Finite Group Databasebeta

← #22561587

Subgroups — #22561587

Order 8576.

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

normal subgroups only

This group has 248 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×#14523974C211yesmaximal, characteristic
2C2×C4⋊(C67⋊C8)C211yesmaximal, characteristic
3C2×#14523966C211yesmaximal, characteristic
4C2×#14523966C211yesmaximal, characteristic
5#16863302C211yesmaximal, characteristic
6#16863158C211yesmaximal, characteristic
7#389×C67C211yesmaximal, characteristic
8C22×Dic134C2211yescharacteristic
9C22×C67⋊C8C2211yescharacteristic
10C22×C67⋊C8C2211yescharacteristic
11C2×C4⋊Dic67C2211yescharacteristic
12#14523974—22no—
13C4⋊(C67⋊C8)—22no—
14#14523966—22no—
15#14523966—22no—
16C67⋊#95—21no—
17C67⋊#95—21no—
18C2×C4⋊C4×C67—21no—
19C2×C4⋊C4×C67C2211yescharacteristic
20C2×C4⋊C4×C67C2211yescharacteristic
21C2×C42×C67C2211yescharacteristic
22#95×C67—21no—
23C2×Dic134—21no—
24C2×Dic134—21no—
25C2×Dic134—21no—
26C2×Dic134—21no—
27C2×Dic134—21no—
28C2×Dic134Q812yes—
29C22×Dic67—21no—
30C22×Dic67—21no—
31C2×C67⋊C8—21no—
32C2×C67⋊C8—21no—
33C2×C67⋊C8—21no—
34C2×C67⋊C8—21no—
35C2×C67⋊C8—21no—
36C2×C67⋊C8D412yes—
37C4⋊Dic67—21no—
38C4⋊Dic67—21no—
39C22×C4×C67—21no—
40C22×C4×C67—21no—
41C22×C4×C67D411yescharacteristic
42C22×C4×C67D411yescharacteristic
43C22×C4×C67C2311yescharacteristic
44C4⋊C4×C67—21no—
45C4⋊C4×C67—21no—
46C4⋊C4×C67—21no—
47C4⋊C4×C67—42no—
48C4⋊C4×C67D412yes—
49C42×C67—21no—
50C42×C67—21no—
51C23×C67C2×D411yescharacteristic
52C2×C4×C67—21no—
53C2×C4×C67—21no—
54C2×C4×C67—21no—
55C2×C4×C67—22no—
56C2×C4×C67—21no—
57C2×C4×C67—21no—
58C2×C4×C67—41no—
59C2×C4×C67—41no—
60C2×C4×C67—41no—
61C2×C4×C67—41no—
62C2×C4×C67—41no—
63C2×C4×C67SD1612yes—
64C2×C4×C67C2×D411yescharacteristic
65C2×C4×C67C2×D411yescharacteristic
66C2×C4×C67C2×Q811yescharacteristic
67C2×C4×C67#4111yescharacteristic
68C2×C4×C67#4111yescharacteristic
69C2×C4×C67#4111yescharacteristic
70C2×Dic67—22no—
71C2×Dic67—41no—
72C2×Dic67—41no—
73C2×Dic67—41no—
74C2×Dic67—41no—
75C2×Dic67—41no—
76Dic134—22no—
77Dic134—22no—
78Dic134—41no—
79Dic134—41no—
80C67⋊C8—22no—
81C67⋊C8—41no—
82C22×C67#12111yescharacteristic
83C22×C67#12111yescharacteristic
84C22×C67C22⋊Q811yescharacteristic
85C22×C67C2×SD1611yescharacteristic
86C22×C67#13511yescharacteristic
87C22×C67#13711yescharacteristic
88C22×C67#13711yescharacteristic
89C4×C67—22no—
90C4×C67—42no—
91C4×C67—41no—
92C4×C67—81no—
93C4×C67#12111yescharacteristic
94C4×C67C22⋊Q811yescharacteristic
95C4×C67C22⋊Q811yescharacteristic
96C4×C67#12611yescharacteristic
97Dic67—42no—
98Dic67—81no—
99C2×C67#39611yescharacteristic
100C2×C67#46111yescharacteristic
101C2×C67#46411yescharacteristic
102C2×C67#46511yescharacteristic
103C2×C67#47011yescharacteristic
104C2×C67#47511yescharacteristic
105C2×C67#47911yescharacteristic
106#2066—671nomaximal, Sylow
107C67#206611yescharacteristic, complemented, Sylow
108C2×#106—671no—
109C2×C4⋊C8—671no—
110C2×#103—671no—
111C2×#103—671no—
112#391—671no—
113#389D6711yescharacteristic
114#340—671no—
115C22×Q8—671no—
116C22×C8—671no—
117C22×C8—671no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—671no—
120C2×C4⋊C4C2×D6711yescharacteristic
121C2×C4⋊C4C2×D6711yescharacteristic
122C2×C42C2×D6711yescharacteristic
123#106—1342no—
124C4⋊C8—1342no—
125#103—1342no—
126#103—1342no—
127#95—21no—
128#95—1341no—
129#95—1341no—
130C2×Q8—672no—
131C2×Q8—1341no—
132C2×Q8—1341no—
133C2×Q8—1341no—
134C2×Q8—1341no—
135C2×Q8—1341no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—1341no—
139C22×C4—1341no—
140C22×C4C22⋊D6711yescharacteristic
141C22×C4C22⋊D6711yescharacteristic
142C22×C4C22×D6711yescharacteristic
143C2×C8—672no—
144C2×C8—1341no—
145C2×C8—1341no—
146C2×C8—1341no—
147C2×C8—1341no—
148C2×C8—1341no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—42no—
153C4⋊C4—1341no—
154C4⋊C4—1341no—
155C4⋊C4D26812yes—
156C42—21no—
157C42—21no—
158C23C2×C22⋊D6711yescharacteristic
159Q8—2681no—
160Q8—2681no—
161Q8—1342no—
162Q8—1342no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—2681no—
175C2×C4—2681no—
176C2×C4—2681no—
177C2×C4—2681no—
178C2×C4—2681no—
179C2×C4—1342no—
180C2×C4#1176161612yes—
181C2×C4D4×D6711yescharacteristic
182C2×C4C2×D26811yescharacteristic
183C2×C4Q8×D6711yescharacteristic
184C2×C4#1176162711yescharacteristic
185C2×C4#1176162811yescharacteristic
186C2×C4#1176162911yescharacteristic
187C8—2681no—
188C8—1342no—
189C22#1452401511yescharacteristic
190C22#1452401711yescharacteristic
191C22#1452401911yescharacteristic
192C22C2×#1176161611yescharacteristic
193C22#1452406311yescharacteristic
194C22#1452407311yescharacteristic
195C22#1452407411yescharacteristic
196C4—22no—
197C4—42no—
198C4—41no—
199C4—81no—
200C4—2682no—
201C4—5361no—
202C4#1452401811yescharacteristic
203C4#1452402111yescharacteristic
204C4#1452402311yescharacteristic
205C4#1452403811yescharacteristic
206C2#1686331811yescharacteristic
207C2#1686360111yescharacteristic
208C2#1686361811yescharacteristic
209C2#1686362311yescharacteristic
210C2#1686365211yescharacteristic
211C2#1686367811yescharacteristic
212C2#1686370011yescharacteristic
subgroupG/H
centerC23C2×C22⋊D67
commutatorC22×C4×C67C23
FrattiniC22×C4C22×D67
Fitting#389×C67C2
socleC23×C67C2×D4
hypercenter#389D67
hypocenterC67#2066
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
107. C67#2066semidirect