Finite Group Databasebeta

← #14666667

Subgroups — #14666667

Order 2816.

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

normal subgroups only

This group has 360 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#13076799C211yesmaximal, characteristic
2#13067641C211yesmaximal, characteristic
3#13067607C211yesmaximal, characteristic
4#13066639C211yesmaximal, characteristic
5#13066615C211yesmaximal, characteristic
6#13066564C211yesmaximal, characteristic
7C11×#2062C211yesmaximal, characteristic
8C11×#543C2211yescharacteristic
9C11×#385—21no—
10C11×#385C2211yescharacteristic
11#10622823—21no—
12#10622657—21no—
13#10622656—21no—
14#10622597—21no—
15#10622593—21no—
16#10622566C2211yescharacteristic
17#10622565—21no—
18#10622562C2211yescharacteristic
19C11⋊#401—21no—
20#10622270—21no—
21C11×#342—21no—
22C11×#342C2211yescharacteristic
23#10622176—21no—
24#10622176—21no—
25#10622163C2211yescharacteristic
26#10622163C2211yescharacteristic
27C23×C4×C11D411yescharacteristic
28C11×C22⋊Q8—21no—
29C11×C22⋊Q8—21no—
30C11×C22⋊Q8—41no—
31C11×C22⋊Q8—41no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—41no—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4D411yescharacteristic
37C2×C11×C22⋊C4C2311yescharacteristic
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C4⋊Dic11D411yescharacteristic
41C2×C4⋊Dic11D411yescharacteristic
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C11×#95—21no—
47C11×#95—41no—
48#66899—41no—
49#66899—41no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95D411yescharacteristic
57C11⋊#95D411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66872—41no—
61#66871—41no—
62#12232—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×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11—81no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—81no—
84C11×C4⋊C4—82no—
85C11×C22⋊C4—22no—
86C11×C22⋊C4—21no—
87C11×C22⋊C4—21no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C22⋊Dic11—41no—
93C22⋊Dic11—41no—
94C22⋊Dic11—81no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97Dic11⋊C4—81no—
98Dic11⋊C4—81no—
99Dic11⋊C4—81no—
100Dic11⋊C4—81no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103#2834—111no—
104#2062D1111yescharacteristic
105#1614—111no—
106#1608—111no—
107#1352—111no—
108#1344—111no—
109#1326—111no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11#12011yescharacteristic
115C23×C11#13511yescharacteristic
116C23×C11#13711yescharacteristic
117Q8×C11—81no—
118Q8×C11—81no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—42no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—42no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—81no—
134C2×C4×C11—81no—
135C2×C4×C11—81no—
136C2×C4×C11—81no—
137C2×C4×C11—81no—
138C2×Dic11—41no—
139C2×Dic11—41no—
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—
150C11⋊C8—81no—
151C11⋊C8—81no—
152#543C2×D1111yescharacteristic
153#484—221no—
154#483—221no—
155#401—221no—
156#399—111no—
157#398—221no—
158#398—221no—
159#398—221no—
160#397—111no—
161#397—221no—
162#385—21no—
163#385—221no—
164#385C2×D1111yescharacteristic
165#342—21no—
166#342C2×D1111yescharacteristic
167#328—221no—
168#328—221no—
169#323—111no—
170#323—111no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—81no—
180C22×C11#45211yescharacteristic
181C22×C11#45611yescharacteristic
182C22×C11B(4,𝔽2)11yescharacteristic
183C4×C11—41no—
184C4×C11—41no—
185C4×C11—81no—
186C4×C11—82no—
187C4×C11—81no—
188C4×C11—81no—
189C4×C11—81no—
190Dic11—81no—
191Dic11—81no—
192Dic11—81no—
193Dic11—81no—
194C23×C4C22⋊D1111yescharacteristic
195C22⋊Q8—21no—
196C22⋊Q8—21no—
197C22⋊Q8—41no—
198C22⋊Q8—41no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—41no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—221no—
210C2×C22⋊C4—221no—
211C2×C22⋊C4C22⋊D1111yescharacteristic
212C2×C22⋊C4C22×D1111yescharacteristic
213#107—441no—
214#106—441no—
215#103—441no—
216#103—441no—
217C22⋊C8—221no—
218C22⋊C8—221no—
219#95—21no—
220#95—41no—
221#95—111no—
222#95—111no—
223#95—221no—
224#95—221no—
225#95—221no—
226#95—221no—
227#95—221no—
228#95—221no—
229C2×C11—21no—
230C2×C11—21no—
231C2×C11—41no—
232C2×C11—41no—
233C2×C11#160311yescharacteristic
234C2×C11#220011yescharacteristic
235C2×C11#220111yescharacteristic
236C24C2×C22⋊D1111yescharacteristic
237C2×Q8—21no—
238C2×Q8—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—81no—
246C22×C4—221no—
247C22×C4—221no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4D4×D1111yescharacteristic
251C22×C4D4×D1111yescharacteristic
252C2×C8—441no—
253C2×C8—441no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—81no—
259C4⋊C4—82no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C4⋊C4—881no—
263C4⋊C4—881no—
264C4⋊C4—881no—
265C4⋊C4—881no—
266C22⋊C4—22no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—441no—
274C22⋊C4—441no—
275C22⋊C4—881no—
276C11#1223211yescharacteristic, complemented, Sylow
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23#6699011yescharacteristic
282C23#6699511yescharacteristic
283C23#6700311yescharacteristic
284Q8—81no—
285Q8—81no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C8—881no—
318C8—881no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—81no—
328C22#1062264511yescharacteristic
329C22#1062266011yescharacteristic
330C22#1062270811yescharacteristic
331C4—41no—
332C4—41no—
333C4—81no—
334C4—82no—
335C4—81no—
336C4—81no—
337C4—81no—
338C4—881no—
339C4—881no—
340C4—881no—
341C4—881no—
342C2—21no—
343C2—21no—
344C2—41no—
345C2—41no—
346C2#1306757711yescharacteristic
347C2#1307062111yescharacteristic
348C2#1307062711yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2062C2
socleC22×C11B(4,𝔽2)
prime radicalC24×C11C2×D4
hypercenter#2062D11
hypocenterC11#12232
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2062

Complements

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

NH ≅ G/Ntype
276. C11#12232semidirect

Maximal subgroups

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

subgroupindex
#130767992
#130676412
#130676072
#130666392
#130666152
#130665642
C11×#20622
#1223211