Finite Group Databasebeta

← #21446923

Subgroups — #21446923

Order 7808.

350 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 69 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#16840562C211yesmaximal, characteristic, complemented
2#16840560C212yesmaximal, complemented
3#16839728C212yesmaximal, complemented
4#16839520C211yesmaximal, characteristic, complemented
5C61×#408C211yesmaximal, characteristic, complemented
6C2×#11758222C2212yes—
7#14519810—22no—
8#14519808—22no—
9#14519807—22no—
10#14519805—22no—
11#14519803—22no—
12#14519802—22no—
13#14519799—22no—
14#14519797—24no—
15C2×#11758194C2212yes—
16#14519689—24no—
17C2×#41×C61C2211yescharacteristic
18C2×M16×C61C2211yescharacteristic
19C22×C8×C61C2211yescharacteristic
20C22⋊C8×C61—22no—
21#41×C61—22no—
22#41×C61—22no—
23C2×Q8×C61D411yescharacteristic
24C2×D4×C61—21no—
25C2×D4×C61D411yescharacteristic
26C22×C4×C61—21no—
27C22×C4×C61C2311yescharacteristic
28C2×C22⋊D61—22no—
29#11758222—22no—
30#11758222—22no—
31#11758222—22no—
32#11758222—22no—
33C2×D244D412yes—
34C2×C4×D61—22no—
35C2×Dic122D412yes—
36M16×C61—22no—
37C2×C8×C61—21no—
38C2×C8×C61—22no—
39C2×C8×C61D412yes—
40#11758202—24no—
41#11758201—24no—
42#11758200—24no—
43#11758199—24no—
44#11758194—22no—
45#11758194—22no—
46C2×#92418D414yes—
47Dic244—22no—
48D488—22no—
49#11758190—24no—
50C23×C61—21no—
51C23×C61#4111yescharacteristic
52C22×D61—22no—
53Q8×C61—22no—
54D4×C61—22no—
55D4×C61—42no—
56C2×C4×C61—21no—
57C2×C4×C61—41no—
58C2×C4×C61—41no—
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×D412yes—
61C2×C4×C61C2×D412yes—
62C2×C4×C61C2×D411yescharacteristic
63C22⋊D61—42no—
64C22⋊D61—42no—
65C2×Dic61—22no—
66D244—22no—
67D244—22no—
68C4×D61—42no—
69C4×D61—42no—
70Dic122—22no—
71Dic122—22no—
72C8×C61—22no—
73C8×C61—41no—
74#92418—24no—
75C22×C61—41no—
76C22×C61—42no—
77C22×C61—41no—
78C22×C61#12112yes—
79C22×C61#12111yescharacteristic
80C2×D61—44no—
81C2×D61—42no—
82C4×C61—41no—
83C4×C61#12011yescharacteristic
84C4×C61#12012yes—
85C4×C61#12711yescharacteristic
86Dic61—42no—
87#2017—611nomaximal, Sylow
88C2×C61—22no—
89C2×C61—21no—
90C2×C61—81no—
91C2×C61#39211yescharacteristic
92D61—82no—
93#575—612no—
94#575—611no—
95#408—612no—
96#408D6111yescharacteristic, complemented
97#338—611no—
98C61#201711yescharacteristic, complemented, Sylow
99C2×#41—612no—
100C2×#41C2×D6111yescharacteristic
101#137—1222no—
102#137—1222no—
103#137—1222no—
104AGL(1,ℤ/8)—1222no—
105AGL(1,ℤ/8)—1222no—
106AGL(1,ℤ/8)—1222no—
107#135—1224no—
108#135—1222no—
109C2×M16—612no—
110C2×M16C2×D6111yescharacteristic
111C22×C8C2×D6111yescharacteristic
112C22⋊C8—22no—
113C22⋊C8—1224no—
114#41—22no—
115#41—22no—
116#41—1222no—
117#41—1222no—
118#41—1222no—
119#41—1222no—
120C2×Q8—612no—
121C2×Q8D24411yescharacteristic
122C2×D4—21no—
123C2×D4—612no—
124C2×D4—1222no—
125C2×D4D24411yescharacteristic
126C22×C4—21no—
127C22×C4—1222no—
128C22×C4C22×D6111yescharacteristic
129Q16—1222no—
130Q16—1224no—
131SD16—1224no—
132SD16—1224no—
133SD16—1224no—
134D8—1222no—
135D8—1224no—
136M16—22no—
137M16—1222no—
138M16—1222no—
139C2×C8—22no—
140C2×C8—21no—
141C2×C8—614no—
142C2×C8C22⋊D6112yes—
143C23—21no—
144C23—1222no—
145C23#1175822211yescharacteristic
146Q8—22no—
147Q8—1222no—
148Q8—1222no—
149D4—22no—
150D4—42no—
151D4—1222no—
152D4—1222no—
153D4—2442no—
154D4—2442no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—1222no—
159C2×C4—2442no—
160C2×C4—2442no—
161C2×C4C2×D24411yescharacteristic
162C2×C4D4×D6112yes—
163C2×C4D4×D6112yes—
164C2×C4C2×C22⋊D6111yescharacteristic
165C8—22no—
166C8—41no—
167C8—1224no—
168C22—41no—
169C22—42no—
170C22—41no—
171C22—2444no—
172C22—2442no—
173C22#1451975012yes—
174C22#1451975111yescharacteristic
175C4—41no—
176C4—2442no—
177C4#1451974511yescharacteristic
178C4#1451974712yes—
179C4#1451977311yescharacteristic
180C2—21no—
181C2—22no—
182C2—81no—
183C2—4882no—
184C2#1683967111yescharacteristic
subgroupG/H
centerC4#14519773
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#408C2
socleC2×C61#392
hypercenter#408D61
hypocenterC61#2017
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #16840562C2semidirect
2. #16840560C2semidirect
3. #16839728C2semidirect
4. #16839520C2semidirect
5. C61×#408C2semidirect
96. #408D61semidirect
98. C61#2017semidirect