Finite Group Databasebeta

← #14650405

Subgroups — #14650405

Order 2816.

426 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 89 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#13079568C211yesmaximal, characteristic
2#13077691C211yesmaximal, characteristic
3#13067231C211yesmaximal, characteristic, complemented
4#13067228C211yesmaximal, characteristic
5#13066479C211yesmaximal, characteristic, complemented
6#13066446C211yesmaximal, characteristic, complemented
7C11×#1497C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9#10623008C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#431C2211yescharacteristic
12#10622706C411yescharacteristic
13#10622705C411yescharacteristic
14#10622701C411yescharacteristic
15#10622698C411yescharacteristic
16#10622660—22no—
17#10622641—22no—
18#10622539C2211yescharacteristic
19#10622538C2211yescharacteristic
20C2×#66867C2211yescharacteristic
21#10622449—22no—
22#10622340—22no—
23#10622301—21no—
24C8×D44—21no—
25C11×Q8⋊C8—21no—
26C11×Q8⋊C8—21no—
27#10622181—22no—
28#10622102—22no—
29C2×#4339D412yes—
30C11×C4⋊Q8C2×C411yescharacteristic
31C11×C4⋊Q8C2×C411yescharacteristic
32C11×#125—21no—
33C11×C22⋊Q8—21no—
34C11×C22⋊Q8—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C11×#117—21no—
38C2×C42×C11C2311yescharacteristic
39C2×#4326—22no—
40C2×#4325—22no—
41#66983—21no—
42#66983—21no—
43C22×C11⋊C8—21no—
44C2×#4313—22no—
45C2×C8×D11—22no—
46#66928D412yes—
47#66927C2×C411yescharacteristic
48C4×D44—21no—
49C4×D44—21no—
50#66922C2×C411yescharacteristic
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C22⋊C8—21no—
54C11×C22⋊C8—21no—
55C11×#97—21no—
56C4×C8×C11D411yescharacteristic
57C4×C8×C11D411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60(C2×D11)⋊C8—22no—
61(C2×D11)⋊C8—22no—
62#66874—22no—
63#66873—22no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66#66867—21no—
67#66867—21no—
68#66867D412yes—
69C4×C11⋊C8C2×C411yescharacteristic
70C4×C11⋊C8C2×C411yescharacteristic
71#9285—111nomaximal, Sylow
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11#4111yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C2×C22⋊D11—22no—
78#4339—82no—
79C2×D44—21no—
80C2×D44—21no—
81C2×D44C22⋊C412yes—
82C2×C4×D11—22no—
83C2×Dic22C22⋊C412yes—
84C2×C8×C11—21no—
85C2×C8×C11—21no—
86C2×C8×C11—41no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C22⋊C4—41no—
94C42×C11—41no—
95C42×C11C22×C411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99#4326—82no—
100#4325—82no—
101(C2×D11)⋊C4—22no—
102(C2×D11)⋊C4—22no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105C2×C11⋊C8—22no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—21no—
108C2×C11⋊C8—22no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111#4313—82no—
112C8×D11—82no—
113#3210—111no—
114#2981—111no—
115#1531—111no—
116#1530—111no—
117#1497D1111yescharacteristic, complemented
118#1287—111no—
119#1275—111no—
120C23×C11#12311yescharacteristic
121C22×D11—22no—
122Q8×C11—42no—
123Q8×C11—41no—
124Q8×C11—41no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11C2×C22⋊C411yescharacteristic
132C2×C4×C11C4×D411yescharacteristic
133C2×C4×C11C4×D411yescharacteristic
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C22⋊D11—82no—
138C2×Dic11—22no—
139D44—42no—
140D44—41no—
141D44—41no—
142D44—81no—
143C4×D11—42no—
144C4×D11—42no—
145Dic22—42no—
146C8×C11—41no—
147C8×C11—41no—
148C8×C11—81no—
149C11⋊C8—42no—
150C11⋊C8—42no—
151C11⋊C8—41no—
152C11⋊C8—41no—
153#533C2×D1111yescharacteristic
154#532—111no—
155#494—111no—
156#492—111no—
157#487—111no—
158#486—111no—
159#464—222no—
160#452—222no—
161#436—221no—
162#435—222no—
163C8×D4—221no—
164#432—111no—
165#432C2×D1111yescharacteristic
166#431—111no—
167#431C2×D1111yescharacteristic
168#408—222no—
169C2×#97—111no—
170#330—222no—
171#329—222no—
172Q8⋊C8—21no—
173Q8⋊C8—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11#38611yescharacteristic
178C2×D11—42no—
179C2×D11—42no—
180C2×D11—42no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—81no—
187C4×C11—81no—
188C4×C11#44311yescharacteristic
189C4×C11#44411yescharacteristic
190Dic11—42no—
191C2×#41—112no—
192C2×Q16—222no—
193C2×SD16—222no—
194C2×M16—222no—
195C22×C8—222no—
196C22×C8—221no—
197C4⋊Q8—111no—
198C4⋊Q8C4×D1111yescharacteristic
199C4⋊Q8C4×D1111yescharacteristic
200#127—111no—
201#125—21no—
202#124—112no—
203C22⋊Q8—21no—
204C22⋊Q8—21no—
205#121—221no—
206#121—221no—
207C4×Q8—21no—
208C4×Q8—21no—
209C4×D4—221no—
210C4×D4—221no—
211#117—21no—
212C2×C42C22×D1111yescharacteristic
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—221no—
216C4⋊C8—221no—
217#103—222no—
218#102—222no—
219C22⋊C8—21no—
220C22⋊C8—21no—
221C22⋊C8—222no—
222C22⋊C8—222no—
223C22⋊C8—221no—
224C22⋊C8—221no—
225#97—21no—
226#97—112no—
227#97—221no—
228#97—221no—
229C4×C8—111no—
230C4×C8—111no—
231C4×C8C22⋊D1111yescharacteristic
232C4×C8C22⋊D1111yescharacteristic
233C2×C11—41no—
234C2×C11#187611yescharacteristic
235C2×C11#190211yescharacteristic
236C2×C11#191111yescharacteristic
237D11—82no—
238#41—882no—
239C2×Q8—21no—
240C2×Q8—21no—
241C2×Q8—112no—
242C2×D4—112no—
243C2×D4—222no—
244C2×D4—221no—
245C2×D4—221no—
246C22×C4—222no—
247C22×C4#433911yescharacteristic
248C22×C4D4×D1111yescharacteristic
249C22×C4#434111yescharacteristic
250Q16—882no—
251SD16—882no—
252M16—882no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—41no—
256C2×C8—222no—
257C2×C8—221no—
258C2×C8—221no—
259C2×C8—222no—
260C2×C8—441no—
261C2×C8—441no—
262C2×C8—882no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C22⋊C4—41no—
272C22⋊C4—222no—
273C22⋊C4—222no—
274C42—41no—
275C42C2×C4×D1111yescharacteristic
276C42D4×D1111yescharacteristic
277C42D4×D1111yescharacteristic
278C42C2×C22⋊D1111yescharacteristic
279C11#928511yescharacteristic, complemented, Sylow
280C23—222no—
281C23#6693611yescharacteristic
282Q8—42no—
283Q8—41no—
284Q8—41no—
285Q8—442no—
286D4—442no—
287D4—441no—
288D4—441no—
289D4—881no—
290D4—882no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—222no—
298C2×C4—442no—
299C2×C4—442no—
300C2×C4C22⋊C4×D1111yescharacteristic
301C2×C4(C22⋊D11)⋊C411yescharacteristic
302C2×C4#6693711yescharacteristic
303C2×C4C4×C22⋊D1111yescharacteristic
304C2×C4#6699011yescharacteristic
305C2×C4#6699111yescharacteristic
306C8—41no—
307C8—41no—
308C8—81no—
309C8—442no—
310C8—442no—
311C8—441no—
312C8—441no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—442no—
317C22—442no—
318C22—442no—
319C22#1062256911yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—81no—
326C4—81no—
327C4—442no—
328C4#1062275711yescharacteristic
329C4#1062275811yescharacteristic
330C2—41no—
331C2—882no—
332C2#1306894611yescharacteristic
333C2#1306908611yescharacteristic
334C2#1306914511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1497C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1497D11
hypocenterC11#9285
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1497

Complements

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

NH ≅ G/Ntype
3. #13067231C2semidirect
5. #13066479C2semidirect
6. #13066446C2semidirect
7. C11×#1497C2semidirect
117. #1497D11semidirect
279. C11#9285semidirect

Maximal subgroups

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

subgroupindex
#130795682
#130776912
#130672312
#130672282
#130664792
#130664462
C11×#14972
#928511