Finite Group Databasebeta

← #14666359

Subgroups — #14666359

Order 2816.

362 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 57 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#13076882C211yesmaximal, characteristic, complemented
2#13069837C211yesmaximal, characteristic
3#13067653C211yesmaximal, characteristic
4#13066646C211yesmaximal, characteristic, complemented
5#13066644C211yesmaximal, characteristic, complemented
6#13066561C211yesmaximal, characteristic, complemented
7C11×#1604C211yesmaximal, characteristic
8C11×#537C2211yescharacteristic
9C11×#448—21no—
10C11×#395C2211yescharacteristic
11C2×#66901—21no—
12#10622845—21no—
13#10622842—21no—
14#10622647—21no—
15#10622599C2211yescharacteristic
16#10622597—21no—
17#10622593—21no—
18#10622589C2211yescharacteristic
19#10622271—21no—
20#10622270—21no—
21#10622264—21no—
22C11×#327—21no—
23C11×#324C2211yescharacteristic
24#10622175—21no—
25#10622168C2211yescharacteristic
26#10622166C2211yescharacteristic
27C2×C11×#41—21no—
28C22×Q8×C11D411yescharacteristic
29C2×C11×SD16—41no—
30C11×C22⋊Q8—41no—
31C11×#121—21no—
32C11×#121—21no—
33C11×#121—41no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4C2311yescharacteristic
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11D411yescharacteristic
44C2×#4318—21no—
45C11×#103—41no—
46C11×C22⋊C8—21no—
47C11×#95—21no—
48C11×#95D411yescharacteristic
49#66901—42no—
50#66899—41no—
51#66896—41no—
52#66896—41no—
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#12183—111nomaximal, Sylow
64C11×#41—41no—
65C11×#41—41no—
66C11×#41—41no—
67C11×#41—41no—
68C2×Q8×C11—21no—
69C2×Q8×C11—41no—
70C2×Q8×C11—81no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—41no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—41no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C11×SD16—82no—
86C2×C8×C11—41no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—81no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95Dic11⋊C4—81no—
96Dic11⋊C4—81no—
97Dic11⋊C4—81no—
98Dic11⋊C4—81no—
99Dic11⋊C4—81no—
100C4×Dic11—21no—
101C4×Dic11SD1612yescomplemented
102#4318—41no—
103#4318—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106#2843—111no—
107#2039—111no—
108#1616—111no—
109#1604D1111yescharacteristic
110#1354—111no—
111#1353—111no—
112#1325—111no—
113C23×C11—41no—
114C23×C11#12011yescharacteristic
115Q8×C11—41no—
116Q8×C11—41no—
117Q8×C11—42no—
118Q8×C11—81no—
119D4×C11—41no—
120D4×C11—41no—
121D4×C11—81no—
122D4×C11—81no—
123D4×C11—81no—
124D4×C11—81no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
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—81no—
139C2×C4×C11—81no—
140C2×C4×C11C2×SD1611yescharacteristic
141C2×C4×C11#13711yescharacteristic
142C2×Dic11—22no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—42no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C8×C11—81no—
154C11⋊C8—81no—
155C11⋊C8—81no—
156#537C2×D1111yescharacteristic
157#481—221no—
158#448—21no—
159C2×#104—221no—
160#417—221no—
161#400—111no—
162#400—221no—
163#398—221no—
164#398—221no—
165#398—221no—
166#395—221no—
167#395C2×D1111yescharacteristic
168#384—111no—
169#383—221no—
170#343—111no—
171#327—21no—
172#327—221no—
173#324—111no—
174#324C2×D1111yescharacteristic
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—81no—
178C22×C11—81no—
179C22×C11—81no—
180C22×C11#44811yescharacteristic
181C22×C11#45411yescharacteristic
182C22×C11B(4,𝔽2)11yescharacteristic
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11—81no—
188C4×C11—81no—
189C4×C11—81no—
190Dic11—42no—
191Dic11—81no—
192Dic11—81no—
193Dic11—81no—
194C2×#41—21no—
195C22×Q8C22⋊D1111yescharacteristic
196C2×SD16—41no—
197C2×M16—221no—
198C22⋊Q8—41no—
199#121—21no—
200#121—21no—
201#121—41no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—111no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4C22×D1111yescharacteristic
211C2×C42—111no—
212#106—441no—
213#104—442no—
214#103—41no—
215#103—441no—
216#102—441no—
217#102—441no—
218C22⋊C8—21no—
219C22⋊C8—221no—
220#95—21no—
221#95—111no—
222#95—221no—
223#95—221no—
224#95—221no—
225#95—221no—
226#95—221no—
227#95—221no—
228#95—221no—
229#95C22⋊D1111yescharacteristic
230C2×C11—21no—
231C2×C11—21no—
232C2×C11—161no—
233C2×C11#159911yescharacteristic
234C2×C11#220011yescharacteristic
235C2×C11#220311yescharacteristic
236#41—41no—
237#41—41no—
238#41—41no—
239#41—41no—
240C2×Q8—21no—
241C2×Q8—41no—
242C2×Q8—81no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—41no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4D4×D1111yescharacteristic
255C22×C4D4×D1111yescharacteristic
256C22×C4C2×C22⋊D1111yescharacteristic
257SD16—82no—
258M16—441no—
259M16—441no—
260C2×C8—41no—
261C2×C8—441no—
262C2×C8—441no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—41no—
266C4⋊C4—81no—
267C4⋊C4—441no—
268C4⋊C4—441no—
269C4⋊C4—881no—
270C4⋊C4—881no—
271C4⋊C4—881no—
272C4⋊C4—881no—
273C4⋊C4—881no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C42—112no—
277C42—221no—
278C11#1218311yescharacteristic, complemented, Sylow
279C23—41no—
280C23#6699011yescharacteristic
281Q8—41no—
282Q8—41no—
283Q8—42no—
284Q8—81no—
285D4—41no—
286D4—41no—
287D4—81no—
288D4—81no—
289D4—81no—
290D4—81no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—222no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—442no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4SD16×D1111yescharacteristic
318C2×C4#6696811yescharacteristic
319C8—81no—
320C8—881no—
321C8—881no—
322C22—21no—
323C22—21no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22#1062264511yescharacteristic
328C22#1062278311yescharacteristic
329C22#1062281411yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—81no—
335C4—81no—
336C4—81no—
337C4—442no—
338C4—881no—
339C4—881no—
340C4—881no—
341C2—21no—
342C2—21no—
343C2—161no—
344C2#1306755411yescharacteristic
345C2#1307062111yescharacteristic
346C2#1307063511yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1604C2
socleC22×C11B(4,𝔽2)
prime radicalC11×#537C22
hypercenter#1604D11
hypocenterC11#12183
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1604

Complements

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

NH ≅ G/Ntype
1. #13076882C2semidirect
4. #13066646C2semidirect
5. #13066644C2semidirect
6. #13066561C2semidirect
101. C4×Dic11SD16semidirect
278. C11#12183semidirect

Maximal subgroups

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

subgroupindex
#130768822
#130698372
#130676532
#130666462
#130666442
#130665612
C11×#16042
#1218311