Finite Group Databasebeta

← #32999360

Subgroups — #32999360

Order 18688.

318 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 318 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#22612143C212yesmaximal, complemented
2#22611506C211yesmaximal, characteristic, complemented
3#22607916C212yesmaximal, complemented
4#22607882C211yesmaximal, characteristic, complemented
5C73×#3253C211yesmaximal, characteristic
6#17988636C2211yescharacteristic
7#17988409—22no—
8#17988400—22no—
9#17988369C2212yes—
10#17988359—21no—
11#17988347—21no—
12#17988344C2211yescharacteristic
13#532×C73—21no—
14#476×C73—22no—
15#469×C73—21no—
16#469×C73C2212yes—
17#459×C73—22no—
18#423×C73C2211yescharacteristic
19C2×#11924012—21no—
20#14556550—21no—
21#14556531—22no—
22#14556527—22no—
23C2×#41×C73—41no—
24C2×D8×C73—21no—
25C2×D8×C73D412yes—
26C2×M16×C73D411yescharacteristic
27C2×M16×C73C2311yescharacteristic
28C4⋊Q8×C73—21no—
29#127×C73—21no—
30#124×C73—41no—
31#121×C73—22no—
32#121×C73—41no—
33C4×D4×C73—22no—
34C4×D4×C73—41no—
35C2×C42×C73D411yescharacteristic
36#106×C73—21no—
37#106×C73D412yes—
38C4⋊C8×C73—22no—
39#102×C73—22no—
40#102×C73—22no—
41#11924012—41no—
42#11924012—41no—
43C2×#10596831—41no—
44C4⋊Dic73—41no—
45C22⋊Dic73—41no—
46C4×Dic73—41no—
47#11924003—42no—
48#41×C73—84no—
49C2×Q8×C73—41no—
50C2×D4×C73—22no—
51C2×D4×C73—41no—
52C2×D4×C73—41no—
53C2×D4×C73—42no—
54C22×C4×C73—21no—
55C22×C4×C73—42no—
56C22×C4×C73C2×D411yescharacteristic
57D8×C73—42no—
58D8×C73—81no—
59M16×C73—41no—
60M16×C73—41no—
61C2×C8×C73—21no—
62C2×C8×C73C2×D412yes—
63C4⋊C4×C73—22no—
64C4⋊C4×C73—41no—
65C22⋊C4×C73—42no—
66C22⋊C4×C73—42no—
67C42×C73—21no—
68C42×C73SD1611yescharacteristic
69C42×C73SD1611yescharacteristic
70C23×C73—42no—
71C23×C73AGL(1,ℤ/8)11yescharacteristic
72Q8×C73—82no—
73D4×C73—42no—
74D4×C73—42no—
75D4×C73—82no—
76D4×C73—82no—
77D4×C73—84no—
78C2×C4×C73—21no—
79C2×C4×C73—21no—
80C2×C4×C73—21no—
81C2×C4×C73—21no—
82C2×C4×C73—42no—
83C2×C4×C73—42no—
84C2×C4×C73—84no—
85C2×C4×C73#12011yescharacteristic
86C2×C4×C73C2×SD1611yescharacteristic
87C2×Dic73—81no—
88C8×C73—22no—
89C8×C73—41no—
90#10596831—81no—
91C22×C73—21no—
92C22×C73—41no—
93C22×C73—82no—
94C22×C73—82no—
95C22×C73—82no—
96C22×C73#45011yescharacteristic
97C4×C73—22no—
98C4×C73—21no—
99C4×C73—41no—
100C4×C73—82no—
101C4×C73#45411yescharacteristic
102C4×C73#45811yescharacteristic
103Dic73—161no—
104#12307—731nomaximal, Sylow
105C2×C73—21no—
106C2×C73—41no—
107C2×C73—162no—
108C2×C73#161611yescharacteristic
109#3253D7311yescharacteristic
110#2238—732no—
111#2102—731no—
112#1339—732no—
113#1327—731no—
114C73#1230711yescharacteristic, complemented, Sylow
115#532—21no—
116#476—22no—
117#469—21no—
118#469C2×D7312yes—
119#459—22no—
120#430—731no—
121#423C2×D7311yescharacteristic
122#365—1462no—
123#361—1462no—
124#349—732no—
125#344—1461no—
126#339—1461no—
127H(3,ℤ/4)—731no—
128C2×#41—41no—
129C2×D8—21no—
130C2×D8C22⋊D7312yes—
131C2×M16—1461no—
132C2×M16C22⋊D7311yescharacteristic
133C2×M16C22×D7311yescharacteristic
134C4⋊Q8—21no—
135#127—21no—
136#124—41no—
137#121—22no—
138#121—41no—
139C4×D4—22no—
140C4×D4—41no—
141#117—1461no—
142C2×C42C22⋊D7311yescharacteristic
143M32—1462no—
144#108—1462no—
145#106—21no—
146#106C22⋊D7312yes—
147C4⋊C8—22no—
148#102—22no—
149#102—22no—
150#41—84no—
151C2×Q8—41no—
152C2×D4—22no—
153C2×D4—41no—
154C2×D4—41no—
155C2×D4—42no—
156C22×C4—21no—
157C22×C4—42no—
158C22×C4C2×C22⋊D7311yescharacteristic
159D8—42no—
160D8—81no—
161M16—41no—
162M16—41no—
163M16—2921no—
164M16—2921no—
165C2×C8—21no—
166C2×C8—2921no—
167C2×C8C2×C22⋊D7312yes—
168C4⋊C4—22no—
169C4⋊C4—41no—
170C4⋊C4—2921no—
171C22⋊C4—42no—
172C22⋊C4—42no—
173C22⋊C4—2921no—
174C42—21no—
175C42—2921no—
176C42#1192401611yescharacteristic
177C42#1192401611yescharacteristic
178C16—2922no—
179C23—42no—
180C23#1455661711yescharacteristic
181Q8—82no—
182D4—42no—
183D4—42no—
184D4—82no—
185D4—82no—
186D4—84no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—84no—
194C2×C4—5841no—
195C2×C4#1455656011yescharacteristic
196C2×C4C2×#1192401611yescharacteristic
197C8—22no—
198C8—41no—
199C8—5841no—
200C22—21no—
201C22—41no—
202C22—82no—
203C22—82no—
204C22—82no—
205C22#1798873811yescharacteristic
206C4—22no—
207C4—21no—
208C4—41no—
209C4—82no—
210C4—11681no—
211C4#1798876011yescharacteristic
212C4#1798877711yescharacteristic
213C2—21no—
214C2—41no—
215C2—162no—
216C2#2260896811yescharacteristic
subgroupG/H
centerC2#22608968
commutator, cosocleC2×M16×C73C23
FrattiniC2×M16C22×D73
Fitting, prime radicalC73×#3253C2
socleC2×C73#1616
hypercenter#3253D73
hypocenterC73#12307
LCSG ▷ C2×M16×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3253

Complements

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

NH ≅ G/Ntype
1. #22612143C2semidirect
2. #22611506C2semidirect
3. #22607916C2semidirect
4. #22607882C2semidirect
114. C73#12307semidirect

Maximal subgroups

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

subgroupindex
#226121432
#226115062
#226079162
#226078822
C73×#32532
#1230773