Finite Group Databasebeta

← #34005284

Subgroups — #34005284

Order 18688.

498 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C2×#17989430C212yesmaximal
2#22624774C214yesmaximal, complemented
3#22612527C211yesmaximal, characteristic
4C2×C22⋊#10596833C2214yes—
5#17989430—22no—
6#17989430—22no—
7C22×C22⋊Dic73C2211yescharacteristic
8#17988481—22no—
9#17988475—22no—
10#17988445C412yes—
11#17988443C411yescharacteristic
12C22⋊C4×Dic73C2212yes—
13#379×C73C411yescharacteristic
14C22×#10596833—24no—
15C22⋊#10596833—24no—
16C22⋊#10596833—24no—
17C23×Dic73C2×C411yescharacteristic
18C23×Dic73C2311yescharacteristic
19C2×#11924007—22no—
20C2×C22⋊Dic73—24no—
21C2×C22⋊Dic73—21no—
22C2×C22⋊Dic73—21no—
23C2×C22⋊Dic73C2×C412yes—
24C2×C22⋊Dic73D412yes—
25C2×C22⋊Dic73D412yes—
26C2×C4×Dic73—22no—
27#14556498—22no—
28#14556498—22no—
29C25×C73C2×C411yescharacteristic
30C2×C22⋊C4×C73—21no—
31C2×C22⋊C4×C73—21no—
32C2×C22⋊C4×C73C2×C412yes—
33C2×#10596833—44no—
34C2×#10596833—84no—
35C22×Dic73—22no—
36C22×Dic73—22no—
37C22×Dic73—81no—
38C22×Dic73—81no—
39C22×Dic73C22⋊C412yes—
40C22×Dic73C2×D412yes—
41C22×Dic73#4114yes—
42#11924007—82no—
43C22⋊Dic73—24no—
44C22⋊Dic73—24no—
45C22⋊Dic73—24no—
46C22⋊Dic73—81no—
47C22⋊Dic73—81no—
48C4×Dic73—82no—
49C24×C73—22no—
50C24×C73—24no—
51C24×C73—81no—
52C24×C73—81no—
53C24×C73C22⋊C411yescharacteristic
54C24×C73C22⋊C411yescharacteristic
55C24×C73C22×C411yescharacteristic
56C22×C4×C73—22no—
57C22⋊C4×C73—24no—
58C22⋊C4×C73—81no—
59C22⋊C4×C73—81no—
60C23×C73—21no—
61C23×C73—21no—
62C23×C73—22no—
63C23×C73—22no—
64C23×C73—41no—
65C23×C73—41no—
66C23×C73—41no—
67C23×C73—41no—
68C23×C73—41no—
69C23×C73—41no—
70C23×C73—44no—
71C23×C73—82no—
72C23×C73—82no—
73C23×C73—88no—
74C23×C73C2×C22⋊C411yescharacteristic
75C23×C73#11712yes—
76C23×C73#13114yes—
77C2×C4×C73—42no—
78C2×C4×C73—42no—
79C2×C4×C73—42no—
80C2×Dic73—22no—
81C2×Dic73—42no—
82C2×Dic73—44no—
83C2×Dic73—42no—
84C2×Dic73—42no—
85C2×Dic73—42no—
86C2×Dic73—42no—
87C2×Dic73—82no—
88C2×Dic73#12314yes—
89#10596833—84no—
90C22×C73—21no—
91C22×C73—22no—
92C22×C73—21no—
93C22×C73—22no—
94C22×C73—44no—
95C22×C73—41no—
96C22×C73—41no—
97C22×C73—41no—
98C22×C73—41no—
99C22×C73—41no—
100C22×C73—41no—
101C22×C73—82no—
102C22×C73—82no—
103C22×C73—88no—
104C22×C73#38111yescharacteristic
105C22×C73#40812yes—
106C22×C73#43314yes—
107C4×C73—82no—
108Dic73—24no—
109Dic73—42no—
110Dic73—82no—
111#8736—731nomaximal, Sylow
112C2×C73—22no—
113C2×C73—24no—
114C2×C73—81no—
115C2×C73—81no—
116C2×C73#181811yescharacteristic
117C2×C73#182811yescharacteristic
118C2×C73#182911yescharacteristic
119#2312—731no—
120C2×#323—732no—
121#1282—734no—
122C73#873611yescharacteristic, complemented, Sylow
123C22×C22⋊C4—731no—
124C2×C22⋊C8—734no—
125#388—1462no—
126#388—1462no—
127#380—732no—
128#379—731no—
129#379#6440811yescharacteristic
130C4×C22⋊C4—732no—
131#323—1462no—
132#323—1462no—
133C25C2×#6440811yescharacteristic
134C23×C4—731no—
135C23×C4—731no—
136C22×C8—1464no—
137C2×C4⋊C4—1462no—
138C2×C22⋊C4—21no—
139C2×C22⋊C4—21no—
140C2×C22⋊C4—732no—
141C2×C22⋊C4—732no—
142C2×C22⋊C4—732no—
143C2×C22⋊C4—1461no—
144C2×C22⋊C4—1461no—
145C2×C22⋊C4—1464no—
146C2×C22⋊C4C2×#6440812yes—
147C2×C42—1462no—
148C22⋊C8—1464no—
149C22⋊C8—1464no—
150#95—1462no—
151#95—1462no—
152C24—24no—
153C24—22no—
154C24—81no—
155C24—81no—
156C24C22⋊#6440811yescharacteristic
157C24C22⋊#6440811yescharacteristic
158C24C22×#6440811yescharacteristic
159C22×C4—22no—
160C22×C4—5841no—
161C22×C4—5841no—
162C22×C4—732no—
163C22×C4—734no—
164C22×C4—732no—
165C22×C4—1462no—
166C22×C4—1462no—
167C2×C8—2924no—
168C2×C8—5844no—
169C4⋊C4—5842no—
170C22⋊C4—24no—
171C22⋊C4—81no—
172C22⋊C4—81no—
173C22⋊C4—5841no—
174C22⋊C4—5841no—
175C22⋊C4—1464no—
176C22⋊C4—1464no—
177C22⋊C4—1464no—
178C42—5842no—
179C23—21no—
180C23—21no—
181C23—22no—
182C23—22no—
183C23—41no—
184C23—41no—
185C23—41no—
186C23—41no—
187C23—41no—
188C23—41no—
189C23—44no—
190C23—82no—
191C23—82no—
192C23—88no—
193C23C2×C22⋊#6440811yescharacteristic
194C23#1455667012yes—
195C23#1455667814yes—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—2922no—
200C2×C4—2922no—
201C2×C4—2922no—
202C2×C4—2922no—
203C2×C4—2922no—
204C2×C4—2924no—
205C2×C4—5842no—
206C2×C4—734no—
207C2×C4—1462no—
208C8—5844no—
209C22—21no—
210C22—22no—
211C22—21no—
212C22—22no—
213C22—44no—
214C22—41no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—41no—
219C22—41no—
220C22—82no—
221C22—82no—
222C22—88no—
223C22#1798953011yescharacteristic
224C22#1798956012yes—
225C22#1798961114yes—
226C4—82no—
227C4—2922no—
228C4—5842no—
229C4—1464no—
230C2—22no—
231C2—24no—
232C2—81no—
233C2—81no—
234C2#2262582411yescharacteristic
235C2#2262584211yescharacteristic
236C2#2262584411yescharacteristic
subgroupG/H
centerC22#17989530
commutatorC24×C73C22×C4
FrattiniC24C22×#64408
Fitting#379×C73C4
socleC22×C73#381
prime radicalC25×C73C2×C4
cosocleC23×Dic73C23
hypercenter#379#64408
hypocenterC73#8736
LCSG ▷ C24×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
2. #22624774C2semidirect
122. C73#8736semidirect

Maximal subgroups

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

subgroupindex
C2×#179894302
#226247742
#226125272
#873673