Finite Group Databasebeta

← #14654385

Subgroups — #14654385

Order 2816.

716 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 83 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#13079391C211yesmaximal, characteristic, complemented
2#13077876C212yesmaximal
3#13066979C212yesmaximal, complemented
4#13066493C211yesmaximal, characteristic, complemented
5C11×#1780C211yesmaximal, characteristic
6C22×C11×#41C2211yescharacteristic
7C2×#67004—22no—
8C2×#66977C2212yes—
9C2×C11×C22⋊C8—22no—
10C2×C11×C22⋊C8C2211yescharacteristic
11C2×C11×C22⋊C8C2211yescharacteristic
12#10622852—24no—
13#10622845—22no—
14#10622841—22no—
15#10622831—22no—
16#10622820C2212yes—
17#10622729—22no—
18#10622352—22no—
19#10622335—22no—
20#10622107—24no—
21C2×C11×#41—22no—
22C2×C11×#41—22no—
23C2×C11×#41—44no—
24C22×Q8×C11D411yescharacteristic
25C22×D4×C11—21no—
26C22×D4×C11D411yescharacteristic
27C23×C4×C11—21no—
28C23×C4×C11C2311yescharacteristic
29C22×Dic22D412yes—
30C22×C8×C11—21no—
31C22×C8×C11D412yes—
32C2×C22⋊Dic11—22no—
33#67004—48no—
34C2×#4326—24no—
35C2×#4324—24no—
36C2×C4⋊Dic11D412yes—
37#66977—22no—
38#66977—22no—
39#66977—22no—
40#66977—22no—
41C2×Dic11⋊C4—22no—
42C2×#4318—22no—
43C2×Dic44—22no—
44C11×C22⋊C8—22no—
45C11×C22⋊C8—22no—
46C11×C22⋊C8—44no—
47#66899—24no—
48#66896—24no—
49C22⋊(C11⋊C8)—22no—
50C22⋊(C11⋊C8)D414yes—
51#66882—22no—
52#66880—24no—
53#9976—111nomaximal, Sylow
54C24×C11—21no—
55C24×C11#4111yescharacteristic
56C11×#41—28no—
57C11×#41—44no—
58C11×#41—44no—
59C11×#41—44no—
60C2×Q8×C11—22no—
61C2×Q8×C11—42no—
62C2×D4×C11—22no—
63C2×D4×C11—42no—
64C2×D4×C11—42no—
65C2×D4×C11—42no—
66C2×D4×C11—42no—
67C22×C4×C11—24no—
68C22×C4×C11—21no—
69C22×C4×C11—42no—
70C22×C4×C11—42no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11C2×D412yes—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D412yes—
77C22×Dic11—22no—
78C22×Dic11—22no—
79C2×Dic22—22no—
80C2×Dic22—22no—
81C2×Dic22—44no—
82C2×C8×C11—22no—
83C2×C8×C11—42no—
84C2×C8×C11—42no—
85C2×C8×C11—41no—
86C22⋊Dic11—42no—
87C22⋊Dic11—42no—
88#4326—48no—
89#4324—48no—
90C4⋊Dic11—22no—
91C4⋊Dic11—22no—
92Dic11⋊C4—42no—
93Dic11⋊C4—42no—
94#4318—44no—
95C2×C11⋊C8—24no—
96Dic44—82no—
97#3189—111no—
98#3007—112no—
99#1780D1111yescharacteristic
100#1472—112no—
101#1293—111no—
102C23×C11—22no—
103C23×C11—22no—
104C23×C11—41no—
105C23×C11—41no—
106C23×C11—41no—
107C23×C11—42no—
108C23×C11—41no—
109C23×C11—42no—
110C23×C11#12112yes—
111C23×C11#12111yescharacteristic
112Q8×C11—24no—
113Q8×C11—42no—
114D4×C11—24no—
115D4×C11—42no—
116D4×C11—48no—
117C2×C4×C11—24no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—41no—
121C2×C4×C11—42no—
122C2×C4×C11—44no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—44no—
126C2×C4×C11#12012yes—
127C2×C4×C11#12011yescharacteristic
128C2×C4×C11#12711yescharacteristic
129C2×Dic11—44no—
130C2×Dic11—42no—
131C2×Dic11—42no—
132C2×Dic11—82no—
133Dic22—44no—
134Dic22—44no—
135C8×C11—42no—
136C8×C11—81no—
137C11⋊C8—44no—
138C22×#41C2×D1111yescharacteristic
139C2×#137—222no—
140C2×C22⋊Q8—112no—
141#484—222no—
142#467—222no—
143#452—224no—
144#451—222no—
145#451—222no—
146#450—222no—
147#417—222no—
148#407—112no—
149C2×C22⋊C8—22no—
150C2×C22⋊C8C2×D1111yescharacteristic
151C2×C22⋊C8C2×D1111yescharacteristic
152#324—224no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—22no—
156C22×C11—22no—
157C22×C11—22no—
158C22×C11—44no—
159C22×C11—42no—
160C22×C11—82no—
161C22×C11—82no—
162C22×C11—81no—
163C22×C11—81no—
164C22×C11#39211yescharacteristic
165C22×C11#47312yes—
166C4×C11—21no—
167C4×C11—22no—
168C4×C11—42no—
169C4×C11B(4,𝔽2)12yes—
170Dic11—82no—
171Dic11—82no—
172C2×#41—22no—
173C2×#41—22no—
174C2×#41—44no—
175C22×Q8—112no—
176C22×Q8D4411yescharacteristic
177C22×D4—21no—
178C22×D4D4411yescharacteristic
179C23×C4—21no—
180C23×C4C22×D1111yescharacteristic
181#137—448no—
182C2×Q16—222no—
183C2×Q16—224no—
184C2×SD16—224no—
185C2×M16—222no—
186C22×C8—21no—
187C22×C8C22⋊D1112yes—
188C22⋊Q8—222no—
189C22⋊Q8—222no—
190C22⋊Q8—222no—
191C22⋊Q8—222no—
192C2×C4⋊C4—112no—
193C2×C4⋊C4—222no—
194C2×C22⋊C4—222no—
195#107—222no—
196#103—224no—
197#103—224no—
198#102—224no—
199C22⋊C8—22no—
200C22⋊C8—22no—
201C22⋊C8—44no—
202C22⋊C8—114no—
203C22⋊C8—222no—
204C2×C11—22no—
205C2×C11—42no—
206C2×C11—82no—
207C2×C11#201711yescharacteristic
208C2×C11#202011yescharacteristic
209C2×C11#202111yescharacteristic
210C24—21no—
211C24#433911yescharacteristic
212#41—28no—
213#41—44no—
214#41—44no—
215#41—44no—
216C2×Q8—22no—
217C2×Q8—42no—
218C2×Q8—222no—
219C2×Q8—222no—
220C2×Q8—444no—
221C2×D4—22no—
222C2×D4—42no—
223C2×D4—42no—
224C2×D4—42no—
225C2×D4—42no—
226C22×C4—24no—
227C22×C4—21no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—222no—
233C22×C4—222no—
234C22×C4C2×D4411yescharacteristic
235C22×C4D4×D1112yes—
236C22×C4D4×D1112yes—
237C22×C4C2×C22⋊D1111yescharacteristic
238Q16—448no—
239Q16—882no—
240SD16—448no—
241M16—444no—
242C2×C8—22no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—41no—
246C2×C8—224no—
247C4⋊C4—222no—
248C4⋊C4—222no—
249C4⋊C4—442no—
250C4⋊C4—442no—
251C22⋊C4—442no—
252C22⋊C4—442no—
253C11#997611yescharacteristic, complemented, Sylow
254C23—22no—
255C23—22no—
256C23—41no—
257C23—41no—
258C23—41no—
259C23—42no—
260C23—42no—
261C23—41no—
262C23#6693712yes—
263C23#6698311yescharacteristic
264Q8—24no—
265Q8—42no—
266Q8—444no—
267Q8—444no—
268D4—24no—
269D4—42no—
270D4—48no—
271C2×C4—22no—
272C2×C4—24no—
273C2×C4—22no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—44no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—44no—
280C2×C4—444no—
281C2×C4—442no—
282C2×C4—442no—
283C2×C4—882no—
284C2×C4#6693512yes—
285C2×C4#6699011yescharacteristic
286C2×C4#6699311yescharacteristic
287C8—42no—
288C8—81no—
289C8—444no—
290C22—21no—
291C22—21no—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—44no—
296C22—42no—
297C22—82no—
298C22—82no—
299C22—81no—
300C22—81no—
301C22#1062257311yescharacteristic
302C22#1062275612yes—
303C4—21no—
304C4—22no—
305C4—42no—
306C4—882no—
307C4—882no—
308C4#1062264512yes—
309C2—22no—
310C2—42no—
311C2—82no—
312C2#1306972011yescharacteristic
313C2#1306973711yescharacteristic
314C2#1306974211yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1780C2
socleC22×C11#392
prime radicalC22×C11×#41C22
hypercenter#1780D11
hypocenterC11#9976
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1780

Complements

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

NH ≅ G/Ntype
1. #13079391C2semidirect
3. #13066979C2semidirect
4. #13066493C2semidirect
253. C11#9976semidirect

Maximal subgroups

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

subgroupindex
#130793912
#130778762
#130669792
#130664932
C11×#17802
#997611