Finite Group Databasebeta

← #18010587

Subgroups — #18010587

Order 4736.

324 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 70 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×#11924623C211yesmaximal, characteristic, complemented
2C2×#11924600C211yesmaximal, characteristic, complemented
3C2×#11924600C211yesmaximal, characteristic, complemented
4#14558507C211yesmaximal, characteristic, complemented
5#14558409C211yesmaximal, characteristic, complemented
6(C2×#3866)⋊C8C211yesmaximal, characteristic, complemented
7C2×#11924555C211yesmaximal, characteristic
8#11924623—22no—
9#11924623—22no—
10C2×#10596953C2211yescharacteristic
11C2×#10596953C2211yescharacteristic
12C2×#10596957—21no—
13C2×D37⋊C8C2211yescharacteristic
14C22×#64438—21no—
15C2×C4×#3866C2211yescharacteristic
16#11924600—22no—
17#11924600—22no—
18C22⋊#64438—21no—
19C22⋊#64438—21no—
20C2×#10596964C2211yescharacteristic
21C2×#10596964C2211yescharacteristic
22#11924555—22no—
23#11924555—22no—
24C2×Dic148C411yescharacteristic, complemented
25C2×#10596940C411yescharacteristic, complemented
26C2×#10596940C411yescharacteristic, complemented
27C2×C8×D37C2211yescharacteristic
28C2×D8×C37C411yescharacteristic, complemented
29C22×#3866—21no—
30C2×D4×C37C2×C411yescharacteristic
31C2×D4×C37C2×C411yescharacteristic
32C2×C22⋊D37—21no—
33C2×C22⋊D37—21no—
34C22×Dic37—21no—
35C22×Dic37—21no—
36#10596964—21no—
37#10596964—21no—
38#10596964—21no—
39#10596964—21no—
40#10596964—21no—
41#10596964—21no—
42#10596964D412yes—
43#10596964D412yes—
44C2×C4×D37C2311yescharacteristic
45C2×Dic74C2×C411yescharacteristic
46C2×Dic74C2×C411yescharacteristic
47#10596957—24no—
48C2×#64438—24no—
49C2×#64438—21no—
50C2×#64438—21no—
51C2×#64438D411yescharacteristic
52C2×#64438D411yescharacteristic
53C4×#3866—21no—
54C4×#3866—21no—
55#10596953—21no—
56#10596953—21no—
57#10596953—21no—
58#10596953D412yes—
59D37⋊C8—21no—
60D37⋊C8—21no—
61D8×C37—22no—
62C2×C8×C37C2×C411yescharacteristic
63#10596940—22no—
64#10596940—22no—
65C2×#64436C2×C411yescharacteristic
66Dic148—22no—
67C8×D37—21no—
68C8×D37—21no—
69C23×C37—21no—
70C23×C37—21no—
71C22×D37#4111yescharacteristic
72C2×#3866—22no—
73C2×#3866—41no—
74C2×#3866—41no—
75D4×C37—21no—
76D4×C37—21no—
77D4×C37—21no—
78D4×C37C22⋊C412yes—
79C2×C4×C37C22×C411yescharacteristic
80C22⋊D37—22no—
81C22⋊D37—22no—
82C22⋊D37—41no—
83C22⋊D37—41no—
84C2×Dic37—21no—
85C2×Dic37—22no—
86C2×Dic37—22no—
87C2×Dic37—21no—
88C2×Dic37—41no—
89C2×Dic37—41no—
90C2×Dic37C2×D411yescharacteristic
91C4×D37C2×D411yescharacteristic
92C4×D37C2×D411yescharacteristic
93C4×D37C2×D411yescharacteristic
94C4×D37#4111yescharacteristic
95Dic74—21no—
96Dic74—21no—
97Dic74—21no—
98Dic74C22⋊C412yes—
99#64438—21no—
100#64438—21no—
101#64438—22no—
102#64438—41no—
103C8×C37—21no—
104#64436—21no—
105C22×C37—22no—
106C22×C37—41no—
107C22×C37—41no—
108C22×C37—41no—
109C22×C37—41no—
110C22×C37—41no—
111C22×C37C4×D411yescharacteristic
112C2×D37—21no—
113C2×D37—21no—
114C2×D37#12111yescharacteristic
115C2×D37#12311yescharacteristic
116#3866—42no—
117C4×C37C2×C22⋊C411yescharacteristic
118C4×C37C4×D411yescharacteristic
119Dic37—22no—
120Dic37—41no—
121Dic37#12011yescharacteristic
122Dic37#12111yescharacteristic
123#1876—371nomaximal, Sylow
124C2×C37—42no—
125C2×C37—81no—
126C2×C37#38611yescharacteristic
127C2×C37#44311yescharacteristic
128C2×C37#44411yescharacteristic
129D37—21no—
130D37—21no—
131C2×#135—371no—
132C2×#131—371no—
133C2×#104—371no—
134C2×#104—371no—
135#408—371no—
136#341—371no—
137#336—371no—
138C37#187611yescharacteristic, complemented, Sylow
139C2×#41—371no—
140C2×#41—371no—
141#135—742no—
142#135—742no—
143C2×Q16—371no—
144C2×SD16—371no—
145C2×SD16—371no—
146C2×D8#386611yescharacteristic, complemented
147#131—742no—
148#131—742no—
149C2×M16—371no—
150C2×M16—371no—
151C2×M16—741no—
152C22×C8—371no—
153C22×C8—371no—
154C22×C8—741no—
155C2×C42—371no—
156#104—742no—
157#104—742no—
158C22⋊C8—741no—
159C22⋊C8—741no—
160#41—372no—
161#41—372no—
162#41—741no—
163#41—741no—
164#41—741no—
165#41—741no—
166#41—741no—
167#41—741no—
168C2×Q8—371no—
169C2×Q8—371no—
170C2×D4—741no—
171C2×D4—741no—
172C2×D4C2×#386611yescharacteristic
173C2×D4C2×#386611yescharacteristic
174C22×C4—371no—
175C22×C4—741no—
176C22×C4—741no—
177C22×C4—741no—
178Q16—742no—
179SD16—742no—
180SD16—742no—
181D8—22no—
182M16—372no—
183M16—741no—
184M16—744no—
185M16—741no—
186M16—741no—
187C2×C8—371no—
188C2×C8—371no—
189C2×C8—371no—
190C2×C8—741no—
191C2×C8—741no—
192C2×C8—741no—
193C2×C8—741no—
194C2×C8—741no—
195C2×C8—744no—
196C2×C8—741no—
197C2×C8C2×#386611yescharacteristic
198C42—741no—
199C42—741no—
200C23—21no—
201C23—21no—
202C23—371no—
203Q8—372no—
204Q8—741no—
205Q8—741no—
206Q8—741no—
207D4—21no—
208D4—21no—
209D4—21no—
210D4—742no—
211D4—742no—
212D4—1481no—
213D4—1481no—
214D4C22⋊#386612yes—
215C2×C4—371no—
216C2×C4—371no—
217C2×C4—371no—
218C2×C4—371no—
219C2×C4—371no—
220C2×C4—742no—
221C2×C4—742no—
222C2×C4—741no—
223C2×C4—742no—
224C2×C4—741no—
225C2×C4—1481no—
226C2×C4—1481no—
227C2×C4—1481no—
228C2×C4—1481no—
229C2×C4C22×#386611yescharacteristic
230C8—21no—
231C8—741no—
232C8—741no—
233C8—742no—
234C8—741no—
235C8—1481no—
236C22—22no—
237C22—41no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—371no—
243C22—371no—
244C22—741no—
245C22—741no—
246C22D4×#386611yescharacteristic
247C4—371no—
248C4—371no—
249C4—742no—
250C4—1482no—
251C4—1481no—
252C4C2×C22⋊#386611yescharacteristic
253C4D4×#386611yescharacteristic
254C2—42no—
255C2—81no—
256C2—741no—
257C2—741no—
258C2#1455848111yescharacteristic
259C2#1455857511yescharacteristic
260C2#1455858011yescharacteristic
subgroupG/H
centerC22D4×#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×D8×C37C4
socleC22×C37C4×D4
prime radicalC2×#11924555C2
cosocleC2×C4×D37C23
hypercenterC2×D8#3866
hypocenterC37#1876
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#11924623C2semidirect
2. C2×#11924600C2semidirect
3. C2×#11924600C2semidirect
4. #14558507C2semidirect
5. #14558409C2semidirect
6. (C2×#3866)⋊C8C2semidirect
24. C2×Dic148C4semidirect
25. C2×#10596940C4semidirect
26. C2×#10596940C4semidirect
28. C2×D8×C37C4semidirect
138. C37#1876semidirect
146. C2×D8#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119246232
C2×#119246002
#145585072
#145584092
(C2×#3866)⋊C82
C2×#119245552
#187637