Finite Group Databasebeta

← #49170609

Subgroups — #49170609

Order 37504.

462 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 141 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#34036836C211yesmaximal, characteristic, complemented
2#34036475C211yesmaximal, characteristic, complemented
3#34036445C212yesmaximal, complemented
4#34036419C211yesmaximal, characteristic, complemented
5#34036356C212yesmaximal, complemented
6#34036326C211yesmaximal, characteristic, complemented
7#34036280C212yesmaximal, complemented
8C4×#17989790C211yesmaximal, characteristic, complemented
9D4×#14556873C211yesmaximal, characteristic, complemented
10C2×#22627545C212yesmaximal, complemented
11D42×C293C211yesmaximal, characteristic
12C2×#17989790C2211yescharacteristic
13C2×#17989790C2212yescomplemented
14C22×#14556873C2212yescomplemented
15#22627624C2211yescharacteristic, complemented
16#22627615—21no—
17#22627603C2212yescomplemented
18#22627601—22no—
19C4×Dic586C2211yescharacteristic, complemented
20D4×Dic293—21no—
21C2×C4⋊Dic293C2212yescomplemented
22#22627555C2212yescomplemented
23#22627555C2211yescharacteristic, complemented
24C4⋊#14556873C2211yescharacteristic, complemented
25#22627547C2211yescharacteristic, complemented
26#22627545C2212yes—
27#22627545C2211yescharacteristic
28#22627545C2212yescomplemented
29#22627545C2212yescomplemented
30#22627545C2212yescomplemented
31C22⋊#14556873C2212yescomplemented
32C4×#14556873C2211yescharacteristic, complemented
33C22×D4×C293—21no—
34C22×D4×C293C2212yes—
35#127×C293C2211yescharacteristic
36#121×C293—21no—
37#121×C293C2212yes—
38#120×C293—22no—
39C4×D4×C293C2211yescharacteristic
40C4×D4×C293C2211yescharacteristic
41C2×Dic586—21no—
42C2×Dic586C2311yescharacteristic
43C22×Dic293—22no—
44#17989790—22no—
45#17989790—42no—
46C2×#14556873—42no—
47C2×#14556873C2311yescharacteristic
48C2×#14556873C2312yes—
49C2×#14556873C2311yescharacteristic
50C4⋊Dic293—21no—
51C4⋊Dic293—22no—
52C4⋊Dic293C2311yescharacteristic
53C4⋊Dic293C2312yes—
54#17989781—21no—
55#17989781—22no—
56C22⋊Dic293—22no—
57C4×Dic293—21no—
58C24×C293—22no—
59C2×D4×C293—24no—
60C2×D4×C293—22no—
61C2×D4×C293—22no—
62C2×D4×C293—21no—
63C2×D4×C293—21no—
64C2×D4×C293—42no—
65C2×D4×C293—44no—
66C2×D4×C293D411yescharacteristic
67C2×D4×C293C2312yes—
68C2×D4×C293C2311yescharacteristic
69C22×C4×C293—21no—
70C22×C4×C293C2312yes—
71C4⋊C4×C293D411yescharacteristic
72C4⋊C4×C293C2311yescharacteristic
73C22⋊C4×C293—21no—
74C22⋊C4×C293—22no—
75C22⋊C4×C293D412yes—
76C42×C293C2311yescharacteristic
77Dic586—21no—
78Dic586—21no—
79Dic586—81no—
80C2×Dic293—21no—
81C2×Dic293—21no—
82C2×Dic293—22no—
83C2×Dic293—82no—
84#14556873—21no—
85#14556873—21no—
86#14556873—22no—
87C23×C293—21no—
88C23×C293—22no—
89C23×C293—44no—
90C23×C293—44no—
91C23×C293—82no—
92C23×C293C2×D412yes—
93D4×C293—22no—
94D4×C293—21no—
95D4×C293—22no—
96D4×C293—44no—
97D4×C293—44no—
98D4×C293—42no—
99D4×C293—81no—
100D4×C293SD1614yescomplemented
101D4×C293#4112yes—
102C2×C4×C293—22no—
103C2×C4×C293—22no—
104C2×C4×C293—21no—
105C2×C4×C293—42no—
106C2×C4×C293C2×D411yescharacteristic
107C2×C4×C293C2×D412yes—
108C2×C4×C293C2×D411yescharacteristic
109C2×C4×C293C2411yescharacteristic
110C22×C293—22no—
111C22×C293—22no—
112C22×C293—22no—
113C22×C293—41no—
114C22×C293—41no—
115C22×C293—42no—
116C22×C293—42no—
117C22×C293—42no—
118C22×C293—88no—
119C22×C293C2×SD1614yes—
120C22×C293C22×D411yescharacteristic
121C4×C293—22no—
122C4×C293—21no—
123C4×C293—41no—
124C4×C293C2×SD1612yes—
125C4×C293C2×#4111yescharacteristic
126C4×C293H(5,𝔽2)11yescharacteristic
127Dic293—41no—
128Dic293—41no—
129Dic293—42no—
130C2×C293—24no—
131C2×C293—42no—
132C2×C293—82no—
133C2×C293#54611yescharacteristic
134C2×C293C22×SD1611yescharacteristic
135C2×C293#57611yescharacteristic
136C293#329511yescharacteristic, complemented, Sylow
137#3295—2931nomaximal, Sylow
138#554—2931no—
139D42D29311yescharacteristic
140#486—2931no—
141#481—2932no—
142#476—2931no—
143#465—2932no—
144#460—2931no—
145#450—2932no—
146C4×SD16—2931no—
147C8×D4—2931no—
148C2×#102—2932no—
149C22×D4—21no—
150C22×D4C2×D29312yes—
151C2×SD16—2931no—
152C2×SD16—2932no—
153C22×C8—2932no—
154C4⋊Q8—2931no—
155#127C2×D29311yescharacteristic
156#125—5861no—
157C22⋊Q8—2932no—
158C22⋊Q8—5862no—
159#121—21no—
160#121C2×D29312yes—
161#120—22no—
162C4×Q8—2931no—
163C4×D4—5861no—
164C4×D4C2×D29311yescharacteristic
165C4×D4C2×D29311yescharacteristic
166C2×C4⋊C4—2932no—
167#106—2931no—
168#106—2932no—
169C4⋊C8—2931no—
170#103—2931no—
171#102—2931no—
172#102—2932no—
173#102—2932no—
174#102—2932no—
175#102—2932no—
176C22⋊C8—2932no—
177C4×C8—2931no—
178C24—22no—
179C2×Q8—2931no—
180C2×Q8—5861no—
181C2×D4—24no—
182C2×D4—22no—
183C2×D4—22no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—42no—
187C2×D4—44no—
188C2×D4C22⋊D29311yescharacteristic
189C2×D4C22×D29312yes—
190C2×D4C22×D29311yescharacteristic
191C22×C4—21no—
192C22×C4—5862no—
193C22×C4C22×D29312yes—
194SD16—5862no—
195SD16—11722no—
196C2×C8—2931no—
197C2×C8—2931no—
198C2×C8—2932no—
199C2×C8—11722no—
200C4⋊C4—2931no—
201C4⋊C4—2932no—
202C4⋊C4—5862no—
203C4⋊C4—5861no—
204C4⋊C4—5861no—
205C4⋊C4—5862no—
206C4⋊C4C22⋊D29311yescharacteristic
207C4⋊C4C22×D29311yescharacteristic
208C22⋊C4—21no—
209C22⋊C4—22no—
210C22⋊C4—5862no—
211C22⋊C4C22⋊D29312yes—
212C42—5861no—
213C42C22×D29311yescharacteristic
214C23—21no—
215C23—22no—
216C23—44no—
217C23—44no—
218C23—82no—
219C23C2×C22⋊D29312yes—
220Q8—23441no—
221Q8—5861no—
222Q8—5861no—
223D4—22no—
224D4—21no—
225D4—22no—
226D4—44no—
227D4—44no—
228D4—42no—
229D4—81no—
230D4#1798979014yescomplemented
231D4#1798980112yes—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—23442no—
237C2×C4—5861no—
238C2×C4—5861no—
239C2×C4—5862no—
240C2×C4C2×C22⋊D29311yescharacteristic
241C2×C4C2×C22⋊D29312yes—
242C2×C4C2×C22⋊D29311yescharacteristic
243C2×C4C23×D29311yescharacteristic
244C8—5861no—
245C8—5861no—
246C8—5862no—
247C22—22no—
248C22—22no—
249C22—22no—
250C22—41no—
251C22—41no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—88no—
256C22C2×#1798979014yes—
257C22C22×C22⋊D29311yescharacteristic
258C4—22no—
259C4—21no—
260C4—41no—
261C4—11721no—
262C4—11721no—
263C4—11722no—
264C4C2×#1798979012yes—
265C4C2×#1798980111yescharacteristic
266C4#2262766911yescharacteristic
267C2—24no—
268C2—42no—
269C2—82no—
270C2#3403677311yescharacteristic
271C2C22×#1798979011yescharacteristic
272C2#3403693211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting, prime radicalD42×C293C2
socleC22×C293C22×D4
hypercenterD42D293
hypocenterC293#3295
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #34036836C2semidirect
2. #34036475C2semidirect
3. #34036445C2semidirect
4. #34036419C2semidirect
5. #34036356C2semidirect
6. #34036326C2semidirect
7. #34036280C2semidirect
8. C4×#17989790C2semidirect
9. D4×#14556873C2semidirect
10. C2×#22627545C2semidirect
13. C2×#17989790C22semidirect
14. C22×#14556873C22semidirect
15. #22627624C22semidirect
17. #22627603C22semidirect
19. C4×Dic586C22semidirect
21. C2×C4⋊Dic293C22semidirect
22. #22627555C22semidirect
23. #22627555C22semidirect
24. C4⋊#14556873C22semidirect
25. #22627547C22semidirect
28. #22627545C22semidirect
29. #22627545C22semidirect
30. #22627545C22semidirect
31. C22⋊#14556873C22semidirect
32. C4×#14556873C22semidirect
100. D4×C293SD16semidirect
136. C293#3295semidirect
230. D4#17989790semidirect

Maximal subgroups

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

subgroupindex
#340368362
#340364752
#340364452
#340364192
#340363562
#340363262
#340362802
C4×#179897902
D4×#145568732
C2×#226275452
D42×C2932
#3295293