Finite Group Databasebeta

← #34010187

Subgroups — #34010187

Order 18688.

270 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 70 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#22626305C212yesmaximal
2#22624880C212yesmaximal
3#22624877C212yesmaximal
4#22618865C211yesmaximal, characteristic
5#17989509—22no—
6#17989483C2214yes—
7#17989480—22no—
8#17989144C411yescharacteristic
9#17988717—22no—
10C8×Dic146—22no—
11#17988613C411yescharacteristic
12#17988613C2211yescharacteristic
13#17988611C2211yescharacteristic
14#17988542C411yescharacteristic
15#17988542C2211yescharacteristic
16C2×C4×C8×C73C411yescharacteristic
17#14556665—24no—
18C2×#11924012C2×C411yescharacteristic
19C2×#11924012C2311yescharacteristic
20#14556591—21no—
21#14556583—21no—
22#14556570—22no—
23C4×Dic146—22no—
24#14556550C2×C411yescharacteristic
25#14556550C2×C411yescharacteristic
26C4⋊#10596831—22no—
27#14556520—22no—
28#14556520—22no—
29#14556501—21no—
30#14556501D412yes—
31C8×Dic73—21no—
32C8×Dic73D412yes—
33C22×C8×C73C2×C411yescharacteristic
34C22×C8×C73C2×C411yescharacteristic
35C2×C42×C73C2×C411yescharacteristic
36C4×C8×C73—21no—
37C4×C8×C73—21no—
38#11924031—44no—
39C2×Dic146—22no—
40#11924012—41no—
41#11924012—41no—
42C2×#10596831—21no—
43C2×#10596831C2×D412yes—
44C4⋊Dic73—22no—
45C4⋊Dic73—21no—
46C4⋊Dic73—21no—
47#11924007—24no—
48C22⋊Dic73—21no—
49C22⋊Dic73M1612yes—
50C4×Dic73—21no—
51C4×Dic73C22⋊C412yes—
52C22×C4×C73—21no—
53C22×C4×C73C22×C411yescharacteristic
54C2×C8×C73—22no—
55C2×C8×C73—21no—
56C2×C8×C73—41no—
57C2×C8×C73C22⋊C411yescharacteristic
58C2×C8×C73C22⋊C411yescharacteristic
59C42×C73—21no—
60C42×C73M1611yescharacteristic
61C42×C73M1611yescharacteristic
62C23×C73C2×M1611yescharacteristic
63C2×C4×C73—21no—
64C2×C4×C73—21no—
65C2×C4×C73—21no—
66C2×C4×C73—21no—
67C2×C4×C73—42no—
68C2×C4×C73C2×C22⋊C411yescharacteristic
69C2×C4×C73C2×M1611yescharacteristic
70C2×Dic73—22no—
71C2×Dic73—22no—
72Dic146—44no—
73C8×C73—21no—
74C8×C73—41no—
75C8×C73#10112yes—
76#10596831—22no—
77#10596831—41no—
78C22×C73—21no—
79C22×C73—41no—
80C22×C73#40711yescharacteristic
81C4×C73—22no—
82C4×C73—21no—
83C4×C73—41no—
84C4×C73#41011yescharacteristic
85C4×C73C2×#10111yescharacteristic
86Dic73—42no—
87Dic73—42no—
88#11539—731nomaximal, Sylow
89C2×C73—21no—
90C2×C73—41no—
91C2×C73#146711yescharacteristic
92#2960—731no—
93#2166—732no—
94#1328—732no—
95#1327—732no—
96C73#1153911yescharacteristic, complemented, Sylow
97#533—731no—
98#446—1462no—
99C8×Q8—1462no—
100#424—731no—
101#424—731no—
102#423—731no—
103#405—731no—
104#405—731no—
105C2×C4×C8#6440811yescharacteristic
106#364—1462no—
107#349—734no—
108#347—1462no—
109C2×M16—731no—
110C2×M16—731no—
111C22×C8C2×#6440811yescharacteristic
112C22×C8C2×#6440811yescharacteristic
113C4⋊Q8—1461no—
114#125—1461no—
115C22⋊Q8—1462no—
116C4×Q8—1462no—
117#117—731no—
118#117—731no—
119C2×C42C2×#6440811yescharacteristic
120M32—1464no—
121C4⋊C8—1462no—
122C4⋊C8—1462no—
123C4⋊C8—1462no—
124#97—732no—
125#97—1461no—
126C4×C8—21no—
127C4×C8—21no—
128C4×C8—732no—
129C4×C8—1461no—
130C2×Q8—1462no—
131C22×C4—21no—
132C22×C4C22×#6440811yescharacteristic
133M16—2921no—
134M16—2921no—
135C2×C8—22no—
136C2×C8—21no—
137C2×C8—41no—
138C2×C8—732no—
139C2×C8—1461no—
140C2×C8C22⋊#6440811yescharacteristic
141C2×C8C22⋊#6440811yescharacteristic
142C4⋊C4—1464no—
143C4⋊C4—1462no—
144C4⋊C4—1461no—
145C4⋊C4—1461no—
146C22⋊C4—732no—
147C22⋊C4—1461no—
148C42—21no—
149C42—732no—
150C42—1461no—
151C42#1192403811yescharacteristic
152C42#1192403811yescharacteristic
153C16—2924no—
154C23D73⋊M1611yescharacteristic
155Q8—2924no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—42no—
161C2×C4—1462no—
162C2×C4—1462no—
163C2×C4C2×C22⋊#6440811yescharacteristic
164C2×C4C2×#1192403811yescharacteristic
165C8—21no—
166C8—41no—
167C8—2921no—
168C8—1462no—
169C8#1455665212yes—
170C22—21no—
171C22—41no—
172C22#1798955811yescharacteristic
173C4—22no—
174C4—21no—
175C4—41no—
176C4—2922no—
177C4—2922no—
178C4#1798956611yescharacteristic
179C4C2×#1455665211yescharacteristic
180C2—21no—
181C2—41no—
182C2#2262519311yescharacteristic
subgroupG/H
centerC4#17989566
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
FittingC2×C4×C8×C73C4
socleC2×C73#1467
prime radicalC23×C73C2×M16
cosocleC2×#11924012C23
hypercenterC2×C4×C8#64408
hypocenterC73#11539
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C8 ◁ C22×C8 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
96. C73#11539semidirect

Maximal subgroups

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

subgroupindex
#226263052
#226248802
#226248772
#226188652
#1153973