Finite Group Databasebeta

← #18010684

Subgroups — #18010684

Order 4736.

216 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 56 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#14558548C211yesmaximal, characteristic, complemented
2#14558531C211yesmaximal, characteristic
3C2×#11924600C211yesmaximal, characteristic
4M16×#3866C211yesmaximal, characteristic, complemented
5#14558416C211yesmaximal, characteristic, complemented
6#14558405C211yesmaximal, characteristic, complemented
7#14557514C211yesmaximal, characteristic
8C2×#10596953C2211yescharacteristic
9D37⋊M16C2211yescharacteristic
10#11924615C2211yescharacteristic
11C2×C4×#3866C2211yescharacteristic
12#11924607—21no—
13#11924606—21no—
14#11924600—21no—
15#11924600—21no—
16#11924600—21no—
17#11924600—21no—
18#11924590—21no—
19C8×#3866—21no—
20C2×#10596964C2211yescharacteristic
21M16×D37C2211yescharacteristic
22M16×D37C2211yescharacteristic
23#11924454C411yescharacteristic, complemented
24#11924454C411yescharacteristic, complemented
25#11924453C411yescharacteristic, complemented
26#100×C37C411yescharacteristic, complemented
27C22×#3866—21no—
28C2×D4×C37C2×C411yescharacteristic
29C2×C22⋊D37—21no—
30C22×Dic37—21no—
31#10596964—21no—
32#10596964—21no—
33#10596964—21no—
34#10596964—21no—
35C2×C4×D37C2311yescharacteristic
36C2×Dic74C2×C411yescharacteristic
37C22⋊#3866—21no—
38#10596957—21no—
39C2×#64438—21no—
40C4⋊#3866—21no—
41C4×#3866—21no—
42C4×#3866—21no—
43C4×#3866D411yescharacteristic
44C4×#3866D411yescharacteristic
45#10596953—21no—
46#10596953—21no—
47#10596953D411yescharacteristic
48#10596953D411yescharacteristic
49D37⋊C8—21no—
50M16×C37C2×C411yescharacteristic
51M16×C37C2×C411yescharacteristic
52#10596934C2×C411yescharacteristic
53#10596934C2×C411yescharacteristic
54#10596929—21no—
55#10596929—21no—
56C8×D37—21no—
57C8×D37—21no—
58C23×C37—21no—
59C22×D37#4111yescharacteristic
60C2×#3866—21no—
61C2×#3866—21no—
62C2×#3866—42no—
63C2×#3866—41no—
64D4×C37—21no—
65D4×C37—21no—
66C2×C4×C37C22×C411yescharacteristic
67C22⋊D37—41no—
68C22⋊D37—41no—
69C2×Dic37—21no—
70C2×Dic37—41no—
71C2×Dic37—41no—
72C2×Dic37#4111yescharacteristic
73C4×D37C2×D411yescharacteristic
74C4×D37C2×D411yescharacteristic
75C4×D37#4111yescharacteristic
76C4×D37#4111yescharacteristic
77Dic74—21no—
78Dic74—21no—
79#64438—21no—
80#64438—21no—
81#64438—41no—
82C8×C37—21no—
83C8×C37—21no—
84#64436—21no—
85#64436—21no—
86C22×C37—41no—
87C22×C37—81no—
88C22×C37#11711yescharacteristic
89C2×D37—41no—
90C2×D37#12311yescharacteristic
91C2×D37#12411yescharacteristic
92#3866—22no—
93#3866—41no—
94#3866—81no—
95C4×C37C4×D411yescharacteristic
96C4×C37C4×D411yescharacteristic
97Dic37—41no—
98Dic37#12111yescharacteristic
99Dic37#12611yescharacteristic
100#1932—371nomaximal, Sylow
101C2×C37—21no—
102C2×C37—81no—
103C2×C37#38811yescharacteristic
104D37—21no—
105D37—21no—
106#430—371no—
107#421—371no—
108C2×#104—371no—
109#413—371no—
110C4×M16—371no—
111#344—371no—
112#339—371no—
113C37#193211yescharacteristic, complemented, Sylow
114C2×#41—371no—
115C2×M16—371no—
116C2×M16—371no—
117C2×M16—371no—
118C2×M16—371no—
119#117—371no—
120C2×C42—371no—
121#108—741no—
122#108—741no—
123#104—741no—
124#104—741no—
125#104—741no—
126#104—741no—
127#101—371no—
128#101—371no—
129#100—371no—
130#100#386611yescharacteristic, complemented
131#97—741no—
132C4×C8—741no—
133#41—741no—
134#41—741no—
135#41—741no—
136#41—741no—
137C2×Q8—371no—
138C2×D4—741no—
139C2×D4C2×#386611yescharacteristic
140C22×C4—371no—
141C22×C4—741no—
142C22×C4—741no—
143M16—371no—
144M16—371no—
145M16—371no—
146M16—371no—
147M16—741no—
148M16—741no—
149M16—741no—
150M16—741no—
151M16—741no—
152M16C2×#386611yescharacteristic
153M16C2×#386611yescharacteristic
154C2×C8—741no—
155C2×C8—741no—
156C2×C8—741no—
157C2×C8—741no—
158C4⋊C4—741no—
159C22⋊C4—741no—
160C42—371no—
161C42—371no—
162C42—741no—
163C42—741no—
164C23—21no—
165C23—371no—
166Q8—741no—
167Q8—741no—
168D4—21no—
169D4—21no—
170D4—1481no—
171D4—1481no—
172C2×C4—371no—
173C2×C4—371no—
174C2×C4—371no—
175C2×C4—371no—
176C2×C4—371no—
177C2×C4—741no—
178C2×C4—741no—
179C2×C4—741no—
180C2×C4—1481no—
181C2×C4—1481no—
182C2×C4—1481no—
183C2×C4—1482no—
184C2×C4C22×#386611yescharacteristic
185C8—21no—
186C8—21no—
187C8—741no—
188C8—741no—
189C8—741no—
190C8—741no—
191C8—1481no—
192C22—41no—
193C22—81no—
194C22—371no—
195C22—371no—
196C22—1481no—
197C22#1192461511yescharacteristic
198C4—371no—
199C4—371no—
200C4—2961no—
201C4—742no—
202C4—1481no—
203C4—1481no—
204C4D4×#386611yescharacteristic
205C4D4×#386611yescharacteristic
206C2—21no—
207C2—81no—
208C2—741no—
209C2—741no—
210C2#1455848311yescharacteristic
subgroupG/H
centerC2#14558483
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#100×C37C4
socleC2×C37#388
prime radicalC2×#10596964C22
cosocleC2×C4×D37C23
hypercenter#100#3866
hypocenterC37#1932
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

Complements

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

NH ≅ G/Ntype
1. #14558548C2semidirect
4. M16×#3866C2semidirect
5. #14558416C2semidirect
6. #14558405C2semidirect
23. #11924454C4semidirect
24. #11924454C4semidirect
25. #11924453C4semidirect
26. #100×C37C4semidirect
113. C37#1932semidirect
130. #100#3866semidirect

Maximal subgroups

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

subgroupindex
#145585482
#145585312
C2×#119246002
M16×#38662
#145584162
#145584052
#145575142
#193237