Finite Group Databasebeta

← #34000947

Subgroups — #34000947

Order 18688.

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

normal subgroups only

This group has 198 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#22624839C211yesmaximal, characteristic, complemented
3#22611215C211yesmaximal, characteristic
4#17989590—21no—
5#17989483—21no—
6#17988610C2211yescharacteristic
7C2×#14556518—21no—
8#17988571—21no—
9#17988345C411yescharacteristic
10#575×C73C411yescharacteristic
11C2×#11924037—22no—
12#14556665—41no—
13#14556658—41no—
14C4⋊#10596833—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
28#11924037—82no—
29C2×#10596833—42no—
30#11924031—81no—
31C22×Dic73—21no—
32#11924012—41no—
33#11924012—41no—
34#11924012—41no—
35C2×#10596831—21no—
36C2×#10596831—41no—
37C4×Dic73—21no—
38C4×Dic73D811yescharacteristic
39C4×Dic73SD1611yescharacteristic
40#41×C73—41no—
41#41×C73—41no—
42#41×C73—41no—
43#41×C73—41no—
44C2×Q8×C73—21no—
45C2×D4×C73—21no—
46C2×D4×C73—41no—
47C22×C4×C73—41no—
48C22×C4×C73C22⋊C411yescharacteristic
49Q16×C73—41no—
50SD16×C73—42no—
51D8×C73—41no—
52M16×C73—41no—
53C2×C8×C73—21no—
54C23×C73—41no—
55C23×C73#10411yescharacteristic
56Q8×C73—41no—
57Q8×C73—41no—
58D4×C73—41no—
59D4×C73—41no—
60D4×C73—81no—
61D4×C73—81no—
62C2×C4×C73—21no—
63C2×C4×C73—21no—
64C2×C4×C73—41no—
65C2×C4×C73—81no—
66C2×C4×C73—81no—
67C2×C4×C73#9911yescharacteristic
68C2×C4×C73#10211yescharacteristic
69C2×Dic73—21no—
70C2×Dic73—21no—
71C2×Dic73—41no—
72C2×Dic73—41no—
73#10596833—82no—
74C8×C73—41no—
75#10596831—41no—
76#10596831—81no—
77C22×C73—21no—
78C22×C73—41no—
79C22×C73—81no—
80C22×C73—161no—
81C22×C73#32711yescharacteristic
82C4×C73—21no—
83C4×C73—81no—
84C4×C73AΣL(1,𝔽16)11yescharacteristic
85C4×C73#35511yescharacteristic
86Dic73—21no—
87Dic73—21no—
88Dic73—41no—
89#7414—731nomaximal, Sylow
90C2×C73—21no—
91C2×C73—41no—
92C2×C73—161no—
93C2×C73#134511yescharacteristic
94#2050—731no—
95#1327—731no—
96#1309—731no—
97C73#741411yescharacteristic, complemented, Sylow
98#575#6440811yescharacteristic
99#423—731no—
100#423—1461no—
101C2×#104—1461no—
102#413—1461no—
103#349—1461no—
104#338—731no—
105C2×#41—21no—
106#137—41no—
107AGL(1,ℤ/8)—41no—
108#135—41no—
109C2×M16—731no—
110C2×M16—1461no—
111C2×M16—1462no—
112C2×M16C2×#6440811yescharacteristic
113C2×C42—731no—
114M32—2921no—
115C4⋊C8—2921no—
116C4⋊C8—2921no—
117C4⋊C8—2921no—
118#104—2921no—
119#104—2921no—
120#101—2921no—
121#100—2921no—
122#41—41no—
123#41—41no—
124#41—41no—
125#41—41no—
126C2×Q8—21no—
127C2×D4—21no—
128C2×D4—41no—
129C22×C4—41no—
130C22×C4—1461no—
131C22×C4C22⋊#6440811yescharacteristic
132Q16—41no—
133SD16—42no—
134D8—41no—
135M16—41no—
136M16—2921no—
137M16—2921no—
138M16—2921no—
139M16—5842no—
140C2×C8—21no—
141C2×C8—2921no—
142C2×C8—2922no—
143C2×C8—1461no—
144C42—731no—
145C42—731no—
146C42—1461no—
147C16—5841no—
148C23—41no—
149C23#1455665511yescharacteristic
150Q8—41no—
151Q8—41no—
152D4—41no—
153D4—41no—
154D4—81no—
155D4—81no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4—2921no—
162C2×C4—2921no—
163C2×C4—1461no—
164C2×C4—1461no—
165C2×C4#1455664911yescharacteristic
166C2×C4#1455665311yescharacteristic
167C8—41no—
168C8—2921no—
169C8—5841no—
170C8—5842no—
171C22—21no—
172C22—41no—
173C22—81no—
174C22—161no—
175C22#1798943811yescharacteristic
176C4—21no—
177C4—81no—
178C4—2921no—
179C4—1461no—
180C4—1461no—
181C4#1798948711yescharacteristic
182C4#1798949511yescharacteristic
183C2—21no—
184C2—41no—
185C2—161no—
186C2#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#7414
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. #22624839C2semidirect
97. C73#7414semidirect

Maximal subgroups

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

subgroupindex
#226248782
#226248392
#226112152
#741473