Finite Group Databasebeta

← #14673163

Subgroups — #14673163

Order 2816.

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

normal subgroups only

This group has 436 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
1C2×#10622794C211yesmaximal, characteristic
2C2×#10622134C211yesmaximal, characteristic
3#13070337C211yesmaximal, characteristic
4#13070336C211yesmaximal, characteristic
5#13069362C211yesmaximal, characteristic
6#13066697C211yesmaximal, characteristic
7C2×C11×#362C211yesmaximal, characteristic
8C22×C11×Q16C2211yescharacteristic
9C2×#66997—21no—
10C22×#4326—21no—
11C22×Dic44C2211yescharacteristic
12C2×C11×M32C2211yescharacteristic
13C2×C11×#108C2211yescharacteristic
14#10622794—22no—
15#10622794—22no—
16#10622732—21no—
17#10622719C2211yescharacteristic
18C2×C8×Dic11C2211yescharacteristic
19C2×#66876C2211yescharacteristic
20C11×#362—22no—
21#10622202—22no—
22#10622193—21no—
23#10622141—22no—
24#10622134—22no—
25C22×Q8×C11—21no—
26C22×Dic22—21no—
27C2×C11×Q16—21no—
28C2×C11×Q16—21no—
29C2×C11×Q16—21no—
30C2×C11×Q16—21no—
31C2×C11×Q16—21no—
32C2×C11×Q16D412yes—
33C2×C11×M16—21no—
34C22×C8×C11C2311yescharacteristic
35#66997—24no—
36#66997—42no—
37C2×#4326—24no—
38C2×#4326—42no—
39C2×#4326—42no—
40#66979—21no—
41C2×Dic11⋊C4—42no—
42C2×C4×Dic11D411yescharacteristic
43C22×C11⋊C8D411yescharacteristic
44C2×Dic44—21no—
45C2×Dic44—21no—
46C2×Dic44—21no—
47C2×Dic44—21no—
48C2×Dic44—21no—
49C2×Dic44D412yes—
50C11×M32—21no—
51C11×M32—21no—
52C2×C11×C16—21no—
53C11×#108—21no—
54C11×#108—21no—
55#66882D412yes—
56#66881—21no—
57Dic11⋊C8—42no—
58C8×Dic11—21no—
59C8×Dic11—21no—
60#66876—21no—
61#66876—21no—
62C2×C11⋊C16—21no—
63#13415—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×C11C2×D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—41no—
74C2×Dic22—22no—
75C2×Dic22—41no—
76C2×Dic22—41no—
77C2×Dic22—41no—
78C2×Dic22—41no—
79C2×Dic22—41no—
80C11×Q16—22no—
81C11×Q16—22no—
82C11×Q16—41no—
83C11×Q16—41no—
84C11×M16—41no—
85C11×M16—41no—
86C2×C8×C11—41no—
87C2×C8×C11C2×D411yescharacteristic
88C2×C8×C11C2×D411yescharacteristic
89C2×C8×C11C2×D411yescharacteristic
90C2×C8×C11#4111yescharacteristic
91C2×C8×C11#4111yescharacteristic
92C2×C8×C11#4111yescharacteristic
93C22⋊Dic11—41no—
94#4326—48no—
95C4⋊Dic11—22no—
96Dic11⋊C4—48no—
97C4×Dic11—21no—
98C4×Dic11—41no—
99C4×Dic11SD1612yes—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—21no—
102C2×C11⋊C8D812yes—
103Dic44—22no—
104Dic44—22no—
105Dic44—41no—
106Dic44—41no—
107C11×C16—41no—
108C11⋊C16—41no—
109C2×#494—111no—
110C2×#362—111no—
111C2×#362D1111yescharacteristic
112#2141—111no—
113#2141—111no—
114#1945—111no—
115#1376—111no—
116C23×C11AGL(1,ℤ/8)11yescharacteristic
117Q8×C11—42no—
118Q8×C11—42no—
119Q8×C11—81no—
120Q8×C11—81no—
121C2×C4×C11—42no—
122C2×C4×C11—81no—
123C2×C4×C11—81no—
124C2×C4×C11#12011yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12411yescharacteristic
127C2×C4×C11C2×D811yescharacteristic
128C2×C4×C11C2×SD1611yescharacteristic
129C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
130C2×Dic11—24no—
131C2×Dic11—22no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—81no—
135C2×Dic11—81no—
136Dic22—42no—
137Dic22—42no—
138Dic22—81no—
139Dic22—81no—
140C8×C11—81no—
141C8×C11#12111yescharacteristic
142C8×C11#12111yescharacteristic
143C8×C11#12311yescharacteristic
144C8×C11#12311yescharacteristic
145C11⋊C8—22no—
146C22×Q16—111no—
147C22×Q16—221no—
148C22×Q16C2×D1111yescharacteristic
149C2×C4⋊Q8—221no—
150C2×M32—111no—
151C2×M32C2×D1111yescharacteristic
152#494—222no—
153#494—222no—
154C2×#108C2×D1111yescharacteristic
155#427—111no—
156#424—221no—
157C2×C4×C8—111no—
158#362—22no—
159#362—222no—
160#358—222no—
161#358—222no—
162#339—221no—
163C22×C11—22no—
164C22×C11#45011yescharacteristic
165C22×C11#45911yescharacteristic
166C22×C11#49011yescharacteristic
167C4×C11—82no—
168C4×C11#39411yescharacteristic
169C4×C11#44711yescharacteristic
170C4×C11#46011yescharacteristic
171C4×C11#48611yescharacteristic
172Dic11—24no—
173Dic11—82no—
174Dic11—82no—
175C22×Q8—21no—
176C22×Q8—221no—
177C2×Q16—21no—
178C2×Q16—21no—
179C2×Q16—21no—
180C2×Q16—21no—
181C2×Q16—21no—
182C2×Q16—112no—
183C2×Q16—224no—
184C2×Q16—221no—
185C2×Q16—221no—
186C2×Q16—221no—
187C2×Q16—221no—
188C2×Q16—221no—
189C2×Q16—442no—
190C2×Q16—442no—
191C2×Q16C22⋊D1112yes—
192C2×M16—21no—
193C22×C8—111no—
194C22×C8C22×D1111yescharacteristic
195C4⋊Q8—224no—
196C4⋊Q8—442no—
197#117—221no—
198C2×C4⋊C4—442no—
199C2×C42—111no—
200M32—21no—
201M32—21no—
202M32—221no—
203M32—221no—
204C2×C16—21no—
205C2×C16—221no—
206#108—21no—
207#108—21no—
208#107—112no—
209#106—221no—
210C4⋊C8—442no—
211C4×C8—221no—
212C4×C8—221no—
213C2×C11—21no—
214C2×C11—21no—
215C2×C11#204111yescharacteristic
216C2×C11#221412yes—
217C2×Q8—22no—
218C2×Q8—41no—
219C2×Q8—41no—
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8—41no—
223C2×Q8—222no—
224C2×Q8—441no—
225C2×Q8—441no—
226C2×Q8—441no—
227C2×Q8—441no—
228C2×Q8—441no—
229C22×C4—41no—
230C22×C4—221no—
231C22×C4—441no—
232C22×C4D4×D1111yescharacteristic
233Q16—22no—
234Q16—22no—
235Q16—41no—
236Q16—41no—
237Q16—222no—
238Q16—222no—
239Q16—448no—
240Q16—441no—
241Q16—441no—
242M16—41no—
243M16—41no—
244C2×C8—41no—
245C2×C8—112no—
246C2×C8—221no—
247C2×C8—221no—
248C2×C8#433911yescharacteristic
249C2×C8#433911yescharacteristic
250C2×C8D4×D1111yescharacteristic
251C2×C8D4×D1111yescharacteristic
252C2×C8#434111yescharacteristic
253C2×C8C2×C22⋊D1111yescharacteristic
254C4⋊C4—222no—
255C4⋊C4—448no—
256C22⋊C4—441no—
257C42—112no—
258C42—221no—
259C42—441no—
260C16—41no—
261C16—441no—
262C11#1341511yescharacteristic, complemented, Sylow
263C23#6696711yescharacteristic
264Q8—42no—
265Q8—42no—
266Q8—81no—
267Q8—81no—
268Q8—442no—
269Q8—442no—
270Q8—881no—
271Q8—881no—
272C2×C4—42no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—224no—
276C2×C4—222no—
277C2×C4—442no—
278C2×C4—442no—
279C2×C4—881no—
280C2×C4—881no—
281C2×C4#6693711yescharacteristic
282C2×C4#6693811yescharacteristic
283C2×C4D8×D1111yescharacteristic
284C2×C4#6696411yescharacteristic
285C2×C4SD16×D1111yescharacteristic
286C2×C4#6699011yescharacteristic
287C8—81no—
288C8—222no—
289C8#6693611yescharacteristic
290C8#6693711yescharacteristic
291C8#6698211yescharacteristic
292C8#6699211yescharacteristic
293C22—22no—
294C22#1062237711yescharacteristic
295C22#1062239911yescharacteristic
296C22#1062278211yescharacteristic
297C4—82no—
298C4—224no—
299C4—882no—
300C4—882no—
301C4#1062237311yescharacteristic
302C4#1062237511yescharacteristic
303C4#1062257211yescharacteristic
304C4#1062276911yescharacteristic
305C2—21no—
306C2—21no—
307C2#1306984811yescharacteristic
308C2#1307069612yes—
subgroupG/H
centerC22#10622399
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×#362C2
socleC22×C11#459
prime radicalC23×C11AGL(1,ℤ/8)
hypercenterC2×#362D11
hypocenterC11#13415
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#362

Complements

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

NH ≅ G/Ntype
262. C11#13415semidirect

Maximal subgroups

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

subgroupindex
C2×#106227942
C2×#106221342
#130703372
#130703362
#130693622
#130666972
C2×C11×#3622
#1341511