Finite Group Databasebeta

← #14664151

Subgroups — #14664151

Order 2816.

402 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 73 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#13071906C211yesmaximal, characteristic
2#13068411C211yesmaximal, characteristic
3#13066938C211yesmaximal, characteristic
4#13066646C211yesmaximal, characteristic
5#13066623C211yesmaximal, characteristic
6#13066621C211yesmaximal, characteristic
7C11×#1354C211yesmaximal, characteristic
8C2×Q8×Dic11C411yescharacteristic
9C2×#66940C2211yescharacteristic
10C11×#395C2211yescharacteristic
11#10622842C411yescharacteristic
12C2×#66888—21no—
13M16×Dic11—21no—
14#10622597—21no—
15#10622596C2211yescharacteristic
16C4⋊C4×Dic11—21no—
17#10622331—21no—
18#10622274C411yescharacteristic
19#10622269—21no—
20#10622262—21no—
21#10622261C411yescharacteristic
22C11×#343C2211yescharacteristic
23C11×#324C2211yescharacteristic
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622107—21no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×Dic22D411yescharacteristic
29C2×C11×M16—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4C2311yescharacteristic
32Q8×Dic11—41no—
33Q8×Dic11—41no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11C2×C411yescharacteristic
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4C2×C411yescharacteristic
40C2×Dic11⋊C4D411yescharacteristic
41C2×C4×Dic11—21no—
42C2×C4×Dic11—21no—
43C2×C4×Dic11C2×C411yescharacteristic
44C2×C4×Dic11D411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C2×#4318—21no—
47#66940—41no—
48#66940—41no—
49C11×C22⋊C8—21no—
50C11×#95—21no—
51C11×#95C2×C411yescharacteristic
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95C2×C411yescharacteristic
57C22⋊(C11⋊C8)—21no—
58#66888—24no—
59#66879—41no—
60Dic11⋊C8—41no—
61C8×Dic11—41no—
62C8×Dic11—41no—
63#11736—111nomaximal, Sylow
64C2×Q8×C11—42no—
65C2×Q8×C11—41no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C411yescharacteristic
75C22×Dic11C22⋊C411yescharacteristic
76C22×Dic11C22⋊C411yescharacteristic
77C2×Dic22—22no—
78C2×Dic22—21no—
79C2×Dic22—21no—
80C2×Dic22—41no—
81C11×M16—22no—
82C11×M16—41no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—42no—
87C4⋊Dic11—41no—
88C4⋊Dic11—42no—
89C4⋊Dic11—42no—
90Dic11⋊C4—41no—
91Dic11⋊C4—41no—
92Dic11⋊C4—42no—
93Dic11⋊C4—41no—
94Dic11⋊C4—41no—
95C4×Dic11—24no—
96C4×Dic11—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—41no—
103C4×Dic11—41no—
104#4318—22no—
105#4318—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108#2399—111no—
109C4×#101—111no—
110#1461—111no—
111#1354—111no—
112#1354D1111yescharacteristic
113#1346—111no—
114#1346—111no—
115C23×C11C2×C22⋊C411yescharacteristic
116Q8×C11—42no—
117Q8×C11—42no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—22no—
121C2×C4×C11—22no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11#13511yescharacteristic
131C2×C4×C11#13511yescharacteristic
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—22no—
135C2×Dic11—22no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11#9911yescharacteristic
147C2×Dic11#9911yescharacteristic
148C2×Dic11#10412yes—
149Dic22—42no—
150Dic22—42no—
151C8×C11—42no—
152C8×C11—81no—
153C11⋊C8—42no—
154C11⋊C8—81no—
155C2×C4×Q8—111no—
156C2×C4×Q8—111no—
157#431—221no—
158C2×#101—221no—
159C4×M16—221no—
160#398—111no—
161#398—111no—
162#398—221no—
163#395—111no—
164#395—221no—
165#395C2×D1111yescharacteristic
166C4×C4⋊C4—221no—
167C4×C4⋊C4—221no—
168#376—111no—
169#343—111no—
170#343C2×D1111yescharacteristic
171#324—111no—
172#324—221no—
173#324C2×D1111yescharacteristic
174C22×C11—21no—
175C22×C11—21no—
176C22×C11C2×#9911yescharacteristic
177C22×C11#41611yescharacteristic
178C22×C11C2×#10411yescharacteristic
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—42no—
182C4×C11—42no—
183C4×C11—41no—
184C4×C11—41no—
185Dic11—21no—
186Dic11—22no—
187Dic11—42no—
188Dic11—41no—
189Dic11—41no—
190Dic11—81no—
191Dic11#35612yes—
192C22×Q8—111no—
193C22×Q8C4×D1111yescharacteristic
194C2×M16—21no—
195C2×M16—221no—
196C4×Q8—441no—
197C4×Q8—441no—
198C4×Q8—441no—
199C4×Q8—441no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—111no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4C22×D1111yescharacteristic
209C2×C42—111no—
210C2×C42—111no—
211C2×C42—111no—
212C2×C42—221no—
213C2×C42—221no—
214C4⋊C8—441no—
215#101—224no—
216C22⋊C8—21no—
217C22⋊C8—221no—
218#97—441no—
219C4×C8—441no—
220C4×C8—441no—
221#95—21no—
222#95—111no—
223#95—221no—
224#95—221no—
225#95—221no—
226#95—221no—
227#95C4×D1111yescharacteristic
228C2×C11—21no—
229C2×C11—21no—
230C2×C11#150111yescharacteristic
231C2×C11#212011yescharacteristic
232C2×C11C2×#35611yescharacteristic
233C2×Q8—42no—
234C2×Q8—41no—
235C2×Q8—222no—
236C2×Q8—221no—
237C2×Q8—221no—
238C2×Q8—441no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—111no—
242C22×C4—111no—
243C22×C4—111no—
244C22×C4—111no—
245C22×C4—221no—
246C22×C4—221no—
247C22×C4C2×C4×D1111yescharacteristic
248C22×C4D4×D1111yescharacteristic
249C22×C4D4×D1111yescharacteristic
250M16—22no—
251M16—41no—
252M16—222no—
253M16—441no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—441no—
257C2×C8—441no—
258C4⋊C4—41no—
259C4⋊C4—42no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4—442no—
264C4⋊C4—442no—
265C4⋊C4—442no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C42—221no—
269C42—221no—
270C42—221no—
271C42—221no—
272C42—221no—
273C42—221no—
274C42—224no—
275C42—441no—
276C42—441no—
277C11#1173611yescharacteristic, complemented, Sylow
278C23C22⋊C4×D1111yescharacteristic
279Q8—42no—
280Q8—42no—
281Q8—442no—
282Q8—442no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—111no—
296C2×C4—111no—
297C2×C4—112no—
298C2×C4—222no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—222no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4#6696911yescharacteristic
313C2×C4#6697211yescharacteristic
314C8—42no—
315C8—81no—
316C8—442no—
317C8—881no—
318C22—21no—
319C22—21no—
320C22D11×#9911yescharacteristic
321C22#1062241711yescharacteristic
322C22D11×#10411yescharacteristic
323C4—21no—
324C4—21no—
325C4—42no—
326C4—41no—
327C4—42no—
328C4—41no—
329C4—112no—
330C4—222no—
331C4—221no—
332C4—442no—
333C4—441no—
334C4—441no—
335C4—881no—
336C2—21no—
337C2—21no—
338C2#1306710611yescharacteristic
339C2#1307025411yescharacteristic
340C2D11×#35611yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1354C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1354D11
hypocenterC11#11736
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
277. C11#11736semidirect

Maximal subgroups

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

subgroupindex
#130719062
#130684112
#130669382
#130666462
#130666232
#130666212
C11×#13542
#1173611