Finite Group Databasebeta

← #26136637

Subgroups — #26136637

Order 12032.

318 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 71 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#20253733C211yesmaximal, characteristic
2#20245073C211yesmaximal, characteristic
3#20241560C214yesmaximal, complemented
4C47×#2132C211yesmaximal, characteristic
5#15689680C411yescharacteristic
6#15689491C2212yes—
7#15689487C412yes—
8#15689482—21no—
9#15689482—21no—
10#15689119—21no—
11#15689119—21no—
12#15689107—21no—
13C2×#13093935C411yescharacteristic
14#15688922C2212yes—
15#15688920—21no—
16C47×#532C2211yescharacteristic
17C47×#413—21no—
18C47×#356C2212yes—
19C47×#355—21no—
20C2×#10625329—41no—
21C22×C47⋊C8—21no—
22#13094024—21no—
23#13094016C2×C412yes—
24#13094003—41no—
25C4×Dic94—41no—
26#13093983—21no—
27#13093948—22no—
28#13093948—22no—
29#13093945—22no—
30#13093945—22no—
31#13093943—22no—
32#13093941—41no—
33#13093935—21no—
34#13093935C2×C412yes—
35C2×#41×C47D411yescharacteristic
36C2×#41×C47D411yescharacteristic
37C2×M16×C47—41no—
38C4⋊Q8×C47C2311yescharacteristic
39#127×C47C2×C411yescharacteristic
40#124×C47D411yescharacteristic
41#124×C47D411yescharacteristic
42#121×C47—41no—
43C4×D4×C47—41no—
44C2×C42×C47C2×C411yescharacteristic
45#101×C47—22no—
46#100×C47—41no—
47#41×C47—41no—
48#41×C47—41no—
49#41×C47—41no—
50#41×C47—41no—
51C2×Q8×C47C2×D411yescharacteristic
52C2×Q8×C47C2×D411yescharacteristic
53C2×D4×C47—21no—
54C2×D4×C47—21no—
55C2×D4×C47—41no—
56C2×D4×C47C22⋊C411yescharacteristic
57C2×D4×C47C22⋊C411yescharacteristic
58C22×C4×C47—21no—
59C22×C4×C47—21no—
60C22×C4×C47—21no—
61C22×C4×C47C22⋊C411yescharacteristic
62C2×Dic94—41no—
63M16×C47—42no—
64M16×C47—81no—
65C2×C8×C47—81no—
66C4⋊C4×C47—41no—
67C22⋊C4×C47—41no—
68C22⋊C4×C47—41no—
69C42×C47—21no—
70C42×C47C22⋊C411yescharacteristic
71C42×C47C22×C411yescharacteristic
72C22⋊Dic47—41no—
73C4⋊Dic47—22no—
74C4⋊Dic47—41no—
75Dic47⋊C4—42no—
76C4×Dic47—41no—
77#10625329—42no—
78#10625329—81no—
79C2×C47⋊C8—22no—
80C2×C47⋊C8—41no—
81C2×C47⋊C8—41no—
82C2×C47⋊C8—81no—
83C23×C47—21no—
84C23×C47—21no—
85C23×C47#9911yescharacteristic
86Q8×C47—41no—
87Q8×C47—41no—
88D4×C47—41no—
89D4×C47—41no—
90D4×C47—81no—
91D4×C47—81no—
92D4×C47—82no—
93C2×C4×C47—21no—
94C2×C4×C47—21no—
95C2×C4×C47—21no—
96C2×C4×C47—21no—
97C2×C4×C47—21no—
98C2×C4×C47—21no—
99C2×C4×C47—41no—
100C2×C4×C47—41no—
101C2×C4×C47—41no—
102C2×C4×C47—41no—
103C2×C4×C47—81no—
104C2×C4×C47#9911yescharacteristic
105C2×C4×C47C2×C22⋊C411yescharacteristic
106C2×Dic47—42no—
107Dic94—82no—
108C8×C47—82no—
109C47⋊C8—42no—
110C47⋊C8—82no—
111#13598—471nomaximal, Sylow
112C22×C47—21no—
113C22×C47—41no—
114C22×C47—41no—
115C22×C47—41no—
116C22×C47—81no—
117C22×C47—81no—
118C22×C47C2×#9911yescharacteristic
119C4×C47—21no—
120C4×C47—41no—
121C4×C47—41no—
122C4×C47—41no—
123C4×C47—41no—
124C4×C47#35411yescharacteristic
125C4×C47#35411yescharacteristic
126Dic47—82no—
127#3135—471no—
128#2132—471no—
129#2132D4711yescharacteristic
130#1413—474no—
131C2×C47—21no—
132C2×C47—41no—
133C2×C47—81no—
134C2×C47—81no—
135C2×C47C2×#35411yescharacteristic
136#533—471no—
137#532C2×D4711yescharacteristic
138#491—472no—
139#490—472no—
140#489—941no—
141#489—941no—
142#416—941no—
143#416—941no—
144#413—21no—
145#413—941no—
146C2×#97—471no—
147#356—472no—
148#356C2×D4712yes—
149#355—21no—
150#355—941no—
151C47#1359811yescharacteristic, complemented, Sylow
152C2×#41D18811yescharacteristic
153C2×#41C22⋊D4711yescharacteristic
154C2×M16—41no—
155C2×M16—1881no—
156C22×C8—941no—
157C4⋊Q8—941no—
158C4⋊Q8C22×D4711yescharacteristic
159#127C4×D4711yescharacteristic
160#125—472no—
161#124D18811yescharacteristic
162#124C22⋊D4711yescharacteristic
163C22⋊Q8—1881no—
164#121—41no—
165C4×Q8—1881no—
166C4×D4—41no—
167#117—941no—
168C2×C42C4×D4711yescharacteristic
169#103—942no—
170#103—942no—
171#102—942no—
172#102—942no—
173#101—22no—
174#101—942no—
175#100—41no—
176#100—1881no—
177#97—472no—
178#97—941no—
179#41—41no—
180#41—41no—
181#41—41no—
182#41—41no—
183C2×Q8—1881no—
184C2×Q8C2×D18811yescharacteristic
185C2×Q8C2×C22⋊D4711yescharacteristic
186C2×D4—21no—
187C2×D4—21no—
188C2×D4—41no—
189C2×D4(C2×D47)⋊C411yescharacteristic
190C2×D4(C2×D47)⋊C411yescharacteristic
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4(C2×D47)⋊C411yescharacteristic
195M16—42no—
196M16—81no—
197M16—3761no—
198M16—1882no—
199C2×C8—81no—
200C2×C8—942no—
201C2×C8—3761no—
202C2×C8—1881no—
203C2×C8—1881no—
204C4⋊C4—41no—
205C4⋊C4—942no—
206C4⋊C4—1882no—
207C4⋊C4—1881no—
208C22⋊C4—41no—
209C22⋊C4—41no—
210C22⋊C4—1881no—
211C42—21no—
212C42—1881no—
213C42(C2×D47)⋊C411yescharacteristic
214C42C2×C4×D4711yescharacteristic
215C23—21no—
216C23—21no—
217C23#1309393811yescharacteristic
218Q8—41no—
219Q8—41no—
220Q8—3762no—
221D4—41no—
222D4—41no—
223D4—81no—
224D4—81no—
225D4—82no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—81no—
237C2×C4—1882no—
238C2×C4#1309393811yescharacteristic
239C2×C4C2×(C2×D47)⋊C411yescharacteristic
240C8—82no—
241C8—3762no—
242C8—1882no—
243C22—21no—
244C22—41no—
245C22—41no—
246C22—41no—
247C22—81no—
248C22—81no—
249C22C2×#1309393811yescharacteristic
250C4—21no—
251C4—41no—
252C4—41no—
253C4—41no—
254C4—41no—
255C4—3762no—
256C4#1568891711yescharacteristic
257C4#1568891711yescharacteristic
258C2—21no—
259C2—41no—
260C2—81no—
261C2—81no—
262C2C2×#1568891711yescharacteristic
subgroupG/H
centerC4#15688917
commutatorC42×C47C22×C4
FrattiniC4⋊Q8C22×D47
FittingC47×#2132C2
socleC2×C47C2×#354
prime radicalC47×#532C22
cosocleC4⋊Q8×C47C23
hypercenter#2132D47
hypocenterC47#13598
LCSG ▷ C42×C47 ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #2132

Complements

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

NH ≅ G/Ntype
3. #20241560C2semidirect
151. C47#13598semidirect

Maximal subgroups

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

subgroupindex
#202537332
#202450732
#202415602
C47×#21322
#1359847