Finite Group Databasebeta

← #22570453

Subgroups — #22570453

Order 8576.

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

normal subgroups only

This group has 418 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, complemented
2#16863870C211yesmaximal, characteristic, complemented
3#16863721C212yesmaximal, complemented
4#16863697C212yesmaximal, complemented
5#16863592C212yesmaximal, complemented
6#16863532C212yesmaximal, complemented
7#16863509C212yesmaximal, complemented
8C4×D536C212yesmaximal, complemented
9#433×C67C211yesmaximal, characteristic, complemented
10C22×D268C2211yescharacteristic
11C2×D536C2212yes—
12C2×D536C2212yes—
13#14524040C2211yescharacteristic, complemented
14#14524035C2211yescharacteristic, complemented
15#14524028—22no—
16#14524017C2212yes—
17#14524016—22no—
18C4×D268C2212yes—
19C4×D268C2212yes—
20C4×D268C2212yescomplemented
21#14524005—22no—
22#14524002C2211yescharacteristic
23C22⋊C4×D67—22no—
24#14523977C2212yescomplemented
25#14523975C2212yescomplemented
26#14523965C2212yes—
27#14523965C2212yes—
28#14523965C2212yescomplemented
29#14523965C2212yescomplemented
30#117×C67C2211yescharacteristic
31C4⋊C8×C67C2212yescomplemented
32C22⋊C8×C67C2212yes—
33#97×C67C2211yescharacteristic, complemented
34C4×C8×C67C2211yescharacteristic, complemented
35C23×D67—21no—
36C2×D268—21no—
37C2×D268—24no—
38C2×D268—22no—
39C2×D268C2312yes—
40C2×D268C2312yes—
41C2×C22⋊D67—22no—
42C2×C4×D67—22no—
43C2×C4×D67—22no—
44C2×C4×D67—22no—
45D536—24no—
46D536—24no—
47C4⋊Dic67C2312yes—
48C4⋊Dic67C2312yes—
49Dic67⋊C4—22no—
50C22⋊Dic67—21no—
51(C2×D67)⋊C4—22no—
52(C2×D67)⋊C4—22no—
53(C2×D67)⋊C4—22no—
54(C2×D67)⋊C4—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—
65C22×D67—24no—
66C22×D67—22no—
67C22×D67—82no—
68C2×C4×C67—22no—
69C2×C4×C67C2×D412yes—
70C2×C4×C67C2×D412yes—
71C2×C4×C67C2×D411yescharacteristic
72C2×C4×C67C2411yescharacteristic
73C22⋊D67—82no—
74C2×Dic67—22no—
75C2×Dic67—22no—
76D268—24no—
77D268—22no—
78D268—22no—
79D268—22no—
80D268—82no—
81D268#4114yes—
82C4×D67—82no—
83C4×D67—82no—
84C4×D67—82no—
85C8×C67—22no—
86C8×C67—22no—
87C22×C67—21no—
88C22×C67—22no—
89C22×C67C22×D411yescharacteristic
90C2×D67—24no—
91C2×D67—42no—
92C2×D67—42no—
93C2×D67—42no—
94C2×D67—42no—
95C2×D67—42no—
96C2×D67—84no—
97C4×C67—21no—
98C4×C67—22no—
99C4×C67—22no—
100C4×C67C2×#4112yes—
101Dic67—42no—
102Dic67—42no—
103C2×C67—41no—
104C2×C67#52511yescharacteristic
105C2×C67#57612yes—
106D67—44no—
107D67—82no—
108#3122—671nomaximal, Sylow
109C67#312211yescharacteristic, complemented, Sylow
110#540—671no—
111#518—671no—
112#482—672no—
113#478—672no—
114#459—672no—
115#447—672no—
116#442—672no—
117C4×D8—672no—
118#433D6711yescharacteristic, complemented
119C22×D4—671no—
120C2×D8—672no—
121C2×D8—672no—
122#127—671no—
123#125—671no—
124#123—1342no—
125#121—672no—
126#121—1342no—
127C4×D4—672no—
128C4×D4—672no—
129C4×D4—672no—
130C4×D4—1342no—
131#117—671no—
132#117C2×D6711yescharacteristic
133C2×C22⋊C4—1342no—
134#107—672no—
135#106—672no—
136C4⋊C8C2×D6712yescomplemented
137#102—672no—
138#102—672no—
139#102—672no—
140#102—672no—
141C22⋊C8C2×D6712yes—
142#97C2×D6711yescharacteristic, complemented
143C4×C8C2×D6711yescharacteristic, complemented
144C24—1341no—
145C2×D4—672no—
146C2×D4—672no—
147C2×D4—1344no—
148C2×D4—1342no—
149C2×D4—1342no—
150C2×D4—1341no—
151C22×C4—1342no—
152C22×C4—1342no—
153C22×C4—1342no—
154C22×C4C22×D6711yescharacteristic
155D8—1344no—
156D8—1344no—
157C2×C8C22×D6712yes—
158C2×C8C22×D6712yes—
159C4⋊C4—672no—
160C4⋊C4—672no—
161C4⋊C4—1342no—
162C4⋊C4D26812yes—
163C22⋊C4—1341no—
164C22⋊C4—1342no—
165C22⋊C4—1342no—
166C22⋊C4—1342no—
167C22⋊C4—1342no—
168C22⋊C4D26812yes—
169C42—1341no—
170C42C22×D6711yescharacteristic
171C42C22×D6711yescharacteristic
172C23—5362no—
173C23—1344no—
174C23—1342no—
175C23—1342no—
176C23C2×D26811yescharacteristic
177D4—5362no—
178D4—5362no—
179D4—674no—
180D4—1344no—
181D4—1342no—
182D4—1342no—
183D4—1342no—
184C2×C4—22no—
185C2×C4—5362no—
186C2×C4—5362no—
187C2×C4—5362no—
188C2×C4—1342no—
189C2×C4—1342no—
190C2×C4C2×D26811yescharacteristic
191C2×C4C2×D26812yes—
192C2×C4C2×D26812yes—
193C2×C4C23×D6711yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—2682no—
199C22—2682no—
200C22—2682no—
201C22—2682no—
202C22—2682no—
203C22—5364no—
204C22—1344no—
205C22C22×D26811yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—2682no—
210C4—2682no—
211C4#41×D6712yes—
212C2—41no—
213C2—2684no—
214C2—5362no—
215C2#1686390811yescharacteristic
216C2#1686420112yes—
subgroupG/H
centerC22C22×D268
commutatorC2×C4×C67C24
FrattiniC2×C4C23×D67
Fitting#433×C67C2
socleC22×C67C22×D4
hypercenter#433D67
hypocenterC67#3122
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
1. #16864001C2semidirect
2. #16863870C2semidirect
3. #16863721C2semidirect
4. #16863697C2semidirect
5. #16863592C2semidirect
6. #16863532C2semidirect
7. #16863509C2semidirect
8. C4×D536C2semidirect
9. #433×C67C2semidirect
13. #14524040C22semidirect
14. #14524035C22semidirect
20. C4×D268C22semidirect
24. #14523977C22semidirect
25. #14523975C22semidirect
28. #14523965C22semidirect
29. #14523965C22semidirect
31. C4⋊C8×C67C22semidirect
33. #97×C67C22semidirect
34. C4×C8×C67C22semidirect
109. C67#3122semidirect
118. #433D67semidirect
136. C4⋊C8C2×D67semidirect
142. #97C2×D67semidirect
143. C4×C8C2×D67semidirect