Finite Group Databasebeta

← #34001463

Subgroups — #34001463

Order 18688.

440 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 110 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#22625858C212yesmaximal
2#22624752C214yesmaximal
3#22612498C211yesmaximal, characteristic
4#17989453—22no—
5#17989453—22no—
6#17989453C2214yes—
7C2×#14556591C411yescharacteristic
8C2×#14556556C412yes—
9#17988492C2212yes—
10#17988483—22no—
11C4⋊C4×Dic73—22no—
12C42×Dic73C2211yescharacteristic
13#384×C73C411yescharacteristic
14C22×#10596833—24no—
15C22×Dic146C2×C412yes—
16#14556591—22no—
17#14556591C814yescomplemented
18#14556556—44no—
19C2×C4⋊Dic73—22no—
20C2×#11924007—22no—
21C2×C4×Dic73—22no—
22C2×C4×Dic73C2×C411yescharacteristic
23C2×C4×Dic73D412yes—
24C2×C4×Dic73D412yes—
25C2×C4×Dic73C2311yescharacteristic
26#14556498—24no—
27C2×C4⋊C4×C73—22no—
28C2×C4⋊C4×C73C2×C412yes—
29C2×C42×C73C2×C411yescharacteristic
30C2×#10596833—44no—
31C2×#10596833—44no—
32C2×#10596833—44no—
33C2×Dic146—22no—
34C2×Dic146—42no—
35C2×Dic146—42no—
36C2×Dic146C2×C814yes—
37C22×Dic73—22no—
38C22×Dic73C22⋊C411yescharacteristic
39C22×Dic73C22⋊C411yescharacteristic
40C22×Dic73C2×D412yes—
41C4⋊Dic73—28no—
42#11924007—44no—
43C4×Dic73—22no—
44C4×Dic73—24no—
45C4×Dic73—42no—
46C4×Dic73—41no—
47C4×Dic73—44no—
48C22×C4×C73—22no—
49C22×C4×C73C22⋊C412yes—
50C22×C4×C73C22×C411yescharacteristic
51C4⋊C4×C73—42no—
52C4⋊C4×C73—44no—
53C42×C73C2×C812yes—
54C42×C73M1612yes—
55C23×C73C2×C22⋊C411yescharacteristic
56C2×C4×C73—21no—
57C2×C4×C73—21no—
58C2×C4×C73—22no—
59C2×C4×C73—22no—
60C2×C4×C73—42no—
61C2×C4×C73—44no—
62C2×C4×C73C22⋊C814yes—
63C2×C4×C73C22×C811yescharacteristic
64C2×C4×C73C2×M1611yescharacteristic
65C2×Dic73—22no—
66C2×Dic73—22no—
67C2×Dic73—22no—
68C2×Dic73—24no—
69C2×Dic73—21no—
70C2×Dic73—22no—
71C2×Dic73—42no—
72C2×Dic73—42no—
73C2×Dic73#10012yes—
74C2×Dic73#13714yes—
75Dic146—44no—
76Dic146—44no—
77#10596833—84no—
78C22×C73C2×C22⋊C811yescharacteristic
79C22×C73#41011yescharacteristic
80C22×C73C2×#10011yescharacteristic
81C22×C73#41912yes—
82C22×C73#42112yes—
83C4×C73—21no—
84C4×C73—21no—
85C4×C73—24no—
86C4×C73—82no—
87Dic73—22no—
88Dic73—24no—
89Dic73—41no—
90Dic73—44no—
91#7605—731nomaximal, Sylow
92C2×C73#146011yescharacteristic
93C2×C73#147912yes—
94C2×C73#151512yes—
95C2×C73#153611yescharacteristic
96C2×C73#155811yescharacteristic
97C4×C4⋊Q8—731no—
98#1839—732no—
99#1272—734no—
100C73#760511yescharacteristic, complemented, Sylow
101C2×C4⋊Q8—731no—
102C2×C4×Q8—732no—
103#391—732no—
104#389—1462no—
105#384#6440811yescharacteristic
106C4×C4⋊C4—1462no—
107C43—731no—
108#336—734no—
109#336—1462no—
110#336—1462no—
111C22×Q8—732no—
112C22×C8—1464no—
113C4⋊Q8—734no—
114C4⋊Q8—1462no—
115C4×Q8—2924no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—1462no—
118C2×C4⋊C4—1462no—
119C2×C4⋊C4C2×#6440812yes—
120C2×C42—732no—
121C2×C42—731no—
122C2×C42—732no—
123C2×C42—731no—
124C2×C42—1462no—
125C2×C42C2×#6440811yescharacteristic
126#95—1464no—
127C2×Q8—2922no—
128C2×Q8—2922no—
129C2×Q8—734no—
130C2×Q8—1462no—
131C22×C4—22no—
132C22×C4—731no—
133C22×C4—732no—
134C22×C4—731no—
135C22×C4—1462no—
136C22×C4C22⋊#6440812yes—
137C22×C4C22×#6440811yescharacteristic
138C2×C8—2924no—
139C2×C8—2924no—
140C2×C8—2924no—
141C4⋊C4—42no—
142C4⋊C4—44no—
143C4⋊C4—2924no—
144C4⋊C4—1468no—
145C42—2921no—
146C42—2922no—
147C42—2924no—
148C42—1464no—
149C42—1462no—
150C42#1192403612yes—
151C42#1192403812yes—
152C23C2×C22⋊#6440811yescharacteristic
153Q8—2924no—
154Q8—2924no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—42no—
160C2×C4—44no—
161C2×C4—2922no—
162C2×C4—2922no—
163C2×C4—732no—
164C2×C4—734no—
165C2×C4—1464no—
166C2×C4—1461no—
167C2×C4—1462no—
168C2×C4—1462no—
169C2×C4—1462no—
170C2×C4—1462no—
171C2×C4#1455664814yes—
172C2×C4C2×#1192403611yescharacteristic
173C2×C4C2×#1192403811yescharacteristic
174C8—5844no—
175C22C2×#1455664811yescharacteristic
176C22#1798956811yescharacteristic
177C22D73⋊#10011yescharacteristic
178C22#1798958012yes—
179C22#1798958512yes—
180C4—21no—
181C4—21no—
182C4—24no—
183C4—82no—
184C4—2921no—
185C4—2924no—
186C4—1464no—
187C4—1462no—
188C2#2262517211yescharacteristic
189C2#2262523512yes—
190C2#2262535412yes—
191C2#2262542011yescharacteristic
192C2#2262546511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C22×C8
FrattiniC22×C4C22×#64408
Fitting#384×C73C4
socle, prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4×Dic73C23
hypercenter#384#64408
hypocenterC73#7605
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
17. #14556591C8semidirect
100. C73#7605semidirect

Maximal subgroups

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

subgroupindex
#226258582
#226247522
#226124982
#760573