Finite Group Databasebeta

← #18010449

Subgroups — #18010449

Order 4736.

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

normal subgroups only

This group has 536 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#14558531C212yesmaximal, complemented
2#14558526C212yesmaximal, complemented
3#14558519C211yesmaximal, characteristic, complemented
4#14558512C211yesmaximal, characteristic, complemented
5C2×#11924583C211yesmaximal, characteristic
6D37⋊M16C2212yes—
7#11924615C2212yes—
8#11924600—24no—
9#11924599—24no—
10#11924597—21no—
11#11924596—21no—
12#11924595—21no—
13#11924594—21no—
14#11924583—24no—
15#11924583—24no—
16C2×#10596962—21no—
17C2×#10596962C2211yescharacteristic
18C2×#10596964—21no—
19C2×#10596964—21no—
20C2×#10596964C411yescharacteristic, complemented
21C2×#10596964C2211yescharacteristic
22C22×Dic74—21no—
23C22×Dic74C411yescharacteristic, complemented
24C2×Q8×D37C411yescharacteristic, complemented
25C2×Q8×D37C2211yescharacteristic
26C2×#41×C37C411yescharacteristic, complemented
27#41×C37—22no—
28#41×C37—22no—
29C2×Q8×C37C2×C411yescharacteristic
30C2×D4×C37—21no—
31C2×D4×C37C2×C411yescharacteristic
32C22×C4×C37—21no—
33C22×C4×C37C2×C411yescharacteristic
34C2×C22⋊D37—21no—
35C2×C22⋊D37—21no—
36C2×C22⋊D37D411yescharacteristic
37C2×C22⋊D37D411yescharacteristic
38C22×Dic37—21no—
39C22×Dic37—21no—
40C22×Dic37—21no—
41Q8×D37—22no—
42Q8×D37—22no—
43Q8×D37—22no—
44Q8×D37D414yes—
45#10596964—28no—
46#10596964—28no—
47#10596964—22no—
48#10596964—22no—
49#10596964—22no—
50#10596964D414yes—
51#10596962—28no—
52#10596962—22no—
53#10596962—22no—
54C2×D148D411yescharacteristic
55C2×C4×D37—21no—
56C2×C4×D37—21no—
57C2×C4×D37C2×C411yescharacteristic
58C2×C4×D37C2311yescharacteristic
59C2×Dic74—28no—
60C2×Dic74—21no—
61C2×Dic74—21no—
62C2×Dic74—21no—
63C2×Dic74—22no—
64C2×Dic74—22no—
65C2×Dic74C2×C411yescharacteristic
66C2×Dic74C2×C411yescharacteristic
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×D37C22⋊C411yescharacteristic
77C22×D37C2×D411yescharacteristic
78C2×#3866—42no—
79Q8×C37—21no—
80Q8×C37C22⋊C412yes—
81D4×C37—24no—
82D4×C37—21no—
83D4×C37C22⋊C412yes—
84C2×C4×C37—24no—
85C2×C4×C37—21no—
86C2×C4×C37—21no—
87C2×C4×C37—21no—
88C2×C4×C37C22⋊C411yescharacteristic
89C2×C4×C37C22×C411yescharacteristic
90C22⋊D37—24no—
91C22⋊D37—22no—
92C22⋊D37—24no—
93C22⋊D37—22no—
94C2×Dic37—24no—
95C2×Dic37—24no—
96C2×Dic37—21no—
97C2×Dic37—21no—
98C2×Dic37—24no—
99C2×Dic37C22⋊C411yescharacteristic
100C2×Dic37C2×D411yescharacteristic
101D148—22no—
102C4×D37—24no—
103C4×D37—24no—
104C4×D37—21no—
105C4×D37—21no—
106C4×D37C2×D412yes—
107C4×D37C2×D412yes—
108Dic74—24no—
109Dic74—24no—
110Dic74—21no—
111Dic74—21no—
112Dic74—22no—
113Dic74—24no—
114Dic74C22⋊C412yes—
115Dic74C22⋊C412yes—
116#64438—42no—
117C22×C37—21no—
118C22×C37—22no—
119C22×C37—41no—
120C22×C37—42no—
121C22×C37C2×C22⋊C411yescharacteristic
122C2×D37—21no—
123C2×D37—41no—
124C2×D37—41no—
125C2×D37#12012yes—
126#3866—82no—
127C4×C37—21no—
128C4×C37—22no—
129C4×C37C2×C22⋊C411yescharacteristic
130C4×C37C2×C22⋊C411yescharacteristic
131Dic37—21no—
132Dic37—22no—
133Dic37—22no—
134Dic37#12012yes—
135#1796—371nomaximal, Sylow
136C2×C37—21no—
137C2×C37—41no—
138C2×C37—42no—
139C2×C37#37911yescharacteristic
140D37—22no—
141D37—41no—
142C2×2−1+4—371no—
143#421—372no—
144#419—372no—
145#413—371no—
146#410—371no—
147C37#179611yescharacteristic, complemented, Sylow
1482−1+4—744no—
1492−1+4—744no—
150C2×#41—371no—
151C2×#41—371no—
152C2×#41—371no—
153C2×#41—741no—
154C2×#41—741no—
155C2×#41—741no—
156C2×#41#386611yescharacteristic, complemented
157C22×Q8—371no—
158C22×Q8—371no—
159C22×Q8—371no—
160C22×Q8—741no—
161C2×M16—372no—
162#117—372no—
163#104—744no—
164#103—744no—
165#101—741no—
166#100—741no—
167#99—741no—
168#99—741no—
169#41—22no—
170#41—22no—
171#41—374no—
172#41—742no—
173#41—742no—
174#41—748no—
175#41—742no—
176#41—742no—
177#41—748no—
178#41—748no—
179#41—742no—
180C2×Q8—371no—
181C2×Q8—374no—
182C2×Q8—371no—
183C2×Q8—371no—
184C2×Q8—741no—
185C2×Q8—741no—
186C2×Q8—742no—
187C2×Q8—742no—
188C2×Q8—748no—
189C2×Q8—742no—
190C2×Q8—742no—
191C2×Q8—742no—
192C2×Q8—741no—
193C2×Q8C2×#386611yescharacteristic
194C2×D4—21no—
195C2×D4—371no—
196C2×D4—371no—
197C2×D4—371no—
198C2×D4—741no—
199C2×D4—741no—
200C2×D4C2×#386611yescharacteristic
201C22×C4—21no—
202C22×C4—371no—
203C22×C4—371no—
204C22×C4—741no—
205C22×C4—741no—
206C22×C4—741no—
207C22×C4—741no—
208C22×C4—741no—
209C22×C4C2×#386611yescharacteristic
210M16—742no—
211M16—742no—
212C2×C8—742no—
213C4⋊C4—742no—
214C22⋊C4—742no—
215C42—742no—
216C23—21no—
217C23—371no—
218C23—371no—
219C23C22⋊#386611yescharacteristic
220Q8—21no—
221Q8—372no—
222Q8—372no—
223Q8—742no—
224Q8—744no—
225Q8—744no—
226Q8—744no—
227Q8—741no—
228Q8—741no—
229Q8C22⋊#386612yes—
230D4—24no—
231D4—21no—
232D4—742no—
233D4—742no—
234D4—742no—
235D4—744no—
236D4—744no—
237D4C22⋊#386612yes—
238C2×C4—24no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—371no—
243C2×C4—372no—
244C2×C4—372no—
245C2×C4—371no—
246C2×C4—744no—
247C2×C4—744no—
248C2×C4—744no—
249C2×C4—744no—
250C2×C4—744no—
251C2×C4—741no—
252C2×C4—741no—
253C2×C4—741no—
254C2×C4—741no—
255C2×C4—1482no—
256C2×C4C22⋊#386611yescharacteristic
257C2×C4C22×#386611yescharacteristic
258C8—1482no—
259C22—21no—
260C22—22no—
261C22—41no—
262C22—42no—
263C22—372no—
264C22—741no—
265C22—1481no—
266C22—1481no—
267C22C2×C22⋊#386611yescharacteristic
268C4—21no—
269C4—22no—
270C4—372no—
271C4—2962no—
272C4—741no—
273C4—742no—
274C4—742no—
275C4C2×C22⋊#386611yescharacteristic
276C4C2×C22⋊#386611yescharacteristic
277C2—21no—
278C2—42no—
279C2—41no—
280C2—742no—
281C2—1481no—
282C2#1455847411yescharacteristic
subgroupG/H
centerC2#14558474
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×#41×C37C4
socleC2×C37#379
prime radicalC2×#11924583C2
cosocleC2×C4×D37C23
hypercenterC2×#41#3866
hypocenterC37#1796
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. #14558531C2semidirect
2. #14558526C2semidirect
3. #14558519C2semidirect
4. #14558512C2semidirect
20. C2×#10596964C4semidirect
23. C22×Dic74C4semidirect
24. C2×Q8×D37C4semidirect
26. C2×#41×C37C4semidirect
147. C37#1796semidirect
156. C2×#41#3866semidirect

Maximal subgroups

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

subgroupindex
#145585312
#145585262
#145585192
#145585122
C2×#119245832
#179637