Finite Group Databasebeta

← #22561027

Subgroups — #22561027

Order 8576.

308 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 99 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
2C2×#14523968C211yesmaximal, characteristic
3C2×#14523967C211yesmaximal, characteristic
4C2×#14523966C211yesmaximal, characteristic
5C2×#14523953C211yesmaximal, characteristic
6#16863261C211yesmaximal, characteristic
7C2×#103×C67C211yesmaximal, characteristic
8C22×Dic134C2211yescharacteristic
9C22×C67⋊C8C2211yescharacteristic
10#14524041—22no—
11#14524041C414yescomplemented
12C2×C4⋊Dic67C2211yescharacteristic
13C2×Dic67⋊C4—22no—
14C2×C4×Dic67C2211yescharacteristic
15#14523968—22no—
16#14523967—22no—
17#14523966—22no—
18#14523953—22no—
19C67⋊#95—22no—
20C22×Q8×C67C2211yescharacteristic
21C22×C8×C67C2211yescharacteristic
22C2×C4⋊C4×C67C2211yescharacteristic
23#103×C67—22no—
24C2×Dic134—21no—
25C2×Dic134—21no—
26C2×Dic134—21no—
27C2×Dic134—21no—
28C2×Dic134—21no—
29C2×Dic134C2×C412yes—
30C22×Dic67—21no—
31C22×Dic67—21no—
32C22×Dic67D412yes—
33C2×C67⋊C8—21no—
34C2×C67⋊C8—21no—
35C2×C67⋊C8D412yes—
36C4⋊Dic67—21no—
37C4⋊Dic67—21no—
38Dic67⋊C4—28no—
39C4×Dic67C2×C412yes—
40C4×Dic67D412yes—
41C2×Q8×C67—21no—
42C2×Q8×C67—21no—
43C2×Q8×C67—21no—
44C2×Q8×C67—21no—
45C2×Q8×C67—21no—
46C2×Q8×C67C2×C412yes—
47C22×C4×C67—21no—
48C22×C4×C67—21no—
49C22×C4×C67C2311yescharacteristic
50C2×C8×C67—21no—
51C2×C8×C67—21no—
52C2×C8×C67D412yes—
53C4⋊C4×C67—21no—
54C4⋊C4×C67—21no—
55C23×C67C2×D411yescharacteristic
56Q8×C67—22no—
57Q8×C67—22no—
58Q8×C67—41no—
59Q8×C67—41no—
60C2×C4×C67—22no—
61C2×C4×C67—41no—
62C2×C4×C67—41no—
63C2×C4×C67—41no—
64C2×C4×C67—42no—
65C2×C4×C67C22×C411yescharacteristic
66C2×C4×C67C2×D411yescharacteristic
67C2×C4×C67C2×D411yescharacteristic
68C2×C4×C67C2×D411yescharacteristic
69C2×C4×C67#4111yescharacteristic
70C2×C4×C67#4111yescharacteristic
71C2×Dic67—22no—
72C2×Dic67—22no—
73C2×Dic67—22no—
74C2×Dic67—41no—
75C2×Dic67—41no—
76C2×Dic67—41no—
77C2×Dic67—42no—
78C2×Dic67C22⋊C414yes—
79Dic134—22no—
80Dic134—22no—
81Dic134—41no—
82Dic134—41no—
83C8×C67—22no—
84C67⋊C8—22no—
85C22×C67C2×C22⋊C411yescharacteristic
86C22×C67#12411yescharacteristic
87C22×C67#12711yescharacteristic
88C22×C67#13712yes—
89C22×C67#13712yes—
90C4×C67—42no—
91C4×C67—81no—
92C4×C67C4×D411yescharacteristic
93C4×C67C4×D411yescharacteristic
94C4×C67#12111yescharacteristic
95C4×C67#12111yescharacteristic
96Dic67—24no—
97Dic67—42no—
98Dic67—81no—
99C2×C67#39011yescharacteristic
100C2×C67#41912yes—
101C2×C67#49112yes—
102C2×C67#49711yescharacteristic
103C2×C67#49711yescharacteristic
104#1960—671nomaximal, Sylow
105C67#196011yescharacteristic, complemented, Sylow
106C2×C4⋊Q8—671no—
107C2×#103—671no—
108C2×#103—671no—
109C2×#103—671no—
110C2×#103D6711yescharacteristic
111C2×#97—671no—
112#382—671no—
113C22×Q8—671no—
114C22×Q8C2×D6711yescharacteristic
115C22×C8—671no—
116C22×C8C2×D6711yescharacteristic
117C4⋊Q8—674no—
118C4⋊Q8—1342no—
119C2×C4⋊C4—671no—
120C2×C4⋊C4—1342no—
121C2×C4⋊C4C2×D6711yescharacteristic
122C2×C42—671no—
123#103—22no—
124#103—1342no—
125#103—1342no—
126#103—1342no—
127#97—1342no—
128#95—1342no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—672no—
135C2×Q8—1341no—
136C2×Q8—1341no—
137C2×Q8—1341no—
138C2×Q8—1341no—
139C2×Q8—1341no—
140C2×Q8C4×D6712yes—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—672no—
144C22×C4—1341no—
145C22×C4—1341no—
146C22×C4C22×D6711yescharacteristic
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—672no—
150C2×C8—1341no—
151C2×C8—1341no—
152C2×C8C22⋊D6712yes—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—1348no—
156C4⋊C4—1341no—
157C4⋊C4—1341no—
158C42—672no—
159C42—672no—
160C23D4×D6711yescharacteristic
161Q8—22no—
162Q8—22no—
163Q8—41no—
164Q8—41no—
165Q8—2681no—
166Q8—2681no—
167Q8—1342no—
168Q8—1342no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—42no—
174C2×C4—2681no—
175C2×C4—2681no—
176C2×C4—2681no—
177C2×C4—2682no—
178C2×C4—674no—
179C2×C4—1342no—
180C2×C4—1342no—
181C2×C4—1342no—
182C2×C4C2×C4×D6711yescharacteristic
183C2×C4D4×D6711yescharacteristic
184C2×C4D4×D6711yescharacteristic
185C2×C4C2×C22⋊D6711yescharacteristic
186C2×C4#1176162711yescharacteristic
187C2×C4#1176162811yescharacteristic
188C8—22no—
189C8—1342no—
190C22C22⋊C4×D6711yescharacteristic
191C22#1452402911yescharacteristic
192C22#1452403911yescharacteristic
193C22#1452407212yes—
194C22#1452407512yes—
195C4—42no—
196C4—81no—
197C4—2682no—
198C4—5361no—
199C4—1344no—
200C4(C22⋊D67)⋊C411yescharacteristic
201C4C4×C22⋊D6711yescharacteristic
202C4#1452401511yescharacteristic
203C4#1452401611yescharacteristic
204C2#1686329611yescharacteristic
205C2#1686340312yes—
206C2#1686376312yes—
207C2#1686378711yescharacteristic
208C2#1686378911yescharacteristic
subgroupG/H
centerC23D4×D67
commutatorC2×C4×C67C22×C4
FrattiniC22×C4C22×D67
FittingC2×#103×C67C2
socleC23×C67C2×D4
hypercenterC2×#103D67
hypocenterC67#1960
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
11. #14524041C4semidirect
105. C67#1960semidirect