Finite Group Databasebeta

← #14651871

Subgroups — #14651871

Order 2816.

428 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 103 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#13077711C211yesmaximal, characteristic, complemented
2#13067346C211yesmaximal, characteristic, complemented
3#13067041C211yesmaximal, characteristic
4#13066957C211yesmaximal, characteristic
5#13066526C211yesmaximal, characteristic, complemented
6#13066479C211yesmaximal, characteristic, complemented
7C11×#3110C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C11×#484C412yes—
11C11×#474—21no—
12C11×#461—21no—
13C11×#450C412yes—
14C11×#440—22no—
15C11×#432C2211yescharacteristic
16#10622637—22no—
17#10622637—21no—
18Q8×C11⋊C8—21no—
19#10622613—22no—
20#10622539C2211yescharacteristic
21#10622539C2211yescharacteristic
22#10622538C2211yescharacteristic
23#10622537C2211yescharacteristic
24#10622185—21no—
25#10622184—21no—
26D4⋊(C11⋊C8)—21no—
27D4⋊(C11⋊C8)—21no—
28#10622163—22no—
29C22×D4×C11C2×C411yescharacteristic
30C23×C4×C11—21no—
31C2×C11×SD16—22no—
32C11×C4⋊Q8D411yescharacteristic
33C11×C4⋊Q8D411yescharacteristic
34C11×#125—21no—
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8C2×C412yes—
37C4×Q8×C11—21no—
38C4×Q8×C11D412yes—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C11×#117—21no—
44C2×C11×C4⋊C4C2×C411yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C42×C11C2311yescharacteristic
47C2×#4318—21no—
48C11×#107—22no—
49C11×C4⋊C8—21no—
50C11×#103—22no—
51C11×#102—22no—
52C11×C22⋊C8C2×C412yes—
53C11×#97—21no—
54C22⋊(C11⋊C8)—21no—
55C22⋊(C11⋊C8)—21no—
56C22⋊(C11⋊C8)D412yes—
57C4⋊(C11⋊C8)—22no—
58C4⋊(C11⋊C8)—22no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64#66867—22no—
65#66867—21no—
66#66867—21no—
67C4×C11⋊C8—22no—
68C4×C11⋊C8D411yescharacteristic
69C4×C11⋊C8D411yescharacteristic
70#9530—111nomaximal, Sylow
71C24×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11C22⋊C412yes—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—42no—
77C22×C4×C11—21no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—81no—
81C22×C4×C11—81no—
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C11×SD16—44no—
86C2×C8×C11—22no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4C22⋊C412yes—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C42×C11—22no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11#4111yescharacteristic
103#4318—81no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—22no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109#3110D1111yescharacteristic
110#2985—111no—
111#1559—111no—
112#1486—111no—
113#1466—111no—
114#1307—111no—
115#1287—111no—
116C23×C11—22no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—81no—
120C23×C11—81no—
121C23×C11C4×D411yescharacteristic
122Q8×C11—42no—
123Q8×C11—41no—
124Q8×C11—41no—
125D4×C11—22no—
126D4×C11—22no—
127D4×C11—41no—
128D4×C11—41no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—82no—
137C2×C4×C11—81no—
138C2×C4×C11—81no—
139C2×C4×C11—81no—
140C2×C4×C11C2×C22⋊C411yescharacteristic
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12311yescharacteristic
146C8×C11—42no—
147C11⋊C8—41no—
148C11⋊C8—42no—
149C11⋊C8—41no—
150C11⋊C8—81no—
151C11⋊C8—81no—
152#533C2×D1111yescharacteristic
153C2×C4×D4C2×D1111yescharacteristic
154#484Dic1112yes—
155#474—21no—
156#461—21no—
157#450Dic1112yes—
158#446—221no—
159#446—222no—
160C8×Q8—221no—
161#440—22no—
162#433—222no—
163#432—111no—
164#432—111no—
165#432C2×D1111yescharacteristic
166#431—111no—
167#423—111no—
168#333—221no—
169#332—221no—
170D4⋊C8—221no—
171D4⋊C8—221no—
172#323—222no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—42no—
177C22×C11—82no—
178C22×C11—82no—
179C22×C11—81no—
180C22×C11—81no—
181C22×C11#38611yescharacteristic
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—42no—
188C4×C11—42no—
189C4×C11—81no—
190C4×C11#47111yescharacteristic
191C4×C11#47211yescharacteristic
192C22×D4C2×Dic1111yescharacteristic
193C23×C4—21no—
194C2×SD16—22no—
195C2×M16—221no—
196C4⋊Q8C22⋊D1111yescharacteristic
197C4⋊Q8C22⋊D1111yescharacteristic
198#125—21no—
199C22⋊Q8—21no—
200C22⋊Q8C2×Dic1112yes—
201C4×Q8—21no—
202C4×Q8C22⋊D1112yes—
203C4×D4—21no—
204C4×D4—21no—
205C4×D4—21no—
206C4×D4—21no—
207#117—21no—
208C2×C4⋊C4C2×Dic1111yescharacteristic
209C2×C22⋊C4—21no—
210C2×C42C22×D1111yescharacteristic
211#107—22no—
212C4⋊C8—21no—
213C4⋊C8—222no—
214C4⋊C8—222no—
215C4⋊C8—221no—
216C4⋊C8—221no—
217C4⋊C8—221no—
218C4⋊C8—221no—
219C4⋊C8—221no—
220#103—22no—
221#102—22no—
222C22⋊C8—112no—
223C22⋊C8—221no—
224C22⋊C8—221no—
225C22⋊C8C2×Dic1112yes—
226#97—21no—
227#97—222no—
228#97—221no—
229#97—221no—
230C4×C8—111no—
231C4×C8—111no—
232C4×C8—222no—
233C2×C11—41no—
234C2×C11—82no—
235C2×C11#189111yescharacteristic
236C2×C11#190511yescharacteristic
237C2×C11#190711yescharacteristic
238C24—21no—
239C2×Q8—21no—
240C2×Q8C22⋊Dic1112yes—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—42no—
244C22×C4—21no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—81no—
248C22×C4—81no—
249C22×C4D4×D1111yescharacteristic
250C22×C4#434111yescharacteristic
251C22×C4C22×Dic1111yescharacteristic
252SD16—44no—
253M16—881no—
254C2×C8—22no—
255C2×C8—221no—
256C2×C8—221no—
257C2×C8—222no—
258C2×C8—441no—
259C2×C8—441no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4C22⋊Dic1112yes—
268C22⋊C4—22no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C42—22no—
272C42D4×D1111yescharacteristic
273C42#434111yescharacteristic
274C42C2×C22⋊D1111yescharacteristic
275C42C2×C22⋊D1111yescharacteristic
276C11#953011yescharacteristic, complemented, Sylow
277C23—22no—
278C23—41no—
279C23—41no—
280C23—81no—
281C23—81no—
282C23D4×Dic1111yescharacteristic
283Q8—42no—
284Q8—41no—
285Q8—41no—
286D4—22no—
287D4—22no—
288D4—41no—
289D4—41no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—82no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4D4×Dic1111yescharacteristic
302C2×C4#6698811yescharacteristic
303C2×C4#6699011yescharacteristic
304C2×C4#6699211yescharacteristic
305C2×C4#6699211yescharacteristic
306C2×C4C2×C22⋊Dic1111yescharacteristic
307C8—42no—
308C8—441no—
309C8—441no—
310C8—442no—
311C8—881no—
312C8—881no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—42no—
317C22—82no—
318C22—82no—
319C22—81no—
320C22—81no—
321C22#1062283311yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—42no—
328C4—42no—
329C4—81no—
330C4#1062281211yescharacteristic
331C4#1062281311yescharacteristic
332C2—41no—
333C2—82no—
334C2#1306903511yescharacteristic
335C2#1306911211yescharacteristic
336C2#1306912611yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3110C2
socleC22×C11#386
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenter#3110D11
hypocenterC11#9530
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3110

Complements

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

NH ≅ G/Ntype
1. #13077711C2semidirect
2. #13067346C2semidirect
5. #13066526C2semidirect
6. #13066479C2semidirect
276. C11#9530semidirect

Maximal subgroups

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

subgroupindex
#130777112
#130673462
#130670412
#130669572
#130665262
#130664792
C11×#31102
#953011