Finite Group Databasebeta

← #30622495

Subgroups — #30622495

Order 15616.

762 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462564C211yesmaximal, characteristic, complemented
2#21462519C211yesmaximal, characteristic, complemented
3#21461973C211yesmaximal, characteristic, complemented
4#21461971C211yesmaximal, characteristic, complemented
5#21461956C211yesmaximal, characteristic, complemented
6#21461934C211yesmaximal, characteristic, complemented
7#21461902C211yesmaximal, characteristic, complemented
8#21461901C211yesmaximal, characteristic, complemented
9#21461809C211yesmaximal, characteristic, complemented
10#21461808C211yesmaximal, characteristic, complemented
11#21461608C211yesmaximal, characteristic, complemented
12#21461598C211yesmaximal, characteristic, complemented
13#21461596C211yesmaximal, characteristic, complemented
14#21461583C211yesmaximal, characteristic, complemented
15#21455273C211yesmaximal, characteristic
16C2×#14519865C2211yescharacteristic
17C2×#14519864C2211yescharacteristic
18#16840795—21no—
19#16840794—21no—
20#16840791—21no—
21#16840789—21no—
22#16840787—21no—
23#16840787—21no—
24#16840784—21no—
25#16840781—21no—
26C2×#14519847C2211yescharacteristic
27C2×#14519847C2211yescharacteristic
28#16840766C2211yescharacteristic
29D61⋊(C4⋊C8)C2211yescharacteristic
30C2×#14519842C2211yescharacteristic
31C2×#14519842C2211yescharacteristic
32C2×#14519842C2211yescharacteristic
33C2×#14519842C2211yescharacteristic
34C2×#14519841C2211yescharacteristic
35C2×#14519841C2211yescharacteristic
36#16840737C2211yescharacteristic
37#16840737C2211yescharacteristic
38#16840737C2211yescharacteristic
39#16840736C2211yescharacteristic
40#16840727C2211yescharacteristic
41#16840727C2211yescharacteristic
42C4×#11758213C2211yescharacteristic
43C2×#14519831C2211yescharacteristic
44C2×C8×#6923C2211yescharacteristic
45#16840698C2211yescharacteristic
46#16840638C2211yescharacteristic
47#16840638C2211yescharacteristic
48#16840632C2211yescharacteristic
49#16840632C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C2×#14519800C2211yescharacteristic
53C2×#14519798C2211yescharacteristic
54#16840311C2211yescharacteristic
55C4×#11758226C2211yescharacteristic
56#16839984C411yescharacteristic, complemented
57#16839978C411yescharacteristic, complemented
58#16839974C411yescharacteristic, complemented
59#16839970C411yescharacteristic, complemented
60#16839966C411yescharacteristic, complemented
61#16839960C411yescharacteristic, complemented
62#16839956C411yescharacteristic, complemented
63C4⋊C8×D61C2211yescharacteristic
64#16839757C2211yescharacteristic
65#16839755C2211yescharacteristic
66C61×#464C411yescharacteristic, complemented
67#14519865—22no—
68#14519865—41no—
69#14519864—22no—
70#14519864—41no—
71C2×#11758213—21no—
72C2×#11758213C2311yescharacteristic
73C2×#11758213C2311yescharacteristic
74C2×#11758213C2311yescharacteristic
75C2×#11758213C2311yescharacteristic
76C2×#11758217—21no—
77C2×D61⋊C8—21no—
78C2×D61⋊C8C2311yescharacteristic
79C2×D61⋊C8C2311yescharacteristic
80C22×#92420—21no—
81C2×C4×#6923C2311yescharacteristic
82C2×C4×#6923C2311yescharacteristic
83#14519847—41no—
84#14519847—41no—
85#14519844D411yescharacteristic
86#14519844D411yescharacteristic
87C4⋊#92420—21no—
88C4⋊#92420—21no—
89C4⋊#92420D411yescharacteristic
90C4⋊#92420D411yescharacteristic
91#14519842—22no—
92#14519842—22no—
93#14519842—22no—
94#14519842—41no—
95#14519841—22no—
96#14519841—41no—
97#14519834—21no—
98#14519834—21no—
99#14519834—21no—
100#14519834—21no—
101#14519834—21no—
102#14519834—21no—
103C22⋊#92420—21no—
104C22⋊#92420—21no—
105#14519832—21no—
106#14519832—21no—
107#14519832—21no—
108#14519831—41no—
109C4×#92420—21no—
110C4×#92420—21no—
111C4×#92420—21no—
112C8×#6923—41no—
113(C2×#6923)⋊C4—21no—
114(C2×#6923)⋊C4—21no—
115C2×#11758226C2311yescharacteristic
116C2×#11758226C2311yescharacteristic
117C2×#11758224C2311yescharacteristic
118#14519800—41no—
119#14519800—41no—
120#14519798—41no—
121#14519798—41no—
122C2×#11758202C2×C411yescharacteristic
123C2×#11758190C2×C411yescharacteristic
124C2×#11758201C2×C411yescharacteristic
125C2×#11758201C2×C411yescharacteristic
126C2×D488C2×C411yescharacteristic
127C2×#11758199C2×C411yescharacteristic
128C2×C8×D61C2311yescharacteristic
129C2×C8×D61C2311yescharacteristic
130#14519775C2×C411yescharacteristic
131#14519773C2×C411yescharacteristic
132#14519765C2×C411yescharacteristic
133#14519750—21no—
134#14519750—21no—
135Q8×Dic61C2×C411yescharacteristic
136C4×D244—21no—
137C4×D244C2×C411yescharacteristic
138#14519739—21no—
139#14519739C2×C411yescharacteristic
140#14519737—21no—
141#14519737—21no—
142#14519735—21no—
143#14519735C2311yescharacteristic
144C42×D61—21no—
145C42×D61C2311yescharacteristic
146C4⋊#92418C2×C411yescharacteristic
147#14519706C2×C411yescharacteristic
148#14519706C2×C411yescharacteristic
149#14519702C2×C411yescharacteristic
150#14519701C2×C411yescharacteristic
151#14519700C2×C411yescharacteristic
152#14519699C2×C411yescharacteristic
153#14519698C2×C411yescharacteristic
154#14519697C2×C411yescharacteristic
155C2×Q16×C61C2×C411yescharacteristic
156C2×SD16×C61C2×C411yescharacteristic
157#124×C61C2×C411yescharacteristic
158C4×Q8×C61C2×C411yescharacteristic
159C4⋊C8×C61C2×C411yescharacteristic
160#103×C61C2×C411yescharacteristic
161#102×C61C2×C411yescharacteristic
162C22×#6923—21no—
163C22×#6923—21no—
164C2×Q8×C61C22×C411yescharacteristic
165C2×Q8×C61C22×C411yescharacteristic
166C2×D4×C61C22×C411yescharacteristic
167C2×C22⋊D61—21no—
168C2×C22⋊D61—21no—
169C2×C22⋊D61—21no—
170C22×Dic61—21no—
171#11758226—21no—
172#11758226—21no—
173#11758226—21no—
174#11758226—21no—
175#11758226—21no—
176#11758226—21no—
177#11758226—21no—
178#11758226—21no—
179#11758224—21no—
180#11758224—21no—
181#11758224—21no—
182#11758224—21no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244C22×C411yescharacteristic
186C2×D244C22×C411yescharacteristic
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61#4111yescharacteristic
192C2×C4×D61#4111yescharacteristic
193C2×C4×D61C2411yescharacteristic
194C2×Dic122C22×C411yescharacteristic
195#11758217—42no—
196C2×#92420—21no—
197C2×#92420—21no—
198C2×#92420—21no—
199C2×#92420—21no—
200C2×#92420—42no—
201C2×#92420C2×D411yescharacteristic
202C2×#92420C2×D411yescharacteristic
203C2×#92420C2×D411yescharacteristic
204C2×#92420C2×D411yescharacteristic
205C4×#6923—21no—
206C4×#6923—21no—
207C4×#6923—21no—
208C4×#6923#4112yes—
209#11758213—21no—
210#11758213—21no—
211#11758213—21no—
212#11758213—21no—
213#11758213—21no—
214#11758213—21no—
215#11758213—21no—
216#11758213—42no—
217#11758213#4112yes—
218D61⋊C8—21no—
219D61⋊C8—21no—
220D61⋊C8—21no—
221D61⋊C8—21no—
222D61⋊C8—42no—
223Q16×C61—41no—
224SD16×C61—41no—
225C2×C8×C61C22×C411yescharacteristic
226C2×C8×C61C22×C411yescharacteristic
227C4⋊C4×C61—21no—
228C4⋊C4×C61C22×C411yescharacteristic
229C22⋊C4×C61—21no—
230C22⋊C4×C61—21no—
231C42×C61—21no—
232C42×C61C22×C411yescharacteristic
233#11758202—41no—
234#11758201—41no—
235#11758201—41no—
236#11758199—41no—
237#11758198—21no—
238#11758198—21no—
239#11758198—21no—
240#11758198—21no—
241#11758198—21no—
242C4⋊Dic61—21no—
243C4⋊Dic61C22×C411yescharacteristic
244#11758196—21no—
245#11758196—21no—
246C4×Dic61—21no—
247C4×Dic61—21no—
248C4×Dic61C22×C411yescharacteristic
249C4×Dic61C2×D411yescharacteristic
250C4×Dic61C2×D411yescharacteristic
251C2×#92418C22×C411yescharacteristic
252C2×#92418C22×C411yescharacteristic
253D488—41no—
254#11758190—41no—
255C8×D61—21no—
256C8×D61—21no—
257C8×D61—21no—
258C8×D61—21no—
259C23×C61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61C2×#4111yescharacteristic
263C2×#6923—22no—
264C2×#6923—41no—
265C2×#6923—41no—
266C2×#6923—41no—
267C2×#6923—41no—
268C2×#6923—41no—
269Q8×C61—21no—
270Q8×C61—21no—
271Q8×C61—21no—
272Q8×C61—21no—
273D4×C61—21no—
274D4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61C4×D411yescharacteristic
279C2×C4×C61C4×D411yescharacteristic
280C2×C4×C61C23×C411yescharacteristic
281C22⋊D61—42no—
282C22⋊D61—41no—
283C22⋊D61—41no—
284C22⋊D61—81no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61C4×D411yescharacteristic
290C2×Dic61C4×D411yescharacteristic
291C2×Dic61C22×D411yescharacteristic
292D244—21no—
293D244—21no—
294D244—21no—
295D244—21no—
296D244—41no—
297D244—41no—
298D244—41no—
299D244—41no—
300C4×D61—41no—
301C4×D61—41no—
302C4×D61—42no—
303C4×D61—41no—
304C4×D61—41no—
305C4×D61—41no—
306C4×D61—41no—
307C4×D61—81no—
308C4×D61C2×#4111yescharacteristic
309C4×D61C2×#4111yescharacteristic
310C4×D61H(5,𝔽2)11yescharacteristic
311C4×D61H(5,𝔽2)11yescharacteristic
312Dic122—21no—
313Dic122—21no—
314#92420—21no—
315#92420—21no—
316#92420—21no—
317#92420—21no—
318#92420—22no—
319#92420—41no—
320#92420—41no—
321#92420—41no—
322C8×C61—21no—
323C8×C61—21no—
324#92418—21no—
325#92418—21no—
326#23115—611nomaximal, Sylow
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61C2×C4×D411yescharacteristic
331C2×D61—21no—
332C2×D61—21no—
333C2×D61—41no—
334C2×D61—41no—
335C2×D61—41no—
336C2×D61—41no—
337C2×D61—41no—
338C2×D61—41no—
339C2×D61#55311yescharacteristic
340C2×D61#55511yescharacteristic
341#6923—42no—
342#6923—81no—
343C4×C61—21no—
344C4×C61—21no—
345C4×C61—41no—
346C4×C61—41no—
347C4×C61—41no—
348C4×C61C4×#4111yescharacteristic
349C4×C61#51811yescharacteristic
350Dic61—21no—
351Dic61—21no—
352Dic61—41no—
353Dic61—41no—
354Dic61#54611yescharacteristic
355Dic61#55011yescharacteristic
356#3035—611no—
357#2935—611no—
358#2925—611no—
359#1975—611no—
360#1974—611no—
361#1963—611no—
362#1950—611no—
363#1929—611no—
364#1929—611no—
365#1876—611no—
366#1876—611no—
367#1768—611no—
368#1765—611no—
369#1764—611no—
370#1759—611no—
371C2×C61—81no—
372C2×C61#236311yescharacteristic
373C2×C61#295511yescharacteristic
374C2×C61#295711yescharacteristic
375D61—21no—
376D61—21no—
377D61—81no—
378D61—81no—
379C2×#135—611no—
380C2×#135—611no—
381C2×#131—611no—
382C2×#131—611no—
383#532—611no—
384C4×#41—611no—
385#464—611no—
386#464#692311yescharacteristic, complemented
387#463—611no—
388#463—611no—
389#462—611no—
390#461—611no—
391#460—611no—
392#459—611no—
393#436—1221no—
394#435—1221no—
395#435—1221no—
396C8×D4—1221no—
397#433—1221no—
398#433—1221no—
399#432—1221no—
400#431—1221no—
401C2×#108—611no—
402C2×#108—611no—
403#423—611no—
404C2×C4⋊C8—611no—
405C2×C4⋊C8—611no—
406C2×#104—611no—
407C2×#104—611no—
408C2×#104—611no—
409C2×#104—611no—
410C2×#104—611no—
411C2×#104—611no—
412#416—611no—
413#416—611no—
414#408—611no—
415#408—611no—
416#408—611no—
417#408—611no—
418#405—611no—
419#405—611no—
420C4×M16—611no—
421C2×#97—611no—
422C2×C4×C8—611no—
423#376—611no—
424#341—611no—
425#341—611no—
426#339—611no—
427#339—611no—
428#336—611no—
429#336—611no—
430C61#2311511yescharacteristic, complemented, Sylow
431C2×#41—611no—
432C2×#41—611no—
433C2×#41—611no—
434#135—2441no—
435#135—2441no—
436#135—2441no—
437#135—2441no—
438C2×Q16—611no—
439C2×Q16C2×#692311yescharacteristic
440C2×SD16—611no—
441C2×SD16—611no—
442C2×SD16—611no—
443C2×SD16C2×#692311yescharacteristic
444C2×D8—611no—
445C2×D8—611no—
446#131—1222no—
447#131—1222no—
448#131—2441no—
449#131—2441no—
450C2×M16—611no—
451C2×M16—611no—
452C2×M16—611no—
453C2×M16—611no—
454C2×M16—1221no—
455C2×M16—1221no—
456C22×C8—611no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8—1221no—
461C22×C8—1221no—
462C4⋊Q8—611no—
463#127—611no—
464#124—611no—
465#124C2×#692311yescharacteristic
466#121—1221no—
467#121—1221no—
468C4×Q8—611no—
469C4×Q8C2×#692311yescharacteristic
470C4×D4—611no—
471C4×D4—611no—
472C4×D4—1221no—
473C4×D4—1221no—
474C4×D4—1221no—
475C4×D4—1221no—
476#117—611no—
477#117—1221no—
478C2×C42—611no—
479C2×C42—611no—
480C2×C42—611no—
481C2×C42—1221no—
482#108—2441no—
483#108—2441no—
484C4⋊C8—611no—
485C4⋊C8—611no—
486C4⋊C8—611no—
487C4⋊C8—611no—
488C4⋊C8—611no—
489C4⋊C8—611no—
490C4⋊C8—611no—
491C4⋊C8—1221no—
492C4⋊C8—1221no—
493C4⋊C8C2×#692311yescharacteristic
494#104—1222no—
495#104—1222no—
496#104—1222no—
497#104—1222no—
498#104—2441no—
499#104—2441no—
500#103—611no—
501#103—611no—
502#103—611no—
503#103C2×#692311yescharacteristic
504#102—611no—
505#102—611no—
506#102—611no—
507#102C2×#692311yescharacteristic
508C22⋊C8—1221no—
509C22⋊C8—1221no—
510C22⋊C8—1221no—
511C22⋊C8—1221no—
512C22⋊C8—1221no—
513C22⋊C8—1221no—
514C22⋊C8—1221no—
515C22⋊C8—1221no—
516#97—1221no—
517#97—1221no—
518#97—1221no—
519#97—2441no—
520C4×C8—1221no—
521C4×C8—1221no—
522C4×C8—1221no—
523C4×C8—2441no—
524#95—1221no—
525#95—1221no—
526#41—1221no—
527#41—1221no—
528#41—1221no—
529#41—1221no—
530#41—1221no—
531#41—1221no—
532#41—1221no—
533#41—1221no—
534#41—1221no—
535#41—1221no—
536#41—1221no—
537#41—1221no—
538C2×Q8—611no—
539C2×Q8C22×#692311yescharacteristic
540C2×Q8C22×#692311yescharacteristic
541C2×D4—611no—
542C2×D4—611no—
543C2×D4—1221no—
544C2×D4—1221no—
545C2×D4—1221no—
546C2×D4—1221no—
547C2×D4—1221no—
548C2×D4C22×#692311yescharacteristic
549C22×C4—611no—
550C22×C4—611no—
551C22×C4—611no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559Q16—41no—
560Q16—2441no—
561SD16—41no—
562SD16—2441no—
563SD16—2441no—
564SD16—2441no—
565D8—2441no—
566D8—2441no—
567M16—612no—
568M16—1221no—
569M16—1221no—
570M16—1221no—
571M16—1221no—
572M16—1221no—
573M16—1221no—
574M16—1221no—
575M16—2442no—
576M16—2442no—
577C2×C8—611no—
578C2×C8—611no—
579C2×C8—611no—
580C2×C8—611no—
581C2×C8—611no—
582C2×C8—611no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—2442no—
596C2×C8—2442no—
597C2×C8C22×#692311yescharacteristic
598C2×C8C22×#692311yescharacteristic
599C4⋊C4—21no—
600C4⋊C4—611no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4C22×#692311yescharacteristic
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—1221no—
608C22⋊C4—1221no—
609C22⋊C4—1221no—
610C22⋊C4—1221no—
611C22⋊C4—1221no—
612C42—21no—
613C42—611no—
614C42—611no—
615C42—611no—
616C42—612no—
617C42—1221no—
618C42—1221no—
619C42—1221no—
620C42—1221no—
621C42—1221no—
622C42C22×#692311yescharacteristic
623C23—21no—
624C23—611no—
625C23—1221no—
626C23—1221no—
627Q8—21no—
628Q8—21no—
629Q8—21no—
630Q8—21no—
631Q8—1221no—
632Q8—1221no—
633D4—21no—
634D4—21no—
635D4—1221no—
636D4—1221no—
637D4—1221no—
638D4—1221no—
639D4—4881no—
640D4—2441no—
641D4—2441no—
642D4—2441no—
643D4—2441no—
644D4—2442no—
645D4—2441no—
646D4—2441no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—611no—
651C2×C4—611no—
652C2×C4—611no—
653C2×C4—611no—
654C2×C4—611no—
655C2×C4—611no—
656C2×C4—611no—
657C2×C4—1222no—
658C2×C4—1221no—
659C2×C4—1221no—
660C2×C4—4881no—
661C2×C4—2441no—
662C2×C4—2441no—
663C2×C4—2442no—
664C2×C4—2441no—
665C2×C4—2441no—
666C2×C4—2441no—
667C2×C4—2441no—
668C2×C4—2441no—
669C2×C4—2441no—
670C2×C4—2441no—
671C2×C4—2441no—
672C2×C4—2441no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4D4×#692311yescharacteristic
676C2×C4D4×#692311yescharacteristic
677C2×C4C23×#692311yescharacteristic
678C8—21no—
679C8—21no—
680C8—1221no—
681C8—1221no—
682C8—1221no—
683C8—1221no—
684C8—1222no—
685C8—1221no—
686C8—1221no—
687C8—2441no—
688C8—2441no—
689C8—2441no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—611no—
694C22—611no—
695C22—1221no—
696C22—1221no—
697C22—2441no—
698C22—2441no—
699C22—2441no—
700C22—2441no—
701C22—2441no—
702C22—2441no—
703C22C2×D4×#692311yescharacteristic
704C4—21no—
705C4—21no—
706C4—41no—
707C4—41no—
708C4—41no—
709C4—611no—
710C4—611no—
711C4—1221no—
712C4—1221no—
713C4—4881no—
714C4—2442no—
715C4—2441no—
716C4—2441no—
717C4#41×#692311yescharacteristic
718C4#1684082911yescharacteristic
719C2—81no—
720C2—1221no—
721C2—1221no—
722C2—4881no—
723C2—4881no—
724C2#2146234611yescharacteristic
725C2#2146259211yescharacteristic
726C2#2146259811yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#464C4
socleC22×C61C2×C4×D4
prime radical#21455273C2
cosocleC2×C4×D61C24
hypercenter#464#6923
hypocenterC61#23115
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #21462564C2semidirect
2. #21462519C2semidirect
3. #21461973C2semidirect
4. #21461971C2semidirect
5. #21461956C2semidirect
6. #21461934C2semidirect
7. #21461902C2semidirect
8. #21461901C2semidirect
9. #21461809C2semidirect
10. #21461808C2semidirect
11. #21461608C2semidirect
12. #21461598C2semidirect
13. #21461596C2semidirect
14. #21461583C2semidirect
56. #16839984C4semidirect
57. #16839978C4semidirect
58. #16839974C4semidirect
59. #16839970C4semidirect
60. #16839966C4semidirect
61. #16839960C4semidirect
62. #16839956C4semidirect
66. C61×#464C4semidirect
386. #464#6923semidirect
430. C61#23115semidirect

Maximal subgroups

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

subgroupindex
#214625642
#214625192
#214619732
#214619712
#214619562
#214619342
#214619022
#214619012
#214618092
#214618082
#214616082
#214615982
#214615962
#214615832
#214552732
#2311561