Finite Group Databasebeta

← #22608921

Subgroups — #22608921

Order 9344.

228 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 53 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#17989213C211yesmaximal, characteristic
2#17988917C212yesmaximal, complemented
3#17988323C212yesmaximal, complemented
4#17988311C211yesmaximal, characteristic
5#397×C73C211yesmaximal, characteristic
6#14556570—21no—
7#14556570C2212yes—
8#14556568—22no—
9#14556568—22no—
10C2×C22⋊Dic73—21no—
11#14556522—22no—
12#14556514—22no—
13C22⋊#10596831C2212yes—
14C2×C4⋊C4×C73C2211yescharacteristic
15C2×C22⋊C4×C73—21no—
16C2×C22⋊C4×C73C2211yescharacteristic
17#95×C73—21no—
18#95×C73C2211yescharacteristic
19C2×Dic146—21no—
20C2×Dic146D412yes—
21C22×Dic73—21no—
22C22×Dic73—21no—
23C2×#10596831—22no—
24C4⋊Dic73—21no—
25C4⋊Dic73D412yes—
26#11924007—22no—
27#11924007—22no—
28C22⋊Dic73—22no—
29C22⋊Dic73—22no—
30C24×C73D411yescharacteristic
31C22×C4×C73—21no—
32C22×C4×C73—21no—
33C22×C4×C73D411yescharacteristic
34C22×C4×C73C2311yescharacteristic
35C4⋊C4×C73—22no—
36C22⋊C4×C73—22no—
37C22⋊C4×C73—42no—
38C23×C73—21no—
39C23×C73—21no—
40C23×C73—41no—
41C23×C73—41no—
42C23×C73SD1612yes—
43C23×C73C2×D411yescharacteristic
44C2×C4×C73—21no—
45C2×C4×C73—41no—
46C2×C4×C73—41no—
47C2×C4×C73—41no—
48C2×C4×C73—41no—
49C2×C4×C73—41no—
50C2×C4×C73—41no—
51C2×C4×C73—41no—
52C2×C4×C73—41no—
53C2×C4×C73C2×D412yes—
54C2×Dic73—22no—
55C2×Dic73—22no—
56C2×Dic73—81no—
57C2×Dic73—81no—
58Dic146—42no—
59Dic146—81no—
60#10596831—42no—
61C22×C73—21no—
62C22×C73—21no—
63C22×C73—22no—
64C22×C73—42no—
65C22×C73—41no—
66C22×C73—41no—
67C22×C73—81no—
68C22×C73#12011yescharacteristic
69C22×C73C2×SD1611yescharacteristic
70C22×C73#13711yescharacteristic
71C4×C73—22no—
72C4×C73—41no—
73C4×C73—81no—
74C4×C73—81no—
75Dic73—42no—
76Dic73—42no—
77C2×C73—21no—
78C2×C73—21no—
79C2×C73—42no—
80C2×C73#44811yescharacteristic
81C2×C73#45511yescharacteristic
82C2×C73#45811yescharacteristic
83#1608—731nomaximal, Sylow
84C73#160811yescharacteristic, complemented, Sylow
85#543—731no—
86#483—732no—
87#397D7311yescharacteristic
88#328—732no—
89#323—731no—
90C22⋊Q8—732no—
91C22⋊Q8—1462no—
92C22⋊Q8—1462no—
93C22⋊Q8—1461no—
94C2×C4⋊C4C2×D7311yescharacteristic
95C2×C22⋊C4—21no—
96C2×C22⋊C4—1461no—
97C2×C22⋊C4C2×D7311yescharacteristic
98#106—1462no—
99#103—1462no—
100C22⋊C8—732no—
101#95—21no—
102#95C2×D7311yescharacteristic
103C24C22⋊D7311yescharacteristic
104C2×Q8—732no—
105C2×Q8—1461no—
106C22×C4—21no—
107C22×C4—21no—
108C22×C4—1461no—
109C22×C4—1461no—
110C22×C4C22⋊D7311yescharacteristic
111C22×C4C22×D7311yescharacteristic
112C2×C8—1462no—
113C4⋊C4—22no—
114C4⋊C4—732no—
115C4⋊C4—1462no—
116C4⋊C4—1461no—
117C4⋊C4—1462no—
118C22⋊C4—22no—
119C22⋊C4—42no—
120C22⋊C4—1462no—
121C22⋊C4—1462no—
122C23—21no—
123C23—21no—
124C23—41no—
125C23—41no—
126C23#1192401612yes—
127C23C2×C22⋊D7311yescharacteristic
128Q8—2922no—
129Q8—5841no—
130C2×C4—21no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—5841no—
140C2×C4—5841no—
141C2×C4—1462no—
142C2×C4—1462no—
143C2×C4D4×D7312yes—
144C8—2922no—
145C22—21no—
146C22—21no—
147C22—22no—
148C22—42no—
149C22—41no—
150C22—41no—
151C22—81no—
152C22#1455655911yescharacteristic
153C22C2×#1192401611yescharacteristic
154C22#1455662111yescharacteristic
155C4—22no—
156C4—41no—
157C4—81no—
158C4—81no—
159C4—2922no—
160C4—2922no—
161C2—21no—
162C2—21no—
163C2—42no—
164C2#1798872511yescharacteristic
165C2#1798876411yescharacteristic
166C2#1798877611yescharacteristic
subgroupG/H
centerC22#14556559
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#397×C73C2
socleC22×C73#120
hypercenter#397D73
hypocenterC73#1608
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #17988917C2semidirect
3. #17988323C2semidirect
84. C73#1608semidirect