Finite Group Databasebeta

← #21447795

Subgroups — #21447795

Order 7808.

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

normal subgroups only

This group has 206 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
2#16840203C211yesmaximal, characteristic, complemented
3C2×#14519723C211yesmaximal, characteristic, complemented
4#16839577C211yesmaximal, characteristic, complemented
5#16839568C211yesmaximal, characteristic, complemented
6#16839546C211yesmaximal, characteristic, complemented
7C61×#473C211yesmaximal, characteristic, complemented
8#14519824—21no—
9#14519810—21no—
10#14519810—22no—
11#14519799—21no—
12#14519799C2211yescharacteristic
13C2×Dic244—21no—
14C2×Dic244C2211yescharacteristic
15#14519723—21no—
16#14519723—22no—
17#14519720—21no—
18#14519717C2211yescharacteristic
19C2×#11758185C2211yescharacteristic
20#137×C61—21no—
21C2×Q16×C61C2211yescharacteristic
22#131×C61C2211yescharacteristic
23#108×C61C2211yescharacteristic
24#101×C61—21no—
25#41×C61D411yescharacteristic
26C2×Q8×C61—21no—
27Q8×D61—41no—
28#11758224—42no—
29#11758224—41no—
30#11758222—22no—
31#11758222—21no—
32C2×Dic122—22no—
33C2×Dic122—21no—
34Q16×C61—21no—
35Q16×C61—21no—
36Q16×C61—41no—
37SD16×C61—41no—
38M16×C61—21no—
39M16×C61—21no—
40M16×C61D411yescharacteristic
41C2×C8×C61—21no—
42C2×C8×C61C2311yescharacteristic
43Dic244—22no—
44Dic244—21no—
45Dic244D412yes—
46Dic244D411yescharacteristic
47D488D411yescharacteristic
48#11758190—22no—
49#11758190—21no—
50#11758185—21no—
51#11758185—21no—
52Q8×C61—41no—
53Q8×C61—41no—
54Q8×C61D811yescharacteristic
55D4×C61—21no—
56D4×C61D811yescharacteristic
57C2×C4×C61—21no—
58C2×C4×C61—41no—
59C2×C4×C61C2×D411yescharacteristic
60C22⋊D61—42no—
61C22⋊D61—41no—
62C2×Dic61—42no—
63C2×Dic61—41no—
64D244—21no—
65C4×D61—42no—
66C4×D61—41no—
67Dic122—22no—
68Dic122—21no—
69Dic122—42no—
70Dic122—41no—
71C8×C61—21no—
72C8×C61—41no—
73C8×C61C2×D411yescharacteristic
74C8×C61C2×D411yescharacteristic
75C22×C61—21no—
76C22×C61AGL(1,ℤ/8)11yescharacteristic
77C2×D61—41no—
78C4×C61—21no—
79C4×C61—81no—
80C4×C61#12011yescharacteristic
81C4×C61C2×D811yescharacteristic
82Dic61—41no—
83Dic61—42no—
84#2195—611nomaximal, Sylow
85C2×C61—21no—
86C2×C61—41no—
87C2×C61#44711yescharacteristic
88D61—81no—
89#578—611no—
90#510—611no—
91C2×Q32—611no—
92#473D6111yescharacteristic, complemented
93#362—611no—
94#359—611no—
95#350—611no—
96C61#219511yescharacteristic, complemented, Sylow
972−1+4—1221no—
98#137—21no—
99#137—1222no—
100#137—1221no—
101#135—611no—
102#135—1221no—
103C2×Q16—611no—
104C2×Q16—1221no—
105C2×Q16C2×D6111yescharacteristic
106#131C2×D6111yescharacteristic
107Q32—1222no—
108Q32—1221no—
109SD32—1221no—
110M32—611no—
111C2×C16—611no—
112#108C2×D6111yescharacteristic
113#101—21no—
114#41—1222no—
115#41—1221no—
116#41—2442no—
117#41—2441no—
118#41C22⋊D6111yescharacteristic
119C2×Q8—21no—
120C2×Q8—1222no—
121C2×Q8—1221no—
122C2×Q8—2441no—
123Q16—21no—
124Q16—21no—
125Q16—41no—
126Q16—612no—
127Q16—611no—
128Q16—1222no—
129Q16—1221no—
130SD16—41no—
131SD16—1222no—
132SD16—1221no—
133D8—611no—
134M16—21no—
135M16—21no—
136M16C22⋊D6111yescharacteristic
137C2×C8—21no—
138C2×C8C22×D6111yescharacteristic
139C16—1221no—
140C16—1221no—
141Q8—41no—
142Q8—41no—
143Q8—1222no—
144Q8—1221no—
145Q8—2442no—
146Q8—2441no—
147Q8#1175819911yescharacteristic
148D4—21no—
149D4—1221no—
150D4—2442no—
151D4—2441no—
152D4#1175819911yescharacteristic
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—2442no—
156C2×C4—2442no—
157C2×C4—2441no—
158C2×C4—2441no—
159C2×C4C2×C22⋊D6111yescharacteristic
160C8—21no—
161C8—41no—
162C8D4×D6111yescharacteristic
163C8D4×D6111yescharacteristic
164C22—21no—
165C22—2441no—
166C22#1451980211yescharacteristic
167C4—21no—
168C4—81no—
169C4—2442no—
170C4—2441no—
171C4#1451974511yescharacteristic
172C4C2×#1175819911yescharacteristic
173C2—21no—
174C2—41no—
175C2—4881no—
176C2#1683989511yescharacteristic
subgroupG/H
centerC2#16839895
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#473C2
socleC2×C61#447
hypercenter#473D61
hypocenterC61#2195
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #473

Complements

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

NH ≅ G/Ntype
2. #16840203C2semidirect
3. C2×#14519723C2semidirect
4. #16839577C2semidirect
5. #16839568C2semidirect
6. #16839546C2semidirect
7. C61×#473C2semidirect
92. #473D61semidirect
96. C61#2195semidirect