Finite Group Databasebeta

← #14673562

Subgroups — #14673562

Order 2816.

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

normal subgroups only

This group has 318 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#13070402C211yesmaximal, characteristic
2C2×#10622149C211yesmaximal, characteristic
3C2×#10622134C211yesmaximal, characteristic
4#13070337C211yesmaximal, characteristic
5#13069475C211yesmaximal, characteristic
6#13069362C211yesmaximal, characteristic
7C11×#1387C211yesmaximal, characteristic
8C22×Dic44C2211yescharacteristic
9C2×C11×M32C2211yescharacteristic
10C2×C11×#108C2211yescharacteristic
11C2×C11×#107C2211yescharacteristic
12#10622732—21no—
13#10622719C2211yescharacteristic
14C2×C8×Dic11C2211yescharacteristic
15C2×#66876C2211yescharacteristic
16#10622587—21no—
17C2×#66874—21no—
18#10622193—21no—
19#10622149—22no—
20#10622141—21no—
21#10622141—21no—
22#10622134—22no—
23#10622128—21no—
24#10622127—21no—
25C22×Dic22—21no—
26C2×C11×M16—21no—
27C22×C8×C11C2311yescharacteristic
28C2×C11×C4⋊C4—21no—
29#66979—21no—
30C2×C4×Dic11D411yescharacteristic
31C22×C11⋊C8D411yescharacteristic
32C2×Dic44—21no—
33C2×Dic44—21no—
34C2×Dic44—21no—
35C2×Dic44—21no—
36C2×Dic44—21no—
37C2×Dic44Q812yes—
38C11×M32—21no—
39C11×M32—21no—
40C2×C11×C16—21no—
41C11×#108—21no—
42C11×#108—21no—
43C11×#107—21no—
44C11×#107—21no—
45C11⋊#95—42no—
46#66882D411yescharacteristic
47#66882D411yescharacteristic
48#66881—21no—
49Dic11⋊C8—42no—
50C8×Dic11—21no—
51C8×Dic11—21no—
52#66876—21no—
53#66876D412yes—
54C2×C11⋊C16—21no—
55#66874—42no—
56#13479—111nomaximal, Sylow
57C22×C4×C11—41no—
58C22×C4×C11C2×D411yescharacteristic
59C22×Dic11—21no—
60C22×Dic11—41no—
61C2×Dic22—22no—
62C2×Dic22—41no—
63C2×Dic22—41no—
64C2×Dic22—41no—
65C2×Dic22—41no—
66C2×Dic22—41no—
67C11×M16—41no—
68C11×M16—41no—
69C2×C8×C11—41no—
70C2×C8×C11C2×D411yescharacteristic
71C2×C8×C11C2×D411yescharacteristic
72C2×C8×C11C2×Q811yescharacteristic
73C2×C8×C11#4111yescharacteristic
74C2×C8×C11#4111yescharacteristic
75C2×C8×C11#4111yescharacteristic
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C22⋊Dic11—41no—
79C4⋊Dic11—21no—
80C4⋊Dic11—21no—
81C4×Dic11—21no—
82C4×Dic11—21no—
83C4×Dic11—41no—
84C2×C11⋊C8—21no—
85C2×C11⋊C8—21no—
86C2×C11⋊C8D812yes—
87Dic44—22no—
88Dic44—22no—
89Dic44—41no—
90Dic44—41no—
91C11×C16—41no—
92C11⋊C16—22no—
93#2159—111no—
94C2×#364—111no—
95C2×#362—111no—
96#2141—111no—
97#1969—111no—
98#1945—111no—
99#1387D1111yescharacteristic
100C23×C11AGL(1,ℤ/8)11yescharacteristic
101C2×C4×C11—82no—
102C2×C4×C11—81no—
103C2×C4×C11#12111yescharacteristic
104C2×C4×C11#12111yescharacteristic
105C2×C4×C11C22⋊Q811yescharacteristic
106C2×C4×C11C2×D811yescharacteristic
107C2×C4×C11#13511yescharacteristic
108C2×C4×C11#13711yescharacteristic
109C2×Dic11—22no—
110C2×Dic11—41no—
111C2×Dic11—41no—
112C2×Dic11—41no—
113C2×Dic11—41no—
114C2×Dic11—42no—
115C2×Dic11—81no—
116C2×Dic11—81no—
117Dic22—42no—
118Dic22—42no—
119Dic22—81no—
120Dic22—81no—
121C8×C11—81no—
122C8×C11#12111yescharacteristic
123C8×C11C22⋊Q811yescharacteristic
124C8×C11C22⋊Q811yescharacteristic
125C8×C11#12611yescharacteristic
126C11⋊C8—22no—
127C22×Q16—111no—
128C2×M32—111no—
129C2×M32C2×D1111yescharacteristic
130C2×#108C2×D1111yescharacteristic
131#427—111no—
132C2×#107C2×D1111yescharacteristic
133#424—221no—
134C2×#103—221no—
135C2×C4×C8—111no—
136#391—221no—
137#367—221no—
138#366—221no—
139#364—222no—
140#362—222no—
141#358—221no—
142#358—221no—
143#339—221no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11#45911yescharacteristic
147C22×C11#46811yescharacteristic
148C22×C11#47811yescharacteristic
149C4×C11—161no—
150C4×C11#39611yescharacteristic
151C4×C11#46411yescharacteristic
152C4×C11#46611yescharacteristic
153C4×C11#47411yescharacteristic
154Dic11—42no—
155Dic11—82no—
156Dic11—81no—
157Dic11—81no—
158C22×Q8—221no—
159C2×Q16—112no—
160C2×Q16—221no—
161C2×Q16—221no—
162C2×Q16—221no—
163C2×Q16—221no—
164C2×Q16—221no—
165C2×M16—21no—
166C22×C8—111no—
167C22×C8C22×D1111yescharacteristic
168#117—221no—
169C2×C4⋊C4—21no—
170C2×C42—111no—
171M32—21no—
172M32—21no—
173M32—112no—
174M32—221no—
175C2×C16—21no—
176C2×C16—221no—
177#108—21no—
178#108—21no—
179#107—21no—
180#107—21no—
181#107—111no—
182#107—111no—
183#106—221no—
184C4⋊C8—442no—
185#103—442no—
186C4×C8—221no—
187C4×C8—221no—
188#95—442no—
189C2×C11—21no—
190C2×C11—21no—
191C2×C11#206711yescharacteristic
192C2×C11#221211yescharacteristic
193C2×C11#221411yescharacteristic
194C2×Q8—222no—
195C2×Q8—441no—
196C2×Q8—441no—
197C2×Q8—441no—
198C2×Q8—441no—
199C2×Q8—441no—
200C22×C4—41no—
201C22×C4—221no—
202C22×C4—441no—
203C22×C4D4×D1111yescharacteristic
204Q16—222no—
205Q16—222no—
206Q16—441no—
207Q16—441no—
208M16—41no—
209M16—41no—
210C2×C8—41no—
211C2×C8—112no—
212C2×C8—221no—
213C2×C8—221no—
214C2×C8#433911yescharacteristic
215C2×C8#433911yescharacteristic
216C2×C8#433911yescharacteristic
217C2×C8D4×D1111yescharacteristic
218C2×C8D4×D1111yescharacteristic
219C2×C8Q8×D1111yescharacteristic
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—221no—
223C4⋊C4—221no—
224C22⋊C4—441no—
225C42—221no—
226C42—221no—
227C42—441no—
228C16—41no—
229C16—222no—
230C11#1347911yescharacteristic, complemented, Sylow
231C23#6696711yescharacteristic
232Q8—442no—
233Q8—442no—
234Q8—881no—
235Q8—881no—
236C2×C4—82no—
237C2×C4—81no—
238C2×C4—222no—
239C2×C4—441no—
240C2×C4—441no—
241C2×C4—442no—
242C2×C4—441no—
243C2×C4—441no—
244C2×C4—881no—
245C2×C4—881no—
246C2×C4#6693711yescharacteristic
247C2×C4#6693711yescharacteristic
248C2×C4#6694911yescharacteristic
249C2×C4D8×D1111yescharacteristic
250C2×C4#6696911yescharacteristic
251C2×C4#6697111yescharacteristic
252C8—81no—
253C8—222no—
254C8#6692911yescharacteristic
255C8#6693711yescharacteristic
256C8#6694911yescharacteristic
257C8#6694911yescharacteristic
258C22—21no—
259C22—21no—
260C22#1062239911yescharacteristic
261C22#1062242511yescharacteristic
262C22#1062248411yescharacteristic
263C4—161no—
264C4—442no—
265C4—881no—
266C4—881no—
267C4—882no—
268C4#1062228911yescharacteristic
269C4#1062238811yescharacteristic
270C4#1062241111yescharacteristic
271C4#1062250311yescharacteristic
272C2—21no—
273C2—21no—
274C2#1307000511yescharacteristic
275C2#1307068411yescharacteristic
276C2#1307069611yescharacteristic
subgroupG/H
centerC22#10622399
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1387C2
socleC22×C11#459
prime radicalC23×C11AGL(1,ℤ/8)
hypercenter#1387D11
hypocenterC11#13479
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1387

Complements

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

NH ≅ G/Ntype
230. C11#13479semidirect

Maximal subgroups

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

subgroupindex
#130704022
C2×#106221492
C2×#106221342
#130703372
#130694752
#130693622
C11×#13872
#1347911