Finite Group Databasebeta

← #22621381

Subgroups — #22621381

Order 9344.

322 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 117 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#17988894C212yesmaximal, complemented
3#17988891C212yesmaximal, complemented
4#17988843C212yesmaximal
5#17988826C212yesmaximal
6#17988797C212yesmaximal, complemented
7#17988794C212yesmaximal, complemented
8#17988614C211yesmaximal, characteristic
9#541×C73C211yesmaximal, characteristic
10C2×#11924018C2212yes—
11C2×#11924018C2212yes—
12C2×#11924012C2211yescharacteristic
13C22×#10596831C2211yescharacteristic
14#14556591C2211yescharacteristic
15#14556584—22no—
16#14556583C2211yescharacteristic
17#14556581—22no—
18#14556570C2212yes—
19C4×Dic146C2212yes—
20#14556524C2212yes—
21#14556522C2212yes—
22C4⋊#10596831C2212yes—
23C4⋊#10596831C2212yes—
24#14556515C2212yes—
25#14556515C2212yes—
26#14556514C2212yes—
27#14556514C2212yes—
28C4⋊Q8×C73C2211yescharacteristic
29#126×C73—22no—
30#125×C73—22no—
31#125×C73C2211yescharacteristic
32C22⋊Q8×C73C2212yes—
33C4×Q8×C73C2212yes—
34#117×C73C2211yescharacteristic
35C2×Dic146C2312yes—
36#11924018—42no—
37#11924018—42no—
38#11924012—41no—
39C2×#10596831—41no—
40C2×#10596831C2312yes—
41C2×#10596831C2312yes—
42C4⋊Dic73—22no—
43C4⋊Dic73C2312yes—
44#11924007—22no—
45#11924007—22no—
46#11924007—22no—
47C22⋊Dic73—22no—
48C4×Dic73—22no—
49C2×Q8×C73C2312yes—
50C22×C4×C73C2311yescharacteristic
51C4⋊C4×C73—22no—
52C4⋊C4×C73—22no—
53C4⋊C4×C73—22no—
54C4⋊C4×C73—22no—
55C4⋊C4×C73D412yes—
56C4⋊C4×C73C2312yes—
57C22⋊C4×C73—22no—
58C22⋊C4×C73D412yes—
59C42×C73—22no—
60C42×C73C2311yescharacteristic
61C42×C73C2311yescharacteristic
62C23×C73C2×D411yescharacteristic
63Q8×C73—22no—
64Q8×C73—22no—
65C2×C4×C73—21no—
66C2×C4×C73—21no—
67C2×C4×C73—22no—
68C2×C4×C73—22no—
69C2×C4×C73C2×D412yes—
70C2×C4×C73C2×D412yes—
71C2×C4×C73C2×D411yescharacteristic
72C2×C4×C73C2411yescharacteristic
73C2×Dic73—22no—
74C2×Dic73—22no—
75Dic146—22no—
76Dic146—22no—
77#10596831—22no—
78#10596831—22no—
79C22×C73—21no—
80C22×C73—22no—
81C22×C73C22×D411yescharacteristic
82C4×C73—21no—
83C4×C73—22no—
84C4×C73—22no—
85C4×C73—42no—
86C4×C73—42no—
87C4×C73H(5,𝔽2)11yescharacteristic
88C4×C732−1+411yescharacteristic
89Dic73—42no—
90Dic73—42no—
91C2×C73—41no—
92C2×C73#53711yescharacteristic
93C2×C73#57812yes—
94#3261—731nomaximal, Sylow
95C73#326111yescharacteristic, complemented, Sylow
96#541—731no—
97#541D7311yescharacteristic
98#479—732no—
99#479—732no—
100#470—732no—
101#467—732no—
102#462—732no—
103#462—732no—
104#424—731no—
105C2×Q16—732no—
106C2×Q16—732no—
107C2×M16—731no—
108C22×C8—731no—
109C4⋊Q8—731no—
110C4⋊Q8C2×D7311yescharacteristic
111#126—22no—
112#126—1462no—
113#125—22no—
114#125—731no—
115#125—1462no—
116#125C2×D7311yescharacteristic
117C22⋊Q8—732no—
118C22⋊Q8C2×D7312yes—
119C4×Q8—732no—
120C4×Q8C2×D7312yes—
121#117C2×D7311yescharacteristic
122#107—732no—
123#106—732no—
124C4⋊C8—732no—
125C4⋊C8—732no—
126#103—732no—
127#103—732no—
128#103—732no—
129#103—732no—
130C2×Q8—732no—
131C2×Q8C22×D7312yes—
132C22×C4C22×D7311yescharacteristic
133Q16—2922no—
134Q16—2922no—
135M16—2921no—
136C2×C8—2921no—
137C2×C8—732no—
138C2×C8—732no—
139C4⋊C4—22no—
140C4⋊C4—22no—
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—22no—
151C22⋊C4—1462no—
152C22⋊C4C22⋊D7312yes—
153C42—22no—
154C42—1462no—
155C42C22×D7311yescharacteristic
156C42C22×D7311yescharacteristic
157C23C2×C22⋊D7311yescharacteristic
158Q8—22no—
159Q8—22no—
160Q8—1462no—
161Q8—1462no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—1462no—
167C2×C4—1462no—
168C2×C4C2×C22⋊D7312yes—
169C2×C4C2×C22⋊D7312yes—
170C2×C4C2×C22⋊D7311yescharacteristic
171C2×C4C23×D7311yescharacteristic
172C8—1462no—
173C8—1462no—
174C22—22no—
175C22—21no—
176C22C22×C22⋊D7311yescharacteristic
177C4—22no—
178C4—22no—
179C4—21no—
180C4—42no—
181C4—42no—
182C4—2922no—
183C4—2922no—
184C4#1455663711yescharacteristic
185C4#1455663811yescharacteristic
186C2—41no—
187C2#1798916511yescharacteristic
188C2#1798940212yes—
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#541×C73C2
socleC22×C73C22×D4
hypercenter#541D73
hypocenterC73#3261
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #17988894C2semidirect
3. #17988891C2semidirect
6. #17988797C2semidirect
7. #17988794C2semidirect
95. C73#3261semidirect