Finite Group Databasebeta

← #33006612

Subgroups — #33006612

Order 18688.

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#22612244C211yesmaximal, characteristic
2#22611816C211yesmaximal, characteristic, complemented
3#22611807C211yesmaximal, characteristic, complemented
4#22608138C211yesmaximal, characteristic, complemented
5#22608119C211yesmaximal, characteristic, complemented
6#22608066C211yesmaximal, characteristic, complemented
7C73×#1419C211yesmaximal, characteristic, complemented
8#17989019C2211yescharacteristic
9#17988703—21no—
10D8×Dic73—21no—
11#17988425C412yescomplemented
12#17988422C412yescomplemented
13#17988421C2211yescharacteristic
14#17988415C2211yescharacteristic
15#17988393—21no—
16#17988388—21no—
17#17988362C2211yescharacteristic
18C2×D16×C73C2211yescharacteristic
19M64×C73C2211yescharacteristic
20#368×C73C2211yescharacteristic
21#14556613—21no—
22#14556599—41no—
23D4×Dic73—41no—
24Dic584C2×C411yescharacteristic, complemented
25#14556536—21no—
26D1168C2×C411yescharacteristic, complemented
27C2×#11924003D411yescharacteristic
28#14556525—21no—
29#14556517—41no—
30#14556512—41no—
31C8×Dic73D411yescharacteristic
32#14556497C2×C412yescomplemented
33C2×D8×C73—21no—
34D16×C73—21no—
35D16×C73C2×C412yes—
36C2×C16×C73C2311yescharacteristic
37#108×C73—21no—
38C32×C73—21no—
39#11924028—41no—
40C22×Dic73—81no—
41Dic292—21no—
42#11924017—41no—
43D584—21no—
44#11924011—81no—
45C2×#10596831D811yescharacteristic
46C8×D73—81no—
47C4⋊Dic73—41no—
48C22⋊Dic73—81no—
49C4×Dic73D811yescharacteristic
50#11924003—21no—
51C2×D4×C73—41no—
52D8×C73—22no—
53D8×C73—41no—
54M16×C73—41no—
55C2×C8×C73C2×D411yescharacteristic
56C16×C73C22×C411yescharacteristic
57C16×C73#4111yescharacteristic
58C23×C73—81no—
59D4×C73—42no—
60D4×C73—81no—
61C2×C4×C73C2×D811yescharacteristic
62C22⋊D73—81no—
63C2×Dic73—21no—
64C2×Dic73—81no—
65C2×Dic73—162no—
66D292—41no—
67C4×D73—81no—
68Dic146—41no—
69C8×C73—81no—
70C8×C73C4×D411yescharacteristic
71C8×C73#13511yescharacteristic
72#10596831—21no—
73C22×C73—82no—
74C22×C73—161no—
75C22×C73—161no—
76C22×C73#50911yescharacteristic
77C2×D73—81no—
78C4×C73C4×D811yescharacteristic
79C4×C73#50911yescharacteristic
80Dic73—41no—
81Dic73—81no—
82Dic73—161no—
83#13658—731nomaximal, Sylow
84C2×C73—21no—
85C2×C73—162no—
86C2×C73#217711yescharacteristic
87D73—161no—
88#2263—731no—
89#2179—731no—
90#2177—731no—
91#1426—731no—
92#1419D7311yescharacteristic, complemented
93#1418—731no—
94#1398—731no—
95C73#1365811yescharacteristic, complemented, Sylow
96#508—731no—
97C2×D16C2×D7311yescharacteristic
98#443—1461no—
99C4×D8—1461no—
100SD64—732no—
101D32—732no—
102M64—731no—
103M64C2×D7311yescharacteristic
104#368C2×D7311yescharacteristic
105#367—731no—
106#359—1461no—
107#357—1461no—
108#346—731no—
109#135—1461no—
110C2×D8—21no—
111#131—2921no—
112C4×D4—2921no—
113Q32—731no—
114SD32—1461no—
115D16—21no—
116D16—731no—
117D16C4×D7312yes—
118C2×C16—731no—
119C2×C16C22×D7311yescharacteristic
120#108—21no—
121#107—1461no—
122#104—2921no—
123#102—2921no—
124C4×C8—731no—
125C32—21no—
126C32—732no—
127#41—2921no—
128C2×D4—41no—
129C22×C4—5841no—
130Q16—1461no—
131SD16—2921no—
132D8—22no—
133D8—41no—
134D8—1461no—
135M16—41no—
136M16—5841no—
137C2×C8—5841no—
138C2×C8—731no—
139C2×C8D4×D7311yescharacteristic
140C4⋊C4—2921no—
141C22⋊C4—5841no—
142C42—731no—
143C16—1461no—
144C16C2×C4×D7311yescharacteristic
145C16#1192402711yescharacteristic
146C23—81no—
147Q8—2921no—
148D4—42no—
149D4—81no—
150D4—2921no—
151D4—5841no—
152C2×C4—5841no—
153C2×C4—5841no—
154C2×C4—11682no—
155C2×C4—1461no—
156C2×C4D8×D7311yescharacteristic
157C8—81no—
158C8—1461no—
159C8#1455655111yescharacteristic
160C8#1455661211yescharacteristic
161C22—82no—
162C22—161no—
163C22—161no—
164C22—5841no—
165C22#1798902411yescharacteristic
166C4—2921no—
167C4—5841no—
168C4—11681no—
169C4#1798866711yescharacteristic
170C4#1798902111yescharacteristic
171C2—21no—
172C2—162no—
173C2—11681no—
174C2#2261180411yescharacteristic
subgroupG/H
centerC2#22611804
commutatorC16×C73C22×C4
FrattiniC2×C16C22×D73
FittingC73×#1419C2
socleC2×C73#2177
prime radical#22612244C2
cosocleC2×C16×C73C23
hypercenter#1419D73
hypocenterC73#13658
LCSG ▷ C16×C73 ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1419

Complements

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

NH ≅ G/Ntype
2. #22611816C2semidirect
3. #22611807C2semidirect
4. #22608138C2semidirect
5. #22608119C2semidirect
6. #22608066C2semidirect
7. C73×#1419C2semidirect
11. #17988425C4semidirect
12. #17988422C4semidirect
24. Dic584C2×C4semidirect
26. D1168C2×C4semidirect
32. #14556497C2×C4semidirect
92. #1419D73semidirect
95. C73#13658semidirect

Maximal subgroups

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

subgroupindex
#226122442
#226118162
#226118072
#226081382
#226081192
#226080662
C73×#14192
#1365873