Finite Group Databasebeta

← #22560991

Subgroups — #22560991

Order 8576.

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

normal subgroups only

This group has 196 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×#14523978C211yesmaximal, characteristic
2#16863439C211yesmaximal, characteristic
3C2×#14523976C211yesmaximal, characteristic
4#16863352C211yesmaximal, characteristic
5#16863165C211yesmaximal, characteristic
6#16863164C211yesmaximal, characteristic
7#428×C67C211yesmaximal, characteristic
8C2×#11761612C2211yescharacteristic
9C2×#11761612C2211yescharacteristic
10C22×C67⋊C8C2211yescharacteristic
11C2×C4⋊Dic67C2211yescharacteristic
12#14523978C414yescomplemented
13#14523976—21no—
14#14523976—21no—
15#14523976—21no—
16#14523974—21no—
17#14523954—21no—
18C4×C67⋊C8—21no—
19C2×M16×C67C2211yescharacteristic
20#117×C67C2211yescharacteristic
21C2×C4⋊C4×C67C2211yescharacteristic
22#107×C67—21no—
23#106×C67—21no—
24C22×Dic67—21no—
25#11761612—21no—
26#11761612—21no—
27#11761612C2×C412yes—
28#11761612Q812yes—
29C2×C67⋊C8—21no—
30C2×C67⋊C8—21no—
31C2×C67⋊C8C2×C412yes—
32C2×C67⋊C8D411yescharacteristic
33C2×C67⋊C8D411yescharacteristic
34C2×C67⋊C8Q812yes—
35C4⋊Dic67—21no—
36C4⋊Dic67—21no—
37C22×C4×C67—21no—
38C22×C4×C67C2311yescharacteristic
39M16×C67—21no—
40M16×C67C2×C412yes—
41C2×C8×C67—21no—
42C4⋊C4×C67—21no—
43C4⋊C4×C67—21no—
44C4⋊C4×C67D411yescharacteristic
45C4⋊C4×C67D411yescharacteristic
46C22⋊C4×C67—21no—
47C42×C67—21no—
48C23×C67#4111yescharacteristic
49C2×C4×C67—21no—
50C2×C4×C67—21no—
51C2×C4×C67—41no—
52C2×C4×C67—81no—
53C2×C4×C67C22×C411yescharacteristic
54C2×C4×C67C2×D411yescharacteristic
55C2×C4×C67C2×D411yescharacteristic
56C2×C4×C67C2×Q811yescharacteristic
57C2×C4×C67C2×Q811yescharacteristic
58C2×C4×C67#4111yescharacteristic
59C2×Dic67—41no—
60C2×Dic67—81no—
61C8×C67—22no—
62C67⋊C8—22no—
63C67⋊C8—22no—
64C67⋊C8C4⋊C412yes—
65C67⋊C8C4⋊C412yes—
66C22×C67—21no—
67C22×C67—21no—
68C22×C67C4×Q811yescharacteristic
69C22×C67#12111yescharacteristic
70C22×C67#12511yescharacteristic
71C4×C67—41no—
72C4×C67—41no—
73C4×C67—81no—
74C4×C67C2×C4⋊C411yescharacteristic
75C4×C67C4×D411yescharacteristic
76C4×C67C22⋊Q811yescharacteristic
77C4×C67C4⋊Q811yescharacteristic
78Dic67—81no—
79C2×C67—21no—
80C2×C67—21no—
81C2×C67#38911yescharacteristic
82C2×C67#47211yescharacteristic
83C2×C67#47311yescharacteristic
84#1952—671nomaximal, Sylow
85C67#195211yescharacteristic, complemented, Sylow
86C2×#108—671no—
87#428—671no—
88#428D6711yescharacteristic
89C2×#107—671no—
90#405—671no—
91#343—671no—
92#343—671no—
93C2×M16—671no—
94C2×M16—671no—
95C2×M16C2×D6711yescharacteristic
96C22×C8—671no—
97#117C2×D6711yescharacteristic
98C2×C4⋊C4—671no—
99C2×C4⋊C4C2×D6711yescharacteristic
100#108—674no—
101#107—21no—
102#107—1341no—
103#107—1341no—
104#107—1341no—
105#106—21no—
106#106—1341no—
107#97—1341no—
108C4×C8—1341no—
109C22×C4—21no—
110C22×C4—1341no—
111C22×C4C22×D6711yescharacteristic
112M16—21no—
113M16—672no—
114M16—672no—
115M16—1341no—
116M16—1341no—
117M16C4×D6712yes—
118C2×C8—21no—
119C2×C8—672no—
120C2×C8—671no—
121C2×C8—671no—
122C2×C8—672no—
123C2×C8—1341no—
124C2×C8—1341no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—1341no—
128C4⋊C4—1341no—
129C4⋊C4C22⋊D6711yescharacteristic
130C4⋊C4C22⋊D6711yescharacteristic
131C22⋊C4—21no—
132C42—21no—
133C23#1176162711yescharacteristic
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—81no—
138C2×C4—2681no—
139C2×C4—5361no—
140C2×C4C2×C4×D6711yescharacteristic
141C2×C4D4×D6711yescharacteristic
142C2×C4C2×C22⋊D6711yescharacteristic
143C2×C4Q8×D6711yescharacteristic
144C2×C4Q8×D6711yescharacteristic
145C2×C4#1176162811yescharacteristic
146C8—22no—
147C8—672no—
148C8—672no—
149C8—1342no—
150C8—1342no—
151C22—21no—
152C22—21no—
153C22#1452400811yescharacteristic
154C22#1452401511yescharacteristic
155C22#1452403311yescharacteristic
156C4—41no—
157C4—41no—
158C4—81no—
159C4—5361no—
160C4C4⋊C4×D6711yescharacteristic
161C4C4×C22⋊D6711yescharacteristic
162C4#1452402111yescharacteristic
163C4#1452404111yescharacteristic
164C2—21no—
165C2—21no—
166C2#1686329111yescharacteristic
167C2#1686366411yescharacteristic
168C2#1686366911yescharacteristic
subgroupG/H
centerC22#14524015
commutatorC2×C4×C67C22×C4
FrattiniC22×C4C22×D67
Fitting#428×C67C2
socleC22×C67#121
hypercenter#428D67
hypocenterC67#1952
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
12. #14523978C4semidirect
85. C67#1952semidirect