Finite Group Databasebeta

← #22610825

Subgroups — #22610825

Order 9344.

292 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 97 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×#14556527C211yesmaximal, characteristic, complemented
2C2×#14556518C212yesmaximal, complemented
3#17988554C212yesmaximal, complemented
4C2×#14556501C211yesmaximal, characteristic, complemented
5C2×#135×C73C211yesmaximal, characteristic
6C2×#11924012C2212yes—
7C22×#10596831C2211yescharacteristic
8C2×C4×Dic73C2211yescharacteristic
9#14556527—22no—
10#14556518—24no—
11C22⋊#10596831—24no—
12#14556501—22no—
13C2×#41×C73C2212yes—
14#135×C73—22no—
15#135×C73—22no—
16C2×Q16×C73C411yescharacteristic, complemented
17C2×SD16×C73C412yescomplemented
18C2×D8×C73C411yescharacteristic, complemented
19C22×C8×C73C2211yescharacteristic
20C22×Dic73—21no—
21#11924012—22no—
22#11924012—22no—
23C2×#10596831—21no—
24C2×#10596831—21no—
25C2×#10596831—22no—
26C2×#10596831D412yes—
27C4×Dic73—21no—
28C4×Dic73D412yes—
29#41×C73—22no—
30#41×C73—22no—
31#41×C73—22no—
32#41×C73—22no—
33C2×Q8×C73C2×C412yes—
34C2×D4×C73—22no—
35C2×D4×C73C2×C412yes—
36C22×C4×C73—22no—
37C22×C4×C73C2311yescharacteristic
38Q16×C73—22no—
39SD16×C73—24no—
40D8×C73—22no—
41C2×C8×C73C2×C411yescharacteristic
42C2×C8×C73C2×C411yescharacteristic
43C2×C8×C73D412yes—
44C2×C8×C73D412yes—
45C23×C73—22no—
46C23×C73#4111yescharacteristic
47Q8×C73—22no—
48Q8×C73—22no—
49D4×C73—22no—
50D4×C73—22no—
51D4×C73—42no—
52D4×C73—42no—
53C2×C4×C73—22no—
54C2×C4×C73—42no—
55C2×C4×C73—42no—
56C2×C4×C73C22×C411yescharacteristic
57C2×C4×C73C2×D411yescharacteristic
58C2×C4×C73C2×D411yescharacteristic
59C2×C4×C73C2×D411yescharacteristic
60C2×C4×C73C2×D411yescharacteristic
61C2×C4×C73#4111yescharacteristic
62C2×Dic73—22no—
63C2×Dic73—42no—
64C8×C73C22⋊C412yes—
65C8×C73C22⋊C412yes—
66#10596831—22no—
67#10596831—42no—
68C22×C73—22no—
69C22×C73—42no—
70C22×C73—44no—
71C22×C73C4×D411yescharacteristic
72C22×C73#12111yescharacteristic
73C22×C73#12411yescharacteristic
74C4×C73—42no—
75C4×C73C2×C22⋊C411yescharacteristic
76C4×C73C4×D411yescharacteristic
77C4×C73#12111yescharacteristic
78C4×C73#12711yescharacteristic
79Dic73—42no—
80C2×C73—21no—
81C2×C73—21no—
82C2×C73—82no—
83C2×C73#39011yescharacteristic
84C2×C73#44412yes—
85#1975—731nomaximal, Sylow
86C73#197511yescharacteristic, complemented, Sylow
87C2×#135D7311yescharacteristic
88C2×#108—731no—
89C2×#104—732no—
90#408—732no—
91C2×#97—731no—
92C2×#41C2×D7312yes—
93#135—22no—
94#135—22no—
95C2×Q16Dic7311yescharacteristic, complemented
96C2×SD16Dic7312yescomplemented
97C2×D8Dic7311yescharacteristic, complemented
98C2×M16—732no—
99C22×C8—731no—
100C22×C8C2×D7311yescharacteristic
101C2×C42—731no—
102#108—1462no—
103#104—1464no—
104C22⋊C8—1464no—
105#97—1462no—
106#41—22no—
107#41—22no—
108#41—22no—
109#41—22no—
110C2×Q8C2×Dic7312yes—
111C2×D4—22no—
112C2×D4C2×Dic7312yes—
113C22×C4—22no—
114C22×C4—1461no—
115C22×C4C22×D7311yescharacteristic
116Q16—22no—
117SD16—24no—
118D8—22no—
119M16—1462no—
120M16—1462no—
121C2×C8—732no—
122C2×C8—1462no—
123C2×C8—1461no—
124C2×C8—1461no—
125C2×C8C2×Dic7311yescharacteristic
126C2×C8C2×Dic7311yescharacteristic
127C2×C8C22⋊D7312yes—
128C2×C8C22⋊D7312yes—
129C42—732no—
130C42—1461no—
131C23—22no—
132C23#1192402711yescharacteristic
133Q8—22no—
134Q8—22no—
135D4—22no—
136D4—22no—
137D4—42no—
138D4—42no—
139C2×C4—22no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—2922no—
143C2×C4—1462no—
144C2×C4C22×Dic7311yescharacteristic
145C2×C4D4×D7311yescharacteristic
146C2×C4D4×D7311yescharacteristic
147C2×C4C2×C22⋊D7311yescharacteristic
148C2×C4C2×C22⋊D7311yescharacteristic
149C2×C4#1192402711yescharacteristic
150C8—2922no—
151C8—1462no—
152C8C22⋊Dic7312yes—
153C8C22⋊Dic7312yes—
154C22—22no—
155C22—44no—
156C22—42no—
157C22D4×Dic7311yescharacteristic
158C22#1455656211yescharacteristic
159C22#1455657811yescharacteristic
160C4—42no—
161C4—2922no—
162C4C2×C22⋊Dic7311yescharacteristic
163C4D4×Dic7311yescharacteristic
164C4#1455656211yescharacteristic
165C4#1455658711yescharacteristic
166C2—21no—
167C2—21no—
168C2—82no—
169C2#1798849011yescharacteristic
170C2#1798870912yes—
subgroupG/H
centerC2×C4D4×D73
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
FittingC2×#135×C73C2
socleC22×C73C4×D4
hypercenterC2×#135D73
hypocenterC73#1975
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#14556527C2semidirect
2. C2×#14556518C2semidirect
3. #17988554C2semidirect
4. C2×#14556501C2semidirect
16. C2×Q16×C73C4semidirect
17. C2×SD16×C73C4semidirect
18. C2×D8×C73C4semidirect
86. C73#1975semidirect
95. C2×Q16Dic73semidirect
96. C2×SD16Dic73semidirect
97. C2×D8Dic73semidirect