Finite Group Databasebeta

← #14656963

Subgroups — #14656963

Order 2816.

390 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 75 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#13074268C211yesmaximal, characteristic, complemented
2#13067163C211yesmaximal, characteristic
3#13067124C211yesmaximal, characteristic
4#13066510C211yesmaximal, characteristic, complemented
5#13066481C211yesmaximal, characteristic, complemented
6#13066472C211yesmaximal, characteristic, complemented
7C11×#1980C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×#104—21no—
10C2×C11×#104—21no—
11C4×C11×M16C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13#10622597—21no—
14#10622597—21no—
15#10622550C2211yescharacteristic
16#10622546—21no—
17#10622545C2211yescharacteristic
18#10622541—21no—
19#10622539C2211yescharacteristic
20#10622539C2211yescharacteristic
21#10622268—21no—
22#10622260—21no—
23#10622175—21no—
24#10622175—21no—
25#10622175—21no—
26#10622175—21no—
27C2×C11×#41—21no—
28C2×C11×M16—21no—
29C11×C4⋊Q8Q811yescharacteristic
30C11×#127Q811yescharacteristic
31C11×#124—21no—
32C11×#121—21no—
33C11×#121—21no—
34C4×D4×C11—21no—
35C4×D4×C11—21no—
36C2×C11×C4⋊C4—21no—
37C2×C42×C11D411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C42×C11C2311yescharacteristic
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×C4×Dic11—21no—
47C11×#104—42no—
48C11×#104—42no—
49C11×#97—21no—
50C4×C8×C11—21no—
51C11×#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95D411yescharacteristic
58C11⋊#95D411yescharacteristic
59C11⋊#95D411yescharacteristic
60C11⋊#95D411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62C22⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65#66867—21no—
66#66867—21no—
67#10380—111nomaximal, Sylow
68C11×#41—41no—
69C11×#41—41no—
70C11×#41—41no—
71C11×#41—41no—
72C2×Q8×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—41no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—41no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C11×M16—22no—
88C11×M16—41no—
89C2×C8×C11—41no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—42no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C42×C11—41no—
96C42×C11—41no—
97C42×C11C2×Q811yescharacteristic
98C42×C11#4111yescharacteristic
99C42×C11#4111yescharacteristic
100C42×C11#4111yescharacteristic
101C4⋊Dic11—42no—
102C4⋊Dic11—81no—
103Dic11⋊C4—42no—
104Dic11⋊C4—42no—
105Dic11⋊C4—42no—
106Dic11⋊C4—81no—
107C4×Dic11—42no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110#2606—111no—
111#1980D1111yescharacteristic
112#1514—111no—
113#1505—111no—
114#1300—111no—
115#1288—111no—
116#1285—111no—
117C23×C11—41no—
118C23×C11#12011yescharacteristic
119Q8×C11—41no—
120Q8×C11—41no—
121D4×C11—41no—
122D4×C11—41no—
123D4×C11—81no—
124D4×C11—81no—
125D4×C11—81no—
126D4×C11—81no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—22no—
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×C11C22⋊Q811yescharacteristic
141C2×C4×C11C22⋊Q811yescharacteristic
142C2×C4×C11C22⋊Q811yescharacteristic
143C2×C4×C11#12411yescharacteristic
144C2×C4×C11#12411yescharacteristic
145C2×C4×C11#12411yescharacteristic
146C2×Dic11—22no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C8×C11—42no—
159C11⋊C8—81no—
160C11⋊C8—81no—
161#532C2×D1111yescharacteristic
162#432—111no—
163#432—111no—
164C2×#104—21no—
165C2×#104—21no—
166C4×M16C2×D1111yescharacteristic
167#398—221no—
168#398—221no—
169#389—221no—
170#389—221no—
171#387—221no—
172#387—221no—
173#383—111no—
174C4×C4⋊C4C2×D1111yescharacteristic
175#376—111no—
176#327—221no—
177#327—221no—
178#327—221no—
179#327—221no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11#39311yescharacteristic
186C22×C11#45311yescharacteristic
187C22×C11#45411yescharacteristic
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—42no—
195C4×C11—81no—
196C4×C11—81no—
197Dic11—42no—
198Dic11—81no—
199Dic11—81no—
200Dic11—81no—
201C2×#41—21no—
202C2×M16—21no—
203C4⋊Q8Dic2211yescharacteristic
204#127Dic2211yescharacteristic
205#124—21no—
206#121—21no—
207#121—21no—
208C4×D4—21no—
209C4×D4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C42—221no—
218C2×C42C22⋊D1111yescharacteristic
219C2×C42C22⋊D1111yescharacteristic
220C2×C42C22×D1111yescharacteristic
221C4⋊C8—221no—
222C4⋊C8—221no—
223#104—42no—
224#104—42no—
225C22⋊C8—221no—
226C22⋊C8—221no—
227#97—21no—
228#97—221no—
229#97—221no—
230C4×C8—21no—
231#95—21no—
232#95—111no—
233#95—111no—
234#95—111no—
235#95—111no—
236#95—221no—
237#95—221no—
238#95—221no—
239#95—221no—
240#95—221no—
241C2×C11—21no—
242C2×C11—21no—
243C2×C11—161no—
244C2×C11#202711yescharacteristic
245C2×C11#203111yescharacteristic
246C2×C11#203111yescharacteristic
247#41—41no—
248#41—41no—
249#41—41no—
250#41—41no—
251C2×Q8—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—41no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—41no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4—221no—
263C22×C4D4×D1111yescharacteristic
264C22×C4D4×D1111yescharacteristic
265C22×C4C2×C22⋊D1111yescharacteristic
266M16—22no—
267M16—41no—
268C2×C8—41no—
269C2×C8—441no—
270C2×C8—441no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—42no—
274C4⋊C4—442no—
275C4⋊C4—442no—
276C4⋊C4—442no—
277C4⋊C4—442no—
278C4⋊C4—881no—
279C4⋊C4—881no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C42—41no—
283C42—41no—
284C42—442no—
285C42C2×Dic2211yescharacteristic
286C42#433911yescharacteristic
287C42#434111yescharacteristic
288C42#434111yescharacteristic
289C11#1038011yescharacteristic, complemented, Sylow
290C23—41no—
291C23#6699011yescharacteristic
292Q8—41no—
293Q8—41no—
294D4—41no—
295D4—41no—
296D4—81no—
297D4—81no—
298D4—81no—
299D4—81no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—222no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4#6693111yescharacteristic
326C2×C4#6693111yescharacteristic
327C2×C4#6693811yescharacteristic
328C2×C4#6693811yescharacteristic
329C2×C4#6697711yescharacteristic
330C2×C4#6698911yescharacteristic
331C8—42no—
332C8—881no—
333C8—881no—
334C22—21no—
335C22—21no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22#1062256011yescharacteristic
340C22#1062267511yescharacteristic
341C22#1062269011yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—42no—
349C4—81no—
350C4—81no—
351C4—442no—
352C4—881no—
353C4—881no—
354C4—881no—
355C2—21no—
356C2—21no—
357C2—161no—
358C2#1306977211yescharacteristic
359C2#1306978611yescharacteristic
360C2#1306978811yescharacteristic
subgroupG/H
centerC22#10622560
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1980C2
socleC22×C11#393
prime radicalC11×#532C22
hypercenter#1980D11
hypocenterC11#10380
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1980

Complements

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

NH ≅ G/Ntype
1. #13074268C2semidirect
4. #13066510C2semidirect
5. #13066481C2semidirect
6. #13066472C2semidirect
289. C11#10380semidirect

Maximal subgroups

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

subgroupindex
#130742682
#130671632
#130671242
#130665102
#130664812
#130664722
C11×#19802
#1038011