Finite Group Databasebeta

← #49170604

Subgroups — #49170604

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
2#34036763C211yesmaximal, characteristic
3#34036474C211yesmaximal, characteristic, complemented
4#34036449C211yesmaximal, characteristic, complemented
5#34036445C211yesmaximal, characteristic, complemented
6#34036418C211yesmaximal, characteristic, complemented
7#34036361C211yesmaximal, characteristic, complemented
8#34036327C211yesmaximal, characteristic, complemented
9#34036279C211yesmaximal, characteristic, complemented
10#34036278C211yesmaximal, characteristic, complemented
11#34036214C211yesmaximal, characteristic, complemented
12C8×C22⋊D293C211yesmaximal, characteristic, complemented
13C2×#22627546C211yesmaximal, characteristic, complemented
14#102×D293C211yesmaximal, characteristic, complemented
15#465×C293C211yesmaximal, characteristic, complemented
16C22×D1172C2211yescharacteristic
17C2×D4×D293—21no—
18C2×D4×D293C2211yescharacteristic
19C2×#17989789C2211yescharacteristic
20C2×#17989789C2211yescharacteristic, complemented
21C2×C8×D293C2211yescharacteristic, complemented
22#22627623C2211yescharacteristic, complemented
23#22627620C2211yescharacteristic
24#22627614—21no—
25#22627604—21no—
26#22627601—21no—
27#22627600C2211yescharacteristic, complemented
28#22627599C2211yescharacteristic
29#22627597—21no—
30#22627594—21no—
31#22627592—21no—
32Q8×Dic293C2211yescharacteristic, complemented
33#22627586C2211yescharacteristic
34C4×C22⋊D293C2211yescharacteristic
35#22627584—21no—
36C2×C4⋊Dic293C2211yescharacteristic, complemented
37C4⋊C4×D293C2211yescharacteristic, complemented
38#22627555C2211yescharacteristic, complemented
39#22627555C2211yescharacteristic, complemented
40#22627553C2211yescharacteristic, complemented
41#22627546C2211yescharacteristic
42#22627546C2211yescharacteristic
43#22627546C2211yescharacteristic, complemented
44#22627546C2211yescharacteristic, complemented
45#22627545C2211yescharacteristic, complemented
46#22627545C2211yescharacteristic, complemented
47#22627544C2211yescharacteristic
48#22627544C2211yescharacteristic, complemented
49C22⋊#14556873C2211yescharacteristic, complemented
50#22627536C2211yescharacteristic, complemented
51C8×Dic293C2211yescharacteristic, complemented
52C2×SD16×C293C2211yescharacteristic, complemented
53C22×C8×C293C2211yescharacteristic, complemented
54C22⋊Q8×C293C2211yescharacteristic, complemented
55#121×C293C2211yescharacteristic
56#106×C293C2211yescharacteristic, complemented
57#103×C293C2211yescharacteristic, complemented
58#102×C293C2211yescharacteristic, complemented
59C23×D293—21no—
60C23×D293—21no—
61C2×Dic586—21no—
62C2×D1172—22no—
63C2×D1172—21no—
64C2×D1172—21no—
65C2×D1172—41no—
66C2×D1172C2311yescharacteristic
67C2×D1172C2311yescharacteristic
68C2×C22⋊D293—21no—
69C2×C22⋊D293—21no—
70C2×C22⋊D293—21no—
71C2×C22⋊D293D411yescharacteristic
72D4×D293—22no—
73D4×D293—41no—
74D4×D293—44no—
75C22×Dic293—21no—
76C2×C4×D293—21no—
77C2×C4×D293—21no—
78C2×C4×D293C2311yescharacteristic
79#17989789—22no—
80#17989789—41no—
81C2×#14556873C2311yescharacteristic
82C2×#14556873C2311yescharacteristic
83C8×D293—41no—
84C4⋊Dic293—21no—
85C4⋊Dic293—21no—
86C4⋊Dic293C2311yescharacteristic
87C4⋊Dic293C2311yescharacteristic
88#17989781—21no—
89#17989781—21no—
90#17989781—21no—
91#17989781D411yescharacteristic
92C22⋊Dic293D411yescharacteristic
93#17989779—21no—
94#17989779—21no—
95#17989779—21no—
96#17989779D411yescharacteristic
97C4×Dic293—21no—
98C4×Dic293C2311yescharacteristic
99C2×Q8×C293C2311yescharacteristic
100C2×D4×C293—21no—
101C2×D4×C293C2311yescharacteristic
102C22×C4×C293C2311yescharacteristic
103SD16×C293—41no—
104C2×C8×C293—41no—
105C2×C8×C293C2311yescharacteristic
106C2×C8×C293C2311yescharacteristic
107C4⋊C4×C293—21no—
108C4⋊C4×C293C2311yescharacteristic
109C4⋊C4×C293C2311yescharacteristic
110C22⋊C4×C293—21no—
111C22⋊C4×C293—21no—
112C22×D293—21no—
113C22×D293—21no—
114C22×D293—42no—
115C22×D293—42no—
116C22×D293—42no—
117C22×D293—42no—
118C22×D293—81no—
119C22×D293—81no—
120C22×D293C2×D411yescharacteristic
121Dic586—81no—
122D1172—21no—
123D1172—21no—
124D1172—21no—
125D1172—42no—
126D1172—42no—
127D1172#4112yes—
128C22⋊D293—42no—
129C22⋊D293—42no—
130C22⋊D293—81no—
131C22⋊D293SD1614yescomplemented
132C2×Dic293—21no—
133C2×Dic293—21no—
134C2×Dic293—81no—
135C2×Dic293C2×D411yescharacteristic
136C2×Dic293C2×D411yescharacteristic
137C2×Dic293C2×D411yescharacteristic
138C4×D293—21no—
139C4×D293—21no—
140C4×D293—42no—
141C4×D293—81no—
142#14556873—21no—
143#14556873—21no—
144C23×C293—21no—
145C23×C293C2×D411yescharacteristic
146Q8×C293—21no—
147Q8×C293—21no—
148D4×C293—21no—
149D4×C293—21no—
150D4×C293—42no—
151C2×C4×C293—21no—
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—41no—
163C22×C293—41no—
164C22×C293—41no—
165C22×C293C2×SD1612yes—
166C22×C293C22×D411yescharacteristic
167C2×D293—21no—
168C2×D293—21no—
169C2×D293—22no—
170C2×D293—41no—
171C2×D293—41no—
172C2×D293—41no—
173C2×D293—41no—
174C2×D293—41no—
175C2×D293—84no—
176C2×D293—84no—
177C2×D293C2×SD1612yes—
178C4×C293—21no—
179C4×C293—41no—
180C4×C293—41no—
181C4×C293—41no—
182C4×C293C2×#4111yescharacteristic
183C4×C293H(5,𝔽2)11yescharacteristic
184Dic293—21no—
185Dic293—21no—
186Dic293—41no—
187Dic293—41no—
188Dic293C2×SD1612yes—
189C2×C293—22no—
190C2×C293—81no—
191C2×C293#54611yescharacteristic
192C2×C293C22×SD1611yescharacteristic
193C2×C293#57611yescharacteristic
194D293—22no—
195D293—42no—
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#465D29311yescharacteristic, complemented
207#460—2931no—
208#450—2931no—
209#450—2931no—
210C4×SD16—2931no—
211C8×D4—2931no—
212C2×#102—2931no—
213C2×#102—2931no—
214C22×D4—2931no—
215C22×D4—2931no—
216C22×D4—5861no—
217C2×SD16—2931no—
218C2×SD16—2931no—
219C2×SD16C2×D29311yescharacteristic, complemented
220C22×C8—2931no—
221C22×C8C2×D29311yescharacteristic, complemented
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—5861no—
231#121C2×D29311yescharacteristic
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#106C2×D29311yescharacteristic, complemented
243C4⋊C8—2931no—
244#103C2×D29311yescharacteristic, complemented
245#102—2931no—
246#102—2931no—
247#102—2931no—
248#102—2931no—
249#102—2931no—
250#102—2931no—
251#102—2931no—
252#102—2931no—
253#102C2×D29311yescharacteristic, complemented
254C22⋊C8—2931no—
255C22⋊C8—2931no—
256C4×C8—2931no—
257C24—5861no—
258C24—5861no—
259C2×Q8—5861no—
260C2×Q8C22×D29311yescharacteristic
261C2×D4—21no—
262C2×D4—2931no—
263C2×D4—2931no—
264C2×D4—2931no—
265C2×D4—5862no—
266C2×D4—5861no—
267C2×D4—5861no—
268C2×D4—5861no—
269C2×D4—5861no—
270C2×D4—5862no—
271C2×D4—5861no—
272C2×D4—11721no—
273C2×D4—11721no—
274C2×D4—11724no—
275C2×D4C22×D29311yescharacteristic
276C22×C4—2931no—
277C22×C4—5861no—
278C22×C4—5861no—
279C22×C4—5861no—
280C22×C4C22×D29311yescharacteristic
281SD16—41no—
282SD16—5862no—
283SD16—11721no—
284C2×C8—41no—
285C2×C8—2931no—
286C2×C8—2931no—
287C2×C8—11721no—
288C2×C8C22×D29311yescharacteristic
289C2×C8C22×D29311yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—2931no—
292C4⋊C4—2931no—
293C4⋊C4—2931no—
294C4⋊C4—5861no—
295C4⋊C4—5861no—
296C4⋊C4—5861no—
297C4⋊C4—5861no—
298C4⋊C4—5861no—
299C4⋊C4C22×D29311yescharacteristic
300C4⋊C4C22×D29311yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—2931no—
304C22⋊C4—2931no—
305C22⋊C4—5861no—
306C22⋊C4—5861no—
307C22⋊C4—5861no—
308C42—2931no—
309C42—5861no—
310C23—21no—
311C23—2931no—
312C23—23441no—
313C23—23441no—
314C23—5861no—
315C23—5861no—
316C23—11722no—
317C23—11722no—
318C23—11722no—
319C23—11722no—
320C23D4×D29311yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—23441no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—2934no—
328D4—2932no—
329D4—23441no—
330D4—5861no—
331D4—5861no—
332D4—5861no—
333D4—11722no—
334D4—11722no—
335D4—11722no—
336D4—11722no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—2931no—
343C2×C4—2931no—
344C2×C4—2931no—
345C2×C4—23441no—
346C2×C4—23441no—
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—41no—
361C22—41no—
362C22—41no—
363C22—2932no—
364C22—23444no—
365C22—23444no—
366C22—5861no—
367C22—5861no—
368C22—5862no—
369C22—11721no—
370C22—11721no—
371C22—11721no—
372C22—11721no—
373C22—11721no—
374C22SD16×D29312yes—
375C22C2×D4×D29311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—2932no—
381C4—5861no—
382C4—5861no—
383C4—11721no—
384C4—11721no—
385C4#41×D29311yescharacteristic
386C4#2262766911yescharacteristic
387C2—22no—
388C2—81no—
389C2—23441no—
390C2—5862no—
391C2—11722no—
392C2#3403676811yescharacteristic
393C2C2×SD16×D29311yescharacteristic
394C2#3403693111yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#465×C293C2
socleC22×C293C22×D4
prime radical#34036763C2
hypercenter#465D293
hypocenterC293#3295
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #34036837C2semidirect
3. #34036474C2semidirect
4. #34036449C2semidirect
5. #34036445C2semidirect
6. #34036418C2semidirect
7. #34036361C2semidirect
8. #34036327C2semidirect
9. #34036279C2semidirect
10. #34036278C2semidirect
11. #34036214C2semidirect
12. C8×C22⋊D293C2semidirect
13. C2×#22627546C2semidirect
14. #102×D293C2semidirect
15. #465×C293C2semidirect
20. C2×#17989789C22semidirect
21. C2×C8×D293C22semidirect
22. #22627623C22semidirect
27. #22627600C22semidirect
32. Q8×Dic293C22semidirect
36. C2×C4⋊Dic293C22semidirect
37. C4⋊C4×D293C22semidirect
38. #22627555C22semidirect
39. #22627555C22semidirect
40. #22627553C22semidirect
43. #22627546C22semidirect
44. #22627546C22semidirect
45. #22627545C22semidirect
46. #22627545C22semidirect
48. #22627544C22semidirect
49. C22⋊#14556873C22semidirect
50. #22627536C22semidirect
51. C8×Dic293C22semidirect
52. C2×SD16×C293C22semidirect
53. C22×C8×C293C22semidirect
54. C22⋊Q8×C293C22semidirect
56. #106×C293C22semidirect
57. #103×C293C22semidirect
58. #102×C293C22semidirect
131. C22⋊D293SD16semidirect
197. C293#3295semidirect
206. #465D293semidirect
219. C2×SD16C2×D293semidirect
221. C22×C8C2×D293semidirect
228. C22⋊Q8C2×D293semidirect
242. #106C2×D293semidirect
244. #103C2×D293semidirect
253. #102C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340368372
#340367632
#340364742
#340364492
#340364452
#340364182
#340363612
#340363272
#340362792
#340362782
#340362142
C8×C22⋊D2932
C2×#226275462
#102×D2932
#465×C2932
#3295293