Finite Group Databasebeta

← #21446922

Subgroups — #21446922

Order 7808.

350 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 71 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#16840560C212yesmaximal, complemented
2#16839730C211yesmaximal, characteristic, complemented
3#16839729C212yesmaximal, complemented
4#16839520C211yesmaximal, characteristic, complemented
5C61×#575C211yesmaximal, characteristic, complemented
6C2×#11758222C2211yescharacteristic
7#14519808—22no—
8#14519807—22no—
9#14519803—22no—
10#14519802—22no—
11#14519797—24no—
12C2×#11758194C2212yes—
13C22×#92418C2211yescharacteristic
14C22⋊#92418—24no—
15#14519689—22no—
16C2×#41×C61C2212yes—
17#137×C61—22no—
18AGL(1,ℤ/8)×C61—22no—
19#135×C61—22no—
20C2×M16×C61C2211yescharacteristic
21#41×C61—22no—
22#41×C61—22no—
23#41×C61—22no—
24#41×C61—22no—
25C2×Q8×C61D412yes—
26C2×D4×C61—22no—
27C2×D4×C61D412yes—
28C22×C4×C61—22no—
29C22×C4×C61C2311yescharacteristic
30C2×C22⋊D61—21no—
31#11758222—22no—
32#11758222—22no—
33C2×D244D411yescharacteristic
34C2×C4×D61—21no—
35C2×Dic122D411yescharacteristic
36Q16×C61—22no—
37SD16×C61—24no—
38D8×C61—22no—
39M16×C61—22no—
40C2×C8×C61D412yes—
41#11758202—24no—
42#11758201—24no—
43#11758200—24no—
44#11758199—24no—
45#11758194—22no—
46#11758194—22no—
47C2×#92418—21no—
48C2×#92418—22no—
49C2×#92418D414yes—
50C23×C61—22no—
51C23×C61#4111yescharacteristic
52C22×D61—21no—
53Q8×C61—22no—
54Q8×C61—22no—
55D4×C61—22no—
56D4×C61—22no—
57D4×C61—42no—
58D4×C61—42no—
59C2×C4×C61—22no—
60C2×C4×C61—42no—
61C2×C4×C61—42no—
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D412yes—
64C2×C4×C61C2×D412yes—
65C2×C4×C61C2×D411yescharacteristic
66C22⋊D61—42no—
67C2×Dic61—21no—
68D244—22no—
69C4×D61—41no—
70C4×D61—41no—
71Dic122—22no—
72C8×C61—22no—
73#92418—24no—
74#92418—41no—
75C22×C61—41no—
76C22×C61—44no—
77C22×C61—42no—
78C22×C61#12111yescharacteristic
79C22×C61#12112yes—
80C2×D61—42no—
81C2×D61—41no—
82C4×C61—42no—
83C4×C61#12012yes—
84C4×C61#12011yescharacteristic
85C4×C61#12711yescharacteristic
86Dic61—41no—
87#2017—611nomaximal, Sylow
88C2×C61—21no—
89C2×C61—22no—
90C2×C61—82no—
91C2×C61#39211yescharacteristic
92D61—81no—
93#575—612no—
94#575D6111yescharacteristic, complemented
95#408—612no—
96#408—611no—
97#338—611no—
98C61#201711yescharacteristic, complemented, Sylow
99C2×#41—611no—
100C2×#41C2×D6112yes—
101#137—22no—
102#137—1222no—
103#137—1222no—
104AGL(1,ℤ/8)—22no—
105AGL(1,ℤ/8)—1222no—
106AGL(1,ℤ/8)—1222no—
107#135—22no—
108#135—1224no—
109C2×M16—612no—
110C2×M16C2×D6111yescharacteristic
111C22×C8—611no—
112C22⋊C8—1224no—
113C22⋊C8—1222no—
114#41—22no—
115#41—22no—
116#41—22no—
117#41—22no—
118#41—1222no—
119#41—1222no—
120C2×Q8—611no—
121C2×Q8C22⋊D6112yes—
122C2×D4—22no—
123C2×D4—611no—
124C2×D4—1221no—
125C2×D4C22⋊D6112yes—
126C22×C4—22no—
127C22×C4—1221no—
128C22×C4C22×D6111yescharacteristic
129Q16—22no—
130Q16—1224no—
131SD16—24no—
132SD16—1224no—
133SD16—1224no—
134D8—22no—
135D8—1224no—
136M16—22no—
137M16—1222no—
138M16—1222no—
139C2×C8—614no—
140C2×C8—1222no—
141C2×C8—1221no—
142C2×C8C22⋊D6112yes—
143C23—22no—
144C23—1221no—
145C23#1175822411yescharacteristic
146Q8—22no—
147Q8—22no—
148Q8—1222no—
149D4—22no—
150D4—22no—
151D4—42no—
152D4—42no—
153D4—1222no—
154D4—2442no—
155C2×C4—22no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—1221no—
159C2×C4—2441no—
160C2×C4—2441no—
161C2×C4D4×D6111yescharacteristic
162C2×C4D4×D6112yes—
163C2×C4C2×C22⋊D6112yes—
164C2×C4C2×C22⋊D6111yescharacteristic
165C8—22no—
166C8—1224no—
167C8—2441no—
168C22—41no—
169C22—44no—
170C22—42no—
171C22—2442no—
172C22—2441no—
173C22#1451974811yescharacteristic
174C22#1451974912yes—
175C4—42no—
176C4—2441no—
177C4#1451974512yes—
178C4#1451974611yescharacteristic
179C4#1451977311yescharacteristic
180C2—22no—
181C2—21no—
182C2—82no—
183C2—4881no—
184C2#1683967011yescharacteristic
subgroupG/H
centerC4#14519773
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#575C2
socleC2×C61#392
hypercenter#575D61
hypocenterC61#2017
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #16840560C2semidirect
2. #16839730C2semidirect
3. #16839729C2semidirect
4. #16839520C2semidirect
5. C61×#575C2semidirect
94. #575D61semidirect
98. C61#2017semidirect