Finite Group Databasebeta

← #14666923

Subgroups — #14666923

Order 2816.

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

normal subgroups only

This group has 396 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#13073859C211yesmaximal, characteristic
2#13069774C211yesmaximal, characteristic, complemented
3#13067658C211yesmaximal, characteristic, complemented
4#13066644C211yesmaximal, characteristic, complemented
5#13066619C211yesmaximal, characteristic
6#13066549C211yesmaximal, characteristic, complemented
7C11×#1599C211yesmaximal, characteristic
8C11×#544C2211yescharacteristic
9C11×#450—21no—
10C11×#394C2211yescharacteristic
11#10622833—21no—
12#10622657—21no—
13#10622617—21no—
14#10622599C2211yescharacteristic
15#10622587C2211yescharacteristic
16#10622564—21no—
17#10622560—21no—
18#10622556—21no—
19C22⋊C4×Dic11—21no—
20#10622264—21no—
21C11×#328—21no—
22C11×#324C2211yescharacteristic
23#10622176—21no—
24#10622170—21no—
25#10622168C2211yescharacteristic
26#10622166C2211yescharacteristic
27C22×D4×C11D411yescharacteristic
28C23×Dic11—21no—
29C22×Dic22D411yescharacteristic
30C2×C11×SD16—41no—
31C11×C4⋊Q8—41no—
32C11×#125—41no—
33C11×C22⋊Q8—21no—
34C11×C22⋊Q8—21no—
35C11×#117—21no—
36C2×C11×C4⋊C4C2311yescharacteristic
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11—21no—
42C2×C4⋊Dic11D411yescharacteristic
43C2×C4×Dic11—21no—
44C2×C4×Dic11D411yescharacteristic
45C2×#4318—21no—
46C11×#102—41no—
47C11×C22⋊C8—21no—
48C11×#95D411yescharacteristic
49#66899—41no—
50C11⋊#95—21no—
51C11⋊#95—21no—
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#66874—41no—
61#66871—41no—
62#12271—111nomaximal, Sylow
63C24×C11—21no—
64C2×Q8×C11—21no—
65C2×Q8×C11—21no—
66C2×D4×C11—41no—
67C2×D4×C11—42no—
68C22×C4×C11—21no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—42no—
77C22×Dic11—42no—
78C22×Dic11—81no—
79C2×Dic22—21no—
80C2×Dic22—21no—
81C2×Dic22—41no—
82C2×Dic22—41no—
83C11×SD16—82no—
84C2×C8×C11—41no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C22⋊C4—42no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C42×C11—41no—
97C22⋊Dic11—42no—
98C22⋊Dic11—81no—
99C22⋊Dic11—81no—
100C4⋊Dic11—41no—
101C4×Dic11—41no—
102C4×Dic11—42no—
103#4318—41no—
104#4318—41no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107#2572—111no—
108#2028—111no—
109#1617—111no—
110#1599D1111yescharacteristic
111#1353—111no—
112#1345—111no—
113#1319—111no—
114C23×C11—22no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11#12011yescharacteristic
122Q8×C11—81no—
123Q8×C11—81no—
124D4×C11—42no—
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#13511yescharacteristic
138C2×C4×C11#13711yescharacteristic
139C2×Dic11—22no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—84no—
152Dic22—42no—
153Dic22—81no—
154C8×C11—81no—
155C11⋊C8—81no—
156C11⋊C8—81no—
157#544C2×D1111yescharacteristic
158#484—221no—
159#450—21no—
160#419—221no—
161#400—111no—
162#394C2×D1111yescharacteristic
163#393—221no—
164#391—111no—
165#388—221no—
166#386—221no—
167#383—221no—
168#381—221no—
169C4×C22⋊C4—221no—
170#343—111no—
171#339—221no—
172#328—21no—
173#328—221no—
174#324—111no—
175#324C2×D1111yescharacteristic
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—42no—
179C22×C11—42no—
180C22×C11—42no—
181C22×C11—81no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11#45211yescharacteristic
186C22×C11#45511yescharacteristic
187C22×C11B(4,𝔽2)11yescharacteristic
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—41no—
191C4×C11—41no—
192C4×C11—81no—
193C4×C11—81no—
194C4×C11—81no—
195Dic11—42no—
196Dic11—81no—
197Dic11—81no—
198Dic11—81no—
199C22×Q8—111no—
200C22×D4C22⋊D1111yescharacteristic
201C23×C4—221no—
202C2×SD16—41no—
203C2×M16—221no—
204C4⋊Q8—41no—
205#125—41no—
206C22⋊Q8—21no—
207C22⋊Q8—21no—
208#117—21no—
209C2×C4⋊C4—111no—
210C2×C4⋊C4C22×D1111yescharacteristic
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—221no—
214C2×C22⋊C4—221no—
215C2×C22⋊C4—221no—
216C2×C42—111no—
217C2×C42—221no—
218#107—441no—
219#103—441no—
220#103—441no—
221#103—441no—
222#102—41no—
223C22⋊C8—21no—
224C22⋊C8—221no—
225#95—111no—
226#95—221no—
227#95—221no—
228#95—221no—
229#95—221no—
230#95—221no—
231#95—221no—
232#95—221no—
233#95C22⋊D1111yescharacteristic
234C2×C11—21no—
235C2×C11—21no—
236C2×C11—82no—
237C2×C11#160611yescharacteristic
238C2×C11#219711yescharacteristic
239C2×C11#220411yescharacteristic
240C24—21no—
241C2×Q8—21no—
242C2×Q8—21no—
243C2×Q8—221no—
244C2×Q8—221no—
245C2×Q8—441no—
246C2×Q8—441no—
247C2×D4—41no—
248C2×D4—42no—
249C22×C4—21no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—442no—
255C22×C4—442no—
256C22×C4—881no—
257C22×C4D4×D1111yescharacteristic
258C22×C4D4×D1111yescharacteristic
259C22×C4C2×C22⋊D1111yescharacteristic
260SD16—82no—
261M16—441no—
262M16—441no—
263C2×C8—41no—
264C2×C8—441no—
265C2×C8—441no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—441no—
274C22⋊C4—42no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—442no—
279C22⋊C4—881no—
280C22⋊C4—881no—
281C42—41no—
282C42—441no—
283C42—442no—
284C11#1227111yescharacteristic, complemented, Sylow
285C23—22no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23#6699011yescharacteristic
293Q8—81no—
294Q8—81no—
295Q8—442no—
296Q8—881no—
297D4—42no—
298D4—81no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—222no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—884no—
323C2×C4#6696811yescharacteristic
324C2×C4#6696911yescharacteristic
325C8—81no—
326C8—881no—
327C8—881no—
328C22—21no—
329C22—21no—
330C22—42no—
331C22—42no—
332C22—42no—
333C22—81no—
334C22—81no—
335C22—81no—
336C22—81no—
337C22#1062264511yescharacteristic
338C22#1062278611yescharacteristic
339C22#1062281511yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—81no—
345C4—81no—
346C4—81no—
347C4—442no—
348C4—881no—
349C4—881no—
350C4—881no—
351C2—21no—
352C2—21no—
353C2—82no—
354C2#1306759311yescharacteristic
355C2#1307060411yescharacteristic
356C2#1307064011yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1599C2
socleC22×C11B(4,𝔽2)
prime radicalC22×D4×C11D4
hypercenter#1599D11
hypocenterC11#12271
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1599

Complements

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

NH ≅ G/Ntype
2. #13069774C2semidirect
3. #13067658C2semidirect
4. #13066644C2semidirect
6. #13066549C2semidirect
284. C11#12271semidirect

Maximal subgroups

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

subgroupindex
#130738592
#130697742
#130676582
#130666442
#130666192
#130665492
C11×#15992
#1227111