Finite Group Databasebeta

← #32973202

Subgroups — #32973202

Order 18688.

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

normal subgroups only

This group has 324 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#22610229C211yesmaximal, characteristic
2#22608249C211yesmaximal, characteristic
3C73×#1460C211yesmaximal, characteristic
4C22×#11924012C411yescharacteristic
5C2×C22⋊#10596831—21no—
6C2×C22⋊#10596831—21no—
7C2×C22⋊#10596831C411yescharacteristic
8#17988342—21no—
9#17988313C412yes—
10#17988311—21no—
11C2×C4×D4×C73C2211yescharacteristic
12#431×C73—21no—
13#323×C73—21no—
14#323×C73C412yes—
15C2×#11924012—41no—
16C2×#11924012—42no—
17C22×#10596831—21no—
18C22×#10596831—21no—
19C22×#10596831—41no—
20C22⋊#10596831—22no—
21C22⋊#10596831—41no—
22C22⋊#10596831—41no—
23C22⋊#10596831—42no—
24C22×D4×C73Q811yescharacteristic
25C23×C4×C73C2×C411yescharacteristic
26C23×C4×C73D411yescharacteristic
27C4×D4×C73—41no—
28C4×D4×C73—41no—
29C2×C4⋊C4×C73C2×C411yescharacteristic
30C2×C22⋊C4×C73C2×C411yescharacteristic
31C2×C22⋊C4×C73D411yescharacteristic
32C2×C42×C73D411yescharacteristic
33C4⋊C8×C73—41no—
34C22⋊C8×C73—22no—
35C4×C8×C73—41no—
36#11924012—42no—
37#11924012—42no—
38C2×#10596831—22no—
39C2×#10596831—41no—
40C2×#10596831—41no—
41C2×#10596831—42no—
42C2×#10596831—41no—
43C2×#10596831—41no—
44C2×#10596831—41no—
45C2×#10596831—81no—
46C2×#10596831—81no—
47C24×C73C4⋊C411yescharacteristic
48C24×C73C4⋊C411yescharacteristic
49C2×D4×C73—22no—
50C2×D4×C73—22no—
51C2×D4×C73—41no—
52C22×C4×C73—21no—
53C22×C4×C73—21no—
54C22×C4×C73—21no—
55C22×C4×C73—21no—
56C22×C4×C73—41no—
57C22×C4×C73—41no—
58C22×C4×C73—41no—
59C22×C4×C73—41no—
60C22×C4×C73C4211yescharacteristic
61C22×C4×C73C22⋊C411yescharacteristic
62C22×C4×C73C22⋊C411yescharacteristic
63C22×C4×C73C22⋊C411yescharacteristic
64C22×C4×C73C4⋊C411yescharacteristic
65C2×C8×C73—42no—
66C4⋊C4×C73—41no—
67C22⋊C4×C73—41no—
68C22⋊C4×C73—41no—
69C42×C73—21no—
70C42×C73—21no—
71C23×C73—21no—
72C23×C73—21no—
73C23×C73—21no—
74C23×C73—21no—
75C23×C73—21no—
76C23×C73—41no—
77C23×C73—41no—
78C23×C73—41no—
79C23×C73—41no—
80C23×C73#9511yescharacteristic
81C23×C73#10812yes—
82D4×C73—44no—
83C2×C4×C73—21no—
84C2×C4×C73—21no—
85C2×C4×C73—21no—
86C2×C4×C73—21no—
87C2×C4×C73—21no—
88C2×C4×C73—21no—
89C2×C4×C73—21no—
90C2×C4×C73—42no—
91C2×C4×C73—41no—
92C2×C4×C73—41no—
93C2×C4×C73—41no—
94C2×C4×C73—41no—
95C2×C4×C73—41no—
96C2×C4×C73—41no—
97C2×C4×C73—41no—
98C2×C4×C73—81no—
99C2×C4×C73#9911yescharacteristic
100C2×C4×C73#9911yescharacteristic
101C2×C4×C73#10812yes—
102C8×C73—82no—
103#10596831—42no—
104#10596831—81no—
105#10596831—82no—
106C22×C73—21no—
107C22×C73—21no—
108C22×C73—22no—
109C22×C73—42no—
110C22×C73—41no—
111C22×C73—41no—
112C22×C73—41no—
113C22×C73—41no—
114C22×C73—41no—
115C22×C73—81no—
116C22×C73—81no—
117C22×C73—81no—
118C22×C73#34111yescharacteristic
119C22×C73#34111yescharacteristic
120C22×C73#34211yescharacteristic
121C4×C73—22no—
122C4×C73—21no—
123C4×C73—41no—
124C4×C73—41no—
125C4×C73—41no—
126C4×C73AΣL(1,𝔽16)11yescharacteristic
127C4×C73#35211yescharacteristic
128#7285—731nomaximal, Sylow
129C2×C73—21no—
130C2×C73—21no—
131C2×C73—42no—
132C2×C73—81no—
133C2×C73#129811yescharacteristic
134C2×C73#139011yescharacteristic
135C2×C73#139511yescharacteristic
136#1870—731no—
137#1460D7311yescharacteristic
138#1459—731no—
139C73#728511yescharacteristic, complemented, Sylow
140C22×M16—731no—
141C2×C4×D4C2×D7311yescharacteristic
142#431—21no—
143C2×C22⋊C8—731no—
144C2×C22⋊C8—1461no—
145C2×C22⋊C8—1461no—
146#336—1461no—
147#324—732no—
148#323—21no—
149#323—1461no—
150#323Dic7312yes—
151C22×D4Dic14611yescharacteristic
152C23×C4C4×D7311yescharacteristic
153C23×C4D29211yescharacteristic
154C2×M16—2922no—
155C2×M16—2921no—
156C22×C8—2921no—
157C22×C8—1461no—
158C22×C8—1461no—
159C4×D4—41no—
160C4×D4—41no—
161C2×C4⋊C4C4×D7311yescharacteristic
162C2×C22⋊C4C2×Dic7311yescharacteristic
163C2×C22⋊C4C22⋊D7311yescharacteristic
164C2×C42C22⋊D7311yescharacteristic
165C4⋊C8—41no—
166C22⋊C8—22no—
167C22⋊C8—2921no—
168C22⋊C8—2922no—
169C22⋊C8—2921no—
170C22⋊C8—1462no—
171C4×C8—41no—
172C24#1192400711yescharacteristic
173C24C4⋊Dic7311yescharacteristic
174C2×D4—22no—
175C2×D4—22no—
176C2×D4—41no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4C4×Dic7311yescharacteristic
186C22×C4#1192400511yescharacteristic
187C22×C4#1192400511yescharacteristic
188C22×C4C22⋊Dic7311yescharacteristic
189C22×C4#1192400711yescharacteristic
190M16—2922no—
191M16—2922no—
192C2×C8—42no—
193C2×C8—2921no—
194C2×C8—2921no—
195C2×C8—2921no—
196C2×C8—2922no—
197C2×C8—2921no—
198C2×C8—2921no—
199C2×C8—5841no—
200C2×C8—5841no—
201C2×C8—1462no—
202C4⋊C4—41no—
203C22⋊C4—41no—
204C22⋊C4—41no—
205C42—21no—
206C42—21no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—21no—
212C23—41no—
213C23—41no—
214C23—41no—
215C23—41no—
216C23#1455649811yescharacteristic
217C23#1455652712yes—
218D4—44no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—81no—
235C2×C4#1455650511yescharacteristic
236C2×C4#1455650511yescharacteristic
237C2×C4#1455652612yes—
238C8—82no—
239C8—2922no—
240C8—5841no—
241C8—5842no—
242C22—21no—
243C22—21no—
244C22—22no—
245C22—42no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—41no—
251C22—81no—
252C22—81no—
253C22—81no—
254C22#1798835111yescharacteristic
255C22#1798835211yescharacteristic
256C22#1798835311yescharacteristic
257C4—21no—
258C4—22no—
259C4—41no—
260C4—41no—
261C4—41no—
262C4#1798837511yescharacteristic
263C4#1798837811yescharacteristic
264C2—21no—
265C2—21no—
266C2—42no—
267C2—81no—
268C2#2260781911yescharacteristic
269C2#2260805011yescharacteristic
270C2#2260805911yescharacteristic
subgroupG/H
centerC2×C4#14556505
commutatorC22×C4×C73C42
FrattiniC2×C4×D4C2×D73
FittingC73×#1460C2
socleC22×C73#342
prime radicalC22×D4×C73Q8
cosocleC2×C4×D4×C73C22
hypercenter#1460D73
hypocenterC73#7285
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1460

Complements

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

NH ≅ G/Ntype
139. C73#7285semidirect

Maximal subgroups

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

subgroupindex
#226102292
#226082492
C73×#14602
#728573