Finite Group Databasebeta

← #18003887

Subgroups — #18003887

Order 4736.

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

normal subgroups only

This group has 700 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
1C2×#11924584C211yesmaximal, characteristic
2C2×#11924567C211yesmaximal, characteristic, complemented
3#14558107C211yesmaximal, characteristic, complemented
4#14557694C214yesmaximal, complemented
5#14557687C214yesmaximal, complemented
6#14557542C211yesmaximal, characteristic, complemented
7#14557530C211yesmaximal, characteristic, complemented
8#14557499C211yesmaximal, characteristic, complemented
9C22×Q16×C37C211yesmaximal, characteristic, complemented
10#11924584—24no—
11#11924584—24no—
12C2×#10596966—21no—
13C2×#10596966C2212yes—
14C2×#10596962—22no—
15C2×#10596962C2211yescharacteristic
16C2×#10596962C2211yescharacteristic
17C2×Q8×D37—21no—
18C2×Q8×D37C2212yes—
19#11924567—24no—
20C2×#10596942C2212yes—
21C2×#10596941C2212yes—
22C2×#10596934C2211yescharacteristic
23#11924534—21no—
24#11924525—21no—
25#11924519—22no—
26#11924512C2214yes—
27#11924495C2211yescharacteristic
28#11924461C2212yes—
29#11924460C2214yes—
30#11924458C2212yes—
31#11924448C2214yes—
32C22×Q8×C37C2211yescharacteristic
33C22×Q8×C37C2211yescharacteristic
34C2×Q16×C37—24no—
35C2×Q16×C37C2214yes—
36C22×C8×C37C2211yescharacteristic
37C2×Q8×C37—21no—
38C2×Q8×C37—22no—
39C2×Q8×C37—21no—
40C2×Q8×C37—22no—
41C2×Q8×C37—22no—
42C2×Q8×C37D414yes—
43C2×Q8×C37C2312yes—
44C2×Q8×C37C2312yes—
45C22×C4×C37—21no—
46C22×C4×C37—21no—
47C22×C4×C37C2311yescharacteristic
48C2×C22⋊D37—21no—
49C2×C22⋊D37D412yes—
50#10596966—28no—
51#10596966—24no—
52#10596966—24no—
53Q8×D37—28no—
54Q8×D37—24no—
55Q8×D37—24no—
56#10596962—216no—
57#10596962—22no—
58#10596962—22no—
59#10596962—22no—
60#10596962D414yes—
61C2×D148—22no—
62C2×D148D411yescharacteristic
63C2×D148C2311yescharacteristic
64C2×C4×D37—22no—
65C2×C4×D37—21no—
66C2×C4×D37—22no—
67C2×C4×D37C2312yes—
68C2×Dic74—22no—
69C2×Dic74D411yescharacteristic
70C2×Dic74C2311yescharacteristic
71Q16×C37—28no—
72C2×C8×C37—22no—
73C2×C8×C37C2312yes—
74C22⋊Dic37—21no—
75#10596942—24no—
76#10596941—24no—
77#10596938—24no—
78C4⋊Dic37C2312yes—
79#10596936—24no—
80C4×Dic37—21no—
81#10596934—22no—
82C2×#64436C2312yes—
83C23×C37C2×D411yescharacteristic
84C22×D37—21no—
85C22×D37C2×D412yes—
86Q8×C37—24no—
87Q8×C37—22no—
88Q8×C37—22no—
89Q8×C37—22no—
90Q8×C37—42no—
91Q8×C37C2×D414yes—
92C2×C4×C37—24no—
93C2×C4×C37—22no—
94C2×C4×C37—22no—
95C2×C4×C37—42no—
96C2×C4×C37C2×D411yescharacteristic
97C2×C4×C37C2×D412yes—
98C2×C4×C37C2×D412yes—
99C2×C4×C37C2411yescharacteristic
100C22⋊D37—24no—
101C22⋊D37—24no—
102C2×Dic37—21no—
103C2×Dic37—22no—
104C2×Dic37C2×D412yes—
105D148—28no—
106D148—22no—
107D148—21no—
108D148C2×D412yes—
109C4×D37—28no—
110C4×D37—28no—
111C4×D37—24no—
112C4×D37—22no—
113C4×D37—22no—
114Dic74—28no—
115Dic74—22no—
116Dic74—21no—
117Dic74C2×D412yes—
118C8×C37—22no—
119#64436—22no—
120C22×C37—22no—
121C22×C37#12012yes—
122C22×C37C22×D411yescharacteristic
123C2×D37—22no—
124C2×D37—22no—
125C2×D37—24no—
126C2×D37—42no—
127C4×C37—24no—
128C4×C37—42no—
129C4×C37#12012yes—
130C4×C37C22×D411yescharacteristic
131C4×C37C22×D411yescharacteristic
132Dic37—22no—
133Dic37—22no—
134Dic37—42no—
135#3011—371nomaximal, Sylow
136C2×C37—22no—
137C2×C37C2×#12011yescharacteristic
138C2×C37#57812yes—
139D37—42no—
140D37—42no—
141C2×2−1+4—371no—
142C2×#137—371no—
143C22×Q16D3711yescharacteristic, complemented
144#536—371no—
145#452—374no—
146#451—374no—
147#419—371no—
148#416—371no—
149#408—371no—
150C37#301111yescharacteristic, complemented, Sylow
1512−1+4—744no—
1522−1+4—744no—
153C2×#41—371no—
154C2×#41—372no—
155C2×#41—371no—
156C2×#41—742no—
157C2×#41—741no—
158C22×Q8—372no—
159C22×Q8—741no—
160C22×Q8C2×D3711yescharacteristic
161C22×Q8C2×D3711yescharacteristic
162#137—744no—
163C2×Q16—24no—
164C2×Q16—372no—
165C2×Q16C2×D3714yes—
166C2×SD16—372no—
167C2×M16—371no—
168C22×C8C2×D3711yescharacteristic
169C4⋊Q8—741no—
170#124—741no—
171#123—742no—
172C22⋊Q8—374no—
173#117—371no—
174#103—374no—
175#103—372no—
176#102—372no—
177C22⋊C8—374no—
178#41—374no—
179#41—7416no—
180#41—744no—
181#41—748no—
182#41—744no—
183#41—742no—
184#41—742no—
185#41—742no—
186C2×Q8—21no—
187C2×Q8—22no—
188C2×Q8—21no—
189C2×Q8—22no—
190C2×Q8—22no—
191C2×Q8—371no—
192C2×Q8—371no—
193C2×Q8—742no—
194C2×Q8—744no—
195C2×Q8—748no—
196C2×Q8—744no—
197C2×Q8C22⋊D3714yes—
198C2×Q8C22×D3712yes—
199C2×Q8C22×D3712yes—
200C2×D4—372no—
201C2×D4—371no—
202C2×D4—371no—
203C2×D4—742no—
204C2×D4—741no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—372no—
208C22×C4—742no—
209C22×C4—742no—
210C22×C4—741no—
211C22×C4C22×D3711yescharacteristic
212Q16—28no—
213Q16—744no—
214SD16—744no—
215M16—742no—
216C2×C8—22no—
217C2×C8—372no—
218C2×C8C22×D3712yes—
219C4⋊C4—372no—
220C4⋊C4—744no—
221C22⋊C4—744no—
222C22⋊C4—741no—
223C42—741no—
224C23—372no—
225C23—741no—
226C23D4×D3711yescharacteristic
227Q8—24no—
228Q8—22no—
229Q8—22no—
230Q8—22no—
231Q8—42no—
232Q8—372no—
233Q8—748no—
234Q8—742no—
235Q8—741no—
236Q8C2×C22⋊D3714yes—
237D4—372no—
238D4—748no—
239D4—744no—
240D4—744no—
241D4—742no—
242D4—741no—
243C2×C4—24no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—372no—
248C2×C4—748no—
249C2×C4—748no—
250C2×C4—741no—
251C2×C4—744no—
252C2×C4—742no—
253C2×C4—742no—
254C2×C4—742no—
255C2×C4D4×D3711yescharacteristic
256C2×C4D4×D3712yes—
257C2×C4C2×C22⋊D3712yes—
258C2×C4C23×D3711yescharacteristic
259C8—22no—
260C8—742no—
261C22—22no—
262C22—742no—
263C22—742no—
264C22—744no—
265C22—1482no—
266C22#1192450412yes—
267C22C2×D4×D3711yescharacteristic
268C4—24no—
269C4—42no—
270C4—742no—
271C4—742no—
272C4—1482no—
273C4#1192450412yes—
274C4C2×D4×D3711yescharacteristic
275C4C22×C22⋊D3711yescharacteristic
276C2—22no—
277C2—1482no—
278C2—1482no—
279C2C2×#1192450411yescharacteristic
280C2#1455834612yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC22×Q16×C37C2
socleC22×C37C22×D4
prime radicalC2×#11924584C2
hypercenterC22×Q16D37
hypocenterC37#3011
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
2. C2×#11924567C2semidirect
3. #14558107C2semidirect
4. #14557694C2semidirect
5. #14557687C2semidirect
6. #14557542C2semidirect
7. #14557530C2semidirect
8. #14557499C2semidirect
9. C22×Q16×C37C2semidirect
143. C22×Q16D37semidirect
150. C37#3011semidirect

Maximal subgroups

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

subgroupindex
C2×#119245842
C2×#119245672
#145581072
#145576942
#145576872
#145575422
#145575302
#145574992
C22×Q16×C372
#301137