Finite Group Databasebeta

← #22626125

Subgroups — #22626125

Order 9344.

228 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 70 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#17989590C211yesmaximal, characteristic
2C4×#11924037C211yesmaximal, characteristic
3#17989467C212yesmaximal
4#17989467C212yesmaximal
5C2×#14556581C211yesmaximal, characteristic
6C2×#11924037C2212yes—
7C2×#11924037C2212yes—
8#14556658—21no—
9C4⋊#10596833—21no—
10#14556646—21no—
11C4×#10596833—21no—
12#14556581—21no—
13#14556581—21no—
14#14556581—21no—
15#14556581—21no—
16C2×C4⋊Dic73C411yescharacteristic
17C2×#11924007C411yescharacteristic
18C2×#11924007C411yescharacteristic
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×C4×Dic73C2211yescharacteristic
22C2×C4⋊C4×C73C411yescharacteristic
23#11924037—22no—
24#11924037—24no—
25#11924037Q814yes—
26C2×#10596833—22no—
27C2×#10596833—22no—
28C22×Dic73C2×C411yescharacteristic
29C22×Dic73C2×C411yescharacteristic
30C22×Dic73C2×C411yescharacteristic
31C22×Dic73C2311yescharacteristic
32C4⋊Dic73—21no—
33C4⋊Dic73—21no—
34#11924007—21no—
35#11924007—21no—
36#11924007—21no—
37#11924007—21no—
38#11924007—21no—
39#11924007—21no—
40#11924007—21no—
41#11924007—21no—
42C4×Dic73D411yescharacteristic
43C4×Dic73D411yescharacteristic
44C4×Dic73D411yescharacteristic
45C4×Dic73D411yescharacteristic
46C22×C4×C73C2×C411yescharacteristic
47C22×C4×C73C2×C411yescharacteristic
48C22×C4×C73C2×C411yescharacteristic
49C4⋊C4×C73—21no—
50C4⋊C4×C73—21no—
51C23×C73C22×C411yescharacteristic
52C2×C4×C73—21no—
53C2×C4×C73—21no—
54C2×C4×C73—41no—
55C2×C4×C73—41no—
56C2×C4×C73—41no—
57C2×C4×C73C22⋊C411yescharacteristic
58C2×C4×C73C22⋊C411yescharacteristic
59C2×Dic73—21no—
60C2×Dic73—21no—
61C2×Dic73—41no—
62C2×Dic73—41no—
63C2×Dic73—41no—
64C2×Dic73C22⋊C411yescharacteristic
65C2×Dic73C22⋊C411yescharacteristic
66C2×Dic73C2×D411yescharacteristic
67C2×Dic73C2×D411yescharacteristic
68C2×Dic73C2×Q812yes—
69C2×Dic73#4112yes—
70#10596833—24no—
71#10596833—42no—
72C22×C73—21no—
73C22×C73—21no—
74C22×C73C2×C22⋊C411yescharacteristic
75C22×C73C4×Q812yes—
76C4×C73—21no—
77C4×C73—21no—
78C4×C73—41no—
79C4×C73—41no—
80Dic73—21no—
81Dic73—21no—
82Dic73—41no—
83Dic73—41no—
84Dic73C22⋊Q812yes—
85Dic73#12411yescharacteristic
86Dic73C4⋊Q811yescharacteristic
87C2×C73—22no—
88C2×C73#39111yescharacteristic
89C2×C73#41311yescharacteristic
90C2×C73#41311yescharacteristic
91#1998—731nomaximal, Sylow
92C73#199811yescharacteristic, complemented, Sylow
93C2×#125—731no—
94#423—731no—
95C4×M16—731no—
96#343—732no—
97#343—732no—
98C2×M16—732no—
99C2×M16—732no—
100#125—1461no—
101#125—1461no—
102#125—1461no—
103#125—1461no—
104C2×C4⋊C4—731no—
105C2×C4⋊C4—731no—
106C2×C4⋊C4—731no—
107C2×C4⋊C4—731no—
108C2×C4⋊C4—731no—
109C2×C4⋊C4#6440811yescharacteristic
110C2×C42—731no—
111C4⋊C8—1461no—
112C4⋊C8—1461no—
113#97—1461no—
114C4×C8—1461no—
115C22×C4—731no—
116C22×C4—731no—
117C22×C4—731no—
118C22×C4—731no—
119C22×C4C2×#6440811yescharacteristic
120C22×C4C2×#6440811yescharacteristic
121C22×C4C2×#6440811yescharacteristic
122M16—734no—
123M16—1464no—
124M16—1462no—
125C2×C8—1462no—
126C2×C8—1462no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—1461no—
130C4⋊C4—1461no—
131C4⋊C4—1461no—
132C4⋊C4—1461no—
133C4⋊C4—1461no—
134C4⋊C4—1461no—
135C4⋊C4—1461no—
136C4⋊C4—1461no—
137C4⋊C4—1461no—
138C4⋊C4—1461no—
139C42—731no—
140C42—731no—
141C42—731no—
142C42—731no—
143C23C22×#6440811yescharacteristic
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—2921no—
150C2×C4—2921no—
151C2×C4—2921no—
152C2×C4—732no—
153C2×C4—732no—
154C2×C4—731no—
155C2×C4—731no—
156C2×C4—731no—
157C2×C4—731no—
158C2×C4—1461no—
159C2×C4—1461no—
160C2×C4C22⋊#6440811yescharacteristic
161C2×C4C22⋊#6440811yescharacteristic
162C8—2922no—
163C8—1464no—
164C22—21no—
165C22—21no—
166C22C2×C22⋊#6440811yescharacteristic
167C22Q8×#6440812yes—
168C4—21no—
169C4—21no—
170C4—41no—
171C4—41no—
172C4—2921no—
173C4—2921no—
174C4—731no—
175C4—732no—
176C4—731no—
177C4—1461no—
178C4—1461no—
179C2—22no—
180C2(C2×#64408)⋊Q811yescharacteristic
181C2#1798957311yescharacteristic
182C2#1798957411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
FittingC2×C4⋊C4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC2×C4⋊C4#64408
hypocenterC73#1998
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
92. C73#1998semidirect