Finite Group Databasebeta

← #16828775

Subgroups — #16828775

Order 3712.

732 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745365C211yesmaximal, characteristic, complemented
2C2×#11745273C211yesmaximal, characteristic, complemented
3C2×SD16×D29C211yesmaximal, characteristic, complemented
4#14271729C211yesmaximal, characteristic, complemented
5#14271309C211yesmaximal, characteristic, complemented
6#14271308C211yesmaximal, characteristic, complemented
7#14271305C211yesmaximal, characteristic, complemented
8#14271304C211yesmaximal, characteristic, complemented
9#14271303C211yesmaximal, characteristic, complemented
10#14271301C211yesmaximal, characteristic, complemented
11#14271300C211yesmaximal, characteristic, complemented
12#14271170C211yesmaximal, characteristic, complemented
13#14271156C211yesmaximal, characteristic, complemented
14#14271128C211yesmaximal, characteristic, complemented
15C29×#449C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic, complemented
17#11745365—24no—
18#11745365—24no—
19C2×Q8×D29C2211yescharacteristic
20C2×Q8×D29C2211yescharacteristic, complemented
21C2×#90807—21no—
22C2×#90807—21no—
23C2×#90807C2211yescharacteristic
24C2×#90807C2211yescharacteristic, complemented
25C2×D4×D29C2211yescharacteristic
26C2×#90805—21no—
27C2×#90805C2211yescharacteristic
28C22×Dic58—21no—
29C22×Dic58C2211yescharacteristic, complemented
30C2×SD16×C29C2211yescharacteristic
31C2×D8×C29C2211yescharacteristic
32C29×#121C2211yescharacteristic
33C2×#90784C2211yescharacteristic
34#11745302—21no—
35#11745300C2211yescharacteristic
36#11745299—21no—
37C2×#90783C2211yescharacteristic
38C2×#90783C2211yescharacteristic
39C2×#90782C2211yescharacteristic
40#11745292C2211yescharacteristic
41SD16×D29—24no—
42#11745273—24no—
43C2×#90773C2211yescharacteristic
44C2×#90773C2211yescharacteristic
45C2×#90772C2211yescharacteristic
46C2×C8×D29C2211yescharacteristic
47#11745257C2211yescharacteristic
48#11745254C2211yescharacteristic
49#11745247—21no—
50#11745244—21no—
51C29×#103C2211yescharacteristic, complemented
52C29×#102C2211yescharacteristic, complemented
53C29×C22⋊C8C2211yescharacteristic, complemented
54#11745183C2211yescharacteristic, complemented
55#11745180C2211yescharacteristic, complemented
56C22⋊#6597C2211yescharacteristic, complemented
57#11745168C2211yescharacteristic, complemented
58#11745168C2211yescharacteristic, complemented
59#11745164C2211yescharacteristic, complemented
60#11745164C2211yescharacteristic, complemented
61#11745158C2211yescharacteristic, complemented
62#11745158C2211yescharacteristic, complemented
63C23×D29—21no—
64#41×C29—22no—
65#41×C29—22no—
66C2×Q8×C29C2311yescharacteristic
67C2×D4×C29—21no—
68C2×D4×C29—21no—
69C2×D4×C29C2311yescharacteristic
70C2×D4×C29C2311yescharacteristic
71C22×C4×C29—21no—
72C22×C4×C29C2311yescharacteristic
73C2×C22⋊D29—21no—
74C2×C22⋊D29—21no—
75C2×C22⋊D29—21no—
76C2×C22⋊D29—21no—
77C2×C22⋊D29—21no—
78C2×C22⋊D29D411yescharacteristic
79C2×C22⋊D29D411yescharacteristic
80C22×Dic29—21no—
81C22×Dic29—21no—
82C22×Dic29—21no—
83Q8×D29—22no—
84Q8×D29—22no—
85Q8×D29—22no—
86Q8×D29D414yescomplemented
87#90807—28no—
88#90807—28no—
89#90807—22no—
90#90807—22no—
91#90807—22no—
92#90807D414yescomplemented
93D4×D29—22no—
94D4×D29—22no—
95#90805—28no—
96#90805—22no—
97#90805—22no—
98C2×D116—21no—
99C2×D116D411yescharacteristic
100C2×D116C2311yescharacteristic
101C2×C4×D29—21no—
102C2×C4×D29—21no—
103C2×C4×D29C2311yescharacteristic
104C2×C4×D29C2311yescharacteristic
105C2×Dic58—28no—
106C2×Dic58—21no—
107C2×Dic58—21no—
108C2×Dic58—21no—
109C2×Dic58—22no—
110C2×Dic58—22no—
111C2×Dic58D411yescharacteristic
112C2×Dic58C2311yescharacteristic
113C2×Dic58C2311yescharacteristic
114SD16×C29—22no—
115D8×C29—22no—
116C2×C8×C29C2311yescharacteristic
117C2×C8×C29C2311yescharacteristic
118C4⋊C4×C29C2311yescharacteristic
119C22⋊C4×C29—21no—
120C22⋊Dic29—21no—
121#90784—22no—
122#90783—22no—
123#90783—22no—
124#90782—22no—
125#90781—21no—
126#90781—21no—
127#90781—21no—
128C4⋊Dic29C2311yescharacteristic
129C4×Dic29—21no—
130C2×#6597C2311yescharacteristic
131C2×#6597C2311yescharacteristic
132#90773—22no—
133#90773—22no—
134#90772—22no—
135C8×D29—22no—
136C23×C29—21no—
137C23×C29—21no—
138C23×C29C2×D411yescharacteristic
139C22×D29—21no—
140C22×D29—42no—
141C22×D29—81no—
142C22×D29—81no—
143C22×D29C2×D411yescharacteristic
144C22×D29C2×D411yescharacteristic
145Q8×C29—21no—
146Q8×C29C2×D412yes—
147D4×C29—24no—
148D4×C29—21no—
149D4×C29—21no—
150D4×C29—21no—
151D4×C29—81no—
152D4×C29C2×D412yes—
153C2×C4×C29—24no—
154C2×C4×C29—21no—
155C2×C4×C29—21no—
156C2×C4×C29—21no—
157C2×C4×C29—21no—
158C2×C4×C29C2×D411yescharacteristic
159C2×C4×C29C2411yescharacteristic
160C22⋊D29—24no—
161C22⋊D29—22no—
162C22⋊D29—24no—
163C22⋊D29—22no—
164C22⋊D29—42no—
165C22⋊D29—81no—
166C22⋊D29—81no—
167C2×Dic29—24no—
168C2×Dic29—24no—
169C2×Dic29—21no—
170C2×Dic29—21no—
171C2×Dic29—24no—
172C2×Dic29—21no—
173C2×Dic29C2×D411yescharacteristic
174C2×Dic29C2×D411yescharacteristic
175D116—22no—
176D116—21no—
177D116—21no—
178D116—81no—
179C4×D29—24no—
180C4×D29—24no—
181C4×D29—21no—
182C4×D29—21no—
183C4×D29C2×D412yes—
184C4×D29C2×D412yes—
185Dic58—24no—
186Dic58—24no—
187Dic58—21no—
188Dic58—21no—
189Dic58—22no—
190Dic58—24no—
191Dic58C2×D412yes—
192Dic58C2×D412yes—
193C8×C29—21no—
194C8×C29—21no—
195#6597—21no—
196#6597—21no—
197#3010—291nomaximal, Sylow
198C22×C29—21no—
199C22×C29—22no—
200C22×C29—21no—
201C22×C29—21no—
202C22×C29—41no—
203C22×C29—41no—
204C22×C29—41no—
205C22×C29—41no—
206C22×C29—41no—
207C22×C29C22×D411yescharacteristic
208C2×D29—21no—
209C2×D29—21no—
210C2×D29—21no—
211C2×D29—21no—
212C2×D29—21no—
213C2×D29—41no—
214C2×D29—41no—
215C2×D29—41no—
216C2×D29—84no—
217C2×D29#12012yes—
218C4×C29—21no—
219C4×C29—22no—
220C4×C29—41no—
221C4×C29C22×D411yescharacteristic
222C4×C29C22×D411yescharacteristic
223Dic29—21no—
224Dic29—22no—
225Dic29—22no—
226Dic29—41no—
227Dic29#12012yes—
228C2×2−1+4—291no—
229C2×AGL(1,ℤ/8)—291no—
230C22×SD16—291no—
231#535—291no—
232#449—291no—
233#449—291no—
234#449—291no—
235#449D2911yescharacteristic, complemented
236#448—291no—
237#448—291no—
238#448—291no—
239#448—291no—
240#419—291no—
241#416—291no—
242#408—291no—
243C2×C29—41no—
244C2×C29—42no—
245C2×C29—81no—
246C2×C29C2×#12011yescharacteristic
247C2×C29#57711yescharacteristic
248C2×C29#57711yescharacteristic
249D29—22no—
250D29—41no—
251D29—81no—
2522−1+4—584no—
2532−1+4—584no—
254C2×#41—291no—
255C2×#41—291no—
256C2×#41—291no—
257C2×#41—581no—
258C2×#41—581no—
259C2×#41—581no—
260C2×#41C2×D2911yescharacteristic, complemented
261C22×Q8—291no—
262C22×Q8—291no—
263C22×Q8—291no—
264C22×Q8—581no—
265C22×D4—291no—
266AGL(1,ℤ/8)—584no—
267C2×SD16—291no—
268C2×SD16—291no—
269C2×SD16—291no—
270C2×SD16—291no—
271C2×SD16—291no—
272C2×SD16—584no—
273C2×SD16C2×D2911yescharacteristic
274C2×D8—291no—
275C2×D8C2×D2911yescharacteristic
276C2×M16—291no—
277C22×C8—291no—
278#127—581no—
279#124—581no—
280#121—291no—
281#121—291no—
282#121—291no—
283#121C2×D2911yescharacteristic
284#120—581no—
285#120—581no—
286#117—291no—
287#103—291no—
288#103—291no—
289#103—291no—
290#103—291no—
291#103—291no—
292#103C2×D2911yescharacteristic, complemented
293#102—291no—
294#102C2×D2911yescharacteristic, complemented
295C22⋊C8—291no—
296C22⋊C8—291no—
297C22⋊C8—291no—
298C22⋊C8C2×D2911yescharacteristic, complemented
299C29#301011yescharacteristic, complemented, Sylow
300C24—581no—
301#41—22no—
302#41—22no—
303#41—294no—
304#41—582no—
305#41—582no—
306#41—588no—
307#41—582no—
308#41—582no—
309#41—588no—
310#41—588no—
311#41—582no—
312C2×Q8—291no—
313C2×Q8—294no—
314C2×Q8—291no—
315C2×Q8—291no—
316C2×Q8—581no—
317C2×Q8—581no—
318C2×Q8—582no—
319C2×Q8—582no—
320C2×Q8—588no—
321C2×Q8—582no—
322C2×Q8—582no—
323C2×Q8—582no—
324C2×Q8—581no—
325C2×Q8C22×D2911yescharacteristic
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—291no—
329C2×D4—291no—
330C2×D4—291no—
331C2×D4—291no—
332C2×D4—581no—
333C2×D4—582no—
334C2×D4—582no—
335C2×D4—581no—
336C2×D4—581no—
337C2×D4—581no—
338C2×D4—581no—
339C2×D4—581no—
340C2×D4C22×D2911yescharacteristic
341C2×D4C22×D2911yescharacteristic
342C22×C4—21no—
343C22×C4—291no—
344C22×C4—291no—
345C22×C4—581no—
346C22×C4—581no—
347C22×C4—581no—
348C22×C4—581no—
349C22×C4—581no—
350C22×C4C22×D2911yescharacteristic
351SD16—22no—
352SD16—582no—
353SD16—582no—
354SD16—582no—
355SD16—582no—
356SD16—582no—
357D8—22no—
358D8—582no—
359M16—582no—
360C2×C8—291no—
361C2×C8—291no—
362C2×C8—582no—
363C2×C8C22×D2911yescharacteristic
364C2×C8C22×D2911yescharacteristic
365C4⋊C4—291no—
366C4⋊C4C22×D2911yescharacteristic
367C22⋊C4—21no—
368C22⋊C4—581no—
369C22⋊C4—581no—
370C22⋊C4—581no—
371C22⋊C4—581no—
372C42—581no—
373C23—21no—
374C23—21no—
375C23—291no—
376C23—291no—
377C23—581no—
378C23—1162no—
379C23—2321no—
380C23—2321no—
381C23D4×D2911yescharacteristic
382Q8—21no—
383Q8—292no—
384Q8—292no—
385Q8—582no—
386Q8—584no—
387Q8—584no—
388Q8—584no—
389Q8—581no—
390Q8—581no—
391Q8D4×D2912yes—
392D4—24no—
393D4—21no—
394D4—21no—
395D4—21no—
396D4—81no—
397D4—582no—
398D4—582no—
399D4—582no—
400D4—584no—
401D4—584no—
402D4—581no—
403D4—581no—
404D4—1162no—
405D4—2321no—
406D4—2321no—
407D4—2321no—
408D4D4×D2912yes—
409C2×C4—24no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—291no—
415C2×C4—292no—
416C2×C4—292no—
417C2×C4—291no—
418C2×C4—584no—
419C2×C4—584no—
420C2×C4—584no—
421C2×C4—584no—
422C2×C4—584no—
423C2×C4—581no—
424C2×C4—581no—
425C2×C4—581no—
426C2×C4—581no—
427C2×C4—581no—
428C2×C4D4×D2911yescharacteristic
429C2×C4C23×D2911yescharacteristic
430C8—21no—
431C8—21no—
432C8—581no—
433C8—581no—
434C22—21no—
435C22—22no—
436C22—21no—
437C22—21no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—292no—
444C22—581no—
445C22—581no—
446C22—581no—
447C22—581no—
448C22—581no—
449C22—1161no—
450C22—1161no—
451C22—1161no—
452C22—2324no—
453C22C2×D4×D2911yescharacteristic
454C4—21no—
455C4—22no—
456C4—41no—
457C4—292no—
458C4—581no—
459C4—582no—
460C4—582no—
461C4—1161no—
462C4C2×D4×D2911yescharacteristic
463C4C2×D4×D2911yescharacteristic
464C2—41no—
465C2—42no—
466C2—81no—
467C2—582no—
468C2—1161no—
469C2—2321no—
470C2#120×D2911yescharacteristic
471C2#1427197011yescharacteristic
472C2#1427197311yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#449C2
socleC22×C29C22×D4
hypercenter#449D29
hypocenterC29#3010
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#11745365C2semidirect
2. C2×#11745273C2semidirect
3. C2×SD16×D29C2semidirect
4. #14271729C2semidirect
5. #14271309C2semidirect
6. #14271308C2semidirect
7. #14271305C2semidirect
8. #14271304C2semidirect
9. #14271303C2semidirect
10. #14271301C2semidirect
11. #14271300C2semidirect
12. #14271170C2semidirect
13. #14271156C2semidirect
14. #14271128C2semidirect
15. C29×#449C2semidirect
16. C2×#41×C29C22semidirect
20. C2×Q8×D29C22semidirect
24. C2×#90807C22semidirect
29. C22×Dic58C22semidirect
51. C29×#103C22semidirect
52. C29×#102C22semidirect
53. C29×C22⋊C8C22semidirect
54. #11745183C22semidirect
55. #11745180C22semidirect
56. C22⋊#6597C22semidirect
57. #11745168C22semidirect
58. #11745168C22semidirect
59. #11745164C22semidirect
60. #11745164C22semidirect
61. #11745158C22semidirect
62. #11745158C22semidirect
86. Q8×D29D4semidirect
92. #90807D4semidirect
235. #449D29semidirect
260. C2×#41C2×D29semidirect
292. #103C2×D29semidirect
294. #102C2×D29semidirect
298. C22⋊C8C2×D29semidirect
299. C29#3010semidirect

Maximal subgroups

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

subgroupindex
C2×#117453652
C2×#117452732
C2×SD16×D292
#142717292
#142713092
#142713082
#142713052
#142713042
#142713032
#142713012
#142713002
#142711702
#142711562
#142711282
C29×#4492
#301029