Finite Group Databasebeta

← #14664657

Subgroups — #14664657

Order 2816.

432 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 79 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#13074303C211yesmaximal, characteristic
2#13068693C211yesmaximal, characteristic, complemented
3#13066638C212yesmaximal, complemented
4#13066614C212yesmaximal
5C11×#1458C211yesmaximal, characteristic, complemented
6C2×C11×#117C2211yescharacteristic
7C2×#66928C411yescharacteristic, complemented
8C11×#431—21no—
9#10622826—21no—
10#10622824—21no—
11#10622604C411yescharacteristic, complemented
12#10622603—21no—
13#10622592C411yescharacteristic, complemented
14#10622573C2211yescharacteristic
15#10622570—21no—
16#10622560C2211yescharacteristic
17#10622553—21no—
18#10622545C411yescharacteristic, complemented
19C11×#324—21no—
20C11×#323C2212yes—
21#10622164—21no—
22#10622164C2212yes—
23C23×C4×C11D411yescharacteristic
24C22×C22⋊D11—21no—
25C22×D44C2×C411yescharacteristic
26C22×Dic22C2×C411yescharacteristic
27C11×#117—41no—
28C11×#117—41no—
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C22⋊C4D411yescharacteristic
32C2×C11×C22⋊C4C2311yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C22⋊Dic11—22no—
36C2×C22⋊Dic11—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11—21no—
44#66928—41no—
45#66928—41no—
46C11×C4⋊C8—41no—
47C11×C22⋊C8—22no—
48C4×C8×C11—41no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—41no—
53C11⋊#95—41no—
54C11⋊#95C2×C411yescharacteristic
55C11⋊#95C2×C411yescharacteristic
56#11844—111nomaximal, Sylow
57C24×C11C2×D411yescharacteristic
58C23×D11—21no—
59C22×C4×C11—22no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—41no—
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C2×C22⋊D11—42no—
70C2×C22⋊D11—42no—
71C2×C22⋊D11—81no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—42no—
76C2×D44—41no—
77C2×D44—81no—
78C2×Dic22—41no—
79C2×Dic22—81no—
80C2×C8×C11—42no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—41no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—21no—
89C22⋊Dic11—42no—
90C22⋊Dic11—42no—
91C22⋊Dic11—81no—
92(C2×D11)⋊C4—42no—
93(C2×D11)⋊C4—42no—
94(C2×D11)⋊C4—42no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—41no—
97(C2×D11)⋊C4—81no—
98Dic11⋊C4—81no—
99C4×Dic11—42no—
100#2610—111no—
101#1820—111no—
102#1458D1111yescharacteristic, complemented
103#1351—112no—
104#1343—112no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11C2×C22⋊C411yescharacteristic
110C23×C11#13512yes—
111C22×D11—41no—
112C22×D11—41no—
113C22×D11—41no—
114C22×D11—41no—
115C22×D11—41no—
116C22×D11—41no—
117C22×D11—41no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
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×C11—42no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11#9911yescharacteristic
134C2×C4×C11#9911yescharacteristic
135C22⋊D11—84no—
136C2×Dic11—22no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—82no—
146C2×Dic11—82no—
147C2×Dic11—82no—
148D44—82no—
149Dic22—82no—
150C8×C11—82no—
151C2×#124—111no—
152C2×#117C2×D1111yescharacteristic
153#431—21no—
154#395—111no—
155#394—111no—
156#393—111no—
157#392—111no—
158#390—221no—
159#388—221no—
160#388—221no—
161#386—221no—
162#381—221no—
163#376—111no—
164#342—112no—
165#342—221no—
166#324—21no—
167#323C2×D1112yes—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—22no—
171C22×C11—42no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—81no—
175C22×C11C2×#9911yescharacteristic
176C22×C11#41611yescharacteristic
177C22×C11#42111yescharacteristic
178C2×D11—81no—
179C2×D11—81no—
180C2×D11—81no—
181C2×D11—81no—
182C2×D11—81no—
183C2×D11—81no—
184C2×D11—81no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—41no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—41no—
192Dic11—42no—
193Dic11—81no—
194Dic11—81no—
195Dic11—162no—
196C22×Q8—111no—
197C22×D4—111no—
198C22×D4—221no—
199C23×C4D4411yescharacteristic
200#124—441no—
201#124—441no—
202#117—41no—
203#117—41no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4C4×D1111yescharacteristic
206C2×C4⋊C4C22⋊D1111yescharacteristic
207C2×C22⋊C4—221no—
208C2×C22⋊C4—221no—
209C2×C22⋊C4—221no—
210C2×C22⋊C4—221no—
211C2×C22⋊C4—222no—
212C2×C22⋊C4—221no—
213C2×C22⋊C4—221no—
214C2×C22⋊C4D4411yescharacteristic
215C2×C22⋊C4C22×D1111yescharacteristic
216C2×C42—221no—
217C2×C42C4×D1111yescharacteristic
218C2×C42C22⋊D1111yescharacteristic
219C4⋊C8—41no—
220C22⋊C8—22no—
221C4×C8—41no—
222#95—111no—
223#95—111no—
224#95—221no—
225#95—221no—
226#95—221no—
227#95—441no—
228#95—441no—
229C2×C11—21no—
230C2×C11—21no—
231C2×C11—42no—
232C2×C11#151611yescharacteristic
233C2×C11#212211yescharacteristic
234C2×C11#212611yescharacteristic
235D11—161no—
236C24—221no—
237C24C2×D4411yescharacteristic
238C2×Q8—441no—
239C2×Q8—881no—
240C2×D4—441no—
241C2×D4—442no—
242C2×D4—442no—
243C2×D4—881no—
244C2×D4—881no—
245C22×C4—22no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—41no—
249C22×C4—221no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—442no—
253C22×C4(C2×D11)⋊C411yescharacteristic
254C22×C4(C2×D11)⋊C411yescharacteristic
255C22×C4(C2×D11)⋊C411yescharacteristic
256C22×C4(C2×D11)⋊C411yescharacteristic
257C22×C4C2×C4×D1111yescharacteristic
258C22×C4C2×C22⋊D1111yescharacteristic
259C2×C8—42no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—881no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—442no—
266C22⋊C4—442no—
267C22⋊C4—442no—
268C22⋊C4—441no—
269C22⋊C4—441no—
270C22⋊C4—442no—
271C22⋊C4—442no—
272C22⋊C4—881no—
273C22⋊C4—881no—
274C42—21no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42—442no—
279C11#1184411yescharacteristic, complemented, Sylow
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—441no—
285C23—441no—
286C23—441no—
287C23—441no—
288C23—441no—
289C23—441no—
290C23—441no—
291C23#6695712yes—
292C23C2×(C2×D11)⋊C411yescharacteristic
293Q8—882no—
294D4—882no—
295D4—884no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—222no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—882no—
321C2×C4—882no—
322C2×C4—882no—
323C2×C4#6687011yescharacteristic
324C2×C4#6687011yescharacteristic
325C8—82no—
326C22—21no—
327C22—21no—
328C22—22no—
329C22—42no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22—881no—
334C22—881no—
335C22—881no—
336C22—881no—
337C22—881no—
338C22—881no—
339C22—881no—
340C22C2×#6687011yescharacteristic
341C22#1062272611yescharacteristic
342C22#1062275211yescharacteristic
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—442no—
351C4—881no—
352C4—881no—
353C4—1762no—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—1761no—
358C2#1306717311yescharacteristic
359C2#1307026711yescharacteristic
360C2#1307027911yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1458C2
socleC22×C11C2×#99
prime radical#10622573C22
cosocleC2×C11×C22⋊C4C23
hypercenter#1458D11
hypocenterC11#11844
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
2. #13068693C2semidirect
3. #13066638C2semidirect
5. C11×#1458C2semidirect
7. C2×#66928C4semidirect
11. #10622604C4semidirect
13. #10622592C4semidirect
18. #10622545C4semidirect
102. #1458D11semidirect
279. C11#11844semidirect

Maximal subgroups

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

subgroupindex
#130743032
#130686932
#130666382
#130666142
C11×#14582
#1184411