Finite Group Databasebeta

← #29646604

Subgroups — #29646604

Order 15616.

920 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459246C211yesmaximal, characteristic
2#21454930C211yesmaximal, characteristic, complemented
3#21444241C212yesmaximal, complemented
4#21444233C212yesmaximal, complemented
5#21444228C212yesmaximal, complemented
6#21444223C212yesmaximal, complemented
7#21444215C211yesmaximal, characteristic, complemented
8#21444207C211yesmaximal, characteristic, complemented
9#21444202C211yesmaximal, characteristic, complemented
10C2×#16839494C211yesmaximal, characteristic, complemented
11C61×#2965C211yesmaximal, characteristic, complemented
12#16840390C411yescharacteristic
13#16840383C412yes—
14#16840377—21no—
15#16840374C412yes—
16#16840370—21no—
17#16840354—22no—
18#16840340C411yescharacteristic
19#16840338C411yescharacteristic
20#16840333C411yescharacteristic
21#16840319C2212yes—
22#16840316—21no—
23#16840296C2212yes—
24#16840294—21no—
25#16840292—22no—
26C4×#11758222C2211yescharacteristic
27C2×C4×Dic122C2211yescharacteristic
28Q8×#92418—21no—
29D4×#92418—22no—
30D4×#92418—21no—
31#16839815C2211yescharacteristic
32#16839815C2212yes—
33C2×C4⋊#92418C2211yescharacteristic
34C2×C4⋊#92418C2212yes—
35#16839494C2212yes—
36#16839494C2212yes—
37#16839494C2211yescharacteristic
38#16839494C2211yescharacteristic
39#16839494C2212yes—
40#16839494C2212yes—
41#16839494C2212yes—
42#16839491C2211yescharacteristic
43#16839491C2211yescharacteristic
44#16839491C2212yes—
45C4×#41×C61C2211yescharacteristic
46C61×#446—21no—
47C61×#436—21no—
48C61×#435—22no—
49C61×#431C2211yescharacteristic
50C61×#431C2212yes—
51C4×M16×C61C2212yes—
52C2×C4×C8×C61C2211yescharacteristic
53C2×#11758222C2×C411yescharacteristic
54C22×Dic122C2×C411yescharacteristic
55C22×#92418—21no—
56C22×#92418—22no—
57#14519777C2×C412yes—
58#14519777C2×C412yes—
59#14519776—21no—
60#14519775—21no—
61#14519772—22no—
62#14519771—22no—
63#14519770—22no—
64#14519770—22no—
65#14519769—22no—
66#14519769C2×C412yes—
67#14519768—21no—
68#14519767—22no—
69#14519767—22no—
70#14519765C2×C412yes—
71#14519764—21no—
72#14519763—22no—
73#14519761—22no—
74#14519760—22no—
75#14519759—22no—
76#14519758—22no—
77#14519757—21no—
78#14519757—21no—
79#14519756—22no—
80#14519756C2×C412yes—
81#14519756C2×C412yes—
82#14519756C2×C412yes—
83#14519755—22no—
84#14519754—22no—
85#14519753—21no—
86#14519751C2×C412yes—
87#14519749—22no—
88#14519748—21no—
89C4×Dic122—21no—
90C4×Dic122—21no—
91C4×Dic122—22no—
92C4×Dic122C2×C412yes—
93C4×Dic122C2×C411yescharacteristic
94C4×Dic122C2312yes—
95C4×Dic122C2311yescharacteristic
96C4×D244C2×C411yescharacteristic
97C4×D244C2311yescharacteristic
98C4×C22⋊D61—21no—
99C4×C22⋊D61—21no—
100C4×C22⋊D61—22no—
101#14519736—22no—
102#14519736C2×C411yescharacteristic
103#14519734—21no—
104#14519734—22no—
105C2×C4⋊Dic61C2×C411yescharacteristic
106C2×#11758196—21no—
107C2×C4×Dic61—21no—
108C42×D61—21no—
109C4⋊#92418—21no—
110C4⋊#92418—22no—
111C4⋊#92418C2311yescharacteristic
112C4⋊#92418C2312yes—
113C4⋊#92418C2311yescharacteristic
114C22⋊#92418—21no—
115C22⋊#92418—22no—
116C4×#92418—21no—
117C4×#92418—22no—
118C2×#41×C61C2×C411yescharacteristic
119C2×M16×C61—22no—
120C22×C8×C61—21no—
121C4×Q8×C61D411yescharacteristic
122C4×Q8×C61D411yescharacteristic
123C4×D4×C61D412yes—
124C4×D4×C61D411yescharacteristic
125C4×D4×C61D412yes—
126C4×D4×C61D411yescharacteristic
127#117×C61C2×C411yescharacteristic
128#117×C61C2×C412yes—
129C2×C42×C61C2311yescharacteristic
130C2×C42×C61C2312yes—
131C4⋊C8×C61—22no—
132C4⋊C8×C61—21no—
133C22⋊C8×C61—21no—
134C22⋊C8×C61—22no—
135#97×C61—22no—
136C4×C8×C61—21no—
137C4×C8×C61C2311yescharacteristic
138C4×C8×C61C2311yescharacteristic
139C4×C8×C61C2312yes—
140#41×C61—24no—
141C2×Q8×C61C22⋊C411yescharacteristic
142C2×D4×C61C22⋊C411yescharacteristic
143C2×D4×C61C22⋊C412yes—
144C22×C4×C61C22×C412yes—
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D412yes—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D412yes—
150C2×C22⋊D61—21no—
151C2×C22⋊D61—22no—
152C22×Dic61—21no—
153C22×Dic61—21no—
154#11758222—24no—
155C2×D244C22×C411yescharacteristic
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×Dic122—24no—
160C2×Dic122—21no—
161C2×Dic122—22no—
162C2×Dic122C22×C412yes—
163C2×Dic122C22×C411yescharacteristic
164M16×C61—44no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—22no—
168C2×C8×C61—42no—
169C4⋊C4×C61C22⋊C412yes—
170C4⋊C4×C61C22⋊C411yescharacteristic
171C4⋊C4×C61C22⋊C411yescharacteristic
172C4⋊C4×C61C22⋊C412yes—
173C22⋊C4×C61C22⋊C412yes—
174C22⋊C4×C61C22⋊C412yes—
175C22⋊C4×C61C22⋊C412yes—
176C42×C61C22×C411yescharacteristic
177C42×C61C22×C412yes—
178C42×C61C2×D411yescharacteristic
179C42×C61C2×D412yes—
180C42×C61C2×D411yescharacteristic
181C42×C61C2×D412yes—
182C42×C61C2411yescharacteristic
183C22⋊Dic61—22no—
184C22⋊Dic61—22no—
185C22⋊Dic61—21no—
186C22⋊Dic61—22no—
187#11758198—21no—
188#11758198—22no—
189#11758198—22no—
190#11758198—22no—
191#11758198—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—22no—
194C4⋊Dic61—22no—
195C4⋊Dic61—22no—
196C4⋊Dic61C22×C412yes—
197C4⋊Dic61C22×C411yescharacteristic
198C4⋊Dic61C22×C411yescharacteristic
199#11758196—22no—
200#11758196—21no—
201#11758196—22no—
202#11758196—22no—
203#11758196—22no—
204#11758196—22no—
205#11758196—22no—
206#11758196—22no—
207#11758196—21no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210C4×Dic61—22no—
211C4×Dic61—21no—
212C4×Dic61—22no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—22no—
216C2×#92418—81no—
217C2×#92418—82no—
218C23×C61C2×C22⋊C412yes—
219C23×C61C2×C22⋊C411yescharacteristic
220C22×D61—21no—
221Q8×C61—22no—
222D4×C61—24no—
223D4×C61—22no—
224C2×C4×C61—24no—
225C2×C4×C61—21no—
226C2×C4×C61—22no—
227C2×C4×C61—21no—
228C2×C4×C61—22no—
229C2×C4×C61—41no—
230C2×C4×C61—42no—
231C2×C4×C61C2×C22⋊C411yescharacteristic
232C2×C4×C61C2×C22⋊C411yescharacteristic
233C2×C4×C61C2×C22⋊C412yes—
234C2×C4×C61C2×C22⋊C412yes—
235C2×C4×C61C2×C22⋊C412yes—
236C2×C4×C61C2×C22⋊C411yescharacteristic
237C2×C4×C61#13114yes—
238C2×C4×C61C23×C411yescharacteristic
239C2×C4×C61C22×D411yescharacteristic
240C2×C4×C61C22×D411yescharacteristic
241C22⋊D61—42no—
242C22⋊D61—82no—
243C2×Dic61—21no—
244C2×Dic61—22no—
245C2×Dic61—21no—
246C2×Dic61—22no—
247C2×Dic61—21no—
248C2×Dic61—42no—
249C2×Dic61—81no—
250D244—22no—
251C4×D61—41no—
252C4×D61—41no—
253C4×D61—42no—
254C4×D61—81no—
255Dic122—24no—
256Dic122—22no—
257Dic122—42no—
258Dic122—82no—
259C8×C61—22no—
260C8×C61—41no—
261C8×C61—42no—
262#92418—41no—
263#92418—42no—
264#92418—41no—
265#17469—611nomaximal, Sylow
266C22×C61—21no—
267C22×C61—21no—
268C22×C61—22no—
269C22×C61—22no—
270C22×C61—22no—
271C22×C61#40812yes—
272C22×C61C22×C22⋊C411yescharacteristic
273C2×D61—41no—
274C2×D61—41no—
275C2×D61—41no—
276C4×C61—22no—
277C4×C61—21no—
278C4×C61—22no—
279C4×C61—21no—
280C4×C61—22no—
281C4×C61—21no—
282C4×C61#40812yes—
283C4×C61C2×#13112yes—
284C4×C61#57711yescharacteristic
285C4×C61#57811yescharacteristic
286Dic61—42no—
287Dic61—41no—
288Dic61—41no—
289Dic61—41no—
290Dic61—42no—
291#3461—611no—
292#2988—611no—
293#2965D6111yescharacteristic, complemented
294#1485—612no—
295#1483—612no—
296#1482—612no—
297#1481—612no—
298#1479—611no—
299#1477—611no—
300#1476—611no—
301C2×Q8⋊C8—611no—
302C2×C61—22no—
303C2×C61—42no—
304C2×C61C2×#40811yescharacteristic
305C2×C61#289811yescharacteristic
306C2×C61#290111yescharacteristic
307D61—81no—
308#544—611no—
309#542—612no—
310#542—1221no—
311#541—612no—
312#541—1221no—
313#539—1222no—
314#537—611no—
315#536—611no—
316#536—611no—
317#533—612no—
318#533—1221no—
319#529—612no—
320#529—1222no—
321#529—1221no—
322C4×#41—611no—
323C4×#41C2×D6111yescharacteristic
324C2×C4×Q8—611no—
325#446—21no—
326C8×Q8—1221no—
327#436—21no—
328#435—22no—
329C8×D4—1221no—
330C8×D4—1222no—
331#431—611no—
332#431—612no—
333#431C2×D6111yescharacteristic
334#431C2×D6112yes—
335C2×C4⋊C8—611no—
336C2×C4⋊C8—612no—
337C4×M16C2×D6112yes—
338C2×C4×C8C2×D6111yescharacteristic
339Q8⋊C8—612no—
340Q8⋊C8—612no—
341Q8⋊C8—611no—
342Q8⋊C8—611no—
343Q8⋊C8—612no—
344Q8⋊C8—612no—
345Q8⋊C8—612no—
346D4⋊C8—611no—
347D4⋊C8—611no—
348D4⋊C8—612no—
349C61#1746911yescharacteristic, complemented, Sylow
350C2×#41—611no—
351C2×#41C4×D6111yescharacteristic
352C22×Q8—611no—
353C2×M16—22no—
354C22×C8—21no—
355C22×C8—1221no—
356C22×C8—1222no—
357C4⋊Q8—612no—
358C4⋊Q8—612no—
359C4⋊Q8—1221no—
360C4⋊Q8—1221no—
361#126—1222no—
362#126—1222no—
363#126—1222no—
364#126—1222no—
365#125—612no—
366#125—1222no—
367#125—1221no—
368#125—1222no—
369#125—1222no—
370#124—612no—
371#124—1221no—
372#124—1222no—
373#123—1222no—
374#123—1222no—
375#123—1222no—
376#123—1222no—
377C22⋊Q8—612no—
378C22⋊Q8—612no—
379C22⋊Q8—612no—
380C22⋊Q8—1221no—
381C22⋊Q8—1222no—
382C22⋊Q8—1221no—
383C22⋊Q8—1221no—
384C22⋊Q8—1222no—
385C22⋊Q8—1222no—
386#121—612no—
387#121—1222no—
388#121—1221no—
389C4×Q8—612no—
390C4×Q8—611no—
391C4×Q8—612no—
392C4×Q8—611no—
393C4×Q8—1221no—
394C4×Q8—1222no—
395C4×Q8—1221no—
396C4×Q8D24411yescharacteristic
397C4×Q8C22⋊D6111yescharacteristic
398C4×D4—611no—
399C4×D4—611no—
400C4×D4—1221no—
401C4×D4—1222no—
402C4×D4—1221no—
403C4×D4D24411yescharacteristic
404C4×D4D24412yes—
405C4×D4C22⋊D6112yes—
406C4×D4C22⋊D6111yescharacteristic
407#117—611no—
408#117—1222no—
409#117—1222no—
410#117—1221no—
411#117C4×D6111yescharacteristic
412#117C4×D6112yes—
413C2×C4⋊C4—611no—
414C2×C4⋊C4—1221no—
415C2×C42—1221no—
416C2×C42—1221no—
417C2×C42C22×D6111yescharacteristic
418C2×C42C22×D6112yes—
419C4⋊C8—22no—
420C4⋊C8—21no—
421C4⋊C8—611no—
422C4⋊C8—612no—
423C4⋊C8—611no—
424C4⋊C8—1221no—
425C4⋊C8—1222no—
426C22⋊C8—21no—
427C22⋊C8—22no—
428C22⋊C8—1221no—
429C22⋊C8—1222no—
430#97—22no—
431C4×C8—21no—
432C4×C8—1221no—
433C4×C8—1222no—
434C4×C8C22×D6111yescharacteristic
435C4×C8C22×D6111yescharacteristic
436C4×C8C22×D6112yes—
437#41—24no—
438#41—1224no—
439C2×Q8—612no—
440C2×Q8—611no—
441C2×Q8—1222no—
442C2×Q8—1221no—
443C2×Q8—1224no—
444C2×Q8#1175819811yescharacteristic
445C2×D4—611no—
446C2×D4—1222no—
447C2×D4—1221no—
448C2×D4#1175819812yes—
449C2×D4#1175819811yescharacteristic
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4—1221no—
453C22×C4—1221no—
454C22×C4—1221no—
455C22×C4C2×C4×D6112yes—
456C22×C4C2×C4×D6111yescharacteristic
457C22×C4C2×D24411yescharacteristic
458C22×C4C2×D24412yes—
459C22×C4C2×C22⋊D6111yescharacteristic
460C22×C4C2×C22⋊D6112yes—
461M16—44no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—22no—
465C2×C8—42no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1222no—
469C2×C8—4881no—
470C2×C8—4882no—
471C4⋊C4—612no—
472C4⋊C4—611no—
473C4⋊C4—611no—
474C4⋊C4—1222no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1222no—
478C4⋊C4—1221no—
479C4⋊C4—1222no—
480C4⋊C4—1222no—
481C4⋊C4—1222no—
482C4⋊C4—1222no—
483C4⋊C4—1222no—
484C4⋊C4—1222no—
485C4⋊C4—1222no—
486C4⋊C4—1222no—
487C4⋊C4#1175819811yescharacteristic
488C4⋊C4#1175819812yes—
489C4⋊C4#1175819812yes—
490C4⋊C4#1175819811yescharacteristic
491C22⋊C4—1221no—
492C22⋊C4—1222no—
493C22⋊C4—1222no—
494C22⋊C4—1222no—
495C22⋊C4—1221no—
496C22⋊C4—1221no—
497C22⋊C4—1222no—
498C22⋊C4—1222no—
499C22⋊C4—1222no—
500C22⋊C4#1175819812yes—
501C22⋊C4#1175819812yes—
502C22⋊C4#1175819812yes—
503C42—1221no—
504C42—1222no—
505C42—1221no—
506C42—1221no—
507C42—1222no—
508C42C2×C4×D6111yescharacteristic
509C42C2×C4×D6112yes—
510C42C2×D24411yescharacteristic
511C42C2×D24412yes—
512C42C2×C22⋊D6111yescharacteristic
513C42C2×C22⋊D6112yes—
514C42C23×D6111yescharacteristic
515C23—1221no—
516C23C2×#1175819812yes—
517C23C2×#1175819811yescharacteristic
518Q8—22no—
519Q8—1224no—
520Q8—1222no—
521Q8—4882no—
522Q8—2442no—
523D4—24no—
524D4—22no—
525D4—1222no—
526D4—4882no—
527D4—2442no—
528C2×C4—24no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—1222no—
538C2×C4—1222no—
539C2×C4—1221no—
540C2×C4—4881no—
541C2×C4—4881no—
542C2×C4—2442no—
543C2×C4—2442no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4C2×#1175819811yescharacteristic
547C2×C4C2×#1175819811yescharacteristic
548C2×C4C2×#1175819812yes—
549C2×C4C2×#1175819812yes—
550C2×C4C2×#1175819812yes—
551C2×C4C2×#1175819811yescharacteristic
552C2×C4#1451978514yes—
553C2×C4C22×C4×D6111yescharacteristic
554C2×C4C22×C22⋊D6111yescharacteristic
555C2×C4C22×D24411yescharacteristic
556C8—22no—
557C8—41no—
558C8—42no—
559C8—2441no—
560C8—2442no—
561C8—2441no—
562C22—21no—
563C22—21no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—2441no—
568C22—2441no—
569C22—2441no—
570C22#1683973012yes—
571C22C22×#1175819811yescharacteristic
572C4—21no—
573C4—22no—
574C4—21no—
575C4—21no—
576C4—22no—
577C4—22no—
578C4—2441no—
579C4—2442no—
580C4—2441no—
581C4—2441no—
582C4—2442no—
583C4#1683973012yes—
584C4C2×#1451978512yes—
585C4#1684057411yescharacteristic
586C4#1684057911yescharacteristic
587C2—22no—
588C2—42no—
589C2—4881no—
590C2C2×#1683973011yescharacteristic
591C2#2145435311yescharacteristic
592C2#2145436711yescharacteristic
subgroupG/H
centerC2×C4C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2965C2
socleC22×C61C22×C22⋊C4
prime radical#16840340C4
cosocleC42×C61C24
hypercenter#2965D61
hypocenterC61#17469
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2965

Complements

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

NH ≅ G/Ntype
2. #21454930C2semidirect
3. #21444241C2semidirect
4. #21444233C2semidirect
5. #21444228C2semidirect
6. #21444223C2semidirect
7. #21444215C2semidirect
8. #21444207C2semidirect
9. #21444202C2semidirect
10. C2×#16839494C2semidirect
11. C61×#2965C2semidirect
293. #2965D61semidirect
349. C61#17469semidirect

Maximal subgroups

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

subgroupindex
#214592462
#214549302
#214442412
#214442332
#214442282
#214442232
#214442152
#214442072
#214442022
C2×#168394942
C61×#29652
#1746961