Finite Group Databasebeta

← #21451602

Subgroups — #21451602

Order 7808.

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

normal subgroups only

This group has 526 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×#14519760C211yesmaximal, characteristic
2C22×C4⋊Dic61C211yesmaximal, characteristic, complemented
3#16839702C212yesmaximal, complemented
4#16839699C212yesmaximal, complemented
5#16839694C212yesmaximal, complemented
6#16839689C212yesmaximal, complemented
7#16839639C212yesmaximal
8#16839637C212yesmaximal, complemented
9C61×#381C211yesmaximal, characteristic, complemented
10C22×C22⋊D61C2211yescharacteristic
11C23×Dic61C2212yes—
12#14519760—24no—
13C2×C4⋊Dic61—24no—
14C2×C4⋊Dic61C2212yes—
15C2×C4⋊Dic61C2212yes—
16C2×C4⋊Dic61C2214yes—
17C2×#11758196C2211yescharacteristic
18C2×#11758196C2211yescharacteristic
19C2×C22⋊Dic61C2211yescharacteristic
20C2×#11758198C2211yescharacteristic
21C2×#11758198C2211yescharacteristic
22C2×#11758198C2214yes—
23#14519684C2214yes—
24#14519684C2214yes—
25C23×C4×C61C2211yescharacteristic
26C2×C22⋊C4×C61C2212yes—
27#95×C61C2212yes—
28#95×C61C2212yes—
29C24×C61C2311yescharacteristic
30C23×D61C2311yescharacteristic
31C22×C4×C61—24no—
32C22×C4×C61D414yes—
33C22×C4×C61C2314yes—
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C2×C22⋊D61—22no—
37C2×C22⋊D61—24no—
38C22×Dic61—24no—
39C22×Dic61—44no—
40C22×Dic61C2314yes—
41C22×Dic61C2311yescharacteristic
42C22×Dic61C2311yescharacteristic
43C22×Dic61C2311yescharacteristic
44C22⋊C4×C61—24no—
45C22⋊Dic61—22no—
46#11758198—22no—
47#11758198—22no—
48#11758198—44no—
49C4⋊Dic61—24no—
50C4⋊Dic61—24no—
51C4⋊Dic61—44no—
52#11758196—22no—
53#11758196—22no—
54C23×C61—22no—
55C23×C61—22no—
56C23×C61C2×D412yes—
57C23×C61#4114yes—
58C23×C61C2411yescharacteristic
59C22×D61—21no—
60C22×D61—22no—
61C22×D61—22no—
62C22×D61—22no—
63C2×C4×C61—28no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—24no—
67C2×C4×C61—24no—
68C2×C4×C61—24no—
69C2×C4×C61C2×D412yes—
70C2×C4×C61C2×D412yes—
71C22⋊D61—44no—
72C2×Dic61—21no—
73C2×Dic61—21no—
74C2×Dic61—21no—
75C2×Dic61—24no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—24no—
79C2×Dic61—24no—
80C2×Dic61—22no—
81C2×Dic61—48no—
82C22×C61—22no—
83C22×C61—22no—
84C22×C61—28no—
85C22×C61#12314yes—
86C22×C61C22×D411yescharacteristic
87C22×C61C2×#4112yes—
88C22×C61H(5,𝔽2)12yes—
89C22×C612−1+412yes—
90C2×D61—41no—
91C2×D61—41no—
92C2×D61—41no—
93C2×D61—44no—
94C4×C61—22no—
95C4×C61—22no—
96C4×C61—44no—
97Dic61—41no—
98Dic61—41no—
99Dic61—44no—
100Dic61—41no—
101#2623—611nomaximal, Sylow
102C2×C61—24no—
103C2×C61C2×#12311yescharacteristic
104C2×C61#53511yescharacteristic
105C2×C61#53611yescharacteristic
106C2×C61#53914yes—
107D61—81no—
108C2×#123—611no—
109C22×C4⋊C4—611no—
110#400—612no—
111#399—612no—
112#398—612no—
113#397—612no—
114#386—612no—
115#385—612no—
116#381D6111yescharacteristic, complemented
117C61#262311yescharacteristic, complemented, Sylow
118C22×D4—611no—
119C23×C4—612no—
120C23×C4C2×D6111yescharacteristic
121#123—1224no—
122C2×C4⋊C4—612no—
123C2×C4⋊C4—612no—
124C2×C4⋊C4—611no—
125C2×C4⋊C4—611no—
126C2×C4⋊C4—614no—
127C2×C4⋊C4—1224no—
128C2×C22⋊C4—611no—
129C2×C22⋊C4—611no—
130C2×C22⋊C4—611no—
131C2×C22⋊C4—614no—
132C2×C22⋊C4C2×D6112yes—
133#95—614no—
134#95—614no—
135#95C2×D6112yes—
136#95C2×D6112yes—
137C24—611no—
138C24C22×D6111yescharacteristic
139C2×D4—1222no—
140C2×D4—1224no—
141C22×C4—24no—
142C22×C4—611no—
143C22×C4—611no—
144C22×C4—614no—
145C22×C4—611no—
146C22×C4—1224no—
147C22×C4—2444no—
148C22×C4D24414yes—
149C22×C4C22×D6114yes—
150C22×C4C22×D6111yescharacteristic
151C22×C4C22×D6111yescharacteristic
152C4⋊C4—1224no—
153C4⋊C4—1224no—
154C4⋊C4—1222no—
155C4⋊C4—1222no—
156C4⋊C4—2444no—
157C22⋊C4—24no—
158C22⋊C4—1222no—
159C22⋊C4—1222no—
160C22⋊C4—1222no—
161C22⋊C4—2444no—
162C23—22no—
163C23—22no—
164C23—1221no—
165C23—1222no—
166C23—1222no—
167C23—1222no—
168C23C2×D24412yes—
169C23#1175822414yes—
170C23C23×D6111yescharacteristic
171D4—2444no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—28no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—1221no—
179C2×C4—1221no—
180C2×C4—1224no—
181C2×C4—1221no—
182C2×C4—1222no—
183C2×C4—1224no—
184C2×C4—1222no—
185C2×C4—1224no—
186C2×C4—1222no—
187C2×C4—2448no—
188C2×C4C2×D24412yes—
189C2×C4C2×D24412yes—
190C22—22no—
191C22—22no—
192C22—28no—
193C22—2441no—
194C22—2441no—
195C22—2441no—
196C22—2444no—
197C22#1451976114yes—
198C22C22×D24411yescharacteristic
199C22C2×#1175822412yes—
200C22#1451982312yes—
201C22#1451982412yes—
202C4—22no—
203C4—22no—
204C4—44no—
205C4—2441no—
206C4—2441no—
207C4—2444no—
208C4—2441no—
209C2—24no—
210C2—4881no—
211C2C2×#1451976111yescharacteristic
212C2#1684033111yescharacteristic
213C2#1684033811yescharacteristic
214C2#1684035614yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#381C2
hypercenter#381D61
hypocenterC61#2623
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊Dic61C2semidirect
3. #16839702C2semidirect
4. #16839699C2semidirect
5. #16839694C2semidirect
6. #16839689C2semidirect
8. #16839637C2semidirect
9. C61×#381C2semidirect
116. #381D61semidirect
117. C61#2623semidirect