Finite Group Databasebeta

← #49172197

Subgroups — #49172197

Order 37504.

1160 conjugacy classes of subgroups; only the 471 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 471 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#34036728C216yesmaximal, complemented
2#34036719C216yesmaximal, complemented
3#34036691C213yesmaximal, complemented
4#34036665C216yesmaximal, complemented
5#34036642C216yesmaximal, complemented
6C2×#22627584C213yesmaximal, complemented
7#543×C293C211yesmaximal, characteristic, complemented
8C2×#17989803C2212yescomplemented
9C22×C22⋊D293C2213yes—
10C23×Dic293C2211yescharacteristic
11C22×C4×D293C2213yescomplemented
12#22627619C22112yescomplemented
13#22627615C2216yescomplemented
14#22627613C2216yescomplemented
15#22627609C22112yescomplemented
16#22627608C22112yescomplemented
17#22627600C2216yescomplemented
18#22627599C2216yescomplemented
19#22627598C2216yes—
20#22627598C2216yes—
21#22627594C22112yescomplemented
22Q8×Dic293C2212yescomplemented
23#22627586C2216yescomplemented
24#22627584C22112yescomplemented
25#22627584C22112yescomplemented
26#22627582C2216yescomplemented
27C2×#17989781C2213yescomplemented
28C2×#17989779C2213yescomplemented
29C2×C4×Dic293C2213yescomplemented
30C22⋊Q8×C293C2216yescomplemented
31C22⋊Q8×C293C2216yescomplemented
32C2×C22⋊C4×C293C2213yes—
33C23×D293C2313yes—
34#17989803—44no—
35C2×D1172C2316yes—
36C2×D1172C2316yes—
37C2×C22⋊D293—212no—
38C2×C22⋊D293C23112yes—
39C22×Dic293—42no—
40C22×Dic293C2313yes—
41C22×Dic293C2313yes—
42C22×Dic293C2313yes—
43C2×C4×D293—46no—
44C2×C4×D293C2316yes—
45C2×C4×D293C2316yes—
46C4⋊Dic293C2316yes—
47C4⋊Dic293C2316yes—
48#17989781C23112yes—
49#17989779C23112yes—
50#17989779C23112yes—
51#17989779C23112yes—
52C4×Dic293C2316yes—
53C4×Dic293C2316yes—
54C24×C293C2311yescharacteristic
55C2×Q8×C293C2312yes—
56C2×Q8×C293C2312yes—
57C22×C4×C293C2313yes—
58C22×C4×C293C2313yes—
59C4⋊C4×C293C2316yes—
60C4⋊C4×C293C2316yes—
61C22⋊C4×C293C23112yes—
62C22×D293—26no—
63C22×D293—43no—
64C22×D293—43no—
65C22×D293C2416yes—
66D1172—46no—
67D1172—46no—
68C22⋊D293—224no—
69C2×Dic293—26no—
70C2×Dic293—26no—
71C2×Dic293—43no—
72C2×Dic293C2413yes—
73C2×Dic293C2416yes—
74C2×Dic293C2411yescharacteristic
75C4×D293—212no—
76C4×D293—46no—
77C23×C293—41no—
78C23×C293—41no—
79C23×C293#4114yescomplemented
80C23×C293C2413yes—
81Q8×C293—42no—
82Q8×C293—42no—
83C2×C4×C293—43no—
84C2×C4×C293—43no—
85C2×C4×C293C2416yes—
86C2×C4×C293C2416yes—
87C22×C293—23no—
88C22×C293—23no—
89C22×C293—44no—
90C22×C293C2×#4116yes—
91C22×C293C2511yescharacteristic
92C2×D293—26no—
93C2×D293—26no—
94C2×D293—26no—
95C2×D293—412no—
96C4×C293—26no—
97C4×C293—26no—
98Dic293—26no—
99Dic293—23no—
100Dic293H(5,𝔽2)12yes—
101C2×C293—26no—
102C2×C293C22×#4111yescharacteristic
103C2×C293C2×H(5,𝔽2)11yescharacteristic
104C2×C293#58511yescharacteristic
105D293—46no—
106C293#345911yescharacteristic, complemented, Sylow
107#3459—2931nomaximal, Sylow
108#543D29311yescharacteristic, complemented
109#539—2936no—
110#538—2936no—
111#534—2933no—
112#529—2936no—
113#525—2936no—
114C2×C4×D4—2933no—
115C2×#41—2932no—
116C22×D4—2933no—
117C23×C4—2931no—
118C23×C4—2933no—
119#126—29312no—
120#125—2936no—
121#124—2936no—
122#123—29312no—
123#123—29312no—
124C22⋊Q8—2936no—
125C22⋊Q8C2×D29316yescomplemented
126C22⋊Q8C2×D29316yescomplemented
127#121—2936no—
128#121—2936no—
129#121—2936no—
130#120—29312no—
131C4×Q8—2932no—
132C4×D4—2936no—
133C4×D4—29312no—
134C4×D4—29312no—
135#117—2936no—
136C2×C4⋊C4—2933no—
137C2×C22⋊C4—2933no—
138C2×C22⋊C4C2×D29313yes—
139C2×C42—2933no—
140C24—2933no—
141C24C22×D29311yescharacteristic
142#41—11724no—
143C2×Q8C22×D29312yes—
144C2×Q8C22×D29312yes—
145C2×D4—29312no—
146C2×D4—2936no—
147C2×D4—2936no—
148C2×D4—58612no—
149C22×C4—2933no—
150C22×C4—2933no—
151C22×C4—2933no—
152C22×C4—2936no—
153C22×C4—2936no—
154C22×C4—11726no—
155C22×C4—11722no—
156C22×C4C22×D29313yes—
157C22×C4C22×D29313yes—
158C4⋊C4—29312no—
159C4⋊C4—2936no—
160C4⋊C4—2936no—
161C4⋊C4C22×D29316yes—
162C4⋊C4C22×D29316yes—
163C22⋊C4—29312no—
164C22⋊C4—29312no—
165C22⋊C4—29312no—
166C22⋊C4C22×D293112yes—
167C42—2936no—
168C42—2936no—
169C23—41no—
170C23—41no—
171C23—2936no—
172C23—5866no—
173C23—11723no—
174C23—11723no—
175C23#1798980314yescomplemented
176C23C23×D29313yes—
177Q8—42no—
178Q8—42no—
179D4—58624no—
180D4—11726no—
181D4—11726no—
182C2×C4—43no—
183C2×C4—43no—
184C2×C4—2931no—
185C2×C4—2936no—
186C2×C4—2933no—
187C2×C4—58612no—
188C2×C4—5866no—
189C2×C4—5866no—
190C2×C4—11726no—
191C2×C4—11723no—
192C2×C4C23×D29316yes—
193C2×C4C23×D29316yes—
194C22—23no—
195C22—23no—
196C22—44no—
197C22—5866no—
198C22—5866no—
199C22—5866no—
200C22—117212no—
201C22C2×#1798980316yes—
202C22C24×D29311yescharacteristic
203C4—26no—
204C4—26no—
205C4—2932no—
206C4—5866no—
207C4—5863no—
208C2—26no—
209C2—11726no—
210C2C22×#1798980311yescharacteristic
211C2H(5,𝔽2)×D29311yescharacteristic
212C2#3403696411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D293
commutator, socle, cosocleC22×C293C25
Fitting#543×C293C2
hypercenter#543D293
hypocenterC293#3459
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ #543

Complements

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

NH ≅ G/Ntype
1. #34036728C2semidirect
2. #34036719C2semidirect
3. #34036691C2semidirect
4. #34036665C2semidirect
5. #34036642C2semidirect
6. C2×#22627584C2semidirect
7. #543×C293C2semidirect
8. C2×#17989803C22semidirect
11. C22×C4×D293C22semidirect
12. #22627619C22semidirect
13. #22627615C22semidirect
14. #22627613C22semidirect
15. #22627609C22semidirect
16. #22627608C22semidirect
17. #22627600C22semidirect
18. #22627599C22semidirect
21. #22627594C22semidirect
22. Q8×Dic293C22semidirect
23. #22627586C22semidirect
24. #22627584C22semidirect
25. #22627584C22semidirect
26. #22627582C22semidirect
27. C2×#17989781C22semidirect
28. C2×#17989779C22semidirect
29. C2×C4×Dic293C22semidirect
30. C22⋊Q8×C293C22semidirect
31. C22⋊Q8×C293C22semidirect
79. C23×C293#41semidirect
106. C293#3459semidirect
108. #543D293semidirect
125. C22⋊Q8C2×D293semidirect
126. C22⋊Q8C2×D293semidirect
175. C23#17989803semidirect

Maximal subgroups

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

subgroupindex
#340367282
#340367192
#340366912
#340366652
#340366422
C2×#226275842
#543×C2932
#3459293