Finite Group Databasebeta

← #26104594

Subgroups — #26104594

Order 12032.

384 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 99 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#20245947C211yesmaximal, characteristic
2#20243530C211yesmaximal, characteristic
3#20243530C211yesmaximal, characteristic
4#20241212C211yesmaximal, characteristic
5#20241211C211yesmaximal, characteristic
6#20241210C211yesmaximal, characteristic
7C47×#1271C211yesmaximal, characteristic
8C2×#13094015C411yescharacteristic
9#15689021C2211yescharacteristic
10#15689008—21no—
11#15689004—21no—
12#15688988C411yescharacteristic
13C4⋊C4×Dic47—21no—
14C4⋊C4×Dic47C411yescharacteristic
15C4⋊C4×Dic47C411yescharacteristic
16#15688974—21no—
17C42×Dic47C2211yescharacteristic
18#15688878C2211yescharacteristic
19#15688878C2211yescharacteristic
20#15688877—21no—
21#15688877—21no—
22#15688877—21no—
23#15688877—21no—
24C47×#389C2211yescharacteristic
25C47×#336C2211yescharacteristic
26C47×#336C2211yescharacteristic
27C22×C47⋊C8—21no—
28C22×C47⋊C8—21no—
29#13094015—22no—
30#13094015—22no—
31C2×C4⋊Dic47—21no—
32C2×C4⋊Dic47C2×C411yescharacteristic
33C2×C4⋊Dic47C2×C411yescharacteristic
34C2×Dic47⋊C4—21no—
35C2×Dic47⋊C4—21no—
36C2×C4×Dic47—21no—
37C2×C4×Dic47—21no—
38C2×C4×Dic47C2×C411yescharacteristic
39C2×C4×Dic47C2×C411yescharacteristic
40C2×C4×Dic47D411yescharacteristic
41C2×C4×Dic47D411yescharacteristic
42C2×C4×Dic47D411yescharacteristic
43C2×C4×Dic47D411yescharacteristic
44C47⋊#95—21no—
45C47⋊#95—21no—
46C47⋊#95—21no—
47C47⋊#95—21no—
48C47⋊#95—21no—
49C22×C8×C47—21no—
50C22×C8×C47—21no—
51C2×C4⋊C4×C47—21no—
52C2×C4⋊C4×C47C2×C411yescharacteristic
53C2×C4⋊C4×C47C2×C411yescharacteristic
54C2×C42×C47C2311yescharacteristic
55#95×C47—21no—
56C22×C4×C47—21no—
57C22×C4×C47—21no—
58C22×C4×C47C22×C411yescharacteristic
59C22×C4×C47C2×D411yescharacteristic
60C22×C4×C47C2×D411yescharacteristic
61C22×Dic47—21no—
62C22×Dic47—21no—
63C22×Dic47C22⋊C411yescharacteristic
64C22×Dic47C22⋊C411yescharacteristic
65C22×Dic47C22⋊C411yescharacteristic
66C22×Dic47C22⋊C411yescharacteristic
67C2×C8×C47—41no—
68C2×C8×C47—41no—
69C2×C8×C47—41no—
70C2×C8×C47—41no—
71C2×C8×C47—41no—
72C2×C8×C47—41no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47—41no—
75C4⋊C4×C47—41no—
76C4⋊C4×C47—41no—
77C4⋊C4×C47M1612yes—
78C42×C47—41no—
79C4⋊Dic47—24no—
80C4⋊Dic47—21no—
81C4⋊Dic47—41no—
82C4⋊Dic47M1612yes—
83Dic47⋊C4—24no—
84Dic47⋊C4—41no—
85Dic47⋊C4—41no—
86C4×Dic47—21no—
87C4×Dic47—21no—
88C4×Dic47—21no—
89C4×Dic47—21no—
90C4×Dic47—21no—
91C4×Dic47—21no—
92C4×Dic47—22no—
93C4×Dic47—41no—
94C4×Dic47—41no—
95C4×Dic47—42no—
96C4×Dic47—42no—
97C2×C47⋊C8—41no—
98C2×C47⋊C8—41no—
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—22no—
111C2×C4×C47—41no—
112C2×C4×C47—41no—
113C2×C4×C47—41no—
114C2×C4×C47—41no—
115C2×C4×C47—41no—
116C2×C4×C47C2×M1611yescharacteristic
117C2×C4×C47C2×M1611yescharacteristic
118C2×C4×C47#13511yescharacteristic
119C2×C4×C47#13511yescharacteristic
120C2×C4×C47#13511yescharacteristic
121C2×C4×C47#13511yescharacteristic
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—22no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—41no—
135C2×Dic47—41no—
136C2×Dic47—41no—
137C2×Dic47—41no—
138C2×Dic47—41no—
139C2×Dic47#10112yes—
140C8×C47—81no—
141C8×C47—81no—
142C47⋊C8—81no—
143C47⋊C8—81no—
144#7650—471nomaximal, Sylow
145C22×C47#40711yescharacteristic
146C22×C47#41011yescharacteristic
147C22×C47C2×#10111yescharacteristic
148C22×C47#41611yescharacteristic
149C22×C47#41611yescharacteristic
150C22×C47#42111yescharacteristic
151C22×C47#42111yescharacteristic
152C4×C47—21no—
153C4×C47—21no—
154C4×C47—21no—
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—42no—
159C4×C47—81no—
160Dic47—22no—
161Dic47—41no—
162Dic47—41no—
163Dic47—41no—
164Dic47—42no—
165Dic47—81no—
166C4×#125—471no—
167#1839—471no—
168#1839—471no—
169#1271—471no—
170#1271—471no—
171#1271—471no—
172#1271D4711yescharacteristic
173C2×C47#146711yescharacteristic
174C2×C47#148811yescharacteristic
175C2×C47#148811yescharacteristic
176C2×C47#152111yescharacteristic
177C2×C47#152111yescharacteristic
178C2×C47#153411yescharacteristic
179C2×C47#154411yescharacteristic
180C2×#125—471no—
181#389—471no—
182#389C2×D4711yescharacteristic
183#387—941no—
184#387—941no—
185#382—471no—
186C4×C4⋊C4—471no—
187C4×C4⋊C4—471no—
188C4×C4⋊C4—941no—
189C4×C4⋊C4—941no—
190C43—471no—
191#336—471no—
192#336—471no—
193#336—941no—
194#336—941no—
195#336—941no—
196#336—941no—
197#336C2×D4711yescharacteristic
198#336C2×D4711yescharacteristic
199C47#765011yescharacteristic, complemented, Sylow
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—941no—
203C22×C8—941no—
204#125—942no—
205#125—942no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—471no—
208C2×C4⋊C4—471no—
209C2×C4⋊C4—941no—
210C2×C4⋊C4—941no—
211C2×C4⋊C4—941no—
212C2×C4⋊C4C4×D4711yescharacteristic
213C2×C4⋊C4C4×D4711yescharacteristic
214C2×C42—471no—
215C2×C42—471no—
216C2×C42—471no—
217C2×C42—471no—
218C2×C42—471no—
219C2×C42—471no—
220C2×C42—941no—
221C2×C42—941no—
222C2×C42C22×D4711yescharacteristic
223#95—21no—
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—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—1881no—
247C2×C8—1881no—
248C2×C8—1881no—
249C2×C8—1881no—
250C2×C8—1881no—
251C2×C8—1881no—
252C4⋊C4—21no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—472no—
257C4⋊C4—944no—
258C4⋊C4—944no—
259C4⋊C4—941no—
260C4⋊C4—1881no—
261C4⋊C4—1881no—
262C4⋊C4—1881no—
263C4⋊C4#1062532412yes—
264C42—41no—
265C42—942no—
266C42—941no—
267C42—941no—
268C42—941no—
269C42—941no—
270C42—941no—
271C42—941no—
272C42—1881no—
273C42—1881no—
274C42—1882no—
275C42—1882no—
276C23C22⋊C4×D4711yescharacteristic
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—472no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—942no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—1881no—
303C2×C4—1881no—
304C2×C4—1881no—
305C2×C4—1881no—
306C2×C4—1881no—
307C2×C4M16×D4711yescharacteristic
308C2×C4C2×#1062532411yescharacteristic
309C2×C4#1309404311yescharacteristic
310C2×C4#1309404511yescharacteristic
311C2×C4#1309404511yescharacteristic
312C2×C4#1309404711yescharacteristic
313C8—81no—
314C8—81no—
315C8—3761no—
316C8—3761no—
317C22#1568908511yescharacteristic
318C22#1568909511yescharacteristic
319C22#101×D4711yescharacteristic
320C22#1568911611yescharacteristic
321C22#1568911811yescharacteristic
322C22#1568913811yescharacteristic
323C22#1568913811yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—42no—
331C4—81no—
332C4—942no—
333C4—3761no—
334C4—1881no—
335C4—1881no—
336C4—1881no—
337C4—1882no—
338C2#2024173011yescharacteristic
339C2#2024181911yescharacteristic
340C2#2024182111yescharacteristic
341C2#2024196211yescharacteristic
342C2#2024196411yescharacteristic
343C2#2024201311yescharacteristic
344C2#2024205111yescharacteristic
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#7650
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
199. C47#7650semidirect

Maximal subgroups

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

subgroupindex
#202459472
#202435302
#202412122
#202412112
#202412102
C47×#12712
#765047