Finite Group Databasebeta

← #14666926

Subgroups — #14666926

Order 2816.

396 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 59 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#13069777C211yesmaximal, characteristic, complemented
2#13067657C211yesmaximal, characteristic, complemented
3#13067555C211yesmaximal, characteristic
4#13066643C211yesmaximal, characteristic, complemented
5#13066619C211yesmaximal, characteristic
6#13066550C211yesmaximal, characteristic, complemented
7C11×#2572C211yesmaximal, characteristic
8#10623031C2211yescharacteristic
9C11×#400C2211yescharacteristic
10C11×#394C2211yescharacteristic
11C11×#393—21no—
12C11×#391C2211yescharacteristic
13C11×#388—21no—
14C11×#386—21no—
15C11×#383—21no—
16C11×#381—21no—
17C4×C11×C22⋊C4—21no—
18#10622838—21no—
19#10622831—21no—
20#10622583—21no—
21#10622168C2211yescharacteristic
22#10622166C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622161—21no—
25#10622090—21no—
26#10622090—21no—
27C22×Q8×C11D411yescharacteristic
28C22×D4×C11D411yescharacteristic
29C23×C4×C11—21no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C42×C11—21no—
38C2×C42×C11D411yescharacteristic
39C2×#4324—41no—
40#66979—21no—
41#66977—21no—
42#66977—21no—
43C2×#4318—21no—
44#66943—41no—
45#66941—41no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95D411yescharacteristic
54C11×#95D411yescharacteristic
55#66899—41no—
56#66899—41no—
57#66896—41no—
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66874—41no—
61#66871—41no—
62#12271—111nomaximal, Sylow
63C24×C11—21no—
64C2×Q8×C11—21no—
65C2×Q8×C11—21no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C2×D4×C11—41no—
69C2×D4×C11—42no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—42no—
76C22×C4×C11—42no—
77C22×C4×C11—81no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C2×Dic22—21no—
82C2×Dic22—21no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C22⋊C4—42no—
86C11×C22⋊C4—42no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—81no—
90C11×C22⋊C4—81no—
91C42×C11—42no—
92C42×C11—41no—
93C22⋊Dic11—41no—
94#4324—82no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99Dic11⋊C4—41no—
100Dic11⋊C4—41no—
101C4×Dic11—41no—
102#4318—41no—
103#4318—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107#2572D1111yescharacteristic
108#2028—111no—
109#1617—111no—
110#1599—111no—
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—42no—
123Q8×C11—81no—
124D4×C11—42no—
125D4×C11—81no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—22no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
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—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—84no—
148C2×C4×C11#13511yescharacteristic
149C2×C4×C11#13711yescharacteristic
150C2×Dic11—41no—
151C2×Dic11—41no—
152Dic22—81no—
153Dic22—81no—
154C11⋊C8—81no—
155C11⋊C8—81no—
156C11⋊C8—81no—
157#544—111no—
158#484—221no—
159#450—221no—
160#419—221no—
161#400C2×D1111yescharacteristic
162#394C2×D1111yescharacteristic
163#393—21no—
164#391C2×D1111yescharacteristic
165#388—21no—
166#386—21no—
167#383—21no—
168#381—21no—
169C4×C22⋊C4—21no—
170#343—111no—
171#339—221no—
172#328—221no—
173#328—221no—
174#324—111no—
175#324—111no—
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—42no—
191C4×C11—41no—
192C4×C11—41no—
193C4×C11—81no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11—81no—
197Dic11—81no—
198Dic11—81no—
199C22×Q8C22⋊D1111yescharacteristic
200C22×D4C22⋊D1111yescharacteristic
201C23×C4—21no—
202C2×SD16—441no—
203C2×M16—221no—
204C4⋊Q8—441no—
205#125—441no—
206C22⋊Q8—221no—
207C22⋊Q8—221no—
208#117—221no—
209C2×C4⋊C4C22⋊D1111yescharacteristic
210C2×C4⋊C4C22×D1111yescharacteristic
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C42—21no—
217C2×C42C22⋊D1111yescharacteristic
218#107—441no—
219#103—441no—
220#103—441no—
221#103—441no—
222#102—441no—
223C22⋊C8—221no—
224C22⋊C8—221no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95C22⋊D1111yescharacteristic
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—41no—
244C2×Q8—41no—
245C2×Q8—221no—
246C2×Q8—221no—
247C2×D4—41no—
248C2×D4—42no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—81no—
257C22×C4C2×C22⋊D1111yescharacteristic
258C22×C4C2×C22⋊D1111yescharacteristic
259C22×C4C2×C22⋊D1111yescharacteristic
260SD16—882no—
261M16—441no—
262M16—441no—
263C2×C8—441no—
264C2×C8—441no—
265C2×C8—441no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—441no—
273C4⋊C4—441no—
274C22⋊C4—42no—
275C22⋊C4—42no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—81no—
279C22⋊C4—81no—
280C22⋊C4—441no—
281C42—41no—
282C42—42no—
283C42—441no—
284C11#1227111yescharacteristic, complemented, Sylow
285C23—22no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23#6700611yescharacteristic
293Q8—42no—
294Q8—81no—
295Q8—881no—
296Q8—881no—
297D4—42no—
298D4—81no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—22no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—84no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4#6700311yescharacteristic
324C2×C4#6700411yescharacteristic
325C8—881no—
326C8—881no—
327C8—881no—
328C22—21no—
329C22—21no—
330C22—42no—
331C22—42no—
332C22—42no—
333C22—81no—
334C22—81no—
335C22—81no—
336C22—81no—
337C22#1062285211yescharacteristic
338C22#1062285511yescharacteristic
339C22#1062285711yescharacteristic
340C4—21no—
341C4—21no—
342C4—42no—
343C4—41no—
344C4—41no—
345C4—81no—
346C4—81no—
347C4—81no—
348C4—81no—
349C4—881no—
350C4—881no—
351C2—21no—
352C2—21no—
353C2—82no—
354C2#1306759611yescharacteristic
355C2#1307060611yescharacteristic
356C2#1307064211yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2572C2
socleC22×C11B(4,𝔽2)
prime radicalC22×D4×C11D4
hypercenter#2572D11
hypocenterC11#12271
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2572

Complements

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

NH ≅ G/Ntype
1. #13069777C2semidirect
2. #13067657C2semidirect
4. #13066643C2semidirect
6. #13066550C2semidirect
284. C11#12271semidirect

Maximal subgroups

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

subgroupindex
#130697772
#130676572
#130675552
#130666432
#130666192
#130665502
C11×#25722
#1227111