Finite Group Databasebeta

← #14666954

Subgroups — #14666954

Order 2816.

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

normal subgroups only

This group has 372 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#13067589C211yesmaximal, characteristic, complemented
3#13067555C211yesmaximal, characteristic
4#13066646C211yesmaximal, characteristic, complemented
5#13066619C211yesmaximal, characteristic
6#13066550C211yesmaximal, characteristic, complemented
7C11×#2832C211yesmaximal, characteristic
8#10623031C2211yescharacteristic
9C11×#400—21no—
10C11×#397—21no—
11C11×#395C2211yescharacteristic
12C11×#394—21no—
13C11×#394C2211yescharacteristic
14C11×#393—21no—
15C11×#393—21no—
16C11×#391C2211yescharacteristic
17C11×#388—21no—
18#10622841—21no—
19#10622838—21no—
20#10622831—21no—
21#10622168C2211yescharacteristic
22#10622166C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622161—21no—
25#10622090—21no—
26#10622090—21no—
27C22×Q8×C11D411yescharacteristic
28C22×Q8×C11D411yescharacteristic
29C22×D4×C11D411yescharacteristic
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4C2311yescharacteristic
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C42×C11D411yescharacteristic
40C2×#4326—41no—
41C2×#4324—41no—
42#66979—21no—
43#66977—21no—
44#66977—21no—
45C2×#4318—21no—
46#66943—41no—
47#66941—41no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95D411yescharacteristic
55C11×#95D411yescharacteristic
56#66899—41no—
57#66899—41no—
58#66899—41no—
59#66896—41no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#12275—111nomaximal, Sylow
63C24×C11—21no—
64C2×Q8×C11—21no—
65C2×Q8×C11—21no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C2×Q8×C11—41no—
69C2×Q8×C11—81no—
70C2×D4×C11—41no—
71C2×D4×C11—81no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C2×Dic22—21no—
81C2×Dic22—21no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—81no—
84C11×C4⋊C4—81no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—81no—
88C11×C22⋊C4—81no—
89C11×C22⋊C4—81no—
90C11×C22⋊C4—81no—
91C11×C22⋊C4—81no—
92C42×C11—41no—
93C22⋊Dic11—41no—
94#4326—82no—
95#4324—82no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100Dic11⋊C4—41no—
101Dic11⋊C4—41no—
102C4×Dic11—41no—
103#4318—41no—
104#4318—41no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108#2832D1111yescharacteristic
109#2028—111no—
110#1605—111no—
111#1599—111no—
112#1354—111no—
113#1345—111no—
114#1319—111no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11#12011yescharacteristic
123Q8×C11—42no—
124Q8×C11—42no—
125Q8×C11—81no—
126Q8×C11—81no—
127D4×C11—42no—
128D4×C11—81no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
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—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11#13511yescharacteristic
151C2×C4×C11#13711yescharacteristic
152C2×Dic11—41no—
153C2×Dic11—41no—
154Dic22—81no—
155Dic22—81no—
156C11⋊C8—81no—
157C11⋊C8—81no—
158C11⋊C8—81no—
159#544—111no—
160#451—221no—
161#450—221no—
162#419—221no—
163#400—21no—
164#397—21no—
165#395C2×D1111yescharacteristic
166#394—21no—
167#394C2×D1111yescharacteristic
168#393—21no—
169#393—21no—
170#391C2×D1111yescharacteristic
171#388—21no—
172#343—111no—
173#339—221no—
174#328—221no—
175#328—221no—
176#324—111no—
177#324—111no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—81no—
181C22×C11—81no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11#45211yescharacteristic
188C22×C11#45511yescharacteristic
189C22×C11B(4,𝔽2)11yescharacteristic
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11—81no—
198C4×C11—81no—
199Dic11—81no—
200Dic11—81no—
201C22×Q8C22⋊D1111yescharacteristic
202C22×Q8C22⋊D1111yescharacteristic
203C22×D4C22⋊D1111yescharacteristic
204C2×Q16—441no—
205C2×SD16—441no—
206C2×M16—221no—
207C4⋊Q8—441no—
208#125—441no—
209C22⋊Q8—221no—
210C22⋊Q8—221no—
211#117—221no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4C22×D1111yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C42C22⋊D1111yescharacteristic
222#103—441no—
223#103—441no—
224#103—441no—
225#102—441no—
226C22⋊C8—221no—
227C22⋊C8—221no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95C22⋊D1111yescharacteristic
235#95C22⋊D1111yescharacteristic
236C2×C11—21no—
237C2×C11—21no—
238C2×C11—161no—
239C2×C11#160611yescharacteristic
240C2×C11#219911yescharacteristic
241C2×C11#220311yescharacteristic
242C24—21no—
243C2×Q8—21no—
244C2×Q8—21no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—81no—
249C2×Q8—221no—
250C2×Q8—221no—
251C2×D4—41no—
252C2×D4—81no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4C2×C22⋊D1111yescharacteristic
259C22×C4C2×C22⋊D1111yescharacteristic
260C22×C4C2×C22⋊D1111yescharacteristic
261Q16—882no—
262SD16—882no—
263M16—441no—
264M16—441no—
265C2×C8—441no—
266C2×C8—441no—
267C2×C8—441no—
268C4⋊C4—41no—
269C4⋊C4—81no—
270C4⋊C4—81no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—81no—
280C22⋊C4—81no—
281C22⋊C4—81no—
282C22⋊C4—81no—
283C22⋊C4—81no—
284C22⋊C4—441no—
285C42—41no—
286C42—441no—
287C11#1227511yescharacteristic, complemented, Sylow
288C23—41no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23#6700611yescharacteristic
296Q8—42no—
297Q8—42no—
298Q8—81no—
299Q8—81no—
300Q8—881no—
301Q8—881no—
302D4—42no—
303D4—81no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
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—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4#6700311yescharacteristic
328C2×C4#6700411yescharacteristic
329C8—881no—
330C8—881no—
331C8—881no—
332C22—21no—
333C22—21no—
334C22—81no—
335C22—81no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22#1062285211yescharacteristic
342C22#1062285511yescharacteristic
343C22#1062285711yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4—81no—
352C4—81no—
353C4—881no—
354C4—881no—
355C2—21no—
356C2—21no—
357C2—161no—
358C2#1306759611yescharacteristic
359C2#1307061711yescharacteristic
360C2#1307063711yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2832C2
socleC22×C11B(4,𝔽2)
prime radicalC22×D4×C11D4
hypercenter#2832D11
hypocenterC11#12275
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2832

Complements

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

NH ≅ G/Ntype
1. #13069777C2semidirect
2. #13067589C2semidirect
4. #13066646C2semidirect
6. #13066550C2semidirect
287. C11#12275semidirect

Maximal subgroups

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

subgroupindex
#130697772
#130675892
#130675552
#130666462
#130666192
#130665502
C11×#28322
#1227511