Finite Group Databasebeta

← #21447786

Subgroups — #21447786

Order 7808.

210 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 47 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#16840575C211yesmaximal, characteristic, complemented
2#16840200C211yesmaximal, characteristic, complemented
3C2×#14519720C211yesmaximal, characteristic, complemented
4#16840033C211yesmaximal, characteristic, complemented
5#16839568C211yesmaximal, characteristic, complemented
6#16839547C211yesmaximal, characteristic, complemented
7C61×#362C211yesmaximal, characteristic, complemented
8#14519825—21no—
9#14519809—22no—
10#14519808—21no—
11#14519805—21no—
12#14519800—21no—
13#14519799C2211yescharacteristic
14Q16×D61—21no—
15C2×D488C2211yescharacteristic
16#14519783C2211yescharacteristic
17#14519722—21no—
18#14519720—22no—
19D976—21no—
20C2×#11758185C2211yescharacteristic
21#14519693—21no—
22C2×Q16×C61C2211yescharacteristic
23M32×C61C2211yescharacteristic
24#108×C61C2211yescharacteristic
25C2×Q8×C61—21no—
26#11758226—22no—
27#11758226—41no—
28Q8×D61—22no—
29Q8×D61—41no—
30#11758222—21no—
31#11758222—42no—
32#11758222D411yescharacteristic
33C2×D244—21no—
34Q16×C61—21no—
35Q16×C61D412yes—
36M16×C61—21no—
37C2×C8×C61C2311yescharacteristic
38#11758202—22no—
39#11758201—22no—
40#11758194D411yescharacteristic
41Dic244D411yescharacteristic
42D488—21no—
43D488—21no—
44D488—41no—
45D488D411yescharacteristic
46#11758190—21no—
47#11758190—41no—
48#11758189—21no—
49C8×D61—21no—
50C16×C61—21no—
51#11758185—21no—
52C22×D61—41no—
53Q8×C61—22no—
54Q8×C61—41no—
55C2×C4×C61—41no—
56C2×C4×C61C2×D411yescharacteristic
57C22⋊D61—21no—
58C22⋊D61—41no—
59D244—21no—
60D244—42no—
61D244—41no—
62D244—41no—
63D244D811yescharacteristic
64C4×D61—21no—
65C4×D61—42no—
66C4×D61—42no—
67C4×D61—41no—
68Dic122—21no—
69Dic122—42no—
70Dic122D811yescharacteristic
71C8×C61—41no—
72C8×C61C2×D411yescharacteristic
73C8×C61C2×D411yescharacteristic
74#92418—21no—
75C22×C61AGL(1,ℤ/8)11yescharacteristic
76C2×D61—21no—
77C2×D61—41no—
78C2×D61—81no—
79C2×D61—161no—
80C4×C61—42no—
81C4×C61#12011yescharacteristic
82C4×C61C2×D811yescharacteristic
83Dic61—21no—
84Dic61—41no—
85#2193—611nomaximal, Sylow
86C2×C61—21no—
87C2×C61#44711yescharacteristic
88D61—41no—
89D61—81no—
90D61—161no—
91#578—611no—
92#509—611no—
93C2×SD32—611no—
94#472—611no—
95#362D6111yescharacteristic, complemented
96#359—611no—
97#350—611no—
98C61#219311yescharacteristic, complemented, Sylow
992−1+4—1221no—
100#137—1221no—
101#137—1222no—
102AGL(1,ℤ/8)—1221no—
103#135—611no—
104#135—1221no—
105C2×Q16—1221no—
106C2×Q16C2×D6111yescharacteristic
107C2×D8—611no—
108#131—611no—
109SD32—1221no—
110SD32—1222no—
111D16—1221no—
112M32C2×D6111yescharacteristic
113C2×C16—611no—
114#108C2×D6111yescharacteristic
115#100—1221no—
116#41—611no—
117#41—1222no—
118#41—1221no—
119#41—2442no—
120#41—2441no—
121C2×Q8—21no—
122C2×Q8—1222no—
123C2×Q8—2441no—
124C2×D4—1221no—
125Q16—21no—
126Q16—611no—
127Q16—1222no—
128Q16D24412yes—
129SD16—1222no—
130SD16—1221no—
131SD16—2441no—
132D8—611no—
133D8—1221no—
134D8—1221no—
135D8—2441no—
136M16—21no—
137M16—611no—
138M16—1221no—
139C2×C8—1221no—
140C2×C8C22×D6111yescharacteristic
141C16—21no—
142C16—1221no—
143C23—2441no—
144Q8—22no—
145Q8—41no—
146Q8—611no—
147Q8—1221no—
148Q8—2442no—
149D4—611no—
150D4—1221no—
151D4—1221no—
152D4—2442no—
153D4—2441no—
154D4—2441no—
155D4—2441no—
156C2×C4—41no—
157C2×C4—1221no—
158C2×C4—2442no—
159C2×C4—2442no—
160C2×C4—2441no—
161C2×C4D4×D6111yescharacteristic
162C8—41no—
163C8—1221no—
164C8C2×D24411yescharacteristic
165C8D4×D6111yescharacteristic
166C22—1221no—
167C22—9761no—
168C22—4881no—
169C22—2441no—
170C22#1451980411yescharacteristic
171C4—42no—
172C4—1221no—
173C4—2441no—
174C4#1451974711yescharacteristic
175C4D8×D6111yescharacteristic
176C2—21no—
177C2—9761no—
178C2—4881no—
179C2—2441no—
180C2#1683989711yescharacteristic
subgroupG/H
centerC2#16839897
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#362C2
socleC2×C61#447
hypercenter#362D61
hypocenterC61#2193
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #362

Complements

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

NH ≅ G/Ntype
1. #16840575C2semidirect
2. #16840200C2semidirect
3. C2×#14519720C2semidirect
4. #16840033C2semidirect
5. #16839568C2semidirect
6. #16839547C2semidirect
7. C61×#362C2semidirect
95. #362D61semidirect
98. C61#2193semidirect