Finite Group Databasebeta

← #14666109

Subgroups — #14666109

Order 2816.

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

normal subgroups only

This group has 354 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#13076436C211yesmaximal, characteristic, complemented
2#13067653C211yesmaximal, characteristic
3#13067619C211yesmaximal, characteristic
4#13066642C211yesmaximal, characteristic, complemented
5#13066621C211yesmaximal, characteristic, complemented
6#13066562C211yesmaximal, characteristic, complemented
7C11×#2039C211yesmaximal, characteristic
8C11×#537C2211yescharacteristic
9C2×C11×#104—21no—
10C11×#417—21no—
11C11×#384C2211yescharacteristic
12#10622647—21no—
13#10622646—21no—
14#10622599C2211yescharacteristic
15#10622596C2211yescharacteristic
16#10622595—21no—
17#10622595—21no—
18#10622594—21no—
19#10622594—21no—
20#10622591—21no—
21#10622546—21no—
22C11×#343C2211yescharacteristic
23#10622175—21no—
24#10622175—21no—
25#10622166C2211yescharacteristic
26#10622166C2211yescharacteristic
27C2×C11×#41—21no—
28C2×C11×M16—21no—
29C11×C22⋊Q8—41no—
30C11×#121—21no—
31C11×#121—21no—
32C11×#121—41no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4C2311yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×C4⋊Dic11D411yescharacteristic
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×C4×Dic11—21no—
43C11×#104—42no—
44C11×#103—41no—
45C11×#102—41no—
46#66896—41no—
47#66896—41no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95D411yescharacteristic
58C11⋊#95D411yescharacteristic
59C22⋊(C11⋊C8)—21no—
60C22⋊(C11⋊C8)—21no—
61#66872—41no—
62#66871—41no—
63#12142—111nomaximal, Sylow
64C11×#41—41no—
65C11×#41—41no—
66C11×#41—41no—
67C11×#41—41no—
68C2×Q8×C11—21no—
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—41no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—41no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C11×M16—41no—
84C11×M16—41no—
85C2×C8×C11—41no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—42no—
90C11×C4⋊C4—42no—
91C11×C4⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C42×C11—21no—
95C42×C11—21no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98Dic11⋊C4—42no—
99Dic11⋊C4—41no—
100Dic11⋊C4—41no—
101C4×Dic11—81no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104#2794—111no—
105#2039D1111yescharacteristic
106#1616—111no—
107#1610—111no—
108#1353—111no—
109#1346—111no—
110#1325—111no—
111C23×C11—41no—
112C23×C11#12011yescharacteristic
113Q8×C11—41no—
114Q8×C11—41no—
115D4×C11—41no—
116D4×C11—41no—
117D4×C11—81no—
118D4×C11—81no—
119D4×C11—81no—
120D4×C11—81no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—22no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—81no—
135C2×C4×C11—81no—
136C2×C4×C11#13511yescharacteristic
137C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—42no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C8×C11—81no—
150C11⋊C8—81no—
151C11⋊C8—81no—
152#537C2×D1111yescharacteristic
153#481—221no—
154#480—221no—
155C2×#104—21no—
156#417—21no—
157#400—111no—
158#400—221no—
159#400—221no—
160#398—111no—
161#387—221no—
162#387—221no—
163#387—221no—
164#387—221no—
165#384C2×D1111yescharacteristic
166#343C2×D1111yescharacteristic
167#327—221no—
168#327—221no—
169#324—111no—
170#324—111no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—81no—
174C22×C11—81no—
175C22×C11—81no—
176C22×C11#44911yescharacteristic
177C22×C11#45411yescharacteristic
178C22×C11B(4,𝔽2)11yescharacteristic
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—42no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—81no—
185C4×C11—81no—
186Dic11—81no—
187Dic11—81no—
188Dic11—81no—
189Dic11—81no—
190C2×#41—21no—
191C2×M16—21no—
192C22⋊Q8—41no—
193#121—21no—
194#121—21no—
195#121—41no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—111no—
199C2×C4⋊C4—111no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4C22⋊D1111yescharacteristic
203C2×C4⋊C4C22×D1111yescharacteristic
204C2×C42—221no—
205C2×C42C22⋊D1111yescharacteristic
206#107—441no—
207#106—441no—
208#104—42no—
209#103—41no—
210#102—41no—
211#102—441no—
212#102—441no—
213C22⋊C8—221no—
214C22⋊C8—221no—
215#95—111no—
216#95—111no—
217#95—221no—
218#95—221no—
219#95—221no—
220#95—221no—
221#95—221no—
222#95—221no—
223#95—221no—
224#95—221no—
225#95—221no—
226C2×C11—21no—
227C2×C11—21no—
228C2×C11—161no—
229C2×C11#159711yescharacteristic
230C2×C11#219811yescharacteristic
231C2×C11#220311yescharacteristic
232#41—41no—
233#41—41no—
234#41—41no—
235#41—41no—
236C2×Q8—21no—
237C2×D4—21no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—41no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—41no—
244C22×C4—221no—
245C22×C4—221no—
246C22×C4—221no—
247C22×C4—221no—
248C22×C4D4×D1111yescharacteristic
249C22×C4D4×D1111yescharacteristic
250C22×C4C2×C22⋊D1111yescharacteristic
251M16—41no—
252M16—41no—
253C2×C8—41no—
254C2×C8—441no—
255C2×C8—441no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—442no—
265C4⋊C4—441no—
266C4⋊C4—441no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C42—21no—
270C42—21no—
271C42—881no—
272C11#1214211yescharacteristic, complemented, Sylow
273C23—41no—
274C23#6699011yescharacteristic
275Q8—41no—
276Q8—41no—
277D4—41no—
278D4—41no—
279D4—81no—
280D4—81no—
281D4—81no—
282D4—81no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—442no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4#6698511yescharacteristic
310C2×C4#6700311yescharacteristic
311C8—81no—
312C8—881no—
313C8—881no—
314C22—21no—
315C22—21no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22#1062264511yescharacteristic
320C22#1062265011yescharacteristic
321C22#1062267511yescharacteristic
322C4—21no—
323C4—21no—
324C4—42no—
325C4—41no—
326C4—41no—
327C4—81no—
328C4—81no—
329C4—881no—
330C4—881no—
331C4—881no—
332C4—881no—
333C2—21no—
334C2—21no—
335C2—161no—
336C2#1306754311yescharacteristic
337C2#1307061111yescharacteristic
338C2#1307063511yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2039C2
socleC22×C11B(4,𝔽2)
prime radicalC11×#537C22
hypercenter#2039D11
hypocenterC11#12142
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2039

Complements

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

NH ≅ G/Ntype
1. #13076436C2semidirect
4. #13066642C2semidirect
5. #13066621C2semidirect
6. #13066562C2semidirect
272. C11#12142semidirect

Maximal subgroups

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

subgroupindex
#130764362
#130676532
#130676192
#130666422
#130666212
#130665622
C11×#20392
#1214211