Finite Group Databasebeta

← #29683237

Subgroups — #29683237

Order 15616.

800 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519797C211yesmaximal, characteristic
2#21454461C211yesmaximal, characteristic, complemented
3#21446467C212yesmaximal, complemented
4#21446418C212yesmaximal, complemented
5#21446146C212yesmaximal
6#21446094C212yesmaximal, complemented
7C4×#14519712C211yesmaximal, characteristic, complemented
8C4×#14519703C211yesmaximal, characteristic, complemented
9C4×#14519704C211yesmaximal, characteristic, complemented
10#21445564C211yesmaximal, characteristic, complemented
11C4×#131×C61C211yesmaximal, characteristic, complemented
12C2×#14519797C2211yescharacteristic
13C4×#11758222C2211yescharacteristic
14C4×#11758202C411yescharacteristic, complemented
15C4×#11758202C411yescharacteristic, complemented
16C4×#11758201C411yescharacteristic, complemented
17C4×#11758201C411yescharacteristic, complemented
18C4×#11758200C411yescharacteristic, complemented
19C4×#11758200C411yescharacteristic, complemented
20C4×#11758199C411yescharacteristic, complemented
21C4×#11758199C411yescharacteristic, complemented
22#16839821—22no—
23#16839813—21no—
24#16839813—21no—
25C2×#14519712C2212yes—
26#16839798C2211yescharacteristic
27#16839788C2212yes—
28C2×#14519704C2212yes—
29C2×#14519703C2212yes—
30#16839758C2211yescharacteristic
31#16839756C2211yescharacteristic
32#16839728C2212yes—
33C4×#11758194C2211yescharacteristic
34C2×C4×#92418C2211yescharacteristic
35C42×Dic61C2211yescharacteristic
36#16839526C2212yes—
37#16839523C2212yes—
38#16839521C2212yes—
39#16839516C2212yes—
40#16839516C2212yes—
41C2×#131×C61C2212yes—
42C4×#41×C61C2211yescharacteristic
43C61×#405—22no—
44C61×#405C2212yes—
45C4×M16×C61—21no—
46C4×M16×C61C2211yescharacteristic
47C2×C4×C8×C61—21no—
48C2×C4×C8×C61C2211yescharacteristic
49C2×#11758222C2311yescharacteristic
50#14519797—24no—
51C2×#11758202C2×C411yescharacteristic
52C2×#11758200C2×C411yescharacteristic
53C2×#11758201C2×C411yescharacteristic
54C2×#11758199C2×C411yescharacteristic
55C2×#11758194C2312yes—
56C22×#92418C2311yescharacteristic
57C22×#92418C2311yescharacteristic
58C4×Dic122C2×C411yescharacteristic
59C4×Dic122C2×C411yescharacteristic
60C4×D244C2×C411yescharacteristic
61C4×D244C2×C411yescharacteristic
62C4×C22⋊D61—21no—
63C4×C22⋊D61—21no—
64#14519736C2311yescharacteristic
65#14519734—21no—
66C2×C4×Dic61—21no—
67C2×C4×Dic61—21no—
68C2×C4×Dic61C2312yes—
69C42×D61—21no—
70#14519712—24no—
71#14519710C2×C411yescharacteristic
72#14519710C2×C411yescharacteristic
73#14519708C2×C411yescharacteristic
74#14519708C2×C411yescharacteristic
75#14519706—22no—
76#14519706—22no—
77#14519704—24no—
78#14519703—24no—
79#14519701C2×C411yescharacteristic
80#14519701C2×C411yescharacteristic
81#14519700C2×C411yescharacteristic
82#14519700C2×C411yescharacteristic
83#14519698C2×C411yescharacteristic
84#14519698C2×C411yescharacteristic
85#14519697C2×C411yescharacteristic
86#14519697C2×C411yescharacteristic
87#14519689—22no—
88#14519689—22no—
89#14519688—21no—
90C4×#92418—21no—
91C4×#92418C2×C411yescharacteristic
92C4×#92418C2×C411yescharacteristic
93C4×#92418C2×C411yescharacteristic
94C4×#92418C2×C411yescharacteristic
95C2×#41×C61C2311yescharacteristic
96#131×C61—24no—
97#131×C61—24no—
98C2×M16×C61—22no—
99C2×M16×C61C2312yes—
100C22×C8×C61—22no—
101C22×C8×C61C2312yes—
102C4×Q8×C61C2×C411yescharacteristic
103C4×Q8×C61C2×C411yescharacteristic
104C4×D4×C61—21no—
105C4×D4×C61—21no—
106C4×D4×C61C2×C411yescharacteristic
107C4×D4×C61C2×C411yescharacteristic
108#117×C61—21no—
109#117×C61C2311yescharacteristic
110C2×C42×C61—21no—
111C2×C42×C61C2311yescharacteristic
112#97×C61—22no—
113#97×C61—21no—
114C4×C8×C61—22no—
115C4×C8×C61—21no—
116C4×C8×C61D411yescharacteristic
117C4×C8×C61D411yescharacteristic
118C4×C8×C61D412yes—
119#41×C61—22no—
120#41×C61#4114yes—
121C2×Q8×C61C22×C411yescharacteristic
122C2×D4×C61—21no—
123C2×D4×C61C22×C411yescharacteristic
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61#4111yescharacteristic
128C22×C4×C61#4111yescharacteristic
129C22×C4×C61C2411yescharacteristic
130C2×C22⋊D61—21no—
131C22×Dic61—22no—
132#11758222—22no—
133#11758222—22no—
134C2×D244C22×C411yescharacteristic
135C2×C4×D61—21no—
136C2×C4×D61—21no—
137C2×C4×D61—21no—
138C2×Dic122C22×C411yescharacteristic
139M16×C61—28no—
140M16×C61—22no—
141M16×C61#4114yes—
142C2×C8×C61—28no—
143C2×C8×C61—22no—
144C2×C8×C61—22no—
145C2×C8×C61—22no—
146C2×C8×C61C2×D412yes—
147C2×C8×C61C2×D412yes—
148C4⋊C4×C61—21no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61C22×C411yescharacteristic
151C4⋊C4×C61C22×C411yescharacteristic
152C22⋊C4×C61—21no—
153C22⋊C4×C61—21no—
154C22⋊C4×C61—21no—
155C42×C61—21no—
156C42×C61—21no—
157C42×C61—21no—
158C42×C61C22×C411yescharacteristic
159C42×C61C22×C411yescharacteristic
160C42×C61C2×D411yescharacteristic
161C42×C61C2×D411yescharacteristic
162C22⋊Dic61—21no—
163#11758202—22no—
164#11758201—22no—
165#11758200—22no—
166#11758199—22no—
167#11758198—21no—
168#11758198—21no—
169C4⋊Dic61C22×C411yescharacteristic
170C4⋊Dic61C22×C411yescharacteristic
171#11758196—21no—
172#11758196—21no—
173C4×Dic61—24no—
174C4×Dic61—21no—
175C4×Dic61—21no—
176C4×Dic61—21no—
177C4×Dic61—22no—
178C4×Dic61—22no—
179C4×Dic61—42no—
180#11758194—22no—
181#11758194—22no—
182C2×#92418—22no—
183C2×#92418—22no—
184C2×#92418—22no—
185C2×#92418C22×C411yescharacteristic
186C2×#92418C22×C411yescharacteristic
187C2×#92418C22×C411yescharacteristic
188C2×#92418C22×C411yescharacteristic
189C23×C61—21no—
190C23×C61C2×#4111yescharacteristic
191C22×D61—21no—
192Q8×C61—21no—
193Q8×C61#11712yes—
194D4×C61—24no—
195D4×C61—21no—
196D4×C61#11712yes—
197C2×C4×C61—21no—
198C2×C4×C61—24no—
199C2×C4×C61—22no—
200C2×C4×C61—22no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—42no—
204C2×C4×C61—42no—
205C2×C4×C61C4×D411yescharacteristic
206C2×C4×C61C4×D411yescharacteristic
207C2×C4×C61C4×D411yescharacteristic
208C2×C4×C61C4×D411yescharacteristic
209C2×C4×C61C23×C411yescharacteristic
210C2×C4×C61C22×D411yescharacteristic
211C2×C4×C61C2×#4112yes—
212C2×C4×C61C2×#4112yes—
213C22⋊D61—42no—
214C2×Dic61—24no—
215C2×Dic61—21no—
216C2×Dic61—21no—
217C2×Dic61—21no—
218C2×Dic61—42no—
219C2×Dic61—42no—
220D244—21no—
221D244—21no—
222C4×D61—42no—
223C4×D61—42no—
224C4×D61—42no—
225Dic122—21no—
226Dic122—21no—
227C8×C61—22no—
228C8×C61—24no—
229C8×C61—22no—
230#92418—21no—
231#92418—21no—
232#92418—21no—
233#92418—21no—
234#92418—42no—
235#21137—611nomaximal, Sylow
236C22×C61—21no—
237C22×C61—21no—
238C22×C61—22no—
239C22×C61—41no—
240C22×C61—41no—
241C22×C61C2×C4×D411yescharacteristic
242C22×C61#52912yes—
243C2×D61—41no—
244C2×D61—41no—
245C2×D61—41no—
246C4×C61—21no—
247C4×C61—21no—
248C4×C61—22no—
249C4×C61—41no—
250C4×C61—41no—
251C4×C61#44312yes—
252C4×C61#44412yes—
253C4×C61C2×#11711yescharacteristic
254C4×C61C4×#4111yescharacteristic
255C4×C61#52512yes—
256Dic61—44no—
257Dic61—41no—
258Dic61—41no—
259Dic61—41no—
260C4×#135—611no—
261#2922—611no—
262C4×#131D6111yescharacteristic, complemented
263#1929—612no—
264#1922—612no—
265#1876—612no—
266#1866—612no—
267C4×#108—611no—
268C4×#104—611no—
269C4×#104—611no—
270#1744—611no—
271C2×C61—22no—
272C2×C61—42no—
273C2×C61#229011yescharacteristic
274C2×C61C2×#44311yescharacteristic
275C2×C61C2×#44411yescharacteristic
276D61—81no—
277C2×#135—611no—
278C2×#131C2×D6112yes—
279C4×#41—611no—
280C4×#41C2×D6111yescharacteristic
281C4×Q16—611no—
282C4×Q16—611no—
283C4×SD16—611no—
284C4×SD16—611no—
285C4×SD16—611no—
286C4×SD16—611no—
287C4×D8—611no—
288C4×D8—611no—
289#433—1222no—
290#431—1221no—
291#431—1221no—
292C2×#108—612no—
293#427—611no—
294#424—612no—
295C2×#104—612no—
296C2×#104—612no—
297#416—611no—
298#416—611no—
299#408—612no—
300#405—22no—
301#405C2×D6112yes—
302C4×M16—21no—
303C4×M16—611no—
304C4×M16C2×D6111yescharacteristic
305C2×C4×C8—21no—
306C2×C4×C8—611no—
307C2×C4×C8C2×D6111yescharacteristic
308C43—611no—
309#341—612no—
310#339—612no—
311#339—612no—
312#336—612no—
313#336—612no—
314C61#2113711yescharacteristic, complemented, Sylow
315C2×#41—611no—
316C2×#41C22×D6111yescharacteristic
317#135—1224no—
318C2×Q16—611no—
319C2×SD16—611no—
320C2×SD16—611no—
321C2×D8—611no—
322#131—24no—
323#131—24no—
324C2×M16—22no—
325C2×M16—612no—
326C2×M16C22×D6112yes—
327C22×C8—22no—
328C22×C8—611no—
329C22×C8—611no—
330C22×C8C22×D6112yes—
331C4×Q8—611no—
332C4×Q8—611no—
333C4×Q8C4×D6111yescharacteristic
334C4×Q8C4×D6111yescharacteristic
335C4×D4—21no—
336C4×D4—21no—
337C4×D4—611no—
338C4×D4—611no—
339C4×D4—1221no—
340C4×D4—1221no—
341C4×D4C4×D6111yescharacteristic
342C4×D4C4×D6111yescharacteristic
343#117—21no—
344#117—611no—
345#117—1221no—
346#117C22×D6111yescharacteristic
347C2×C42—21no—
348C2×C42—612no—
349C2×C42—1221no—
350C2×C42—1221no—
351C2×C42—1221no—
352C2×C42C22×D6111yescharacteristic
353#108—1224no—
354#107—611no—
355#107—611no—
356#106—611no—
357#106—611no—
358C4⋊C8—1222no—
359C4⋊C8—1222no—
360#104—1224no—
361#104—1224no—
362#103—611no—
363#103—611no—
364#103—611no—
365#103—611no—
366#102—611no—
367#102—611no—
368#102—611no—
369#102—611no—
370C22⋊C8—1222no—
371C22⋊C8—1222no—
372#97—22no—
373#97—21no—
374#97—1221no—
375C4×C8—22no—
376C4×C8—21no—
377C4×C8—611no—
378C4×C8—611no—
379C4×C8—611no—
380C4×C8—611no—
381C4×C8—1221no—
382C4×C8C22⋊D6112yes—
383C4×C8C22⋊D6111yescharacteristic
384C4×C8C22⋊D6111yescharacteristic
385#41—22no—
386#41—1222no—
387#41—1222no—
388#41#1175822214yes—
389C2×Q8—611no—
390C2×Q8C2×C4×D6111yescharacteristic
391C2×D4—21no—
392C2×D4—611no—
393C2×D4—1221no—
394C2×D4C2×C4×D6111yescharacteristic
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—1222no—
399C22×C4—1221no—
400C22×C4—1221no—
401C22×C4—1221no—
402C22×C4#1175822211yescharacteristic
403C22×C4#1175822211yescharacteristic
404C22×C4C23×D6111yescharacteristic
405Q16—1222no—
406SD16—1222no—
407SD16—1222no—
408D8—1222no—
409M16—28no—
410M16—22no—
411M16—1222no—
412M16—1222no—
413M16#1175822214yes—
414C2×C8—28no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—611no—
419C2×C8—611no—
420C2×C8—611no—
421C2×C8—611no—
422C2×C8—1222no—
423C2×C8—1222no—
424C2×C8—1222no—
425C2×C8C2×C22⋊D6112yes—
426C2×C8C2×C22⋊D6112yes—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—611no—
430C4⋊C4—611no—
431C4⋊C4—1221no—
432C4⋊C4—1221no—
433C4⋊C4C2×C4×D6111yescharacteristic
434C4⋊C4C2×C4×D6111yescharacteristic
435C22⋊C4—21no—
436C22⋊C4—21no—
437C22⋊C4—21no—
438C22⋊C4—1221no—
439C22⋊C4—1221no—
440C22⋊C4—1221no—
441C42—21no—
442C42—21no—
443C42—21no—
444C42—1224no—
445C42—1221no—
446C42—1221no—
447C42—1221no—
448C42—1222no—
449C42—1222no—
450C42—2442no—
451C42C2×C4×D6111yescharacteristic
452C42C2×C4×D6111yescharacteristic
453C42C2×C22⋊D6111yescharacteristic
454C42C2×C22⋊D6111yescharacteristic
455C23—21no—
456C23—1221no—
457C23C2×#1175822211yescharacteristic
458Q8—21no—
459Q8—1221no—
460Q8—1221no—
461Q8#1451973412yes—
462D4—24no—
463D4—21no—
464D4—1221no—
465D4—1221no—
466D4—2442no—
467D4#1451973412yes—
468C2×C4—21no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—1224no—
477C2×C4—1221no—
478C2×C4—1221no—
479C2×C4—1221no—
480C2×C4—2442no—
481C2×C4—2442no—
482C2×C4—2442no—
483C2×C4—2442no—
484C2×C4—2442no—
485C2×C4C4×C22⋊D6111yescharacteristic
486C2×C4C4×C22⋊D6111yescharacteristic
487C2×C4C4×C22⋊D6111yescharacteristic
488C2×C4C4×C22⋊D6111yescharacteristic
489C2×C4C22×C4×D6111yescharacteristic
490C2×C4C22×C22⋊D6111yescharacteristic
491C2×C4C2×#1175822212yes—
492C2×C4C2×#1175822212yes—
493C8—22no—
494C8—24no—
495C8—22no—
496C8—1221no—
497C8—1221no—
498C8—1221no—
499C8—1221no—
500C8—2442no—
501C22—21no—
502C22—21no—
503C22—22no—
504C22—41no—
505C22—41no—
506C22—2441no—
507C22—2441no—
508C22—2441no—
509C22C2×C4×C22⋊D6111yescharacteristic
510C22#1684029612yes—
511C4—22no—
512C4—21no—
513C4—21no—
514C4—41no—
515C4—41no—
516C4—2444no—
517C4—2441no—
518C4—2441no—
519C4—2441no—
520C4#1683987712yes—
521C4#1683988212yes—
522C4C2×#1451973411yescharacteristic
523C4C4×#1175822211yescharacteristic
524C4#1684027312yes—
525C2—22no—
526C2—42no—
527C2—4881no—
528C2#2144826211yescharacteristic
529C2C2×#1683987711yescharacteristic
530C2C2×#1683988211yescharacteristic
subgroupG/H
centerC42C2×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#131×C61C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519797C22
cosocleC22×C4×C61C24
hypercenterC4×#131D61
hypocenterC61#21137
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C42 ◁ C2×C4×C8 ◁ C4×#131

Complements

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

NH ≅ G/Ntype
2. #21454461C2semidirect
3. #21446467C2semidirect
4. #21446418C2semidirect
6. #21446094C2semidirect
7. C4×#14519712C2semidirect
8. C4×#14519703C2semidirect
9. C4×#14519704C2semidirect
10. #21445564C2semidirect
11. C4×#131×C61C2semidirect
14. C4×#11758202C4semidirect
15. C4×#11758202C4semidirect
16. C4×#11758201C4semidirect
17. C4×#11758201C4semidirect
18. C4×#11758200C4semidirect
19. C4×#11758200C4semidirect
20. C4×#11758199C4semidirect
21. C4×#11758199C4semidirect
262. C4×#131D61semidirect
314. C61#21137semidirect

Maximal subgroups

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

subgroupindex
C4×#145197972
#214544612
#214464672
#214464182
#214461462
#214460942
C4×#145197122
C4×#145197032
C4×#145197042
#214455642
C4×#131×C612
#2113761