Finite Group Databasebeta

← #22625304

Subgroups — #22625304

Order 9344.

238 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 60 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#17989606C211yesmaximal, characteristic, complemented
2#17989523C211yesmaximal, characteristic, complemented
3#17989441C212yesmaximal, complemented
4#17989439C212yesmaximal
5#17989124C211yesmaximal, characteristic
6C2×C4×#64408—21no—
7C4⋊#10596833—21no—
8#14556648C2212yes—
9C4×#10596833—21no—
10(C2×#64408)⋊C4—21no—
11(C2×#64408)⋊C4C2212yes—
12#14556586—21no—
13#14556582C411yescharacteristic, complemented
14#14556580C411yescharacteristic, complemented
15#14556576—21no—
16#14556567C2211yescharacteristic
17#14556566C2211yescharacteristic
18C4×D292—21no—
19C4×D292C411yescharacteristic, complemented
20#14556548—21no—
21C42×D73C2211yescharacteristic
22C4×Q8×C73C411yescharacteristic, complemented
23C22×#64408—22no—
24C2×#10596833—22no—
25C4×#64408—24no—
26C2×D292—21no—
27C2×D292C2×C411yescharacteristic
28C2×C4×D73—21no—
29C2×C4×D73D411yescharacteristic
30C2×C4×D73D411yescharacteristic
31C2×C4×D73C2311yescharacteristic
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×Dic73C2×C411yescharacteristic
42C4×Dic73D411yescharacteristic
43C4×Dic73D411yescharacteristic
44C2×Q8×C73C2×C411yescharacteristic
45C4⋊C4×C73—21no—
46C4⋊C4×C73C2×C411yescharacteristic
47C42×C73—21no—
48C42×C73C2×C411yescharacteristic
49C22×D73—21no—
50C22×D73C2×D411yescharacteristic
51C2×#64408—24no—
52C2×#64408—42no—
53C2×#64408—42no—
54Q8×C73—41no—
55C2×C4×C73—21no—
56C2×C4×C73—21no—
57C2×C4×C73C22⋊C411yescharacteristic
58C2×C4×C73C22⋊C411yescharacteristic
59C2×C4×C73C22×C411yescharacteristic
60C2×Dic73—21no—
61C2×Dic73C22⋊C411yescharacteristic
62C2×Dic73C22⋊C411yescharacteristic
63C2×Dic73C2×D411yescharacteristic
64D292—41no—
65D292—42no—
66C4×D73—22no—
67C4×D73—22no—
68C4×D73—41no—
69C4×D73—42no—
70#10596833—42no—
71C22×C73C2×C22⋊C411yescharacteristic
72C2×D73—21no—
73C2×D73—21no—
74C2×D73—41no—
75C2×D73—41no—
76C2×D73—41no—
77C2×D73#13512yes—
78#64408—44no—
79C4×C73—21no—
80C4×C73—21no—
81C4×C73—41no—
82C4×C73—41no—
83C4×C73#10412yes—
84Dic73—21no—
85Dic73—21no—
86Dic73—21no—
87Dic73—41no—
88C2×C73#41011yescharacteristic
89C2×C73#41611yescharacteristic
90C2×C73C2×#10411yescharacteristic
91D73—22no—
92D73—81no—
93#1500—731nomaximal, Sylow
94C73#150011yescharacteristic, complemented, Sylow
95#529—731no—
96#431—731no—
97#376—731no—
98#328—732no—
99#327—732no—
100#126—1461no—
101#125—731no—
102#124—731no—
103#123—1461no—
104C22⋊Q8—731no—
105#121—731no—
106C4×Q8#6440811yescharacteristic, complemented
107C4×D4—731no—
108C4×D4—1461no—
109#117—1461no—
110C2×C42—731no—
111C2×C42—1461no—
112C4⋊C8—1461no—
113C22⋊C8—732no—
114C4×C8—1461no—
115#95—732no—
116#95—1461no—
117C2×Q8C2×#6440811yescharacteristic
118C2×D4—731no—
119C2×D4—1461no—
120C22×C4—731no—
121C22×C4—731no—
122C22×C4—731no—
123C22×C4—1462no—
124C22×C4—1461no—
125C2×C8—1462no—
126C4⋊C4—21no—
127C4⋊C4—731no—
128C4⋊C4—1461no—
129C4⋊C4—1461no—
130C4⋊C4—1461no—
131C4⋊C4C2×#6440811yescharacteristic
132C22⋊C4—1461no—
133C22⋊C4—1461no—
134C22⋊C4—1461no—
135C22⋊C4—1461no—
136C22⋊C4—1461no—
137C42—21no—
138C42—731no—
139C42—731no—
140C42—731no—
141C42—1464no—
142C42C2×#6440811yescharacteristic
143C23—731no—
144C23—1461no—
145Q8—41no—
146D4—2921no—
147D4—2922no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—2921no—
151C2×C4—2922no—
152C2×C4—2922no—
153C2×C4—2922no—
154C2×C4—731no—
155C2×C4—731no—
156C2×C4—731no—
157C2×C4—1462no—
158C2×C4—1464no—
159C2×C4—1461no—
160C2×C4—1462no—
161C2×C4C22⋊#6440811yescharacteristic
162C2×C4C22⋊#6440811yescharacteristic
163C2×C4C22×#6440811yescharacteristic
164C8—2922no—
165C22—2921no—
166C22—2921no—
167C22—2921no—
168C22—732no—
169C22—1461no—
170C22—1461no—
171C22C2×C22⋊#6440811yescharacteristic
172C4—21no—
173C4—21no—
174C4—41no—
175C4—41no—
176C4—2924no—
177C4—2921no—
178C4—1461no—
179C4—1461no—
180C4—1461no—
181C4#1455665612yes—
182C2—5841no—
183C2—1462no—
184C2#1798956611yescharacteristic
185C2#1798957711yescharacteristic
186C2C2×#1455665611yescharacteristic
subgroupG/H
centerC2×C4C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4×Q8×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC4×Q8#64408
hypocenterC73#1500
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #17989606C2semidirect
2. #17989523C2semidirect
3. #17989441C2semidirect
13. #14556582C4semidirect
14. #14556580C4semidirect
19. C4×D292C4semidirect
22. C4×Q8×C73C4semidirect
94. C73#1500semidirect
106. C4×Q8#64408semidirect