Finite Group Databasebeta

← #14651866

Subgroups — #14651866

Order 2816.

428 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 89 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#13078715C211yesmaximal, characteristic
2#13077710C211yesmaximal, characteristic, complemented
3#13067344C211yesmaximal, characteristic, complemented
4#13066957C211yesmaximal, characteristic
5#13066527C211yesmaximal, characteristic, complemented
6#13066478C211yesmaximal, characteristic, complemented
7C11×#1486C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12#10622831C412yes—
13#10622632—21no—
14#10622631—22no—
15#10622620—21no—
16#10622583C412yes—
17#10622539C2211yescharacteristic
18#10622539C2211yescharacteristic
19#10622539C2211yescharacteristic
20#10622441—22no—
21#10622333—22no—
22#10622292—21no—
23C8×Dic22—21no—
24C11×D4⋊C8—21no—
25C11×D4⋊C8—21no—
26#10622163—22no—
27#10622120—21no—
28#10622119—21no—
29C22×D4×C11C2×C411yescharacteristic
30C23×C4×C11—21no—
31C2×C11×M16—21no—
32C4×D4×C11—21no—
33C4×D4×C11—21no—
34C4×D4×C11—21no—
35C4×D4×C11—21no—
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C22⋊C4—21no—
38C2×C42×C11C2311yescharacteristic
39C2×#4324—22no—
40#66979—21no—
41#66977—21no—
42#66977C2×C412yes—
43#66923—21no—
44#66922D411yescharacteristic
45#66922D411yescharacteristic
46C4×Dic22—21no—
47C4×Dic22D412yes—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C22⋊C8—21no—
52C4×C8×C11D411yescharacteristic
53C4×C8×C11D411yescharacteristic
54#66896—22no—
55C22⋊(C11⋊C8)—21no—
56C22⋊(C11⋊C8)C2×C412yes—
57C22⋊(C11⋊C8)D412yes—
58#66879—22no—
59Dic11⋊C8—22no—
60Dic11⋊C8—22no—
61C8×Dic11—22no—
62#66874—22no—
63#66871—22no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67#66867—21no—
68#66867—21no—
69#66867—21no—
70#9530—111nomaximal, Sylow
71C24×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—42no—
75C22×C4×C11—21no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—81no—
79C22×C4×C11—81no—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C2×Dic22—21no—
84C2×Dic22C22⋊C412yes—
85C11×M16—81no—
86C2×C8×C11—21no—
87C2×C8×C11—21no—
88C2×C8×C11—41no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11C2×D411yescharacteristic
96C42×C11#4111yescharacteristic
97C22⋊Dic11—22no—
98#4324—44no—
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11C22⋊C412yes—
103Dic11⋊C4—22no—
104Dic11⋊C4—22no—
105C4×Dic11—22no—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—22no—
108C2×C11⋊C8—41no—
109#3110—111no—
110#2985—111no—
111#1559—111no—
112#1486D1111yescharacteristic
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
122D4×C11—22no—
123D4×C11—22no—
124D4×C11—41no—
125D4×C11—41no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—82no—
132C2×C4×C11—81no—
133C2×C4×C11—81no—
134C2×C4×C11—81no—
135C2×C4×C11C2×C22⋊C411yescharacteristic
136C2×C4×C11C4×D411yescharacteristic
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12311yescharacteristic
141C2×Dic11—22no—
142C2×Dic11—22no—
143Dic22—41no—
144Dic22—41no—
145Dic22—42no—
146C8×C11—41no—
147C8×C11—41no—
148C8×C11—81no—
149C11⋊C8—42no—
150C11⋊C8—42no—
151C11⋊C8—81no—
152#533—111no—
153C2×C4×D4C2×D1111yescharacteristic
154#484—112no—
155#474—221no—
156#461—221no—
157#450—112no—
158#446—222no—
159#446—221no—
160C8×Q8—221no—
161#440—222no—
162#433—222no—
163#432—111no—
164#432—111no—
165#432—111no—
166#431C2×D1111yescharacteristic
167#423C2×D1111yescharacteristic
168#333—221no—
169#332—221no—
170D4⋊C8—21no—
171D4⋊C8—21no—
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—81no—
188C4×C11#47111yescharacteristic
189C4×C11#47211yescharacteristic
190Dic11—42no—
191Dic11—42no—
192C22×D4C4×D1111yescharacteristic
193C23×C4—21no—
194C2×SD16—222no—
195C2×M16—21no—
196C4⋊Q8—111no—
197C4⋊Q8—111no—
198#125—221no—
199C22⋊Q8—112no—
200C22⋊Q8—221no—
201C4×Q8—112no—
202C4×Q8—221no—
203C4×D4—21no—
204C4×D4—21no—
205C4×D4—21no—
206C4×D4—21no—
207#117—221no—
208C2×C4⋊C4C4×D1111yescharacteristic
209C2×C22⋊C4—21no—
210C2×C42C22×D1111yescharacteristic
211#107—222no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—222no—
216C4⋊C8—222no—
217C4⋊C8—221no—
218C4⋊C8—221no—
219C4⋊C8—221no—
220#103—222no—
221#102—222no—
222C22⋊C8—21no—
223C22⋊C8—112no—
224C22⋊C8—112no—
225C22⋊C8—221no—
226#97—222no—
227#97—221no—
228#97—221no—
229#97—221no—
230C4×C8—222no—
231C4×C8C22⋊D1111yescharacteristic
232C4×C8C22⋊D1111yescharacteristic
233C2×C11—41no—
234C2×C11—82no—
235C2×C11#189111yescharacteristic
236C2×C11#190511yescharacteristic
237C2×C11#190711yescharacteristic
238C24—21no—
239C2×Q8—112no—
240C2×Q8—221no—
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×C4C2×C4×D1111yescharacteristic
250C22×C4D4×D1111yescharacteristic
251C22×C4#434111yescharacteristic
252SD16—444no—
253M16—81no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—41no—
257C2×C8—222no—
258C2×C8—222no—
259C2×C8—441no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—112no—
263C4⋊C4—222no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—222no—
267C4⋊C4—221no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—222no—
271C42—222no—
272C42#433911yescharacteristic
273C42D4×D1111yescharacteristic
274C42D4×D1111yescharacteristic
275C42C2×C22⋊D1111yescharacteristic
276C11#953011yescharacteristic, complemented, Sylow
277C23—22no—
278C23—41no—
279C23—41no—
280C23—81no—
281C23—81no—
282C23(C22⋊D11)⋊C411yescharacteristic
283Q8—442no—
284Q8—441no—
285Q8—441no—
286D4—22no—
287D4—22no—
288D4—41no—
289D4—41no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—82no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—222no—
300C2×C4—222no—
301C2×C4C22⋊C4×D1111yescharacteristic
302C2×C4#6693611yescharacteristic
303C2×C4#6693711yescharacteristic
304C2×C4C4×C22⋊D1111yescharacteristic
305C2×C4#6699011yescharacteristic
306C2×C4#6699111yescharacteristic
307C8—41no—
308C8—41no—
309C8—81no—
310C8—442no—
311C8—442no—
312C8—881no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—42no—
317C22—82no—
318C22—82no—
319C22—81no—
320C22—81no—
321C22#1062256911yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—81no—
328C4—442no—
329C4—442no—
330C4#1062277311yescharacteristic
331C4#1062279011yescharacteristic
332C2—41no—
333C2—82no—
334C2#1306903111yescharacteristic
335C2#1306910711yescharacteristic
336C2#1306912711yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1486C2
socleC22×C11#386
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenter#1486D11
hypocenterC11#9530
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #13077710C2semidirect
3. #13067344C2semidirect
5. #13066527C2semidirect
6. #13066478C2semidirect
276. C11#9530semidirect

Maximal subgroups

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

subgroupindex
#130787152
#130777102
#130673442
#130669572
#130665272
#130664782
C11×#14862
#953011