Finite Group Databasebeta

← #14664297

Subgroups — #14664297

Order 2816.

420 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 83 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#13074314C211yesmaximal, characteristic
2#13066950C211yesmaximal, characteristic
3#13066642C212yesmaximal, complemented
4#13066621C212yesmaximal, complemented
5C11×#1742C211yesmaximal, characteristic
6C22×C11×M16—21no—
7C2×C11×#117C2211yescharacteristic
8C2×#66923C411yescharacteristic
9#10622823—21no—
10#10622599C2211yescharacteristic
11#10622596C2211yescharacteristic
12#10622585—21no—
13#10622566C411yescharacteristic
14#10622562C411yescharacteristic
15#10622558—21no—
16#10622546—21no—
17#10622545C411yescharacteristic
18#10622539—21no—
19C11×#343—21no—
20C11×#343C2212yes—
21#10622166C2212yes—
22#10622163—21no—
23C23×C4×C11D411yescharacteristic
24C2×C11×M16—24no—
25C2×C11×M16—22no—
26C2×C11×M16—41no—
27C2×C11×M16—42no—
28C22×C8×C11—41no—
29C11×#117—41no—
30C11×#117—41no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C4⋊C4C2311yescharacteristic
33C2×C11×C22⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11—21no—
46#66923—41no—
47#66923—41no—
48C11⋊#95—21no—
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—
57#66867—41no—
58#11767—111nomaximal, Sylow
59C24×C11C22⋊C411yescharacteristic
60C22×C4×C11—22no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C11×M16—24no—
76C11×M16—44no—
77C11×M16—42no—
78C2×C8×C11—44no—
79C2×C8×C11—42no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C22⋊C4—41no—
83C11×C22⋊C4—41no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11—21no—
88C22⋊Dic11—42no—
89C22⋊Dic11—42no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92Dic11⋊C4—42no—
93Dic11⋊C4—42no—
94Dic11⋊C4—41no—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97Dic11⋊C4—41no—
98C4×Dic11—42no—
99C2×C11⋊C8—42no—
100#2611—111no—
101#1742D1111yescharacteristic
102#1464—111no—
103#1353—112no—
104#1346—112no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11#10412yes—
110C23×C11C2×C22⋊C411yescharacteristic
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11#9911yescharacteristic
128C2×C4×C11#9911yescharacteristic
129C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C11#13711yescharacteristic
131C2×Dic11—22no—
132C2×Dic11—41no—
133C2×Dic11—41no—
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—
143C8×C11—44no—
144C11⋊C8—82no—
145C22×M16—21no—
146C2×#125—111no—
147C2×#117C2×D1111yescharacteristic
148#432—221no—
149#400—111no—
150#399—111no—
151#398—111no—
152#397—111no—
153#389—221no—
154#388—221no—
155#387—221no—
156#385—221no—
157#376—111no—
158#343—21no—
159#343C2×D1112yes—
160#324—112no—
161#323—221no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—22no—
165C22×C11—42no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—81no—
169C22×C11C2×#9911yescharacteristic
170C22×C11#41711yescharacteristic
171C22×C11C2×#10411yescharacteristic
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—41no—
180Dic11—42no—
181Dic11—81no—
182Dic11—81no—
183Dic11—81no—
184C23×C4C22⋊D1111yescharacteristic
185C2×M16—24no—
186C2×M16—22no—
187C2×M16—41no—
188C2×M16—42no—
189C22×C8—41no—
190#125—441no—
191#125—441no—
192#117—41no—
193#117—41no—
194C2×C4⋊C4—111no—
195C2×C4⋊C4—111no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4C22⋊D1111yescharacteristic
201C2×C4⋊C4C22×D1111yescharacteristic
202C2×C22⋊C4—221no—
203C2×C22⋊C4—221no—
204C2×C22⋊C4C4×D1111yescharacteristic
205C2×C22⋊C4D4411yescharacteristic
206C2×C42—221no—
207C2×C42C4×D1111yescharacteristic
208C2×C42D4411yescharacteristic
209C4⋊C8—441no—
210C22⋊C8—222no—
211#97—441no—
212#95—111no—
213#95—111no—
214#95—221no—
215#95—221no—
216#95—221no—
217#95—221no—
218#95—221no—
219C2×C11—21no—
220C2×C11—21no—
221C2×C11—42no—
222C2×C11#150411yescharacteristic
223C2×C11#212311yescharacteristic
224C2×C11#213211yescharacteristic
225C24(C2×D11)⋊C411yescharacteristic
226C22×C4—22no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—221no—
232C22×C4—221no—
233C22×C4—221no—
234C22×C4—221no—
235C22×C4(C2×D11)⋊C411yescharacteristic
236C22×C4(C2×D11)⋊C411yescharacteristic
237C22×C4(C2×D11)⋊C411yescharacteristic
238C22×C4C2×C4×D1111yescharacteristic
239C22×C4C2×D4411yescharacteristic
240C22×C4C2×C22⋊D1111yescharacteristic
241M16—24no—
242M16—44no—
243M16—42no—
244C2×C8—44no—
245C2×C8—42no—
246C2×C8—442no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—441no—
250C4⋊C4—441no—
251C4⋊C4—442no—
252C4⋊C4—442no—
253C4⋊C4—441no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C4⋊C4—441no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—442no—
260C22⋊C4—442no—
261C42—21no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—442no—
266C11#1176711yescharacteristic, complemented, Sylow
267C23—21no—
268C23—21no—
269C23—41no—
270C23—41no—
271C23#6686912yes—
272C23C2×(C2×D11)⋊C411yescharacteristic
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—222no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4#6687011yescharacteristic
302C2×C4#6687011yescharacteristic
303C2×C4#6698511yescharacteristic
304C2×C4#6699511yescharacteristic
305C8—44no—
306C8—882no—
307C22—21no—
308C22—21no—
309C22—22no—
310C22—42no—
311C22—41no—
312C22—41no—
313C22—81no—
314C22C2×#6686911yescharacteristic
315C22C2×#6687011yescharacteristic
316C22#1062257911yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—442no—
326C4—881no—
327C4—881no—
328C4—881no—
329C2—21no—
330C2—21no—
331C2—42no—
332C2#1306711811yescharacteristic
333C2#1307027111yescharacteristic
334C2#1307029911yescharacteristic
subgroupG/H
centerC22C2×#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#11767
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1742

Complements

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

NH ≅ G/Ntype
3. #13066642C2semidirect
4. #13066621C2semidirect
266. C11#11767semidirect

Maximal subgroups

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

subgroupindex
#130743142
#130669502
#130666422
#130666212
C11×#17422
#1176711