Finite Group Databasebeta

← #17997808

Subgroups — #17997808

Order 4736.

944 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 944 conjugacy classes of subgroups — too many to draw. Only its 167 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
1C22×#10596964C211yesmaximal, characteristic, complemented
2C2×D4×Dic37C212yesmaximal, complemented
3C2×#11924496C211yesmaximal, characteristic, complemented
4#14557454C211yesmaximal, characteristic, complemented
5#14557449C212yesmaximal, complemented
6#14557447C211yesmaximal, characteristic, complemented
7#14557445C211yesmaximal, characteristic, complemented
8#14557441C212yesmaximal, complemented
9C22⋊C4×Dic37C212yesmaximal, complemented
10#14557380C211yesmaximal, characteristic, complemented
11C37×#392C211yesmaximal, characteristic, complemented
12C2×#10596964—28no—
13C2×#10596964—24no—
14C22×Dic74C2211yescharacteristic
15C22×C22⋊D37C2211yescharacteristic
16C22×C22⋊D37C2212yes—
17C23×Dic37C2211yescharacteristic
18C23×Dic37C2212yes—
19C22×C4×D37C2211yescharacteristic
20D4×Dic37—28no—
21#11924496—24no—
22C2×C4⋊Dic37C2212yes—
23C2×#10596936C2211yescharacteristic
24C2×C22⋊Dic37C2212yes—
25C2×C22⋊Dic37C2212yes—
26C2×C22⋊Dic37C2212yes—
27C2×#10596938C2212yes—
28C2×#10596938C2211yescharacteristic
29C2×C4×Dic37C2211yescharacteristic
30C2×C4×Dic37C2212yes—
31#11924443C2212yes—
32#11924443C2211yescharacteristic
33#11924443C2212yes—
34C22×D4×C37C2212yes—
35C22×D4×C37C2211yescharacteristic
36C2×C22⋊C4×C37C2211yescharacteristic
37C2×C22⋊C4×C37C2212yes—
38#95×C37C2211yescharacteristic
39C24×C37C2312yes—
40C24×C37C2311yescharacteristic
41C23×D37C2311yescharacteristic
42C2×D4×C37—24no—
43C2×D4×C37—24no—
44C2×D4×C37—24no—
45C2×D4×C37—22no—
46C2×D4×C37—24no—
47C22×C4×C37C2311yescharacteristic
48C22×C4×C37C2311yescharacteristic
49C22×C4×C37C2312yes—
50C2×C22⋊D37—24no—
51C2×C22⋊D37—22no—
52C2×C22⋊D37—22no—
53C2×C22⋊D37—24no—
54C2×C22⋊D37—24no—
55C2×C22⋊D37—22no—
56C22×Dic37—24no—
57C22×Dic37—24no—
58C22×Dic37—22no—
59C22×Dic37—24no—
60C22×Dic37D418yescomplemented
61C22×Dic37C2312yes—
62C22×Dic37C2311yescharacteristic
63C22×Dic37C2312yes—
64C22×Dic37C2311yescharacteristic
65C22×Dic37C2311yescharacteristic
66#10596964—232no—
67C2×C4×D37—24no—
68C2×C4×D37D414yescomplemented
69C2×Dic74—22no—
70C2×Dic74—24no—
71C22⋊C4×C37—22no—
72C22⋊C4×C37—24no—
73C22⋊Dic37—24no—
74C22⋊Dic37—24no—
75C22⋊Dic37—24no—
76#10596938—22no—
77#10596938—24no—
78C4⋊Dic37—24no—
79#10596936—22no—
80C4×Dic37—22no—
81C4×Dic37—24no—
82C23×C37—22no—
83C23×C37—21no—
84C23×C37—22no—
85C23×C37—22no—
86C23×C37—22no—
87C23×C37—22no—
88C23×C37—21no—
89C23×C37—22no—
90C23×C37—22no—
91C23×C37—22no—
92C23×C37C2×D414yes—
93C23×C37#4112yescomplemented
94C23×C37C2411yescharacteristic
95C22×D37—22no—
96C22×D37—22no—
97C22×D37—21no—
98C22×D37—21no—
99C22×D37C2×D412yes—
100D4×C37—28no—
101D4×C37—216no—
102C2×C4×C37—22no—
103C2×C4×C37—22no—
104C2×C4×C37—22no—
105C2×C4×C37—21no—
106C2×C4×C37—22no—
107C2×C4×C37C2×D412yes—
108C2×C4×C37#4114yescomplemented
109C22⋊D37—216no—
110C22⋊D37—28no—
111C2×Dic37—21no—
112C2×Dic37—22no—
113C2×Dic37—22no—
114C2×Dic37—21no—
115C2×Dic37—216no—
116C2×Dic37—22no—
117C2×Dic37—21no—
118C2×Dic37—22no—
119C2×Dic37—22no—
120C2×Dic37—22no—
121C2×Dic37—44no—
122C2×Dic37C2×D414yes—
123C2×Dic37C2×D414yes—
124C2×Dic37C2×D412yes—
125C2×Dic37#4112yescomplemented
126C4×D37—28no—
127Dic74—28no—
128C22×C37—24no—
129C22×C37—22no—
130C22×C37—24no—
131C22×C37—24no—
132C22×C37—24no—
133C22×C37—41no—
134C22×C37—42no—
135C22×C37—42no—
136C22×C37—42no—
137C22×C37—42no—
138C22×C37—41no—
139C22×C37—42no—
140C22×C37C22×D411yescharacteristic
141C22×C37C22×D412yes—
142C22×C37C2×#4111yescharacteristic
143C22×C37C2×#4111yescharacteristic
144C22×C37C2×#4112yes—
145C2×D37—22no—
146C2×D37—22no—
147C2×D37—22no—
148C2×D37—42no—
149C2×D37—42no—
150C4×C37—22no—
151C4×C37—24no—
152C4×C37—41no—
153Dic37—24no—
154Dic37—22no—
155Dic37—41no—
156Dic37—42no—
157Dic37#12014yes—
158#2388—371nomaximal, Sylow
159C2×C37—44no—
160C2×C37—42no—
161C2×C37C2×#12011yescharacteristic
162C2×C37#52512yes—
163C2×C37#52511yescharacteristic
164C2×C37#53212yes—
165C2×C37#53211yescharacteristic
166D37—42no—
167C22×#41—371no—
168C2×C4×D4—372no—
169C2×C4×D4—371no—
170#395—371no—
171#394—371no—
172#394—372no—
173#393—371no—
174#392—372no—
175#392D3711yescharacteristic, complemented
176C4×C22⋊C4—372no—
177C4×C22⋊C4—371no—
178C37#238811yescharacteristic, complemented, Sylow
179C2×#41—748no—
180C2×#41—744no—
181C22×Q8—371no—
182C22×D4—371no—
183C22×D4—372no—
184C22×D4C2×D3712yes—
185C22×D4C2×D3711yescharacteristic
186C23×C4—372no—
187C23×C4—371no—
188C23×C4—371no—
189C4×D4—744no—
190C4×D4—748no—
191C2×C4⋊C4—371no—
192C2×C4⋊C4—372no—
193C2×C22⋊C4—372no—
194C2×C22⋊C4—372no—
195C2×C22⋊C4—372no—
196C2×C22⋊C4—371no—
197C2×C22⋊C4—372no—
198C2×C22⋊C4C2×D3711yescharacteristic
199C2×C22⋊C4C2×D3712yes—
200C2×C42—371no—
201C2×C42—372no—
202#95—372no—
203#95—372no—
204#95—371no—
205#95C2×D3711yescharacteristic
206C24—371no—
207C24C22×D3712yes—
208C24C22×D3711yescharacteristic
209#41—7432no—
210C2×Q8—744no—
211C2×Q8—742no—
212C2×D4—24no—
213C2×D4—24no—
214C2×D4—24no—
215C2×D4—22no—
216C2×D4—24no—
217C2×D4—742no—
218C2×D4—744no—
219C2×D4—742no—
220C2×D4—744no—
221C2×D4—744no—
222C2×D4—742no—
223C22×C4—371no—
224C22×C4—378no—
225C22×C4—371no—
226C22×C4—372no—
227C22×C4—374no—
228C22×C4—372no—
229C22×C4—371no—
230C22×C4—744no—
231C22×C4—744no—
232C22×C4—744no—
233C22×C4—742no—
234C22×C4—744no—
235C22×C4C22×D3711yescharacteristic
236C22×C4C22×D3711yescharacteristic
237C22×C4C22×D3712yes—
238C4⋊C4—744no—
239C4⋊C4—742no—
240C22⋊C4—22no—
241C22⋊C4—24no—
242C22⋊C4—742no—
243C22⋊C4—744no—
244C22⋊C4—744no—
245C22⋊C4—744no—
246C22⋊C4—744no—
247C42—744no—
248C42—742no—
249C23—21no—
250C23—22no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—21no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—22no—
259C23—372no—
260C23—742no—
261C23—741no—
262C23—742no—
263C23—741no—
264C23D4×D3714yes—
265C23#1059696412yescomplemented
266C23C23×D3711yescharacteristic
267Q8—748no—
268D4—28no—
269D4—216no—
270D4—7416no—
271D4—748no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—374no—
278C2×C4—372no—
279C2×C4—374no—
280C2×C4—372no—
281C2×C4—748no—
282C2×C4—7416no—
283C2×C4—741no—
284C2×C4—742no—
285C2×C4—742no—
286C2×C4—741no—
287C2×C4—742no—
288C2×C4—742no—
289C2×C4—741no—
290C2×C4—742no—
291C2×C4—742no—
292C2×C4—1484no—
293C2×C4D4×D3712yes—
294C2×C4#1059696414yescomplemented
295C22—24no—
296C22—24no—
297C22—24no—
298C22—22no—
299C22—24no—
300C22—41no—
301C22—42no—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—41no—
306C22—42no—
307C22—742no—
308C22—742no—
309C22—742no—
310C22—1482no—
311C22—1482no—
312C22C2×D4×D3712yes—
313C22C2×D4×D3711yescharacteristic
314C22#41×D3711yescharacteristic
315C22C2×#1059696411yescharacteristic
316C22C2×#1059696412yes—
317C4—22no—
318C4—24no—
319C4—41no—
320C4—374no—
321C4—744no—
322C4—742no—
323C4—1481no—
324C4—1482no—
325C2—44no—
326C2—42no—
327C2—1482no—
328C2#120×D3711yescharacteristic
329C2#1455803912yes—
330C2#1455804311yescharacteristic
331C2#1455807812yes—
332C2#1455808111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutator, socle, cosocleC23×C37C24
FittingC37×#392C2
hypercenter#392D37
hypocenterC37#2388
LCSG ▷ C23×C37 ▷ C37
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×#10596964C2semidirect
2. C2×D4×Dic37C2semidirect
3. C2×#11924496C2semidirect
4. #14557454C2semidirect
5. #14557449C2semidirect
6. #14557447C2semidirect
7. #14557445C2semidirect
8. #14557441C2semidirect
9. C22⋊C4×Dic37C2semidirect
10. #14557380C2semidirect
11. C37×#392C2semidirect
60. C22×Dic37D4semidirect
68. C2×C4×D37D4semidirect
93. C23×C37#41semidirect
108. C2×C4×C37#41semidirect
125. C2×Dic37#41semidirect
175. #392D37semidirect
178. C37#2388semidirect
265. C23#10596964semidirect
294. C2×C4#10596964semidirect

Maximal subgroups

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

subgroupindex
C22×#105969642
C2×D4×Dic372
C2×#119244962
#145574542
#145574492
#145574472
#145574452
#145574412
C22⋊C4×Dic372
#145573802
C37×#3922
#238837