Finite Group Databasebeta

← #32989231

Subgroups — #32989231

Order 18688.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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#22610030C212yesmaximal
3#22607839C211yesmaximal, characteristic
4#22607783C212yesmaximal
5C73×#1820C211yesmaximal, characteristic
6#17988551C2212yes—
7#17988510—22no—
8#17988484—22no—
9#17988470—22no—
10C4×C22⋊Dic73C2212yes—
11#17988346—22no—
12#17988346—22no—
13C2×#117×C73C2211yescharacteristic
14#381×C73C2211yescharacteristic
15#381×C73C2211yescharacteristic
16#342×C73—22no—
17C2×#11924012—22no—
18C2×C4⋊Dic73—22no—
19C2×#11924007—22no—
20C2×#11924007—22no—
21C2×C22⋊Dic73—22no—
22C2×C4×Dic73D412yes—
23C2×C4×Dic73D412yes—
24C22⋊#10596831—22no—
25C22⋊#10596831—22no—
26#14556498—22no—
27#14556498—22no—
28C23×C4×C73C2311yescharacteristic
29#117×C73—22no—
30#117×C73—22no—
31C2×C4⋊C4×C73Q812yes—
32C2×C22⋊C4×C73—21no—
33C2×C22⋊C4×C73—21no—
34C2×C22⋊C4×C73D412yes—
35C2×C42×C73—21no—
36#95×C73—22no—
37#95×C73—22no—
38C22×Dic73—22no—
39C22×Dic73—22no—
40#11924012—42no—
41#11924012—42no—
42C2×#10596831—42no—
43C4⋊Dic73—44no—
44#11924007—44no—
45#11924007—82no—
46C22⋊Dic73—44no—
47C4×Dic73—42no—
48C4×Dic73—42no—
49C24×C73C2×D411yescharacteristic
50C22×C4×C73—22no—
51C22×C4×C73—22no—
52C22×C4×C73—42no—
53C22×C4×C73—41no—
54C22×C4×C73C2×D412yes—
55C22×C4×C73C2×Q811yescharacteristic
56C22×C4×C73#4112yes—
57C22×C4×C73#4111yescharacteristic
58C4⋊C4×C73—24no—
59C22⋊C4×C73—41no—
60C22⋊C4×C73—41no—
61C22⋊C4×C73—42no—
62C22⋊C4×C73—42no—
63C42×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—42no—
73C2×C4×C73—41no—
74C2×C4×C73—42no—
75C2×C4×C73—42no—
76C2×C4×C73—42no—
77C2×C4×C73—42no—
78C2×C4×C73—82no—
79C2×C4×C73—81no—
80C2×C4×C73—82no—
81C2×C4×C73C22⋊Q812yes—
82C2×C4×C73#12412yes—
83C2×Dic73—24no—
84C2×Dic73—42no—
85C2×Dic73—42no—
86C2×Dic73—42no—
87C2×Dic73—42no—
88C2×Dic73—42no—
89#10596831—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—
101C4×C73—82no—
102C4×C73—161no—
103Dic73—44no—
104Dic73—82no—
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#1820D7311yescharacteristic
114#1306—731no—
115#1284—732no—
116C73#1038911yescharacteristic, complemented, Sylow
117C2×#117C2×D7311yescharacteristic
118#407—732no—
119#396—1462no—
120#389—1462no—
121#387—1462no—
122#381C2×D7311yescharacteristic
123#381C2×D7311yescharacteristic
124C4×C22⋊C4—732no—
125#342—22no—
126#339—1462no—
127#339—1462no—
128C23×C4C22×D7311yescharacteristic
129C2×M16—1462no—
130#117—22no—
131#117—22no—
132C2×C4⋊C4—1462no—
133C2×C4⋊C4—1462no—
134C2×C4⋊C4—1462no—
135C2×C4⋊C4Dic14612yes—
136C2×C22⋊C4—21no—
137C2×C22⋊C4—21no—
138C2×C22⋊C4—1462no—
139C2×C22⋊C4C22⋊D7312yes—
140C2×C42—21no—
141C2×C42—732no—
142C2×C42—732no—
143C22⋊C8—1462no—
144C22⋊C8—1462no—
145#95—22no—
146#95—22no—
147#95—1462no—
148#95—1462no—
149C24C2×C22⋊D7311yescharacteristic
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—42no—
153C22×C4—41no—
154C22×C4—1462no—
155C22×C4—1462no—
156C22×C4D4×D7312yes—
157C22×C4C2×Dic14611yescharacteristic
158C22×C4#1192402712yes—
159C22×C4#1192402811yescharacteristic
160M16—2922no—
161M16—2922no—
162C2×C8—2922no—
163C4⋊C4—24no—
164C4⋊C4—2924no—
165C4⋊C4—2924no—
166C4⋊C4—5842no—
167C22⋊C4—41no—
168C22⋊C4—41no—
169C22⋊C4—42no—
170C22⋊C4—42no—
171C22⋊C4—2924no—
172C42—42no—
173C42—2922no—
174C42—2922no—
175C23—22no—
176C23—42no—
177C23#1455655911yescharacteristic
178C23#1455657011yescharacteristic
179C23#1455657811yescharacteristic
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—41no—
183C2×C4—42no—
184C2×C4—41no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—82no—
190C2×C4—81no—
191C2×C4—82no—
192C2×C4—2922no—
193C2×C4—2922no—
194C2×C4—2922no—
195C2×C4—2922no—
196C2×C4—2922no—
197C2×C4—1464no—
198C2×C4#1455656812yes—
199C2×C4#1455657712yes—
200C8—5842no—
201C22—22no—
202C22—21no—
203C22—21no—
204C22—22no—
205C22—22no—
206C22—82no—
207C22#1798849911yescharacteristic
208C22#1798877612yes—
209C4—22no—
210C4—22no—
211C4—82no—
212C4—82no—
213C4—161no—
214C4—2924no—
215C4—5842no—
216C2—22no—
217C2—41no—
218C2—41no—
219C2#2261109811yescharacteristic
220C2#2261110512yes—
subgroupG/H
centerC22#17988499
commutator, cosocleC23×C4×C73C23
FrattiniC23×C4C22×D73
FittingC73×#1820C2
socleC22×C73#393
prime radicalC24×C73C2×D4
hypercenter#1820D73
hypocenterC73#10389
LCSG ▷ C23×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

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
#226100302
#226078392
#226077832
C73×#18202
#1038973