Finite Group Databasebeta

← #26105225

Subgroups — #26105225

Order 12032.

380 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 83 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#20244721C211yesmaximal, characteristic
2#20244716C211yesmaximal, characteristic
3#20244634C211yesmaximal, characteristic
4#20241211C211yesmaximal, characteristic
5#20241211C211yesmaximal, characteristic
6#20241211C211yesmaximal, characteristic
7C47×#2810C211yesmaximal, characteristic
8C2×#13094024C2211yescharacteristic
9C2×#13093957—21no—
10C2×#13093955—21no—
11C2×#13093947—21no—
12C2×#13093947—21no—
13#15688885—21no—
14#15688885—21no—
15#15688878C2211yescharacteristic
16#15688878C2211yescharacteristic
17#15688878C2211yescharacteristic
18C47×#400—21no—
19C47×#400—21no—
20C47×#400—21no—
21C47×#389C2211yescharacteristic
22C47×#389C2211yescharacteristic
23C47×#389C2211yescharacteristic
24C47×#387—21no—
25C47×#387—21no—
26C47×#387—21no—
27C22×Dic94—21no—
28C22×C47⋊C8—21no—
29C22×C47⋊C8—21no—
30C22×C47⋊C8—21no—
31#13094024—42no—
32C2×C4⋊Dic47—21no—
33C2×C4⋊Dic47—21no—
34#13093957—42no—
35#13093955—42no—
36#13093947—42no—
37#13093947—42no—
38C2×C4⋊C4×C47—21no—
39C2×C4⋊C4×C47—21no—
40C2×C4⋊C4×C47—21no—
41C2×C4⋊C4×C47D411yescharacteristic
42C2×C4⋊C4×C47D411yescharacteristic
43C2×C4⋊C4×C47D411yescharacteristic
44C2×C4⋊C4×C47D411yescharacteristic
45C2×C4⋊C4×C47D411yescharacteristic
46C2×C4⋊C4×C47D411yescharacteristic
47C2×C42×C47—21no—
48C2×C42×C47C2311yescharacteristic
49#95×C47—21no—
50#95×C47—21no—
51#95×C47—21no—
52#95×C47—21no—
53#95×C47—21no—
54#95×C47—21no—
55#95×C47—21no—
56#95×C47—21no—
57#95×C47—21no—
58#95×C47—21no—
59C22×C4×C47—21no—
60C22×C4×C47—21no—
61C22×C4×C47—21no—
62C22×C4×C47—21no—
63C22×C4×C47—21no—
64C22×C4×C47—21no—
65C22×C4×C47C2×D411yescharacteristic
66C22×C4×C47C2×D411yescharacteristic
67C22×C4×C47C2×D411yescharacteristic
68C22×Dic47—41no—
69C2×Dic94—22no—
70C2×Dic94—41no—
71C2×Dic94—41no—
72C2×Dic94—41no—
73C2×Dic94—41no—
74C2×Dic94—41no—
75C4⋊C4×C47—21no—
76C4⋊C4×C47—21no—
77C4⋊C4×C47—21no—
78C4⋊C4×C47—21no—
79C4⋊C4×C47—21no—
80C4⋊C4×C47—21no—
81C4⋊C4×C47—41no—
82C4⋊C4×C47—41no—
83C4⋊C4×C47—41no—
84C4⋊C4×C47—41no—
85C4⋊C4×C47—41no—
86C4⋊C4×C47—41no—
87C4⋊C4×C47—41no—
88C4⋊C4×C47—41no—
89C4⋊C4×C47—41no—
90C42×C47—41no—
91C42×C47—81no—
92C4⋊Dic47—22no—
93C4⋊Dic47—22no—
94C4⋊Dic47—41no—
95C4⋊Dic47—41no—
96C2×C47⋊C8—22no—
97C2×C47⋊C8—22no—
98C2×C47⋊C8—41no—
99C2×C47⋊C8—41no—
100C2×C47⋊C8—41no—
101C2×C47⋊C8—41no—
102C2×C47⋊C8—41no—
103C2×C47⋊C8—41no—
104C2×C47⋊C8—41no—
105C23×C47#12011yescharacteristic
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—41no—
113C2×C4×C47—41no—
114C2×C4×C47—41no—
115C2×C4×C47—41no—
116C2×C4×C47—41no—
117C2×C4×C47—41no—
118C2×C4×C47—41no—
119C2×C4×C47—41no—
120C2×C4×C47—41no—
121C2×C4×C47—41no—
122C2×C4×C47—41no—
123C2×C4×C47—41no—
124C2×C4×C47—41no—
125C2×C4×C47—41no—
126C2×C4×C47—41no—
127C2×C4×C47—41no—
128C2×C4×C47—41no—
129C2×C4×C47—41no—
130C2×C4×C47#13511yescharacteristic
131C2×C4×C47#13511yescharacteristic
132C2×C4×C47#13511yescharacteristic
133C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C47#13711yescharacteristic
135C2×C4×C47#13711yescharacteristic
136C2×Dic47—42no—
137C2×Dic47—81no—
138C2×Dic47—81no—
139Dic94—42no—
140Dic94—42no—
141Dic94—81no—
142Dic94—81no—
143C47⋊C8—42no—
144C47⋊C8—42no—
145C47⋊C8—81no—
146#7775—471nomaximal, Sylow
147C22×C47#44911yescharacteristic
148C22×C47#45211yescharacteristic
149C22×C47#45211yescharacteristic
150C22×C47#45411yescharacteristic
151C22×C47#45611yescharacteristic
152C22×C47#45611yescharacteristic
153C22×C47B(4,𝔽2)11yescharacteristic
154C4×C47—21no—
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—21no—
159C4×C47—21no—
160C4×C47—81no—
161C4×C47—81no—
162C4×C47—81no—
163C4×C47—81no—
164C4×C47—81no—
165C4×C47—81no—
166Dic47—82no—
167#2810D4711yescharacteristic
168#2058—471no—
169#2057—471no—
170#2043—471no—
171#1271—471no—
172#1271—471no—
173#1271—471no—
174C2×C47#159711yescharacteristic
175C2×C47#160311yescharacteristic
176C2×C47#160311yescharacteristic
177C2×C47#163811yescharacteristic
178C2×C47#165011yescharacteristic
179C2×C47#165211yescharacteristic
180C2×C47#166311yescharacteristic
181C2×C4⋊Q8—471no—
182C2×#107—941no—
183C2×#106—941no—
184C2×#103—941no—
185C2×#103—941no—
186#400—21no—
187#400—21no—
188#400—21no—
189#389C2×D4711yescharacteristic
190#389C2×D4711yescharacteristic
191#389C2×D4711yescharacteristic
192#387—21no—
193#387—21no—
194#387—21no—
195#340—941no—
196#340—941no—
197#336—471no—
198#336—471no—
199#336—471no—
200C47#777511yescharacteristic, complemented, Sylow
201C22×Q8—941no—
202C22×C8—941no—
203C22×C8—941no—
204C22×C8—941no—
205C4⋊Q8—1882no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—941no—
210C2×C4⋊C4—941no—
211C2×C4⋊C4C22⋊D4711yescharacteristic
212C2×C4⋊C4C22⋊D4711yescharacteristic
213C2×C4⋊C4C22⋊D4711yescharacteristic
214C2×C4⋊C4C22⋊D4711yescharacteristic
215C2×C4⋊C4C22⋊D4711yescharacteristic
216C2×C4⋊C4C22⋊D4711yescharacteristic
217C2×C42—21no—
218C2×C42C22×D4711yescharacteristic
219#107—1882no—
220#106—1882no—
221#103—1882no—
222#103—1882no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233C2×Q8—942no—
234C2×Q8—1881no—
235C2×Q8—1881no—
236C2×Q8—1881no—
237C2×Q8—1881no—
238C2×Q8—1881no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—1881no—
246C22×C4C2×C22⋊D4711yescharacteristic
247C22×C4C2×C22⋊D4711yescharacteristic
248C22×C4C2×C22⋊D4711yescharacteristic
249C2×C8—942no—
250C2×C8—942no—
251C2×C8—1881no—
252C2×C8—1881no—
253C2×C8—1881no—
254C2×C8—1881no—
255C2×C8—1881no—
256C2×C8—1881no—
257C2×C8—1881no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—942no—
274C4⋊C4—942no—
275C4⋊C4—1881no—
276C4⋊C4—1881no—
277C42—41no—
278C42—81no—
279C23#1309399311yescharacteristic
280Q8—3761no—
281Q8—3761no—
282Q8—1882no—
283Q8—1882no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—3761no—
309C2×C4—3761no—
310C2×C4—1882no—
311C2×C4#1309404411yescharacteristic
312C2×C4#1309404411yescharacteristic
313C2×C4#1309404411yescharacteristic
314C2×C4#1309404911yescharacteristic
315C2×C4#1309405411yescharacteristic
316C2×C4#1309405411yescharacteristic
317C8—3761no—
318C8—1882no—
319C8—1882no—
320C22#1568926811yescharacteristic
321C22#1568928511yescharacteristic
322C22#1568928511yescharacteristic
323C22#1568929611yescharacteristic
324C22#1568930611yescharacteristic
325C22#1568930611yescharacteristic
326C22#1568931011yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—81no—
334C4—81no—
335C4—81no—
336C4—81no—
337C4—81no—
338C4—81no—
339C4—3762no—
340C2#2024231711yescharacteristic
341C2#2024235111yescharacteristic
342C2#2024235111yescharacteristic
343C2#2024256011yescharacteristic
344C2#2024264411yescharacteristic
345C2#2024265811yescharacteristic
346C2#2024271611yescharacteristic
subgroupG/H
centerC23#13093993
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#2810C2
socle, prime radicalC23×C47#120
hypercenter#2810D47
hypocenterC47#7775
LCSG ▷ C2×C42×C47 ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2810

Complements

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

NH ≅ G/Ntype
200. C47#7775semidirect

Maximal subgroups

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

subgroupindex
#202447212
#202447162
#202446342
#202412112
C47×#28102
#777547