Finite Group Databasebeta

← #14667235

Subgroups — #14667235

Order 2816.

384 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 69 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#13080375C211yesmaximal, characteristic
2#13070872C211yesmaximal, characteristic, complemented
3#13070666C211yesmaximal, characteristic, complemented
4#13067982C211yesmaximal, characteristic, complemented
5#13066661C211yesmaximal, characteristic, complemented
6#13066572C211yesmaximal, characteristic, complemented
7C11×#1332C211yesmaximal, characteristic, complemented
8C2×#66972—21no—
9#10623108—21no—
10C4×C11×Q16C2211yescharacteristic
11C2×#66893—21no—
12#10622640—21no—
13C2×#66864—22no—
14#10622496—21no—
15#10622459—21no—
16#10622424—22no—
17#10622312C2211yescharacteristic
18#10622308C2211yescharacteristic
19C8×D44C2211yescharacteristic
20C4×C11×C16C2211yescharacteristic
21C11×#335C2211yescharacteristic
22#10622130—21no—
23#10622124—21no—
24C4⋊(C11⋊C16)C2211yescharacteristic
25C2×#4343—22no—
26C2×C11×Q16D411yescharacteristic
27C4×Q8×C11—21no—
28C2×#4325—22no—
29#66972—42no—
30#66972—42no—
31C2×Dic44—21no—
32C2×Dic44—21no—
33C2×D88—21no—
34C2×D88D412yes—
35C2×C8×D11—21no—
36#66948—22no—
37#66948—42no—
38#66927—21no—
39#66927—41no—
40C4×D44—41no—
41C4×D44D411yescharacteristic
42#66922—21no—
43C2×C11×C16—21no—
44C11×#107D411yescharacteristic
45C11×C4⋊C8—21no—
46C11×#103—21no—
47C4×C8×C11C2311yescharacteristic
48#66893—42no—
49#66885—41no—
50(C2×D11)⋊C8—21no—
51#66882—41no—
52C2×C11⋊C16—21no—
53#66873—22no—
54C4⋊(C11⋊C8)D411yescharacteristic
55#66864—44no—
56#12321—111nomaximal, Sylow
57C2×Q8×C11—21no—
58#4343—44no—
59#4343—82no—
60C2×D44—22no—
61C2×D44—42no—
62C2×D44—42no—
63C2×D44—41no—
64C2×D44—41no—
65C2×D44D811yescharacteristic
66C2×C4×D11—21no—
67C2×C4×D11—42no—
68C2×Dic22—41no—
69C11×Q16—21no—
70C11×Q16D812yes—
71C2×C8×C11—41no—
72C2×C8×C11C2×D411yescharacteristic
73C2×C8×C11C2×D411yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4—41no—
76C42×C11—41no—
77C42×C11C2×D411yescharacteristic
78#4325—44no—
79(C2×D11)⋊C4—21no—
80(C2×D11)⋊C4—42no—
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83C4⋊Dic11D811yescharacteristic
84C2×C11⋊C8—21no—
85Dic44—42no—
86Dic44—41no—
87Dic44—41no—
88D88—42no—
89D88—41no—
90D88—41no—
91C8×D11—41no—
92C8×D11—41no—
93C11×C16—22no—
94C11⋊C16—41no—
95#3287—111no—
96#2248—111no—
97#2209—111no—
98#1669—111no—
99#1361—111no—
100#1332D1111yescharacteristic, complemented
101D4⋊C16—111no—
102C22×D11—21no—
103C22×D11—42no—
104Q8×C11—22no—
105Q8×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11#12011yescharacteristic
109C2×C4×C11C2×D811yescharacteristic
110C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
111C2×Dic11—21no—
112C2×Dic11—81no—
113D44—21no—
114D44—21no—
115D44—42no—
116D44—42no—
117D44—84no—
118D44—81no—
119D44—81no—
120D44—161no—
121D44—162no—
122C4×D11—41no—
123C4×D11—41no—
124C4×D11—84no—
125Dic22—81no—
126Dic22—81no—
127C8×C11—21no—
128C8×C11—81no—
129C8×C11C2×D811yescharacteristic
130C8×C11AGL(1,ℤ/8)11yescharacteristic
131C11⋊C8—41no—
132C2×#135—221no—
133#550—221no—
134C2×Q32—221no—
135C2×SD32—222no—
136#494—111no—
137#493—111no—
138#474—221no—
139#466—221no—
140#460—221no—
141#449—222no—
142C4×Q16C2×D1111yescharacteristic
143C8×D4—111no—
144C4⋊C16—111no—
145#358—221no—
146C4×C16C2×D1111yescharacteristic
147#335C2×D1111yescharacteristic
148#332—221no—
149C22×C11#44711yescharacteristic
150C2×D11—41no—
151C2×D11—41no—
152C2×D11—41no—
153C2×D11—82no—
154C2×D11—82no—
155C2×D11—82no—
156C4×C11—21no—
157C4×C11—42no—
158C4×C11—81no—
159C4×C11#44711yescharacteristic
160C4×C11#45311yescharacteristic
161C4×C11#50811yescharacteristic
162C4×C11#51011yescharacteristic
163Dic11—41no—
164Dic11—161no—
165C2×#41—222no—
166#135—442no—
167#135—442no—
168C2×Q16—221no—
169C2×Q16—221no—
170C2×Q16D4411yescharacteristic
171C2×SD16—222no—
172C2×D8—112no—
173C2×D8—221no—
174C22×C8—221no—
175C4⋊Q8—221no—
176#127—221no—
177#127—441no—
178#121—222no—
179#121—442no—
180C4×Q8—21no—
181C4×D4—111no—
182C4×D4—441no—
183Q32—442no—
184SD32—444no—
185C2×C16—21no—
186C2×C16—221no—
187#107—441no—
188#107D4411yescharacteristic
189C4⋊C8—21no—
190C4⋊C8—111no—
191#103—21no—
192#102—222no—
193#102—441no—
194C22⋊C8—221no—
195C4×C8C22×D1111yescharacteristic
196C2×C11#161911yescharacteristic
197C2×C11#218911yescharacteristic
198C2×C11#219411yescharacteristic
199D11—81no—
200D11—162no—
201#41—444no—
202#41—882no—
203C2×Q8—21no—
204C2×Q8—441no—
205C2×D4—111no—
206C2×D4—222no—
207C2×D4—442no—
208C2×D4—442no—
209C2×D4—441no—
210C2×D4—441no—
211C22×C4—221no—
212C22×C4—442no—
213Q16—21no—
214Q16—442no—
215Q16—441no—
216Q16—441no—
217Q16D8812yes—
218SD16—444no—
219D8—442no—
220D8—441no—
221D8—441no—
222C2×C8—41no—
223C2×C8—221no—
224C2×C8—441no—
225C2×C8—441no—
226C2×C8C2×D4411yescharacteristic
227C2×C8D4×D1111yescharacteristic
228C4⋊C4—21no—
229C4⋊C4—41no—
230C4⋊C4—111no—
231C4⋊C4—441no—
232C4⋊C4—441no—
233C22⋊C4—221no—
234C22⋊C4—442no—
235C42—41no—
236C42D4×D1111yescharacteristic
237C16—22no—
238C16—441no—
239C11#1232111yescharacteristic, complemented, Sylow
240C23—221no—
241C23—442no—
242Q8—22no—
243Q8—41no—
244Q8—881no—
245Q8—881no—
246D4—221no—
247D4—221no—
248D4—442no—
249D4—442no—
250D4—884no—
251D4—881no—
252D4—881no—
253D4—1761no—
254D4—1762no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—221no—
258C2×C4—441no—
259C2×C4—441no—
260C2×C4—884no—
261C2×C4—881no—
262C2×C4#6693511yescharacteristic
263C2×C4D8×D1111yescharacteristic
264C2×C4#6696711yescharacteristic
265C8—21no—
266C8—81no—
267C8—441no—
268C8C2×D8811yescharacteristic
269C8#6696111yescharacteristic
270C22—441no—
271C22—441no—
272C22—441no—
273C22—882no—
274C22—882no—
275C22—882no—
276C22#1062238611yescharacteristic
277C4—21no—
278C4—42no—
279C4—81no—
280C4—441no—
281C4—1761no—
282C4#1062234511yescharacteristic
283C4#1062243511yescharacteristic
284C4#1062252911yescharacteristic
285C4#1062253111yescharacteristic
286C2—881no—
287C2—1762no—
288C2#1306767211yescharacteristic
289C2#1307055911yescharacteristic
290C2#1307058811yescharacteristic
subgroupG/H
centerC22#10622386
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1332C2
socleC22×C11#447
prime radical#13080375C2
hypercenter#1332D11
hypocenterC11#12321
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1332

Complements

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

NH ≅ G/Ntype
2. #13070872C2semidirect
3. #13070666C2semidirect
4. #13067982C2semidirect
5. #13066661C2semidirect
6. #13066572C2semidirect
7. C11×#1332C2semidirect
100. #1332D11semidirect
239. C11#12321semidirect

Maximal subgroups

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

subgroupindex
#130803752
#130708722
#130706662
#130679822
#130666612
#130665722
C11×#13322
#1232111