Finite Group Databasebeta

← #26105239

Subgroups — #26105239

Order 12032.

392 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 87 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#20244716C211yesmaximal, characteristic
2#20244634C211yesmaximal, characteristic
3#20244529C211yesmaximal, characteristic
4#20241214C211yesmaximal, characteristic
5#20241211C211yesmaximal, characteristic
6#20241211C211yesmaximal, characteristic
7C47×#2805C211yesmaximal, characteristic
8C2×#13094024C2211yescharacteristic
9C2×#13093957—21no—
10C2×#13093948—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×#395—21no—
21C47×#391C2211yescharacteristic
22C47×#389—21no—
23C47×#389C2211yescharacteristic
24C47×#389C2211yescharacteristic
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#13093948—42no—
36#13093947—42no—
37#13093947—42no—
38C22×Q8×C47D411yescharacteristic
39C2×C4⋊C4×C47—21no—
40C2×C4⋊C4×C47—21no—
41C2×C4⋊C4×C47—21no—
42C2×C4⋊C4×C47—21no—
43C2×C4⋊C4×C47D411yescharacteristic
44C2×C4⋊C4×C47D411yescharacteristic
45C2×C4⋊C4×C47D411yescharacteristic
46C2×C4⋊C4×C47D411yescharacteristic
47C2×C4⋊C4×C47D411yescharacteristic
48C2×C42×C47—21no—
49C2×C42×C47C2311yescharacteristic
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—
59C2×Q8×C47—21no—
60C2×Q8×C47—21no—
61C2×Q8×C47—41no—
62C2×Q8×C47—41no—
63C22×C4×C47—21no—
64C22×C4×C47—21no—
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47—21no—
68C22×C4×C47—21no—
69C22×C4×C47C2×D411yescharacteristic
70C22×C4×C47C2×D411yescharacteristic
71C22×C4×C47C2×D411yescharacteristic
72C22×Dic47—41no—
73C2×Dic94—22no—
74C2×Dic94—41no—
75C2×Dic94—41no—
76C2×Dic94—41no—
77C2×Dic94—41no—
78C2×Dic94—41no—
79C4⋊C4×C47—21no—
80C4⋊C4×C47—21no—
81C4⋊C4×C47—21no—
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—81no—
90C4⋊C4×C47—81no—
91C4⋊C4×C47Q1612yes—
92C42×C47—41no—
93C42×C47—81no—
94C4⋊Dic47—22no—
95C4⋊Dic47—22no—
96C4⋊Dic47—41no—
97C4⋊Dic47—41no—
98C2×C47⋊C8—22no—
99C2×C47⋊C8—41no—
100C2×C47⋊C8—41no—
101C2×C47⋊C8—41no—
102C2×C47⋊C8—41no—
103C2×C47⋊C8—41no—
104C2×C47⋊C8—41no—
105C2×C47⋊C8—41no—
106C2×C47⋊C8—41no—
107C23×C47#12011yescharacteristic
108Q8×C47—42no—
109Q8×C47—81no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—22no—
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—41no—
131C2×C4×C47—41no—
132C2×C4×C47—41no—
133C2×C4×C47—41no—
134C2×C4×C47C2×Q1611yescharacteristic
135C2×C4×C47#13511yescharacteristic
136C2×C4×C47#13511yescharacteristic
137C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C47#13711yescharacteristic
139C2×C4×C47#13711yescharacteristic
140C2×Dic47—42no—
141C2×Dic47—81no—
142C2×Dic47—81no—
143Dic94—42no—
144Dic94—42no—
145Dic94—81no—
146Dic94—81no—
147C47⋊C8—42no—
148C47⋊C8—81no—
149C47⋊C8—81no—
150#7777—471nomaximal, Sylow
151C22×C47#44911yescharacteristic
152C22×C47#45111yescharacteristic
153C22×C47#45211yescharacteristic
154C22×C47#45411yescharacteristic
155C22×C47#45511yescharacteristic
156C22×C47#45611yescharacteristic
157C22×C47B(4,𝔽2)11yescharacteristic
158C4×C47—21no—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—21no—
162C4×C47—21no—
163C4×C47—21no—
164C4×C47—42no—
165C4×C47—81no—
166C4×C47—81no—
167C4×C47—81no—
168C4×C47—81no—
169C4×C47—81no—
170Dic47—82no—
171#2805D4711yescharacteristic
172#2057—471no—
173#2043—471no—
174#2024—471no—
175#1272—471no—
176#1271—471no—
177#1271—471no—
178C2×C47#159711yescharacteristic
179C2×C47#160511yescharacteristic
180C2×C47#160611yescharacteristic
181C2×C47#163611yescharacteristic
182C2×C47#164411yescharacteristic
183C2×C47#165011yescharacteristic
184C2×C47#166411yescharacteristic
185C2×C4⋊Q8—471no—
186C2×#107—941no—
187C2×#103—941no—
188C2×#103—941no—
189C2×#103—941no—
190#400—21no—
191#400—21no—
192#395—21no—
193#391C2×D4711yescharacteristic
194#389—21no—
195#389C2×D4711yescharacteristic
196#389C2×D4711yescharacteristic
197#387—21no—
198#387—21no—
199#340—941no—
200#340—941no—
201#336—471no—
202#336—471no—
203#336—471no—
204C47#777711yescharacteristic, complemented, Sylow
205C22×Q8—941no—
206C22×Q8C22⋊D4711yescharacteristic
207C22×C8—941no—
208C22×C8—941no—
209C22×C8—941no—
210C4⋊Q8—1882no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—941no—
216C2×C4⋊C4—941no—
217C2×C4⋊C4C22⋊D4711yescharacteristic
218C2×C4⋊C4C22⋊D4711yescharacteristic
219C2×C4⋊C4C22⋊D4711yescharacteristic
220C2×C4⋊C4C22⋊D4711yescharacteristic
221C2×C4⋊C4C22⋊D4711yescharacteristic
222C2×C42—21no—
223C2×C42C22×D4711yescharacteristic
224#107—1882no—
225#103—1882no—
226#103—1882no—
227#103—1882no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—942no—
242C2×Q8—1881no—
243C2×Q8—1881no—
244C2×Q8—1881no—
245C2×Q8—1881no—
246C2×Q8—1881no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—1881no—
254C22×C4C2×C22⋊D4711yescharacteristic
255C22×C4C2×C22⋊D4711yescharacteristic
256C22×C4C2×C22⋊D4711yescharacteristic
257C2×C8—942no—
258C2×C8—1881no—
259C2×C8—1881no—
260C2×C8—1881no—
261C2×C8—1881no—
262C2×C8—1881no—
263C2×C8—1881no—
264C2×C8—1881no—
265C2×C8—1881no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—81no—
277C4⋊C4—81no—
278C4⋊C4—942no—
279C4⋊C4—942no—
280C4⋊C4—1881no—
281C4⋊C4—1881no—
282C4⋊C4#1062533712yes—
283C42—41no—
284C42—81no—
285C23#1309399311yescharacteristic
286Q8—42no—
287Q8—81no—
288Q8—3761no—
289Q8—3761no—
290Q8—1882no—
291Q8—1882no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
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—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—3761no—
317C2×C4—3761no—
318C2×C4—1882no—
319C2×C4C2×#1062533711yescharacteristic
320C2×C4#1309404411yescharacteristic
321C2×C4#1309404411yescharacteristic
322C2×C4#1309404911yescharacteristic
323C2×C4#1309405411yescharacteristic
324C2×C4#1309405511yescharacteristic
325C8—3761no—
326C8—3761no—
327C8—1882no—
328C22#1568926811yescharacteristic
329C22#1568927911yescharacteristic
330C22#1568928511yescharacteristic
331C22#1568929611yescharacteristic
332C22#1568930111yescharacteristic
333C22#1568930611yescharacteristic
334C22#1568931011yescharacteristic
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—81no—
343C4—81no—
344C4—81no—
345C4—81no—
346C4—81no—
347C4—3762no—
348C2#2024231711yescharacteristic
349C2#2024236211yescharacteristic
350C2#2024236811yescharacteristic
351C2#2024254611yescharacteristic
352C2#2024260211yescharacteristic
353C2#2024264411yescharacteristic
354C2#2024272211yescharacteristic
subgroupG/H
centerC23#13093993
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#2805C2
socle, prime radicalC23×C47#120
hypercenter#2805D47
hypocenterC47#7777
LCSG ▷ C2×C42×C47 ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2805

Complements

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

NH ≅ G/Ntype
204. C47#7777semidirect

Maximal subgroups

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

subgroupindex
#202447162
#202446342
#202445292
#202412142
#202412112
C47×#28052
#777747