Finite Group Databasebeta

← #29686863

Subgroups — #29686863

Order 15616.

938 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455425C211yesmaximal, characteristic
2C2×#16839882C211yesmaximal, characteristic, complemented
3#21454522C211yesmaximal, characteristic, complemented
4C2×M16×Dic61C211yesmaximal, characteristic, complemented
5#21446706C211yesmaximal, characteristic, complemented
6#21446564C211yesmaximal, characteristic, complemented
7#21446533C211yesmaximal, characteristic, complemented
8#21446529C211yesmaximal, characteristic, complemented
9#21446263C211yesmaximal, characteristic, complemented
10#21446260C211yesmaximal, characteristic, complemented
11#21445859C211yesmaximal, characteristic, complemented
12#21445704C211yesmaximal, characteristic, complemented
13#21445658C211yesmaximal, characteristic, complemented
14#21445654C211yesmaximal, characteristic, complemented
15C61×#2930C211yesmaximal, characteristic, complemented
16C2×#14519797C2211yescharacteristic
17C2×#14519783C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19#16840273C2211yescharacteristic
20C22×C4×Dic61C2211yescharacteristic
21#16840018C412yescomplemented
22#16840013C412yescomplemented
23#16840010C412yescomplemented
24#16840006C412yescomplemented
25#16839882—24no—
26#16839838—22no—
27#16839831—22no—
28C2×#14519712C2211yescharacteristic
29C2×#14519712C2211yescharacteristic
30#16839798C2211yescharacteristic
31#16839788C2211yescharacteristic
32C2×#14519704C2211yescharacteristic
33C2×#14519704C2211yescharacteristic
34C2×#14519703C2211yescharacteristic
35C2×#14519703C2211yescharacteristic
36#16839758C2211yescharacteristic
37#16839756C2211yescharacteristic
38#16839728C2211yescharacteristic
39#16839726C2211yescharacteristic
40#16839717C2211yescharacteristic
41M16×Dic61—24no—
42C2×#14519687C2211yescharacteristic
43C2×#14519687C2211yescharacteristic
44C2×C8×Dic61C2211yescharacteristic
45C2×C8×Dic61C2211yescharacteristic
46#16839526C2211yescharacteristic
47#16839526C2211yescharacteristic
48#16839523C2211yescharacteristic
49#16839523C2211yescharacteristic
50#16839521C2211yescharacteristic
51#16839521C2211yescharacteristic
52C2×#131×C61C2211yescharacteristic
53C22×M16×C61C2211yescharacteristic
54C61×#525C2211yescharacteristic
55C61×#436—22no—
56C61×#435—22no—
57C61×#424C2211yescharacteristic
58C61×#408C2211yescharacteristic
59C61×#407C2211yescharacteristic
60C61×#405C2211yescharacteristic
61C2×#11758222C2311yescharacteristic
62C23×Dic61—21no—
63#14519797—22no—
64#14519797—22no—
65C2×#11758202C2×C411yescharacteristic, complemented
66C2×#11758200C2×C411yescharacteristic, complemented
67C2×#11758201C2×C411yescharacteristic, complemented
68C2×#11758199C2×C411yescharacteristic, complemented
69#14519783—22no—
70#14519783—22no—
71C2×#11758194—22no—
72C2×#11758194—22no—
73C2×#11758194C2×C412yes—
74C2×#11758194C2×C412yes—
75C2×#11758194C2311yescharacteristic
76C2×#11758194C2311yescharacteristic
77C2×#11758189—21no—
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C2×C8×D61—21no—
81#14519760—21no—
82#14519756C2×C412yes—
83#14519751C2×C412yes—
84#14519746—21no—
85C4×C22⋊D61—22no—
86#14519736C2311yescharacteristic
87C2×C4×Dic61—21no—
88C2×C4×Dic61—22no—
89C2×C4×Dic61—22no—
90C2×C4×Dic61C2311yescharacteristic
91C2×C4×Dic61C2311yescharacteristic
92#14519712—22no—
93#14519712—22no—
94#14519710C2×C412yescomplemented
95#14519708C2×C412yescomplemented
96#14519706—22no—
97#14519704—22no—
98#14519704—22no—
99#14519703—22no—
100#14519703—22no—
101#14519701C2×C412yescomplemented
102#14519700C2×C412yescomplemented
103#14519698C2×C412yescomplemented
104#14519697C2×C412yescomplemented
105C22⋊#92418—22no—
106#14519689—22no—
107#14519687—21no—
108#14519687—22no—
109#14519687D414yescomplemented
110C8×Dic61—22no—
111C8×Dic61—21no—
112C8×Dic61—22no—
113C2×#41×C61C2311yescharacteristic
114C23×C4×C61C2311yescharacteristic
115#131×C61—22no—
116#131×C61—22no—
117C2×M16×C61—22no—
118C2×M16×C61—21no—
119C2×M16×C61—22no—
120C2×M16×C61D412yes—
121C2×M16×C61D412yes—
122C2×M16×C61C2311yescharacteristic
123C2×M16×C61C2311yescharacteristic
124C22×C8×C61—21no—
125C22×C8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127#123×C61—21no—
128C22⋊Q8×C61C2×C412yes—
129#121×C61C2×C412yes—
130#120×C61—21no—
131C4×D4×C61—22no—
132#117×C61C2311yescharacteristic
133C4⋊C8×C61—22no—
134C22⋊C8×C61—22no—
135C22⋊C8×C61—22no—
136#97×C61—21no—
137C4×C8×C61—21no—
138C24×C61#4111yescharacteristic
139#41×C61—21no—
140#41×C61—21no—
141#41×C61—21no—
142#41×C61—21no—
143C2×Q8×C61C22×C411yescharacteristic
144C2×D4×C61—21no—
145C2×D4×C61—22no—
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61C22×C412yes—
153C22×C4×C61C2×D412yes—
154C22×C4×C61#4111yescharacteristic
155C22×C4×C61C2411yescharacteristic
156C2×C22⋊D61—21no—
157C2×C22⋊D61—22no—
158C22×Dic61—21no—
159C22×Dic61—24no—
160C22×Dic61—21no—
161C22×Dic61—44no—
162#11758222—21no—
163#11758222—21no—
164#11758222—21no—
165#11758222—21no—
166C2×D244C22×C411yescharacteristic
167C2×C4×D61—21no—
168C2×Dic122C22×C411yescharacteristic
169M16×C61—24no—
170M16×C61—24no—
171M16×C61—21no—
172M16×C61—21no—
173M16×C61—21no—
174M16×C61—21no—
175M16×C61—42no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—42no—
181C2×C8×C61C2×D412yes—
182C2×C8×C61C2×D412yes—
183C2×C8×C61C2×D411yescharacteristic
184C2×C8×C61C2×D411yescharacteristic
185C2×C8×C61#4112yes—
186C4⋊C4×C61—22no—
187C4⋊C4×C61C22×C412yes—
188C22⋊C4×C61—22no—
189C22⋊C4×C61—21no—
190C22⋊C4×C61—22no—
191C42×C61—21no—
192C22⋊Dic61—22no—
193C22⋊Dic61—21no—
194#11758202—22no—
195#11758201—22no—
196#11758200—22no—
197#11758199—22no—
198#11758198—22no—
199C4⋊Dic61C22×C412yes—
200#11758196—22no—
201C4×Dic61—24no—
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61—21no—
205C4×Dic61C2×D412yes—
206C4×Dic61#4112yes—
207#11758194—24no—
208#11758194—24no—
209#11758194—21no—
210#11758194—21no—
211#11758194—21no—
212#11758194—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418C22×C412yes—
218C2×#92418C22×C411yescharacteristic
219C2×#92418C22×C411yescharacteristic
220C2×#92418C2×D412yes—
221C2×#92418#4112yes—
222#11758189—42no—
223C8×D61—42no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61—21no—
227C23×C61—42no—
228C23×C61C4×D412yes—
229C23×C61C2×#4111yescharacteristic
230C22×D61—21no—
231Q8×C61—21no—
232Q8×C61—21no—
233D4×C61—21no—
234D4×C61—21no—
235D4×C61—41no—
236D4×C61—41no—
237D4×C61—82no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—22no—
245C2×C4×C61—21no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61C4×D412yes—
249C2×C4×C61C23×C411yescharacteristic
250C2×C4×C61C22×D411yescharacteristic
251C2×C4×C61C22×D411yescharacteristic
252C2×C4×C61C2×#4111yescharacteristic
253C2×C4×C61C2×#4111yescharacteristic
254C2×C4×C61C2×#4111yescharacteristic
255C22⋊D61—41no—
256C22⋊D61—41no—
257C22⋊D61—82no—
258C2×Dic61—24no—
259C2×Dic61—22no—
260C2×Dic61—22no—
261C2×Dic61—21no—
262C2×Dic61—22no—
263C2×Dic61—48no—
264C2×Dic61—42no—
265D244—21no—
266D244—21no—
267C4×D61—41no—
268C4×D61—41no—
269Dic122—21no—
270Dic122—21no—
271C8×C61—22no—
272C8×C61—41no—
273C8×C61—41no—
274C8×C61#12112yes—
275C8×C61#12112yes—
276#92418—22no—
277#92418—41no—
278#92418—41no—
279#92418C4×D412yes—
280#92418C4×D412yes—
281#21551—611nomaximal, Sylow
282C22×C61—22no—
283C22×C61—22no—
284C22×C61—22no—
285C22×C61—22no—
286C22×C61—42no—
287C22×C61—42no—
288C22×C61—42no—
289C22×C61—41no—
290C22×C61C2×C4×D411yescharacteristic
291C22×C61#52511yescharacteristic
292C22×C61#52911yescharacteristic
293C2×D61—42no—
294C2×D61—41no—
295C4×C61—22no—
296C4×C61—42no—
297C4×C61—41no—
298C4×C61C2×C4×D411yescharacteristic
299C4×C61C4×#4111yescharacteristic
300C4×C61C2×#12111yescharacteristic
301C4×C61#53211yescharacteristic
302Dic61—24no—
303Dic61—42no—
304Dic61—42no—
305Dic61—41no—
306#3054—611no—
307C2×#444—611no—
308#2930—611no—
309#2930D6111yescharacteristic, complemented
310C2×C4×M16—611no—
311#1974—611no—
312#1945—611no—
313#1938—611no—
314#1938—611no—
315#1896—611no—
316#1896—611no—
317#1811—611no—
318#1773—611no—
319#1764—611no—
320#1764—611no—
321C2×C61—21no—
322C2×C61—21no—
323C2×C61—42no—
324C2×C61—81no—
325C2×C61C4×#12111yescharacteristic
326C2×C61#295612yes—
327D61—81no—
328C2×#135—611no—
329C2×#131—611no—
330C2×#131C2×D6111yescharacteristic
331C22×M16—611no—
332C22×M16C2×D6111yescharacteristic
333#525—611no—
334#525C2×D6111yescharacteristic
335C22×C42—611no—
336#470—612no—
337#469—612no—
338#468—612no—
339#468—612no—
340#444—1224no—
341#436—22no—
342#436—1222no—
343#435—22no—
344#435—1222no—
345C2×#108—611no—
346C2×#108—611no—
347#427—611no—
348#424—611no—
349#424C2×D6111yescharacteristic
350C2×#104—611no—
351C2×#104—611no—
352C2×#104—611no—
353C2×#104—611no—
354#416—611no—
355#416—611no—
356#408—611no—
357#408C2×D6111yescharacteristic
358#407—611no—
359#407C2×D6111yescharacteristic
360#405—611no—
361#405C2×D6111yescharacteristic
362C4×M16—1224no—
363C2×#97—611no—
364C2×#97—611no—
365C2×C4×C8—611no—
366C2×C4×C8—611no—
367#341—611no—
368#341—611no—
369#339—611no—
370#339—611no—
371#339—611no—
372#339—611no—
373C61#2155111yescharacteristic, complemented, Sylow
374C2×#41—611no—
375C2×#41C22×D6111yescharacteristic
376C23×C4—1221no—
377C23×C4C22×D6111yescharacteristic
378#135—1222no—
379#135—1222no—
380C2×Q16—611no—
381C2×SD16—611no—
382C2×SD16—611no—
383C2×D8—611no—
384#131—22no—
385#131—22no—
386#131—1222no—
387#131—1222no—
388C2×M16—22no—
389C2×M16—22no—
390C2×M16—21no—
391C2×M16—612no—
392C2×M16—612no—
393C2×M16—611no—
394C2×M16—611no—
395C2×M16—1222no—
396C2×M16—1222no—
397C2×M16—1221no—
398C2×M16C22⋊D6112yes—
399C2×M16C22⋊D6112yes—
400C2×M16C22×D6111yescharacteristic
401C2×M16C22×D6111yescharacteristic
402C22×C8—21no—
403C22×C8—611no—
404C22×C8—611no—
405C22×C8—1221no—
406C22×C8C22×D6111yescharacteristic
407C22×C8C22×D6111yescharacteristic
408#123—21no—
409#123—1221no—
410C22⋊Q8—612no—
411C22⋊Q8C4×D6112yes—
412#121—612no—
413#121C4×D6112yes—
414#120—21no—
415#120—1221no—
416C4×D4—22no—
417C4×D4—1222no—
418#117—611no—
419#117C22×D6111yescharacteristic
420C2×C42—611no—
421C2×C42—611no—
422C2×C42—1222no—
423C2×C42—1222no—
424C2×C42—1221no—
425#108—1222no—
426#108—1222no—
427#107—612no—
428#106—612no—
429C4⋊C8—22no—
430C4⋊C8—1222no—
431#104—1222no—
432#104—1222no—
433#104—1222no—
434#104—1222no—
435#103—612no—
436#103—612no—
437#102—612no—
438#102—612no—
439C22⋊C8—22no—
440C22⋊C8—22no—
441C22⋊C8—1222no—
442C22⋊C8—1222no—
443#97—21no—
444#97—614no—
445#97—1222no—
446#97—1221no—
447C4×C8—21no—
448C4×C8—1222no—
449C4×C8—1222no—
450C4×C8—1221no—
451C24#1175822211yescharacteristic
452#41—21no—
453#41—21no—
454#41—21no—
455#41—21no—
456#41—1221no—
457#41—1221no—
458#41—1221no—
459#41—1221no—
460C2×Q8—611no—
461C2×Q8C2×C4×D6111yescharacteristic
462C2×D4—21no—
463C2×D4—22no—
464C2×D4—611no—
465C2×D4—1222no—
466C2×D4—1221no—
467C2×D4C2×C4×D6111yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—1221no—
474C22×C4—1224no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—2444no—
478C22×C4C2×C4×D6112yes—
479C22×C4#1175822211yescharacteristic
480C22×C4C2×C22⋊D6112yes—
481C22×C4C23×D6111yescharacteristic
482Q16—1222no—
483SD16—1222no—
484SD16—1222no—
485D8—1222no—
486M16—24no—
487M16—24no—
488M16—21no—
489M16—21no—
490M16—21no—
491M16—21no—
492M16—42no—
493M16—1224no—
494M16—1224no—
495M16—1221no—
496M16—1221no—
497M16—1221no—
498M16—1221no—
499M16—2442no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—42no—
505C2×C8—611no—
506C2×C8—611no—
507C2×C8—612no—
508C2×C8—612no—
509C2×C8—612no—
510C2×C8—1221no—
511C2×C8—1221no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—2442no—
515C2×C8D4×D6112yes—
516C2×C8#1175822412yes—
517C2×C8C2×C22⋊D6112yes—
518C2×C8C2×C22⋊D6111yescharacteristic
519C2×C8C2×C22⋊D6111yescharacteristic
520C4⋊C4—22no—
521C4⋊C4—612no—
522C4⋊C4—1222no—
523C4⋊C4C2×C4×D6112yes—
524C22⋊C4—21no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—1221no—
528C22⋊C4—1222no—
529C22⋊C4—1222no—
530C42—21no—
531C42—612no—
532C42—612no—
533C42—1224no—
534C42—1221no—
535C42—1221no—
536C42—1221no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—42no—
541C23—1221no—
542C23C4×C22⋊D6112yes—
543C23C2×#1175822211yescharacteristic
544Q8—21no—
545Q8—21no—
546Q8—1221no—
547Q8—1221no—
548D4—21no—
549D4—21no—
550D4—41no—
551D4—41no—
552D4—82no—
553D4—1221no—
554D4—1221no—
555D4—4882no—
556D4—2441no—
557D4—2441no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—1224no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—1221no—
572C2×C4—1222no—
573C2×C4—2448no—
574C2×C4—2442no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4C4×C22⋊D6112yes—
578C2×C4C22×C4×D6111yescharacteristic
579C2×C4C2×D4×D6111yescharacteristic
580C2×C4C22×C22⋊D6111yescharacteristic
581C2×C4#41×D6111yescharacteristic
582C2×C4#41×D6111yescharacteristic
583C2×C4C2×#1175822411yescharacteristic
584C8—22no—
585C8—41no—
586C8—41no—
587C8—612no—
588C8—612no—
589C8—1222no—
590C8—2441no—
591C8—2441no—
592C8#1451974912yes—
593C8#1451974912yes—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—41no—
602C22—2442no—
603C22—2441no—
604C22C2×C4×C22⋊D6111yescharacteristic
605C22#1684027111yescharacteristic
606C22#1684029211yescharacteristic
607C4—22no—
608C4—42no—
609C4—41no—
610C4—1224no—
611C4—2442no—
612C4—2442no—
613C4—2441no—
614C4C4×D4×D6111yescharacteristic
615C4C4×#1175822411yescharacteristic
616C4C2×#1451974911yescharacteristic
617C4#1684030811yescharacteristic
618C2—21no—
619C2—21no—
620C2—42no—
621C2—81no—
622C2—4881no—
623C2C4×#1451974911yescharacteristic
624C2#2145472612yes—
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2930C2
socleC22×C61C2×C4×D4
prime radical#21455425C2
cosocleC22×C4×C61C24
hypercenter#2930D61
hypocenterC61#21551
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ #2930

Complements

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

NH ≅ G/Ntype
2. C2×#16839882C2semidirect
3. #21454522C2semidirect
4. C2×M16×Dic61C2semidirect
5. #21446706C2semidirect
6. #21446564C2semidirect
7. #21446533C2semidirect
8. #21446529C2semidirect
9. #21446263C2semidirect
10. #21446260C2semidirect
11. #21445859C2semidirect
12. #21445704C2semidirect
13. #21445658C2semidirect
14. #21445654C2semidirect
15. C61×#2930C2semidirect
21. #16840018C4semidirect
22. #16840013C4semidirect
23. #16840010C4semidirect
24. #16840006C4semidirect
65. C2×#11758202C2×C4semidirect
66. C2×#11758200C2×C4semidirect
67. C2×#11758201C2×C4semidirect
68. C2×#11758199C2×C4semidirect
94. #14519710C2×C4semidirect
95. #14519708C2×C4semidirect
101. #14519701C2×C4semidirect
102. #14519700C2×C4semidirect
103. #14519698C2×C4semidirect
104. #14519697C2×C4semidirect
109. #14519687D4semidirect
309. #2930D61semidirect
373. C61#21551semidirect

Maximal subgroups

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

subgroupindex
#214554252
C2×#168398822
#214545222
C2×M16×Dic612
#214467062
#214465642
#214465332
#214465292
#214462632
#214462602
#214458592
#214457042
#214456582
#214456542
C61×#29302
#2155161