Finite Group Databasebeta

← #21458909

Subgroups — #21458909

Order 7808.

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

normal subgroups only

This group has 380 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#16840497C212yesmaximal, complemented
2#16840151C212yesmaximal, complemented
3#16840146C211yesmaximal, characteristic, complemented
4#16839985C212yesmaximal, complemented
5#16839978C212yesmaximal, complemented
6#16839958C212yesmaximal, complemented
7#16839864C212yesmaximal, complemented
8C4×D488C211yesmaximal, characteristic, complemented
9C61×#446C211yesmaximal, characteristic, complemented
10C2×Dic244C2211yescharacteristic
11C2×#11758190C2212yes—
12C2×#11758190C2212yes—
13C2×D488C2211yescharacteristic
14C2×D488C2211yescharacteristic
15C2×D488C2212yes—
16#14519774C2212yes—
17#14519766—22no—
18#14519765C2212yes—
19#14519765C2212yes—
20#14519762—22no—
21#14519762—22no—
22C4×Dic122C2212yes—
23C4×D244C2212yes—
24C4×D244C2212yes—
25#14519739—22no—
26#14519711C2211yescharacteristic
27#14519702C2212yes—
28#14519699C2212yes—
29#14519699C2212yes—
30C4×Q8×C61C2211yescharacteristic
31C4⋊C8×C61C2212yes—
32C4⋊C8×C61C2211yescharacteristic
33#97×C61C2212yes—
34C4×C8×C61C2211yescharacteristic
35C2×Q8×C61D411yescharacteristic
36C2×D244—22no—
37C2×D244—22no—
38C2×D244C2312yes—
39C2×D244C2312yes—
40C2×C4×D61—22no—
41C2×C4×D61—22no—
42C2×Dic122C2312yes—
43C2×C8×C61C2311yescharacteristic
44C2×C8×C61C2312yes—
45C2×C8×C61C2311yescharacteristic
46C4⋊C4×C61D412yes—
47C4⋊C4×C61D411yescharacteristic
48C42×C61C2311yescharacteristic
49C42×C61C2312yes—
50#11758198—22no—
51#11758198—22no—
52#11758198—22no—
53#11758198—22no—
54#11758198—22no—
55#11758198—22no—
56C4⋊Dic61C2312yes—
57#11758196—22no—
58C4×Dic61—22no—
59Dic244—41no—
60D488—22no—
61D488—42no—
62D488—41no—
63#11758190—24no—
64#11758190—42no—
65C22×D61—22no—
66C22×D61—22no—
67Q8×C61—41no—
68C2×C4×C61C2×D412yes—
69C2×C4×C61C2×D412yes—
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2411yescharacteristic
73C2×Dic61—22no—
74C2×Dic61—22no—
75D244—22no—
76D244—22no—
77D244—22no—
78D244—22no—
79D244—44no—
80D244—82no—
81C4×D61—82no—
82C4×D61—82no—
83Dic122—22no—
84Dic122—22no—
85C8×C61—22no—
86C8×C61—21no—
87C8×C61#4112yes—
88C22×C61C22×D411yescharacteristic
89C2×D61—42no—
90C2×D61—42no—
91C2×D61—42no—
92C2×D61—42no—
93C2×D61—42no—
94C2×D61—42no—
95C4×C61—22no—
96C4×C61—21no—
97C4×C61—21no—
98C4×C61—22no—
99C4×C61C2×#4111yescharacteristic
100C4×C61H(5,𝔽2)11yescharacteristic
101Dic61—42no—
102Dic61—42no—
103#3403—611nomaximal, Sylow
104C2×C61#55011yescharacteristic
105C2×C61#57511yescharacteristic
106C2×C61#57611yescharacteristic
107D61—82no—
108D61—82no—
109#559—612no—
110#496—612no—
111#495—611no—
112#464—612no—
113#463—612no—
114#459—612no—
115#446D6111yescharacteristic, complemented
116#440—612no—
117C4×D8—611no—
118C61#340311yescharacteristic, complemented, Sylow
119C2×Q16—611no—
120C2×SD16—612no—
121C2×SD16—612no—
122C2×D8—611no—
123C2×D8—611no—
124C2×D8—612no—
125#127—612no—
126#124—612no—
127#124—612no—
128#124—1222no—
129#123—1222no—
130#123—1222no—
131C4×Q8—612no—
132C4×Q8C2×D6111yescharacteristic
133C4×D4—612no—
134C4×D4—612no—
135C4×D4—1222no—
136#107—611no—
137C4⋊C8C2×D6112yes—
138C4⋊C8C2×D6111yescharacteristic
139#103—612no—
140#102—612no—
141#102—612no—
142#97C2×D6112yes—
143C4×C8C2×D6111yescharacteristic
144C2×Q8—612no—
145C2×Q8D24411yescharacteristic
146C2×D4—612no—
147C2×D4—612no—
148C2×D4—1222no—
149C2×D4—1222no—
150C22×C4—1222no—
151C22×C4—1222no—
152Q16—2441no—
153SD16—1224no—
154SD16—2442no—
155D8—1222no—
156D8—2442no—
157D8—2441no—
158C2×C8C22×D6111yescharacteristic
159C2×C8C22×D6112yes—
160C2×C8C22×D6111yescharacteristic
161C4⋊C4—612no—
162C4⋊C4—1222no—
163C4⋊C4D24412yes—
164C4⋊C4D24411yescharacteristic
165C22⋊C4—1222no—
166C22⋊C4—1222no—
167C22⋊C4—1222no—
168C22⋊C4—1222no—
169C22⋊C4—1222no—
170C22⋊C4—1222no—
171C42—1222no—
172C42C22×D6111yescharacteristic
173C42C22×D6112yes—
174C23—1222no—
175C23—1222no—
176Q8—41no—
177Q8—1222no—
178Q8—1222no—
179D4—1222no—
180D4—1222no—
181D4—1222no—
182D4—1222no—
183D4—4882no—
184D4—2444no—
185C2×C4—1222no—
186C2×C4—1222no—
187C2×C4—4882no—
188C2×C4—4882no—
189C2×C4C2×D24412yes—
190C2×C4C2×D24411yescharacteristic
191C2×C4C2×D24411yescharacteristic
192C2×C4C2×D24412yes—
193C2×C4C23×D6111yescharacteristic
194C8—22no—
195C8—21no—
196C8#1175822612yes—
197C22—2442no—
198C22—2442no—
199C22—2442no—
200C22—2442no—
201C22—2442no—
202C22—2442no—
203C22C22×D24411yescharacteristic
204C4—22no—
205C4—21no—
206C4—21no—
207C4—22no—
208C4—2442no—
209C4—2442no—
210C4C2×#1175822611yescharacteristic
211C4#1451982311yescharacteristic
212C2—4882no—
213C2—4882no—
214C2#1684043411yescharacteristic
215C2#1684056211yescharacteristic
216C2#1684056711yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#446C2
socleC22×C61C22×D4
hypercenter#446D61
hypocenterC61#3403
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #16840497C2semidirect
2. #16840151C2semidirect
3. #16840146C2semidirect
4. #16839985C2semidirect
5. #16839978C2semidirect
6. #16839958C2semidirect
7. #16839864C2semidirect
8. C4×D488C2semidirect
9. C61×#446C2semidirect
115. #446D61semidirect
118. C61#3403semidirect