Finite Group Databasebeta

← #22561547

Subgroups — #22561547

Order 8576.

250 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14524035C211yesmaximal, characteristic
2C2×#14523976C211yesmaximal, characteristic
3C2×#14523974C211yesmaximal, characteristic
4#16863158C211yesmaximal, characteristic
5#16863158C211yesmaximal, characteristic
6#16863151C211yesmaximal, characteristic
7#389×C67C211yesmaximal, characteristic
8C22×C67⋊C8C2211yescharacteristic
9C22×C67⋊C8C2211yescharacteristic
10#14524035—22no—
11#14524035—22no—
12C2×C4⋊Dic67C2211yescharacteristic
13C2×C4⋊Dic67C2211yescharacteristic
14C2×Dic67⋊C4—21no—
15C2×Dic67⋊C4—21no—
16#14523976—22no—
17#14523974—22no—
18C2×C4⋊C4×C67—21no—
19C2×C4⋊C4×C67C2211yescharacteristic
20C2×C4⋊C4×C67C2211yescharacteristic
21C2×C42×C67C2211yescharacteristic
22#95×C67—21no—
23C22×Dic67—21no—
24C22×Dic67—21no—
25C2×C67⋊C8—21no—
26C2×C67⋊C8—21no—
27C2×C67⋊C8—21no—
28C2×C67⋊C8—21no—
29C2×C67⋊C8Q812yes—
30C2×C67⋊C8Q812yes—
31C4⋊Dic67—21no—
32C4⋊Dic67—21no—
33C4⋊Dic67D412yes—
34C4⋊Dic67D412yes—
35Dic67⋊C4—24no—
36Dic67⋊C4—24no—
37C22×C4×C67—21no—
38C22×C4×C67—21no—
39C22×C4×C67D411yescharacteristic
40C22×C4×C67D411yescharacteristic
41C22×C4×C67C2311yescharacteristic
42C4⋊C4×C67—21no—
43C4⋊C4×C67—21no—
44C4⋊C4×C67—21no—
45C4⋊C4×C67—42no—
46C4⋊C4×C67Q812yes—
47C42×C67—21no—
48C42×C67—21no—
49C23×C67C2×D411yescharacteristic
50C2×C4×C67—21no—
51C2×C4×C67—21no—
52C2×C4×C67—22no—
53C2×C4×C67—21no—
54C2×C4×C67—21no—
55C2×C4×C67—21no—
56C2×C4×C67—21no—
57C2×C4×C67—41no—
58C2×C4×C67—41no—
59C2×C4×C67—41no—
60C2×C4×C67—41no—
61C2×C4×C67—41no—
62C2×C4×C67C2×D411yescharacteristic
63C2×C4×C67C2×D411yescharacteristic
64C2×C4×C67C2×Q811yescharacteristic
65C2×C4×C67C2×Q811yescharacteristic
66C2×C4×C67C2×Q811yescharacteristic
67C2×C4×C67#4111yescharacteristic
68C2×Dic67—22no—
69C2×Dic67—22no—
70C2×Dic67—41no—
71C2×Dic67—41no—
72C2×Dic67—41no—
73C2×Dic67—41no—
74C67⋊C8—22no—
75C67⋊C8—22no—
76C22×C67#12011yescharacteristic
77C22×C67C22⋊Q811yescharacteristic
78C22×C67C4⋊Q811yescharacteristic
79C22×C67#13511yescharacteristic
80C22×C67#13511yescharacteristic
81C22×C67AGL(1,ℤ/8)11yescharacteristic
82C22×C67#13711yescharacteristic
83C4×C67—41no—
84C4×C67—41no—
85C4×C67—42no—
86C4×C67—81no—
87C4×C67C22⋊Q811yescharacteristic
88C4×C67C22⋊Q811yescharacteristic
89C4×C67C4⋊Q811yescharacteristic
90C4×C67C4⋊Q811yescharacteristic
91Dic67—42no—
92Dic67—42no—
93C2×C67#39511yescharacteristic
94C2×C67#44911yescharacteristic
95C2×C67#45211yescharacteristic
96C2×C67#47811yescharacteristic
97C2×C67#47911yescharacteristic
98C2×C67#49911yescharacteristic
99C2×C67#50111yescharacteristic
100#2059—671nomaximal, Sylow
101C67#205911yescharacteristic, complemented, Sylow
102C2×#125—671no—
103C2×#107—671no—
104C2×#106—671no—
105#389D6711yescharacteristic
106#340—671no—
107#340—671no—
108#336—671no—
109C22×C8—671no—
110C22×C8—671no—
111#125—1342no—
112#125—1342no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—671no—
115C2×C4⋊C4—671no—
116C2×C4⋊C4—1341no—
117C2×C4⋊C4—1341no—
118C2×C4⋊C4C2×D6711yescharacteristic
119C2×C4⋊C4C2×D6711yescharacteristic
120C2×C42C2×D6711yescharacteristic
121#107—1342no—
122#106—1342no—
123#95—21no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—1341no—
127C22×C4—1341no—
128C22×C4C22⋊D6711yescharacteristic
129C22×C4C22⋊D6711yescharacteristic
130C22×C4C22×D6711yescharacteristic
131C2×C8—672no—
132C2×C8—672no—
133C2×C8—1341no—
134C2×C8—1341no—
135C2×C8—1341no—
136C2×C8—1341no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—42no—
141C4⋊C4—672no—
142C4⋊C4—672no—
143C4⋊C4—1344no—
144C4⋊C4—1344no—
145C4⋊C4—1341no—
146C4⋊C4—1341no—
147C4⋊C4Dic13412yes—
148C42—21no—
149C42—21no—
150C23C2×C22⋊D6711yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—2681no—
164C2×C4—2681no—
165C2×C4—2681no—
166C2×C4—2681no—
167C2×C4—1342no—
168C2×C4—1342no—
169C2×C4D4×D6711yescharacteristic
170C2×C4D4×D6711yescharacteristic
171C2×C4Q8×D6711yescharacteristic
172C2×C4Q8×D6711yescharacteristic
173C2×C4C2×Dic13411yescharacteristic
174C2×C4#1176162811yescharacteristic
175C8—1342no—
176C8—1342no—
177C22#1452401111yescharacteristic
178C22#1452402211yescharacteristic
179C22#1452404111yescharacteristic
180C22#1452406311yescharacteristic
181C22#1452406311yescharacteristic
182C22#1452406911yescharacteristic
183C22#1452407411yescharacteristic
184C4—41no—
185C4—41no—
186C4—42no—
187C4—81no—
188C4—2682no—
189C4—2682no—
190C4#1452402111yescharacteristic
191C4#1452402111yescharacteristic
192C4#1452404211yescharacteristic
193C4#1452404211yescharacteristic
194C2#1686331611yescharacteristic
195C2#1686353911yescharacteristic
196C2#1686355611yescharacteristic
197C2#1686369611yescharacteristic
198C2#1686370311yescharacteristic
199C2#1686379511yescharacteristic
200C2#1686380211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D67
commutatorC22×C4×C67C23
FrattiniC22×C4C22×D67
Fitting#389×C67C2
socleC23×C67C2×D4
hypercenter#389D67
hypocenterC67#2059
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
101. C67#2059semidirect