Finite Group Databasebeta

← #14642000

Subgroups — #14642000

Order 2816.

594 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C2×#10622541C211yesmaximal, characteristic
2#13068378C211yesmaximal, characteristic
3#13066440C214yesmaximal, complemented
4C11×#1749C211yesmaximal, characteristic
5C22×C42×C11C2211yescharacteristic
6C22×C4⋊Dic11C411yescharacteristic
7C22×C4⋊Dic11C411yescharacteristic
8C22×Dic11⋊C4—21no—
9C2×C11×C22⋊C8—21no—
10C2×C11×#97—21no—
11C2×C11⋊#95—21no—
12C2×C22⋊(C11⋊C8)—21no—
13#10622541—21no—
14#10622541—21no—
15#10622541C412yes—
16#10622541C2212yes—
17C2×#66867—21no—
18C11×#336C2212yes—
19#10622162C2212yes—
20C23×C4×C11C2×C411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×Dic11—21no—
24C23×Dic11—21no—
25C22×C8×C11—22no—
26C2×C42×C11—42no—
27C2×C42×C11C2×C411yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11C2311yescharacteristic
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—24no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—42no—
35C2×C4⋊Dic11C2×C412yes—
36C2×C4⋊Dic11C2×C412yes—
37C2×Dic11⋊C4—22no—
38C2×Dic11⋊C4—22no—
39C2×Dic11⋊C4—44no—
40C22×C11⋊C8—22no—
41C11×C22⋊C8—24no—
42C11×#97—42no—
43C11⋊#95—22no—
44C11⋊#95—22no—
45C22⋊(C11⋊C8)—24no—
46#66867—42no—
47#7627—111nomaximal, Sylow
48C24×C11C22⋊C411yescharacteristic
49C22×C4×C11—22no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—41no—
57C22×C4×C11—41no—
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22×C411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×Dic11—24no—
65C22×Dic11—22no—
66C22×Dic11—22no—
67C22×Dic11—42no—
68C22×Dic11—42no—
69C22×Dic11—42no—
70C22×Dic11—42no—
71C22×Dic11—42no—
72C2×C8×C11—24no—
73C2×C8×C11—42no—
74C2×C8×C11—42no—
75C42×C11—22no—
76C42×C11—22no—
77C42×C11—41no—
78C42×C11—41no—
79C4⋊Dic11—24no—
80C4⋊Dic11—22no—
81C4⋊Dic11—42no—
82C4⋊Dic11—42no—
83C4⋊Dic11M1614yes—
84Dic11⋊C4—44no—
85Dic11⋊C4—44no—
86C2×C11⋊C8—24no—
87C2×C11⋊C8—42no—
88C2×C11⋊C8—42no—
89C2×#389—111no—
90#1749—111no—
91#1749D1111yescharacteristic
92#1271—114no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11#10112yes—
98C23×C11#10412yes—
99C23×C11#10412yes—
100C23×C11C2×C22⋊C411yescharacteristic
101C2×C4×C11—28no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
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—21no—
116C2×C4×C11—44no—
117C2×C4×C11—44no—
118C2×C4×C11#9912yes—
119C2×C4×C11C2×M1612yes—
120C2×C4×C11AGL(1,ℤ/8)12yes—
121C2×C4×C11#13712yes—
122C2×Dic11—24no—
123C2×Dic11—48no—
124C2×Dic11—42no—
125C2×Dic11—42no—
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11—42no—
129C2×Dic11—84no—
130C8×C11—44no—
131C11⋊C8—44no—
132C22×C4⋊C4—111no—
133C22×C4⋊C4—111no—
134C22×C4⋊C4—221no—
135C22×C42C2×D1111yescharacteristic
136C2×C22⋊C8—21no—
137C2×C22⋊C8—221no—
138C2×#97—21no—
139C2×#97—221no—
140#389—112no—
141#389—112no—
142#389—221no—
143#389—221no—
144C2×#95—221no—
145#336—112no—
146#336C2×D1112yes—
147C22×C11—22no—
148C22×C11—22no—
149C22×C11—22no—
150C22×C11—22no—
151C22×C11—22no—
152C22×C11—22no—
153C22×C11#33014yes—
154C22×C11#40711yescharacteristic
155C22×C11C2×#9911yescharacteristic
156C22×C11C2×#10111yescharacteristic
157C22×C11#41811yescharacteristic
158C22×C11#41911yescharacteristic
159C22×C11C2×#10411yescharacteristic
160C22×C11C2×#10411yescharacteristic
161C4×C11—22no—
162C4×C11—22no—
163C4×C11—22no—
164C4×C11—22no—
165C4×C11—41no—
166C4×C11—41no—
167Dic11—44no—
168Dic11—82no—
169C23×C4—221no—
170C23×C4—221no—
171C23×C4C4×D1111yescharacteristic
172C23×C4D4411yescharacteristic
173C23×C4C22⋊D1111yescharacteristic
174C22×C8—22no—
175C22×C8—222no—
176C2×C4⋊C4—112no—
177C2×C4⋊C4—112no—
178C2×C4⋊C4—224no—
179C2×C4⋊C4—221no—
180C2×C4⋊C4—221no—
181C2×C4⋊C4—222no—
182C2×C4⋊C4—222no—
183C2×C4⋊C4—444no—
184C2×C4⋊C4—442no—
185C2×C42—42no—
186C2×C42C4×D1111yescharacteristic
187C2×C42D4411yescharacteristic
188C2×C42C22⋊D1111yescharacteristic
189C2×C42C22×D1111yescharacteristic
190C22⋊C8—24no—
191C22⋊C8—224no—
192#97—42no—
193#97—442no—
194#95—222no—
195#95—222no—
196C2×C11—24no—
197C2×C11#146311yescharacteristic
198C2×C11#149011yescharacteristic
199C2×C11#149111yescharacteristic
200C2×C11#150711yescharacteristic
201C2×C11#150811yescharacteristic
202C2×C11C2×#33011yescharacteristic
203C2×C11#155611yescharacteristic
204C24(C2×D11)⋊C411yescharacteristic
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—224no—
215C22×C4—222no—
216C22×C4—222no—
217C22×C4—442no—
218C22×C4—442no—
219C22×C4—442no—
220C22×C4—442no—
221C22×C4—442no—
222C22×C4(C2×D11)⋊C411yescharacteristic
223C22×C4(C2×D11)⋊C411yescharacteristic
224C22×C4(C2×D11)⋊C411yescharacteristic
225C22×C4C2×C4×D1111yescharacteristic
226C22×C4C2×D4411yescharacteristic
227C22×C4C2×C22⋊D1111yescharacteristic
228C2×C8—24no—
229C2×C8—42no—
230C2×C8—42no—
231C2×C8—224no—
232C2×C8—442no—
233C2×C8—442no—
234C4⋊C4—114no—
235C4⋊C4—224no—
236C4⋊C4—222no—
237C4⋊C4—442no—
238C4⋊C4—444no—
239C4⋊C4—442no—
240C4⋊C4—444no—
241C42—22no—
242C42—22no—
243C42—41no—
244C42—41no—
245C11#762711yescharacteristic, complemented, Sylow
246C23—21no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23#6686912yes—
251C23#6688812yes—
252C23#6688912yes—
253C23C2×(C2×D11)⋊C411yescharacteristic
254C2×C4—28no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—44no—
270C2×C4—44no—
271C2×C4—224no—
272C2×C4—448no—
273C2×C4—442no—
274C2×C4—442no—
275C2×C4—442no—
276C2×C4—442no—
277C2×C4—442no—
278C2×C4—884no—
279C2×C4#6687012yes—
280C2×C4M16×D1112yes—
281C2×C4#6696212yes—
282C2×C4#6700212yes—
283C8—44no—
284C8—444no—
285C22—22no—
286C22—22no—
287C22—22no—
288C22—22no—
289C22—22no—
290C22—22no—
291C22#1062210314yes—
292C22C2×#6686911yescharacteristic
293C22C2×#6687011yescharacteristic
294C22#1062261411yescharacteristic
295C22#1062273311yescharacteristic
296C22#1062273911yescharacteristic
297C22C2×#6688811yescharacteristic
298C22C2×#6688911yescharacteristic
299C4—22no—
300C4—22no—
301C4—22no—
302C4—22no—
303C4—41no—
304C4—41no—
305C4—444no—
306C4—882no—
307C2—24no—
308C2#1306694511yescharacteristic
309C2#1306705811yescharacteristic
310C2#1306706411yescharacteristic
311C2#1306713111yescharacteristic
312C2#1306713711yescharacteristic
313C2C2×#1062210311yescharacteristic
314C2#1306733411yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1749C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1749D11
hypocenterC11#7627
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
3. #13066440C2semidirect
245. C11#7627semidirect

Maximal subgroups

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

subgroupindex
C2×#106225412
#130683782
#130664402
C11×#17492
#762711