Finite Group Databasebeta

← #26126675

Subgroups — #26126675

Order 12032.

358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 83 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#20249264C211yesmaximal, characteristic
2#20241712C211yesmaximal, characteristic
3#20241414C212yesmaximal
4#20241393C212yesmaximal
5C4×#101×C47C211yesmaximal, characteristic
6C2×#13094016C411yescharacteristic
7#15689176—21no—
8#15689062C411yescharacteristic
9#15689062C2211yescharacteristic
10#15689061—21no—
11#15689053C411yescharacteristic
12#15689053C2211yescharacteristic
13#15689042—21no—
14#15689007—21no—
15#15689007—21no—
16#15688991C411yescharacteristic
17#15688849—21no—
18#15688849C2212yes—
19C2×C4×Q8×C47C2211yescharacteristic
20C2×#101×C47—21no—
21C4×M16×C47—21no—
22C47×#343C2212yes—
23#13094016—41no—
24#13094016—41no—
25C2×C4⋊Dic47C2×C411yescharacteristic
26C2×C4⋊Dic47C2×C411yescharacteristic
27C2×Dic47⋊C4—21no—
28C2×Dic47⋊C4—21no—
29C2×Dic47⋊C4—21no—
30C2×Dic47⋊C4—21no—
31C4⋊(C47⋊C8)—41no—
32C22⋊(C47⋊C8)—22no—
33C4×C47⋊C8—41no—
34C47⋊#95—21no—
35C47⋊#95—21no—
36C47⋊#95—21no—
37C47⋊#95—21no—
38C47⋊#95—21no—
39C47⋊#95—21no—
40C47⋊#95—21no—
41C47⋊#95—21no—
42C47⋊#95C2×C411yescharacteristic
43C47⋊#95C2×C411yescharacteristic
44C22×Q8×C47D411yescharacteristic
45C2×M16×C47—22no—
46C4×Q8×C47—41no—
47C4×Q8×C47—41no—
48C2×C4⋊C4×C47C2×C411yescharacteristic
49C2×C4⋊C4×C47D411yescharacteristic
50C2×C4⋊C4×C47C2311yescharacteristic
51C2×C42×C47C2×C411yescharacteristic
52C2×C42×C47D411yescharacteristic
53C2×C42×C47D411yescharacteristic
54#101×C47—24no—
55#97×C47—41no—
56C4×C8×C47—41no—
57C2×Q8×C47—22no—
58C2×Q8×C47—22no—
59C2×Q8×C47—41no—
60C22×C4×C47C22⋊C411yescharacteristic
61C22×C4×C47C22⋊C411yescharacteristic
62C22×C4×C47C22⋊C411yescharacteristic
63C22×C4×C47C22⋊C411yescharacteristic
64C22×C4×C47C22×C411yescharacteristic
65C22×C4×C47C2×D411yescharacteristic
66C22×C4×C47C2×D411yescharacteristic
67C22×Dic47—21no—
68C22×Dic47—21no—
69C22×Dic47—21no—
70C22×Dic47—21no—
71M16×C47—24no—
72M16×C47—42no—
73C2×C8×C47—42no—
74C4⋊C4×C47—41no—
75C4⋊C4×C47—41no—
76C4⋊C4×C47—41no—
77C42×C47—21no—
78C42×C47—21no—
79C42×C47—21no—
80C42×C47—21no—
81C42×C47—21no—
82C42×C47—21no—
83C4⋊Dic47—41no—
84C4⋊Dic47—41no—
85Dic47⋊C4—42no—
86Dic47⋊C4—41no—
87Dic47⋊C4—41no—
88Dic47⋊C4—42no—
89Dic47⋊C4—42no—
90C2×C47⋊C8—42no—
91C23×C47C2×C22⋊C411yescharacteristic
92Q8×C47—44no—
93C2×C4×C47—21no—
94C2×C4×C47—21no—
95C2×C4×C47—21no—
96C2×C4×C47—21no—
97C2×C4×C47—21no—
98C2×C4×C47—21no—
99C2×C4×C47—21no—
100C2×C4×C47—21no—
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47—41no—
104C2×C4×C47—41no—
105C2×C4×C47—41no—
106C2×C4×C47—41no—
107C2×C4×C47#9911yescharacteristic
108C2×C4×C47#9911yescharacteristic
109C2×C4×C47#10412yes—
110C2×C4×C47#13512yes—
111C2×Dic47—41no—
112C2×Dic47—41no—
113C2×Dic47—41no—
114C2×Dic47—41no—
115C2×Dic47—42no—
116C2×Dic47—41no—
117C2×Dic47—41no—
118C2×Dic47—41no—
119C2×Dic47—41no—
120C2×Dic47—41no—
121C2×Dic47—41no—
122C8×C47—44no—
123C47⋊C8—82no—
124#11740—471nomaximal, Sylow
125C22×C47—21no—
126C22×C47—21no—
127C22×C47C2×#9911yescharacteristic
128C22×C47#41611yescharacteristic
129C22×C47C2×#10411yescharacteristic
130C4×C47—21no—
131C4×C47—21no—
132C4×C47—22no—
133C4×C47—22no—
134C4×C47—41no—
135C4×C47—41no—
136C4×C47—41no—
137C4×C47—41no—
138Dic47—81no—
139Dic47—81no—
140Dic47—81no—
141Dic47—81no—
142#2634—471no—
143C4×#101D4711yescharacteristic
144#1461—471no—
145#1353—472no—
146#1346—472no—
147C2×C47—21no—
148C2×C47—21no—
149C2×C47#150111yescharacteristic
150C2×C47#212311yescharacteristic
151C2×C47#213311yescharacteristic
152C2×#125—471no—
153C2×C4×Q8C2×D4711yescharacteristic
154#431—941no—
155C2×#101—21no—
156C4×M16—21no—
157#400—471no—
158#400—471no—
159#400—941no—
160#398—471no—
161#398—471no—
162#395—941no—
163#387—941no—
164#387—941no—
165#383—471no—
166#343C2×D4712yes—
167#324—472no—
168#324—941no—
169C47#1174011yescharacteristic, complemented, Sylow
170C22×Q8C22⋊D4711yescharacteristic
171C2×M16—22no—
172#125—1881no—
173#125—1881no—
174C4×Q8—41no—
175C4×Q8—41no—
176C2×C4⋊C4—471no—
177C2×C4⋊C4—471no—
178C2×C4⋊C4—941no—
179C2×C4⋊C4—941no—
180C2×C4⋊C4—941no—
181C2×C4⋊C4—941no—
182C2×C4⋊C4C4×D4711yescharacteristic
183C2×C4⋊C4D18811yescharacteristic
184C2×C4⋊C4C22×D4711yescharacteristic
185C2×C42C4×D4711yescharacteristic
186C2×C42D18811yescharacteristic
187C2×C42C22⋊D4711yescharacteristic
188C4⋊C8—1881no—
189#101—24no—
190C22⋊C8—942no—
191#97—41no—
192C4×C8—41no—
193C4×C8—1881no—
194#95—471no—
195#95—471no—
196#95—941no—
197#95—941no—
198#95—941no—
199#95—941no—
200#95—941no—
201#95—941no—
202#95—941no—
203#95—941no—
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8—41no—
207C22×C4—941no—
208C22×C4—941no—
209C22×C4—941no—
210C22×C4—941no—
211C22×C4(C2×D47)⋊C411yescharacteristic
212C22×C4(C2×D47)⋊C411yescharacteristic
213C22×C4(C2×D47)⋊C411yescharacteristic
214C22×C4(C2×D47)⋊C411yescharacteristic
215C22×C4C2×C4×D4711yescharacteristic
216C22×C4C2×D18811yescharacteristic
217C22×C4C2×C22⋊D4711yescharacteristic
218M16—24no—
219M16—42no—
220C2×C8—42no—
221C2×C8—1882no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—1881no—
226C4⋊C4—1881no—
227C4⋊C4—1882no—
228C4⋊C4—1881no—
229C4⋊C4—1881no—
230C4⋊C4—1882no—
231C4⋊C4—1882no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—21no—
237C42—21no—
238C23C2×(C2×D47)⋊C411yescharacteristic
239Q8—44no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—1881no—
255C2×C4—1881no—
256C2×C4—1881no—
257C2×C4—1881no—
258C2×C4—1882no—
259C2×C4—1881no—
260C2×C4—1881no—
261C2×C4—1881no—
262C2×C4—1881no—
263C2×C4—1881no—
264C2×C4—1881no—
265C2×C4#1309393811yescharacteristic
266C2×C4#1309393811yescharacteristic
267C2×C4#1309395212yes—
268C2×C4#1309404412yes—
269C8—44no—
270C8—3762no—
271C22—21no—
272C22—21no—
273C22C2×#1309393811yescharacteristic
274C22#1568911711yescharacteristic
275C22C2×#1309395211yescharacteristic
276C4—21no—
277C4—21no—
278C4—22no—
279C4—22no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—3761no—
285C4—3761no—
286C4—3761no—
287C4—3761no—
288C2—21no—
289C2—21no—
290C2#2024187711yescharacteristic
291C2#2024504311yescharacteristic
292C2#2024507511yescharacteristic
subgroupG/H
centerC22C2×#13093938
commutatorC22×C4×C47C22×C4
FrattiniC2×C4⋊C4C22×D47
FittingC4×#101×C47C2
socleC22×C47C2×#99
prime radicalC23×C47C2×C22⋊C4
cosocleC2×C4⋊C4×C47C23
hypercenterC4×#101D47
hypocenterC47#11740
LCSG ▷ C22×C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
169. C47#11740semidirect

Maximal subgroups

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

subgroupindex
#202492642
#202417122
#202414142
#202413932
C4×#101×C472
#1174047