Finite Group Databasebeta

← #22620420

Subgroups — #22620420

Order 9344.

532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14556622C212yesmaximal, complemented
2C2×#14556613C211yesmaximal, characteristic
3#17989161C212yesmaximal, complemented
4#17988980C214yesmaximal, complemented
5#17988972C212yesmaximal, complemented
6#17988965C212yesmaximal, complemented
7#17988542C211yesmaximal, characteristic, complemented
8C22×Q16×C73C211yesmaximal, characteristic, complemented
9C2×#11924028C2212yes—
10#14556622—28no—
11#14556613—24no—
12C2×Dic292C2211yescharacteristic
13C2×#11924018C2214yes—
14C2×#11924017C2212yes—
15C2×#11924015C2214yes—
16C2×D584C2211yescharacteristic
17C2×#11924012C2211yescharacteristic
18#14556589C2214yes—
19#14556580C2214yes—
20#14556574—24no—
21#14556567—24no—
22#14556550C2211yescharacteristic
23#14556501C2212yes—
24C8×Dic73C2212yes—
25C22×Q8×C73C2212yes—
26C2×Q16×C73—24no—
27C2×Q16×C73C2212yes—
28C2×Q16×C73C2212yes—
29C22×C8×C73C2211yescharacteristic
30#11924028—24no—
31#11924028—24no—
32C2×Dic146C2312yes—
33C2×D292C2312yes—
34C2×C22⋊D73—22no—
35C2×C4×D73—22no—
36Dic292—22no—
37#11924018—28no—
38#11924017—24no—
39#11924015—28no—
40D584—22no—
41#11924012D414yes—
42C2×#10596831C2312yes—
43C4⋊Dic73D412yes—
44#11924007—28no—
45C22⋊Dic73D412yes—
46#11924005—28no—
47C4×Dic73C2312yes—
48C2×Q8×C73—22no—
49C2×Q8×C73—24no—
50C2×Q8×C73—24no—
51C2×Q8×C73C2314yes—
52C22×C4×C73—22no—
53C22×C4×C73C2311yescharacteristic
54Q16×C73—24no—
55Q16×C73—24no—
56C2×C8×C73D414yes—
57C2×C8×C73C2311yescharacteristic
58C2×C8×C73C2311yescharacteristic
59C23×C73C2×D411yescharacteristic
60C22×D73—22no—
61Q8×C73—24no—
62Q8×C73—24no—
63Q8×C73—44no—
64C2×C4×C73—24no—
65C2×C4×C73—44no—
66C2×C4×C73C2×D411yescharacteristic
67C2×C4×C73C2×D412yes—
68C2×C4×C73C2×D412yes—
69C2×C4×C73C2411yescharacteristic
70C22⋊D73—44no—
71C2×Dic73—22no—
72C2×Dic73C2×D414yes—
73D292—22no—
74D292—22no—
75C4×D73—44no—
76Dic146—22no—
77Dic146—22no—
78C8×C73C2×D412yes—
79C8×C73C2×D412yes—
80#10596831C2×D414yes—
81C22×C73—22no—
82C22×C73#12712yes—
83C22×C73C22×D411yescharacteristic
84C2×D73—42no—
85C2×D73—44no—
86C4×C73—44no—
87C4×C73#12712yes—
88C4×C73C22×D411yescharacteristic
89C4×C73C22×D411yescharacteristic
90Dic73—24no—
91Dic73—42no—
92C2×C73—22no—
93C2×C73C2×#12711yescharacteristic
94C2×C73#57812yes—
95D73—82no—
96#3156—731nomaximal, Sylow
97C73#315611yescharacteristic, complemented, Sylow
98C2×#137—732no—
99C2×#135—731no—
100C22×Q16D7311yescharacteristic, complemented
101#536—732no—
102#497—734no—
103#495—732no—
104#494—732no—
105#405—731no—
106C2×#41—732no—
107C22×Q8C2×D7312yes—
108#137—1468no—
109#135—1464no—
110C2×Q16—24no—
111C2×Q16—734no—
112C2×Q16—731no—
113C2×Q16C2×D7312yes—
114C2×Q16C2×D7312yes—
115C2×SD16—734no—
116C2×SD16—732no—
117C2×D8—731no—
118C2×M16—731no—
119C22×C8C2×D7311yescharacteristic
120C4⋊Q8—734no—
121#124—734no—
122#123—1464no—
123C22⋊Q8—1464no—
124#117—731no—
125#97—732no—
126C4×C8—732no—
127#41—1464no—
128#41—1464no—
129C2×Q8—22no—
130C2×Q8—24no—
131C2×Q8—24no—
132C2×Q8—732no—
133C2×Q8C22×D7314yes—
134C2×D4—732no—
135C2×D4—1462no—
136C22×C4—22no—
137C22×C4—1462no—
138C22×C4C22×D7311yescharacteristic
139Q16—24no—
140Q16—24no—
141Q16—1468no—
142Q16—1462no—
143SD16—1468no—
144SD16—1464no—
145D8—1462no—
146M16—734no—
147C2×C8—732no—
148C2×C8C22⋊D7314yes—
149C2×C8C22×D7311yescharacteristic
150C2×C8C22×D7311yescharacteristic
151C4⋊C4—732no—
152C4⋊C4—1468no—
153C22⋊C4—732no—
154C22⋊C4—1468no—
155C42—732no—
156C23—1462no—
157C23D4×D7311yescharacteristic
158Q8—24no—
159Q8—24no—
160Q8—44no—
161Q8—1462no—
162Q8—1462no—
163D4—2924no—
164D4—1462no—
165D4—1462no—
166C2×C4—24no—
167C2×C4—44no—
168C2×C4—2924no—
169C2×C4—734no—
170C2×C4—1462no—
171C2×C4D4×D7311yescharacteristic
172C2×C4D4×D7312yes—
173C2×C4C2×C22⋊D7312yes—
174C2×C4C23×D7311yescharacteristic
175C8—734no—
176C8C2×C22⋊D7312yes—
177C8C2×C22⋊D7312yes—
178C22—22no—
179C22—2922no—
180C22—2924no—
181C22#1455658712yes—
182C22C2×D4×D7311yescharacteristic
183C4—44no—
184C4—2922no—
185C4—1464no—
186C4#1455658712yes—
187C4C2×D4×D7311yescharacteristic
188C4C22×C22⋊D7311yescharacteristic
189C2—22no—
190C2—5842no—
191C2C2×#1455658711yescharacteristic
192C2#1798940012yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC22×Q16×C73C2
socleC22×C73C22×D4
hypercenterC22×Q16D73
hypocenterC73#3156
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#14556622C2semidirect
3. #17989161C2semidirect
4. #17988980C2semidirect
5. #17988972C2semidirect
6. #17988965C2semidirect
7. #17988542C2semidirect
8. C22×Q16×C73C2semidirect
97. C73#3156semidirect
100. C22×Q16D73semidirect