Finite Group Databasebeta

← #32973366

Subgroups — #32973366

Order 18688.

268 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 43 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#22610736C211yesmaximal, characteristic
2#22607877C211yesmaximal, characteristic, complemented
3C73×#1325C211yesmaximal, characteristic, complemented
4C2×#14556588C411yescharacteristic
5C2×#14556511—21no—
6C2×#14556511—21no—
7C2×C4×#10596831C411yescharacteristic
8#17988313—21no—
9#384×C73C2211yescharacteristic
10#324×C73—21no—
11C22×D292—21no—
12C22×D292—41no—
13C22×#10596831—21no—
14#14556588—21no—
15#14556588—41no—
16#14556588C812yescomplemented
17#14556511—42no—
18#14556511—42no—
19C22⋊#10596831—41no—
20C4×#10596831—41no—
21C2×C4⋊C4×C73—41no—
22C2×C4⋊C4×C73D411yescharacteristic
23C2×C4⋊C4×C73D411yescharacteristic
24C2×C42×C73C2×C411yescharacteristic
25C22⋊C8×C73—41no—
26C23×D73—41no—
27C2×D292—22no—
28C2×D292—41no—
29C2×D292—41no—
30C2×D292—41no—
31C2×D292—41no—
32C2×D292—42no—
33C2×D292—42no—
34C2×D292—41no—
35C2×D292—82no—
36C2×D292—82no—
37C2×#10596831—22no—
38C2×#10596831—41no—
39C2×#10596831—41no—
40C2×#10596831—81no—
41C22×C4×C73—21no—
42C22×C4×C73—21no—
43C22×C4×C73—21no—
44C22×C4×C73C22⋊C411yescharacteristic
45C2×C8×C73—81no—
46C4⋊C4×C73—41no—
47C4⋊C4×C73—41no—
48C4⋊C4×C73—82no—
49C42×C73—21no—
50C42×C73C2×C811yescharacteristic
51C42×C73M1611yescharacteristic
52C23×C73#9911yescharacteristic
53C22×D73—42no—
54C22×D73—82no—
55C22×D73—82no—
56C22×D73—81no—
57C22×D73—81no—
58C2×C4×C73—22no—
59C2×C4×C73—22no—
60C2×C4×C73—21no—
61C2×C4×C73—21no—
62C2×C4×C73—21no—
63C2×C4×C73—21no—
64C2×C4×C73—41no—
65C2×C4×C73—41no—
66C2×C4×C73—81no—
67C2×C4×C73—81no—
68C2×C4×C73C22⋊C811yescharacteristic
69C2×C4×C73#10011yescharacteristic
70D292—42no—
71D292—42no—
72D292—81no—
73D292—81no—
74D292—84no—
75D292—84no—
76C8×C73—161no—
77#10596831—42no—
78#10596831—161no—
79C22×C73—21no—
80C22×C73—21no—
81C22×C73#32311yescharacteristic
82C22×C73#35311yescharacteristic
83C22×C73#35511yescharacteristic
84C2×D73—84no—
85C2×D73—82no—
86C2×D73—162no—
87C2×D73—161no—
88C2×D73—161no—
89C4×C73—22no—
90C4×C73—22no—
91C4×C73—21no—
92C4×C73—21no—
93C4×C73—81no—
94C4×C73—81no—
95#7354—731nomaximal, Sylow
96C2×C73—21no—
97C2×C73—21no—
98C2×C73#131811yescharacteristic
99C2×C73#140811yescharacteristic
100C2×C73#141011yescharacteristic
101D73—162no—
102#1957—731no—
103#1325—731no—
104#1325D7311yescharacteristic, complemented
105C73#735411yescharacteristic, complemented, Sylow
106C2×#127—731no—
107C2×#102—1461no—
108C2×#102—1461no—
109C2×C4×C8—731no—
110#384C2×D7311yescharacteristic
111#324—21no—
112#324—1461no—
113C22×D4—2921no—
114C22×D4—1461no—
115C22×C8—1461no—
116#127—2921no—
117#127—732no—
118#127—1461no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4D29211yescharacteristic
121C2×C4⋊C4C22⋊D7311yescharacteristic
122C2×C42C4×D7311yescharacteristic
123#102—2922no—
124#102—2922no—
125C22⋊C8—41no—
126C22⋊C8—2921no—
127C4×C8—2921no—
128C24—2921no—
129C2×D4—2921no—
130C2×D4—2921no—
131C2×D4—2921no—
132C2×D4—2921no—
133C2×D4—2922no—
134C2×D4—2922no—
135C2×D4—2921no—
136C2×D4—5842no—
137C2×D4—5842no—
138C2×D4—1462no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4#1192400511yescharacteristic
143C2×C8—81no—
144C2×C8—2921no—
145C2×C8—2921no—
146C2×C8—5841no—
147C2×C8—1462no—
148C4⋊C4—41no—
149C4⋊C4—41no—
150C4⋊C4—82no—
151C42—21no—
152C42C8×D7311yescharacteristic
153C42#1192401111yescharacteristic
154C23—2922no—
155C23—5842no—
156C23—5842no—
157C23—5841no—
158C23—5841no—
159C23#1455650511yescharacteristic
160D4—2922no—
161D4—2922no—
162D4—5841no—
163D4—5841no—
164D4—5844no—
165D4—5844no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—81no—
175C2×C4—81no—
176C2×C4#1455650311yescharacteristic
177C2×C4#1455650711yescharacteristic
178C8—161no—
179C8—2922no—
180C8—11681no—
181C22—21no—
182C22—21no—
183C22—5844no—
184C22—5842no—
185C22—11682no—
186C22—11681no—
187C22—11681no—
188C22#1798831011yescharacteristic
189C22#1798837911yescharacteristic
190C22#1798838311yescharacteristic
191C4—22no—
192C4—22no—
193C4—21no—
194C4—21no—
195C4—81no—
196C4—81no—
197C2—21no—
198C2—21no—
199C2—11682no—
200C2#2260786211yescharacteristic
201C2#2260809311yescharacteristic
202C2#2260809711yescharacteristic
subgroupG/H
centerC22#17988379
commutatorC42×C73C2×C8
Frattini#384C2×D73
FittingC73×#1325C2
socleC22×C73#353
prime radicalC2×#14556588C4
cosocle#384×C73C22
hypercenter#1325D73
hypocenterC73#7354
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #384 ◁ #1325

Complements

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

NH ≅ G/Ntype
2. #22607877C2semidirect
3. C73×#1325C2semidirect
16. #14556588C8semidirect
104. #1325D73semidirect
105. C73#7354semidirect

Maximal subgroups

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

subgroupindex
#226107362
#226078772
C73×#13252
#735473