Finite Group Databasebeta

← #49170599

Subgroups — #49170599

Order 37504.

494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 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#34036783C211yesmaximal, characteristic, complemented
2D4×D1172C211yesmaximal, characteristic, complemented
3#34036476C211yesmaximal, characteristic, complemented
4#34036443C212yesmaximal, complemented
5#34036410C211yesmaximal, characteristic, complemented
6#34036365C212yesmaximal, complemented
7#34036325C211yesmaximal, characteristic, complemented
8#34036265C212yesmaximal, complemented
9C4×D2344C211yesmaximal, characteristic, complemented
10C2×#22627546C212yesmaximal, complemented
11C8×D4×C293C211yesmaximal, characteristic, complemented
12C2×#17989801—21no—
13C22×D1172C2212yes—
14C2×D4×D293—21no—
15C2×D2344C2211yescharacteristic
16C2×D2344C2212yescomplemented
17#22627624C2211yescharacteristic, complemented
18#22627621C2211yescharacteristic
19#22627608—22no—
20#22627604—21no—
21#22627599—21no—
22#22627598C2212yes—
23#22627598C2212yescomplemented
24#22627594—22no—
25C4×D1172C2211yescharacteristic
26C4×D1172C2211yescharacteristic, complemented
27C2×C4⋊Dic293C2212yescomplemented
28#22627558C2212yescomplemented
29#22627558C2211yescharacteristic, complemented
30#22627546C2212yes—
31#22627546C2211yescharacteristic
32#22627546C2212yescomplemented
33#22627546C2212yescomplemented
34#22627546C2211yescharacteristic, complemented
35#22627546C2212yescomplemented
36C22×C8×C293C2212yescomplemented
37C4×D4×C293C2211yescharacteristic
38C4⋊C8×C293C2211yescharacteristic, complemented
39C22⋊C8×C293C2212yescomplemented
40C4×C8×C293C2211yescharacteristic, complemented
41C23×D293—22no—
42#17989801—44no—
43C2×Dic586—21no—
44C2×D1172—24no—
45C2×D1172—22no—
46C2×D1172—21no—
47C2×D1172—21no—
48C2×D1172—42no—
49C2×D1172C2311yescharacteristic
50C2×D1172C2312yes—
51C2×D1172C2311yescharacteristic
52C2×C22⋊D293—22no—
53C2×C22⋊D293—22no—
54D4×D293—44no—
55C22×Dic293—22no—
56C2×C4×D293—21no—
57C2×C4×D293—21no—
58D2344—22no—
59D2344—42no—
60C4⋊Dic293—22no—
61C4⋊Dic293—21no—
62C4⋊Dic293C2311yescharacteristic
63C4⋊Dic293C2311yescharacteristic
64C4⋊Dic293C2312yes—
65#17989779—21no—
66#17989779—21no—
67#17989779—22no—
68#17989779—22no—
69C2×D4×C293D411yescharacteristic
70C22×C4×C293C2312yes—
71C2×C8×C293—42no—
72C2×C8×C293C2311yescharacteristic
73C2×C8×C293C2312yes—
74C2×C8×C293C2311yescharacteristic
75C4⋊C4×C293D411yescharacteristic
76C22⋊C4×C293D412yes—
77C42×C293C2311yescharacteristic
78C22×D293—21no—
79C22×D293—21no—
80C22×D293—22no—
81C22×D293—44no—
82C22×D293—44no—
83C22×D293—82no—
84Dic586—42no—
85D1172—21no—
86D1172—22no—
87D1172—21no—
88D1172—21no—
89D1172—22no—
90D1172—44no—
91D1172—42no—
92D1172—81no—
93D1172#4112yescomplemented
94C22⋊D293—44no—
95C22⋊D293—44no—
96C2×Dic293—21no—
97C2×Dic293—21no—
98C2×Dic293—22no—
99C2×Dic293—44no—
100C4×D293—42no—
101C4×D293—42no—
102C23×C293C2×D412yes—
103D4×C293D814yescomplemented
104C2×C4×C293—22no—
105C2×C4×C293—22no—
106C2×C4×C293C2×D411yescharacteristic
107C2×C4×C293C2×D412yes—
108C2×C4×C293C2×D411yescharacteristic
109C2×C4×C293C2411yescharacteristic
110C8×C293—21no—
111C8×C293—21no—
112C8×C293—22no—
113C22×C293—22no—
114C22×C293—22no—
115C22×C293C2×D814yes—
116C22×C293C22×D411yescharacteristic
117C2×D293—22no—
118C2×D293—41no—
119C2×D293—41no—
120C2×D293—42no—
121C2×D293—41no—
122C2×D293—41no—
123C2×D293—42no—
124C2×D293—42no—
125C2×D293—41no—
126C2×D293—88no—
127C4×C293—22no—
128C4×C293—21no—
129C4×C293C2×D812yes—
130C4×C293C2×#4111yescharacteristic
131C4×C293H(5,𝔽2)11yescharacteristic
132Dic293—41no—
133Dic293—41no—
134Dic293—42no—
135C2×C293—24no—
136C2×C293#54611yescharacteristic
137C2×C293C22×D811yescharacteristic
138C2×C293#57711yescharacteristic
139D293—42no—
140D293—81no—
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×D8—2931no—
153C8×D4D29311yescharacteristic, complemented
154C2×#102—2932no—
155C2×#41—5861no—
156C22×D4—2932no—
157C22×D4—5861no—
158C2×D8—2931no—
159C2×D8—2932no—
160C22×C8C2×D29312yescomplemented
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×D4—2931no—
171C4×D4C2×D29311yescharacteristic
172C2×C4⋊C4—2932no—
173#107—2931no—
174#107—2932no—
175C4⋊C8C2×D29311yescharacteristic, complemented
176#102—2931no—
177#102—2932no—
178#102—2932no—
179#102—2932no—
180#102—2931no—
181#102—2932no—
182C22⋊C8C2×D29312yescomplemented
183C4×C8C2×D29311yescharacteristic, complemented
184C24—5862no—
185#41—11724no—
186C2×Q8—5861no—
187C2×D4—2931no—
188C2×D4—2932no—
189C2×D4—2931no—
190C2×D4—5864no—
191C2×D4—5862no—
192C2×D4—5862no—
193C2×D4—5861no—
194C2×D4—5862no—
195C2×D4—5861no—
196C2×D4—11722no—
197C2×D4—11724no—
198C2×D4D117211yescharacteristic
199C22×C4—5862no—
200C22×C4—5861no—
201C22×C4—5861no—
202C22×C4C22×D29312yes—
203D8—5862no—
204D8—11722no—
205C2×C8—42no—
206C2×C8C22×D29311yescharacteristic
207C2×C8C22×D29311yescharacteristic
208C2×C8C22×D29312yes—
209C4⋊C4—2931no—
210C4⋊C4—2932no—
211C4⋊C4—2931no—
212C4⋊C4—5862no—
213C4⋊C4—5861no—
214C4⋊C4D117211yescharacteristic
215C22⋊C4—5861no—
216C22⋊C4—5861no—
217C22⋊C4—5862no—
218C22⋊C4—5862no—
219C22⋊C4D117212yes—
220C42C22×D29311yescharacteristic
221C23—23442no—
222C23—5861no—
223C23—5861no—
224C23—5862no—
225C23—11724no—
226C23—11724no—
227C23C2×D117212yes—
228Q8—11722no—
229D4—2932no—
230D4—23441no—
231D4—5861no—
232D4—5862no—
233D4—5861no—
234D4—5861no—
235D4—5862no—
236D4—11724no—
237D4—11724no—
238D4—11724no—
239D4—11722no—
240D4D234414yescomplemented
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—5861no—
244C2×C4—5861no—
245C2×C4—5862no—
246C2×C4—11724no—
247C2×C4—11722no—
248C2×C4—11722no—
249C2×C4C2×D117211yescharacteristic
250C2×C4C2×D117212yes—
251C2×C4C2×D117211yescharacteristic
252C2×C4C23×D29311yescharacteristic
253C8—21no—
254C8—21no—
255C8—22no—
256C22—22no—
257C22—22no—
258C22—23448no—
259C22—5862no—
260C22—11722no—
261C22—11721no—
262C22—11721no—
263C22—11722no—
264C22—11722no—
265C22—11721no—
266C22—11721no—
267C22—11721no—
268C22C2×D234414yes—
269C22C22×D117211yescharacteristic
270C4—22no—
271C4—21no—
272C4—11721no—
273C4—11721no—
274C4—11722no—
275C4C2×D234412yes—
276C4#41×D29311yescharacteristic
277C4#2262766911yescharacteristic
278C2—24no—
279C2—23442no—
280C2—23441no—
281C2—11722no—
282C2#3403677411yescharacteristic
283C2C22×D234411yescharacteristic
284C2#3403694111yescharacteristic
subgroupG/H
centerC22C22×D1172
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC8×D4×C293C2
socleC22×C293C22×D4
hypercenterC8×D4D293
hypocenterC293#3294
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #34036783C2semidirect
2. D4×D1172C2semidirect
3. #34036476C2semidirect
4. #34036443C2semidirect
5. #34036410C2semidirect
6. #34036365C2semidirect
7. #34036325C2semidirect
8. #34036265C2semidirect
9. C4×D2344C2semidirect
10. C2×#22627546C2semidirect
11. C8×D4×C293C2semidirect
16. C2×D2344C22semidirect
17. #22627624C22semidirect
23. #22627598C22semidirect
26. C4×D1172C22semidirect
27. C2×C4⋊Dic293C22semidirect
28. #22627558C22semidirect
29. #22627558C22semidirect
32. #22627546C22semidirect
33. #22627546C22semidirect
34. #22627546C22semidirect
35. #22627546C22semidirect
36. C22×C8×C293C22semidirect
38. C4⋊C8×C293C22semidirect
39. C22⋊C8×C293C22semidirect
40. C4×C8×C293C22semidirect
93. D1172#41semidirect
103. D4×C293D8semidirect
142. C293#3294semidirect
153. C8×D4D293semidirect
160. C22×C8C2×D293semidirect
175. C4⋊C8C2×D293semidirect
182. C22⋊C8C2×D293semidirect
183. C4×C8C2×D293semidirect
240. D4D2344semidirect

Maximal subgroups

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

subgroupindex
#340367832
D4×D11722
#340364762
#340364432
#340364102
#340363652
#340363252
#340362652
C4×D23442
C2×#226275462
C8×D4×C2932
#3294293