Finite Group Databasebeta

← #22625398

Subgroups — #22625398

Order 9344.

216 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 58 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#17989609C211yesmaximal, characteristic, complemented
2C4×#11924038C211yesmaximal, characteristic, complemented
3#17989444C212yesmaximal, complemented
4#17989443C212yesmaximal, complemented
5#17989124C211yesmaximal, characteristic
6C2×#11924038—21no—
7C4⋊#10596833—21no—
8#14556648—21no—
9#14556646C2212yes—
10#14556646C2212yes—
11C4×#10596833—21no—
12#14556586—21no—
13#14556582C2211yescharacteristic
14#14556580C2211yescharacteristic
15#14556576—21no—
16#14556567C411yescharacteristic
17#14556566C411yescharacteristic
18C4×D292—21no—
19C4×D292C411yescharacteristic
20#14556548—21no—
21C42×D73C2211yescharacteristic
22C4×Q8×C73C411yescharacteristic
23#11924038—24no—
24C2×#10596833—22no—
25C2×#10596833—22no—
26C2×D292—21no—
27C2×D292C2×C411yescharacteristic
28C2×C4×D73—21no—
29C2×C4×D73C2×C411yescharacteristic
30C2×C4×D73D411yescharacteristic
31C2×C4×D73D411yescharacteristic
32C4⋊Dic73—21no—
33C4⋊Dic73C2×C411yescharacteristic
34#11924007—21no—
35#11924007—21no—
36#11924005—21no—
37#11924005—21no—
38#11924005—21no—
39#11924005—21no—
40#11924005—21no—
41C4×Dic73D411yescharacteristic
42C4×Dic73D411yescharacteristic
43C4×Dic73C2311yescharacteristic
44C2×Q8×C73C2×C411yescharacteristic
45C4⋊C4×C73—21no—
46C4⋊C4×C73C2×C411yescharacteristic
47C42×C73—21no—
48C42×C73C2×C411yescharacteristic
49C22×D73—21no—
50C22×D73C22⋊C411yescharacteristic
51Q8×C73—41no—
52C2×C4×C73—21no—
53C2×C4×C73—21no—
54C2×C4×C73C22⋊C411yescharacteristic
55C2×C4×C73C22⋊C411yescharacteristic
56C2×C4×C73C22×C411yescharacteristic
57C2×Dic73—21no—
58C2×Dic73C22⋊C411yescharacteristic
59C2×Dic73C2×D411yescharacteristic
60C2×Dic73C2×D411yescharacteristic
61D292—41no—
62D292—42no—
63C4×D73—22no—
64C4×D73—41no—
65C4×D73—41no—
66C4×D73—42no—
67#10596833—24no—
68#10596833—42no—
69C22×C73C2×C22⋊C411yescharacteristic
70C2×D73—21no—
71C2×D73—21no—
72C2×D73—21no—
73C2×D73—41no—
74C2×D73—41no—
75C2×D73—41no—
76C4×C73—21no—
77C4×C73—21no—
78C4×C73—41no—
79C4×C73—41no—
80C4×C73#10412yes—
81Dic73—21no—
82Dic73—21no—
83Dic73—21no—
84Dic73—41no—
85C2×C73#41311yescharacteristic
86C2×C73C2×#10411yescharacteristic
87C2×C73#42111yescharacteristic
88D73—41no—
89D73—81no—
90#1529—731nomaximal, Sylow
91C73#152911yescharacteristic, complemented, Sylow
92#529—731no—
93#432—731no—
94C4×M16—731no—
95#330—732no—
96#329—732no—
97C2×M16—1461no—
98#126—1461no—
99#125—731no—
100#124—731no—
101#123—1461no—
102C22⋊Q8—731no—
103#121—731no—
104C4×Q8#6440811yescharacteristic
105C4×D4—731no—
106C4×D4—1461no—
107#117—1461no—
108C2×C42—731no—
109C4⋊C8—1461no—
110C22⋊C8—1461no—
111#97—732no—
112#97—732no—
113C4×C8—1461no—
114C2×Q8C2×#6440811yescharacteristic
115C2×D4—731no—
116C2×D4—1461no—
117C22×C4—731no—
118C22×C4—731no—
119C22×C4—731no—
120C22×C4—1461no—
121M16—1464no—
122C2×C8—1462no—
123C2×C8—1462no—
124C4⋊C4—21no—
125C4⋊C4—731no—
126C4⋊C4—1461no—
127C4⋊C4—1461no—
128C4⋊C4—1461no—
129C4⋊C4C2×#6440811yescharacteristic
130C22⋊C4—1461no—
131C22⋊C4—1461no—
132C22⋊C4—1461no—
133C22⋊C4—1461no—
134C22⋊C4—1461no—
135C42—21no—
136C42—731no—
137C42—731no—
138C42—731no—
139C42C2×#6440811yescharacteristic
140C23—731no—
141C23—1461no—
142Q8—41no—
143D4—2921no—
144D4—2922no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—2921no—
148C2×C4—2921no—
149C2×C4—2922no—
150C2×C4—731no—
151C2×C4—731no—
152C2×C4—731no—
153C2×C4—1461no—
154C2×C4—1462no—
155C2×C4C22⋊#6440811yescharacteristic
156C2×C4C22⋊#6440811yescharacteristic
157C2×C4C22×#6440811yescharacteristic
158C8—2922no—
159C8—1464no—
160C22—2921no—
161C22—2921no—
162C22—2921no—
163C22—1461no—
164C22—1461no—
165C22—1461no—
166C22C2×C22⋊#6440811yescharacteristic
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—2921no—
172C4—1461no—
173C4—1461no—
174C4—1461no—
175C4#1455665612yes—
176C2—2921no—
177C2—5841no—
178C2#1798957311yescharacteristic
179C2C2×#1455665611yescharacteristic
180C2#1798958411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4×Q8×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC4×Q8#64408
hypocenterC73#1529
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #17989609C2semidirect
2. C4×#11924038C2semidirect
3. #17989444C2semidirect
4. #17989443C2semidirect
91. C73#1529semidirect