Finite Group Databasebeta

← #14650421

Subgroups — #14650421

Order 2816.

410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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#13079764C211yesmaximal, characteristic
2#13077557C211yesmaximal, characteristic
3#13069588C211yesmaximal, characteristic
4#13067296C211yesmaximal, characteristic
5#13066474C211yesmaximal, characteristic
6#13066446C211yesmaximal, characteristic
7C11×#1518C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#382C2211yescharacteristic
12#10622694C412yescomplemented
13#10622691C412yescomplemented
14#10622657—22no—
15#10622637—22no—
16#10622637—22no—
17#10622634—22no—
18#10622612—21no—
19#10622610—21no—
20#10622538C2211yescharacteristic
21#10622537C2211yescharacteristic
22C2×#66867C2211yescharacteristic
23C11×#328—22no—
24#10622167—21no—
25#10622167—21no—
26#10622119—22no—
27C22×Dic22—21no—
28C11×C4⋊Q8C2×C411yescharacteristic
29C11×C4⋊Q8C2×C411yescharacteristic
30C11×#125—21no—
31C11×C22⋊Q8—21no—
32C11×C22⋊Q8D412yes—
33C4×Q8×C11—21no—
34C4×Q8×C11D412yes—
35C11×#117—21no—
36C2×C11×C4⋊C4—21no—
37C2×C42×C11C2311yescharacteristic
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×#4318—21no—
41C22×C11⋊C8D411yescharacteristic
42C22×C11⋊C8D411yescharacteristic
43#66922—21no—
44#66922—21no—
45#66922—21no—
46#66922C2×C412yes—
47C11×C4⋊C8—21no—
48C11×C22⋊C8—21no—
49C4×C8×C11—21no—
50C11×#95—21no—
51C11×#95—21no—
52#66899—24no—
53C22⋊(C11⋊C8)—21no—
54#66871—24no—
55C4⋊(C11⋊C8)—24no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)D412yes—
59#66867—22no—
60#66867—21no—
61#66867—21no—
62C4×C11⋊C8—22no—
63C4×C11⋊C8C2×C412yes—
64#9288—111nomaximal, Sylow
65C2×Q8×C11—21no—
66C2×Q8×C11C22⋊C412yes—
67C22×C4×C11—41no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4111yescharacteristic
71C22×Dic11—41no—
72C2×Dic22—22no—
73C2×Dic22—41no—
74C2×Dic22—82no—
75C2×C8×C11—41no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4C22⋊C412yes—
84C11×C22⋊C4—22no—
85C42×C11—22no—
86C42×C11C22×C411yescharacteristic
87C42×C11C2×D411yescharacteristic
88C42×C11C2×D411yescharacteristic
89C42×C11#4111yescharacteristic
90C4⋊Dic11—22no—
91C4⋊Dic11—22no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94#4318—41no—
95#4318—41no—
96C2×C11⋊C8—22no—
97C2×C11⋊C8—21no—
98C2×C11⋊C8—22no—
99C2×C11⋊C8—21no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8Q1612yes—
104#3230—111no—
105#2961—111no—
106#1993—111no—
107#1548—111no—
108#1518D1111yescharacteristic
109#1286—111no—
110#1275—111no—
111C23×C11#12111yescharacteristic
112Q8×C11—42no—
113Q8×C11—81no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—81no—
119C2×C4×C11—81no—
120C2×C4×C11—81no—
121C2×C4×C11C2×C22⋊C411yescharacteristic
122C2×C4×C11C4×D411yescharacteristic
123C2×C4×C11C4×D411yescharacteristic
124C2×C4×C11#12011yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12311yescharacteristic
127C2×C4×C11C2×Q1611yescharacteristic
128C2×C4×C11#13511yescharacteristic
129C2×C4×C11#13711yescharacteristic
130C2×C4×C11#13711yescharacteristic
131C2×Dic11—42no—
132C2×Dic11—82no—
133Dic22—82no—
134Dic22—82no—
135C8×C11—81no—
136C11⋊C8—22no—
137C11⋊C8—42no—
138C11⋊C8—41no—
139C11⋊C8—42no—
140#533C2×D1111yescharacteristic
141C2×C4⋊Q8—111no—
142#500—112no—
143#487—112no—
144#484—222no—
145#477—222no—
146#446—222no—
147#446—222no—
148#431—111no—
149#431C2×D1111yescharacteristic
150#424—221no—
151#423—111no—
152#405—221no—
153C2×#97—111no—
154#382C2×D1111yescharacteristic
155#340—221no—
156#340—221no—
157#333—222no—
158#328—22no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11#38611yescharacteristic
162C22×C11#46211yescharacteristic
163C22×C11#46411yescharacteristic
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—42no—
169C4×C11—42no—
170C4×C11—161no—
171C4×C11C4×Q1611yescharacteristic
172C4×C11#44111yescharacteristic
173C4×C11#45111yescharacteristic
174C4×C11#45211yescharacteristic
175Dic11—82no—
176C22×Q8—221no—
177C2×M16—221no—
178C22×C8—111no—
179C22×C8—111no—
180C4⋊Q8—112no—
181C4⋊Q8—221no—
182C4⋊Q8—221no—
183C4⋊Q8—221no—
184C4⋊Q8C4×D1111yescharacteristic
185C4⋊Q8C4×D1111yescharacteristic
186#125—21no—
187C22⋊Q8—21no—
188C22⋊Q8C22⋊D1112yes—
189C4×Q8—21no—
190C4×Q8D4412yes—
191#117—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—221no—
194C2×C4⋊C4—221no—
195C2×C42C22×D1111yescharacteristic
196#107—224no—
197C4⋊C8—21no—
198C4⋊C8—112no—
199C4⋊C8—224no—
200C4⋊C8—221no—
201C4⋊C8—221no—
202#103—224no—
203C22⋊C8—21no—
204C22⋊C8—221no—
205#97—222no—
206#97—221no—
207#97—221no—
208C4×C8—21no—
209C4×C8—112no—
210C4×C8—222no—
211#95—21no—
212#95—21no—
213C2×C11—21no—
214C2×C11—21no—
215C2×C11#187811yescharacteristic
216C2×C11#190311yescharacteristic
217C2×C11#190911yescharacteristic
218C2×Q8—21no—
219C2×Q8—222no—
220C2×Q8—441no—
221C2×Q8—882no—
222C2×Q8(C2×D11)⋊C412yes—
223C22×C4—41no—
224C22×C4—441no—
225C22×C4D4×D1111yescharacteristic
226C22×C4#434111yescharacteristic
227C22×C4C2×C22⋊D1111yescharacteristic
228M16—441no—
229M16—441no—
230C2×C8—41no—
231C2×C8—112no—
232C2×C8—221no—
233C2×C8—221no—
234C2×C8—222no—
235C2×C8—221no—
236C2×C8—221no—
237C2×C8—221no—
238C2×C8—222no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—222no—
247C4⋊C4—222no—
248C4⋊C4—441no—
249C4⋊C4—441no—
250C4⋊C4(C2×D11)⋊C412yes—
251C22⋊C4—22no—
252C42—22no—
253C42C2×C4×D1111yescharacteristic
254C42C2×D4411yescharacteristic
255C42D4×D1111yescharacteristic
256C42#434111yescharacteristic
257C11#928811yescharacteristic, complemented, Sylow
258C23#6699211yescharacteristic
259Q8—42no—
260Q8—81no—
261Q8—882no—
262Q8—882no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—442no—
271C2×C4—882no—
272C2×C4(C22⋊D11)⋊C411yescharacteristic
273C2×C4(C22⋊D11)⋊C411yescharacteristic
274C2×C4#6693511yescharacteristic
275C2×C4#6693911yescharacteristic
276C2×C4#6696811yescharacteristic
277C2×C4#6696911yescharacteristic
278C2×C4Q16×D1111yescharacteristic
279C2×C4#6697111yescharacteristic
280C2×C4C2×(C2×D11)⋊C411yescharacteristic
281C2×C4#6699211yescharacteristic
282C8—81no—
283C8—222no—
284C8—442no—
285C8—441no—
286C8—442no—
287C22—21no—
288C22—21no—
289C22#1062257111yescharacteristic
290C22#1062277911yescharacteristic
291C22#1062279511yescharacteristic
292C4—21no—
293C4—21no—
294C4—21no—
295C4—21no—
296C4—42no—
297C4—42no—
298C4—161no—
299C4—882no—
300C4#1062240211yescharacteristic
301C4#1062240311yescharacteristic
302C4#1062242111yescharacteristic
303C4#1062242311yescharacteristic
304C2—21no—
305C2—21no—
306C2#1306895511yescharacteristic
307C2#1306909411yescharacteristic
308C2#1306913611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1518C2
socleC22×C11#386
prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1518D11
hypocenterC11#9288
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
12. #10622694C4semidirect
13. #10622691C4semidirect
257. C11#9288semidirect

Maximal subgroups

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

subgroupindex
#130797642
#130775572
#130695882
#130672962
#130664742
#130664462
C11×#15182
#928811