Finite Group Databasebeta

← #16831098

Subgroups — #16831098

Order 3712.

520 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745276C211yesmaximal, characteristic, complemented
2C2×#11745273C211yesmaximal, characteristic, complemented
3#14271808C211yesmaximal, characteristic, complemented
4#14271806C211yesmaximal, characteristic, complemented
5#14271545C211yesmaximal, characteristic, complemented
6#14271412C211yesmaximal, characteristic, complemented
7#14271408C211yesmaximal, characteristic, complemented
8#14271379C211yesmaximal, characteristic, complemented
9#14271328C211yesmaximal, characteristic, complemented
10#14271322C211yesmaximal, characteristic, complemented
11#14271298C211yesmaximal, characteristic, complemented
12#14271295C211yesmaximal, characteristic, complemented
13C4×#90782C211yesmaximal, characteristic, complemented
14#14271240C211yesmaximal, characteristic, complemented
15C29×#463C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C2×#90807C2211yescharacteristic
18C2×D4×D29C2211yescharacteristic, complemented
19C2×D4×D29C2211yescharacteristic, complemented
20C2×SD16×C29C2211yescharacteristic, complemented
21C2×D8×C29C2211yescharacteristic
22C29×#124C2211yescharacteristic, complemented
23C4×D4×C29C2211yescharacteristic, complemented
24#11745308C2211yescharacteristic, complemented
25C2×#90785C2211yescharacteristic, complemented
26C2×#90784C2211yescharacteristic, complemented
27#11745300C2211yescharacteristic
28C2×#90783C2211yescharacteristic, complemented
29C2×#90782C2211yescharacteristic
30C2×#90782C2211yescharacteristic
31#11745292—21no—
32C2×#90781—21no—
33#11745276—24no—
34#11745273—24no—
35C2×D232C2211yescharacteristic
36C2×#90773C2211yescharacteristic, complemented
37C2×#90772C2211yescharacteristic, complemented
38C2×#90772C2211yescharacteristic, complemented
39#11745259C2211yescharacteristic, complemented
40#11745257C2211yescharacteristic
41#11745248—21no—
42#11745246—21no—
43#11745245—21no—
44#11745244—21no—
45#11745244—21no—
46C22⋊C4×D29—21no—
47#11745237C2211yescharacteristic, complemented
48C4×D116C2211yescharacteristic
49C4×D116C2211yescharacteristic, complemented
50C29×C4⋊C8C2211yescharacteristic, complemented
51C29×#103C2211yescharacteristic, complemented
52C29×#102C2211yescharacteristic, complemented
53#11745180C2211yescharacteristic, complemented
54#11745169C2211yescharacteristic, complemented
55#11745168C2211yescharacteristic, complemented
56#11745168C2211yescharacteristic, complemented
57#11745164C2211yescharacteristic, complemented
58#11745157C2211yescharacteristic, complemented
59#11745155C2211yescharacteristic, 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—41no—
74#90807—22no—
75#90807—41no—
76D4×D29—22no—
77D4×D29—22no—
78D4×D29—41no—
79D4×D29—41no—
80C2×D116—21no—
81C2×D116—21no—
82C2×D116D411yescharacteristic
83C2×D116C2311yescharacteristic
84C2×D116C2311yescharacteristic
85C2×C4×D29—21no—
86C2×C4×D29—21no—
87C2×C4×D29C2311yescharacteristic
88C2×C4×D29C2311yescharacteristic
89C2×Dic58C2311yescharacteristic
90SD16×C29—22no—
91D8×C29—22no—
92C2×C8×C29C2311yescharacteristic
93C2×C8×C29C2311yescharacteristic
94C4⋊C4×C29C2311yescharacteristic
95C22⋊C4×C29—21no—
96C22⋊C4×C29—21no—
97C22⋊C4×C29—21no—
98C42×C29C2311yescharacteristic
99C22⋊Dic29—21no—
100#90785—41no—
101#90784—22no—
102#90783—22no—
103#90782—41no—
104#90782D414yescomplemented
105#90781—21no—
106#90781—21no—
107#90781—21no—
108#90781—21no—
109#90781—21no—
110#90781—21no—
111#90781D411yescharacteristic
112#90781D411yescharacteristic
113C4⋊Dic29—21no—
114C4⋊Dic29D411yescharacteristic
115C4⋊Dic29C2311yescharacteristic
116#90779—21no—
117C2×#6597C2311yescharacteristic
118C2×#6597C2311yescharacteristic
119D232—22no—
120#90773—22no—
121#90772—22no—
122#90772—22no—
123C23×C29—21no—
124C23×C29—21no—
125C22×D29—21no—
126C22×D29—21no—
127C22×D29—42no—
128C22×D29—42no—
129C22×D29—42no—
130C22×D29—42no—
131C22×D29—81no—
132C22×D29—81no—
133C22×D29C2×D411yescharacteristic
134C22×D29C2×D411yescharacteristic
135Q8×C29—21no—
136Q8×C29—21no—
137D4×C29—21no—
138D4×C29—21no—
139D4×C29—21no—
140D4×C29C2×D412yes—
141C2×C4×C29—21no—
142C2×C4×C29—21no—
143C2×C4×C29—81no—
144C2×C4×C29C2×D411yescharacteristic
145C2×C4×C29C2×D411yescharacteristic
146C2×C4×C29C2411yescharacteristic
147C22⋊D29—42no—
148C22⋊D29—42no—
149C22⋊D29—42no—
150C22⋊D29—81no—
151C2×Dic29—21no—
152C2×Dic29—21no—
153C2×Dic29—42no—
154C2×Dic29C2×D411yescharacteristic
155C2×Dic29C2×D411yescharacteristic
156D116—21no—
157D116—21no—
158D116—21no—
159D116—41no—
160D116—42no—
161D116—81no—
162D116C2×D412yes—
163C4×D29—21no—
164C4×D29—21no—
165C4×D29—21no—
166C4×D29—21no—
167C4×D29—42no—
168C4×D29—81no—
169Dic58—21no—
170Dic58—21no—
171C8×C29—21no—
172C8×C29—21no—
173#6597—21no—
174#6597C2×D412yes—
175#3273—291nomaximal, Sylow
176C22×C29—22no—
177C22×C29—41no—
178C22×C29—41no—
179C22×C29—41no—
180C22×C29—41no—
181C22×C29—41no—
182C22×C29C22×D411yescharacteristic
183C2×D29—21no—
184C2×D29—21no—
185C2×D29—22no—
186C2×D29—21no—
187C2×D29—21no—
188C2×D29—21no—
189C2×D29—21no—
190C2×D29—41no—
191C2×D29—41no—
192C2×D29—41no—
193C2×D29—41no—
194C2×D29—41no—
195C2×D29—84no—
196C2×D29—84no—
197C4×C29—21no—
198C4×C29—21no—
199C4×C29—41no—
200C4×C29—41no—
201C4×C29C22×D411yescharacteristic
202C4×C29H(5,𝔽2)11yescharacteristic
203Dic29—21no—
204Dic29—21no—
205Dic29—41no—
206Dic29—41no—
207C2×AGL(1,ℤ/8)—291no—
208C2×AGL(1,ℤ/8)—291no—
209#546—291no—
210#546—291no—
211#495—291no—
212#468—291no—
213#468—291no—
214#463—291no—
215#463D2911yescharacteristic, complemented
216#452—291no—
217#452—291no—
218#447—291no—
219#447—291no—
220C4×D8—291no—
221#436—291no—
222C2×C29—42no—
223C2×C29—81no—
224C2×C29D4211yescharacteristic
225C2×C29#57511yescharacteristic
226C2×C29#57611yescharacteristic
227D29—41no—
228D29—41no—
229D29—42no—
230D29—81no—
231C2×#41—291no—
232C2×#41—291no—
233C22×D4—291no—
234C22×D4—291no—
235AGL(1,ℤ/8)—584no—
236AGL(1,ℤ/8)—584no—
237C2×Q16—291no—
238C2×SD16—291no—
239C2×SD16—291no—
240C2×SD16—291no—
241C2×SD16C2×D2911yescharacteristic, complemented
242C2×D8—291no—
243C2×D8—291no—
244C2×D8—291no—
245C2×D8C2×D2911yescharacteristic
246C2×M16—291no—
247C2×M16—291no—
248#124—291no—
249#124C2×D2911yescharacteristic, complemented
250#123—581no—
251#123—581no—
252C22⋊Q8—291no—
253C22⋊Q8—291no—
254#121—291no—
255#121—291no—
256#121—581no—
257#121—581no—
258#120—581no—
259#120—581no—
260C4×D4—291no—
261C4×D4—291no—
262C4×D4C2×D2911yescharacteristic, complemented
263C2×C22⋊C4—581no—
264C2×C22⋊C4—581no—
265#107—291no—
266C4⋊C8C2×D2911yescharacteristic, complemented
267#103—291no—
268#103C2×D2911yescharacteristic, complemented
269#102—291no—
270#102—291no—
271#102—291no—
272#102C2×D2911yescharacteristic, complemented
273C22⋊C8—291no—
274C22⋊C8—291no—
275C4×C8—291no—
276C29#327311yescharacteristic, complemented, Sylow
277C24—581no—
278C24—581no—
279#41—582no—
280#41—582no—
281#41—1161no—
282#41—1161no—
283C2×Q8—291no—
284C2×Q8C22×D2911yescharacteristic
285C2×D4—291no—
286C2×D4—291no—
287C2×D4—291no—
288C2×D4—581no—
289C2×D4—581no—
290C2×D4—581no—
291C2×D4—581no—
292C2×D4—582no—
293C2×D4—582no—
294C2×D4—581no—
295C2×D4—581no—
296C2×D4—1161no—
297C2×D4—1161no—
298C2×D4C22×D2911yescharacteristic
299C2×D4C22×D2911yescharacteristic
300C22×C4—21no—
301C22×C4—291no—
302C22×C4—291no—
303C22×C4—581no—
304C22×C4—581no—
305C22×C4—581no—
306Q16—1161no—
307SD16—22no—
308SD16—582no—
309SD16—582no—
310SD16—582no—
311D8—22no—
312D8—294no—
313D8—582no—
314D8—1161no—
315M16—582no—
316M16—582no—
317C2×C8—291no—
318C2×C8—291no—
319C2×C8C22×D2911yescharacteristic
320C2×C8C22×D2911yescharacteristic
321C4⋊C4—291no—
322C4⋊C4—291no—
323C4⋊C4—581no—
324C4⋊C4—581no—
325C4⋊C4C22×D2911yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—291no—
330C22⋊C4—291no—
331C22⋊C4—581no—
332C22⋊C4—581no—
333C22⋊C4—581no—
334C22⋊C4—581no—
335C22⋊C4—581no—
336C22⋊C4—581no—
337C22⋊C4—581no—
338C42C22×D2911yescharacteristic
339C23—21no—
340C23—21no—
341C23—291no—
342C23—291no—
343C23—581no—
344C23—581no—
345C23—1162no—
346C23—1162no—
347C23—1162no—
348C23—1162no—
349C23—2321no—
350C23—2321no—
351Q8—21no—
352Q8—21no—
353Q8—581no—
354Q8—581no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—292no—
359D4—581no—
360D4—581no—
361D4—581no—
362D4—1161no—
363D4—1162no—
364D4—1162no—
365D4—1162no—
366D4—1162no—
367D4—2321no—
368D4—2321no—
369D4D4×D2912yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—291no—
374C2×C4—291no—
375C2×C4—581no—
376C2×C4—581no—
377C2×C4—581no—
378C2×C4—581no—
379C2×C4—581no—
380C2×C4—581no—
381C2×C4—1162no—
382C2×C4—1162no—
383C2×C4—2321no—
384C2×C4D4×D2911yescharacteristic
385C2×C4D4×D2911yescharacteristic
386C2×C4C23×D2911yescharacteristic
387C8—21no—
388C8—21no—
389C8—292no—
390C8—581no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—581no—
398C22—581no—
399C22—582no—
400C22—581no—
401C22—581no—
402C22—581no—
403C22—581no—
404C22—1161no—
405C22—1161no—
406C22—1161no—
407C22—1161no—
408C22—1161no—
409C22—2324no—
410C22—2324no—
411C22C2×D4×D2911yescharacteristic
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—581no—
417C4—581no—
418C4—1161no—
419C4—1161no—
420C4C2×D4×D2911yescharacteristic
421C4#1174536411yescharacteristic
422C2—42no—
423C2—81no—
424C2—1161no—
425C2—1161no—
426C2—1162no—
427C2—2321no—
428C2#1427179711yescharacteristic
429C2#1427196011yescharacteristic
430C2#1427196711yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#463C2
socleC22×C29C22×D4
hypercenter#463D29
hypocenterC29#3273
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×#11745273C2semidirect
3. #14271808C2semidirect
4. #14271806C2semidirect
5. #14271545C2semidirect
6. #14271412C2semidirect
7. #14271408C2semidirect
8. #14271379C2semidirect
9. #14271328C2semidirect
10. #14271322C2semidirect
11. #14271298C2semidirect
12. #14271295C2semidirect
13. C4×#90782C2semidirect
14. #14271240C2semidirect
15. C29×#463C2semidirect
18. C2×D4×D29C22semidirect
19. C2×D4×D29C22semidirect
20. C2×SD16×C29C22semidirect
22. C29×#124C22semidirect
23. C4×D4×C29C22semidirect
24. #11745308C22semidirect
25. C2×#90785C22semidirect
26. C2×#90784C22semidirect
28. C2×#90783C22semidirect
36. C2×#90773C22semidirect
37. C2×#90772C22semidirect
38. C2×#90772C22semidirect
39. #11745259C22semidirect
47. #11745237C22semidirect
49. C4×D116C22semidirect
50. C29×C4⋊C8C22semidirect
51. C29×#103C22semidirect
52. C29×#102C22semidirect
53. #11745180C22semidirect
54. #11745169C22semidirect
55. #11745168C22semidirect
56. #11745168C22semidirect
57. #11745164C22semidirect
58. #11745157C22semidirect
59. #11745155C22semidirect
60. C4×#6597C22semidirect
104. #90782D4semidirect
215. #463D29semidirect
241. C2×SD16C2×D29semidirect
249. #124C2×D29semidirect
262. C4×D4C2×D29semidirect
266. C4⋊C8C2×D29semidirect
268. #103C2×D29semidirect
272. #102C2×D29semidirect
276. C29#3273semidirect

Maximal subgroups

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

subgroupindex
C2×#117452762
C2×#117452732
#142718082
#142718062
#142715452
#142714122
#142714082
#142713792
#142713282
#142713222
#142712982
#142712952
C4×#907822
#142712402
C29×#4632
#327329