Finite Group Databasebeta

← #17995058

Subgroups — #17995058

Order 4736.

390 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 85 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×M16×D37C211yesmaximal, characteristic, complemented
2C2×#11924511C211yesmaximal, characteristic
3C2×#11924452C211yesmaximal, characteristic, complemented
4C2×#11924452C211yesmaximal, characteristic, complemented
5#14557496C211yesmaximal, characteristic, complemented
6#14557302C211yesmaximal, characteristic, complemented
7C37×#343C211yesmaximal, characteristic, complemented
8C22×D148C412yes—
9C22×D148C2211yescharacteristic
10C22×C4×D37C2211yescharacteristic
11C2×#10596934C2211yescharacteristic
12C2×#10596934C2211yescharacteristic
13C2×#10596929—21no—
14M16×D37—22no—
15M16×D37—22no—
16C2×C8×D37—21no—
17#11924511—21no—
18#11924511—21no—
19#11924511—21no—
20#11924511—21no—
21C2×#10596938C412yes—
22#11924452—22no—
23#11924452—22no—
24#11924448—21no—
25#11924448—21no—
26C2×M16×C37C2211yescharacteristic
27C2×M16×C37C2211yescharacteristic
28C2×C4⋊C4×C37C2211yescharacteristic
29C23×D37C2×C411yescharacteristic
30C23×D37C2×C412yes—
31C22×C4×C37C2×C412yes—
32C22×C4×C37C2311yescharacteristic
33C22×Dic37C2×C411yescharacteristic
34C2×D148—22no—
35C2×D148—22no—
36C2×D148—21no—
37C2×D148—21no—
38C2×D148—21no—
39C2×D148—21no—
40C2×D148—21no—
41C2×D148—21no—
42C2×D148—44no—
43C2×C4×D37—21no—
44C2×C4×D37—21no—
45C2×C4×D37—21no—
46C2×C4×D37—21no—
47C2×C4×D37D411yescharacteristic
48C2×C4×D37D411yescharacteristic
49C2×C4×D37D411yescharacteristic
50C2×C4×D37D411yescharacteristic
51M16×C37—21no—
52M16×C37—21no—
53M16×C37—21no—
54M16×C37D412yescomplemented
55C2×C8×C37—21no—
56C2×C8×C37—21no—
57C4⋊C4×C37—21no—
58C4⋊C4×C37—21no—
59#10596938—22no—
60#10596938—22no—
61#10596934—21no—
62#10596934—21no—
63#10596934—21no—
64#10596934D412yescomplemented
65C2×#64436—21no—
66C2×#64436—21no—
67#10596929—24no—
68C8×D37—24no—
69C23×C37C22×C411yescharacteristic
70C22×D37—21no—
71C22×D37—21no—
72C22×D37—22no—
73C22×D37—22no—
74C22×D37—22no—
75C22×D37—22no—
76C22×D37—41no—
77C22×D37—42no—
78C22×D37—42no—
79C22×D37C22⋊C411yescharacteristic
80C22×D37C22⋊C411yescharacteristic
81C2×C4×C37—22no—
82C2×C4×C37—42no—
83C2×C4×C37C2×D411yescharacteristic
84C2×C4×C37C2×D411yescharacteristic
85C2×C4×C37C2×D411yescharacteristic
86C2×C4×C37C2×D411yescharacteristic
87C2×C4×C37#4111yescharacteristic
88C2×C4×C37#4111yescharacteristic
89C2×Dic37—21no—
90C2×Dic37—21no—
91C2×Dic37C22⋊C411yescharacteristic
92C2×Dic37C22⋊C411yescharacteristic
93D148—44no—
94D148—44no—
95D148—41no—
96D148—41no—
97D148—41no—
98D148—41no—
99C4×D37—21no—
100C4×D37—21no—
101C4×D37—21no—
102C4×D37—21no—
103C4×D37—21no—
104C4×D37—21no—
105C4×D37—21no—
106C4×D37—21no—
107C8×C37—22no—
108C8×C37—41no—
109#64436—22no—
110#64436—41no—
111C22×C37—21no—
112C22×C37—21no—
113C22×C37C2×C22⋊C411yescharacteristic
114C22×C37C4×D411yescharacteristic
115C22×C37C4×D411yescharacteristic
116C2×D37—21no—
117C2×D37—21no—
118C2×D37—21no—
119C2×D37—21no—
120C2×D37—21no—
121C2×D37—42no—
122C2×D37—42no—
123C2×D37—42no—
124C2×D37—42no—
125C2×D37—42no—
126C2×D37—82no—
127C2×D37—82no—
128C2×D37#10012yescomplemented
129C4×C37—42no—
130C4×C37#12011yescharacteristic
131C4×C37#12111yescharacteristic
132C4×C37#12111yescharacteristic
133C4×C37#12311yescharacteristic
134Dic37—21no—
135Dic37—21no—
136#1900—371nomaximal, Sylow
137C2×C37—21no—
138C2×C37—21no—
139C2×C37#38611yescharacteristic
140C2×C37C2×#10011yescharacteristic
141C2×C37#41311yescharacteristic
142D37—22no—
143D37—41no—
144D37—82no—
145C22×M16—371no—
146C2×#121—371no—
147C2×#100—371no—
148C2×#100—371no—
149#407—371no—
150#343—371no—
151#343D3711yescharacteristic, complemented
152C37#190011yescharacteristic, complemented, Sylow
153C22×D4—372no—
154C22×D4—371no—
155C23×C4—371no—
156C2×M16—371no—
157C2×M16—371no—
158C2×M16—741no—
159C2×M16—742no—
160C2×M16—742no—
161C2×M16C2×D3711yescharacteristic
162C2×M16C2×D3711yescharacteristic
163C22×C8—741no—
164#121—741no—
165#121—741no—
166#121—741no—
167#121—741no—
168C2×C4⋊C4C2×D3711yescharacteristic
169C2×C22⋊C4—372no—
170#100—742no—
171#100—742no—
172C22⋊C8—741no—
173C22⋊C8—741no—
174C24—371no—
175C24—372no—
176C2×D4—742no—
177C2×D4—742no—
178C2×D4—741no—
179C2×D4—741no—
180C2×D4—741no—
181C2×D4—741no—
182C2×D4—741no—
183C2×D4—741no—
184C2×D4—1484no—
185C22×C4—371no—
186C22×C4—371no—
187C22×C4—371no—
188C22×C4—371no—
189C22×C4—371no—
190C22×C4—741no—
191C22×C4—741no—
192C22×C4—741no—
193C22×C4—741no—
194C22×C4C4×D3712yes—
195C22×C4C22×D3711yescharacteristic
196M16—21no—
197M16—21no—
198M16—21no—
199M16—372no—
200M16—744no—
201M16—741no—
202M16—741no—
203M16—741no—
204M16D14812yescomplemented
205C2×C8—21no—
206C2×C8—21no—
207C2×C8—744no—
208C2×C8—741no—
209C2×C8—741no—
210C4⋊C4—21no—
211C4⋊C4—21no—
212C22⋊C4—742no—
213C22⋊C4—742no—
214C23—371no—
215C23—371no—
216C23—742no—
217C23—742no—
218C23—742no—
219C23—741no—
220C23—741no—
221C23—742no—
222C23—1482no—
223C23—1482no—
224C23—1481no—
225C23C2×C4×D3711yescharacteristic
226D4—1484no—
227D4—1484no—
228D4—1481no—
229D4—1481no—
230D4—1481no—
231D4—1481no—
232C2×C4—22no—
233C2×C4—42no—
234C2×C4—371no—
235C2×C4—371no—
236C2×C4—741no—
237C2×C4—741no—
238C2×C4—741no—
239C2×C4—741no—
240C2×C4—741no—
241C2×C4—741no—
242C2×C4—741no—
243C2×C4—741no—
244C2×C4—741no—
245C2×C4—741no—
246C2×C4C2×D14811yescharacteristic
247C2×C4#1059696211yescharacteristic
248C2×C4D4×D3711yescharacteristic
249C2×C4D4×D3711yescharacteristic
250C2×C4D4×D3711yescharacteristic
251C2×C4#1059696611yescharacteristic
252C8—22no—
253C8—41no—
254C8—742no—
255C8—1481no—
256C22—21no—
257C22—21no—
258C22—372no—
259C22—2962no—
260C22—2962no—
261C22—741no—
262C22—741no—
263C22—741no—
264C22—741no—
265C22—741no—
266C22—1482no—
267C22—1482no—
268C22—1482no—
269C22—1482no—
270C22—1482no—
271C22C22⋊C4×D3711yescharacteristic
272C22#1192449811yescharacteristic
273C22C4×D14811yescharacteristic
274C4—42no—
275C4—741no—
276C4—741no—
277C4#1192450611yescharacteristic
278C4#1192450911yescharacteristic
279C4#1192451111yescharacteristic
280C4#1192452111yescharacteristic
281C2—21no—
282C2—21no—
283C2—2962no—
284C2—742no—
285C2—1481no—
286C2#1455741111yescharacteristic
287C2#100×D3711yescharacteristic
288C2#1455751611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC23×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#343C2
socleC22×C37C2×C22⋊C4
prime radicalC2×#11924511C2
cosocleC22×C4×C37C23
hypercenter#343D37
hypocenterC37#1900
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×M16×D37C2semidirect
3. C2×#11924452C2semidirect
4. C2×#11924452C2semidirect
5. #14557496C2semidirect
6. #14557302C2semidirect
7. C37×#343C2semidirect
54. M16×C37D4semidirect
64. #10596934D4semidirect
128. C2×D37#100semidirect
151. #343D37semidirect
152. C37#1900semidirect
204. M16D148semidirect

Maximal subgroups

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

subgroupindex
C2×M16×D372
C2×#119245112
C2×#119244522
#145574962
#145573022
C37×#3432
#190037