Finite Group Databasebeta

← #14653185

Subgroups — #14653185

Order 2816.

418 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 97 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#13079198C211yesmaximal, characteristic
2#13068303C211yesmaximal, characteristic
3#13067377C211yesmaximal, characteristic
4#13067232C211yesmaximal, characteristic
5#13067231C211yesmaximal, characteristic
6#13067127C211yesmaximal, characteristic
7C11×#1506C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#376C2211yescharacteristic
12#10622706C411yescharacteristic, complemented
13#10622705C411yescharacteristic, complemented
14#10622694C411yescharacteristic, complemented
15#10622691C411yescharacteristic, complemented
16#10622664—21no—
17#10622664—21no—
18C4×#4326—21no—
19C4×#4326—21no—
20#10622539C2211yescharacteristic
21C2×#66867—21no—
22C2×#66867C2211yescharacteristic
23C2×C4×C11⋊C8—21no—
24C2×C4×C11⋊C8C2211yescharacteristic
25C11×#328—22no—
26#10622181—22no—
27#10622118—21no—
28#10622117—21no—
29#10622103—22no—
30#10622090—22no—
31C11×C4⋊Q8C2×C411yescharacteristic
32C11×C4⋊Q8C2×C411yescharacteristic
33C11×#125—21no—
34C11×C22⋊Q8—21no—
35C11×C22⋊Q8—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C11×#117—21no—
39C2×C42×C11—21no—
40C2×C42×C11C2311yescharacteristic
41C2×#4326—21no—
42C2×#4326—21no—
43#66979—21no—
44#66977—21no—
45#66977—21no—
46C22×C11⋊C8—21no—
47C22×C11⋊C8D411yescharacteristic
48C22×C11⋊C8D411yescharacteristic
49#66923—21no—
50#66922C2×C411yescharacteristic
51#66922C2×C411yescharacteristic
52C4×Dic22—21no—
53C4×Dic22—21no—
54C11×C4⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×#97—21no—
57C11×#95—21no—
58C11×#95D412yes—
59#66899—21no—
60#66899—21no—
61C22⋊(C11⋊C8)—21no—
62#66874—21no—
63#66874—21no—
64#66871—21no—
65#66871—21no—
66C4⋊(C11⋊C8)—21no—
67#66867—24no—
68#66867—21no—
69#66867—21no—
70#66867D412yes—
71C4×C11⋊C8—24no—
72C4×C11⋊C8C2×C411yescharacteristic
73C4×C11⋊C8C2×C411yescharacteristic
74C4×C11⋊C8D411yescharacteristic
75C4×C11⋊C8D411yescharacteristic
76#9763—111nomaximal, Sylow
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C22×C4×C11—22no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C2×Dic22—21no—
84C2×Dic22—21no—
85C2×C8×C11—41no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C22⋊C4—41no—
93C42×C11—22no—
94C42×C11—22no—
95C42×C11—41no—
96C42×C11C22×C411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11#4111yescharacteristic
100C22⋊Dic11—41no—
101#4326—42no—
102#4326—42no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107Dic11⋊C4—41no—
108Dic11⋊C4—41no—
109C4×Dic11—41no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8C22⋊C411yescharacteristic
117C2×C11⋊C8C22⋊C411yescharacteristic
118C2×C11⋊C8C22⋊C411yescharacteristic
119C2×C11⋊C8C22⋊C411yescharacteristic
120#3170—111no—
121#1726—111no—
122#1568—111no—
123#1531—111no—
124#1531—111no—
125#1506—111no—
126#1506D1111yescharacteristic
127C23×C11#12111yescharacteristic
128Q8×C11—41no—
129Q8×C11—41no—
130Q8×C11—81no—
131C2×C4×C11—22no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—24no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11C2×C22⋊C411yescharacteristic
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11C4×D411yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12411yescharacteristic
145C2×C4×C11#12711yescharacteristic
146C2×Dic11—41no—
147C2×Dic11—41no—
148Dic22—41no—
149Dic22—41no—
150Dic22—81no—
151C8×C11—81no—
152C11⋊C8—24no—
153C11⋊C8—21no—
154C11⋊C8—21no—
155C11⋊C8—81no—
156C11⋊C8#10412yes—
157C11⋊C8#10412yes—
158#533—111no—
159#533C2×D1111yescharacteristic
160#500—111no—
161#494—111no—
162#487—111no—
163#487—111no—
164#467—221no—
165#467—221no—
166C4×Q16—221no—
167C4×Q16—221no—
168#432—111no—
169#432C2×D1111yescharacteristic
170C2×#97—111no—
171C2×#97—221no—
172C2×C4×C8—111no—
173C2×C4×C8—221no—
174#376C2×D1111yescharacteristic
175#335—221no—
176#334—221no—
177#330—222no—
178#330—222no—
179#328—22no—
180#328—222no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11#39011yescharacteristic
184C22×C11#47312yes—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—44no—
191C4×C11—81no—
192C4×C11—81no—
193C4×C11C2×#10411yescharacteristic
194C4×C11C2×#10411yescharacteristic
195Dic11—81no—
196Dic11—81no—
197C2×Q16—221no—
198C2×Q16—221no—
199C22×C8—111no—
200C22×C8—111no—
201C22×C8—221no—
202C4⋊Q8—111no—
203C4⋊Q8—111no—
204C4⋊Q8C4×D1111yescharacteristic
205C4⋊Q8C4×D1111yescharacteristic
206#125—21no—
207#125—221no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C22⋊Q8—221no—
211C22⋊Q8—221no—
212C4×Q8—21no—
213C4×Q8—21no—
214C4×Q8—221no—
215C4×Q8—221no—
216#117—21no—
217#117—221no—
218C2×C42—21no—
219C2×C42C22×D1111yescharacteristic
220#107—221no—
221#107—221no—
222C4⋊C8—21no—
223C4⋊C8—221no—
224#103—221no—
225#103—221no—
226#103—221no—
227#103—221no—
228C22⋊C8—21no—
229C22⋊C8—221no—
230#97—21no—
231#97—112no—
232#97—224no—
233#97—221no—
234#97—221no—
235C4×C8—111no—
236C4×C8—111no—
237C4×C8—111no—
238C4×C8—111no—
239C4×C8—224no—
240#95—21no—
241#95C22⋊D1112yes—
242C2×C11—22no—
243C2×C11#196211yescharacteristic
244C2×C11#197611yescharacteristic
245C2×C11#197911yescharacteristic
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—221no—
249C2×Q8—221no—
250C22×C4—22no—
251C22×C4D4×D1111yescharacteristic
252C22×C4#434111yescharacteristic
253C22×C4C2×C22⋊D1111yescharacteristic
254Q16—442no—
255Q16—442no—
256C2×C8—41no—
257C2×C8—111no—
258C2×C8—111no—
259C2×C8—111no—
260C2×C8—111no—
261C2×C8—222no—
262C2×C8—222no—
263C2×C8—222no—
264C2×C8—222no—
265C2×C8—222no—
266C2×C8—441no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C22⋊C4—41no—
280C22⋊C4—441no—
281C42—22no—
282C42—22no—
283C42—41no—
284C42—441no—
285C42C2×C4×D1111yescharacteristic
286C42#433911yescharacteristic
287C42D4×D1111yescharacteristic
288C42D4×D1111yescharacteristic
289C11#976311yescharacteristic, complemented, Sylow
290C23#6699211yescharacteristic
291Q8—41no—
292Q8—41no—
293Q8—81no—
294Q8—441no—
295Q8—441no—
296Q8—881no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—24no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4C22⋊C4×D1111yescharacteristic
309C2×C4(C22⋊D11)⋊C411yescharacteristic
310C2×C4#6693711yescharacteristic
311C2×C4#6693811yescharacteristic
312C2×C4C4×C22⋊D1111yescharacteristic
313C2×C4#6699311yescharacteristic
314C8—81no—
315C8—112no—
316C8—112no—
317C8—224no—
318C8—221no—
319C8—221no—
320C8—881no—
321C22—21no—
322C22—21no—
323C22#1062257011yescharacteristic
324C22#1062281712yes—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—44no—
331C4—81no—
332C4—81no—
333C4—881no—
334C4—881no—
335C4D11×#10411yescharacteristic
336C4D11×#10411yescharacteristic
337C2—22no—
338C2#1306944211yescharacteristic
339C2#1306951111yescharacteristic
340C2#1306953011yescharacteristic
subgroupG/H
centerC22#10622570
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1506C2
socleC22×C11#390
prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1506D11
hypocenterC11#9763
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1506

Complements

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

NH ≅ G/Ntype
12. #10622706C4semidirect
13. #10622705C4semidirect
14. #10622694C4semidirect
15. #10622691C4semidirect
289. C11#9763semidirect

Maximal subgroups

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

subgroupindex
#130791982
#130683032
#130673772
#130672322
#130672312
#130671272
C11×#15062
#976311