Finite Group Databasebeta

← #21456826

Subgroups — #21456826

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#16840312C211yesmaximal, characteristic
2#16840154C212yesmaximal, complemented
3#16840124C212yesmaximal, complemented
4#16839972C212yesmaximal, complemented
5#16839962C212yesmaximal, complemented
6#16839922C214yesmaximal, complemented
7#16839819C211yesmaximal, characteristic, complemented
8C61×#533C211yesmaximal, characteristic, complemented
9C2×#11758222C2212yes—
10C2×#11758202C2214yes—
11C2×#11758201C2214yes—
12#14519777C2211yescharacteristic
13#14519774C2211yescharacteristic
14#14519765C2212yes—
15#14519751—21no—
16#14519751—21no—
17C4×D244—21no—
18C4×D244—21no—
19C4⋊#92418C2212yes—
20#14519700C2214yes—
21#14519697C2214yes—
22C22⋊#92418C2212yes—
23#14519688C2212yes—
24C4⋊Q8×C61C2211yescharacteristic
25C4⋊Q8×C61C2211yescharacteristic
26#125×C61—21no—
27C22⋊Q8×C61—21no—
28C22⋊Q8×C61C2212yes—
29C4×Q8×C61—21no—
30C4×Q8×C61C2212yes—
31#117×C61—21no—
32C2×C42×C61C2211yescharacteristic
33C2×Q8×C61—21no—
34C2×Q8×C61C2312yes—
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×Dic122C2312yes—
45C4⋊C4×C61—21no—
46C4⋊C4×C61—21no—
47C4⋊C4×C61—21no—
48C4⋊C4×C61—22no—
49C4⋊C4×C61—22no—
50C4⋊C4×C61C2312yes—
51C22⋊C4×C61—22no—
52C42×C61—22no—
53C42×C61D411yescharacteristic
54C42×C61D411yescharacteristic
55C42×C61C2311yescharacteristic
56C42×C61C2311yescharacteristic
57#11758202—44no—
58#11758201—44no—
59#11758198—22no—
60#11758198—22no—
61C4⋊Dic61—21no—
62C4⋊Dic61—21no—
63C2×#92418C2314yes—
64C23×C61C2×D411yescharacteristic
65C22×D61—22no—
66Q8×C61—22no—
67Q8×C61—22no—
68Q8×C61—42no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—41no—
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2411yescharacteristic
80C22⋊D61—44no—
81C2×Dic61—22no—
82D244—24no—
83D244—42no—
84D244—42no—
85C4×D61—44no—
86Dic122—24no—
87#92418—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—42no—
100C4×C61—42no—
101C4×C61#13712yes—
102C4×C61H(5,𝔽2)12yes—
103Dic61—42no—
104#3216—611nomaximal, Sylow
105C2×C61—41no—
106C2×C61#53511yescharacteristic
107C2×C61C2×#13711yescharacteristic
108C2×C61#57511yescharacteristic
109D61—82no—
110#533D6111yescharacteristic, complemented
111#532—611no—
112#497—612no—
113#489—612no—
114#462—612no—
115#460—612no—
116#452—614no—
117#432—611no—
118C61#321611yescharacteristic, complemented, Sylow
119C2×#41—612no—
120C2×Q16—614no—
121C2×SD16—614no—
122C4⋊Q8—611no—
123C4⋊Q8C2×D6111yescharacteristic
124C4⋊Q8C2×D6111yescharacteristic
125#127—611no—
126#125—21no—
127#124—612no—
128C22⋊Q8—21no—
129C22⋊Q8C2×D6112yes—
130#121—1221no—
131#121—1221no—
132C4×Q8—21no—
133C4×Q8C2×D6112yes—
134C4×D4—1221no—
135C4×D4—1221no—
136#117—21no—
137C2×C42C2×D6111yescharacteristic
138C4⋊C8—612no—
139#103—614no—
140#102—614no—
141C22⋊C8—612no—
142#97—612no—
143#41—2444no—
144C2×Q8—21no—
145C2×Q8—612no—
146C2×Q8C22×D6112yes—
147C2×D4—612no—
148C2×D4—1222no—
149C2×D4—1221no—
150C2×D4—1221no—
151C22×C4—1222no—
152C22×C4C22⋊D6111yescharacteristic
153C22×C4C22⋊D6111yescharacteristic
154C22×C4C22×D6111yescharacteristic
155Q16—2444no—
156SD16—2444no—
157C2×C8—614no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—1221no—
164C4⋊C4—1221no—
165C4⋊C4C22×D6112yes—
166C22⋊C4—22no—
167C22⋊C4—1222no—
168C22⋊C4—1222no—
169C42—22no—
170C42C22⋊D6111yescharacteristic
171C42C22⋊D6111yescharacteristic
172C42C22×D6111yescharacteristic
173C42C22×D6111yescharacteristic
174C23—1222no—
175C23C2×C22⋊D6111yescharacteristic
176Q8—22no—
177Q8—22no—
178Q8—42no—
179Q8—1224no—
180D4—1224no—
181D4—2442no—
182D4—2444no—
183D4—2442no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—1222no—
190C2×C4—2444no—
191C2×C4C2×C22⋊D6111yescharacteristic
192C2×C4C2×C22⋊D6111yescharacteristic
193C2×C4C2×C22⋊D6111yescharacteristic
194C2×C4C2×C22⋊D6111yescharacteristic
195C2×C4C2×C22⋊D6111yescharacteristic
196C2×C4C23×D6111yescharacteristic
197C8—1224no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—2442no—
202C22—2442no—
203C22—2442no—
204C22C22×C22⋊D6111yescharacteristic
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—42no—
210C4—42no—
211C4—2442no—
212C4#1451980812yes—
213C4#1451982312yes—
214C2—41no—
215C2—4882no—
216C2#1684032611yescharacteristic
217C2C2×#1451980811yescharacteristic
218C2#1684056011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#533C2
socleC22×C61C22×D4
hypercenter#533D61
hypocenterC61#3216
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #16840154C2semidirect
3. #16840124C2semidirect
4. #16839972C2semidirect
5. #16839962C2semidirect
6. #16839922C2semidirect
7. #16839819C2semidirect
8. C61×#533C2semidirect
110. #533D61semidirect
118. C61#3216semidirect