Finite Group Databasebeta

← #18010630

Subgroups — #18010630

Order 4736.

346 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 66 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#14558600C211yesmaximal, characteristic, complemented
2#14558531C211yesmaximal, characteristic, complemented
3#14558525C211yesmaximal, characteristic, complemented
4#14558513C211yesmaximal, characteristic, complemented
5#14558415C211yesmaximal, characteristic, complemented
6#14558401C211yesmaximal, characteristic, complemented
7C2×#11924560C211yesmaximal, characteristic
8D37⋊M16C2211yescharacteristic
9D4×#3866—22no—
10D4×#3866—22no—
11#11924615C2211yescharacteristic
12#11924615C2211yescharacteristic
13#11924615C2211yescharacteristic
14C2×C22⋊#3866—22no—
15#11924600—22no—
16#11924598—22no—
17#11924594—22no—
18C2×#10596964C2211yescharacteristic
19C2×D4×D37C2211yescharacteristic
20#11924560—22no—
21#11924560—22no—
22C2×#10596930C411yescharacteristic, complemented
23C2×#10596940C411yescharacteristic, complemented
24C2×#10596939C411yescharacteristic, complemented
25C2×#10596929C2211yescharacteristic
26C2×D8×C37C411yescharacteristic, complemented
27C23×D37—21no—
28C22×#3866—24no—
29C2×D4×C37C2×C411yescharacteristic
30C2×D4×C37C2×C411yescharacteristic, complemented
31C2×C22⋊D37—21no—
32C2×C22⋊D37—21no—
33C22×Dic37—21no—
34#10596964—21no—
35#10596964—21no—
36#10596964—21no—
37#10596964—21no—
38D4×D37—21no—
39D4×D37—21no—
40D4×D37D412yes—
41D4×D37D412yes—
42C2×D148C2×C411yescharacteristic
43C2×C4×D37C2311yescharacteristic
44C2×Dic74C2×C411yescharacteristic, complemented
45C22⋊#3866—24no—
46C22⋊#3866—21no—
47C22⋊#3866—21no—
48C22⋊#3866D412yes—
49#10596957—21no—
50C4⋊#3866—21no—
51C4⋊#3866—21no—
52C4⋊#3866—21no—
53C4×#3866—21no—
54C4×#3866—21no—
55C4×#3866D412yes—
56#10596953—21no—
57D37⋊C8—21no—
58D8×C37—22no—
59C2×C8×C37C2×C411yescharacteristic, complemented
60#10596940—22no—
61#10596939—22no—
62C2×#64436C2×C411yescharacteristic, complemented
63#10596930—22no—
64#10596929—21no—
65#10596929—21no—
66C23×C37—21no—
67C23×C37—21no—
68C22×D37—21no—
69C22×D37—22no—
70C22×D37—22no—
71C22×D37—82no—
72C22×D37C2×D411yescharacteristic
73C2×#3866—22no—
74C2×#3866—22no—
75C2×#3866—41no—
76C2×#3866—84no—
77D4×C37—21no—
78D4×C37—21no—
79D4×C37—21no—
80D4×C37C22⋊C412yes—
81C2×C4×C37C22×C411yescharacteristic
82C22⋊D37—22no—
83C22⋊D37—22no—
84C22⋊D37—41no—
85C22⋊D37—41no—
86C2×Dic37—21no—
87C2×Dic37—41no—
88C2×Dic37—41no—
89C2×Dic37#4111yescharacteristic
90D148—21no—
91D148C22⋊C412yes—
92C4×D37C2×D411yescharacteristic
93C4×D37C2×D411yescharacteristic
94C4×D37C2×D411yescharacteristic
95C4×D37#4111yescharacteristic
96Dic74—21no—
97Dic74—21no—
98#64438—41no—
99C8×C37—21no—
100#64436—21no—
101C22×C37—22no—
102C22×C37—41no—
103C22×C37—81no—
104C22×C37—81no—
105C22×C37C4×D411yescharacteristic
106C2×D37—22no—
107C2×D37—41no—
108C2×D37—44no—
109C2×D37—82no—
110C2×D37—81no—
111C2×D37#12011yescharacteristic
112C2×D37#12111yescharacteristic
113#3866—42no—
114#3866—42no—
115#3866—81no—
116C4×C37C2×C22⋊C411yescharacteristic
117C4×C37C4×D411yescharacteristic
118Dic37—41no—
119Dic37#12111yescharacteristic
120Dic37#12311yescharacteristic
121#1904—371nomaximal, Sylow
122C2×C37—21no—
123C2×C37—42no—
124C2×C37—81no—
125C2×C37#38611yescharacteristic
126D37—21no—
127D37—21no—
128D37—42no—
129C2×AGL(1,ℤ/8)—371no—
130#518—371no—
131#421—371no—
132#418—371no—
133#410—371no—
134#344—371no—
135H(3,ℤ/4)—371no—
136C37#190411yescharacteristic, complemented, Sylow
137C2×#41—371no—
138C22×D4—371no—
139AGL(1,ℤ/8)—742no—
140AGL(1,ℤ/8)—742no—
141C2×SD16—371no—
142C2×SD16—371no—
143C2×D8—371no—
144C2×D8#386611yescharacteristic, complemented
145C2×M16—371no—
146C2×M16—371no—
147C4×D4—742no—
148C4×D4—742no—
149#117—371no—
150#117—371no—
151#117—371no—
152C2×C22⋊C4—742no—
153#104—742no—
154#102—742no—
155#99—742no—
156C24—741no—
157#41—741no—
158#41—741no—
159#41—741no—
160#41—741no—
161C2×Q8—371no—
162C2×D4—372no—
163C2×D4—372no—
164C2×D4—371no—
165C2×D4—741no—
166C2×D4—741no—
167C2×D4—741no—
168C2×D4—741no—
169C2×D4C2×#386611yescharacteristic
170C2×D4C2×#386611yescharacteristic, complemented
171C22×C4—371no—
172C22×C4—741no—
173C22×C4—744no—
174SD16—742no—
175SD16—742no—
176D8—22no—
177D8—742no—
178M16—741no—
179M16—741no—
180M16—741no—
181M16—741no—
182C2×C8—371no—
183C2×C8—741no—
184C2×C8C2×#386611yescharacteristic, complemented
185C4⋊C4—741no—
186C4⋊C4—741no—
187C4⋊C4—741no—
188C22⋊C4—372no—
189C22⋊C4—741no—
190C22⋊C4—744no—
191C22⋊C4—741no—
192C42—372no—
193C42—741no—
194C42—741no—
195C23—21no—
196C23—21no—
197C23—371no—
198C23—2962no—
199C23—742no—
200C23—742no—
201C23—741no—
202Q8—741no—
203Q8—741no—
204D4—21no—
205D4—21no—
206D4—21no—
207D4—372no—
208D4—742no—
209D4—742no—
210D4—741no—
211D4—1481no—
212D4—1481no—
213D4C22⋊#386612yes—
214C2×C4—371no—
215C2×C4—371no—
216C2×C4—371no—
217C2×C4—371no—
218C2×C4—371no—
219C2×C4—2964no—
220C2×C4—742no—
221C2×C4—742no—
222C2×C4—741no—
223C2×C4—1481no—
224C2×C4—1481no—
225C2×C4—1481no—
226C2×C4C22×#386611yescharacteristic
227C8—21no—
228C8—741no—
229C8—1481no—
230C22—22no—
231C22—41no—
232C22—81no—
233C22—81no—
234C22—371no—
235C22—371no—
236C22—2961no—
237C22—2962no—
238C22—742no—
239C22—1481no—
240C22—1484no—
241C22D4×#386611yescharacteristic
242C4—371no—
243C4—371no—
244C4—2961no—
245C4—1482no—
246C4—1482no—
247C4—1481no—
248C4C2×C22⋊#386611yescharacteristic
249C4D4×#386611yescharacteristic
250C2—21no—
251C2—42no—
252C2—81no—
253C2—741no—
254C2—741no—
255C2—1482no—
256C2#1455848111yescharacteristic
subgroupG/H
centerC2#14558481
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×D8×C37C4
socleC2×C37#386
prime radicalC2×#11924560C2
cosocleC2×C4×D37C23
hypercenterC2×D8#3866
hypocenterC37#1904
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #14558600C2semidirect
2. #14558531C2semidirect
3. #14558525C2semidirect
4. #14558513C2semidirect
5. #14558415C2semidirect
6. #14558401C2semidirect
22. C2×#10596930C4semidirect
23. C2×#10596940C4semidirect
24. C2×#10596939C4semidirect
26. C2×D8×C37C4semidirect
30. C2×D4×C37C2×C4semidirect
44. C2×Dic74C2×C4semidirect
59. C2×C8×C37C2×C4semidirect
62. C2×#64436C2×C4semidirect
136. C37#1904semidirect
144. C2×D8#3866semidirect
170. C2×D4C2×#3866semidirect
184. C2×C8C2×#3866semidirect

Maximal subgroups

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

subgroupindex
#145586002
#145585312
#145585252
#145585132
#145584152
#145584012
C2×#119245602
#190437