Finite Group Databasebeta

← #26108921

Subgroups — #26108921

Order 12032.

778 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 778 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C22×#13094014C211yesmaximal, characteristic
2#20243466C212yesmaximal
3#20241718C211yesmaximal, characteristic
4#20241717C212yesmaximal
5C47×#1463C211yesmaximal, characteristic
6C2×#13094014—24no—
7C2×#13094014—24no—
8C2×#13094014—22no—
9C2×#13094014—22no—
10C22×C4⋊Dic47C2211yescharacteristic
11C22×Dic47⋊C4C411yescharacteristic
12C22×Dic47⋊C4C411yescharacteristic
13C22×Dic47⋊C4C411yescharacteristic
14C22×Dic47⋊C4C2211yescharacteristic
15C22×C4×Dic47C411yescharacteristic
16#15689087C2212yes—
17#15688891—24no—
18#15688849—22no—
19#15688848—24no—
20C22×C4⋊C4×C47C2211yescharacteristic
21C47×#407C2212yes—
22C47×#324—22no—
23C23×Dic47C2×C411yescharacteristic
24C23×Dic47C2×C411yescharacteristic
25C23×Dic47C2×C411yescharacteristic
26C23×Dic47C2×C411yescharacteristic
27C2×#10625329—22no—
28#13094014—216no—
29#13094014—216no—
30C2×C4⋊Dic47—21no—
31C2×C4⋊Dic47—22no—
32C2×C4⋊Dic47—21no—
33C2×C4⋊Dic47D414yes—
34C2×Dic47⋊C4—22no—
35C2×Dic47⋊C4—22no—
36C2×Dic47⋊C4—22no—
37C2×Dic47⋊C4—22no—
38C2×Dic47⋊C4—21no—
39C2×Dic47⋊C4—21no—
40C2×Dic47⋊C4—22no—
41C2×Dic47⋊C4—22no—
42C2×Dic47⋊C4—22no—
43C2×Dic47⋊C4—22no—
44C2×Dic47⋊C4—22no—
45C2×Dic47⋊C4—22no—
46C2×Dic47⋊C4D414yes—
47C2×C4×Dic47—22no—
48C2×C4×Dic47—22no—
49C2×C4×Dic47—22no—
50C22⋊(C47⋊C8)—22no—
51C22⋊(C47⋊C8)—22no—
52C23×C4×C47C2×C411yescharacteristic
53C23×C4×C47C2×C411yescharacteristic
54C23×C4×C47C2311yescharacteristic
55C2×M16×C47—22no—
56C2×C4⋊C4×C47—22no—
57C2×C4⋊C4×C47—22no—
58C2×C4⋊C4×C47D412yes—
59C2×C4⋊C4×C47D412yes—
60C22⋊C8×C47—22no—
61C22⋊C8×C47—22no—
62C24×C47C22×C411yescharacteristic
63C22×C4×C47—21no—
64C22×C4×C47—21no—
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47—42no—
68C22×C4×C47—42no—
69C22×C4×C47—42no—
70C22×C4×C47C22⋊C412yes—
71C22×C4×C47C22⋊C412yes—
72C22×C4×C47C2×D412yes—
73C22×C4×C47C2×D411yescharacteristic
74C22×C4×C47C2×D412yes—
75C22×C4×C47C2×D411yescharacteristic
76C22×Dic47—21no—
77C22×Dic47—21no—
78C22×Dic47—24no—
79C22×Dic47—21no—
80C22×Dic47—21no—
81C22×Dic47—21no—
82C22×Dic47—21no—
83C22×Dic47—21no—
84C22×Dic47—21no—
85C22×Dic47—42no—
86C22×Dic47—42no—
87C22×Dic47—42no—
88C22×Dic47C22⋊C412yes—
89C22×Dic47C22⋊C412yes—
90C22×Dic47C22⋊C412yes—
91C22×Dic47C22⋊C412yes—
92M16×C47—44no—
93C2×C8×C47—42no—
94C4⋊C4×C47—24no—
95C4⋊C4×C47—24no—
96C4⋊Dic47—24no—
97C4⋊Dic47—24no—
98Dic47⋊C4—28no—
99Dic47⋊C4—28no—
100Dic47⋊C4—28no—
101Dic47⋊C4—24no—
102Dic47⋊C4—24no—
103C4×Dic47—28no—
104#10625329—44no—
105C2×C47⋊C8—42no—
106C23×C47—22no—
107C23×C47—22no—
108C23×C47—22no—
109C23×C47C2×C22⋊C411yescharacteristic
110C23×C47C2×C22⋊C411yescharacteristic
111C23×C47C2×C22⋊C411yescharacteristic
112C2×C4×C47—24no—
113C2×C4×C47—22no—
114C2×C4×C47—22no—
115C2×C4×C47—24no—
116C2×C4×C47—41no—
117C2×C4×C47—42no—
118C2×C4×C47—41no—
119C2×C4×C47—42no—
120C2×C4×C47—42no—
121C2×C4×C47—42no—
122C2×C4×C47—42no—
123C2×C4×C47—42no—
124C2×C4×C47#12012yes—
125C2×C4×C47#12012yes—
126C2×Dic47—24no—
127C2×Dic47—24no—
128C2×Dic47—22no—
129C2×Dic47—22no—
130C2×Dic47—22no—
131C2×Dic47—22no—
132C2×Dic47—22no—
133C2×Dic47—42no—
134C2×Dic47—42no—
135C2×Dic47—42no—
136C2×Dic47—42no—
137C2×Dic47—42no—
138C2×Dic47—42no—
139C2×Dic47—42no—
140C2×Dic47—42no—
141C2×Dic47—42no—
142C2×Dic47#10114yes—
143C8×C47—82no—
144C47⋊C8—82no—
145#8554—471nomaximal, Sylow
146C22×C47—28no—
147C22×C47—21no—
148C22×C47—21no—
149C22×C47—21no—
150C22×C47—21no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47#37911yescharacteristic
154C22×C47#41012yes—
155C22×C47C2×#10112yes—
156C22×C47#41312yes—
157C4×C47—22no—
158C4×C47—22no—
159C4×C47—42no—
160C4×C47—42no—
161Dic47—24no—
162Dic47—42no—
163Dic47—42no—
164Dic47—42no—
165C22×#125—471no—
166#1821—472no—
167#1463—472no—
168#1463—471no—
169#1463D4711yescharacteristic
170C2×C47—22no—
171C2×C47—22no—
172C2×C47—22no—
173C2×C47#178211yescharacteristic
174C2×C47#178411yescharacteristic
175C2×C47#178511yescharacteristic
176C2×#125—944no—
177C2×#125—944no—
178C2×#125—942no—
179C2×#125—942no—
180C22×C4⋊C4—471no—
181C22×C4⋊C4—471no—
182C22×C4⋊C4—471no—
183C22×C4⋊C4—471no—
184C22×C4⋊C4—471no—
185C22×C4⋊C4C2×D4711yescharacteristic
186C22×C42—471no—
187#407—472no—
188#407C2×D4712yes—
189#343—944no—
190#324—22no—
191#324—944no—
192#324—942no—
193C47#855411yescharacteristic, complemented, Sylow
194C23×C4—471no—
195C23×C4—471no—
196C23×C4—471no—
197C23×C4—471no—
198C23×C4C4×D4711yescharacteristic
199C23×C4C4×D4711yescharacteristic
200C23×C4C22×D4711yescharacteristic
201C2×M16—22no—
202C2×M16—942no—
203#125—9416no—
204#125—9416no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—474no—
208C2×C4⋊C4—474no—
209C2×C4⋊C4—942no—
210C2×C4⋊C4—942no—
211C2×C4⋊C4—942no—
212C2×C4⋊C4—942no—
213C2×C4⋊C4—942no—
214C2×C4⋊C4—942no—
215C2×C4⋊C4—942no—
216C2×C4⋊C4—942no—
217C2×C4⋊C4—942no—
218C2×C4⋊C4—941no—
219C2×C4⋊C4—941no—
220C2×C4⋊C4—942no—
221C2×C4⋊C4—942no—
222C2×C4⋊C4—941no—
223C2×C4⋊C4—941no—
224C2×C4⋊C4D18812yes—
225C2×C4⋊C4C22⋊D4712yes—
226C2×C42—942no—
227C2×C42—942no—
228C2×C42—942no—
229C22⋊C8—22no—
230C22⋊C8—22no—
231C22⋊C8—942no—
232C22⋊C8—942no—
233C24C2×C4×D4711yescharacteristic
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—472no—
242C22×C4—472no—
243C22×C4—472no—
244C22×C4—472no—
245C22×C4—944no—
246C22×C4—941no—
247C22×C4—941no—
248C22×C4—941no—
249C22×C4—941no—
250C22×C4—941no—
251C22×C4—941no—
252C22×C4—941no—
253C22×C4—941no—
254C22×C4—1882no—
255C22×C4—1882no—
256C22×C4—1882no—
257C22×C4(C2×D47)⋊C412yes—
258C22×C4(C2×D47)⋊C412yes—
259C22×C4C2×D18811yescharacteristic
260C22×C4D4×D4712yes—
261C22×C4D4×D4712yes—
262C22×C4C2×C22⋊D4711yescharacteristic
263M16—44no—
264M16—1884no—
265C2×C8—42no—
266C2×C8—1882no—
267C4⋊C4—24no—
268C4⋊C4—24no—
269C4⋊C4—948no—
270C4⋊C4—948no—
271C4⋊C4—948no—
272C4⋊C4—944no—
273C4⋊C4—944no—
274C4⋊C4—944no—
275C4⋊C4—944no—
276C42—948no—
277C23—22no—
278C23—22no—
279C23—22no—
280C23C22⋊C4×D4711yescharacteristic
281C23C22⋊C4×D4711yescharacteristic
282C23C2×(C2×D47)⋊C411yescharacteristic
283C2×C4—24no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—24no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—474no—
296C2×C4—944no—
297C2×C4—944no—
298C2×C4—942no—
299C2×C4—942no—
300C2×C4—942no—
301C2×C4—942no—
302C2×C4—942no—
303C2×C4—1882no—
304C2×C4—1882no—
305C2×C4—1882no—
306C2×C4—1882no—
307C2×C4—1882no—
308C2×C4—1882no—
309C2×C4—1882no—
310C2×C4—1882no—
311C2×C4—1882no—
312C2×C4#1309399212yes—
313C2×C4#1309399412yes—
314C8—82no—
315C8—3762no—
316C22—28no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22#1568897811yescharacteristic
324C22#1568909512yes—
325C22#101×D4712yes—
326C22#1568910512yes—
327C4—22no—
328C4—22no—
329C4—42no—
330C4—42no—
331C4—944no—
332C4—1882no—
333C4—1882no—
334C4—1882no—
335C2—22no—
336C2—22no—
337C2—22no—
338C2#2024330411yescharacteristic
339C2#2024331011yescharacteristic
340C2#2024331411yescharacteristic
subgroupG/H
centerC22#15688978
commutator, prime radicalC24×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#1463C2
socleC22×C47#379
cosocleC23×C4×C47C23
hypercenter#1463D47
hypocenterC47#8554
LCSG ▷ C24×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
193. C47#8554semidirect

Maximal subgroups

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

subgroupindex
C22×#130940142
#202434662
#202417182
#202417172
C47×#14632
#855447