Finite Group Databasebeta

← #16831035

Subgroups — #16831035

Order 3712.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745311C211yesmaximal, characteristic, complemented
2C2×#11745281C211yesmaximal, characteristic, complemented
3#14271832C211yesmaximal, characteristic, complemented
4#14271804C211yesmaximal, characteristic, complemented
5#14271549C211yesmaximal, characteristic, complemented
6#14271411C211yesmaximal, characteristic, complemented
7#14271398C211yesmaximal, characteristic, complemented
8#14271387C211yesmaximal, characteristic, complemented
9#14271357C211yesmaximal, characteristic, complemented
10#14271311C211yesmaximal, characteristic, complemented
11#14271307C211yesmaximal, characteristic, complemented
12#14271299C211yesmaximal, characteristic, complemented
13#14271266C211yesmaximal, characteristic, complemented
14#14271237C211yesmaximal, characteristic, complemented
15C29×#452C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C2×#90809C2211yescharacteristic
18C2×#90809C2211yescharacteristic, complemented
19C22×D116C2211yescharacteristic
20C2×Q16×C29C2211yescharacteristic, complemented
21C2×SD16×C29C2211yescharacteristic, complemented
22C29×C22⋊Q8C2211yescharacteristic
23#11745311—24no—
24#11745309C2211yescharacteristic
25Q8×Dic29C2211yescharacteristic, complemented
26C2×#90784C2211yescharacteristic
27C2×#90784C2211yescharacteristic
28C2×#90784C2211yescharacteristic, complemented
29#11745302—21no—
30#11745302C2211yescharacteristic, complemented
31#11745300—21no—
32#11745300C2211yescharacteristic, complemented
33C2×#90782C2211yescharacteristic
34C2×#90782C2211yescharacteristic
35#11745292—21no—
36#11745292C2211yescharacteristic
37C4×C22⋊D29—21no—
38C4×C22⋊D29C2211yescharacteristic
39C2×#90777C2211yescharacteristic
40#11745281—24no—
41C2×D232C2211yescharacteristic
42C2×D232C2211yescharacteristic
43C2×C8×D29C2211yescharacteristic, complemented
44#11745257—21no—
45#11745257C2211yescharacteristic
46#11745256—21no—
47#11745255C2211yescharacteristic
48#11745244—21no—
49C22⋊C4×D29—21no—
50C29×#103C2211yescharacteristic, complemented
51C29×#102C2211yescharacteristic, complemented
52C29×C22⋊C8C2211yescharacteristic
53#11745183C2211yescharacteristic, complemented
54#11745169C2211yescharacteristic
55#11745169C2211yescharacteristic
56#11745168C2211yescharacteristic, complemented
57#11745163C2211yescharacteristic, complemented
58#11745162C2211yescharacteristic, complemented
59#11745157C2211yescharacteristic, complemented
60#11745155C2211yescharacteristic, complemented
61C23×D29—21no—
62#41×C29—22no—
63#41×C29—41no—
64C2×Q8×C29C2311yescharacteristic
65C2×Q8×C29C2311yescharacteristic
66C2×D4×C29—21no—
67C2×D4×C29C2311yescharacteristic
68C22×C4×C29—21no—
69C22×C4×C29C2311yescharacteristic
70C2×C22⋊D29—21no—
71C2×C22⋊D29—21no—
72C2×C22⋊D29—21no—
73C2×C22⋊D29—21no—
74C2×C22⋊D29D411yescharacteristic
75#90809—22no—
76#90809—22no—
77#90809—41no—
78#90809—41no—
79C2×D116—22no—
80C2×D116—21no—
81C2×D116—21no—
82C2×D116—21no—
83C2×D116—21no—
84C2×D116—41no—
85C2×D116C2311yescharacteristic
86C2×D116C2311yescharacteristic
87C2×D116C2311yescharacteristic
88C2×C4×D29—21no—
89C2×C4×D29—21no—
90C2×C4×D29—21no—
91C2×C4×D29C2311yescharacteristic
92Q16×C29—22no—
93SD16×C29—41no—
94C2×C8×C29C2311yescharacteristic
95C2×C8×C29C2311yescharacteristic
96C4⋊C4×C29—21no—
97C4⋊C4×C29C2311yescharacteristic
98C22⋊C4×C29—21no—
99C22⋊Dic29—21no—
100C22⋊Dic29D411yescharacteristic
101#90784—22no—
102#90784—22no—
103#90784D414yescomplemented
104#90782—22no—
105#90782—22no—
106#90781—21no—
107#90781—21no—
108#90781—21no—
109#90781—21no—
110#90781—21no—
111#90781D411yescharacteristic
112C4⋊Dic29—21no—
113C4⋊Dic29C2311yescharacteristic
114#90779D411yescharacteristic
115C4×Dic29—21no—
116C4×Dic29C2311yescharacteristic
117#90777—22no—
118C2×#6597C2311yescharacteristic
119C2×#6597C2311yescharacteristic
120D232—22no—
121D232—41no—
122C8×D29—22no—
123C23×C29—21no—
124C23×C29C2×D411yescharacteristic
125C22×D29—21no—
126C22×D29—21no—
127C22×D29—21no—
128C22×D29—42no—
129C22×D29—42no—
130C22×D29—81no—
131C22×D29C2×D411yescharacteristic
132Q8×C29—21no—
133Q8×C29—21no—
134Q8×C29—21no—
135Q8×C29C2×D412yes—
136D4×C29—21no—
137D4×C29—21no—
138D4×C29—42no—
139C2×C4×C29—21no—
140C2×C4×C29—21no—
141C2×C4×C29—21no—
142C2×C4×C29—21no—
143C2×C4×C29—21no—
144C2×C4×C29—42no—
145C2×C4×C29C2×D411yescharacteristic
146C2×C4×C29C2411yescharacteristic
147C22⋊D29—41no—
148C22⋊D29—42no—
149C22⋊D29—81no—
150C22⋊D29—81no—
151C22⋊D29—81no—
152C2×Dic29—21no—
153C2×Dic29C2×D411yescharacteristic
154C2×Dic29C2×D411yescharacteristic
155C2×Dic29C2×D411yescharacteristic
156D116—21no—
157D116—21no—
158D116—21no—
159D116—21no—
160D116—21no—
161D116—42no—
162D116—42no—
163D116—42no—
164D116—81no—
165D116C2×D412yes—
166C4×D29—21no—
167C4×D29—21no—
168C4×D29—42no—
169C4×D29—42no—
170C4×D29—81no—
171C8×C29—21no—
172C8×C29—21no—
173#6597—21no—
174#6597C2×D412yes—
175#3268—291nomaximal, Sylow
176C22×C29—21no—
177C22×C29—21no—
178C22×C29—21no—
179C22×C29—41no—
180C22×C29—41no—
181C22×C29—41no—
182C22×C29C22×D411yescharacteristic
183C2×D29—21no—
184C2×D29—22no—
185C2×D29—21no—
186C2×D29—21no—
187C2×D29—41no—
188C2×D29—41no—
189C2×D29—41no—
190C2×D29—41no—
191C2×D29—41no—
192C2×D29—41no—
193C2×D29—41no—
194C2×D29—41no—
195C2×D29—84no—
196C4×C29—22no—
197C4×C29—21no—
198C4×C29—41no—
199C4×C29—41no—
200C4×C29C22×D411yescharacteristic
201C4×C29H(5,𝔽2)11yescharacteristic
202Dic29—21no—
203Dic29—21no—
204Dic29—21no—
205Dic29—41no—
206C2×AGL(1,ℤ/8)—291no—
207C2×#135—291no—
208#550—291no—
209#546—291no—
210#496—291no—
211#468—291no—
212#466—291no—
213#464—291no—
214#459—291no—
215#452D2911yescharacteristic, complemented
216#449—291no—
217#449—291no—
218#447—291no—
219#440—291no—
220#435—291no—
221C2×C29—41no—
222C2×C29—81no—
223C2×C29D4211yescharacteristic
224C2×C29#57511yescharacteristic
225C2×C29#57611yescharacteristic
226D29—41no—
227D29—42no—
228D29—81no—
229D29—81no—
230C2×#41—291no—
231C2×#41—291no—
232C2×#41C2×D2911yescharacteristic
233C22×D4—291no—
234AGL(1,ℤ/8)—584no—
235#135—584no—
236C2×Q16C2×D2911yescharacteristic, complemented
237C2×SD16—291no—
238C2×SD16—291no—
239C2×SD16—291no—
240C2×SD16C2×D2911yescharacteristic, complemented
241C2×D8—291no—
242C2×D8—291no—
243C2×D8—291no—
244C2×D8—291no—
245C2×M16—291no—
246C22×C8—291no—
247#127—291no—
248#127—581no—
249#124—291no—
250#123—581no—
251C22⋊Q8C2×D2911yescharacteristic
252#121—291no—
253#121—291no—
254#121—291no—
255#121—581no—
256#121—581no—
257#121—581no—
258#120—581no—
259C4×Q8—291no—
260C4×D4—291no—
261C4×D4—291no—
262C4×D4—581no—
263C2×C22⋊C4—581no—
264#107—291no—
265C4⋊C8—291no—
266#103—291no—
267#103C2×D2911yescharacteristic, complemented
268#102—291no—
269#102—291no—
270#102—291no—
271#102C2×D2911yescharacteristic, complemented
272C22⋊C8—291no—
273C22⋊C8C2×D2911yescharacteristic
274#97—291no—
275C29#326811yescharacteristic, complemented, Sylow
276C24—581no—
277#41—22no—
278#41—41no—
279#41—582no—
280#41—582no—
281#41—1161no—
282#41—1161no—
283C2×Q8C22×D2911yescharacteristic
284C2×Q8C22×D2911yescharacteristic
285C2×D4—21no—
286C2×D4—291no—
287C2×D4—291no—
288C2×D4—291no—
289C2×D4—291no—
290C2×D4—582no—
291C2×D4—581no—
292C2×D4—581no—
293C2×D4—581no—
294C2×D4—581no—
295C2×D4—581no—
296C2×D4—581no—
297C2×D4—581no—
298C2×D4—581no—
299C2×D4—1161no—
300C2×D4C22×D2911yescharacteristic
301C22×C4—21no—
302C22×C4—291no—
303C22×C4—581no—
304C22×C4—581no—
305C22×C4—581no—
306C22×C4C22×D2911yescharacteristic
307Q16—22no—
308SD16—41no—
309SD16—294no—
310SD16—582no—
311SD16—582no—
312D8—582no—
313D8—582no—
314D8—582no—
315D8—1161no—
316M16—582no—
317C2×C8—291no—
318C2×C8—291no—
319C2×C8—582no—
320C2×C8C22×D2911yescharacteristic
321C2×C8C22×D2911yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—291no—
324C4⋊C4—291no—
325C4⋊C4—581no—
326C4⋊C4C22×D2911yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—291no—
329C22⋊C4—291no—
330C22⋊C4—581no—
331C22⋊C4—581no—
332C22⋊C4—581no—
333C22⋊C4—581no—
334C22⋊C4—581no—
335C22⋊C4—581no—
336C42—291no—
337C42—581no—
338C23—21no—
339C23—291no—
340C23—581no—
341C23—581no—
342C23—581no—
343C23—1162no—
344C23—1162no—
345C23—2321no—
346C23D4×D2911yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—21no—
350Q8D4×D2912yes—
351D4—21no—
352D4—21no—
353D4—42no—
354D4—292no—
355D4—581no—
356D4—581no—
357D4—581no—
358D4—581no—
359D4—581no—
360D4—1162no—
361D4—1162no—
362D4—1162no—
363D4—1161no—
364D4—1162no—
365D4—2321no—
366D4—2321no—
367D4—2321no—
368D4—2321no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—291no—
376C2×C4—291no—
377C2×C4—291no—
378C2×C4—581no—
379C2×C4—581no—
380C2×C4—581no—
381C2×C4—1162no—
382C2×C4—1162no—
383C2×C4—2321no—
384C2×C4D4×D2911yescharacteristic
385C2×C4C23×D2911yescharacteristic
386C8—21no—
387C8—21no—
388C8—292no—
389C8—581no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—581no—
397C22—582no—
398C22—581no—
399C22—581no—
400C22—1161no—
401C22—1161no—
402C22—1161no—
403C22—1161no—
404C22—1161no—
405C22—1161no—
406C22—1161no—
407C22—1161no—
408C22—2324no—
409C22C2×D4×D2911yescharacteristic
410C4—21no—
411C4—22no—
412C4—41no—
413C4—41no—
414C4—581no—
415C4—581no—
416C4—581no—
417C4—1161no—
418C4C2×D4×D2911yescharacteristic
419C4#1174535911yescharacteristic
420C2—41no—
421C2—81no—
422C2—1161no—
423C2—1162no—
424C2—2321no—
425C2—2321no—
426C2#1427179511yescharacteristic
427C2#1427196211yescharacteristic
428C2#1427196511yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#452C2
socleC22×C29C22×D4
hypercenter#452D29
hypocenterC29#3268
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#11745311C2semidirect
2. C2×#11745281C2semidirect
3. #14271832C2semidirect
4. #14271804C2semidirect
5. #14271549C2semidirect
6. #14271411C2semidirect
7. #14271398C2semidirect
8. #14271387C2semidirect
9. #14271357C2semidirect
10. #14271311C2semidirect
11. #14271307C2semidirect
12. #14271299C2semidirect
13. #14271266C2semidirect
14. #14271237C2semidirect
15. C29×#452C2semidirect
18. C2×#90809C22semidirect
20. C2×Q16×C29C22semidirect
21. C2×SD16×C29C22semidirect
25. Q8×Dic29C22semidirect
28. C2×#90784C22semidirect
30. #11745302C22semidirect
32. #11745300C22semidirect
43. C2×C8×D29C22semidirect
50. C29×#103C22semidirect
51. C29×#102C22semidirect
53. #11745183C22semidirect
56. #11745168C22semidirect
57. #11745163C22semidirect
58. #11745162C22semidirect
59. #11745157C22semidirect
60. #11745155C22semidirect
103. #90784D4semidirect
215. #452D29semidirect
236. C2×Q16C2×D29semidirect
240. C2×SD16C2×D29semidirect
267. #103C2×D29semidirect
271. #102C2×D29semidirect
275. C29#3268semidirect

Maximal subgroups

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

subgroupindex
C2×#117453112
C2×#117452812
#142718322
#142718042
#142715492
#142714112
#142713982
#142713872
#142713572
#142713112
#142713072
#142712992
#142712662
#142712372
C29×#4522
#326829