Finite Group Databasebeta

← #29740497

Subgroups — #29740497

Order 15616.

734 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455365C211yesmaximal, characteristic
2#21454692C211yesmaximal, characteristic
3#21454411C211yesmaximal, characteristic, complemented
4#21447369C211yesmaximal, characteristic, complemented
5#21447327C211yesmaximal, characteristic, complemented
6#21447264C211yesmaximal, characteristic, complemented
7#21447033C211yesmaximal, characteristic, complemented
8#21446477C211yesmaximal, characteristic, complemented
9#21446420C211yesmaximal, characteristic, complemented
10#21446337C211yesmaximal, characteristic, complemented
11#21446185C211yesmaximal, characteristic, complemented
12#21446149C211yesmaximal, characteristic
13#21446052C211yesmaximal, characteristic, complemented
14#21446049C211yesmaximal, characteristic, complemented
15C61×#3097C211yesmaximal, characteristic, complemented
16C2×#14519808C2211yescharacteristic
17C2×#14519797C2211yescharacteristic
18C2×#14519783C2211yescharacteristic
19#16840242C2211yescharacteristic
20#16840242C2211yescharacteristic
21#16839981—21no—
22#16839974—21no—
23#16839969—21no—
24#16839964—21no—
25#16839862—21no—
26#16839860—21no—
27C4×#11758202—21no—
28C4×#11758199—21no—
29#16839805C2211yescharacteristic
30#16839805C2211yescharacteristic
31#16839803—21no—
32#16839803—21no—
33#16839797—21no—
34C2×#14519710C2211yescharacteristic
35C2×#14519709C2211yescharacteristic
36#106×D61—21no—
37#16839789C2211yescharacteristic
38C2×#14519704C2211yescharacteristic
39C2×#14519703C2211yescharacteristic
40#16839763C2211yescharacteristic
41#16839763C2211yescharacteristic
42#16839761C2211yescharacteristic
43C2×#14519701C2211yescharacteristic
44C2×#14519696C2211yescharacteristic
45#16839718C2211yescharacteristic
46#16839669C2211yescharacteristic
47#16839627C2211yescharacteristic
48#16839531C2211yescharacteristic
49#16839530C2211yescharacteristic
50#16839530C2211yescharacteristic
51#16839527C2211yescharacteristic
52#16839526C2211yescharacteristic
53#16839521C2211yescharacteristic
54#16839521C2211yescharacteristic
55#16839516C2211yescharacteristic
56C61×#536C2211yescharacteristic
57C61×#520C2211yescharacteristic
58C61×#485—21no—
59C61×#485—21no—
60C61×#484—21no—
61C61×#483—21no—
62C61×#428C2211yescharacteristic
63C61×#427C2211yescharacteristic
64C61×#419C2211yescharacteristic
65C2×#103×C61C2211yescharacteristic
66C61×#408C2211yescharacteristic
67C2×#11758222C2311yescharacteristic
68#14519808—22no—
69#14519808—22no—
70#14519797—22no—
71#14519797—22no—
72C2×#11758202—21no—
73C2×#11758202D411yescharacteristic
74C2×#11758200D411yescharacteristic
75C2×#11758201—21no—
76C2×#11758201D411yescharacteristic
77C2×#11758199D411yescharacteristic
78#14519783—22no—
79#14519783—22no—
80C2×#11758194C2311yescharacteristic
81C2×#11758194C2311yescharacteristic
82C2×#11758194C2311yescharacteristic
83C2×#11758189—21no—
84C22×#92418C2311yescharacteristic
85C2×C8×D61—21no—
86C4×Dic122—21no—
87C4×Dic122—21no—
88C4×D244—21no—
89C4×D244—21no—
90#14519737—41no—
91#14519737—41no—
92#14519735—21no—
93#14519735—21no—
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C4⋊C4×D61—21no—
97C4⋊C4×D61—21no—
98C2×C4×Dic61C2311yescharacteristic
99#14519710—21no—
100#14519710—21no—
101#14519710—21no—
102#14519710—21no—
103#14519709—21no—
104#14519709—21no—
105#14519708—21no—
106#14519708—21no—
107C4⋊#92418—21no—
108C4⋊#92418—21no—
109#14519704—22no—
110#14519703—22no—
111#14519701—21no—
112#14519701—21no—
113#14519701—21no—
114#14519701—21no—
115#14519700—21no—
116#14519698—21no—
117#14519698—21no—
118#14519697—21no—
119#14519696—22no—
120#14519688—21no—
121C4×#92418—21no—
122#14519684—41no—
123#14519684—41no—
124C2×#41×C61C2311yescharacteristic
125C22×Q8×C61C2311yescharacteristic
126C2×M16×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C4⋊Q8×C61—21no—
129#124×C61—21no—
130#123×C61—41no—
131C22⋊Q8×C61—21no—
132C22⋊Q8×C61—21no—
133C4×Q8×C61—21no—
134C4×D4×C61—21no—
135C4×D4×C61—41no—
136#117×C61—21no—
137#117×C61C2311yescharacteristic
138#117×C61C2311yescharacteristic
139C2×C4⋊C4×C61—21no—
140C2×C4⋊C4×C61C2311yescharacteristic
141#107×C61—21no—
142#107×C61D411yescharacteristic
143#107×C61D411yescharacteristic
144#106×C61—21no—
145#106×C61D411yescharacteristic
146#106×C61D411yescharacteristic
147#103×C61—21no—
148#103×C61—21no—
149#103×C61—21no—
150#103×C61—21no—
151C22⋊C8×C61—21no—
152C22⋊C8×C61—21no—
153#41×C61—21no—
154#41×C61—21no—
155#41×C61—21no—
156#41×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61C2×D411yescharacteristic
164C2×D4×C61—21no—
165C2×D4×C61C2×D411yescharacteristic
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—41no—
170C22×C4×C61C2411yescharacteristic
171C2×C22⋊D61—21no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175#11758222—21no—
176#11758222—21no—
177#11758222#4112yes—
178#11758222#4112yes—
179C2×D244C2×D411yescharacteristic
180C2×C4×D61—21no—
181C2×C4×D61—41no—
182C2×C4×D61—41no—
183C2×Dic122C2×D411yescharacteristic
184M16×C61—21no—
185M16×C61—21no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61C2×D411yescharacteristic
190C2×C8×C61C2×D411yescharacteristic
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—41no—
194C4⋊C4×C61—41no—
195C4⋊C4×C61—41no—
196C4⋊C4×C61C2×D411yescharacteristic
197C4⋊C4×C61C2×D411yescharacteristic
198C4⋊C4×C61C2×D411yescharacteristic
199C4⋊C4×C61C2×D411yescharacteristic
200C22⋊C4×C61—21no—
201C22⋊C4×C61—21no—
202C22⋊C4×C61—41no—
203C22⋊C4×C61—41no—
204C22⋊C4×C61—41no—
205C42×C61—21no—
206C42×C61—21no—
207C42×C61—41no—
208#11758202—22no—
209#11758202—42no—
210#11758201—22no—
211#11758201—42no—
212#11758200—22no—
213#11758199—22no—
214#11758198—41no—
215#11758198—41no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220#11758196—41no—
221#11758196—41no—
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61—41no—
225C4×Dic61—41no—
226#11758194—21no—
227#11758194—21no—
228#11758194—21no—
229#11758194—21no—
230#11758194—21no—
231#11758194#4112yes—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418C2×D411yescharacteristic
238C2×#92418C2×D411yescharacteristic
239#11758189—24no—
240C8×D61—24no—
241C23×C61—21no—
242C23×C61H(5,𝔽2)11yescharacteristic
243C22×D61—21no—
244Q8×C61—21no—
245Q8×C61—21no—
246Q8×C61—41no—
247Q8×C61—41no—
248Q8×C61—41no—
249Q8×C61—41no—
250D4×C61—21no—
251D4×C61—21no—
252D4×C61—41no—
253D4×C61—41no—
254C2×C4×C61—21no—
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—41no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—81no—
266C2×C4×C61—161no—
267C2×C4×C61C22×D411yescharacteristic
268C2×C4×C61C22×D411yescharacteristic
269C2×C4×C61C2×#4111yescharacteristic
270C2×C4×C61C2×#4111yescharacteristic
271C2×C4×C61C2×#4111yescharacteristic
272C2×C4×C612−1+411yescharacteristic
273C22⋊D61—22no—
274C22⋊D61—22no—
275C2×Dic61—21no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—81no—
282C2×Dic61—81no—
283D244—21no—
284D244#12312yes—
285C4×D61—22no—
286C4×D61—22no—
287C4×D61—161no—
288C4×D61—161no—
289Dic122—21no—
290Dic122#12312yes—
291C8×C61—21no—
292C8×C61—21no—
293C8×C61—41no—
294#92418—21no—
295#92418—21no—
296#92418—22no—
297#92418—41no—
298#92418—41no—
299#26192—611nomaximal, Sylow
300C22×C61—21no—
301C22×C61—21no—
302C22×C61—41no—
303C22×C61—41no—
304C22×C61—41no—
305C22×C61#53911yescharacteristic
306C22×C61D4211yescharacteristic
307C22×C61#55311yescharacteristic
308C2×D61—22no—
309C2×D61—41no—
310C2×D61—41no—
311C4×C61—41no—
312C4×C61—41no—
313C4×C61—41no—
314C4×C61—41no—
315C4×C61—41no—
316C4×C61—81no—
317C4×C61—81no—
318C4×C61C2×#12311yescharacteristic
319C4×C61#52511yescharacteristic
320C4×C61#54711yescharacteristic
321C4×C61#54811yescharacteristic
322Dic61—22no—
323Dic61—81no—
324Dic61—81no—
325Dic61—81no—
326#3097D6111yescharacteristic, complemented
327#3046—611no—
328#2951—611no—
329#2912—611no—
330#2097—611no—
331#2089—611no—
332#2079—611no—
333#2038—611no—
334#1930—611no—
335#1922—611no—
336#1908—611no—
337#1882—611no—
338#1876—611no—
339#1860—611no—
340#1860—611no—
341C2×C61—21no—
342C2×C61—21no—
343C2×C61—81no—
344C2×C61#244311yescharacteristic
345C2×C61#328911yescharacteristic
346C2×C61#329011yescharacteristic
347D61—42no—
348C2×#137—611no—
349C2×#135—611no—
350C2×#131—611no—
351#536C2×D6111yescharacteristic
352#520—611no—
353#520—611no—
354#520C2×D6111yescharacteristic
355#485—21no—
356#485—21no—
357#484—21no—
358#483—21no—
359#464—1221no—
360#463—1221no—
361#462—1221no—
362#461—1221no—
363#440—1221no—
364#440—1221no—
365C4×Q16—1221no—
366C4×D8—1221no—
367#428—611no—
368#428—611no—
369#428—1221no—
370#428—1221no—
371#428C2×D6111yescharacteristic
372#427—1221no—
373#427C2×D6111yescharacteristic
374C2×#107—611no—
375C2×#106—611no—
376C2×#106—1221no—
377#424—611no—
378C2×#104—611no—
379C2×#104—611no—
380#419C2×D6111yescharacteristic
381#417—611no—
382#417—611no—
383#417—611no—
384C2×#103—611no—
385C2×#103C2×D6111yescharacteristic
386C2×#101—611no—
387#408C2×D6111yescharacteristic
388#405—611no—
389#391—611no—
390#382—611no—
391#343—611no—
392#343—611no—
393#343—611no—
394#341—611no—
395#341—611no—
396#339—611no—
397#339—611no—
398#336—611no—
399C61#2619211yescharacteristic, complemented, Sylow
400C2×#41—611no—
401C2×#41C22×D6111yescharacteristic
402C22×Q8C22×D6111yescharacteristic
403#137—1222no—
404#137—1222no—
405#135—1222no—
406#135—1222no—
407C2×Q16—611no—
408C2×Q16—1221no—
409C2×SD16—611no—
410C2×SD16—611no—
411C2×SD16—1221no—
412C2×D8—611no—
413#131—1222no—
414#131—1222no—
415C2×M16—611no—
416C2×M16—611no—
417C2×M16—611no—
418C2×M16—1221no—
419C2×M16C22×D6111yescharacteristic
420C22×C8—611no—
421C22×C8—1221no—
422C22×C8C22×D6111yescharacteristic
423C4⋊Q8—21no—
424#124—21no—
425#123—41no—
426C22⋊Q8—21no—
427C22⋊Q8—21no—
428C4×Q8—21no—
429C4×Q8—1221no—
430C4×Q8—1221no—
431C4×D4—21no—
432C4×D4—41no—
433C4×D4—1221no—
434C4×D4—1221no—
435C4×D4—2441no—
436C4×D4—2441no—
437#117—21no—
438#117—1221no—
439#117—1221no—
440#117C22×D6111yescharacteristic
441#117C22×D6111yescharacteristic
442C2×C4⋊C4—21no—
443C2×C4⋊C4—611no—
444C2×C4⋊C4—611no—
445C2×C4⋊C4—1221no—
446C2×C4⋊C4—1221no—
447C2×C4⋊C4C22×D6111yescharacteristic
448C2×C42—611no—
449#107—21no—
450#107—1221no—
451#107—1221no—
452#107—1221no—
453#107—1221no—
454#107C22⋊D6111yescharacteristic
455#107C22⋊D6111yescharacteristic
456#106—21no—
457#106—1221no—
458#106—1221no—
459#106—1221no—
460#106—1221no—
461#106C22⋊D6111yescharacteristic
462#106C22⋊D6111yescharacteristic
463C4⋊C8—1221no—
464C4⋊C8—1221no—
465#104—1222no—
466#104—1222no—
467#103—21no—
468#103—21no—
469#103—21no—
470#103—21no—
471#103—1221no—
472#103—1221no—
473#103—1221no—
474#103—1221no—
475#103—1221no—
476#102—1221no—
477#102—1221no—
478#102—1221no—
479#101—1222no—
480C22⋊C8—21no—
481C22⋊C8—21no—
482#97—1221no—
483C4×C8—1221no—
484#95—2441no—
485#95—2441no—
486#41—21no—
487#41—21no—
488#41—21no—
489#41—21no—
490#41—612no—
491#41—612no—
492#41—1221no—
493#41—1221no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—611no—
501C2×Q8D4×D6111yescharacteristic
502C2×D4—21no—
503C2×D4—611no—
504C2×D4—1221no—
505C2×D4D4×D6111yescharacteristic
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—41no—
510C22×C4—1221no—
511C22×C4—1221no—
512C22×C4—1221no—
513C22×C4—1221no—
514C22×C4—2441no—
515C22×C4—2441no—
516C22×C4C23×D6111yescharacteristic
517Q16—1222no—
518Q16—2442no—
519SD16—1222no—
520SD16—1222no—
521SD16—2442no—
522D8—1222no—
523M16—21no—
524M16—21no—
525M16—612no—
526M16—1224no—
527M16—1221no—
528M16—1221no—
529M16—1221no—
530M16—1221no—
531M16—1221no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—611no—
536C2×C8—611no—
537C2×C8—1224no—
538C2×C8—1221no—
539C2×C8—1221no—
540C2×C8—1221no—
541C2×C8—1221no—
542C2×C8—1221no—
543C2×C8C2×C22⋊D6111yescharacteristic
544C2×C8C2×C22⋊D6111yescharacteristic
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—41no—
548C4⋊C4—41no—
549C4⋊C4—41no—
550C4⋊C4—1221no—
551C4⋊C4—1221no—
552C4⋊C4—1221no—
553C4⋊C4—1221no—
554C4⋊C4—2441no—
555C4⋊C4—2441no—
556C4⋊C4C2×C22⋊D6111yescharacteristic
557C4⋊C4C2×C22⋊D6111yescharacteristic
558C4⋊C4C2×C22⋊D6111yescharacteristic
559C4⋊C4C2×C22⋊D6111yescharacteristic
560C22⋊C4—21no—
561C22⋊C4—21no—
562C22⋊C4—41no—
563C22⋊C4—41no—
564C22⋊C4—41no—
565C22⋊C4—2441no—
566C22⋊C4—2441no—
567C42—21no—
568C42—21no—
569C42—41no—
570C42—1221no—
571C42—1221no—
572C42—2441no—
573C42—2441no—
574C23—21no—
575C23—1221no—
576C23#1451982211yescharacteristic
577Q8—21no—
578Q8—21no—
579Q8—41no—
580Q8—41no—
581Q8—41no—
582Q8—41no—
583Q8—612no—
584Q8—1221no—
585D4—21no—
586D4—21no—
587D4—41no—
588D4—41no—
589D4—612no—
590D4—1222no—
591D4—1222no—
592D4—1221no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—81no—
605C2×C4—161no—
606C2×C4—1221no—
607C2×C4—1222no—
608C2×C4—1222no—
609C2×C4—9761no—
610C2×C4—9761no—
611C2×C4—4881no—
612C2×C4—4881no—
613C2×C4—2441no—
614C2×C4—2441no—
615C2×C4—2441no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4C2×D4×D6111yescharacteristic
619C2×C4C22×C22⋊D6111yescharacteristic
620C2×C4#41×D6111yescharacteristic
621C2×C4#41×D6111yescharacteristic
622C2×C4#41×D6111yescharacteristic
623C2×C4#1451982411yescharacteristic
624C8—21no—
625C8—21no—
626C8—41no—
627C8—1221no—
628C8—1221no—
629C8—1222no—
630C8—2441no—
631C8—2441no—
632C22—21no—
633C22—21no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—1222no—
638C22—2441no—
639C22—2441no—
640C22#1684035511yescharacteristic
641C22D4×C22⋊D6111yescharacteristic
642C22#1684045711yescharacteristic
643C4—41no—
644C4—41no—
645C4—41no—
646C4—41no—
647C4—41no—
648C4—81no—
649C4—81no—
650C4—1222no—
651C4—4881no—
652C4—4881no—
653C4—4881no—
654C4#123×D6111yescharacteristic
655C4#1684026911yescharacteristic
656C4#1684041011yescharacteristic
657C4#1684041911yescharacteristic
658C2—21no—
659C2—21no—
660C2—81no—
661C2—2442no—
662C2#2144955111yescharacteristic
663C2#2145759011yescharacteristic
664C2#2145759911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#3097C2
socleC22×C61D42
prime radicalC2×#14519797C22
hypercenter#3097D61
hypocenterC61#26192
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #3097

Complements

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

NH ≅ G/Ntype
3. #21454411C2semidirect
4. #21447369C2semidirect
5. #21447327C2semidirect
6. #21447264C2semidirect
7. #21447033C2semidirect
8. #21446477C2semidirect
9. #21446420C2semidirect
10. #21446337C2semidirect
11. #21446185C2semidirect
13. #21446052C2semidirect
14. #21446049C2semidirect
15. C61×#3097C2semidirect
326. #3097D61semidirect
399. C61#26192semidirect

Maximal subgroups

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

subgroupindex
#214553652
#214546922
#214544112
#214473692
#214473272
#214472642
#214470332
#214464772
#214464202
#214463372
#214461852
#214461492
#214460522
#214460492
C61×#30972
#2619261