Finite Group Databasebeta

← #21456832

Subgroups — #21456832

Order 7808.

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

normal subgroups only

This group has 390 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#16840319C211yesmaximal, characteristic, complemented
2#16840312C211yesmaximal, characteristic
3#16840156C212yesmaximal, complemented
4#16840122C212yesmaximal, complemented
5#16839973C212yesmaximal, complemented
6#16839963C212yesmaximal, complemented
7#16839926C214yesmaximal, complemented
8C61×#432C211yesmaximal, characteristic, complemented
9C2×#11758222C2212yes—
10C2×Dic244C2214yes—
11C2×#11758190C2214yes—
12#14519777C2211yescharacteristic
13#14519777C2211yescharacteristic
14#14519777C2211yescharacteristic
15#14519774C2211yescharacteristic
16#14519769—21no—
17#14519765C2212yes—
18#14519756—21no—
19#14519756C2212yes—
20#14519751—21no—
21#14519751—21no—
22C4×Dic122—21no—
23C4×Dic122C2212yes—
24C4×D244—21no—
25C4×D244—21no—
26#14519736—21no—
27#14519702C2214yes—
28#14519699C2214yes—
29C2×C42×C61C2211yescharacteristic
30C4⋊C8×C61C2212yes—
31C22⋊C8×C61C2212yes—
32#97×C61C2212yes—
33C22×C4×C61D411yescharacteristic
34C22×C4×C61D411yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C2×C22⋊D61—22no—
37#11758222—44no—
38C2×D244—21no—
39C2×D244—21no—
40C2×D244C2312yes—
41C2×C4×D61—22no—
42C2×Dic122—21no—
43C2×Dic122C2312yes—
44C2×Dic122C2312yes—
45C2×C8×C61C2314yes—
46C42×C61D411yescharacteristic
47C42×C61D411yescharacteristic
48C42×C61C2311yescharacteristic
49C42×C61C2311yescharacteristic
50C22⋊Dic61—22no—
51#11758198—22no—
52#11758198—22no—
53C4⋊Dic61—21no—
54C4⋊Dic61—21no—
55C4⋊Dic61—21no—
56C4⋊Dic61—21no—
57C4⋊Dic61—21no—
58C4⋊Dic61C2312yes—
59#11758196—22no—
60#11758196—22no—
61C4×Dic61—22no—
62Dic244—44no—
63#11758190—44no—
64C23×C61C2×D411yescharacteristic
65C22×D61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—41no—
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2411yescharacteristic
75C22⋊D61—44no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79D244—24no—
80D244—42no—
81D244—42no—
82C4×D61—44no—
83Dic122—22no—
84Dic122—22no—
85Dic122—24no—
86Dic122—42no—
87C8×C61—24no—
88C22×C61—21no—
89C22×C61—21no—
90C22×C61—21no—
91C22×C61C22×D411yescharacteristic
92C2×D61—42no—
93C2×D61—42no—
94C2×D61—42no—
95C4×C61—21no—
96C4×C61—21no—
97C4×C61—21no—
98C4×C61—21no—
99C4×C61#13712yes—
100C4×C61H(5,𝔽2)12yes—
101Dic61—42no—
102Dic61—42no—
103Dic61—42no—
104#3216—611nomaximal, Sylow
105C2×C61—41no—
106C2×C61#53511yescharacteristic
107C2×C61C2×#13711yescharacteristic
108C2×C61#57511yescharacteristic
109D61—82no—
110#533—611no—
111#532—611no—
112#497—612no—
113#489—612no—
114#462—612no—
115#460—612no—
116#452—614no—
117#432D6111yescharacteristic, complemented
118C61#321611yescharacteristic, complemented, Sylow
119C2×#41—612no—
120C2×Q16—614no—
121C2×SD16—614no—
122C4⋊Q8—611no—
123C4⋊Q8—611no—
124C4⋊Q8—611no—
125#127—611no—
126#125—1221no—
127#124—612no—
128C22⋊Q8—612no—
129C22⋊Q8—1221no—
130#121—1221no—
131#121—1221no—
132C4×Q8—612no—
133C4×Q8—1221no—
134C4×D4—1221no—
135C4×D4—1221no—
136#117—1221no—
137C2×C42C2×D6111yescharacteristic
138C4⋊C8C2×D6112yes—
139#103—614no—
140#102—614no—
141C22⋊C8C2×D6112yes—
142#97C2×D6112yes—
143#41—2444no—
144C2×Q8—612no—
145C2×Q8—612no—
146C2×Q8—1221no—
147C2×D4—612no—
148C2×D4—1222no—
149C2×D4—1221no—
150C2×D4—1221no—
151C22×C4—1222no—
152C22×C4D24411yescharacteristic
153C22×C4D24411yescharacteristic
154C22×C4C22×D6111yescharacteristic
155Q16—2444no—
156SD16—2444no—
157C2×C8C22×D6114yes—
158C4⋊C4—612no—
159C4⋊C4—1222no—
160C4⋊C4—1222no—
161C4⋊C4—1221no—
162C4⋊C4—1221no—
163C4⋊C4—1221no—
164C4⋊C4—1221no—
165C4⋊C4—1221no—
166C22⋊C4—1222no—
167C22⋊C4—1222no—
168C22⋊C4—1222no—
169C42—1222no—
170C42D24411yescharacteristic
171C42D24411yescharacteristic
172C42C22×D6111yescharacteristic
173C42C22×D6111yescharacteristic
174C23—1222no—
175C23C2×D24411yescharacteristic
176Q8—1222no—
177Q8—1222no—
178Q8—1224no—
179Q8—2442no—
180D4—1224no—
181D4—2442no—
182D4—2444no—
183D4—2442no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—41no—
187C2×C4—1222no—
188C2×C4—1222no—
189C2×C4—1222no—
190C2×C4—2444no—
191C2×C4C2×D24411yescharacteristic
192C2×C4C2×D24411yescharacteristic
193C2×C4C2×D24411yescharacteristic
194C2×C4C2×D24411yescharacteristic
195C2×C4C2×D24411yescharacteristic
196C2×C4C23×D6111yescharacteristic
197C8—24no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—2442no—
202C22—2442no—
203C22—2442no—
204C22C22×D24411yescharacteristic
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—2442no—
210C4—2442no—
211C4—2442no—
212C4#1451981012yes—
213C4#1451982312yes—
214C2—41no—
215C2—4882no—
216C2#1684033111yescharacteristic
217C2C2×#1451981011yescharacteristic
218C2#1684056211yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#432C2
socleC22×C61C22×D4
hypercenter#432D61
hypocenterC61#3216
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #16840319C2semidirect
3. #16840156C2semidirect
4. #16840122C2semidirect
5. #16839973C2semidirect
6. #16839963C2semidirect
7. #16839926C2semidirect
8. C61×#432C2semidirect
117. #432D61semidirect
118. C61#3216semidirect