Finite Group Databasebeta

← #33244127

Subgroups — #33244127

Order 18688.

466 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 127 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#508×D73C212yesmaximal, complemented
2#22612250C212yesmaximal, complemented
3#22612247C212yesmaximal, complemented
4#22612245C212yesmaximal, complemented
5#22612242C212yesmaximal, complemented
6#22612240C211yesmaximal, characteristic, complemented
7#22612238C212yesmaximal, complemented
8C2×#17988420C211yesmaximal, characteristic, complemented
9C73×#2262C211yesmaximal, characteristic, complemented
10#135×D73—22no—
11#17989020C2212yes—
12#17989019C2212yescomplemented
13#17989018—22no—
14#17989017—22no—
15#17989016C2212yes—
16Q32×D73C2212yescomplemented
17SD32×D73—22no—
18D16×D73C2212yescomplemented
19C2×C16×D73C2211yescharacteristic
20Dic1168C2211yescharacteristic, complemented
21#17988427C2212yescomplemented
22#17988426C2212yescomplemented
23#17988425C2212yescomplemented
24#17988424C2212yescomplemented
25D2336C2211yescharacteristic, complemented
26#17988422C2212yescomplemented
27#17988420C2212yescomplemented
28#17988420C2212yescomplemented
29C2×#14556497C2211yescharacteristic, complemented
30#508×C73C2212yescomplemented
31Q64×C73C2211yescharacteristic, complemented
32SD64×C73C2212yescomplemented
33D32×C73C2211yescharacteristic, complemented
34C2×C32×C73C2211yescharacteristic, complemented
35#41×D73—42no—
36#14556614—22no—
37#14556613—22no—
38#14556612—42no—
39#14556611—42no—
40#14556610—22no—
41Q16×D73—22no—
42SD16×D73—42no—
43D8×D73—22no—
44C2×C8×D73D411yescharacteristic
45Dic584C2312yes—
46#14556537—22no—
47#14556536—22no—
48#14556535—22no—
49#14556534—22no—
50D1168C2312yes—
51#14556532—22no—
52C2×#11924003D411yescharacteristic
53C16×D73D412yes—
54C16×D73C2312yes—
55#14556497C2312yes—
56#135×C73—22no—
57Q32×C73C2312yes—
58SD32×C73—22no—
59D16×C73C2312yes—
60C2×C16×C73C2311yescharacteristic
61C32×C73C2311yescharacteristic
62C32×C73C2311yescharacteristic
63#11924029—42no—
64#11924028—42no—
65#11924028—82no—
66#11924027—42no—
67#11924027—82no—
68Q8×D73—42no—
69D4×D73—42no—
70D4×D73—82no—
71C2×C4×D73—82no—
72C2×C4×D73D811yescharacteristic
73Dic292—22no—
74#11924018—42no—
75#11924017—42no—
76#11924016—42no—
77#11924015—42no—
78D584—22no—
79#11924013—42no—
80C2×#10596831D811yescharacteristic
81C8×D73D812yes—
82C8×D73C2×D412yes—
83#11924003C2×D412yes—
84#41×C73—42no—
85Q16×C73—22no—
86SD16×C73—42no—
87D8×C73—22no—
88C2×C8×C73C2×D411yescharacteristic
89C16×C73C2×D411yescharacteristic
90C16×C73C2411yescharacteristic
91C22×D73—82no—
92C22×D73D1611yescharacteristic
93Q8×C73—42no—
94D4×C73—42no—
95D4×C73—82no—
96C2×C4×C73—82no—
97C2×C4×C73C2×D811yescharacteristic
98C22⋊D73—82no—
99C22⋊D73—82no—
100C22⋊D73—82no—
101C2×Dic73—82no—
102C2×Dic73D1611yescharacteristic
103D292—42no—
104D292—82no—
105C4×D73—82no—
106C4×D73—82no—
107C4×D73—82no—
108C4×D73D1612yes—
109C4×D73C2×D812yes—
110Dic146—42no—
111Dic146—82no—
112C8×C73C2×D811yescharacteristic
113C8×C73C22×D411yescharacteristic
114#10596831C2×D812yes—
115C22×C73—82no—
116C22×C73C2×D1611yescharacteristic
117C2×D73—41no—
118C2×D73—82no—
119C2×D73—164no—
120C2×D73C2×D1612yes—
121C4×C73—82no—
122C4×C73C2×D1611yescharacteristic
123C4×C73C22×D811yescharacteristic
124Dic73—82no—
125Dic73C2×D1612yes—
126#33981—731nomaximal, Sylow
127C2×C73—21no—
128C2×C73—162no—
129C2×C73C22×D1611yescharacteristic
130D73—22no—
131D73—162no—
132C2×#508—732no—
133#2264—732no—
134#2264—732no—
135#2263—732no—
136#2263—732no—
137#2262—732no—
138#2262—731no—
139#2262D7311yescharacteristic, complemented
140C2×M64—731no—
141C73#3398111yescharacteristic, complemented, Sylow
142C2×#135—1462no—
143#508—732no—
144#508—732no—
145#508—732no—
146#508—1462no—
147#508—1462no—
148#508C2×D7312yescomplemented
149C2×Q32—732no—
150C2×SD32—1462no—
151C2×D16—732no—
152C22×C16—731no—
153Q64—732no—
154Q64—731no—
155Q64C2×D7311yescharacteristic, complemented
156SD64—732no—
157SD64—732no—
158SD64—732no—
159SD64C2×D7312yescomplemented
160D32—732no—
161D32—731no—
162D32C2×D7311yescharacteristic, complemented
163M64—732no—
164M64—732no—
165C2×C32—731no—
166C2×C32C2×D7311yescharacteristic, complemented
167C2×#41—2922no—
168#135—22no—
169#135—2922no—
170#135—2922no—
171#135—1462no—
172#135—1462no—
173#135—1462no—
174C2×Q16—1462no—
175C2×SD16—2922no—
176C2×D8—1462no—
177C22×C8—731no—
178Q32—732no—
179Q32—1462no—
180Q32C22×D7312yes—
181SD32—22no—
182SD32—1462no—
183SD32—1462no—
184SD32—1462no—
185D16—732no—
186D16—1462no—
187D16C22×D7312yes—
188C2×C16—731no—
189C2×C16—732no—
190C2×C16—732no—
191C2×C16C22×D7311yescharacteristic
192C32—732no—
193C32C22×D7311yescharacteristic
194C32C22×D7311yescharacteristic
195#41—42no—
196#41—2922no—
197#41—2922no—
198#41—2922no—
199#41—5842no—
200#41—5842no—
201C2×Q8—2922no—
202C2×D4—2922no—
203C2×D4—5842no—
204C22×C4—5842no—
205C22×C4—731no—
206Q16—22no—
207Q16—2922no—
208Q16—1462no—
209SD16—42no—
210SD16—2922no—
211SD16—2922no—
212SD16—2922no—
213D8—22no—
214D8—2922no—
215D8—1462no—
216C2×C8—731no—
217C2×C8—732no—
218C2×C8—732no—
219C2×C8D4×D7311yescharacteristic
220C16—732no—
221C16D4×D7311yescharacteristic
222C16C23×D7311yescharacteristic
223C23—5842no—
224C23—731no—
225Q8—42no—
226Q8—2922no—
227Q8—5842no—
228D4—42no—
229D4—82no—
230D4—2922no—
231D4—5842no—
232D4—5842no—
233D4—5842no—
234D4—5842no—
235C2×C4—82no—
236C2×C4—5842no—
237C2×C4—5842no—
238C2×C4—5842no—
239C2×C4—5842no—
240C2×C4—731no—
241C2×C4—732no—
242C2×C4—732no—
243C2×C4D8×D7311yescharacteristic
244C8—732no—
245C8D8×D7311yescharacteristic
246C8C2×D4×D7311yescharacteristic
247C22—82no—
248C22—2921no—
249C22—5842no—
250C22—732no—
251C22—11684no—
252C22D16×D7311yescharacteristic
253C4—82no—
254C4—5842no—
255C4—732no—
256C4D16×D7311yescharacteristic
257C4C2×D8×D7311yescharacteristic
258C2—21no—
259C2—162no—
260C2—11682no—
261C2—1462no—
262C2C2×D16×D7311yescharacteristic
subgroupG/H
centerC4D16×D73
commutator, cosocleC16×C73C24
FrattiniC16C23×D73
FittingC73×#2262C2
socleC2×C73C22×D16
hypercenter#2262D73
hypocenterC73#33981
LCSG ▷ C16×C73 ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2262

Complements

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

NH ≅ G/Ntype
1. #508×D73C2semidirect
2. #22612250C2semidirect
3. #22612247C2semidirect
4. #22612245C2semidirect
5. #22612242C2semidirect
6. #22612240C2semidirect
7. #22612238C2semidirect
8. C2×#17988420C2semidirect
9. C73×#2262C2semidirect
12. #17989019C22semidirect
16. Q32×D73C22semidirect
18. D16×D73C22semidirect
20. Dic1168C22semidirect
21. #17988427C22semidirect
22. #17988426C22semidirect
23. #17988425C22semidirect
24. #17988424C22semidirect
25. D2336C22semidirect
26. #17988422C22semidirect
27. #17988420C22semidirect
28. #17988420C22semidirect
29. C2×#14556497C22semidirect
30. #508×C73C22semidirect
31. Q64×C73C22semidirect
32. SD64×C73C22semidirect
33. D32×C73C22semidirect
34. C2×C32×C73C22semidirect
139. #2262D73semidirect
141. C73#33981semidirect
148. #508C2×D73semidirect
155. Q64C2×D73semidirect
159. SD64C2×D73semidirect
162. D32C2×D73semidirect
166. C2×C32C2×D73semidirect

Maximal subgroups

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

subgroupindex
#508×D732
#226122502
#226122472
#226122452
#226122422
#226122402
#226122382
C2×#179884202
C73×#22622
#3398173