Finite Group Databasebeta

← #30610298

Subgroups — #30610298

Order 15616.

1002 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462508C212yesmaximal, complemented
2#21461095C212yesmaximal, complemented
3#21461089C212yesmaximal, complemented
4#21461088C212yesmaximal, complemented
5#21461075C211yesmaximal, characteristic, complemented
6#21461073C211yesmaximal, characteristic, complemented
7#21461070C211yesmaximal, characteristic, complemented
8#21461055C211yesmaximal, characteristic, complemented
9#21461053C211yesmaximal, characteristic, complemented
10#21461050C211yesmaximal, characteristic, complemented
11C2×#16840476C211yesmaximal, characteristic
12#16840786—22no—
13#16840786—22no—
14#16840783C2212yes—
15#16840782C2212yes—
16#16840779C2212yes—
17#16840778C2212yes—
18#16840768—22no—
19#16840732C2212yes—
20C2×C22⋊#92420C2212yes—
21#16840726—22no—
22#16840607C2211yescharacteristic
23#16840607C2211yescharacteristic
24#16840607C2211yescharacteristic
25#16840607C2211yescharacteristic
26#16840606C2212yes—
27#16840606C2212yes—
28#16840605C2212yes—
29#16840605C2212yes—
30#16840605C2212yes—
31#16840605C2212yes—
32#16840476—22no—
33#16840476—22no—
34#16840476—22no—
35#16840476—22no—
36C2×#14519776C411yescharacteristic
37C2×#14519764C411yescharacteristic
38C2×#14519764C2211yescharacteristic
39C2×#14519763C411yescharacteristic
40C2×#14519763C2211yescharacteristic
41C2×#14519749C411yescharacteristic
42C2×#14519749C2211yescharacteristic
43C2×#14519748C411yescharacteristic
44C2×D4×Dic61C2211yescharacteristic
45C2×C4×C22⋊D61C411yescharacteristic
46C2×#14519736C2211yescharacteristic
47C2×#14519735C2211yescharacteristic
48C2×#14519733C411yescharacteristic
49C2×#14519733C2211yescharacteristic
50C2×#121×C61C411yescharacteristic
51C2×#11758217—22no—
52C22×#92420—22no—
53#14519844—22no—
54#14519844—22no—
55C4⋊#92420—22no—
56C4⋊#92420—22no—
57C22⋊#92420—22no—
58C22⋊#92420—22no—
59C22⋊#92420C2312yes—
60C22⋊#92420C2312yes—
61C22⋊#92420C2312yes—
62C22⋊#92420C2312yes—
63#14519832—22no—
64#14519832—22no—
65C4×#92420—22no—
66C4×#92420—22no—
67C22×Dic122C2×C411yescharacteristic
68C22×Dic122C2×C411yescharacteristic
69C22×C22⋊D61C2×C411yescharacteristic
70C22×C22⋊D61C2×C411yescharacteristic
71C22×C22⋊D61C2×C411yescharacteristic
72C23×Dic61C2×C411yescharacteristic
73C23×Dic61C2311yescharacteristic
74C22×C4×D61C2×C411yescharacteristic
75#14519776—22no—
76#14519776—22no—
77#14519764—22no—
78#14519764—22no—
79#14519764—22no—
80#14519764—22no—
81#14519763—22no—
82#14519763—22no—
83#14519763—22no—
84#14519763—22no—
85#14519749—22no—
86#14519749—22no—
87#14519749—22no—
88#14519749—22no—
89#14519748—22no—
90#14519748—22no—
91D4×Dic61—22no—
92D4×Dic61—22no—
93C4×C22⋊D61—21no—
94C4×C22⋊D61—21no—
95C4×C22⋊D61—21no—
96C4×C22⋊D61—21no—
97#14519736—22no—
98#14519736—22no—
99#14519735—22no—
100#14519735—22no—
101#14519733—21no—
102#14519733—21no—
103#14519733—21no—
104#14519733—21no—
105#14519733D412yes—
106#14519733D412yes—
107#14519733D412yes—
108#14519733D412yes—
109C2×C4⋊Dic61C2×C411yescharacteristic
110C2×C4⋊Dic61C2311yescharacteristic
111C2×#11758196C2×C411yescharacteristic
112C2×#11758196C2×C411yescharacteristic
113C2×#11758196C2×C411yescharacteristic
114C2×C22⋊Dic61C2×C411yescharacteristic
115C2×C22⋊Dic61C2×C411yescharacteristic
116C2×C22⋊Dic61C2×C411yescharacteristic
117C2×C22⋊Dic61C2×C411yescharacteristic
118C2×C22⋊Dic61C2×C411yescharacteristic
119C2×C22⋊Dic61C2311yescharacteristic
120C2×C22⋊Dic61C2311yescharacteristic
121C2×#11758198C2×C411yescharacteristic
122C2×#11758198C2×C411yescharacteristic
123C2×#11758198C2311yescharacteristic
124C2×C4×Dic61C2×C411yescharacteristic
125C2×C4×Dic61C2×C411yescharacteristic
126C2×C4×Dic61C2×C411yescharacteristic
127C2×C4×Dic61C2311yescharacteristic
128C2×C4×Dic61C2311yescharacteristic
129C22×D4×C61C2×C411yescharacteristic
130C22×D4×C61C2×C411yescharacteristic
131C22×D4×C61C2×C411yescharacteristic
132C23×C4×C61C2×C411yescharacteristic
133#121×C61—22no—
134#121×C61—22no—
135C2×C4⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2×C411yescharacteristic
137C2×C22⋊C4×C61C2×C411yescharacteristic
138C24×C61C22×C411yescharacteristic
139C24×C61C22×C411yescharacteristic
140C24×C61C22×C411yescharacteristic
141C23×D61C22×C411yescharacteristic
142C2×D4×C61—22no—
143C2×D4×C61—22no—
144C2×D4×C61—22no—
145C2×D4×C61—22no—
146C2×D4×C61—41no—
147C2×D4×C61—81no—
148C2×D4×C61—81no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—22no—
152C22×C4×C61—41no—
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C2×C22⋊D61—22no—
158C2×C22⋊D61—21no—
159C2×C22⋊D61—21no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—42no—
162C2×C22⋊D61—81no—
163C2×C22⋊D61—81no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—42no—
167C22×Dic61—42no—
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61C22×C411yescharacteristic
172C22×Dic61C22×C411yescharacteristic
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C2×D412yes—
175C22×Dic61C2×D412yes—
176C22×Dic61C2411yescharacteristic
177C2×C4×D61—22no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—41no—
181C2×Dic122—22no—
182C2×Dic122—22no—
183C2×Dic122—81no—
184C2×Dic122—81no—
185#11758217—44no—
186C2×#92420—22no—
187C2×#92420—22no—
188C2×#92420—22no—
189C2×#92420—22no—
190C2×#92420—44no—
191C4⋊C4×C61—22no—
192C22⋊C4×C61—21no—
193C22⋊C4×C61—21no—
194C22⋊C4×C61C22⋊C412yes—
195C22⋊C4×C61C22⋊C412yes—
196C22⋊Dic61—22no—
197C22⋊Dic61—21no—
198C22⋊Dic61—21no—
199C22⋊Dic61—22no—
200C22⋊Dic61—21no—
201C22⋊Dic61—21no—
202C22⋊Dic61—22no—
203C22⋊Dic61—22no—
204C22⋊Dic61C22⋊C412yes—
205C22⋊Dic61C22⋊C412yes—
206#11758198—22no—
207#11758198—21no—
208#11758198—21no—
209#11758198—22no—
210C4⋊Dic61—22no—
211C4⋊Dic61—22no—
212#11758196—21no—
213#11758196—21no—
214#11758196C22⋊C411yescharacteristic
215#11758196C22⋊C411yescharacteristic
216#11758196C22⋊C411yescharacteristic
217#11758196C22⋊C411yescharacteristic
218#11758196C22⋊C412yes—
219#11758196C22⋊C412yes—
220C4×Dic61—21no—
221C4×Dic61—21no—
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61—21no—
226C4×Dic61C2×D412yes—
227C4×Dic61C2×D412yes—
228C4×Dic61C2×D412yes—
229C4×Dic61C2×D412yes—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61C2×C22⋊C412yes—
245C23×C61C23×C411yescharacteristic
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—41no—
250C22×D61—41no—
251D4×C61—44no—
252D4×C61—82no—
253D4×C61—82no—
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—42no—
261C2×C4×C61—42no—
262C2×C4×C61—41no—
263C2×C4×C61C2×C22⋊C411yescharacteristic
264C2×C4×C61C2×C22⋊C411yescharacteristic
265C2×C4×C61C2×C22⋊C412yes—
266C2×C4×C61#13112yes—
267C22⋊D61—42no—
268C22⋊D61—42no—
269C22⋊D61—82no—
270C22⋊D61—82no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—24no—
274C2×Dic61—22no—
275C2×Dic61—21no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—41no—
279C2×Dic61—42no—
280C2×Dic61—41no—
281C2×Dic61—42no—
282C2×Dic61—42no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61C2×C22⋊C411yescharacteristic
287C2×Dic61C2×C22⋊C411yescharacteristic
288C2×Dic61C2×C22⋊C411yescharacteristic
289C2×Dic61C2×C22⋊C412yes—
290C2×Dic61C2×C22⋊C411yescharacteristic
291C2×Dic61C22×D412yes—
292C4×D61—42no—
293C4×D61—42no—
294Dic122—82no—
295Dic122—82no—
296#92420—42no—
297#92420—42no—
298#92420—42no—
299#92420—42no—
300#17418—611nomaximal, Sylow
301C22×C61—21no—
302C22×C61—21no—
303C22×C61—22no—
304C22×C61—22no—
305C22×C61—22no—
306C22×C61—41no—
307C22×C61—41no—
308C22×C61—41no—
309C22×C61—41no—
310C22×C61—41no—
311C22×C61—41no—
312C22×C61—81no—
313C22×C61—81no—
314C22×C61—81no—
315C22×C61—81no—
316C22×C61—81no—
317C22×C61—81no—
318C22×C61C22×C22⋊C411yescharacteristic
319C22×C61C2×#13111yescharacteristic
320C22×C61#56811yescharacteristic
321C2×D61—41no—
322C2×D61—41no—
323C2×D61—41no—
324C2×D61—81no—
325C2×D61—81no—
326C4×C61—22no—
327C4×C61—21no—
328C4×C61—21no—
329C4×C61—22no—
330C4×C61—41no—
331Dic61—21no—
332Dic61—21no—
333Dic61—22no—
334Dic61—21no—
335Dic61—22no—
336Dic61—41no—
337Dic61—41no—
338Dic61—41no—
339Dic61#41012yes—
340C2×#555—611no—
341#2924—612no—
342#1471—612no—
343#1469—612no—
344#1469—612no—
345#1465—611no—
346#1464—611no—
347#1464—611no—
348#1459—611no—
349#1458—611no—
350#1458—611no—
351C2×C61—21no—
352C2×C61—21no—
353C2×C61—42no—
354C2×C61—81no—
355C2×C61—81no—
356C2×C61#288011yescharacteristic
357C2×C61C2×#41011yescharacteristic
358C2×C61#288811yescharacteristic
359D61—81no—
360#555—1222no—
361#555—1222no—
362#555—1222no—
363#555—1222no—
364C2×C4⋊Q8—611no—
365C2×#124—611no—
366C2×#124—611no—
367C2×#124—611no—
368C2×#124—611no—
369C2×#121—611no—
370C2×#121—611no—
371C2×#121—611no—
372C2×#121#692311yescharacteristic
373C2×C4×D4—611no—
374C2×C4×D4—611no—
375C2×#117—611no—
376C2×#117—611no—
377C2×#117—611no—
378C2×#117—611no—
379#433—1222no—
380#433—1222no—
381#432—612no—
382#432—612no—
383#431—612no—
384#431—612no—
385#424—1222no—
386#407—612no—
387C2×C22⋊C8—612no—
388#405—1222no—
389#324—611no—
390#324—611no—
391#324—611no—
392#324—611no—
393#323—612no—
394#323—612no—
395#323—612no—
396#323—612no—
397#323—612no—
398#323—612no—
399C61#1741811yescharacteristic, complemented, Sylow
400C22×Q8—611no—
401C22×Q8—611no—
402C22×D4—611no—
403C22×D4—611no—
404C22×D4—611no—
405C22×D4C2×#692311yescharacteristic
406C22×D4C2×#692311yescharacteristic
407C22×D4C2×#692311yescharacteristic
408C23×C4—611no—
409C23×C4—611no—
410C23×C4—611no—
411C23×C4C2×#692311yescharacteristic
412C2×M16—1222no—
413C22×C8—1222no—
414C4⋊Q8—1222no—
415C4⋊Q8—1222no—
416#124—1222no—
417#124—1222no—
418#124—1222no—
419#124—1222no—
420#124—1222no—
421#124—1222no—
422#124—1222no—
423#124—1222no—
424#121—22no—
425#121—22no—
426#121—1222no—
427#121—1222no—
428#121—1222no—
429#121—1222no—
430#121—1222no—
431#121—1222no—
432C4×D4—1221no—
433C4×D4—1221no—
434C4×D4—1221no—
435C4×D4—1221no—
436C4×D4—1222no—
437C4×D4—1222no—
438#117—612no—
439#117—612no—
440#117—612no—
441#117—612no—
442#117—1222no—
443#117—1222no—
444#117—1222no—
445#117—1222no—
446#117—1221no—
447#117—1221no—
448#117—1221no—
449#117—1221no—
450C2×C4⋊C4—611no—
451C2×C4⋊C4—611no—
452C2×C4⋊C4—611no—
453C2×C4⋊C4—611no—
454C2×C4⋊C4—611no—
455C2×C4⋊C4C2×#692311yescharacteristic
456C2×C22⋊C4—611no—
457C2×C22⋊C4—611no—
458C2×C22⋊C4—611no—
459C2×C22⋊C4—611no—
460C2×C22⋊C4—611no—
461C2×C22⋊C4—611no—
462C2×C22⋊C4—611no—
463C2×C22⋊C4—611no—
464C2×C22⋊C4—611no—
465C2×C22⋊C4—611no—
466C2×C22⋊C4C2×#692311yescharacteristic
467C2×C22⋊C4C2×#692311yescharacteristic
468C2×C42—611no—
469C2×C42—611no—
470C2×C42—611no—
471C2×C42—611no—
472C2×C42—611no—
473C4⋊C8—1222no—
474C4⋊C8—1222no—
475C4⋊C8—1222no—
476C4⋊C8—1222no—
477C22⋊C8—612no—
478C22⋊C8—612no—
479C22⋊C8—612no—
480C22⋊C8—612no—
481C22⋊C8—1222no—
482C22⋊C8—1222no—
483#97—1222no—
484#97—1222no—
485C4×C8—1222no—
486C4×C8—1222no—
487C24—611no—
488C24C22×#692311yescharacteristic
489C24C22×#692311yescharacteristic
490C24C22×#692311yescharacteristic
491C2×Q8—1222no—
492C2×Q8—1222no—
493C2×Q8—4881no—
494C2×Q8—4881no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—41no—
500C2×D4—81no—
501C2×D4—81no—
502C2×D4—1222no—
503C2×D4—1221no—
504C2×D4—1221no—
505C2×D4—1222no—
506C2×D4—4881no—
507C2×D4—4881no—
508C2×D4—2442no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—41no—
513C22×C4—612no—
514C22×C4—611no—
515C22×C4—611no—
516C22×C4—612no—
517C22×C4—611no—
518C22×C4—611no—
519C22×C4—611no—
520C22×C4—611no—
521C22×C4—611no—
522C22×C4—1221no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4—1221no—
526C22×C4—1222no—
527C22×C4—2441no—
528C22×C4—2442no—
529C22×C4—2442no—
530C22×C4C22×#692311yescharacteristic
531C22×C4C22×#692311yescharacteristic
532C22×C4C22×#692311yescharacteristic
533C22×C4C22×#692311yescharacteristic
534M16—2444no—
535C2×C8—1222no—
536C2×C8—1222no—
537C2×C8—1222no—
538C2×C8—1222no—
539C2×C8—2444no—
540C4⋊C4—22no—
541C4⋊C4—611no—
542C4⋊C4—611no—
543C4⋊C4—611no—
544C4⋊C4—611no—
545C4⋊C4—612no—
546C4⋊C4—612no—
547C4⋊C4—1221no—
548C4⋊C4—1221no—
549C4⋊C4—1222no—
550C4⋊C4—1222no—
551C22⋊C4—21no—
552C22⋊C4—21no—
553C22⋊C4—612no—
554C22⋊C4—612no—
555C22⋊C4—1222no—
556C22⋊C4—1221no—
557C22⋊C4—1221no—
558C22⋊C4—1222no—
559C22⋊C4—1222no—
560C22⋊C4—1221no—
561C22⋊C4—1221no—
562C22⋊C4—1222no—
563C22⋊C4—1222no—
564C22⋊C4—1222no—
565C22⋊C4—1221no—
566C22⋊C4—1221no—
567C22⋊C4C22⋊#692312yes—
568C22⋊C4C22⋊#692312yes—
569C42—612no—
570C42—612no—
571C42—612no—
572C42—612no—
573C42—1221no—
574C42—1221no—
575C42—1221no—
576C42—1221no—
577C42—1221no—
578C42—1221no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—1221no—
594C23—1221no—
595C23—1221no—
596C23—2441no—
597C23—2441no—
598C23C2×C22⋊#692312yes—
599C23C23×#692311yescharacteristic
600Q8—4882no—
601Q8—4882no—
602D4—44no—
603D4—82no—
604D4—82no—
605D4—4882no—
606D4—4882no—
607D4—2442no—
608D4—2442no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—41no—
618C2×C4—611no—
619C2×C4—611no—
620C2×C4—611no—
621C2×C4—612no—
622C2×C4—611no—
623C2×C4—612no—
624C2×C4—1224no—
625C2×C4—1222no—
626C2×C4—1221no—
627C2×C4—1221no—
628C2×C4—1221no—
629C2×C4—1221no—
630C2×C4—1221no—
631C2×C4—2442no—
632C2×C4—2442no—
633C2×C4—2442no—
634C2×C4—2441no—
635C2×C4—2442no—
636C2×C4—2441no—
637C2×C4—2442no—
638C2×C4—2441no—
639C2×C4—2441no—
640C2×C4—2441no—
641C2×C4C2×C22⋊#692311yescharacteristic
642C2×C4C2×C22⋊#692311yescharacteristic
643C2×C4C2×C22⋊#692312yes—
644C2×C4#1451986412yes—
645C8—2442no—
646C8—2442no—
647C8—2442no—
648C8—2442no—
649C22—21no—
650C22—21no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22—4881no—
667C22—4881no—
668C22—2441no—
669C22—2441no—
670C22—2441no—
671C22C22×C22⋊#692311yescharacteristic
672C22C2×#1451986411yescharacteristic
673C22#1684084011yescharacteristic
674C4—22no—
675C4—21no—
676C4—21no—
677C4—22no—
678C4—41no—
679C4—612no—
680C4—1221no—
681C4—1221no—
682C4—1222no—
683C4—1221no—
684C4—1222no—
685C4—2441no—
686C4—2441no—
687C4—2441no—
688C2—21no—
689C2—21no—
690C2—42no—
691C2—81no—
692C2—81no—
693C2—4881no—
694C2#2146240711yescharacteristic
695C2D61⋊#41011yescharacteristic
696C2#2146242911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#121×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840476C2
cosocleC22×Dic61C24
hypercenterC2×#121#6923
hypocenterC61#17418
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #21462508C2semidirect
2. #21461095C2semidirect
3. #21461089C2semidirect
4. #21461088C2semidirect
5. #21461075C2semidirect
6. #21461073C2semidirect
7. #21461070C2semidirect
8. #21461055C2semidirect
9. #21461053C2semidirect
10. #21461050C2semidirect
399. C61#17418semidirect

Maximal subgroups

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

subgroupindex
#214625082
#214610952
#214610892
#214610882
#214610752
#214610732
#214610702
#214610552
#214610532
#214610502
C2×#168404762
#1741861