Finite Group Databasebeta

← #26112274

Subgroups — #26112274

Order 12032.

436 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 99 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#20252473C211yesmaximal, characteristic
2#20249264C211yesmaximal, characteristic
3#20241989C212yesmaximal
4#20241253C212yesmaximal
5C4×#101×C47C211yesmaximal, characteristic
6C2×#13094016C2211yescharacteristic
7#15689254—24no—
8#15689180—21no—
9#15689180C2212yes—
10#15689176—21no—
11#15689062C411yescharacteristic
12#15689062C411yescharacteristic
13#15689061—21no—
14#15689053C411yescharacteristic
15#15689053C411yescharacteristic
16#15689042—21no—
17#15689007—21no—
18#15689007—21no—
19#15688991C2211yescharacteristic
20#15688864—24no—
21C2×C4×Q8×C47C2211yescharacteristic
22C2×#101×C47—21no—
23C4×M16×C47C2212yes—
24C47×#343—21no—
25#13094016—22no—
26#13094016—22no—
27C2×C4⋊Dic47C2×C411yescharacteristic
28C2×C4⋊Dic47C2×C411yescharacteristic
29C2×Dic47⋊C4—21no—
30C2×Dic47⋊C4—21no—
31C2×Dic47⋊C4—21no—
32C2×Dic47⋊C4—21no—
33C4⋊(C47⋊C8)—22no—
34C4⋊(C47⋊C8)—22no—
35C4⋊(C47⋊C8)—22no—
36C22⋊(C47⋊C8)—22no—
37#13093935—22no—
38#13093935D414yes—
39C4×C47⋊C8—22no—
40C47⋊#95—21no—
41C47⋊#95—21no—
42C47⋊#95—21no—
43C47⋊#95—21no—
44C47⋊#95—21no—
45C47⋊#95—21no—
46C47⋊#95—21no—
47C47⋊#95—21no—
48C47⋊#95C2×C411yescharacteristic
49C47⋊#95C2×C411yescharacteristic
50C22×Q8×C47D411yescharacteristic
51C2×M16×C47—22no—
52C4×Q8×C47—22no—
53C4×Q8×C47—22no—
54C2×C4⋊C4×C47C2×C411yescharacteristic
55C2×C4⋊C4×C47C2×C411yescharacteristic
56C2×C4⋊C4×C47D411yescharacteristic
57C2×C42×C47D411yescharacteristic
58C2×C42×C47D411yescharacteristic
59C2×C42×C47C2311yescharacteristic
60#101×C47—24no—
61#97×C47—22no—
62C4×C8×C47—22no—
63C2×Q8×C47—22no—
64C2×Q8×C47—22no—
65C2×Q8×C47—41no—
66C22×C4×C47C22⋊C411yescharacteristic
67C22×C4×C47C22⋊C411yescharacteristic
68C22×C4×C47C22⋊C411yescharacteristic
69C22×C4×C47C22⋊C411yescharacteristic
70C22×C4×C47C22×C411yescharacteristic
71C22×C4×C47C2×D411yescharacteristic
72C22×C4×C47C2×D411yescharacteristic
73C22×Dic47—21no—
74C22×Dic47—21no—
75C22×Dic47—21no—
76C22×Dic47—21no—
77M16×C47—24no—
78M16×C47—42no—
79C2×C8×C47—42no—
80C4⋊C4×C47—22no—
81C4⋊C4×C47—22no—
82C4⋊C4×C47—22no—
83C42×C47—21no—
84C42×C47—21no—
85C42×C47—21no—
86C42×C47—21no—
87C42×C47C2×D412yes—
88C42×C47#4112yes—
89C4⋊Dic47—22no—
90C4⋊Dic47—22no—
91Dic47⋊C4—42no—
92Dic47⋊C4—42no—
93Dic47⋊C4—41no—
94Dic47⋊C4—42no—
95Dic47⋊C4—41no—
96C2×C47⋊C8—24no—
97C23×C47C2×C22⋊C411yescharacteristic
98Q8×C47—44no—
99C2×C4×C47—21no—
100C2×C4×C47—21no—
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47—21no—
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—41no—
109C2×C4×C47—41no—
110C2×C4×C47—41no—
111C2×C4×C47—41no—
112C2×C4×C47#10412yes—
113C2×C4×C47C4×D412yes—
114C2×C4×C47#12011yescharacteristic
115C2×C4×C47#12112yes—
116C2×C4×C47#12311yescharacteristic
117C2×Dic47—41no—
118C2×Dic47—41no—
119C2×Dic47—41no—
120C2×Dic47—41no—
121C2×Dic47—42no—
122C2×Dic47—41no—
123C2×Dic47—41no—
124C2×Dic47—41no—
125C2×Dic47—41no—
126C2×Dic47—41no—
127C2×Dic47—41no—
128C8×C47—44no—
129C47⋊C8—44no—
130#9190—471nomaximal, Sylow
131C22×C47—21no—
132C22×C47—21no—
133C22×C47#38611yescharacteristic
134C22×C47C2×#10411yescharacteristic
135C22×C47#42111yescharacteristic
136C4×C47—22no—
137C4×C47—22no—
138C4×C47—21no—
139C4×C47—21no—
140C4×C47—22no—
141C4×C47—41no—
142C4×C47—41no—
143C4×C47—41no—
144Dic47—81no—
145Dic47—81no—
146Dic47—81no—
147Dic47—81no—
148#2983—471no—
149#2634—471no—
150C4×#101D4711yescharacteristic
151#1528—472no—
152#1288—472no—
153C2×C47—21no—
154C2×C47—21no—
155C2×C47#187111yescharacteristic
156C2×C47#191211yescharacteristic
157C2×C47#191511yescharacteristic
158C2×#125—471no—
159C2×C4×Q8C2×D4711yescharacteristic
160#446—944no—
161#432—472no—
162#432—941no—
163#431—941no—
164C2×#101—21no—
165C4×M16C2×D4712yes—
166#400—471no—
167#400—471no—
168#400—941no—
169#398—471no—
170#398—471no—
171#395—941no—
172#387—941no—
173#387—941no—
174#383—471no—
175#343—21no—
176#330—944no—
177C47#919011yescharacteristic, complemented, Sylow
178C22×Q8C22⋊D4711yescharacteristic
179C2×M16—22no—
180#125—942no—
181#125—942no—
182C4×Q8—22no—
183C4×Q8—22no—
184C2×C4⋊C4—471no—
185C2×C4⋊C4—471no—
186C2×C4⋊C4—941no—
187C2×C4⋊C4—941no—
188C2×C4⋊C4—941no—
189C2×C4⋊C4—941no—
190C2×C4⋊C4C4×D4711yescharacteristic
191C2×C4⋊C4C4×D4711yescharacteristic
192C2×C4⋊C4C22⋊D4711yescharacteristic
193C2×C42D18811yescharacteristic
194C2×C42D18811yescharacteristic
195C2×C42C22×D4711yescharacteristic
196C4⋊C8—942no—
197C4⋊C8—942no—
198C4⋊C8—942no—
199#101—24no—
200C22⋊C8—942no—
201#97—22no—
202#97—474no—
203#97—942no—
204C4×C8—22no—
205C4×C8—942no—
206#95—471no—
207#95—471no—
208#95—941no—
209#95—941no—
210#95—941no—
211#95—941no—
212#95—941no—
213#95—941no—
214#95—941no—
215#95—941no—
216C2×Q8—22no—
217C2×Q8—22no—
218C2×Q8—41no—
219C22×C4—941no—
220C22×C4—941no—
221C22×C4—941no—
222C22×C4—941no—
223C22×C4(C2×D47)⋊C411yescharacteristic
224C22×C4(C2×D47)⋊C411yescharacteristic
225C22×C4(C2×D47)⋊C411yescharacteristic
226C22×C4(C2×D47)⋊C411yescharacteristic
227C22×C4C2×C4×D4711yescharacteristic
228C22×C4C2×D18811yescharacteristic
229C22×C4C2×C22⋊D4711yescharacteristic
230M16—24no—
231M16—42no—
232C2×C8—42no—
233C2×C8—944no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—942no—
238C4⋊C4—942no—
239C4⋊C4—1882no—
240C4⋊C4—1882no—
241C4⋊C4—1881no—
242C4⋊C4—1882no—
243C4⋊C4—1881no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42D4×D4712yes—
249C42#1062535212yes—
250C23C2×(C2×D47)⋊C411yescharacteristic
251Q8—44no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—1881no—
266C2×C4—1881no—
267C2×C4—1881no—
268C2×C4—1881no—
269C2×C4—1882no—
270C2×C4—1881no—
271C2×C4—1881no—
272C2×C4—1881no—
273C2×C4—1881no—
274C2×C4—1881no—
275C2×C4—1881no—
276C2×C4#1309395212yes—
277C2×C4(C22⋊D47)⋊C412yes—
278C2×C4#1309399411yescharacteristic
279C2×C4#1309399612yes—
280C2×C4#1309400811yescharacteristic
281C8—44no—
282C8—1884no—
283C22—21no—
284C22—21no—
285C22#1568900011yescharacteristic
286C22C2×#1309395211yescharacteristic
287C22#1568914111yescharacteristic
288C4—21no—
289C4—21no—
290C4—22no—
291C4—22no—
292C4—22no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—3761no—
297C4—3761no—
298C4—3761no—
299C4—3761no—
300C2—21no—
301C2—21no—
302C2#2024368811yescharacteristic
303C2#2024392311yescharacteristic
304C2#2024393811yescharacteristic
subgroupG/H
centerC22#15689000
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC4×#101×C47C2
socleC22×C47#386
prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenterC4×#101D47
hypocenterC47#9190
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
177. C47#9190semidirect

Maximal subgroups

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

subgroupindex
#202524732
#202492642
#202419892
#202412532
C4×#101×C472
#919047