Finite Group Databasebeta

← #16830988

Subgroups — #16830988

Order 3712.

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×#11745311C211yesmaximal, characteristic, complemented
2C22×#90784C211yesmaximal, characteristic, complemented
3D4×D116C211yesmaximal, characteristic, complemented
4#14271553C211yesmaximal, characteristic, complemented
5#14271411C211yesmaximal, characteristic, complemented
6#14271397C211yesmaximal, characteristic, complemented
7#14271375C211yesmaximal, characteristic, complemented
8#14271363C211yesmaximal, characteristic, complemented
9#14271313C211yesmaximal, characteristic, complemented
10#14271308C211yesmaximal, characteristic, complemented
11#14271302C211yesmaximal, characteristic, complemented
12#14271296C211yesmaximal, characteristic, complemented
13#14271261C211yesmaximal, characteristic, complemented
14#14271235C211yesmaximal, characteristic, complemented
15C29×#548C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic, complemented
17C22×Q8×C29C2211yescharacteristic, complemented
18C2×D4×D29—21no—
19C22×D116C2211yescharacteristic
20C22×D116C2211yescharacteristic
21C29×#124—21no—
22C29×#124C2211yescharacteristic, complemented
23C29×C22⋊Q8—21no—
24C29×C22⋊Q8C2211yescharacteristic, complemented
25C29×#121—21no—
26C29×#121C2211yescharacteristic, complemented
27C4×Q8×C29C2211yescharacteristic, complemented
28C4×D4×C29—21no—
29C4×D4×C29C2211yescharacteristic
30#11745311—24no—
31C2×#90784—24no—
32C2×#90784C2211yescharacteristic
33C2×#90784C2211yescharacteristic
34C2×#90784C2211yescharacteristic, complemented
35C2×#90784C2211yescharacteristic, complemented
36C2×#90784C2211yescharacteristic, complemented
37C2×#90784C2211yescharacteristic, complemented
38C2×#90782C2211yescharacteristic
39C2×#90782C2211yescharacteristic, complemented
40C2×#90782C2211yescharacteristic, complemented
41#11745292C2211yescharacteristic
42#11745292C2211yescharacteristic
43C2×#90777C2211yescharacteristic, complemented
44C22×#6597C2211yescharacteristic, complemented
45#11745257—21no—
46#11745244—21no—
47#11745244—21no—
48#11745236C2211yescharacteristic
49C4×D116C2211yescharacteristic
50#11745183C2211yescharacteristic, complemented
51#11745183C2211yescharacteristic, complemented
52#11745180C2211yescharacteristic, complemented
53C22⋊#6597C2211yescharacteristic, complemented
54C22⋊#6597C2211yescharacteristic, complemented
55#11745157C2211yescharacteristic
56#11745157C2211yescharacteristic, complemented
57#11745157C2211yescharacteristic, complemented
58#11745155C2211yescharacteristic, complemented
59C4⋊#6597C2211yescharacteristic, complemented
60#11745151C2211yescharacteristic, complemented
61C23×D29—21no—
62C23×D29—21no—
63#41×C29—22no—
64#41×C29—41no—
65C2×Q8×C29—21no—
66C2×Q8×C29—22no—
67C2×Q8×C29—41no—
68C2×Q8×C29C2311yescharacteristic
69C2×Q8×C29C2311yescharacteristic
70C2×D4×C29—21no—
71C2×D4×C29—21no—
72C2×D4×C29D411yescharacteristic
73C2×D4×C29C2311yescharacteristic
74C22×C4×C29—21no—
75C22×C4×C29—21no—
76C22×C4×C29C2311yescharacteristic
77C22×C4×C29C2311yescharacteristic
78C2×C22⋊D29—21no—
79C2×C22⋊D29—21no—
80D4×D29—44no—
81C2×D116—22no—
82C2×D116—22no—
83C2×D116—21no—
84C2×D116—21no—
85C2×D116—21no—
86C2×D116—21no—
87C2×D116—41no—
88C2×D116—41no—
89C2×D116C2311yescharacteristic
90C2×D116C2311yescharacteristic
91C2×D116C2311yescharacteristic
92C2×C4×D29—21no—
93C4⋊C4×C29—21no—
94C4⋊C4×C29—21no—
95C4⋊C4×C29D411yescharacteristic
96C4⋊C4×C29C2311yescharacteristic
97C22⋊C4×C29—21no—
98C22⋊C4×C29—21no—
99C22⋊C4×C29—21no—
100C22⋊C4×C29—21no—
101C22⋊C4×C29D411yescharacteristic
102C22⋊C4×C29D411yescharacteristic
103C42×C29—21no—
104C42×C29C2311yescharacteristic
105#90784—22no—
106#90784—22no—
107#90784—22no—
108#90784—22no—
109#90784—41no—
110#90784D414yescomplemented
111#90782—22no—
112#90782—22no—
113#90782—41no—
114#90781—21no—
115#90781—21no—
116#90781—21no—
117C4⋊Dic29C2311yescharacteristic
118#90777—22no—
119C2×#6597—22no—
120C2×#6597C2311yescharacteristic
121C2×#6597C2311yescharacteristic
122C2×#6597C2311yescharacteristic
123C2×#6597C2311yescharacteristic
124C23×C29—21no—
125C23×C29C2×D411yescharacteristic
126C23×C29C2×D411yescharacteristic
127C22×D29—21no—
128C22×D29—21no—
129C22×D29—21no—
130C22×D29—42no—
131C22×D29—42no—
132C22×D29—42no—
133C22×D29—42no—
134C22×D29—81no—
135C22×D29—81no—
136Q8×C29—21no—
137Q8×C29—21no—
138Q8×C29—21no—
139Q8×C29—42no—
140Q8×C29C2×D412yescomplemented
141D4×C29—22no—
142D4×C29—21no—
143D4×C29—21no—
144D4×C29—42no—
145D4×C29—42no—
146C2×C4×C29—21no—
147C2×C4×C29—21no—
148C2×C4×C29—21no—
149C2×C4×C29—21no—
150C2×C4×C29—21no—
151C2×C4×C29—21no—
152C2×C4×C29—21no—
153C2×C4×C29—42no—
154C2×C4×C29—42no—
155C2×C4×C29C2×D411yescharacteristic
156C2×C4×C29C2×D411yescharacteristic
157C2×C4×C29C2×D411yescharacteristic
158C2×C4×C29C2×D411yescharacteristic
159C2×C4×C29C2411yescharacteristic
160C22⋊D29—42no—
161C22⋊D29—42no—
162C2×Dic29—21no—
163D116—21no—
164D116—21no—
165D116—21no—
166D116—21no—
167D116—21no—
168D116—42no—
169D116—42no—
170D116—42no—
171D116—81no—
172D116C2×D412yes—
173C4×D29—42no—
174#6597—21no—
175#6597—21no—
176#6597—21no—
177#6597C2×D412yescomplemented
178#3265—291nomaximal, Sylow
179C22×C29—21no—
180C22×C29—21no—
181C22×C29—21no—
182C22×C29—21no—
183C22×C29—21no—
184C22×C29—41no—
185C22×C29—41no—
186C22×C29—41no—
187C22×C29AGL(1,ℤ/8)12yescomplemented
188C22×C29C22×D411yescharacteristic
189C2×D29—22no—
190C2×D29—41no—
191C2×D29—41no—
192C2×D29—41no—
193C2×D29—41no—
194C2×D29—41no—
195C2×D29—41no—
196C2×D29—41no—
197C2×D29—41no—
198C2×D29—84no—
199C2×D29—84no—
200C4×C29—21no—
201C4×C29—21no—
202C4×C29—22no—
203C4×C29—21no—
204C4×C29—21no—
205C4×C29—41no—
206C4×C29—41no—
207C4×C29C22×D411yescharacteristic
208C4×C29H(5,𝔽2)11yescharacteristic
209Dic29—41no—
210C2×AGL(1,ℤ/8)—291no—
211C22×SD16—291no—
212#548D2911yescharacteristic, complemented
213D42—291no—
214#496—291no—
215#468—291no—
216#466—291no—
217#463—291no—
218#460—291no—
219#450—291no—
220#449—291no—
221#448—291no—
222#447—291no—
223#440—291no—
224#435—291no—
225C2×C29—22no—
226C2×C29—41no—
227C2×C29—81no—
228C2×C29D4211yescharacteristic
229C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
230C2×C29#57711yescharacteristic
231D29—42no—
232D29—81no—
233D29—81no—
234C2×#41C2×D2911yescharacteristic, complemented
235C22×Q8C2×D2911yescharacteristic, complemented
236C22×D4—291no—
237C22×D4—291no—
238C22×D4—581no—
239AGL(1,ℤ/8)—584no—
240C2×SD16—291no—
241C2×SD16—291no—
242C2×SD16—291no—
243C2×SD16—291no—
244C2×SD16—291no—
245C2×SD16—291no—
246C2×SD16—584no—
247C2×D8—291no—
248C2×D8—291no—
249C2×D8—291no—
250C2×M16—291no—
251C22×C8—291no—
252#127—291no—
253#124—21no—
254#124C2×D2911yescharacteristic, complemented
255C22⋊Q8—21no—
256C22⋊Q8C2×D2911yescharacteristic, complemented
257#121—21no—
258#121—291no—
259#121—291no—
260#121—581no—
261#121C2×D2911yescharacteristic, complemented
262#120—581no—
263#120—581no—
264C4×Q8C2×D2911yescharacteristic, complemented
265C4×D4—21no—
266C4×D4—291no—
267C4×D4C2×D2911yescharacteristic
268#107—291no—
269C4⋊C8—291no—
270#103—291no—
271#103—291no—
272#102—291no—
273#102—291no—
274#102—291no—
275#102—291no—
276C22⋊C8—291no—
277C22⋊C8—291no—
278#97—291no—
279C29#326511yescharacteristic, complemented, Sylow
280C24—581no—
281C24—581no—
282#41—22no—
283#41—41no—
284C2×Q8—21no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×Q8C22×D2911yescharacteristic
288C2×Q8C22×D2911yescharacteristic
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—291no—
292C2×D4—291no—
293C2×D4—291no—
294C2×D4—582no—
295C2×D4—582no—
296C2×D4—581no—
297C2×D4—581no—
298C2×D4—581no—
299C2×D4—581no—
300C2×D4—581no—
301C2×D4—581no—
302C2×D4—1161no—
303C2×D4—1161no—
304C2×D4—1164no—
305C2×D4C22⋊D2911yescharacteristic
306C2×D4C22×D2911yescharacteristic
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—581no—
310C22×C4C22×D2911yescharacteristic
311C22×C4C22×D2911yescharacteristic
312SD16—294no—
313SD16—582no—
314SD16—582no—
315SD16—582no—
316SD16—582no—
317SD16—1161no—
318D8—582no—
319D8—582no—
320D8—1161no—
321M16—582no—
322C2×C8—291no—
323C2×C8—291no—
324C2×C8—291no—
325C2×C8—291no—
326C2×C8—582no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—291no—
330C4⋊C4C22⋊D2911yescharacteristic
331C4⋊C4C22×D2911yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—581no—
337C22⋊C4—581no—
338C22⋊C4—581no—
339C22⋊C4C22⋊D2911yescharacteristic
340C22⋊C4C22⋊D2911yescharacteristic
341C42—21no—
342C42C22×D2911yescharacteristic
343C23—21no—
344C23—581no—
345C23—581no—
346C23—581no—
347C23—1162no—
348C23—1162no—
349C23—1162no—
350C23—1162no—
351C23—2321no—
352C23—2321no—
353C23C2×C22⋊D2911yescharacteristic
354C23C2×C22⋊D2911yescharacteristic
355Q8—21no—
356Q8—21no—
357Q8—21no—
358Q8—42no—
359Q8D4×D2912yescomplemented
360D4—22no—
361D4—21no—
362D4—21no—
363D4—42no—
364D4—42no—
365D4—292no—
366D4—581no—
367D4—581no—
368D4—581no—
369D4—581no—
370D4—581no—
371D4—1162no—
372D4—1162no—
373D4—1162no—
374D4—1162no—
375D4—1162no—
376D4—2321no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—581no—
387C2×C4—1162no—
388C2×C4C2×C22⋊D2911yescharacteristic
389C2×C4C2×C22⋊D2911yescharacteristic
390C2×C4C2×C22⋊D2911yescharacteristic
391C2×C4C2×C22⋊D2911yescharacteristic
392C2×C4C23×D2911yescharacteristic
393C8—292no—
394C8—581no—
395C8—581no—
396C8—581no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—582no—
406C22—1161no—
407C22—1161no—
408C22—1161no—
409C22—1161no—
410C22—1161no—
411C22—1161no—
412C22—1161no—
413C22—1161no—
414C22—2324no—
415C22—2324no—
416C22#1174531112yescomplemented
417C22C22×C22⋊D2911yescharacteristic
418C4—21no—
419C4—21no—
420C4—22no—
421C4—21no—
422C4—21no—
423C4—41no—
424C4—41no—
425C4—1161no—
426C4C2×D4×D2911yescharacteristic
427C4#1174535911yescharacteristic
428C2—22no—
429C2—41no—
430C2—81no—
431C2—1162no—
432C2—2321no—
433C2—2321no—
434C2D4×C22⋊D2911yescharacteristic
435C2C2×#1174531111yescharacteristic
436C2#1427197111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#548C2
socleC22×C29C22×D4
hypercenter#548D29
hypocenterC29#3265
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#11745311C2semidirect
2. C22×#90784C2semidirect
3. D4×D116C2semidirect
4. #14271553C2semidirect
5. #14271411C2semidirect
6. #14271397C2semidirect
7. #14271375C2semidirect
8. #14271363C2semidirect
9. #14271313C2semidirect
10. #14271308C2semidirect
11. #14271302C2semidirect
12. #14271296C2semidirect
13. #14271261C2semidirect
14. #14271235C2semidirect
15. C29×#548C2semidirect
16. C2×#41×C29C22semidirect
17. C22×Q8×C29C22semidirect
22. C29×#124C22semidirect
24. C29×C22⋊Q8C22semidirect
26. C29×#121C22semidirect
27. C4×Q8×C29C22semidirect
34. C2×#90784C22semidirect
35. C2×#90784C22semidirect
36. C2×#90784C22semidirect
37. C2×#90784C22semidirect
39. C2×#90782C22semidirect
40. C2×#90782C22semidirect
43. C2×#90777C22semidirect
44. C22×#6597C22semidirect
50. #11745183C22semidirect
51. #11745183C22semidirect
52. #11745180C22semidirect
53. C22⋊#6597C22semidirect
54. C22⋊#6597C22semidirect
56. #11745157C22semidirect
57. #11745157C22semidirect
58. #11745155C22semidirect
59. C4⋊#6597C22semidirect
60. #11745151C22semidirect
110. #90784D4semidirect
140. Q8×C29C2×D4semidirect
177. #6597C2×D4semidirect
187. C22×C29AGL(1,ℤ/8)semidirect
212. #548D29semidirect
234. C2×#41C2×D29semidirect
235. C22×Q8C2×D29semidirect
254. #124C2×D29semidirect
256. C22⋊Q8C2×D29semidirect
261. #121C2×D29semidirect
264. C4×Q8C2×D29semidirect
279. C29#3265semidirect
359. Q8D4×D29semidirect
416. C22#11745311semidirect

Maximal subgroups

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

subgroupindex
C2×#117453112
C22×#907842
D4×D1162
#142715532
#142714112
#142713972
#142713752
#142713632
#142713132
#142713082
#142713022
#142712962
#142712612
#142712352
C29×#5482
#326529