Finite Group Databasebeta

← #21446250

Subgroups — #21446250

Order 7808.

360 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 105 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
1C22×#11758194C211yesmaximal, characteristic
2C2×#14519756C211yesmaximal, characteristic
3C2×#14519700C212yesmaximal, complemented
4#16839524C212yesmaximal, complemented
5C61×#380C211yesmaximal, characteristic
6C22×Dic122C2211yescharacteristic
7C2×#11758194—22no—
8C2×#11758194—24no—
9C22×#92418C2212yes—
10#14519756—22no—
11#14519756C414yescomplemented
12C2×C4⋊Dic61C2211yescharacteristic
13C2×#11758196—21no—
14C2×C22⋊Dic61—21no—
15#14519700—24no—
16C23×C4×C61C2211yescharacteristic
17C2×C4⋊C4×C61C2212yes—
18C2×C22⋊C4×C61—21no—
19#95×C61—21no—
20C24×C61D411yescharacteristic
21C22×C4×C61—22no—
22C22×C4×C61—22no—
23C22×C4×C61—22no—
24C22×C4×C61C2×C412yes—
25C22×C4×C61D411yescharacteristic
26C22×C4×C61D412yes—
27C22×C4×C61C2311yescharacteristic
28C22×Dic61—21no—
29C22×Dic61—21no—
30C2×Dic122—22no—
31C2×Dic122—22no—
32C2×Dic122—21no—
33C2×Dic122C2×C412yes—
34C4⋊C4×C61—22no—
35C4⋊C4×C61—22no—
36C22⋊C4×C61—42no—
37C22⋊Dic61—24no—
38C4⋊Dic61—21no—
39C4⋊Dic61C2×C412yes—
40#11758196—24no—
41#11758194—28no—
42C2×#92418—22no—
43C2×#92418—22no—
44C2×#92418D414yes—
45C23×C61—22no—
46C23×C61—21no—
47C23×C61—21no—
48C23×C61—22no—
49C23×C61C22⋊C412yes—
50C23×C61C2×D411yescharacteristic
51C2×C4×C61—22no—
52C2×C4×C61—24no—
53C2×C4×C61—22no—
54C2×C4×C61—22no—
55C2×C4×C61—42no—
56C2×C4×C61—42no—
57C2×C4×C61—42no—
58C2×C4×C61C22⋊C412yes—
59C2×C4×C61C22×C411yescharacteristic
60C2×C4×C61C2×D412yes—
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61#4112yes—
63C2×Dic61—22no—
64C2×Dic61—22no—
65C2×Dic61—42no—
66C2×Dic61—41no—
67C2×Dic61—41no—
68Dic122—24no—
69Dic122—41no—
70Dic122—41no—
71#92418—24no—
72C22×C61—22no—
73C22×C61—22no—
74C22×C61—22no—
75C22×C61—42no—
76C22×C61—42no—
77C22×C61C2×C22⋊C411yescharacteristic
78C22×C61#12112yes—
79C22×C61AGL(1,ℤ/8)11yescharacteristic
80C22×C61#13711yescharacteristic
81C22×C61#13712yes—
82C4×C61—22no—
83C4×C61—82no—
84C4×C61C4×D412yes—
85C4×C61#12011yescharacteristic
86C4×C61#12311yescharacteristic
87Dic61—42no—
88Dic61—42no—
89#1894—611nomaximal, Sylow
90C2×C61—42no—
91C2×C61#38611yescharacteristic
92C2×C61#41711yescharacteristic
93C2×C61#41911yescharacteristic
94C2×C61#46812yes—
95C2×C61#47012yes—
96C22×M16—611no—
97C2×C22⋊Q8—611no—
98C2×#103—612no—
99#380D6111yescharacteristic
100#340—612no—
101C61#189411yescharacteristic, complemented, Sylow
102C22×Q8—611no—
103C23×C4C2×D6111yescharacteristic
104C2×M16—1224no—
105C2×M16—1222no—
106C22×C8—612no—
107C22⋊Q8—614no—
108C22⋊Q8—1222no—
109C2×C4⋊C4—611no—
110C2×C4⋊C4—1221no—
111C2×C4⋊C4C2×D6112yes—
112C2×C22⋊C4—21no—
113C2×C22⋊C4—1221no—
114#103—1224no—
115#95—21no—
116C24C22⋊D6111yescharacteristic
117C2×Q8—612no—
118C2×Q8—1221no—
119C2×Q8—1222no—
120C2×Q8—1222no—
121C22×C4—22no—
122C22×C4—22no—
123C22×C4—22no—
124C22×C4—1221no—
125C22×C4—1221no—
126C22×C4C4×D6112yes—
127C22×C4D24412yes—
128C22×C4C22⋊D6111yescharacteristic
129C22×C4C22×D6111yescharacteristic
130M16—1228no—
131C2×C8—614no—
132C2×C8—1222no—
133C2×C8—1222no—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—612no—
137C4⋊C4—1224no—
138C4⋊C4—1221no—
139C22⋊C4—42no—
140C22⋊C4—1224no—
141C23—21no—
142C23—22no—
143C23—21no—
144C23—22no—
145C23#1175819812yes—
146C23C2×C22⋊D6111yescharacteristic
147Q8—1224no—
148Q8—2441no—
149Q8—2441no—
150C2×C4—22no—
151C2×C4—24no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—1222no—
158C2×C4—1222no—
159C2×C4—2441no—
160C2×C4—2442no—
161C2×C4—2441no—
162C2×C4#1175819812yes—
163C2×C4C2×C4×D6111yescharacteristic
164C2×C4C2×D24411yescharacteristic
165C2×C4D4×D6112yes—
166C2×C4#1175822412yes—
167C8—1224no—
168C22—22no—
169C22—22no—
170C22—22no—
171C22—42no—
172C22—42no—
173C22C2×#1175819811yescharacteristic
174C22#1451974912yes—
175C22#1451980311yescharacteristic
176C22#1451980712yes—
177C22#1451980811yescharacteristic
178C4—22no—
179C4—82no—
180C4—2442no—
181C4—2442no—
182C4#1451973712yes—
183C4#1451974711yescharacteristic
184C4#1451976111yescharacteristic
185C2—42no—
186C2#1683963911yescharacteristic
187C2#1683976111yescharacteristic
188C2#1683977011yescharacteristic
189C2#1684000612yes—
190C2#1684001812yes—
subgroupG/H
centerC23C2×C22⋊D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#380C2
socleC23×C61C2×D4
hypercenter#380D61
hypocenterC61#1894
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. C2×#14519700C2semidirect
4. #16839524C2semidirect
11. #14519756C4semidirect
101. C61#1894semidirect