Finite Group Databasebeta

← #22611352

Subgroups — #22611352

Order 9344.

222 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C2×#14556515C211yesmaximal, characteristic
2#17988494C211yesmaximal, characteristic
3#17988452C211yesmaximal, characteristic
4#17988350C211yesmaximal, characteristic
5#17988349C211yesmaximal, characteristic
6#17988341C211yesmaximal, characteristic
7C2×#103×C73C211yesmaximal, characteristic
8C22×#10596831C2211yescharacteristic
9C2×C4⋊Dic73C2211yescharacteristic
10C2×C4⋊Dic73C2211yescharacteristic
11C2×C4×Dic73C2211yescharacteristic
12#14556515—22no—
13#14556498—21no—
14#14556498—21no—
15#14556498—21no—
16#14556498—21no—
17C22×Q8×C73C2211yescharacteristic
18C22×C8×C73C2211yescharacteristic
19C2×C4⋊C4×C73C2211yescharacteristic
20#103×C73—22no—
21C22×Dic73—21no—
22C22×Dic73—21no—
23C22×Dic73D411yescharacteristic
24C22×Dic73D411yescharacteristic
25C2×#10596831—21no—
26C2×#10596831—21no—
27C2×#10596831—21no—
28C4⋊Dic73—21no—
29C4⋊Dic73—21no—
30C4⋊Dic73—21no—
31C4⋊Dic73—21no—
32C4×Dic73—21no—
33C4×Dic73—21no—
34C2×Q8×C73—21no—
35C2×Q8×C73—21no—
36C2×Q8×C73—21no—
37C2×Q8×C73—21no—
38C2×Q8×C73—21no—
39C2×Q8×C73D412yes—
40C22×C4×C73—21no—
41C22×C4×C73—21no—
42C22×C4×C73C2311yescharacteristic
43C2×C8×C73—21no—
44C2×C8×C73—21no—
45C2×C8×C73—21no—
46C4⋊C4×C73—21no—
47C4⋊C4×C73—21no—
48C23×C73C2×D411yescharacteristic
49Q8×C73—22no—
50Q8×C73—22no—
51Q8×C73—41no—
52Q8×C73—41no—
53C2×C4×C73—22no—
54C2×C4×C73—41no—
55C2×C4×C73—41no—
56C2×C4×C73—41no—
57C2×C4×C73—41no—
58C2×C4×C73—41no—
59C2×C4×C73C2×D411yescharacteristic
60C2×C4×C73#4111yescharacteristic
61C2×C4×C73#4111yescharacteristic
62C2×C4×C73#4111yescharacteristic
63C2×C4×C73#4111yescharacteristic
64C2×C4×C73#4111yescharacteristic
65C2×Dic73—21no—
66C2×Dic73—21no—
67C2×Dic73—21no—
68C2×Dic73—21no—
69C2×Dic73—21no—
70C2×Dic73—21no—
71C2×Dic73—41no—
72C2×Dic73—41no—
73C2×Dic73—41no—
74C2×Dic73—41no—
75C2×Dic73—41no—
76C2×Dic73—41no—
77C8×C73—41no—
78#10596831—41no—
79C22×C73#12111yescharacteristic
80C22×C73#12311yescharacteristic
81C22×C73#12411yescharacteristic
82C22×C73#13511yescharacteristic
83C22×C73#13511yescharacteristic
84C22×C73#13711yescharacteristic
85C22×C73#13711yescharacteristic
86C4×C73—42no—
87C4×C73—81no—
88C4×C73#12311yescharacteristic
89C4×C73#12311yescharacteristic
90C4×C73#12611yescharacteristic
91C4×C73#12611yescharacteristic
92Dic73—41no—
93Dic73—41no—
94Dic73—81no—
95Dic73—81no—
96C2×C73#39711yescharacteristic
97C2×C73#46411yescharacteristic
98C2×C73#46411yescharacteristic
99C2×C73#48511yescharacteristic
100C2×C73#48511yescharacteristic
101C2×C73#48811yescharacteristic
102C2×C73#49111yescharacteristic
103#2074—731nomaximal, Sylow
104C73#207411yescharacteristic, complemented, Sylow
105C2×#103—731no—
106C2×#103D7311yescharacteristic
107#391—731no—
108#382—731no—
109#340—731no—
110#340—731no—
111#336—731no—
112C22×Q8C2×D7311yescharacteristic
113C22×C8—731no—
114C22×C8C2×D7311yescharacteristic
115C2×C4⋊C4—731no—
116C2×C4⋊C4—731no—
117C2×C4⋊C4C2×D7311yescharacteristic
118C2×C42—731no—
119#103—22no—
120#103—1462no—
121#95—1461no—
122#95—1461no—
123#95—1461no—
124#95—1461no—
125C2×Q8—21no—
126C2×Q8—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8C22⋊D7312yes—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—731no—
134C22×C4—731no—
135C22×C4—1461no—
136C22×C4—1461no—
137C22×C4C22×D7311yescharacteristic
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—1461no—
142C2×C8—1461no—
143C2×C8—1461no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—1461no—
147C4⋊C4—1461no—
148C4⋊C4—1461no—
149C4⋊C4—1461no—
150C42—1461no—
151C42—1461no—
152C23D4×D7311yescharacteristic
153Q8—22no—
154Q8—22no—
155Q8—41no—
156Q8—41no—
157C2×C4—22no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—2921no—
164C2×C4—2921no—
165C2×C4—2921no—
166C2×C4—2921no—
167C2×C4—2921no—
168C2×C4—2921no—
169C2×C4—1461no—
170C2×C4—1461no—
171C2×C4—1461no—
172C2×C4—1461no—
173C2×C4—1461no—
174C2×C4—1461no—
175C2×C4C2×C22⋊D7311yescharacteristic
176C2×C4#1192402711yescharacteristic
177C2×C4#1192402711yescharacteristic
178C2×C4#1192402711yescharacteristic
179C2×C4#1192402811yescharacteristic
180C2×C4#1192402811yescharacteristic
181C8—41no—
182C8—2921no—
183C22#1455656311yescharacteristic
184C22#1455657311yescharacteristic
185C22#1455657711yescharacteristic
186C22#1455661211yescharacteristic
187C22#1455661411yescharacteristic
188C22#1455662011yescharacteristic
189C22#1455662311yescharacteristic
190C4—42no—
191C4—81no—
192C4—2921no—
193C4—2921no—
194C4—5841no—
195C4—5841no—
196C4#1455657211yescharacteristic
197C4#1455657411yescharacteristic
198C4#1455658411yescharacteristic
199C4#1455658411yescharacteristic
200C2#1798851511yescharacteristic
201C2#1798880711yescharacteristic
202C2#1798881111yescharacteristic
203C2#1798892611yescharacteristic
204C2#1798892711yescharacteristic
205C2#1798894311yescharacteristic
206C2#1798895411yescharacteristic
subgroupG/H
centerC23D4×D73
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
FittingC2×#103×C73C2
socleC23×C73C2×D4
hypercenterC2×#103D73
hypocenterC73#2074
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
104. C73#2074semidirect