Finite Group Databasebeta

← #49170746

Subgroups — #49170746

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#34036783C211yesmaximal, characteristic, complemented
2#34036488C211yesmaximal, characteristic, complemented
3#34036457C211yesmaximal, characteristic, complemented
4#34036445C211yesmaximal, characteristic, complemented
5#34036419C211yesmaximal, characteristic, complemented
6#34036380C211yesmaximal, characteristic, complemented
7#34036360C211yesmaximal, characteristic, complemented
8#34036341C211yesmaximal, characteristic, complemented
9#34036274C211yesmaximal, characteristic, complemented
10#34036263C211yesmaximal, characteristic, complemented
11#34036239C211yesmaximal, characteristic, complemented
12#34036201C211yesmaximal, characteristic, complemented
13#34036130C211yesmaximal, characteristic, complemented
14C2×#22627545C211yesmaximal, characteristic, complemented
15#546×C293C211yesmaximal, characteristic, complemented
16C2×#17989801—21no—
17C2×#17989789C2211yescharacteristic, complemented
18C2×#17989787C2211yescharacteristic
19C2×#17989787C2211yescharacteristic
20C2×#17989786C2211yescharacteristic, complemented
21C22×#14556873C2211yescharacteristic
22#22627624C2211yescharacteristic, complemented
23#22627608—21no—
24#22627608—21no—
25#22627604—21no—
26#22627598C2211yescharacteristic
27#22627598C2211yescharacteristic, complemented
28C4×D1172C2211yescharacteristic, complemented
29C2×C4⋊Dic293C2211yescharacteristic
30C2×C4⋊Dic293C2211yescharacteristic, complemented
31#22627555C2211yescharacteristic, complemented
32#22627555C2211yescharacteristic, complemented
33#22627555C2211yescharacteristic, complemented
34C4⋊#14556873C2211yescharacteristic, complemented
35#22627548C2211yescharacteristic, complemented
36#22627548C2211yescharacteristic, complemented
37#22627548C2211yescharacteristic, complemented
38#22627545C2211yescharacteristic
39#22627545C2211yescharacteristic
40#22627545C2211yescharacteristic
41#22627545C2211yescharacteristic
42#22627545C2211yescharacteristic
43#22627545C2211yescharacteristic
44#22627544C2211yescharacteristic, complemented
45C22⋊#14556873C2211yescharacteristic
46C22⋊#14556873C2211yescharacteristic, complemented
47#22627535C2211yescharacteristic, 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—
59#17989801—44no—
60C2×Dic586—21no—
61C2×D1172C2311yescharacteristic
62C2×C22⋊D293—21no—
63C2×C22⋊D293—21no—
64C22×Dic293—21no—
65C22×Dic293—21no—
66C2×C4×D293—21no—
67#17989789—41no—
68#17989787—22no—
69#17989787—41no—
70#17989786—41no—
71C2×#14556873—41no—
72C2×#14556873C2311yescharacteristic
73C2×#14556873C2311yescharacteristic
74C2×#14556873C2311yescharacteristic
75C2×#14556873C2311yescharacteristic
76C4⋊Dic293—21no—
77C4⋊Dic293—21no—
78C4⋊Dic293—21no—
79C4⋊Dic293C2311yescharacteristic
80C4⋊Dic293C2311yescharacteristic
81C4⋊Dic293C2311yescharacteristic
82#17989779—21no—
83#17989779—21no—
84#17989779—21no—
85C24×C293—21no—
86#41×C293—22no—
87#41×C293—41no—
88C2×Q8×C293C2311yescharacteristic
89C2×D4×C293—22no—
90C2×D4×C293—21no—
91C2×D4×C293—21no—
92C2×D4×C293—21no—
93C2×D4×C293—41no—
94C2×D4×C293D411yescharacteristic
95C2×D4×C293C2311yescharacteristic
96C2×D4×C293C2311yescharacteristic
97C22×C4×C293—21no—
98C22×C4×C293—21no—
99C22×C4×C293C2311yescharacteristic
100C22×C4×C293C2311yescharacteristic
101C4⋊C4×C293—21no—
102C4⋊C4×C293D411yescharacteristic
103C4⋊C4×C293C2311yescharacteristic
104C22⋊C4×C293—21no—
105C22⋊C4×C293—21no—
106C22⋊C4×C293—21no—
107C22⋊C4×C293—21no—
108C22⋊C4×C293—21no—
109C22⋊C4×C293D411yescharacteristic
110C22⋊C4×C293D411yescharacteristic
111C42×C293C2311yescharacteristic
112C22×D293—21no—
113Dic586—42no—
114D1172—21no—
115D1172—21no—
116C22⋊D293—42no—
117C22⋊D293—42no—
118C2×Dic293—21no—
119C2×Dic293—21no—
120C2×Dic293—21no—
121C2×Dic293—42no—
122C2×Dic293—42no—
123C4×D293—42no—
124#14556873—21no—
125#14556873—21no—
126#14556873—21no—
127#14556873—21no—
128C23×C293—21no—
129C23×C293—21no—
130C23×C293—42no—
131C23×C293—42no—
132C23×C293—81no—
133C23×C293C2×D411yescharacteristic
134C23×C293C2×D411yescharacteristic
135Q8×C293—21no—
136Q8×C293—21no—
137D4×C293—22no—
138D4×C293—21no—
139D4×C293—21no—
140D4×C293—21no—
141D4×C293—42no—
142D4×C293—42no—
143D4×C293—81no—
144D4×C293#4112yescomplemented
145C2×C4×C293—21no—
146C2×C4×C293—21no—
147C2×C4×C293—21no—
148C2×C4×C293—21no—
149C2×C4×C293—21no—
150C2×C4×C293—21no—
151C2×C4×C293—42no—
152C2×C4×C293—81no—
153C2×C4×C293C2×D411yescharacteristic
154C2×C4×C293C2×D411yescharacteristic
155C2×C4×C293C2×D411yescharacteristic
156C2×C4×C293C2×D411yescharacteristic
157C2×C4×C293C2411yescharacteristic
158C22×C293—21no—
159C22×C293—21no—
160C22×C293—21no—
161C22×C293—22no—
162C22×C293—21no—
163C22×C293—21no—
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—41no—
173C2×D293—41no—
174C2×D293—41no—
175C4×C293—21no—
176C4×C293—21no—
177C4×C293—21no—
178C4×C293—21no—
179C4×C293—41no—
180C4×C293—41no—
181C4×C293C2×#4111yescharacteristic
182C4×C293H(5,𝔽2)11yescharacteristic
183Dic293—41no—
184Dic293—41no—
185Dic293—41no—
186C2×C293—22no—
187C2×C293—41no—
188C2×C293—42no—
189C2×C293—81no—
190C2×C293#54611yescharacteristic
191C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C293#57711yescharacteristic
193D293—81no—
194C293#330611yescharacteristic, complemented, Sylow
195#3306—2931nomaximal, Sylow
196#547—2931no—
197#546D29311yescharacteristic, complemented
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#447—2931no—
207#442—2931no—
208#435—2931no—
209#417—2931no—
210C2×#102—2931no—
211C2×#41—5861no—
212C2×#41C2×D29311yescharacteristic
213C22×D4C2×D29311yescharacteristic
214C2×SD16—2931no—
215C2×D8—2931no—
216C2×D8—2931no—
217C2×M16—2931no—
218C22×C8—2931no—
219C4⋊Q8—2931no—
220#124C2×D29311yescharacteristic
221#123—21no—
222#123—5861no—
223#123—5861no—
224C22⋊Q8—5861no—
225C22⋊Q8C2×D29311yescharacteristic
226#121—21no—
227#121—2931no—
228#121—2931no—
229#121C2×D29311yescharacteristic
230#120—21no—
231C4×D4—2931no—
232C4×D4C2×D29311yescharacteristic
233C4×D4C2×D29311yescharacteristic
234C2×C4⋊C4—2931no—
235C2×C4⋊C4—2931no—
236C2×C22⋊C4—21no—
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#102—2931no—
250#102—2931no—
251C22⋊C8—2931no—
252C22⋊C8—2931no—
253#97—2931no—
254C24—21no—
255#41—22no—
256#41—41no—
257#41—11724no—
258C2×Q8—5861no—
259C2×Q8C22×D29311yescharacteristic
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—2931no—
266C2×D4—5861no—
267C2×D4—5861no—
268C2×D4C22⋊D29311yescharacteristic
269C2×D4C22×D29311yescharacteristic
270C2×D4C22×D29311yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—5861no—
274C22×C4—5861no—
275C22×C4—5861no—
276C22×C4C22×D29311yescharacteristic
277C22×C4C22×D29311yescharacteristic
278SD16—11721no—
279D8—5862no—
280D8—11721no—
281M16—11721no—
282C2×C8—2931no—
283C2×C8—2931no—
284C2×C8—2931no—
285C2×C8—2931no—
286C2×C8—11721no—
287C4⋊C4—21no—
288C4⋊C4—2931no—
289C4⋊C4—2931no—
290C4⋊C4—2931no—
291C4⋊C4—5861no—
292C4⋊C4—5861no—
293C4⋊C4—5861no—
294C4⋊C4C22⋊D29311yescharacteristic
295C4⋊C4C22×D29311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—5861no—
302C22⋊C4—5861no—
303C22⋊C4—5861no—
304C22⋊C4C22⋊D29311yescharacteristic
305C22⋊C4C22⋊D29311yescharacteristic
306C42C22×D29311yescharacteristic
307C23—21no—
308C23—21no—
309C23—42no—
310C23—42no—
311C23—81no—
312C23—5861no—
313C23C2×C22⋊D29311yescharacteristic
314C23C2×C22⋊D29311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—11722no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—42no—
324D4—81no—
325D4—5861no—
326D4—5861no—
327D4—11722no—
328D4—11722no—
329D4#1798980112yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—81no—
338C2×C4—5861no—
339C2×C4—5861no—
340C2×C4—5861no—
341C2×C4—11722no—
342C2×C4—11722no—
343C2×C4—11722no—
344C2×C4C2×C22⋊D29311yescharacteristic
345C2×C4C2×C22⋊D29311yescharacteristic
346C2×C4C2×C22⋊D29311yescharacteristic
347C2×C4C2×C22⋊D29311yescharacteristic
348C2×C4C23×D29311yescharacteristic
349C8—5861no—
350C8—5861no—
351C8—5861no—
352C8—5861no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—21no—
358C22—21no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—84no—
365C22—11721no—
366C22—11721no—
367C22—11721no—
368C22#2262764912yes—
369C22C22×C22⋊D29311yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—11721no—
377C4—11721no—
378C4—11721no—
379C4C2×#1798980111yescharacteristic
380C4#2262766911yescharacteristic
381C2—22no—
382C2—41no—
383C2—42no—
384C2—81no—
385C2—23441no—
386C2#3403677311yescharacteristic
387C2C2×#2262764911yescharacteristic
388C2#3403694011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#546×C293C2
socleC22×C293C22×D4
hypercenter#546D293
hypocenterC293#3306
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. #34036783C2semidirect
2. #34036488C2semidirect
3. #34036457C2semidirect
4. #34036445C2semidirect
5. #34036419C2semidirect
6. #34036380C2semidirect
7. #34036360C2semidirect
8. #34036341C2semidirect
9. #34036274C2semidirect
10. #34036263C2semidirect
11. #34036239C2semidirect
12. #34036201C2semidirect
13. #34036130C2semidirect
14. C2×#22627545C2semidirect
15. #546×C293C2semidirect
17. C2×#17989789C22semidirect
20. C2×#17989786C22semidirect
22. #22627624C22semidirect
27. #22627598C22semidirect
28. C4×D1172C22semidirect
30. C2×C4⋊Dic293C22semidirect
31. #22627555C22semidirect
32. #22627555C22semidirect
33. #22627555C22semidirect
34. C4⋊#14556873C22semidirect
35. #22627548C22semidirect
36. #22627548C22semidirect
37. #22627548C22semidirect
44. #22627544C22semidirect
46. C22⋊#14556873C22semidirect
47. #22627535C22semidirect
144. D4×C293#41semidirect
194. C293#3306semidirect
197. #546D293semidirect
329. D4#17989801semidirect

Maximal subgroups

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

subgroupindex
#340367832
#340364882
#340364572
#340364452
#340364192
#340363802
#340363602
#340363412
#340362742
#340362632
#340362392
#340362012
#340361302
C2×#226275452
#546×C2932
#3306293