Finite Group Databasebeta

← #26113697

Subgroups — #26113697

Order 12032.

450 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 109 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#20252471C211yesmaximal, characteristic
2#20248603C211yesmaximal, characteristic
3#20243381C211yesmaximal, characteristic
4#20242074C211yesmaximal, characteristic
5#20242072C211yesmaximal, characteristic
6#20241291C211yesmaximal, characteristic
7C47×#1303C211yesmaximal, characteristic
8C2×#13094024C2211yescharacteristic
9C2×C4×Dic94C2211yescharacteristic
10#15689253—22no—
11#15689250—22no—
12#15689177—22no—
13#15689176C2211yescharacteristic
14#15689147C2211yescharacteristic
15C2×#13093942—21no—
16#15689063C414yes—
17#15689029—21no—
18#15689028—22no—
19#15688989—21no—
20#15688891—21no—
21#15688870—22no—
22#15688868—22no—
23C47×#431C2211yescharacteristic
24C47×#423C2211yescharacteristic
25C4×C4⋊C4×C47C2211yescharacteristic
26C22×Dic94—21no—
27C22×Dic94D411yescharacteristic
28C2×#10625329—21no—
29#13094024—21no—
30#13094024—21no—
31#13094024—21no—
32#13094024—21no—
33C4×Dic94—21no—
34C4×Dic94—21no—
35C4×Dic94—21no—
36C4×Dic94—21no—
37C2×C4⋊Dic47—21no—
38C2×C4⋊Dic47C2×C412yes—
39C2×C4⋊Dic47D411yescharacteristic
40C2×Dic47⋊C4C2×C412yes—
41C2×C4×Dic47D412yes—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)—21no—
44C4⋊(C47⋊C8)D412yes—
45Dic47⋊C8—24no—
46#13093942—42no—
47C22⋊(C47⋊C8)—21no—
48#13093934—24no—
49C4×C47⋊C8—21no—
50C47⋊#95—24no—
51C47⋊#95—24no—
52C2×M16×C47—21no—
53C2×C4⋊C4×C47—21no—
54C2×C42×C47—21no—
55C2×C42×C47C2311yescharacteristic
56C4⋊C8×C47—21no—
57C4⋊C8×C47—21no—
58C4⋊C8×C47D412yes—
59C22⋊C8×C47—21no—
60C4×C8×C47—21no—
61#95×C47C2×C412yes—
62C22×C4×C47—22no—
63C22×C4×C47C22×C411yescharacteristic
64C22×C4×C47C2×D411yescharacteristic
65C22×C4×C47C2×D411yescharacteristic
66C22×Dic47—22no—
67C22×Dic47C22⋊C412yes—
68C22×Dic47C22⋊C412yes—
69C2×Dic94—21no—
70C2×Dic94—21no—
71C2×Dic94—21no—
72C2×Dic94—21no—
73C2×Dic94—21no—
74C2×Dic94—21no—
75C2×Dic94—44no—
76C2×Dic94—41no—
77C2×Dic94—41no—
78M16×C47—41no—
79M16×C47—41no—
80C2×C8×C47—22no—
81C2×C8×C47—41no—
82C4⋊C4×C47—42no—
83C42×C47—41no—
84C42×C47—41no—
85C42×C47C2×D411yescharacteristic
86C42×C47C2×D411yescharacteristic
87C42×C47#4111yescharacteristic
88C42×C47#4111yescharacteristic
89C4⋊Dic47—21no—
90C4⋊Dic47—21no—
91C4⋊Dic47—22no—
92C4⋊Dic47—22no—
93C4⋊Dic47—41no—
94C4⋊Dic47—41no—
95Dic47⋊C4—22no—
96Dic47⋊C4—22no—
97C4×Dic47—22no—
98C4×Dic47—22no—
99#10625329—41no—
100#10625329—41no—
101C2×C47⋊C8—22no—
102C2×C47⋊C8—41no—
103C23×C47C2×C22⋊C411yescharacteristic
104C2×C4×C47—22no—
105C2×C4×C47—41no—
106C2×C4×C47—42no—
107C2×C4×C47—42no—
108C2×C4×C47—42no—
109C2×C4×C47C4×D411yescharacteristic
110C2×C4×C47C4×D411yescharacteristic
111C2×C4×C47#12011yescharacteristic
112C2×C4×C47#12111yescharacteristic
113C2×C4×C47#12111yescharacteristic
114C2×C4×C47#12311yescharacteristic
115C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C47#13711yescharacteristic
117C2×C4×C47#13711yescharacteristic
118C2×C4×C47#13711yescharacteristic
119C2×Dic47—22no—
120C2×Dic47—22no—
121C2×Dic47—22no—
122C2×Dic47—22no—
123C2×Dic47—42no—
124C2×Dic47—44no—
125C2×Dic47—42no—
126Dic94—41no—
127Dic94—41no—
128Dic94—41no—
129Dic94—41no—
130Dic94—82no—
131Dic94—82no—
132C8×C47—42no—
133C8×C47—81no—
134C47⋊C8—42no—
135C47⋊C8—81no—
136#9404—471nomaximal, Sylow
137C22×C47—21no—
138C22×C47—21no—
139C22×C47#38611yescharacteristic
140C22×C47#41711yescharacteristic
141C22×C47#41911yescharacteristic
142C4×C47—21no—
143C4×C47—21no—
144C4×C47—21no—
145C4×C47—82no—
146C4×C47#45412yes—
147C4×C47#46811yescharacteristic
148C4×C47#46811yescharacteristic
149C4×C47#47011yescharacteristic
150C4×C47#47011yescharacteristic
151Dic47—42no—
152Dic47—42no—
153Dic47—82no—
154#2983—471no—
155#2568—471no—
156#1801—471no—
157#1549—471no—
158#1549—471no—
159#1303—471no—
160#1303D4711yescharacteristic
161C2×C47—21no—
162C2×C47—21no—
163C2×C47#188811yescharacteristic
164C2×C47#189411yescharacteristic
165C2×C47#191511yescharacteristic
166C2×C4⋊Q8—471no—
167C2×C4×Q8—471no—
168#446—942no—
169#446—942no—
170#432—942no—
171#431—471no—
172#431C2×D4711yescharacteristic
173#423—471no—
174#423C2×D4711yescharacteristic
175C2×#101—941no—
176#400—474no—
177#391—941no—
178#391—942no—
179#382—941no—
180C4×C4⋊C4C2×D4711yescharacteristic
181#343—941no—
182#332—942no—
183#332—942no—
184C47#940411yescharacteristic, complemented, Sylow
185C22×Q8—471no—
186C22×Q8—941no—
187C2×M16—21no—
188C2×M16—941no—
189C4⋊Q8—941no—
190C4⋊Q8—941no—
191C4⋊Q8—941no—
192C4⋊Q8—941no—
193C4×Q8—941no—
194C4×Q8—941no—
195C4×Q8—941no—
196C4×Q8—941no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—472no—
199C2×C4⋊C4—471no—
200C2×C4⋊C4—472no—
201C2×C4⋊C4—941no—
202C2×C42—21no—
203C2×C42—472no—
204C2×C42C22×D4711yescharacteristic
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—472no—
208C4⋊C8—944no—
209C4⋊C8—941no—
210C4⋊C8—941no—
211C4⋊C8D18812yes—
212#101—1882no—
213C22⋊C8—21no—
214C22⋊C8—941no—
215#97—944no—
216C4×C8—21no—
217C4×C8—941no—
218#95—944no—
219#95—944no—
220#95C4×D4712yes—
221C2×Q8—941no—
222C2×Q8—941no—
223C2×Q8—941no—
224C2×Q8—941no—
225C2×Q8—941no—
226C2×Q8—941no—
227C2×Q8—1884no—
228C2×Q8—1881no—
229C2×Q8—1881no—
230C22×C4—22no—
231C22×C4—472no—
232C22×C4—472no—
233C22×C4—942no—
234C22×C4C2×C4×D4711yescharacteristic
235C22×C4D4×D4711yescharacteristic
236C22×C4D4×D4711yescharacteristic
237M16—41no—
238M16—41no—
239M16—1881no—
240M16—1881no—
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—942no—
244C2×C8—1881no—
245C4⋊C4—42no—
246C4⋊C4—942no—
247C4⋊C4—942no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4—942no—
251C4⋊C4—942no—
252C4⋊C4—1881no—
253C4⋊C4—1881no—
254C42—41no—
255C42—41no—
256C42—942no—
257C42—942no—
258C42C2×D18811yescharacteristic
259C42#1062535011yescharacteristic
260C42D4×D4711yescharacteristic
261C42#1062535411yescharacteristic
262C23C22⋊C4×D4711yescharacteristic
263Q8—3762no—
264Q8—3762no—
265Q8—1881no—
266Q8—1881no—
267Q8—1881no—
268Q8—1881no—
269C2×C4—22no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—942no—
275C2×C4—942no—
276C2×C4—942no—
277C2×C4—942no—
278C2×C4—1884no—
279C2×C4—1882no—
280C2×C4—1882no—
281C2×C4#1309398611yescharacteristic
282C2×C4C4×D18811yescharacteristic
283C2×C4#1309399411yescharacteristic
284C2×C4#1309399711yescharacteristic
285C2×C4#1309399911yescharacteristic
286C2×C4#1309400911yescharacteristic
287C2×C4#1309404811yescharacteristic
288C2×C4#1309405311yescharacteristic
289C2×C4#1309405311yescharacteristic
290C2×C4#1309405611yescharacteristic
291C8—42no—
292C8—81no—
293C8—3761no—
294C8—1882no—
295C22—21no—
296C22—21no—
297C22#1568900111yescharacteristic
298C22#1568912111yescharacteristic
299C22#1568913011yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—82no—
304C4—3762no—
305C4—1882no—
306C4—1882no—
307C4#1568929712yes—
308C4#1568936811yescharacteristic
309C4#1568937011yescharacteristic
310C4#1568938011yescharacteristic
311C4#1568938211yescharacteristic
312C2—21no—
313C2—21no—
314C2#2024379011yescharacteristic
315C2#2024382011yescharacteristic
316C2#2024393911yescharacteristic
subgroupG/H
centerC22#15689001
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1303C2
socleC22×C47#386
prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1303D47
hypocenterC47#9404
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
184. C47#9404semidirect

Maximal subgroups

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

subgroupindex
#202524712
#202486032
#202433812
#202420742
#202420722
#202412912
C47×#13032
#940447