Finite Group Databasebeta

← #18010447

Subgroups — #18010447

Order 4736.

588 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 82 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#14558532C212yesmaximal, complemented
2#14558525C212yesmaximal, complemented
3#14558519C211yesmaximal, characteristic, complemented
4#14558512C211yesmaximal, characteristic, complemented
5C2×#11924582C211yesmaximal, characteristic
6D37⋊M16C2212yescomplemented
7#11924615C2212yescomplemented
8#11924601—24no—
9#11924598—24no—
10#11924597—21no—
11#11924596—21no—
12#11924595—21no—
13#11924594—21no—
14#11924582—24no—
15#11924582—24no—
16C2×#10596966C411yescharacteristic, complemented
17C2×#10596966C2211yescharacteristic
18C2×#10596962—21no—
19C2×#10596962C2211yescharacteristic
20C22×D148—21no—
21C22×D148C411yescharacteristic, complemented
22C2×D4×D37—21no—
23C2×D4×D37—21no—
24C2×D4×D37C411yescharacteristic, complemented
25C2×D4×D37C2211yescharacteristic
26C2×#41×C37C411yescharacteristic, complemented
27C23×D37—21no—
28C23×D37—21no—
29C23×D37—21no—
30#41×C37—22no—
31#41×C37—22no—
32C2×Q8×C37C2×C411yescharacteristic
33C2×D4×C37—21no—
34C2×D4×C37C2×C411yescharacteristic
35C22×C4×C37—21no—
36C22×C4×C37C2×C411yescharacteristic
37C2×C22⋊D37—21no—
38C2×C22⋊D37—21no—
39C2×C22⋊D37D411yescharacteristic
40C2×C22⋊D37D411yescharacteristic
41#10596966—22no—
42#10596966—22no—
43#10596966—22no—
44#10596966D414yes—
45D4×D37—28no—
46D4×D37—28no—
47D4×D37—22no—
48D4×D37—22no—
49D4×D37—22no—
50D4×D37D414yes—
51#10596962—28no—
52#10596962—22no—
53#10596962—22no—
54C2×D148—28no—
55C2×D148—21no—
56C2×D148—21no—
57C2×D148—21no—
58C2×D148—22no—
59C2×D148—22no—
60C2×D148C2×C411yescharacteristic
61C2×D148C2×C411yescharacteristic
62C2×D148D411yescharacteristic
63C2×C4×D37—21no—
64C2×C4×D37—21no—
65C2×C4×D37C2×C411yescharacteristic
66C2×C4×D37C2311yescharacteristic
67C2×Dic74D411yescharacteristic
68C22⋊#3866—22no—
69#10596957—22no—
70C4⋊#3866—22no—
71C4×#3866—22no—
72#10596953—22no—
73D37⋊C8—22no—
74C23×C37—21no—
75C23×C37C22⋊C411yescharacteristic
76C22×D37—21no—
77C22×D37—21no—
78C22×D37—24no—
79C22×D37—24no—
80C22×D37—24no—
81C22×D37—82no—
82C22×D37—82no—
83C22×D37—82no—
84C22×D37C22⋊C411yescharacteristic
85C22×D37C2×D411yescharacteristic
86C2×#3866—42no—
87Q8×C37—21no—
88Q8×C37C22⋊C412yes—
89D4×C37—24no—
90D4×C37—21no—
91D4×C37C22⋊C412yes—
92C2×C4×C37—24no—
93C2×C4×C37—21no—
94C2×C4×C37—21no—
95C2×C4×C37—21no—
96C2×C4×C37C22⋊C411yescharacteristic
97C2×C4×C37C22×C411yescharacteristic
98C22⋊D37—24no—
99C22⋊D37—22no—
100C22⋊D37—22no—
101C22⋊D37—24no—
102C2×Dic37C22⋊C411yescharacteristic
103C2×Dic37C2×D411yescharacteristic
104D148—24no—
105D148—24no—
106D148—22no—
107D148—24no—
108D148—21no—
109D148—21no—
110D148C22⋊C412yes—
111D148C22⋊C412yes—
112C4×D37—24no—
113C4×D37—21no—
114C4×D37—21no—
115C4×D37—24no—
116C4×D37C2×D412yes—
117C4×D37C2×D412yes—
118Dic74—22no—
119#64438—42no—
120C22×C37—21no—
121C22×C37—22no—
122C22×C37—41no—
123C22×C37—42no—
124C22×C37C2×C22⋊C411yescharacteristic
125C2×D37—21no—
126C2×D37—22no—
127C2×D37—22no—
128C2×D37—41no—
129C2×D37—42no—
130C2×D37—42no—
131C2×D37—41no—
132C2×D37—84no—
133C2×D37—84no—
134C2×D37—84no—
135C2×D37#12012yes—
136#3866—82no—
137C4×C37—21no—
138C4×C37—22no—
139C4×C37C2×C22⋊C411yescharacteristic
140C4×C37C2×C22⋊C411yescharacteristic
141Dic37—21no—
142Dic37#12012yes—
143#1795—371nomaximal, Sylow
144C2×C37—21no—
145C2×C37—41no—
146C2×C37—42no—
147C2×C37#37911yescharacteristic
148D37—22no—
149D37—42no—
150D37—42no—
151D37—41no—
152C2×H(5,𝔽2)—371no—
153#421—372no—
154#418—372no—
155#413—371no—
156#410—371no—
157C37#179511yescharacteristic, complemented, Sylow
158H(5,𝔽2)—744no—
159H(5,𝔽2)—744no—
160C2×#41—371no—
161C2×#41—371no—
162C2×#41—371no—
163C2×#41—741no—
164C2×#41#386611yescharacteristic, complemented
165C22×D4—371no—
166C22×D4—371no—
167C22×D4—371no—
168C22×D4—741no—
169C22×D4—741no—
170C22×D4—741no—
171C2×M16—372no—
172#117—372no—
173#104—744no—
174#102—744no—
175#101—741no—
176#100—741no—
177#99—741no—
178#99—741no—
179C24—741no—
180C24—741no—
181C24—741no—
182#41—22no—
183#41—22no—
184#41—374no—
185#41—742no—
186#41—742no—
187#41—748no—
188#41—742no—
189#41—742no—
190#41—742no—
191C2×Q8—371no—
192C2×Q8C2×#386611yescharacteristic
193C2×D4—21no—
194C2×D4—374no—
195C2×D4—371no—
196C2×D4—371no—
197C2×D4—371no—
198C2×D4—371no—
199C2×D4—371no—
200C2×D4—742no—
201C2×D4—742no—
202C2×D4—741no—
203C2×D4—741no—
204C2×D4—748no—
205C2×D4—742no—
206C2×D4—741no—
207C2×D4—741no—
208C2×D4—742no—
209C2×D4—748no—
210C2×D4—748no—
211C2×D4—742no—
212C2×D4—741no—
213C2×D4C2×#386611yescharacteristic
214C22×C4—21no—
215C22×C4—371no—
216C22×C4—371no—
217C22×C4—741no—
218C22×C4—741no—
219C22×C4C2×#386611yescharacteristic
220M16—742no—
221M16—742no—
222C2×C8—742no—
223C4⋊C4—742no—
224C22⋊C4—742no—
225C42—742no—
226C23—21no—
227C23—371no—
228C23—371no—
229C23—2962no—
230C23—2962no—
231C23—2962no—
232C23—744no—
233C23—744no—
234C23—744no—
235C23—741no—
236C23—741no—
237C23C22⋊#386611yescharacteristic
238Q8—21no—
239Q8—742no—
240Q8C22⋊#386612yes—
241D4—24no—
242D4—21no—
243D4—372no—
244D4—372no—
245D4—742no—
246D4—744no—
247D4—744no—
248D4—744no—
249D4—742no—
250D4—744no—
251D4—742no—
252D4—744no—
253D4—741no—
254D4—741no—
255D4C22⋊#386612yes—
256C2×C4—24no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—371no—
261C2×C4—372no—
262C2×C4—372no—
263C2×C4—371no—
264C2×C4—744no—
265C2×C4—744no—
266C2×C4—741no—
267C2×C4—741no—
268C2×C4—1482no—
269C2×C4C22⋊#386611yescharacteristic
270C2×C4C22×#386611yescharacteristic
271C8—1482no—
272C22—21no—
273C22—22no—
274C22—41no—
275C22—42no—
276C22—372no—
277C22—2964no—
278C22—2964no—
279C22—2964no—
280C22—742no—
281C22—742no—
282C22—741no—
283C22—1481no—
284C22—1481no—
285C22—1482no—
286C22—1482no—
287C22C2×C22⋊#386611yescharacteristic
288C4—21no—
289C4—22no—
290C4—372no—
291C4—2962no—
292C4—741no—
293C4C2×C22⋊#386611yescharacteristic
294C4C2×C22⋊#386611yescharacteristic
295C2—21no—
296C2—42no—
297C2—41no—
298C2—742no—
299C2—1482no—
300C2—1482no—
301C2—1481no—
302C2#1455847411yescharacteristic
subgroupG/H
centerC2#14558474
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×#41×C37C4
socleC2×C37#379
prime radicalC2×#11924582C2
cosocleC2×C4×D37C23
hypercenterC2×#41#3866
hypocenterC37#1795
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #14558532C2semidirect
2. #14558525C2semidirect
3. #14558519C2semidirect
4. #14558512C2semidirect
6. D37⋊M16C22semidirect
7. #11924615C22semidirect
16. C2×#10596966C4semidirect
21. C22×D148C4semidirect
24. C2×D4×D37C4semidirect
26. C2×#41×C37C4semidirect
157. C37#1795semidirect
164. C2×#41#3866semidirect

Maximal subgroups

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

subgroupindex
#145585322
#145585252
#145585192
#145585122
C2×#119245822
#179537