Finite Group Databasebeta

← #29684434

Subgroups — #29684434

Order 15616.

730 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454617C211yesmaximal, characteristic
2#21454464C211yesmaximal, characteristic, complemented
3#21454463C211yesmaximal, 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
13#21445630C211yesmaximal, characteristic, complemented
14#21445506C211yesmaximal, characteristic, complemented
15C61×#1759C211yesmaximal, characteristic, complemented
16C2×#14519797C2211yescharacteristic
17C4×#11758222C2211yescharacteristic
18#16839872C412yescomplemented
19#16839867C412yescomplemented
20#16839862C412yescomplemented
21#16839860C412yescomplemented
22#16839824—22no—
23#16839823—22no—
24#16839815—22no—
25#16839813—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×C4×#92418C2211yescharacteristic
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
56C61×#376C2211yescharacteristic
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—
101C4×#92418—21no—
102C4×#92418—22no—
103C4×#92418—22no—
104C4×#92418D412yes—
105C4×#92418D412yes—
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×C61C2311yescharacteristic
116C2×C42×C61C2311yescharacteristic
117C2×C42×C61C2311yescharacteristic
118#104×C61—22no—
119#104×C61—22no—
120#97×C61—21no—
121C4×C8×C61—21no—
122#95×C61—22no—
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—22no—
133C22×C4×C61—21no—
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—22no—
143C2×C4×D61—21no—
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×C61C22×C412yes—
160C42×C61C2×D411yescharacteristic
161C42×C61C2×D411yescharacteristic
162C42×C61#4112yes—
163C42×C61#4112yes—
164C22⋊Dic61—21no—
165#11758202—22no—
166#11758201—22no—
167#11758200—22no—
168#11758199—22no—
169#11758198—22no—
170C4⋊Dic61C22×C412yes—
171#11758196—22no—
172C4×Dic61—22no—
173C4×Dic61—21no—
174#11758194—21no—
175#11758194—21no—
176#11758194—21no—
177#11758194—21no—
178C2×#92418—21no—
179C2×#92418—21no—
180C2×#92418—21no—
181C2×#92418—21no—
182C2×#92418—21no—
183C2×#92418—21no—
184C2×#92418—21no—
185C2×#92418—21no—
186C2×#92418C22×C412yes—
187C2×#92418C22×C411yescharacteristic
188C2×#92418C22×C411yescharacteristic
189C2×#92418C2×D412yes—
190C2×#92418C2×D412yes—
191C2×#92418#4112yes—
192C2×#92418#4112yes—
193C23×C61—21no—
194C23×C61C2×#4111yescharacteristic
195C22×D61—21no—
196Q8×C61—21no—
197Q8×C61—21no—
198D4×C61—21no—
199D4×C61—21no—
200D4×C61—41no—
201D4×C61—41no—
202C2×C4×C61—22no—
203C2×C4×C61—21no—
204C2×C4×C61—22no—
205C2×C4×C61—22no—
206C2×C4×C61—42no—
207C2×C4×C61—44no—
208C2×C4×C61—42no—
209C2×C4×C61—42no—
210C2×C4×C61—41no—
211C2×C4×C61—41no—
212C2×C4×C61C4×D412yes—
213C2×C4×C61C4×D412yes—
214C2×C4×C61C23×C411yescharacteristic
215C2×C4×C61C22×D411yescharacteristic
216C2×C4×C61C2×#4111yescharacteristic
217C2×C4×C61C2×#4111yescharacteristic
218C2×C4×C61C2×#4111yescharacteristic
219C2×C4×C61C2×#4111yescharacteristic
220C22⋊D61—41no—
221C22⋊D61—41no—
222C2×Dic61—21no—
223C2×Dic61—22no—
224D244—21no—
225D244—21no—
226C4×D61—44no—
227C4×D61—41no—
228C4×D61—41no—
229Dic122—21no—
230Dic122—21no—
231C8×C61—41no—
232C8×C61—41no—
233#92418—22no—
234#92418—22no—
235#92418—22no—
236#92418—41no—
237#92418—41no—
238#92418#11712yes—
239#92418#11712yes—
240#21296—611nomaximal, Sylow
241C22×C61—22no—
242C22×C61—42no—
243C22×C61—41no—
244C22×C61C2×C4×D411yescharacteristic
245C22×C61#52911yescharacteristic
246C22×C61#52911yescharacteristic
247C2×D61—42no—
248C2×D61—41no—
249C4×C61—22no—
250C4×C61—22no—
251C4×C61—42no—
252C4×C61—42no—
253C4×C61—42no—
254C4×C61—41no—
255C4×C61C2×#11711yescharacteristic
256C4×C61C4×#4111yescharacteristic
257C4×C61#53211yescharacteristic
258C4×C61#53211yescharacteristic
259Dic61—42no—
260Dic61—41no—
261#2943—611no—
262#2922—611no—
263#2922—611no—
264#1975—611no—
265#1974—611no—
266#1946—611no—
267#1945—611no—
268#1938—611no—
269#1938—611no—
270#1937—611no—
271#1937—611no—
272#1778—611no—
273#1759—611no—
274#1759D6111yescharacteristic, complemented
275#1726—611no—
276C2×C61—21no—
277C2×C61—21no—
278C2×C61—81no—
279C2×C61#229311yescharacteristic
280C2×C61#295512yes—
281D61—81no—
282C2×#135—611no—
283C4×#41—611no—
284C4×#41C2×D6111yescharacteristic
285#442—612no—
286#441—612no—
287#440—612no—
288#440—612no—
289#433—1222no—
290#433—1222no—
291#431—1222no—
292#431—1222no—
293C2×#108—611no—
294C2×#108—611no—
295#427—611no—
296#424—611no—
297#424—611no—
298#424—611no—
299#424—611no—
300C2×#104—611no—
301C2×#104—611no—
302C2×#104C2×D6111yescharacteristic
303C2×#104C2×D6111yescharacteristic
304#416—611no—
305#416—611no—
306#408—611no—
307#408—611no—
308#408—611no—
309#408—611no—
310C4×M16—611no—
311C4×M16C2×D6111yescharacteristic
312C2×#97—611no—
313C2×#97—611no—
314C2×#97—611no—
315C2×C4×C8—611no—
316C2×C4×C8—611no—
317C2×C4×C8—611no—
318#376C2×D6111yescharacteristic
319#341—611no—
320#341—611no—
321#339—611no—
322#339—611no—
323#339C2×D6111yescharacteristic
324#339C2×D6111yescharacteristic
325C61#2129611yescharacteristic, complemented, Sylow
326C2×#41—611no—
327C2×#41C22×D6111yescharacteristic
328#135—1222no—
329#135—1222no—
330C2×Q16—611no—
331C2×SD16—611no—
332C2×SD16—611no—
333C2×D8—611no—
334C2×M16—611no—
335C2×M16—611no—
336C2×M16C22×D6111yescharacteristic
337C2×M16C22×D6111yescharacteristic
338C22×C8—611no—
339C22×C8—611no—
340C22×C8—611no—
341C22×C8—611no—
342C4×Q8—612no—
343C4×Q8C4×D6112yes—
344C4×D4—22no—
345C4×D4—612no—
346C4×D4—1222no—
347C4×D4C4×D6112yes—
348#117—21no—
349#117—611no—
350#117—1221no—
351#117C22×D6111yescharacteristic
352C2×C42—21no—
353C2×C42—1221no—
354C2×C42C22×D6111yescharacteristic
355C2×C42C22×D6111yescharacteristic
356C2×C42C22×D6111yescharacteristic
357#108—1222no—
358#108—1222no—
359#107—612no—
360#106—612no—
361C4⋊C8—1222no—
362C4⋊C8—1222no—
363C4⋊C8—1222no—
364C4⋊C8—1222no—
365#104—22no—
366#104—22no—
367#104—1222no—
368#104—1222no—
369#103—612no—
370#103—612no—
371#102—612no—
372#102—612no—
373C22⋊C8—1222no—
374C22⋊C8—1222no—
375C22⋊C8—1222no—
376C22⋊C8—1222no—
377#97—21no—
378#97—612no—
379#97—612no—
380#97—1222no—
381#97—1222no—
382#97—1221no—
383C4×C8—21no—
384C4×C8—612no—
385C4×C8—612no—
386C4×C8—1222no—
387C4×C8—1222no—
388C4×C8—1221no—
389#95—22no—
390#41—21no—
391#41—21no—
392#41—21no—
393#41—21no—
394#41—1221no—
395#41—1221no—
396#41—1221no—
397#41—1221no—
398C2×Q8—611no—
399C2×Q8C2×C4×D6111yescharacteristic
400C2×D4—21no—
401C2×D4—611no—
402C2×D4—1221no—
403C2×D4C2×C4×D6111yescharacteristic
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—1221no—
409C22×C4—1222no—
410C22×C4#1175822412yes—
411C22×C4C23×D6111yescharacteristic
412Q16—1222no—
413SD16—1222no—
414SD16—1222no—
415D8—1222no—
416M16—21no—
417M16—21no—
418M16—21no—
419M16—21no—
420M16—1221no—
421M16—1221no—
422M16—1221no—
423M16—1221no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—611no—
427C2×C8—611no—
428C2×C8—612no—
429C2×C8—612no—
430C2×C8—612no—
431C2×C8—612no—
432C2×C8—612no—
433C2×C8—1221no—
434C2×C8—1221no—
435C2×C8—1221no—
436C2×C8—1221no—
437C2×C8—1221no—
438C2×C8—1221no—
439C2×C8—1221no—
440C2×C8—1221no—
441C4⋊C4—22no—
442C4⋊C4—612no—
443C4⋊C4—1222no—
444C4⋊C4C2×C4×D6112yes—
445C22⋊C4—21no—
446C22⋊C4—22no—
447C22⋊C4—1221no—
448C22⋊C4—1222no—
449C42—21no—
450C42—21no—
451C42—21no—
452C42—22no—
453C42—1221no—
454C42—1222no—
455C42C2×C4×D6112yes—
456C42#1175822212yes—
457C42#1175822212yes—
458C42D4×D6111yescharacteristic
459C42D4×D6111yescharacteristic
460C23—21no—
461C23—1221no—
462C23C2×#1175822411yescharacteristic
463Q8—21no—
464Q8—21no—
465Q8—1221no—
466Q8—1221no—
467D4—21no—
468D4—21no—
469D4—41no—
470D4—41no—
471D4—1221no—
472D4—1221no—
473D4—2441no—
474D4—2441no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—42no—
480C2×C4—44no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—1222no—
486C2×C4—1221no—
487C2×C4—2444no—
488C2×C4—2441no—
489C2×C4—2441no—
490C2×C4#1451973712yes—
491C2×C4#1451973712yes—
492C2×C4C22×C4×D6111yescharacteristic
493C2×C4C2×D4×D6111yescharacteristic
494C2×C4#41×D6111yescharacteristic
495C2×C4#41×D6111yescharacteristic
496C2×C4C2×#1175822211yescharacteristic
497C2×C4C2×#1175822211yescharacteristic
498C8—41no—
499C8—41no—
500C8—612no—
501C8—612no—
502C8—1222no—
503C8—1222no—
504C8—1222no—
505C8—2441no—
506C8—2441no—
507C22—22no—
508C22—41no—
509C22—42no—
510C22—2441no—
511C22—2442no—
512C22C2×#1451973711yescharacteristic
513C22#1684029211yescharacteristic
514C22#1684029211yescharacteristic
515C4—22no—
516C4—22no—
517C4—42no—
518C4—42no—
519C4—41no—
520C4—42no—
521C4—2441no—
522C4—2442no—
523C4#117×D6111yescharacteristic
524C4C4×#1175822211yescharacteristic
525C4#1684030911yescharacteristic
526C4#1684030911yescharacteristic
527C2—21no—
528C2—21no—
529C2—81no—
530C2—4881no—
531C2#2144828211yescharacteristic
532C2#2145471812yes—
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1759C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519797C22
cosocleC22×C4×C61C24
hypercenter#1759D61
hypocenterC61#21296
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1759

Complements

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

NH ≅ G/Ntype
2. #21454464C2semidirect
3. #21454463C2semidirect
6. #21446571C2semidirect
7. #21446566C2semidirect
8. #21446531C2semidirect
9. #21446527C2semidirect
10. #21446524C2semidirect
11. #21446520C2semidirect
12. #21445726C2semidirect
13. #21445630C2semidirect
14. #21445506C2semidirect
15. C61×#1759C2semidirect
18. #16839872C4semidirect
19. #16839867C4semidirect
20. #16839862C4semidirect
21. #16839860C4semidirect
274. #1759D61semidirect
325. C61#21296semidirect

Maximal subgroups

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

subgroupindex
#214546172
#214544642
#214544632
#214467092
#214467042
#214465712
#214465662
#214465312
#214465272
#214465242
#214465202
#214457262
#214456302
#214455062
C61×#17592
#2129661