Finite Group Databasebeta

← #32989232

Subgroups — #32989232

Order 18688.

406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 73 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#22615601C211yesmaximal, characteristic
2#22610028C212yesmaximal
3#22610006C211yesmaximal, characteristic
4#22607785C212yesmaximal
5C73×#1306C211yesmaximal, characteristic
6C2×#14556550C2211yescharacteristic
7#17988510—22no—
8#17988484—22no—
9#17988470—22no—
10#17988450C2211yescharacteristic
11C4×C22⋊Dic73C2212yes—
12#17988353—22no—
13#17988348—22no—
14#17988348—22no—
15#407×C73C2212yes—
16#381×C73C2211yescharacteristic
17#14556550—22no—
18#14556550—22no—
19C2×C4⋊Dic73—22no—
20C2×C4⋊Dic73Q812yes—
21C2×#11924007—22no—
22C2×#11924007—22no—
23C2×C22⋊Dic73—21no—
24C2×C22⋊Dic73—22no—
25C2×C22⋊Dic73—21no—
26C2×C4×Dic73—21no—
27C2×C4×Dic73D412yes—
28C2×C4×Dic73D412yes—
29#14556498—22no—
30#14556498—22no—
31#14556498—22no—
32C23×C4×C73C2311yescharacteristic
33C2×M16×C73—22no—
34C2×C22⋊C4×C73D412yes—
35C22⋊C8×C73—22no—
36C22⋊C8×C73—22no—
37#95×C73—22no—
38C22×Dic73—22no—
39C22×Dic73—22no—
40C22×Dic73—22no—
41C22×Dic73—41no—
42C4⋊Dic73—24no—
43C4⋊Dic73—44no—
44#11924007—44no—
45#11924007—82no—
46C22⋊Dic73—44no—
47C22⋊Dic73—41no—
48C22⋊Dic73—41no—
49C22⋊Dic73—42no—
50C4×Dic73—42no—
51C4×Dic73—42no—
52C4×Dic73—42no—
53C24×C73C2×D411yescharacteristic
54C22×C4×C73—22no—
55C22×C4×C73—42no—
56C22×C4×C73C2×D412yes—
57C22×C4×C73C2×Q811yescharacteristic
58C22×C4×C73#4111yescharacteristic
59C22×C4×C73#4112yes—
60M16×C73—42no—
61M16×C73—42no—
62C2×C8×C73—42no—
63C22⋊C4×C73—42no—
64C23×C73—22no—
65C23×C73—42no—
66C23×C73#12011yescharacteristic
67C23×C73C22⋊Q811yescharacteristic
68C23×C73#12411yescharacteristic
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—41no—
72C2×C4×C73—41no—
73C2×C4×C73—42no—
74C2×C4×C73—42no—
75C2×C4×C73—42no—
76C2×C4×C73—42no—
77C2×C4×C73C22⋊Q812yes—
78C2×C4×C73#12412yes—
79C2×Dic73—24no—
80C2×Dic73—42no—
81C2×Dic73—42no—
82C2×Dic73—42no—
83C2×Dic73—42no—
84C2×Dic73—42no—
85C2×Dic73—42no—
86C2×Dic73—82no—
87C2×Dic73—81no—
88C2×Dic73—82no—
89C8×C73—82no—
90C22×C73—22no—
91C22×C73—21no—
92C22×C73—21no—
93C22×C73—22no—
94C22×C73—22no—
95C22×C73—82no—
96C22×C73#39311yescharacteristic
97C22×C73#45812yes—
98C4×C73—22no—
99C4×C73—22no—
100C4×C73—82no—
101Dic73—44no—
102Dic73—82no—
103Dic73—82no—
104Dic73—161no—
105#10389—731nomaximal, Sylow
106C2×C73—22no—
107C2×C73—41no—
108C2×C73—41no—
109C2×C73#203011yescharacteristic
110C2×C73#203112yes—
111#2608—731no—
112#1826—732no—
113#1820—731no—
114#1306D7311yescharacteristic
115#1284—732no—
116C73#1038911yescharacteristic, complemented, Sylow
117C2×#117—731no—
118#407C2×D7312yes—
119#396—1462no—
120#389—1462no—
121#387—1462no—
122#381—731no—
123#381C2×D7311yescharacteristic
124C4×C22⋊C4—732no—
125#342—1462no—
126#339—1462no—
127#339—1462no—
128C23×C4C22×D7311yescharacteristic
129C2×M16—22no—
130#117—1462no—
131#117—1462no—
132C2×C4⋊C4—732no—
133C2×C4⋊C4—1462no—
134C2×C4⋊C4—1462no—
135C2×C4⋊C4—1462no—
136C2×C22⋊C4—1461no—
137C2×C22⋊C4—1461no—
138C2×C22⋊C4—1462no—
139C2×C22⋊C4D29212yes—
140C2×C42—732no—
141C2×C42—732no—
142C2×C42—1461no—
143C22⋊C8—22no—
144C22⋊C8—22no—
145#95—22no—
146#95—1462no—
147#95—1462no—
148#95—1462no—
149C24C2×D29211yescharacteristic
150C22×C4—22no—
151C22×C4—42no—
152C22×C4—2921no—
153C22×C4—1462no—
154C22×C4—1462no—
155C22×C4—1462no—
156C22×C4D4×D7312yes—
157C22×C4Q8×D7311yescharacteristic
158C22×C4#1192402711yescharacteristic
159C22×C4#1192402812yes—
160M16—42no—
161M16—42no—
162C2×C8—42no—
163C4⋊C4—2924no—
164C4⋊C4—2924no—
165C4⋊C4—5842no—
166C4⋊C4—1464no—
167C22⋊C4—42no—
168C22⋊C4—2921no—
169C22⋊C4—2921no—
170C22⋊C4—2924no—
171C22⋊C4—2922no—
172C42—2922no—
173C42—2922no—
174C42—2922no—
175C23—22no—
176C23—42no—
177C23#1455656111yescharacteristic
178C23#1455657111yescharacteristic
179C23#1455657911yescharacteristic
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—2922no—
189C2×C4—2922no—
190C2×C4—2922no—
191C2×C4—2922no—
192C2×C4—2922no—
193C2×C4—2922no—
194C2×C4—5842no—
195C2×C4—5841no—
196C2×C4—5842no—
197C2×C4—1464no—
198C2×C4#1455656912yes—
199C2×C4#1455657712yes—
200C8—82no—
201C22—22no—
202C22—21no—
203C22—21no—
204C22—22no—
205C22—22no—
206C22—82no—
207C22#1798850011yescharacteristic
208C22#1798877812yes—
209C4—22no—
210C4—22no—
211C4—82no—
212C4—2924no—
213C4—5842no—
214C4—5842no—
215C4—11681no—
216C2—22no—
217C2—41no—
218C2—41no—
219C2#2261109911yescharacteristic
220C2#2261110612yes—
subgroupG/H
centerC22#17988500
commutator, cosocleC23×C4×C73C23
FrattiniC23×C4C22×D73
FittingC73×#1306C2
socleC22×C73#393
prime radicalC24×C73C2×D4
hypercenter#1306D73
hypocenterC73#10389
LCSG ▷ C23×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1306

Complements

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

NH ≅ G/Ntype
116. C73#10389semidirect

Maximal subgroups

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

subgroupindex
#226156012
#226100282
#226100062
#226077852
C73×#13062
#1038973