Finite Group Databasebeta

← #26119952

Subgroups — #26119952

Order 12032.

376 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#15689419C211yesmaximal, characteristic
2#20243381C211yesmaximal, characteristic
3#20242162C211yesmaximal, characteristic
4#20242072C211yesmaximal, characteristic
5#20242070C211yesmaximal, characteristic
6#20241784C211yesmaximal, characteristic
7C47×#1301C211yesmaximal, characteristic
8C2×#13094024C2211yescharacteristic
9C2×C4×Dic94C2211yescharacteristic
10#15689419—22no—
11#15689419—22no—
12#15689176C2211yescharacteristic
13C2×#13093958—21no—
14#15689147C2211yescharacteristic
15C2×#13093949—21no—
16C2×#13093942—21no—
17#15688891—21no—
18#15688875—22no—
19#15688871—22no—
20#15688870—22no—
21#15688855—22no—
22C47×#431C2211yescharacteristic
23C47×#423C2211yescharacteristic
24C2×C4⋊C8×C47C2211yescharacteristic
25C22×Dic94—21no—
26C22×Dic94D411yescharacteristic
27C2×#10625329—21no—
28#13094024—21no—
29#13094024—21no—
30#13094024—21no—
31#13094024D412yes—
32C4×Dic94—21no—
33C4×Dic94—21no—
34C4×Dic94—21no—
35C4×Dic94—21no—
36C2×C4⋊Dic47—21no—
37C2×C4⋊Dic47—21no—
38C2×C4⋊Dic47D411yescharacteristic
39C2×Dic47⋊C4—21no—
40C2×C4×Dic47—21no—
41#13093958—24no—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)—21no—
44C4⋊(C47⋊C8)D412yes—
45#13093949—24no—
46#13093942—42no—
47C22⋊(C47⋊C8)—21no—
48C4×C47⋊C8—21no—
49C2×M16×C47—21no—
50C22×C8×C47—21no—
51C2×C42×C47C2311yescharacteristic
52C4⋊C8×C47—21no—
53C4⋊C8×C47—21no—
54C4⋊C8×C47—21no—
55C4⋊C8×C47—21no—
56C4⋊C8×C47D412yes—
57C22⋊C8×C47—21no—
58C4×C8×C47—21no—
59C22×C4×C47C2×D411yescharacteristic
60C22×C4×C47#4111yescharacteristic
61C22×C4×C47#4111yescharacteristic
62C22×Dic47—21no—
63C22×Dic47—21no—
64C22×Dic47—41no—
65C2×Dic94—21no—
66C2×Dic94—21no—
67C2×Dic94—21no—
68C2×Dic94—21no—
69C2×Dic94—21no—
70C2×Dic94—22no—
71C2×Dic94—41no—
72C2×Dic94—82no—
73C2×Dic94Q1612yes—
74M16×C47—41no—
75M16×C47—41no—
76C2×C8×C47—22no—
77C2×C8×C47—41no—
78C2×C8×C47—41no—
79C2×C8×C47—41no—
80C2×C8×C47—41no—
81C42×C47C2×D411yescharacteristic
82C42×C47C2×D411yescharacteristic
83C42×C47C2×D411yescharacteristic
84C42×C47#4111yescharacteristic
85C4⋊Dic47—22no—
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47—22no—
89C4⋊Dic47—41no—
90C4⋊Dic47—41no—
91Dic47⋊C4—41no—
92Dic47⋊C4—41no—
93C4×Dic47—41no—
94C4×Dic47—41no—
95#10625329—41no—
96#10625329—41no—
97C2×C47⋊C8—22no—
98C2×C47⋊C8—41no—
99C23×C47#12311yescharacteristic
100C2×C4×C47—22no—
101C2×C4×C47—41no—
102C2×C4×C47#12011yescharacteristic
103C2×C4×C47#12111yescharacteristic
104C2×C4×C47#12111yescharacteristic
105C2×C4×C47#12111yescharacteristic
106C2×C4×C47#12311yescharacteristic
107C2×C4×C47#12411yescharacteristic
108C2×C4×C47C2×Q1611yescharacteristic
109C2×C4×C47#13511yescharacteristic
110C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
111C2×C4×C47#13711yescharacteristic
112C2×Dic47—22no—
113C2×Dic47—41no—
114C2×Dic47—41no—
115C2×Dic47—41no—
116C2×Dic47—42no—
117C2×Dic47—82no—
118C2×Dic47—81no—
119Dic94—22no—
120Dic94—22no—
121Dic94—41no—
122Dic94—41no—
123Dic94—82no—
124Dic94—82no—
125C8×C47—42no—
126C8×C47—81no—
127C8×C47—81no—
128C47⋊C8—42no—
129C47⋊C8—81no—
130#10455—471nomaximal, Sylow
131C22×C47—21no—
132C22×C47—21no—
133C22×C47#39411yescharacteristic
134C22×C47#48411yescharacteristic
135C22×C47#48511yescharacteristic
136C4×C47—21no—
137C4×C47—21no—
138C4×C47—21no—
139C4×C47#44911yescharacteristic
140C4×C47#45111yescharacteristic
141C4×C47#46711yescharacteristic
142C4×C47#46811yescharacteristic
143C4×C47#47312yes—
144Dic47—42no—
145Dic47—82no—
146Dic47—81no—
147C2×#477—471no—
148#1801—471no—
149#1571—471no—
150#1549—471no—
151#1548—471no—
152#1479—471no—
153#1301D4711yescharacteristic
154C2×C47—21no—
155C2×C47—21no—
156C2×C47#203611yescharacteristic
157C2×C47#204711yescharacteristic
158C2×C47#204811yescharacteristic
159C2×C4⋊Q8—471no—
160C2×C4×Q8—471no—
161#477—942no—
162#477—942no—
163#431—471no—
164#431C2×D4711yescharacteristic
165C2×#107—941no—
166#423—471no—
167#423C2×D4711yescharacteristic
168C2×C4⋊C8C2×D4711yescharacteristic
169C2×#103—941no—
170C2×#101—941no—
171#343—941no—
172#335—942no—
173#333—942no—
174#332—942no—
175Q8⋊C8—942no—
176C47#1045511yescharacteristic, complemented, Sylow
177C22×Q8—471no—
178C22×Q8—941no—
179C2×M16—21no—
180C2×M16—941no—
181C22×C8—21no—
182C4⋊Q8—472no—
183C4⋊Q8—941no—
184C4⋊Q8—941no—
185C4⋊Q8—941no—
186C4×Q8—941no—
187C4×Q8—941no—
188C4×Q8—941no—
189C4×Q8—941no—
190C2×C4⋊C4—471no—
191C2×C4⋊C4—941no—
192C2×C4⋊C4—941no—
193C2×C4⋊C4—941no—
194C2×C42—941no—
195C2×C42C22×D4711yescharacteristic
196#107—944no—
197C4⋊C8—21no—
198C4⋊C8—21no—
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—472no—
202C4⋊C8—941no—
203C4⋊C8—941no—
204C4⋊C8D18812yes—
205#103—944no—
206#101—1882no—
207C22⋊C8—21no—
208C22⋊C8—941no—
209C4×C8—21no—
210C4×C8—941no—
211C2×Q8—472no—
212C2×Q8—941no—
213C2×Q8—941no—
214C2×Q8—941no—
215C2×Q8—942no—
216C2×Q8—941no—
217C2×Q8—941no—
218C2×Q8—3762no—
219C2×Q8—1881no—
220C22×C4—941no—
221C22×C4—941no—
222C22×C4—1881no—
223C22×C4#1062535011yescharacteristic
224C22×C4D4×D4711yescharacteristic
225C22×C4#1062535411yescharacteristic
226M16—41no—
227M16—41no—
228M16—1881no—
229M16—1881no—
230C2×C8—22no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—942no—
236C2×C8—1881no—
237C4⋊C4—942no—
238C4⋊C4—941no—
239C4⋊C4—941no—
240C4⋊C4—942no—
241C4⋊C4—1881no—
242C4⋊C4—1881no—
243C4⋊C4—1881no—
244C4⋊C4—1881no—
245C42—1881no—
246C42—1881no—
247C42C2×D18811yescharacteristic
248C42#1062535011yescharacteristic
249C42D4×D4711yescharacteristic
250C42D4×D4711yescharacteristic
251C23#1309400911yescharacteristic
252Q8—942no—
253Q8—942no—
254Q8—3762no—
255Q8—3762no—
256Q8—1881no—
257Q8—1881no—
258C2×C4—22no—
259C2×C4—41no—
260C2×C4—942no—
261C2×C4—3762no—
262C2×C4—3761no—
263C2×C4—1881no—
264C2×C4—1882no—
265C2×C4—1881no—
266C2×C4—1881no—
267C2×C4#1309399411yescharacteristic
268C2×C4#1309399711yescharacteristic
269C2×C4#1309399711yescharacteristic
270C2×C4#1309399911yescharacteristic
271C2×C4#1309400911yescharacteristic
272C2×C4#1309401211yescharacteristic
273C2×C4Q16×D4711yescharacteristic
274C2×C4#1309404511yescharacteristic
275C2×C4#1309404811yescharacteristic
276C2×C4#1309405311yescharacteristic
277C8—42no—
278C8—81no—
279C8—81no—
280C8—3761no—
281C8—1882no—
282C22—21no—
283C22—21no—
284C22#1568904111yescharacteristic
285C22#1568946011yescharacteristic
286C22#1568946711yescharacteristic
287C4—21no—
288C4—21no—
289C4—21no—
290C4—3762no—
291C4—3761no—
292C4—1882no—
293C4#1568926911yescharacteristic
294C4#1568928011yescharacteristic
295C4#1568936311yescharacteristic
296C4#1568936811yescharacteristic
297C4#1568939912yes—
298C2—21no—
299C2—21no—
300C2#2024459411yescharacteristic
301C2#2024465711yescharacteristic
302C2#2024466411yescharacteristic
subgroupG/H
centerC22#15689041
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1301C2
socleC22×C47#394
prime radicalC23×C47#123
hypercenter#1301D47
hypocenterC47#10455
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
176. C47#10455semidirect

Maximal subgroups

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

subgroupindex
C2×#156894192
#202433812
#202421622
#202420722
#202420702
#202417842
C47×#13012
#1045547