Finite Group Databasebeta

← #14647261

Subgroups — #14647261

Order 2816.

450 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 99 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#13071100C211yesmaximal, characteristic
2#13066950C211yesmaximal, characteristic
3#13066473C212yesmaximal, complemented
4#13066471C212yesmaximal, complemented
5C11×#1464C211yesmaximal, characteristic
6C2×C11×#117C2211yescharacteristic
7C2×#66979C411yescharacteristic
8C22×C4×Dic11C411yescharacteristic
9C11×#432C2212yes—
10#10622598—21no—
11#10622598—21no—
12#10622563—21no—
13#10622563—21no—
14C4×C4⋊Dic11C411yescharacteristic
15C4×C4⋊Dic11C411yescharacteristic
16C4×C4⋊Dic11C2211yescharacteristic
17C4×C4⋊Dic11C2211yescharacteristic
18#10622539C2212yes—
19C11×#324—21no—
20C11×#323—21no—
21#10622166—21no—
22#10622163—21no—
23C23×C4×C11C2×C411yescharacteristic
24C23×Dic11—21no—
25C11×#117—22no—
26C11×#117—22no—
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C22⋊C4D411yescharacteristic
30C2×C11×C22⋊C4D411yescharacteristic
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×C22⋊Dic11—21no—
34#66979—42no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4×Dic11—21no—
41C2×C4×Dic11—42no—
42C2×C4×Dic11C2×C411yescharacteristic
43C2×C4×Dic11C2×C411yescharacteristic
44C2×C4×Dic11C2×C411yescharacteristic
45C2×C4×Dic11C2×C411yescharacteristic
46C11×C4⋊C8—22no—
47C11×C22⋊C8—22no—
48C11×#97—22no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C22⋊(C11⋊C8)—22no—
54C4⋊(C11⋊C8)—22no—
55#66867—22no—
56#8743—111nomaximal, Sylow
57C24×C11C22⋊C411yescharacteristic
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—42no—
73C22×Dic11—42no—
74C22×Dic11—42no—
75C2×C8×C11—42no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4—22no—
78C11×C22⋊C4—22no—
79C11×C22⋊C4—22no—
80C42×C11—21no—
81C42×C11—21no—
82C42×C11#4112yes—
83C42×C11#4112yes—
84C22⋊Dic11—42no—
85C4⋊Dic11—42no—
86C4⋊Dic11—42no—
87C4⋊Dic11—42no—
88C4⋊Dic11—42no—
89C4⋊Dic11—42no—
90C4×Dic11—41no—
91C4×Dic11—41no—
92C4×Dic11—41no—
93C4×Dic11—41no—
94C4×Dic11—42no—
95C2×C11⋊C8—42no—
96#2296—111no—
97#1464—111no—
98#1464D1111yescharacteristic
99#1285—112no—
100#1285—112no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—41no—
104C23×C11—41no—
105C23×C11#10112yes—
106C23×C11C2×C22⋊C411yescharacteristic
107C2×C4×C11—24no—
108C2×C4×C11—24no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11#10012yes—
120C2×C4×C11#11711yescharacteristic
121C2×C4×C11#11711yescharacteristic
122C2×C4×C11#12312yes—
123C2×C4×C11#12312yes—
124C2×Dic11—22no—
125C2×Dic11—22no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11—48no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C8×C11—82no—
138C11⋊C8—82no—
139C2×#117—111no—
140C2×#117C2×D1111yescharacteristic
141C22×C42—111no—
142#432—112no—
143#432C2×D1112yes—
144#389—221no—
145#389—221no—
146#385—221no—
147#385—221no—
148C4×C4⋊C4—111no—
149C4×C4⋊C4—111no—
150C4×C4⋊C4—111no—
151C4×C4⋊C4—111no—
152#324—21no—
153#324—221no—
154#323—21no—
155#323—221no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—22no—
159C22×C11—42no—
160C22×C11—42no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11#38111yescharacteristic
164C22×C11C2×#10011yescharacteristic
165C22×C11C2×#10111yescharacteristic
166C4×C11—22no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—22no—
170C4×C11—22no—
171C4×C11—41no—
172C4×C11—41no—
173Dic11—42no—
174Dic11—42no—
175Dic11—81no—
176Dic11—81no—
177C23×C4—221no—
178C23×C4C4×D1111yescharacteristic
179#117—22no—
180#117—22no—
181#117—442no—
182C2×C4⋊C4—221no—
183C2×C4⋊C4—221no—
184C2×C4⋊C4—221no—
185C2×C4⋊C4—221no—
186C2×C4⋊C4—221no—
187C2×C4⋊C4D4411yescharacteristic
188C2×C4⋊C4C22⋊D1111yescharacteristic
189C2×C22⋊C4—221no—
190C2×C22⋊C4D4411yescharacteristic
191C2×C22⋊C4C22⋊D1111yescharacteristic
192C2×C42—111no—
193C2×C42—111no—
194C2×C42—111no—
195C2×C42—111no—
196C2×C42—221no—
197C2×C42—442no—
198C2×C42C4×D1111yescharacteristic
199C2×C42C22×D1111yescharacteristic
200C4⋊C8—22no—
201C4⋊C8—222no—
202C22⋊C8—22no—
203C22⋊C8—222no—
204#97—22no—
205#97—222no—
206#95—221no—
207#95—221no—
208#95—221no—
209#95—221no—
210C2×C11—21no—
211C2×C11—21no—
212C2×C11—42no—
213C2×C11#182111yescharacteristic
214C2×C11#182711yescharacteristic
215C2×C11#182711yescharacteristic
216C24(C2×D11)⋊C411yescharacteristic
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—221no—
222C22×C4—221no—
223C22×C4—221no—
224C22×C4—221no—
225C22×C4—442no—
226C22×C4—442no—
227C22×C4—442no—
228C22×C4(C2×D11)⋊C411yescharacteristic
229C22×C4(C2×D11)⋊C411yescharacteristic
230C22×C4(C2×D11)⋊C411yescharacteristic
231C22×C4C2×C4×D1111yescharacteristic
232C22×C4C2×D4411yescharacteristic
233C22×C4C2×C22⋊D1111yescharacteristic
234C2×C8—42no—
235C2×C8—442no—
236C4⋊C4—22no—
237C4⋊C4—22no—
238C4⋊C4—442no—
239C4⋊C4—442no—
240C4⋊C4—442no—
241C4⋊C4—442no—
242C4⋊C4—442no—
243C22⋊C4—22no—
244C22⋊C4—22no—
245C22⋊C4—442no—
246C42—21no—
247C42—21no—
248C42—441no—
249C42—441no—
250C42—441no—
251C42—441no—
252C42—442no—
253C42#434112yes—
254C42#434112yes—
255C11#874311yescharacteristic, complemented, Sylow
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23#6688812yes—
261C23C2×(C2×D11)⋊C411yescharacteristic
262C2×C4—24no—
263C2×C4—24no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—222no—
275C2×C4—222no—
276C2×C4—441no—
277C2×C4—441no—
278C2×C4—448no—
279C2×C4—441no—
280C2×C4—441no—
281C2×C4—441no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4#6688712yes—
288C2×C4#6693011yescharacteristic
289C2×C4#6693011yescharacteristic
290C2×C4#6693912yes—
291C2×C4#6698812yes—
292C8—82no—
293C8—882no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22#1062255611yescharacteristic
302C22C2×#6688711yescharacteristic
303C22C2×#6688811yescharacteristic
304C4—22no—
305C4—21no—
306C4—21no—
307C4—22no—
308C4—22no—
309C4—41no—
310C4—41no—
311C4—442no—
312C4—442no—
313C4—881no—
314C4—881no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2#1306869411yescharacteristic
319C2#1306871711yescharacteristic
320C2#1306872111yescharacteristic
subgroupG/H
centerC22#10622556
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1464C2
socleC22×C11#381
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1464D11
hypocenterC11#8743
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #13066473C2semidirect
4. #13066471C2semidirect
255. C11#8743semidirect

Maximal subgroups

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

subgroupindex
#130711002
#130669502
#130664732
#130664712
C11×#14642
#874311