Finite Group Databasebeta

← #22620231

Subgroups — #22620231

Order 9344.

358 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 125 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#17989199C211yesmaximal, characteristic
2#17988928C212yesmaximal
3#17988894C212yesmaximal, complemented
4#17988797C212yesmaximal, complemented
5#17988743C212yesmaximal
6#17988692C212yesmaximal, complemented
7C4×#11924018C212yesmaximal, complemented
8#17988648C211yesmaximal, characteristic
9#519×C73C211yesmaximal, characteristic
10C2×#11924018C2212yes—
11C2×#11924018C2212yes—
12#14556591C2211yescharacteristic
13#14556584—22no—
14#14556583C2211yescharacteristic
15#14556581—22no—
16#14556570C2212yes—
17C4×Dic146C2212yes—
18#14556524C2212yes—
19#14556522C2212yes—
20C4⋊#10596831C2212yes—
21#14556515C2212yes—
22#14556515C2212yes—
23#14556514C2212yes—
24#14556514C2212yes—
25C22⋊#10596831C2212yes—
26#14556502C2211yescharacteristic
27C4×#10596831C2211yescharacteristic
28C22×Q8×C73C2211yescharacteristic
29C4×Q8×C73—22no—
30C4×Q8×C73C2212yes—
31C4×Q8×C73C2212yes—
32#117×C73—22no—
33#117×C73C2211yescharacteristic
34#117×C73C2211yescharacteristic
35C2×Dic146C2312yes—
36#11924018—24no—
37#11924018—24no—
38C2×#10596831C2312yes—
39C2×#10596831C2312yes—
40C4⋊Dic73—22no—
41C4⋊Dic73C2312yes—
42#11924007—22no—
43#11924007—22no—
44#11924007—22no—
45C22⋊Dic73—22no—
46C4×Dic73—22no—
47C2×Q8×C73—24no—
48C2×Q8×C73—21no—
49C2×Q8×C73C2312yes—
50C22×C4×C73—21no—
51C22×C4×C73C2311yescharacteristic
52C4⋊C4×C73—22no—
53C4⋊C4×C73—22no—
54C4⋊C4×C73D412yes—
55C4⋊C4×C73C2312yes—
56C22⋊C4×C73—21no—
57C22⋊C4×C73D412yes—
58C42×C73—22no—
59C42×C73—22no—
60C42×C73—21no—
61C42×C73C2311yescharacteristic
62C42×C73C2311yescharacteristic
63C23×C73C2×D411yescharacteristic
64Q8×C73—24no—
65Q8×C73—22no—
66Q8×C73#4114yes—
67C2×C4×C73—24no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73C2×D412yes—
72C2×C4×C73C2×D412yes—
73C2×C4×C73C2×D411yescharacteristic
74C2×C4×C73C2411yescharacteristic
75C2×Dic73—22no—
76C2×Dic73—22no—
77Dic146—22no—
78Dic146—22no—
79#10596831—22no—
80#10596831—22no—
81C22×C73—21no—
82C22×C73—22no—
83C22×C73C22×D411yescharacteristic
84C4×C73—24no—
85C4×C73—21no—
86C4×C73—22no—
87C4×C73—22no—
88C4×C73—42no—
89C4×C73C2×#4112yes—
90Dic73—42no—
91Dic73—42no—
92C2×C73—41no—
93C2×C73#52511yescharacteristic
94C2×C73#57812yes—
95#3127—731nomaximal, Sylow
96C73#312711yescharacteristic, complemented, Sylow
97#541—731no—
98#519D7311yescharacteristic
99#485—732no—
100#479—732no—
101#462—732no—
102#451—732no—
103#441—732no—
104C4×Q16—732no—
105#433—731no—
106C22×Q8C2×D7311yescharacteristic
107C2×Q16—732no—
108C2×Q16—732no—
109C4⋊Q8—731no—
110#126—1462no—
111#125—731no—
112#125—1462no—
113C22⋊Q8—732no—
114C4×Q8—22no—
115C4×Q8—732no—
116C4×Q8C2×D7312yes—
117C4×Q8C2×D7312yes—
118#117—22no—
119#117C2×D7311yescharacteristic
120#117C2×D7311yescharacteristic
121#107—732no—
122#106—732no—
123C4⋊C8—732no—
124#103—732no—
125#103—732no—
126#103—732no—
127#103—732no—
128C22⋊C8—732no—
129#97—731no—
130C4×C8—731no—
131C2×Q8—24no—
132C2×Q8—21no—
133C2×Q8—732no—
134C2×Q8C22×D7312yes—
135C22×C4—21no—
136C22×C4C22×D7311yescharacteristic
137Q16—1464no—
138Q16—1464no—
139C2×C8—732no—
140C2×C8—732no—
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—732no—
144C4⋊C4—1462no—
145C4⋊C4—1462no—
146C4⋊C4—1462no—
147C4⋊C4—1462no—
148C4⋊C4C22⋊D7312yes—
149C4⋊C4C22×D7312yes—
150C22⋊C4—21no—
151C22⋊C4—1462no—
152C22⋊C4C22⋊D7312yes—
153C42—22no—
154C42—22no—
155C42—21no—
156C42—1462no—
157C42C22×D7311yescharacteristic
158C42C22×D7311yescharacteristic
159C23C2×C22⋊D7311yescharacteristic
160Q8—24no—
161Q8—22no—
162Q8—1462no—
163Q8—1462no—
164Q8#1192402814yes—
165C2×C4—24no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—1462no—
170C2×C4—1462no—
171C2×C4C2×C22⋊D7312yes—
172C2×C4C2×C22⋊D7312yes—
173C2×C4C2×C22⋊D7311yescharacteristic
174C2×C4C23×D7311yescharacteristic
175C8—1462no—
176C8—1462no—
177C22—22no—
178C22—21no—
179C22C22×C22⋊D7311yescharacteristic
180C4—22no—
181C4—22no—
182C4—24no—
183C4—21no—
184C4—42no—
185C4—2922no—
186C4—2922no—
187C4C2×#1192402812yes—
188C2—41no—
189C2#1798909811yescharacteristic
190C2#1798940212yes—
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#519×C73C2
socleC22×C73C22×D4
hypercenter#519D73
hypocenterC73#3127
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
3. #17988894C2semidirect
4. #17988797C2semidirect
6. #17988692C2semidirect
7. C4×#11924018C2semidirect
96. C73#3127semidirect