Finite Group Databasebeta

← #14673164

Subgroups — #14673164

Order 2816.

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

normal subgroups only

This group has 436 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
1C2×#10622794C211yesmaximal, characteristic
2C2×#10622155C211yesmaximal, characteristic
3C2×#10622203C211yesmaximal, characteristic
4#13070335C211yesmaximal, characteristic
5#13069365C211yesmaximal, characteristic
6#13066697C211yesmaximal, characteristic
7C11×#2141C211yesmaximal, characteristic
8C22×C11×Q16C2211yescharacteristic
9C2×#66997—21no—
10C22×#4326—21no—
11C22×Dic44C2211yescharacteristic
12C2×C11×M32C2211yescharacteristic
13C11×#427C2211yescharacteristic
14#10622794—22no—
15#10622794—22no—
16C2×#66883C2211yescharacteristic
17C2×C8×Dic11C2211yescharacteristic
18C2×#66876C2211yescharacteristic
19#10622612—21no—
20C11×#358—22no—
21#10622203—22no—
22#10622170—21no—
23#10622155—22no—
24#10622130—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—
33C22×C8×C11C2311yescharacteristic
34C11×#117—21no—
35#66997—24no—
36#66997—42no—
37C2×#4326—24no—
38C2×#4326—42no—
39C2×#4326—42no—
40C2×Dic11⋊C4—42no—
41C2×C4×Dic11D411yescharacteristic
42C2×#4318—21no—
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×#107D412yes—
54C11×#106—21no—
55#66883—21no—
56#66883—21no—
57C8×Dic11—21no—
58C8×Dic11—21no—
59#66876—21no—
60#66876—21no—
61C2×C11⋊C16—21no—
62C4⋊(C11⋊C8)—42no—
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—
84C2×C8×C11C2×D411yescharacteristic
85C2×C8×C11C2×D411yescharacteristic
86C2×C8×C11C2×D411yescharacteristic
87C2×C8×C11#4111yescharacteristic
88C2×C8×C11#4111yescharacteristic
89C2×C8×C11#4111yescharacteristic
90C11×C4⋊C4—22no—
91C11×C22⋊C4—41no—
92C42×C11—41no—
93#4326—48no—
94Dic11⋊C4—48no—
95C4×Dic11—21no—
96C4×Dic11SD1612yes—
97#4318—41no—
98#4318—41no—
99C2×C11⋊C8—21no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8D812yes—
103Dic44—22no—
104Dic44—22no—
105Dic44—41no—
106Dic44—41no—
107C11×C16—41no—
108C11⋊C16—41no—
109C2×#494—111no—
110C2×#362—111no—
111C2×#362—111no—
112#2141—111no—
113#2141D1111yescharacteristic
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—42no—
123C2×C4×C11—81no—
124C2×C4×C11—81no—
125C2×C4×C11#12011yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12411yescharacteristic
128C2×C4×C11C2×D811yescharacteristic
129C2×C4×C11C2×SD1611yescharacteristic
130C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
131C2×Dic11—24no—
132C2×Dic11—22no—
133C2×Dic11—42no—
134C2×Dic11—81no—
135C2×Dic11—81no—
136Dic22—42no—
137Dic22—42no—
138Dic22—81no—
139Dic22—81no—
140C8×C11#12111yescharacteristic
141C8×C11#12111yescharacteristic
142C8×C11#12311yescharacteristic
143C8×C11#12311yescharacteristic
144C11⋊C8—22no—
145C11⋊C8—81no—
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×#108—111no—
155#427C2×D1111yescharacteristic
156#424—221no—
157C2×C4×C8—111no—
158#362—222no—
159#362—222no—
160#358—22no—
161#358—222no—
162#339—221no—
163C22×C11—22no—
164C22×C11#45011yescharacteristic
165C22×C11#45911yescharacteristic
166C22×C11#49011yescharacteristic
167C4×C11—82no—
168C4×C11—82no—
169C4×C11#39411yescharacteristic
170C4×C11#44711yescharacteristic
171C4×C11#46011yescharacteristic
172C4×C11#48611yescharacteristic
173Dic11—24no—
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×Q16D4412yes—
192C2×M16—221no—
193C22×C8—111no—
194C22×C8C22×D1111yescharacteristic
195C4⋊Q8—224no—
196C4⋊Q8—442no—
197#117—21no—
198C2×C4⋊C4—442no—
199C2×C42—111no—
200M32—21no—
201M32—21no—
202M32—221no—
203M32—221no—
204C2×C16—21no—
205C2×C16—221no—
206#108—221no—
207#108—221no—
208#107C22⋊D1112yes—
209#106—21no—
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—441no—
243M16—441no—
244C2×C8—112no—
245C2×C8—221no—
246C2×C8—221no—
247C2×C8—441no—
248C2×C8C2×D4411yescharacteristic
249C2×C8#433911yescharacteristic
250C2×C8D4×D1111yescharacteristic
251C2×C8#434111yescharacteristic
252C2×C8#434111yescharacteristic
253C2×C8C2×C22⋊D1111yescharacteristic
254C4⋊C4—22no—
255C4⋊C4—448no—
256C22⋊C4—41no—
257C42—41no—
258C42—112no—
259C42—221no—
260C16—41no—
261C16—441no—
262C11#1341511yescharacteristic, complemented, Sylow
263C23#6696411yescharacteristic
264Q8—42no—
265Q8—42no—
266Q8—81no—
267Q8—81no—
268Q8—442no—
269Q8—442no—
270Q8—881no—
271Q8—881no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—224no—
277C2×C4—222no—
278C2×C4—442no—
279C2×C4—881no—
280C2×C4—881no—
281C2×C4#6693511yescharacteristic
282C2×C4#6693811yescharacteristic
283C2×C4D8×D1111yescharacteristic
284C2×C4SD16×D1111yescharacteristic
285C2×C4#6696711yescharacteristic
286C2×C4#6699211yescharacteristic
287C8—222no—
288C8—881no—
289C8#6693611yescharacteristic
290C8#6693911yescharacteristic
291C8#6698311yescharacteristic
292C8#6699111yescharacteristic
293C22—22no—
294C22#1062237711yescharacteristic
295C22#1062238911yescharacteristic
296C22#1062276311yescharacteristic
297C4—82no—
298C4—82no—
299C4—224no—
300C4—882no—
301C4#1062237311yescharacteristic
302C4#1062238611yescharacteristic
303C4#1062257411yescharacteristic
304C4#1062277611yescharacteristic
305C2—21no—
306C2—21no—
307C2#1306984911yescharacteristic
308C2#1307069512yes—
subgroupG/H
centerC22#10622763
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#2141C2
socleC22×C11#459
prime radicalC23×C11AGL(1,ℤ/8)
hypercenter#2141D11
hypocenterC11#13415
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2141

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×#106221552
C2×#106222032
#130703352
#130693652
#130666972
C11×#21412
#1341511