Finite Group Databasebeta

← #26111591

Subgroups — #26111591

Order 12032.

404 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 97 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#20253898C211yesmaximal, characteristic
2#20252489C211yesmaximal, characteristic
3#20241982C211yesmaximal, characteristic
4#20241809C211yesmaximal, characteristic
5#20241226C211yesmaximal, characteristic
6#20241224C211yesmaximal, characteristic
7C47×#1485C211yesmaximal, characteristic
8#15689680C2211yescharacteristic
9#15689526C411yescharacteristic
10#15689526C411yescharacteristic
11#15689522—22no—
12#15689519C411yescharacteristic
13#15689519C411yescharacteristic
14#15689253—21no—
15#15689250—21no—
16C8×Dic94—21no—
17#15689247—21no—
18#15689181—22no—
19#15689176C2211yescharacteristic
20#15689159—22no—
21C4×#10625329C2211yescharacteristic
22C2×C4×C47⋊C8C2211yescharacteristic
23#15688864—22no—
24Q8⋊(C47⋊C8)—21no—
25Q8⋊(C47⋊C8)—21no—
26C47×#533C2211yescharacteristic
27C47×#431C2211yescharacteristic
28C4×M16×C47C2211yescharacteristic
29C47×Q8⋊C8—21no—
30C47×Q8⋊C8—21no—
31C2×#10625329—21no—
32C22×C47⋊C8—21no—
33#13094024C2×C411yescharacteristic
34#13094024C2×C411yescharacteristic
35#13094016D412yes—
36#13094003—21no—
37#13094003—21no—
38C4×Dic94—21no—
39C4×Dic94—21no—
40#13093983D412yes—
41#13093957—22no—
42#13093957—22no—
43#13093955—22no—
44#13093955—22no—
45C4⋊(C47⋊C8)D411yescharacteristic
46C4⋊(C47⋊C8)D411yescharacteristic
47Dic47⋊C8—22no—
48Dic47⋊C8—22no—
49C22⋊(C47⋊C8)—21no—
50#13093935—21no—
51#13093934—22no—
52C4×C47⋊C8—21no—
53C4×C47⋊C8—21no—
54C4×C47⋊C8—21no—
55C4×C47⋊C8C2×C411yescharacteristic
56C4×C47⋊C8C2×C411yescharacteristic
57C8×Dic47—22no—
58C2×M16×C47—21no—
59C4⋊Q8×C47C2×C411yescharacteristic
60C4⋊Q8×C47C2×C411yescharacteristic
61#125×C47—21no—
62C22⋊Q8×C47—21no—
63C22⋊Q8×C47—21no—
64C4×Q8×C47—21no—
65C4×Q8×C47—21no—
66#117×C47—21no—
67C2×C42×C47C2311yescharacteristic
68C4⋊C8×C47D411yescharacteristic
69C4⋊C8×C47D411yescharacteristic
70C22⋊C8×C47—21no—
71#97×C47—21no—
72C4×C8×C47—21no—
73C4×C8×C47—21no—
74C2×Q8×C47—21no—
75C2×Q8×C47—21no—
76C22×C4×C47C2×D411yescharacteristic
77C22×C4×C47#4111yescharacteristic
78C22×C4×C47#4111yescharacteristic
79C2×Dic94—21no—
80C2×Dic94—21no—
81M16×C47—22no—
82M16×C47—41no—
83C2×C8×C47—21no—
84C2×C8×C47—21no—
85C2×C8×C47—41no—
86C4⋊C4×C47—21no—
87C4⋊C4×C47—21no—
88C4⋊C4×C47—21no—
89C4⋊C4×C47—21no—
90C4⋊C4×C47—41no—
91C4⋊C4×C47—41no—
92C22⋊C4×C47—41no—
93C42×C47—41no—
94C42×C47C22×C411yescharacteristic
95C42×C47C2×D411yescharacteristic
96C42×C47C2×D411yescharacteristic
97C42×C47C2×D411yescharacteristic
98C22⋊Dic47—22no—
99C4⋊Dic47—21no—
100C4⋊Dic47—21no—
101C4⋊Dic47C22⋊C412yes—
102C4⋊Dic47C22⋊C412yes—
103Dic47⋊C4—22no—
104Dic47⋊C4—22no—
105C4×Dic47—22no—
106#10625329—22no—
107#10625329—41no—
108C2×C47⋊C8—22no—
109C2×C47⋊C8—22no—
110C2×C47⋊C8—21no—
111C2×C47⋊C8—21no—
112C2×C47⋊C8—21no—
113C2×C47⋊C8—21no—
114C2×C47⋊C8—41no—
115C23×C47#12311yescharacteristic
116Q8×C47—41no—
117Q8×C47—41no—
118Q8×C47—41no—
119Q8×C47—41no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—41no—
127C2×C4×C47—41no—
128C2×C4×C47C2×C22⋊C411yescharacteristic
129C2×C4×C47C4×D411yescharacteristic
130C2×C4×C47C4×D411yescharacteristic
131C2×C4×C47#12011yescharacteristic
132C2×C4×C47#12111yescharacteristic
133C2×C4×C47#12111yescharacteristic
134C2×Dic47—22no—
135C2×Dic47—22no—
136Dic94—41no—
137Dic94—41no—
138Dic94—41no—
139Dic94—41no—
140C8×C47—42no—
141C8×C47—41no—
142C8×C47—41no—
143C47⋊C8—22no—
144C47⋊C8—22no—
145C47⋊C8—42no—
146C47⋊C8—41no—
147C47⋊C8—41no—
148#9068—471nomaximal, Sylow
149C22×C47—21no—
150C22×C47—21no—
151C22×C47—21no—
152C22×C47#38611yescharacteristic
153C4×C47—21no—
154C4×C47—21no—
155C4×C47—21no—
156C4×C47—81no—
157C4×C47—81no—
158C4×C47#44311yescharacteristic
159C4×C47#44311yescharacteristic
160C4×C47#44411yescharacteristic
161C4×C47#44411yescharacteristic
162C4×C47#45611yescharacteristic
163C4×C47#45611yescharacteristic
164Dic47—42no—
165Dic47—42no—
166#3160—471no—
167#2986—471no—
168#1526—471no—
169#1485—471no—
170#1485D4711yescharacteristic
171#1278—471no—
172#1278—471no—
173C2×C47—41no—
174C2×C47#187611yescharacteristic
175C2×C47#187611yescharacteristic
176C2×C47#188611yescharacteristic
177#533—471no—
178#533C2×D4711yescharacteristic
179#500—471no—
180#500—471no—
181#499—942no—
182#498—471no—
183#498—471no—
184#446—941no—
185#446—941no—
186C8×Q8—941no—
187C8×Q8—941no—
188#433—942no—
189#431—471no—
190#431C2×D4711yescharacteristic
191#427—942no—
192C4×M16—471no—
193C4×M16C2×D4711yescharacteristic
194C2×C4×C8—471no—
195#330—942no—
196Q8⋊C8—21no—
197Q8⋊C8—21no—
198Q8⋊C8—941no—
199Q8⋊C8—941no—
200C47#906811yescharacteristic, complemented, Sylow
201C2×M16—21no—
202C2×M16—941no—
203C22×C8—941no—
204C4⋊Q8—471no—
205C4⋊Q8—471no—
206C4⋊Q8C4×D4711yescharacteristic
207C4⋊Q8C4×D4711yescharacteristic
208#125—21no—
209#125—472no—
210C22⋊Q8—21no—
211C22⋊Q8—21no—
212C22⋊Q8—941no—
213C22⋊Q8—941no—
214C4×Q8—21no—
215C4×Q8—21no—
216C4×Q8—941no—
217C4×Q8—941no—
218#117—21no—
219#117—472no—
220C2×C42C22×D4711yescharacteristic
221#107—942no—
222#107—942no—
223#106—942no—
224#106—942no—
225C4⋊C8—471no—
226C4⋊C8—471no—
227C4⋊C8—942no—
228C4⋊C8—942no—
229C4⋊C8C22⋊D4711yescharacteristic
230C4⋊C8C22⋊D4711yescharacteristic
231C22⋊C8—21no—
232C22⋊C8—941no—
233#97—21no—
234#97—942no—
235#97—941no—
236C4×C8—21no—
237C4×C8—21no—
238C4×C8—471no—
239C4×C8—471no—
240C4×C8—942no—
241C4×C8—941no—
242C4×C8—941no—
243C4×C8—941no—
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—941no—
247C2×Q8—941no—
248C22×C4#1062535011yescharacteristic
249C22×C4D4×D4711yescharacteristic
250C22×C4#1062535211yescharacteristic
251M16—22no—
252M16—41no—
253M16—942no—
254M16—1881no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—41no—
258C2×C8—942no—
259C2×C8—942no—
260C2×C8—941no—
261C2×C8—941no—
262C2×C8—941no—
263C2×C8—941no—
264C2×C8—1881no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—472no—
272C4⋊C4—472no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4—942no—
276C4⋊C4—942no—
277C22⋊C4—41no—
278C22⋊C4—942no—
279C42—41no—
280C42—942no—
281C42C2×C4×D4711yescharacteristic
282C42D4×D4711yescharacteristic
283C42D4×D4711yescharacteristic
284C42C2×C22⋊D4711yescharacteristic
285C23#1309400611yescharacteristic
286Q8—41no—
287Q8—41no—
288Q8—41no—
289Q8—41no—
290Q8—1881no—
291Q8—1881no—
292Q8—1881no—
293Q8—1881no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—942no—
303C2×C4—942no—
304C2×C4C22⋊C4×D4711yescharacteristic
305C2×C4(C22⋊D47)⋊C411yescharacteristic
306C2×C4C4×C22⋊D4711yescharacteristic
307C2×C4#1309399211yescharacteristic
308C2×C4#1309399511yescharacteristic
309C2×C4#1309399711yescharacteristic
310C8—42no—
311C8—41no—
312C8—41no—
313C8—942no—
314C8—942no—
315C8—1882no—
316C8—1881no—
317C8—1881no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22#1568899911yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—81no—
326C4—81no—
327C4—1882no—
328C4—1882no—
329C4#1568923711yescharacteristic
330C4#1568923811yescharacteristic
331C4#1568924211yescharacteristic
332C4#1568924311yescharacteristic
333C4#1568930411yescharacteristic
334C4#1568930411yescharacteristic
335C2—41no—
336C2#2024371211yescharacteristic
337C2#2024371811yescharacteristic
338C2#2024377811yescharacteristic
subgroupG/H
centerC2×C4#13093992
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1485C2
socleC22×C47#386
prime radicalC23×C47#123
cosocleC2×C42×C47C23
hypercenter#1485D47
hypocenterC47#9068
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1485

Complements

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

NH ≅ G/Ntype
200. C47#9068semidirect

Maximal subgroups

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

subgroupindex
#202538982
#202524892
#202419822
#202418092
#202412262
#202412242
C47×#14852
#906847