Finite Group Databasebeta

← #16831030

Subgroups — #16831030

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×#11745294C211yesmaximal, characteristic, complemented
2C2×#11745274C211yesmaximal, characteristic, complemented
3#14271831C211yesmaximal, characteristic, complemented
4#14271807C211yesmaximal, characteristic, complemented
5#14271551C211yesmaximal, characteristic, complemented
6#14271407C211yesmaximal, characteristic, complemented
7#14271398C211yesmaximal, characteristic, complemented
8#14271384C211yesmaximal, characteristic, complemented
9#14271356C211yesmaximal, characteristic, complemented
10#14271327C211yesmaximal, characteristic, complemented
11#14271309C211yesmaximal, characteristic, complemented
12#14271305C211yesmaximal, characteristic, complemented
13#14271260C211yesmaximal, characteristic, complemented
14#14271237C211yesmaximal, characteristic, complemented
15C29×#447C211yesmaximal, characteristic, complemented
16C22×D4×C29C2211yescharacteristic
17C2×#90807C2211yescharacteristic
18C2×#90807C2211yescharacteristic, complemented
19C2×#90805C2211yescharacteristic
20C2×D8×C29C2211yescharacteristic
21C2×D8×C29C2211yescharacteristic
22C29×#121C2211yescharacteristic
23#11745315—21no—
24C2×C22⋊Dic29—21no—
25#11745302—21no—
26#11745302C2211yescharacteristic, complemented
27#11745301—21no—
28#11745301—21no—
29#11745300C2211yescharacteristic
30#11745298C2211yescharacteristic
31#11745297—21no—
32D4×Dic29C2211yescharacteristic
33C2×#90783C2211yescharacteristic
34C2×#90783C2211yescharacteristic
35C2×#90783C2211yescharacteristic, complemented
36#11745294—24no—
37C2×#90782C2211yescharacteristic
38C2×#90782C2211yescharacteristic
39C4×C22⋊D29C2211yescharacteristic
40#11745286C2211yescharacteristic
41C2×#90777C2211yescharacteristic
42#11745274—24no—
43C2×Dic116C2211yescharacteristic, complemented
44C2×#90773C2211yescharacteristic, complemented
45C2×C8×D29C2211yescharacteristic, complemented
46#11745257C2211yescharacteristic, complemented
47#11745249C2211yescharacteristic, complemented
48#11745246—21no—
49#11745243—21no—
50C29×#102C2211yescharacteristic
51C29×#102C2211yescharacteristic
52C29×C22⋊C8C2211yescharacteristic
53#11745180C2211yescharacteristic, complemented
54#11745169C2211yescharacteristic, complemented
55#11745168C2211yescharacteristic, complemented
56#11745164C2211yescharacteristic, complemented
57#11745163C2211yescharacteristic, complemented
58#11745162C2211yescharacteristic, complemented
59#11745158C2211yescharacteristic, complemented
60#11745155C2211yescharacteristic, complemented
61C24×C29—21no—
62C2×D4×C29—22no—
63C2×D4×C29—21no—
64C2×D4×C29—21no—
65C2×D4×C29—41no—
66C2×D4×C29C2311yescharacteristic
67C2×D4×C29C2311yescharacteristic
68C2×D4×C29C2311yescharacteristic
69C22×C4×C29C2311yescharacteristic
70C2×C22⋊D29—21no—
71C2×C22⋊D29—21no—
72C2×C22⋊D29—21no—
73C2×C22⋊D29—21no—
74C2×C22⋊D29—21no—
75C2×C22⋊D29—21no—
76C2×C22⋊D29D411yescharacteristic
77C22×Dic29—21no—
78C22×Dic29—21no—
79C22×Dic29—21no—
80#90807—22no—
81#90807—22no—
82#90807—41no—
83#90807—41no—
84#90805—22no—
85#90805—41no—
86C2×D116—21no—
87C2×D116C2311yescharacteristic
88C2×C4×D29—21no—
89C2×C4×D29C2311yescharacteristic
90C2×Dic58C2311yescharacteristic
91C2×Dic58C2311yescharacteristic
92D8×C29—22no—
93D8×C29—41no—
94C2×C8×C29C2311yescharacteristic
95C2×C8×C29C2311yescharacteristic
96C4⋊C4×C29C2311yescharacteristic
97C22⋊C4×C29—21no—
98C22⋊Dic29—21no—
99C22⋊Dic29—21no—
100C22⋊Dic29—21no—
101C22⋊Dic29—21no—
102C22⋊Dic29—21no—
103C22⋊Dic29D411yescharacteristic
104#90783—22no—
105#90783—22no—
106#90783D414yescomplemented
107#90782—22no—
108#90782—22no—
109#90781—21no—
110#90781D411yescharacteristic
111C4⋊Dic29C2311yescharacteristic
112#90779—21no—
113#90779—21no—
114#90779D411yescharacteristic
115C4×Dic29—21no—
116C4×Dic29C2311yescharacteristic
117#90777—22no—
118C2×#6597C2311yescharacteristic
119C2×#6597C2311yescharacteristic
120Dic116—22no—
121#90773—41no—
122C8×D29—22no—
123C23×C29—21no—
124C23×C29—21no—
125C23×C29—21no—
126C23×C29—42no—
127C23×C29—42no—
128C23×C29—81no—
129C23×C29C2×D411yescharacteristic
130C22×D29—21no—
131C22×D29C2×D411yescharacteristic
132D4×C29—21no—
133D4×C29—21no—
134D4×C29—21no—
135D4×C29—21no—
136D4×C29—21no—
137D4×C29—42no—
138D4×C29—81no—
139D4×C29C2×D412yes—
140C2×C4×C29—21no—
141C2×C4×C29—21no—
142C2×C4×C29—21no—
143C2×C4×C29C2×D411yescharacteristic
144C2×C4×C29C2411yescharacteristic
145C22⋊D29—41no—
146C22⋊D29—42no—
147C22⋊D29—42no—
148C22⋊D29—42no—
149C22⋊D29—42no—
150C22⋊D29—81no—
151C22⋊D29—81no—
152C2×Dic29—21no—
153C2×Dic29—21no—
154C2×Dic29—21no—
155C2×Dic29—42no—
156C2×Dic29—42no—
157C2×Dic29—81no—
158C2×Dic29C2×D411yescharacteristic
159C2×Dic29C2×D411yescharacteristic
160C2×Dic29C2×D411yescharacteristic
161D116—21no—
162D116—21no—
163D116—81no—
164C4×D29—21no—
165C4×D29—21no—
166C4×D29—42no—
167Dic58—21no—
168Dic58—21no—
169Dic58—21no—
170Dic58C2×D412yes—
171C8×C29—21no—
172C8×C29—21no—
173#6597—21no—
174#6597C2×D412yes—
175#3268—291nomaximal, Sylow
176C22×C29—22no—
177C22×C29—21no—
178C22×C29—21no—
179C22×C29—21no—
180C22×C29—41no—
181C22×C29—41no—
182C22×C29—41no—
183C22×C29—41no—
184C22×C29—41no—
185C22×C29—41no—
186C22×C29—41no—
187C22×C29—41no—
188C22×C29—84no—
189C22×C29C22×D411yescharacteristic
190C2×D29—21no—
191C2×D29—21no—
192C2×D29—21no—
193C2×D29—41no—
194C2×D29—41no—
195C2×D29—41no—
196C4×C29—21no—
197C4×C29—41no—
198C4×C29C22×D411yescharacteristic
199C4×C29H(5,𝔽2)11yescharacteristic
200Dic29—22no—
201Dic29—21no—
202Dic29—21no—
203Dic29—21no—
204Dic29—41no—
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#452—291no—
216#449—291no—
217#449—291no—
218#447D2911yescharacteristic, complemented
219#440—291no—
220#435—291no—
221C2×C29—41no—
222C2×C29—42no—
223C2×C29—81no—
224C2×C29—81no—
225C2×C29D4211yescharacteristic
226C2×C29#57511yescharacteristic
227C2×C29#57611yescharacteristic
228D29—41no—
229D29—81no—
230C2×#41—291no—
231C2×#41—291no—
232C2×#41—291no—
233C22×D4C2×D2911yescharacteristic
234AGL(1,ℤ/8)—584no—
235#135—584no—
236C2×Q16—291no—
237C2×SD16—291no—
238C2×SD16—291no—
239C2×SD16—291no—
240C2×SD16—291no—
241C2×D8—291no—
242C2×D8—291no—
243C2×D8C2×D2911yescharacteristic
244C2×D8C2×D2911yescharacteristic
245C2×M16—291no—
246C22×C8—291no—
247#127—291no—
248#127—581no—
249#124—291no—
250#123—581no—
251C22⋊Q8—291no—
252#121—291no—
253#121—291no—
254#121—581no—
255#121—581no—
256#121—581no—
257#121C2×D2911yescharacteristic
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#103—291no—
268#102—291no—
269#102—291no—
270#102C2×D2911yescharacteristic
271#102C2×D2911yescharacteristic
272C22⋊C8—291no—
273C22⋊C8C2×D2911yescharacteristic
274#97—291no—
275C29#326811yescharacteristic, complemented, Sylow
276C24—21no—
277#41—582no—
278#41—582no—
279#41—582no—
280#41—1161no—
281#41—1161no—
282#41—1161no—
283C2×Q8—291no—
284C2×Q8—291no—
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—291no—
290C2×D4—291no—
291C2×D4—581no—
292C2×D4—581no—
293C2×D4—581no—
294C2×D4—581no—
295C2×D4—581no—
296C2×D4—581no—
297C2×D4—581no—
298C2×D4C22×D2911yescharacteristic
299C2×D4C22×D2911yescharacteristic
300C2×D4C22×D2911yescharacteristic
301C22×C4—291no—
302C22×C4—581no—
303C22×C4—581no—
304C22×C4—581no—
305C22×C4—581no—
306C22×C4C22×D2911yescharacteristic
307Q16—582no—
308SD16—294no—
309SD16—582no—
310SD16—582no—
311SD16—1161no—
312D8—22no—
313D8—41no—
314D8—582no—
315D8—582no—
316M16—582no—
317C2×C8—291no—
318C2×C8—291no—
319C2×C8—582no—
320C2×C8C22×D2911yescharacteristic
321C2×C8C22×D2911yescharacteristic
322C4⋊C4—291no—
323C4⋊C4—291no—
324C4⋊C4—581no—
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—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—291no—
345C23—581no—
346C23D4×D2911yescharacteristic
347Q8—292no—
348Q8—581no—
349Q8—581no—
350Q8—581no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—42no—
357D4—81no—
358D4—581no—
359D4—581no—
360D4—1161no—
361D4—1162no—
362D4—1162no—
363D4—1162no—
364D4—1162no—
365D4—2321no—
366D4—2321no—
367D4—2321no—
368D4D4×D2912yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—291no—
373C2×C4—291no—
374C2×C4—291no—
375C2×C4—581no—
376C2×C4—581no—
377C2×C4—581no—
378C2×C4—581no—
379C2×C4—581no—
380C2×C4—1162no—
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—22no—
392C22—21no—
393C22—21no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—84no—
403C22—581no—
404C22—581no—
405C22—581no—
406C22—1161no—
407C22—1161no—
408C22—1161no—
409C22C2×D4×D2911yescharacteristic
410C4—21no—
411C4—41no—
412C4—581no—
413C4—582no—
414C4—581no—
415C4—581no—
416C4—1161no—
417C4—1161no—
418C4C2×D4×D2911yescharacteristic
419C4#1174535911yescharacteristic
420C2—41no—
421C2—42no—
422C2—81no—
423C2—81no—
424C2—1161no—
425C2—2321no—
426C2#1427179511yescharacteristic
427C2#1427195911yescharacteristic
428C2#1427196411yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#447C2
socleC22×C29C22×D4
hypercenter#447D29
hypocenterC29#3268
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#11745294C2semidirect
2. C2×#11745274C2semidirect
3. #14271831C2semidirect
4. #14271807C2semidirect
5. #14271551C2semidirect
6. #14271407C2semidirect
7. #14271398C2semidirect
8. #14271384C2semidirect
9. #14271356C2semidirect
10. #14271327C2semidirect
11. #14271309C2semidirect
12. #14271305C2semidirect
13. #14271260C2semidirect
14. #14271237C2semidirect
15. C29×#447C2semidirect
18. C2×#90807C22semidirect
26. #11745302C22semidirect
35. C2×#90783C22semidirect
43. C2×Dic116C22semidirect
44. C2×#90773C22semidirect
45. C2×C8×D29C22semidirect
46. #11745257C22semidirect
47. #11745249C22semidirect
53. #11745180C22semidirect
54. #11745169C22semidirect
55. #11745168C22semidirect
56. #11745164C22semidirect
57. #11745163C22semidirect
58. #11745162C22semidirect
59. #11745158C22semidirect
60. #11745155C22semidirect
106. #90783D4semidirect
218. #447D29semidirect
275. C29#3268semidirect

Maximal subgroups

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

subgroupindex
C2×#117452942
C2×#117452742
#142718312
#142718072
#142715512
#142714072
#142713982
#142713842
#142713562
#142713272
#142713092
#142713052
#142712602
#142712372
C29×#4472
#326829