Finite Group Databasebeta

← #22560599

Subgroups — #22560599

Order 8576.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#14524041C211yesmaximal, characteristic
2#16863873C211yesmaximal, characteristic
3#16863405C211yesmaximal, characteristic
4C2×#14523961C211yesmaximal, characteristic
5#16863157C211yesmaximal, characteristic
6#16863155C211yesmaximal, characteristic
7#419×C67C211yesmaximal, characteristic
8C22×Dic134C2211yescharacteristic
9C2×#11761612C2211yescharacteristic
10#14524041—22no—
11#14524041C414yescomplemented
12C4×Dic134—22no—
13#14524008—22no—
14#14524002C2211yescharacteristic
15#14523999—22no—
16C2×Dic67⋊C4—22no—
17C2×C4×Dic67C2211yescharacteristic
18#14523967—22no—
19#14523961—22no—
20C22×Q8×C67C2211yescharacteristic
21C2×M16×C67C2211yescharacteristic
22#117×C67C2211yescharacteristic
23#103×C67—22no—
24C2×Dic134—21no—
25C2×Dic134—21no—
26C2×Dic134—21no—
27C2×Dic134—21no—
28C2×Dic134C2×C412yes—
29C2×Dic134D412yes—
30C22×Dic67—21no—
31C22×Dic67D412yes—
32#11761612—21no—
33#11761612—21no—
34C2×C67⋊C8—21no—
35C4⋊Dic67D412yes—
36Dic67⋊C4—24no—
37Dic67⋊C4—28no—
38C22⋊Dic67—21no—
39C4×Dic67—24no—
40C4×Dic67—21no—
41C4×Dic67—21no—
42C4×Dic67C2×C412yes—
43C2×Q8×C67—21no—
44C2×Q8×C67—21no—
45C2×Q8×C67—21no—
46C2×Q8×C67—21no—
47C2×Q8×C67—21no—
48C2×Q8×C67C2×C412yes—
49C22×C4×C67—21no—
50C22×C4×C67C2311yescharacteristic
51M16×C67—21no—
52M16×C67—21no—
53C2×C8×C67—21no—
54C4⋊C4×C67D412yes—
55C22⋊C4×C67—21no—
56C42×C67—21no—
57C23×C67C2×D411yescharacteristic
58Q8×C67—22no—
59Q8×C67—22no—
60Q8×C67—41no—
61Q8×C67—41no—
62C2×C4×C67—22no—
63C2×C4×C67—22no—
64C2×C4×C67—41no—
65C2×C4×C67—41no—
66C2×C4×C67C22×C411yescharacteristic
67C2×C4×C67C2×D411yescharacteristic
68C2×C4×C67C2×D411yescharacteristic
69C2×C4×C67C2×D411yescharacteristic
70C2×C4×C67#4111yescharacteristic
71C2×C4×C67#4111yescharacteristic
72C2×Dic67—24no—
73C2×Dic67—22no—
74C2×Dic67—22no—
75C2×Dic67—22no—
76C2×Dic67—22no—
77C2×Dic67C22⋊C414yes—
78Dic134—22no—
79Dic134—22no—
80Dic134—22no—
81Dic134—22no—
82C8×C67—41no—
83C67⋊C8—41no—
84C22×C67—22no—
85C22×C67C2×C22⋊C411yescharacteristic
86C22×C67#12011yescharacteristic
87C22×C67#12311yescharacteristic
88C4×C67—42no—
89C4×C67—42no—
90C4×C67C4×D411yescharacteristic
91C4×C67C4×D411yescharacteristic
92C4×C67#12111yescharacteristic
93C4×C67#12111yescharacteristic
94Dic67—24no—
95Dic67—24no—
96Dic67—42no—
97C2×C67—21no—
98C2×C67—21no—
99C2×C67#38611yescharacteristic
100C2×C67#45612yes—
101#1886—671nomaximal, Sylow
102C67#188611yescharacteristic, complemented, Sylow
103C2×C4⋊Q8—671no—
104#519—671no—
105#419—671no—
106#419D6711yescharacteristic
107C2×#101—671no—
108#339—671no—
109#339—671no—
110C22×Q8—671no—
111C22×Q8C2×D6711yescharacteristic
112C2×M16—671no—
113C2×M16C2×D6711yescharacteristic
114C4⋊Q8—674no—
115C4⋊Q8—1342no—
116C4×Q8—1342no—
117C4×Q8—1342no—
118#117—671no—
119#117—1342no—
120#117C2×D6711yescharacteristic
121C2×C4⋊C4—1342no—
122C2×C42—671no—
123#103—22no—
124#103—1342no—
125#101—1342no—
126C2×Q8—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—672no—
132C2×Q8—672no—
133C2×Q8—1341no—
134C2×Q8—1341no—
135C2×Q8—1341no—
136C2×Q8—1341no—
137C2×Q8C4×D6712yes—
138C22×C4—21no—
139C22×C4—672no—
140C22×C4—1341no—
141C22×C4C22×D6711yescharacteristic
142M16—21no—
143M16—21no—
144M16—1341no—
145M16—1341no—
146C2×C8—21no—
147C2×C8—1341no—
148C4⋊C4—672no—
149C4⋊C4—1348no—
150C4⋊C4—1344no—
151C4⋊C4C22⋊D6712yes—
152C22⋊C4—21no—
153C22⋊C4—1341no—
154C42—21no—
155C42—672no—
156C42—1344no—
157C42—1341no—
158C42—1341no—
159C23D4×D6711yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—41no—
163Q8—41no—
164Q8—1342no—
165Q8—1342no—
166Q8—1342no—
167Q8—1342no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—674no—
173C2×C4—1342no—
174C2×C4—1344no—
175C2×C4—1342no—
176C2×C4—1342no—
177C2×C4—1342no—
178C2×C4C2×C4×D6711yescharacteristic
179C2×C4D4×D6711yescharacteristic
180C2×C4D4×D6711yescharacteristic
181C2×C4C2×C22⋊D6711yescharacteristic
182C2×C4#1176162711yescharacteristic
183C2×C4#1176162811yescharacteristic
184C8—41no—
185C8—2681no—
186C22—22no—
187C22C22⋊C4×D6711yescharacteristic
188C22#1452401111yescharacteristic
189C22#1452402511yescharacteristic
190C4—42no—
191C4—42no—
192C4—2682no—
193C4—1344no—
194C4—1344no—
195C4(C22⋊D67)⋊C411yescharacteristic
196C4C4×C22⋊D6711yescharacteristic
197C4#1452401411yescharacteristic
198C4#1452401611yescharacteristic
199C2—21no—
200C2—21no—
201C2#1686327211yescharacteristic
202C2#1686357712yes—
subgroupG/H
centerC22#14524011
commutatorC2×C4×C67C22×C4
FrattiniC22×C4C22×D67
Fitting#419×C67C2
socleC22×C67#120
hypercenter#419D67
hypocenterC67#1886
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
11. #14524041C4semidirect
102. C67#1886semidirect