Finite Group Databasebeta

← #22609013

Subgroups — #22609013

Order 9344.

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

normal subgroups only

This group has 240 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#17989302C211yesmaximal, characteristic, complemented
2#17988959C211yesmaximal, characteristic, complemented
3#17988779C211yesmaximal, characteristic, complemented
4#17988335C211yesmaximal, characteristic, complemented
5D4⋊#10596831C211yesmaximal, characteristic, complemented
6#17988314C211yesmaximal, characteristic, complemented
7#459×C73C211yesmaximal, characteristic, complemented
8C2×#11924016—22no—
9C2×#11924013—21no—
10#14556591C2211yescharacteristic
11#14556577—22no—
12#14556565—21no—
13#14556562—21no—
14C4×D292C2211yescharacteristic
15#14556550—21no—
16#14556549—21no—
17C4⋊#10596831C2211yescharacteristic
18#14556512—21no—
19C4×#10596831C2211yescharacteristic
20C2×D8×C73—21no—
21#127×C73C2211yescharacteristic
22C4×D4×C73C2211yescharacteristic
23C4⋊C8×C73C2211yescharacteristic
24#102×C73—21no—
25C2×Dic146D412yes—
26C2×D292D411yescharacteristic
27C2×C22⋊D73—22no—
28C2×C4×D73—21no—
29#11924016—44no—
30#11924013—42no—
31C2×#10596831—21no—
32C2×#10596831—21no—
33C4⋊Dic73—21no—
34C4⋊Dic73—21no—
35C4⋊Dic73D411yescharacteristic
36C22⋊Dic73—22no—
37#11924005—22no—
38#11924005—21no—
39C4×Dic73—22no—
40C2×D4×C73—21no—
41C2×D4×C73—21no—
42C2×D4×C73—21no—
43C2×D4×C73D411yescharacteristic
44C22×C4×C73—21no—
45D8×C73—42no—
46C2×C8×C73—21no—
47C4⋊C4×C73D411yescharacteristic
48C22⋊C4×C73—21no—
49C42×C73C2311yescharacteristic
50C23×C73—21no—
51C23×C73—41no—
52C22×D73—21no—
53D4×C73—21no—
54D4×C73—21no—
55D4×C73—42no—
56D4×C73—41no—
57D4×C73—41no—
58D4×C73—41no—
59D4×C73—41no—
60C2×C4×C73—21no—
61C2×C4×C73—41no—
62C2×C4×C73—41no—
63C2×C4×C73C2×D411yescharacteristic
64C2×C4×C73C2×D411yescharacteristic
65C2×C4×C73C2×D411yescharacteristic
66C22⋊D73—82no—
67C2×Dic73—21no—
68C2×Dic73—22no—
69D292—21no—
70D292—21no—
71C4×D73—41no—
72C4×D73—41no—
73Dic146—42no—
74C8×C73—41no—
75#10596831—22no—
76#10596831—41no—
77C22×C73—41no—
78C22×C73—41no—
79C22×C73—41no—
80C22×C73—81no—
81C22×C73—81no—
82C22×C73—81no—
83C22×C73#12011yescharacteristic
84C2×D73—41no—
85C2×D73—41no—
86C2×D73—41no—
87C4×C73—21no—
88C4×C73—41no—
89C4×C73#13511yescharacteristic
90C4×C73#13511yescharacteristic
91C4×C73AGL(1,ℤ/8)11yescharacteristic
92C4×C73AGL(1,ℤ/8)11yescharacteristic
93Dic73—41no—
94Dic73—42no—
95C2×C73—81no—
96C2×C73—161no—
97C2×C73#44911yescharacteristic
98C2×C73#44911yescharacteristic
99C2×C73#45311yescharacteristic
100D73—81no—
101#1624—731nomaximal, Sylow
102C73#162411yescharacteristic, complemented, Sylow
103#555—731no—
104#492—731no—
105#459—731no—
106#459D7311yescharacteristic, complemented
107#333—731no—
108D4⋊C8—731no—
109D4⋊C8—731no—
110C2×SD16—1462no—
111C2×D8—21no—
112C2×D8—1461no—
113C4⋊Q8—731no—
114#127C2×D7311yescharacteristic
115#124—1462no—
116#121—1461no—
117#121—1461no—
118C4×D4—731no—
119C4×D4C2×D7311yescharacteristic
120#117—1461no—
121#117—1461no—
122C4⋊C8—731no—
123C4⋊C8C2×D7311yescharacteristic
124#102—21no—
125#102—1461no—
126C4×C8—731no—
127C2×Q8—732no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—731no—
132C2×D4—1462no—
133C2×D4C22⋊D7311yescharacteristic
134C22×C4—21no—
135C22×C4—1461no—
136SD16—2924no—
137D8—42no—
138D8—2922no—
139C2×C8—21no—
140C2×C8—1461no—
141C2×C8—1461no—
142C4⋊C4—731no—
143C4⋊C4—1461no—
144C4⋊C4—1461no—
145C4⋊C4C22⋊D7311yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—1462no—
148C22⋊C4—1462no—
149C22⋊C4—1461no—
150C42—1462no—
151C42C22×D7311yescharacteristic
152C23—21no—
153C23—41no—
154C23—1461no—
155Q8—2922no—
156D4—21no—
157D4—21no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—5842no—
164D4—1461no—
165D4—1461no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—2921no—
170C2×C4—2921no—
171C2×C4—1461no—
172C2×C4—1462no—
173C2×C4D4×D7311yescharacteristic
174C2×C4D4×D7311yescharacteristic
175C2×C4C2×C22⋊D7311yescharacteristic
176C8—41no—
177C8—2921no—
178C8—1462no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—81no—
183C22—81no—
184C22—81no—
185C22—2921no—
186C22—2921no—
187C22—2921no—
188C22#1455655911yescharacteristic
189C4—21no—
190C4—41no—
191C4—2921no—
192C4—2922no—
193C4#1455661011yescharacteristic
194C4#1455661111yescharacteristic
195C4#1455661511yescharacteristic
196C4#1455661711yescharacteristic
197C2—81no—
198C2—161no—
199C2—5841no—
200C2#1798872911yescharacteristic
201C2#1798873011yescharacteristic
202C2#1798875311yescharacteristic
subgroupG/H
centerC22#14556559
commutatorC42×C73C23
FrattiniC42C22×D73
Fitting#459×C73C2
socleC22×C73#120
hypercenter#459D73
hypocenterC73#1624
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #17989302C2semidirect
2. #17988959C2semidirect
3. #17988779C2semidirect
4. #17988335C2semidirect
5. D4⋊#10596831C2semidirect
6. #17988314C2semidirect
7. #459×C73C2semidirect
102. C73#1624semidirect
106. #459D73semidirect