Finite Group Databasebeta

← #29729820

Subgroups — #29729820

Order 15616.

722 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456208C211yesmaximal, characteristic, complemented
2#21455612C211yesmaximal, characteristic, complemented
3C2×#16839978C211yesmaximal, characteristic
4#21447185C211yesmaximal, characteristic, complemented
5#21447178C211yesmaximal, characteristic, complemented
6#21447082C211yesmaximal, characteristic, complemented
7#21447075C211yesmaximal, characteristic
8#21446729C211yesmaximal, characteristic
9#21446722C211yesmaximal, characteristic, complemented
10#21446668C211yesmaximal, characteristic, complemented
11#21446595C211yesmaximal, characteristic, complemented
12#21446481C211yesmaximal, characteristic, complemented
13#21446474C211yesmaximal, characteristic, complemented
14C4×#14519693C211yesmaximal, characteristic, complemented
15C61×#2962C211yesmaximal, characteristic, complemented
16C22×#11758190C2211yescharacteristic
17C22×D488C2211yescharacteristic
18C2×#14519765C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20#16840124—21no—
21#16840124—21no—
22#16840119—21no—
23#16840119—21no—
24#16840059—21no—
25#16840059—21no—
26#16840049—21no—
27#16840039—21no—
28#16839978—21no—
29#16839978—21no—
30#16839978—21no—
31#16839978—21no—
32C2×#14519713C2211yescharacteristic
33C2×#14519713C2211yescharacteristic
34#16839805C2211yescharacteristic
35#16839805C2211yescharacteristic
36#16839786C2211yescharacteristic
37#16839770C2211yescharacteristic
38#16839770C2211yescharacteristic
39#16839766C2211yescharacteristic
40#16839766C2211yescharacteristic
41#16839766C2211yescharacteristic
42#16839766C2211yescharacteristic
43C2×#14519702C2211yescharacteristic
44C2×#14519699C2211yescharacteristic
45C2×#14519695C2211yescharacteristic
46C2×#14519695C2211yescharacteristic
47C2×#14519693C2211yescharacteristic
48C2×#14519693C2211yescharacteristic
49C2×#14519693C2211yescharacteristic
50C2×#14519693C2211yescharacteristic
51C4×#11758194C2211yescharacteristic
52#16839530C2211yescharacteristic
53#16839530C2211yescharacteristic
54#16839527C2211yescharacteristic
55#16839527C2211yescharacteristic
56C61×#533C2211yescharacteristic
57C61×#446—21no—
58C61×#446—21no—
59C61×#446—21no—
60C8×Q8×C61—21no—
61C61×#424C2211yescharacteristic
62C61×#424C2211yescharacteristic
63C2×C4⋊C8×C61C2211yescharacteristic
64C61×#405C2211yescharacteristic
65C61×#405C2211yescharacteristic
66C4×M16×C61C2211yescharacteristic
67C22×Dic122C2311yescharacteristic
68C22×D244C2311yescharacteristic
69C22×D244C2311yescharacteristic
70C22×C4×D61—21no—
71C2×#11758190—22no—
72C2×#11758190—21no—
73C2×#11758190—21no—
74C2×#11758190—41no—
75C2×D488—22no—
76C2×D488—21no—
77C2×D488—21no—
78C2×D488—41no—
79C2×#11758194C2311yescharacteristic
80C2×#11758194C2311yescharacteristic
81C2×#11758194C2311yescharacteristic
82C2×#11758194C2311yescharacteristic
83#14519765—21no—
84#14519765—21no—
85#14519765—21no—
86#14519765—21no—
87C4×D244—21no—
88C4×D244—21no—
89C4×D244—21no—
90C4×D244—21no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95#14519713—41no—
96#14519713—41no—
97#14519710—21no—
98#14519710—21no—
99#14519708—21no—
100#14519708—21no—
101C4⋊#92418—21no—
102C4⋊#92418—21no—
103#14519702—21no—
104#14519702—21no—
105#14519700—21no—
106#14519700—21no—
107#14519700—21no—
108#14519700—21no—
109#14519699—21no—
110#14519699—21no—
111#14519697—21no—
112#14519697—21no—
113#14519697—21no—
114#14519697—21no—
115#14519697—21no—
116#14519697—21no—
117#14519697—21no—
118#14519697—21no—
119#14519695—22no—
120#14519695—41no—
121#14519693—22no—
122#14519693—22no—
123#14519693—22no—
124#14519693—41no—
125#14519688—21no—
126C4×#92418—21no—
127C2×M16×C61C2311yescharacteristic
128C2×M16×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C4⋊Q8×C61D411yescharacteristic
132C4⋊Q8×C61D411yescharacteristic
133#125×C61D411yescharacteristic
134#125×C61D411yescharacteristic
135C22⋊Q8×C61—21no—
136C22⋊Q8×C61—21no—
137C4×Q8×C61—21no—
138C4×Q8×C61—21no—
139#117×C61C2311yescharacteristic
140#117×C61C2311yescharacteristic
141C2×C42×C61C2311yescharacteristic
142C4⋊C8×C61—21no—
143C4⋊C8×C61—21no—
144C4⋊C8×C61—21no—
145C4⋊C8×C61—21no—
146C4⋊C8×C61D411yescharacteristic
147C4⋊C8×C61D411yescharacteristic
148C4⋊C8×C61D411yescharacteristic
149C4⋊C8×C61D411yescharacteristic
150#97×C61—21no—
151#97×C61—21no—
152#97×C61—21no—
153C4×C8×C61—21no—
154C4×C8×C61—21no—
155C4×C8×C61—21no—
156C23×D61—21no—
157C23×D61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C22×C4×C61#4111yescharacteristic
161C22×C4×C61#4111yescharacteristic
162C22×C4×C61C2411yescharacteristic
163C22×Dic61—21no—
164C22×Dic61—21no—
165C2×D244—21no—
166C2×D244—21no—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244#4112yes—
177C2×C4×D61—41no—
178C2×C4×D61—41no—
179C2×C4×D61—82no—
180C2×Dic122—21no—
181C2×Dic122—21no—
182C2×Dic122—21no—
183C2×Dic122—21no—
184C2×Dic122—21no—
185C2×Dic122—21no—
186M16×C61—21no—
187M16×C61—21no—
188M16×C61—21no—
189M16×C61#4112yes—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61C2×D411yescharacteristic
197C2×C8×C61C2×D411yescharacteristic
198C2×C8×C61C2×D411yescharacteristic
199C2×C8×C61C2×D411yescharacteristic
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61C2×D411yescharacteristic
207C4⋊C4×C61C2×D411yescharacteristic
208C4⋊C4×C61C2×D411yescharacteristic
209C4⋊C4×C61C2×D411yescharacteristic
210C22⋊C4×C61—21no—
211C22⋊C4×C61—21no—
212C42×C61—21no—
213C42×C61—21no—
214C42×C61C2×D411yescharacteristic
215C42×C61C2×D411yescharacteristic
216C42×C61C2×D411yescharacteristic
217C42×C61C2×D411yescharacteristic
218#11758198—41no—
219#11758198—41no—
220#11758198—41no—
221#11758198—41no—
222#11758198—41no—
223#11758198—41no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226#11758194—21no—
227#11758194—21no—
228#11758194—21no—
229#11758194—21no—
230#11758194—21no—
231#11758194—21no—
232#11758194—21no—
233#11758194—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238D488—42no—
239D488—42no—
240#11758190—42no—
241#11758190—42no—
242C23×C61C2×#4111yescharacteristic
243C22×D61—22no—
244C22×D61—41no—
245C22×D61—41no—
246C22×D61—41no—
247C22×D61—41no—
248C22×D61—41no—
249C22×D61—81no—
250C22×D61—81no—
251C22×D61—81no—
252C22×D61—81no—
253Q8×C61—42no—
254Q8×C61—81no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61#12111yescharacteristic
262C2×C4×C61#12111yescharacteristic
263C2×C4×C61#12111yescharacteristic
264C2×C4×C61#12111yescharacteristic
265C2×C4×C61C22×D411yescharacteristic
266C2×C4×C61C22×D411yescharacteristic
267C2×C4×C61C2×#4111yescharacteristic
268C2×C4×C61C2×#4111yescharacteristic
269C2×C4×C61H(5,𝔽2)11yescharacteristic
270C2×C4×C612−1+411yescharacteristic
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—81no—
276D244—22no—
277D244—22no—
278D244—41no—
279D244—41no—
280D244—41no—
281D244—41no—
282D244—41no—
283D244—41no—
284C4×D61—82no—
285C4×D61—82no—
286Dic122—41no—
287Dic122—41no—
288Dic122—41no—
289Dic122—41no—
290C8×C61—21no—
291C8×C61—21no—
292C8×C61—21no—
293C8×C61—21no—
294C8×C61—22no—
295C8×C61—41no—
296#92418—41no—
297#92418—41no—
298#92418—41no—
299#92418—41no—
300#25316—611nomaximal, Sylow
301C22×C61—21no—
302C22×C61—21no—
303C22×C61C2×#12111yescharacteristic
304C22×C61#52911yescharacteristic
305C22×C61#54211yescharacteristic
306C2×D61—42no—
307C2×D61—82no—
308C2×D61—81no—
309C2×D61—81no—
310C2×D61—82no—
311C2×D61—81no—
312C2×D61—81no—
313C2×D61—81no—
314C2×D61—161no—
315C2×D61—161no—
316C4×C61—21no—
317C4×C61—21no—
318C4×C61—21no—
319C4×C61—21no—
320C4×C61—41no—
321C4×C61—41no—
322C4×C61—41no—
323C4×C61—41no—
324C4×C61#54611yescharacteristic
325C4×C61#54811yescharacteristic
326C4×C61#54811yescharacteristic
327C4×C61#55011yescharacteristic
328Dic61—81no—
329Dic61—81no—
330#3140—611no—
331#3077—611no—
332C2×#463—611no—
333#2962D6111yescharacteristic, complemented
334#2064—611no—
335#2063—611no—
336#2046—611no—
337#2045—611no—
338#1978—611no—
339#1977—611no—
340#1967—611no—
341#1950—611no—
342#1931—611no—
343#1930—611no—
344C4×#100—611no—
345C2×C61—21no—
346C2×C61—21no—
347C2×C61#242611yescharacteristic
348C2×C61#306711yescharacteristic
349C2×C61#306811yescharacteristic
350D61—82no—
351D61—161no—
352C22×SD16—611no—
353C22×D8—611no—
354#533C2×D6111yescharacteristic
355C2×#124—611no—
356C2×C4×D4—611no—
357#489—1221no—
358#489—1221no—
359#488—1221no—
360#488—1221no—
361#478—1221no—
362#478—1221no—
363#476—1221no—
364#474—1221no—
365#463—1221no—
366#463—1221no—
367#463—1221no—
368#463—1221no—
369#446—21no—
370#446—21no—
371#446—21no—
372C8×Q8—21no—
373C2×#108—611no—
374C2×#108—611no—
375#428—611no—
376#428—611no—
377#424C2×D6111yescharacteristic
378#424C2×D6111yescharacteristic
379#423—611no—
380C2×C4⋊C8C2×D6111yescharacteristic
381#419—611no—
382#419—611no—
383#418—611no—
384#418—611no—
385#418—611no—
386#418—611no—
387C2×#103—611no—
388C2×#102—611no—
389C2×#101—611no—
390C2×#101—611no—
391C2×#100—611no—
392C2×#100—611no—
393C2×#100—611no—
394C2×#100—611no—
395#405C2×D6111yescharacteristic
396#405C2×D6111yescharacteristic
397C4×M16—611no—
398C4×M16C2×D6111yescharacteristic
399#343—611no—
400#343—611no—
401#341—611no—
402#341—611no—
403C61#2531611yescharacteristic, complemented, Sylow
404C22×Q8—611no—
405C22×D4—611no—
406C22×D4—611no—
407C23×C4—1221no—
408C2×SD16—1222no—
409C2×SD16—1221no—
410C2×SD16—1221no—
411C2×SD16—2441no—
412C2×D8—1222no—
413C2×D8—1221no—
414C2×D8—1221no—
415C2×D8—2441no—
416C2×M16—611no—
417C2×M16—611no—
418C2×M16—611no—
419C2×M16—611no—
420C2×M16C22×D6111yescharacteristic
421C2×M16C22×D6111yescharacteristic
422C22×C8C22×D6111yescharacteristic
423C22×C8C22×D6111yescharacteristic
424C4⋊Q8D24411yescharacteristic
425C4⋊Q8D24411yescharacteristic
426#125D24411yescharacteristic
427#125D24411yescharacteristic
428#124—1221no—
429#124—1221no—
430#124—1221no—
431#124—1221no—
432C22⋊Q8—21no—
433C22⋊Q8—21no—
434C4×Q8—21no—
435C4×Q8—21no—
436C4×D4—1221no—
437C4×D4—1221no—
438C4×D4—1221no—
439C4×D4—1221no—
440#117C22×D6111yescharacteristic
441#117C22×D6111yescharacteristic
442C2×C4⋊C4—611no—
443C2×C22⋊C4—1221no—
444C2×C22⋊C4—1221no—
445C2×C22⋊C4—1221no—
446C2×C42C22×D6111yescharacteristic
447#108—2441no—
448#108—2441no—
449#107—1221no—
450#107—1221no—
451#106—1221no—
452#106—1221no—
453C4⋊C8—21no—
454C4⋊C8—21no—
455C4⋊C8—21no—
456C4⋊C8—21no—
457C4⋊C8—1221no—
458C4⋊C8—1221no—
459C4⋊C8C22⋊D6111yescharacteristic
460C4⋊C8C22⋊D6111yescharacteristic
461C4⋊C8C22⋊D6111yescharacteristic
462C4⋊C8C22⋊D6111yescharacteristic
463#103—1221no—
464#103—1221no—
465#103—1221no—
466#103—1221no—
467#103—1221no—
468#103—1221no—
469#102—1221no—
470#102—1221no—
471#102—1221no—
472#102—1221no—
473#102—1221no—
474#102—1221no—
475#102—1221no—
476#102—1221no—
477#102—1221no—
478#102—1221no—
479#101—1222no—
480#101—2441no—
481#100—1222no—
482#100—1222no—
483#100—1222no—
484#100—2441no—
485#97—21no—
486#97—21no—
487#97—21no—
488#97—1221no—
489C4×C8—21no—
490C4×C8—21no—
491C4×C8—21no—
492C4×C8—1221no—
493C24—1221no—
494C24—1221no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—1221no—
498C2×Q8—1221no—
499C2×Q8—1221no—
500C2×Q8—1221no—
501C2×Q8—1221no—
502C2×Q8—1221no—
503C2×D4—612no—
504C2×D4—1221no—
505C2×D4—1221no—
506C2×D4—1221no—
507C2×D4—1221no—
508C2×D4—1221no—
509C2×D4—1221no—
510C2×D4—1221no—
511C2×D4—1221no—
512C2×D4—1221no—
513C2×D4—1221no—
514C2×D4—1221no—
515C22×C4—1221no—
516C22×C4—1221no—
517C22×C4—4882no—
518C22×C4—2441no—
519C22×C4—2441no—
520C22×C4#1175822211yescharacteristic
521C22×C4#1175822211yescharacteristic
522C22×C4C23×D6111yescharacteristic
523SD16—2442no—
524SD16—2442no—
525D8—2442no—
526D8—2442no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—1221no—
531M16—1221no—
532M16—1221no—
533M16—1221no—
534M16—1221no—
535M16—1221no—
536M16—1221no—
537M16—1221no—
538M16#1175822612yes—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—1221no—
546C2×C8—1221no—
547C2×C8—1221no—
548C2×C8—1221no—
549C2×C8C2×C22⋊D6111yescharacteristic
550C2×C8C2×C22⋊D6111yescharacteristic
551C2×C8C2×C22⋊D6111yescharacteristic
552C2×C8C2×C22⋊D6111yescharacteristic
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—1221no—
560C4⋊C4—1221no—
561C4⋊C4C2×D24411yescharacteristic
562C4⋊C4C2×D24411yescharacteristic
563C4⋊C4C2×D24411yescharacteristic
564C4⋊C4C2×D24411yescharacteristic
565C22⋊C4—21no—
566C22⋊C4—21no—
567C22⋊C4—2441no—
568C22⋊C4—2441no—
569C22⋊C4—2441no—
570C22⋊C4—2441no—
571C22⋊C4—2441no—
572C22⋊C4—2441no—
573C42—21no—
574C42—21no—
575C42C2×D24411yescharacteristic
576C42C2×D24411yescharacteristic
577C42C2×C22⋊D6111yescharacteristic
578C42C2×C22⋊D6111yescharacteristic
579C23—1222no—
580C23—4881no—
581C23—4881no—
582C23—4881no—
583C23—4881no—
584C23—2441no—
585C23—2441no—
586C23—2441no—
587C23—2441no—
588C23—2441no—
589C23C2×#1175822211yescharacteristic
590Q8—42no—
591Q8—81no—
592Q8—2441no—
593Q8—2441no—
594Q8—2441no—
595Q8—2441no—
596D4—1222no—
597D4—1222no—
598D4—2441no—
599D4—2441no—
600D4—2441no—
601D4—2441no—
602D4—2441no—
603D4—2441no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—4882no—
611C2×C4—4882no—
612C2×C4—4881no—
613C2×C4—2441no—
614C2×C4—2441no—
615C2×C4—2441no—
616C2×C4—2441no—
617C2×C4#1451975111yescharacteristic
618C2×C4#1451975111yescharacteristic
619C2×C4#1451975111yescharacteristic
620C2×C4#1451975111yescharacteristic
621C2×C4C22×C22⋊D6111yescharacteristic
622C2×C4C22×D24411yescharacteristic
623C2×C4#41×D6111yescharacteristic
624C2×C4C2×#1175822611yescharacteristic
625C2×C4#1451982311yescharacteristic
626C2×C4#1451982511yescharacteristic
627C8—21no—
628C8—21no—
629C8—21no—
630C8—21no—
631C8—22no—
632C8—41no—
633C8—2441no—
634C8—2441no—
635C8—2441no—
636C8—2441no—
637C22—21no—
638C22—21no—
639C22—9761no—
640C22—9761no—
641C22—4882no—
642C22—4882no—
643C22—4881no—
644C22—4881no—
645C22—4881no—
646C22—4881no—
647C22—4881no—
648C22—2442no—
649C22C2×#1451975111yescharacteristic
650C22#1684029911yescharacteristic
651C22#1684038411yescharacteristic
652C4—21no—
653C4—21no—
654C4—21no—
655C4—21no—
656C4—41no—
657C4—41no—
658C4—41no—
659C4—41no—
660C4—4881no—
661C4—4881no—
662C4#1684040011yescharacteristic
663C4#1684042311yescharacteristic
664C4#1684042411yescharacteristic
665C4#1684043411yescharacteristic
666C2—21no—
667C2—21no—
668C2—9761no—
669C2—4882no—
670C2#2144937911yescharacteristic
671C2#2145553911yescharacteristic
672C2#2145554711yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2962C2
socleC22×C61C2×#121
prime radicalC22×D488C22
hypercenter#2962D61
hypocenterC61#25316
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2962

Complements

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

NH ≅ G/Ntype
1. #21456208C2semidirect
2. #21455612C2semidirect
4. #21447185C2semidirect
5. #21447178C2semidirect
6. #21447082C2semidirect
9. #21446722C2semidirect
10. #21446668C2semidirect
11. #21446595C2semidirect
12. #21446481C2semidirect
13. #21446474C2semidirect
14. C4×#14519693C2semidirect
15. C61×#2962C2semidirect
333. #2962D61semidirect
403. C61#25316semidirect

Maximal subgroups

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

subgroupindex
#214562082
#214556122
C2×#168399782
#214471852
#214471782
#214470822
#214470752
#214467292
#214467222
#214466682
#214465952
#214464812
#214464742
C4×#145196932
C61×#29622
#2531661