Finite Group Databasebeta

← #18010682

Subgroups — #18010682

Order 4736.

232 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 58 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#14558544C211yesmaximal, characteristic, complemented
2#14558525C211yesmaximal, characteristic
3C2×#11924598C211yesmaximal, characteristic
4#14558499C211yesmaximal, characteristic, complemented
5#14558412C211yesmaximal, characteristic, complemented
6#14558408C211yesmaximal, characteristic, complemented
7#100×D37C211yesmaximal, characteristic
8D37⋊M16C2211yescharacteristic
9C2×D37⋊C8C2211yescharacteristic
10#11924615C2211yescharacteristic
11C2×C4⋊#3866C2211yescharacteristic
12#11924605—21no—
13#11924604—21no—
14#11924598—21no—
15#11924598—21no—
16#11924598—21no—
17#11924598—21no—
18#11924590—21no—
19C8×#3866—21no—
20C2×D4×D37C2211yescharacteristic
21M16×D37C2211yescharacteristic
22M16×D37C2211yescharacteristic
23#11924453C411yescharacteristic, complemented
24#11924452C411yescharacteristic, complemented
25#11924452C411yescharacteristic, complemented
26#100×C37C411yescharacteristic, complemented
27C23×D37—21no—
28C22×#3866—21no—
29C2×D4×C37C2×C411yescharacteristic
30C2×C22⋊D37—21no—
31D4×D37—21no—
32D4×D37—21no—
33D4×D37—21no—
34D4×D37—21no—
35C2×D148C2×C411yescharacteristic
36C2×C4×D37C2311yescharacteristic
37C22⋊#3866—21no—
38#10596957—21no—
39C2×#64438—21no—
40C4⋊#3866—21no—
41C4⋊#3866—21no—
42C4⋊#3866D411yescharacteristic
43C4⋊#3866D411yescharacteristic
44C4×#3866—21no—
45#10596953—21no—
46D37⋊C8—21no—
47D37⋊C8—21no—
48D37⋊C8D411yescharacteristic
49D37⋊C8D411yescharacteristic
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—21no—
60C22×D37—41no—
61C22×D37—41no—
62C22×D37—81no—
63C22×D37—81no—
64C22×D37#4111yescharacteristic
65C2×#3866—21no—
66C2×#3866—21no—
67C2×#3866—41no—
68C2×#3866—81no—
69D4×C37—21no—
70D4×C37—21no—
71C2×C4×C37C22×C411yescharacteristic
72C22⋊D37—41no—
73C22⋊D37—41no—
74C2×Dic37#4111yescharacteristic
75D148—21no—
76D148—21no—
77C4×D37C2×D411yescharacteristic
78C4×D37C2×D411yescharacteristic
79C4×D37#4111yescharacteristic
80C4×D37#4111yescharacteristic
81#64438—21no—
82#64438—21no—
83#64438—41no—
84C8×C37—21no—
85C8×C37—21no—
86#64436—21no—
87#64436—21no—
88C22×C37—41no—
89C22×C37—81no—
90C22×C37#11711yescharacteristic
91C2×D37—21no—
92C2×D37—21no—
93C2×D37—41no—
94C2×D37—82no—
95C2×D37—81no—
96C2×D37—81no—
97C2×D37—81no—
98C2×D37#12111yescharacteristic
99C2×D37#12611yescharacteristic
100#3866—41no—
101#3866—41no—
102#3866—81no—
103C4×C37C4×D411yescharacteristic
104C4×C37C4×D411yescharacteristic
105Dic37#12311yescharacteristic
106Dic37#12411yescharacteristic
107#1931—371nomaximal, Sylow
108C2×C37—21no—
109C2×C37—81no—
110C2×C37#38811yescharacteristic
111D37—21no—
112D37—81no—
113D37#47111yescharacteristic
114D37#47211yescharacteristic
115#428—371no—
116#418—371no—
117C2×#102—371no—
118C2×#100—371no—
119#405—371no—
120#343—371no—
121#341—371no—
122C37#193111yescharacteristic, complemented, Sylow
123C22×D4—371no—
124C2×M16—371no—
125C2×M16—371no—
126C2×M16—371no—
127C22×C8—371no—
128#117—371no—
129C2×C4⋊C4—371no—
130#107—741no—
131#106—741no—
132#102—741no—
133#102—741no—
134#102—741no—
135#102—741no—
136#100—371no—
137#100—371no—
138#100—371no—
139#100#386611yescharacteristic, complemented
140#97—741no—
141C4×C8—741no—
142C24—741no—
143C2×D4—371no—
144C2×D4—741no—
145C2×D4—741no—
146C2×D4—741no—
147C2×D4—741no—
148C2×D4—741no—
149C2×D4C2×#386611yescharacteristic
150C22×C4—371no—
151C22×C4—741no—
152M16—371no—
153M16—371no—
154M16—741no—
155M16—741no—
156M16—741no—
157M16—741no—
158M16C2×#386611yescharacteristic
159M16C2×#386611yescharacteristic
160C2×C8—371no—
161C2×C8—371no—
162C2×C8—741no—
163C2×C8—741no—
164C2×C8—741no—
165C2×C8—741no—
166C2×C8—741no—
167C4⋊C4—371no—
168C4⋊C4—371no—
169C4⋊C4—741no—
170C4⋊C4—741no—
171C22⋊C4—741no—
172C42—741no—
173C23—21no—
174C23—371no—
175C23—2961no—
176C23—2961no—
177C23—741no—
178C23—1481no—
179C23—1481no—
180D4—21no—
181D4—21no—
182D4—741no—
183D4—741no—
184D4—1481no—
185D4—1481no—
186C2×C4—371no—
187C2×C4—371no—
188C2×C4—371no—
189C2×C4—371no—
190C2×C4—371no—
191C2×C4—2961no—
192C2×C4—741no—
193C2×C4—741no—
194C2×C4—1481no—
195C2×C4C22×#386611yescharacteristic
196C8—21no—
197C8—21no—
198C8—741no—
199C8—741no—
200C8—741no—
201C8—741no—
202C8—1481no—
203C22—41no—
204C22—81no—
205C22—371no—
206C22—371no—
207C22—2961no—
208C22—2961no—
209C22—2961no—
210C22—2962no—
211C22—741no—
212C22—741no—
213C22—1481no—
214C22#1192461511yescharacteristic
215C4—371no—
216C4—371no—
217C4—2961no—
218C4—1481no—
219C4—1481no—
220C4D4×#386611yescharacteristic
221C4D4×#386611yescharacteristic
222C2—21no—
223C2—81no—
224C2—371no—
225C2—371no—
226C2—2961no—
227C2—741no—
228C2#1455848311yescharacteristic
subgroupG/H
centerC2#14558483
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#100×C37C4
socleC2×C37#388
prime radicalC2×D4×D37C22
cosocleC2×C4×D37C23
hypercenter#100#3866
hypocenterC37#1931
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. #14558544C2semidirect
4. #14558499C2semidirect
5. #14558412C2semidirect
6. #14558408C2semidirect
23. #11924453C4semidirect
24. #11924452C4semidirect
25. #11924452C4semidirect
26. #100×C37C4semidirect
122. C37#1931semidirect
139. #100#3866semidirect

Maximal subgroups

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

subgroupindex
#145585442
#145585252
C2×#119245982
#145584992
#145584122
#145584082
#100×D372
#193137