Finite Group Databasebeta

← #26113637

Subgroups — #26113637

Order 12032.

486 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 117 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#20252468C211yesmaximal, characteristic
2#20248596C211yesmaximal, characteristic
3#20243381C211yesmaximal, characteristic
4#20242070C211yesmaximal, characteristic
5#20242068C211yesmaximal, characteristic
6#20241291C211yesmaximal, characteristic
7C47×#1303C211yesmaximal, characteristic
8C2×#13094024C2211yescharacteristic
9C2×C4×Dic94C2211yescharacteristic
10C8×Dic94—22no—
11#15689247—22no—
12#15689176C2211yescharacteristic
13#15689173—22no—
14#15689147C2211yescharacteristic
15C2×#13093942—21no—
16#15689044C414yes—
17#15689029—21no—
18#15689022—22no—
19#15688993—21no—
20#15688891—21no—
21#15688871—22no—
22#15688871—22no—
23C47×#431C2211yescharacteristic
24C47×#423C2211yescharacteristic
25C4×C4⋊C4×C47C2211yescharacteristic
26C22×Dic94C2×C412yes—
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⋊Dic47—21no—
39C2×C4⋊Dic47—24no—
40C2×C4⋊Dic47D411yescharacteristic
41C2×Dic47⋊C4C2×C412yes—
42C2×C4×Dic47D412yes—
43C4⋊(C47⋊C8)—21no—
44C4⋊(C47⋊C8)—21no—
45C4⋊(C47⋊C8)D412yes—
46Dic47⋊C8—24no—
47#13093942—42no—
48C22⋊(C47⋊C8)—21no—
49C4×C47⋊C8—21no—
50C8×Dic47—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—22no—
74C2×Dic94—22no—
75C2×Dic94—82no—
76C2×Dic94SD1612yes—
77C2×Dic94Q1612yes—
78M16×C47—41no—
79M16×C47—41no—
80C2×C8×C47—22no—
81C2×C8×C47—41no—
82C4⋊C4×C47—24no—
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—41no—
92C4⋊Dic47—41no—
93C4⋊Dic47—41no—
94C4⋊Dic47—41no—
95C4⋊Dic47—84no—
96Dic47⋊C4—22no—
97Dic47⋊C4—22no—
98C4×Dic47—22no—
99C4×Dic47—22no—
100#10625329—41no—
101#10625329—41no—
102C2×C47⋊C8—22no—
103C2×C47⋊C8—41no—
104C23×C47C2×C22⋊C411yescharacteristic
105C2×C4×C47—22no—
106C2×C4×C47—24no—
107C2×C4×C47—41no—
108C2×C4×C47—42no—
109C2×C4×C47—42no—
110C2×C4×C47C4×D411yescharacteristic
111C2×C4×C47C4×D411yescharacteristic
112C2×C4×C47#12011yescharacteristic
113C2×C4×C47#12111yescharacteristic
114C2×C4×C47#12111yescharacteristic
115C2×C4×C47#12311yescharacteristic
116C2×C4×C47C2×SD1611yescharacteristic
117C2×C4×C47C2×Q1611yescharacteristic
118C2×C4×C47#13511yescharacteristic
119C2×C4×C47#13511yescharacteristic
120C2×Dic47—22no—
121C2×Dic47—22no—
122C2×Dic47—22no—
123C2×Dic47—42no—
124C2×Dic47—44no—
125C2×Dic47—42no—
126C2×Dic47#10314yes—
127Dic94—22no—
128Dic94—22no—
129Dic94—22no—
130Dic94—22no—
131Dic94—82no—
132Dic94—82no—
133C8×C47—42no—
134C8×C47—81no—
135C47⋊C8—42no—
136C47⋊C8—81no—
137#9392—471nomaximal, Sylow
138C22×C47—21no—
139C22×C47—21no—
140C22×C47#38611yescharacteristic
141C22×C47C2×#10311yescharacteristic
142C22×C47#41611yescharacteristic
143C4×C47—21no—
144C4×C47—21no—
145C4×C47—21no—
146C4×C47—44no—
147C4×C47#45612yes—
148C4×C47#46511yescharacteristic
149C4×C47#46511yescharacteristic
150C4×C47#46711yescharacteristic
151C4×C47#46711yescharacteristic
152Dic47—24no—
153Dic47—42no—
154Dic47—82no—
155#2982—471no—
156#2567—471no—
157#1801—471no—
158#1548—471no—
159#1548—471no—
160#1303—471no—
161#1303D4711yescharacteristic
162C2×C47—21no—
163C2×C47—21no—
164C2×C47#188611yescharacteristic
165C2×C47#189211yescharacteristic
166C2×C47#191411yescharacteristic
167C2×C4⋊Q8—471no—
168C2×C4×Q8—471no—
169C8×Q8—942no—
170C8×Q8—942no—
171#431—471no—
172#431—942no—
173#431C2×D4711yescharacteristic
174#423—471no—
175#423C2×D4711yescharacteristic
176C2×#101—941no—
177#395—474no—
178#391—941no—
179#389—942no—
180#384—941no—
181C4×C4⋊C4C2×D4711yescharacteristic
182#343—941no—
183#333—942no—
184#333—942no—
185C47#939211yescharacteristic, complemented, Sylow
186C22×Q8—471no—
187C22×Q8—472no—
188C2×M16—21no—
189C2×M16—941no—
190C4⋊Q8—941no—
191C4⋊Q8—941no—
192C4⋊Q8—941no—
193C4⋊Q8—941no—
194C4×Q8—941no—
195C4×Q8—941no—
196C4×Q8—941no—
197C4×Q8—941no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—472no—
200C2×C4⋊C4—471no—
201C2×C4⋊C4—944no—
202C2×C4⋊C4—941no—
203C2×C4⋊C4—941no—
204C2×C42—21no—
205C2×C42—472no—
206C2×C42C22×D4711yescharacteristic
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—472no—
210C4⋊C8—944no—
211C4⋊C8—941no—
212C4⋊C8—941no—
213C4⋊C8D18812yes—
214#101—1882no—
215C22⋊C8—21no—
216C22⋊C8—941no—
217C4×C8—21no—
218C4×C8—944no—
219C4×C8—941no—
220#95—944no—
221#95C4×D4712yes—
222C2×Q8—472no—
223C2×Q8—472no—
224C2×Q8—941no—
225C2×Q8—941no—
226C2×Q8—941no—
227C2×Q8—941no—
228C2×Q8—942no—
229C2×Q8—942no—
230C2×Q8—3762no—
231C22×C4—22no—
232C22×C4—472no—
233C22×C4—472no—
234C22×C4—942no—
235C22×C4C2×C4×D4711yescharacteristic
236C22×C4D4×D4711yescharacteristic
237C22×C4D4×D4711yescharacteristic
238M16—41no—
239M16—41no—
240M16—1881no—
241M16—1881no—
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—942no—
245C2×C8—1881no—
246C4⋊C4—24no—
247C4⋊C4—942no—
248C4⋊C4—942no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4—3764no—
252C4⋊C4—1881no—
253C4⋊C4—1881no—
254C4⋊C4—1881no—
255C4⋊C4—1881no—
256C42—41no—
257C42—41no—
258C42—942no—
259C42—942no—
260C42C2×D18811yescharacteristic
261C42#1062535011yescharacteristic
262C42D4×D4711yescharacteristic
263C42#1062535411yescharacteristic
264C23C22⋊C4×D4711yescharacteristic
265Q8—942no—
266Q8—942no—
267Q8—942no—
268Q8—942no—
269Q8—3762no—
270Q8—3762no—
271C2×C4—22no—
272C2×C4—24no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—474no—
277C2×C4—942no—
278C2×C4—942no—
279C2×C4—942no—
280C2×C4—1884no—
281C2×C4—1882no—
282C2×C4—1882no—
283C2×C4#1309398611yescharacteristic
284C2×C4C4×D18811yescharacteristic
285C2×C4#1309399411yescharacteristic
286C2×C4#1309399711yescharacteristic
287C2×C4#1309399911yescharacteristic
288C2×C4#1309400911yescharacteristic
289C2×C4SD16×D4711yescharacteristic
290C2×C4Q16×D4711yescharacteristic
291C2×C4#1309404311yescharacteristic
292C2×C4#1309404511yescharacteristic
293C8—42no—
294C8—81no—
295C8—3761no—
296C8—1882no—
297C22—21no—
298C22—21no—
299C22#1568900111yescharacteristic
300C22#103×D4711yescharacteristic
301C22#1568911611yescharacteristic
302C4—21no—
303C4—21no—
304C4—21no—
305C4—44no—
306C4—944no—
307C4—3762no—
308C4—1882no—
309C4#1568930712yes—
310C4#1568935111yescharacteristic
311C4#1568935311yescharacteristic
312C4#1568936311yescharacteristic
313C4#1568936511yescharacteristic
314C2—21no—
315C2—21no—
316C2#2024378011yescharacteristic
317C2#2024381011yescharacteristic
318C2#2024393411yescharacteristic
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#9392
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
185. C47#9392semidirect

Maximal subgroups

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

subgroupindex
#202524682
#202485962
#202433812
#202420702
#202420682
#202412912
C47×#13032
#939247