Finite Group Databasebeta

← #49170600

Subgroups — #49170600

Order 37504.

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

normal subgroups only

This group has 494 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#34036784C211yesmaximal, characteristic, complemented
2D4×D1172C211yesmaximal, characteristic, complemented
3#34036476C211yesmaximal, characteristic, complemented
4#34036444C212yesmaximal, complemented
5#34036409C211yesmaximal, characteristic, complemented
6#34036364C212yesmaximal, complemented
7#34036324C211yesmaximal, characteristic, complemented
8#34036261C212yesmaximal, complemented
9C8×D1172C211yesmaximal, characteristic, complemented
10#102×D293C212yesmaximal, complemented
11C4×D8×C293C211yesmaximal, characteristic, complemented
12C2×#17989802—21no—
13C22×D1172—21no—
14C2×D4×D293C2212yes—
15C2×#17989787C2212yescomplemented
16C2×C8×D293C2212yescomplemented
17#22627624C2211yescharacteristic, complemented
18#22627621C2211yescharacteristic
19#22627606—22no—
20#22627603—21no—
21#22627599C2212yes—
22#22627598—21no—
23#22627595C2212yescomplemented
24#22627594—22no—
25C4×D1172C2211yescharacteristic
26C4⋊C4×D293C2212yescomplemented
27#22627557C2212yescomplemented
28C4⋊#14556873C2211yescharacteristic, complemented
29#22627546C2212yescomplemented
30#22627546C2212yescomplemented
31#22627545C2212yes—
32#22627544C2212yescomplemented
33#22627536C2212yescomplemented
34C2×D8×C293C2211yescharacteristic
35C4×D4×C293C2211yescharacteristic
36C4×D4×C293C2211yescharacteristic, complemented
37#107×C293C2211yescharacteristic, complemented
38#102×C293C2211yescharacteristic
39#102×C293C2211yescharacteristic, complemented
40C4×C8×C293C2211yescharacteristic, complemented
41C23×D293—22no—
42#17989802—44no—
43C2×Dic586—21no—
44C2×D1172—22no—
45C2×D1172—21no—
46C2×D1172—21no—
47C2×D1172—44no—
48C2×D1172D411yescharacteristic
49C2×D1172C2312yes—
50C2×C22⋊D293—22no—
51C2×C22⋊D293—22no—
52D4×D293—24no—
53D4×D293—42no—
54C2×C4×D293—22no—
55C2×C4×D293C2312yes—
56#17989787—42no—
57C2×#14556873C2312yes—
58C8×D293—42no—
59C4⋊Dic293—21no—
60C4⋊Dic293D411yescharacteristic
61C4⋊Dic293C2312yes—
62#17989781—22no—
63C22⋊Dic293—22no—
64#17989779—22no—
65#17989779D412yes—
66C2×D4×C293C2311yescharacteristic
67C2×D4×C293C2311yescharacteristic
68C22×C4×C293—21no—
69C22×C4×C293—21no—
70D8×C293—22no—
71C2×C8×C293C2311yescharacteristic
72C2×C8×C293C2311yescharacteristic
73C4⋊C4×C293C2311yescharacteristic
74C4⋊C4×C293C2311yescharacteristic
75C22⋊C4×C293—21no—
76C22⋊C4×C293—21no—
77C42×C293C2311yescharacteristic
78C22×D293—22no—
79C22×D293—44no—
80C22×D293—44no—
81C22×D293—82no—
82C22×D293C2×D412yes—
83Dic586—42no—
84D1172—22no—
85D1172—22no—
86D1172—44no—
87D1172—42no—
88D1172—81no—
89D1172D814yescomplemented
90C22⋊D293—44no—
91C22⋊D293—44no—
92C2×Dic293—22no—
93C2×Dic293C2×D412yes—
94C4×D293—22no—
95C4×D293—22no—
96C4×D293—44no—
97#14556873—22no—
98C23×C293—21no—
99C23×C293—21no—
100D4×C293—21no—
101D4×C293—21no—
102D4×C293—21no—
103D4×C293#4112yescomplemented
104C2×C4×C293—21no—
105C2×C4×C293—21no—
106C2×C4×C293—42no—
107C2×C4×C293—42no—
108C2×C4×C293C2×D411yescharacteristic
109C2×C4×C293C2×D411yescharacteristic
110C2×C4×C293C2411yescharacteristic
111C8×C293—21no—
112C8×C293—21no—
113C22×C293—22no—
114C22×C293—41no—
115C22×C293—41no—
116C22×C293—41no—
117C22×C293—41no—
118C22×C293—41no—
119C22×C293C22×D411yescharacteristic
120C2×D293—22no—
121C2×D293—22no—
122C2×D293—42no—
123C2×D293—42no—
124C2×D293—42no—
125C2×D293—88no—
126C2×D293C2×D814yes—
127C4×C293—21no—
128C4×C293—41no—
129C4×C293—41no—
130C4×C293C2×D812yes—
131C4×C293C2×#4111yescharacteristic
132C4×C293H(5,𝔽2)11yescharacteristic
133Dic293—22no—
134Dic293—42no—
135C2×C293—42no—
136C2×C293—81no—
137C2×C293#54611yescharacteristic
138C2×C293C22×D811yescharacteristic
139C2×C293#57711yescharacteristic
140D293—24no—
141D293—82no—
142C293#329411yescharacteristic, complemented, Sylow
143#3294—2931nomaximal, Sylow
144#547—2931no—
145D42—2931no—
146#486—2931no—
147#480—2932no—
148#474—2931no—
149#466—2932no—
150#459—2931no—
151#447—2932no—
152C4×D8D29311yescharacteristic, complemented
153C8×D4—2931no—
154C2×#102—2932no—
155C2×#41—5861no—
156C22×D4—2932no—
157C22×D4—5861no—
158C2×D8—2932no—
159C2×D8C2×D29311yescharacteristic
160C22×C8—2932no—
161C4⋊Q8—2931no—
162#127—2931no—
163#123—5862no—
164C22⋊Q8—5861no—
165#121—2932no—
166#121—2932no—
167#121—5861no—
168#120—5862no—
169C4×D4—2931no—
170C4×D4C2×D29311yescharacteristic
171C4×D4C2×D29311yescharacteristic, complemented
172C2×C4⋊C4—2932no—
173#107—2932no—
174#107C2×D29311yescharacteristic, complemented
175C4⋊C8—2931no—
176#102—2932no—
177#102—2932no—
178#102—2932no—
179#102—2932no—
180#102C2×D29311yescharacteristic
181#102C2×D29311yescharacteristic, complemented
182C22⋊C8—2932no—
183C4×C8C2×D29311yescharacteristic, complemented
184C24—5862no—
185#41—11724no—
186C2×Q8—5861no—
187C2×D4—2931no—
188C2×D4—2932no—
189C2×D4—5862no—
190C2×D4—5862no—
191C2×D4—5864no—
192C2×D4—5862no—
193C2×D4—5861no—
194C2×D4—5861no—
195C2×D4—11724no—
196C2×D4—11722no—
197C2×D4C22×D29311yescharacteristic
198C2×D4C22×D29311yescharacteristic
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—2932no—
202C22×C4—5862no—
203D8—22no—
204D8—11722no—
205C2×C8—2932no—
206C2×C8—11722no—
207C2×C8C22×D29311yescharacteristic
208C2×C8C22×D29311yescharacteristic
209C4⋊C4—2931no—
210C4⋊C4—2932no—
211C4⋊C4—5862no—
212C4⋊C4—5861no—
213C4⋊C4C22×D29311yescharacteristic
214C4⋊C4C22×D29311yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—21no—
217C22⋊C4—2932no—
218C22⋊C4—5862no—
219C22⋊C4—5862no—
220C42C22×D29311yescharacteristic
221C23—21no—
222C23—21no—
223C23—2932no—
224C23—23442no—
225C23—5862no—
226C23—11724no—
227C23—11724no—
228Q8—11722no—
229D4—21no—
230D4—21no—
231D4—21no—
232D4—2934no—
233D4—23441no—
234D4—5862no—
235D4—5862no—
236D4—11724no—
237D4—11724no—
238D4—11724no—
239D4—11722no—
240D4#1798980212yescomplemented
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—2932no—
246C2×C4—5862no—
247C2×C4—5862no—
248C2×C4—5862no—
249C2×C4—11724no—
250C2×C4D4×D29311yescharacteristic
251C2×C4D4×D29311yescharacteristic
252C2×C4C23×D29311yescharacteristic
253C8—21no—
254C8—21no—
255C8—5862no—
256C22—22no—
257C22—41no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—2934no—
263C22—23448no—
264C22—5862no—
265C22—5862no—
266C22—11722no—
267C22—11722no—
268C22—11722no—
269C22C2×D4×D29311yescharacteristic
270C4—21no—
271C4—41no—
272C4—41no—
273C4—5862no—
274C4—11722no—
275C4D8×D29312yes—
276C4C2×#1798980211yescharacteristic
277C4#2262767011yescharacteristic
278C2—42no—
279C2—81no—
280C2—23442no—
281C2—5864no—
282C2#3403677511yescharacteristic
283C2C2×D8×D29311yescharacteristic
284C2#3403693611yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC4×D8×C293C2
socleC22×C293C22×D4
hypercenterC4×D8D293
hypocenterC293#3294
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #34036784C2semidirect
2. D4×D1172C2semidirect
3. #34036476C2semidirect
4. #34036444C2semidirect
5. #34036409C2semidirect
6. #34036364C2semidirect
7. #34036324C2semidirect
8. #34036261C2semidirect
9. C8×D1172C2semidirect
10. #102×D293C2semidirect
11. C4×D8×C293C2semidirect
15. C2×#17989787C22semidirect
16. C2×C8×D293C22semidirect
17. #22627624C22semidirect
23. #22627595C22semidirect
26. C4⋊C4×D293C22semidirect
27. #22627557C22semidirect
28. C4⋊#14556873C22semidirect
29. #22627546C22semidirect
30. #22627546C22semidirect
32. #22627544C22semidirect
33. #22627536C22semidirect
36. C4×D4×C293C22semidirect
37. #107×C293C22semidirect
39. #102×C293C22semidirect
40. C4×C8×C293C22semidirect
89. D1172D8semidirect
103. D4×C293#41semidirect
142. C293#3294semidirect
152. C4×D8D293semidirect
171. C4×D4C2×D293semidirect
174. #107C2×D293semidirect
181. #102C2×D293semidirect
183. C4×C8C2×D293semidirect
240. D4#17989802semidirect

Maximal subgroups

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

subgroupindex
#340367842
D4×D11722
#340364762
#340364442
#340364092
#340363642
#340363242
#340362612
C8×D11722
#102×D2932
C4×D8×C2932
#3294293