Finite Group Databasebeta

← #22571417

Subgroups — #22571417

Order 8576.

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

normal subgroups only

This group has 324 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#16863953C211yesmaximal, characteristic
2C2×#14524035C211yesmaximal, characteristic
3#16863805C212yesmaximal, complemented
4#16863765C212yesmaximal, complemented
5#16863732C212yesmaximal
6#16863727C212yesmaximal
7#16863704C214yesmaximal, complemented
8#432×C67C211yesmaximal, characteristic
9#14524043C2211yescharacteristic
10#14524043C2211yescharacteristic
11#14524035—21no—
12#14524035—21no—
13#14524035—21no—
14#14524035C2212yes—
15#14524035C2212yes—
16#14524022—21no—
17#14524022C2212yes—
18C4×Dic134—21no—
19C4×Dic134C2212yes—
20#14524002—21no—
21C2×C4⋊Dic67C2211yescharacteristic
22C2×C4⋊Dic67C2211yescharacteristic
23C2×Dic67⋊C4—21no—
24C2×Dic67⋊C4—21no—
25#14523977C2214yes—
26#14523975C2214yes—
27#14523968C2214yes—
28#14523968C2214yes—
29C2×C42×C67C2211yescharacteristic
30C4⋊C8×C67C2212yes—
31C22⋊C8×C67C2212yes—
32#97×C67C2212yes—
33C2×Dic134—21no—
34C2×Dic134C2312yes—
35C22×Dic67—21no—
36C22×Dic67—21no—
37C4⋊Dic67—21no—
38C4⋊Dic67—21no—
39C4⋊Dic67—21no—
40C4⋊Dic67—21no—
41C4⋊Dic67—21no—
42C4⋊Dic67C2312yes—
43C4⋊Dic67C2312yes—
44C4⋊Dic67C2312yes—
45Dic67⋊C4—22no—
46Dic67⋊C4—22no—
47Dic67⋊C4—22no—
48Dic67⋊C4—22no—
49Dic67⋊C4—22no—
50Dic67⋊C4—22no—
51C22⋊Dic67—22no—
52C4×Dic67—22no—
53C22×C4×C67D411yescharacteristic
54C22×C4×C67D411yescharacteristic
55C22×C4×C67C2311yescharacteristic
56C2×C8×C67C2314yes—
57C42×C67D411yescharacteristic
58C42×C67D411yescharacteristic
59C42×C67C2311yescharacteristic
60C42×C67C2311yescharacteristic
61C23×C67C2×D411yescharacteristic
62C2×C4×C67—22no—
63C2×C4×C67—22no—
64C2×C4×C67—41no—
65C2×C4×C67C2×D411yescharacteristic
66C2×C4×C67C2×D411yescharacteristic
67C2×C4×C67C2×D411yescharacteristic
68C2×C4×C67C2×D411yescharacteristic
69C2×C4×C67C2×D411yescharacteristic
70C2×C4×C67C2411yescharacteristic
71C2×Dic67—22no—
72C2×Dic67—22no—
73C2×Dic67—22no—
74C2×Dic67—22no—
75C2×Dic67—42no—
76C2×Dic67—42no—
77Dic134—24no—
78Dic134—42no—
79C8×C67—24no—
80C22×C67—21no—
81C22×C67—21no—
82C22×C67#13712yes—
83C22×C67C22×D411yescharacteristic
84C4×C67—21no—
85C4×C67—21no—
86C4×C67—21no—
87C4×C67—21no—
88C4×C67—21no—
89C4×C672−1+412yes—
90Dic67—42no—
91Dic67—42no—
92Dic67—42no—
93Dic67—42no—
94C2×C67—22no—
95C2×C67#53611yescharacteristic
96C2×C67C2×#13711yescharacteristic
97C2×C67#57511yescharacteristic
98#3236—671nomaximal, Sylow
99C67#323611yescharacteristic, complemented, Sylow
100#533—671no—
101C2×#125—671no—
102#501—672no—
103#491—672no—
104#484—672no—
105#483—672no—
106#479—674no—
107#432D6711yescharacteristic
108C4⋊Q8—671no—
109C4⋊Q8—671no—
110#125—672no—
111#125—672no—
112#125—1341no—
113#125—1341no—
114#125—1341no—
115C22⋊Q8—672no—
116C22⋊Q8—1341no—
117C4×Q8—672no—
118C4×Q8—1341no—
119#117—1341no—
120C2×C4⋊C4—671no—
121C2×C4⋊C4—671no—
122C2×C4⋊C4—1341no—
123C2×C4⋊C4—1341no—
124C2×C42C2×D6711yescharacteristic
125#107—674no—
126#106—674no—
127C4⋊C8C2×D6712yes—
128#103—674no—
129#103—674no—
130C22⋊C8C2×D6712yes—
131#97C2×D6712yes—
132C2×Q8—672no—
133C2×Q8—1341no—
134C22×C4—1341no—
135C22×C4—1341no—
136C22×C4D26811yescharacteristic
137C22×C4D26811yescharacteristic
138C22×C4C22×D6711yescharacteristic
139C2×C8C22×D6714yes—
140C4⋊C4—672no—
141C4⋊C4—672no—
142C4⋊C4—672no—
143C4⋊C4—1341no—
144C4⋊C4—1341no—
145C4⋊C4—1342no—
146C4⋊C4—1342no—
147C4⋊C4—1342no—
148C4⋊C4—1342no—
149C4⋊C4—1341no—
150C4⋊C4—1341no—
151C4⋊C4—1342no—
152C4⋊C4—1342no—
153C4⋊C4—1341no—
154C22⋊C4—1342no—
155C42—1342no—
156C42D26811yescharacteristic
157C42D26811yescharacteristic
158C42C22×D6711yescharacteristic
159C42C22×D6711yescharacteristic
160C23C2×D26811yescharacteristic
161Q8—2682no—
162Q8—1344no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—41no—
166C2×C4—2682no—
167C2×C4—2682no—
168C2×C4—1342no—
169C2×C4—1342no—
170C2×C4—1342no—
171C2×C4—1342no—
172C2×C4C2×D26811yescharacteristic
173C2×C4C2×D26811yescharacteristic
174C2×C4C2×D26811yescharacteristic
175C2×C4C2×D26811yescharacteristic
176C2×C4C2×D26811yescharacteristic
177C2×C4C23×D6711yescharacteristic
178C8—24no—
179C22—21no—
180C22—21no—
181C22#1452407612yes—
182C22C22×D26811yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—21no—
187C4—21no—
188C4—2682no—
189C4—2682no—
190C4—2682no—
191C4—2682no—
192C4#1452409012yes—
193C2—22no—
194C2#1686397211yescharacteristic
195C2C2×#1452407611yescharacteristic
196C2#1686419611yescharacteristic
subgroupG/H
centerC22C22×D268
commutatorC2×C4×C67C24
FrattiniC2×C4C23×D67
Fitting#432×C67C2
socleC22×C67C22×D4
hypercenter#432D67
hypocenterC67#3236
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
3. #16863805C2semidirect
4. #16863765C2semidirect
7. #16863704C2semidirect
99. C67#3236semidirect