Finite Group Databasebeta

← #14666108

Subgroups — #14666108

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#13076440C211yesmaximal, characteristic, complemented
2#13069837C211yesmaximal, characteristic
3#13067653C211yesmaximal, characteristic
4#13066644C211yesmaximal, characteristic, complemented
5#13066622C211yesmaximal, characteristic, complemented
6#13066561C211yesmaximal, characteristic, complemented
7C11×#1610C211yesmaximal, characteristic
8C11×#537C2211yescharacteristic
9C11×#480—21no—
10C11×#398C2211yescharacteristic
11C2×#66901—21no—
12#10622845—21no—
13#10622647—21no—
14#10622599C2211yescharacteristic
15#10622594—21no—
16#10622591—21no—
17#10622591—21no—
18#10622589C2211yescharacteristic
19#10622271—21no—
20#10622271—21no—
21#10622268—21no—
22C11×#327—21no—
23C11×#324C2211yescharacteristic
24#10622175—21no—
25#10622168C2211yescharacteristic
26#10622166C2211yescharacteristic
27C2×C11×#41—21no—
28C11×C22⋊Q8—41no—
29C11×#121—21no—
30C11×#121—21no—
31C11×#121—41no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C4⋊Dic11D411yescharacteristic
36C2×C4⋊Dic11D411yescharacteristic
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×C4×Dic11—21no—
41C2×C4×Dic11D411yescharacteristic
42C2×#4318—21no—
43C11×#107—41no—
44C11×#102—41no—
45C11×C22⋊C8—21no—
46C11×#95—21no—
47C11×#95D411yescharacteristic
48#66901—42no—
49#66899—41no—
50#66896—41no—
51#66896—41no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95D411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62#66872—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—
83C2×C8×C11—41no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94Dic11⋊C4—42no—
95Dic11⋊C4—42no—
96Dic11⋊C4—42no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—81no—
100#4318—41no—
101#4318—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104#2794—111no—
105#2039—111no—
106#1616—111no—
107#1610D1111yescharacteristic
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—21no—
124C2×C4×C11—21no—
125C2×C4×C11—41no—
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—22no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—42no—
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—21no—
155C2×#104—221no—
156#417—221no—
157#400—111no—
158#400—221no—
159#400—221no—
160#398C2×D1111yescharacteristic
161#387—221no—
162#387—221no—
163#387—221no—
164#387—221no—
165#384—111no—
166#343—111no—
167#327—21no—
168#327—221no—
169#324—111no—
170#324C2×D1111yescharacteristic
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—41no—
182C4×C11—41no—
183C4×C11—81no—
184C4×C11—81no—
185C4×C11—81no—
186Dic11—42no—
187Dic11—81no—
188Dic11—81no—
189Dic11—81no—
190C2×#41—21no—
191C2×M16—221no—
192C22⋊Q8—41no—
193#121—21no—
194#121—21no—
195#121—41no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—111no—
198C2×C4⋊C4—111no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4C22⋊D1111yescharacteristic
203C2×C4⋊C4C22×D1111yescharacteristic
204C2×C42—111no—
205C2×C42—221no—
206#107—41no—
207#106—441no—
208#104—442no—
209#103—441no—
210#102—41no—
211#102—441no—
212#102—441no—
213C22⋊C8—21no—
214C22⋊C8—221no—
215#95—21no—
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#95C22⋊D1111yescharacteristic
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—441no—
252M16—441no—
253C2×C8—41no—
254C2×C8—441no—
255C2×C8—441no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—442no—
265C4⋊C4—442no—
266C4⋊C4—442no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C42—221no—
270C42—221no—
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—21no—
286C2×C4—21no—
287C2×C4—41no—
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—222no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—442no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4#6696411yescharacteristic
310C2×C4#6696511yescharacteristic
311C8—81no—
312C8—881no—
313C8—881no—
314C22—21no—
315C22—21no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22#1062264511yescharacteristic
320C22#1062277111yescharacteristic
321C22#1062281411yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—81no—
327C4—81no—
328C4—81no—
329C4—442no—
330C4—881no—
331C4—881no—
332C4—881no—
333C2—21no—
334C2—21no—
335C2—161no—
336C2#1306754211yescharacteristic
337C2#1307061011yescharacteristic
338C2#1307063511yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1610C2
socleC22×C11B(4,𝔽2)
prime radicalC11×#537C22
hypercenter#1610D11
hypocenterC11#12142
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1610

Complements

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

NH ≅ G/Ntype
1. #13076440C2semidirect
4. #13066644C2semidirect
5. #13066622C2semidirect
6. #13066561C2semidirect
272. C11#12142semidirect

Maximal subgroups

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

subgroupindex
#130764402
#130698372
#130676532
#130666442
#130666222
#130665612
C11×#16102
#1214211