Finite Group Databasebeta

← #17994614

Subgroups — #17994614

Order 4736.

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

normal subgroups only

This group has 312 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
1#41×Dic37C211yesmaximal, characteristic
2#14557556C211yesmaximal, characteristic, complemented
3C2×#11924463C211yesmaximal, characteristic
4C4×#10596936C211yesmaximal, characteristic, complemented
5#14557294C211yesmaximal, characteristic, complemented
6#14557293C211yesmaximal, characteristic, complemented
7C2×#104×C37C211yesmaximal, characteristic
8C2×#10596934C2211yescharacteristic
9Q8×Dic37C411yescharacteristic, complemented
10Q8×Dic37C411yescharacteristic, complemented
11D4×Dic37—21no—
12D4×Dic37—21no—
13D4×Dic37C411yescharacteristic, complemented
14D4×Dic37C411yescharacteristic, complemented
15#11924495—21no—
16#11924495C2211yescharacteristic
17C2×#10596936—21no—
18C2×C4×Dic37—21no—
19C2×C4×Dic37C2211yescharacteristic
20C2×C4×Dic37C2211yescharacteristic
21#11924465—21no—
22#11924465—21no—
23#11924463—22no—
24#11924443—21no—
25C2×#41×C37C2211yescharacteristic
26C2×M16×C37C2211yescharacteristic
27C2×C42×C37C2211yescharacteristic
28#104×C37—22no—
29#41×C37—21no—
30#41×C37—21no—
31#41×C37D412yes—
32#41×C37Q812yes—
33C2×Q8×C37C2×C411yescharacteristic
34C2×D4×C37—21no—
35C2×D4×C37C2×C411yescharacteristic
36C22×C4×C37—21no—
37C22×C4×C37—21no—
38C22×C4×C37C2311yescharacteristic
39C22×Dic37—21no—
40C22×Dic37—21no—
41C22×Dic37—21no—
42C22×Dic37D411yescharacteristic
43C22×Dic37D411yescharacteristic
44M16×C37—21no—
45M16×C37—21no—
46C2×C8×C37—21no—
47C42×C37—21no—
48C42×C37—21no—
49C22⋊Dic37—21no—
50C22⋊Dic37—21no—
51C22⋊Dic37—21no—
52C4⋊Dic37—21no—
53C4⋊Dic37—21no—
54C4⋊Dic37C2×C411yescharacteristic
55C4⋊Dic37C2×C411yescharacteristic
56#10596936—24no—
57C4×Dic37—21no—
58C4×Dic37—21no—
59C4×Dic37—21no—
60C4×Dic37—21no—
61C4×Dic37—21no—
62C4×Dic37C2×C411yescharacteristic
63C4×Dic37C2×C411yescharacteristic
64C4×Dic37D411yescharacteristic
65C4×Dic37D411yescharacteristic
66#10596934—21no—
67#10596934—21no—
68C2×#64436—21no—
69C23×C37—21no—
70C23×C37C2×D411yescharacteristic
71Q8×C37—21no—
72Q8×C37C4⋊C412yescomplemented
73D4×C37—22no—
74D4×C37—22no—
75D4×C37—21no—
76D4×C37C4⋊C412yescomplemented
77C2×C4×C37—21no—
78C2×C4×C37—22no—
79C2×C4×C37—22no—
80C2×C4×C37—22no—
81C2×C4×C37—41no—
82C2×C4×C37—41no—
83C2×C4×C37C22×C411yescharacteristic
84C2×C4×C37C2×D411yescharacteristic
85C2×C4×C37C2×D411yescharacteristic
86C2×C4×C37C2×Q811yescharacteristic
87C2×C4×C37#4111yescharacteristic
88C2×C4×C37#4111yescharacteristic
89C2×Dic37—22no—
90C2×Dic37—22no—
91C2×Dic37—21no—
92C2×Dic37—21no—
93C2×Dic37—41no—
94C2×Dic37—42no—
95C2×Dic37—41no—
96C2×Dic37—41no—
97C2×Dic37—42no—
98C2×Dic37C22⋊C411yescharacteristic
99C2×Dic37C22⋊C411yescharacteristic
100C2×Dic37C22⋊C411yescharacteristic
101C2×Dic37C22⋊C411yescharacteristic
102C8×C37—41no—
103#64436—41no—
104C22×C37—21no—
105C22×C37—21no—
106C22×C37—22no—
107C22×C37—41no—
108C22×C37—41no—
109C22×C37C2×C22⋊C411yescharacteristic
110C22×C37#12111yescharacteristic
111C22×C37C22⋊Q811yescharacteristic
112C4×C37—22no—
113C4×C37—42no—
114C4×C37C2×C4⋊C411yescharacteristic
115C4×C37#11711yescharacteristic
116C4×C37#12111yescharacteristic
117C4×C37C22⋊Q811yescharacteristic
118Dic37—21no—
119Dic37—21no—
120Dic37—21no—
121Dic37—42no—
122Dic37—41no—
123Dic37—41no—
124Dic37#10412yescomplemented
125#1806—371nomaximal, Sylow
126C2×C37—21no—
127C2×C37—21no—
128C2×C37—42no—
129C2×C37#38011yescharacteristic
130C2×C37C2×#10411yescharacteristic
131C2×C37#42111yescharacteristic
132C4×#41—371no—
133#423—371no—
134C2×#104—371no—
135C2×#104D3711yescharacteristic
136C4×C4⋊C4—371no—
137#339—371no—
138#339—371no—
139C37#180611yescharacteristic, complemented, Sylow
140C2×#41C2×D3711yescharacteristic
141C2×M16—371no—
142C2×M16C2×D3711yescharacteristic
143C4×Q8—371no—
144C4×Q8—371no—
145C4×D4—371no—
146C4×D4—371no—
147C4×D4—741no—
148C4×D4—741no—
149#117—371no—
150#117—741no—
151C2×C4⋊C4—741no—
152C2×C42—371no—
153C2×C42—371no—
154C2×C42—741no—
155C2×C42C2×D3711yescharacteristic
156C4⋊C8—741no—
157C4⋊C8—741no—
158#104—22no—
159#104—742no—
160#95—741no—
161#41—21no—
162#41—21no—
163#41Dic7412yes—
164#41C22⋊D3712yes—
165C2×Q8C4×D3711yescharacteristic
166C2×D4—21no—
167C2×D4C4×D3711yescharacteristic
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—371no—
171C22×C4—371no—
172C22×C4—741no—
173C22×C4—741no—
174C22×C4—741no—
175C22×C4C22×D3711yescharacteristic
176M16—21no—
177M16—21no—
178M16—741no—
179M16—741no—
180C2×C8—21no—
181C2×C8—741no—
182C4⋊C4—371no—
183C4⋊C4—371no—
184C4⋊C4—741no—
185C4⋊C4—741no—
186C4⋊C4—744no—
187C22⋊C4—741no—
188C22⋊C4—741no—
189C22⋊C4—741no—
190C42—21no—
191C42—21no—
192C42—371no—
193C42—371no—
194C42—371no—
195C42—371no—
196C42—741no—
197C42—741no—
198C42—741no—
199C42—741no—
200C42—741no—
201C23—21no—
202C23D4×D3711yescharacteristic
203Q8—21no—
204Q8#1059693612yescomplemented
205D4—22no—
206D4—22no—
207D4—21no—
208D4#1059693612yescomplemented
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—371no—
216C2×C4—371no—
217C2×C4—371no—
218C2×C4—371no—
219C2×C4—742no—
220C2×C4—742no—
221C2×C4—741no—
222C2×C4—741no—
223C2×C4—1482no—
224C2×C4—1481no—
225C2×C4—1482no—
226C2×C4—1481no—
227C2×C4—1481no—
228C2×C4C2×Dic7411yescharacteristic
229C2×C4C2×C4×D3711yescharacteristic
230C2×C4D4×D3711yescharacteristic
231C2×C4#1059696411yescharacteristic
232C2×C4#1059696411yescharacteristic
233C2×C4C2×C22⋊D3711yescharacteristic
234C8—41no—
235C8—1481no—
236C22—21no—
237C22—21no—
238C22—22no—
239C22—41no—
240C22—41no—
241C22C22⋊C4×D3711yescharacteristic
242C22#1192450811yescharacteristic
243C22#1192451311yescharacteristic
244C4—22no—
245C4—42no—
246C4—372no—
247C4—741no—
248C4—741no—
249C4—741no—
250C4—1482no—
251C4—1481no—
252C4—1481no—
253C4C2×#1059693611yescharacteristic
254C4#1192449211yescharacteristic
255C4#1192450811yescharacteristic
256C4#1192451311yescharacteristic
257C2—21no—
258C2—21no—
259C2—42no—
260C2#1455739111yescharacteristic
261C2#104×D3711yescharacteristic
262C2#1455754811yescharacteristic
subgroupG/H
centerC2×C4D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC2×#104×C37C2
socleC22×C37C2×C22⋊C4
prime radicalC2×#41×C37C22
cosocleC22×C4×C37C23
hypercenterC2×#104D37
hypocenterC37#1806
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #14557556C2semidirect
4. C4×#10596936C2semidirect
5. #14557294C2semidirect
6. #14557293C2semidirect
9. Q8×Dic37C4semidirect
10. Q8×Dic37C4semidirect
13. D4×Dic37C4semidirect
14. D4×Dic37C4semidirect
72. Q8×C37C4⋊C4semidirect
76. D4×C37C4⋊C4semidirect
124. Dic37#104semidirect
139. C37#1806semidirect
204. Q8#10596936semidirect
208. D4#10596936semidirect

Maximal subgroups

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

subgroupindex
#41×Dic372
#145575562
C2×#119244632
C4×#105969362
#145572942
#145572932
C2×#104×C372
#180637