Finite Group Databasebeta

← #14647376

Subgroups — #14647376

Order 2816.

446 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 95 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#13071556C211yesmaximal, characteristic
2C4×#66897C211yesmaximal, characteristic
3#13066508C212yesmaximal, complemented
4#13066482C212yesmaximal, complemented
5C11×#1466C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C11×#432C2212yes—
8#10622833—21no—
9C2×#66897—21no—
10#10622825C411yescharacteristic
11#10622824C411yescharacteristic
12C4×C22⋊Dic11C411yescharacteristic
13C2×C11⋊#95C411yescharacteristic
14#10622594—21no—
15#10622564—21no—
16C22⋊C4×Dic11—21no—
17#10622550C2211yescharacteristic
18#10622545C2211yescharacteristic
19C4×#4318C2212yes—
20C11×#323—21no—
21C11×#323—21no—
22#10622168—21no—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11C2×C411yescharacteristic
26C23×Dic11—21no—
27C4×D4×C11—22no—
28C4×D4×C11—22no—
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C22⋊C4D411yescharacteristic
31C2×C11×C22⋊C4D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×C22⋊Dic11—21no—
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4×Dic11—21no—
38C2×C4×Dic11—21no—
39C2×#4318—22no—
40C11×C4⋊C8—22no—
41C11×C22⋊C8—22no—
42C11×#97—22no—
43#66897—24no—
44C11⋊#95—21no—
45C11⋊#95—21no—
46C11⋊#95—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95C2×C411yescharacteristic
50C11⋊#95C2×C411yescharacteristic
51C11⋊#95C2×C411yescharacteristic
52C11⋊#95C2×C411yescharacteristic
53#66867—22no—
54C4×C11⋊C8—22no—
55#8772—111nomaximal, Sylow
56C24×C11C22⋊C411yescharacteristic
57C24×C11C22⋊C411yescharacteristic
58C2×D4×C11—22no—
59C2×D4×C11—22no—
60C2×D4×C11—41no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—81no—
66C22×C4×C11—81no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—42no—
77C22×Dic11—42no—
78C22×Dic11—81no—
79C2×C8×C11—42no—
80C11×C4⋊C4—22no—
81C11×C22⋊C4—22no—
82C11×C22⋊C4—22no—
83C42×C11#4112yes—
84C42×C11#4112yes—
85C22⋊Dic11—42no—
86C22⋊Dic11—42no—
87C22⋊Dic11—81no—
88C4⋊Dic11—81no—
89C4×Dic11—42no—
90C4×Dic11—81no—
91#4318—24no—
92#4318—42no—
93C2×C11⋊C8—42no—
94#2353—111no—
95C4×#100—111no—
96#1466D1111yescharacteristic
97#1300—112no—
98#1288—112no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—41no—
105C23×C11—41no—
106C23×C11—41no—
107C23×C11—41no—
108C23×C11#10412yes—
109C23×C11C2×C22⋊C411yescharacteristic
110D4×C11—44no—
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—81no—
120C2×C4×C11—81no—
121C2×C4×C11—81no—
122C2×C4×C11—81no—
123C2×C4×C11#11711yescharacteristic
124C2×C4×C11#11711yescharacteristic
125C2×C4×C11#12312yes—
126C2×C4×C11#12312yes—
127C2×Dic11—22no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—84no—
140C8×C11—82no—
141C11⋊C8—44no—
142C2×C4×D4C2×D1111yescharacteristic
143#432C2×D1112yes—
144C2×#100—221no—
145C4×M16—112no—
146#388—221no—
147#387—221no—
148#386—221no—
149#383—111no—
150#381—111no—
151#380—111no—
152C4×C22⋊C4—111no—
153C4×C22⋊C4—221no—
154#376—111no—
155C2×#95—111no—
156#343—221no—
157#323—21no—
158#323—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—22no—
162C22×C11—42no—
163C22×C11—42no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—81no—
170C22×C11—81no—
171C22×C11#38111yescharacteristic
172C22×C11C2×#10411yescharacteristic
173C22×C11#42111yescharacteristic
174C4×C11—22no—
175C4×C11—22no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—41no—
179C4×C11—41no—
180Dic11—42no—
181Dic11—81no—
182Dic11—81no—
183Dic11—81no—
184C22×D4D4411yescharacteristic
185C23×C4—221no—
186C23×C4C4×D1111yescharacteristic
187C23×C4C4×D1111yescharacteristic
188C2×M16—222no—
189C4×D4—22no—
190C4×D4—22no—
191C2×C4⋊C4—221no—
192C2×C4⋊C4D4411yescharacteristic
193C2×C22⋊C4—221no—
194C2×C22⋊C4—221no—
195C2×C22⋊C4—221no—
196C2×C22⋊C4C22⋊D1111yescharacteristic
197C2×C22⋊C4C22⋊D1111yescharacteristic
198C2×C42—221no—
199C2×C42—221no—
200C2×C42C22×D1111yescharacteristic
201C4⋊C8—22no—
202#100—224no—
203C22⋊C8—22no—
204#97—22no—
205#97—222no—
206C4×C8—222no—
207#95—111no—
208#95—111no—
209#95—111no—
210#95—111no—
211#95—221no—
212#95—221no—
213#95—221no—
214#95—221no—
215#95—221no—
216C2×C11—21no—
217C2×C11—21no—
218C2×C11—42no—
219C2×C11—81no—
220C2×C11#182611yescharacteristic
221C2×C11#182711yescharacteristic
222C2×C11#182911yescharacteristic
223C24(C2×D11)⋊C411yescharacteristic
224C24(C2×D11)⋊C411yescharacteristic
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—41no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—81no—
233C22×C4—81no—
234C22×C4—221no—
235C22×C4—221no—
236C22×C4—221no—
237C22×C4—221no—
238C22×C4—442no—
239C22×C4—442no—
240C22×C4—881no—
241C22×C4(C2×D11)⋊C411yescharacteristic
242C22×C4(C2×D11)⋊C411yescharacteristic
243C22×C4C2×C4×D1111yescharacteristic
244C22×C4C2×D4411yescharacteristic
245C22×C4C2×C22⋊D1111yescharacteristic
246M16—224no—
247M16—442no—
248C2×C8—42no—
249C2×C8—442no—
250C4⋊C4—22no—
251C4⋊C4—881no—
252C22⋊C4—22no—
253C22⋊C4—22no—
254C22⋊C4—442no—
255C22⋊C4—442no—
256C22⋊C4—881no—
257C42—442no—
258C42—881no—
259C42#434112yes—
260C42#434112yes—
261C11#877211yescharacteristic, complemented, Sylow
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23#6688912yes—
272C23C2×(C2×D11)⋊C411yescharacteristic
273D4—44no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—222no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4—884no—
299C2×C4#6693011yescharacteristic
300C2×C4#6693011yescharacteristic
301C2×C4#6693912yes—
302C2×C4#6698812yes—
303C8—82no—
304C8—444no—
305C22—21no—
306C22—21no—
307C22—22no—
308C22—42no—
309C22—42no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—81no—
316C22—81no—
317C22#1062255611yescharacteristic
318C22C2×#6688911yescharacteristic
319C22#1062275211yescharacteristic
320C4—22no—
321C4—22no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—442no—
327C4—881no—
328C4—881no—
329C4—881no—
330C2—21no—
331C2—21no—
332C2—42no—
333C2—81no—
334C2#1306871311yescharacteristic
335C2#1306871711yescharacteristic
336C2#1306872511yescharacteristic
subgroupG/H
centerC22#10622556
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1466C2
socleC22×C11#381
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenter#1466D11
hypocenterC11#8772
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1466

Complements

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

NH ≅ G/Ntype
3. #13066508C2semidirect
4. #13066482C2semidirect
261. C11#8772semidirect

Maximal subgroups

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

subgroupindex
#130715562
C4×#668972
#130665082
#130664822
C11×#14662
#877211