Finite Group Databasebeta

← #21447796

Subgroups — #21447796

Order 7808.

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

normal subgroups only

This group has 206 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
2#16840203C211yesmaximal, characteristic, complemented
3#16840034C211yesmaximal, characteristic, complemented
4#16839578C211yesmaximal, characteristic, complemented
5#16839570C211yesmaximal, characteristic, complemented
6#16839545C211yesmaximal, characteristic, complemented
7C2×Q32×C61C211yesmaximal, characteristic, complemented
8#14519825—21no—
9#14519809—22no—
10#14519808—21no—
11#14519808—21no—
12#14519800—21no—
13#14519799C2211yescharacteristic
14Q16×D61—21no—
15#14519783C2211yescharacteristic
16#14519723—21no—
17#14519720—21no—
18#14519717C2211yescharacteristic
19#14519713C2211yescharacteristic
20#14519696—21no—
21C2×Q16×C61C2211yescharacteristic
22C2×Q16×C61C2211yescharacteristic
23Q32×C61—22no—
24C2×C16×C61C2211yescharacteristic
25C2×Q8×C61—21no—
26C2×Q8×C61—21no—
27#11758226—22no—
28#11758226—41no—
29Q8×D61—22no—
30Q8×D61—41no—
31#11758222—21no—
32#11758222—42no—
33#11758222D411yescharacteristic
34Q16×C61—21no—
35Q16×C61—21no—
36Q16×C61—21no—
37Q16×C61D412yes—
38C2×C8×C61C2311yescharacteristic
39#11758202—22no—
40#11758202—41no—
41#11758201—22no—
42#11758201—41no—
43#11758194—21no—
44#11758194D411yescharacteristic
45Dic244D411yescharacteristic
46D488D411yescharacteristic
47#11758190—21no—
48#11758189—21no—
49C8×D61—21no—
50C16×C61—21no—
51#11758185—21no—
52Q8×C61—22no—
53Q8×C61—41no—
54Q8×C61—41no—
55Q8×C61—41no—
56C2×C4×C61—41no—
57C2×C4×C61—41no—
58C2×C4×C61C2×D411yescharacteristic
59C22⋊D61—21no—
60C22⋊D61—41no—
61D244—21no—
62D244—42no—
63D244D811yescharacteristic
64C4×D61—21no—
65C4×D61—42no—
66C4×D61—42no—
67C4×D61—41no—
68Dic122—21no—
69Dic122—42no—
70Dic122D811yescharacteristic
71C8×C61C2×D411yescharacteristic
72C8×C61C2×D411yescharacteristic
73#92418—21no—
74#92418—41no—
75C22×C61AGL(1,ℤ/8)11yescharacteristic
76C2×D61—21no—
77C2×D61—41no—
78C4×C61—42no—
79C4×C61—81no—
80C4×C61#12011yescharacteristic
81C4×C61C2×D811yescharacteristic
82Dic61—21no—
83Dic61—41no—
84#2195—611nomaximal, Sylow
85C2×C61—21no—
86C2×C61#44711yescharacteristic
87D61—41no—
88D61—81no—
89#578—611no—
90#510—611no—
91C2×Q32D6111yescharacteristic, complemented
92#473—611no—
93#362—611no—
94#359—611no—
95#350—611no—
96C61#219511yescharacteristic, complemented, Sylow
972−1+4—1221no—
98#137—1221no—
99#137—1222no—
100#137—1221no—
101#135—611no—
102#135—1221no—
103C2×Q16—1221no—
104C2×Q16C2×D6111yescharacteristic
105C2×Q16C2×D6111yescharacteristic
106#131—611no—
107Q32—22no—
108Q32—1221no—
109SD32—1221no—
110M32—611no—
111C2×C16C2×D6111yescharacteristic
112#108—611no—
113#101—1221no—
114#41—611no—
115#41—1222no—
116#41—1221no—
117#41—2442no—
118#41—2441no—
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—1222no—
122C2×Q8—2441no—
123Q16—21no—
124Q16—21no—
125Q16—21no—
126Q16—611no—
127Q16—1222no—
128Q16—2441no—
129Q16C22⋊D6112yes—
130SD16—1222no—
131SD16—1221no—
132SD16—2441no—
133D8—611no—
134M16—611no—
135M16—1221no—
136M16—1221no—
137C2×C8—1221no—
138C2×C8C22×D6111yescharacteristic
139C16—21no—
140C16—1221no—
141Q8—22no—
142Q8—41no—
143Q8—41no—
144Q8—41no—
145Q8—611no—
146Q8—1221no—
147Q8—2442no—
148D4—611no—
149D4—1221no—
150D4—1221no—
151D4—2442no—
152D4—2441no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—1221no—
156C2×C4—2442no—
157C2×C4—2442no—
158C2×C4—2441no—
159C2×C4D4×D6111yescharacteristic
160C8—1221no—
161C8—2441no—
162C8D4×D6111yescharacteristic
163C8C2×C22⋊D6111yescharacteristic
164C22—1221no—
165C22—2441no—
166C22#1451980111yescharacteristic
167C4—42no—
168C4—81no—
169C4—1221no—
170C4—2441no—
171C4#1451974511yescharacteristic
172C4D8×D6111yescharacteristic
173C2—21no—
174C2—4881no—
175C2—2441no—
176C2#1683989411yescharacteristic
subgroupG/H
centerC2#16839894
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC2×Q32×C61C2
socleC2×C61#447
hypercenterC2×Q32D61
hypocenterC61#2195
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
2. #16840203C2semidirect
3. #16840034C2semidirect
4. #16839578C2semidirect
5. #16839570C2semidirect
6. #16839545C2semidirect
7. C2×Q32×C61C2semidirect
91. C2×Q32D61semidirect
96. C61#2195semidirect