Finite Group Databasebeta

← #33062291

Subgroups — #33062291

Order 18688.

982 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 982 conjugacy classes of subgroups — too many to draw. Only its 179 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#22620311C211yesmaximal, characteristic, complemented
2#22620030C212yesmaximal, complemented
3#22609159C218yesmaximal, complemented
4#22608657C211yesmaximal, characteristic, complemented
5#22608374C212yesmaximal, complemented
6C2×#555×C73C211yesmaximal, characteristic
7#17989144C2211yescharacteristic
8#17988955—22no—
9#17988937C2214yescomplemented
10#17988922—22no—
11#17988867C2214yescomplemented
12#17988792C2214yescomplemented
13#17988738—22no—
14#17988687—24no—
15#17988644C2212yes—
16#17988596—22no—
17C4×#11924012C2211yescharacteristic
18#17988336C2214yescomplemented
19D4⋊#10596831C2218yescomplemented
20#555×C73—22no—
21#555×C73—24no—
22#555×C73C2214yes—
23C2×C4⋊Q8×C73C2211yescharacteristic
24C2×#124×C73—22no—
25C2×#121×C73—22no—
26C2×C4×D4×C73C2212yes—
27C2×#117×C73—22no—
28C2×#11924016—24no—
29C2×#11924012—21no—
30#14556591C2312yes—
31#14556583—21no—
32#14556570—22no—
33C4×Dic146—22no—
34#14556550—21no—
35#14556524—24no—
36C4⋊#10596831C2314yes—
37#14556515—28no—
38#14556514—24no—
39#14556512—24no—
40C22⋊#10596831—22no—
41#14556502—22no—
42#14556502—21no—
43C4×#10596831C2312yes—
44C22×Q8×C73D412yes—
45C22×D4×C73—22no—
46C22×D4×C73D412yes—
47C23×C4×C73—22no—
48C4⋊Q8×C73—22no—
49C4⋊Q8×C73D412yes—
50C4⋊Q8×C73C2312yes—
51#124×C73—28no—
52#124×C73—28no—
53#121×C73—28no—
54#121×C73—28no—
55C4×D4×C73—22no—
56C4×D4×C73—22no—
57C4×D4×C73D414yes—
58C4×D4×C73C2314yes—
59#117×C73—28no—
60#117×C73—28no—
61C2×C4⋊C4×C73—22no—
62C2×C4⋊C4×C73D412yes—
63C2×C22⋊C4×C73—24no—
64C2×C22⋊C4×C73—22no—
65C2×C42×C73—22no—
66C2×C42×C73C2311yescharacteristic
67C2×Dic146—22no—
68#11924016—48no—
69#11924012—42no—
70C2×#10596831—22no—
71C2×#10596831—24no—
72C4⋊Dic73—22no—
73C4⋊Dic73—22no—
74#11924007—42no—
75C22⋊Dic73—41no—
76C4×Dic73—41no—
77C24×C73—22no—
78C2×Q8×C73—22no—
79C2×Q8×C73—44no—
80C2×Q8×C73C2×D414yes—
81C2×D4×C73—28no—
82C2×D4×C73—22no—
83C2×D4×C73—44no—
84C2×D4×C73—84no—
85C2×D4×C73C2×D414yes—
86C22×C4×C73—22no—
87C22×C4×C73—22no—
88C22×C4×C73—24no—
89C22×C4×C73—24no—
90C22×C4×C73—48no—
91C22×C4×C73C2×D411yescharacteristic
92C22×C4×C73C2×D412yes—
93C4⋊C4×C73—24no—
94C4⋊C4×C73—22no—
95C4⋊C4×C73—24no—
96C4⋊C4×C73C2×D414yes—
97C22⋊C4×C73—216no—
98C22⋊C4×C73—24no—
99C22⋊C4×C73—24no—
100C42×C73—28no—
101C42×C73C2×D411yescharacteristic
102C42×C73C2×D412yes—
103C42×C73C2411yescharacteristic
104C23×C73—24no—
105C23×C73—44no—
106C23×C73—44no—
107C23×C73—44no—
108C23×C73#12011yescharacteristic
109Q8×C73—44no—
110Q8×C73—82no—
111D4×C73—24no—
112D4×C73—24no—
113D4×C73—44no—
114D4×C73—88no—
115C2×C4×C73—22no—
116C2×C4×C73—24no—
117C2×C4×C73—24no—
118C2×C4×C73—24no—
119C2×C4×C73—48no—
120C2×C4×C73—44no—
121C2×C4×C73—44no—
122C2×C4×C73—48no—
123C2×C4×C73#12011yescharacteristic
124C2×C4×C73#12012yes—
125C2×C4×C73C22×D411yescharacteristic
126C2×C4×C73C22×D412yes—
127C2×Dic73—42no—
128Dic146—44no—
129#10596831—42no—
130#10596831—44no—
131C22×C73—22no—
132C22×C73—44no—
133C22×C73—44no—
134C22×C73—44no—
135C22×C73—88no—
136C22×C73#45512yes—
137C22×C73C2×#12011yescharacteristic
138C4×C73—22no—
139C4×C73—21no—
140C4×C73—21no—
141C4×C73—44no—
142C4×C73—44no—
143C4×C73#57514yes—
144Dic73—82no—
145#18552—731nomaximal, Sylow
146C2×C73—22no—
147C2×C73—84no—
148C2×C73#300512yes—
149C2×C73C2×#45511yescharacteristic
150C2×#555D7311yescharacteristic
151#3139—731no—
152#3110—732no—
153#1646—738no—
154#1558—731no—
155#1490—732no—
156C73#1855211yescharacteristic, complemented, Sylow
157#555—22no—
158#555—24no—
159#555C2×D7314yes—
160#533—731no—
161C2×C4⋊Q8C2×D7311yescharacteristic
162C2×#124—22no—
163C2×#121—22no—
164C2×C4×D4C2×D7312yes—
165C2×#117—22no—
166#491—1462no—
167#487—734no—
168#484—1462no—
169#474—734no—
170#461—734no—
171#450—1462no—
172#440—1464no—
173#432—732no—
174#419—1462no—
175C4×M16—731no—
176#333—734no—
177D4⋊C8—738no—
178C22×Q8C22⋊D7312yes—
179C22×D4—22no—
180C22×D4C22⋊D7312yes—
181C23×C4—22no—
182C2×SD16—1464no—
183C2×M16—1461no—
184C4⋊Q8—22no—
185C4⋊Q8—732no—
186C4⋊Q8C22⋊D7312yes—
187C4⋊Q8C22×D7312yes—
188#125—1461no—
189#124—28no—
190#124—28no—
191C22⋊Q8—1462no—
192#121—28no—
193#121—28no—
194C4×Q8—1462no—
195C4×D4—22no—
196C4×D4—22no—
197C4×D4C22⋊D7314yes—
198C4×D4C22×D7314yes—
199#117—28no—
200#117—28no—
201#117—1461no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4C22⋊D7312yes—
204C2×C22⋊C4—24no—
205C2×C22⋊C4—22no—
206C2×C42—22no—
207C2×C42C22×D7311yescharacteristic
208#107—1464no—
209C4⋊C8—734no—
210#103—1468no—
211#103—1464no—
212#102—1464no—
213C22⋊C8—1462no—
214#97—1461no—
215#97—1462no—
216C4×C8—732no—
217C24—22no—
218C2×Q8—22no—
219C2×Q8—44no—
220C2×Q8—1462no—
221C2×Q8C2×C22⋊D7314yes—
222C2×D4—28no—
223C2×D4—22no—
224C2×D4—44no—
225C2×D4—84no—
226C2×D4C2×C22⋊D7314yes—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—24no—
230C22×C4—24no—
231C22×C4—48no—
232C22×C4C2×C22⋊D7312yes—
233C22×C4C2×C22⋊D7311yescharacteristic
234SD16—2928no—
235M16—2922no—
236C2×C8—1462no—
237C2×C8—1464no—
238C4⋊C4—24no—
239C4⋊C4—22no—
240C4⋊C4—24no—
241C4⋊C4—2922no—
242C4⋊C4—1462no—
243C4⋊C4—1462no—
244C4⋊C4C2×C22⋊D7314yes—
245C22⋊C4—216no—
246C22⋊C4—24no—
247C22⋊C4—24no—
248C22⋊C4—2921no—
249C42—28no—
250C42—2921no—
251C42C2×C22⋊D7311yescharacteristic
252C42C2×C22⋊D7312yes—
253C42C23×D7311yescharacteristic
254C23—24no—
255C23—44no—
256C23—44no—
257C23—44no—
258C23#1455656011yescharacteristic
259Q8—44no—
260Q8—82no—
261Q8—2924no—
262D4—24no—
263D4—24no—
264D4—44no—
265D4—88no—
266C2×C4—22no—
267C2×C4—24no—
268C2×C4—24no—
269C2×C4—24no—
270C2×C4—48no—
271C2×C4—44no—
272C2×C4—44no—
273C2×C4—48no—
274C2×C4—2922no—
275C2×C4#1455656011yescharacteristic
276C2×C4#1455656012yes—
277C2×C4C22×C22⋊D7311yescharacteristic
278C2×C4C22×C22⋊D7312yes—
279C8—2922no—
280C8—2924no—
281C22—22no—
282C22—44no—
283C22—44no—
284C22—44no—
285C22—88no—
286C22#1798876512yes—
287C22C2×#1455656011yescharacteristic
288C4—22no—
289C4—21no—
290C4—21no—
291C4—44no—
292C4—44no—
293C4—5842no—
294C4#1798938514yes—
295C2—22no—
296C2—84no—
297C2#2261917312yes—
298C2C2×#1798876511yescharacteristic
subgroupG/H
centerC22C2×#14556560
commutator, cosocleC42×C73C24
FrattiniC42C23×D73
Fitting, prime radicalC2×#555×C73C2
socleC22×C73C2×#120
hypercenterC2×#555D73
hypocenterC73#18552
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. #22620311C2semidirect
2. #22620030C2semidirect
3. #22609159C2semidirect
4. #22608657C2semidirect
5. #22608374C2semidirect
9. #17988937C22semidirect
11. #17988867C22semidirect
12. #17988792C22semidirect
18. #17988336C22semidirect
19. D4⋊#10596831C22semidirect
156. C73#18552semidirect

Maximal subgroups

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

subgroupindex
#226203112
#226200302
#226091592
#226086572
#226083742
C2×#555×C732
#1855273