Finite Group Databasebeta

← #31918080

Subgroups — #31918080

Order 18176.

194 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 59 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#22590653C211yesmaximal, characteristic
2#22590225C211yesmaximal, characteristic, complemented
3#22590216C211yesmaximal, characteristic, complemented
4#22586547C211yesmaximal, characteristic, complemented
5#22586528C211yesmaximal, characteristic, complemented
6#22586475C211yesmaximal, characteristic, complemented
7C71×#1419C211yesmaximal, characteristic, complemented
8#17986431C2211yescharacteristic
9#17986115—21no—
10D8×Dic71—21no—
11#17985837C412yescomplemented
12#17985834C412yescomplemented
13#17985833C2211yescharacteristic
14#17985827C2211yescharacteristic
15#17985805—21no—
16#17985800—21no—
17#17985774C2211yescharacteristic
18C2×D16×C71C2211yescharacteristic
19M64×C71C2211yescharacteristic
20#368×C71C2211yescharacteristic
21#14556150—21no—
22#14556136—41no—
23D4×Dic71—41no—
24Dic568C2×C411yescharacteristic, complemented
25#14556073—21no—
26D1136C2×C411yescharacteristic, complemented
27C2×C71⋊C16D411yescharacteristic
28#14556062—21no—
29#14556054—41no—
30#14556049—41no—
31C8×Dic71D411yescharacteristic
32C71⋊C32C2×C412yescomplemented
33C2×D8×C71—21no—
34D16×C71—21no—
35D16×C71C2×C412yes—
36C2×C16×C71C2311yescharacteristic
37#108×C71—21no—
38C32×C71—21no—
39#11765865—41no—
40C22×Dic71—81no—
41Dic284—21no—
42#11765854—41no—
43D568—21no—
44#11765848—81no—
45C2×C71⋊C8D811yescharacteristic
46C8×D71—81no—
47C4⋊Dic71—41no—
48C22⋊Dic71—81no—
49C4×Dic71D811yescharacteristic
50C71⋊C16—21no—
51C2×D4×C71—41no—
52D8×C71—22no—
53D8×C71—41no—
54M16×C71—41no—
55C2×C8×C71C2×D411yescharacteristic
56C16×C71C22×C411yescharacteristic
57C16×C71#4111yescharacteristic
58C23×C71—81no—
59D4×C71—42no—
60D4×C71—81no—
61C2×C4×C71C2×D811yescharacteristic
62C22⋊D71—81no—
63C2×Dic71—21no—
64C2×Dic71—81no—
65C2×Dic71—162no—
66D284—41no—
67C4×D71—81no—
68Dic142—41no—
69C8×C71—81no—
70C8×C71C4×D411yescharacteristic
71C8×C71#13511yescharacteristic
72C71⋊C8—21no—
73C22×C71—82no—
74C22×C71—161no—
75C22×C71—161no—
76C22×C71#50911yescharacteristic
77C2×D71—81no—
78C4×C71C4×D811yescharacteristic
79C4×C71#50911yescharacteristic
80Dic71—41no—
81Dic71—81no—
82Dic71—161no—
83#13658—711nomaximal, Sylow
84C2×C71—21no—
85C2×C71—162no—
86C2×C71#217711yescharacteristic
87D71—161no—
88#2263—711no—
89#2179—711no—
90#2177—711no—
91#1426—711no—
92#1419D7111yescharacteristic, complemented
93#1418—711no—
94#1398—711no—
95C71#1365811yescharacteristic, complemented, Sylow
96#508—711no—
97C2×D16C2×D7111yescharacteristic
98#443—1421no—
99C4×D8—1421no—
100SD64—712no—
101D32—712no—
102M64—711no—
103M64C2×D7111yescharacteristic
104#368C2×D7111yescharacteristic
105#367—711no—
106#359—1421no—
107#357—1421no—
108#346—711no—
109#135—1421no—
110C2×D8—21no—
111#131—2841no—
112C4×D4—2841no—
113Q32—711no—
114SD32—1421no—
115D16—21no—
116D16—711no—
117D16C4×D7112yes—
118C2×C16—711no—
119C2×C16C22×D7111yescharacteristic
120#108—21no—
121#107—1421no—
122#104—2841no—
123#102—2841no—
124C4×C8—711no—
125C32—21no—
126C32—712no—
127#41—2841no—
128C2×D4—41no—
129C22×C4—5681no—
130Q16—1421no—
131SD16—2841no—
132D8—22no—
133D8—41no—
134D8—1421no—
135M16—41no—
136M16—5681no—
137C2×C8—5681no—
138C2×C8—711no—
139C2×C8D4×D7111yescharacteristic
140C4⋊C4—2841no—
141C22⋊C4—5681no—
142C42—711no—
143C16—1421no—
144C16C2×C4×D7111yescharacteristic
145C16#1176586411yescharacteristic
146C23—81no—
147Q8—2841no—
148D4—42no—
149D4—81no—
150D4—2841no—
151D4—5681no—
152C2×C4—5681no—
153C2×C4—5681no—
154C2×C4—11362no—
155C2×C4—1421no—
156C2×C4D8×D7111yescharacteristic
157C8—81no—
158C8—1421no—
159C8(C22⋊D71)⋊C411yescharacteristic
160C8#1455614911yescharacteristic
161C22—82no—
162C22—161no—
163C22—161no—
164C22—5681no—
165C22#1798643611yescharacteristic
166C4—2841no—
167C4—5681no—
168C4—11361no—
169C4#1798607911yescharacteristic
170C4#1798643311yescharacteristic
171C2—21no—
172C2—162no—
173C2—11361no—
174C2#2259021311yescharacteristic
subgroupG/H
centerC2#22590213
commutatorC16×C71C22×C4
FrattiniC2×C16C22×D71
FittingC71×#1419C2
socleC2×C71#2177
prime radical#22590653C2
cosocleC2×C16×C71C23
hypercenter#1419D71
hypocenterC71#13658
LCSG ▷ C16×C71 ▷ C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1419

Complements

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

NH ≅ G/Ntype
2. #22590225C2semidirect
3. #22590216C2semidirect
4. #22586547C2semidirect
5. #22586528C2semidirect
6. #22586475C2semidirect
7. C71×#1419C2semidirect
11. #17985837C4semidirect
12. #17985834C4semidirect
24. Dic568C2×C4semidirect
26. D1136C2×C4semidirect
32. C71⋊C32C2×C4semidirect
92. #1419D71semidirect
95. C71#13658semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#225906532
#225902252
#225902162
#225865472
#225865282
#225864752
C71×#14192
#1365871