Finite Group Databasebeta

← #33004528

Subgroups — #33004528

Order 18688.

308 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 115 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#22618869C211yesmaximal, characteristic
2#22611697C211yesmaximal, characteristic
3#22608016C212yesmaximal
4#22608010C212yesmaximal
5C73×#2110C211yesmaximal, characteristic
6#17989140C411yescharacteristic
7C2×#14556531C2212yes—
8#17988717—22no—
9#17988715—22no—
10#17988615C411yescharacteristic
11#17988614C411yescharacteristic
12#17988610C411yescharacteristic
13#17988542C2211yescharacteristic
14C2×#14556501C2211yescharacteristic
15#17988408—22no—
16C2×M32×C73C2212yes—
17#405×C73C2211yescharacteristic
18#347×C73—22no—
19C2×#11924012C2×C411yescharacteristic
20C22×#10596831C2×C411yescharacteristic
21#14556590—21no—
22#14556582—21no—
23#14556568—22no—
24C4×Dic146—22no—
25#14556550C2×C411yescharacteristic
26C2×C4×Dic73C2×C411yescharacteristic
27#14556531—22no—
28#14556531—22no—
29C2×#11924003—22no—
30C4⋊#10596831—22no—
31#14556520—22no—
32#14556520—22no—
33#14556501—21no—
34#14556501—21no—
35#14556501—21no—
36C8×Dic73—21no—
37C2×M16×C73C2×C411yescharacteristic
38C22×C8×C73C2311yescharacteristic
39#117×C73C2×C411yescharacteristic
40M32×C73—22no—
41M32×C73—22no—
42C2×C16×C73Q814yescomplemented
43#97×C73D412yes—
44C4×C8×C73D412yes—
45C2×Dic146—22no—
46C22×Dic73—21no—
47#11924012—22no—
48C2×#10596831—21no—
49C2×#10596831—21no—
50C2×#10596831—22no—
51C4⋊Dic73—22no—
52C4⋊Dic73—21no—
53#11924007—22no—
54#11924007—22no—
55C22⋊Dic73M1612yes—
56C4×Dic73—21no—
57C4×Dic73—21no—
58C4×Dic73M1611yescharacteristic
59C4×Dic73M1611yescharacteristic
60#11924003—42no—
61C22×C4×C73C22×C411yescharacteristic
62M16×C73—22no—
63C2×C8×C73C22⋊C412yes—
64C2×C8×C73C2×D411yescharacteristic
65C2×C8×C73C2×D411yescharacteristic
66C2×C8×C73C2×Q812yes—
67C2×C8×C73#4112yes—
68C4⋊C4×C73—21no—
69C22⋊C4×C73—21no—
70C42×C73C22⋊C412yes—
71C16×C73—24no—
72C23×C73C2×M1611yescharacteristic
73C2×C4×C73—22no—
74C2×C4×C73C2×C22⋊C411yescharacteristic
75C2×C4×C73C4×Q812yes—
76C2×C4×C73C2×M1611yescharacteristic
77C2×C4×C73#13112yes—
78C2×Dic73—21no—
79C2×Dic73—21no—
80C2×Dic73—22no—
81C2×Dic73—81no—
82Dic146—82no—
83C8×C73—22no—
84C8×C73C22⋊Q812yes—
85C8×C73#12411yescharacteristic
86C8×C73C4⋊Q811yescharacteristic
87#10596831—41no—
88#10596831—41no—
89C22×C73—41no—
90C22×C73#40711yescharacteristic
91C22×C73#44612yes—
92C4×C73—42no—
93C4×C73#39111yescharacteristic
94C4×C73#40811yescharacteristic
95C4×C73#44612yes—
96Dic73—41no—
97Dic73—42no—
98Dic73—41no—
99#13269—731nomaximal, Sylow
100C2×C73—21no—
101C2×C73—22no—
102C2×C73#198511yescharacteristic
103#2961—731no—
104#2153—731no—
105#2110D7311yescharacteristic
106#1378—732no—
107#1375—732no—
108C73#1326911yescharacteristic, complemented, Sylow
109#533—731no—
110C2×M32—732no—
111C2×M32C2×D7312yes—
112#446—1462no—
113#446—1462no—
114#424—731no—
115#424—731no—
116#423—731no—
117#405—731no—
118#405C2×D7311yescharacteristic
119C2×#97—731no—
120#364—1462no—
121#347—22no—
122C2×M16—731no—
123C2×M16C4×D7311yescharacteristic
124C22×C8—731no—
125C22×C8C22×D7311yescharacteristic
126C4⋊Q8—1461no—
127#125—1461no—
128C22⋊Q8—1462no—
129C4×Q8—1462no—
130#117—731no—
131#117C4×D7311yescharacteristic
132C2×C42—731no—
133M32—22no—
134M32—22no—
135M32—1462no—
136M32—1462no—
137C2×C16—1462no—
138C2×C16Dic14614yescomplemented
139C4⋊C8—1462no—
140C4⋊C8—1462no—
141C4⋊C8—1462no—
142#97—1461no—
143#97—1461no—
144#97—1461no—
145#97C22⋊D7312yes—
146C4×C8—1461no—
147C4×C8D29212yes—
148C2×Q8—1462no—
149C22×C4—1461no—
150C22×C4C2×C4×D7311yescharacteristic
151M16—22no—
152M16—1462no—
153C2×C8—1461no—
154C2×C8—1461no—
155C2×C8—1462no—
156C2×C8#1192400512yes—
157C2×C8C2×C22⋊D7311yescharacteristic
158C2×C8C2×D29211yescharacteristic
159C2×C8C2×Dic14612yes—
160C2×C8#1192402812yes—
161C4⋊C4—21no—
162C4⋊C4—1462no—
163C4⋊C4—1462no—
164C4⋊C4—1462no—
165C4⋊C4—1461no—
166C22⋊C4—21no—
167C22⋊C4—732no—
168C42—731no—
169C42—731no—
170C42—1461no—
171C42—1461no—
172C42#1192400512yes—
173C16—24no—
174C16—2922no—
175C23M16×D7311yescharacteristic
176Q8—5842no—
177C2×C4—22no—
178C2×C4—5841no—
179C2×C4—1461no—
180C2×C4—1461no—
181C2×C4—1462no—
182C2×C4C2×#1192400511yescharacteristic
183C2×C4C4×Dic14612yes—
184C2×C4M16×D7311yescharacteristic
185C2×C4#1455659912yes—
186C8—22no—
187C8—2921no—
188C8—2921no—
189C8#1455657012yes—
190C8#1455657911yescharacteristic
191C8#1455659111yescharacteristic
192C22—41no—
193C22#1798855011yescharacteristic
194C22#1798871512yes—
195C4—42no—
196C4—2921no—
197C4—2921no—
198C4—2922no—
199C4#1798849311yescharacteristic
200C4#1798855511yescharacteristic
201C4#1798871512yes—
202C2—21no—
203C2—22no—
204C2#2261087111yescharacteristic
subgroupG/H
centerC4#17988493
commutatorC22×C4×C73C22×C4
FrattiniC22×C8C22×D73
FittingC73×#2110C2
socleC2×C73#1985
prime radicalC23×C73C2×M16
cosocleC22×C8×C73C23
hypercenter#2110D73
hypocenterC73#13269
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C22×C8 ◁ #2110

Complements

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

NH ≅ G/Ntype
42. C2×C16×C73Q8semidirect
108. C73#13269semidirect
138. C2×C16Dic146semidirect

Maximal subgroups

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

subgroupindex
#226188692
#226116972
#226080162
#226080102
C73×#21102
#1326973