Finite Group Databasebeta

← #17995147

Subgroups — #17995147

Order 4736.

308 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 79 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#14558299C211yesmaximal, characteristic
2#14558109C211yesmaximal, characteristic
3#14557515C211yesmaximal, characteristic
4C2×#11924454C211yesmaximal, characteristic, complemented
5C2×#11924454C211yesmaximal, characteristic, complemented
6#14557303C211yesmaximal, characteristic, complemented
7C37×#344C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×Dic74C2211yescharacteristic
10#11924544—22no—
11#11924542—22no—
12C2×#10596934C2211yescharacteristic
13C2×#10596934C2211yescharacteristic
14M16×D37—22no—
15#11924536—21no—
16#11924524—21no—
17#11924520C414yes—
18#11924516—22no—
19#11924454—21no—
20#11924454—22no—
21#11924454—22no—
22#11924452—21no—
23C2×M16×C37C2211yescharacteristic
24C2×M16×C37C2211yescharacteristic
25#117×C37C2211yescharacteristic
26C22×C4×C37C2311yescharacteristic
27C2×C22⋊D37C2×C412yes—
28C22×Dic37C2×C412yes—
29#10596962—21no—
30#10596962—21no—
31#10596962—21no—
32#10596962—21no—
33C2×D148D411yescharacteristic
34C2×C4×D37D412yes—
35C2×Dic74—21no—
36C2×Dic74—21no—
37C2×Dic74—21no—
38C2×Dic74—21no—
39C2×Dic74—21no—
40C2×Dic74—21no—
41C2×Dic74D411yescharacteristic
42M16×C37—21no—
43M16×C37—21no—
44M16×C37—21no—
45M16×C37D412yes—
46C2×C8×C37—21no—
47C2×C8×C37—21no—
48C4⋊C4×C37—21no—
49C22⋊C4×C37C2×C412yes—
50C42×C37—21no—
51#10596938—24no—
52C4⋊Dic37—24no—
53#10596934—21no—
54#10596934—21no—
55#10596934—21no—
56#10596934D412yes—
57C2×#64436—21no—
58C2×#64436—21no—
59#10596929—24no—
60C8×D37—24no—
61C23×C37C22×C411yescharacteristic
62C22×D37C22⋊C412yes—
63C2×C4×C37—22no—
64C2×C4×C37C2×D411yescharacteristic
65C2×C4×C37C2×D411yescharacteristic
66C2×C4×C37C2×D411yescharacteristic
67C2×C4×C37C2×D411yescharacteristic
68C2×C4×C37#4111yescharacteristic
69C2×C4×C37#4111yescharacteristic
70C22⋊D37—22no—
71C22⋊D37—22no—
72C2×Dic37—22no—
73C2×Dic37—22no—
74C2×Dic37—22no—
75C2×Dic37C22⋊C412yes—
76D148—21no—
77D148—21no—
78C4×D37—22no—
79C4×D37—22no—
80Dic74—21no—
81Dic74—21no—
82Dic74—41no—
83Dic74—41no—
84Dic74—41no—
85Dic74—41no—
86C8×C37—22no—
87C8×C37—41no—
88#64436—22no—
89#64436—41no—
90C22×C37—41no—
91C22×C37C2×C22⋊C411yescharacteristic
92C22×C37C4×D411yescharacteristic
93C22×C37C4×D411yescharacteristic
94C2×D37—22no—
95C2×D37—42no—
96C4×C37—42no—
97C4×C37#12011yescharacteristic
98C4×C37#12111yescharacteristic
99C4×C37#12111yescharacteristic
100C4×C37#12311yescharacteristic
101Dic37—22no—
102Dic37—42no—
103#1915—371nomaximal, Sylow
104C2×C37—21no—
105C2×C37—21no—
106C2×C37—21no—
107C2×C37#38611yescharacteristic
108D37—42no—
109#568—371no—
110#536—371no—
111#413—371no—
112C2×#101—371no—
113C2×#101—371no—
114#344—371no—
115#344D3711yescharacteristic, complemented
116C37#191511yescharacteristic, complemented, Sylow
117C2×#41—371no—
118C22×Q8—371no—
119#131—742no—
120#131—742no—
121C2×M16—371no—
122C2×M16—371no—
123C2×M16—742no—
124C2×M16C2×D3711yescharacteristic
125C2×M16C2×D3711yescharacteristic
126C4⋊Q8—741no—
127#124—741no—
128#123—374no—
129C22⋊Q8—742no—
130#117C2×D3711yescharacteristic
131#101—742no—
132#101—741no—
133#101—742no—
134#100—741no—
135#41—741no—
136#41—741no—
137#41—741no—
138#41—741no—
139C2×Q8—371no—
140C2×Q8—741no—
141C2×Q8—741no—
142C2×Q8—741no—
143C2×Q8—741no—
144C2×Q8—741no—
145C2×Q8—741no—
146C2×D4—372no—
147C2×D4—371no—
148C22×C4—372no—
149C22×C4—372no—
150C22×C4C22×D3711yescharacteristic
151M16—21no—
152M16—21no—
153M16—21no—
154M16—372no—
155M16—744no—
156M16—741no—
157M16—741no—
158M16—741no—
159M16D14812yes—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—744no—
163C2×C8—741no—
164C2×C8—741no—
165C4⋊C4—21no—
166C4⋊C4—744no—
167C22⋊C4—744no—
168C22⋊C4C4×D3712yes—
169C42—21no—
170C23—372no—
171C23C2×C4×D3711yescharacteristic
172Q8—741no—
173Q8—741no—
174Q8—1481no—
175Q8—1481no—
176Q8—1481no—
177Q8—1481no—
178D4—742no—
179D4—742no—
180D4—741no—
181D4—741no—
182C2×C4—22no—
183C2×C4—372no—
184C2×C4—742no—
185C2×C4—742no—
186C2×C4—742no—
187C2×C4—742no—
188C2×C4—742no—
189C2×C4C2×D14811yescharacteristic
190C2×C4#1059696211yescharacteristic
191C2×C4D4×D3711yescharacteristic
192C2×C4D4×D3711yescharacteristic
193C2×C4D4×D3711yescharacteristic
194C2×C4#1059696611yescharacteristic
195C8—22no—
196C8—41no—
197C8—742no—
198C8—1481no—
199C22—41no—
200C22—742no—
201C22—1482no—
202C22C22⋊C4×D3711yescharacteristic
203C22#1192449811yescharacteristic
204C22C4×D14811yescharacteristic
205C4—42no—
206C4—742no—
207C4—1482no—
208C4#1192450611yescharacteristic
209C4#1192450911yescharacteristic
210C4#1192451111yescharacteristic
211C4#1192452111yescharacteristic
212C2—21no—
213C2—21no—
214C2—21no—
215C2—1482no—
216C2#1455741111yescharacteristic
subgroupG/H
centerC2#14557411
commutatorC23×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#344C2
socleC2×C37#386
prime radicalC2×#10596962C22
cosocleC22×C4×C37C23
hypercenter#344D37
hypocenterC37#1915
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
4. C2×#11924454C2semidirect
5. C2×#11924454C2semidirect
6. #14557303C2semidirect
7. C37×#344C2semidirect
115. #344D37semidirect
116. C37#1915semidirect

Maximal subgroups

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

subgroupindex
#145582992
#145581092
#145575152
C2×#119244542
#145573032
C37×#3442
#191537