Finite Group Databasebeta

← #14645253

Subgroups — #14645253

Order 2816.

814 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 139 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×#10623001C211yesmaximal, characteristic
2#13068378C211yesmaximal, characteristic
3C2×#10622103C214yesmaximal, complemented
4C11×#1749C211yesmaximal, characteristic
5C22×C42×C11C2211yescharacteristic
6C2×#66979C412yes—
7C2×#66977—21no—
8C2×#66977—21no—
9#10623001—28no—
10C2×#66923C2212yes—
11C2×#66922C411yescharacteristic
12C2×#66922C411yescharacteristic
13C2×C4×Dic22—21no—
14C2×C4×Dic22—21no—
15C2×C11×C22⋊C8—21no—
16C2×C11×#97C2212yes—
17C2×C22⋊(C11⋊C8)—21no—
18C2×#66867C2212yes—
19C11×#336—21no—
20#10622162—21no—
21#10622103—28no—
22C23×C4×C11C2×C411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C22×Dic22—21no—
26C22×Dic22—21no—
27C22×C8×C11—22no—
28C2×C42×C11—24no—
29C2×C42×C11C2×C411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×C22⋊Dic11—22no—
34#66979—24no—
35#66979—24no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11C2×C412yes—
39C2×C4⋊Dic11C2×C412yes—
40#66977—28no—
41#66977—28no—
42C2×Dic11⋊C4—22no—
43C2×Dic11⋊C4—22no—
44C2×C4×Dic11—22no—
45C22×C11⋊C8—22no—
46#66923—24no—
47#66923D418yes—
48#66922—24no—
49#66922—24no—
50C4×Dic22—28no—
51C4×Dic22—28no—
52C11×C22⋊C8—24no—
53C11×#97—24no—
54C22⋊(C11⋊C8)—24no—
55#66867—24no—
56#8338—111nomaximal, Sylow
57C24×C11C22⋊C411yescharacteristic
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—41no—
66C22×C4×C11—41no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—22no—
74C22×Dic11—22no—
75C2×Dic22—24no—
76C2×Dic22—24no—
77C2×Dic22—42no—
78C2×Dic22—42no—
79C2×Dic22—42no—
80C2×Dic22—42no—
81C2×C8×C11—24no—
82C2×C8×C11—42no—
83C2×C8×C11—42no—
84C42×C11—22no—
85C42×C11—22no—
86C42×C11—22no—
87C42×C11C2×D414yes—
88C22⋊Dic11—28no—
89C4⋊Dic11—24no—
90C4⋊Dic11—24no—
91C4⋊Dic11—22no—
92C4⋊Dic11—22no—
93C4⋊Dic11C22⋊C414yes—
94C4⋊Dic11C22⋊C414yes—
95Dic11⋊C4—28no—
96Dic11⋊C4—28no—
97C4×Dic11—28no—
98C2×C11⋊C8—24no—
99C2×C11⋊C8—42no—
100C2×C11⋊C8—42no—
101C2×#533—111no—
102#1749—111no—
103#1749D1111yescharacteristic
104C2×#330—114no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11#10112yes—
112C23×C11C2×C22⋊C411yescharacteristic
113C2×C4×C11—28no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—44no—
127C2×C4×C11—44no—
128C2×C4×C11#10112yes—
129C2×C4×C11#10412yes—
130C2×C4×C11#10412yes—
131C2×C4×C11C2×C22⋊C412yes—
132C2×C4×C11#12012yes—
133C2×C4×C11#12012yes—
134C2×Dic11—24no—
135C2×Dic11—24no—
136C2×Dic11—42no—
137C2×Dic11—42no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140Dic22—48no—
141Dic22—48no—
142C8×C11—44no—
143C11⋊C8—44no—
144#533—228no—
145C2×C4⋊Q8—111no—
146C2×C4⋊Q8—111no—
147C2×#125—112no—
148C2×C22⋊Q8—221no—
149C2×C22⋊Q8—221no—
150C2×C4×Q8—221no—
151C2×C4×Q8—221no—
152C2×#117—112no—
153C22×C42C2×D1111yescharacteristic
154C2×C22⋊C8—21no—
155C2×C22⋊C8—221no—
156C2×#97—112no—
157C2×#97C2×D1112yes—
158#336—21no—
159#336—221no—
160#330—228no—
161C22×C11—22no—
162C22×C11—22no—
163C22×C11—22no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11#37911yescharacteristic
169C22×C11C2×#10111yescharacteristic
170C22×C11C2×#10111yescharacteristic
171C22×C11C2×#10411yescharacteristic
172C22×C11C2×#10411yescharacteristic
173C22×C11#42111yescharacteristic
174C22×C11#42111yescharacteristic
175C4×C11—22no—
176C4×C11—22no—
177C4×C11—22no—
178C4×C11—22no—
179C4×C11—22no—
180C4×C11—22no—
181Dic11—44no—
182Dic11—44no—
183C22×Q8—221no—
184C22×Q8—221no—
185C23×C4C4×D1111yescharacteristic
186C23×C4D4411yescharacteristic
187C23×C4C22⋊D1111yescharacteristic
188C22×C8—22no—
189C22×C8—222no—
190C4⋊Q8—224no—
191C4⋊Q8—224no—
192#125—118no—
193#125—224no—
194C22⋊Q8—228no—
195C22⋊Q8—228no—
196C4×Q8—228no—
197C4×Q8—228no—
198#117—224no—
199#117—224no—
200C2×C4⋊C4—112no—
201C2×C4⋊C4—112no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—222no—
205C2×C4⋊C4—222no—
206C2×C22⋊C4—222no—
207C2×C42—24no—
208C2×C42—222no—
209C2×C42C4×D1111yescharacteristic
210C2×C42D4411yescharacteristic
211C2×C42C22⋊D1111yescharacteristic
212C2×C42C22×D1111yescharacteristic
213C22⋊C8—24no—
214C22⋊C8—224no—
215#97—24no—
216#97—224no—
217C2×C11—42no—
218C2×C11#152611yescharacteristic
219C2×C11#153111yescharacteristic
220C2×C11#153111yescharacteristic
221C2×C11#153711yescharacteristic
222C2×C11#178411yescharacteristic
223C2×C11#178911yescharacteristic
224C2×C11#178911yescharacteristic
225C24(C2×D11)⋊C411yescharacteristic
226C2×Q8—224no—
227C2×Q8—224no—
228C2×Q8—442no—
229C2×Q8—442no—
230C2×Q8—442no—
231C2×Q8—442no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—222no—
242C22×C4—222no—
243C22×C4(C2×D11)⋊C411yescharacteristic
244C22×C4(C2×D11)⋊C411yescharacteristic
245C22×C4(C2×D11)⋊C411yescharacteristic
246C22×C4C2×C4×D1111yescharacteristic
247C22×C4C2×D4411yescharacteristic
248C22×C4C2×C22⋊D1111yescharacteristic
249C2×C8—24no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—224no—
253C2×C8—442no—
254C2×C8—442no—
255C4⋊C4—114no—
256C4⋊C4—114no—
257C4⋊C4—224no—
258C4⋊C4—224no—
259C4⋊C4—222no—
260C4⋊C4—222no—
261C4⋊C4—228no—
262C4⋊C4—228no—
263C22⋊C4—228no—
264C42—22no—
265C42—22no—
266C42—22no—
267C42—228no—
268C42D4×D1114yes—
269C11#833811yescharacteristic, complemented, Sylow
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23#6688812yes—
277C23C2×(C2×D11)⋊C411yescharacteristic
278Q8—448no—
279Q8—448no—
280C2×C4—28no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—224no—
296C2×C4—224no—
297C2×C4—442no—
298C2×C4—442no—
299C2×C4—442no—
300C2×C4—442no—
301C2×C4#6686912yes—
302C2×C4#6688812yes—
303C2×C4#6688912yes—
304C2×C4C22⋊C4×D1112yes—
305C2×C4#6693512yes—
306C2×C4#6699012yes—
307C8—44no—
308C8—444no—
309C22—22no—
310C22—22no—
311C22—22no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22C2×#6686911yescharacteristic
317C22#1062256811yescharacteristic
318C22#1062261811yescharacteristic
319C22C2×#6688811yescharacteristic
320C22C2×#6688811yescharacteristic
321C22C2×#6688911yescharacteristic
322C22#1062275211yescharacteristic
323C4—22no—
324C4—22no—
325C4—22no—
326C4—22no—
327C4—22no—
328C4—22no—
329C4—444no—
330C4—444no—
331C2—42no—
332C2#1306721011yescharacteristic
333C2#1306723011yescharacteristic
334C2#1306723211yescharacteristic
335C2#1306725311yescharacteristic
336C2#1306853911yescharacteristic
337C2#1306855911yescharacteristic
338C2#1306856111yescharacteristic
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#8338
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. C2×#10622103C2semidirect
269. C11#8338semidirect

Maximal subgroups

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

subgroupindex
C2×#106230012
#130683782
C2×#106221032
C11×#17492
#833811