Finite Group Databasebeta

← #32979508

Subgroups — #32979508

Order 18688.

566 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 87 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#22612516C211yesmaximal, characteristic
2#22609854C212yesmaximal
3#22607840C212yesmaximal
4#22607839C211yesmaximal, characteristic
5C73×#1306C211yesmaximal, characteristic
6C23×Dic146C2211yescharacteristic
7C2×#14556547C412yes—
8C2×#14556509—24no—
9#17988551C2212yes—
10#17988491—24no—
11#17988450C2211yescharacteristic
12#17988448C412yes—
13#407×C73C2212yes—
14#381×C73C2211yescharacteristic
15C22×Dic146—21no—
16C22×Dic146—22no—
17C22×Dic146—21no—
18C22×Dic146—44no—
19C22×Dic146D414yes—
20C23×Dic73C2×C411yescharacteristic
21C23×Dic73C2×C411yescharacteristic
22C2×#11924012—22no—
23#14556547—44no—
24C2×#11924007—22no—
25C2×C22⋊Dic73C2×C412yes—
26C2×C4×Dic73—22no—
27#14556509—48no—
28C22⋊#10596831—22no—
29C22⋊#10596831—22no—
30#14556498—24no—
31#14556498—22no—
32C23×C4×C73C2311yescharacteristic
33C2×M16×C73—22no—
34C2×C22⋊C4×C73C2×C412yes—
35C22⋊C8×C73—22no—
36C22⋊C8×C73—22no—
37#95×C73—22no—
38C2×Dic146—24no—
39C2×Dic146—24no—
40C2×Dic146—28no—
41C2×Dic146—44no—
42C2×Dic146—44no—
43C2×Dic146—48no—
44C2×Dic146—44no—
45C22×Dic73—21no—
46C22×Dic73—21no—
47C22×Dic73—24no—
48C22×Dic73—21no—
49C22×Dic73—21no—
50C22×Dic73—22no—
51C22×Dic73—42no—
52C22×Dic73C22⋊C412yes—
53C22×Dic73C22⋊C412yes—
54#11924012—44no—
55C2×#10596831—42no—
56#11924007—44no—
57C22⋊Dic73—42no—
58C4×Dic73—44no—
59C24×C73C22×C411yescharacteristic
60C22×C4×C73—22no—
61C22×C4×C73—42no—
62C22×C4×C73C2×D412yes—
63C22×C4×C73#4111yescharacteristic
64C22×C4×C73#4112yes—
65C22×C4×C73#4111yescharacteristic
66M16×C73—44no—
67C2×C8×C73—42no—
68C22⋊C4×C73—42no—
69C23×C73—22no—
70C23×C73—42no—
71C23×C73C2×C22⋊C411yescharacteristic
72C23×C73#11711yescharacteristic
73C23×C73#11711yescharacteristic
74C2×C4×C73—24no—
75C2×C4×C73—41no—
76C2×C4×C73—42no—
77C2×C4×C73—41no—
78C2×C4×C73—44no—
79C2×C4×C73—42no—
80C2×C4×C73#12312yes—
81C2×C4×C73#12312yes—
82C2×Dic73—24no—
83C2×Dic73—24no—
84C2×Dic73—22no—
85C2×Dic73—22no—
86C2×Dic73—22no—
87C2×Dic73—24no—
88C2×Dic73—42no—
89C2×Dic73—42no—
90C2×Dic73—44no—
91C2×Dic73—42no—
92C2×Dic73#9914yes—
93Dic146—48no—
94Dic146—48no—
95C8×C73—82no—
96#10596831—82no—
97C22×C73—22no—
98C22×C73—21no—
99C22×C73—21no—
100C22×C73—22no—
101C22×C73—22no—
102C22×C73—44no—
103C22×C73#38111yescharacteristic
104C22×C73C2×#9912yes—
105C4×C73—22no—
106C4×C73—22no—
107C4×C73—82no—
108Dic73—24no—
109Dic73—42no—
110Dic73—82no—
111#8754—731nomaximal, Sylow
112C2×C73—22no—
113C2×C73—41no—
114C2×C73—41no—
115C2×C73#181911yescharacteristic
116C2×C73#183012yes—
117#2310—731no—
118#1784—732no—
119#1306—732no—
120#1306—731no—
121#1306D7311yescharacteristic
122C73#875411yescharacteristic, complemented, Sylow
123C23×Q8—731no—
124C2×#117—732no—
125C2×#101—1464no—
126#407—732no—
127#407C2×D7312yes—
128#391—1464no—
129#381—731no—
130#381—732no—
131#381C2×D7311yescharacteristic
132C22×Q8—2924no—
133C22×Q8—734no—
134C22×Q8—1461no—
135C22×Q8—1462no—
136C22×Q8—1461no—
137C23×C4—731no—
138C23×C4—731no—
139C23×C4C22×D7311yescharacteristic
140C2×M16—22no—
141C2×M16—1462no—
142#117—2924no—
143C2×C4⋊C4—1462no—
144C2×C22⋊C4—732no—
145C2×C22⋊C4C4×D7312yes—
146C2×C42—1462no—
147#101—2928no—
148C22⋊C8—22no—
149C22⋊C8—22no—
150C22⋊C8—1462no—
151C22⋊C8—1462no—
152#95—22no—
153#95—1464no—
154#95—1462no—
155C24C2×C4×D7311yescharacteristic
156C2×Q8—2924no—
157C2×Q8—2924no—
158C2×Q8—2928no—
159C2×Q8—2924no—
160C2×Q8—1468no—
161C2×Q8—1464no—
162C2×Q8—1464no—
163C22×C4—22no—
164C22×C4—42no—
165C22×C4—2922no—
166C22×C4—732no—
167C22×C4—732no—
168C22×C4—1462no—
169C22×C4—1461no—
170C22×C4—1461no—
171C22×C4—1464no—
172C22×C4—1461no—
173C22×C4—1461no—
174C22×C4D4×D7312yes—
175C22×C4#1192402711yescharacteristic
176C22×C4#1192402812yes—
177C22×C4#1192402911yescharacteristic
178M16—44no—
179M16—2924no—
180C2×C8—42no—
181C2×C8—2922no—
182C4⋊C4—2924no—
183C22⋊C4—42no—
184C22⋊C4—2922no—
185C42—2924no—
186C23—22no—
187C23—42no—
188C23C22⋊C4×D7311yescharacteristic
189C23#1455654811yescharacteristic
190C23#1455654911yescharacteristic
191Q8—2928no—
192Q8—2928no—
193C2×C4—24no—
194C2×C4—41no—
195C2×C4—42no—
196C2×C4—41no—
197C2×C4—44no—
198C2×C4—42no—
199C2×C4—2922no—
200C2×C4—2922no—
201C2×C4—2924no—
202C2×C4—2922no—
203C2×C4—734no—
204C2×C4—1462no—
205C2×C4—1464no—
206C2×C4—1464no—
207C2×C4—1464no—
208C2×C4—1462no—
209C2×C4—1462no—
210C2×C4#1455657312yes—
211C2×C4#1455657612yes—
212C8—82no—
213C8—5842no—
214C22—22no—
215C22—21no—
216C22—21no—
217C22—22no—
218C22—22no—
219C22—44no—
220C22#1798844911yescharacteristic
221C22#99×D7312yes—
222C4—22no—
223C4—22no—
224C4—82no—
225C4—2922no—
226C4—5842no—
227C4—1464no—
228C2—22no—
229C2—41no—
230C2—41no—
231C2#2261000411yescharacteristic
232C2#2261004412yes—
subgroupG/H
centerC22#17988449
commutator, prime radicalC24×C73C22×C4
FrattiniC23×C4C22×D73
FittingC73×#1306C2
socleC22×C73#381
cosocleC23×C4×C73C23
hypercenter#1306D73
hypocenterC73#8754
LCSG ▷ C24×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1306

Complements

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

NH ≅ G/Ntype
122. C73#8754semidirect

Maximal subgroups

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

subgroupindex
#226125162
#226098542
#226078402
#226078392
C73×#13062
#875473