Finite Group Databasebeta

← #34000940

Subgroups — #34000940

Order 18688.

208 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 36 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#22625025C211yesmaximal, characteristic
2#22624860C211yesmaximal, characteristic
3#22611345C211yesmaximal, characteristic
4C2×#14556650—21no—
5#17989432—21no—
6C2×#14556511—21no—
7#17988489C2211yescharacteristic
8#17988349—21no—
9#17988342C411yescharacteristic, complemented
10#382×C73C411yescharacteristic, complemented
11C2×C22⋊#64408—41no—
12#14556650—22no—
13#14556650—41no—
14C22⋊#10596833—41no—
15C22×D292D411yescharacteristic
16C22×#10596831—21no—
17C2×C4⋊Dic73D411yescharacteristic
18C2×#11924005—41no—
19#14556511—41no—
20#14556511—41no—
21C2×C4⋊C4×C73—21no—
22C2×C42×C73C2×C411yescharacteristic
23#95×C73—41no—
24C22×#64408—81no—
25C2×#10596833—81no—
26C22⋊#64408—42no—
27C22⋊#64408—81no—
28C23×D73—21no—
29C2×D292—21no—
30C2×D292—41no—
31C2×D292—41no—
32C2×D292D811yescharacteristic
33C2×D292SD1611yescharacteristic
34C22×Dic73—21no—
35C2×#10596831—41no—
36C2×#10596831—41no—
37C2×#10596831—41no—
38C4⋊Dic73—41no—
39#11924005—82no—
40C22×C4×C73—21no—
41C22×C4×C73—41no—
42C22×C4×C73C22⋊C411yescharacteristic
43C4⋊C4×C73—41no—
44C4⋊C4×C73—41no—
45C42×C73—41no—
46C23×C73#9911yescharacteristic
47C22×D73—21no—
48C22×D73—21no—
49C22×D73—41no—
50C22×D73—41no—
51C22×D73—81no—
52C22×D73—81no—
53C2×#64408—82no—
54C2×#64408—161no—
55C2×#64408—161no—
56C2×C4×C73—21no—
57C2×C4×C73—21no—
58C2×C4×C73—41no—
59C2×C4×C73—41no—
60C2×C4×C73—41no—
61C2×C4×C73—81no—
62C2×C4×C73—81no—
63C2×C4×C73—81no—
64C2×C4×C73#10211yescharacteristic
65C2×C4×C73#10411yescharacteristic
66C2×Dic73—41no—
67C2×Dic73—81no—
68D292—41no—
69D292—41no—
70D292—81no—
71#10596833—161no—
72#10596831—81no—
73C22×C73—21no—
74C22×C73—21no—
75C22×C73#32711yescharacteristic
76C22×C73#35211yescharacteristic
77C22×C73#35411yescharacteristic
78C2×D73—41no—
79C2×D73—41no—
80C2×D73—81no—
81C2×D73—81no—
82C2×D73—81no—
83C2×D73—81no—
84C2×D73—161no—
85#64408—162no—
86C4×C73—21no—
87C4×C73—21no—
88C4×C73—81no—
89C4×C73—161no—
90Dic73—81no—
91#7412—731nomaximal, Sylow
92C2×C73—21no—
93C2×C73—21no—
94C2×C73#134411yescharacteristic
95C2×C73#141211yescharacteristic
96C2×C73#141411yescharacteristic
97D73—81no—
98D73—81no—
99#2073—731no—
100#1393—731no—
101#1318—731no—
102C73#741211yescharacteristic, complemented, Sylow
103C2×#102—1461no—
104C2×#99—1461no—
105#390—731no—
106#382#6440811yescharacteristic, complemented
107#340—1461no—
108#336—731no—
109#324—1461no—
110C22×D4—731no—
111C22×C8—1461no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—731no—
114C2×C22⋊C4—2921no—
115C2×C22⋊C4—2921no—
116C2×C42C2×#6440811yescharacteristic
117#102—2921no—
118#102—2921no—
119#99—2921no—
120#99—1462no—
121C22⋊C8—2921no—
122#95—41no—
123C24—1461no—
124C2×D4—2921no—
125C2×D4—2921no—
126C2×D4—731no—
127C2×D4—731no—
128C2×D4—1461no—
129C22×C4—21no—
130C22×C4—41no—
131C22×C4—5841no—
132C22×C4—1461no—
133C22×C4C22⋊#6440811yescharacteristic
134C2×C8—2921no—
135C2×C8—2921no—
136C2×C8—2921no—
137C2×C8—5841no—
138C4⋊C4—41no—
139C4⋊C4—41no—
140C4⋊C4—2921no—
141C22⋊C4—2922no—
142C22⋊C4—5842no—
143C22⋊C4—5841no—
144C42—41no—
145C23—2921no—
146C23—2921no—
147C23—5841no—
148C23—5841no—
149C23—1461no—
150C23—1461no—
151C23#1455664911yescharacteristic
152D4—2921no—
153D4—2921no—
154D4—5841no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—81no—
161C2×C4—81no—
162C2×C4—81no—
163C2×C4—2921no—
164C2×C4—5841no—
165C2×C4—5842no—
166C2×C4—11681no—
167C2×C4—11681no—
168C2×C4#1455665311yescharacteristic
169C2×C4#1455665511yescharacteristic
170C8—5841no—
171C8—11681no—
172C22—21no—
173C22—21no—
174C22—2921no—
175C22—2921no—
176C22—5841no—
177C22—5841no—
178C22—5841no—
179C22—5841no—
180C22—11681no—
181C22#1798943811yescharacteristic
182C22#1798948911yescharacteristic
183C22#1798949311yescharacteristic
184C4—21no—
185C4—21no—
186C4—81no—
187C4—161no—
188C4—5841no—
189C4—11682no—
190C2—21no—
191C2—21no—
192C2—5841no—
193C2—5841no—
194C2#2262491111yescharacteristic
195C2#2262507111yescharacteristic
196C2#2262507711yescharacteristic
subgroupG/H
centerC22#17989493
commutatorC2×C42×C73C2×C4
FrattiniC2×C42C2×#64408
Fitting#382×C73C4
socleC22×C73#354
prime radicalC22×D292D4
cosocle#17988489C22
hypercenter#382#64408
hypocenterC73#7412
LCSG ▷ C2×C42×C73 ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
9. #17988342C4semidirect
10. #382×C73C4semidirect
102. C73#7412semidirect
106. #382#64408semidirect

Maximal subgroups

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

subgroupindex
#226250252
#226248602
#226113452
#741273