11)⋊C411yescharacteristic
240C22×C4(C2×D11)⋊C411yescharacteristic
241C22×C4#432412yes—
242C22×C4#432612yes—
243C22×C4C2×C4×D1111yescharacteristic
244C22×C4C2×D4411yescharacteristic
245C22×C4C2×C22⋊D1111yescharacteristic
246M16—24no—
247M16—44no—
248M16—42no—
249C2×C8—42no—
250C2×C8—44no—
251C2×C8—442no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—441no—
255C4⋊C4—442no—
256C4⋊C4—442no—
257C4⋊C4—442no—
258C4⋊C4—442no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—442no—
262C22⋊C4—442no—
263C42—21no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—442no—
268C42—441no—
269C42—441no—
270C11#1172111yescharacteristic, complemented, Sylow
271C23—21no—
272C23—21no—
273C23—41no—
274C23—41no—
275C23#6687412yes—
276C23C2×(C2×D11)⋊C411yescharacteristic
277Q8—442no—
278Q8—442no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—222no—
294C2×C4—222no—
295C2×C4—441no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4#6686912yes—
306C2×C4#6687011yescharacteristic
307C2×C4#6687011yescharacteristic
308C2×C4#6687412yes—
309C2×C4C2×#432411yescharacteristic
310C2×C4C2×#432611yescharacteristic
311C8—44no—
312C8—882no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—42no—
317C22—41no—
318C22—41no—
319C22—81no—
320C22C2×#6686911yescharacteristic
321C22C2×#6687011yescharacteristic
322C22C2×#6687411yescharacteristic
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—442no—
330C4—442no—
331C4—881no—
332C4—881no—
333C4#1062209012yes—
334C4#1062209012yes—
335C2—21no—
336C2—21no—
337C2—42no—
338C2C2×#1062209011yescharacteristic
339C2#1307025811yescharacteristic
340C2#1307029911yescharacteristic
subgroupG/H
centerC2×C4#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1742C2
socleC22×C11C2×#99
prime radicalC24×C11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1742D11
hypocenterC11#11721
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#117 ◁ #1742

Complements

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

NH ≅ G/Ntype
3. #13066645C2semidirect
4. #13066642C2semidirect
270. C11#11721semidirect

Maximal subgroups

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

subgroupindex
#130718842
#130669302
#130666452
#130666422
C11×#17422
#1172111