Finite Group Databasebeta

← #14669400

Subgroups — #14669400

Order 2816.

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

normal subgroups only

This group has 810 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
1#13070285C212yesmaximal, complemented
2C2×#10622183C212yesmaximal, complemented
3#13068724C212yesmaximal, complemented
4C11×#3508C211yesmaximal, characteristic
5C11×#559—22no—
6C11×#550—22no—
7C11×#546—24no—
8C11×#540—22no—
9C11×#535C411yescharacteristic, complemented
10C11×#535C2211yescharacteristic
11C11×#533C411yescharacteristic, complemented
12C11×#532—22no—
13C2×C11×#127C2211yescharacteristic
14C11×#518C411yescharacteristic, complemented
15C11×#518C2211yescharacteristic
16C4×C11×#41C411yescharacteristic, complemented
17C2×#66898C2214yes—
18#10622183—22no—
19#10622183—22no—
20#10622183—22no—
21#10622179—22no—
22#10622165—24no—
23C2×C11×#41—24no—
24C2×C11×#41C2×C411yescharacteristic
25C22×D4×C11—22no—
26C22×D4×C11C2×C411yescharacteristic
27C22×D4×C11C2311yescharacteristic
28C11×C4⋊Q8—21no—
29C11×#127—21no—
30C11×#127—22no—
31C11×#127D412yes—
32C11×#127D412yes—
33C11×#127D412yes—
34C11×#125—21no—
35C11×#124—24no—
36C11×#124—21no—
37C11×#124D412yes—
38C11×#123—24no—
39C11×#123—24no—
40C11×C22⋊Q8—22no—
41C11×#121—24no—
42C11×#121—24no—
43C11×#121—24no—
44C11×#121—22no—
45C11×#121—22no—
46C11×#120—22no—
47C11×#120—22no—
48C4×Q8×C11—21no—
49C4×Q8×C11—22no—
50C4×D4×C11—24no—
51C4×D4×C11—21no—
52C4×D4×C11—22no—
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C11×#117—21no—
58C11×#117C2×C411yescharacteristic
59C11×#117C2×C411yescharacteristic
60C11×#117C2×C411yescharacteristic
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4D414yes—
63C2×C42×C11—21no—
64C2×C42×C11C2×C411yescharacteristic
65C2×C22⋊Dic11—24no—
66#66898—24no—
67#66898—24no—
68#12727—111nomaximal, Sylow
69C24×C11—21no—
70C24×C11C2×D412yes—
71C11×#41—42no—
72C11×#41—88no—
73C2×Q8×C11—22no—
74C2×Q8×C11C22⋊C411yescharacteristic
75C2×D4×C11—21no—
76C2×D4×C11—24no—
77C2×D4×C11—24no—
78C2×D4×C11—24no—
79C2×D4×C11—24no—
80C2×D4×C11—21no—
81C2×D4×C11—42no—
82C2×D4×C11—42no—
83C2×D4×C11—84no—
84C2×D4×C11C22⋊C412yes—
85C2×D4×C11C22⋊C411yescharacteristic
86C2×D4×C11C2×D412yes—
87C2×D4×C11C2×D412yes—
88C22×C4×C11—22no—
89C22×C4×C11—21no—
90C22×C4×C11—24no—
91C22×C4×C11—24no—
92C22×C4×C11—21no—
93C22×C4×C11C22×C411yescharacteristic
94C22×Dic11—44no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C22⋊C4—24no—
103C11×C22⋊C4—22no—
104C11×C22⋊C4—24no—
105C11×C22⋊C4—21no—
106C11×C22⋊C4—24no—
107C11×C22⋊C4—24no—
108C11×C22⋊C4C22⋊C412yes—
109C11×C22⋊C4C22⋊C412yes—
110C42×C11—22no—
111C42×C11—21no—
112C42×C11—21no—
113C42×C11—21no—
114C42×C11C22⋊C411yescharacteristic
115C42×C11C22⋊C411yescharacteristic
116C42×C11C22⋊C412yes—
117C22⋊Dic11—44no—
118C22⋊Dic11—44no—
119#3508D1111yescharacteristic
120#2127—112no—
121C2×#353—112no—
122#1828—112no—
123C23×C11—24no—
124C23×C11—22no—
125C23×C11—21no—
126C23×C11—42no—
127C23×C11—82no—
128C23×C11—82no—
129C23×C11C2×C22⋊C411yescharacteristic
130C23×C11#12014yes—
131Q8×C11—41no—
132Q8×C11—44no—
133D4×C11—42no—
134D4×C11—42no—
135D4×C11—42no—
136D4×C11—41no—
137D4×C11—42no—
138D4×C11—48no—
139D4×C11—42no—
140D4×C11—84no—
141D4×C11—84no—
142D4×C11—84no—
143C2×C4×C11—21no—
144C2×C4×C11—22no—
145C2×C4×C11—21no—
146C2×C4×C11—22no—
147C2×C4×C11—21no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—44no—
153C2×C4×C11—84no—
154C2×C4×C11—84no—
155C2×C4×C11C2×C22⋊C411yescharacteristic
156C2×C4×C11C2×C22⋊C411yescharacteristic
157C2×Dic11—84no—
158C2×Dic11—164no—
159#559—22no—
160#550—22no—
161#546—24no—
162#540—22no—
163#535Dic1111yescharacteristic, complemented
164#535C2×D1111yescharacteristic
165#533Dic1111yescharacteristic, complemented
166#532—22no—
167C2×#127C2×D1111yescharacteristic
168#518Dic1111yescharacteristic, complemented
169#518C2×D1111yescharacteristic
170C4×#41Dic1111yescharacteristic, complemented
171C2×#99—114no—
172#354—222no—
173#353—222no—
174#353—222no—
175#353—222no—
176#342—224no—
177C22×C11—24no—
178C22×C11—41no—
179C22×C11—44no—
180C22×C11—42no—
181C22×C11—44no—
182C22×C11—41no—
183C22×C11—42no—
184C22×C11—84no—
185C22×C11—162no—
186C22×C11#37911yescharacteristic
187C22×C11#41012yes—
188C4×C11—22no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—42no—
192C4×C11—41no—
193C4×C11—42no—
194C4×C11—42no—
195C4×C11—41no—
196Dic11—164no—
197C2×#41—24no—
198C2×#41C2×Dic1111yescharacteristic
199C22×D4—22no—
200C22×D4C2×Dic1111yescharacteristic
201C22×D4C22×D1111yescharacteristic
202C4⋊Q8—21no—
203#127—21no—
204#127—22no—
205#127C22⋊D1112yes—
206#127C22⋊D1112yes—
207#127C22⋊D1112yes—
208#125—21no—
209#124—24no—
210#124—21no—
211#124C22⋊D1112yes—
212#123—24no—
213#123—24no—
214C22⋊Q8—22no—
215#121—24no—
216#121—24no—
217#121—24no—
218#121—22no—
219#121—22no—
220#120—22no—
221#120—22no—
222C4×Q8—21no—
223C4×Q8—22no—
224C4×D4—24no—
225C4×D4—21no—
226C4×D4—22no—
227C4×D4—22no—
228C4×D4—22no—
229C4×D4—22no—
230C4×D4—22no—
231#117—21no—
232#117C2×Dic1111yescharacteristic
233#117C2×Dic1111yescharacteristic
234#117C2×Dic1111yescharacteristic
235C2×C22⋊C4—22no—
236C2×C22⋊C4—224no—
237C2×C22⋊C4C22⋊D1114yes—
238C2×C42—21no—
239C2×C42C2×Dic1111yescharacteristic
240#99—224no—
241#99—224no—
242C2×C11—21no—
243C2×C11—22no—
244C2×C11—44no—
245C2×C11—81no—
246C2×C11—82no—
247C2×C11#178211yescharacteristic
248C24—21no—
249C24C2×C22⋊D1112yes—
250#41—42no—
251#41—88no—
252C2×Q8—22no—
253C2×Q8C22⋊Dic1111yescharacteristic
254C2×D4—21no—
255C2×D4—24no—
256C2×D4—24no—
257C2×D4—24no—
258C2×D4—24no—
259C2×D4—21no—
260C2×D4—42no—
261C2×D4—42no—
262C2×D4—84no—
263C2×D4C22⋊Dic1112yes—
264C2×D4C22⋊Dic1111yescharacteristic
265C2×D4C2×C22⋊D1112yes—
266C2×D4C2×C22⋊D1112yes—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—21no—
272C22×C4—444no—
273C22×C4C22×Dic1111yescharacteristic
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C22⋊C4—24no—
282C22⋊C4—22no—
283C22⋊C4—24no—
284C22⋊C4—21no—
285C22⋊C4—24no—
286C22⋊C4—24no—
287C22⋊C4—444no—
288C22⋊C4—444no—
289C22⋊C4C22⋊Dic1112yes—
290C22⋊C4C22⋊Dic1112yes—
291C42—22no—
292C42—21no—
293C42—21no—
294C42—21no—
295C42C22⋊Dic1111yescharacteristic
296C42C22⋊Dic1111yescharacteristic
297C42C22⋊Dic1112yes—
298C11#1272711yescharacteristic, complemented, Sylow
299C23—24no—
300C23—22no—
301C23—21no—
302C23—42no—
303C23—82no—
304C23—82no—
305C23C2×C22⋊Dic1111yescharacteristic
306C23#6700614yes—
307Q8—41no—
308Q8—44no—
309D4—42no—
310D4—42no—
311D4—42no—
312D4—41no—
313D4—42no—
314D4—48no—
315D4—42no—
316D4—84no—
317D4—84no—
318D4—84no—
319C2×C4—22no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—44no—
329C2×C4—84no—
330C2×C4—84no—
331C2×C4—884no—
332C2×C4—1764no—
333C2×C4C2×C22⋊Dic1111yescharacteristic
334C2×C4C2×C22⋊Dic1111yescharacteristic
335C22—24no—
336C22—41no—
337C22—44no—
338C22—42no—
339C22—44no—
340C22—41no—
341C22—42no—
342C22—84no—
343C22—162no—
344C22#1062285312yes—
345C22#1062286011yescharacteristic
346C4—22no—
347C4—21no—
348C4—21no—
349C4—42no—
350C4—41no—
351C4—42no—
352C4—42no—
353C4—41no—
354C4—1764no—
355C2—21no—
356C2—22no—
357C2—44no—
358C2—82no—
359C2—81no—
360C2#1306853411yescharacteristic
subgroupG/H
centerC2#13068534
commutatorC22×C4×C11C22×C4
FrattiniC22×D4C22×D11
Fitting, prime radicalC11×#3508C2
socleC2×C11#1782
cosocleC22×D4×C11C23
hypercenter#3508D11
hypocenterC11#12727
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C23 ◁ #518 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. #13070285C2semidirect
2. C2×#10622183C2semidirect
3. #13068724C2semidirect
9. C11×#535C4semidirect
11. C11×#533C4semidirect
14. C11×#518C4semidirect
16. C4×C11×#41C4semidirect
163. #535Dic11semidirect
165. #533Dic11semidirect
168. #518Dic11semidirect
170. C4×#41Dic11semidirect
298. C11#12727semidirect

Maximal subgroups

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

subgroupindex
#130702852
C2×#106221832
#130687242
C11×#35082
#1272711