Finite Group Databasebeta

← #18010484

Subgroups — #18010484

Order 4736.

264 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 74 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
1D37⋊#108C211yesmaximal, characteristic, complemented
2C2×#11924604C211yesmaximal, characteristic, complemented
3#14558524C212yesmaximal
4#14558412C212yesmaximal, complemented
5#131×D37C211yesmaximal, characteristic
6D37⋊M16C2212yes—
7C2×C4⋊#3866C2212yes—
8#11924607—21no—
9#11924606—21no—
10#11924604—21no—
11#11924604—21no—
12#11924599—22no—
13#11924598—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
25C22×#3866—22no—
26#41×C37C2×C411yescharacteristic
27#10596966Q811yescharacteristic
28Q8×D37D411yescharacteristic
29#10596964—21no—
30#10596964Q811yescharacteristic
31D4×D37—21no—
32D4×D37D411yescharacteristic
33#10596962—21no—
34#10596962C2×C411yescharacteristic
35C2×C4×D37—21no—
36C2×C4×D37C2311yescharacteristic
37#10596957—22no—
38C4⋊#3866—22no—
39C4⋊#3866—22no—
40#10596953—22no—
41D37⋊C8—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—
63C2×#3866—82no—
64Q8×C37C4⋊C411yescharacteristic
65D4×C37—21no—
66D4×C37C4⋊C411yescharacteristic
67C2×C4×C37—21no—
68C2×C4×C37C22×C411yescharacteristic
69C22⋊D37—21no—
70C22⋊D37—21no—
71C22⋊D37—21no—
72C2×Dic37—21no—
73C2×Dic37#4111yescharacteristic
74D148—21no—
75D148C4⋊C411yescharacteristic
76C4×D37—21no—
77C4×D37—21no—
78C4×D37—21no—
79C4×D37C2×D411yescharacteristic
80C4×D37C2×D411yescharacteristic
81C4×D37C2×D411yescharacteristic
82C4×D37C2×Q811yescharacteristic
83Dic74—21no—
84Dic74C4⋊C411yescharacteristic
85#64438—42no—
86C8×C37—21no—
87C8×C37C22⋊C411yescharacteristic
88C8×C37C22⋊C411yescharacteristic
89#64436—21no—
90#64436C22⋊C411yescharacteristic
91#64436C22⋊C411yescharacteristic
92C22×C37—21no—
93C22×C37#11711yescharacteristic
94C2×D37—22no—
95C2×D37—21no—
96C2×D37—42no—
97C2×D37#12111yescharacteristic
98C2×D37C22⋊Q811yescharacteristic
99#3866—82no—
100C4×C37—21no—
101C4×C37C2×C22⋊C411yescharacteristic
102C4×C37C2×C4⋊C411yescharacteristic
103Dic37—21no—
104Dic37#12111yescharacteristic
105Dic37C22⋊Q811yescharacteristic
106#1815—371nomaximal, Sylow
107C2×C37—21no—
108C2×C37—41no—
109C2×C37#38011yescharacteristic
110D37—21no—
111D37—41no—
112D37#47112yes—
113C2×#131—371no—
114C2×#108—371no—
115C2×#106—371no—
116#417—372no—
117#343—372no—
118C37#181511yescharacteristic, complemented, Sylow
119C2×#41—371no—
120#131—371no—
121#131—371no—
122#131—371no—
123#131—741no—
124#131—741no—
125#131#386611yescharacteristic, complemented
126C2×M16—371no—
127C2×M16—372no—
128C2×M16—741no—
129C22×C8—371no—
130C22×C8—741no—
131C2×C4⋊C4—372no—
132#108—741no—
133#108—741no—
134#106—741no—
135#106—741no—
136#103—742no—
137#102—742no—
138#41—371no—
139#41—371no—
140#41—371no—
141#41—741no—
142#41—741no—
143#41C2×#386611yescharacteristic
144C2×Q8—371no—
145C2×D4—371no—
146C2×D4—741no—
147C22×C4—371no—
148C22×C4—741no—
149C22×C4—742no—
150M16—21no—
151M16—371no—
152M16—741no—
153M16—741no—
154M16—741no—
155M16—741no—
156M16—742no—
157M16—742no—
158M16C2×#386611yescharacteristic
159C2×C8—21no—
160C2×C8—371no—
161C2×C8—371no—
162C2×C8—371no—
163C2×C8—371no—
164C2×C8—371no—
165C2×C8—741no—
166C2×C8—741no—
167C2×C8—741no—
168C2×C8—741no—
169C2×C8—742no—
170C2×C8C2×#386611yescharacteristic
171C4⋊C4—742no—
172C4⋊C4—742no—
173C23—371no—
174C23—741no—
175Q8—371no—
176Q8—741no—
177Q8C4⋊#386611yescharacteristic
178D4—21no—
179D4—371no—
180D4—741no—
181D4—741no—
182D4—741no—
183D4—741no—
184D4C4⋊#386611yescharacteristic
185C2×C4—21no—
186C2×C4—371no—
187C2×C4—371no—
188C2×C4—371no—
189C2×C4—371no—
190C2×C4—371no—
191C2×C4—2962no—
192C2×C4—741no—
193C2×C4—741no—
194C2×C4—741no—
195C2×C4—741no—
196C2×C4—1482no—
197C2×C4C22×#386611yescharacteristic
198C8—21no—
199C8—371no—
200C8—371no—
201C8—741no—
202C8—1482no—
203C8C22⋊#386611yescharacteristic
204C8C22⋊#386611yescharacteristic
205C22—21no—
206C22—371no—
207C22—371no—
208C22—742no—
209C22—741no—
210C22—1482no—
211C22#1192461511yescharacteristic
212C4—21no—
213C4—371no—
214C4—371no—
215C4—2962no—
216C4—741no—
217C4C2×C22⋊#386611yescharacteristic
218C4C2×C4⋊#386611yescharacteristic
219C2—21no—
220C2—41no—
221C2—372no—
222C2—741no—
223C2—1481no—
224C2#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#1815
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. D37⋊#108C2semidirect
2. C2×#11924604C2semidirect
4. #14558412C2semidirect
16. #11924544C4semidirect
17. #11924543C4semidirect
19. #11924542C4semidirect
24. #131×C37C4semidirect
118. C37#1815semidirect
125. #131#3866semidirect

Maximal subgroups

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

subgroupindex
D37⋊#1082
C2×#119246042
#145585242
#145584122
#131×D372
#181537