Finite Group Databasebeta

← #16831099

Subgroups — #16831099

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×#11745294C211yesmaximal, characteristic, complemented
2C2×#11745311C211yesmaximal, characteristic, complemented
3#14271809C211yesmaximal, characteristic, complemented
4#14271545C211yesmaximal, characteristic, complemented
5#14271411C211yesmaximal, characteristic, complemented
6#14271407C211yesmaximal, characteristic, complemented
7#14271378C211yesmaximal, characteristic, complemented
8#14271375C211yesmaximal, characteristic, complemented
9#14271325C211yesmaximal, characteristic, complemented
10#14271323C211yesmaximal, characteristic, complemented
11#14271297C211yesmaximal, characteristic, complemented
12#14271296C211yesmaximal, characteristic, complemented
13C4×#90782C211yesmaximal, characteristic, complemented
14#14271241C211yesmaximal, characteristic, complemented
15C29×#546C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C22×D4×C29C2211yescharacteristic, complemented
18C2×#90805C2211yescharacteristic
19C22×D116C2211yescharacteristic, complemented
20C29×#124C2211yescharacteristic, complemented
21C29×#123—21no—
22C29×C22⋊Q8C2211yescharacteristic, complemented
23C29×#121—21no—
24C29×#121C2211yescharacteristic
25C29×#120—21no—
26C4×D4×C29C2211yescharacteristic
27C4×D4×C29C2211yescharacteristic, complemented
28C2×C22⋊C4×C29—21no—
29#11745311—24no—
30C2×#90785C2211yescharacteristic, complemented
31C2×#90784C2211yescharacteristic, complemented
32C2×#90784C2211yescharacteristic, complemented
33#11745299—21no—
34C2×#90783C2211yescharacteristic, complemented
35C2×#90783C2211yescharacteristic, complemented
36#11745294—24no—
37C2×#90782C2211yescharacteristic
38C2×#90782C2211yescharacteristic
39C2×#90782C2211yescharacteristic
40C2×#90782C2211yescharacteristic
41#11745292C2211yescharacteristic
42#11745286C2211yescharacteristic, complemented
43C2×#90777C2211yescharacteristic, complemented
44C2×#90777C2211yescharacteristic, complemented
45#11745256—21no—
46#11745246—21no—
47C22⋊C4×D29—21no—
48#11745237C2211yescharacteristic, complemented
49C4×D116C2211yescharacteristic, complemented
50#11745183C2211yescharacteristic, complemented
51#11745180C2211yescharacteristic, complemented
52#11745180C2211yescharacteristic, complemented
53C22⋊#6597C2211yescharacteristic, complemented
54C22⋊#6597C2211yescharacteristic, complemented
55#11745158C2211yescharacteristic, complemented
56#11745157C2211yescharacteristic, complemented
57#11745157C2211yescharacteristic, complemented
58#11745155C2211yescharacteristic, complemented
59C4⋊#6597C2211yescharacteristic, complemented
60C4×#6597C2211yescharacteristic, complemented
61C24×C29—21no—
62C23×D29—21no—
63#41×C29—22no—
64#41×C29—41no—
65C2×Q8×C29C2311yescharacteristic
66C2×D4×C29—22no—
67C2×D4×C29—21no—
68C2×D4×C29—21no—
69C2×D4×C29—21no—
70C2×D4×C29—41no—
71C2×D4×C29D411yescharacteristic
72C2×D4×C29C2311yescharacteristic
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—
80#90805—22no—
81#90805—41no—
82C2×D116—22no—
83C2×D116—21no—
84C2×D116—41no—
85C2×D116C2311yescharacteristic
86C2×D116C2311yescharacteristic
87C2×C4×D29—21no—
88C2×C4×D29—21no—
89C2×Dic58C2311yescharacteristic
90C4⋊C4×C29—21no—
91C4⋊C4×C29D411yescharacteristic
92C4⋊C4×C29C2311yescharacteristic
93C22⋊C4×C29—21no—
94C22⋊C4×C29—21no—
95C22⋊C4×C29—21no—
96C22⋊C4×C29—21no—
97C22⋊C4×C29—21no—
98C22⋊C4×C29D411yescharacteristic
99C22⋊C4×C29D411yescharacteristic
100C42×C29C2311yescharacteristic
101C22⋊Dic29—21no—
102#90785—41no—
103#90784—22no—
104#90784—22no—
105#90783—22no—
106#90783—22no—
107#90782—22no—
108#90782—22no—
109#90782—41no—
110#90782D414yescomplemented
111#90781—21no—
112#90781—21no—
113#90781—21no—
114#90781—21no—
115C4⋊Dic29C2311yescharacteristic
116#90779—21no—
117#90777—22no—
118#90777—22no—
119C2×#6597C2311yescharacteristic
120C2×#6597C2311yescharacteristic
121C2×#6597C2311yescharacteristic
122C2×#6597C2311yescharacteristic
123C23×C29—21no—
124C23×C29—21no—
125C23×C29—42no—
126C23×C29—42no—
127C23×C29—81no—
128C23×C29C2×D411yescharacteristic
129C23×C29C2×D411yescharacteristic
130C22×D29—21no—
131C22×D29—21no—
132C22×D29—42no—
133C22×D29—42no—
134C22×D29—81no—
135Q8×C29—21no—
136Q8×C29—21no—
137D4×C29—21no—
138D4×C29—21no—
139D4×C29—21no—
140D4×C29—41no—
141D4×C29—42no—
142D4×C29—42no—
143D4×C29—81no—
144D4×C29C2×D412yes—
145C2×C4×C29—21no—
146C2×C4×C29—21no—
147C2×C4×C29—21no—
148C2×C4×C29—21no—
149C2×C4×C29—21no—
150C2×C4×C29—21no—
151C2×C4×C29—42no—
152C2×C4×C29—81no—
153C2×C4×C29C2×D411yescharacteristic
154C2×C4×C29C2×D411yescharacteristic
155C2×C4×C29C2×D411yescharacteristic
156C2×C4×C29C2×D411yescharacteristic
157C2×C4×C29C2411yescharacteristic
158C22⋊D29—42no—
159C22⋊D29—81no—
160C2×Dic29—21no—
161C2×Dic29—21no—
162D116—21no—
163D116—21no—
164D116—21no—
165D116—42no—
166D116C2×D412yes—
167C4×D29—42no—
168C4×D29—81no—
169Dic58—21no—
170Dic58—21no—
171#6597—21no—
172#6597—21no—
173#6597—21no—
174#6597C2×D412yes—
175#3273—291nomaximal, Sylow
176C22×C29—21no—
177C22×C29—21no—
178C22×C29—22no—
179C22×C29—21no—
180C22×C29—21no—
181C22×C29—21no—
182C22×C29—21no—
183C22×C29—41no—
184C22×C29—41no—
185C22×C29—41no—
186C22×C29—41no—
187C22×C29—41no—
188C22×C29—84no—
189C22×C29C22×D411yescharacteristic
190C2×D29—22no—
191C2×D29—41no—
192C2×D29—41no—
193C2×D29—41no—
194C2×D29—41no—
195C2×D29—41no—
196C2×D29—84no—
197C4×C29—21no—
198C4×C29—21no—
199C4×C29—21no—
200C4×C29—21no—
201C4×C29—41no—
202C4×C29—41no—
203C4×C29C22×D411yescharacteristic
204C4×C29H(5,𝔽2)11yescharacteristic
205Dic29—41no—
206Dic29—41no—
207C2×AGL(1,ℤ/8)—291no—
208C2×AGL(1,ℤ/8)—291no—
209#546—291no—
210#546D2911yescharacteristic, complemented
211#495—291no—
212#468—291no—
213#468—291no—
214#463—291no—
215#463—291no—
216#452—291no—
217#452—291no—
218#447—291no—
219#447—291no—
220C4×D8—291no—
221#436—291no—
222C2×C29—41no—
223C2×C29—41no—
224C2×C29—42no—
225C2×C29—81no—
226C2×C29D4211yescharacteristic
227C2×C29#57511yescharacteristic
228C2×C29#57611yescharacteristic
229D29—42no—
230D29—81no—
231C2×#41—291no—
232C2×#41C2×D2911yescharacteristic
233C22×D4—291no—
234C22×D4C2×D2911yescharacteristic, complemented
235AGL(1,ℤ/8)—584no—
236AGL(1,ℤ/8)—584no—
237C2×Q16—291no—
238C2×SD16—291no—
239C2×SD16—291no—
240C2×SD16—291no—
241C2×SD16—291no—
242C2×D8—291no—
243C2×D8—291no—
244C2×D8—291no—
245C2×D8—291no—
246C2×M16—291no—
247C2×M16—291no—
248#124—291no—
249#124C2×D2911yescharacteristic, complemented
250#123—21no—
251#123—581no—
252C22⋊Q8—291no—
253C22⋊Q8C2×D2911yescharacteristic, complemented
254#121—21no—
255#121—291no—
256#121—581no—
257#121C2×D2911yescharacteristic
258#120—21no—
259#120—581no—
260C4×D4—291no—
261C4×D4C2×D2911yescharacteristic
262C4×D4C2×D2911yescharacteristic, complemented
263C2×C22⋊C4—21no—
264C2×C22⋊C4—581no—
265#107—291no—
266C4⋊C8—291no—
267#103—291no—
268#103—291no—
269#102—291no—
270#102—291no—
271#102—291no—
272#102—291no—
273C22⋊C8—291no—
274C22⋊C8—291no—
275C4×C8—291no—
276C29#327311yescharacteristic, complemented, Sylow
277C24—21no—
278C24—581no—
279#41—22no—
280#41—41no—
281#41—582no—
282#41—1161no—
283C2×Q8—291no—
284C2×Q8C22×D2911yescharacteristic
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—291no—
291C2×D4—291no—
292C2×D4—582no—
293C2×D4—581no—
294C2×D4—581no—
295C2×D4—581no—
296C2×D4—1161no—
297C2×D4C22⋊D2911yescharacteristic
298C2×D4C22×D2911yescharacteristic
299C2×D4C22×D2911yescharacteristic
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—581no—
303C22×C4—581no—
304C22×C4C22×D2911yescharacteristic
305C22×C4C22×D2911yescharacteristic
306Q16—1161no—
307SD16—582no—
308SD16—582no—
309SD16—582no—
310SD16—582no—
311D8—294no—
312D8—582no—
313D8—582no—
314D8—1161no—
315M16—582no—
316M16—582no—
317C2×C8—291no—
318C2×C8—291no—
319C2×C8—291no—
320C2×C8—291no—
321C4⋊C4—21no—
322C4⋊C4—291no—
323C4⋊C4—581no—
324C4⋊C4C22⋊D2911yescharacteristic
325C4⋊C4C22×D2911yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C22⋊C4—21no—
331C22⋊C4—581no—
332C22⋊C4—581no—
333C22⋊C4—581no—
334C22⋊C4—581no—
335C22⋊C4—581no—
336C22⋊C4C22⋊D2911yescharacteristic
337C22⋊C4C22⋊D2911yescharacteristic
338C42C22×D2911yescharacteristic
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—581no—
345C23—581no—
346C23—1162no—
347C23—1162no—
348C23—2321no—
349C23C2×C22⋊D2911yescharacteristic
350C23C2×C22⋊D2911yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—581no—
354Q8—581no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—41no—
359D4—42no—
360D4—42no—
361D4—81no—
362D4—292no—
363D4—581no—
364D4—581no—
365D4—581no—
366D4—1162no—
367D4—1162no—
368D4—2321no—
369D4D4×D2912yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—81no—
378C2×C4—581no—
379C2×C4—581no—
380C2×C4—1162no—
381C2×C4—2321no—
382C2×C4C2×C22⋊D2911yescharacteristic
383C2×C4C2×C22⋊D2911yescharacteristic
384C2×C4C2×C22⋊D2911yescharacteristic
385C2×C4C2×C22⋊D2911yescharacteristic
386C2×C4C23×D2911yescharacteristic
387C8—292no—
388C8—581no—
389C8—581no—
390C8—581no—
391C22—21no—
392C22—21no—
393C22—22no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—84no—
404C22—582no—
405C22—1161no—
406C22—1161no—
407C22—1161no—
408C22—1161no—
409C22—1161no—
410C22—2324no—
411C22C22×C22⋊D2911yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—41no—
417C4—41no—
418C4—1161no—
419C4—1161no—
420C4C2×D4×D2911yescharacteristic
421C4#1174535911yescharacteristic
422C2—41no—
423C2—41no—
424C2—42no—
425C2—81no—
426C2—1162no—
427C2—2321no—
428C2D4×C22⋊D2911yescharacteristic
429C2#1427196111yescharacteristic
430C2#1427196611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#546C2
socleC22×C29C22×D4
hypercenter#546D29
hypocenterC29#3273
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#11745294C2semidirect
2. C2×#11745311C2semidirect
3. #14271809C2semidirect
4. #14271545C2semidirect
5. #14271411C2semidirect
6. #14271407C2semidirect
7. #14271378C2semidirect
8. #14271375C2semidirect
9. #14271325C2semidirect
10. #14271323C2semidirect
11. #14271297C2semidirect
12. #14271296C2semidirect
13. C4×#90782C2semidirect
14. #14271241C2semidirect
15. C29×#546C2semidirect
17. C22×D4×C29C22semidirect
19. C22×D116C22semidirect
20. C29×#124C22semidirect
22. C29×C22⋊Q8C22semidirect
27. C4×D4×C29C22semidirect
30. C2×#90785C22semidirect
31. C2×#90784C22semidirect
32. C2×#90784C22semidirect
34. C2×#90783C22semidirect
35. C2×#90783C22semidirect
42. #11745286C22semidirect
43. C2×#90777C22semidirect
44. C2×#90777C22semidirect
48. #11745237C22semidirect
49. C4×D116C22semidirect
50. #11745183C22semidirect
51. #11745180C22semidirect
52. #11745180C22semidirect
53. C22⋊#6597C22semidirect
54. C22⋊#6597C22semidirect
55. #11745158C22semidirect
56. #11745157C22semidirect
57. #11745157C22semidirect
58. #11745155C22semidirect
59. C4⋊#6597C22semidirect
60. C4×#6597C22semidirect
110. #90782D4semidirect
210. #546D29semidirect
234. C22×D4C2×D29semidirect
249. #124C2×D29semidirect
253. C22⋊Q8C2×D29semidirect
262. C4×D4C2×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×#117452942
C2×#117453112
#142718092
#142715452
#142714112
#142714072
#142713782
#142713752
#142713252
#142713232
#142712972
#142712962
C4×#907822
#142712412
C29×#5462
#327329