Finite Group Databasebeta

← #26119357

Subgroups — #26119357

Order 12032.

476 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 89 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#20251663C211yesmaximal, characteristic, complemented
2#20244212C212yesmaximal
3#20244211C211yesmaximal, characteristic
4#20241270C212yesmaximal, complemented
5C47×#1295C211yesmaximal, characteristic, complemented
6C2×#13094021C2211yescharacteristic
7C2×#13093946—22no—
8C2×#13093946—22no—
9C2×#13093944—22no—
10C2×#13093935C2211yescharacteristic
11#15689057—22no—
12#15689056—22no—
13#15689055—22no—
14#15688989C2212yes—
15C2×#97×C47C2212yes—
16C47×#382C2211yescharacteristic
17C22×D188—21no—
18C22×D188—22no—
19C22×C47⋊C8—21no—
20#13094021—22no—
21#13094021—21no—
22#13094021Q812yes—
23C2×C4⋊Dic47—22no—
24C2×C4⋊Dic47D412yes—
25C2×C4⋊Dic47D412yes—
26C2×Dic47⋊C4—22no—
27C2×Dic47⋊C4—22no—
28#13093946—44no—
29#13093946—44no—
30#13093944—44no—
31#13093935—22no—
32C47⋊#95—22no—
33C47⋊#95—22no—
34C47⋊#95—22no—
35C22×C8×C47—22no—
36C2×C4⋊C4×C47D412yes—
37C2×C42×C47C2311yescharacteristic
38#97×C47—22no—
39#97×C47—22no—
40#95×C47—22no—
41C23×D47—41no—
42C22×C4×C47—22no—
43C22×C4×C47C2×D411yescharacteristic
44C22×C4×C47C2×D412yes—
45C22×Dic47—22no—
46C22×Dic47—22no—
47C2×D188—24no—
48C2×D188—22no—
49C2×D188—42no—
50C2×D188—42no—
51C2×D188—42no—
52C2×D188—42no—
53C2×D188—42no—
54C2×D188—42no—
55C2×D188—42no—
56C2×D188—41no—
57C2×C8×C47—24no—
58C2×C8×C47—42no—
59C2×C8×C47—42no—
60C4⋊C4×C47—42no—
61C42×C47C2×Q811yescharacteristic
62C42×C47#4112yes—
63C42×C47#4111yescharacteristic
64C4⋊Dic47—42no—
65C4⋊Dic47—42no—
66C4⋊Dic47—82no—
67Dic47⋊C4—82no—
68Dic47⋊C4—82no—
69C2×C47⋊C8—22no—
70C2×C47⋊C8—41no—
71C2×C47⋊C8—41no—
72C23×C47#12011yescharacteristic
73C22×D47—42no—
74C22×D47—82no—
75C22×D47—81no—
76C22×D47—82no—
77C22×D47—81no—
78C2×C4×C47—21no—
79C2×C4×C47—22no—
80C2×C4×C47—21no—
81C2×C4×C47—22no—
82C2×C4×C47—42no—
83C2×C4×C47—42no—
84C2×C4×C47—42no—
85C2×C4×C47C22⋊Q812yes—
86C2×C4×C47C22⋊Q811yescharacteristic
87C2×C4×C47#12412yes—
88C2×C4×C47#12411yescharacteristic
89C2×Dic47—42no—
90C2×Dic47—42no—
91C2×Dic47—42no—
92C2×Dic47—42no—
93C2×Dic47—42no—
94C2×Dic47—42no—
95D188—44no—
96D188—44no—
97D188—44no—
98D188—82no—
99D188—82no—
100D188—82no—
101C8×C47—44no—
102C47⋊C8—42no—
103#10360—471nomaximal, Sylow
104C22×C47#39311yescharacteristic
105C22×C47#45312yes—
106C22×C47#45311yescharacteristic
107C22×C47#45412yes—
108C22×C47#45411yescharacteristic
109C2×D47—84no—
110C2×D47—82no—
111C2×D47—162no—
112C2×D47—161no—
113C2×D47—161no—
114C4×C47—21no—
115C4×C47—22no—
116C4×C47—22no—
117C4×C47—21no—
118C4×C47—82no—
119Dic47—82no—
120Dic47—82no—
121#2845—471no—
122#1961—472no—
123#1961—471no—
124#1295—472no—
125#1295D4711yescharacteristic, complemented
126C2×C47#165612yes—
127C2×C47#165611yescharacteristic
128C2×C47#165811yescharacteristic
129C2×C47#202712yes—
130C2×C47#202711yescharacteristic
131D47—162no—
132C2×#127—471no—
133C2×#102—942no—
134C2×#102—942no—
135C2×#102—942no—
136C2×#97—471no—
137C2×#97C2×D4712yes—
138#398—942no—
139#398—942no—
140#398—942no—
141#382—472no—
142#382C2×D4711yescharacteristic
143C47#1036011yescharacteristic, complemented, Sylow
144C22×D4—941no—
145C22×D4—942no—
146C22×C8—22no—
147C22×C8—941no—
148#127—472no—
149#127—942no—
150#127—941no—
151C2×C4⋊C4—472no—
152C2×C4⋊C4—472no—
153C2×C4⋊C4—942no—
154C2×C4⋊C4—942no—
155C2×C4⋊C4—942no—
156C2×C4⋊C4D18812yes—
157C2×C42C22×D4711yescharacteristic
158#102—1884no—
159#102—1884no—
160#102—1884no—
161#97—22no—
162#97—22no—
163#97—942no—
164#95—22no—
165#95—942no—
166#95—942no—
167#95—942no—
168C24—1881no—
169C2×D4—944no—
170C2×D4—942no—
171C2×D4—1882no—
172C2×D4—1882no—
173C2×D4—1882no—
174C2×D4—1882no—
175C2×D4—1882no—
176C2×D4—1882no—
177C2×D4—1882no—
178C2×D4—1881no—
179C22×C4—22no—
180C22×C4—942no—
181C22×C4—942no—
182C22×C4C2×D18811yescharacteristic
183C22×C4D4×D4712yes—
184C2×C8—24no—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—942no—
188C2×C8—1881no—
189C2×C8—1881no—
190C4⋊C4—42no—
191C4⋊C4—3762no—
192C4⋊C4—3762no—
193C4⋊C4—3762no—
194C4⋊C4—1882no—
195C4⋊C4—1882no—
196C42#1062535012yes—
197C42#1062535211yescharacteristic
198C42Q8×D4711yescharacteristic
199C23—3762no—
200C23—3761no—
201C23—3762no—
202C23—3761no—
203C23—1882no—
204C23#1309399411yescharacteristic
205D4—3762no—
206D4—3762no—
207D4—3762no—
208D4—1884no—
209D4—1884no—
210D4—1884no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—1882no—
219C2×C4—1882no—
220C2×C4—1882no—
221C2×C4—1882no—
222C2×C4—1882no—
223C2×C4—1882no—
224C2×C4#1309400212yes—
225C2×C4#1309400411yescharacteristic
226C2×C4#1309401012yes—
227C2×C4#1309401211yescharacteristic
228C8—44no—
229C8—1882no—
230C22—3764no—
231C22—3762no—
232C22—7521no—
233C22—7522no—
234C22—7521no—
235C22#1568903611yescharacteristic
236C22#1568929212yes—
237C22#1568929311yescharacteristic
238C22#1568929712yes—
239C22#1568929811yescharacteristic
240C4—22no—
241C4—22no—
242C4—21no—
243C4—21no—
244C4—82no—
245C4—3762no—
246C4—3762no—
247C2—7522no—
248C2#2024268212yes—
249C2#2024268311yescharacteristic
250C2#2024269111yescharacteristic
251C2#2024454312yes—
252C2#2024454511yescharacteristic
subgroupG/H
centerC23#13093994
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1295C2
socleC23×C47#120
prime radicalC2×#13094021C22
hypercenter#1295D47
hypocenterC47#10360
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
1. #20251663C2semidirect
4. #20241270C2semidirect
5. C47×#1295C2semidirect
125. #1295D47semidirect
143. C47#10360semidirect

Maximal subgroups

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

subgroupindex
#202516632
#202442122
#202442112
#202412702
C47×#12952
#1036047