Finite Group Databasebeta

← #22570501

Subgroups — #22570501

Order 8576.

382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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#16864001C211yesmaximal, characteristic
2#16863873C211yesmaximal, characteristic, complemented
3#16863721C212yesmaximal, complemented
4#16863704C212yesmaximal, complemented
5#16863597C212yesmaximal, complemented
6#16863537C212yesmaximal, complemented
7#16863498C212yesmaximal, complemented
8C4×#11761617C212yesmaximal, complemented
9#433×C67C211yesmaximal, characteristic, complemented
10C22×Dic134C2211yescharacteristic
11C2×#11761617C2212yes—
12C2×#11761617C2212yes—
13#14524040C2211yescharacteristic
14#14524035C2211yescharacteristic
15#14524028—22no—
16#14524017C2212yes—
17#14524016—22no—
18C4×Dic134C2212yes—
19C4×Dic134C2212yes—
20#14524008—22no—
21C4×D268C2212yes—
22#14524002C2211yescharacteristic
23#14523999—22no—
24#14523977C2212yes—
25#14523975C2212yes—
26#14523968C2212yes—
27#14523968C2212yes—
28#14523965C2212yes—
29#14523965C2212yes—
30#117×C67C2211yescharacteristic
31C4⋊C8×C67C2212yes—
32C22⋊C8×C67C2212yes—
33#97×C67C2211yescharacteristic
34C4×C8×C67C2211yescharacteristic
35C2×Dic134—21no—
36C2×Dic134—24no—
37C2×Dic134C2312yes—
38C2×D268—22no—
39C2×D268C2312yes—
40C2×C22⋊D67—22no—
41C22×Dic67—21no—
42C2×C4×D67—22no—
43#11761617—24no—
44#11761617—24no—
45C4⋊Dic67C2312yes—
46C4⋊Dic67C2312yes—
47Dic67⋊C4—22no—
48Dic67⋊C4—22no—
49Dic67⋊C4—22no—
50C22⋊Dic67—21no—
51(C2×D67)⋊C4—22no—
52(C2×D67)⋊C4—22no—
53C4×Dic67—22no—
54C4×Dic67—22no—
55C4×Dic67—21no—
56C22×C4×C67C2311yescharacteristic
57C2×C8×C67C2312yes—
58C2×C8×C67C2312yes—
59C4⋊C4×C67D412yes—
60C22⋊C4×C67D412yes—
61C42×C67C2311yescharacteristic
62C42×C67C2311yescharacteristic
63C23×C67C2×D411yescharacteristic
64C22×D67—22no—
65C2×C4×C67—22no—
66C2×C4×C67C2×D412yes—
67C2×C4×C67C2×D412yes—
68C2×C4×C67C2×D411yescharacteristic
69C2×C4×C67C2411yescharacteristic
70C22⋊D67—82no—
71C2×Dic67—24no—
72C2×Dic67—22no—
73C2×Dic67—22no—
74C2×Dic67—22no—
75D268—22no—
76D268—22no—
77D268—82no—
78C4×D67—82no—
79Dic134—24no—
80Dic134—22no—
81Dic134#4114yes—
82C8×C67—22no—
83C8×C67—22no—
84C22×C67—21no—
85C22×C67—22no—
86C22×C67C22×D411yescharacteristic
87C2×D67—42no—
88C2×D67—42no—
89C2×D67—42no—
90C4×C67—21no—
91C4×C67—22no—
92C4×C67—22no—
93C4×C67C2×#4112yes—
94Dic67—24no—
95Dic67—42no—
96Dic67—42no—
97C2×C67—41no—
98C2×C67#52511yescharacteristic
99C2×C67#57712yes—
100D67—82no—
101#3126—671nomaximal, Sylow
102C67#312611yescharacteristic, complemented, Sylow
103#540—671no—
104#519—671no—
105#482—672no—
106#479—672no—
107#460—672no—
108#448—672no—
109#440—672no—
110C4×SD16—672no—
111#433D6711yescharacteristic, complemented
112C22×Q8—671no—
113C2×SD16—672no—
114C2×SD16—672no—
115#127—671no—
116#125—671no—
117#123—1342no—
118#121—672no—
119#121—1342no—
120C4×Q8—672no—
121C4×Q8—672no—
122C4×Q8—1342no—
123C4×D4—672no—
124#117—671no—
125#117—1342no—
126#117C2×D6711yescharacteristic
127#107—672no—
128#106—672no—
129C4⋊C8C2×D6712yes—
130#103—672no—
131#103—672no—
132#102—672no—
133#102—672no—
134C22⋊C8C2×D6712yes—
135#97C2×D6711yescharacteristic
136C4×C8C2×D6711yescharacteristic
137C2×Q8—672no—
138C2×Q8—1344no—
139C2×Q8—1341no—
140C2×D4—672no—
141C2×D4—1342no—
142C2×D4—1342no—
143C22×C4—1342no—
144C22×C4—1341no—
145C22×C4C22×D6711yescharacteristic
146SD16—1344no—
147SD16—1344no—
148C2×C8C22×D6712yes—
149C2×C8C22×D6712yes—
150C4⋊C4—672no—
151C4⋊C4—672no—
152C4⋊C4—1342no—
153C4⋊C4—1342no—
154C4⋊C4—1342no—
155C4⋊C4D26812yes—
156C22⋊C4—1341no—
157C22⋊C4—1342no—
158C22⋊C4—1342no—
159C22⋊C4D26812yes—
160C42—1341no—
161C42—1342no—
162C42—1342no—
163C42C22×D6711yescharacteristic
164C42C22×D6711yescharacteristic
165C23—1342no—
166C23C2×D26811yescharacteristic
167Q8—674no—
168Q8—1344no—
169Q8—1342no—
170D4—5362no—
171D4—5362no—
172D4—1342no—
173D4—1342no—
174C2×C4—22no—
175C2×C4—5362no—
176C2×C4—1342no—
177C2×C4—1342no—
178C2×C4—1344no—
179C2×C4—1342no—
180C2×C4C2×D26812yes—
181C2×C4C2×D26812yes—
182C2×C4C2×D26811yescharacteristic
183C2×C4C23×D6711yescharacteristic
184C8—22no—
185C8—22no—
186C22—21no—
187C22—22no—
188C22—2682no—
189C22—2682no—
190C22—2682no—
191C22C22×D26811yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—2682no—
196C4—2682no—
197C4—1344no—
198C4#41×D6712yes—
199C2—41no—
200C2—5362no—
201C2#1686390811yescharacteristic
202C2#1686420812yes—
subgroupG/H
centerC22C22×D268
commutatorC2×C4×C67C24
FrattiniC2×C4C23×D67
Fitting#433×C67C2
socleC22×C67C22×D4
hypercenter#433D67
hypocenterC67#3126
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #16863873C2semidirect
3. #16863721C2semidirect
4. #16863704C2semidirect
5. #16863597C2semidirect
6. #16863537C2semidirect
7. #16863498C2semidirect
8. C4×#11761617C2semidirect
9. #433×C67C2semidirect
102. C67#3126semidirect
111. #433D67semidirect