Finite Group Databasebeta

← #21447785

Subgroups — #21447785

Order 7808.

210 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 49 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#16840579C211yesmaximal, characteristic, complemented
2#16840200C211yesmaximal, characteristic, complemented
3C2×#14519722C211yesmaximal, characteristic, complemented
4#16840032C211yesmaximal, characteristic, complemented
5#16839579C211yesmaximal, characteristic, complemented
6#16839570C211yesmaximal, characteristic, complemented
7C61×#350C211yesmaximal, characteristic, complemented
8#14519824—21no—
9#14519810—21no—
10#14519810—22no—
11#14519802—21no—
12#14519799—21no—
13#14519799C2211yescharacteristic
14C2×Dic244—21no—
15C2×Dic244C2211yescharacteristic
16C2×D488C2211yescharacteristic
17#14519722—21no—
18#14519722—22no—
19D976—21no—
20#14519713C2211yescharacteristic
21#14519693—21no—
22#131×C61C2211yescharacteristic
23M32×C61C2211yescharacteristic
24C2×C16×C61C2211yescharacteristic
25#41×C61D411yescharacteristic
26Q8×D61—41no—
27#11758224—42no—
28#11758224—41no—
29#11758222—22no—
30#11758222—21no—
31C2×D244—21no—
32C2×Dic122—22no—
33C2×Dic122—21no—
34M16×C61—21no—
35M16×C61D411yescharacteristic
36C2×C8×C61—21no—
37C2×C8×C61C2311yescharacteristic
38#11758201—41no—
39#11758199—41no—
40#11758194—21no—
41Dic244—22no—
42Dic244—21no—
43Dic244D412yes—
44Dic244D411yescharacteristic
45D488—21no—
46D488—21no—
47D488D411yescharacteristic
48#11758190—22no—
49#11758190—21no—
50C16×C61—21no—
51C16×C61—21no—
52C22×D61—41no—
53Q8×C61D811yescharacteristic
54D4×C61—21no—
55D4×C61D811yescharacteristic
56C2×C4×C61—21no—
57C2×C4×C61C2×D411yescharacteristic
58C22⋊D61—42no—
59C22⋊D61—41no—
60C2×Dic61—42no—
61C2×Dic61—41no—
62D244—21no—
63D244—41no—
64D244—41no—
65C4×D61—42no—
66C4×D61—41no—
67Dic122—22no—
68Dic122—21no—
69Dic122—42no—
70Dic122—41no—
71C8×C61—21no—
72C8×C61C2×D411yescharacteristic
73C8×C61C2×D411yescharacteristic
74#92418—41no—
75C22×C61—21no—
76C22×C61AGL(1,ℤ/8)11yescharacteristic
77C2×D61—41no—
78C2×D61—81no—
79C2×D61—161no—
80C4×C61—21no—
81C4×C61#12011yescharacteristic
82C4×C61C2×D811yescharacteristic
83Dic61—41no—
84Dic61—42no—
85#2193—611nomaximal, Sylow
86C2×C61—21no—
87C2×C61—41no—
88C2×C61#44711yescharacteristic
89D61—81no—
90D61—161no—
91#578—611no—
92#509—611no—
93C2×SD32—611no—
94#472—611no—
95#362—611no—
96#359—611no—
97#350D6111yescharacteristic, complemented
98C61#219311yescharacteristic, complemented, Sylow
992−1+4—1221no—
100#137—1222no—
101#137—1221no—
102AGL(1,ℤ/8)—1221no—
103#135—611no—
104#135—1221no—
105C2×Q16—611no—
106C2×Q16—1221no—
107C2×D8—611no—
108#131C2×D6111yescharacteristic
109SD32—1222no—
110SD32—1221no—
111D16—1221no—
112M32C2×D6111yescharacteristic
113C2×C16C2×D6111yescharacteristic
114#108—611no—
115#100—1221no—
116#41—1222no—
117#41—1221no—
118#41—2442no—
119#41—2441no—
120#41D24411yescharacteristic
121C2×Q8—1222no—
122C2×Q8—1221no—
123C2×Q8—2441no—
124C2×D4—1221no—
125Q16—612no—
126Q16—611no—
127Q16—1222no—
128Q16—1221no—
129SD16—1222no—
130SD16—1221no—
131SD16—2441no—
132D8—611no—
133D8—1221no—
134D8—1221no—
135D8—2441no—
136M16—21no—
137M16—1221no—
138M16D24411yescharacteristic
139C2×C8—21no—
140C2×C8C22×D6111yescharacteristic
141C16—21no—
142C16—21no—
143C23—2441no—
144Q8—1222no—
145Q8—1221no—
146Q8—2442no—
147Q8—2441no—
148Q8D48811yescharacteristic
149D4—21no—
150D4—1221no—
151D4—2442no—
152D4—2441no—
153D4—2441no—
154D4—2441no—
155D4D48811yescharacteristic
156C2×C4—21no—
157C2×C4—2442no—
158C2×C4—2442no—
159C2×C4—2441no—
160C2×C4—2441no—
161C2×C4C2×D24411yescharacteristic
162C8—21no—
163C8—2441no—
164C8D4×D6111yescharacteristic
165C8D4×D6111yescharacteristic
166C22—21no—
167C22—9761no—
168C22—4881no—
169C22—2441no—
170C22#1451980511yescharacteristic
171C4—21no—
172C4—2442no—
173C4—2441no—
174C4#1451974711yescharacteristic
175C4C2×D48811yescharacteristic
176C2—21no—
177C2—41no—
178C2—9761no—
179C2—4881no—
180C2#1683989811yescharacteristic
subgroupG/H
centerC2#16839898
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#350C2
socleC2×C61#447
hypercenter#350D61
hypocenterC61#2193
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #350

Complements

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

NH ≅ G/Ntype
1. #16840579C2semidirect
2. #16840200C2semidirect
3. C2×#14519722C2semidirect
4. #16840032C2semidirect
5. #16839579C2semidirect
6. #16839570C2semidirect
7. C61×#350C2semidirect
97. #350D61semidirect
98. C61#2193semidirect