Finite Group Databasebeta

← #18010859

Subgroups — #18010859

Order 4736.

234 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 52 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#14558520C211yesmaximal, characteristic
2#14558513C211yesmaximal, characteristic
3#14558436C212yesmaximal, complemented
4#14558435C212yesmaximal, complemented
5#14558105C211yesmaximal, characteristic
6C2×#10596957—21no—
7#11924615—21no—
8#11924597—21no—
9#11924596C2212yes—
10#11924594—21no—
11#11924594C2212yes—
12C2×#10596964C2211yescharacteristic
13C22×Dic74C411yescharacteristic, complemented
14#11924535—21no—
15#11924522—21no—
16#11924520C2211yescharacteristic
17#11924519C2211yescharacteristic
18#11924517C411yescharacteristic, complemented
19#11924514—21no—
20#11924513—21no—
21#11924492C411yescharacteristic, complemented
22#123×C37C411yescharacteristic, complemented
23C2×D4×C37C2×C411yescharacteristic
24C22×C4×C37C2×C411yescharacteristic
25C2×C22⋊D37D411yescharacteristic
26C2×C22⋊D37C2311yescharacteristic
27C22×Dic37C2×C411yescharacteristic
28C22×Dic37C2×C411yescharacteristic
29C22×Dic37D411yescharacteristic
30#10596964—41no—
31#10596964—41no—
32C2×C4×D37D411yescharacteristic
33C2×Dic74—21no—
34C2×Dic74—21no—
35C2×Dic74—41no—
36C2×Dic74—41no—
37C2×Dic74D411yescharacteristic
38C22⋊#3866—22no—
39#10596957—22no—
40#10596957—41no—
41C2×#64438—41no—
42C4⋊#3866—41no—
43C4×#3866—41no—
44C4⋊C4×C37—21no—
45C22⋊C4×C37—21no—
46C22⋊C4×C37C2×C411yescharacteristic
47C22⋊Dic37—21no—
48C22⋊Dic37C2×C411yescharacteristic
49#10596938—21no—
50#10596938—21no—
51C4⋊Dic37—21no—
52#10596936—21no—
53#10596936—21no—
54#10596936—21no—
55C4×Dic37—21no—
56C23×C37C22⋊C411yescharacteristic
57C23×C37C22×C411yescharacteristic
58C22×D37C2×D411yescharacteristic
59C2×#3866—42no—
60D4×C37—41no—
61C2×C4×C37—21no—
62C2×C4×C37—21no—
63C2×C4×C37—41no—
64C2×C4×C37C22⋊C411yescharacteristic
65C22⋊D37—41no—
66C22⋊D37—41no—
67C2×Dic37—21no—
68C2×Dic37—21no—
69C2×Dic37—21no—
70C2×Dic37—21no—
71C2×Dic37—21no—
72C2×Dic37—21no—
73C2×Dic37—41no—
74C2×Dic37C22⋊C411yescharacteristic
75C2×Dic37C22⋊C411yescharacteristic
76C2×Dic37C2×D411yescharacteristic
77C4×D37—21no—
78C4×D37—21no—
79Dic74—41no—
80Dic74—42no—
81Dic74—41no—
82Dic74—41no—
83#64438—42no—
84C22×C37—21no—
85C22×C37—21no—
86C22×C37—41no—
87C22×C37—41no—
88C22×C37C2×C22⋊C411yescharacteristic
89C2×D37—21no—
90C2×D37—41no—
91#3866—82no—
92C4×C37—21no—
93C4×C37—41no—
94C4×C37—41no—
95Dic37—21no—
96Dic37—21no—
97Dic37—41no—
98Dic37—41no—
99Dic37#9911yescharacteristic
100Dic37#9911yescharacteristic
101#2123—371nomaximal, Sylow
102C2×C37—21no—
103C2×C37—41no—
104C2×C37—41no—
105C2×C37C2×#9911yescharacteristic
106D37—41no—
107#536—371no—
108#413—371no—
109#410—371no—
110#352—372no—
111#352—372no—
112C37#212311yescharacteristic, complemented, Sylow
113C2×#41—371no—
114C22×Q8—371no—
115C2×M16—741no—
116C4⋊Q8—741no—
117#124—741no—
118#123—371no—
119#123—371no—
120#123—371no—
121#123#386611yescharacteristic, complemented
122C22⋊Q8—741no—
123C22⋊Q8—741no—
124#117—371no—
125#117—741no—
126#101—741no—
127#100—372no—
128#99—372no—
129#99—741no—
130#41—1481no—
131#41—1481no—
132C2×Q8—371no—
133C2×Q8—741no—
134C2×Q8—741no—
135C2×Q8—1481no—
136C2×Q8—1481no—
137C2×D4—371no—
138C2×D4—371no—
139C2×D4C2×#386611yescharacteristic
140C22×C4—371no—
141C22×C4—371no—
142C22×C4—371no—
143C22×C4—371no—
144C22×C4C2×#386611yescharacteristic
145M16—742no—
146M16—1481no—
147C2×C8—1481no—
148C4⋊C4—21no—
149C4⋊C4—741no—
150C4⋊C4—741no—
151C4⋊C4—741no—
152C4⋊C4—741no—
153C4⋊C4—1481no—
154C22⋊C4—21no—
155C22⋊C4—371no—
156C22⋊C4—741no—
157C22⋊C4—741no—
158C22⋊C4—741no—
159C22⋊C4—742no—
160C22⋊C4C2×#386611yescharacteristic
161C42—741no—
162C42—1481no—
163C23—371no—
164C23C22⋊#386611yescharacteristic
165C23C22×#386611yescharacteristic
166Q8—1481no—
167Q8—1481no—
168Q8—1481no—
169Q8—1482no—
170D4—41no—
171D4—1481no—
172D4—1481no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—371no—
177C2×C4—371no—
178C2×C4—371no—
179C2×C4—741no—
180C2×C4—741no—
181C2×C4—741no—
182C2×C4—741no—
183C2×C4—741no—
184C2×C4—741no—
185C2×C4—741no—
186C2×C4—741no—
187C2×C4—1482no—
188C2×C4—1481no—
189C2×C4C22⋊#386611yescharacteristic
190C8—1482no—
191C22—21no—
192C22—21no—
193C22—41no—
194C22—41no—
195C22—741no—
196C22—1481no—
197C22C2×C22⋊#386611yescharacteristic
198C4—21no—
199C4—41no—
200C4—41no—
201C4—371no—
202C4—371no—
203C4—2962no—
204C4—741no—
205C4—741no—
206C4—1481no—
207C4—1481no—
208C2—21no—
209C2—41no—
210C2—41no—
211C2—1481no—
212C2D37⋊#9911yescharacteristic
subgroupG/H
centerC2D37⋊#99
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
Fitting#123×C37C4
socleC2×C37C2×#99
prime radicalC2×#10596964C22
cosocleC2×C22⋊D37C23
hypercenter#123#3866
hypocenterC37#2123
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #123

Complements

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

NH ≅ G/Ntype
3. #14558436C2semidirect
4. #14558435C2semidirect
13. C22×Dic74C4semidirect
18. #11924517C4semidirect
21. #11924492C4semidirect
22. #123×C37C4semidirect
112. C37#2123semidirect
121. #123#3866semidirect

Maximal subgroups

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

subgroupindex
#145585202
#145585132
#145584362
#145584352
#145581052
#212337