Finite Group Databasebeta

← #22561777

Subgroups — #22561777

Order 8576.

198 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 81 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#16863262C211yesmaximal, characteristic
2#16863158C211yesmaximal, characteristic
3#16863158C211yesmaximal, characteristic
4#16863158C211yesmaximal, characteristic
5#16863158C211yesmaximal, characteristic
6#16863151C211yesmaximal, characteristic
7#389×C67C211yesmaximal, characteristic
8C22×C67⋊C8C2211yescharacteristic
9C22×C67⋊C8C2211yescharacteristic
10C2×C4⋊Dic67C2211yescharacteristic
11C2×C4⋊Dic67C2211yescharacteristic
12C67⋊#95—21no—
13C67⋊#95—21no—
14C2×C4⋊C4×C67—21no—
15C2×C4⋊C4×C67C2211yescharacteristic
16C2×C4⋊C4×C67C2211yescharacteristic
17C2×C42×C67C2211yescharacteristic
18#95×C67—21no—
19C22×Dic67—21no—
20C22×Dic67—21no—
21C2×C67⋊C8—21no—
22C2×C67⋊C8—21no—
23C2×C67⋊C8—21no—
24C2×C67⋊C8—21no—
25C2×C67⋊C8—21no—
26C2×C67⋊C8—21no—
27C4⋊Dic67—21no—
28C4⋊Dic67—21no—
29C4⋊Dic67—21no—
30C4⋊Dic67—21no—
31C22×C4×C67—21no—
32C22×C4×C67—21no—
33C22×C4×C67D411yescharacteristic
34C22×C4×C67D411yescharacteristic
35C22×C4×C67C2311yescharacteristic
36C4⋊C4×C67—21no—
37C4⋊C4×C67—21no—
38C4⋊C4×C67—21no—
39C4⋊C4×C67—42no—
40C4⋊C4×C67Q812yes—
41C42×C67—21no—
42C42×C67—21no—
43C23×C67C2×D411yescharacteristic
44C2×C4×C67—22no—
45C2×C4×C67—21no—
46C2×C4×C67—21no—
47C2×C4×C67—21no—
48C2×C4×C67—21no—
49C2×C4×C67—21no—
50C2×C4×C67—21no—
51C2×C4×C67—41no—
52C2×C4×C67—41no—
53C2×C4×C67—41no—
54C2×C4×C67—41no—
55C2×C4×C67—41no—
56C2×C4×C67C2×Q811yescharacteristic
57C2×C4×C67#4111yescharacteristic
58C2×C4×C67#4111yescharacteristic
59C2×C4×C67#4111yescharacteristic
60C2×C4×C67#4111yescharacteristic
61C2×C4×C67#4111yescharacteristic
62C2×Dic67—41no—
63C2×Dic67—41no—
64C2×Dic67—41no—
65C2×Dic67—41no—
66C2×Dic67—41no—
67C2×Dic67—41no—
68C67⋊C8—41no—
69C67⋊C8—41no—
70C22×C67C22⋊Q811yescharacteristic
71C22×C67#12311yescharacteristic
72C22×C67#12411yescharacteristic
73C22×C67#13511yescharacteristic
74C22×C67#13511yescharacteristic
75C22×C67AGL(1,ℤ/8)11yescharacteristic
76C22×C67#13711yescharacteristic
77C4×C67—42no—
78C4×C67—41no—
79C4×C67—41no—
80C4×C67—81no—
81C4×C67#12511yescharacteristic
82C4×C67#12511yescharacteristic
83C4×C67#12611yescharacteristic
84C4×C67#12611yescharacteristic
85Dic67—81no—
86Dic67—81no—
87C2×C67#40011yescharacteristic
88C2×C67#47811yescharacteristic
89C2×C67#47911yescharacteristic
90C2×C67#48211yescharacteristic
91C2×C67#48511yescharacteristic
92C2×C67#48811yescharacteristic
93C2×C67#48911yescharacteristic
94#2101—671nomaximal, Sylow
95C67#210111yescharacteristic, complemented, Sylow
96#389D6711yescharacteristic
97#382—671no—
98#340—671no—
99#340—671no—
100#340—671no—
101#340—671no—
102#336—671no—
103C22×C8—671no—
104C22×C8—671no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—671no—
107C2×C4⋊C4—671no—
108C2×C4⋊C4C2×D6711yescharacteristic
109C2×C4⋊C4C2×D6711yescharacteristic
110C2×C42C2×D6711yescharacteristic
111#95—21no—
112#95—1341no—
113#95—1341no—
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—1341no—
117C22×C4—1341no—
118C22×C4C22⋊D6711yescharacteristic
119C22×C4C22⋊D6711yescharacteristic
120C22×C4C22×D6711yescharacteristic
121C2×C8—1341no—
122C2×C8—1341no—
123C2×C8—1341no—
124C2×C8—1341no—
125C2×C8—1341no—
126C2×C8—1341no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—42no—
131C4⋊C4—1341no—
132C4⋊C4—1341no—
133C4⋊C4—1341no—
134C4⋊C4—1341no—
135C4⋊C4Dic13412yes—
136C42—21no—
137C42—21no—
138C23C2×C22⋊D6711yescharacteristic
139C2×C4—22no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—2681no—
152C2×C4—2681no—
153C2×C4—2681no—
154C2×C4—2681no—
155C2×C4—2681no—
156C2×C4—2681no—
157C2×C4C2×Dic13411yescharacteristic
158C2×C4#1176162711yescharacteristic
159C2×C4#1176162711yescharacteristic
160C2×C4#1176162811yescharacteristic
161C2×C4#1176162911yescharacteristic
162C2×C4#1176162911yescharacteristic
163C8—2681no—
164C8—2681no—
165C22#1452402211yescharacteristic
166C22#1452402411yescharacteristic
167C22#1452403211yescharacteristic
168C22#1452406311yescharacteristic
169C22#1452406311yescharacteristic
170C22#1452406911yescharacteristic
171C22#1452407411yescharacteristic
172C4—42no—
173C4—41no—
174C4—41no—
175C4—81no—
176C4—5361no—
177C4—5361no—
178C4#1452403411yescharacteristic
179C4#1452403411yescharacteristic
180C4#1452403811yescharacteristic
181C4#1452403811yescharacteristic
182C2#1686333511yescharacteristic
183C2#1686369611yescharacteristic
184C2#1686370311yescharacteristic
185C2#1686371711yescharacteristic
186C2#1686373411yescharacteristic
187C2#1686375311yescharacteristic
188C2#1686375811yescharacteristic
subgroupG/H
centerC23C2×C22⋊D67
commutatorC22×C4×C67C23
FrattiniC22×C4C22×D67
Fitting#389×C67C2
socleC23×C67C2×D4
hypercenter#389D67
hypocenterC67#2101
LCSG ▷ C22×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
95. C67#2101semidirect