Finite Group Databasebeta

← #14656965

Subgroups — #14656965

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#13074273C211yesmaximal, characteristic, complemented
2#13069536C211yesmaximal, characteristic
3#13067163C211yesmaximal, characteristic
4#13066509C211yesmaximal, characteristic, complemented
5#13066482C211yesmaximal, characteristic, complemented
6#13066473C211yesmaximal, characteristic, complemented
7C11×#1505C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C11×#432C2211yescharacteristic
10C11×#376C2211yescharacteristic
11C2×#66901—21no—
12C2×#66901—21no—
13#10622550C2211yescharacteristic
14C4×C4⋊Dic11C2211yescharacteristic
15#10622546—21no—
16#10622541—21no—
17#10622539C2211yescharacteristic
18C4×#4318C2211yescharacteristic
19#10622274—21no—
20#10622270—21no—
21#10622267—21no—
22#10622260—21no—
23C11×#327—21no—
24C11×#327—21no—
25#10622175—21no—
26#10622175—21no—
27C2×C11×#41—21no—
28C11×C4⋊Q8Q811yescharacteristic
29C11×#127Q811yescharacteristic
30C11×#124—21no—
31C11×#121—21no—
32C11×#121—21no—
33C4×D4×C11—21no—
34C4×D4×C11—21no—
35C2×C42×C11—21no—
36C2×C42×C11C2311yescharacteristic
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×C4×Dic11D411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C2×#4318—21no—
47C11×C4⋊C8—21no—
48C11×C22⋊C8—21no—
49C11×#97—21no—
50C11×#95—21no—
51C11×#95D411yescharacteristic
52C11×#95D411yescharacteristic
53#66901—42no—
54#66901—42no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95D411yescharacteristic
61C11⋊#95D411yescharacteristic
62C22⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64#66867—21no—
65#66867—21no—
66C4×C11⋊C8—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—
87C2×C8×C11—41no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C42×C11—42no—
93C42×C11C2×Q811yescharacteristic
94C42×C11#4111yescharacteristic
95C42×C11#4111yescharacteristic
96C42×C11#4111yescharacteristic
97C4⋊Dic11—42no—
98C4⋊Dic11—42no—
99C4⋊Dic11—42no—
100Dic11⋊C4—42no—
101Dic11⋊C4—42no—
102Dic11⋊C4—81no—
103Dic11⋊C4—81no—
104C4×Dic11—41no—
105C4×Dic11—41no—
106#4318—22no—
107#4318—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110#2606—111no—
111#1980—111no—
112#1514—111no—
113#1505D1111yescharacteristic
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—81no—
159C11⋊C8—42no—
160C11⋊C8—81no—
161#532C2×D1111yescharacteristic
162#432—111no—
163#432C2×D1111yescharacteristic
164C2×#104—221no—
165C2×#104—221no—
166C4×M16—111no—
167#398—221no—
168#398—221no—
169#389—221no—
170#389—221no—
171#387—221no—
172#387—221no—
173#383—111no—
174C4×C4⋊C4—111no—
175#376C2×D1111yescharacteristic
176#327—21no—
177#327—21no—
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—221no—
203C4⋊Q8Dic2211yescharacteristic
204#127Dic2211yescharacteristic
205#124—21no—
206#121—21no—
207#121—21no—
208C4×D4—21no—
209C4×D4—21no—
210C2×C4⋊C4—221no—
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—21no—
218C2×C42—111no—
219C2×C42—111no—
220C2×C42C22×D1111yescharacteristic
221C4⋊C8—21no—
222C4⋊C8—221no—
223#104—442no—
224#104—442no—
225C22⋊C8—21no—
226C22⋊C8—221no—
227#97—21no—
228#97—221no—
229#97—221no—
230C4×C8—221no—
231#95—21no—
232#95—111no—
233#95—111no—
234#95—221no—
235#95—221no—
236#95—221no—
237#95—221no—
238#95—221no—
239#95C22⋊D1111yescharacteristic
240#95C22⋊D1111yescharacteristic
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—222no—
267M16—441no—
268C2×C8—41no—
269C2×C8—441no—
270C2×C8—441no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—442no—
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—42no—
283C42—441no—
284C42—441no—
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—81no—
332C8—442no—
333C8—881no—
334C22—21no—
335C22—21no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22#1062256011yescharacteristic
340C22#1062281111yescharacteristic
341C22#1062281411yescharacteristic
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#1306977011yescharacteristic
359C2#1306978811yescharacteristic
360C2#1306979011yescharacteristic
subgroupG/H
centerC22#10622560
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1505C2
socleC22×C11#393
prime radicalC11×#532C22
hypercenter#1505D11
hypocenterC11#10380
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1505

Complements

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

NH ≅ G/Ntype
1. #13074273C2semidirect
4. #13066509C2semidirect
5. #13066482C2semidirect
6. #13066473C2semidirect
289. C11#10380semidirect

Maximal subgroups

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

subgroupindex
#130742732
#130695362
#130671632
#130665092
#130664822
#130664732
C11×#15052
#1038011