Finite Group Databasebeta

← #14672876

Subgroups — #14672876

Order 2816.

358 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 95 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#13079152C211yesmaximal, characteristic
2#13070336C211yesmaximal, characteristic
3#13069532C211yesmaximal, characteristic
4#13066724C211yesmaximal, characteristic
5#13066712C211yesmaximal, characteristic
6#13066704C211yesmaximal, characteristic
7C2×C11×#358C211yesmaximal, characteristic
8C22×C11×Q16C2211yescharacteristic
9#10623031—21no—
10C22×C11×C16C2211yescharacteristic
11C2×C11×#107C2211yescharacteristic
12C2×#66900—21no—
13#10622838—21no—
14C2×#66883C2211yescharacteristic
15#10622719C2211yescharacteristic
16#10622714C2211yescharacteristic
17C2×#66876C2211yescharacteristic
18#10622577—21no—
19#10622491—21no—
20#10622489—22no—
21#10622487—21no—
22C11×#358—22no—
23#10622202—21no—
24#10622202—21no—
25C22×Q8×C11—21no—
26C2×C11×Q16—21no—
27C2×C11×Q16—21no—
28C2×C11×Q16—21no—
29C2×C11×Q16—21no—
30C2×C11×Q16—21no—
31C2×C11×Q16Q812yescomplemented
32C22×C8×C11C2311yescharacteristic
33C2×C11×C4⋊C4—21no—
34#66979—21no—
35#66979D411yescharacteristic
36#66977—42no—
37C2×#4318—21no—
38C2×#4318D411yescharacteristic
39#66943—22no—
40#66943—41no—
41#66941—22no—
42#66941—41no—
43C2×C11×C16—21no—
44C2×C11×C16—21no—
45C2×C11×C16—21no—
46C11×#107—21no—
47C11×#107D412yes—
48#66900—42no—
49#66899—41no—
50#66899—41no—
51#66883—21no—
52#66883—21no—
53#66882D411yescharacteristic
54#66882D411yescharacteristic
55#66881—21no—
56#66879—21no—
57C8×Dic11—21no—
58#66876—21no—
59#66876—21no—
60C2×C11⋊C16—21no—
61#66872—22no—
62#66871—22no—
63#13370—111nomaximal, Sylow
64C2×Q8×C11—22no—
65C2×Q8×C11—41no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C2×Q8×C11—41no—
69C2×Q8×C11—41no—
70C22×C4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11C2×D411yescharacteristic
73C2×Dic22—42no—
74C11×Q16—22no—
75C11×Q16—22no—
76C11×Q16—41no—
77C11×Q16—41no—
78C2×C8×C11C2×D411yescharacteristic
79C2×C8×C11C2×D411yescharacteristic
80C2×C8×C11C2×Q811yescharacteristic
81C2×C8×C11#4111yescharacteristic
82C2×C8×C11#4111yescharacteristic
83C2×C8×C11#4111yescharacteristic
84C11×C4⋊C4—22no—
85C11×C4⋊C4—41no—
86C22⋊Dic11—21no—
87C22⋊Dic11—41no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11—42no—
91C4⋊Dic11D811yescharacteristic
92C4⋊Dic11D811yescharacteristic
93Dic11⋊C4—42no—
94Dic11⋊C4—42no—
95C4×Dic11—21no—
96C4×Dic11—41no—
97#4318—21no—
98#4318—41no—
99#4318—41no—
100#4318SD1612yes—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—41no—
103C11×C16—41no—
104C11⋊C16—41no—
105#3164—111no—
106#2141—111no—
107C2×#358D1111yescharacteristic
108#1979—111no—
109#1387—111no—
110#1382—111no—
111#1379—111no—
112C23×C11AGL(1,ℤ/8)11yescharacteristic
113Q8×C11—42no—
114Q8×C11—42no—
115Q8×C11—81no—
116Q8×C11—81no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—81no—
120C2×C4×C11—81no—
121C2×C4×C11—161no—
122C2×C4×C11#12011yescharacteristic
123C2×C4×C11C22⋊Q811yescharacteristic
124C2×C4×C11#12411yescharacteristic
125C2×C4×C11C2×D811yescharacteristic
126C2×C4×C11C2×SD1611yescharacteristic
127C2×C4×C11#13711yescharacteristic
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132Dic22—162no—
133C8×C11C22⋊Q811yescharacteristic
134C8×C11C22⋊Q811yescharacteristic
135C8×C11#12411yescharacteristic
136C8×C11#12411yescharacteristic
137C11⋊C8—22no—
138C11⋊C8—81no—
139C22×Q16C2×D1111yescharacteristic
140#544—221no—
141C2×M32—111no—
142C22×C16C2×D1111yescharacteristic
143#501—222no—
144#500—221no—
145#499—221no—
146C2×#108—111no—
147#428—221no—
148#427—111no—
149C2×#107C2×D1111yescharacteristic
150#419—221no—
151C2×#101—221no—
152#405—111no—
153#358—22no—
154#358—221no—
155#358—221no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11#44711yescharacteristic
159C22×C11#47611yescharacteristic
160C22×C11#48911yescharacteristic
161C4×C11—82no—
162C4×C11—82no—
163C4×C11#39311yescharacteristic
164C4×C11#44811yescharacteristic
165C4×C11#47411yescharacteristic
166C4×C11#48611yescharacteristic
167Dic11—41no—
168Dic11—41no—
169Dic11—81no—
170Dic11—81no—
171C22×Q8—21no—
172C2×Q16—21no—
173C2×Q16—21no—
174C2×Q16—21no—
175C2×Q16—21no—
176C2×Q16—21no—
177C2×Q16Dic2212yescomplemented
178C2×M16—111no—
179C2×M16—221no—
180C22×C8C22×D1111yescharacteristic
181C4⋊Q8—222no—
182C4⋊Q8—441no—
183#125—222no—
184#125—441no—
185C22⋊Q8—442no—
186#117—111no—
187#117—221no—
188C2×C4⋊C4—21no—
189M32—221no—
190M32—221no—
191C2×C16—21no—
192C2×C16—21no—
193C2×C16—21no—
194C2×C16—221no—
195#108—221no—
196#108—221no—
197#107—21no—
198#107—111no—
199#107—111no—
200#107—222no—
201#107C22⋊D1112yes—
202#106—222no—
203#106—221no—
204#103—441no—
205#103—441no—
206#101—442no—
207#97—221no—
208C4×C8—221no—
209C2×C11—21no—
210C2×C11—21no—
211C2×C11#202311yescharacteristic
212C2×C11#219411yescharacteristic
213C2×C11#219511yescharacteristic
214C2×Q8—22no—
215C2×Q8—41no—
216C2×Q8—41no—
217C2×Q8—41no—
218C2×Q8—41no—
219C2×Q8—41no—
220C2×Q8—442no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4D4×D1111yescharacteristic
224Q16—22no—
225Q16—22no—
226Q16—41no—
227Q16—41no—
228M16—112no—
229M16—221no—
230M16—441no—
231M16—441no—
232C2×C8—221no—
233C2×C8—441no—
234C2×C8C2×Dic2211yescharacteristic
235C2×C8#433911yescharacteristic
236C2×C8D4×D1111yescharacteristic
237C2×C8#434111yescharacteristic
238C2×C8#434111yescharacteristic
239C2×C8C2×C22⋊D1111yescharacteristic
240C4⋊C4—22no—
241C4⋊C4—41no—
242C4⋊C4—111no—
243C4⋊C4—111no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4—442no—
247C4⋊C4—442no—
248C4⋊C4—442no—
249C22⋊C4—221no—
250C22⋊C4—441no—
251C42—221no—
252C42—441no—
253C16—41no—
254C16—441no—
255C11#1337011yescharacteristic, complemented, Sylow
256C23#6696411yescharacteristic
257Q8—42no—
258Q8—42no—
259Q8—81no—
260Q8—81no—
261Q8—1762no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—161no—
267C2×C4—221no—
268C2×C4—221no—
269C2×C4—441no—
270C2×C4—441no—
271C2×C4#6693111yescharacteristic
272C2×C4#6693811yescharacteristic
273C2×C4D8×D1111yescharacteristic
274C2×C4SD16×D1111yescharacteristic
275C2×C4#6696811yescharacteristic
276C2×C4#6699011yescharacteristic
277C8—222no—
278C8—881no—
279C8#6693111yescharacteristic
280C8#6693811yescharacteristic
281C8#6697711yescharacteristic
282C8#6698911yescharacteristic
283C22—21no—
284C22—21no—
285C22#1062237411yescharacteristic
286C22#1062237811yescharacteristic
287C22#1062276911yescharacteristic
288C4—82no—
289C4—82no—
290C4—441no—
291C4—441no—
292C4—881no—
293C4—881no—
294C4#1062237211yescharacteristic
295C4#1062237311yescharacteristic
296C4#1062256011yescharacteristic
297C4#1062278311yescharacteristic
298C2—21no—
299C2—21no—
300C2#1306975011yescharacteristic
301C2#1307058611yescharacteristic
302C2#1307059311yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×#358C2
socleC22×C11#447
prime radicalC23×C11AGL(1,ℤ/8)
hypercenterC2×#358D11
hypocenterC11#13370
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
31. C2×C11×Q16Q8semidirect
177. C2×Q16Dic22semidirect
255. C11#13370semidirect

Maximal subgroups

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

subgroupindex
#130791522
#130703362
#130695322
#130667242
#130667122
#130667042
C2×C11×#3582
#1337011