Finite Group Databasebeta

← #49170602

Subgroups — #49170602

Order 37504.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036837C211yesmaximal, characteristic, complemented
2D4×C22⋊D293C211yesmaximal, characteristic
3#34036474C211yesmaximal, characteristic, complemented
4#34036448C211yesmaximal, characteristic, complemented
5#34036446C211yesmaximal, characteristic, complemented
6#34036417C211yesmaximal, characteristic, complemented
7#34036360C211yesmaximal, characteristic, complemented
8#34036355C211yesmaximal, characteristic, complemented
9#34036327C211yesmaximal, characteristic, complemented
10#34036278C211yesmaximal, characteristic, complemented
11SD16×Dic293C211yesmaximal, characteristic, complemented
12#34036192C211yesmaximal, characteristic, complemented
13C2×#22627545C211yesmaximal, characteristic, complemented
14#102×D293C211yesmaximal, characteristic, complemented
15#450×C293C211yesmaximal, characteristic, complemented
16C22×C22⋊D293—21no—
17C2×D4×D293C2211yescharacteristic
18C2×#17989789C2211yescharacteristic, complemented
19C22×#14556873C2211yescharacteristic, complemented
20C2×C8×D293C2211yescharacteristic, complemented
21#22627623C2211yescharacteristic, complemented
22#22627620C2211yescharacteristic
23#22627614—21no—
24#22627604—21no—
25#22627601—21no—
26#22627600C2211yescharacteristic, complemented
27#22627598C2211yescharacteristic
28#22627596—21no—
29#22627595C2211yescharacteristic
30#22627593—21no—
31#22627592—21no—
32Q8×Dic293C2211yescharacteristic, complemented
33D4×Dic293C2211yescharacteristic
34C4×C22⋊D293C2211yescharacteristic
35#22627584—21no—
36C2×C4⋊Dic293C2211yescharacteristic, complemented
37C4⋊C4×D293C2211yescharacteristic, complemented
38#22627556C2211yescharacteristic, complemented
39#22627556C2211yescharacteristic, complemented
40#22627555C2211yescharacteristic, complemented
41#22627553C2211yescharacteristic, complemented
42#22627548C2211yescharacteristic, complemented
43#22627546C2211yescharacteristic, complemented
44#22627546C2211yescharacteristic, complemented
45#22627545C2211yescharacteristic
46#22627545C2211yescharacteristic
47#22627545C2211yescharacteristic, complemented
48#22627545C2211yescharacteristic, complemented
49#22627544C2211yescharacteristic, complemented
50#22627536C2211yescharacteristic, complemented
51C8×Dic293C2211yescharacteristic, complemented
52C22×D4×C293C2211yescharacteristic
53C2×SD16×C293C2211yescharacteristic
54C2×SD16×C293C2211yescharacteristic, complemented
55C22⋊Q8×C293C2211yescharacteristic, complemented
56#102×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic, complemented
58C22⋊C8×C293C2211yescharacteristic, complemented
59C23×D293—21no—
60C2×Dic586—21no—
61C2×D1172C2311yescharacteristic
62C2×C22⋊D293—21no—
63C2×C22⋊D293—21no—
64C2×C22⋊D293—21no—
65C2×C22⋊D293—21no—
66C2×C22⋊D293—21no—
67C2×C22⋊D293—44no—
68C2×C22⋊D293D411yescharacteristic
69D4×D293—22no—
70D4×D293—41no—
71C22×Dic293—21no—
72C22×Dic293—21no—
73C2×C4×D293—21no—
74C2×C4×D293C2311yescharacteristic
75#17989789—41no—
76C2×#14556873—41no—
77C2×#14556873C2311yescharacteristic
78C2×#14556873C2311yescharacteristic
79C8×D293—41no—
80C4⋊Dic293—21no—
81C4⋊Dic293—21no—
82C4⋊Dic293C2311yescharacteristic
83C4⋊Dic293C2311yescharacteristic
84C4⋊Dic293C2311yescharacteristic
85#17989781—21no—
86#17989781—21no—
87#17989781—21no—
88#17989781D411yescharacteristic
89C22⋊Dic293—21no—
90C22⋊Dic293—21no—
91C22⋊Dic293D411yescharacteristic
92#17989779—21no—
93#17989779—21no—
94#17989779D411yescharacteristic
95C4×Dic293—21no—
96C4×Dic293C2311yescharacteristic
97C24×C293—21no—
98C2×Q8×C293C2311yescharacteristic
99C2×D4×C293—22no—
100C2×D4×C293—21no—
101C2×D4×C293—41no—
102C2×D4×C293C2311yescharacteristic
103C2×D4×C293C2311yescharacteristic
104C22×C4×C293C2311yescharacteristic
105SD16×C293—22no—
106SD16×C293—41no—
107C2×C8×C293C2311yescharacteristic
108C2×C8×C293C2311yescharacteristic
109C4⋊C4×C293—21no—
110C4⋊C4×C293C2311yescharacteristic
111C22⋊C4×C293—21no—
112C22×D293—21no—
113C22×D293—42no—
114C22×D293—42no—
115C22×D293—81no—
116C22×D293C2×D411yescharacteristic
117Dic586—81no—
118D1172—21no—
119D1172—21no—
120C22⋊D293—42no—
121C22⋊D293—42no—
122C22⋊D293—42no—
123C22⋊D293—42no—
124C22⋊D293—81no—
125C22⋊D293SD1614yescomplemented
126C2×Dic293—21no—
127C2×Dic293—21no—
128C2×Dic293—21no—
129C2×Dic293—42no—
130C2×Dic293—81no—
131C2×Dic293C2×D411yescharacteristic
132C2×Dic293C2×D411yescharacteristic
133C2×Dic293C2×D411yescharacteristic
134C4×D293—21no—
135C4×D293—21no—
136C4×D293—81no—
137#14556873—21no—
138#14556873—21no—
139C23×C293—21no—
140C23×C293—21no—
141C23×C293—42no—
142C23×C293—42no—
143C23×C293—81no—
144C23×C293C2×D411yescharacteristic
145Q8×C293—21no—
146Q8×C293—21no—
147D4×C293—21no—
148D4×C293—21no—
149D4×C293—21no—
150D4×C293—42no—
151D4×C293#4112yes—
152C2×C4×C293—21no—
153C2×C4×C293—21no—
154C2×C4×C293—21no—
155C2×C4×C293—21no—
156C2×C4×C293C2×D411yescharacteristic
157C2×C4×C293C2411yescharacteristic
158C8×C293—21no—
159C8×C293—21no—
160C22×C293—21no—
161C22×C293—21no—
162C22×C293—22no—
163C22×C293—41no—
164C22×C293—41no—
165C22×C293—41no—
166C22×C293—41no—
167C22×C293—41no—
168C22×C293—84no—
169C22×C293C2×SD1612yes—
170C22×C293C22×D411yescharacteristic
171C2×D293—21no—
172C2×D293—21no—
173C2×D293—41no—
174C2×D293—41no—
175C2×D293—41no—
176C2×D293—84no—
177C2×D293C2×SD1612yes—
178C4×C293—21no—
179C4×C293—41no—
180C4×C293—41no—
181C4×C293C2×#4111yescharacteristic
182C4×C293H(5,𝔽2)11yescharacteristic
183Dic293—21no—
184Dic293—21no—
185Dic293—41no—
186Dic293—41no—
187Dic293—41no—
188Dic293C2×SD1612yes—
189C2×C293—22no—
190C2×C293—42no—
191C2×C293—81no—
192C2×C293#54611yescharacteristic
193C2×C293C22×SD1611yescharacteristic
194C2×C293#57611yescharacteristic
195D293—22no—
196D293—81no—
197C293#329511yescharacteristic, complemented, Sylow
198#3295—2931nomaximal, Sylow
199#554—2931no—
200D42—2931no—
201#486—2931no—
202#481—2931no—
203#481—2931no—
204#476—2931no—
205#465—2931no—
206#465—2931no—
207#460—2931no—
208#450—2931no—
209#450D29311yescharacteristic, complemented
210C4×SD16—2931no—
211C8×D4—2931no—
212C2×#102—2931no—
213C2×#102—2931no—
214C22×D4—2931no—
215C22×D4—5861no—
216C22×D4C2×D29311yescharacteristic
217C2×SD16—2931no—
218C2×SD16C2×D29311yescharacteristic
219C2×SD16C2×D29311yescharacteristic, complemented
220C22×C8—2931no—
221C22×C8—2931no—
222C4⋊Q8—2931no—
223#127—2931no—
224#125—5861no—
225C22⋊Q8—2931no—
226C22⋊Q8—5861no—
227C22⋊Q8—5861no—
228C22⋊Q8C2×D29311yescharacteristic, complemented
229#121—2931no—
230#121—2931no—
231#121—5861no—
232#120—5861no—
233#120—5861no—
234C4×Q8—2931no—
235C4×D4—2931no—
236C4×D4—2931no—
237C4×D4—5861no—
238C2×C4⋊C4—2931no—
239C2×C4⋊C4—2931no—
240#106—2931no—
241#106—2931no—
242#106—2931no—
243C4⋊C8—2931no—
244#103—2931no—
245#102—2931no—
246#102—2931no—
247#102—2931no—
248#102—2931no—
249#102—2931no—
250#102—2931no—
251#102—2931no—
252#102C2×D29311yescharacteristic
253#102C2×D29311yescharacteristic, complemented
254C22⋊C8—2931no—
255C22⋊C8C2×D29311yescharacteristic, complemented
256C4×C8—2931no—
257C24—21no—
258C24—5861no—
259C2×Q8—5861no—
260C2×Q8C22×D29311yescharacteristic
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—2931no—
265C2×D4—2931no—
266C2×D4—5861no—
267C2×D4—5861no—
268C2×D4—5861no—
269C2×D4—5862no—
270C2×D4—5861no—
271C2×D4—5861no—
272C2×D4—11721no—
273C2×D4—11724no—
274C2×D4C22×D29311yescharacteristic
275C2×D4C22×D29311yescharacteristic
276C22×C4—2931no—
277C22×C4—5861no—
278C22×C4—5861no—
279C22×C4—5861no—
280C22×C4C22×D29311yescharacteristic
281SD16—22no—
282SD16—41no—
283SD16—11721no—
284C2×C8—2931no—
285C2×C8—2931no—
286C2×C8—11721no—
287C2×C8—11721no—
288C2×C8C22×D29311yescharacteristic
289C2×C8C22×D29311yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—2931no—
292C4⋊C4—2931no—
293C4⋊C4—2931no—
294C4⋊C4—2931no—
295C4⋊C4—5861no—
296C4⋊C4—5861no—
297C4⋊C4—5861no—
298C4⋊C4—5861no—
299C4⋊C4—5861no—
300C4⋊C4C22×D29311yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—2931no—
303C22⋊C4—2931no—
304C22⋊C4—5861no—
305C22⋊C4—5861no—
306C22⋊C4—5861no—
307C22⋊C4—5861no—
308C42—2931no—
309C42—5861no—
310C23—21no—
311C23—21no—
312C23—42no—
313C23—42no—
314C23—81no—
315C23—2931no—
316C23—23441no—
317C23—5861no—
318C23—11722no—
319C23—11722no—
320C23D4×D29311yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—23441no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—2934no—
329D4—23441no—
330D4—5861no—
331D4—5861no—
332D4—11722no—
333D4—11722no—
334D4—11722no—
335D4—11722no—
336D4#1798980112yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—2931no—
342C2×C4—2931no—
343C2×C4—2931no—
344C2×C4—23441no—
345C2×C4—23441no—
346C2×C4—5861no—
347C2×C4—5861no—
348C2×C4—5861no—
349C2×C4—5861no—
350C2×C4—5861no—
351C2×C4—11722no—
352C2×C4D4×D29311yescharacteristic
353C2×C4C23×D29311yescharacteristic
354C8—21no—
355C8—21no—
356C8—5861no—
357C8—5861no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—84no—
367C22—2932no—
368C22—23444no—
369C22—5861no—
370C22—5861no—
371C22—11721no—
372C22—11721no—
373C22—11721no—
374C22SD16×D29312yes—
375C22C2×D4×D29311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—2932no—
380C4—5861no—
381C4—5861no—
382C4—11721no—
383C4—11721no—
384C4—11721no—
385C4C2×#1798980111yescharacteristic
386C4#2262766911yescharacteristic
387C2—22no—
388C2—42no—
389C2—81no—
390C2—23441no—
391C2—5862no—
392C2#3403676611yescharacteristic
393C2C2×SD16×D29311yescharacteristic
394C2#3403693311yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#450×C293C2
socleC22×C293C22×D4
prime radicalD4×C22⋊D293C2
hypercenter#450D293
hypocenterC293#3295
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #34036837C2semidirect
3. #34036474C2semidirect
4. #34036448C2semidirect
5. #34036446C2semidirect
6. #34036417C2semidirect
7. #34036360C2semidirect
8. #34036355C2semidirect
9. #34036327C2semidirect
10. #34036278C2semidirect
11. SD16×Dic293C2semidirect
12. #34036192C2semidirect
13. C2×#22627545C2semidirect
14. #102×D293C2semidirect
15. #450×C293C2semidirect
18. C2×#17989789C22semidirect
19. C22×#14556873C22semidirect
20. C2×C8×D293C22semidirect
21. #22627623C22semidirect
26. #22627600C22semidirect
32. Q8×Dic293C22semidirect
36. C2×C4⋊Dic293C22semidirect
37. C4⋊C4×D293C22semidirect
38. #22627556C22semidirect
39. #22627556C22semidirect
40. #22627555C22semidirect
41. #22627553C22semidirect
42. #22627548C22semidirect
43. #22627546C22semidirect
44. #22627546C22semidirect
47. #22627545C22semidirect
48. #22627545C22semidirect
49. #22627544C22semidirect
50. #22627536C22semidirect
51. C8×Dic293C22semidirect
54. C2×SD16×C293C22semidirect
55. C22⋊Q8×C293C22semidirect
57. #102×C293C22semidirect
58. C22⋊C8×C293C22semidirect
125. C22⋊D293SD16semidirect
197. C293#3295semidirect
209. #450D293semidirect
219. C2×SD16C2×D293semidirect
228. C22⋊Q8C2×D293semidirect
253. #102C2×D293semidirect
255. C22⋊C8C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340368372
D4×C22⋊D2932
#340364742
#340364482
#340364462
#340364172
#340363602
#340363552
#340363272
#340362782
SD16×Dic2932
#340361922
C2×#226275452
#102×D2932
#450×C2932
#3295293