Finite Group Databasebeta

← #32999364

Subgroups — #32999364

Order 18688.

274 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 55 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#22621325C211yesmaximal, characteristic
2#22612150C212yesmaximal
3#22607918C212yesmaximal
4#22607882C211yesmaximal, characteristic
5C73×#2102C211yesmaximal, characteristic
6#17989144—21no—
7#17988873—22no—
8#17988845—21no—
9#17988845C2212yes—
10#17988798—22no—
11#17988411—22no—
12#17988402—22no—
13#17988369C2212yes—
14#430×C73C2211yescharacteristic
15#423×C73C2211yescharacteristic
16#344×C73—21no—
17#339×C73—21no—
18H(3,ℤ/4)×C73C2211yescharacteristic
19C2×Dic292—21no—
20C2×Dic292D412yes—
21#14556591—21no—
22#14556591—21no—
23#14556583—41no—
24#14556570—22no—
25#14556570—41no—
26C4×Dic146—22no—
27C4×Dic146—41no—
28#14556550—41no—
29#14556531—22no—
30#14556523—21no—
31#14556523D412yes—
32#14556516—22no—
33#14556516—22no—
34C2×M16×C73—21no—
35C2×M16×C73D411yescharacteristic
36C2×M16×C73C2311yescharacteristic
37#117×C73—21no—
38C2×C42×C73D411yescharacteristic
39#108×C73—22no—
40C4⋊C8×C73—22no—
41C2×Dic146—22no—
42C2×Dic146—41no—
43Dic292—42no—
44Dic292—81no—
45C4⋊Dic73—22no—
46C4⋊Dic73—41no—
47C4⋊Dic73—41no—
48C4⋊Dic73—41no—
49#11924007—42no—
50#11924007—42no—
51C22⋊Dic73—42no—
52C4×Dic73—42no—
53#11924003—42no—
54C22×C4×C73—21no—
55C22×C4×C73C2×D411yescharacteristic
56M16×C73—41no—
57M16×C73—41no—
58M16×C73—41no—
59M16×C73—41no—
60C2×C8×C73—21no—
61C2×C8×C73—41no—
62C2×C8×C73C2×D412yes—
63C4⋊C4×C73—41no—
64C22⋊C4×C73—41no—
65C42×C73—21no—
66C42×C73—41no—
67C42×C73SD1611yescharacteristic
68C42×C73SD1611yescharacteristic
69C23×C73AGL(1,ℤ/8)11yescharacteristic
70C2×C4×C73—21no—
71C2×C4×C73—21no—
72C2×C4×C73—21no—
73C2×C4×C73—21no—
74C2×C4×C73—42no—
75C2×C4×C73—81no—
76C2×C4×C73#12011yescharacteristic
77C2×C4×C73C2×SD1611yescharacteristic
78C2×Dic73—42no—
79C2×Dic73—42no—
80Dic146—42no—
81Dic146—42no—
82Dic146—82no—
83C8×C73—22no—
84C8×C73—41no—
85C8×C73—81no—
86C22×C73—21no—
87C22×C73—41no—
88C22×C73#45011yescharacteristic
89C4×C73—22no—
90C4×C73—21no—
91C4×C73—41no—
92C4×C73—161no—
93C4×C73#45411yescharacteristic
94C4×C73#45811yescharacteristic
95Dic73—82no—
96Dic73—82no—
97#12308—731nomaximal, Sylow
98C2×C73—21no—
99C2×C73—41no—
100C2×C73#161611yescharacteristic
101#3255—731no—
102#2239—732no—
103#2102D7311yescharacteristic
104#1340—732no—
105#1327—731no—
106C73#1230811yescharacteristic, complemented, Sylow
107#533—1461no—
108#475—1462no—
109#470—732no—
110#470—1461no—
111#462—1462no—
112#430C2×D7311yescharacteristic
113#423C2×D7311yescharacteristic
114#365—1462no—
115#362—1462no—
116#349—732no—
117#344—21no—
118#339—21no—
119H(3,ℤ/4)C2×D7311yescharacteristic
120C2×Q16—732no—
121C2×Q16—1461no—
122C2×M16—21no—
123C2×M16C22⋊D7311yescharacteristic
124C2×M16C22×D7311yescharacteristic
125C4⋊Q8—1461no—
126C4⋊Q8—1461no—
127#125—2921no—
128C22⋊Q8—2921no—
129C22⋊Q8—1462no—
130C4×Q8—2921no—
131C4×Q8—1462no—
132#117—21no—
133#117—2921no—
134C2×C42C22⋊D7311yescharacteristic
135M32—1462no—
136#108—22no—
137#106—732no—
138#106—1461no—
139C4⋊C8—22no—
140#103—1462no—
141#103—1462no—
142C2×Q8—2921no—
143C2×Q8—1462no—
144C22×C4—21no—
145C22×C4C2×C22⋊D7311yescharacteristic
146Q16—2922no—
147Q16—5841no—
148M16—41no—
149M16—41no—
150M16—41no—
151M16—41no—
152C2×C8—21no—
153C2×C8—41no—
154C2×C8D4×D7312yes—
155C4⋊C4—41no—
156C4⋊C4—2922no—
157C4⋊C4—2921no—
158C4⋊C4—2921no—
159C4⋊C4—2921no—
160C4⋊C4—2922no—
161C4⋊C4—1462no—
162C22⋊C4—41no—
163C22⋊C4—2922no—
164C42—21no—
165C42—41no—
166C42—2922no—
167C42#1192401511yescharacteristic
168C42#1192401511yescharacteristic
169C16—2922no—
170C23#1455661611yescharacteristic
171Q8—2922no—
172Q8—2922no—
173Q8—5842no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—81no—
180C2×C4—2922no—
181C2×C4—2922no—
182C2×C4#1455655911yescharacteristic
183C2×C4C2×#1192401511yescharacteristic
184C8—22no—
185C8—41no—
186C8—81no—
187C22—21no—
188C22—41no—
189C22#1798873711yescharacteristic
190C4—22no—
191C4—21no—
192C4—41no—
193C4—161no—
194C4—5842no—
195C4—5842no—
196C4#1798875911yescharacteristic
197C4#1798877611yescharacteristic
198C2—21no—
199C2—41no—
200C2#2260896711yescharacteristic
subgroupG/H
centerC2#22608967
commutator, cosocleC2×M16×C73C23
FrattiniC2×M16C22×D73
FittingC73×#2102C2
socleC2×C73#1616
prime radicalC23×C73AGL(1,ℤ/8)
hypercenter#2102D73
hypocenterC73#12308
LCSG ▷ C2×M16×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2102

Complements

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

NH ≅ G/Ntype
106. C73#12308semidirect

Maximal subgroups

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

subgroupindex
#226213252
#226121502
#226079182
#226078822
C73×#21022
#1230873