Finite Group Databasebeta

← #32995491

Subgroups — #32995491

Order 18688.

270 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 71 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#22618864C211yesmaximal, characteristic
2#22611744C212yesmaximal
3#22607884C211yesmaximal, characteristic
4#22607881C212yesmaximal
5C73×#1328C211yesmaximal, characteristic
6#17989140C411yescharacteristic
7#17988716—22no—
8#17988711—22no—
9#17988613C411yescharacteristic
10#17988610C2211yescharacteristic
11#17988545C2211yescharacteristic
12#17988543C411yescharacteristic
13C2×C8×Dic73C411yescharacteristic
14#17988407—22no—
15#17988369C2212yes—
16#17988364—22no—
17#424×C73C2211yescharacteristic
18#349×C73C2212yes—
19C2×#11924012C2×C411yescharacteristic
20C22×#10596831C2×C411yescharacteristic
21#14556590—21no—
22#14556582—21no—
23#14556568—22no—
24C4×Dic146—22no—
25#14556550C2×C411yescharacteristic
26C2×C4×Dic73C2×C411yescharacteristic
27#14556531—22no—
28#14556520—22no—
29#14556520—22no—
30#14556502—21no—
31#14556501D412yes—
32C4×#10596831—21no—
33C8×Dic73—21no—
34C8×Dic73—21no—
35C8×Dic73D412yes—
36C2×M16×C73C2311yescharacteristic
37C22×C8×C73C2×C411yescharacteristic
38#117×C73C2×C411yescharacteristic
39M32×C73—22no—
40C4⋊C8×C73—22no—
41C2×Dic146—22no—
42C22×Dic73—21no—
43#11924012—41no—
44C2×#10596831—22no—
45C2×#10596831—21no—
46C2×#10596831C22⋊C411yescharacteristic
47C2×#10596831C22⋊C411yescharacteristic
48C4⋊Dic73—22no—
49C4⋊Dic73—21no—
50#11924007—22no—
51#11924007—22no—
52C22⋊Dic73—21no—
53C4×Dic73—21no—
54C4×Dic73C22⋊C412yes—
55C4×Dic73M1611yescharacteristic
56C4×Dic73M1611yescharacteristic
57#11924003—42no—
58C22×C4×C73C22×C411yescharacteristic
59M16×C73—41no—
60C2×C8×C73—21no—
61C2×C8×C73—41no—
62C2×C8×C73C2×D412yes—
63C4⋊C4×C73—21no—
64C22⋊C4×C73M1612yes—
65C42×C73—21no—
66C16×C73—42no—
67C23×C73C2×M1611yescharacteristic
68C2×C4×C73—21no—
69C2×C4×C73—21no—
70C2×C4×C73—22no—
71C2×C4×C73C2×C22⋊C411yescharacteristic
72C2×C4×C73C2×M1611yescharacteristic
73C2×Dic73—21no—
74C2×Dic73—21no—
75C2×Dic73—22no—
76C2×Dic73—42no—
77Dic146—44no—
78C8×C73—22no—
79C8×C73—41no—
80#10596831—21no—
81#10596831—41no—
82#10596831#10112yes—
83C22×C73—21no—
84C22×C73—41no—
85C22×C73#40711yescharacteristic
86C4×C73—21no—
87C4×C73—42no—
88C4×C73#41011yescharacteristic
89C4×C73C2×#10111yescharacteristic
90Dic73—22no—
91Dic73—42no—
92Dic73—41no—
93#11539—731nomaximal, Sylow
94C2×C73—21no—
95C2×C73—41no—
96C2×C73#146711yescharacteristic
97#2960—731no—
98#2166—732no—
99#1328—731no—
100#1328D7311yescharacteristic
101#1327—732no—
102C73#1153911yescharacteristic, complemented, Sylow
103#533—731no—
104#446—1462no—
105C8×Q8—1462no—
106#424—731no—
107#424C2×D7311yescharacteristic
108#423—731no—
109#405—731no—
110#405—731no—
111C2×C4×C8—731no—
112#364—1462no—
113#349—732no—
114#349C2×D7312yes—
115#347—1462no—
116C2×M16—731no—
117C2×M16C22×D7311yescharacteristic
118C22×C8—731no—
119C22×C8C4×D7311yescharacteristic
120C4⋊Q8—1461no—
121#125—1461no—
122C22⋊Q8—1462no—
123C4×Q8—1462no—
124#117—731no—
125#117C4×D7311yescharacteristic
126C2×C42—731no—
127M32—22no—
128M32—1462no—
129C4⋊C8—22no—
130C4⋊C8—1462no—
131C4⋊C8—1462no—
132#97—732no—
133#97—1461no—
134C4×C8—732no—
135C4×C8—1461no—
136C4×C8—1461no—
137C4×C8—1461no—
138C2×Q8—1462no—
139C22×C4—1461no—
140C22×C4C2×C4×D7311yescharacteristic
141M16—41no—
142M16—2921no—
143C2×C8—21no—
144C2×C8—41no—
145C2×C8—731no—
146C2×C8—731no—
147C2×C8—1461no—
148C2×C8—1462no—
149C2×C8D4×D7312yes—
150C4⋊C4—21no—
151C4⋊C4—1462no—
152C4⋊C4—1462no—
153C4⋊C4—1462no—
154C4⋊C4—1461no—
155C22⋊C4—1461no—
156C22⋊C4#1192401112yes—
157C42—21no—
158C42—732no—
159C42—731no—
160C42—731no—
161C42—1461no—
162C16—42no—
163C16—2922no—
164C23C2×#1192401111yescharacteristic
165Q8—2924no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—2922no—
170C2×C4—1461no—
171C2×C4—1462no—
172C2×C4—1461no—
173C2×C4C22⋊C4×D7311yescharacteristic
174C2×C4M16×D7311yescharacteristic
175C8—22no—
176C8—41no—
177C8—2921no—
178C8—732no—
179C8—1461no—
180C22—21no—
181C22—41no—
182C22#1798854911yescharacteristic
183C4—21no—
184C4—42no—
185C4—2921no—
186C4—2922no—
187C4—1462no—
188C4#1798855911yescharacteristic
189C4#101×D7311yescharacteristic
190C2—21no—
191C2—41no—
192C2#2260827311yescharacteristic
subgroupG/H
centerC4#17988559
commutatorC22×C4×C73C22×C4
FrattiniC2×M16C22×D73
FittingC73×#1328C2
socleC2×C73#1467
prime radicalC23×C73C2×M16
cosocleC2×M16×C73C23
hypercenter#1328D73
hypocenterC73#11539
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1328

Complements

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

NH ≅ G/Ntype
102. C73#11539semidirect

Maximal subgroups

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

subgroupindex
#226188642
#226117442
#226078842
#226078812
C73×#13282
#1153973