Finite Group Databasebeta

← #18010482

Subgroups — #18010482

Order 4736.

256 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 72 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×#11924606C211yesmaximal, characteristic, complemented
2#14558543C211yesmaximal, characteristic, complemented
3#14558530C212yesmaximal
4#14558416C212yesmaximal, complemented
5#131×D37C211yesmaximal, characteristic
6C2×#10596953C2212yes—
7#11924615C2212yes—
8#11924606—21no—
9#11924606—21no—
10#11924605—21no—
11#11924604—21no—
12#11924601—22no—
13#11924600—22no—
14#41×D37C2211yescharacteristic
15#11924544—21no—
16#11924544C411yescharacteristic, complemented
17#11924543C411yescharacteristic, complemented
18#11924542—21no—
19#11924542C411yescharacteristic, complemented
20M16×D37—21no—
21M16×D37C2211yescharacteristic
22C2×C8×D37—21no—
23C2×C8×D37C2211yescharacteristic
24#131×C37C411yescharacteristic, complemented
25#41×C37C2×C411yescharacteristic
26#10596966D411yescharacteristic
27Q8×D37Q811yescharacteristic
28#10596964—21no—
29#10596964D411yescharacteristic
30D4×D37—21no—
31D4×D37Q811yescharacteristic
32#10596962—21no—
33#10596962C2×C411yescharacteristic
34C2×C4×D37—21no—
35C2×C4×D37C2311yescharacteristic
36C22⋊#3866—22no—
37C2×#64438—22no—
38C4⋊#3866—22no—
39C4×#3866—22no—
40#10596953—22no—
41#10596953—22no—
42M16×C37—21no—
43M16×C37C2×C411yescharacteristic
44C2×C8×C37—21no—
45C2×C8×C37C2×C411yescharacteristic
46#10596934—21no—
47#10596934C2×C411yescharacteristic
48C2×#64436—21no—
49C2×#64436C2×C411yescharacteristic
50#10596929—21no—
51#10596929—21no—
52#10596929—21no—
53C8×D37—21no—
54C8×D37—21no—
55C8×D37—21no—
56C8×D37D411yescharacteristic
57C8×D37D411yescharacteristic
58C8×D37D411yescharacteristic
59C8×D37D411yescharacteristic
60C22×D37—21no—
61C22×D37#4111yescharacteristic
62C2×#3866—42no—
63Q8×C37C4⋊C411yescharacteristic
64D4×C37—21no—
65D4×C37C4⋊C411yescharacteristic
66C2×C4×C37—21no—
67C2×C4×C37C22×C411yescharacteristic
68C22⋊D37—21no—
69C22⋊D37—21no—
70C22⋊D37—21no—
71C2×Dic37—21no—
72C2×Dic37#4111yescharacteristic
73D148—21no—
74D148C4⋊C411yescharacteristic
75C4×D37—21no—
76C4×D37—21no—
77C4×D37—21no—
78C4×D37C2×D411yescharacteristic
79C4×D37C2×D411yescharacteristic
80C4×D37C2×D411yescharacteristic
81C4×D37C2×Q811yescharacteristic
82Dic74—21no—
83Dic74C4⋊C411yescharacteristic
84#64438—42no—
85C8×C37—21no—
86C8×C37C22⋊C411yescharacteristic
87C8×C37C22⋊C411yescharacteristic
88#64436—21no—
89#64436C22⋊C411yescharacteristic
90#64436C22⋊C411yescharacteristic
91C22×C37—21no—
92C22×C37#11711yescharacteristic
93C2×D37—21no—
94C2×D37—41no—
95C2×D37—42no—
96C2×D37#12111yescharacteristic
97C2×D37C22⋊Q811yescharacteristic
98#3866—82no—
99C4×C37—21no—
100C4×C37C2×C22⋊C411yescharacteristic
101C4×C37C2×C4⋊C411yescharacteristic
102Dic37—21no—
103Dic37#12111yescharacteristic
104Dic37C22⋊Q811yescharacteristic
105#1814—371nomaximal, Sylow
106C2×C37—21no—
107C2×C37—41no—
108C2×C37#38011yescharacteristic
109D37—21no—
110D37—21no—
111D37—41no—
112C2×#131—371no—
113C2×#108—371no—
114#427—371no—
115#421—372no—
116#344—372no—
117C37#181411yescharacteristic, complemented, Sylow
118C2×#41—371no—
119#131—371no—
120#131—371no—
121#131—371no—
122#131—741no—
123#131—741no—
124#131#386611yescharacteristic, complemented
125C2×M16—371no—
126C2×M16—372no—
127C2×M16—741no—
128C22×C8—371no—
129C22×C8—741no—
130#117—372no—
131#108—741no—
132#108—741no—
133#107—741no—
134#106—741no—
135#104—742no—
136#104—742no—
137#41—371no—
138#41—371no—
139#41—371no—
140#41—741no—
141#41—741no—
142#41C2×#386611yescharacteristic
143C2×Q8—371no—
144C2×D4—371no—
145C2×D4—741no—
146C22×C4—371no—
147C22×C4—741no—
148M16—21no—
149M16—371no—
150M16—741no—
151M16—741no—
152M16—741no—
153M16—741no—
154M16—742no—
155M16—742no—
156M16C2×#386611yescharacteristic
157C2×C8—21no—
158C2×C8—371no—
159C2×C8—371no—
160C2×C8—371no—
161C2×C8—371no—
162C2×C8—371no—
163C2×C8—741no—
164C2×C8—741no—
165C2×C8—741no—
166C2×C8—741no—
167C2×C8—742no—
168C2×C8C2×#386611yescharacteristic
169C4⋊C4—742no—
170C22⋊C4—742no—
171C42—742no—
172C23—371no—
173C23—741no—
174Q8—371no—
175Q8—741no—
176Q8C4⋊#386611yescharacteristic
177D4—21no—
178D4—371no—
179D4—741no—
180D4—741no—
181D4—741no—
182D4—741no—
183D4C4⋊#386611yescharacteristic
184C2×C4—21no—
185C2×C4—371no—
186C2×C4—371no—
187C2×C4—371no—
188C2×C4—371no—
189C2×C4—371no—
190C2×C4—741no—
191C2×C4—741no—
192C2×C4—741no—
193C2×C4—741no—
194C2×C4—1482no—
195C2×C4C22×#386611yescharacteristic
196C8—21no—
197C8—371no—
198C8—371no—
199C8—741no—
200C8—1482no—
201C8C22⋊#386611yescharacteristic
202C8C22⋊#386611yescharacteristic
203C22—21no—
204C22—371no—
205C22—371no—
206C22—741no—
207C22—1481no—
208C22—1482no—
209C22#1192461511yescharacteristic
210C4—21no—
211C4—371no—
212C4—371no—
213C4—2962no—
214C4—741no—
215C4C2×C22⋊#386611yescharacteristic
216C4C2×C4⋊#386611yescharacteristic
217C2—21no—
218C2—41no—
219C2—741no—
220C2—741no—
221C2—1481no—
222C2#1455847511yescharacteristic
subgroupG/H
centerC2#14558475
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#131×C37C4
socleC2×C37#380
prime radical#41×D37C22
cosocleC2×C4×D37C23
hypercenter#131#3866
hypocenterC37#1814
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131

Complements

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

NH ≅ G/Ntype
1. C2×#11924606C2semidirect
2. #14558543C2semidirect
4. #14558416C2semidirect
16. #11924544C4semidirect
17. #11924543C4semidirect
19. #11924542C4semidirect
24. #131×C37C4semidirect
117. C37#1814semidirect
124. #131#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119246062
#145585432
#145585302
#145584162
#131×D372
#181437