Finite Group Databasebeta

← #14666821

Subgroups — #14666821

Order 2816.

378 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 57 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#13076587C211yesmaximal, characteristic
2#13069968C211yesmaximal, characteristic
3#13067641C211yesmaximal, characteristic
4#13066641C211yesmaximal, characteristic
5#13066640C211yesmaximal, characteristic
6#13066563C211yesmaximal, characteristic
7C11×#1614C211yesmaximal, characteristic
8C11×#543C2211yescharacteristic
9C11×#484—21no—
10C11×#399C2211yescharacteristic
11#10622657—21no—
12#10622598—21no—
13#10622596—21no—
14#10622595—21no—
15#10622563—21no—
16#10622562C2211yescharacteristic
17#10622559—21no—
18#10622559C2211yescharacteristic
19#10622558—21no—
20#10622260—21no—
21C11×#328—21no—
22C11×#323C2211yescharacteristic
23#10622176—21no—
24#10622164—21no—
25#10622164C2211yescharacteristic
26#10622163C2211yescharacteristic
27C23×Dic11D411yescharacteristic
28C11×C22⋊Q8—21no—
29C11×C22⋊Q8—21no—
30C11×C22⋊Q8—41no—
31C11×C22⋊Q8—41no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4C2311yescharacteristic
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11D411yescharacteristic
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11D411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—41no—
47C2×C4×Dic11—21no—
48C11×#107—41no—
49C11×#103—41no—
50C11×C22⋊C8—21no—
51C11×#95D411yescharacteristic
52#66899—41no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—41no—
59C11⋊#95D411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61#66871—41no—
62#12255—111nomaximal, Sylow
63C24×C11C2×D411yescharacteristic
64C2×Q8×C11—21no—
65C2×Q8×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—41no—
77C22×Dic11—41no—
78C22×Dic11—81no—
79C2×C8×C11—41no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—42no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—42no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C22⋊Dic11—22no—
91C22⋊Dic11—21no—
92C22⋊Dic11—41no—
93C22⋊Dic11—81no—
94C22⋊Dic11Q1612yes—
95C4⋊Dic11—41no—
96C4⋊Dic11—81no—
97C4⋊Dic11—81no—
98Dic11⋊C4—42no—
99Dic11⋊C4—81no—
100Dic11⋊C4—81no—
101Dic11⋊C4—82no—
102C4×Dic11—81no—
103C2×C11⋊C8—41no—
104#2807—111no—
105#2062—111no—
106#1614—111no—
107#1614D1111yescharacteristic
108#1352—111no—
109#1352—111no—
110#1326—111no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11#12011yescharacteristic
116C23×C11C2×Q1611yescharacteristic
117C23×C11#13711yescharacteristic
118Q8×C11—81no—
119Q8×C11—81no—
120C2×C4×C11—22no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—41no—
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—41no—
131C2×C4×C11—41no—
132C2×C4×C11—81no—
133C2×C4×C11—81no—
134C2×Dic11—22no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—81no—
149C2×Dic11—81no—
150C2×Dic11—81no—
151C8×C11—81no—
152C11⋊C8—81no—
153#543C2×D1111yescharacteristic
154#484—21no—
155#484—221no—
156#400—221no—
157#399—111no—
158#399C2×D1111yescharacteristic
159#398—221no—
160#389—221no—
161#389—221no—
162#388—221no—
163#385—111no—
164#385—221no—
165#385—221no—
166#342—111no—
167#342—221no—
168#328—21no—
169#328—221no—
170#323—111no—
171#323C2×D1111yescharacteristic
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—81no—
181C22×C11#45111yescharacteristic
182C22×C11#45611yescharacteristic
183C22×C11B(4,𝔽2)11yescharacteristic
184C4×C11—42no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11—81no—
188C4×C11—81no—
189C4×C11—81no—
190Dic11—42no—
191Dic11—81no—
192Dic11—82no—
193Dic11—81no—
194Dic11—81no—
195C23×C4—111no—
196C22⋊Q8—21no—
197C22⋊Q8—21no—
198C22⋊Q8—41no—
199C22⋊Q8—41no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—441no—
208C2×C4⋊C4C22⋊D1111yescharacteristic
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—111no—
212C2×C22⋊C4—221no—
213C2×C22⋊C4—221no—
214C2×C22⋊C4C22×D1111yescharacteristic
215C2×C42—221no—
216#107—41no—
217#107—441no—
218#103—41no—
219#103—441no—
220C22⋊C8—21no—
221C22⋊C8—221no—
222#95—111no—
223#95—221no—
224#95—221no—
225#95—221no—
226#95—221no—
227#95—221no—
228#95—441no—
229#95C22⋊D1111yescharacteristic
230C2×C11—21no—
231C2×C11—21no—
232C2×C11—41no—
233C2×C11—41no—
234C2×C11#160511yescharacteristic
235C2×C11#219811yescharacteristic
236C2×C11#220011yescharacteristic
237C24D4×D1111yescharacteristic
238C2×Q8—21no—
239C2×Q8—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—221no—
245C22×C4—221no—
246C22×C4—221no—
247C22×C4—221no—
248C22×C4—441no—
249C22×C4—441no—
250C22×C4—881no—
251C22×C4D4×D1111yescharacteristic
252C22×C4C2×C22⋊D1111yescharacteristic
253C2×C8—41no—
254C2×C8—441no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—41no—
258C4⋊C4—42no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—441no—
262C4⋊C4—442no—
263C4⋊C4—881no—
264C4⋊C4—881no—
265C4⋊C4—881no—
266C4⋊C4—881no—
267C4⋊C4—882no—
268C22⋊C4—41no—
269C22⋊C4—42no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—112no—
273C22⋊C4—221no—
274C22⋊C4—222no—
275C22⋊C4—441no—
276C22⋊C4—881no—
277C42—881no—
278C11#1225511yescharacteristic, complemented, Sylow
279C23—21no—
280C23—21no—
281C23—41no—
282C23—41no—
283C23Q16×D1111yescharacteristic
284C23#6697111yescharacteristic
285C23#6699011yescharacteristic
286Q8—81no—
287Q8—81no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—222no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—442no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—442no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—881no—
317C2×C4—881no—
318C2×C4—881no—
319C8—81no—
320C8—881no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—81no—
330C22#1062264511yescharacteristic
331C22#1062279911yescharacteristic
332C22#1062281811yescharacteristic
333C4—42no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—81no—
338C4—81no—
339C4—442no—
340C4—881no—
341C4—882no—
342C4—881no—
343C4—881no—
344C2—21no—
345C2—21no—
346C2—41no—
347C2—41no—
348C2#1306758811yescharacteristic
349C2#1307061111yescharacteristic
350C2#1307062011yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1614C2
socleC22×C11B(4,𝔽2)
prime radicalC24×C11C2×D4
hypercenter#1614D11
hypocenterC11#12255
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1614

Complements

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

NH ≅ G/Ntype
278. C11#12255semidirect

Maximal subgroups

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

subgroupindex
#130765872
#130699682
#130676412
#130666412
#130666402
#130665632
C11×#16142
#1225511