Finite Group Databasebeta

← #22611405

Subgroups — #22611405

Order 9344.

230 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14556524C211yesmaximal, characteristic
2#17988486C211yesmaximal, characteristic
3#17988456C211yesmaximal, characteristic
4#17988350C211yesmaximal, characteristic
5#17988349C211yesmaximal, characteristic
6#17988341C211yesmaximal, characteristic
7C2×#107×C73C211yesmaximal, characteristic
8C22×#10596831C2211yescharacteristic
9C2×C4⋊Dic73—21no—
10C2×C4⋊Dic73C2211yescharacteristic
11C2×C4⋊Dic73C2211yescharacteristic
12C2×#11924007—21no—
13C2×#11924007—21no—
14C2×C4×Dic73C2211yescharacteristic
15#14556524—22no—
16#14556498—21no—
17C22×C8×C73C2211yescharacteristic
18C2×C4⋊C4×C73C2211yescharacteristic
19C2×C4⋊C4×C73C2211yescharacteristic
20#107×C73—22no—
21C22×Dic73—21no—
22C22×Dic73—21no—
23C22×Dic73D411yescharacteristic
24C22×Dic73D411yescharacteristic
25C2×#10596831—21no—
26C2×#10596831—21no—
27C2×#10596831Q812yes—
28C4⋊Dic73—21no—
29C4⋊Dic73—21no—
30C4⋊Dic73—21no—
31C4⋊Dic73—21no—
32C4⋊Dic73—42no—
33#11924007—42no—
34#11924007—42no—
35C4×Dic73—21no—
36C4×Dic73—21no—
37C22×C4×C73—21no—
38C22×C4×C73—21no—
39C22×C4×C73C2311yescharacteristic
40C2×C8×C73—21no—
41C2×C8×C73—21no—
42C2×C8×C73Q812yes—
43C4⋊C4×C73—21no—
44C4⋊C4×C73—21no—
45C4⋊C4×C73—21no—
46C4⋊C4×C73D412yes—
47C23×C73C2×D411yescharacteristic
48C2×C4×C73—22no—
49C2×C4×C73—41no—
50C2×C4×C73—41no—
51C2×C4×C73—41no—
52C2×C4×C73—41no—
53C2×C4×C73—41no—
54C2×C4×C73C2×D411yescharacteristic
55C2×C4×C73C2×Q811yescharacteristic
56C2×C4×C73C2×Q811yescharacteristic
57C2×C4×C73#4111yescharacteristic
58C2×C4×C73#4111yescharacteristic
59C2×C4×C73#4111yescharacteristic
60C2×Dic73—21no—
61C2×Dic73—21no—
62C2×Dic73—21no—
63C2×Dic73—21no—
64C2×Dic73—41no—
65C2×Dic73—41no—
66C2×Dic73—41no—
67C2×Dic73—41no—
68C2×Dic73—41no—
69C2×Dic73—41no—
70C2×Dic73D812yes—
71C2×Dic73Q1612yes—
72C8×C73—22no—
73#10596831—22no—
74C22×C73#12111yescharacteristic
75C22×C73#12311yescharacteristic
76C22×C73C4⋊Q811yescharacteristic
77C22×C73C2×D811yescharacteristic
78C22×C73C2×Q1611yescharacteristic
79C22×C73AGL(1,ℤ/8)11yescharacteristic
80C22×C73#13711yescharacteristic
81C4×C73—42no—
82C4×C73—81no—
83C4×C73C22⋊Q811yescharacteristic
84C4×C73C22⋊Q811yescharacteristic
85C4×C73#12511yescharacteristic
86C4×C73#12511yescharacteristic
87Dic73—22no—
88Dic73—22no—
89Dic73—81no—
90Dic73—81no—
91C2×C73#39811yescharacteristic
92C2×C73#45911yescharacteristic
93C2×C73#46211yescharacteristic
94C2×C73#48011yescharacteristic
95C2×C73#48411yescharacteristic
96C2×C73#50011yescharacteristic
97C2×C73#50111yescharacteristic
98#2083—731nomaximal, Sylow
99C73#208311yescharacteristic, complemented, Sylow
100C2×#107—731no—
101C2×#107D7311yescharacteristic
102#389—731no—
103#384—731no—
104#340—731no—
105#340—731no—
106#336—731no—
107C22×C8—731no—
108C22×C8C2×D7311yescharacteristic
109C2×C4⋊C4—731no—
110C2×C4⋊C4—731no—
111C2×C4⋊C4—1461no—
112C2×C4⋊C4—1461no—
113C2×C4⋊C4—1461no—
114C2×C4⋊C4C2×D7311yescharacteristic
115C2×C4⋊C4C2×D7311yescharacteristic
116C2×C42—731no—
117#107—22no—
118#107—1462no—
119#95—1461no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—731no—
123C22×C4—731no—
124C22×C4—1461no—
125C22×C4—1461no—
126C22×C4C22×D7311yescharacteristic
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—732no—
130C2×C8—1461no—
131C2×C8—1461no—
132C2×C8Dic14612yes—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—2922no—
137C4⋊C4—2922no—
138C4⋊C4—2922no—
139C4⋊C4—1461no—
140C4⋊C4—1461no—
141C4⋊C4—1461no—
142C4⋊C4—1461no—
143C4⋊C4C22⋊D7312yes—
144C42—1461no—
145C42—1461no—
146C23D4×D7311yescharacteristic
147C2×C4—22no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—2921no—
154C2×C4—2921no—
155C2×C4—2921no—
156C2×C4—2921no—
157C2×C4—2921no—
158C2×C4—2921no—
159C2×C4—732no—
160C2×C4—732no—
161C2×C4—1461no—
162C2×C4—1461no—
163C2×C4—1461no—
164C2×C4—1461no—
165C2×C4C2×C22⋊D7311yescharacteristic
166C2×C4Q8×D7311yescharacteristic
167C2×C4C2×Dic14611yescharacteristic
168C2×C4#1192402711yescharacteristic
169C2×C4#1192402811yescharacteristic
170C2×C4#1192402911yescharacteristic
171C8—22no—
172C8—1462no—
173C22#1455656311yescharacteristic
174C22#1455657611yescharacteristic
175C22#1455659011yescharacteristic
176C22D8×D7311yescharacteristic
177C22Q16×D7311yescharacteristic
178C22#1455661511yescharacteristic
179C22#1455662311yescharacteristic
180C4—42no—
181C4—81no—
182C4—5841no—
183C4—5841no—
184C4—1462no—
185C4—1462no—
186C4#1455656711yescharacteristic
187C4#1455657011yescharacteristic
188C4#1455658111yescharacteristic
189C4#1455658211yescharacteristic
190C2#1798852011yescharacteristic
191C2#1798878011yescharacteristic
192C2#1798879511yescharacteristic
193C2#1798890211yescharacteristic
194C2#1798892411yescharacteristic
195C2#1798899111yescharacteristic
196C2#1798899511yescharacteristic
subgroupG/H
centerC23D4×D73
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
FittingC2×#107×C73C2
socleC23×C73C2×D4
hypercenterC2×#107D73
hypocenterC73#2083
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
99. C73#2083semidirect