Finite Group Databasebeta

← #14667233

Subgroups — #14667233

Order 2816.

384 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 67 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#13080374C211yesmaximal, characteristic
2#13070871C211yesmaximal, characteristic, complemented
3#13070667C211yesmaximal, characteristic, complemented
4#13067982C211yesmaximal, characteristic, complemented
5#13066579C211yesmaximal, characteristic, complemented
6#13066570C211yesmaximal, characteristic, complemented
7C11×#1361C211yesmaximal, characteristic, complemented
8C2×#66965—21no—
9#10623249—21no—
10C11×#493C2211yescharacteristic
11#10622771—22no—
12#10622770—21no—
13C2×#66891—22no—
14#10622688—21no—
15C2×Dic88—21no—
16#10622459—21no—
17#10622312C2211yescharacteristic
18C4×Dic44C2211yescharacteristic
19C8×D44C2211yescharacteristic
20C11×C4⋊C16C2211yescharacteristic
21C11×#335C2211yescharacteristic
22#10622141—21no—
23#10622124—21no—
24C4×C11⋊C16C2211yescharacteristic
25C2×#4341—22no—
26C2×C11×D8—21no—
27C2×C11×D8D412yes—
28C11×#127—21no—
29#66993—41no—
30#66992—42no—
31#66991—22no—
32D4×Dic11—41no—
33C2×#4324—22no—
34#66965—42no—
35#66965—42no—
36C2×Dic44—21no—
37C2×Dic44—21no—
38C2×Dic44D411yescharacteristic
39C2×C8×D11—21no—
40C4×D44D411yescharacteristic
41#66922—21no—
42C4×Dic22—21no—
43C2×C11×C16—21no—
44C11×C4⋊C8—21no—
45C4×C8×C11C2311yescharacteristic
46#66896—22no—
47#66891—44no—
48#66885—41no—
49(C2×D11)⋊C8—21no—
50#66882—41no—
51#66882D411yescharacteristic
52#66880—21no—
53C2×C11⋊C16—21no—
54C4⋊(C11⋊C8)D411yescharacteristic
55Dic88—42no—
56#12321—111nomaximal, Sylow
57C2×D4×C11—22no—
58C2×D4×C11—41no—
59C2×D4×C11—41no—
60C2×C22⋊D11—42no—
61C2×C22⋊D11—42no—
62C22×Dic11—42no—
63#4341—44no—
64#4341—82no—
65C2×D44D811yescharacteristic
66C2×C4×D11—21no—
67C2×Dic22—21no—
68C2×Dic22—41no—
69C11×D8—41no—
70C11×D8—41no—
71C11×D8—42no—
72C2×C8×C11—41no—
73C2×C8×C11C2×D411yescharacteristic
74C2×C8×C11C2×D411yescharacteristic
75C42×C11C2×D411yescharacteristic
76C22⋊Dic11—42no—
77#4324—44no—
78(C2×D11)⋊C4—21no—
79C4⋊Dic11—21no—
80C4⋊Dic11—41no—
81C4⋊Dic11—41no—
82C4⋊Dic11D811yescharacteristic
83Dic11⋊C4—41no—
84C4×Dic11—41no—
85C2×C11⋊C8—21no—
86Dic44—21no—
87Dic44—42no—
88Dic44—41no—
89Dic44—41no—
90Dic44D812yes—
91C8×D11—41no—
92C8×D11—41no—
93C11×C16—41no—
94C11⋊C16—22no—
95#3287—111no—
96#2248—111no—
97#2209—111no—
98#1669—111no—
99#1361D1111yescharacteristic, complemented
100#1332—111no—
101D4⋊C16—111no—
102C23×C11—42no—
103C22×D11—21no—
104D4×C11—42no—
105D4×C11—42no—
106D4×C11—81no—
107D4×C11—81no—
108D4×C11—161no—
109C2×C4×C11#12011yescharacteristic
110C2×C4×C11C2×D811yescharacteristic
111C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
112C22⋊D11—84no—
113C22⋊D11—162no—
114C2×Dic11—21no—
115C2×Dic11—41no—
116C2×Dic11—41no—
117C2×Dic11—84no—
118C2×Dic11—81no—
119D44—21no—
120D44—21no—
121C4×D11—41no—
122C4×D11—41no—
123Dic22—22no—
124Dic22—41no—
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#493C2×D1111yescharacteristic
138#474—221no—
139#466—221no—
140#460—221no—
141#449—222no—
142C4×Q16—111no—
143C8×D4—111no—
144C4⋊C16C2×D1111yescharacteristic
145#358—221no—
146C4×C16—111no—
147#335C2×D1111yescharacteristic
148#332—221no—
149C22×C11—82no—
150C22×C11—82no—
151C22×C11—82no—
152C22×C11#44711yescharacteristic
153C2×D11—41no—
154C2×D11—41no—
155C2×D11—41no—
156C4×C11—21no—
157C4×C11#44711yescharacteristic
158C4×C11#45311yescharacteristic
159C4×C11#50811yescharacteristic
160C4×C11#51011yescharacteristic
161Dic11—42no—
162Dic11—41no—
163Dic11—81no—
164Dic11—161no—
165C2×#41—222no—
166#135—442no—
167#135—442no—
168C2×Q16—111no—
169C2×Q16—221no—
170C2×Q16—221no—
171C2×SD16—222no—
172C2×D8—21no—
173C2×D8D4412yes—
174C22×C8—221no—
175C4⋊Q8—221no—
176#127—21no—
177#127—441no—
178#121—222no—
179#121—442no—
180C4×Q8—221no—
181C4×D4—111no—
182C4×D4—441no—
183Q32—442no—
184SD32—444no—
185C2×C16—21no—
186C2×C16—221no—
187#107—111no—
188#107—441no—
189C4⋊C8—21no—
190C4⋊C8—111no—
191#103—221no—
192#102—222no—
193#102—441no—
194C22⋊C8—221no—
195C4×C8C22×D1111yescharacteristic
196C2×C11—162no—
197C2×C11#161911yescharacteristic
198C2×C11#218911yescharacteristic
199C2×C11#219411yescharacteristic
200D11—81no—
201#41—444no—
202#41—882no—
203C2×Q8—221no—
204C2×Q8—441no—
205C2×D4—22no—
206C2×D4—41no—
207C2×D4—41no—
208C2×D4—111no—
209C2×D4—442no—
210C2×D4—442no—
211C22×C4—221no—
212C22×C4—442no—
213Q16—112no—
214Q16—221no—
215Q16—442no—
216Q16—441no—
217Q16—441no—
218SD16—444no—
219D8—42no—
220D8—41no—
221D8—41no—
222C2×C8—41no—
223C2×C8—221no—
224C2×C8—441no—
225C2×C8—441no—
226C2×C8C2×D4411yescharacteristic
227C2×C8D4×D1111yescharacteristic
228C4⋊C4—111no—
229C4⋊C4—221no—
230C4⋊C4—441no—
231C4⋊C4—441no—
232C4⋊C4—441no—
233C22⋊C4—221no—
234C22⋊C4—442no—
235C42—441no—
236C42D4×D1111yescharacteristic
237C16—41no—
238C16—222no—
239C11#1232111yescharacteristic, complemented, Sylow
240C23—42no—
241C23—221no—
242Q8—222no—
243Q8—441no—
244Q8—881no—
245Q8—881no—
246D4—42no—
247D4—42no—
248D4—81no—
249D4—81no—
250D4—161no—
251D4—221no—
252D4—221no—
253D4—884no—
254D4—1762no—
255C2×C4—221no—
256C2×C4—441no—
257C2×C4—441no—
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—
268C8D8×D1111yescharacteristic
269C8#6696711yescharacteristic
270C22—82no—
271C22—82no—
272C22—82no—
273C22—441no—
274C22—441no—
275C22—441no—
276C22#1062238611yescharacteristic
277C4—21no—
278C4—441no—
279C4—442no—
280C4—881no—
281C4—1761no—
282C4#1062236011yescharacteristic
283C4#1062238611yescharacteristic
284C4#1062252511yescharacteristic
285C4#1062252811yescharacteristic
286C2—162no—
287C2—881no—
288C2#1306767111yescharacteristic
289C2#1307055711yescharacteristic
290C2#1307059011yescharacteristic
subgroupG/H
centerC22#10622386
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1361C2
socleC22×C11#447
prime radical#13080374C2
hypercenter#1361D11
hypocenterC11#12321
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
2. #13070871C2semidirect
3. #13070667C2semidirect
4. #13067982C2semidirect
5. #13066579C2semidirect
6. #13066570C2semidirect
7. C11×#1361C2semidirect
99. #1361D11semidirect
239. C11#12321semidirect

Maximal subgroups

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

subgroupindex
#130803742
#130708712
#130706672
#130679822
#130665792
#130665702
C11×#13612
#1232111