Finite Group Databasebeta

← #32973368

Subgroups — #32973368

Order 18688.

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

normal subgroups only

This group has 216 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#22610732C211yesmaximal, characteristic
2#22607877C211yesmaximal, characteristic
3C73×#1325C211yesmaximal, characteristic
4C2×#14556591C411yescharacteristic
5C2×#14556514—21no—
6C2×#14556514—21no—
7C2×C4×#10596831C411yescharacteristic
8#17988313—21no—
9#384×C73C2211yescharacteristic
10#324×C73—21no—
11C22×Dic146—21no—
12C22×#10596831—21no—
13#14556591—21no—
14#14556591—41no—
15#14556591C812yescomplemented
16C2×C4⋊Dic73—41no—
17#14556514—42no—
18#14556514—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—
26C2×Dic146—22no—
27C2×Dic146—41no—
28C2×Dic146—41no—
29C2×Dic146—41no—
30C2×Dic146—41no—
31C2×Dic146—41no—
32C22×Dic73—41no—
33C2×#10596831—22no—
34C2×#10596831—41no—
35C2×#10596831—41no—
36C2×#10596831—81no—
37C4⋊Dic73—42no—
38C4⋊Dic73—42no—
39C22×C4×C73—21no—
40C22×C4×C73—21no—
41C22×C4×C73—21no—
42C22×C4×C73C22⋊C411yescharacteristic
43C2×C8×C73—81no—
44C4⋊C4×C73—41no—
45C4⋊C4×C73—41no—
46C4⋊C4×C73—82no—
47C42×C73—21no—
48C42×C73C2×C811yescharacteristic
49C42×C73M1611yescharacteristic
50C23×C73#9911yescharacteristic
51C2×C4×C73—22no—
52C2×C4×C73—22no—
53C2×C4×C73—21no—
54C2×C4×C73—21no—
55C2×C4×C73—21no—
56C2×C4×C73—21no—
57C2×C4×C73—41no—
58C2×C4×C73—41no—
59C2×C4×C73—81no—
60C2×C4×C73—81no—
61C2×C4×C73C22⋊C811yescharacteristic
62C2×C4×C73#10011yescharacteristic
63C2×Dic73—42no—
64C2×Dic73—81no—
65C2×Dic73—81no—
66Dic146—42no—
67Dic146—42no—
68Dic146—81no—
69Dic146—81no—
70C8×C73—161no—
71#10596831—42no—
72#10596831—161no—
73C22×C73—21no—
74C22×C73—21no—
75C22×C73#32311yescharacteristic
76C22×C73#35311yescharacteristic
77C22×C73#35511yescharacteristic
78C4×C73—22no—
79C4×C73—22no—
80C4×C73—21no—
81C4×C73—21no—
82C4×C73—81no—
83C4×C73—81no—
84Dic73—82no—
85#7355—731nomaximal, Sylow
86C2×C73—21no—
87C2×C73—21no—
88C2×C73#131811yescharacteristic
89C2×C73#140911yescharacteristic
90C2×C73#141111yescharacteristic
91#1956—731no—
92#1325—731no—
93#1325D7311yescharacteristic
94C73#735511yescharacteristic, complemented, Sylow
95C2×C4⋊Q8—731no—
96C2×#103—1461no—
97C2×#103—1461no—
98C2×C4×C8—731no—
99#384C2×D7311yescharacteristic
100#324—21no—
101#324—1461no—
102C22×Q8—1461no—
103C22×C8—1461no—
104C4⋊Q8—2921no—
105C4⋊Q8—732no—
106C4⋊Q8—1461no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4—2921no—
109C2×C4⋊C4D29211yescharacteristic
110C2×C4⋊C4C22⋊D7311yescharacteristic
111C2×C42C4×D7311yescharacteristic
112#103—2922no—
113#103—2922no—
114C22⋊C8—41no—
115C22⋊C8—2921no—
116C4×C8—2921no—
117C2×Q8—2921no—
118C2×Q8—2921no—
119C2×Q8—2921no—
120C2×Q8—2921no—
121C2×Q8—2921no—
122C2×Q8—1462no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—2921no—
127C22×C4#1192400511yescharacteristic
128C2×C8—81no—
129C2×C8—2921no—
130C2×C8—2921no—
131C2×C8—5841no—
132C2×C8—1462no—
133C4⋊C4—41no—
134C4⋊C4—41no—
135C4⋊C4—82no—
136C4⋊C4—2922no—
137C4⋊C4—2922no—
138C42—21no—
139C42C8×D7311yescharacteristic
140C42#1192401111yescharacteristic
141C23#1455650511yescharacteristic
142Q8—2922no—
143Q8—2922no—
144Q8—5841no—
145Q8—5841no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—81no—
155C2×C4—81no—
156C2×C4—2922no—
157C2×C4—5841no—
158C2×C4—5841no—
159C2×C4#1455650311yescharacteristic
160C2×C4#1455650711yescharacteristic
161C8—161no—
162C8—2922no—
163C8—11681no—
164C22—21no—
165C22—21no—
166C22#1798831011yescharacteristic
167C22#1798837911yescharacteristic
168C22#1798838311yescharacteristic
169C4—22no—
170C4—22no—
171C4—21no—
172C4—21no—
173C4—81no—
174C4—81no—
175C4—5842no—
176C2—21no—
177C2—21no—
178C2#2260786211yescharacteristic
179C2#2260809511yescharacteristic
180C2#2260809911yescharacteristic
subgroupG/H
centerC22#17988379
commutatorC42×C73C2×C8
Frattini#384C2×D73
FittingC73×#1325C2
socleC22×C73#353
prime radicalC23×C73#99
cosocle#384×C73C22
hypercenter#1325D73
hypocenterC73#7355
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
15. #14556591C8semidirect
94. C73#7355semidirect

Maximal subgroups

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

subgroupindex
#226107322
#226078772
C73×#13252
#735573