Finite Group Databasebeta

← #14657533

Subgroups — #14657533

Order 2816.

398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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#13078409C211yesmaximal, characteristic
2#13068627C211yesmaximal, characteristic
3#13067386C211yesmaximal, characteristic, complemented
4#13067180C211yesmaximal, characteristic, complemented
5#13066936C211yesmaximal, characteristic
6#13066475C211yesmaximal, characteristic, complemented
7C11×#1542C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C4×D44C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×#66885—21no—
13#10622700—21no—
14#10622697—21no—
15#10622679—22no—
16#10622614—21no—
17#10622608—21no—
18#10622549C2211yescharacteristic
19#10622538C2211yescharacteristic
20#10622537C2211yescharacteristic
21C11×#333—21no—
22C11×#332—21no—
23#10622189—21no—
24#10622176—22no—
25#10622118—22no—
26#10622106—22no—
27C22×D44D411yescharacteristic
28C22×C4×D11—21no—
29C22×C8×C11—21no—
30C11×C4⋊Q8D411yescharacteristic
31C11×C4⋊Q8D411yescharacteristic
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×(C2×D11)⋊C4—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11D411yescharacteristic
42C2×#4318—21no—
43C4×D44—21no—
44C4×D44—21no—
45C4×D44—21no—
46C4×D44—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C22⋊C8—21no—
51C4×C8×C11—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C22⋊(C11⋊C8)D412yes—
55#66885—42no—
56#66873—22no—
57#66873—22no—
58#66872—22no—
59#66871—22no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)D412yes—
63C4×C11⋊C8—21no—
64#10468—111nomaximal, Sylow
65C23×D11—21no—
66C2×Q8×C11—21no—
67C2×Q8×C11—21no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4111yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—41no—
73C2×D44—21no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44SD1612yes—
79C2×C4×D11—41no—
80C2×C4×D11—41no—
81C2×C4×D11—82no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
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—41no—
94C42×C11C2×D411yescharacteristic
95C42×C11C2×D411yescharacteristic
96C42×C11#4111yescharacteristic
97C42×C11#4111yescharacteristic
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—41no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104#4318—41no—
105#4318—41no—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—22no—
108#3077—111no—
109#1804—111no—
110#1570—111no—
111#1542D1111yescharacteristic, complemented
112#1518—111no—
113#1460—111no—
114#1286—111no—
115C23×C11#12111yescharacteristic
116C22×D11—22no—
117C22×D11—41no—
118C22×D11—41no—
119C22×D11—81no—
120C22×D11—81no—
121Q8×C11—81no—
122Q8×C11—81no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11#12011yescharacteristic
128C2×C4×C11#12111yescharacteristic
129C2×C4×C11#12111yescharacteristic
130C2×C4×C11#12311yescharacteristic
131C2×C4×C11#12311yescharacteristic
132C2×C4×C11#12411yescharacteristic
133C2×C4×C11C2×SD1611yescharacteristic
134C2×C4×C11#13511yescharacteristic
135C2×C4×C11#13711yescharacteristic
136C2×C4×C11#13711yescharacteristic
137C2×Dic11—41no—
138C2×Dic11—81no—
139C2×Dic11—81no—
140C2×Dic11—81no—
141C2×Dic11—81no—
142D44—22no—
143D44—22no—
144D44—41no—
145D44—41no—
146C4×D11—82no—
147C4×D11—82no—
148C8×C11—81no—
149C8×C11—81no—
150C11⋊C8—42no—
151C11⋊C8—42no—
152#533C2×D1111yescharacteristic
153C2×C4×D4—111no—
154#478—222no—
155#476—221no—
156#474—221no—
157#431—111no—
158#431C2×D1111yescharacteristic
159#428—221no—
160#423—111no—
161C2×C4⋊C8C2×D1111yescharacteristic
162#418—221no—
163C2×#102—221no—
164#382—111no—
165#340—221no—
166#334—222no—
167#333—21no—
168#332—21no—
169#328—222no—
170#323—222no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11#39411yescharacteristic
174C22×C11#46511yescharacteristic
175C22×C11#47011yescharacteristic
176C2×D11—42no—
177C2×D11—82no—
178C2×D11—81no—
179C2×D11—81no—
180C2×D11—82no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—81no—
186C4×C11—81no—
187C4×C11#44811yescharacteristic
188C4×C11#45211yescharacteristic
189C4×C11#48311yescharacteristic
190C4×C11#48511yescharacteristic
191Dic11—81no—
192Dic11—161no—
193C22×D4—111no—
194C23×C4—221no—
195C2×M16—221no—
196C22×C8—21no—
197C4⋊Q8C22⋊D1111yescharacteristic
198C4⋊Q8C22⋊D1111yescharacteristic
199#125—21no—
200C22⋊Q8—21no—
201C22⋊Q8—21no—
202C4×Q8—21no—
203C4×Q8—21no—
204C4×D4—221no—
205C4×D4—221no—
206C4×D4—221no—
207C4×D4—221no—
208#117—21no—
209C2×C4⋊C4—111no—
210C2×C4⋊C4—221no—
211C2×C22⋊C4—221no—
212C2×C42C22×D1111yescharacteristic
213#107—222no—
214#106—222no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—112no—
219C4⋊C8—221no—
220C4⋊C8—221no—
221#102—222no—
222#102—222no—
223#102—442no—
224C22⋊C8—21no—
225C22⋊C8—112no—
226C4×C8—21no—
227C4×C8—221no—
228#95—221no—
229#95—221no—
230C2×C11—21no—
231C2×C11—21no—
232C2×C11#203511yescharacteristic
233C2×C11#204811yescharacteristic
234C2×C11#205311yescharacteristic
235D11—82no—
236C24—221no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×D4—112no—
240C2×D4—221no—
241C2×D4—221no—
242C2×D4—221no—
243C2×D4—221no—
244C2×D4—221no—
245C22×C4—221no—
246C22×C4—441no—
247C22×C4—441no—
248C22×C4—441no—
249C22×C4—882no—
250C22×C4#433911yescharacteristic
251C22×C4D4×D1111yescharacteristic
252C22×C4D4×D1111yescharacteristic
253M16—441no—
254M16—441no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—222no—
260C2×C8—222no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C22⋊C4—41no—
272C22⋊C4—441no—
273C22⋊C4—441no—
274C42—41no—
275C42#433911yescharacteristic
276C42D4×D1111yescharacteristic
277C42#434111yescharacteristic
278C42C2×C22⋊D1111yescharacteristic
279C11#1046811yescharacteristic, complemented, Sylow
280C23—222no—
281C23—441no—
282C23—441no—
283C23—881no—
284C23—881no—
285C23#6693711yescharacteristic
286Q8—81no—
287Q8—81no—
288D4—222no—
289D4—222no—
290D4—441no—
291D4—441no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—441no—
297C2×C4—882no—
298C2×C4—882no—
299C2×C4—881no—
300C2×C4—881no—
301C2×C4—881no—
302C2×C4—881no—
303C2×C4#6693611yescharacteristic
304C2×C4#6693711yescharacteristic
305C2×C4#6693811yescharacteristic
306C2×C4SD16×D1111yescharacteristic
307C2×C4#6696811yescharacteristic
308C2×C4#6697111yescharacteristic
309C2×C4#6697211yescharacteristic
310C2×C4#6698211yescharacteristic
311C2×C4#6699011yescharacteristic
312C2×C4#6699211yescharacteristic
313C8—81no—
314C8—81no—
315C8—442no—
316C8—442no—
317C22—21no—
318C22—21no—
319C22—442no—
320C22—882no—
321C22—882no—
322C22—881no—
323C22—881no—
324C22#1062242011yescharacteristic
325C22#1062242911yescharacteristic
326C22#1062257211yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—81no—
332C4—81no—
333C4—881no—
334C4—1761no—
335C4#1062241811yescharacteristic
336C4#1062242711yescharacteristic
337C4#1062278311yescharacteristic
338C4#1062280011yescharacteristic
339C2—21no—
340C2—21no—
341C2—882no—
342C2#1306981011yescharacteristic
343C2#1306988911yescharacteristic
344C2#1306992011yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1542C2
socleC22×C11#394
prime radicalC22×D44D4
hypercenter#1542D11
hypocenterC11#10468
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
3. #13067386C2semidirect
4. #13067180C2semidirect
6. #13066475C2semidirect
7. C11×#1542C2semidirect
111. #1542D11semidirect
279. C11#10468semidirect

Maximal subgroups

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

subgroupindex
#130784092
#130686272
#130673862
#130671802
#130669362
#130664752
C11×#15422
#1046811