Finite Group Databasebeta

← #26104716

Subgroups — #26104716

Order 12032.

396 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 97 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#20251774C211yesmaximal, characteristic
2#20243236C211yesmaximal, characteristic
3#20243135C211yesmaximal, characteristic
4#20241212C211yesmaximal, characteristic
5#20241211C211yesmaximal, characteristic
6#20241210C211yesmaximal, characteristic
7C47×#1271C211yesmaximal, characteristic
8C2×Dic47⋊C8—21no—
9C2×#13093934—21no—
10C2×C8×Dic47—21no—
11#15689022C411yescharacteristic
12#15689021C2211yescharacteristic
13#15689019C411yescharacteristic
14#15689009—21no—
15#15689008—21no—
16#15689005—21no—
17#15689004—21no—
18#15688988C411yescharacteristic
19#15688988C411yescharacteristic
20C42×Dic47C2211yescharacteristic
21#15688878C2211yescharacteristic
22#15688878C2211yescharacteristic
23#15688877—21no—
24C47×#389C2211yescharacteristic
25C47×#336C2211yescharacteristic
26C47×#336C2211yescharacteristic
27C22×C47⋊C8—21no—
28C22×C47⋊C8—21no—
29C2×C4⋊Dic47—21no—
30C2×C4⋊Dic47C2×C411yescharacteristic
31C2×C4⋊Dic47C2×C411yescharacteristic
32C2×Dic47⋊C4—21no—
33C2×Dic47⋊C4—21no—
34C2×C4×Dic47C2×C411yescharacteristic
35C2×C4×Dic47C2×C411yescharacteristic
36C2×C4×Dic47D411yescharacteristic
37C2×C4×Dic47D411yescharacteristic
38C2×C4×Dic47D411yescharacteristic
39C2×C4×Dic47D411yescharacteristic
40Dic47⋊C8—24no—
41#13093934—24no—
42C8×Dic47—42no—
43C47⋊#95—21no—
44C47⋊#95—21no—
45C47⋊#95—21no—
46C47⋊#95—21no—
47C47⋊#95—21no—
48C47⋊#95—21no—
49C47⋊#95—21no—
50C22×C8×C47—21no—
51C22×C8×C47—21no—
52C2×C4⋊C4×C47—21no—
53C2×C4⋊C4×C47C2×C411yescharacteristic
54C2×C4⋊C4×C47C2×C411yescharacteristic
55C2×C42×C47C2311yescharacteristic
56#95×C47—21no—
57C22×C4×C47—21no—
58C22×C4×C47—21no—
59C22×C4×C47C22×C411yescharacteristic
60C22×C4×C47C2×D411yescharacteristic
61C22×C4×C47C2×D411yescharacteristic
62C22×Dic47—21no—
63C22×Dic47—21no—
64C22×Dic47C22⋊C411yescharacteristic
65C22×Dic47C22⋊C411yescharacteristic
66C22×Dic47C22⋊C411yescharacteristic
67C22×Dic47C22⋊C411yescharacteristic
68C2×C8×C47—22no—
69C2×C8×C47—22no—
70C2×C8×C47—41no—
71C2×C8×C47—41no—
72C2×C8×C47—41no—
73C2×C8×C47—41no—
74C4⋊C4×C47—21no—
75C4⋊C4×C47—21no—
76C4⋊C4×C47—41no—
77C4⋊C4×C47—41no—
78C4⋊C4×C47—41no—
79C42×C47—41no—
80C4⋊Dic47—21no—
81C4⋊Dic47—21no—
82C4⋊Dic47—42no—
83C4⋊Dic47—41no—
84Dic47⋊C4—41no—
85Dic47⋊C4—41no—
86Dic47⋊C4—42no—
87C4×Dic47—21no—
88C4×Dic47—21no—
89C4×Dic47—21no—
90C4×Dic47—21no—
91C4×Dic47—21no—
92C4×Dic47—21no—
93C4×Dic47—22no—
94C4×Dic47—22no—
95C4×Dic47—22no—
96C2×C47⋊C8—22no—
97C2×C47⋊C8—22no—
98C2×C47⋊C8—41no—
99C2×C47⋊C8—41no—
100C2×C47⋊C8—41no—
101C2×C47⋊C8—41no—
102C23×C47C2×C22⋊C411yescharacteristic
103C2×C4×C47—21no—
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—41no—
110C2×C4×C47—41no—
111C2×C4×C47—41no—
112C2×C4×C47—41no—
113C2×C4×C47—41no—
114C2×C4×C47—41no—
115C2×C4×C47#13111yescharacteristic
116C2×C4×C47#13111yescharacteristic
117C2×C4×C47#13511yescharacteristic
118C2×C4×C47#13511yescharacteristic
119C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C47#13711yescharacteristic
121C2×Dic47—21no—
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#10112yes—
137C2×Dic47#10412yes—
138C2×Dic47#10412yes—
139C8×C47—42no—
140C8×C47—42no—
141C47⋊C8—42no—
142C47⋊C8—42no—
143#7677—471nomaximal, Sylow
144C22×C47#40811yescharacteristic
145C22×C47#41011yescharacteristic
146C22×C47C2×#10111yescharacteristic
147C22×C47#41611yescharacteristic
148C22×C47#41711yescharacteristic
149C22×C47C2×#10411yescharacteristic
150C22×C47C2×#10411yescharacteristic
151C4×C47—21no—
152C4×C47—21no—
153C4×C47—21no—
154C4×C47—21no—
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—81no—
158C4×C47—81no—
159Dic47—22no—
160Dic47—22no—
161Dic47—22no—
162Dic47—41no—
163Dic47—81no—
164Dic47—81no—
165#2864—471no—
166C4×C4⋊C8—471no—
167#1745—471no—
168#1271—471no—
169#1271—471no—
170#1271—471no—
171#1271D4711yescharacteristic
172C2×C47#147011yescharacteristic
173C2×C47#148311yescharacteristic
174C2×C47#149411yescharacteristic
175C2×C47#150011yescharacteristic
176C2×C47#150911yescharacteristic
177C2×C47#152611yescharacteristic
178C2×C47#155211yescharacteristic
179C2×C4⋊C8—941no—
180C2×#97—941no—
181C2×C4×C8—941no—
182#389—471no—
183#389—471no—
184#389—471no—
185#389C2×D4711yescharacteristic
186#387—941no—
187#387—941no—
188#387—941no—
189#387—941no—
190#382—471no—
191#382—471no—
192C43—471no—
193#336—471no—
194#336—471no—
195#336—941no—
196#336C2×D4711yescharacteristic
197#336C2×D4711yescharacteristic
198C47#767711yescharacteristic, complemented, Sylow
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—941no—
202C22×C8—941no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—471no—
205C2×C4⋊C4—471no—
206C2×C4⋊C4—941no—
207C2×C4⋊C4—941no—
208C2×C4⋊C4—941no—
209C2×C4⋊C4C4×D4711yescharacteristic
210C2×C4⋊C4C4×D4711yescharacteristic
211C2×C42—471no—
212C2×C42—471no—
213C2×C42—471no—
214C2×C42—471no—
215C2×C42—471no—
216C2×C42—471no—
217C2×C42C22×D4711yescharacteristic
218C4⋊C8—944no—
219#97—944no—
220C4×C8—1882no—
221#95—21no—
222#95—941no—
223#95—941no—
224#95—941no—
225#95—941no—
226#95—941no—
227#95—941no—
228#95—941no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—471no—
232C22×C4—471no—
233C22×C4—471no—
234C22×C4—471no—
235C22×C4—941no—
236C22×C4—941no—
237C22×C4C2×C4×D4711yescharacteristic
238C22×C4D4×D4711yescharacteristic
239C22×C4D4×D4711yescharacteristic
240C2×C8—22no—
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—942no—
247C2×C8—942no—
248C2×C8—1881no—
249C2×C8—1881no—
250C2×C8—1881no—
251C2×C8—1881no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4—1881no—
260C4⋊C4—1882no—
261C4⋊C4—1882no—
262C4⋊C4—1881no—
263C4⋊C4—1881no—
264C42—41no—
265C42—942no—
266C42—942no—
267C42—942no—
268C42—941no—
269C42—941no—
270C42—941no—
271C42—941no—
272C42—941no—
273C42—941no—
274C23C22⋊C4×D4711yescharacteristic
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—472no—
288C2×C4—472no—
289C2×C4—472no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—1881no—
300C2×C4—1881no—
301C2×C4—1881no—
302C2×C4—1881no—
303C2×C4—1881no—
304C2×C4—1881no—
305C2×C4#1309403011yescharacteristic
306C2×C4#1309403211yescharacteristic
307C2×C4#1309404511yescharacteristic
308C2×C4#1309404711yescharacteristic
309C2×C4#1309404811yescharacteristic
310C2×C4#1309405311yescharacteristic
311C8—42no—
312C8—42no—
313C8—1882no—
314C8—1882no—
315C22#1568908811yescharacteristic
316C22#1568909511yescharacteristic
317C22#101×D4711yescharacteristic
318C22#1568911811yescharacteristic
319C22#1568912111yescharacteristic
320C22#104×D4711yescharacteristic
321C22#104×D4711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—81no—
329C4—81no—
330C4—942no—
331C4—942no—
332C4—942no—
333C4—3761no—
334C4—3761no—
335C4—1881no—
336C2#2024174211yescharacteristic
337C2#2024179811yescharacteristic
338C2#2024184711yescharacteristic
339C2#2024187311yescharacteristic
340C2#2024191011yescharacteristic
341C2#2024198111yescharacteristic
342C2#2024208711yescharacteristic
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#7677
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
198. C47#7677semidirect

Maximal subgroups

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

subgroupindex
#202517742
#202432362
#202431352
#202412122
#202412112
#202412102
C47×#12712
#767747