Finite Group Databasebeta

← #21456283

Subgroups — #21456283

Order 7808.

572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519808C212yesmaximal, complemented
2C2×#14519803C212yesmaximal, complemented
3#16840312C211yesmaximal, characteristic, complemented
4#16840157C212yesmaximal, complemented
5#16840152C212yesmaximal, complemented
6#16840144C214yesmaximal, complemented
7C4×#11758194C211yesmaximal, characteristic, complemented
8C2×#124×C61C211yesmaximal, characteristic, complemented
9C2×#11758222C2212yes—
10#14519808—28no—
11#14519803—28no—
12C2×#11758202C2214yescomplemented
13C2×#11758200C2214yes—
14C2×#11758201C2214yescomplemented
15C2×#11758199C2214yes—
16C2×#11758194C2212yes—
17#14519777C2211yescharacteristic, complemented
18#14519774C2211yescharacteristic, complemented
19#14519765C2212yescomplemented
20#14519751—22no—
21C4×D244—22no—
22#14519688C2212yescomplemented
23C4×#92418C2212yescomplemented
24C22×Q8×C61C2211yescharacteristic
25C22×D4×C61C2211yescharacteristic
26#124×C61—22no—
27#124×C61C2212yes—
28#124×C61C2212yes—
29C2×C22⋊C4×C61—22no—
30C2×C42×C61C2211yescharacteristic
31C24×C61—21no—
32C2×Q8×C61—21no—
33C2×Q8×C61—24no—
34C2×Q8×C61C2312yes—
35C2×D4×C61—24no—
36C2×D4×C61—21no—
37C2×D4×C61C2312yes—
38C22×C4×C61—21no—
39C22×C4×C61D412yes—
40C22×C4×C61C2311yescharacteristic
41C2×C22⋊D61—22no—
42#11758222—24no—
43#11758222—24no—
44C2×D244—22no—
45C2×D244C2312yes—
46C2×C4×D61—22no—
47C2×Dic122C2312yes—
48C22⋊C4×C61—24no—
49C22⋊C4×C61—24no—
50C42×C61D412yes—
51C42×C61C2311yescharacteristic
52C42×C61C2311yescharacteristic
53#11758202—28no—
54#11758201—28no—
55#11758200—28no—
56#11758199—28no—
57#11758198—24no—
58C4⋊Dic61—22no—
59#11758194D418yescomplemented
60C2×#92418C2314yes—
61C23×C61—22no—
62C23×C61—44no—
63C23×C61—42no—
64C23×C61C2×D411yescharacteristic
65C22×D61—22no—
66Q8×C61—24no—
67Q8×C61—42no—
68D4×C61—24no—
69D4×C61—42no—
70C2×C4×C61—22no—
71C2×C4×C61—42no—
72C2×C4×C61—42no—
73C2×C4×C61C2×D412yes—
74C2×C4×C61C2×D412yes—
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D414yes—
77C2×C4×C61C2411yescharacteristic
78C22⋊D61—44no—
79C2×Dic61—22no—
80D244—22no—
81D244—22no—
82D244—44no—
83C4×D61—44no—
84Dic122—22no—
85Dic122—22no—
86#92418C2×D418yes—
87C22×C61—22no—
88C22×C61—42no—
89C22×C61—44no—
90C22×C61—84no—
91C22×C61#12712yes—
92C22×C61C22×D411yescharacteristic
93C2×D61—42no—
94C2×D61—44no—
95C4×C61—22no—
96C4×C61—22no—
97C4×C61—42no—
98C4×C61#12712yes—
99C4×C61C22×D412yes—
100Dic61—42no—
101#3153—611nomaximal, Sylow
102C2×C61—22no—
103C2×C61—82no—
104C2×C61C2×#12711yescharacteristic
105C2×C61#57512yes—
106D61—82no—
107C2×#137—612no—
108C2×AGL(1,ℤ/8)—612no—
109#532—611no—
110C2×#124D6111yescharacteristic, complemented
111#497—612no—
112#496—612no—
113#495—614no—
114C4×M16—611no—
115C61#315311yescharacteristic, complemented, Sylow
116C2×#41—612no—
117C22×Q8C2×D6111yescharacteristic
118C22×D4C2×D6111yescharacteristic
119#137—1228no—
120AGL(1,ℤ/8)—1228no—
121C2×Q16—614no—
122C2×SD16—614no—
123C2×SD16—614no—
124C2×D8—614no—
125C2×M16—612no—
126C4⋊Q8—611no—
127#127—611no—
128#124—22no—
129#124—612no—
130#124C2×D6112yes—
131#124C2×D6112yes—
132#121—1222no—
133C4×D4—1222no—
134C2×C22⋊C4—22no—
135C2×C42C2×D6111yescharacteristic
136#97—612no—
137C4×C8—612no—
138C24—21no—
139#41—1224no—
140#41—1224no—
141C2×Q8—21no—
142C2×Q8—24no—
143C2×Q8—612no—
144C2×Q8C22×D6112yes—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—612no—
148C2×D4—1222no—
149C2×D4—1222no—
150C2×D4C22×D6112yes—
151C22×C4—21no—
152C22×C4—1222no—
153C22×C4C22⋊D6112yes—
154C22×C4C22×D6111yescharacteristic
155Q16—1228no—
156SD16—1228no—
157SD16—1228no—
158D8—1228no—
159M16—618no—
160C2×C8—614no—
161C4⋊C4—1222no—
162C22⋊C4—24no—
163C22⋊C4—24no—
164C22⋊C4—1224no—
165C42C22⋊D6112yes—
166C42C22×D6111yescharacteristic
167C42C22×D6111yescharacteristic
168C23—22no—
169C23—44no—
170C23—42no—
171C23—1222no—
172C23C2×C22⋊D6111yescharacteristic
173Q8—24no—
174Q8—42no—
175Q8—1222no—
176Q8—1222no—
177D4—24no—
178D4—42no—
179D4—1222no—
180D4—1222no—
181D4—2444no—
182D4—2444no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—1222no—
187C2×C4—2444no—
188C2×C4D4×D6114yes—
189C2×C4C2×C22⋊D6112yes—
190C2×C4C2×C22⋊D6112yes—
191C2×C4C2×C22⋊D6111yescharacteristic
192C2×C4C23×D6111yescharacteristic
193C8—618no—
194C22—22no—
195C22—42no—
196C22—44no—
197C22—84no—
198C22—2442no—
199C22—2444no—
200C22#1451977312yes—
201C22C22×C22⋊D6111yescharacteristic
202C4—22no—
203C4—22no—
204C4—42no—
205C4—2442no—
206C4#1451977312yes—
207C4C2×D4×D6112yes—
208C2—22no—
209C2—82no—
210C2—4882no—
211C2C2×#1451977311yescharacteristic
212C2#1684056012yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#124×C61C2
socleC22×C61C22×D4
hypercenterC2×#124D61
hypocenterC61#3153
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#14519808C2semidirect
2. C2×#14519803C2semidirect
3. #16840312C2semidirect
4. #16840157C2semidirect
5. #16840152C2semidirect
6. #16840144C2semidirect
7. C4×#11758194C2semidirect
8. C2×#124×C61C2semidirect
12. C2×#11758202C22semidirect
14. C2×#11758201C22semidirect
17. #14519777C22semidirect
18. #14519774C22semidirect
19. #14519765C22semidirect
22. #14519688C22semidirect
23. C4×#92418C22semidirect
59. #11758194D4semidirect
110. C2×#124D61semidirect
115. C61#3153semidirect