Finite Group Databasebeta

← #14657438

Subgroups — #14657438

Order 2816.

376 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 99 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×#10622634C211yesmaximal, characteristic
2#13068612C211yesmaximal, characteristic
3#13067387C211yesmaximal, characteristic
4#13067300C211yesmaximal, characteristic
5#13067296C211yesmaximal, characteristic
6#13066512C211yesmaximal, characteristic
7C11×#1479C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C2×#66900—21no—
13C2×#66899—21no—
14#10622634—22no—
15#10622634—22no—
16C2×#66871—21no—
17#10622537C2211yescharacteristic
18#10622537C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C11×Q8⋊C8—22no—
21#10622168—21no—
22#10622120—22no—
23#10622119—22no—
24#10622095—22no—
25C22×Q8×C11D411yescharacteristic
26C22×Dic22—21no—
27C4×Q8×C11—21no—
28C4×Q8×C11—21no—
29C4×Q8×C11—21no—
30C4×Q8×C11—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C42×C11—21no—
34C2×C42×C11C2311yescharacteristic
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×#4318—21no—
38C2×#4318—21no—
39C22×C11⋊C8—21no—
40#66922—21no—
41#66922—21no—
42#66922—21no—
43#66922D412yes—
44C11×C4⋊C8—21no—
45C11×C4⋊C8D412yes—
46C11×C22⋊C8—21no—
47C11×C22⋊C8—21no—
48C4×C8×C11—21no—
49C4×C8×C11—21no—
50#66900—42no—
51#66899—24no—
52#66871—24no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)D412yes—
59#10454—111nomaximal, Sylow
60C2×Q8×C11—21no—
61C2×Q8×C11—21no—
62C2×Q8×C11—21no—
63C2×Q8×C11—21no—
64C2×Q8×C11—21no—
65C2×Q8×C11SD1612yes—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11#4111yescharacteristic
70C22×C4×C11#4111yescharacteristic
71C22×Dic11—41no—
72C2×Dic22—22no—
73C2×Dic22—41no—
74C2×Dic22—82no—
75C2×C8×C11—22no—
76C2×C8×C11—41no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C42×C11—41no—
82C42×C11—41no—
83C42×C11C2×D411yescharacteristic
84C42×C11C2×D411yescharacteristic
85C42×C11C2×D411yescharacteristic
86C42×C11#4111yescharacteristic
87C4⋊Dic11—22no—
88C4⋊Dic11—22no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91#4318—41no—
92#4318—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#1548—111no—
105#1479D1111yescharacteristic
106#1301—111no—
107C23×C11#12311yescharacteristic
108Q8×C11—22no—
109Q8×C11—22no—
110Q8×C11—41no—
111Q8×C11—41no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—81no—
119C2×C4×C11#12011yescharacteristic
120C2×C4×C11#12111yescharacteristic
121C2×C4×C11#12111yescharacteristic
122C2×C4×C11#12111yescharacteristic
123C2×C4×C11#12311yescharacteristic
124C2×C4×C11#12411yescharacteristic
125C2×C4×C11C2×SD1611yescharacteristic
126C2×C4×C11#13511yescharacteristic
127C2×C4×C11#13711yescharacteristic
128C2×C4×C11#13711yescharacteristic
129C2×Dic11—42no—
130C2×Dic11—82no—
131Dic22—82no—
132Dic22—82no—
133C8×C11—42no—
134C8×C11—81no—
135C11⋊C8—42no—
136C11⋊C8—81no—
137C11⋊C8—81no—
138C2×C4⋊Q8—111no—
139C2×C4×Q8C2×D1111yescharacteristic
140#477—222no—
141#477—222no—
142#431C2×D1111yescharacteristic
143#431C2×D1111yescharacteristic
144C2×#107—221no—
145#423—111no—
146#423—111no—
147C2×C4⋊C8—111no—
148C2×#103—221no—
149C2×#101—221no—
150#343—221no—
151#334—222no—
152#333—222no—
153#332—222no—
154Q8⋊C8—22no—
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—42no—
164C4×C11—81no—
165C4×C11#44811yescharacteristic
166C4×C11#45211yescharacteristic
167C4×C11#46511yescharacteristic
168C4×C11#47011yescharacteristic
169C4×C11#47312yes—
170Dic11—82no—
171C22×Q8—221no—
172C22×Q8D4411yescharacteristic
173C2×M16—221no—
174C2×M16—221no—
175C22×C8—221no—
176C4⋊Q8—112no—
177C4⋊Q8—221no—
178C4⋊Q8—221no—
179C4⋊Q8—221no—
180C4×Q8—21no—
181C4×Q8—21no—
182C4×Q8—21no—
183C4×Q8—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—221no—
186C2×C4⋊C4—221no—
187C2×C4⋊C4D4411yescharacteristic
188C2×C42—21no—
189C2×C42C22×D1111yescharacteristic
190#107—224no—
191C4⋊C8—21no—
192C4⋊C8—112no—
193C4⋊C8—221no—
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—21no—
203C4×C8—21no—
204C4×C8—21no—
205C2×C11—21no—
206C2×C11—21no—
207C2×C11#203511yescharacteristic
208C2×C11#204711yescharacteristic
209C2×C11#204811yescharacteristic
210C2×Q8—21no—
211C2×Q8—21no—
212C2×Q8—21no—
213C2×Q8—21no—
214C2×Q8—21no—
215C2×Q8—222no—
216C2×Q8—441no—
217C2×Q8—882no—
218C2×Q8#431412yes—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—441no—
222C22×C4C2×D4411yescharacteristic
223C22×C4#434111yescharacteristic
224C22×C4#434111yescharacteristic
225M16—441no—
226M16—441no—
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—21no—
237C4⋊C4—21no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—222no—
241C4⋊C4—222no—
242C4⋊C4—441no—
243C4⋊C4—441no—
244C42—41no—
245C42—41no—
246C42#433911yescharacteristic
247C42D4×D1111yescharacteristic
248C42D4×D1111yescharacteristic
249C42C2×C22⋊D1111yescharacteristic
250C11#1045411yescharacteristic, complemented, Sylow
251C23#6693911yescharacteristic
252Q8—22no—
253Q8—22no—
254Q8—41no—
255Q8—41no—
256Q8—882no—
257Q8—882no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—81no—
265C2×C4—442no—
266C2×C4—882no—
267C2×C4#6693511yescharacteristic
268C2×C4#6693611yescharacteristic
269C2×C4#6693811yescharacteristic
270C2×C4C2×#431411yescharacteristic
271C2×C4#6695711yescharacteristic
272C2×C4#6696211yescharacteristic
273C2×C4#6696211yescharacteristic
274C2×C4#6698311yescharacteristic
275C2×C4#6699111yescharacteristic
276C2×C4#6699211yescharacteristic
277C8—42no—
278C8—81no—
279C8—442no—
280C8—881no—
281C8—881no—
282C22—21no—
283C22—21no—
284C22#1062233411yescharacteristic
285C22#1062233611yescharacteristic
286C22#1062257411yescharacteristic
287C4—21no—
288C4—21no—
289C4—21no—
290C4—42no—
291C4—81no—
292C4—882no—
293C4#1062234611yescharacteristic
294C4#1062235111yescharacteristic
295C4#1062272711yescharacteristic
296C4#1062275011yescharacteristic
297C4#1062281712yes—
298C2—21no—
299C2—21no—
300C2#1306981311yescharacteristic
301C2#1306988311yescharacteristic
302C2#1306989011yescharacteristic
subgroupG/H
centerC22#10622574
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1479C2
socleC22×C11#394
prime radicalC23×C11#123
hypercenter#1479D11
hypocenterC11#10454
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

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×#106226342
#130686122
#130673872
#130673002
#130672962
#130665122
C11×#14792
#1045411