Finite Group Databasebeta

← #49170286

Subgroups — #49170286

Order 37504.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22627648C211yesmaximal, characteristic, complemented
2C2×SD16×D293C211yesmaximal, characteristic, complemented
3#34036787C211yesmaximal, characteristic, complemented
4D4×D1172C211yesmaximal, characteristic, complemented
5#34036519C211yesmaximal, characteristic, complemented
6#34036378C211yesmaximal, characteristic, complemented
7#34036364C211yesmaximal, characteristic, complemented
8#34036330C211yesmaximal, characteristic, complemented
9#34036278C211yesmaximal, characteristic, complemented
10#34036275C211yesmaximal, characteristic, complemented
11#34036269C211yesmaximal, characteristic, complemented
12#34036261C211yesmaximal, characteristic, complemented
13#34036229C211yesmaximal, characteristic, complemented
14#34036199C211yesmaximal, characteristic, complemented
15#463×C293C211yesmaximal, characteristic, complemented
16C2×#17989801C2211yescharacteristic, complemented
17C2×Q8×D293C2211yescharacteristic, complemented
18C22×D1172—21no—
19C2×D4×D293C2211yescharacteristic
20C2×D4×D293C2211yescharacteristic
21#22627648—24no—
22C2×#17989791C2211yescharacteristic, complemented
23C2×#17989791C2211yescharacteristic, complemented
24C2×#17989790C2211yescharacteristic
25C2×#17989789C2211yescharacteristic, complemented
26C2×#17989789C2211yescharacteristic, complemented
27SD16×D293—24no—
28C2×#17989787C2211yescharacteristic, complemented
29C2×#17989787C2211yescharacteristic, complemented
30C2×#17989785C2211yescharacteristic, complemented
31C2×C8×D293C2211yescharacteristic, complemented
32#22627621C2211yescharacteristic
33#22627610—21no—
34#22627601—21no—
35#22627600C2211yescharacteristic, complemented
36#22627599C2211yescharacteristic
37#22627599C2211yescharacteristic
38#22627598—21no—
39#22627597—21no—
40#22627595C2211yescharacteristic, complemented
41#22627594—21no—
42#22627594—21no—
43C4×Dic586C2211yescharacteristic, complemented
44C4×D1172C2211yescharacteristic
45#22627584—21no—
46#22627557C2211yescharacteristic, complemented
47#22627547C2211yescharacteristic, complemented
48#22627546C2211yescharacteristic, complemented
49#22627546C2211yescharacteristic, complemented
50#22627545C2211yescharacteristic
51#22627536C2211yescharacteristic, complemented
52#22627536C2211yescharacteristic, complemented
53#22627535C2211yescharacteristic, complemented
54C2×SD16×C293C2211yescharacteristic
55C2×D8×C293C2211yescharacteristic
56#124×C293C2211yescharacteristic, complemented
57C4×D4×C293C2211yescharacteristic
58C4⋊C8×C293C2211yescharacteristic, complemented
59#103×C293C2211yescharacteristic, complemented
60#102×C293C2211yescharacteristic, complemented
61C23×D293—21no—
62C23×D293—21no—
63#17989801—22no—
64#17989801—41no—
65C2×Dic586—21no—
66C2×Dic586C2311yescharacteristic
67Q8×D293—22no—
68Q8×D293—41no—
69C2×D1172—21no—
70C2×D1172—21no—
71C2×D1172—21no—
72C2×D1172—21no—
73C2×D1172—44no—
74C2×D1172D411yescharacteristic
75C2×D1172C2311yescharacteristic
76C2×D1172C2311yescharacteristic
77C2×C22⋊D293—21no—
78C2×C22⋊D293—21no—
79C2×C22⋊D293—21no—
80C2×C22⋊D293—21no—
81D4×D293—22no—
82D4×D293—22no—
83D4×D293—41no—
84D4×D293—41no—
85C22×Dic293—21no—
86C2×C4×D293—21no—
87C2×C4×D293C2311yescharacteristic
88C2×C4×D293C2311yescharacteristic
89#17989791—22no—
90#17989791—22no—
91#17989790D414yescomplemented
92#17989789—22no—
93#17989789—41no—
94#17989787—22no—
95#17989787—41no—
96#17989785—22no—
97C2×#14556873C2311yescharacteristic
98C2×#14556873C2311yescharacteristic
99C8×D293—22no—
100C4⋊Dic293D411yescharacteristic
101C4⋊Dic293C2311yescharacteristic
102#17989781—21no—
103#17989781—21no—
104C22⋊Dic293—21no—
105#17989779—21no—
106#17989779—21no—
107#17989779—21no—
108#17989779D411yescharacteristic
109#17989779D411yescharacteristic
110C4×Dic293—21no—
111C2×Q8×C293C2311yescharacteristic
112C2×D4×C293C2311yescharacteristic
113C2×D4×C293C2311yescharacteristic
114C22×C4×C293—21no—
115SD16×C293—22no—
116D8×C293—22no—
117C2×C8×C293C2311yescharacteristic
118C2×C8×C293C2311yescharacteristic
119C4⋊C4×C293C2311yescharacteristic
120C22⋊C4×C293—21no—
121C22⋊C4×C293—21no—
122C22⋊C4×C293—21no—
123C42×C293C2311yescharacteristic
124C22×D293—21no—
125C22×D293—21no—
126C22×D293—42no—
127C22×D293—42no—
128C22×D293—42no—
129C22×D293—42no—
130C22×D293—81no—
131C22×D293—81no—
132C22×D293C2×D411yescharacteristic
133C22×D293C2×D411yescharacteristic
134Dic586—21no—
135Dic586—42no—
136Dic586C2×D412yescomplemented
137D1172—22no—
138D1172—21no—
139D1172—21no—
140D1172—21no—
141D1172—21no—
142D1172—42no—
143D1172—42no—
144D1172—42no—
145D1172—81no—
146C22⋊D293—42no—
147C22⋊D293—42no—
148C22⋊D293—42no—
149C22⋊D293—42no—
150C2×Dic293—21no—
151C2×Dic293—21no—
152C2×Dic293—42no—
153C2×Dic293C2×D411yescharacteristic
154C2×Dic293C2×D411yescharacteristic
155C4×D293—21no—
156C4×D293—21no—
157C4×D293—21no—
158C4×D293—21no—
159C4×D293—42no—
160#14556873—21no—
161#14556873C2×D412yescomplemented
162C23×C293—21no—
163C23×C293—21no—
164Q8×C293—21no—
165Q8×C293—21no—
166D4×C293—21no—
167D4×C293—21no—
168D4×C293—21no—
169D4×C293C2×D412yes—
170C2×C4×C293—21no—
171C2×C4×C293—21no—
172C2×C4×C293—42no—
173C2×C4×C293C2×D411yescharacteristic
174C2×C4×C293C2×D411yescharacteristic
175C2×C4×C293C2411yescharacteristic
176C8×C293—21no—
177C8×C293—21no—
178C22×C293—22no—
179C22×C293—41no—
180C22×C293—41no—
181C22×C293—41no—
182C22×C293—41no—
183C22×C293—41no—
184C22×C293C22×D411yescharacteristic
185C2×D293—21no—
186C2×D293—21no—
187C2×D293—21no—
188C2×D293—21no—
189C2×D293—21no—
190C2×D293—41no—
191C2×D293—41no—
192C2×D293—41no—
193C2×D293—41no—
194C2×D293—41no—
195C2×D293—41no—
196C2×D293—84no—
197C2×D293—84no—
198C2×D293AGL(1,ℤ/8)12yescomplemented
199C4×C293—21no—
200C4×C293—21no—
201C4×C293—41no—
202C4×C293—41no—
203C4×C293C22×D411yescharacteristic
204C4×C293H(5,𝔽2)11yescharacteristic
205Dic293—21no—
206Dic293—21no—
207Dic293—22no—
208Dic293—41no—
209C2×C293—42no—
210C2×C293—81no—
211C2×C293D4211yescharacteristic
212C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
213C2×C293#57711yescharacteristic
214D293—22no—
215D293—41no—
216D293—81no—
217D293—81no—
218C293#326511yescharacteristic, complemented, Sylow
219#3265—2931nomaximal, Sylow
220C2×AGL(1,ℤ/8)—2931no—
221C22×SD16—2931no—
222#548—2931no—
223D42—2931no—
224#496—2931no—
225#468—2931no—
226#466—2931no—
227#463D29311yescharacteristic, complemented
228#460—2931no—
229#450—2931no—
230#449—2931no—
231#448—2931no—
232#447—2931no—
233#440—2931no—
234#435—2931no—
235C2×#41—2931no—
236C22×Q8—2931no—
237C22×D4—2931no—
238C22×D4—2931no—
239C22×D4—5861no—
240AGL(1,ℤ/8)—5864no—
241C2×SD16—2931no—
242C2×SD16—2931no—
243C2×SD16—2931no—
244C2×SD16—2931no—
245C2×SD16—2931no—
246C2×SD16—5864no—
247C2×SD16C2×D29311yescharacteristic
248C2×D8—2931no—
249C2×D8—2931no—
250C2×D8C2×D29311yescharacteristic
251C2×M16—2931no—
252C22×C8—2931no—
253#127—2931no—
254#124—5861no—
255#124C2×D29311yescharacteristic, complemented
256C22⋊Q8—2931no—
257C22⋊Q8—5861no—
258#121—2931no—
259#121—2931no—
260#121—2931no—
261#121—5861no—
262#121—5861no—
263#120—5861no—
264#120—5861no—
265C4×Q8—2931no—
266C4×D4—2931no—
267C4×D4—5861no—
268C4×D4C2×D29311yescharacteristic
269#107—2931no—
270C4⋊C8C2×D29311yescharacteristic, complemented
271#103—2931no—
272#103C2×D29311yescharacteristic, complemented
273#102—2931no—
274#102—2931no—
275#102—2931no—
276#102C2×D29311yescharacteristic, complemented
277C22⋊C8—2931no—
278C22⋊C8—2931no—
279#97—2931no—
280C24—5861no—
281C24—5861no—
282#41—5862no—
283#41—11721no—
284C2×Q8—2931no—
285C2×Q8—5861no—
286C2×Q8—5862no—
287C2×Q8—11721no—
288C2×Q8C22×D29311yescharacteristic
289C2×D4—2931no—
290C2×D4—2931no—
291C2×D4—2931no—
292C2×D4—5861no—
293C2×D4—5861no—
294C2×D4—5861no—
295C2×D4—5861no—
296C2×D4—5862no—
297C2×D4—5862no—
298C2×D4—5861no—
299C2×D4—5861no—
300C2×D4—5861no—
301C2×D4—5861no—
302C2×D4—11724no—
303C2×D4—11721no—
304C2×D4—11721no—
305C2×D4C22×D29311yescharacteristic
306C2×D4C22×D29311yescharacteristic
307C22×C4—21no—
308C22×C4—2931no—
309C22×C4—2931no—
310C22×C4—5861no—
311C22×C4—5861no—
312SD16—22no—
313SD16—2934no—
314SD16—5862no—
315SD16—5862no—
316SD16—5862no—
317SD16—11721no—
318D8—22no—
319D8—5862no—
320D8—11721no—
321M16—5862no—
322C2×C8—2931no—
323C2×C8—2931no—
324C2×C8—5862no—
325C2×C8C22×D29311yescharacteristic
326C2×C8C22×D29311yescharacteristic
327C4⋊C4—2931no—
328C4⋊C4—2931no—
329C4⋊C4—5861no—
330C4⋊C4—5861no—
331C4⋊C4C22×D29311yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—2931no—
336C22⋊C4—2931no—
337C22⋊C4—5861no—
338C22⋊C4—5861no—
339C22⋊C4—5861no—
340C22⋊C4—5861no—
341C42—5861no—
342C42C22×D29311yescharacteristic
343C23—21no—
344C23—21no—
345C23—2931no—
346C23—2931no—
347C23—23441no—
348C23—23441no—
349C23—5861no—
350C23—5861no—
351C23—11722no—
352C23—11722no—
353C23—11722no—
354C23—11722no—
355Q8—21no—
356Q8—21no—
357Q8—2932no—
358Q8—5861no—
359Q8—11722no—
360D4—21no—
361D4—21no—
362D4—21no—
363D4—23441no—
364D4—5862no—
365D4—5861no—
366D4—5861no—
367D4—5861no—
368D4—5861no—
369D4—11722no—
370D4—11722no—
371D4—11722no—
372D4—11722no—
373D4—11722no—
374D4—11722no—
375D4—11722no—
376D4D4×D29312yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—42no—
380C2×C4—2931no—
381C2×C4—2931no—
382C2×C4—5861no—
383C2×C4—5861no—
384C2×C4—5861no—
385C2×C4—5861no—
386C2×C4—5861no—
387C2×C4—5861no—
388C2×C4—11722no—
389C2×C4—11722no—
390C2×C4D4×D29311yescharacteristic
391C2×C4D4×D29311yescharacteristic
392C2×C4C23×D29311yescharacteristic
393C8—21no—
394C8—21no—
395C8—2932no—
396C8—5861no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—2932no—
404C22—23444no—
405C22—23444no—
406C22—5861no—
407C22—5861no—
408C22—5861no—
409C22—5861no—
410C22—5861no—
411C22—11721no—
412C22—11721no—
413C22—11721no—
414C22—11721no—
415C22—11721no—
416C22—11721no—
417C22C2×D4×D29311yescharacteristic
418C4—21no—
419C4—21no—
420C4—41no—
421C4—41no—
422C4—5861no—
423C4—5861no—
424C4—5862no—
425C4—11721no—
426C4C2×D4×D29311yescharacteristic
427C4#2262767011yescharacteristic
428C2—42no—
429C2—81no—
430C2—23441no—
431C2—23441no—
432C2—5862no—
433C2—11721no—
434C2#3403676311yescharacteristic
435C2AGL(1,ℤ/8)×D29311yescharacteristic
436C2#3403693611yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#463×C293C2
socleC22×C293C22×D4
hypercenter#463D293
hypocenterC293#3265
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#22627648C2semidirect
2. C2×SD16×D293C2semidirect
3. #34036787C2semidirect
4. D4×D1172C2semidirect
5. #34036519C2semidirect
6. #34036378C2semidirect
7. #34036364C2semidirect
8. #34036330C2semidirect
9. #34036278C2semidirect
10. #34036275C2semidirect
11. #34036269C2semidirect
12. #34036261C2semidirect
13. #34036229C2semidirect
14. #34036199C2semidirect
15. #463×C293C2semidirect
16. C2×#17989801C22semidirect
17. C2×Q8×D293C22semidirect
22. C2×#17989791C22semidirect
23. C2×#17989791C22semidirect
25. C2×#17989789C22semidirect
26. C2×#17989789C22semidirect
28. C2×#17989787C22semidirect
29. C2×#17989787C22semidirect
30. C2×#17989785C22semidirect
31. C2×C8×D293C22semidirect
35. #22627600C22semidirect
40. #22627595C22semidirect
43. C4×Dic586C22semidirect
46. #22627557C22semidirect
47. #22627547C22semidirect
48. #22627546C22semidirect
49. #22627546C22semidirect
51. #22627536C22semidirect
52. #22627536C22semidirect
53. #22627535C22semidirect
56. #124×C293C22semidirect
58. C4⋊C8×C293C22semidirect
59. #103×C293C22semidirect
60. #102×C293C22semidirect
91. #17989790D4semidirect
136. Dic586C2×D4semidirect
161. #14556873C2×D4semidirect
198. C2×D293AGL(1,ℤ/8)semidirect
218. C293#3265semidirect
227. #463D293semidirect
255. #124C2×D293semidirect
270. C4⋊C8C2×D293semidirect
272. #103C2×D293semidirect
276. #102C2×D293semidirect

Maximal subgroups

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

subgroupindex
C2×#226276482
C2×SD16×D2932
#340367872
D4×D11722
#340365192
#340363782
#340363642
#340363302
#340362782
#340362752
#340362692
#340362612
#340362292
#340361992
#463×C2932
#3265293