Finite Group Databasebeta

← #14670516

Subgroups — #14670516

Order 2816.

396 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 107 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×#10622466C211yesmaximal, characteristic
2C2×#10622134C211yesmaximal, characteristic
3#13070337C211yesmaximal, characteristic
4#13069367C211yesmaximal, characteristic
5#13066723C211yesmaximal, characteristic
6#13066695C211yesmaximal, characteristic
7C2×C11×#365C211yesmaximal, characteristic
8C22×Dic44C2211yescharacteristic
9C2×#66940—21no—
10C2×C11×M32C2211yescharacteristic
11C2×C11×#108C2211yescharacteristic
12C2×C11×#106C2211yescharacteristic
13#10622732—21no—
14#10622719C2211yescharacteristic
15C2×#66879C2211yescharacteristic
16C2×#66876C2211yescharacteristic
17C2×#66874—21no—
18#10622466—22no—
19#10622466—22no—
20C11×#365—22no—
21#10622193—21no—
22#10622141C414yescomplemented
23#10622134—22no—
24C22×Dic22—21no—
25C2×C11×M16—21no—
26C22×C8×C11C2311yescharacteristic
27C2×C11×C4⋊C4—21no—
28#66979—21no—
29C2×Dic11⋊C4—41no—
30C2×C4×Dic11—41no—
31C2×C4×Dic11D411yescharacteristic
32C22×C11⋊C8D411yescharacteristic
33C2×Dic44—21no—
34C2×Dic44—21no—
35C2×Dic44—21no—
36C2×Dic44C2×C412yes—
37C2×Dic44D412yes—
38C2×Dic44Q812yes—
39#66940—24no—
40#66940—42no—
41C11×M32—21no—
42C11×M32—21no—
43C2×C11×C16C2×C412yes—
44C11×#108—21no—
45C11×#108—21no—
46C11×#106—21no—
47C11×#106D412yes—
48#66882C2×C412yes—
49#66881—21no—
50#66879—21no—
51#66879—21no—
52Dic11⋊C8—42no—
53#66876—21no—
54#66876—21no—
55C2×C11⋊C16—21no—
56#66874—24no—
57#12957—111nomaximal, Sylow
58C22×C4×C11—41no—
59C22×C4×C11C2×D411yescharacteristic
60C22×Dic11—21no—
61C22×Dic11—41no—
62C2×Dic22—22no—
63C2×Dic22—22no—
64C2×Dic22—22no—
65C2×Dic22—41no—
66C2×Dic22—41no—
67C2×Dic22—41no—
68C11×M16—41no—
69C11×M16—41no—
70C2×C8×C11—41no—
71C2×C8×C11C22×C411yescharacteristic
72C2×C8×C11C2×D411yescharacteristic
73C2×C8×C11C2×D411yescharacteristic
74C2×C8×C11C2×Q811yescharacteristic
75C2×C8×C11#4111yescharacteristic
76C2×C8×C11#4111yescharacteristic
77C11×C4⋊C4—22no—
78C11×C4⋊C4—41no—
79C22⋊Dic11—41no—
80C4⋊Dic11—22no—
81Dic11⋊C4—44no—
82C4×Dic11—21no—
83C4×Dic11—44no—
84C4×Dic11—41no—
85C4×Dic11SD1612yes—
86C2×C11⋊C8—21no—
87C2×C11⋊C8—21no—
88C2×C11⋊C8—21no—
89Dic44—22no—
90Dic44—22no—
91Dic44—22no—
92Dic44C4⋊C414yes—
93C11×C16—22no—
94C11⋊C16—41no—
95C2×#441—111no—
96C2×#365D1111yescharacteristic
97C2×#362—111no—
98#2141—111no—
99#1946—111no—
100#1386—111no—
101#1375—111no—
102C23×C11AGL(1,ℤ/8)11yescharacteristic
103C2×C4×C11—42no—
104C2×C4×C11—82no—
105C2×C4×C11C4×D411yescharacteristic
106C2×C4×C11#12011yescharacteristic
107C2×C4×C11C22⋊Q811yescharacteristic
108C2×C4×C11C2×SD1611yescharacteristic
109C2×C4×C11#13511yescharacteristic
110C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
111C2×Dic11—22no—
112C2×Dic11—42no—
113C2×Dic11—42no—
114C2×Dic11—42no—
115C2×Dic11—42no—
116C2×Dic11—42no—
117Dic22—24no—
118Dic22—42no—
119Dic22—42no—
120Dic22—42no—
121C8×C11—81no—
122C8×C11C2×C4⋊C411yescharacteristic
123C8×C11C4×D411yescharacteristic
124C8×C11C22⋊Q811yescharacteristic
125C8×C11#12311yescharacteristic
126C11⋊C8—41no—
127C22×Q16—111no—
128C2×C4×Q8—221no—
129C2×M32—111no—
130C2×M32C2×D1111yescharacteristic
131#441—222no—
132#441—222no—
133C2×#108C2×D1111yescharacteristic
134#427—111no—
135C2×#106C2×D1111yescharacteristic
136#424—221no—
137C2×#103—221no—
138C2×#97—111no—
139#365—22no—
140#362—222no—
141#358—114no—
142#339—221no—
143C22×C11—22no—
144C22×C11#44211yescharacteristic
145C22×C11#45011yescharacteristic
146C22×C11#47811yescharacteristic
147C4×C11—82no—
148C4×C11#38511yescharacteristic
149C4×C11C4×SD1611yescharacteristic
150C4×C11#44911yescharacteristic
151C4×C11#47611yescharacteristic
152Dic11—42no—
153Dic11—44no—
154Dic11—82no—
155C22×Q8—221no—
156C2×Q16—112no—
157C2×Q16—112no—
158C2×Q16—112no—
159C2×Q16—221no—
160C2×Q16—221no—
161C2×Q16—221no—
162C2×M16—21no—
163C22×C8—111no—
164C22×C8C22×D1111yescharacteristic
165C4×Q8—224no—
166C4×Q8—442no—
167#117—221no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—441no—
170C2×C42—111no—
171C2×C42—441no—
172M32—21no—
173M32—21no—
174M32—221no—
175M32—221no—
176C2×C16—221no—
177C2×C16C4×D1112yes—
178#108—21no—
179#108—21no—
180#107—112no—
181#106—21no—
182#106—221no—
183#106C22⋊D1112yes—
184C4⋊C8—442no—
185#103—224no—
186#97—221no—
187#97—221no—
188C2×C11—21no—
189C2×C11—21no—
190C2×C11#186411yescharacteristic
191C2×C11#218012yes—
192C2×Q8—222no—
193C2×Q8—222no—
194C2×Q8—222no—
195C2×Q8—441no—
196C2×Q8—441no—
197C2×Q8—441no—
198C22×C4—41no—
199C22×C4—221no—
200C22×C4—441no—
201C22×C4D4×D1111yescharacteristic
202Q16—114no—
203Q16—222no—
204Q16—222no—
205Q16—222no—
206M16—41no—
207M16—41no—
208C2×C8—41no—
209C2×C8—221no—
210C2×C8—221no—
211C2×C8—221no—
212C2×C8C2×C4×D1111yescharacteristic
213C2×C8#433911yescharacteristic
214C2×C8D4×D1111yescharacteristic
215C2×C8Q8×D1111yescharacteristic
216C2×C8#434311yescharacteristic
217C2×C8C2×C22⋊D1111yescharacteristic
218C4⋊C4—22no—
219C4⋊C4—41no—
220C4⋊C4—222no—
221C4⋊C4—444no—
222C22⋊C4—441no—
223C42—112no—
224C42—221no—
225C42—444no—
226C42—441no—
227C16—22no—
228C16—441no—
229C11#1295711yescharacteristic, complemented, Sylow
230C23#6696711yescharacteristic
231Q8—224no—
232Q8—442no—
233Q8—442no—
234Q8—442no—
235C2×C4—42no—
236C2×C4—82no—
237C2×C4—222no—
238C2×C4—442no—
239C2×C4—442no—
240C2×C4—442no—
241C2×C4—442no—
242C2×C4—442no—
243C2×C4#6694611yescharacteristic
244C2×C4#6694911yescharacteristic
245C2×C4SD16×D1111yescharacteristic
246C2×C4#6696711yescharacteristic
247C2×C4#6696911yescharacteristic
248C2×C4#6699011yescharacteristic
249C8—81no—
250C8—441no—
251C8C4⋊C4×D1111yescharacteristic
252C8#6694711yescharacteristic
253C8C4×C22⋊D1111yescharacteristic
254C8#6699911yescharacteristic
255C22—22no—
256C22#1062248211yescharacteristic
257C22#1062248411yescharacteristic
258C22#1062278211yescharacteristic
259C4—82no—
260C4—442no—
261C4—444no—
262C4—882no—
263C4#1062246511yescharacteristic
264C4#1062248311yescharacteristic
265C4#1062260211yescharacteristic
266C4#1062278511yescharacteristic
267C2—21no—
268C2—21no—
269C2#1306887411yescharacteristic
270C2#1307050612yes—
subgroupG/H
centerC22#10622482
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#365C2
socleC22×C11#442
prime radicalC23×C11AGL(1,ℤ/8)
cosocleC22×C8×C11C23
hypercenterC2×#365D11
hypocenterC11#12957
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

Complements

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

NH ≅ G/Ntype
22. #10622141C4semidirect
229. C11#12957semidirect

Maximal subgroups

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

subgroupindex
C2×#106224662
C2×#106221342
#130703372
#130693672
#130667232
#130666952
C2×C11×#3652
#1295711