Finite Group Databasebeta

← #29684445

Subgroups — #29684445

Order 15616.

738 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454617C211yesmaximal, characteristic
2#21454471C211yesmaximal, characteristic, complemented
3#21454470C211yesmaximal, characteristic, complemented
4#21446709C211yesmaximal, characteristic
5#21446704C211yesmaximal, characteristic
6#21446571C211yesmaximal, characteristic, complemented
7#21446566C211yesmaximal, characteristic, complemented
8#21446531C211yesmaximal, characteristic, complemented
9#21446527C211yesmaximal, characteristic, complemented
10#21446524C211yesmaximal, characteristic, complemented
11#21446520C211yesmaximal, characteristic, complemented
12#21445726C211yesmaximal, characteristic, complemented
13C4×#14519705C211yesmaximal, characteristic, complemented
14C4×#14519688C211yesmaximal, characteristic, complemented
15C4×#104×C61C211yesmaximal, characteristic, complemented
16C2×#14519797C2211yescharacteristic
17C4×#11758222C2211yescharacteristic
18#16839872C412yescomplemented
19#16839867C412yescomplemented
20#16839862C412yescomplemented
21#16839860C412yescomplemented
22#16839823—22no—
23#16839821—22no—
24#16839819—22no—
25#16839817—22no—
26C2×#14519712C2211yescharacteristic
27C2×#14519712C2211yescharacteristic
28#16839798C2211yescharacteristic
29#16839790C2211yescharacteristic
30#16839790C2211yescharacteristic
31#16839789C2211yescharacteristic
32#16839789C2211yescharacteristic
33C2×#14519705C2211yescharacteristic
34C2×#14519705C2211yescharacteristic
35#16839758C2211yescharacteristic
36#16839756C2211yescharacteristic
37#16839730C2211yescharacteristic
38#16839730C2211yescharacteristic
39#16839729C2211yescharacteristic
40#16839729C2211yescharacteristic
41C4×#11758194C2211yescharacteristic
42C2×#14519688C2211yescharacteristic
43C2×#14519688C2211yescharacteristic
44C2×#14519688C2211yescharacteristic
45C2×#14519688C2211yescharacteristic
46C2×C4×#92418C2211yescharacteristic
47C2×C4×#92418C2211yescharacteristic
48#16839526C2211yescharacteristic
49#16839526C2211yescharacteristic
50#16839522C2211yescharacteristic
51#16839522C2211yescharacteristic
52C4×#41×C61C2211yescharacteristic
53C2×#104×C61C2211yescharacteristic
54C2×#104×C61C2211yescharacteristic
55C4×M16×C61C2211yescharacteristic
56C43×C61C2211yescharacteristic
57C61×#339C2211yescharacteristic
58C61×#339C2211yescharacteristic
59C2×#11758222C2311yescharacteristic
60#14519797—22no—
61#14519797—22no—
62C2×#11758202C2×C411yescharacteristic
63C2×#11758200C2×C411yescharacteristic
64C2×#11758201C2×C411yescharacteristic
65C2×#11758199C2×C411yescharacteristic
66C2×#11758194C2311yescharacteristic
67C2×#11758194C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C4×Dic122C2×C412yes—
73C4×D244C2×C412yes—
74C4×C22⋊D61—22no—
75#14519736C2311yescharacteristic
76#14519734—21no—
77C42×D61—21no—
78#14519712—22no—
79#14519712—22no—
80#14519710C2×C412yes—
81#14519708C2×C412yes—
82C4⋊#92418—22no—
83C4⋊#92418—22no—
84#14519706—22no—
85#14519706—22no—
86#14519705—22no—
87#14519705—22no—
88#14519701C2×C412yes—
89#14519700C2×C412yes—
90#14519698C2×C412yes—
91#14519697C2×C412yes—
92C22⋊#92418—22no—
93C22⋊#92418—22no—
94#14519689—22no—
95#14519689—22no—
96#14519688—21no—
97#14519688—22no—
98#14519688—22no—
99#14519688C2×C412yes—
100#14519688C2×C412yes—
101#14519688D412yes—
102#14519688D412yes—
103C4×#92418—21no—
104C4×#92418—22no—
105C4×#92418—22no—
106C2×#41×C61C2311yescharacteristic
107C2×M16×C61C2311yescharacteristic
108C2×M16×C61C2311yescharacteristic
109C4×Q8×C61C2×C412yes—
110C4×D4×C61—22no—
111C4×D4×C61C2×C412yes—
112#117×C61—21no—
113#117×C61C2311yescharacteristic
114C2×C42×C61—21no—
115C2×C42×C61—22no—
116C2×C42×C61C2311yescharacteristic
117C2×C42×C61C2311yescharacteristic
118C2×C42×C61C2311yescharacteristic
119#104×C61—22no—
120#104×C61—22no—
121#97×C61—21no—
122C4×C8×C61—21no—
123#41×C61—21no—
124#41×C61—21no—
125#41×C61—21no—
126#41×C61—21no—
127C2×Q8×C61C22×C411yescharacteristic
128C2×D4×C61—21no—
129C2×D4×C61C22×C411yescharacteristic
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—22no—
134C22×C4×C61#4112yes—
135C22×C4×C61C2411yescharacteristic
136C2×C22⋊D61—21no—
137#11758222—21no—
138#11758222—21no—
139#11758222—21no—
140#11758222—21no—
141C2×D244C22×C411yescharacteristic
142C2×C4×D61—21no—
143C2×C4×D61—22no—
144C2×Dic122C22×C411yescharacteristic
145M16×C61—21no—
146M16×C61—21no—
147M16×C61—21no—
148M16×C61—21no—
149C2×C8×C61—21no—
150C2×C8×C61—21no—
151C4⋊C4×C61—22no—
152C4⋊C4×C61C22×C412yes—
153C22⋊C4×C61—21no—
154C22⋊C4×C61—22no—
155C42×C61—22no—
156C42×C61—21no—
157C42×C61—21no—
158C42×C61—21no—
159C42×C61—44no—
160C42×C61C22×C412yes—
161C42×C61C2×D411yescharacteristic
162C42×C61C2×D411yescharacteristic
163C42×C61#4112yes—
164C42×C61#4112yes—
165C22⋊Dic61—21no—
166#11758202—22no—
167#11758201—22no—
168#11758200—22no—
169#11758199—22no—
170#11758198—22no—
171C4⋊Dic61C22×C412yes—
172#11758196—22no—
173C4×Dic61—22no—
174C4×Dic61—21no—
175#11758194—21no—
176#11758194—21no—
177#11758194—21no—
178#11758194—21no—
179C2×#92418—21no—
180C2×#92418—21no—
181C2×#92418—21no—
182C2×#92418—21no—
183C2×#92418—21no—
184C2×#92418—21no—
185C2×#92418—21no—
186C2×#92418—21no—
187C2×#92418C22×C412yes—
188C2×#92418C22×C411yescharacteristic
189C2×#92418C22×C411yescharacteristic
190C2×#92418C2×D412yes—
191C2×#92418C2×D412yes—
192C2×#92418#4112yes—
193C2×#92418#4112yes—
194C23×C61—21no—
195C23×C61C2×#4111yescharacteristic
196C22×D61—21no—
197Q8×C61—21no—
198Q8×C61—21no—
199D4×C61—21no—
200D4×C61—21no—
201D4×C61—41no—
202D4×C61—41no—
203C2×C4×C61—24no—
204C2×C4×C61—22no—
205C2×C4×C61—22no—
206C2×C4×C61—21no—
207C2×C4×C61—22no—
208C2×C4×C61—42no—
209C2×C4×C61—42no—
210C2×C4×C61—41no—
211C2×C4×C61—41no—
212C2×C4×C61—82no—
213C2×C4×C61C4×D412yes—
214C2×C4×C61C4×D412yes—
215C2×C4×C61C23×C411yescharacteristic
216C2×C4×C61C22×D411yescharacteristic
217C2×C4×C61C2×#4111yescharacteristic
218C2×C4×C61C2×#4111yescharacteristic
219C2×C4×C61C2×#4111yescharacteristic
220C2×C4×C61C2×#4111yescharacteristic
221C22⋊D61—41no—
222C22⋊D61—41no—
223C2×Dic61—21no—
224C2×Dic61—22no—
225D244—21no—
226D244—21no—
227C4×D61—41no—
228C4×D61—41no—
229C4×D61—82no—
230Dic122—21no—
231Dic122—21no—
232C8×C61—41no—
233C8×C61—41no—
234#92418—22no—
235#92418—22no—
236#92418—22no—
237#92418—41no—
238#92418—41no—
239#92418#11712yes—
240#92418#11712yes—
241#21297—611nomaximal, Sylow
242C22×C61—22no—
243C22×C61—42no—
244C22×C61—41no—
245C22×C61C2×C4×D411yescharacteristic
246C22×C61#52911yescharacteristic
247C22×C61#52911yescharacteristic
248C2×D61—42no—
249C2×D61—41no—
250C4×C61—24no—
251C4×C61—22no—
252C4×C61—22no—
253C4×C61—42no—
254C4×C61—42no—
255C4×C61—41no—
256C4×C61C2×#11711yescharacteristic
257C4×C61C4×#4111yescharacteristic
258C4×C61#53211yescharacteristic
259C4×C61#53211yescharacteristic
260Dic61—42no—
261Dic61—41no—
262#2943—611no—
263#2923—611no—
264#2923—611no—
265#1975—611no—
266#1974—611no—
267#1946—611no—
268#1945—611no—
269#1938—611no—
270#1938—611no—
271#1937—611no—
272#1937—611no—
273#1778—611no—
274C4×#104—611no—
275C4×#104D6111yescharacteristic, complemented
276C4×#97—611no—
277C2×C61—21no—
278C2×C61—21no—
279C2×C61—81no—
280C2×C61#229311yescharacteristic
281C2×C61#295612yes—
282D61—81no—
283C2×#135—611no—
284C4×#41—611no—
285C4×#41C2×D6111yescharacteristic
286#442—612no—
287#441—612no—
288#440—612no—
289#440—612no—
290#433—1222no—
291#433—1222no—
292#432—1222no—
293#432—1222no—
294C2×#108—611no—
295C2×#108—611no—
296#427—611no—
297#424—611no—
298#424—611no—
299#424—611no—
300#424—611no—
301C2×#104—611no—
302C2×#104—611no—
303C2×#104C2×D6111yescharacteristic
304C2×#104C2×D6111yescharacteristic
305#416—611no—
306#416—611no—
307#408—611no—
308#408—611no—
309#408—611no—
310#408—611no—
311C4×M16—611no—
312C4×M16C2×D6111yescharacteristic
313C2×#97—611no—
314C2×#97—611no—
315C2×#97—611no—
316C2×#97—611no—
317C2×C4×C8—611no—
318C2×C4×C8—611no—
319C43C2×D6111yescharacteristic
320#341—611no—
321#341—611no—
322#339—611no—
323#339—611no—
324#339C2×D6111yescharacteristic
325#339C2×D6111yescharacteristic
326C61#2129711yescharacteristic, complemented, Sylow
327C2×#41—611no—
328C2×#41C22×D6111yescharacteristic
329#135—1222no—
330#135—1222no—
331C2×Q16—611no—
332C2×SD16—611no—
333C2×SD16—611no—
334C2×D8—611no—
335C2×M16—611no—
336C2×M16—611no—
337C2×M16C22×D6111yescharacteristic
338C2×M16C22×D6111yescharacteristic
339C22×C8—611no—
340C22×C8—611no—
341C22×C8—611no—
342C22×C8—611no—
343C4×Q8—612no—
344C4×Q8C4×D6112yes—
345C4×D4—22no—
346C4×D4—612no—
347C4×D4—1222no—
348C4×D4C4×D6112yes—
349#117—21no—
350#117—611no—
351#117—1221no—
352#117C22×D6111yescharacteristic
353C2×C42—21no—
354C2×C42—22no—
355C2×C42—1221no—
356C2×C42C22×D6111yescharacteristic
357C2×C42C22×D6111yescharacteristic
358C2×C42C22×D6111yescharacteristic
359#108—1222no—
360#108—1222no—
361#107—612no—
362#106—612no—
363C4⋊C8—1222no—
364C4⋊C8—1222no—
365C4⋊C8—1222no—
366C4⋊C8—1222no—
367#104—22no—
368#104—22no—
369#104—1222no—
370#104—1222no—
371#103—612no—
372#103—612no—
373#102—612no—
374#102—612no—
375C22⋊C8—1222no—
376C22⋊C8—1222no—
377C22⋊C8—1222no—
378C22⋊C8—1222no—
379#97—21no—
380#97—612no—
381#97—612no—
382#97—612no—
383#97—612no—
384#97—1222no—
385#97—1222no—
386#97—1221no—
387C4×C8—21no—
388C4×C8—1222no—
389C4×C8—1222no—
390C4×C8—1221no—
391#41—21no—
392#41—21no—
393#41—21no—
394#41—21no—
395#41—1221no—
396#41—1221no—
397#41—1221no—
398#41—1221no—
399C2×Q8—611no—
400C2×Q8C2×C4×D6111yescharacteristic
401C2×D4—21no—
402C2×D4—611no—
403C2×D4—1221no—
404C2×D4C2×C4×D6111yescharacteristic
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—1222no—
410C22×C4—1221no—
411C22×C4#1175822412yes—
412C22×C4C23×D6111yescharacteristic
413Q16—1222no—
414SD16—1222no—
415SD16—1222no—
416D8—1222no—
417M16—21no—
418M16—21no—
419M16—21no—
420M16—21no—
421M16—1221no—
422M16—1221no—
423M16—1221no—
424M16—1221no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—611no—
428C2×C8—611no—
429C2×C8—612no—
430C2×C8—612no—
431C2×C8—612no—
432C2×C8—612no—
433C2×C8—612no—
434C2×C8—1221no—
435C2×C8—1221no—
436C2×C8—1221no—
437C2×C8—1221no—
438C2×C8—1221no—
439C2×C8—1221no—
440C2×C8—1221no—
441C2×C8—1221no—
442C4⋊C4—22no—
443C4⋊C4—612no—
444C4⋊C4—1222no—
445C4⋊C4C2×C4×D6112yes—
446C22⋊C4—21no—
447C22⋊C4—22no—
448C22⋊C4—1221no—
449C22⋊C4—1222no—
450C42—21no—
451C42—21no—
452C42—21no—
453C42—22no—
454C42—44no—
455C42—1221no—
456C42—1222no—
457C42C2×C4×D6112yes—
458C42#1175822212yes—
459C42#1175822212yes—
460C42D4×D6111yescharacteristic
461C42D4×D6111yescharacteristic
462C23—21no—
463C23—1221no—
464C23C2×#1175822411yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—1221no—
468Q8—1221no—
469D4—21no—
470D4—21no—
471D4—41no—
472D4—41no—
473D4—1221no—
474D4—1221no—
475D4—2441no—
476D4—2441no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—82no—
487C2×C4—1222no—
488C2×C4—1221no—
489C2×C4—4882no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4#1451973712yes—
493C2×C4#1451973712yes—
494C2×C4C22×C4×D6111yescharacteristic
495C2×C4C2×D4×D6111yescharacteristic
496C2×C4#41×D6111yescharacteristic
497C2×C4#41×D6111yescharacteristic
498C2×C4C2×#1175822211yescharacteristic
499C2×C4C2×#1175822211yescharacteristic
500C8—41no—
501C8—41no—
502C8—612no—
503C8—612no—
504C8—1222no—
505C8—1222no—
506C8—1222no—
507C8—2441no—
508C8—2441no—
509C22—22no—
510C22—41no—
511C22—42no—
512C22—2441no—
513C22—2442no—
514C22C2×#1451973711yescharacteristic
515C22#1684029211yescharacteristic
516C22#1684029211yescharacteristic
517C4—24no—
518C4—22no—
519C4—22no—
520C4—42no—
521C4—41no—
522C4—42no—
523C4—2441no—
524C4—2442no—
525C4#117×D6111yescharacteristic
526C4C4×#1175822211yescharacteristic
527C4#1684030911yescharacteristic
528C4#1684030911yescharacteristic
529C2—21no—
530C2—21no—
531C2—81no—
532C2—4881no—
533C2#2144828211yescharacteristic
534C2#2145472512yes—
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#104×C61C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519797C22
cosocleC22×C4×C61C24
hypercenterC4×#104D61
hypocenterC61#21297
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#104

Complements

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

NH ≅ G/Ntype
2. #21454471C2semidirect
3. #21454470C2semidirect
6. #21446571C2semidirect
7. #21446566C2semidirect
8. #21446531C2semidirect
9. #21446527C2semidirect
10. #21446524C2semidirect
11. #21446520C2semidirect
12. #21445726C2semidirect
13. C4×#14519705C2semidirect
14. C4×#14519688C2semidirect
15. C4×#104×C61C2semidirect
18. #16839872C4semidirect
19. #16839867C4semidirect
20. #16839862C4semidirect
21. #16839860C4semidirect
275. C4×#104D61semidirect
326. C61#21297semidirect

Maximal subgroups

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

subgroupindex
#214546172
#214544712
#214544702
#214467092
#214467042
#214465712
#214465662
#214465312
#214465272
#214465242
#214465202
#214457262
C4×#145197052
C4×#145196882
C4×#104×C612
#2129761