Finite Group Databasebeta

← #29683238

Subgroups — #29683238

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×#14519799C211yesmaximal, characteristic
2#21454461C211yesmaximal, characteristic, complemented
3C4×#14519783C211yesmaximal, characteristic, complemented
4#21446468C212yesmaximal, complemented
5#21446419C212yesmaximal, complemented
6#21446145C212yesmaximal
7#21446097C212yesmaximal, complemented
8C4×#14519713C211yesmaximal, characteristic, complemented
9C4×#14519705C211yesmaximal, characteristic, complemented
10C4×#14519705C211yesmaximal, characteristic, complemented
11C61×#1744C211yesmaximal, characteristic, complemented
12C2×#14519799C2211yescharacteristic
13C2×#14519783C2212yes—
14C4×#11758222C2211yescharacteristic
15C4×#11758222C2211yescharacteristic
16C4×Dic244C411yescharacteristic, complemented
17C4×Dic244C411yescharacteristic, complemented
18C4×#11758190C411yescharacteristic, complemented
19C4×#11758190C411yescharacteristic, complemented
20C4×#11758190C411yescharacteristic, complemented
21C4×#11758190C411yescharacteristic, complemented
22C4×D488C411yescharacteristic, complemented
23C4×D488C411yescharacteristic, complemented
24#16839821—22no—
25#16839813—21no—
26#16839813—21no—
27C2×#14519713C2212yes—
28#16839800C2211yescharacteristic
29#16839788C2212yes—
30C2×#14519705C2212yes—
31C2×#14519705C2212yes—
32#16839759C2211yescharacteristic
33#16839759C2211yescharacteristic
34#16839728C2212yes—
35#16839717C2212yes—
36#16839716—22no—
37C4×#11758194C2211yescharacteristic
38C4×#11758194C2211yescharacteristic
39C4×#11758189—21no—
40C4×C8×D61—21no—
41#16839527C2212yes—
42#16839522C2212yes—
43#16839522C2212yes—
44C2×C4×C8×C61C2211yescharacteristic
45C2×C4×C8×C61C2211yescharacteristic
46C43×C61C2211yescharacteristic
47C61×#336C2212yes—
48C61×#336C2212yes—
49C2×#11758222C2311yescharacteristic
50C2×#11758222C2311yescharacteristic
51#14519799—24no—
52C2×Dic244C2×C411yescharacteristic
53C2×#11758190C2×C411yescharacteristic
54C2×#11758190C2×C411yescharacteristic
55C2×D488C2×C411yescharacteristic
56#14519783—24no—
57#14519783—24no—
58C2×#11758194C2312yes—
59C2×#11758194C2312yes—
60C2×#11758189—22no—
61C2×C8×D61—22no—
62C4×Dic122C2×C411yescharacteristic
63C4×Dic122C2×C411yescharacteristic
64C4×Dic122C2×C411yescharacteristic
65C4×Dic122C2×C411yescharacteristic
66C4×D244C2×C411yescharacteristic
67C4×D244C2×C411yescharacteristic
68C4×D244C2×C411yescharacteristic
69C4×D244C2×C411yescharacteristic
70C4×C22⋊D61—21no—
71C4×C22⋊D61—21no—
72C4×C22⋊D61—21no—
73C4×C22⋊D61—21no—
74#14519736C2311yescharacteristic
75#14519736C2311yescharacteristic
76#14519734—21no—
77#14519734—21no—
78C42×D61—21no—
79C42×D61—21no—
80#14519713—24no—
81#14519711C2×C411yescharacteristic
82#14519711C2×C411yescharacteristic
83#14519709C2×C411yescharacteristic
84#14519709C2×C411yescharacteristic
85#14519706—22no—
86#14519706—22no—
87#14519705—24no—
88#14519705—24no—
89#14519702C2×C411yescharacteristic
90#14519702C2×C411yescharacteristic
91#14519702C2×C411yescharacteristic
92#14519702C2×C411yescharacteristic
93#14519699C2×C411yescharacteristic
94#14519699C2×C411yescharacteristic
95#14519699C2×C411yescharacteristic
96#14519699C2×C411yescharacteristic
97#14519689—22no—
98#14519689—22no—
99#14519688—21no—
100#14519688—21no—
101#14519687—22no—
102C4×#92418—21no—
103C4×#92418—21no—
104C8×Dic61—22no—
105C22×C8×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C22×C8×C61C2312yes—
108C2×C42×C61—21no—
109C2×C42×C61—21no—
110C2×C42×C61C2312yes—
111C2×C42×C61C2311yescharacteristic
112C4×C8×C61C2×C411yescharacteristic
113C4×C8×C61C2×C411yescharacteristic
114C4×C8×C61C2×C411yescharacteristic
115C4×C8×C61C2×C411yescharacteristic
116C4×C8×C61D411yescharacteristic
117C4×C8×C61D411yescharacteristic
118C4×C8×C61D412yes—
119C22×C4×C61—22no—
120C22×C4×C61#4111yescharacteristic
121C22×C4×C61#4111yescharacteristic
122C22×C4×C61C2411yescharacteristic
123C2×C22⋊D61—21no—
124C2×C22⋊D61—21no—
125#11758222—22no—
126#11758222—22no—
127#11758222—22no—
128#11758222#4114yes—
129C2×D244C22×C411yescharacteristic
130C2×D244C22×C411yescharacteristic
131C2×C4×D61—21no—
132C2×C4×D61—21no—
133C2×C4×D61—21no—
134C2×C4×D61—21no—
135C2×C4×D61—21no—
136C2×C4×D61—21no—
137C2×Dic122C22×C411yescharacteristic
138C2×Dic122C22×C411yescharacteristic
139C2×C8×C61—22no—
140C2×C8×C61—22no—
141C2×C8×C61—22no—
142C2×C8×C61—22no—
143C2×C8×C61C22×C411yescharacteristic
144C2×C8×C61C22×C411yescharacteristic
145C2×C8×C61C22×C411yescharacteristic
146C2×C8×C61C22×C411yescharacteristic
147C2×C8×C61C2×D412yes—
148C2×C8×C61C2×D412yes—
149C42×C61—24no—
150C42×C61—22no—
151C42×C61—22no—
152C42×C61—42no—
153C42×C61C22×C411yescharacteristic
154C42×C61C22×C411yescharacteristic
155C42×C61C2×D411yescharacteristic
156C42×C61C2×D411yescharacteristic
157C22⋊Dic61—21no—
158C22⋊Dic61—21no—
159#11758198—21no—
160#11758198—21no—
161#11758198—21no—
162#11758198—21no—
163C4⋊Dic61C22×C411yescharacteristic
164C4⋊Dic61C22×C411yescharacteristic
165C4⋊Dic61C22×C411yescharacteristic
166C4⋊Dic61C22×C411yescharacteristic
167#11758196—21no—
168#11758196—21no—
169#11758196—21no—
170#11758196—21no—
171C4×Dic61—21no—
172C4×Dic61—21no—
173C4×Dic61—21no—
174C4×Dic61—21no—
175C4×Dic61—21no—
176C4×Dic61—21no—
177#11758194—22no—
178#11758194—22no—
179#11758194—22no—
180#11758194#4114yes—
181C2×#92418—22no—
182C2×#92418—22no—
183Dic244—22no—
184D488—22no—
185#11758190—22no—
186#11758190—22no—
187#11758189—28no—
188C8×D61—28no—
189C23×C61C2×#4111yescharacteristic
190C22×D61—21no—
191C22×D61—21no—
192C2×C4×C61—22no—
193C2×C4×C61—22no—
194C2×C4×C61—24no—
195C2×C4×C61—42no—
196C2×C4×C61—42no—
197C2×C4×C61C4×D411yescharacteristic
198C2×C4×C61C4×D411yescharacteristic
199C2×C4×C61C4×D411yescharacteristic
200C2×C4×C61C4×D411yescharacteristic
201C2×C4×C61C23×C411yescharacteristic
202C2×C4×C61C22×D411yescharacteristic
203C2×C4×C61C2×#4112yes—
204C2×C4×C61C2×#4112yes—
205C22⋊D61—24no—
206C22⋊D61—42no—
207C2×Dic61—21no—
208C2×Dic61—21no—
209C2×Dic61—21no—
210C2×Dic61—21no—
211C2×Dic61—21no—
212C2×Dic61—21no—
213D244—21no—
214D244—21no—
215D244—21no—
216D244#11712yes—
217C4×D61—24no—
218C4×D61—42no—
219C4×D61—42no—
220C4×D61—42no—
221C4×D61—42no—
222C4×D61—42no—
223Dic122—21no—
224Dic122—21no—
225Dic122—21no—
226Dic122#11712yes—
227C8×C61—21no—
228C8×C61—21no—
229C8×C61—21no—
230C8×C61—21no—
231C8×C61—22no—
232C8×C61—22no—
233#92418—24no—
234#92418—42no—
235#21137—611nomaximal, Sylow
236C22×C61—21no—
237C22×C61—21no—
238C22×C61C2×C4×D411yescharacteristic
239C22×C61#52912yes—
240C2×D61—22no—
241C2×D61—41no—
242C2×D61—41no—
243C2×D61—41no—
244C2×D61—41no—
245C2×D61—41no—
246C4×C61—21no—
247C4×C61—21no—
248C4×C61—44no—
249C4×C61#44312yes—
250C4×C61#44412yes—
251C4×C61C2×#11711yescharacteristic
252C4×C61C4×#4111yescharacteristic
253C4×C61#52512yes—
254Dic61—22no—
255Dic61—41no—
256Dic61—41no—
257Dic61—41no—
258Dic61—41no—
259Dic61—41no—
260C4×#135—611no—
261#2922—611no—
262C4×#131—611no—
263#1929—612no—
264#1922—612no—
265#1876—612no—
266#1866—612no—
267C4×#108—611no—
268C4×#104—611no—
269C4×#104—611no—
270#1744D6111yescharacteristic, complemented
271C2×C61—22no—
272C2×C61#229011yescharacteristic
273C2×C61C2×#44311yescharacteristic
274C2×C61C2×#44411yescharacteristic
275D61—42no—
276D61—81no—
277C2×#135—611no—
278C2×#131—612no—
279C4×#41—611no—
280C4×#41—611no—
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—612no—
301#405—1222no—
302C4×M16—611no—
303C4×M16—611no—
304C4×M16—1221no—
305C2×C4×C8—1221no—
306C2×C4×C8C2×D6111yescharacteristic
307C2×C4×C8C2×D6111yescharacteristic
308C43C2×D6111yescharacteristic
309#341—612no—
310#339—612no—
311#339—612no—
312#336C2×D6112yes—
313#336C2×D6112yes—
314C61#2113711yescharacteristic, complemented, Sylow
315C2×#41—611no—
316C2×#41—611no—
317#135—1224no—
318C2×Q16—611no—
319C2×SD16—611no—
320C2×SD16—611no—
321C2×D8—611no—
322#131—1224no—
323#131—1224no—
324C2×M16—612no—
325C2×M16—612no—
326C2×M16—1222no—
327C22×C8—1222no—
328C22×C8C22×D6111yescharacteristic
329C22×C8C22×D6111yescharacteristic
330C22×C8C22×D6112yes—
331C4×Q8—611no—
332C4×Q8—611no—
333C4×Q8—611no—
334C4×Q8—611no—
335C4×D4—611no—
336C4×D4—611no—
337C4×D4—611no—
338C4×D4—611no—
339C4×D4—1221no—
340C4×D4—1221no—
341C4×D4—1221no—
342C4×D4—1221no—
343#117—611no—
344#117—611no—
345#117—1221no—
346#117—1221no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—1221no—
350C2×C42—1221no—
351C2×C42C22×D6112yes—
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—1222no—
373#97—1221no—
374#97—1221no—
375C4×C8—1222no—
376C4×C8—1221no—
377C4×C8—1221no—
378C4×C8C4×D6111yescharacteristic
379C4×C8C4×D6111yescharacteristic
380C4×C8C4×D6111yescharacteristic
381C4×C8C4×D6111yescharacteristic
382C4×C8D24412yes—
383C4×C8D24411yescharacteristic
384C4×C8D24411yescharacteristic
385#41—614no—
386#41—1222no—
387#41—1222no—
388#41—1222no—
389C2×Q8—611no—
390C2×Q8—611no—
391C2×D4—611no—
392C2×D4—611no—
393C2×D4—1221no—
394C2×D4—1221no—
395C22×C4—22no—
396C22×C4—1221no—
397C22×C4—1221no—
398C22×C4—1221no—
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—614no—
410M16—1228no—
411M16—1222no—
412M16—1222no—
413M16—1222no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—1228no—
419C2×C8—1222no—
420C2×C8—1222no—
421C2×C8C2×C4×D6111yescharacteristic
422C2×C8C2×C4×D6111yescharacteristic
423C2×C8C2×C4×D6111yescharacteristic
424C2×C8C2×C4×D6111yescharacteristic
425C2×C8C2×D24412yes—
426C2×C8C2×D24412yes—
427C4⋊C4—611no—
428C4⋊C4—611no—
429C4⋊C4—611no—
430C4⋊C4—611no—
431C4⋊C4—1221no—
432C4⋊C4—1221no—
433C4⋊C4—1221no—
434C4⋊C4—1221no—
435C22⋊C4—1221no—
436C22⋊C4—1221no—
437C22⋊C4—1221no—
438C22⋊C4—1221no—
439C22⋊C4—1221no—
440C22⋊C4—1221no—
441C42—24no—
442C42—22no—
443C42—22no—
444C42—42no—
445C42—1221no—
446C42—1221no—
447C42—1221no—
448C42—1221no—
449C42—1221no—
450C42—1221no—
451C42C2×C4×D6111yescharacteristic
452C42C2×C4×D6111yescharacteristic
453C42C2×D24411yescharacteristic
454C42C2×D24411yescharacteristic
455C23—1221no—
456C23—1221no—
457C23C2×#1175822211yescharacteristic
458Q8—612no—
459Q8—1221no—
460Q8—1221no—
461Q8—1221no—
462D4—612no—
463D4—1224no—
464D4—1221no—
465D4—1221no—
466D4—1221no—
467D4—2442no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—1221no—
474C2×C4—1224no—
475C2×C4—1221no—
476C2×C4—1221no—
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×D24411yescharacteristic
486C2×C4C4×D24411yescharacteristic
487C2×C4C4×D24411yescharacteristic
488C2×C4C4×D24411yescharacteristic
489C2×C4C22×C4×D6111yescharacteristic
490C2×C4C22×D24411yescharacteristic
491C2×C4#41×D6112yes—
492C2×C4#41×D6112yes—
493C8—21no—
494C8—21no—
495C8—21no—
496C8—21no—
497C8—22no—
498C8—22no—
499C8—1224no—
500C8—2442no—
501C22—21no—
502C22—21no—
503C22—1222no—
504C22—2441no—
505C22—2441no—
506C22—2441no—
507C22—2441no—
508C22—2441no—
509C22C2×C4×D24411yescharacteristic
510C22#1684029012yes—
511C4—21no—
512C4—21no—
513C4—44no—
514C4—1222no—
515C4—2441no—
516C4—2441no—
517C4—2441no—
518C4—2441no—
519C4—2441no—
520C4#1683988012yes—
521C4#1683988512yes—
522C4#117×D6111yescharacteristic
523C4#1684023011yescharacteristic
524C4#1684027412yes—
525C2—22no—
526C2—4881no—
527C2—2442no—
528C2#2144826311yescharacteristic
529C2C2×#1683988011yescharacteristic
530C2C2×#1683988511yescharacteristic
subgroupG/H
centerC42C2×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1744C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519799C22
cosocleC22×C4×C61C24
hypercenter#1744D61
hypocenterC61#21137
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C42 ◁ C2×C4×C8 ◁ #1744

Complements

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

NH ≅ G/Ntype
2. #21454461C2semidirect
3. C4×#14519783C2semidirect
4. #21446468C2semidirect
5. #21446419C2semidirect
7. #21446097C2semidirect
8. C4×#14519713C2semidirect
9. C4×#14519705C2semidirect
10. C4×#14519705C2semidirect
11. C61×#1744C2semidirect
16. C4×Dic244C4semidirect
17. C4×Dic244C4semidirect
18. C4×#11758190C4semidirect
19. C4×#11758190C4semidirect
20. C4×#11758190C4semidirect
21. C4×#11758190C4semidirect
22. C4×D488C4semidirect
23. C4×D488C4semidirect
270. #1744D61semidirect
314. C61#21137semidirect

Maximal subgroups

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

subgroupindex
C4×#145197992
#214544612
C4×#145197832
#214464682
#214464192
#214461452
#214460972
C4×#145197132
C4×#145197052
C61×#17442
#2113761