Finite Group Databasebeta

← #14664597

Subgroups — #14664597

Order 2816.

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

normal subgroups only

This group has 382 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#13074476C211yesmaximal, characteristic
2#13066960C211yesmaximal, characteristic, complemented
3#13066645C212yesmaximal, complemented
4#13066618C212yesmaximal
5C11×#1801C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#66928C411yescharacteristic
8C11×#423—21no—
9C2×C11×#101—21no—
10#10622844—21no—
11#10622605—21no—
12#10622604C411yescharacteristic
13#10622604C2211yescharacteristic
14#10622592C411yescharacteristic
15#10622592C2211yescharacteristic
16#10622553—21no—
17#10622553—21no—
18#10622550C411yescharacteristic
19#10622539—21no—
20C11×#343C2212yes—
21#10622166—21no—
22#10622166C2212yes—
23C22×Q8×C11D411yescharacteristic
24C22×D44C2×C411yescharacteristic
25C22×Dic22C2×C411yescharacteristic
26C2×C11×M16—22no—
27C4×Q8×C11—41no—
28C4×Q8×C11—41no—
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43#66928—41no—
44#66928—41no—
45C11×C4⋊C8—41no—
46C11×C4⋊C8—41no—
47C11×#101—42no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95C2×C411yescharacteristic
53C11⋊#95C2×C411yescharacteristic
54C22⋊(C11⋊C8)—22no—
55C4⋊(C11⋊C8)—41no—
56#66867—41no—
57#11833—111nomaximal, Sylow
58C23×D11—21no—
59C2×Q8×C11—21no—
60C2×Q8×C11—21no—
61C2×Q8×C11—41no—
62C2×Q8×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
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—21no—
73C2×D44—41no—
74C2×D44—81no—
75C2×Dic22—41no—
76C2×Dic22—81no—
77C11×M16—42no—
78C11×M16—42no—
79C2×C8×C11—42no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C42×C11—21no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—21no—
89(C2×D11)⋊C4—42no—
90(C2×D11)⋊C4—42no—
91(C2×D11)⋊C4—41no—
92(C2×D11)⋊C4—41no—
93(C2×D11)⋊C4—41no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—81no—
96(C2×D11)⋊C4—81no—
97Dic11⋊C4—81no—
98Dic11⋊C4—81no—
99C2×C11⋊C8—42no—
100#2632—111no—
101#1801D1111yescharacteristic, complemented
102#1467—111no—
103#1354—112no—
104#1345—112no—
105C23×C11C2×C22⋊C411yescharacteristic
106C22×D11—41no—
107C22×D11—41no—
108C22×D11—41no—
109C22×D11—41no—
110C22×D11—41no—
111C22×D11—41no—
112C22×D11—41no—
113Q8×C11—42no—
114Q8×C11—42no—
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—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11#9911yescharacteristic
131C2×C4×C11#9911yescharacteristic
132C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C11#13711yescharacteristic
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—
143D44—82no—
144Dic22—82no—
145C8×C11—82no—
146C11⋊C8—82no—
147C2×#124—111no—
148C2×C4×Q8C2×D1111yescharacteristic
149#432—221no—
150#423—21no—
151C2×#101—21no—
152#399—221no—
153#395—111no—
154#395—111no—
155#394—111no—
156#394—111no—
157#393—221no—
158#388—221no—
159#388—221no—
160#383—111no—
161#343C2×D1112yes—
162#324—112no—
163#324—221no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11C2×#9911yescharacteristic
167C22×C11#41711yescharacteristic
168C22×C11#42111yescharacteristic
169C2×D11—81no—
170C2×D11—81no—
171C2×D11—81no—
172C2×D11—81no—
173C2×D11—81no—
174C2×D11—81no—
175C2×D11—81no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—41no—
185Dic11—81no—
186Dic11—81no—
187Dic11—81no—
188C22×Q8—111no—
189C22×Q8C22⋊D1111yescharacteristic
190C22×D4—111no—
191C2×M16—22no—
192#124—441no—
193#124—441no—
194C4×Q8—41no—
195C4×Q8—41no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4C4×D1111yescharacteristic
199C2×C4⋊C4D4411yescharacteristic
200C2×C4⋊C4C22×D1111yescharacteristic
201C2×C22⋊C4—221no—
202C2×C22⋊C4—221no—
203C2×C22⋊C4—221no—
204C2×C22⋊C4—221no—
205C2×C22⋊C4—221no—
206C2×C22⋊C4—221no—
207C2×C42C4×D1111yescharacteristic
208C2×C42D4411yescharacteristic
209C2×C42C22⋊D1111yescharacteristic
210C4⋊C8—41no—
211C4⋊C8—41no—
212C4⋊C8—441no—
213#101—42no—
214C22⋊C8—222no—
215#97—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#151311yescharacteristic
225C2×C11#212211yescharacteristic
226C2×C11#213311yescharacteristic
227D11—161no—
228C24—221no—
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—441no—
234C2×Q8—881no—
235C2×D4—441no—
236C2×D4—881no—
237C22×C4—221no—
238C22×C4—221no—
239C22×C4—221no—
240C22×C4(C2×D11)⋊C411yescharacteristic
241C22×C4(C2×D11)⋊C411yescharacteristic
242C22×C4(C2×D11)⋊C411yescharacteristic
243C22×C4(C2×D11)⋊C411yescharacteristic
244C22×C4C2×C4×D1111yescharacteristic
245C22×C4C2×D4411yescharacteristic
246C22×C4C2×C22⋊D1111yescharacteristic
247M16—42no—
248M16—42no—
249C2×C8—42no—
250C2×C8—442no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—881no—
255C4⋊C4—881no—
256C22⋊C4—442no—
257C22⋊C4—442no—
258C22⋊C4—441no—
259C22⋊C4—441no—
260C22⋊C4—441no—
261C22⋊C4—441no—
262C22⋊C4—881no—
263C22⋊C4—881no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C11#1183311yescharacteristic, complemented, Sylow
271C23—441no—
272C23—441no—
273C23—441no—
274C23—441no—
275C23—441no—
276C23—441no—
277C23—441no—
278C23C2×(C2×D11)⋊C411yescharacteristic
279Q8—42no—
280Q8—42no—
281Q8—882no—
282D4—882no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4#6687011yescharacteristic
308C2×C4#6687011yescharacteristic
309C2×C4#6698511yescharacteristic
310C2×C4#6699511yescharacteristic
311C8—82no—
312C8—882no—
313C22—21no—
314C22—21no—
315C22—881no—
316C22—881no—
317C22—881no—
318C22—881no—
319C22—881no—
320C22—881no—
321C22—881no—
322C22C2×#6687011yescharacteristic
323C22#1062257911yescharacteristic
324C22#1062261811yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—881no—
335C4—881no—
336C4—881no—
337C2—21no—
338C2—21no—
339C2—1761no—
340C2#1306715711yescharacteristic
341C2#1307026711yescharacteristic
342C2#1307030311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1801C2
socleC22×C11C2×#99
prime radicalC22×D44C2×C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1801D11
hypocenterC11#11833
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
2. #13066960C2semidirect
3. #13066645C2semidirect
5. C11×#1801C2semidirect
101. #1801D11semidirect
270. C11#11833semidirect

Maximal subgroups

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

subgroupindex
#130744762
#130669602
#130666452
#130666182
C11×#18012
#1183311