Finite Group Databasebeta

← #49170620

Subgroups — #49170620

Order 37504.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036819C211yesmaximal, characteristic, complemented
2#34036483C211yesmaximal, characteristic, complemented
3#34036457C211yesmaximal, characteristic, complemented
4#34036450C211yesmaximal, characteristic, complemented
5#34036429C211yesmaximal, characteristic, complemented
6#34036368C211yesmaximal, characteristic, complemented
7#34036356C211yesmaximal, characteristic, complemented
8#34036348C211yesmaximal, characteristic, complemented
9#34036291C211yesmaximal, characteristic, complemented
10#34036280C211yesmaximal, characteristic, complemented
11C4×#17989790C211yesmaximal, characteristic, complemented
12D4×#14556873C211yesmaximal, characteristic, complemented
13#34036125C211yesmaximal, characteristic, complemented
14C2×#22627545C211yesmaximal, characteristic, complemented
15#546×C293C211yesmaximal, characteristic
16C2×#17989792C2211yescharacteristic, complemented
17C2×#17989790C2211yescharacteristic
18C2×#17989790C2211yescharacteristic
19C22×#14556873C2211yescharacteristic
20C22×#14556873C2211yescharacteristic, complemented
21#22627617—21no—
22#22627616C2211yescharacteristic, complemented
23#22627614—21no—
24#22627605—21no—
25#22627603C2211yescharacteristic
26#22627603C2211yescharacteristic, complemented
27C4×Dic586C2211yescharacteristic, complemented
28#22627583C2211yescharacteristic, complemented
29#22627580—21no—
30C2×C4⋊Dic293C2211yescharacteristic
31#22627557C2211yescharacteristic, complemented
32#22627555C2211yescharacteristic, complemented
33#22627555C2211yescharacteristic, complemented
34C4⋊#14556873C2211yescharacteristic, complemented
35#22627548C2211yescharacteristic, complemented
36#22627548C2211yescharacteristic, complemented
37#22627548C2211yescharacteristic, complemented
38#22627547C2211yescharacteristic, complemented
39#22627545C2211yescharacteristic
40#22627545C2211yescharacteristic
41#22627545C2211yescharacteristic
42#22627545C2211yescharacteristic
43#22627545C2211yescharacteristic
44#22627545C2211yescharacteristic
45C22⋊#14556873C2211yescharacteristic
46C22⋊#14556873C2211yescharacteristic, complemented
47C4×#14556873C2211yescharacteristic, complemented
48C2×#41×C293C2211yescharacteristic
49C22×D4×C293C2211yescharacteristic
50#124×C293C2211yescharacteristic
51#123×C293—21no—
52C22⋊Q8×C293C2211yescharacteristic
53#121×C293—21no—
54#121×C293C2211yescharacteristic
55#120×C293—21no—
56C4×D4×C293C2211yescharacteristic
57C4×D4×C293C2211yescharacteristic
58C2×C22⋊C4×C293—21no—
59C2×Dic586C2311yescharacteristic
60C22×Dic293—21no—
61#17989792—41no—
62#17989790—22no—
63#17989790—41no—
64C2×#14556873—41no—
65C2×#14556873—41no—
66C2×#14556873C2311yescharacteristic
67C2×#14556873C2311yescharacteristic
68C2×#14556873C2311yescharacteristic
69C2×#14556873C2311yescharacteristic
70C4⋊Dic293—21no—
71C4⋊Dic293C2311yescharacteristic
72C4⋊Dic293C2311yescharacteristic
73C4⋊Dic293C2311yescharacteristic
74#17989781—21no—
75#17989781—21no—
76#17989781—21no—
77#17989781—21no—
78#17989781—21no—
79C22⋊Dic293—21no—
80C22⋊Dic293—21no—
81C22⋊Dic293—21no—
82C4×Dic293—21no—
83C4×Dic293—21no—
84C24×C293—21no—
85#41×C293—22no—
86#41×C293—41no—
87C2×Q8×C293C2311yescharacteristic
88C2×D4×C293—22no—
89C2×D4×C293—21no—
90C2×D4×C293—21no—
91C2×D4×C293—21no—
92C2×D4×C293—41no—
93C2×D4×C293D411yescharacteristic
94C2×D4×C293C2311yescharacteristic
95C2×D4×C293C2311yescharacteristic
96C22×C4×C293—21no—
97C22×C4×C293—21no—
98C22×C4×C293C2311yescharacteristic
99C22×C4×C293C2311yescharacteristic
100C4⋊C4×C293—21no—
101C4⋊C4×C293D411yescharacteristic
102C4⋊C4×C293C2311yescharacteristic
103C22⋊C4×C293—21no—
104C22⋊C4×C293—21no—
105C22⋊C4×C293—21no—
106C22⋊C4×C293—21no—
107C22⋊C4×C293—21no—
108C22⋊C4×C293D411yescharacteristic
109C22⋊C4×C293D411yescharacteristic
110C42×C293C2311yescharacteristic
111Dic586—21no—
112Dic586—21no—
113C2×Dic293—21no—
114C2×Dic293—21no—
115C2×Dic293—21no—
116C2×Dic293—21no—
117C2×Dic293—42no—
118#14556873—21no—
119#14556873—21no—
120#14556873—21no—
121#14556873—21no—
122C23×C293—21no—
123C23×C293—21no—
124C23×C293—42no—
125C23×C293—42no—
126C23×C293—81no—
127C23×C293C2×D411yescharacteristic
128C23×C293C2×D411yescharacteristic
129Q8×C293—21no—
130Q8×C293—21no—
131D4×C293—22no—
132D4×C293—21no—
133D4×C293—21no—
134D4×C293—21no—
135D4×C293—42no—
136D4×C293—42no—
137D4×C293—81no—
138D4×C293#4112yes—
139C2×C4×C293—21no—
140C2×C4×C293—21no—
141C2×C4×C293—21no—
142C2×C4×C293—21no—
143C2×C4×C293—21no—
144C2×C4×C293—21no—
145C2×C4×C293—42no—
146C2×C4×C293—81no—
147C2×C4×C293C2×D411yescharacteristic
148C2×C4×C293C2×D411yescharacteristic
149C2×C4×C293C2×D411yescharacteristic
150C2×C4×C293C2×D411yescharacteristic
151C2×C4×C293C2411yescharacteristic
152C22×C293—21no—
153C22×C293—21no—
154C22×C293—21no—
155C22×C293—22no—
156C22×C293—21no—
157C22×C293—21no—
158C22×C293—41no—
159C22×C293—41no—
160C22×C293—41no—
161C22×C293—41no—
162C22×C293—41no—
163C22×C293—84no—
164C22×C293#13512yes—
165C22×C293C22×D411yescharacteristic
166C4×C293—21no—
167C4×C293—21no—
168C4×C293—21no—
169C4×C293—21no—
170C4×C293—41no—
171C4×C293—41no—
172C4×C293C2×#4111yescharacteristic
173C4×C293H(5,𝔽2)11yescharacteristic
174Dic293—41no—
175Dic293—41no—
176Dic293—41no—
177Dic293—41no—
178C2×C293—22no—
179C2×C293—41no—
180C2×C293—42no—
181C2×C293—81no—
182C2×C293#54611yescharacteristic
183C2×C293C2×#13511yescharacteristic
184C2×C293#57711yescharacteristic
185C293#329611yescharacteristic, complemented, Sylow
186#3296—2931nomaximal, Sylow
187#552—2931no—
188#546D29311yescharacteristic
189#488—2931no—
190#483—2931no—
191#482—2931no—
192#478—2931no—
193#467—2931no—
194#465—2931no—
195#464—2931no—
196#452—2931no—
197#450—2931no—
198C4×SD16—2931no—
199C8×D4—2931no—
200#416—2931no—
201C2×#102—2931no—
202C2×#41C2×D29311yescharacteristic
203C22×D4C2×D29311yescharacteristic
204C2×Q16—2931no—
205C2×SD16—2931no—
206C2×SD16—2931no—
207C22×C8—2931no—
208C22×C8—2931no—
209#126—5861no—
210#125—2931no—
211#125—5861no—
212#124C2×D29311yescharacteristic
213#123—21no—
214#123—5861no—
215C22⋊Q8—2931no—
216C22⋊Q8—2931no—
217C22⋊Q8C2×D29311yescharacteristic
218#121—21no—
219#121C2×D29311yescharacteristic
220#120—21no—
221C4×Q8—2931no—
222C4×D4C2×D29311yescharacteristic
223C4×D4C2×D29311yescharacteristic
224#117—2931no—
225#117—5861no—
226C2×C4⋊C4—2931no—
227C2×C22⋊C4—21no—
228#107—2931no—
229#106—2931no—
230#106—2931no—
231C4⋊C8—2931no—
232#103—2931no—
233#103—2931no—
234#103—2931no—
235#103—2931no—
236#102—2931no—
237#102—2931no—
238#102—2931no—
239#102—2931no—
240#102—2931no—
241#102—2931no—
242C22⋊C8—2931no—
243C22⋊C8—2931no—
244C4×C8—2931no—
245C24—21no—
246#41—22no—
247#41—41no—
248C2×Q8—2931no—
249C2×Q8C22×D29311yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—41no—
255C2×D4C22⋊D29311yescharacteristic
256C2×D4C22×D29311yescharacteristic
257C2×D4C22×D29311yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—5861no—
261C22×C4C22×D29311yescharacteristic
262C22×C4C22×D29311yescharacteristic
263Q16—11721no—
264SD16—5862no—
265SD16—11721no—
266C2×C8—2931no—
267C2×C8—2931no—
268C2×C8—2931no—
269C2×C8—2931no—
270C2×C8—11721no—
271C2×C8—11721no—
272C4⋊C4—21no—
273C4⋊C4—2931no—
274C4⋊C4—2931no—
275C4⋊C4—2931no—
276C4⋊C4—5861no—
277C4⋊C4—5861no—
278C4⋊C4—5861no—
279C4⋊C4—5861no—
280C4⋊C4—5861no—
281C4⋊C4—5861no—
282C4⋊C4C22⋊D29311yescharacteristic
283C4⋊C4C22×D29311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—5861no—
290C22⋊C4—5861no—
291C22⋊C4—5861no—
292C22⋊C4C22⋊D29311yescharacteristic
293C22⋊C4C22⋊D29311yescharacteristic
294C42—5861no—
295C42—5861no—
296C42C22×D29311yescharacteristic
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23C2×C22⋊D29311yescharacteristic
303C23C2×C22⋊D29311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—5861no—
307Q8—5861no—
308D4—22no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—42no—
314D4—81no—
315D4#1798980112yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—81no—
324C2×C4—5861no—
325C2×C4—5861no—
326C2×C4—5861no—
327C2×C4—5861no—
328C2×C4—11722no—
329C2×C4C2×C22⋊D29311yescharacteristic
330C2×C4C2×C22⋊D29311yescharacteristic
331C2×C4C2×C22⋊D29311yescharacteristic
332C2×C4C2×C22⋊D29311yescharacteristic
333C2×C4C23×D29311yescharacteristic
334C8—5861no—
335C8—5861no—
336C8—5861no—
337C8—5861no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—84no—
350C22#2262764412yes—
351C22C22×C22⋊D29311yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—11721no—
359C4—11721no—
360C4—11721no—
361C4—11721no—
362C4C2×#1798980111yescharacteristic
363C4#2262766911yescharacteristic
364C2—22no—
365C2—41no—
366C2—42no—
367C2—81no—
368C2#3403677311yescharacteristic
369C2C2×#2262764411yescharacteristic
370C2#3403694011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting, prime radical#546×C293C2
socleC22×C293C22×D4
hypercenter#546D293
hypocenterC293#3296
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #34036819C2semidirect
2. #34036483C2semidirect
3. #34036457C2semidirect
4. #34036450C2semidirect
5. #34036429C2semidirect
6. #34036368C2semidirect
7. #34036356C2semidirect
8. #34036348C2semidirect
9. #34036291C2semidirect
10. #34036280C2semidirect
11. C4×#17989790C2semidirect
12. D4×#14556873C2semidirect
13. #34036125C2semidirect
14. C2×#22627545C2semidirect
16. C2×#17989792C22semidirect
20. C22×#14556873C22semidirect
22. #22627616C22semidirect
26. #22627603C22semidirect
27. C4×Dic586C22semidirect
28. #22627583C22semidirect
31. #22627557C22semidirect
32. #22627555C22semidirect
33. #22627555C22semidirect
34. C4⋊#14556873C22semidirect
35. #22627548C22semidirect
36. #22627548C22semidirect
37. #22627548C22semidirect
38. #22627547C22semidirect
46. C22⋊#14556873C22semidirect
47. C4×#14556873C22semidirect
185. C293#3296semidirect

Maximal subgroups

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

subgroupindex
#340368192
#340364832
#340364572
#340364502
#340364292
#340363682
#340363562
#340363482
#340362912
#340362802
C4×#179897902
D4×#145568732
#340361252
C2×#226275452
#546×C2932
#3296293