Finite Group Databasebeta

← #29683254

Subgroups — #29683254

Order 15616.

780 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454619C211yesmaximal, characteristic
2#21454469C211yesmaximal, characteristic, complemented
3#21454246C211yesmaximal, characteristic, complemented
4#21446467C211yesmaximal, characteristic, complemented
5#21446465C211yesmaximal, characteristic, complemented
6#21446420C211yesmaximal, characteristic, complemented
7#21446147C211yesmaximal, characteristic
8#21446145C211yesmaximal, characteristic
9#21446095C211yesmaximal, characteristic, complemented
10#21446093C211yesmaximal, characteristic, complemented
11#21445724C211yesmaximal, characteristic, complemented
12#21445623C211yesmaximal, characteristic, complemented
13#21445623C211yesmaximal, characteristic, complemented
14#21445566C211yesmaximal, characteristic, complemented
15C61×#1922C211yesmaximal, characteristic, complemented
16C2×#14519799C2211yescharacteristic
17C2×#14519785C2211yescharacteristic
18C2×#14519783C2211yescharacteristic
19#16840230C2211yescharacteristic
20#16840230C2211yescharacteristic
21#16839873C411yescharacteristic, complemented
22#16839873C411yescharacteristic, complemented
23#16839868C411yescharacteristic, complemented
24#16839868C411yescharacteristic, complemented
25#16839861C411yescharacteristic, complemented
26#16839861C411yescharacteristic, complemented
27#16839861C411yescharacteristic, complemented
28#16839861C411yescharacteristic, complemented
29#16839822—21no—
30#16839822—21no—
31#16839818—21no—
32#16839818—21no—
33C2×#14519712C2211yescharacteristic
34C2×#14519712C2211yescharacteristic
35#16839789C2211yescharacteristic
36C2×#14519705C2211yescharacteristic
37C2×#14519705C2211yescharacteristic
38C2×#14519703C2211yescharacteristic
39C2×#14519703C2211yescharacteristic
40#16839756C2211yescharacteristic
41#16839756C2211yescharacteristic
42#16839730C2211yescharacteristic
43#16839728C2211yescharacteristic
44#16839719—21no—
45#16839718C2211yescharacteristic
46#16839716—21no—
47M16×Dic61C2211yescharacteristic
48M16×Dic61C2211yescharacteristic
49C4×#11758189—21no—
50C2×#14519687C2211yescharacteristic
51C2×#14519687C2211yescharacteristic
52#97×D61—21no—
53C42×Dic61C2211yescharacteristic
54#16839527C2211yescharacteristic
55#16839521C2211yescharacteristic
56#16839521C2211yescharacteristic
57#16839517C2211yescharacteristic
58#16839516C2211yescharacteristic
59#16839516C2211yescharacteristic
60C61×#427C2211yescharacteristic
61C61×#424C2211yescharacteristic
62C61×#405C2211yescharacteristic
63C61×#341C2211yescharacteristic
64C61×#339C2211yescharacteristic
65C61×#339C2211yescharacteristic
66C61×#336C2211yescharacteristic
67C2×#11758222C2311yescharacteristic
68C2×#11758222C2311yescharacteristic
69#14519799—22no—
70#14519799—22no—
71C2×Dic244C2×C411yescharacteristic
72C2×#11758190C2×C411yescharacteristic
73C2×#11758190C2×C411yescharacteristic
74C2×D488C2×C411yescharacteristic
75#14519785—22no—
76#14519785—22no—
77#14519783—22no—
78#14519783—22no—
79C2×#11758194C2311yescharacteristic
80C2×#11758194C2311yescharacteristic
81C2×#11758189—21no—
82C2×#11758189—21no—
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C2×C8×D61—21no—
86C2×C8×D61—21no—
87#14519742C2×C411yescharacteristic
88#14519742C2×C411yescharacteristic
89#14519742C2×C411yescharacteristic
90#14519742C2×C411yescharacteristic
91#14519739C2×C411yescharacteristic
92#14519739C2×C411yescharacteristic
93#14519739C2×C411yescharacteristic
94#14519739C2×C411yescharacteristic
95#14519737—21no—
96#14519737—21no—
97#14519737—21no—
98#14519737—21no—
99#14519734—21no—
100#14519734—21no—
101C2×C4×Dic61—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61C2311yescharacteristic
104C2×C4×Dic61C2311yescharacteristic
105C42×D61—21no—
106C42×D61—21no—
107#14519712—22no—
108#14519712—22no—
109C4⋊#92418—21no—
110C4⋊#92418—21no—
111#14519705—22no—
112#14519705—22no—
113#14519703—22no—
114#14519703—22no—
115#14519700C2×C411yescharacteristic
116#14519700C2×C411yescharacteristic
117#14519700C2×C411yescharacteristic
118#14519700C2×C411yescharacteristic
119#14519697C2×C411yescharacteristic
120#14519697C2×C411yescharacteristic
121#14519697C2×C411yescharacteristic
122#14519697C2×C411yescharacteristic
123#14519689—21no—
124#14519689—21no—
125#14519689—21no—
126#14519689—21no—
127#14519688—21no—
128#14519687—21no—
129#14519687—21no—
130#14519687C2×C411yescharacteristic
131#14519687C2×C411yescharacteristic
132#14519687C2×C411yescharacteristic
133#14519687C2×C411yescharacteristic
134#14519687D411yescharacteristic
135#14519687D411yescharacteristic
136#14519687D411yescharacteristic
137#14519687D411yescharacteristic
138C4×#92418—21no—
139C8×Dic61—21no—
140C8×Dic61—21no—
141C2×M16×C61C2311yescharacteristic
142C2×M16×C61C2311yescharacteristic
143C22×C8×C61C2311yescharacteristic
144C22×C8×C61C2311yescharacteristic
145#117×C61C2311yescharacteristic
146#117×C61C2311yescharacteristic
147C2×C42×C61C2311yescharacteristic
148#107×C61C2×C411yescharacteristic
149#107×C61C2×C411yescharacteristic
150#106×C61C2×C411yescharacteristic
151#106×C61C2×C411yescharacteristic
152C4⋊C8×C61—21no—
153C4⋊C8×C61—21no—
154#97×C61—21no—
155C4×C8×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61C2411yescharacteristic
158C2×C22⋊D61—21no—
159C2×C22⋊D61—21no—
160C22×Dic61—21no—
161C22×Dic61#4111yescharacteristic
162C22×Dic61#4111yescharacteristic
163#11758222—21no—
164#11758222—21no—
165#11758222—21no—
166#11758222—21no—
167#11758222—21no—
168#11758222—21no—
169#11758222#4112yes—
170#11758222#4112yes—
171C2×D244C22×C411yescharacteristic
172C2×D244C22×C411yescharacteristic
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×Dic122C22×C411yescharacteristic
180C2×Dic122C22×C411yescharacteristic
181M16×C61—21no—
182M16×C61—21no—
183M16×C61—21no—
184M16×C61#4112yes—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61C22×C411yescharacteristic
192C2×C8×C61C22×C411yescharacteristic
193C2×C8×C61C2×D411yescharacteristic
194C2×C8×C61C2×D411yescharacteristic
195C4⋊C4×C61C22×C411yescharacteristic
196C4⋊C4×C61C22×C411yescharacteristic
197C4⋊C4×C61C22×C411yescharacteristic
198C4⋊C4×C61C22×C411yescharacteristic
199C22⋊C4×C61—21no—
200C22⋊C4×C61—21no—
201C42×C61—21no—
202C42×C61—21no—
203C42×C61—21no—
204C42×C61—21no—
205#11758198—21no—
206#11758198—21no—
207#11758198—21no—
208#11758198—21no—
209#11758196—21no—
210#11758196—21no—
211#11758196—21no—
212#11758196—21no—
213C4×Dic61—21no—
214C4×Dic61—21no—
215C4×Dic61—21no—
216C4×Dic61—21no—
217C4×Dic61—21no—
218C4×Dic61—21no—
219C4×Dic61—42no—
220C4×Dic61—42no—
221C4×Dic61C22×C411yescharacteristic
222C4×Dic61C22×C411yescharacteristic
223C4×Dic61C2×D411yescharacteristic
224C4×Dic61C2×D411yescharacteristic
225#11758194—21no—
226#11758194—21no—
227#11758194—21no—
228#11758194#4112yes—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418C22×C411yescharacteristic
236C2×#92418C22×C411yescharacteristic
237C2×#92418C2×D411yescharacteristic
238C2×#92418C2×D411yescharacteristic
239Dic244—22no—
240D488—22no—
241#11758190—22no—
242#11758190—22no—
243#11758189—24no—
244#11758189—24no—
245C8×D61—24no—
246C8×D61—24no—
247C23×C61C2×#4111yescharacteristic
248C22×D61—21no—
249C22×D61—21no—
250C2×C4×C61—22no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61C23×C411yescharacteristic
258C2×C4×C61C22×D411yescharacteristic
259C2×C4×C61C2×#4111yescharacteristic
260C2×C4×C61C2×#4111yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C22⋊D61—22no—
264C22⋊D61—22no—
265C22⋊D61—41no—
266C22⋊D61—41no—
267C2×Dic61—21no—
268C2×Dic61—22no—
269C2×Dic61—21no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61C4×D411yescharacteristic
275C2×Dic61C4×D411yescharacteristic
276C2×Dic61C4×D411yescharacteristic
277C2×Dic61C4×D411yescharacteristic
278D244—21no—
279D244—21no—
280D244—21no—
281D244#11712yes—
282C4×D61—22no—
283C4×D61—22no—
284C4×D61—41no—
285C4×D61—41no—
286C4×D61—81no—
287C4×D61—81no—
288C4×D61—81no—
289C4×D61—81no—
290Dic122—21no—
291Dic122—21no—
292Dic122—21no—
293Dic122#11712yes—
294C8×C61—21no—
295C8×C61—21no—
296C8×C61—21no—
297C8×C61—22no—
298C8×C61—21no—
299C8×C61—41no—
300#92418—21no—
301#92418—21no—
302#92418—21no—
303#92418—22no—
304#92418—21no—
305#92418—41no—
306#21139—611nomaximal, Sylow
307C22×C61—21no—
308C22×C61—21no—
309C22×C61C2×C4×D411yescharacteristic
310C22×C61#52911yescharacteristic
311C22×C61#52911yescharacteristic
312C2×D61—22no—
313C2×D61—41no—
314C2×D61—41no—
315C2×D61—41no—
316C2×D61—41no—
317C2×D61—41no—
318C4×C61—42no—
319C4×C61—41no—
320C4×C61—41no—
321C4×C61—41no—
322C4×C61—41no—
323C4×C61C2×#11711yescharacteristic
324C4×C61C4×#4111yescharacteristic
325C4×C61#52511yescharacteristic
326C4×C61#52511yescharacteristic
327Dic61—21no—
328Dic61—21no—
329Dic61—21no—
330Dic61—21no—
331Dic61—22no—
332Dic61—42no—
333Dic61—41no—
334#2943—611no—
335#2923—611no—
336#2875—611no—
337#1929—611no—
338#1929—611no—
339#1922—611no—
340#1922D6111yescharacteristic, complemented
341#1876—611no—
342#1876—611no—
343#1866—611no—
344#1866—611no—
345#1778—611no—
346C4×#104—611no—
347C4×#104—611no—
348#1745—611no—
349C2×C61—21no—
350C2×C61—21no—
351C2×C61#229011yescharacteristic
352C2×C61#295611yescharacteristic
353C2×C61#295611yescharacteristic
354D61—42no—
355D61—81no—
356C2×#135—611no—
357C2×#131—611no—
358C2×#131—611no—
359C4×#41—611no—
360C4×#41—611no—
361#442—611no—
362#442—611no—
363#441—611no—
364#441—611no—
365#440—611no—
366#440—611no—
367#440—611no—
368#440—611no—
369#433—1221no—
370#433—1221no—
371#432—1221no—
372#432—1221no—
373C2×#108—611no—
374C2×#108—611no—
375#427C2×D6111yescharacteristic
376#424—611no—
377#424C2×D6111yescharacteristic
378C2×#104—611no—
379C2×#104—611no—
380C2×#104—611no—
381C2×#104—611no—
382#416—611no—
383#416—611no—
384#408—611no—
385#408—611no—
386#405—611no—
387#405—1221no—
388#405—1221no—
389#405C2×D6111yescharacteristic
390C4×M16—611no—
391C4×M16—611no—
392C4×M16—1221no—
393C2×#97—611no—
394C2×#97—611no—
395C2×#97—1221no—
396C43—611no—
397#341—611no—
398#341C2×D6111yescharacteristic
399#339—611no—
400#339—611no—
401#339C2×D6111yescharacteristic
402#339C2×D6111yescharacteristic
403#336—611no—
404#336—611no—
405#336—611no—
406#336C2×D6111yescharacteristic
407C61#2113911yescharacteristic, complemented, Sylow
408C2×#41—611no—
409C2×#41—611no—
410#135—1222no—
411#135—1222no—
412C2×Q16—611no—
413C2×SD16—611no—
414C2×SD16—611no—
415C2×D8—611no—
416#131—1222no—
417#131—1222no—
418#131—1222no—
419#131—1222no—
420C2×M16—611no—
421C2×M16—611no—
422C2×M16—1221no—
423C2×M16—1221no—
424C2×M16C22×D6111yescharacteristic
425C2×M16C22×D6111yescharacteristic
426C22×C8—611no—
427C22×C8—611no—
428C22×C8—1221no—
429C22×C8—1221no—
430C22×C8C22×D6111yescharacteristic
431C22×C8C22×D6111yescharacteristic
432C4×Q8—611no—
433C4×Q8—611no—
434C4×Q8—611no—
435C4×Q8—611no—
436C4×D4—611no—
437C4×D4—611no—
438C4×D4—611no—
439C4×D4—611no—
440C4×D4—1221no—
441C4×D4—1221no—
442C4×D4—1221no—
443C4×D4—1221no—
444#117—1221no—
445#117—1221no—
446#117C22×D6111yescharacteristic
447#117C22×D6111yescharacteristic
448C2×C42—611no—
449C2×C42—611no—
450C2×C42—1221no—
451C2×C42—1221no—
452C2×C42—1221no—
453C2×C42—1221no—
454C2×C42C22×D6111yescharacteristic
455#108—1222no—
456#108—1222no—
457#107C4×D6111yescharacteristic
458#107C4×D6111yescharacteristic
459#106C4×D6111yescharacteristic
460#106C4×D6111yescharacteristic
461C4⋊C8—21no—
462C4⋊C8—21no—
463C4⋊C8—1221no—
464C4⋊C8—1221no—
465#104—1222no—
466#104—1222no—
467#104—1222no—
468#104—1222no—
469#103—611no—
470#103—611no—
471#103—611no—
472#103—611no—
473#102—611no—
474#102—611no—
475#102—611no—
476#102—611no—
477C22⋊C8—1221no—
478C22⋊C8—1221no—
479C22⋊C8—1221no—
480C22⋊C8—1221no—
481#97—21no—
482#97—611no—
483#97—611no—
484#97—611no—
485#97—611no—
486#97—611no—
487#97—611no—
488#97—611no—
489#97—611no—
490#97—1221no—
491#97—1221no—
492#97—1221no—
493C4×C8—21no—
494C4×C8—1221no—
495C4×C8—1221no—
496C4×C8—1221no—
497#41—612no—
498#41—612no—
499#41—1221no—
500#41—1221no—
501#41—1221no—
502#41—1221no—
503#41—1221no—
504#41—1221no—
505C2×Q8—611no—
506C2×Q8—611no—
507C2×D4—611no—
508C2×D4—611no—
509C2×D4—1221no—
510C2×D4—1221no—
511C22×C4—21no—
512C22×C4—611no—
513C22×C4—611no—
514C22×C4—1221no—
515C22×C4—1221no—
516C22×C4—1221no—
517C22×C4—1221no—
518C22×C4—1221no—
519C22×C4—1221no—
520C22×C4—1221no—
521C22×C4C23×D6111yescharacteristic
522Q16—1222no—
523SD16—1222no—
524SD16—1222no—
525D8—1222no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—612no—
530M16—1224no—
531M16—1224no—
532M16—1221no—
533M16—1221no—
534M16—1221no—
535M16#1175822612yes—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—611no—
543C2×C8—611no—
544C2×C8—611no—
545C2×C8—611no—
546C2×C8—1224no—
547C2×C8—1224no—
548C2×C8—1221no—
549C2×C8—1221no—
550C2×C8—1221no—
551C2×C8—1221no—
552C2×C8—1221no—
553C2×C8—1221no—
554C2×C8C2×C4×D6111yescharacteristic
555C2×C8C2×C4×D6111yescharacteristic
556C2×C8D4×D6111yescharacteristic
557C2×C8D4×D6111yescharacteristic
558C4⋊C4—1221no—
559C4⋊C4—1221no—
560C4⋊C4—1221no—
561C4⋊C4—1221no—
562C4⋊C4C2×C4×D6111yescharacteristic
563C4⋊C4C2×C4×D6111yescharacteristic
564C4⋊C4C2×C4×D6111yescharacteristic
565C4⋊C4C2×C4×D6111yescharacteristic
566C22⋊C4—21no—
567C22⋊C4—21no—
568C22⋊C4—1221no—
569C22⋊C4—1221no—
570C22⋊C4—1221no—
571C22⋊C4—1221no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—611no—
577C42—611no—
578C42—611no—
579C42—611no—
580C42—1221no—
581C42—1221no—
582C42—1221no—
583C42—1221no—
584C42—1221no—
585C42—1221no—
586C42—2442no—
587C42—2442no—
588C23—1221no—
589C23—1221no—
590C23#41×D6111yescharacteristic
591Q8—612no—
592Q8—1221no—
593Q8—1221no—
594Q8—1221no—
595D4—612no—
596D4—1222no—
597D4—1222no—
598D4—1221no—
599D4—1221no—
600D4—1221no—
601D4—2441no—
602D4—2441no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—611no—
611C2×C4—611no—
612C2×C4—611no—
613C2×C4—611no—
614C2×C4—1221no—
615C2×C4—1222no—
616C2×C4—1222no—
617C2×C4—1222no—
618C2×C4—1221no—
619C2×C4—4881no—
620C2×C4—4881no—
621C2×C4—4881no—
622C2×C4—4881no—
623C2×C4—2441no—
624C2×C4—2441no—
625C2×C4—2441no—
626C2×C4—2441no—
627C2×C4—2441no—
628C2×C4—2441no—
629C2×C4C22×C4×D6111yescharacteristic
630C2×C4C2×D4×D6111yescharacteristic
631C2×C4#41×D6111yescharacteristic
632C2×C4#41×D6111yescharacteristic
633C2×C4#41×D6111yescharacteristic
634C2×C4C2×#1175822611yescharacteristic
635C8—21no—
636C8—21no—
637C8—21no—
638C8—21no—
639C8—22no—
640C8—41no—
641C8—1221no—
642C8—1221no—
643C8—1222no—
644C8—1221no—
645C8—1221no—
646C8—2441no—
647C22—21no—
648C22—21no—
649C22—1222no—
650C22—2441no—
651C22—2441no—
652C22—2441no—
653C22—2441no—
654C22—2441no—
655C22C4×D4×D6111yescharacteristic
656C22#1684029511yescharacteristic
657C22#1684029711yescharacteristic
658C4—42no—
659C4—41no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—1222no—
664C4—1221no—
665C4—1221no—
666C4—1221no—
667C4—1221no—
668C4—2442no—
669C4—2441no—
670C4#117×D6111yescharacteristic
671C4C4×#1175822611yescharacteristic
672C4#1684027011yescharacteristic
673C4#1684027511yescharacteristic
674C2—21no—
675C2—21no—
676C2—4881no—
677C2—2442no—
678C2#2144825711yescharacteristic
679C2#2145472411yescharacteristic
680C2#2145472711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1922C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519799C22
cosocleC22×C4×C61C24
hypercenter#1922D61
hypocenterC61#21139
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1922

Complements

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

NH ≅ G/Ntype
2. #21454469C2semidirect
3. #21454246C2semidirect
4. #21446467C2semidirect
5. #21446465C2semidirect
6. #21446420C2semidirect
9. #21446095C2semidirect
10. #21446093C2semidirect
11. #21445724C2semidirect
12. #21445623C2semidirect
13. #21445623C2semidirect
14. #21445566C2semidirect
15. C61×#1922C2semidirect
21. #16839873C4semidirect
22. #16839873C4semidirect
23. #16839868C4semidirect
24. #16839868C4semidirect
25. #16839861C4semidirect
26. #16839861C4semidirect
27. #16839861C4semidirect
28. #16839861C4semidirect
340. #1922D61semidirect
407. C61#21139semidirect

Maximal subgroups

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

subgroupindex
#214546192
#214544692
#214542462
#214464672
#214464652
#214464202
#214461472
#214461452
#214460952
#214460932
#214457242
#214456232
#214455662
C61×#19222
#2113961