Finite Group Databasebeta

← #49170611

Subgroups — #49170611

Order 37504.

462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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#34036839C211yesmaximal, characteristic, complemented
2D4×D1172C211yesmaximal, characteristic
3#34036476C211yesmaximal, characteristic, complemented
4#34036449C212yesmaximal, complemented
5#34036419C211yesmaximal, characteristic, complemented
6#34036361C212yesmaximal, complemented
7#34036329C211yesmaximal, characteristic, complemented
8#34036278C212yesmaximal, complemented
9C8×D1172C211yesmaximal, characteristic, complemented
10#102×D293C212yesmaximal, complemented
11C4×SD16×C293C211yesmaximal, characteristic, complemented
12C22×D1172—21no—
13C2×D4×D293C2212yes—
14C2×#17989789C2212yescomplemented
15C2×C8×D293C2212yescomplemented
16#22627624C2211yescharacteristic, complemented
17#22627621C2211yescharacteristic
18#22627616—21no—
19#22627602—22no—
20#22627600C2212yescomplemented
21#22627599C2212yes—
22#22627598—21no—
23#22627594—22no—
24C4×D1172—21no—
25C4×D1172C2211yescharacteristic
26C4⋊C4×D293C2212yescomplemented
27#22627555C2212yescomplemented
28C4⋊#14556873C2211yescharacteristic, complemented
29#22627546C2212yescomplemented
30#22627546C2212yescomplemented
31#22627545C2212yes—
32#22627544C2212yescomplemented
33#22627536C2212yescomplemented
34C2×SD16×C293C2211yescharacteristic
35C4×Q8×C293C2211yescharacteristic, complemented
36C4×D4×C293C2211yescharacteristic
37#106×C293C2211yescharacteristic, complemented
38#103×C293C2211yescharacteristic, complemented
39#102×C293C2211yescharacteristic
40C4×C8×C293C2211yescharacteristic, complemented
41C23×D293—22no—
42C2×Dic586—21no—
43C2×D1172—22no—
44C2×D1172—21no—
45C2×D1172—21no—
46C2×D1172—44no—
47C2×D1172D411yescharacteristic
48C2×D1172C2312yes—
49C2×C22⋊D293—22no—
50D4×D293—24no—
51D4×D293—42no—
52C2×C4×D293—22no—
53C2×C4×D293C2312yes—
54#17989789—42no—
55C2×#14556873C2312yes—
56C8×D293—42no—
57C4⋊Dic293—21no—
58C4⋊Dic293D411yescharacteristic
59C4⋊Dic293C2312yes—
60#17989781—22no—
61#17989781—22no—
62#17989779—22no—
63#17989779—22no—
64#17989779D412yes—
65C2×Q8×C293C2311yescharacteristic
66C2×D4×C293C2311yescharacteristic
67C22×C4×C293—21no—
68SD16×C293—22no—
69C2×C8×C293C2311yescharacteristic
70C2×C8×C293C2311yescharacteristic
71C4⋊C4×C293—21no—
72C4⋊C4×C293C2311yescharacteristic
73C4⋊C4×C293C2311yescharacteristic
74C22⋊C4×C293—21no—
75C42×C293—21no—
76C42×C293C2311yescharacteristic
77C22×D293—22no—
78C22×D293—44no—
79C22×D293—44no—
80C22×D293—82no—
81C22×D293C2×D412yes—
82Dic586—81no—
83D1172—22no—
84D1172—22no—
85D1172—44no—
86D1172—42no—
87D1172—81no—
88D1172SD1614yescomplemented
89C22⋊D293—44no—
90C2×Dic293—22no—
91C2×Dic293C2×D412yes—
92C4×D293—22no—
93C4×D293—22no—
94C4×D293—82no—
95#14556873—22no—
96C23×C293—21no—
97Q8×C293—21no—
98Q8×C293—21no—
99D4×C293—21no—
100D4×C293#4112yes—
101C2×C4×C293—21no—
102C2×C4×C293—21no—
103C2×C4×C293—21no—
104C2×C4×C293—42no—
105C2×C4×C293C2×D411yescharacteristic
106C2×C4×C293C2×D411yescharacteristic
107C2×C4×C293C2411yescharacteristic
108C8×C293—21no—
109C8×C293—21no—
110C22×C293—22no—
111C22×C293—41no—
112C22×C293—41no—
113C22×C293C22×D411yescharacteristic
114C2×D293—22no—
115C2×D293—22no—
116C2×D293—42no—
117C2×D293—42no—
118C2×D293—42no—
119C2×D293—88no—
120C2×D293C2×SD1614yes—
121C4×C293—21no—
122C4×C293—41no—
123C4×C293—41no—
124C4×C293—41no—
125C4×C293C2×SD1612yes—
126C4×C293C2×#4111yescharacteristic
127C4×C293H(5,𝔽2)11yescharacteristic
128Dic293—22no—
129Dic293—42no—
130C2×C293—42no—
131C2×C293#54611yescharacteristic
132C2×C293C22×SD1611yescharacteristic
133C2×C293#57611yescharacteristic
134D293—24no—
135D293—82no—
136C293#329511yescharacteristic, complemented, Sylow
137#3295—2931nomaximal, Sylow
138#554—2931no—
139D42—2931no—
140#486—2931no—
141#481—2932no—
142#476—2931no—
143#465—2932no—
144#460—2931no—
145#450—2932no—
146C4×SD16D29311yescharacteristic, complemented
147C8×D4—2931no—
148C2×#102—2932no—
149C22×D4—2932no—
150C22×D4—5861no—
151C2×SD16—2932no—
152C2×SD16C2×D29311yescharacteristic
153C22×C8—2932no—
154C4⋊Q8—2931no—
155#127—2931no—
156#125—5861no—
157C22⋊Q8—2932no—
158C22⋊Q8—5862no—
159#121—2932no—
160#121—5861no—
161#120—5862no—
162C4×Q8C2×D29311yescharacteristic, complemented
163C4×D4—2931no—
164C4×D4—5861no—
165C4×D4C2×D29311yescharacteristic
166C2×C4⋊C4—2932no—
167#106—2932no—
168#106C2×D29311yescharacteristic, complemented
169C4⋊C8—2931no—
170#103C2×D29311yescharacteristic, complemented
171#102—2932no—
172#102—2932no—
173#102—2932no—
174#102—2932no—
175#102C2×D29311yescharacteristic
176C22⋊C8—2932no—
177C4×C8C2×D29311yescharacteristic, complemented
178C24—5862no—
179C2×Q8—5861no—
180C2×Q8C22×D29311yescharacteristic
181C2×D4—2931no—
182C2×D4—2932no—
183C2×D4—5862no—
184C2×D4—5862no—
185C2×D4—5864no—
186C2×D4—5861no—
187C2×D4—5861no—
188C2×D4—11724no—
189C2×D4—11722no—
190C2×D4C22×D29311yescharacteristic
191C22×C4—21no—
192C22×C4—2932no—
193C22×C4—5862no—
194SD16—22no—
195SD16—11722no—
196C2×C8—2932no—
197C2×C8—11722no—
198C2×C8C22×D29311yescharacteristic
199C2×C8C22×D29311yescharacteristic
200C4⋊C4—21no—
201C4⋊C4—2931no—
202C4⋊C4—2932no—
203C4⋊C4—5862no—
204C4⋊C4—5862no—
205C4⋊C4—5861no—
206C4⋊C4C22×D29311yescharacteristic
207C4⋊C4C22×D29311yescharacteristic
208C22⋊C4—21no—
209C22⋊C4—2932no—
210C22⋊C4—5862no—
211C22⋊C4—5862no—
212C42—21no—
213C42C22×D29311yescharacteristic
214C23—21no—
215C23—2932no—
216C23—23442no—
217C23—5862no—
218C23—11724no—
219C23—11724no—
220Q8—21no—
221Q8—21no—
222Q8—23441no—
223D4—21no—
224D4—2934no—
225D4—23441no—
226D4—5862no—
227D4—5862no—
228D4—11724no—
229D4—11724no—
230D4—11722no—
231D4#1798980212yes—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—2932no—
237C2×C4—23442no—
238C2×C4—5862no—
239C2×C4—5862no—
240C2×C4—5862no—
241C2×C4D4×D29311yescharacteristic
242C2×C4D4×D29311yescharacteristic
243C2×C4C23×D29311yescharacteristic
244C8—21no—
245C8—21no—
246C8—5862no—
247C22—22no—
248C22—41no—
249C22—41no—
250C22—2934no—
251C22—23448no—
252C22—5862no—
253C22—5862no—
254C22—11722no—
255C22—11722no—
256C22—11722no—
257C22C2×D4×D29311yescharacteristic
258C4—21no—
259C4—41no—
260C4—41no—
261C4—41no—
262C4—5862no—
263C4—11722no—
264C4SD16×D29312yes—
265C4C2×#1798980211yescharacteristic
266C4#2262767011yescharacteristic
267C2—42no—
268C2—23442no—
269C2—5864no—
270C2#3403677511yescharacteristic
271C2C2×SD16×D29311yescharacteristic
272C2#3403693111yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC4×SD16×C293C2
socleC22×C293C22×D4
prime radicalD4×D1172C2
hypercenterC4×SD16D293
hypocenterC293#3295
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #34036839C2semidirect
3. #34036476C2semidirect
4. #34036449C2semidirect
5. #34036419C2semidirect
6. #34036361C2semidirect
7. #34036329C2semidirect
8. #34036278C2semidirect
9. C8×D1172C2semidirect
10. #102×D293C2semidirect
11. C4×SD16×C293C2semidirect
14. C2×#17989789C22semidirect
15. C2×C8×D293C22semidirect
16. #22627624C22semidirect
20. #22627600C22semidirect
26. C4⋊C4×D293C22semidirect
27. #22627555C22semidirect
28. C4⋊#14556873C22semidirect
29. #22627546C22semidirect
30. #22627546C22semidirect
32. #22627544C22semidirect
33. #22627536C22semidirect
35. C4×Q8×C293C22semidirect
37. #106×C293C22semidirect
38. #103×C293C22semidirect
40. C4×C8×C293C22semidirect
88. D1172SD16semidirect
136. C293#3295semidirect
146. C4×SD16D293semidirect
162. C4×Q8C2×D293semidirect
168. #106C2×D293semidirect
170. #103C2×D293semidirect
177. C4×C8C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340368392
D4×D11722
#340364762
#340364492
#340364192
#340363612
#340363292
#340362782
C8×D11722
#102×D2932
C4×SD16×C2932
#3295293