Finite Group Databasebeta

← #21457009

Subgroups — #21457009

Order 7808.

368 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 121 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#16840312C211yesmaximal, characteristic
2#16840172C212yesmaximal, complemented
3#16840128C212yesmaximal, complemented
4#16840080C212yesmaximal, complemented
5#16840075C212yesmaximal, complemented
6#16840059C214yesmaximal, complemented
7#16839819C211yesmaximal, characteristic, complemented
8C2×#125×C61C211yesmaximal, characteristic, complemented
9C2×#11758222—21no—
10#14519777C2211yescharacteristic
11#14519774C2211yescharacteristic
12#14519765—21no—
13#14519751—21no—
14#14519751C2212yes—
15C4×D244—21no—
16C4×D244C2212yes—
17#14519710C2214yes—
18#14519708C2214yes—
19C4⋊#92418C2212yes—
20#14519697C2214yes—
21#14519697C2214yes—
22C22⋊#92418C2212yes—
23#14519688C2212yes—
24#125×C61—21no—
25#125×C61—21no—
26#125×C61C2212yes—
27#125×C61C2212yes—
28C2×C4⋊C4×C61—21no—
29C2×C4⋊C4×C61—21no—
30C2×C4⋊C4×C61C2211yescharacteristic
31C2×C4⋊C4×C61C2211yescharacteristic
32C2×C42×C61C2211yescharacteristic
33C22×C4×C61—21no—
34C22×C4×C61—21no—
35C22×C4×C61D411yescharacteristic
36C22×C4×C61D411yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C2×C22⋊D61—22no—
39#11758222—44no—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244C2312yes—
43C2×C4×D61—22no—
44C2×Dic122—21no—
45C4⋊C4×C61—22no—
46C4⋊C4×C61—22no—
47C4⋊C4×C61—22no—
48C4⋊C4×C61—22no—
49C4⋊C4×C61—21no—
50C4⋊C4×C61—21no—
51C4⋊C4×C61C2312yes—
52C4⋊C4×C61C2312yes—
53C42×C61D411yescharacteristic
54C42×C61D411yescharacteristic
55C42×C61C2311yescharacteristic
56C42×C61C2311yescharacteristic
57#11758198—22no—
58#11758198—22no—
59C4⋊Dic61—21no—
60C4⋊Dic61C2312yes—
61C2×#92418C2314yes—
62C23×C61C2×D411yescharacteristic
63C22×D61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—41no—
69C2×C4×C61—42no—
70C2×C4×C61—42no—
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2411yescharacteristic
77C22⋊D61—44no—
78C2×Dic61—22no—
79D244—24no—
80D244—42no—
81D244—42no—
82C4×D61—44no—
83Dic122—42no—
84#92418—24no—
85C22×C61—21no—
86C22×C61—21no—
87C22×C61AGL(1,ℤ/8)12yes—
88C22×C61C22×D411yescharacteristic
89C2×D61—42no—
90C2×D61—42no—
91C2×D61—42no—
92C4×C61—21no—
93C4×C61—21no—
94C4×C61—21no—
95C4×C61—21no—
96C4×C61—21no—
97C4×C61—42no—
98C4×C61—42no—
99C4×C612−1+412yes—
100Dic61—42no—
101#3234—611nomaximal, Sylow
102C2×C61—22no—
103C2×C61#53611yescharacteristic
104C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
105C2×C61#57511yescharacteristic
106D61—82no—
107#532—611no—
108C2×#125D6111yescharacteristic, complemented
109#501—612no—
110#490—612no—
111#481—612no—
112#480—612no—
113#478—614no—
114#432—611no—
115C61#323411yescharacteristic, complemented, Sylow
116C2×#41—1221no—
117C4⋊Q8—611no—
118#127—611no—
119#125—21no—
120#125—21no—
121#125C2×D6112yes—
122#125C2×D6112yes—
123#124—1221no—
124#121—612no—
125#121—1221no—
126C4×D4—612no—
127C4×D4—1221no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4C2×D6111yescharacteristic
131C2×C4⋊C4C2×D6111yescharacteristic
132C2×C42C2×D6111yescharacteristic
133#107—614no—
134#106—614no—
135C4⋊C8—612no—
136#102—614no—
137#102—614no—
138C22⋊C8—612no—
139#97—612no—
140#41—2444no—
141C2×Q8—1221no—
142C2×D4—612no—
143C2×D4—1222no—
144C2×D4—1221no—
145C2×D4—1221no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—1222no—
149C22×C4C22⋊D6111yescharacteristic
150C22×C4C22⋊D6111yescharacteristic
151C22×C4C22×D6111yescharacteristic
152C2×C8—614no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—612no—
160C4⋊C4—1221no—
161C4⋊C4C22×D6112yes—
162C4⋊C4C22×D6112yes—
163C22⋊C4—1222no—
164C22⋊C4—1222no—
165C42C22⋊D6111yescharacteristic
166C42C22⋊D6111yescharacteristic
167C42C22×D6111yescharacteristic
168C42C22×D6111yescharacteristic
169C23—1222no—
170C23C2×C22⋊D6111yescharacteristic
171Q8—2442no—
172D4—1224no—
173D4—2442no—
174D4—2442no—
175D4—2444no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—1222no—
184C2×C4—2444no—
185C2×C4C2×C22⋊D6111yescharacteristic
186C2×C4C2×C22⋊D6111yescharacteristic
187C2×C4C2×C22⋊D6111yescharacteristic
188C2×C4C2×C22⋊D6111yescharacteristic
189C2×C4C2×C22⋊D6111yescharacteristic
190C2×C4C23×D6111yescharacteristic
191C8—1224no—
192C22—21no—
193C22—21no—
194C22—2442no—
195C22—2442no—
196C22—2442no—
197C22#1451980212yes—
198C22C22×C22⋊D6111yescharacteristic
199C4—21no—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—21no—
204C4—42no—
205C4—42no—
206C4—2442no—
207C4#1451982512yes—
208C2—22no—
209C2—4882no—
210C2#1684033611yescharacteristic
211C2C2×#1451980211yescharacteristic
212C2#1684056011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#125×C61C2
socleC22×C61C22×D4
hypercenterC2×#125D61
hypocenterC61#3234
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #16840172C2semidirect
3. #16840128C2semidirect
4. #16840080C2semidirect
5. #16840075C2semidirect
6. #16840059C2semidirect
7. #16839819C2semidirect
8. C2×#125×C61C2semidirect
108. C2×#125D61semidirect
115. C61#3234semidirect