Finite Group Databasebeta

← #32998780

Subgroups — #32998780

Order 18688.

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

normal subgroups only

This group has 388 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#22615596C211yesmaximal, characteristic
2#22608956C212yesmaximal
3#22607954C212yesmaximal
4#22607861C211yesmaximal, characteristic
5C73×#2030C211yesmaximal, characteristic
6#17988920—22no—
7#17988523C2212yes—
8#17988499—21no—
9#17988491—22no—
10#17988474—22no—
11C4×C22⋊Dic73—21no—
12#17988324—22no—
13#17988311C2212yes—
14#543×C73C2211yescharacteristic
15#381×C73—21no—
16#381×C73C2211yescharacteristic
17#342×C73—21no—
18#342×C73C2211yescharacteristic
19C22×Dic146—21no—
20C2×C4⋊Dic73D412yes—
21C2×#11924007—22no—
22C2×C22⋊Dic73—22no—
23C2×C4×Dic73—21no—
24C2×C4×Dic73—21no—
25#14556524—42no—
26#14556515—42no—
27C22⋊#10596831—22no—
28#14556498—22no—
29#14556498—21no—
30#14556498—22no—
31#14556498D412yes—
32C23×C4×C73D411yescharacteristic
33C22⋊Q8×C73—22no—
34C22⋊Q8×C73—42no—
35C2×C22⋊C4×C73—21no—
36C2×C22⋊C4×C73—21no—
37C2×C22⋊C4×C73D411yescharacteristic
38C2×C22⋊C4×C73C2311yescharacteristic
39#95×C73—22no—
40#95×C73—42no—
41C2×Dic146—44no—
42C2×Dic146—81no—
43C22×Dic73—22no—
44C22×Dic73—22no—
45C2×#10596831—42no—
46C4⋊Dic73—42no—
47#11924007—44no—
48C22⋊Dic73—44no—
49C4×Dic73—81no—
50C4×Dic73—81no—
51C24×C73C2×D411yescharacteristic
52C2×Q8×C73—22no—
53C22×C4×C73—21no—
54C22×C4×C73—21no—
55C22×C4×C73—21no—
56C22×C4×C73—22no—
57C22×C4×C73—41no—
58C22×C4×C73—41no—
59C22×C4×C73—41no—
60C22×C4×C73Q1612yes—
61C22×C4×C73C2×D412yes—
62C4⋊C4×C73—22no—
63C4⋊C4×C73—42no—
64C22⋊C4×C73—41no—
65C22⋊C4×C73—41no—
66C22⋊C4×C73—41no—
67C22⋊C4×C73—41no—
68C22⋊C4×C73—41no—
69C22⋊C4×C73—41no—
70C23×C73—21no—
71C23×C73—21no—
72C23×C73—42no—
73C23×C73#12011yescharacteristic
74C23×C73C2×Q1611yescharacteristic
75C23×C73#13711yescharacteristic
76Q8×C73—82no—
77C2×C4×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73—41no—
80C2×C4×C73—41no—
81C2×C4×C73—42no—
82C2×C4×C73—42no—
83C2×C4×C73—42no—
84C2×C4×C73—41no—
85C2×C4×C73—42no—
86C2×C4×C73—81no—
87C2×C4×C73—82no—
88C2×C4×C73—81no—
89C2×C4×C73—82no—
90C2×Dic73—24no—
91C2×Dic73—42no—
92C2×Dic73—42no—
93C2×Dic73—42no—
94C2×Dic73—42no—
95C2×Dic73—42no—
96Dic146—84no—
97#10596831—82no—
98C22×C73—22no—
99C22×C73—21no—
100C22×C73—21no—
101C22×C73—41no—
102C22×C73—41no—
103C22×C73—42no—
104C22×C73—81no—
105C22×C73#45111yescharacteristic
106C22×C73#45511yescharacteristic
107C22×C73B(4,𝔽2)11yescharacteristic
108C4×C73—42no—
109C4×C73—42no—
110C4×C73—81no—
111C4×C73—82no—
112C4×C73—161no—
113Dic73—44no—
114Dic73—82no—
115#12216—731nomaximal, Sylow
116C2×C73—21no—
117C2×C73—21no—
118C2×C73—41no—
119C2×C73—41no—
120C2×C73#160211yescharacteristic
121C2×C73#219812yes—
122#2607—731no—
123#2030D7311yescharacteristic
124#1614—732no—
125#1352—732no—
126#1317—731no—
127C73#1221611yescharacteristic, complemented, Sylow
128#543C2×D7311yescharacteristic
129#484—1462no—
130#399—732no—
131#393—1461no—
132#391—1462no—
133#387—1462no—
134#381—21no—
135#381C2×D7311yescharacteristic
136C4×C22⋊C4—1461no—
137#342—21no—
138#342C2×D7311yescharacteristic
139#328—1462no—
140#323—732no—
141C22×Q8—1461no—
142C23×C4C22⋊D7311yescharacteristic
143C22⋊Q8—22no—
144C22⋊Q8—42no—
145C2×C4⋊C4—732no—
146C2×C4⋊C4—1462no—
147C2×C22⋊C4—21no—
148C2×C22⋊C4—21no—
149C2×C22⋊C4—1462no—
150C2×C22⋊C4C22⋊D7311yescharacteristic
151C2×C22⋊C4C22×D7311yescharacteristic
152C2×C42—1461no—
153C2×C42—1461no—
154#107—2922no—
155#103—2922no—
156C22⋊C8—1462no—
157#95—22no—
158#95—42no—
159#95—732no—
160#95—1462no—
161#95—1461no—
162#95—1462no—
163C24C2×C22⋊D7311yescharacteristic
164C2×Q8—22no—
165C2×Q8—2924no—
166C2×Q8—5841no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—22no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—1462no—
175C22×C4—1462no—
176C22×C4#1192401812yes—
177C22×C4D4×D7312yes—
178C2×C8—2922no—
179C4⋊C4—22no—
180C4⋊C4—42no—
181C4⋊C4—2922no—
182C4⋊C4—2924no—
183C22⋊C4—41no—
184C22⋊C4—41no—
185C22⋊C4—41no—
186C22⋊C4—41no—
187C22⋊C4—41no—
188C22⋊C4—41no—
189C22⋊C4—2924no—
190C42—5841no—
191C42—5841no—
192C23—21no—
193C23—21no—
194C23—42no—
195C23#1455655911yescharacteristic
196C23C2×#1192401811yescharacteristic
197C23#1455662111yescharacteristic
198Q8—82no—
199Q8—5844no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—81no—
210C2×C4—82no—
211C2×C4—81no—
212C2×C4—82no—
213C2×C4—2922no—
214C2×C4—2922no—
215C2×C4—2922no—
216C2×C4—2922no—
217C2×C4—2922no—
218C2×C4—1464no—
219C8—5842no—
220C22—22no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22—81no—
227C22#1798874211yescharacteristic
228C22#1798876411yescharacteristic
229C22#1798877311yescharacteristic
230C4—42no—
231C4—42no—
232C4—81no—
233C4—82no—
234C4—161no—
235C4—2924no—
236C4—5842no—
237C2—21no—
238C2—21no—
239C2—41no—
240C2—41no—
241C2#2260888711yescharacteristic
242C2#2261192512yes—
subgroupG/H
centerC22#17988773
commutator, cosocleC2×C22⋊C4×C73C23
FrattiniC2×C22⋊C4C22×D73
FittingC73×#2030C2
socleC22×C73B(4,𝔽2)
prime radicalC24×C73C2×D4
hypercenter#2030D73
hypocenterC73#12216
LCSG ▷ C2×C22⋊C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2030

Complements

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

NH ≅ G/Ntype
127. C73#12216semidirect

Maximal subgroups

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

subgroupindex
#226155962
#226089562
#226079542
#226078612
C73×#20302
#1221673