Finite Group Databasebeta

← #14647813

Subgroups — #14647813

Order 2816.

348 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 95 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#13077700C211yesmaximal, characteristic
2#13069555C211yesmaximal, characteristic
3#13067399C211yesmaximal, characteristic
4#13066939C211yesmaximal, characteristic
5#13066516C211yesmaximal, characteristic
6#13066514C211yesmaximal, characteristic
7C11×#1573C211yesmaximal, characteristic
8C2×C4×Dic22C2211yescharacteristic
9C11×#432C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12#10622539C2211yescharacteristic
13#10622538C2211yescharacteristic
14C2×#66867C2211yescharacteristic
15#10622441—21no—
16#10622441—21no—
17#10622332—21no—
18#10622331—21no—
19#10622314—21no—
20#10622314—21no—
21C11×#335—21no—
22C11×#334—21no—
23#10622188—21no—
24#10622188—21no—
25#10622118—21no—
26#10622117—21no—
27#10622107C412yes—
28#10622107C412yes—
29C22×Dic22Q811yescharacteristic
30C22×C8×C11—21no—
31C2×C42×C11C2311yescharacteristic
32C2×C4⋊Dic11Q811yescharacteristic
33C2×Dic11⋊C4C2×C411yescharacteristic
34C2×Dic11⋊C4C2×C411yescharacteristic
35C2×C4×Dic11D411yescharacteristic
36C2×C4×Dic11D411yescharacteristic
37C22×C11⋊C8—21no—
38C4×Dic22—21no—
39C4×Dic22—21no—
40C4×Dic22—21no—
41C4×Dic22—21no—
42C11×C4⋊C8—21no—
43C11×C4⋊C8—21no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8D411yescharacteristic
46C11×C4⋊C8D411yescharacteristic
47C11×C22⋊C8—21no—
48C11×C22⋊C8C2×C412yes—
49C11×#97—21no—
50C4×C8×C11—21no—
51C22⋊(C11⋊C8)—21no—
52C22⋊(C11⋊C8)C2×C412yes—
53#66879—21no—
54#66879—21no—
55Dic11⋊C8—21no—
56Dic11⋊C8—21no—
57Dic11⋊C8—21no—
58Dic11⋊C8—21no—
59C8×Dic11—21no—
60C8×Dic11—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)D411yescharacteristic
63C4⋊(C11⋊C8)D411yescharacteristic
64#66867—21no—
65#66867—21no—
66#66867—21no—
67C4×C11⋊C8—21no—
68#8865—111nomaximal, Sylow
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×Q811yescharacteristic
72C22×Dic11C4⋊C411yescharacteristic
73C22×Dic11C4⋊C411yescharacteristic
74C22×Dic11C4⋊C411yescharacteristic
75C22×Dic11C4⋊C411yescharacteristic
76C2×Dic22—22no—
77C2×Dic22—21no—
78C2×Dic22—21no—
79C2×Dic22—41no—
80C2×C8×C11—22no—
81C2×C8×C11—21no—
82C2×C8×C11—21no—
83C2×C8×C11—42no—
84C2×C8×C11—41no—
85C42×C11C2×D411yescharacteristic
86C42×C11C2×D411yescharacteristic
87C42×C11#4111yescharacteristic
88C42×C11#4111yescharacteristic
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95C4×Dic11—21no—
96C4×Dic11—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C2×C11⋊C8—22no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105#2983—111no—
106#1985—111no—
107#1573—111no—
108#1573D1111yescharacteristic
109#1461—111no—
110#1302—111no—
111#1302—111no—
112C23×C11C2×C4⋊C411yescharacteristic
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—41no—
118C2×C4×C11C4×D411yescharacteristic
119C2×C4×C11C4×D411yescharacteristic
120C2×C4×C11#12011yescharacteristic
121C2×C4×C11C22⋊Q811yescharacteristic
122C2×C4×C11C22⋊Q811yescharacteristic
123C2×C4×C11#12311yescharacteristic
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11#10812yes—
134Dic22—42no—
135Dic22—42no—
136C8×C11—42no—
137C8×C11—41no—
138C8×C11—41no—
139C8×C11—81no—
140C11⋊C8—42no—
141C11⋊C8—42no—
142C11⋊C8—41no—
143C11⋊C8—41no—
144C2×C4×Q8—111no—
145#446—221no—
146#446—221no—
147#446—221no—
148#446—221no—
149#432—111no—
150#432—221no—
151#432C2×D1111yescharacteristic
152#431—111no—
153#431—221no—
154#431C2×D1111yescharacteristic
155C2×C4⋊C8C2×D1111yescharacteristic
156C2×#97—111no—
157#336—221no—
158#336—221no—
159#335—21no—
160#335—221no—
161#334—21no—
162#334—221no—
163#324—112no—
164#324—112no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11#38511yescharacteristic
168C22×C11C2×#10811yescharacteristic
169C22×C11#43011yescharacteristic
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11#45411yescharacteristic
176C4×C11#45611yescharacteristic
177Dic11—22no—
178Dic11—41no—
179Dic11—41no—
180Dic11—41no—
181C22×Q8—111no—
182C22×C8—21no—
183C22×C8—221no—
184C4×Q8—221no—
185C4×Q8—221no—
186C4×Q8—221no—
187C4×Q8—221no—
188C2×C4⋊C4—111no—
189C2×C4⋊C4—111no—
190C2×C4⋊C4—111no—
191C2×C42—111no—
192C2×C42—111no—
193C2×C42C22×D1111yescharacteristic
194C4⋊C8—21no—
195C4⋊C8—21no—
196C4⋊C8—21no—
197C4⋊C8—111no—
198C4⋊C8—111no—
199C4⋊C8—221no—
200C4⋊C8—221no—
201C4⋊C8—221no—
202C4⋊C8—221no—
203C4⋊C8—221no—
204C4⋊C8C22⋊D1111yescharacteristic
205C4⋊C8C22⋊D1111yescharacteristic
206C22⋊C8—21no—
207C22⋊C8—112no—
208C22⋊C8—221no—
209C22⋊C8C4×D1112yes—
210#97—21no—
211#97—221no—
212#97—221no—
213#97—221no—
214#97—221no—
215#97—221no—
216C4×C8—21no—
217C4×C8—221no—
218C4×C8—221no—
219C4×C8—221no—
220C2×C11—21no—
221C2×C11—21no—
222C2×C11#185511yescharacteristic
223C2×C11#185711yescharacteristic
224C2×C11#186811yescharacteristic
225C2×Q8—222no—
226C2×Q8—221no—
227C2×Q8—221no—
228C2×Q8—441no—
229C22×C4—111no—
230C22×C4—111no—
231C22×C4—111no—
232C22×C4—111no—
233C22×C4C2×C4×D1111yescharacteristic
234C22×C4D4×D1111yescharacteristic
235C22×C4Q8×D1111yescharacteristic
236C2×C8—22no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—42no—
240C2×C8—41no—
241C2×C8—222no—
242C2×C8—222no—
243C2×C8—221no—
244C2×C8—221no—
245C2×C8—441no—
246C2×C8—441no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C42—221no—
254C42—221no—
255C42—221no—
256C42—221no—
257C42#433911yescharacteristic
258C42D4×D1111yescharacteristic
259C42#434311yescharacteristic
260C42C2×C22⋊D1111yescharacteristic
261C11#886511yescharacteristic, complemented, Sylow
262C23C4⋊C4×D1111yescharacteristic
263Q8—442no—
264Q8—442no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—112no—
271C2×C4—221no—
272C2×C4—221no—
273C2×C4—221no—
274C2×C4—221no—
275C2×C4—221no—
276C2×C4—221no—
277C2×C4—221no—
278C2×C4—441no—
279C2×C4—441no—
280C2×C4#6694611yescharacteristic
281C2×C4#6694711yescharacteristic
282C2×C4#6694911yescharacteristic
283C2×C4C4×C22⋊D1111yescharacteristic
284C2×C4#6699011yescharacteristic
285C2×C4#6699911yescharacteristic
286C8—42no—
287C8—41no—
288C8—41no—
289C8—81no—
290C8—442no—
291C8—442no—
292C8—441no—
293C8—441no—
294C22—21no—
295C22—21no—
296C22D11×#10811yescharacteristic
297C22#1062250611yescharacteristic
298C22#1062260211yescharacteristic
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—222no—
305C4—441no—
306C4—441no—
307C4—441no—
308C4#1062281411yescharacteristic
309C4#1062281811yescharacteristic
310C2—21no—
311C2—21no—
312C2#1306881911yescharacteristic
313C2#1306882911yescharacteristic
314C2#1306890011yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1573C2
socleC22×C11#385
prime radicalC23×C11C2×C4⋊C4
cosocleC2×C42×C11C23
hypercenter#1573D11
hypocenterC11#8865
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
261. C11#8865semidirect

Maximal subgroups

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

subgroupindex
#130777002
#130695552
#130673992
#130669392
#130665162
#130665142
C11×#15732
#886511