Finite Group Databasebeta

← #16828993

Subgroups — #16828993

Order 3712.

526 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745276C211yesmaximal, characteristic, complemented
2C2×D8×D29C211yesmaximal, characteristic, complemented
3#14271731C211yesmaximal, characteristic, complemented
4#14271635C211yesmaximal, characteristic, complemented
5#14271381C211yesmaximal, characteristic, complemented
6#14271380C211yesmaximal, characteristic, complemented
7#14271375C211yesmaximal, characteristic, complemented
8#14271359C211yesmaximal, characteristic, complemented
9#14271358C211yesmaximal, characteristic, complemented
10#14271357C211yesmaximal, characteristic, complemented
11#14271356C211yesmaximal, characteristic, complemented
12#14271188C211yesmaximal, characteristic, complemented
13#14271166C211yesmaximal, characteristic, complemented
14#14271158C211yesmaximal, characteristic, complemented
15C29×#463C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C2×D4×D29C2211yescharacteristic
18C2×D4×D29C2211yescharacteristic
19C2×SD16×C29C2211yescharacteristic, complemented
20C2×D8×C29C2211yescharacteristic
21C29×#124C2211yescharacteristic, complemented
22C4×D4×C29C2211yescharacteristic, complemented
23#11745309C2211yescharacteristic, complemented
24C2×#90784C2211yescharacteristic, complemented
25#11745302C2211yescharacteristic, complemented
26D4×Dic29C2211yescharacteristic, complemented
27C2×#90782C2211yescharacteristic
28C2×#90782C2211yescharacteristic
29C2×#90782C2211yescharacteristic, complemented
30C4×C22⋊D29—21no—
31C2×#90781—21no—
32#11745276—24no—
33D8×D29—24no—
34C2×D232C2211yescharacteristic
35C2×D232C2211yescharacteristic, complemented
36C2×#90772C2211yescharacteristic
37C2×C8×D29C2211yescharacteristic
38#11745255C2211yescharacteristic, complemented
39#11745254C2211yescharacteristic
40#11745246—21no—
41#11745246—21no—
42#11745244—21no—
43#11745244—21no—
44#11745243—21no—
45C22⋊C4×D29—21no—
46#11745236C2211yescharacteristic, complemented
47C4×D116C2211yescharacteristic, complemented
48#11745234C2211yescharacteristic
49C29×C4⋊C8C2211yescharacteristic, complemented
50C29×#103C2211yescharacteristic, complemented
51C29×#102C2211yescharacteristic, complemented
52#11745183C2211yescharacteristic, complemented
53#11745180C2211yescharacteristic, complemented
54#11745169C2211yescharacteristic, complemented
55#11745169C2211yescharacteristic, complemented
56#11745162C2211yescharacteristic, complemented
57#11745162C2211yescharacteristic, complemented
58#11745157C2211yescharacteristic, complemented
59#11745157C2211yescharacteristic, complemented
60C4⋊#6597C2211yescharacteristic, complemented
61C23×D29—21no—
62C23×D29—21no—
63C2×Q8×C29C2311yescharacteristic
64C2×D4×C29C2311yescharacteristic
65C2×D4×C29C2311yescharacteristic
66C22×C4×C29—21no—
67C2×C22⋊D29—21no—
68C2×C22⋊D29—21no—
69C2×C22⋊D29—21no—
70C2×C22⋊D29—21no—
71C22×Dic29—21no—
72#90809—22no—
73#90809—22no—
74D4×D29—22no—
75D4×D29—22no—
76D4×D29—22no—
77D4×D29D414yescomplemented
78C2×D116—21no—
79C2×D116—21no—
80C2×D116—21no—
81C2×D116C2311yescharacteristic
82C2×D116C2311yescharacteristic
83C2×D116C2311yescharacteristic
84C2×C4×D29—21no—
85C2×C4×D29—21no—
86C2×C4×D29—21no—
87C2×C4×D29C2311yescharacteristic
88SD16×C29—22no—
89D8×C29—22no—
90C2×C8×C29C2311yescharacteristic
91C2×C8×C29C2311yescharacteristic
92C4⋊C4×C29C2311yescharacteristic
93C22⋊C4×C29—21no—
94C22⋊C4×C29—21no—
95C22⋊C4×C29—21no—
96C42×C29C2311yescharacteristic
97C22⋊Dic29—21no—
98#90784—22no—
99#90782—22no—
100#90782—22no—
101#90782—22no—
102#90781—21no—
103#90781—21no—
104#90781—21no—
105#90781—21no—
106#90781—21no—
107#90781D411yescharacteristic
108#90781D411yescharacteristic
109C4⋊Dic29C2311yescharacteristic
110#90779D411yescharacteristic
111#90779D411yescharacteristic
112C4×Dic29—21no—
113C4×Dic29C2311yescharacteristic
114C2×#6597C2311yescharacteristic
115C2×#6597C2311yescharacteristic
116D232—22no—
117D232—22no—
118#90772—22no—
119C8×D29—22no—
120C23×C29—21no—
121C23×C29—21no—
122C22×D29—21no—
123C22×D29—24no—
124C22×D29—21no—
125C22×D29—21no—
126C22×D29—42no—
127C22×D29—81no—
128C22×D29—81no—
129C22×D29—81no—
130C22×D29—81no—
131C22×D29C2×D411yescharacteristic
132Q8×C29—21no—
133Q8×C29—21no—
134D4×C29—21no—
135D4×C29—21no—
136D4×C29—21no—
137D4×C29C2×D412yes—
138C2×C4×C29—21no—
139C2×C4×C29—21no—
140C2×C4×C29—81no—
141C2×C4×C29C2×D411yescharacteristic
142C2×C4×C29C2×D411yescharacteristic
143C2×C4×C29C2411yescharacteristic
144C22⋊D29—24no—
145C22⋊D29—42no—
146C22⋊D29—81no—
147C22⋊D29—81no—
148C2×Dic29—21no—
149C2×Dic29—81no—
150C2×Dic29C2×D411yescharacteristic
151C2×Dic29C2×D411yescharacteristic
152C2×Dic29C2×D411yescharacteristic
153D116—21no—
154D116—21no—
155D116—21no—
156D116—21no—
157D116—21no—
158D116—42no—
159D116—81no—
160D116—81no—
161D116C2×D412yes—
162C4×D29—42no—
163C4×D29—81no—
164C4×D29—81no—
165C4×D29C2×D412yes—
166C4×D29#4112yes—
167C8×C29—21no—
168C8×C29—21no—
169#6597—21no—
170#6597—21no—
171#3041—291nomaximal, Sylow
172C22×C29—22no—
173C22×C29—41no—
174C22×C29—41no—
175C22×C29—41no—
176C22×C29—41no—
177C22×C29—41no—
178C22×C29C22×D411yescharacteristic
179C2×D29—21no—
180C2×D29—21no—
181C2×D29—22no—
182C2×D29—41no—
183C2×D29—41no—
184C2×D29—41no—
185C2×D29—41no—
186C2×D29—41no—
187C2×D29—41no—
188C2×D29—41no—
189C2×D29—41no—
190C2×D29—84no—
191C2×D29—84no—
192C2×D29#12112yes—
193C4×C29—21no—
194C4×C29—21no—
195C4×C29—41no—
196C4×C29—41no—
197C4×C29C22×D411yescharacteristic
198C4×C29C2×#4111yescharacteristic
199Dic29—21no—
200Dic29—21no—
201Dic29—41no—
202Dic29#12112yes—
203C2×AGL(1,ℤ/8)—291no—
204C22×D8—291no—
205#535—291no—
206#518—291no—
207#463—291no—
208#463—291no—
209#463—291no—
210#463D2911yescharacteristic, complemented
211#459—291no—
212#459—291no—
213#459—291no—
214#459—291no—
215#424—291no—
216#418—291no—
217#416—291no—
218C2×C29—42no—
219C2×C29—81no—
220C2×C29C2×#12111yescharacteristic
221C2×C29#57611yescharacteristic
222C2×C29#57611yescharacteristic
223D29—22no—
224D29—42no—
225D29—81no—
226D29—81no—
227C2×#41—291no—
228C22×D4—291no—
229C22×D4—291no—
230AGL(1,ℤ/8)—584no—
231C2×SD16—291no—
232C2×SD16C2×D2911yescharacteristic, complemented
233C2×D8—291no—
234C2×D8—291no—
235C2×D8—291no—
236C2×D8—291no—
237C2×D8—291no—
238C2×D8—584no—
239C2×D8C2×D2911yescharacteristic
240C2×M16—291no—
241C22×C8—291no—
242#127—291no—
243#127—291no—
244#124—291no—
245#124C2×D2911yescharacteristic, complemented
246#121—581no—
247#121—581no—
248#120—581no—
249#120—581no—
250C4×D4—291no—
251C4×D4—291no—
252C4×D4—291no—
253C4×D4—581no—
254C4×D4—581no—
255C4×D4C2×D2911yescharacteristic, complemented
256#117—291no—
257#117—291no—
258C2×C22⋊C4—581no—
259C2×C22⋊C4—581no—
260C4⋊C8—291no—
261C4⋊C8—291no—
262C4⋊C8—291no—
263C4⋊C8C2×D2911yescharacteristic, complemented
264#103—291no—
265#103C2×D2911yescharacteristic, complemented
266#102—291no—
267#102—291no—
268#102—291no—
269#102—291no—
270#102—291no—
271#102C2×D2911yescharacteristic, complemented
272C29#304111yescharacteristic, complemented, Sylow
273C24—581no—
274C24—581no—
275#41—582no—
276#41—582no—
277C2×Q8C22×D2911yescharacteristic
278C2×D4—294no—
279C2×D4—291no—
280C2×D4—291no—
281C2×D4—291no—
282C2×D4—581no—
283C2×D4—582no—
284C2×D4—582no—
285C2×D4—582no—
286C2×D4—581no—
287C2×D4—581no—
288C2×D4—581no—
289C2×D4—581no—
290C2×D4—581no—
291C2×D4—581no—
292C2×D4C22×D2911yescharacteristic
293C2×D4C22×D2911yescharacteristic
294C22×C4—21no—
295C22×C4—291no—
296C22×C4—581no—
297C22×C4—581no—
298C22×C4—581no—
299C22×C4—581no—
300SD16—22no—
301SD16—582no—
302D8—22no—
303D8—582no—
304D8—582no—
305D8—582no—
306D8—582no—
307D8—582no—
308M16—582no—
309C2×C8—291no—
310C2×C8—291no—
311C2×C8—582no—
312C2×C8C22×D2911yescharacteristic
313C2×C8C22×D2911yescharacteristic
314C4⋊C4—291no—
315C4⋊C4—291no—
316C4⋊C4—291no—
317C4⋊C4C22×D2911yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—291no—
322C22⋊C4—291no—
323C22⋊C4—581no—
324C22⋊C4—581no—
325C22⋊C4—581no—
326C22⋊C4—581no—
327C22⋊C4—581no—
328C22⋊C4—581no—
329C42—291no—
330C42—581no—
331C42C22×D2911yescharacteristic
332C23—21no—
333C23—21no—
334C23—291no—
335C23—584no—
336C23—581no—
337C23—581no—
338C23—581no—
339C23—1162no—
340C23—2321no—
341C23—2321no—
342C23—2321no—
343C23—2321no—
344Q8—21no—
345Q8—21no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—292no—
350D4—584no—
351D4—581no—
352D4—581no—
353D4—581no—
354D4—581no—
355D4—581no—
356D4—1162no—
357D4—1162no—
358D4—2321no—
359D4—2321no—
360D4—2321no—
361D4—2321no—
362D4D4×D2912yes—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—81no—
366C2×C4—291no—
367C2×C4—292no—
368C2×C4—292no—
369C2×C4—291no—
370C2×C4—291no—
371C2×C4—581no—
372C2×C4—1162no—
373C2×C4—2321no—
374C2×C4—2321no—
375C2×C4—2321no—
376C2×C4D4×D2911yescharacteristic
377C2×C4D4×D2911yescharacteristic
378C2×C4C23×D2911yescharacteristic
379C8—21no—
380C8—21no—
381C8—581no—
382C8—581no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—292no—
390C22—581no—
391C22—581no—
392C22—582no—
393C22—1161no—
394C22—1161no—
395C22—1161no—
396C22—1161no—
397C22—1161no—
398C22—1161no—
399C22—1161no—
400C22—1161no—
401C22—2324no—
402C22—2324no—
403C22C2×D4×D2911yescharacteristic
404C4—21no—
405C4—21no—
406C4—41no—
407C4—41no—
408C4—292no—
409C4—581no—
410C4—581no—
411C4—1161no—
412C4C2×D4×D2911yescharacteristic
413C4#41×D2911yescharacteristic
414C2—42no—
415C2—81no—
416C2—582no—
417C2—1162no—
418C2—2321no—
419C2—2321no—
420C2#121×D2911yescharacteristic
421C2#1427196511yescharacteristic
422C2#1427196711yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#463C2
socleC22×C29C22×D4
hypercenter#463D29
hypocenterC29#3041
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#11745276C2semidirect
2. C2×D8×D29C2semidirect
3. #14271731C2semidirect
4. #14271635C2semidirect
5. #14271381C2semidirect
6. #14271380C2semidirect
7. #14271375C2semidirect
8. #14271359C2semidirect
9. #14271358C2semidirect
10. #14271357C2semidirect
11. #14271356C2semidirect
12. #14271188C2semidirect
13. #14271166C2semidirect
14. #14271158C2semidirect
15. C29×#463C2semidirect
19. C2×SD16×C29C22semidirect
21. C29×#124C22semidirect
22. C4×D4×C29C22semidirect
23. #11745309C22semidirect
24. C2×#90784C22semidirect
25. #11745302C22semidirect
26. D4×Dic29C22semidirect
29. C2×#90782C22semidirect
35. C2×D232C22semidirect
38. #11745255C22semidirect
46. #11745236C22semidirect
47. C4×D116C22semidirect
49. C29×C4⋊C8C22semidirect
50. C29×#103C22semidirect
51. C29×#102C22semidirect
52. #11745183C22semidirect
53. #11745180C22semidirect
54. #11745169C22semidirect
55. #11745169C22semidirect
56. #11745162C22semidirect
57. #11745162C22semidirect
58. #11745157C22semidirect
59. #11745157C22semidirect
60. C4⋊#6597C22semidirect
77. D4×D29D4semidirect
210. #463D29semidirect
232. C2×SD16C2×D29semidirect
245. #124C2×D29semidirect
255. C4×D4C2×D29semidirect
263. C4⋊C8C2×D29semidirect
265. #103C2×D29semidirect
271. #102C2×D29semidirect
272. C29#3041semidirect

Maximal subgroups

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

subgroupindex
C2×#117452762
C2×D8×D292
#142717312
#142716352
#142713812
#142713802
#142713752
#142713592
#142713582
#142713572
#142713562
#142711882
#142711662
#142711582
C29×#4632
#304129