Finite Group Databasebeta

← #22626223

Subgroups — #22626223

Order 9344.

250 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 52 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#17989574C212yesmaximal, complemented
2#17989498C212yesmaximal, complemented
3#17989495C212yesmaximal, complemented
4#17989135C211yesmaximal, characteristic
5C2×#11924037—22no—
6#14556652C2214yes—
7#14556651—22no—
8C2×#11924027C411yescharacteristic
9C2×#11924027C2211yescharacteristic
10#14556591C2211yescharacteristic
11#14556578C411yescharacteristic
12#14556578C2211yescharacteristic
13#14556562—22no—
14D4×Dic73—22no—
15C42×D73C411yescharacteristic
16#127×C73C411yescharacteristic
17#11924037—24no—
18#11924037—42no—
19C2×#10596833—42no—
20#11924027—41no—
21#11924027—41no—
22#11924027—41no—
23#11924027—41no—
24C2×Dic146C2×C411yescharacteristic
25C2×Dic146C2311yescharacteristic
26C2×C22⋊D73—21no—
27C2×C22⋊D73D412yes—
28C22×Dic73—21no—
29C22×Dic73D412yes—
30C2×C4×D73—21no—
31C2×C4×D73C2×C411yescharacteristic
32C4⋊Dic73—22no—
33C22⋊Dic73—22no—
34C22⋊Dic73—22no—
35C4×Dic73—21no—
36C4×Dic73C2×C411yescharacteristic
37C2×D4×C73—22no—
38C2×D4×C73C2×C411yescharacteristic
39C2×D4×C73C2×C411yescharacteristic
40C42×C73C2×C411yescharacteristic
41C23×C73—21no—
42C23×C73C22⋊C412yes—
43C22×D73C22⋊C411yescharacteristic
44D4×C73—41no—
45D4×C73—41no—
46D4×C73—44no—
47C2×C4×C73—21no—
48C2×C4×C73C22×C411yescharacteristic
49C22⋊D73—42no—
50C22⋊D73—42no—
51C2×Dic73—22no—
52C2×Dic73—22no—
53C2×Dic73—21no—
54C2×Dic73—21no—
55C2×Dic73—41no—
56C2×Dic73—41no—
57C2×Dic73C22⋊C411yescharacteristic
58C2×Dic73C2×D412yes—
59C4×D73—21no—
60C4×D73—21no—
61C4×D73—42no—
62Dic146—41no—
63Dic146—41no—
64#10596833—44no—
65C22×C73—22no—
66C22×C73—42no—
67C22×C73—42no—
68C22×C73—41no—
69C22×C73C2×C22⋊C411yescharacteristic
70C2×D73—21no—
71C2×D73—41no—
72C4×C73—22no—
73C4×C73—21no—
74Dic73—22no—
75Dic73—41no—
76Dic73—41no—
77Dic73#9911yescharacteristic
78Dic73#9911yescharacteristic
79C2×C73—21no—
80C2×C73—42no—
81C2×C73—81no—
82C2×C73C2×#9911yescharacteristic
83D73—41no—
84#2132—731nomaximal, Sylow
85C73#213211yescharacteristic, complemented, Sylow
86#532—731no—
87#413—732no—
88#356—732no—
89#355—732no—
90C2×#41—731no—
91C2×#41—731no—
92C2×M16—1462no—
93C4⋊Q8—731no—
94#127#6440811yescharacteristic
95#124—731no—
96#124—731no—
97#121—1462no—
98C4×D4—1462no—
99C2×C42—731no—
100#101—734no—
101#100—1462no—
102#41—2921no—
103#41—2921no—
104#41—2921no—
105#41—2921no—
106C2×Q8—731no—
107C2×Q8—731no—
108C2×D4—22no—
109C2×D4—732no—
110C2×D4—1461no—
111C2×D4C2×#6440811yescharacteristic
112C2×D4C2×#6440811yescharacteristic
113C22×C4—732no—
114C22×C4—731no—
115C22×C4—1461no—
116C22×C4—1461no—
117M16—2922no—
118M16—1464no—
119C2×C8—2922no—
120C4⋊C4—1462no—
121C22⋊C4—1462no—
122C22⋊C4—1462no—
123C42—731no—
124C42—1461no—
125C42C2×#6440811yescharacteristic
126C23—21no—
127C23—731no—
128C23C22⋊#6440812yes—
129Q8—2921no—
130Q8—2921no—
131D4—41no—
132D4—41no—
133D4—44no—
134D4—2922no—
135D4—2922no—
136C2×C4—21no—
137C2×C4—2922no—
138C2×C4—2921no—
139C2×C4—2921no—
140C2×C4—731no—
141C2×C4—732no—
142C2×C4—1461no—
143C2×C4—1461no—
144C2×C4—1461no—
145C2×C4—1461no—
146C2×C4—1462no—
147C2×C4—1462no—
148C2×C4C22×#6440811yescharacteristic
149C8—2924no—
150C22—22no—
151C22—42no—
152C22—42no—
153C22—41no—
154C22—2921no—
155C22—1461no—
156C22C2×C22⋊#6440811yescharacteristic
157C4—22no—
158C4—21no—
159C4—2921no—
160C4—2921no—
161C4—731no—
162C4—731no—
163C4—1462no—
164C2—21no—
165C2—42no—
166C2—81no—
167C2—2921no—
168C2D73⋊#9911yescharacteristic
subgroupG/H
centerC2D73⋊#99
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#127×C73C4
socleC2×C73C2×#99
hypercenter#127#64408
hypocenterC73#2132
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #17989574C2semidirect
2. #17989498C2semidirect
3. #17989495C2semidirect
85. C73#2132semidirect