Finite Group Databasebeta

← #14648958

Subgroups — #14648958

Order 2816.

424 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 109 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#13078656C211yesmaximal, characteristic
2#13077556C211yesmaximal, characteristic
3#13069556C211yesmaximal, characteristic
4#13067271C211yesmaximal, characteristic
5#13067046C211yesmaximal, characteristic
6#13066512C211yesmaximal, characteristic
7C11×#1281C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C2×C4×Dic22C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C2×C11×#97C2211yescharacteristic
13#10622715—21no—
14#10622714—21no—
15#10622537C2211yescharacteristic
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17#10622463—21no—
18#10622462—21no—
19#10622352C412yes—
20#10622335C412yes—
21#10622314—22no—
22#10622314—22no—
23C4×Dic44—22no—
24#10622188—21no—
25#10622188—21no—
26#10622120—21no—
27#10622119—21no—
28#10622094—22no—
29C22×Dic22C2×C411yescharacteristic
30C22×C8×C11D411yescharacteristic
31C22×C8×C11D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33#66979—21no—
34C2×C4⋊Dic11C2×C411yescharacteristic
35#66977—21no—
36#66977C2×C412yes—
37C2×Dic11⋊C4—21no—
38C2×C4×Dic11—21no—
39C2×#4318—21no—
40C22×C11⋊C8—21no—
41C2×Dic44—22no—
42#66923—21no—
43#66922D411yescharacteristic
44#66922D411yescharacteristic
45C4×Dic22—21no—
46C4×Dic22—21no—
47C4×Dic22—21no—
48C4×Dic22—21no—
49C4×Dic22—21no—
50C4×Dic22D412yes—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C22⋊C8—21no—
54C11×C22⋊C8C2×C412yes—
55C11×#97—21no—
56C11×#97—21no—
57C4×C8×C11—21no—
58C4×C8×C11—21no—
59#66882—22no—
60#66880—22no—
61#66880—22no—
62#66879—22no—
63Dic11⋊C8—24no—
64C8×Dic11—22no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)D412yes—
69#9048—111nomaximal, Sylow
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×Dic22—21no—
78C2×Dic22—42no—
79C2×Dic22C22⋊C412yes—
80C2×C8×C11—22no—
81C2×C8×C11—21no—
82C2×C8×C11—21no—
83C2×C8×C11—21no—
84C2×C8×C11—21no—
85C2×C8×C11—21no—
86C2×C8×C11—41no—
87C2×C8×C11Q1612yescomplemented
88C42×C11C2×D411yescharacteristic
89C42×C11C2×D411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C42×C11#4111yescharacteristic
92C22⋊Dic11—22no—
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11C22⋊C412yes—
99Dic11⋊C4—22no—
100Dic11⋊C4—22no—
101Dic11⋊C4—41no—
102Dic11⋊C4—41no—
103C4×Dic11—22no—
104C4×Dic11—41no—
105C4×Dic11—41no—
106#4318—41no—
107#4318—41no—
108C2×C11⋊C8—22no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112Dic44—44no—
113#3104—111no—
114#2961—111no—
115#1985—111no—
116#1542—111no—
117#1487—111no—
118#1301—111no—
119#1281D1111yescharacteristic
120C23×C11C4×D411yescharacteristic
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11C2×C22⋊C411yescharacteristic
124C2×C4×C11C4×D411yescharacteristic
125C2×C4×C11#12011yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12111yescharacteristic
128C2×C4×C11#12311yescharacteristic
129C2×C4×C11C2×Q1611yescharacteristic
130C2×C4×C11#13511yescharacteristic
131C2×C4×C11#13711yescharacteristic
132C2×C4×C11#13711yescharacteristic
133C2×Dic11—22no—
134C2×Dic11—22no—
135C2×Dic11—22no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—42no—
139C2×Dic11—41no—
140Dic22—22no—
141Dic22—22no—
142Dic22—41no—
143Dic22—41no—
144Dic22—42no—
145Dic22—81no—
146C8×C11—22no—
147C8×C11—42no—
148C8×C11—41no—
149C8×C11—81no—
150C11⋊C8—42no—
151C11⋊C8—81no—
152#533—111no—
153C2×C4×Q8—111no—
154#484—112no—
155#477—221no—
156#462—221no—
157#451—112no—
158#446—222no—
159#446—222no—
160C4×Q16—222no—
161#431C2×D1111yescharacteristic
162#431C2×D1111yescharacteristic
163#424—221no—
164#423—111no—
165C2×C4⋊C8—111no—
166#405—221no—
167C2×#97C2×D1111yescharacteristic
168#336—221no—
169#336—221no—
170#333—221no—
171#332—221no—
172Q8⋊C8—222no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11#38611yescharacteristic
176C22×C11C4×Q1611yescharacteristic
177C22×C11#44111yescharacteristic
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11#45111yescharacteristic
183C4×C11#45211yescharacteristic
184C4×C11#46211yescharacteristic
185C4×C11#46411yescharacteristic
186Dic11—42no—
187Dic11—42no—
188Dic11—42no—
189Dic11—81no—
190C22×Q8—111no—
191C2×Q16—222no—
192C2×M16—221no—
193C22×C8—221no—
194C22×C8D4411yescharacteristic
195C22×C8D4411yescharacteristic
196C4⋊Q8—111no—
197C4⋊Q8—111no—
198#125—221no—
199C22⋊Q8—112no—
200C22⋊Q8—221no—
201C4×Q8—112no—
202C4×Q8—221no—
203C4×Q8—221no—
204C4×Q8—221no—
205C4×Q8—221no—
206C4×Q8—221no—
207#117—221no—
208C2×C4⋊C4—111no—
209C2×C4⋊C4—221no—
210C2×C42—221no—
211C2×C42C22×D1111yescharacteristic
212#107—222no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—112no—
216C4⋊C8—224no—
217C4⋊C8—221no—
218C4⋊C8—221no—
219C4⋊C8—221no—
220#103—222no—
221#103—222no—
222C22⋊C8—21no—
223C22⋊C8C4×D1112yes—
224#97—21no—
225#97—21no—
226#97—222no—
227C4×C8—21no—
228C4×C8—21no—
229C4×C8—222no—
230C2×C11—21no—
231C2×C11—21no—
232C2×C11#187811yescharacteristic
233C2×C11#188111yescharacteristic
234C2×C11#189111yescharacteristic
235C2×Q8—112no—
236C2×Q8—221no—
237C2×Q8—221no—
238C2×Q8—221no—
239C2×Q8—442no—
240C22×C4—221no—
241C22×C4—221no—
242C22×C4C2×C4×D1111yescharacteristic
243C22×C4C2×D4411yescharacteristic
244C22×C4#433911yescharacteristic
245Q16—444no—
246M16—441no—
247M16—441no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—22no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—41no—
255C2×C8—222no—
256C2×C8—441no—
257C2×C8—441no—
258C2×C8—441no—
259C2×C8Dic4412yescomplemented
260C4⋊C4—112no—
261C4⋊C4—221no—
262C4⋊C4—222no—
263C4⋊C4—222no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—441no—
269C4⋊C4—441no—
270C22⋊C4—222no—
271C42—222no—
272C42—441no—
273C42—441no—
274C42D4×D1111yescharacteristic
275C42D4×D1111yescharacteristic
276C42D4×D1111yescharacteristic
277C42#434311yescharacteristic
278C11#904811yescharacteristic, complemented, Sylow
279C23C4×D4411yescharacteristic
280Q8—222no—
281Q8—222no—
282Q8—442no—
283Q8—441no—
284Q8—441no—
285Q8—881no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—222no—
289C2×C4—222no—
290C2×C4—222no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—442no—
294C2×C4—441no—
295C2×C4C22⋊C4×D1111yescharacteristic
296C2×C4#6693511yescharacteristic
297C2×C4#6693711yescharacteristic
298C2×C4#6694611yescharacteristic
299C2×C4#6694711yescharacteristic
300C2×C4#6694811yescharacteristic
301C2×C4#6695711yescharacteristic
302C2×C4C2×Dic4411yescharacteristic
303C2×C4#6696211yescharacteristic
304C2×C4#6696211yescharacteristic
305C8—22no—
306C8—42no—
307C8—41no—
308C8—81no—
309C8—442no—
310C8—881no—
311C22—21no—
312C22—21no—
313C22#1062227811yescharacteristic
314C22C4×Dic4411yescharacteristic
315C22#1062232911yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—442no—
321C4—442no—
322C4—442no—
323C4—881no—
324C4#1062234611yescharacteristic
325C4#1062235211yescharacteristic
326C4#1062245811yescharacteristic
327C4#1062246211yescharacteristic
328C2—21no—
329C2—21no—
330C2#1306895611yescharacteristic
331C2#1306897711yescharacteristic
332C2#1306903311yescharacteristic
subgroupG/H
centerC2×C4#66935
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1281C2
socleC22×C11#386
prime radicalC23×C11C4×D4
cosocleC2×C42×C11C23
hypercenter#1281D11
hypocenterC11#9048
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1281

Complements

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

NH ≅ G/Ntype
87. C2×C8×C11Q16semidirect
259. C2×C8Dic44semidirect
278. C11#9048semidirect

Maximal subgroups

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

subgroupindex
#130786562
#130775562
#130695562
#130672712
#130670462
#130665122
C11×#12812
#904811