Finite Group Databasebeta

← #22570340

Subgroups — #22570340

Order 8576.

380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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#16863953C211yesmaximal, characteristic
2C2×C4×Dic134C211yesmaximal, characteristic
3#16863727C212yesmaximal
4#16863682C212yesmaximal, complemented
5#16863607C212yesmaximal, complemented
6#16863554C212yesmaximal
7#16863504C214yesmaximal, complemented
8#432×C67C211yesmaximal, characteristic
9C22×Dic134C2211yescharacteristic
10C2×Dic268C2214yes—
11#14524043C2211yescharacteristic
12#14524043C2211yescharacteristic
13#14524035—21no—
14#14524022—21no—
15#14524022C2212yes—
16C4×Dic134—21no—
17C4×Dic134—21no—
18C4×Dic134—21no—
19C4×Dic134C2212yes—
20C4×Dic134C2212yes—
21C4×Dic134C2212yes—
22#14524002—21no—
23C2×C4⋊Dic67C2211yescharacteristic
24C2×Dic67⋊C4—21no—
25C2×C4×Dic67—21no—
26#14523975C2214yes—
27#14523968C2214yes—
28#14523968C2214yes—
29C2×C42×C67C2211yescharacteristic
30C4⋊C8×C67C2212yes—
31C22⋊C8×C67C2212yes—
32#97×C67C2212yes—
33C2×Dic134—21no—
34C2×Dic134—24no—
35C2×Dic134—21no—
36C2×Dic134C2312yes—
37C2×Dic134C2312yes—
38C22×Dic67—21no—
39C22×Dic67—21no—
40Dic268—28no—
41C4⋊Dic67—21no—
42C4⋊Dic67—21no—
43C4⋊Dic67—21no—
44C4⋊Dic67—21no—
45C4⋊Dic67C2312yes—
46C4⋊Dic67C2312yes—
47Dic67⋊C4—22no—
48Dic67⋊C4—22no—
49Dic67⋊C4—22no—
50Dic67⋊C4—22no—
51C22⋊Dic67—22no—
52C4×Dic67—22no—
53C4×Dic67—22no—
54C4×Dic67—22no—
55C22×C4×C67D411yescharacteristic
56C22×C4×C67D411yescharacteristic
57C22×C4×C67C2311yescharacteristic
58C2×C8×C67C2314yes—
59C42×C67D411yescharacteristic
60C42×C67D411yescharacteristic
61C42×C67C2311yescharacteristic
62C42×C67C2311yescharacteristic
63C23×C67C2×D411yescharacteristic
64C2×C4×C67—22no—
65C2×C4×C67—22no—
66C2×C4×C67—22no—
67C2×C4×C67C2×D411yescharacteristic
68C2×C4×C67C2×D411yescharacteristic
69C2×C4×C67C2×D411yescharacteristic
70C2×C4×C67C2×D411yescharacteristic
71C2×C4×C67C2×D411yescharacteristic
72C2×C4×C67C2411yescharacteristic
73C2×Dic67—24no—
74C2×Dic67—22no—
75C2×Dic67—22no—
76C2×Dic67—22no—
77C2×Dic67—22no—
78C2×Dic67—42no—
79Dic134—24no—
80Dic134—22no—
81Dic134—24no—
82Dic134—42no—
83Dic134#4114yes—
84C8×C67—24no—
85C22×C67—21no—
86C22×C67—21no—
87C22×C67#13712yes—
88C22×C67C22×D411yescharacteristic
89C4×C67—21no—
90C4×C67—21no—
91C4×C67—21no—
92C4×C67—21no—
93C4×C67#13712yes—
94C4×C67C2×#4112yes—
95Dic67—24no—
96Dic67—42no—
97Dic67—42no—
98Dic67—42no—
99C2×C67—22no—
100C2×C67#52511yescharacteristic
101C2×C67C2×#13711yescharacteristic
102C2×C67C2×#13711yescharacteristic
103#3113—671nomaximal, Sylow
104C67#311311yescharacteristic, complemented, Sylow
105#533—671no—
106C2×C4×Q8—671no—
107#483—672no—
108#475—672no—
109#462—672no—
110#451—672no—
111#441—674no—
112#432D6711yescharacteristic
113C22×Q8—671no—
114C2×Q16—674no—
115C4⋊Q8—671no—
116C4⋊Q8—671no—
117#125—1341no—
118C22⋊Q8—672no—
119C22⋊Q8—1341no—
120C4×Q8—672no—
121C4×Q8—672no—
122C4×Q8—672no—
123C4×Q8—1341no—
124C4×Q8—1341no—
125C4×Q8—1341no—
126#117—1341no—
127C2×C4⋊C4—671no—
128C2×C4⋊C4—1341no—
129C2×C42—1341no—
130C2×C42C2×D6711yescharacteristic
131#106—674no—
132C4⋊C8C2×D6712yes—
133#103—674no—
134#103—674no—
135C22⋊C8C2×D6712yes—
136#97C2×D6712yes—
137C2×Q8—672no—
138C2×Q8—672no—
139C2×Q8—1344no—
140C2×Q8—1341no—
141C2×Q8—1341no—
142C22×C4—1341no—
143C22×C4—1341no—
144C22×C4D26811yescharacteristic
145C22×C4D26811yescharacteristic
146C22×C4C22×D6711yescharacteristic
147Q16—1348no—
148C2×C8C22×D6714yes—
149C4⋊C4—672no—
150C4⋊C4—672no—
151C4⋊C4—1341no—
152C4⋊C4—1342no—
153C4⋊C4—1342no—
154C4⋊C4—1341no—
155C4⋊C4—1341no—
156C4⋊C4—1342no—
157C4⋊C4—1342no—
158C4⋊C4—1341no—
159C22⋊C4—1342no—
160C42—1342no—
161C42—1342no—
162C42—1342no—
163C42D26811yescharacteristic
164C42D26811yescharacteristic
165C42C22×D6711yescharacteristic
166C42C22×D6711yescharacteristic
167C23C2×D26811yescharacteristic
168Q8—2682no—
169Q8—674no—
170Q8—1344no—
171Q8—1344no—
172Q8—1342no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—2682no—
177C2×C4—1342no—
178C2×C4—1342no—
179C2×C4—1342no—
180C2×C4—1344no—
181C2×C4—1342no—
182C2×C4C2×D26811yescharacteristic
183C2×C4C2×D26811yescharacteristic
184C2×C4C2×D26811yescharacteristic
185C2×C4C2×D26811yescharacteristic
186C2×C4C2×D26811yescharacteristic
187C2×C4C23×D6711yescharacteristic
188C8—24no—
189C22—21no—
190C22—21no—
191C22#1452407612yes—
192C22C22×D26811yescharacteristic
193C4—21no—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—2682no—
198C4—2682no—
199C4—2682no—
200C4—1344no—
201C4#1452407612yes—
202C4#41×D6712yes—
203C2—22no—
204C2#1686390811yescharacteristic
205C2C2×#1452407611yescharacteristic
206C2C2×#1452407611yescharacteristic
subgroupG/H
centerC22C22×D268
commutatorC2×C4×C67C24
FrattiniC2×C4C23×D67
Fitting#432×C67C2
socleC22×C67C22×D4
hypercenter#432D67
hypocenterC67#3113
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
4. #16863682C2semidirect
5. #16863607C2semidirect
7. #16863504C2semidirect
104. C67#3113semidirect