Finite Group Databasebeta

← #26120615

Subgroups — #26120615

Order 12032.

364 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 101 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#20253934C211yesmaximal, characteristic
2#20244163C211yesmaximal, characteristic
3#20242076C211yesmaximal, characteristic
4#20242068C211yesmaximal, characteristic
5C2×#15688870C211yesmaximal, characteristic
6#20241792C211yesmaximal, characteristic
7C47×#1283C211yesmaximal, characteristic
8#15689680C2211yescharacteristic
9C2×#13094024C2211yescharacteristic
10#15689532—22no—
11#15689528—21no—
12#15689521—21no—
13C2×#13093959—21no—
14#15689165—21no—
15#15689165—21no—
16#15689147C2211yescharacteristic
17C2×C4⋊(C47⋊C8)C2211yescharacteristic
18#15688887—21no—
19#15688871—22no—
20#15688871—21no—
21#15688870—21no—
22#15688870—22no—
23#15688855—22no—
24C47×#431C2211yescharacteristic
25C2×C4⋊C8×C47C2211yescharacteristic
26C4×M16×C47C2211yescharacteristic
27C22×Dic94—21no—
28C2×#10625329—21no—
29C22×C47⋊C8—21no—
30#13094024—21no—
31#13094024—21no—
32#13094024—21no—
33#13094024D411yescharacteristic
34#13094024D411yescharacteristic
35#13094024D412yes—
36#13094016—21no—
37#13094003—21no—
38#13094003—21no—
39C4×Dic94—21no—
40C4×Dic94—21no—
41#13093983—21no—
42C2×C4⋊Dic47—21no—
43C2×C4⋊Dic47—21no—
44#13093959—42no—
45#13093958—22no—
46#13093958—22no—
47#13093956—22no—
48#13093956—22no—
49C4⋊(C47⋊C8)—21no—
50C4⋊(C47⋊C8)—21no—
51C4⋊(C47⋊C8)—21no—
52C4⋊(C47⋊C8)D412yes—
53C2×M16×C47D411yescharacteristic
54C2×M16×C47D411yescharacteristic
55C22×C8×C47—21no—
56C2×C42×C47C2311yescharacteristic
57C4⋊C8×C47—21no—
58C4⋊C8×C47—21no—
59C4⋊C8×C47—21no—
60C22⋊C8×C47—21no—
61#97×C47—21no—
62C4×C8×C47—21no—
63C4×C8×C47—21no—
64C22×C4×C47C2×D411yescharacteristic
65C22×C4×C47#4111yescharacteristic
66C22×C4×C47#4111yescharacteristic
67C22×Dic47—41no—
68C2×Dic94—21no—
69C2×Dic94—21no—
70C2×Dic94—22no—
71C2×Dic94—41no—
72C2×Dic94—81no—
73C2×Dic94—81no—
74M16×C47—21no—
75M16×C47—21no—
76M16×C47SD1612yes—
77M16×C47Q1612yes—
78C2×C8×C47—21no—
79C2×C8×C47—21no—
80C2×C8×C47—41no—
81C2×C8×C47—41no—
82C2×C8×C47—81no—
83C42×C47C2×D411yescharacteristic
84C42×C47C2×D411yescharacteristic
85C42×C47C2×D411yescharacteristic
86C42×C47#4111yescharacteristic
87C22⋊Dic47—41no—
88C4⋊Dic47—21no—
89C4⋊Dic47—22no—
90C4⋊Dic47—21no—
91C4⋊Dic47—22no—
92C4⋊Dic47—21no—
93C4⋊Dic47—21no—
94C4⋊Dic47—41no—
95C4⋊Dic47—41no—
96Dic47⋊C4—41no—
97Dic47⋊C4—41no—
98C4×Dic47—41no—
99#10625329—41no—
100#10625329—41no—
101C2×C47⋊C8—22no—
102C2×C47⋊C8—41no—
103C2×C47⋊C8—41no—
104C2×C47⋊C8—41no—
105C23×C47#12411yescharacteristic
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—41no—
109C2×C4×C47#12011yescharacteristic
110C2×C4×C47#12111yescharacteristic
111C2×C4×C47#12111yescharacteristic
112C2×C4×C47#12111yescharacteristic
113C2×C4×C47#12311yescharacteristic
114C2×C4×C47#12311yescharacteristic
115C2×C4×C47C2×SD1611yescharacteristic
116C2×C4×C47C2×Q1611yescharacteristic
117C2×C4×C47#13711yescharacteristic
118C2×C4×C47#13711yescharacteristic
119C2×Dic47—41no—
120C2×Dic47—41no—
121C2×Dic47—42no—
122C2×Dic47—82no—
123Dic94—41no—
124Dic94—41no—
125Dic94—81no—
126Dic94—81no—
127Dic94—81no—
128Dic94—82no—
129C8×C47—22no—
130C8×C47—22no—
131C8×C47—81no—
132C8×C47—81no—
133C47⋊C8—42no—
134C47⋊C8—81no—
135#10556—471nomaximal, Sylow
136C22×C47—21no—
137C22×C47—21no—
138C22×C47#39411yescharacteristic
139C22×C47#48711yescharacteristic
140C22×C47#49111yescharacteristic
141C4×C47—21no—
142C4×C47—21no—
143C4×C47—21no—
144C4×C47#44811yescharacteristic
145C4×C47#45111yescharacteristic
146C4×C47#46111yescharacteristic
147C4×C47#46211yescharacteristic
148C4×C47#47111yescharacteristic
149C4×C47#47211yescharacteristic
150Dic47—81no—
151Dic47—81no—
152Dic47—82no—
153#3165—471no—
154#1950—471no—
155#1550—471no—
156#1548—471no—
157C2×#332—471no—
158#1481—471no—
159#1283D4711yescharacteristic
160C2×C47—21no—
161C2×C47—21no—
162C2×C47#204311yescharacteristic
163C2×C47#204911yescharacteristic
164C2×C47#205111yescharacteristic
165#533—471no—
166C2×C4⋊Q8—471no—
167#501—942no—
168#500—941no—
169#498—941no—
170#431C2×D4711yescharacteristic
171C2×#108—941no—
172#428—941no—
173#428—941no—
174#423—471no—
175C2×C4⋊C8—471no—
176C2×C4⋊C8C2×D4711yescharacteristic
177C4×M16C2×D4711yescharacteristic
178#341—941no—
179#333—942no—
180#333—941no—
181#332—942no—
182#332—941no—
183Q8⋊C8—942no—
184C47#1055611yescharacteristic, complemented, Sylow
185C22×Q8—941no—
186C2×M16—941no—
187C2×M16D18811yescharacteristic
188C2×M16D18811yescharacteristic
189C22×C8—21no—
190C22×C8—941no—
191C4⋊Q8—472no—
192C4⋊Q8—471no—
193C4⋊Q8—471no—
194C4⋊Q8—941no—
195C4⋊Q8—941no—
196C4⋊Q8—941no—
197#125—941no—
198C22⋊Q8—941no—
199C22⋊Q8—941no—
200C4×Q8—941no—
201C4×Q8—941no—
202#117—941no—
203C2×C4⋊C4—941no—
204C2×C4⋊C4—941no—
205C2×C42C22×D4711yescharacteristic
206#108—1882no—
207#107—942no—
208#107—942no—
209#106—942no—
210#106—942no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—472no—
215C4⋊C8—941no—
216C4⋊C8—941no—
217C4⋊C8—941no—
218C22⋊C8—21no—
219#97—21no—
220C4×C8—21no—
221C4×C8—21no—
222C2×Q8—941no—
223C2×Q8—941no—
224C2×Q8—942no—
225C2×Q8—3761no—
226C2×Q8—3761no—
227C2×Q8—1881no—
228C22×C4—1881no—
229C22×C4C2×D18811yescharacteristic
230C22×C4#1062535011yescharacteristic
231C22×C4#1062535011yescharacteristic
232M16—21no—
233M16—21no—
234M16—1881no—
235M16—1881no—
236M16#1062532512yes—
237M16Dic18812yes—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—81no—
243C2×C8—942no—
244C2×C8—1881no—
245C2×C8—1881no—
246C2×C8—1881no—
247C4⋊C4—941no—
248C4⋊C4—942no—
249C4⋊C4—941no—
250C4⋊C4—942no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—1881no—
254C4⋊C4—1881no—
255C4⋊C4—1881no—
256C4⋊C4—1881no—
257C22⋊C4—1881no—
258C42—1881no—
259C42D4×D4711yescharacteristic
260C42D4×D4711yescharacteristic
261C42D4×D4711yescharacteristic
262C42#1062535411yescharacteristic
263C23#1309401211yescharacteristic
264Q8—3761no—
265Q8—3762no—
266Q8—3761no—
267Q8—3761no—
268Q8—1881no—
269Q8—1881no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—3762no—
274C2×C4—1881no—
275C2×C4—1881no—
276C2×C4—1882no—
277C2×C4#1309399411yescharacteristic
278C2×C4#1309399711yescharacteristic
279C2×C4#1309399711yescharacteristic
280C2×C4#1309399911yescharacteristic
281C2×C4#1309400911yescharacteristic
282C2×C4#1309400911yescharacteristic
283C2×C4C2×#1062532511yescharacteristic
284C2×C4C2×Dic18811yescharacteristic
285C2×C4#1309405711yescharacteristic
286C2×C4#1309405711yescharacteristic
287C8—22no—
288C8—22no—
289C8—81no—
290C8—81no—
291C8—3761no—
292C8—1882no—
293C22—21no—
294C22—21no—
295C22#1568904111yescharacteristic
296C22#1568947411yescharacteristic
297C22#1568949211yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—3761no—
302C4—3762no—
303C4—3761no—
304C4#1568926411yescharacteristic
305C4#1568928111yescharacteristic
306C4#1568932911yescharacteristic
307C4#1568933411yescharacteristic
308C4#1568938911yescharacteristic
309C4#1568939211yescharacteristic
310C2—21no—
311C2—21no—
312C2#2024463511yescharacteristic
313C2#2024467111yescharacteristic
314C2#2024468311yescharacteristic
subgroupG/H
centerC22#15689041
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1283C2
socleC22×C47#394
prime radicalC23×C47#124
hypercenter#1283D47
hypocenterC47#10556
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1283

Complements

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

NH ≅ G/Ntype
184. C47#10556semidirect

Maximal subgroups

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

subgroupindex
#202539342
#202441632
#202420762
#202420682
C2×#156888702
#202417922
C47×#12832
#1055647