Finite Group Databasebeta

← #26104568

Subgroups — #26104568

Order 12032.

402 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 105 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#20245863C211yesmaximal, characteristic
2#20243530C211yesmaximal, characteristic
3#20243503C211yesmaximal, characteristic
4#20241214C211yesmaximal, characteristic
5#20241212C211yesmaximal, characteristic
6#20241210C211yesmaximal, characteristic
7C47×#1272C211yesmaximal, characteristic
8C2×Q8×Dic47C411yescharacteristic
9C2×Dic47⋊C8—21no—
10#15689030C411yescharacteristic
11#15689021C2211yescharacteristic
12#15689019C411yescharacteristic
13#15689008—21no—
14#15689006—21no—
15C4⋊C4×Dic47C411yescharacteristic
16#15688974—21no—
17#15688968—21no—
18C42×Dic47C2211yescharacteristic
19#15688878C2211yescharacteristic
20#15688878C2211yescharacteristic
21#15688877—21no—
22#15688877—21no—
23#15688877—21no—
24C47×#391C2211yescharacteristic
25C47×#336C2211yescharacteristic
26C47×#336C2211yescharacteristic
27C22×C47⋊C8—21no—
28C22×C47⋊C8—21no—
29Q8×Dic47—22no—
30Q8×Dic47—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
44Dic47⋊C8—42no—
45C47⋊#95—21no—
46C47⋊#95—21no—
47C47⋊#95—21no—
48C47⋊#95—21no—
49C47⋊#95—21no—
50C22×Q8×C47C2×C411yescharacteristic
51C22×C8×C47—21no—
52C22×C8×C47—21no—
53C2×C4⋊C4×C47C2×C411yescharacteristic
54C2×C42×C47C2311yescharacteristic
55#95×C47—21no—
56#95×C47—21no—
57C2×Q8×C47—21no—
58C2×Q8×C47—41no—
59C2×Q8×C47—41no—
60C2×Q8×C47M1612yes—
61C22×C4×C47—21no—
62C22×C4×C47—21no—
63C22×C4×C47C22×C411yescharacteristic
64C22×C4×C47C2×D411yescharacteristic
65C22×C4×C47C2×D411yescharacteristic
66C22×Dic47—21no—
67C22×Dic47—21no—
68C22×Dic47C22⋊C411yescharacteristic
69C22×Dic47C22⋊C411yescharacteristic
70C22×Dic47C22⋊C411yescharacteristic
71C22×Dic47C22⋊C411yescharacteristic
72C2×C8×C47—41no—
73C2×C8×C47—41no—
74C2×C8×C47—41no—
75C2×C8×C47—41no—
76C2×C8×C47—41no—
77C2×C8×C47—41no—
78C4⋊C4×C47—41no—
79C42×C47—41no—
80C4⋊Dic47—24no—
81C4⋊Dic47—21no—
82C4⋊Dic47—41no—
83C4⋊Dic47M1612yes—
84Dic47⋊C4—42no—
85Dic47⋊C4—41no—
86Dic47⋊C4—41no—
87C4×Dic47—24no—
88C4×Dic47—21no—
89C4×Dic47—21no—
90C4×Dic47—21no—
91C4×Dic47—21no—
92C4×Dic47—41no—
93C4×Dic47—41no—
94C4×Dic47—41no—
95C4×Dic47—42no—
96C4×Dic47SD1612yes—
97C4×Dic47Q1612yes—
98C2×C47⋊C8—41no—
99C2×C47⋊C8—41no—
100C2×C47⋊C8—41no—
101C2×C47⋊C8—41no—
102C2×C47⋊C8—41no—
103C2×C47⋊C8—41no—
104C23×C47C2×C22⋊C411yescharacteristic
105Q8×C47—42no—
106Q8×C47—42no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—22no—
114C2×C4×C47—41no—
115C2×C4×C47—41no—
116C2×C4×C47—41no—
117C2×C4×C47—41no—
118C2×C4×C47—41no—
119C2×C4×C47C2×M1611yescharacteristic
120C2×C4×C47C2×M1611yescharacteristic
121C2×C4×C47C2×SD1611yescharacteristic
122C2×C4×C47C2×Q1611yescharacteristic
123C2×C4×C47#13511yescharacteristic
124C2×C4×C47#13511yescharacteristic
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—22no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—41no—
137C2×Dic47—41no—
138C2×Dic47—41no—
139C2×Dic47—41no—
140C2×Dic47—41no—
141C2×Dic47#10312yes—
142C2×Dic47#10312yes—
143C8×C47—81no—
144C8×C47—81no—
145C47⋊C8—81no—
146C47⋊C8—81no—
147#7644—471nomaximal, Sylow
148C22×C47#40711yescharacteristic
149C22×C47#41011yescharacteristic
150C22×C47#41311yescharacteristic
151C22×C47C2×#10311yescharacteristic
152C22×C47#41611yescharacteristic
153C22×C47#42111yescharacteristic
154C22×C47#42111yescharacteristic
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—21no—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—42no—
162C4×C47—81no—
163Dic47—22no—
164Dic47—22no—
165Dic47—41no—
166Dic47—42no—
167Dic47—41no—
168Dic47—81no—
169#2295—471no—
170#1839—471no—
171#1831—471no—
172#1272—471no—
173#1272D4711yescharacteristic
174#1271—471no—
175#1271—471no—
176C2×C47#146411yescharacteristic
177C2×C47#148711yescharacteristic
178C2×C47#148811yescharacteristic
179C2×C47#151811yescharacteristic
180C2×C47#152111yescharacteristic
181C2×C47#153511yescharacteristic
182C2×C47#154211yescharacteristic
183C2×C4×Q8—471no—
184C2×C4⋊C8—941no—
185#391—471no—
186#391C2×D4711yescharacteristic
187#389—471no—
188#389—471no—
189#387—941no—
190#387—941no—
191C4×C4⋊C4—471no—
192C4×C4⋊C4—941no—
193#376—941no—
194C43—471no—
195#336—471no—
196#336—471no—
197#336—941no—
198#336—941no—
199#336—941no—
200#336C2×D4711yescharacteristic
201#336C2×D4711yescharacteristic
202C47#764411yescharacteristic, complemented, Sylow
203C22×Q8C4×D4711yescharacteristic
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—941no—
207C22×C8—941no—
208C4×Q8—942no—
209C4×Q8—942no—
210C2×C4⋊C4—471no—
211C2×C4⋊C4—471no—
212C2×C4⋊C4—941no—
213C2×C4⋊C4—941no—
214C2×C4⋊C4—941no—
215C2×C4⋊C4C4×D4711yescharacteristic
216C2×C42—471no—
217C2×C42—471no—
218C2×C42—471no—
219C2×C42—471no—
220C2×C42—471no—
221C2×C42—471no—
222C2×C42—941no—
223C2×C42—941no—
224C2×C42C22×D4711yescharacteristic
225C4⋊C8—1882no—
226#95—21no—
227#95—21no—
228#95—941no—
229#95—941no—
230#95—941no—
231#95—941no—
232#95—941no—
233C2×Q8—21no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8#1062532412yes—
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—41no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—1881no—
255C2×C8—1881no—
256C2×C8—1881no—
257C2×C8—1881no—
258C2×C8—1881no—
259C2×C8—1881no—
260C4⋊C4—41no—
261C4⋊C4—472no—
262C4⋊C4—944no—
263C4⋊C4—941no—
264C4⋊C4—1881no—
265C4⋊C4—1882no—
266C4⋊C4—1881no—
267C4⋊C4—1881no—
268C42—41no—
269C42—472no—
270C42—472no—
271C42—944no—
272C42—941no—
273C42—941no—
274C42—941no—
275C42—941no—
276C42—1881no—
277C42—1881no—
278C42—1881no—
279C42—1882no—
280C23C22⋊C4×D4711yescharacteristic
281Q8—42no—
282Q8—42no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—472no—
296C2×C4—472no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—942no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—1881no—
309C2×C4—1881no—
310C2×C4—1881no—
311C2×C4—1881no—
312C2×C4—1881no—
313C2×C4M16×D4711yescharacteristic
314C2×C4C2×#1062532411yescharacteristic
315C2×C4SD16×D4711yescharacteristic
316C2×C4Q16×D4711yescharacteristic
317C2×C4#1309404511yescharacteristic
318C2×C4#1309404711yescharacteristic
319C8—81no—
320C8—81no—
321C8—3761no—
322C8—3761no—
323C22#1568908511yescharacteristic
324C22#1568909511yescharacteristic
325C22#1568910411yescharacteristic
326C22#103×D4711yescharacteristic
327C22#1568911811yescharacteristic
328C22#1568913811yescharacteristic
329C22#1568913811yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—42no—
337C4—81no—
338C4—942no—
339C4—942no—
340C4—3761no—
341C4—1881no—
342C4—1881no—
343C4—1882no—
344C2#2024171911yescharacteristic
345C2#2024181511yescharacteristic
346C2#2024182111yescharacteristic
347C2#2024195011yescharacteristic
348C2#2024196411yescharacteristic
349C2#2024201611yescharacteristic
350C2#2024204211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1272C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1272D47
hypocenterC47#7644
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
202. C47#7644semidirect

Maximal subgroups

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

subgroupindex
#202458632
#202435302
#202435032
#202412142
#202412122
#202412102
C47×#12722
#764447