Finite Group Databasebeta

← #26104370

Subgroups — #26104370

Order 12032.

406 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 109 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#20245859C211yesmaximal, characteristic
2#20243530C211yesmaximal, characteristic
3#20243503C211yesmaximal, characteristic
4#20241213C211yesmaximal, characteristic
5#20241213C211yesmaximal, characteristic
6#20241211C211yesmaximal, characteristic
7C47×#1271C211yesmaximal, characteristic
8C2×#13093989C411yescharacteristic
9C2×Dic47⋊C8—21no—
10#15689029C2211yescharacteristic
11#15689028C411yescharacteristic
12#15689022C411yescharacteristic
13#15689010—21no—
14#15689004—21no—
15C4⋊C4×Dic47—21no—
16C4⋊C4×Dic47C411yescharacteristic
17#15688968—21no—
18C42×Dic47C2211yescharacteristic
19#15688878C2211yescharacteristic
20#15688878C2211yescharacteristic
21#15688877—21no—
22#15688877—21no—
23#15688877—21no—
24C47×#389C2211yescharacteristic
25C47×#336C2211yescharacteristic
26C47×#336C2211yescharacteristic
27C22×Dic94C2×C411yescharacteristic
28C22×C47⋊C8—21no—
29C22×C47⋊C8—21no—
30#13093989—22no—
31#13093989C814yescomplemented
32C2×C4⋊Dic47—21no—
33C2×C4⋊Dic47C2×C411yescharacteristic
34C2×Dic47⋊C4—21no—
35C2×C4×Dic47—21no—
36C2×C4×Dic47—21no—
37C2×C4×Dic47C2×C411yescharacteristic
38C2×C4×Dic47C2×C411yescharacteristic
39C2×C4×Dic47D411yescharacteristic
40C2×C4×Dic47D411yescharacteristic
41C2×C4×Dic47D411yescharacteristic
42C2×C4×Dic47D411yescharacteristic
43Dic47⋊C8—42no—
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×Dic94—21no—
69C2×Dic94—41no—
70C2×Dic94—41no—
71C2×Dic94C2×C812yes—
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—21no—
79C4⋊C4×C47—41no—
80C4⋊C4×C47—41no—
81C4⋊C4×C47—41no—
82C4⋊C4×C47C2×C812yes—
83C42×C47—41no—
84C4⋊Dic47—42no—
85C4⋊Dic47—41no—
86Dic47⋊C4—24no—
87C4×Dic47—21no—
88C4×Dic47—21no—
89C4×Dic47—21no—
90C4×Dic47—21no—
91C4×Dic47—24no—
92C4×Dic47—41no—
93C4×Dic47—41no—
94C4×Dic47—41no—
95C4×Dic47—42no—
96C4×Dic47C2×C812yes—
97C4×Dic47M1612yes—
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
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—22no—
112C2×C4×C47—41no—
113C2×C4×C47—41no—
114C2×C4×C47—41no—
115C2×C4×C47—41no—
116C2×C4×C47—41no—
117C2×C4×C47C22×C811yescharacteristic
118C2×C4×C47C2×M1611yescharacteristic
119C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C47#13711yescharacteristic
121C2×C4×C47#13711yescharacteristic
122C2×C4×C47#13711yescharacteristic
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—22no—
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×Dic47C22⋊C812yes—
140C2×Dic47C22⋊C812yes—
141Dic94—42no—
142Dic94—42no—
143C8×C47—81no—
144C8×C47—81no—
145C47⋊C8—81no—
146C47⋊C8—81no—
147#7596—471nomaximal, Sylow
148C22×C47C2×C22⋊C811yescharacteristic
149C22×C47#41011yescharacteristic
150C22×C47#41311yescharacteristic
151C22×C47#41711yescharacteristic
152C22×C47#41911yescharacteristic
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#1272—471no—
174#1271—471no—
175#1271D4711yescharacteristic
176C2×C47#145811yescharacteristic
177C2×C47#147711yescharacteristic
178C2×C47#147911yescharacteristic
179C2×C47#151211yescharacteristic
180C2×C47#151511yescharacteristic
181C2×C47#153511yescharacteristic
182C2×C47#155911yescharacteristic
183C2×C4×Q8—471no—
184C2×C4⋊C8—941no—
185#391—471no—
186#391—471no—
187#389—471no—
188#389C2×D4711yescharacteristic
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#759611yescharacteristic, complemented, Sylow
203C22×Q8—471no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—941no—
207C22×C8—941no—
208C4×Q8—474no—
209C4×Q8—942no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—471no—
212C2×C4⋊C4—941no—
213C2×C4⋊C4—941no—
214C2×C4⋊C4C4×D4711yescharacteristic
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—941no—
228#95—941no—
229#95—941no—
230#95—941no—
231#95—941no—
232#95—941no—
233C2×Q8—472no—
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—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—21no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—944no—
265C4⋊C4—1881no—
266C4⋊C4—1882no—
267C4⋊C4C8×D4712yes—
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—1882no—
282Q8—1882no—
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×C4C2×C8×D4711yescharacteristic
314C2×C4M16×D4711yescharacteristic
315C2×C4#1309404811yescharacteristic
316C2×C4#1309405311yescharacteristic
317C2×C4#1309405311yescharacteristic
318C2×C4#1309405611yescharacteristic
319C8—81no—
320C8—81no—
321C8—3761no—
322C8—3761no—
323C22C22⋊C8×D4711yescharacteristic
324C22#1568909511yescharacteristic
325C22#1568910611yescharacteristic
326C22#1568912111yescharacteristic
327C22#1568913011yescharacteristic
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—1882no—
342C4—1881no—
343C4—1881no—
344C2#2024170111yescharacteristic
345C2#2024177211yescharacteristic
346C2#2024178111yescharacteristic
347C2#2024192311yescharacteristic
348C2#2024193711yescharacteristic
349C2#2024201811yescharacteristic
350C2#2024211711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC47×#1271C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1271D47
hypocenterC47#7596
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
31. #13093989C8semidirect
202. C47#7596semidirect

Maximal subgroups

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

subgroupindex
#202458592
#202435302
#202435032
#202412132
#202412112
C47×#12712
#759647