Finite Group Databasebeta

← #14666722

Subgroups — #14666722

Order 2816.

350 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 55 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#13076416C211yesmaximal, characteristic
2#13069958C211yesmaximal, characteristic
3#13067590C211yesmaximal, characteristic
4#13066647C211yesmaximal, characteristic
5#13066622C211yesmaximal, characteristic
6#13066561C211yesmaximal, characteristic
7C11×#1611C211yesmaximal, characteristic
8C11×#544C2211yescharacteristic
9C11×#483—21no—
10C11×#398C2211yescharacteristic
11#10622663—21no—
12#10622608—21no—
13#10622598—21no—
14#10622596—21no—
15#10622592C2211yescharacteristic
16#10622591—21no—
17#10622589C2211yescharacteristic
18#10622269—21no—
19#10622265—21no—
20#10622260—21no—
21C11×#328—21no—
22C11×#324C2211yescharacteristic
23#10622176—21no—
24#10622170—21no—
25#10622168C2211yescharacteristic
26#10622166C2211yescharacteristic
27C22×Dic22D411yescharacteristic
28C11×C4⋊Q8—41no—
29C11×#125—41no—
30C11×C22⋊Q8—21no—
31C11×C22⋊Q8—21no—
32C11×#117—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4C2311yescharacteristic
36C2×#4326—41no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11D411yescharacteristic
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×C4×Dic11—21no—
45C2×C4×Dic11D411yescharacteristic
46C2×#4318—21no—
47C11×#106—41no—
48C11×#103—41no—
49C11×C22⋊C8—21no—
50C11×#95—21no—
51C11×#95D411yescharacteristic
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95D411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59#66874—41no—
60#66872—41no—
61#66871—41no—
62#12240—111nomaximal, Sylow
63C2×Q8×C11—21no—
64C2×Q8×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C2×Dic22—41no—
75C2×Dic22—81no—
76C2×C8×C11—41no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C22⋊C4—41no—
88C42×C11—41no—
89#4326—82no—
90C4⋊Dic11—41no—
91C4⋊Dic11—81no—
92C4⋊Dic11—81no—
93Dic11⋊C4—24no—
94Dic11⋊C4—81no—
95Dic11⋊C4—81no—
96Dic11⋊C4—81no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—81no—
100#4318—22no—
101#4318—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104#2792—111no—
105#2060—111no—
106#1611D1111yescharacteristic
107#1605—111no—
108#1354—111no—
109#1346—111no—
110#1325—111no—
111C23×C11#12011yescharacteristic
112Q8×C11—81no—
113Q8×C11—81no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—22no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11#13511yescharacteristic
129C2×C4×C11#13711yescharacteristic
130C2×Dic11—22no—
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—
142Dic22—42no—
143Dic22—81no—
144C8×C11—81no—
145C11⋊C8—42no—
146C11⋊C8—81no—
147#544C2×D1111yescharacteristic
148#483—21no—
149#451—221no—
150#428—221no—
151#398—221no—
152#398C2×D1111yescharacteristic
153#395—111no—
154#395—221no—
155#389—221no—
156#389—221no—
157#387—221no—
158#387—221no—
159#384—111no—
160#343—111no—
161#339—221no—
162#328—21no—
163#328—221no—
164#324—111no—
165#324C2×D1111yescharacteristic
166C22×C11—21no—
167C22×C11—21no—
168C22×C11#45211yescharacteristic
169C22×C11#45611yescharacteristic
170C22×C11B(4,𝔽2)11yescharacteristic
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—42no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11—81no—
177C4×C11—81no—
178C4×C11—81no—
179Dic11—42no—
180Dic11—42no—
181Dic11—81no—
182Dic11—81no—
183C22×Q8—111no—
184C2×Q16—441no—
185C2×M16—221no—
186C4⋊Q8—41no—
187#125—41no—
188C22⋊Q8—21no—
189C22⋊Q8—21no—
190#117—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—111no—
193C2×C4⋊C4—221no—
194C2×C4⋊C4—221no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4C22⋊D1111yescharacteristic
200C2×C4⋊C4C22×D1111yescharacteristic
201C2×C42—111no—
202C2×C42—221no—
203#107—441no—
204#106—41no—
205#106—441no—
206#103—41no—
207#103—441no—
208C22⋊C8—21no—
209C22⋊C8—221no—
210#95—21no—
211#95—111no—
212#95—221no—
213#95—221no—
214#95—221no—
215#95—221no—
216#95—221no—
217#95C22⋊D1111yescharacteristic
218C2×C11—21no—
219C2×C11—21no—
220C2×C11#160311yescharacteristic
221C2×C11#220011yescharacteristic
222C2×C11#220511yescharacteristic
223C2×Q8—21no—
224C2×Q8—21no—
225C2×Q8—441no—
226C2×Q8—881no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—221no—
230C22×C4—221no—
231C22×C4—221no—
232C22×C4—221no—
233C22×C4D4×D1111yescharacteristic
234C22×C4D4×D1111yescharacteristic
235C22×C4C2×C22⋊D1111yescharacteristic
236Q16—882no—
237M16—222no—
238M16—441no—
239C2×C8—41no—
240C2×C8—441no—
241C2×C8—441no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—224no—
253C4⋊C4—441no—
254C4⋊C4—881no—
255C4⋊C4—881no—
256C4⋊C4—881no—
257C4⋊C4—881no—
258C4⋊C4—881no—
259C22⋊C4—41no—
260C42—41no—
261C42—221no—
262C42—221no—
263C42—881no—
264C11#1224011yescharacteristic, complemented, Sylow
265C23#6699011yescharacteristic
266Q8—81no—
267Q8—81no—
268Q8—442no—
269Q8—881no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—222no—
285C2×C4—222no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4#6696811yescharacteristic
297C2×C4#6696911yescharacteristic
298C8—81no—
299C8—442no—
300C8—881no—
301C22—21no—
302C22—21no—
303C22#1062264511yescharacteristic
304C22#1062278611yescharacteristic
305C22#1062281811yescharacteristic
306C4—21no—
307C4—21no—
308C4—42no—
309C4—41no—
310C4—41no—
311C4—81no—
312C4—81no—
313C4—81no—
314C4—442no—
315C4—442no—
316C4—881no—
317C4—881no—
318C2—21no—
319C2—21no—
320C2#1306757611yescharacteristic
321C2#1307062011yescharacteristic
322C2#1307064511yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1611C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#1611D11
hypocenterC11#12240
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1611

Complements

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

NH ≅ G/Ntype
264. C11#12240semidirect

Maximal subgroups

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

subgroupindex
#130764162
#130699582
#130675902
#130666472
#130666222
#130665612
C11×#16112
#1224011