Finite Group Databasebeta

← #29708584

Subgroups — #29708584

Order 15616.

1002 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839809C211yesmaximal, characteristic, complemented
2#428×D61C211yesmaximal, characteristic, complemented
3#21454380C211yesmaximal, characteristic, complemented
4#21454337C211yesmaximal, characteristic
5C2×#16839762C211yesmaximal, characteristic
6C2×#16839745C211yesmaximal, characteristic
7#21447186C211yesmaximal, characteristic, complemented
8#21447184C211yesmaximal, characteristic, complemented
9#21447182C211yesmaximal, characteristic, complemented
10#21447180C211yesmaximal, characteristic, complemented
11#21447178C211yesmaximal, characteristic, complemented
12#21447176C211yesmaximal, characteristic, complemented
13#21447174C211yesmaximal, characteristic, complemented
14#343×D61C211yesmaximal, characteristic, complemented
15C61×#2064C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C2×M16×D61C2211yescharacteristic
19C2×M16×D61C2211yescharacteristic
20C2×M16×D61C2211yescharacteristic
21#117×D61C2211yescharacteristic
22C2×C4⋊C4×D61C2211yescharacteristic
23#16839809—24no—
24C2×#14519713C2211yescharacteristic
25C2×#14519712C2211yescharacteristic
26C2×#14519712C2211yescharacteristic
27#16839805C2211yescharacteristic
28#16839804C2211yescharacteristic
29#16839803—21no—
30#16839802C2211yescharacteristic
31#16839801—21no—
32#107×D61—21no—
33#106×D61—21no—
34#16839790C2211yescharacteristic
35#16839789C2211yescharacteristic
36#16839788C2211yescharacteristic
37#16839787—22no—
38#16839784—22no—
39#16839771C2211yescharacteristic
40#16839768C2211yescharacteristic
41#16839766C2211yescharacteristic
42#16839762—22no—
43#16839762—22no—
44#16839762—21no—
45#16839762—21no—
46#16839757—21no—
47#16839757—21no—
48C2×#14519701C2211yescharacteristic
49C2×#14519699C2211yescharacteristic
50C2×#14519697C2211yescharacteristic
51#16839745—24no—
52C2×#14519696C2211yescharacteristic
53C2×#14519693C2211yescharacteristic
54C2×#14519693C2211yescharacteristic
55#16839531C2211yescharacteristic
56#16839530C2211yescharacteristic
57#16839530C2211yescharacteristic
58C2×#108×C61C2211yescharacteristic
59C61×#428C2211yescharacteristic
60C61×#424C2211yescharacteristic
61C61×#419C2211yescharacteristic
62C2×#103×C61C2211yescharacteristic
63C2×#101×C61C2211yescharacteristic
64C61×#343C2211yescharacteristic
65C2×#11758226—22no—
66C2×#11758226—21no—
67C2×#11758226—21no—
68C2×#11758226—21no—
69C2×#11758226—21no—
70C2×#11758226—22no—
71C2×#11758226—22no—
72C2×#11758226Q814yes—
73C22×D244—21no—
74C22×D244C2311yescharacteristic
75C22×C4×D61—21no—
76C22×C4×D61—21no—
77C22×C4×D61C2311yescharacteristic
78C2×#11758194C2311yescharacteristic
79C2×#11758194C2311yescharacteristic
80C2×#11758194C2311yescharacteristic
81C2×#11758189—21no—
82C2×#11758189—22no—
83C2×#11758189—22no—
84C2×#11758189—21no—
85C2×#11758189—21no—
86C2×#11758189D412yes—
87C2×#11758189D412yes—
88M16×D61—22no—
89M16×D61—22no—
90M16×D61—22no—
91M16×D61—22no—
92M16×D61—22no—
93M16×D61D414yes—
94C22×#92418C2311yescharacteristic
95C2×C8×D61—21no—
96C2×C8×D61—21no—
97C2×C8×D61—21no—
98#14519736C2311yescharacteristic
99#14519735D411yescharacteristic
100#14519735D411yescharacteristic
101#14519734—21no—
102#14519733—21no—
103C2×C4⋊Dic61C2311yescharacteristic
104C2×#11758196—21no—
105C4⋊C4×D61—21no—
106C4⋊C4×D61—21no—
107C4⋊C4×D61—21no—
108C4⋊C4×D61—21no—
109C4⋊C4×D61D411yescharacteristic
110C4⋊C4×D61D411yescharacteristic
111C22⋊C4×D61—21no—
112C42×D61—21no—
113#14519713—22no—
114#14519712—22no—
115#14519712—22no—
116#14519711—21no—
117#14519710—21no—
118#14519710—21no—
119#14519709—21no—
120#14519708—21no—
121#14519708—21no—
122C4⋊#92418—22no—
123#14519706—22no—
124#14519706—22no—
125#14519701—21no—
126#14519701—21no—
127#14519701—22no—
128#14519699—22no—
129#14519699—21no—
130#14519699—21no—
131#14519697—21no—
132#14519697—21no—
133#14519697—22no—
134#14519696—22no—
135#14519693—22no—
136#14519693—22no—
137C22×Q8×C61C2311yescharacteristic
138C2×M16×C61C2311yescharacteristic
139C2×M16×C61C2311yescharacteristic
140C2×M16×C61C2311yescharacteristic
141C22×C8×C61C2311yescharacteristic
142#117×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144#108×C61—22no—
145#107×C61—21no—
146#106×C61—21no—
147C4⋊C8×C61—22no—
148#103×C61—22no—
149#103×C61—21no—
150#103×C61—21no—
151#101×C61—22no—
152C23×D61—21no—
153C23×D61#4111yescharacteristic
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61C2×Q812yes—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61C2411yescharacteristic
163C22×Dic61—21no—
164C22×Dic61#4111yescharacteristic
165#11758226—24no—
166#11758226—24no—
167#11758226—24no—
168#11758226—24no—
169#11758226—42no—
170#11758226—42no—
171#11758226—42no—
172#11758226—42no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—24no—
178C2×D244—21no—
179C2×D244—41no—
180C2×D244—41no—
181C2×D244—42no—
182C2×D244C2×Q812yes—
183C2×C4×D61—24no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—41no—
187C2×C4×D61—41no—
188C2×C4×D61—42no—
189C2×C4×D61—41no—
190C2×C4×D61—41no—
191C2×C4×D61—82no—
192C2×C4×D61C2×D412yes—
193C2×C4×D61C2×D411yescharacteristic
194C2×C4×D61C2×D411yescharacteristic
195C2×C4×D61C2×D411yescharacteristic
196C2×C4×D61C2×D411yescharacteristic
197C2×C4×D61C2×Q812yes—
198C2×C4×D61#4112yes—
199C2×C4×D61#4112yes—
200M16×C61—21no—
201M16×C61—21no—
202M16×C61—21no—
203M16×C61—21no—
204M16×C61—21no—
205M16×C61C2×D412yes—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61C2×D412yes—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61C2×D411yescharacteristic
215C4⋊C4×C61C2×D411yescharacteristic
216C22⋊C4×C61—21no—
217C42×C61—21no—
218C22⋊Dic61—21no—
219#11758198—21no—
220#11758198—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61C2×D411yescharacteristic
224C4⋊Dic61C2×D411yescharacteristic
225#11758196—21no—
226#11758196—21no—
227#11758196—41no—
228#11758196—41no—
229C4×Dic61—21no—
230C4×Dic61—21no—
231C4×Dic61—21no—
232#11758194—21no—
233#11758194—21no—
234#11758194—21no—
235#11758194—21no—
236#11758194—21no—
237#11758194C2×D412yes—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418C2×D412yes—
244#11758189—24no—
245#11758189—24no—
246#11758189—24no—
247#11758189—42no—
248#11758189—42no—
249C8×D61—24no—
250C8×D61—42no—
251C8×D61—42no—
252C23×C61C2×#4111yescharacteristic
253C22×D61—22no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—81no—
259C22×D61—81no—
260C22×D61#12111yescharacteristic
261C22×D61#12111yescharacteristic
262C22×D61C22⋊Q812yes—
263C22×D61#12612yes—
264Q8×C61—22no—
265Q8×C61—22no—
266Q8×C61—41no—
267Q8×C61—41no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—22no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—81no—
275C2×C4×C61C22×D411yescharacteristic
276C2×C4×C61C22×D411yescharacteristic
277C2×C4×C61C22×D411yescharacteristic
278C2×C4×C61C22×Q811yescharacteristic
279C2×C4×C61C2×#4111yescharacteristic
280C2×C4×C61C2×#4111yescharacteristic
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—41no—
284C2×Dic61—81no—
285C2×Dic61#12111yescharacteristic
286C2×Dic61#12111yescharacteristic
287C2×Dic61C22⋊Q812yes—
288C2×Dic61#12612yes—
289D244—22no—
290D244—22no—
291D244—44no—
292D244—44no—
293D244—41no—
294D244—41no—
295C4×D61—44no—
296C4×D61—44no—
297C4×D61—81no—
298C4×D61—81no—
299C4×D61—82no—
300C4×D61—82no—
301C4×D61#12112yes—
302C4×D61#12112yes—
303C4×D61#12112yes—
304C4×D61#12112yes—
305C4×D61C22⋊Q812yes—
306C4×D61C22⋊Q812yes—
307C4×D61C22⋊Q812yes—
308C4×D61C22⋊Q812yes—
309C8×C61—22no—
310C8×C61—22no—
311C8×C61—41no—
312C8×C61—41no—
313#92418—22no—
314#92418—22no—
315#92418—41no—
316#92418—41no—
317#23604—611nomaximal, Sylow
318C22×C61—21no—
319C22×C61—21no—
320C22×C61C2×#12111yescharacteristic
321C22×C61C2×C22⋊Q811yescharacteristic
322C22×C61C2×#12611yescharacteristic
323C2×D61—21no—
324C2×D61—21no—
325C2×D61—21no—
326C2×D61—21no—
327C2×D61—42no—
328C2×D61—42no—
329C2×D61—42no—
330C2×D61—82no—
331C2×D61—81no—
332C2×D61—81no—
333C2×D61—82no—
334C2×D61#39612yes—
335C2×D61#39612yes—
336C4×C61—42no—
337C4×C61—41no—
338C4×C61—41no—
339C4×C61—81no—
340C4×C61C2×#12111yescharacteristic
341C4×C61C2×#12111yescharacteristic
342C4×C61C2×C22⋊Q811yescharacteristic
343C4×C61C2×C22⋊Q811yescharacteristic
344Dic61—41no—
345Dic61—41no—
346Dic61—81no—
347Dic61#39612yes—
348Dic61#39612yes—
349C2×#430—611no—
350C2×#428—611no—
351#2905—611no—
352#2896—611no—
353C2×#417—611no—
354C2×#413—611no—
355#2064—611no—
356#2064—611no—
357#2064—611no—
358#2064D6111yescharacteristic, complemented
359#2063—611no—
360#2063—611no—
361#2063—611no—
362#2063—611no—
363C2×#343—611no—
364C2×C61—21no—
365C2×C61—21no—
366C2×C61C2×#39611yescharacteristic
367C2×C61#306811yescharacteristic
368C2×C61#306911yescharacteristic
369D61—22no—
370D61—22no—
371D61—82no—
372C22×#41—611no—
373C22×M16—611no—
374C22×M16—611no—
375C22×M16—611no—
376C22×M16—611no—
377C2×#117—611no—
378C22×C4⋊C4—611no—
379#430—1224no—
380C2×#108—611no—
381C2×#108—611no—
382C2×#108—611no—
383C2×#108C2×D6111yescharacteristic
384#428—611no—
385#428—611no—
386#428—611no—
387#428—1221no—
388#428—1221no—
389#428C2×D6111yescharacteristic
390C2×#107—1221no—
391C2×#106—1221no—
392#424—611no—
393#424—611no—
394#424—611no—
395#424—1222no—
396#424C2×D6111yescharacteristic
397#423—1222no—
398#419—611no—
399#419C2×D6111yescharacteristic
400#418—611no—
401#418—611no—
402#417—1221no—
403#417—1221no—
404#417—1222no—
405#417—1222no—
406#416—1221no—
407#416—1221no—
408C2×#103—611no—
409C2×#103C2×D6111yescharacteristic
410C2×#102—611no—
411C2×#102—611no—
412#413—1224no—
413C2×#101—611no—
414C2×#101C2×D6111yescharacteristic
415C2×#100—611no—
416C2×#100—611no—
417#343—611no—
418#343—611no—
419#343—611no—
420#343C2×D6111yescharacteristic
421C61#2360411yescharacteristic, complemented, Sylow
422C2×#41—614no—
423C2×#41—1222no—
424C2×#41—1222no—
425C2×#41—1222no—
426C2×#41—1221no—
427C2×#41—1221no—
428C2×#41—1221no—
429C2×#41—1221no—
430C22×Q8C22×D6111yescharacteristic
431C22×D4—611no—
432C22×D4—1221no—
433C23×C4—611no—
434C23×C4—1221no—
435C23×C4—1221no—
436C2×M16—612no—
437C2×M16—612no—
438C2×M16—611no—
439C2×M16—614no—
440C2×M16—611no—
441C2×M16—611no—
442C2×M16—1221no—
443C2×M16—1222no—
444C2×M16—1222no—
445C2×M16—1221no—
446C2×M16—1221no—
447C2×M16—1222no—
448C2×M16—1222no—
449C2×M16—1222no—
450C2×M16—1222no—
451C2×M16—1222no—
452C2×M16C22×D6111yescharacteristic
453C2×M16C22×D6111yescharacteristic
454C2×M16C22×D6111yescharacteristic
455C22×C8—611no—
456C22×C8—1221no—
457C22×C8—1221no—
458C22×C8—1221no—
459C22×C8C22×D6111yescharacteristic
460#117—611no—
461#117—611no—
462#117—611no—
463#117—1221no—
464#117—1221no—
465#117C22×D6111yescharacteristic
466C2×C4⋊C4—611no—
467C2×C4⋊C4—611no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—1221no—
470C2×C4⋊C4—1221no—
471C2×C4⋊C4—1221no—
472C2×C4⋊C4—1221no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4C22×D6111yescharacteristic
475C2×C22⋊C4—1221no—
476C2×C42—1221no—
477#108—22no—
478#108—1222no—
479#108—1222no—
480#108—1222no—
481#107—21no—
482#107—1221no—
483#107—1221no—
484#107—1221no—
485#106—21no—
486#106—1221no—
487#106—1221no—
488#106—1221no—
489C4⋊C8—22no—
490C4⋊C8—1222no—
491C4⋊C8—1222no—
492C4⋊C8—1222no—
493#103—22no—
494#103—21no—
495#103—21no—
496#103—1221no—
497#103—1221no—
498#103—1222no—
499#102—1222no—
500#102—1221no—
501#102—1221no—
502#102—1222no—
503#102—1221no—
504#102—1221no—
505#101—22no—
506#101—1222no—
507#100—1222no—
508#100—1222no—
509C24—611no—
510C24—1221no—
511#41—1224no—
512#41—1224no—
513#41—1224no—
514#41—1224no—
515#41—2442no—
516#41—2442no—
517#41—2442no—
518#41—2442no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8Q8×D6112yes—
525C2×D4—612no—
526C2×D4—1224no—
527C2×D4—1221no—
528C2×D4—1221no—
529C2×D4—1221no—
530C2×D4—1221no—
531C2×D4—1221no—
532C2×D4—2441no—
533C2×D4—2441no—
534C2×D4—2442no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—611no—
538C22×C4—611no—
539C22×C4—611no—
540C22×C4—611no—
541C22×C4—611no—
542C22×C4—612no—
543C22×C4—612no—
544C22×C4—612no—
545C22×C4—612no—
546C22×C4—1224no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—4882no—
551C22×C4—2441no—
552C22×C4—2441no—
553C22×C4—2442no—
554C22×C4—2441no—
555C22×C4—2441no—
556C22×C4C23×D6111yescharacteristic
557M16—21no—
558M16—21no—
559M16—21no—
560M16—21no—
561M16—21no—
562M16—612no—
563M16—1224no—
564M16—1224no—
565M16—1224no—
566M16—1221no—
567M16—1221no—
568M16—1221no—
569M16—1221no—
570M16—1221no—
571M16—2442no—
572M16—2442no—
573M16D4×D6112yes—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—612no—
580C2×C8—1224no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—2442no—
587C2×C8—2442no—
588C2×C8D4×D6112yes—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—611no—
592C4⋊C4—611no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—2441no—
598C4⋊C4—2441no—
599C4⋊C4D4×D6111yescharacteristic
600C4⋊C4D4×D6111yescharacteristic
601C22⋊C4—21no—
602C22⋊C4—1221no—
603C22⋊C4—1221no—
604C22⋊C4—1221no—
605C42—21no—
606C42—1221no—
607C42—1221no—
608C42—1221no—
609C23—611no—
610C23—611no—
611C23—612no—
612C23—612no—
613C23—1222no—
614C23—4881no—
615C23—4881no—
616C23—2441no—
617C23—2441no—
618C23—2441no—
619C23—2441no—
620C23#41×D6111yescharacteristic
621Q8—22no—
622Q8—22no—
623Q8—41no—
624Q8—41no—
625D4—1222no—
626D4—1222no—
627D4—2444no—
628D4—2444no—
629D4—2441no—
630D4—2441no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—81no—
638C2×C4—611no—
639C2×C4—611no—
640C2×C4—612no—
641C2×C4—612no—
642C2×C4—612no—
643C2×C4—612no—
644C2×C4—612no—
645C2×C4—612no—
646C2×C4—612no—
647C2×C4—612no—
648C2×C4—612no—
649C2×C4—612no—
650C2×C4—1221no—
651C2×C4—1221no—
652C2×C4—4881no—
653C2×C4—4881no—
654C2×C4—4882no—
655C2×C4—4882no—
656C2×C4—4881no—
657C2×C4—2444no—
658C2×C4—2444no—
659C2×C4—2441no—
660C2×C4C2×D4×D6111yescharacteristic
661C2×C4C2×D4×D6111yescharacteristic
662C2×C4C2×D4×D6111yescharacteristic
663C2×C4C2×Q8×D6111yescharacteristic
664C2×C4#41×D6111yescharacteristic
665C2×C4#41×D6111yescharacteristic
666C8—22no—
667C8—22no—
668C8—41no—
669C8—41no—
670C8—1222no—
671C8—1222no—
672C8—2441no—
673C8—2441no—
674C22—21no—
675C22—21no—
676C22—612no—
677C22—612no—
678C22—1221no—
679C22—1221no—
680C22—1221no—
681C22—1221no—
682C22—4882no—
683C22—4882no—
684C22—4881no—
685C22—4881no—
686C22—2442no—
687C22—2442no—
688C22—2442no—
689C22#121×D6111yescharacteristic
690C22C22⋊Q8×D6111yescharacteristic
691C22#126×D6111yescharacteristic
692C4—42no—
693C4—41no—
694C4—41no—
695C4—81no—
696C4—612no—
697C4—612no—
698C4—4881no—
699C4—2441no—
700C4—2441no—
701C4#121×D6111yescharacteristic
702C4#121×D6111yescharacteristic
703C4C22⋊Q8×D6111yescharacteristic
704C4C22⋊Q8×D6111yescharacteristic
705C2—21no—
706C2—21no—
707C2—1222no—
708C2—1222no—
709C2—4882no—
710C2#396×D6111yescharacteristic
711C2#2145554211yescharacteristic
712C2#2145555411yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2064C2
socleC22×C61C2×#121
prime radicalC22×#11758226C22
hypercenter#2064D61
hypocenterC61#23604
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2064

Complements

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

NH ≅ G/Ntype
1. C2×#16839809C2semidirect
2. #428×D61C2semidirect
3. #21454380C2semidirect
7. #21447186C2semidirect
8. #21447184C2semidirect
9. #21447182C2semidirect
10. #21447180C2semidirect
11. #21447178C2semidirect
12. #21447176C2semidirect
13. #21447174C2semidirect
14. #343×D61C2semidirect
15. C61×#2064C2semidirect
358. #2064D61semidirect
421. C61#23604semidirect

Maximal subgroups

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

subgroupindex
C2×#168398092
#428×D612
#214543802
#214543372
C2×#168397622
C2×#168397452
#214471862
#214471842
#214471822
#214471802
#214471782
#214471762
#214471742
#343×D612
C61×#20642
#2360461