Finite Group Databasebeta

← #14654388

Subgroups — #14654388

Order 2816.

544 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 85 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#13078552C212yesmaximal, complemented
2#13068685C211yesmaximal, characteristic, complemented
3#13066976C212yesmaximal, complemented
4#13066493C211yesmaximal, characteristic, complemented
5C11×#3186C211yesmaximal, characteristic
6C2×C11×#121C2212yes—
7C2×#66979C2211yescharacteristic
8C11×#480—22no—
9C11×#466—22no—
10C11×#447—22no—
11C2×C11×C22⋊C8C2211yescharacteristic
12#10622828—22no—
13#10622820C2212yes—
14C2×C22⋊(C11⋊C8)C2211yescharacteristic
15#10622648—24no—
16#10622647—22no—
17#10622646—22no—
18#10622577—22no—
19#10622188—22no—
20#10622163—24no—
21C22×D4×C11—22no—
22C22×D4×C11D412yes—
23C23×C4×C11C2311yescharacteristic
24C2×C11×D8—22no—
25C22×C8×C11D412yes—
26C11×#121—22no—
27C11×#121—22no—
28C11×#121—22no—
29C11×#121—22no—
30C2×C11×C4⋊C4D412yes—
31C2×C11×C22⋊C4—22no—
32C2×C22⋊Dic11—21no—
33#66979—22no—
34#66979—22no—
35C2×C4⋊Dic11D411yescharacteristic
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4×Dic11—21no—
38C2×#4318—22no—
39C22×C11⋊C8—21no—
40C11×#107—22no—
41C11×#102—24no—
42C11×C22⋊C8—22no—
43#66896—24no—
44#66896—24no—
45C22⋊(C11⋊C8)—22no—
46C22⋊(C11⋊C8)—22no—
47C22⋊(C11⋊C8)D414yes—
48#66872—24no—
49#66871—24no—
50#9977—111nomaximal, Sylow
51C24×C11—22no—
52C24×C11#4111yescharacteristic
53C2×D4×C11—22no—
54C2×D4×C11—22no—
55C2×D4×C11—44no—
56C2×D4×C11—42no—
57C2×D4×C11—42no—
58C2×D4×C11—84no—
59C22×C4×C11—22no—
60C22×C4×C11—42no—
61C22×C4×C11C2×D412yes—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D412yes—
65C22×Dic11—21no—
66C22×Dic11—21no—
67C11×D8—82no—
68C2×C8×C11—22no—
69C2×C8×C11—42no—
70C11×C4⋊C4—22no—
71C11×C4⋊C4—22no—
72C11×C22⋊C4—42no—
73C11×C22⋊C4—42no—
74C22⋊Dic11—42no—
75C4⋊Dic11—22no—
76C4⋊Dic11—22no—
77C4×Dic11—41no—
78C4×Dic11—41no—
79#4318—44no—
80C2×C11⋊C8—24no—
81C2×C11⋊C8—42no—
82C2×C11⋊C8—41no—
83#3186D1111yescharacteristic
84#3094—112no—
85#1818—111no—
86#1471—112no—
87#1293—111no—
88C23×C11—22no—
89C23×C11—41no—
90C23×C11—41no—
91C23×C11—44no—
92C23×C11—42no—
93C23×C11—82no—
94C23×C11—82no—
95C23×C11#12111yescharacteristic
96C23×C11#12112yes—
97D4×C11—44no—
98D4×C11—44no—
99D4×C11—84no—
100D4×C11—84no—
101C2×C4×C11—22no—
102C2×C4×C11—24no—
103C2×C4×C11—41no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11—82no—
107C2×C4×C11#12012yes—
108C2×C4×C11#12011yescharacteristic
109C2×C4×C11#12711yescharacteristic
110C2×Dic11—42no—
111C2×Dic11—41no—
112C2×Dic11—41no—
113C2×Dic11—42no—
114C8×C11—42no—
115C11⋊C8—44no—
116C11⋊C8—81no—
117C2×#121C2×D1112yes—
118C2×#117—111no—
119#482—224no—
120#481—222no—
121#480—22no—
122#480—222no—
123#466—22no—
124#447—22no—
125#428—222no—
126#418—222no—
127#407—112no—
128C2×C22⋊C8—111no—
129C2×C22⋊C8C2×D1111yescharacteristic
130#336—222no—
131#323—224no—
132C22×C11—21no—
133C22×C11—21no—
134C22×C11—22no—
135C22×C11—22no—
136C22×C11—22no—
137C22×C11—82no—
138C22×C11—82no—
139C22×C11—82no—
140C22×C11—82no—
141C22×C11—164no—
142C22×C11#39211yescharacteristic
143C22×C11#47212yes—
144C4×C11—22no—
145C4×C11—21no—
146C4×C11—82no—
147C4×C11#45812yes—
148Dic11—81no—
149Dic11—81no—
150C22×D4—22no—
151C22×D4C22⋊D1112yes—
152C23×C4C22×D1111yescharacteristic
153C2×D8—22no—
154C2×M16—222no—
155C22×C8—221no—
156C22×C8C22⋊D1112yes—
157#121—22no—
158#121—22no—
159#121—22no—
160#121—22no—
161#117—222no—
162#117—222no—
163C2×C4⋊C4—111no—
164C2×C4⋊C4—111no—
165C2×C4⋊C4C22⋊D1112yes—
166C2×C22⋊C4—22no—
167C2×C22⋊C4—221no—
168C2×C42—221no—
169#107—22no—
170#107—224no—
171#106—224no—
172#102—24no—
173#102—224no—
174#102—224no—
175C22⋊C8—22no—
176C22⋊C8—114no—
177C22⋊C8—222no—
178C22⋊C8—222no—
179C2×C11—22no—
180C2×C11—42no—
181C2×C11—162no—
182C2×C11#201711yescharacteristic
183C2×C11#201811yescharacteristic
184C2×C11#202211yescharacteristic
185C24—22no—
186C24#434111yescharacteristic
187C2×D4—22no—
188C2×D4—22no—
189C2×D4—44no—
190C2×D4—42no—
191C2×D4—42no—
192C2×D4—84no—
193C22×C4—22no—
194C22×C4—42no—
195C22×C4—221no—
196C22×C4—221no—
197C22×C4D4×D1111yescharacteristic
198C22×C4D4×D1112yes—
199C22×C4C2×C22⋊D1112yes—
200C22×C4C2×C22⋊D1111yescharacteristic
201D8—82no—
202M16—444no—
203C2×C8—22no—
204C2×C8—42no—
205C2×C8—224no—
206C2×C8—442no—
207C2×C8—441no—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—222no—
211C4⋊C4—222no—
212C22⋊C4—42no—
213C22⋊C4—42no—
214C22⋊C4—442no—
215C42—441no—
216C42—441no—
217C11#997711yescharacteristic, complemented, Sylow
218C23—22no—
219C23—41no—
220C23—41no—
221C23—44no—
222C23—42no—
223C23—82no—
224C23—82no—
225C23#6699111yescharacteristic
226C23#6699212yes—
227D4—44no—
228D4—44no—
229D4—84no—
230D4—84no—
231C2×C4—22no—
232C2×C4—24no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—82no—
237C2×C4—442no—
238C2×C4—442no—
239C2×C4—441no—
240C2×C4—441no—
241C2×C4#6699012yes—
242C2×C4#6699311yescharacteristic
243C2×C4#6700611yescharacteristic
244C8—42no—
245C8—444no—
246C8—881no—
247C22—21no—
248C22—21no—
249C22—22no—
250C22—22no—
251C22—22no—
252C22—82no—
253C22—82no—
254C22—82no—
255C22—82no—
256C22—164no—
257C22#1062277312yes—
258C22#1062283611yescharacteristic
259C4—22no—
260C4—21no—
261C4—82no—
262C4—881no—
263C4—881no—
264C4#1062285612yes—
265C2—22no—
266C2—42no—
267C2—162no—
268C2#1306971911yescharacteristic
269C2#1306972311yescharacteristic
270C2#1306974511yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
Fitting, prime radicalC11×#3186C2
socleC22×C11#392
hypercenter#3186D11
hypocenterC11#9977
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3186

Complements

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

NH ≅ G/Ntype
1. #13078552C2semidirect
2. #13068685C2semidirect
3. #13066976C2semidirect
4. #13066493C2semidirect
217. C11#9977semidirect

Maximal subgroups

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

subgroupindex
#130785522
#130686852
#130669762
#130664932
C11×#31862
#997711