Finite Group Databasebeta

← #32989244

Subgroups — #32989244

Order 18688.

526 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 77 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#22610003C212yesmaximal
2#22610003C211yesmaximal, characteristic
3#22607835C211yesmaximal, characteristic
4#22607835C212yesmaximal
5C73×#2842C211yesmaximal, characteristic
6C22×C22⋊Dic73C2211yescharacteristic
7#17988443C2212yes—
8#17988443C2211yescharacteristic
9#17988353—24no—
10#17988353—22no—
11#399×C73—22no—
12#396×C73—24no—
13#379×C73C2211yescharacteristic
14#379×C73C2212yes—
15C23×Dic73Q812yes—
16C2×C22⋊Dic73—22no—
17C2×C22⋊Dic73—21no—
18C2×C22⋊Dic73—22no—
19C2×C22⋊Dic73—21no—
20C2×C22⋊Dic73—22no—
21C2×C22⋊Dic73—21no—
22C2×C22⋊Dic73—22no—
23C2×C22⋊Dic73—22no—
24C2×C22⋊Dic73—22no—
25C25×C73C2311yescharacteristic
26C2×C4⋊C4×C73—24no—
27C2×C4⋊C4×C73—22no—
28C2×C22⋊C4×C73—22no—
29C2×C22⋊C4×C73—22no—
30C2×C22⋊C4×C73—22no—
31C2×C22⋊C4×C73D414yes—
32C2×C22⋊C4×C73D412yes—
33#95×C73—22no—
34C22×Dic73—22no—
35C22×Dic73—22no—
36C22×Dic73—22no—
37C22×Dic73—42no—
38C22×Dic73—41no—
39C22×Dic73—82no—
40C22⋊Dic73—41no—
41C22⋊Dic73—42no—
42C22⋊Dic73—41no—
43C22⋊Dic73—44no—
44C22⋊Dic73—42no—
45C22⋊Dic73—82no—
46C22⋊Dic73—82no—
47C22⋊Dic73—82no—
48C24×C73—42no—
49C24×C73—82no—
50C24×C73C2×D412yes—
51C24×C73C2×D411yescharacteristic
52C24×C73C2×Q811yescharacteristic
53C24×C73#4112yes—
54C24×C73#4111yescharacteristic
55C22×C4×C73—22no—
56C22×C4×C73—24no—
57C4⋊C4×C73—84no—
58C4⋊C4×C73—82no—
59C22⋊C4×C73—44no—
60C22⋊C4×C73—42no—
61C22⋊C4×C73—82no—
62C22⋊C4×C73—82no—
63C22⋊C4×C73—82no—
64C23×C73—24no—
65C23×C73—22no—
66C23×C73—41no—
67C23×C73—42no—
68C23×C73—42no—
69C23×C73—42no—
70C23×C73—42no—
71C23×C73—41no—
72C23×C73—42no—
73C23×C73—42no—
74C23×C73—42no—
75C23×C73—42no—
76C23×C73—88no—
77C23×C73#12011yescharacteristic
78C23×C73C22⋊Q812yes—
79C23×C73C22⋊Q811yescharacteristic
80C23×C73#12412yes—
81C23×C73#12411yescharacteristic
82C2×C4×C73—44no—
83C2×C4×C73—44no—
84C2×C4×C73—44no—
85C2×C4×C73—44no—
86C2×C4×C73—42no—
87C2×Dic73—42no—
88C2×Dic73—82no—
89C2×Dic73—82no—
90C2×Dic73—82no—
91C2×Dic73—82no—
92C2×Dic73—81no—
93C2×Dic73—82no—
94C2×Dic73—82no—
95C2×Dic73—82no—
96C22×C73—22no—
97C22×C73—22no—
98C22×C73—21no—
99C22×C73—22no—
100C22×C73—21no—
101C22×C73—22no—
102C22×C73—22no—
103C22×C73—22no—
104C22×C73—22no—
105C22×C73—22no—
106C22×C73—22no—
107C22×C73—44no—
108C22×C73—84no—
109C22×C73—82no—
110C22×C73—82no—
111C22×C73—84no—
112C22×C73#39311yescharacteristic
113C22×C73#45812yes—
114C4×C73—82no—
115C4×C73—84no—
116Dic73—82no—
117Dic73—162no—
118Dic73—161no—
119#10393—731nomaximal, Sylow
120C2×C73—22no—
121C2×C73—42no—
122C2×C73—41no—
123C2×C73—42no—
124C2×C73—41no—
125C2×C73#203011yescharacteristic
126C2×C73#203212yes—
127#2842D7311yescharacteristic
128#1819—732no—
129#1819—731no—
130#1304—731no—
131#1304—732no—
132C73#1039311yescharacteristic, complemented, Sylow
133C22×C22⋊C4—731no—
134#399—22no—
135#396—24no—
136#379—732no—
137#379—731no—
138#379C2×D7311yescharacteristic
139#379C2×D7312yes—
140#342—1464no—
141#342—1462no—
142C25C22×D7311yescharacteristic
143C23×C4—732no—
144C2×C4⋊C4—24no—
145C2×C4⋊C4—22no—
146C2×C22⋊C4—22no—
147C2×C22⋊C4—22no—
148C2×C22⋊C4—22no—
149C2×C22⋊C4—1462no—
150C2×C22⋊C4—1461no—
151C2×C22⋊C4—1462no—
152C2×C22⋊C4—1461no—
153C2×C22⋊C4—1461no—
154C2×C22⋊C4—1462no—
155C2×C22⋊C4—1462no—
156C2×C22⋊C4—1462no—
157C2×C22⋊C4—1462no—
158C2×C22⋊C4C22⋊D7314yes—
159C2×C22⋊C4C22⋊D7312yes—
160#95—22no—
161C24—42no—
162C24—82no—
163C24C2×C22⋊D7312yes—
164C24C2×C22⋊D7311yescharacteristic
165C24Q8×D7311yescharacteristic
166C24#1192402912yes—
167C24#1192402911yescharacteristic
168C22×C4—22no—
169C22×C4—24no—
170C22×C4—2922no—
171C22×C4—2921no—
172C22×C4—5842no—
173C22×C4—1462no—
174C22×C4—1462no—
175C22×C4—1462no—
176C4⋊C4—84no—
177C4⋊C4—82no—
178C22⋊C4—44no—
179C22⋊C4—42no—
180C22⋊C4—82no—
181C22⋊C4—82no—
182C22⋊C4—82no—
183C22⋊C4—2921no—
184C22⋊C4—2922no—
185C22⋊C4—2921no—
186C22⋊C4—2924no—
187C22⋊C4—2922no—
188C22⋊C4—5842no—
189C22⋊C4—5842no—
190C22⋊C4—5842no—
191C23—24no—
192C23—22no—
193C23—42no—
194C23—41no—
195C23—42no—
196C23—42no—
197C23—42no—
198C23—42no—
199C23—42no—
200C23—42no—
201C23—41no—
202C23—42no—
203C23—88no—
204C23#1455656011yescharacteristic
205C23#1455656712yes—
206C23#1455656711yescharacteristic
207C23#1455658012yes—
208C23#1455658011yescharacteristic
209C2×C4—44no—
210C2×C4—44no—
211C2×C4—44no—
212C2×C4—44no—
213C2×C4—42no—
214C2×C4—2922no—
215C2×C4—5842no—
216C2×C4—5842no—
217C2×C4—5842no—
218C2×C4—5842no—
219C2×C4—5841no—
220C2×C4—5842no—
221C2×C4—5842no—
222C2×C4—5842no—
223C22—22no—
224C22—22no—
225C22—21no—
226C22—22no—
227C22—21no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—22no—
232C22—22no—
233C22—22no—
234C22—44no—
235C22—84no—
236C22—82no—
237C22—82no—
238C22—84no—
239C22#1798849811yescharacteristic
240C22#1798877712yes—
241C4—82no—
242C4—84no—
243C4—5842no—
244C4—11682no—
245C4—11681no—
246C2—22no—
247C2—42no—
248C2—41no—
249C2—42no—
250C2—41no—
251C2#2261109711yescharacteristic
252C2#2261110712yes—
subgroupG/H
centerC22#17988498
commutator, prime radical, cosocleC25×C73C23
FrattiniC25C22×D73
FittingC73×#2842C2
socleC22×C73#393
hypercenter#2842D73
hypocenterC73#10393
LCSG ▷ C25×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C25 ◁ #2842

Complements

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

NH ≅ G/Ntype
132. C73#10393semidirect

Maximal subgroups

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

subgroupindex
#226100032
#226078352
C73×#28422
#1039373