Finite Group Databasebeta

← #18003894

Subgroups — #18003894

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×#11924583C211yesmaximal, characteristic
2C2×#11924566C211yesmaximal, characteristic, complemented
3C22×Dic148C211yesmaximal, characteristic, complemented
4#14558109C211yesmaximal, characteristic, complemented
5#14557696C214yesmaximal, complemented
6#14557690C214yesmaximal, complemented
7#14557541C211yesmaximal, characteristic, complemented
8#14557499C211yesmaximal, characteristic, complemented
9C37×#416C211yesmaximal, characteristic, complemented
10#11924583—24no—
11#11924583—24no—
12C2×#10596962—21no—
13C2×#10596962C2211yescharacteristic
14C2×#10596964—22no—
15C2×#10596964C2212yes—
16C22×Dic74—21no—
17C22×Dic74C2211yescharacteristic
18C22×Dic74C2211yescharacteristic
19C2×Q8×D37C2212yes—
20#11924566—24no—
21C2×Dic148—24no—
22C2×Dic148C2214yes—
23C2×#10596942C2212yes—
24C2×#10596940C2212yes—
25C2×#10596934C2211yescharacteristic
26#11924536—21no—
27#11924524—21no—
28#11924520—22no—
29#11924516C2214yes—
30#11924459C2214yes—
31#11924448C2214yes—
32C2×#41×C37C2211yescharacteristic
33C22×C8×C37C2211yescharacteristic
34#117×C37C2211yescharacteristic
35#103×C37C2212yes—
36#102×C37C2212yes—
37#41×C37—22no—
38#41×C37D414yes—
39C2×Q8×C37C2311yescharacteristic
40C2×D4×C37—21no—
41C2×D4×C37C2311yescharacteristic
42C22×C4×C37—21no—
43C22×C4×C37C2311yescharacteristic
44C2×C22⋊D37—22no—
45C2×C22⋊D37D412yes—
46C22×Dic37—21no—
47C22×Dic37—22no—
48C22×Dic37—21no—
49Q8×D37—24no—
50Q8×D37—24no—
51#10596964—216no—
52#10596964—24no—
53#10596964—24no—
54#10596962—28no—
55#10596962—22no—
56#10596962—22no—
57C2×D148D411yescharacteristic
58C2×C4×D37—22no—
59C2×C4×D37C2312yes—
60C2×Dic74—28no—
61C2×Dic74—21no—
62C2×Dic74—22no—
63C2×Dic74—22no—
64C2×Dic74—22no—
65C2×Dic74—22no—
66C2×Dic74—21no—
67C2×Dic74D411yescharacteristic
68C2×Dic74D414yes—
69C2×Dic74C2312yes—
70C2×Dic74C2312yes—
71C2×C8×C37—22no—
72C2×C8×C37C2312yes—
73C4⋊C4×C37C2312yes—
74C22⋊C4×C37—21no—
75C42×C37—21no—
76#10596942—24no—
77#10596940—24no—
78#10596938—24no—
79C4⋊Dic37—24no—
80#10596934—22no—
81C2×#64436C2312yes—
82Dic148—28no—
83C23×C37—21no—
84C23×C37C2×D411yescharacteristic
85C22×D37C2×D412yes—
86Q8×C37—21no—
87Q8×C37C2×D412yes—
88D4×C37—24no—
89D4×C37—21no—
90D4×C37C2×D412yes—
91C2×C4×C37—21no—
92C2×C4×C37—24no—
93C2×C4×C37—22no—
94C2×C4×C37C2×D412yes—
95C2×C4×C37C2×D411yescharacteristic
96C2×C4×C37C2×D412yes—
97C2×C4×C37C2411yescharacteristic
98C22⋊D37—28no—
99C22⋊D37—24no—
100C2×Dic37—28no—
101C2×Dic37—24no—
102C2×Dic37—22no—
103C2×Dic37—22no—
104C2×Dic37—42no—
105C2×Dic37C2×D412yes—
106D148—22no—
107C4×D37—28no—
108C4×D37—22no—
109C4×D37—22no—
110Dic74—28no—
111Dic74—22no—
112Dic74—24no—
113Dic74—22no—
114Dic74—22no—
115Dic74—22no—
116Dic74—42no—
117Dic74C2×D414yes—
118C8×C37—22no—
119#64436—22no—
120C22×C37—22no—
121C22×C37—22no—
122C22×C37—42no—
123C22×C37#12012yes—
124C22×C37C22×D411yescharacteristic
125C2×D37—22no—
126C2×D37—24no—
127C4×C37—22no—
128C4×C37—42no—
129C4×C37#12012yes—
130C4×C37C22×D411yescharacteristic
131C4×C37C22×D411yescharacteristic
132Dic37—22no—
133Dic37—24no—
134Dic37—42no—
135#3011—371nomaximal, Sylow
136C2×C37—22no—
137C2×C37—42no—
138C2×C37C2×#12011yescharacteristic
139C2×C37#57812yes—
140D37—42no—
141C2×2−1+4—371no—
142C2×#137—371no—
143C22×Q16—371no—
144#536—371no—
145#452—374no—
146#451—374no—
147#419—371no—
148#416D3711yescharacteristic, complemented
149#408—371no—
150C37#301111yescharacteristic, complemented, Sylow
1512−1+4—744no—
1522−1+4—744no—
153C2×#41—371no—
154C2×#41—372no—
155C2×#41—741no—
156C2×#41—742no—
157C2×#41C2×D3711yescharacteristic
158C22×Q8—372no—
159C22×Q8—371no—
160C22×Q8—371no—
161C22×Q8—741no—
162#137—744no—
163C2×Q16—372no—
164C2×Q16—374no—
165C2×Q16—744no—
166C2×SD16—372no—
167C2×M16—371no—
168C22×C8C2×D3711yescharacteristic
169C4⋊Q8—741no—
170#124—741no—
171#123—742no—
172C22⋊Q8—374no—
173#117C2×D3711yescharacteristic
174#103—374no—
175#103C2×D3712yes—
176#102C2×D3712yes—
177C22⋊C8—374no—
178#41—22no—
179#41—748no—
180#41—744no—
181#41—7416no—
182#41—744no—
183#41—742no—
184#41—742no—
185#41D14814yes—
186C2×Q8—371no—
187C2×Q8—374no—
188C2×Q8—372no—
189C2×Q8—372no—
190C2×Q8—742no—
191C2×Q8—748no—
192C2×Q8—744no—
193C2×Q8—744no—
194C2×Q8—742no—
195C2×Q8—741no—
196C2×Q8—741no—
197C2×Q8—742no—
198C2×Q8—742no—
199C2×Q8C22×D3711yescharacteristic
200C2×D4—21no—
201C2×D4—372no—
202C2×D4—371no—
203C2×D4—742no—
204C2×D4C22×D3711yescharacteristic
205C22×C4—21no—
206C22×C4—372no—
207C22×C4—742no—
208C22×C4—742no—
209C22×C4—741no—
210C22×C4—741no—
211C22×C4C22×D3711yescharacteristic
212Q16—748no—
213Q16—744no—
214SD16—744no—
215M16—742no—
216C2×C8—22no—
217C2×C8—372no—
218C2×C8C22×D3712yes—
219C4⋊C4—744no—
220C4⋊C4C22×D3712yes—
221C22⋊C4—21no—
222C22⋊C4—744no—
223C42—21no—
224C23—21no—
225C23—372no—
226C23D4×D3711yescharacteristic
227Q8—21no—
228Q8—374no—
229Q8—748no—
230Q8—742no—
231Q8—744no—
232Q8—742no—
233Q8—742no—
234Q8—742no—
235Q8—1482no—
236Q8C2×D14812yes—
237D4—24no—
238D4—21no—
239D4—748no—
240D4—744no—
241D4—742no—
242D4C2×D14812yes—
243C2×C4—21no—
244C2×C4—24no—
245C2×C4—22no—
246C2×C4—372no—
247C2×C4—748no—
248C2×C4—748no—
249C2×C4—744no—
250C2×C4—742no—
251C2×C4—742no—
252C2×C4—742no—
253C2×C4—742no—
254C2×C4—1482no—
255C2×C4C2×D14812yes—
256C2×C4D4×D3711yescharacteristic
257C2×C4D4×D3712yes—
258C2×C4C23×D3711yescharacteristic
259C8—22no—
260C8—742no—
261C22—22no—
262C22—22no—
263C22—42no—
264C22—742no—
265C22—744no—
266C22#1192450612yes—
267C22C2×D4×D3711yescharacteristic
268C4—22no—
269C4—42no—
270C4—742no—
271C4—744no—
272C4—1482no—
273C4#1192450612yes—
274C4C2×D4×D3711yescharacteristic
275C4C22×D14811yescharacteristic
276C2—22no—
277C2—42no—
278C2—1482no—
279C2C2×#1192450611yescharacteristic
280C2#1455834712yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#416C2
socleC22×C37C22×D4
prime radicalC2×#11924583C2
hypercenter#416D37
hypocenterC37#3011
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. C2×#11924566C2semidirect
3. C22×Dic148C2semidirect
4. #14558109C2semidirect
5. #14557696C2semidirect
6. #14557690C2semidirect
7. #14557541C2semidirect
8. #14557499C2semidirect
9. C37×#416C2semidirect
148. #416D37semidirect
150. C37#3011semidirect

Maximal subgroups

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

subgroupindex
C2×#119245832
C2×#119245662
C22×Dic1482
#145581092
#145576962
#145576902
#145575412
#145574992
C37×#4162
#301137