Finite Group Databasebeta

← #21452769

Subgroups — #21452769

Order 7808.

416 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519767C212yesmaximal
2#16839696C212yesmaximal
3#16839695C212yesmaximal
4#16839693C212yesmaximal
5#16839660C211yesmaximal, characteristic
6#16839660C211yesmaximal, characteristic
7#16839657C212yesmaximal
8#16839645C212yesmaximal
9C61×#389C211yesmaximal, characteristic
10#14519767—28no—
11C2×C4⋊Dic61C2211yescharacteristic
12C2×C4⋊Dic61C2211yescharacteristic
13C2×C4⋊Dic61C2211yescharacteristic
14C2×C4⋊Dic61C2211yescharacteristic
15C2×#11758196C2212yes—
16C2×#11758196C2212yes—
17C2×#11758196C2212yes—
18C2×#11758196C2212yes—
19C2×#11758196C2212yes—
20C2×#11758196C2212yes—
21C2×C4×Dic61C2212yes—
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26#14519684C2212yes—
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C4⋊C4×C61C2212yes—
29C2×C4⋊C4×C61C2211yescharacteristic
30C2×C42×C61C2211yescharacteristic
31#95×C61C2212yes—
32C22×C4×C61C2312yes—
33C22×C4×C61C2312yes—
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2311yescharacteristic
37C22×Dic61C2312yes—
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C4⋊C4×C61—24no—
42C4⋊C4×C61—22no—
43C4⋊C4×C61—41no—
44C42×C61—41no—
45C4⋊Dic61—41no—
46C4⋊Dic61—41no—
47C4⋊Dic61D414yes—
48C4⋊Dic61Q814yes—
49#11758196—24no—
50#11758196—24no—
51#11758196—24no—
52#11758196—24no—
53#11758196—24no—
54#11758196—42no—
55C4×Dic61—24no—
56C23×C61C2411yescharacteristic
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—21no—
62C2×C4×C61—21no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61C2×D412yes—
70C2×C4×C61C2×Q812yes—
71C2×C4×C61#4112yes—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61C2×D414yes—
83C2×Dic61C2×Q814yes—
84C22×C61C22×D411yescharacteristic
85C22×C61C22×Q811yescharacteristic
86C22×C61C2×#4111yescharacteristic
87C22×C61H(5,𝔽2)11yescharacteristic
88C22×C612−1+411yescharacteristic
89C22×C612−1+411yescharacteristic
90C22×C612−1+411yescharacteristic
91C4×C61—22no—
92C4×C61—22no—
93C4×C61—22no—
94C4×C61—42no—
95C4×C61—42no—
96Dic61—24no—
97Dic61—24no—
98Dic61—42no—
99Dic61—42no—
100#2726—611nomaximal, Sylow
101C2×C61#53711yescharacteristic
102C2×C61#53911yescharacteristic
103C2×C61#54411yescharacteristic
104C2×C61#54711yescharacteristic
105C2×C61D4×Q811yescharacteristic
106C2×C61#55711yescharacteristic
107C2×C61#56411yescharacteristic
108C2×#125—612no—
109#398—612no—
110#398—612no—
111#398—612no—
112#389—612no—
113#389—611no—
114#389—611no—
115#389D6111yescharacteristic
116#387—612no—
117C61#272611yescharacteristic, complemented, Sylow
118#125—1228no—
119C2×C4⋊C4—611no—
120C2×C4⋊C4—611no—
121C2×C4⋊C4—612no—
122C2×C4⋊C4—612no—
123C2×C4⋊C4—612no—
124C2×C4⋊C4—612no—
125C2×C4⋊C4—612no—
126C2×C4⋊C4—612no—
127C2×C4⋊C4—611no—
128C2×C4⋊C4—611no—
129C2×C4⋊C4C2×D6112yes—
130C2×C4⋊C4C2×D6111yescharacteristic
131C2×C4⋊C4C2×D6111yescharacteristic
132C2×C42—612no—
133C2×C42C2×D6111yescharacteristic
134#95—612no—
135#95—612no—
136#95—612no—
137#95—612no—
138#95—612no—
139#95C2×D6112yes—
140C22×C4—612no—
141C22×C4—612no—
142C22×C4—612no—
143C22×C4—612no—
144C22×C4C22×D6112yes—
145C22×C4C22×D6112yes—
146C22×C4C22×D6111yescharacteristic
147C22×C4C22×D6111yescharacteristic
148C22×C4C22×D6111yescharacteristic
149C4⋊C4—22no—
150C4⋊C4—24no—
151C4⋊C4—41no—
152C4⋊C4—614no—
153C4⋊C4—614no—
154C4⋊C4—1224no—
155C4⋊C4—1224no—
156C4⋊C4—1224no—
157C4⋊C4—1224no—
158C4⋊C4—1224no—
159C4⋊C4—2442no—
160C4⋊C4—2441no—
161C4⋊C4—2441no—
162C42—41no—
163C42—1224no—
164C23C23×D6111yescharacteristic
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—614no—
178C2×C4—614no—
179C2×C4—1222no—
180C2×C4—1222no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—1222no—
184C2×C4—1222no—
185C2×C4—1222no—
186C2×C4—1222no—
187C2×C4—1222no—
188C2×C4—1222no—
189C2×C4#1175822212yes—
190C2×C4D4×D6112yes—
191C2×C4Q8×D6112yes—
192C22C2×D4×D6111yescharacteristic
193C22C2×Q8×D6111yescharacteristic
194C22C2×#1175822211yescharacteristic
195C22#1451982211yescharacteristic
196C22#1451982411yescharacteristic
197C22#1451982411yescharacteristic
198C22#1451982511yescharacteristic
199C4—22no—
200C4—22no—
201C4—22no—
202C4—42no—
203C4—42no—
204C4—1224no—
205C4—1224no—
206C4—2442no—
207C4—2442no—
208C2#1684033911yescharacteristic
209C2#1684035911yescharacteristic
210C2#1684039111yescharacteristic
211C2#1684041711yescharacteristic
212C2#1684042711yescharacteristic
213C2#1684049011yescharacteristic
214C2C61⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#389C2
hypercenter#389D61
hypocenterC61#2726
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
117. C61#2726semidirect