Finite Group Databasebeta

← #2842×D73 #33292393

Subgroups — #2842×D73 #33292393

Order 18688.

3294 conjugacy classes of subgroups; only the 579 normal subgroups are shown.

normal subgroups only

This group has 3294 conjugacy classes of subgroups — too many to draw. Only its 579 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#22618196C214yesmaximal, complemented
2#22618195C213yesmaximal, complemented
3#22618194C218yesmaximal, complemented
4#399×D73C214yesmaximal, complemented
5#396×D73C218yesmaximal, complemented
6#379×D73C213yesmaximal
7C73×#2842C211yesmaximal, characteristic, complemented
8C25×D73C2211yescharacteristic
9C2×C4⋊C4×D73C22112yescomplemented
10C2×C22⋊C4×D73C22112yes—
11C2×C22⋊C4×D73C2216yes—
12#17988524C2214yescomplemented
13#17988523C22112yescomplemented
14#17988522C22112yescomplemented
15#17988511C2218yescomplemented
16#17988510C22124yescomplemented
17#17988509C22124yescomplemented
18#17988443C2213yes—
19#17988442C22112yes—
20#17988442C2216yes—
21#95×D73C2214yescomplemented
22#399×C73C2214yescomplemented
23#396×C73C2218yescomplemented
24#379×C73C2213yes—
25C24×D73—412no—
26C24×D73Q818yes—
27C24×D73C2312yes—
28C24×D73C2311yescharacteristic
29C24×D73C2312yes—
30C24×D73C2311yescharacteristic
31C22×C4×D73C23112yes—
32C2×C4⋊Dic73C23112yescomplemented
33C2×#11924007C23124yescomplemented
34C4⋊C4×D73—424no—
35C2×C22⋊Dic73C23112yes—
36C2×C22⋊Dic73C2316yes—
37C2×#11924005C23124yes—
38C2×#11924005C23112yes—
39C22⋊C4×D73—424no—
40C22⋊C4×D73—412no—
41#14556498C23112yescomplemented
42C25×C73C2311yescharacteristic
43C2×C4⋊C4×C73C23112yescomplemented
44C2×C22⋊C4×C73C23112yes—
45C2×C22⋊C4×C73C2316yes—
46#95×C73C2314yescomplemented
47C23×D73—224no—
48C23×D73—212no—
49C23×D73—448no—
50C23×D73—412no—
51C23×D73—46no—
52C23×D73—464no—
53C23×D73C2×Q818yes—
54C23×D73C2×Q814yes—
55C23×D73C2×Q818yes—
56C23×D73C2×Q814yes—
57C23×D73C2412yes—
58C23×D73C2411yescharacteristic
59C23×D73C2411yescharacteristic
60C22×Dic73C24112yes—
61C2×C4×D73—224no—
62C2×C4×D73—248no—
63C4⋊Dic73—412no—
64#11924007—424no—
65C22⋊Dic73—46no—
66C22⋊Dic73—412no—
67#11924005—412no—
68#11924005—424no—
69C24×C73—46no—
70C24×C73C2×Q814yes—
71C24×C73C2412yes—
72C24×C73C2411yescharacteristic
73C22×C4×C73C24112yes—
74C4⋊C4×C73—412no—
75C22⋊C4×C73—412no—
76C22⋊C4×C73—46no—
77C23×C73—212no—
78C23×C73—26no—
79C23×C73—412no—
80C23×C73—416no—
81C23×C73C22×Q814yes—
82C23×C73C22×Q812yes—
83C23×C73C2511yescharacteristic
84C22×D73—26no—
85C22×D73—212no—
86C22×D73—248no—
87C22×D73—224no—
88C22×D73—424no—
89C22×D73—412no—
90C22×D73—432no—
91C22×D73—416no—
92C22×D73—4128no—
93C22×D73—432no—
94C22×D73—416no—
95C22×D73C22×Q814yes—
96C22×D73C22×Q812yes—
97C22×D73C22×Q812yes—
98C22×D73H(5,𝔽2)112yes—
99C2×C4×C73—224no—
100C2×C4×C73—212no—
101C2×Dic73—212no—
102C2×Dic73—224no—
103C4×D73—448no—
104C22×C73—212no—
105C22×C73—26no—
106C22×C73—416no—
107C22×C73—48no—
108C22×C73—44no—
109C22×C73C23×Q811yescharacteristic
110C22×C73C2×H(5,𝔽2)16yes—
111C2×D73—26no—
112C2×D73—212no—
113C2×D73—432no—
114C2×D73—416no—
115C2×D73—44no—
116C2×D73—48no—
117C2×D73—432no—
118C2×D73—416no—
119C2×D73#543112yes—
120C2×D73#560116yes—
121C4×C73—412no—
122Dic73—412no—
123C2×#2842—731nomaximal, Sylow
124C2×C73—44no—
125C2×C73—42no—
126C2×C73C2×#54313yes—
127C2×C73C2×#56014yes—
128D73—42no—
129D73—44no—
130D73#284218yesdirect product factor
131#2842—734no—
132#2842—738no—
133#2842—733no—
134#2842D7311yescharacteristic, direct product factor
135C2×#399—734no—
136C2×#396—738no—
137C2×#379—733no—
138C73C2×#284211yescharacteristic, complemented, Sylow
139C26—731no—
140C22×C4⋊C4—7312no—
141C22×C22⋊C4—7312no—
142C22×C22⋊C4—736no—
143#399—7312no—
144#399—7312no—
145#399—734no—
146#399C2×D7314yescomplemented
147#396—7324no—
148#396—7324no—
149#396—738no—
150#396C2×D7318yescomplemented
151#379—733no—
152#379—7312no—
153#379—736no—
154#379C2×D7313yes—
155C2×#95—734no—
156C25—29212no—
157C25—738no—
158C25—731no—
159C25—732no—
160C25—732no—
161C25—731no—
162C25C22×D7311yescharacteristic
163C23×C4—7312no—
164C2×C4⋊C4—29224no—
165C2×C4⋊C4—7324no—
166C2×C4⋊C4—7312no—
167C2×C4⋊C4C22×D73112yescomplemented
168C2×C22⋊C4—29224no—
169C2×C22⋊C4—29212no—
170C2×C22⋊C4—7312no—
171C2×C22⋊C4—736no—
172C2×C22⋊C4—7324no—
173C2×C22⋊C4—7312no—
174C2×C22⋊C4C22×D73112yes—
175C2×C22⋊C4C22×D7316yes—
176#95—7312no—
177#95C22×D7314yescomplemented
178C24—46no—
179C24—29212no—
180C24—2926no—
181C24—29264no—
182C24—29248no—
183C24—734no—
184C24—738no—
185C24—731no—
186C24—738no—
187C24—734no—
188C24—732no—
189C24—731no—
190C24—14624no—
191C24—14612no—
192C24Q8×D7314yes—
193C24C23×D7312yes—
194C24C23×D7311yescharacteristic
195C22×C4—7312no—
196C22×C4—14648no—
197C22×C4—14624no—
198C22×C4C23×D73112yes—
199C4⋊C4—412no—
200C4⋊C4—29224no—
201C4⋊C4—29212no—
202C22⋊C4—412no—
203C22⋊C4—46no—
204C22⋊C4—29224no—
205C22⋊C4—29212no—
206C22⋊C4—29212no—
207C22⋊C4—2926no—
208C23—212no—
209C23—26no—
210C23—412no—
211C23—416no—
212C23—29224no—
213C23—29212no—
214C23—292128no—
215C23—29232no—
216C23—29216no—
217C23—29232no—
218C23—29216no—
219C23—732no—
220C23—7312no—
221C23—734no—
222C23—732no—
223C23—14648no—
224C23—14624no—
225C23—14612no—
226C23—1466no—
227C23C2×Q8×D7314yes—
228C23C2×Q8×D7312yes—
229C23C24×D7311yescharacteristic
230C2×C4—224no—
231C2×C4—212no—
232C2×C4—29248no—
233C2×C4—14612no—
234C2×C4—14624no—
235C22—212no—
236C22—26no—
237C22—416no—
238C22—48no—
239C22—44no—
240C22—29232no—
241C22—29216no—
242C22—29232no—
243C22—29216no—
244C22—2928no—
245C22—2924no—
246C22—7316no—
247C22—7312no—
248C22—14612no—
249C22—1466no—
250C22C22×Q8×D7311yescharacteristic
251C22H(5,𝔽2)×D7316yes—
252C4—412no—
253C4—29212no—
254C2—44no—
255C2—42no—
256C2—2924no—
257C2—2922no—
258C2—738no—
259C2#543×D7313yes—
260C2#560×D7314yes—
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2842C2
prime radicalC25×D73C22
hypercenter#2842D73
hypocenterC73C2×#2842
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2842

Complements

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

NH ≅ G/Ntype
1. #22618196C2semidirect
2. #22618195C2semidirect
3. #22618194C2semidirect
4. #399×D73C2semidirect
5. #396×D73C2semidirect
7. C73×#2842C2semidirect
9. C2×C4⋊C4×D73C22semidirect
12. #17988524C22semidirect
13. #17988523C22semidirect
14. #17988522C22semidirect
15. #17988511C22semidirect
16. #17988510C22semidirect
17. #17988509C22semidirect
21. #95×D73C22semidirect
22. #399×C73C22semidirect
23. #396×C73C22semidirect
32. C2×C4⋊Dic73C23semidirect
33. C2×#11924007C23semidirect
41. #14556498C23semidirect
43. C2×C4⋊C4×C73C23semidirect
46. #95×C73C23semidirect
130. D73#2842direct (N × H)
134. #2842D73direct (N × H)
138. C73C2×#2842semidirect
146. #399C2×D73semidirect
150. #396C2×D73semidirect
167. C2×C4⋊C4C22×D73semidirect
177. #95C22×D73semidirect

Maximal subgroups

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

subgroupindex
#226181962
#226181952
#226181942
#399×D732
#396×D732
#379×D732
C73×#28422
C2×#284273