Finite Group Databasebeta

← #49170750

Subgroups — #49170750

Order 37504.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036779C211yesmaximal, characteristic, complemented
2#34036773C211yesmaximal, characteristic, complemented
3#34036487C211yesmaximal, characteristic, complemented
4#34036460C211yesmaximal, characteristic, complemented
5#34036446C211yesmaximal, characteristic, complemented
6#34036417C211yesmaximal, characteristic, complemented
7#34036379C211yesmaximal, characteristic, complemented
8#34036356C211yesmaximal, characteristic, complemented
9#34036342C211yesmaximal, characteristic, complemented
10#34036271C211yesmaximal, characteristic, complemented
11#34036241C211yesmaximal, characteristic, complemented
12#34036197C211yesmaximal, characteristic, complemented
13#34036127C211yesmaximal, characteristic, complemented
14C2×#22627545C211yesmaximal, characteristic, complemented
15#447×C293C211yesmaximal, characteristic, complemented
16C2×#17989801—21no—
17C2×#17989801C2211yescharacteristic
18C2×#17989790C2211yescharacteristic, complemented
19C2×#17989785C2211yescharacteristic, complemented
20C22×#14556873C2211yescharacteristic
21#22627623C2211yescharacteristic, complemented
22#22627611C2211yescharacteristic
23#22627606—21no—
24#22627605—21no—
25#22627605—21no—
26#22627603C2211yescharacteristic
27#22627601—21no—
28#22627596—21no—
29#22627595C2211yescharacteristic
30#22627595C2211yescharacteristic, complemented
31#22627593—21no—
32D4×Dic293C2211yescharacteristic
33D4×Dic293C2211yescharacteristic, complemented
34C4×C22⋊D293C2211yescharacteristic
35C2×C4⋊Dic293C2211yescharacteristic
36C4⋊C4×D293C2211yescharacteristic, complemented
37C2×C22⋊Dic293—21no—
38#22627556C2211yescharacteristic, complemented
39#22627556C2211yescharacteristic, 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
51#22627534C2211yescharacteristic, 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—
61#17989801—44no—
62C2×Dic586—21no—
63C2×Dic586C2311yescharacteristic
64C2×C22⋊D293—21no—
65C2×C22⋊D293—21no—
66C2×C22⋊D293—21no—
67C2×C22⋊D293D411yescharacteristic
68C22×Dic293—21no—
69C22×Dic293—21no—
70C22×Dic293—21no—
71C22×Dic293—21no—
72C2×C4×D293—21no—
73C2×C4×D293C2311yescharacteristic
74#17989790—41no—
75#17989785—41no—
76C2×#14556873—41no—
77C2×#14556873C2311yescharacteristic
78C2×#14556873C2311yescharacteristic
79C4⋊Dic293—21no—
80C4⋊Dic293C2311yescharacteristic
81C4⋊Dic293C2311yescharacteristic
82C4⋊Dic293C2311yescharacteristic
83#17989781—21no—
84#17989781—21no—
85#17989781—21no—
86#17989781D411yescharacteristic
87C22⋊Dic293—21no—
88C22⋊Dic293—21no—
89C22⋊Dic293—21no—
90C22⋊Dic293—21no—
91C22⋊Dic293—21no—
92C22⋊Dic293—21no—
93C22⋊Dic293—21no—
94C22⋊Dic293D411yescharacteristic
95#17989779D411yescharacteristic
96C4×Dic293C2311yescharacteristic
97C24×C293—21no—
98C2×D4×C293—22no—
99C2×D4×C293—21no—
100C2×D4×C293—21no—
101C2×D4×C293—41no—
102C2×D4×C293C2311yescharacteristic
103C2×D4×C293C2311yescharacteristic
104C2×D4×C293C2311yescharacteristic
105C22×C4×C293C2311yescharacteristic
106D8×C293—22no—
107D8×C293—41no—
108C2×C8×C293C2311yescharacteristic
109C2×C8×C293C2311yescharacteristic
110C4⋊C4×C293C2311yescharacteristic
111C22⋊C4×C293—21no—
112C22×D293C2×D411yescharacteristic
113Dic586—21no—
114Dic586—21no—
115Dic586—42no—
116C22⋊D293—22no—
117C22⋊D293—42no—
118C22⋊D293—42no—
119C22⋊D293—81no—
120C2×Dic293—21no—
121C2×Dic293—21no—
122C2×Dic293—21no—
123C2×Dic293—21no—
124C2×Dic293—42no—
125C2×Dic293—42no—
126C2×Dic293—42no—
127C2×Dic293—81no—
128C2×Dic293C2×D411yescharacteristic
129C2×Dic293C2×D411yescharacteristic
130C2×Dic293C2×D411yescharacteristic
131C4×D293—21no—
132C4×D293—21no—
133C4×D293—42no—
134#14556873—21no—
135#14556873—21no—
136C23×C293—21no—
137C23×C293—21no—
138C23×C293—21no—
139C23×C293—42no—
140C23×C293—42no—
141C23×C293—81no—
142C23×C293C2×D411yescharacteristic
143D4×C293—21no—
144D4×C293—21no—
145D4×C293—21no—
146D4×C293—21no—
147D4×C293—21no—
148D4×C293—42no—
149D4×C293—42no—
150D4×C293#4112yescomplemented
151C2×C4×C293—21no—
152C2×C4×C293—21no—
153C2×C4×C293—21no—
154C2×C4×C293C2×D411yescharacteristic
155C2×C4×C293C2411yescharacteristic
156C8×C293—21no—
157C8×C293—21no—
158C22×C293—21no—
159C22×C293—21no—
160C22×C293—22no—
161C22×C293—41no—
162C22×C293—41no—
163C22×C293—41no—
164C22×C293—41no—
165C22×C293—41no—
166C22×C293—41no—
167C22×C293—41no—
168C22×C293—41no—
169C22×C293—84no—
170C22×C293AGL(1,ℤ/8)12yes—
171C22×C293C22×D411yescharacteristic
172C2×D293—21no—
173C2×D293—21no—
174C2×D293—21no—
175C4×C293—21no—
176C4×C293—41no—
177C4×C293C2×#4111yescharacteristic
178C4×C293H(5,𝔽2)11yescharacteristic
179Dic293—21no—
180Dic293—21no—
181Dic293—21no—
182Dic293—41no—
183Dic293—41no—
184Dic293—41no—
185Dic293—41no—
186C2×C293—22no—
187C2×C293—42no—
188C2×C293—81no—
189C2×C293—81no—
190C2×C293#54611yescharacteristic
191C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C293#57711yescharacteristic
193D293—41no—
194C293#330611yescharacteristic, complemented, Sylow
195#3306—2931nomaximal, Sylow
196#547—2931no—
197#546—2931no—
198#489—2931no—
199#483—2931no—
200#481—2931no—
201#476—2931no—
202#469—2931no—
203#465—2931no—
204#463—2931no—
205#449—2931no—
206#447D29311yescharacteristic, complemented
207#442—2931no—
208#435—2931no—
209#417—2931no—
210C2×#102—2931no—
211C2×#41—2931no—
212C2×#41—5861no—
213C22×D4C2×D29311yescharacteristic
214C2×SD16—2931no—
215C2×D8C2×D29311yescharacteristic
216C2×D8C2×D29311yescharacteristic
217C2×M16—2931no—
218C22×C8—2931no—
219C4⋊Q8—2931no—
220#124—2931no—
221#123—5861no—
222#123—5861no—
223#123—5861no—
224C22⋊Q8—2931no—
225C22⋊Q8—5861no—
226#121—2931no—
227#121—2931no—
228#121—5861no—
229#121C2×D29311yescharacteristic
230#120—5861no—
231C4×D4—2931no—
232C4×D4—2931no—
233C4×D4—2931no—
234C2×C4⋊C4—2931no—
235C2×C4⋊C4—2931no—
236C2×C22⋊C4—5861no—
237#106—2931no—
238#106—2931no—
239#106—2931no—
240C4⋊C8—2931no—
241#103—2931no—
242#103—2931no—
243#103—2931no—
244#102—2931no—
245#102—2931no—
246#102—2931no—
247#102—2931no—
248#102—2931no—
249#102C2×D29311yescharacteristic
250#102C2×D29311yescharacteristic
251C22⋊C8—2931no—
252C22⋊C8C2×D29311yescharacteristic
253#97—2931no—
254C24—21no—
255#41—5862no—
256#41—11721no—
257#41—11724no—
258C2×Q8—2931no—
259C2×Q8—5861no—
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—2931no—
265C2×D4—5861no—
266C2×D4—5861no—
267C2×D4—5861no—
268C2×D4C22×D29311yescharacteristic
269C2×D4C22×D29311yescharacteristic
270C2×D4C22×D29311yescharacteristic
271C22×C4—2931no—
272C22×C4—5861no—
273C22×C4—5861no—
274C22×C4—5861no—
275C22×C4—5861no—
276C22×C4—5861no—
277C22×C4C22×D29311yescharacteristic
278SD16—11721no—
279D8—22no—
280D8—41no—
281M16—11721no—
282C2×C8—2931no—
283C2×C8—2931no—
284C2×C8—11721no—
285C2×C8C22×D29311yescharacteristic
286C2×C8C22×D29311yescharacteristic
287C4⋊C4—2931no—
288C4⋊C4—2931no—
289C4⋊C4—2931no—
290C4⋊C4—2931no—
291C4⋊C4—5861no—
292C4⋊C4—5861no—
293C4⋊C4—5861no—
294C4⋊C4—5861no—
295C4⋊C4C22×D29311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—2931no—
298C22⋊C4—2931no—
299C22⋊C4—5861no—
300C22⋊C4—5861no—
301C22⋊C4—5861no—
302C22⋊C4—5861no—
303C22⋊C4—5861no—
304C22⋊C4—5861no—
305C22⋊C4—5861no—
306C42—2931no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—2931no—
314C23D4×D29311yescharacteristic
315Q8—5861no—
316Q8—5861no—
317Q8—11722no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—42no—
324D4—42no—
325D4—23441no—
326D4—5862no—
327D4—11722no—
328D4—11722no—
329D4#1798980112yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—2931no—
334C2×C4—2931no—
335C2×C4—2931no—
336C2×C4—23441no—
337C2×C4—5861no—
338C2×C4—5861no—
339C2×C4—5861no—
340C2×C4—5861no—
341C2×C4—5861no—
342C2×C4—5861no—
343C2×C4—11722no—
344C2×C4—11722no—
345C2×C4—11722no—
346C2×C4—11722no—
347C2×C4D4×D29311yescharacteristic
348C2×C4C23×D29311yescharacteristic
349C8—21no—
350C8—21no—
351C8—5861no—
352C8—5861no—
353C22—21no—
354C22—21no—
355C22—22no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—84no—
365C22—5861no—
366C22—5861no—
367C22—5861no—
368C22#2262764812yes—
369C22C2×D4×D29311yescharacteristic
370C4—21no—
371C4—41no—
372C4—5861no—
373C4—5861no—
374C4—5861no—
375C4—11721no—
376C4—11721no—
377C4—11721no—
378C4—11721no—
379C4C2×#1798980111yescharacteristic
380C4#2262766911yescharacteristic
381C2—22no—
382C2—42no—
383C2—81no—
384C2—81no—
385C2—11721no—
386C2#3403676611yescharacteristic
387C2C2×#2262764811yescharacteristic
388C2#3403693911yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#447×C293C2
socleC22×C293C22×D4
hypercenter#447D293
hypocenterC293#3306
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. #34036779C2semidirect
2. #34036773C2semidirect
3. #34036487C2semidirect
4. #34036460C2semidirect
5. #34036446C2semidirect
6. #34036417C2semidirect
7. #34036379C2semidirect
8. #34036356C2semidirect
9. #34036342C2semidirect
10. #34036271C2semidirect
11. #34036241C2semidirect
12. #34036197C2semidirect
13. #34036127C2semidirect
14. C2×#22627545C2semidirect
15. #447×C293C2semidirect
18. C2×#17989790C22semidirect
19. C2×#17989785C22semidirect
21. #22627623C22semidirect
30. #22627595C22semidirect
33. D4×Dic293C22semidirect
36. C4⋊C4×D293C22semidirect
38. #22627556C22semidirect
39. #22627556C22semidirect
40. #22627555C22semidirect
41. #22627553C22semidirect
42. #22627549C22semidirect
43. #22627549C22semidirect
44. #22627547C22semidirect
49. #22627545C22semidirect
50. #22627536C22semidirect
51. #22627534C22semidirect
150. D4×C293#41semidirect
194. C293#3306semidirect
206. #447D293semidirect
329. D4#17989801semidirect

Maximal subgroups

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

subgroupindex
#340367792
#340367732
#340364872
#340364602
#340364462
#340364172
#340363792
#340363562
#340363422
#340362712
#340362412
#340361972
#340361272
C2×#226275452
#447×C2932
#3306293