Finite Group Databasebeta

← #14657535

Subgroups — #14657535

Order 2816.

398 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 93 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#13078413C211yesmaximal, characteristic
2#13067386C211yesmaximal, characteristic, complemented
3#13067274C211yesmaximal, characteristic, complemented
4#13067179C211yesmaximal, characteristic, complemented
5#13066937C211yesmaximal, characteristic
6#13066474C211yesmaximal, characteristic, complemented
7C11×#1804C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C11×#102—21no—
12C11×#382C2211yescharacteristic
13#10622828—21no—
14#10622622—22no—
15#10622621—21no—
16#10622620—21no—
17#10622577—21no—
18#10622538C2211yescharacteristic
19#10622538C2211yescharacteristic
20#10622537C2211yescharacteristic
21C11×#340—21no—
22#10622163—22no—
23#10622124—21no—
24#10622119—21no—
25#10622118—22no—
26#10622090—22no—
27C22×D4×C11D411yescharacteristic
28C23×C4×C11—21no—
29C22×C8×C11—21no—
30C4×D4×C11—21no—
31C4×D4×C11—21no—
32C4×D4×C11—21no—
33C4×D4×C11—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C42×C11C2311yescharacteristic
38#66979—21no—
39#66977—21no—
40#66977—21no—
41C2×#4318—21no—
42#66923—21no—
43#66922D411yescharacteristic
44#66922D411yescharacteristic
45C4×Dic22—21no—
46C4×Dic22—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×#102—42no—
50C11×#95—21no—
51C11×#95—21no—
52#66896—22no—
53#66896—22no—
54C22⋊(C11⋊C8)—21no—
55C22⋊(C11⋊C8)D412yes—
56#66872—22no—
57#66871—22no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)D412yes—
62C4×C11⋊C8—21no—
63C4×C11⋊C8—21no—
64#10468—111nomaximal, Sylow
65C24×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11—21no—
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11SD1612yes—
72C22×C4×C11—21no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11—82no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C2×Dic22—21no—
81C2×Dic22—21no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—41no—
91C42×C11C2×D411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C42×C11#4111yescharacteristic
94C42×C11#4111yescharacteristic
95C22⋊Dic11—41no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100Dic11⋊C4—41no—
101Dic11⋊C4—41no—
102C4×Dic11—41no—
103#4318—41no—
104#4318—41no—
105C2×C11⋊C8—22no—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—41no—
108#3077—111no—
109#1804D1111yescharacteristic
110#1570—111no—
111#1542—111no—
112#1518—111no—
113#1460—111no—
114#1286—111no—
115C23×C11—22no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—81no—
119C23×C11—81no—
120C23×C11#12111yescharacteristic
121D4×C11—22no—
122D4×C11—22no—
123D4×C11—41no—
124D4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—82no—
129C2×C4×C11—82no—
130C2×C4×C11—81no—
131C2×C4×C11—81no—
132C2×C4×C11—81no—
133C2×C4×C11—81no—
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12311yescharacteristic
138C2×C4×C11#12311yescharacteristic
139C2×C4×C11#12411yescharacteristic
140C2×C4×C11C2×SD1611yescharacteristic
141C2×C4×C11#13511yescharacteristic
142C2×C4×C11#13711yescharacteristic
143C2×C4×C11#13711yescharacteristic
144C2×Dic11—41no—
145C2×Dic11—41no—
146Dic22—81no—
147Dic22—81no—
148C8×C11—81no—
149C11⋊C8—42no—
150C11⋊C8—42no—
151C11⋊C8—81no—
152#533—111no—
153C2×C4×D4C2×D1111yescharacteristic
154#478—222no—
155#476—221no—
156#474—221no—
157#431—111no—
158#431—111no—
159#428—221no—
160#423—111no—
161C2×C4⋊C8C2×D1111yescharacteristic
162#418—221no—
163C2×#102—21no—
164#382C2×D1111yescharacteristic
165#340—21no—
166#334—222no—
167#333—221no—
168#332—221no—
169#328—222no—
170#323—222no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—42no—
174C22×C11—82no—
175C22×C11—82no—
176C22×C11—81no—
177C22×C11—81no—
178C22×C11#39411yescharacteristic
179C22×C11#46511yescharacteristic
180C22×C11#47011yescharacteristic
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—81no—
186C4×C11—161no—
187C4×C11#44811yescharacteristic
188C4×C11#45211yescharacteristic
189C4×C11#48311yescharacteristic
190C4×C11#48511yescharacteristic
191Dic11—81no—
192Dic11—81no—
193C22×D4C22⋊D1111yescharacteristic
194C23×C4—21no—
195C2×M16—221no—
196C22×C8—21no—
197C4⋊Q8—111no—
198C4⋊Q8—111no—
199#125—221no—
200C22⋊Q8—221no—
201C22⋊Q8—221no—
202C4×Q8—221no—
203C4×Q8—221no—
204C4×D4—21no—
205C4×D4—21no—
206C4×D4—21no—
207C4×D4—21no—
208#117—221no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4C22⋊D1111yescharacteristic
211C2×C22⋊C4—21no—
212C2×C42C22×D1111yescharacteristic
213#107—222no—
214#106—222no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—112no—
218C4⋊C8—221no—
219C4⋊C8—221no—
220C4⋊C8—221no—
221#102—42no—
222#102—222no—
223#102—222no—
224C22⋊C8—112no—
225C22⋊C8—221no—
226C4×C8—221no—
227C4×C8—221no—
228#95—21no—
229#95—21no—
230C2×C11—21no—
231C2×C11—21no—
232C2×C11—82no—
233C2×C11#203511yescharacteristic
234C2×C11#204811yescharacteristic
235C2×C11#205311yescharacteristic
236C24—21no—
237C2×Q8—221no—
238C2×Q8—221no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4#432412yes—
245C22×C4—21no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—82no—
250C22×C4D4×D1111yescharacteristic
251C22×C4#434111yescharacteristic
252C22×C4C2×C22⋊D1111yescharacteristic
253M16—441no—
254M16—441no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—222no—
259C2×C8—222no—
260C2×C8—441no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—441no—
274C42—441no—
275C42#433911yescharacteristic
276C42#433911yescharacteristic
277C42D4×D1111yescharacteristic
278C42D4×D1111yescharacteristic
279C11#1046811yescharacteristic, complemented, Sylow
280C23—22no—
281C23—41no—
282C23—41no—
283C23—81no—
284C23—81no—
285C23#6699211yescharacteristic
286Q8—881no—
287Q8—881no—
288D4—22no—
289D4—22no—
290D4—41no—
291D4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—82no—
296C2×C4—82no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4#6693611yescharacteristic
304C2×C4#6693711yescharacteristic
305C2×C4#6693711yescharacteristic
306C2×C4#6693811yescharacteristic
307C2×C4#6698211yescharacteristic
308C2×C4C2×#432411yescharacteristic
309C2×C4#6699011yescharacteristic
310C2×C4#6699511yescharacteristic
311C2×C4#6700311yescharacteristic
312C2×C4#6700411yescharacteristic
313C8—81no—
314C8—442no—
315C8—442no—
316C8—881no—
317C22—21no—
318C22—21no—
319C22—42no—
320C22—82no—
321C22—82no—
322C22—81no—
323C22—81no—
324C22#1062257211yescharacteristic
325C22#1062265411yescharacteristic
326C22#1062266511yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—81no—
332C4—161no—
333C4—881no—
334C4—881no—
335C4#1062258411yescharacteristic
336C4#1062260911yescharacteristic
337C4#1062265311yescharacteristic
338C4#1062266011yescharacteristic
339C2—21no—
340C2—21no—
341C2—82no—
342C2#1306981211yescharacteristic
343C2#1306988711yescharacteristic
344C2#1306992011yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1804C2
socleC22×C11#394
prime radicalC22×D4×C11D4
hypercenter#1804D11
hypocenterC11#10468
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. #13067386C2semidirect
3. #13067274C2semidirect
4. #13067179C2semidirect
6. #13066474C2semidirect
279. C11#10468semidirect

Maximal subgroups

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

subgroupindex
#130784132
#130673862
#130672742
#130671792
#130669372
#130664742
C11×#18042
#1046811