Finite Group Databasebeta

← #18004427

Subgroups — #18004427

Order 4736.

398 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 149 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#14558161C211yesmaximal, characteristic, complemented
2#14557833C212yesmaximal, complemented
3#14557833C212yesmaximal, complemented
4#14557823C212yesmaximal, complemented
5#14557813C212yesmaximal, complemented
6#14557576C211yesmaximal, characteristic, complemented
7#14557569C211yesmaximal, characteristic, complemented
8#14557560C211yesmaximal, characteristic, complemented
9#14557538C211yesmaximal, characteristic
10C2×#11924457C211yesmaximal, characteristic
11C37×#518C211yesmaximal, characteristic
12C2×#10596934C2211yescharacteristic
13C22×#64436C2211yescharacteristic
14#11924536C2212yescomplemented
15#11924535—21no—
16#11924528C2212yescomplemented
17#11924527—21no—
18#11924513—22no—
19#11924495C2211yescharacteristic
20C2×C4⋊Dic37C2211yescharacteristic
21#11924469C2211yescharacteristic, complemented
22#11924469C2212yescomplemented
23#11924469C2211yescharacteristic, complemented
24#11924467C2211yescharacteristic, complemented
25#11924467C2212yescomplemented
26#11924467C2211yescharacteristic, complemented
27C4⋊#64436C2212yescomplemented
28C4⋊#64436C2212yescomplemented
29#11924457C2212yes—
30#11924457C2212yes—
31#11924457C2212yes—
32#11924457C2212yes—
33C22×D4×C37C2211yescharacteristic
34C4×D4×C37—21no—
35C4×D4×C37—21no—
36C4×D4×C37C2212yes—
37C4×D4×C37C2212yes—
38#117×C37C2211yescharacteristic
39#117×C37C2211yescharacteristic
40C2×C22⋊C4×C37—22no—
41C24×C37—21no—
42C2×D4×C37—21no—
43C2×D4×C37—22no—
44C2×D4×C37Q814yescomplemented
45C2×D4×C37C2312yes—
46C22×C4×C37—22no—
47C22×C4×C37—22no—
48C22×C4×C37C2311yescharacteristic
49C22×Dic37—21no—
50C2×Dic74—22no—
51C4⋊C4×C37D411yescharacteristic
52C4⋊C4×C37D411yescharacteristic
53C4⋊C4×C37C2311yescharacteristic
54C4⋊C4×C37C2311yescharacteristic
55C22⋊C4×C37—21no—
56C22⋊C4×C37—22no—
57C22⋊C4×C37—22no—
58C22⋊C4×C37D412yes—
59C42×C37—21no—
60C42×C37C2312yes—
61C22⋊Dic37—21no—
62C4⋊Dic37—21no—
63C4⋊Dic37—22no—
64C4⋊Dic37C2312yes—
65C4⋊Dic37C2311yescharacteristic
66C4⋊Dic37C2311yescharacteristic
67#10596936—22no—
68#10596936—22no—
69C4×Dic37—21no—
70#10596934—22no—
71C2×#64436—22no—
72C2×#64436C2311yescharacteristic
73C2×#64436C2311yescharacteristic
74C2×#64436C2312yes—
75C23×C37—22no—
76C23×C37—24no—
77C23×C37—81no—
78C23×C37—81no—
79C23×C37C2×D411yescharacteristic
80D4×C37—24no—
81D4×C37—22no—
82D4×C37C2×Q814yes—
83C2×C4×C37—21no—
84C2×C4×C37—21no—
85C2×C4×C37—82no—
86C2×C4×C37—82no—
87C2×C4×C37C2×D412yes—
88C2×C4×C37C2×D412yes—
89C2×C4×C37C2×D411yescharacteristic
90C2×C4×C37C2×Q812yes—
91C2×C4×C37#4112yes—
92C2×C4×C37C2411yescharacteristic
93C2×Dic37—21no—
94C2×Dic37—21no—
95C2×Dic37—22no—
96C2×Dic37—81no—
97Dic74—82no—
98#64436—21no—
99#64436—21no—
100#64436—22no—
101C22×C37—21no—
102C22×C37—21no—
103C22×C37—24no—
104C22×C37—42no—
105C22×C37—42no—
106C22×C37—84no—
107C22×C37C22⋊Q812yes—
108C22×C37C22×D411yescharacteristic
109C4×C37—22no—
110C4×C37—22no—
111C4×C37—41no—
112C4×C37—41no—
113C4×C37C22⋊Q812yes—
114C4×C37C22×Q811yescharacteristic
115C4×C37C2×#4111yescharacteristic
116Dic37—41no—
117Dic37—42no—
118Dic37—41no—
119#3081—371nomaximal, Sylow
120C2×C37—22no—
121C2×C37—44no—
122C2×C37C2×C22⋊Q811yescharacteristic
123C2×C37#57611yescharacteristic
124C2×C37#57711yescharacteristic
125#544—371no—
126#518D3711yescharacteristic
127#478—372no—
128#478—372no—
129#476—372no—
130#474—372no—
131#428—371no—
132#427—371no—
133#424—371no—
134#418—371no—
135C2×#102—371no—
136C37#308111yescharacteristic, complemented, Sylow
137C22×D4C2×D3711yescharacteristic
138C2×M16—371no—
139C22×C8—371no—
140C4⋊Q8—372no—
141C4⋊Q8—741no—
142#125—372no—
143#125—741no—
144C22⋊Q8—742no—
145C4×D4—21no—
146C4×D4—21no—
147C4×D4C2×D3712yes—
148C4×D4C2×D3712yes—
149#117—371no—
150#117C2×D3711yescharacteristic
151#117C2×D3711yescharacteristic
152C2×C4⋊C4—371no—
153C2×C22⋊C4—22no—
154#107—371no—
155#107—371no—
156#107—372no—
157#106—371no—
158#106—371no—
159#106—372no—
160C4⋊C8—372no—
161C4⋊C8—372no—
162#102—372no—
163#102—372no—
164#102—372no—
165#102—372no—
166C24—21no—
167C2×Q8—742no—
168C2×D4—22no—
169C2×D4—21no—
170C2×D4Dic7414yescomplemented
171C2×D4C22×D3712yes—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—741no—
175C22×C4C22×D3711yescharacteristic
176M16—742no—
177C2×C8—371no—
178C2×C8—372no—
179C2×C8—371no—
180C2×C8—742no—
181C4⋊C4—372no—
182C4⋊C4—371no—
183C4⋊C4—371no—
184C4⋊C4—742no—
185C4⋊C4—742no—
186C4⋊C4—741no—
187C4⋊C4—742no—
188C4⋊C4C22⋊D3711yescharacteristic
189C4⋊C4C22⋊D3711yescharacteristic
190C4⋊C4C22×D3711yescharacteristic
191C4⋊C4C22×D3711yescharacteristic
192C22⋊C4—21no—
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—741no—
196C22⋊C4C22⋊D3712yes—
197C42—21no—
198C42—741no—
199C42C22×D3712yes—
200C23—22no—
201C23—24no—
202C23—81no—
203C23—81no—
204C23C2×C22⋊D3711yescharacteristic
205Q8—2962no—
206D4—24no—
207D4—22no—
208D4C2×Dic7414yes—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—82no—
212C2×C4—82no—
213C2×C4—2961no—
214C2×C4—741no—
215C2×C4—741no—
216C2×C4—742no—
217C2×C4C2×Dic7412yes—
218C2×C4#1059696212yes—
219C2×C4C2×C22⋊D3712yes—
220C2×C4C2×C22⋊D3712yes—
221C2×C4C2×C22⋊D3711yescharacteristic
222C2×C4C23×D3711yescharacteristic
223C8—741no—
224C8—741no—
225C8—742no—
226C22—21no—
227C22—21no—
228C22—24no—
229C22—42no—
230C22—42no—
231C22—84no—
232C22#1192451512yes—
233C22C22×C22⋊D3711yescharacteristic
234C4—22no—
235C4—22no—
236C4—41no—
237C4—41no—
238C4—1482no—
239C4—1481no—
240C4—1481no—
241C4#1192451512yes—
242C4C22×Dic7411yescharacteristic
243C4C2×#1059696211yescharacteristic
244C2—22no—
245C2—44no—
246C2C2×#1192451511yescharacteristic
247C2#1455833611yescharacteristic
248C2#1455834411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#518C2
socleC22×C37C22×D4
prime radicalC22×D4×C37C22
hypercenter#518D37
hypocenterC37#3081
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #14558161C2semidirect
2. #14557833C2semidirect
3. #14557833C2semidirect
4. #14557823C2semidirect
5. #14557813C2semidirect
6. #14557576C2semidirect
7. #14557569C2semidirect
8. #14557560C2semidirect
14. #11924536C22semidirect
16. #11924528C22semidirect
21. #11924469C22semidirect
22. #11924469C22semidirect
23. #11924469C22semidirect
24. #11924467C22semidirect
25. #11924467C22semidirect
26. #11924467C22semidirect
27. C4⋊#64436C22semidirect
28. C4⋊#64436C22semidirect
44. C2×D4×C37Q8semidirect
136. C37#3081semidirect
170. C2×D4Dic74semidirect

Maximal subgroups

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

subgroupindex
#145581612
#145578332
#145578232
#145578132
#145575762
#145575692
#145575602
#145575382
C2×#119244572
C37×#5182
#308137