Finite Group Databasebeta

← #14656845

Subgroups — #14656845

Order 2816.

400 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 93 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#13069588C212yesmaximal
2#13069435C211yesmaximal, characteristic
3#13066497C211yesmaximal, characteristic
4#13066497C212yesmaximal
5C11×#2844C211yesmaximal, characteristic
6C2×#66922C2211yescharacteristic
7C11×#400—21no—
8C11×#400—22no—
9C11×#395—21no—
10C11×#395—22no—
11C11×#382C2212yes—
12C11×#382C2211yescharacteristic
13C2×#66874—21no—
14C2×#66874—21no—
15C2×#66867C2212yes—
16C2×#66867C2211yescharacteristic
17#10622167—22no—
18#10622167—22no—
19C22×Q8×C11—21no—
20C22×Dic22—21no—
21C2×C11×C4⋊C4—21no—
22C2×C11×C4⋊C4—22no—
23C2×C11×C4⋊C4D411yescharacteristic
24C2×C11×C4⋊C4D411yescharacteristic
25C2×C11×C4⋊C4D412yes—
26C2×C11×C4⋊C4D412yes—
27C2×C42×C11C2311yescharacteristic
28C2×C4⋊Dic11—22no—
29C22×C11⋊C8—21no—
30C22×C11⋊C8—22no—
31#66922—22no—
32#66922—21no—
33#66922Q812yescomplemented
34C11×#95—22no—
35C11×#95—21no—
36C11×#95—21no—
37C11×#95—22no—
38C11×#95—22no—
39C11×#95—22no—
40#66874—42no—
41#66874—42no—
42#66867—22no—
43#66867—22no—
44#66867—22no—
45#10359—111nomaximal, Sylow
46C2×Q8×C11—81no—
47C2×Q8×C11—82no—
48C22×C4×C11—21no—
49C22×C4×C11—22no—
50C22×C4×C11—21no—
51C22×C4×C11—22no—
52C22×C4×C11C2×D412yes—
53C22×C4×C11C2×D411yescharacteristic
54C22×Dic11—41no—
55C2×Dic22—22no—
56C2×Dic22—41no—
57C2×Dic22—41no—
58C2×Dic22—41no—
59C2×Dic22—41no—
60C2×Dic22—41no—
61C11×C4⋊C4—41no—
62C11×C4⋊C4—41no—
63C11×C4⋊C4—42no—
64C11×C4⋊C4—42no—
65C11×C4⋊C4—81no—
66C11×C4⋊C4—82no—
67C42×C11C2×Q811yescharacteristic
68C42×C11#4112yes—
69C42×C11#4111yescharacteristic
70C4⋊Dic11—24no—
71C4⋊Dic11—42no—
72C2×C11⋊C8—22no—
73C2×C11⋊C8—24no—
74C2×C11⋊C8—41no—
75C2×C11⋊C8—42no—
76C2×C11⋊C8—42no—
77C2×C11⋊C8—41no—
78#2844D1111yescharacteristic
79#1993—112no—
80#1960—111no—
81#1295—111no—
82#1295—112no—
83C23×C11#12011yescharacteristic
84Q8×C11—84no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—41no—
90C2×C4×C11—41no—
91C2×C4×C11—42no—
92C2×C4×C11—42no—
93C2×C4×C11—42no—
94C2×C4×C11—42no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11C22⋊Q812yes—
100C2×C4×C11C22⋊Q811yescharacteristic
101C2×C4×C11#12412yes—
102C2×C4×C11#12411yescharacteristic
103C2×Dic11—42no—
104C2×Dic11—81no—
105C2×Dic11—81no—
106Dic22—42no—
107Dic22—42no—
108Dic22—81no—
109Dic22—81no—
110C11⋊C8—42no—
111C11⋊C8—44no—
112C2×C4⋊Q8—111no—
113C2×#103—221no—
114C2×#103—221no—
115C2×#97—111no—
116C2×#97—112no—
117#400—22no—
118#400—21no—
119#395—22no—
120#395—21no—
121#382C2×D1111yescharacteristic
122#382C2×D1112yes—
123#340—222no—
124#340—222no—
125C22×C11#39311yescharacteristic
126C22×C11#45311yescharacteristic
127C22×C11#45411yescharacteristic
128C22×C11#45512yes—
129C22×C11#45612yes—
130C4×C11—21no—
131C4×C11—21no—
132C4×C11—22no—
133C4×C11—22no—
134C4×C11—81no—
135C4×C11—82no—
136C4×C11—81no—
137C4×C11—82no—
138Dic11—82no—
139C22×Q8—21no—
140C22×Q8—221no—
141C22×C8—222no—
142C22×C8—221no—
143C4⋊Q8—112no—
144C4⋊Q8—222no—
145C4⋊Q8—221no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—222no—
149C2×C4⋊C4C22⋊D1112yes—
150C2×C4⋊C4C22⋊D1112yes—
151C2×C4⋊C4C22⋊D1111yescharacteristic
152C2×C4⋊C4C22⋊D1111yescharacteristic
153C2×C42C22×D1111yescharacteristic
154#103—442no—
155#103—442no—
156#97—222no—
157#97—222no—
158#97—222no—
159#95—22no—
160#95—21no—
161#95—21no—
162#95—22no—
163#95—22no—
164#95—22no—
165C2×C11#165911yescharacteristic
166C2×C11#166011yescharacteristic
167C2×C11#166412yes—
168C2×C11#202711yescharacteristic
169C2×C11#202812yes—
170C2×Q8—81no—
171C2×Q8—82no—
172C2×Q8—222no—
173C2×Q8—441no—
174C2×Q8—441no—
175C2×Q8—441no—
176C2×Q8—441no—
177C2×Q8—441no—
178C22×C4—21no—
179C22×C4—22no—
180C22×C4—21no—
181C22×C4—22no—
182C22×C4—441no—
183C22×C4C2×C22⋊D1112yes—
184C22×C4C2×C22⋊D1111yescharacteristic
185C2×C8—222no—
186C2×C8—224no—
187C2×C8—442no—
188C2×C8—441no—
189C2×C8—442no—
190C2×C8—441no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—81no—
196C4⋊C4—82no—
197C4⋊C4—224no—
198C4⋊C4—442no—
199C42Q8×D1111yescharacteristic
200C42#434312yes—
201C42#434311yescharacteristic
202C11#1035911yescharacteristic, complemented, Sylow
203C23#6700611yescharacteristic
204Q8—84no—
205Q8—442no—
206Q8—442no—
207Q8—881no—
208Q8—881no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—442no—
224C2×C4—881no—
225C2×C4—881no—
226C2×C4#6699912yes—
227C2×C4#6699911yescharacteristic
228C2×C4#6700012yes—
229C2×C4#6700011yescharacteristic
230C8—442no—
231C8—444no—
232C22#1062284411yescharacteristic
233C22#1062285411yescharacteristic
234C22#1062285512yes—
235C22#1062285811yescharacteristic
236C22#1062285912yes—
237C4—21no—
238C4—21no—
239C4—22no—
240C4—22no—
241C4—81no—
242C4—82no—
243C4—81no—
244C4—82no—
245C4—882no—
246C2#1306792211yescharacteristic
247C2#1306792711yescharacteristic
248C2#1306795012yes—
249C2#1306976911yescharacteristic
250C2#1306977412yes—
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2844C2
socle, prime radicalC23×C11#120
hypercenter#2844D11
hypocenterC11#10359
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2844

Complements

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

NH ≅ G/Ntype
33. #66922Q8semidirect
202. C11#10359semidirect

Maximal subgroups

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

subgroupindex
#130695882
#130694352
#130664972
C11×#28442
#1035911