Finite Group Databasebeta

← #34000949

Subgroups — #34000949

Order 18688.

190 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 32 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#22624878C211yesmaximal, characteristic, complemented
2#22624837C211yesmaximal, characteristic, complemented
3#22611215C211yesmaximal, characteristic
4#17989608—21no—
5#17989483—21no—
6#17988610C2211yescharacteristic
7C2×#14556518—21no—
8#17988571—21no—
9#17988345C411yescharacteristic
10#575×C73C411yescharacteristic
11#14556665—41no—
12C4⋊#10596833—41no—
13C22⋊#10596833—22no—
14#14556646—41no—
15C2×#11924012—21no—
16C2×#11924012D411yescharacteristic
17C2×C4×Dic73D411yescharacteristic
18#14556520—41no—
19#14556518—41no—
20#14556518—41no—
21#14556510—41no—
22#14556508—41no—
23C2×#41×C73—21no—
24#137×C73—41no—
25AGL(1,ℤ/8)×C73—41no—
26#135×C73—41no—
27C2×M16×C73C2×C411yescharacteristic
28C2×#10596833—42no—
29#11924031—81no—
30C22×Dic73—21no—
31#11924012—41no—
32#11924012—41no—
33#11924012—41no—
34C2×#10596831—21no—
35C2×#10596831—41no—
36C4×Dic73—21no—
37C4×Dic73D811yescharacteristic
38C4×Dic73SD1611yescharacteristic
39#41×C73—41no—
40#41×C73—41no—
41#41×C73—41no—
42#41×C73—41no—
43C2×Q8×C73—21no—
44C2×D4×C73—21no—
45C2×D4×C73—41no—
46C22×C4×C73—41no—
47C22×C4×C73C22⋊C411yescharacteristic
48Q16×C73—41no—
49SD16×C73—42no—
50D8×C73—41no—
51M16×C73—41no—
52C2×C8×C73—21no—
53C23×C73—41no—
54C23×C73#10411yescharacteristic
55Q8×C73—41no—
56Q8×C73—41no—
57D4×C73—41no—
58D4×C73—41no—
59D4×C73—81no—
60D4×C73—81no—
61C2×C4×C73—21no—
62C2×C4×C73—21no—
63C2×C4×C73—41no—
64C2×C4×C73—81no—
65C2×C4×C73—81no—
66C2×C4×C73#9911yescharacteristic
67C2×C4×C73#10211yescharacteristic
68C2×Dic73—21no—
69C2×Dic73—21no—
70C2×Dic73—81no—
71#10596833—82no—
72C8×C73—41no—
73#10596831—41no—
74#10596831—81no—
75C22×C73—21no—
76C22×C73—41no—
77C22×C73—81no—
78C22×C73—161no—
79C22×C73#32711yescharacteristic
80C4×C73—21no—
81C4×C73—81no—
82C4×C73AΣL(1,𝔽16)11yescharacteristic
83C4×C73#35511yescharacteristic
84Dic73—41no—
85Dic73—41no—
86#7415—731nomaximal, Sylow
87C2×C73—21no—
88C2×C73—41no—
89C2×C73—161no—
90C2×C73#134511yescharacteristic
91#2050—731no—
92#1327—731no—
93#1307—731no—
94C73#741511yescharacteristic, complemented, Sylow
95#575#6440811yescharacteristic
96#432—1461no—
97#423—731no—
98C2×#104—1461no—
99#413—1461no—
100#349—1461no—
101#338—731no—
102C2×#41—21no—
103#137—41no—
104AGL(1,ℤ/8)—41no—
105#135—41no—
106C2×M16—731no—
107C2×M16—1461no—
108C2×M16C2×#6440811yescharacteristic
109C2×C42—731no—
110M32—2921no—
111C4⋊C8—2921no—
112C4⋊C8—2921no—
113#104—2921no—
114#104—2921no—
115#101—2921no—
116#100—2921no—
117C22⋊C8—1462no—
118#97—2921no—
119#41—41no—
120#41—41no—
121#41—41no—
122#41—41no—
123C2×Q8—21no—
124C2×D4—21no—
125C2×D4—41no—
126C22×C4—41no—
127C22×C4—1461no—
128C22×C4C22⋊#6440811yescharacteristic
129Q16—41no—
130SD16—42no—
131D8—41no—
132M16—41no—
133M16—2921no—
134M16—2921no—
135M16—2921no—
136C2×C8—21no—
137C2×C8—2921no—
138C2×C8—2922no—
139C2×C8—1461no—
140C42—731no—
141C42—731no—
142C42—1461no—
143C16—5841no—
144C23—41no—
145C23#1455665511yescharacteristic
146Q8—41no—
147Q8—41no—
148D4—41no—
149D4—41no—
150D4—81no—
151D4—81no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—81no—
156C2×C4—81no—
157C2×C4—5841no—
158C2×C4—1461no—
159C2×C4—1461no—
160C2×C4#1455664911yescharacteristic
161C2×C4#1455665311yescharacteristic
162C8—41no—
163C8—2921no—
164C8—5841no—
165C8—5842no—
166C22—21no—
167C22—41no—
168C22—81no—
169C22—161no—
170C22#1798943811yescharacteristic
171C4—21no—
172C4—81no—
173C4—2921no—
174C4—2921no—
175C4#1798948711yescharacteristic
176C4#1798949511yescharacteristic
177C2—21no—
178C2—41no—
179C2—161no—
180C2#2262491311yescharacteristic
subgroupG/H
centerC2#22624913
commutatorC2×M16×C73C2×C4
FrattiniC2×M16C2×#64408
Fitting, prime radical#575×C73C4
socleC2×C73#1345
cosocle#17988610C22
hypercenter#575#64408
hypocenterC73#7415
LCSG ▷ C2×M16×C73 ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #22624878C2semidirect
2. #22624837C2semidirect
94. C73#7415semidirect

Maximal subgroups

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

subgroupindex
#226248782
#226248372
#226112152
#741573