Finite Group Databasebeta

← #26104768

Subgroups — #26104768

Order 12032.

410 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 103 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#20251771C211yesmaximal, characteristic
2#20243240C211yesmaximal, characteristic
3#20243236C211yesmaximal, characteristic
4#20241213C211yesmaximal, characteristic
5#20241213C211yesmaximal, characteristic
6#20241211C211yesmaximal, characteristic
7C47×#1271C211yesmaximal, characteristic
8C2×Dic47⋊C8—21no—
9C2×Dic47⋊C8—21no—
10C2×#13093934—21no—
11C2×C8×Dic47—21no—
12#15689029C2211yescharacteristic
13#15689028C411yescharacteristic
14#15689028C411yescharacteristic
15#15689022C411yescharacteristic
16#15689019C411yescharacteristic
17#15689009—21no—
18#15689006—21no—
19#15689004—21no—
20#15688990—21no—
21C42×Dic47C2211yescharacteristic
22#15688878C2211yescharacteristic
23#15688878C2211yescharacteristic
24C47×#389C2211yescharacteristic
25C47×#336C2211yescharacteristic
26C47×#336C2211yescharacteristic
27C22×Dic94C2×C411yescharacteristic
28C22×C47⋊C8—21no—
29C22×C47⋊C8—21no—
30C2×C4⋊Dic47—21no—
31C2×C4⋊Dic47C2×C411yescharacteristic
32C2×Dic47⋊C4—21no—
33C2×C4×Dic47C2×C411yescharacteristic
34C2×C4×Dic47C2×C411yescharacteristic
35C2×C4×Dic47D411yescharacteristic
36C2×C4×Dic47D411yescharacteristic
37C2×C4×Dic47D411yescharacteristic
38C2×C4×Dic47D411yescharacteristic
39Dic47⋊C8—24no—
40Dic47⋊C8—24no—
41#13093934—42no—
42C8×Dic47—42no—
43C47⋊#95—21no—
44C47⋊#95—21no—
45C47⋊#95—21no—
46C47⋊#95—21no—
47C47⋊#95—21no—
48C47⋊#95—21no—
49C47⋊#95—21no—
50C47⋊#95—21no—
51C22×C8×C47—21no—
52C22×C8×C47—21no—
53C2×C4⋊C4×C47—21no—
54C2×C4⋊C4×C47C2×C411yescharacteristic
55C2×C4⋊C4×C47C2×C411yescharacteristic
56C2×C42×C47C2311yescharacteristic
57#95×C47—21no—
58C22×C4×C47—21no—
59C22×C4×C47—21no—
60C22×C4×C47C22×C411yescharacteristic
61C22×C4×C47C2×D411yescharacteristic
62C22×C4×C47C2×D411yescharacteristic
63C22×Dic47—21no—
64C22×Dic47—21no—
65C22×Dic47C22⋊C411yescharacteristic
66C22×Dic47C22⋊C411yescharacteristic
67C22×Dic47C22⋊C411yescharacteristic
68C22×Dic47C22⋊C411yescharacteristic
69C2×Dic94—21no—
70C2×Dic94—21no—
71C2×Dic94—41no—
72C2×Dic94—41no—
73C2×C8×C47—22no—
74C2×C8×C47—22no—
75C2×C8×C47—41no—
76C2×C8×C47—41no—
77C2×C8×C47—41no—
78C2×C8×C47—41no—
79C4⋊C4×C47—21no—
80C4⋊C4×C47—21no—
81C4⋊C4×C47—41no—
82C4⋊C4×C47—41no—
83C4⋊C4×C47—41no—
84C42×C47—41no—
85C4⋊Dic47—42no—
86C4⋊Dic47—41no—
87Dic47⋊C4—42no—
88C4×Dic47—21no—
89C4×Dic47—21no—
90C4×Dic47—21no—
91C4×Dic47—21no—
92C4×Dic47—22no—
93C4×Dic47—22no—
94C4×Dic47—41no—
95C4×Dic47SD1612yes—
96C4×Dic47Q1612yes—
97C2×C47⋊C8—22no—
98C2×C47⋊C8—22no—
99C2×C47⋊C8—41no—
100C2×C47⋊C8—41no—
101C2×C47⋊C8—41no—
102C2×C47⋊C8—41no—
103C23×C47C2×C22⋊C411yescharacteristic
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—41no—
111C2×C4×C47—41no—
112C2×C4×C47—41no—
113C2×C4×C47—41no—
114C2×C4×C47—41no—
115C2×C4×C47—41no—
116C2×C4×C47#13111yescharacteristic
117C2×C4×C47#13111yescharacteristic
118C2×C4×C47C2×SD1611yescharacteristic
119C2×C4×C47C2×Q1611yescharacteristic
120C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C47#13711yescharacteristic
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—41no—
131C2×Dic47—41no—
132C2×Dic47—41no—
133C2×Dic47—41no—
134C2×Dic47—41no—
135C2×Dic47—41no—
136C2×Dic47#10312yes—
137C2×Dic47#10312yes—
138C2×Dic47#10412yes—
139C2×Dic47#10412yes—
140Dic94—81no—
141Dic94—81no—
142C8×C47—42no—
143C8×C47—42no—
144C47⋊C8—42no—
145C47⋊C8—42no—
146#7689—471nomaximal, Sylow
147C22×C47#40811yescharacteristic
148C22×C47#41011yescharacteristic
149C22×C47#41311yescharacteristic
150C22×C47C2×#10311yescharacteristic
151C22×C47#41711yescharacteristic
152C22×C47C2×#10411yescharacteristic
153C22×C47C2×#10411yescharacteristic
154C4×C47—21no—
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—21no—
159C4×C47—21no—
160C4×C47—81no—
161C4×C47—81no—
162Dic47—22no—
163Dic47—22no—
164Dic47—22no—
165Dic47—22no—
166Dic47—81no—
167Dic47—81no—
168#2863—471no—
169#1767—471no—
170C4×C4⋊C8—471no—
171#1272—471no—
172#1272—471no—
173#1271—471no—
174#1271D4711yescharacteristic
175C2×C47#147311yescharacteristic
176C2×C47#148311yescharacteristic
177C2×C47#149311yescharacteristic
178C2×C47#150311yescharacteristic
179C2×C47#150911yescharacteristic
180C2×C47#152411yescharacteristic
181C2×C47#155011yescharacteristic
182C2×C4⋊C8—941no—
183C2×C4⋊C8—941no—
184C2×#97—941no—
185C2×C4×C8—941no—
186#391—471no—
187#391—471no—
188#391—471no—
189#389—471no—
190#389—471no—
191#389C2×D4711yescharacteristic
192#387—941no—
193#387—941no—
194#387—941no—
195#383—941no—
196C43—471no—
197#336—471no—
198#336—471no—
199#336C2×D4711yescharacteristic
200#336C2×D4711yescharacteristic
201C47#768911yescharacteristic, complemented, Sylow
202C22×Q8—471no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—941no—
206C22×C8—941no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—471no—
209C2×C4⋊C4—941no—
210C2×C4⋊C4—941no—
211C2×C4⋊C4C4×D4711yescharacteristic
212C2×C4⋊C4C4×D4711yescharacteristic
213C2×C42—471no—
214C2×C42—471no—
215C2×C42—471no—
216C2×C42—471no—
217C2×C42—471no—
218C2×C42—471no—
219C2×C42C22×D4711yescharacteristic
220C4⋊C8—944no—
221C4⋊C8—944no—
222#97—1882no—
223C4×C8—1882no—
224#95—21no—
225#95—941no—
226#95—941no—
227#95—941no—
228#95—941no—
229#95—941no—
230#95—941no—
231#95—941no—
232#95—941no—
233C2×Q8—941no—
234C2×Q8—941no—
235C2×Q8—1881no—
236C2×Q8—1881no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—471no—
240C22×C4—471no—
241C22×C4—471no—
242C22×C4—471no—
243C22×C4—941no—
244C22×C4—941no—
245C22×C4C2×C4×D4711yescharacteristic
246C22×C4D4×D4711yescharacteristic
247C22×C4D4×D4711yescharacteristic
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—942no—
255C2×C8—942no—
256C2×C8—1881no—
257C2×C8—1881no—
258C2×C8—1881no—
259C2×C8—1881no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—1881no—
266C4⋊C4—1882no—
267C4⋊C4—1882no—
268C42—41no—
269C42—472no—
270C42—472no—
271C42—942no—
272C42—942no—
273C42—941no—
274C42—941no—
275C42—941no—
276C42—941no—
277C42—1881no—
278C23C22⋊C4×D4711yescharacteristic
279Q8—3761no—
280Q8—3761no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—472no—
294C2×C4—472no—
295C2×C4—472no—
296C2×C4—472no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—1881no—
306C2×C4—1881no—
307C2×C4—1881no—
308C2×C4—1881no—
309C2×C4—1881no—
310C2×C4—1881no—
311C2×C4#1309403011yescharacteristic
312C2×C4#1309403211yescharacteristic
313C2×C4SD16×D4711yescharacteristic
314C2×C4Q16×D4711yescharacteristic
315C2×C4#1309404811yescharacteristic
316C2×C4#1309405311yescharacteristic
317C8—42no—
318C8—42no—
319C8—1882no—
320C8—1882no—
321C22#1568908811yescharacteristic
322C22#1568909511yescharacteristic
323C22#1568910611yescharacteristic
324C22#103×D4711yescharacteristic
325C22#1568912111yescharacteristic
326C22#104×D4711yescharacteristic
327C22#104×D4711yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—81no—
335C4—81no—
336C4—942no—
337C4—942no—
338C4—942no—
339C4—942no—
340C4—3761no—
341C4—3761no—
342C2#2024175611yescharacteristic
343C2#2024179811yescharacteristic
344C2#2024184111yescharacteristic
345C2#2024188511yescharacteristic
346C2#2024191011yescharacteristic
347C2#2024197511yescharacteristic
348C2#2024207711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1271C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1271D47
hypocenterC47#7689
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
201. C47#7689semidirect

Maximal subgroups

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

subgroupindex
#202517712
#202432402
#202432362
#202412132
#202412112
C47×#12712
#768947