Finite Group Databasebeta

← #14657436

Subgroups — #14657436

Order 2816.

376 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#10622704C211yesmaximal, characteristic
2#13068609C211yesmaximal, characteristic
3#13067387C211yesmaximal, characteristic
4#13067301C211yesmaximal, characteristic
5#13067010C211yesmaximal, characteristic
6#13066511C211yesmaximal, characteristic
7C11×#1548C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×Dic22C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×#66888—21no—
13#10622704—22no—
14#10622704—22no—
15C2×#66874—21no—
16C2×#66871—21no—
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C11×#333—22no—
21#10622192—21no—
22#10622185—22no—
23#10622122—22no—
24#10622095—22no—
25C22×Q8×C11—21no—
26C22×Dic22D411yescharacteristic
27C2×C11×M16—21no—
28C11×C4⋊Q8—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8D412yes—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C42×C11C2311yescharacteristic
35C2×C4⋊Dic11D411yescharacteristic
36C2×Dic11⋊C4—21no—
37C2×C4×Dic11—21no—
38C2×#4318—21no—
39C22×C11⋊C8—21no—
40C4×Dic22—21no—
41C4×Dic22—21no—
42C4×Dic22—21no—
43C4×Dic22—21no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8D412yes—
47C11×C22⋊C8—21no—
48C4×C8×C11—21no—
49C22⋊(C11⋊C8)—21no—
50#66888—42no—
51#66874—24no—
52#66871—24no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)D412yes—
58C4×C11⋊C8—21no—
59#10454—111nomaximal, Sylow
60C2×Q8×C11—22no—
61C2×Q8×C11—41no—
62C2×Q8×C11—82no—
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11#4111yescharacteristic
66C22×C4×C11#4111yescharacteristic
67C22×Dic11—21no—
68C22×Dic11—21no—
69C2×Dic22—21no—
70C2×Dic22—21no—
71C2×Dic22—21no—
72C2×Dic22—21no—
73C2×Dic22—21no—
74C2×Dic22SD1612yes—
75C11×M16—41no—
76C11×M16—41no—
77C2×C8×C11—22no—
78C2×C8×C11—41no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C42×C11C2×D411yescharacteristic
84C42×C11C2×D411yescharacteristic
85C42×C11C2×D411yescharacteristic
86C42×C11#4111yescharacteristic
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89Dic11⋊C4—41no—
90Dic11⋊C4—41no—
91C4×Dic11—41no—
92C4×Dic11—41no—
93#4318—41no—
94#4318—41no—
95C2×C11⋊C8—22no—
96C2×C11⋊C8—41no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100C2×#477—111no—
101#1801—111no—
102#1570—111no—
103#1549—111no—
104#1548D1111yescharacteristic
105#1479—111no—
106#1301—111no—
107C23×C11#12311yescharacteristic
108Q8×C11—82no—
109Q8×C11—82no—
110C2×C4×C11—22no—
111C2×C4×C11—41no—
112C2×C4×C11—42no—
113C2×C4×C11—82no—
114C2×C4×C11#12011yescharacteristic
115C2×C4×C11#12111yescharacteristic
116C2×C4×C11#12111yescharacteristic
117C2×C4×C11#12111yescharacteristic
118C2×C4×C11#12311yescharacteristic
119C2×C4×C11#12411yescharacteristic
120C2×C4×C11C2×SD1611yescharacteristic
121C2×C4×C11#13511yescharacteristic
122C2×C4×C11#13711yescharacteristic
123C2×C4×C11#13711yescharacteristic
124C2×Dic11—22no—
125C2×Dic11—41no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11—81no—
129Dic22—22no—
130Dic22—22no—
131Dic22—41no—
132Dic22—41no—
133C8×C11—42no—
134C8×C11—81no—
135C11⋊C8—42no—
136C11⋊C8—81no—
137C11⋊C8—81no—
138C2×C4⋊Q8C2×D1111yescharacteristic
139C2×C4×Q8—111no—
140#477—222no—
141#477—222no—
142#431—111no—
143#431C2×D1111yescharacteristic
144C2×#107—221no—
145#423—111no—
146#423C2×D1111yescharacteristic
147C2×C4⋊C8—111no—
148C2×#103—221no—
149C2×#101—221no—
150#343—221no—
151#334—222no—
152#333—22no—
153#332—222no—
154Q8⋊C8—222no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11#39411yescharacteristic
158C22×C11#48311yescharacteristic
159C22×C11#48511yescharacteristic
160C4×C11—21no—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—82no—
164C4×C11#44811yescharacteristic
165C4×C11#45211yescharacteristic
166C4×C11#46511yescharacteristic
167C4×C11#47011yescharacteristic
168C4×C11#47312yes—
169Dic11—42no—
170Dic11—81no—
171C22×Q8—21no—
172C22×Q8—111no—
173C2×M16—21no—
174C2×M16—221no—
175C22×C8—221no—
176C4⋊Q8—21no—
177C4⋊Q8—21no—
178C4⋊Q8—21no—
179C4⋊Q8D4412yes—
180C4×Q8—221no—
181C4×Q8—221no—
182C4×Q8—221no—
183C4×Q8—221no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—111no—
187C2×C4⋊C4—221no—
188C2×C42—221no—
189C2×C42C22×D1111yescharacteristic
190#107—224no—
191C4⋊C8—21no—
192C4⋊C8—21no—
193C4⋊C8—112no—
194C4⋊C8—221no—
195C4⋊C8—221no—
196C4⋊C8—221no—
197C4⋊C8—221no—
198C4⋊C8C22⋊D1112yes—
199#103—224no—
200#101—442no—
201C22⋊C8—21no—
202C22⋊C8—221no—
203C4×C8—21no—
204C4×C8—221no—
205C2×C11—21no—
206C2×C11—21no—
207C2×C11#203511yescharacteristic
208C2×C11#204711yescharacteristic
209C2×C11#204811yescharacteristic
210C2×Q8—22no—
211C2×Q8—41no—
212C2×Q8—82no—
213C2×Q8—112no—
214C2×Q8—221no—
215C2×Q8—221no—
216C2×Q8—221no—
217C2×Q8—221no—
218C2×Q8—221no—
219C22×C4—41no—
220C22×C4—221no—
221C22×C4—221no—
222C22×C4#433911yescharacteristic
223C22×C4D4×D1111yescharacteristic
224C22×C4#434111yescharacteristic
225M16—41no—
226M16—41no—
227M16—441no—
228M16—441no—
229C2×C8—22no—
230C2×C8—41no—
231C2×C8—222no—
232C2×C8—441no—
233C2×C8—441no—
234C2×C8—441no—
235C2×C8—441no—
236C4⋊C4—22no—
237C4⋊C4—22no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—221no—
241C4⋊C4—221no—
242C4⋊C4—441no—
243C4⋊C4—441no—
244C42—441no—
245C42—441no—
246C42C2×D4411yescharacteristic
247C42D4×D1111yescharacteristic
248C42#434111yescharacteristic
249C42C2×C22⋊D1111yescharacteristic
250C11#1045411yescharacteristic, complemented, Sylow
251C23#6693611yescharacteristic
252Q8—82no—
253Q8—82no—
254Q8—222no—
255Q8—222no—
256Q8—441no—
257Q8—441no—
258C2×C4—22no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—82no—
262C2×C4—222no—
263C2×C4—441no—
264C2×C4—441no—
265C2×C4—441no—
266C2×C4—881no—
267C2×C4#6693511yescharacteristic
268C2×C4#6693811yescharacteristic
269C2×C4#6693911yescharacteristic
270C2×C4SD16×D1111yescharacteristic
271C2×C4#6696911yescharacteristic
272C2×C4#6697111yescharacteristic
273C2×C4#6697111yescharacteristic
274C2×C4#6698311yescharacteristic
275C2×C4#6699111yescharacteristic
276C2×C4#6699211yescharacteristic
277C8—42no—
278C8—81no—
279C8—442no—
280C8—881no—
281C8—881no—
282C22—21no—
283C22—21no—
284C22#1062241811yescharacteristic
285C22#1062242811yescharacteristic
286C22#1062257411yescharacteristic
287C4—21no—
288C4—21no—
289C4—21no—
290C4—82no—
291C4—442no—
292C4—881no—
293C4#1062241911yescharacteristic
294C4#1062242311yescharacteristic
295C4#1062278411yescharacteristic
296C4#1062280211yescharacteristic
297C4#1062281712yes—
298C2—21no—
299C2—21no—
300C2#1306981111yescharacteristic
301C2#1306988311yescharacteristic
302C2#1306988811yescharacteristic
subgroupG/H
centerC22#10622574
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1548C2
socleC22×C11#394
prime radicalC23×C11#123
hypercenter#1548D11
hypocenterC11#10454
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
250. C11#10454semidirect

Maximal subgroups

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

subgroupindex
C2×#106227042
#130686092
#130673872
#130673012
#130670102
#130665112
C11×#15482
#1045411