Finite Group Databasebeta

← #14666207

Subgroups — #14666207

Order 2816.

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

normal subgroups only

This group has 372 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#13076682C211yesmaximal, characteristic, complemented
2#13069842C211yesmaximal, characteristic
3#13067619C211yesmaximal, characteristic
4#13066623C211yesmaximal, characteristic, complemented
5#13066622C211yesmaximal, characteristic, complemented
6#13066559C211yesmaximal, characteristic, complemented
7C11×#1610C211yesmaximal, characteristic
8C11×#537C2211yescharacteristic
9C2×#66942—21no—
10C11×#480—21no—
11C11×#398C2211yescharacteristic
12C2×#66901—21no—
13#10622845—21no—
14#10622646—21no—
15#10622597—21no—
16#10622597—21no—
17#10622596C2211yescharacteristic
18#10622590C2211yescharacteristic
19#10622273—21no—
20#10622271—21no—
21#10622270—21no—
22C11×#327—21no—
23C11×#324C2211yescharacteristic
24#10622175—21no—
25#10622168C2211yescharacteristic
26#10622166C2211yescharacteristic
27C2×C11×#41—21no—
28C11×C22⋊Q8—41no—
29C11×#121—21no—
30C11×#121—21no—
31C11×#121—41no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11D411yescharacteristic
44C2×#4318—21no—
45#66942—42no—
46#66942—42no—
47C11×#107—41no—
48C11×#102—41no—
49C11×C22⋊C8—21no—
50C11×#95—21no—
51C11×#95D411yescharacteristic
52#66901—42no—
53#66899—41no—
54#66896—41no—
55#66896—41no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95D411yescharacteristic
63C22⋊(C11⋊C8)—21no—
64#66871—41no—
65#12157—111nomaximal, Sylow
66C11×#41—41no—
67C11×#41—41no—
68C11×#41—41no—
69C11×#41—41no—
70C2×Q8×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—41no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—41no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C2×C8×C11—41no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96C4⋊Dic11—42no—
97Dic11⋊C4—42no—
98Dic11⋊C4—42no—
99Dic11⋊C4—42no—
100Dic11⋊C4—41no—
101Dic11⋊C4—41no—
102Dic11⋊C4—81no—
103C4×Dic11—21no—
104C4×Dic11D812yes—
105#4318—41no—
106#4318—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109#2822—111no—
110#2040—111no—
111#1610—111no—
112#1610D1111yescharacteristic
113#1346—111no—
114#1346—111no—
115#1324—111no—
116C23×C11—41no—
117C23×C11#12011yescharacteristic
118Q8×C11—41no—
119Q8×C11—41no—
120D4×C11—41no—
121D4×C11—41no—
122D4×C11—81no—
123D4×C11—81no—
124D4×C11—81no—
125D4×C11—81no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—81no—
140C2×C4×C11—81no—
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×Dic11—22no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—42no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C8×C11—81no—
155C11⋊C8—81no—
156C11⋊C8—81no—
157#537C2×D1111yescharacteristic
158C2×#125—221no—
159#480—21no—
160#480—221no—
161C2×#104—221no—
162#417—221no—
163#400—221no—
164#400—221no—
165#398—111no—
166#398—221no—
167#398—221no—
168#398—221no—
169#398C2×D1111yescharacteristic
170#382—111no—
171#343—111no—
172#327—21no—
173#327—221no—
174#324—111no—
175#324C2×D1111yescharacteristic
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—81no—
179C22×C11—81no—
180C22×C11—81no—
181C22×C11#44711yescharacteristic
182C22×C11#45411yescharacteristic
183C22×C11B(4,𝔽2)11yescharacteristic
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11—81no—
189C4×C11—81no—
190C4×C11—81no—
191Dic11—42no—
192Dic11—81no—
193Dic11—81no—
194Dic11—81no—
195C2×#41—21no—
196C2×M16—221no—
197#125—442no—
198#125—442no—
199C22⋊Q8—41no—
200#121—21no—
201#121—21no—
202#121—41no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4C22⋊D1111yescharacteristic
213C2×C4⋊C4C22×D1111yescharacteristic
214C2×C42—111no—
215#107—41no—
216#107—441no—
217#104—442no—
218#103—441no—
219#102—41no—
220#102—441no—
221#102—441no—
222C22⋊C8—21no—
223C22⋊C8—221no—
224#95—21no—
225#95—111no—
226#95—221no—
227#95—221no—
228#95—221no—
229#95—221no—
230#95—221no—
231#95—221no—
232#95C22⋊D1111yescharacteristic
233C2×C11—21no—
234C2×C11—21no—
235C2×C11—161no—
236C2×C11#159811yescharacteristic
237C2×C11#220111yescharacteristic
238C2×C11#220311yescharacteristic
239#41—41no—
240#41—41no—
241#41—41no—
242#41—41no—
243C2×Q8—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—41no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—41no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4D4×D1111yescharacteristic
256C22×C4D4×D1111yescharacteristic
257C22×C4C2×C22⋊D1111yescharacteristic
258M16—441no—
259M16—441no—
260C2×C8—41no—
261C2×C8—441no—
262C2×C8—441no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C4⋊C4—442no—
272C4⋊C4—442no—
273C4⋊C4—442no—
274C4⋊C4—442no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C4⋊C4—881no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C42—112no—
281C42—221no—
282C11#1215711yescharacteristic, complemented, Sylow
283C23—41no—
284C23#6699011yescharacteristic
285Q8—41no—
286Q8—41no—
287D4—41no—
288D4—41no—
289D4—81no—
290D4—81no—
291D4—81no—
292D4—81no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—222no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—442no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4D8×D1111yescharacteristic
320C2×C4#6696411yescharacteristic
321C8—81no—
322C8—881no—
323C8—881no—
324C22—21no—
325C22—21no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22#1062264511yescharacteristic
330C22#1062276911yescharacteristic
331C22#1062281411yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—81no—
338C4—81no—
339C4—442no—
340C4—881no—
341C4—881no—
342C4—881no—
343C2—21no—
344C2—21no—
345C2—161no—
346C2#1306754911yescharacteristic
347C2#1307062711yescharacteristic
348C2#1307063511yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1610C2
socleC22×C11B(4,𝔽2)
prime radicalC11×#537C22
hypercenter#1610D11
hypocenterC11#12157
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1610

Complements

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

NH ≅ G/Ntype
1. #13076682C2semidirect
4. #13066623C2semidirect
5. #13066622C2semidirect
6. #13066559C2semidirect
282. C11#12157semidirect

Maximal subgroups

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

subgroupindex
#130766822
#130698422
#130676192
#130666232
#130666222
#130665592
C11×#16102
#1215711