Finite Group Databasebeta

← #49170639

Subgroups — #49170639

Order 37504.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036831C211yesmaximal, characteristic, complemented
2#34036773C211yesmaximal, characteristic, complemented
3#34036482C211yesmaximal, characteristic, complemented
4#34036465C211yesmaximal, characteristic, complemented
5#34036451C211yesmaximal, characteristic, complemented
6#34036427C211yesmaximal, characteristic, complemented
7#34036362C211yesmaximal, characteristic, complemented
8#34036356C211yesmaximal, characteristic, complemented
9#34036342C211yesmaximal, characteristic, complemented
10#34036271C211yesmaximal, characteristic, complemented
11D8×Dic293C211yesmaximal, characteristic, complemented
12#34036192C211yesmaximal, characteristic, complemented
13#34036122C211yesmaximal, characteristic, complemented
14C2×#22627545C211yesmaximal, characteristic, complemented
15#447×C293C211yesmaximal, characteristic, complemented
16C2×#17989801C2211yescharacteristic
17C2×#17989790C2211yescharacteristic, complemented
18C22×#14556873C2211yescharacteristic
19C2×C8×D293C2211yescharacteristic, complemented
20#22627617—21no—
21#22627615C2211yescharacteristic, complemented
22#22627611C2211yescharacteristic
23#22627608—21no—
24#22627605—21no—
25#22627603C2211yescharacteristic
26#22627596—21no—
27#22627596—21no—
28#22627595C2211yescharacteristic
29#22627595C2211yescharacteristic, complemented
30#22627593—21no—
31D4×Dic293—21no—
32D4×Dic293C2211yescharacteristic
33D4×Dic293C2211yescharacteristic, complemented
34C4×C22⋊D293C2211yescharacteristic
35#22627582C2211yescharacteristic, complemented
36C2×C4⋊Dic293C2211yescharacteristic
37C2×C22⋊Dic293—21no—
38#22627558C2211yescharacteristic, complemented
39#22627558C2211yescharacteristic, complemented
40#22627555C2211yescharacteristic, complemented
41#22627553C2211yescharacteristic, complemented
42#22627549C2211yescharacteristic, complemented
43#22627549C2211yescharacteristic, complemented
44#22627547C2211yescharacteristic, complemented
45#22627545C2211yescharacteristic
46#22627545C2211yescharacteristic
47#22627545C2211yescharacteristic
48#22627545C2211yescharacteristic
49#22627545C2211yescharacteristic, complemented
50#22627536C2211yescharacteristic, complemented
51C8×Dic293C2211yescharacteristic, complemented
52C22×D4×C293C2211yescharacteristic
53C2×D8×C293C2211yescharacteristic
54C2×D8×C293C2211yescharacteristic
55#121×C293C2211yescharacteristic
56#102×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58C22⋊C8×C293C2211yescharacteristic
59#17989801—22no—
60#17989801—41no—
61C2×Dic586C2311yescharacteristic
62C2×C22⋊D293—21no—
63C2×C22⋊D293—21no—
64C2×C22⋊D293—21no—
65C2×C22⋊D293D411yescharacteristic
66C22×Dic293—21no—
67C22×Dic293—21no—
68C22×Dic293—21no—
69C22×Dic293—21no—
70C2×C4×D293C2311yescharacteristic
71#17989790—41no—
72C2×#14556873—41no—
73C2×#14556873C2311yescharacteristic
74C2×#14556873C2311yescharacteristic
75C8×D293—41no—
76C4⋊Dic293—21no—
77C4⋊Dic293—21no—
78C4⋊Dic293C2311yescharacteristic
79C4⋊Dic293C2311yescharacteristic
80C4⋊Dic293C2311yescharacteristic
81#17989781—21no—
82#17989781—21no—
83#17989781D411yescharacteristic
84C22⋊Dic293—21no—
85C22⋊Dic293—21no—
86C22⋊Dic293—21no—
87C22⋊Dic293—21no—
88C22⋊Dic293—21no—
89C22⋊Dic293—21no—
90C22⋊Dic293—21no—
91C22⋊Dic293D411yescharacteristic
92#17989779—21no—
93#17989779D411yescharacteristic
94C4×Dic293—21no—
95C4×Dic293C2311yescharacteristic
96C24×C293—21no—
97C2×D4×C293—22no—
98C2×D4×C293—21no—
99C2×D4×C293—21no—
100C2×D4×C293—41no—
101C2×D4×C293C2311yescharacteristic
102C2×D4×C293C2311yescharacteristic
103C2×D4×C293C2311yescharacteristic
104C22×C4×C293C2311yescharacteristic
105D8×C293—22no—
106D8×C293—41no—
107C2×C8×C293C2311yescharacteristic
108C2×C8×C293C2311yescharacteristic
109C4⋊C4×C293C2311yescharacteristic
110C22⋊C4×C293—21no—
111C22×D293C2×D411yescharacteristic
112Dic586—21no—
113Dic586—21no—
114C22⋊D293—22no—
115C22⋊D293—42no—
116C22⋊D293—81no—
117C22⋊D293—81no—
118C2×Dic293—21no—
119C2×Dic293—21no—
120C2×Dic293—21no—
121C2×Dic293—21no—
122C2×Dic293—42no—
123C2×Dic293—81no—
124C2×Dic293—81no—
125C2×Dic293—81no—
126C2×Dic293C2×D411yescharacteristic
127C2×Dic293C2×D411yescharacteristic
128C2×Dic293C2×D411yescharacteristic
129C4×D293—21no—
130C4×D293—21no—
131#14556873—21no—
132#14556873—21no—
133C23×C293—21no—
134C23×C293—21no—
135C23×C293—21no—
136C23×C293—42no—
137C23×C293—42no—
138C23×C293—81no—
139C23×C293C2×D411yescharacteristic
140D4×C293—21no—
141D4×C293—21no—
142D4×C293—21no—
143D4×C293—21no—
144D4×C293—21no—
145D4×C293—42no—
146D4×C293—42no—
147D4×C293#4112yes—
148C2×C4×C293—21no—
149C2×C4×C293—21no—
150C2×C4×C293—21no—
151C2×C4×C293C2×D411yescharacteristic
152C2×C4×C293C2411yescharacteristic
153C8×C293—21no—
154C8×C293—21no—
155C22×C293—21no—
156C22×C293—21no—
157C22×C293—22no—
158C22×C293—41no—
159C22×C293—41no—
160C22×C293—41no—
161C22×C293—41no—
162C22×C293—41no—
163C22×C293—41no—
164C22×C293—41no—
165C22×C293—41no—
166C22×C293—84no—
167C22×C293#13512yes—
168C22×C293C22×D411yescharacteristic
169C2×D293—21no—
170C2×D293—21no—
171C2×D293—21no—
172C4×C293—21no—
173C4×C293—41no—
174C4×C293C2×#4111yescharacteristic
175C4×C293H(5,𝔽2)11yescharacteristic
176Dic293—21no—
177Dic293—21no—
178Dic293—21no—
179Dic293—41no—
180Dic293—41no—
181Dic293—41no—
182Dic293—41no—
183C2×C293—22no—
184C2×C293—42no—
185C2×C293—81no—
186C2×C293—81no—
187C2×C293#54611yescharacteristic
188C2×C293C2×#13511yescharacteristic
189C2×C293#57611yescharacteristic
190D293—41no—
191C293#329711yescharacteristic, complemented, Sylow
192#3297—2931nomaximal, Sylow
193#553—2931no—
194#546—2931no—
195#488—2931no—
196#484—2931no—
197#482—2931no—
198#478—2931no—
199#466—2931no—
200#465—2931no—
201#463—2931no—
202#449—2931no—
203#447D29311yescharacteristic, complemented
204C4×D8—2931no—
205C8×D4—2931no—
206#416—2931no—
207C2×#102—2931no—
208C2×#41—2931no—
209C22×D4C2×D29311yescharacteristic
210C2×SD16—2931no—
211C2×D8C2×D29311yescharacteristic
212C2×D8C2×D29311yescharacteristic
213C22×C8—2931no—
214C22×C8—2931no—
215#126—5861no—
216#125—2931no—
217#124—2931no—
218#123—5861no—
219#123—5861no—
220C22⋊Q8—2931no—
221#121—2931no—
222#121—2931no—
223#121—5861no—
224#121—5861no—
225#121C2×D29311yescharacteristic
226#120—5861no—
227C4×D4—2931no—
228C4×D4—2931no—
229C4×D4—2931no—
230C4×D4—5861no—
231#117—2931no—
232C2×C4⋊C4—2931no—
233C2×C22⋊C4—5861no—
234#107—2931no—
235#107—2931no—
236#106—2931no—
237C4⋊C8—2931no—
238#103—2931no—
239#103—2931no—
240#103—2931no—
241#102—2931no—
242#102—2931no—
243#102—2931no—
244#102—2931no—
245#102—2931no—
246#102C2×D29311yescharacteristic
247#102C2×D29311yescharacteristic
248C22⋊C8—2931no—
249C22⋊C8C2×D29311yescharacteristic
250C4×C8—2931no—
251C24—21no—
252#41—5862no—
253#41—11721no—
254C2×Q8—2931no—
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C2×D4—2931no—
260C2×D4—5861no—
261C2×D4—5861no—
262C2×D4—5861no—
263C2×D4C22×D29311yescharacteristic
264C2×D4C22×D29311yescharacteristic
265C2×D4C22×D29311yescharacteristic
266C22×C4—2931no—
267C22×C4—5861no—
268C22×C4—5861no—
269C22×C4—5861no—
270C22×C4—5861no—
271C22×C4C22×D29311yescharacteristic
272SD16—11721no—
273D8—22no—
274D8—41no—
275C2×C8—2931no—
276C2×C8—2931no—
277C2×C8—11721no—
278C2×C8—11721no—
279C2×C8C22×D29311yescharacteristic
280C2×C8C22×D29311yescharacteristic
281C4⋊C4—2931no—
282C4⋊C4—2931no—
283C4⋊C4—2931no—
284C4⋊C4—2931no—
285C4⋊C4—5861no—
286C4⋊C4—5861no—
287C4⋊C4—5861no—
288C4⋊C4—5861no—
289C4⋊C4C22×D29311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—2931no—
292C22⋊C4—2931no—
293C22⋊C4—5861no—
294C22⋊C4—5861no—
295C22⋊C4—5861no—
296C22⋊C4—5861no—
297C22⋊C4—5861no—
298C22⋊C4—5861no—
299C22⋊C4—5861no—
300C22⋊C4—5861no—
301C42—2931no—
302C42—5861no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—42no—
307C23—42no—
308C23—81no—
309C23—2931no—
310C23D4×D29311yescharacteristic
311Q8—5861no—
312Q8—5861no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—42no—
319D4—42no—
320D4—23441no—
321D4—23441no—
322D4—5862no—
323D4—11722no—
324D4#1798980112yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—2931no—
329C2×C4—2931no—
330C2×C4—2931no—
331C2×C4—23441no—
332C2×C4—23441no—
333C2×C4—23441no—
334C2×C4—5861no—
335C2×C4—5861no—
336C2×C4—5861no—
337C2×C4—5861no—
338C2×C4—5861no—
339C2×C4—5861no—
340C2×C4—11722no—
341C2×C4D4×D29311yescharacteristic
342C2×C4C23×D29311yescharacteristic
343C8—21no—
344C8—21no—
345C8—5861no—
346C8—5861no—
347C22—21no—
348C22—21no—
349C22—22no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—84no—
359C22—5861no—
360C22—5861no—
361C22—5861no—
362C22#2262764312yes—
363C22C2×D4×D29311yescharacteristic
364C4—21no—
365C4—41no—
366C4—5861no—
367C4—5861no—
368C4—5861no—
369C4—11721no—
370C4—11721no—
371C4—11721no—
372C4—11721no—
373C4C2×#1798980111yescharacteristic
374C4#2262766911yescharacteristic
375C2—22no—
376C2—42no—
377C2—81no—
378C2—81no—
379C2—11721no—
380C2#3403676611yescharacteristic
381C2C2×#2262764311yescharacteristic
382C2#3403693311yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#447×C293C2
socleC22×C293C22×D4
hypercenter#447D293
hypocenterC293#3297
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #34036831C2semidirect
2. #34036773C2semidirect
3. #34036482C2semidirect
4. #34036465C2semidirect
5. #34036451C2semidirect
6. #34036427C2semidirect
7. #34036362C2semidirect
8. #34036356C2semidirect
9. #34036342C2semidirect
10. #34036271C2semidirect
11. D8×Dic293C2semidirect
12. #34036192C2semidirect
13. #34036122C2semidirect
14. C2×#22627545C2semidirect
15. #447×C293C2semidirect
17. C2×#17989790C22semidirect
19. C2×C8×D293C22semidirect
21. #22627615C22semidirect
29. #22627595C22semidirect
33. D4×Dic293C22semidirect
35. #22627582C22semidirect
38. #22627558C22semidirect
39. #22627558C22semidirect
40. #22627555C22semidirect
41. #22627553C22semidirect
42. #22627549C22semidirect
43. #22627549C22semidirect
44. #22627547C22semidirect
49. #22627545C22semidirect
50. #22627536C22semidirect
51. C8×Dic293C22semidirect
191. C293#3297semidirect
203. #447D293semidirect

Maximal subgroups

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

subgroupindex
#340368312
#340367732
#340364822
#340364652
#340364512
#340364272
#340363622
#340363562
#340363422
#340362712
D8×Dic2932
#340361922
#340361222
C2×#226275452
#447×C2932
#3297293