Finite Group Databasebeta

← #18010563

Subgroups — #18010563

Order 4736.

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

normal subgroups only

This group has 270 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
2C2×#11924607C211yesmaximal, characteristic, complemented
3#14558540C211yesmaximal, characteristic, complemented
4C2×#11924600C211yesmaximal, characteristic
5#14558403C211yesmaximal, characteristic, complemented
6(C2×#3866)⋊C8C211yesmaximal, characteristic, complemented
7#14557526C211yesmaximal, characteristic
8#11924623—22no—
9#11924623—22no—
10C2×#10596953C2211yescharacteristic
11C2×#10596953C2211yescharacteristic
12C2×#10596957—21no—
13C2×D37⋊C8C2211yescharacteristic
14C22×#64438—21no—
15C2×C4×#3866C2211yescharacteristic
16#11924607—22no—
17#11924603—21no—
18C4⋊#64438—21no—
19#11924600—22no—
20C2×#10596964C2211yescharacteristic
21C2×C8×D37C2211yescharacteristic
22#11924494C2211yescharacteristic
23#11924461C411yescharacteristic, complemented
24#11924459C411yescharacteristic, complemented
25#11924457C411yescharacteristic, complemented
26#102×C37C411yescharacteristic, complemented
27C22×#3866—21no—
28C2×D4×C37C2×C411yescharacteristic
29C2×C22⋊D37—21no—
30C22×Dic37—21no—
31#10596964—21no—
32#10596964—21no—
33#10596964D412yes—
34#10596964Q812yes—
35C2×C4×D37C2311yescharacteristic
36C2×Dic74C2×C411yescharacteristic
37#10596957—24no—
38C2×#64438—24no—
39C2×#64438—21no—
40C2×#64438—21no—
41C2×#64438D411yescharacteristic
42C2×#64438D411yescharacteristic
43C4×#3866—21no—
44C4×#3866—21no—
45#10596953—21no—
46#10596953—21no—
47#10596953—21no—
48#10596953D412yes—
49D37⋊C8—21no—
50D37⋊C8—21no—
51C2×C8×C37C2×C411yescharacteristic
52C4⋊C4×C37C2×C411yescharacteristic
53#10596938—21no—
54C4⋊Dic37C2×C411yescharacteristic
55C4×Dic37—21no—
56C2×#64436C2×C411yescharacteristic
57C8×D37—21no—
58C8×D37—21no—
59C23×C37—21no—
60C22×D37#4111yescharacteristic
61C2×#3866—22no—
62C2×#3866—41no—
63C2×#3866—41no—
64D4×C37—21no—
65D4×C37C4⋊C412yes—
66C2×C4×C37—21no—
67C2×C4×C37C22×C411yescharacteristic
68C22⋊D37—22no—
69C22⋊D37—22no—
70C2×Dic37—21no—
71C2×Dic37—22no—
72C2×Dic37—22no—
73C2×Dic37—21no—
74C2×Dic37C2×D411yescharacteristic
75C4×D37C2×D411yescharacteristic
76C4×D37C2×D411yescharacteristic
77C4×D37C2×Q811yescharacteristic
78C4×D37#4111yescharacteristic
79Dic74—21no—
80Dic74C4⋊C412yes—
81#64438—21no—
82#64438—21no—
83#64438—22no—
84#64438—41no—
85C8×C37—21no—
86#64436—21no—
87C22×C37—22no—
88C22×C37—41no—
89C22×C37—41no—
90C22×C37C4×D411yescharacteristic
91C2×D37—21no—
92C2×D37—21no—
93C2×D37C22⋊Q811yescharacteristic
94C2×D37#12311yescharacteristic
95#3866—42no—
96C4×C37—41no—
97C4×C37C2×C4⋊C411yescharacteristic
98C4×C37C4×D411yescharacteristic
99Dic37—22no—
100Dic37—41no—
101Dic37#12011yescharacteristic
102Dic37C22⋊Q811yescharacteristic
103#1866—371nomaximal, Sylow
104C2×C37—42no—
105C2×C37#38511yescharacteristic
106C2×C37#44311yescharacteristic
107C2×C37#44411yescharacteristic
108D37—21no—
109D37—21no—
110C2×#131—371no—
111C2×#108—371no—
112#424—371no—
113C2×#104—371no—
114#416—371no—
115#339—371no—
116#336—371no—
117C37#186611yescharacteristic, complemented, Sylow
118C2×#41—371no—
119#131—742no—
120#131—742no—
121C2×M16—371no—
122C2×M16—371no—
123C2×M16—741no—
124C22×C8—371no—
125C22×C8—371no—
126C22×C8—741no—
127#117—371no—
128C2×C42—371no—
129#108—742no—
130C4⋊C8—741no—
131C4⋊C8—741no—
132#104—742no—
133#103—371no—
134#103—371no—
135#102—371no—
136#102#386611yescharacteristic, complemented
137#41—372no—
138#41—372no—
139#41—741no—
140#41—741no—
141C2×Q8—371no—
142C2×D4—741no—
143C2×D4C2×#386611yescharacteristic
144C22×C4—371no—
145C22×C4—741no—
146C22×C4—741no—
147M16—372no—
148M16—741no—
149M16—744no—
150M16—741no—
151M16—741no—
152C2×C8—371no—
153C2×C8—371no—
154C2×C8—371no—
155C2×C8—741no—
156C2×C8—741no—
157C2×C8—741no—
158C2×C8—741no—
159C2×C8—741no—
160C2×C8—744no—
161C2×C8—741no—
162C2×C8C2×#386611yescharacteristic
163C4⋊C4—371no—
164C4⋊C4C2×#386611yescharacteristic
165C22⋊C4—741no—
166C42—741no—
167C42—741no—
168C42—741no—
169C23—21no—
170C23—371no—
171Q8—372no—
172Q8—741no—
173D4—21no—
174D4—742no—
175D4—742no—
176D4C4⋊#386612yes—
177C2×C4—21no—
178C2×C4—371no—
179C2×C4—371no—
180C2×C4—371no—
181C2×C4—371no—
182C2×C4—371no—
183C2×C4—742no—
184C2×C4—742no—
185C2×C4—741no—
186C2×C4—742no—
187C2×C4—741no—
188C2×C4—1481no—
189C2×C4—1481no—
190C2×C4C22×#386611yescharacteristic
191C8—21no—
192C8—741no—
193C8—741no—
194C8—742no—
195C8—741no—
196C8—1481no—
197C22—22no—
198C22—41no—
199C22—41no—
200C22—371no—
201C22—371no—
202C22—741no—
203C22—741no—
204C22D4×#386611yescharacteristic
205C4—41no—
206C4—371no—
207C4—371no—
208C4—742no—
209C4—1482no—
210C4—1481no—
211C4C2×C4⋊#386611yescharacteristic
212C4D4×#386611yescharacteristic
213C2—42no—
214C2—741no—
215C2—741no—
216C2#1455848011yescharacteristic
217C2#1455857511yescharacteristic
218C2#1455857811yescharacteristic
subgroupG/H
centerC22D4×#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#102×C37C4
socleC22×C37C4×D4
prime radicalC2×#10596964C22
cosocleC2×C4×D37C23
hypercenter#102#3866
hypocenterC37#1866
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. C2×#11924607C2semidirect
3. #14558540C2semidirect
5. #14558403C2semidirect
6. (C2×#3866)⋊C8C2semidirect
23. #11924461C4semidirect
24. #11924459C4semidirect
25. #11924457C4semidirect
26. #102×C37C4semidirect
117. C37#1866semidirect
136. #102#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119246232
C2×#119246072
#145585402
C2×#119246002
#145584032
(C2×#3866)⋊C82
#145575262
#186637