Finite Group Databasebeta

← #32996835

Subgroups — #32996835

Order 18688.

280 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 71 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#22620676C211yesmaximal, characteristic
2#22611743C211yesmaximal, characteristic
3#22607924C212yesmaximal
4#22607918C212yesmaximal
5C73×#1841C211yesmaximal, characteristic
6#17989144—21no—
7#17988985C411yescharacteristic, complemented
8#17988967C411yescharacteristic, complemented
9#17988938—21no—
10#17988845—21no—
11#17988845C2212yes—
12#17988695—21no—
13#17988695C412yescomplemented
14#17988408—21no—
15#17988369C2212yes—
16#17988365—21no—
17C4×M16×C73C2211yescharacteristic
18#344×C73—21no—
19#339×C73—21no—
20#338×C73C2211yescharacteristic
21H(3,ℤ/4)×C73C2211yescharacteristic
22C2×Dic292—21no—
23C2×Dic292C2×C412yes—
24#14556591—21no—
25#14556591—21no—
26#14556583—41no—
27#14556570—22no—
28#14556570—41no—
29C4×Dic146—22no—
30C4×Dic146—41no—
31#14556550—41no—
32#14556531—22no—
33#14556523—21no—
34#14556523C2×C412yes—
35#14556516—22no—
36#14556516—22no—
37C2×M16×C73—21no—
38C2×M16×C73D411yescharacteristic
39C2×M16×C73C2311yescharacteristic
40#117×C73—21no—
41C2×C42×C73D411yescharacteristic
42#97×C73C2×C411yescharacteristic
43#97×C73D411yescharacteristic
44C4×C8×C73C2×C411yescharacteristic
45C4×C8×C73D411yescharacteristic
46C2×Dic146—22no—
47C2×Dic146—41no—
48Dic292—42no—
49Dic292—42no—
50C4⋊Dic73—22no—
51C4⋊Dic73—41no—
52C4⋊Dic73—41no—
53C4⋊Dic73—41no—
54#11924007—42no—
55#11924007—42no—
56C22⋊Dic73—42no—
57C4×Dic73—42no—
58#11924003—42no—
59C22×C4×C73—21no—
60C22×C4×C73C2×D411yescharacteristic
61M16×C73—41no—
62M16×C73—41no—
63M16×C73—41no—
64M16×C73—41no—
65C2×C8×C73—41no—
66C2×C8×C73C22⋊C411yescharacteristic
67C2×C8×C73C22⋊C411yescharacteristic
68C2×C8×C73C22×C411yescharacteristic
69C2×C8×C73C2×D411yescharacteristic
70C4⋊C4×C73—41no—
71C22⋊C4×C73—41no—
72C42×C73—21no—
73C42×C73—41no—
74C42×C73C22⋊C411yescharacteristic
75C42×C73C22⋊C411yescharacteristic
76C23×C73AGL(1,ℤ/8)11yescharacteristic
77C2×C4×C73—21no—
78C2×C4×C73—21no—
79C2×C4×C73—21no—
80C2×C4×C73—21no—
81C2×C4×C73—42no—
82C2×C4×C73—81no—
83C2×C4×C73C2×C22⋊C411yescharacteristic
84C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
85C2×Dic73—42no—
86C2×Dic73—42no—
87Dic146—42no—
88Dic146—42no—
89Dic146—82no—
90C8×C73—21no—
91C8×C73—21no—
92C8×C73—21no—
93C8×C73—21no—
94C8×C73—81no—
95C22×C73—21no—
96C22×C73—41no—
97C22×C73#41811yescharacteristic
98C4×C73—22no—
99C4×C73—21no—
100C4×C73—41no—
101C4×C73—161no—
102C4×C73#41011yescharacteristic
103C4×C73#42111yescharacteristic
104Dic73—82no—
105Dic73—82no—
106#11838—731nomaximal, Sylow
107C2×C73—21no—
108C2×C73—41no—
109C2×C73#151411yescharacteristic
110#3185—731no—
111#2165—731no—
112#1841D7311yescharacteristic
113#1342—732no—
114#1340—732no—
115C73#1183811yescharacteristic, complemented, Sylow
116#533—1461no—
117#498—731no—
118#494—731no—
119#487—1461no—
120#470—732no—
121#470—1461no—
122#441—732no—
123#441—1461no—
124C4×M16C2×D7311yescharacteristic
125#364—1461no—
126#349—732no—
127#347—1461no—
128#344—21no—
129#339—21no—
130#338C2×D7311yescharacteristic
131H(3,ℤ/4)C2×D7311yescharacteristic
132C2×Q16—732no—
133C2×Q16—1461no—
134C2×M16—21no—
135C2×M16C22⋊D7311yescharacteristic
136C2×M16C22×D7311yescharacteristic
137C4⋊Q8—1461no—
138C4⋊Q8—1461no—
139#125—2921no—
140C22⋊Q8—2921no—
141C22⋊Q8—1462no—
142C4×Q8—2921no—
143C4×Q8—1462no—
144#117—21no—
145#117—2921no—
146C2×C42C22⋊D7311yescharacteristic
147M32—1462no—
148#106—732no—
149#106—1461no—
150#103—1462no—
151#103—1462no—
152#97C4×D7311yescharacteristic
153#97D29211yescharacteristic
154C4×C8C4×D7311yescharacteristic
155C4×C8D29211yescharacteristic
156C2×Q8—2921no—
157C2×Q8—1462no—
158C22×C4—21no—
159C22×C4C2×C22⋊D7311yescharacteristic
160Q16—2922no—
161Q16—2922no—
162M16—41no—
163M16—41no—
164M16—41no—
165M16—41no—
166C2×C8—41no—
167C2×C8#1192400511yescharacteristic
168C2×C8#1192400511yescharacteristic
169C2×C8C2×C4×D7311yescharacteristic
170C2×C8C2×D29211yescharacteristic
171C4⋊C4—41no—
172C4⋊C4—2922no—
173C4⋊C4—2921no—
174C4⋊C4—2921no—
175C4⋊C4—2921no—
176C4⋊C4—2922no—
177C4⋊C4—1462no—
178C22⋊C4—41no—
179C22⋊C4—2922no—
180C42—21no—
181C42—41no—
182C42—2922no—
183C42#1192400511yescharacteristic
184C42#1192400511yescharacteristic
185C16—2922no—
186C23#1455661611yescharacteristic
187Q8—2922no—
188Q8—2922no—
189Q8—5842no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—42no—
195C2×C4—81no—
196C2×C4—2922no—
197C2×C4—2922no—
198C2×C4C2×#1192400511yescharacteristic
199C2×C4#1455661611yescharacteristic
200C8—21no—
201C8—21no—
202C8—21no—
203C8—21no—
204C8—81no—
205C22—21no—
206C22—41no—
207C22#1798859111yescharacteristic
208C4—22no—
209C4—21no—
210C4—41no—
211C4—161no—
212C4—5842no—
213C4—5842no—
214C4#1798856011yescharacteristic
215C4#1798860511yescharacteristic
216C2—21no—
217C2—41no—
218C2#2260847711yescharacteristic
subgroupG/H
centerC2#22608477
commutatorC2×C8×C73C22×C4
FrattiniC2×M16C22×D73
FittingC73×#1841C2
socleC2×C73#1514
prime radicalC23×C73AGL(1,ℤ/8)
cosocleC2×M16×C73C23
hypercenter#1841D73
hypocenterC73#11838
LCSG ▷ C2×C8×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #1841

Complements

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

NH ≅ G/Ntype
7. #17988985C4semidirect
8. #17988967C4semidirect
13. #17988695C4semidirect
115. C73#11838semidirect

Maximal subgroups

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

subgroupindex
#226206762
#226117432
#226079242
#226079182
C73×#18412
#1183873