Finite Group Databasebeta

← #22566156

Subgroups — #22566156

Order 8576.

416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14524042C211yesmaximal, characteristic
2C2×#14524033C211yesmaximal, characteristic
3#16863338C212yesmaximal
4#16863337C212yesmaximal
5#16863336C211yesmaximal, characteristic
6#16863335C211yesmaximal, characteristic
7#16863334C211yesmaximal, characteristic
8#16863300C212yesmaximal
9#16863300C212yesmaximal
10#16863241C211yesmaximal, characteristic
11#400×C67C211yesmaximal, characteristic
12C22×Dic134C2212yes—
13#14524042—24no—
14#14524033—24no—
15C2×C4⋊Dic67C2211yescharacteristic
16C2×C4⋊Dic67C2211yescharacteristic
17C2×Dic67⋊C4C2211yescharacteristic
18C2×Dic67⋊C4C2211yescharacteristic
19C2×Dic67⋊C4C2211yescharacteristic
20C2×Dic67⋊C4C2211yescharacteristic
21C2×Dic67⋊C4C2212yes—
22C2×C4×Dic67C2212yes—
23C2×C4×Dic67C2211yescharacteristic
24C67⋊#95C2211yescharacteristic
25C67⋊#95C2212yes—
26C67⋊#95C2212yes—
27C67⋊#95C2212yes—
28C67⋊#95C2212yes—
29C67⋊#95C2212yes—
30C67⋊#95C2212yes—
31C67⋊#95C2212yes—
32C2×C4⋊C4×C67C2211yescharacteristic
33C2×C4⋊C4×C67C2211yescharacteristic
34#95×C67C2211yescharacteristic
35#95×C67C2212yes—
36#95×C67C2212yes—
37C2×Dic134—24no—
38C2×Dic134—28no—
39C22×Dic67C2312yes—
40C22×Dic67C2311yescharacteristic
41C22×Dic67C2311yescharacteristic
42C22×Dic67C2312yes—
43C22×Dic67C2311yescharacteristic
44C22×Dic67C2311yescharacteristic
45C4⋊Dic67—22no—
46C4⋊Dic67—22no—
47Dic67⋊C4—22no—
48Dic67⋊C4—22no—
49Dic67⋊C4—22no—
50Dic67⋊C4—22no—
51Dic67⋊C4—24no—
52C4×Dic67—24no—
53C4×Dic67D414yes—
54C22×C4×C67C2311yescharacteristic
55C22×C4×C67C2311yescharacteristic
56C22×C4×C67C2312yes—
57C22×C4×C67C2312yes—
58C22×C4×C67C2311yescharacteristic
59C4⋊C4×C67—22no—
60C4⋊C4×C67—22no—
61C23×C67C2411yescharacteristic
62C2×C4×C67—22no—
63C2×C4×C67—21no—
64C2×C4×C67—21no—
65C2×C4×C67—22no—
66C2×C4×C67—22no—
67C2×C4×C67—24no—
68C2×C4×C67—21no—
69C2×C4×C67—22no—
70C2×C4×C67—22no—
71C2×C4×C67—22no—
72C2×C4×C67—21no—
73C2×C4×C67C2×D412yes—
74C2×Dic67—21no—
75C2×Dic67—21no—
76C2×Dic67—21no—
77C2×Dic67—21no—
78C2×Dic67—22no—
79C2×Dic67—22no—
80C2×Dic67—24no—
81C2×Dic67—22no—
82C2×Dic67—21no—
83C2×Dic67—22no—
84C2×Dic67—21no—
85C2×Dic67—22no—
86C2×Dic67C2×D412yes—
87C2×Dic67C2×D412yes—
88C2×Dic67#4114yes—
89Dic134—48no—
90C22×C67C22×D411yescharacteristic
91C22×C67C2×#4112yes—
92C22×C672−1+411yescharacteristic
93C22×C672−1+412yes—
94C22×C672−1+411yescharacteristic
95C4×C67—22no—
96C4×C67—42no—
97C4×C67—41no—
98C4×C67—41no—
99C4×C67—42no—
100Dic67—22no—
101Dic67—42no—
102Dic67—41no—
103Dic67—41no—
104Dic67—42no—
105Dic67#12414yes—
106C2×C67C2×#12411yescharacteristic
107C2×C67#53611yescharacteristic
108C2×C67#53611yescharacteristic
109C2×C67#54112yes—
110C2×C67#54112yes—
111#2642—671nomaximal, Sylow
112C67#264211yescharacteristic, complemented, Sylow
113C2×C4⋊Q8—671no—
114C2×#125—671no—
115#400—671no—
116#400—671no—
117#400—671no—
118#400—672no—
119#400—672no—
120#400D6711yescharacteristic
121#391—672no—
122#391—672no—
123#376—671no—
124C22×Q8—672no—
125C4⋊Q8—1344no—
126#125—1344no—
127C2×C4⋊C4—671no—
128C2×C4⋊C4—671no—
129C2×C4⋊C4—671no—
130C2×C4⋊C4—671no—
131C2×C4⋊C4—671no—
132C2×C4⋊C4—672no—
133C2×C4⋊C4—671no—
134C2×C4⋊C4C2×D6711yescharacteristic
135C2×C4⋊C4C2×D6711yescharacteristic
136C2×C42—671no—
137C2×C42—672no—
138#95—672no—
139#95—671no—
140#95—672no—
141#95—672no—
142#95—672no—
143#95—672no—
144#95—672no—
145#95—672no—
146#95C2×D6711yescharacteristic
147#95C2×D6712yes—
148#95C2×D6712yes—
149C2×Q8—1344no—
150C2×Q8—1348no—
151C22×C4—671no—
152C22×C4—671no—
153C22×C4—672no—
154C22×C4—671no—
155C22×C4—671no—
156C22×C4—672no—
157C22×C4C22×D6712yes—
158C22×C4C22×D6711yescharacteristic
159C22×C4C22×D6711yescharacteristic
160C22×C4C22×D6712yes—
161C22×C4C22×D6711yescharacteristic
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—1342no—
165C4⋊C4—1342no—
166C4⋊C4—1342no—
167C4⋊C4—1342no—
168C4⋊C4—1344no—
169C4⋊C4—1342no—
170C4⋊C4—1342no—
171C42—674no—
172C42—1344no—
173C23C23×D6711yescharacteristic
174Q8—2688no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—672no—
187C2×C4—674no—
188C2×C4—672no—
189C2×C4—1341no—
190C2×C4—1341no—
191C2×C4—1342no—
192C2×C4—1342no—
193C2×C4—1344no—
194C2×C4—1342no—
195C2×C4—1342no—
196C2×C4—1341no—
197C2×C4—1342no—
198C2×C4—1341no—
199C2×C4—1341no—
200C2×C4—1341no—
201C2×C4D4×D6712yes—
202C22C2×D4×D6711yescharacteristic
203C22#41×D6712yes—
204C22#1452409011yescharacteristic
205C22#1452409012yes—
206C22#1452409111yescharacteristic
207C4—22no—
208C4—42no—
209C4—42no—
210C4—41no—
211C4—41no—
212C4—2682no—
213C4—2682no—
214C4—2681no—
215C4—2681no—
216C4—674no—
217C4—1342no—
218C2#124×D6711yescharacteristic
219C2#1686396811yescharacteristic
220C2#1686396911yescharacteristic
221C2#1686400312yes—
222C2#1686400512yes—
subgroupG/H
center, FrattiniC23C23×D67
commutator, socleC23×C67C24
Fitting#400×C67C2
hypercenter#400D67
hypocenterC67#2642
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
112. C67#2642semidirect