Finite Group Databasebeta

← #30617841

Subgroups — #30617841

Order 15616.

1444 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462498C211yesmaximal, characteristic, complemented
2C4×#14519856C211yesmaximal, characteristic, complemented
3#21461984C214yesmaximal, complemented
4#21461954C214yesmaximal, complemented
5#21461662C212yesmaximal, complemented
6#21461660C212yesmaximal, complemented
7C2×#16840311C211yesmaximal, characteristic
8C2×#14519856—21no—
9#16840785—21no—
10#16840782—21no—
11#16840780—21no—
12#16840779—21no—
13#16840767C2212yescomplemented
14C2×#14519842C2218yescomplemented
15C2×#14519841C2218yescomplemented
16#16840733C2212yes—
17C4×#11758213C2212yescomplemented
18C4×C4⋊#6923—21no—
19C4×C4⋊#6923C2212yescomplemented
20C4×C22⋊#6923—21no—
21C4×C22⋊#6923C2212yes—
22#16840698—21no—
23C42×#6923C2212yescomplemented
24C22×#11758226C2211yescharacteristic
25C22×#11758224C2211yescharacteristic
26#16840311—21no—
27#16840311—21no—
28#16840311—21no—
29#16840311—21no—
30#16840311C412yescomplemented
31#16840311C412yescomplemented
32#16840311C2212yes—
33#16840311C2212yes—
34C2×#14519775C411yescharacteristic, complemented
35C2×#14519773C411yescharacteristic, complemented
36C2×#14519765C411yescharacteristic, complemented
37C2×#14519750—21no—
38C2×#14519750—21no—
39C2×#14519737—21no—
40C2×#14519737—21no—
41C2×C42×D61C2211yescharacteristic
42C2×#124×C61C411yescharacteristic, complemented
43C2×#11758213C2314yes—
44#14519856—28no—
45C2×C4⋊#6923—22no—
46C2×C22⋊#6923—22no—
47C2×C4×#6923—22no—
48C2×C4×#6923—22no—
49C2×C4×#6923C2314yes—
50#14519844—22no—
51#14519844—22no—
52#14519842—48no—
53#14519841—48no—
54#14519834—22no—
55C22⋊#92420—22no—
56#14519832—22no—
57C4×#92420—22no—
58(C2×#6923)⋊C4—22no—
59(C2×#6923)⋊C4—22no—
60C2×#11758226—21no—
61C2×#11758226—21no—
62C2×#11758226—44no—
63C2×#11758226C2×C412yes—
64C2×#11758226C2312yes—
65C2×#11758224—21no—
66C2×#11758224—21no—
67C2×#11758224—44no—
68C2×#11758224C2×C412yes—
69C2×#11758224C2312yes—
70C22×Dic122C2×C411yescharacteristic
71C22×D244—21no—
72C22×D244C2×C411yescharacteristic
73C22×C22⋊D61—21no—
74C22×C22⋊D61—21no—
75C22×C22⋊D61—21no—
76C23×Dic61—21no—
77C22×C4×D61—21no—
78C22×C4×D61D411yescharacteristic
79C22×C4×D61D411yescharacteristic
80C22×C4×D61C2311yescharacteristic
81#14519775—21no—
82#14519775—21no—
83#14519775C2×C412yes—
84#14519775C2×C412yes—
85#14519773—21no—
86#14519773—21no—
87#14519773C2×C412yes—
88#14519773C2×C412yes—
89#14519765—21no—
90#14519765—21no—
91#14519765C2×C412yes—
92#14519765C2×C412yes—
93#14519750—22no—
94#14519750—22no—
95#14519750—22no—
96#14519750—22no—
97#14519750—22no—
98#14519750—22no—
99#14519750—22no—
100#14519750—22no—
101#14519737—22no—
102#14519737—22no—
103#14519737—22no—
104#14519737—22no—
105#14519737—22no—
106#14519737—22no—
107#14519737—22no—
108#14519737—22no—
109C2×#11758196—21no—
110C2×#11758196—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×C4×Dic61C2×C411yescharacteristic
114C2×C4×Dic61D411yescharacteristic
115C2×C4×Dic61D411yescharacteristic
116C42×D61C2×C411yescharacteristic
117C42×D61C2×C411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61D411yescharacteristic
120C42×D61D411yescharacteristic
121C42×D61D411yescharacteristic
122C42×D61C2311yescharacteristic
123C42×D61C2311yescharacteristic
124C22×Q8×C61C2×C411yescharacteristic
125C22×D4×C61C2×C411yescharacteristic
126#124×C61—21no—
127#124×C61—21no—
128#124×C61C2×C412yes—
129#124×C61C2×C412yes—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C42×C61C2×C411yescharacteristic
133C24×C61—21no—
134C23×D61—21no—
135C23×D61C2×D411yescharacteristic
136C22×#6923—24no—
137C2×Q8×C61—21no—
138C2×Q8×C61—42no—
139C2×Q8×C61C22×C412yes—
140C2×D4×C61—21no—
141C2×D4×C61—42no—
142C2×D4×C61C22×C412yes—
143C22×C4×C61—21no—
144C22×C4×C61C22⋊C411yescharacteristic
145C22×C4×C61C22⋊C411yescharacteristic
146C22×C4×C61C22×C411yescharacteristic
147C2×C22⋊D61—22no—
148C2×C22⋊D61—22no—
149C2×C22⋊D61—22no—
150C2×C22⋊D61—22no—
151C2×C22⋊D61—22no—
152C2×C22⋊D61—22no—
153C2×C22⋊D61—44no—
154C2×C22⋊D61—44no—
155C2×C22⋊D61—44no—
156C22×Dic61—21no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—44no—
160C22×Dic61C22⋊C411yescharacteristic
161C22×Dic61C22⋊C411yescharacteristic
162C22×Dic61C2×D411yescharacteristic
163#11758226—28no—
164#11758226—44no—
165#11758226—44no—
166#11758226—44no—
167#11758224—28no—
168#11758224—44no—
169#11758224—44no—
170#11758224—44no—
171C2×D244—22no—
172C2×D244—22no—
173C2×D244—21no—
174C2×D244—42no—
175C2×D244—44no—
176C2×D244C22×C412yes—
177C2×C4×D61—24no—
178C2×C4×D61—24no—
179C2×C4×D61—22no—
180C2×C4×D61—22no—
181C2×C4×D61—42no—
182C2×C4×D61—44no—
183C2×C4×D61C22⋊C411yescharacteristic
184C2×C4×D61C22⋊C411yescharacteristic
185C2×C4×D61C22⋊C411yescharacteristic
186C2×C4×D61C22⋊C411yescharacteristic
187C2×C4×D61C22×C411yescharacteristic
188C2×C4×D61C2×D411yescharacteristic
189C2×C4×D61C2×D411yescharacteristic
190C2×C4×D61C2×D411yescharacteristic
191C2×C4×D61C2×D411yescharacteristic
192C2×C4×D61C2×D411yescharacteristic
193C2×C4×D61C2×D411yescharacteristic
194C2×C4×D61C2411yescharacteristic
195C2×Dic122—21no—
196C2×Dic122—42no—
197C2×Dic122C22×C412yes—
198C22⋊#6923—28no—
199C2×#92420—24no—
200C4⋊#6923—28no—
201C4×#6923—28no—
202C4×#6923—28no—
203C4×#6923—44no—
204#11758213—28no—
205C22⋊C4×C61—22no—
206C22⋊C4×C61—22no—
207C22⋊C4×C61—22no—
208C22⋊C4×C61—22no—
209C42×C61C22⋊C411yescharacteristic
210C42×C61C22⋊C411yescharacteristic
211C42×C61C22×C411yescharacteristic
212C42×C61C22×C411yescharacteristic
213#11758198—22no—
214#11758198—22no—
215#11758198—22no—
216#11758198—22no—
217#11758196—22no—
218#11758196—22no—
219#11758196—22no—
220#11758196—22no—
221C4×Dic61C22⋊C411yescharacteristic
222C4×Dic61C22⋊C411yescharacteristic
223C4×Dic61C22⋊C411yescharacteristic
224C4×Dic61C22⋊C411yescharacteristic
225C4×Dic61C22⋊C411yescharacteristic
226C4×Dic61C22⋊C411yescharacteristic
227C4×Dic61C22×C411yescharacteristic
228C4×Dic61C22×C411yescharacteristic
229C4×Dic61C2×D411yescharacteristic
230C4×Dic61C2×D411yescharacteristic
231C4×Dic61C2×D411yescharacteristic
232C4×Dic61C2×D411yescharacteristic
233C23×C61—22no—
234C23×C61—42no—
235C23×C61—42no—
236C23×C61—42no—
237C23×C61C2×C22⋊C411yescharacteristic
238C22×D61—22no—
239C22×D61—22no—
240C22×D61—22no—
241C22×D61—41no—
242C22×D61—42no—
243C22×D61—42no—
244C22×D61—42no—
245C22×D61C2×C22⋊C411yescharacteristic
246C22×D61C22×D411yescharacteristic
247C2×#6923—28no—
248C2×#6923—44no—
249C2×#6923—44no—
250Q8×C61—24no—
251Q8×C61—42no—
252D4×C61—24no—
253D4×C61—42no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
256C2×C4×C61—22no—
257C2×C4×C61—41no—
258C2×C4×C61—42no—
259C2×C4×C61C2×C22⋊C411yescharacteristic
260C2×C4×C61C2×C22⋊C411yescharacteristic
261C2×C4×C61C2×C22⋊C411yescharacteristic
262C2×C4×C61C2×C22⋊C411yescharacteristic
263C2×C4×C61C2×C22⋊C411yescharacteristic
264C2×C4×C61C23×C411yescharacteristic
265C22⋊D61—44no—
266C22⋊D61—44no—
267C22⋊D61—44no—
268C22⋊D61—44no—
269C22⋊D61—44no—
270C22⋊D61—44no—
271C2×Dic61—22no—
272C2×Dic61—22no—
273C2×Dic61—22no—
274C2×Dic61—44no—
275C2×Dic61—42no—
276C2×Dic61—44no—
277C2×Dic61#10414yescomplemented
278C2×Dic61C2×C22⋊C411yescharacteristic
279C2×Dic61C2×C22⋊C411yescharacteristic
280C2×Dic61C2×C22⋊C411yescharacteristic
281C2×Dic61C2×C22⋊C411yescharacteristic
282C2×Dic61C2×C22⋊C411yescharacteristic
283C2×Dic61C22×D411yescharacteristic
284D244—24no—
285D244—42no—
286D244—44no—
287D244—44no—
288C4×D61—22no—
289C4×D61—22no—
290C4×D61—22no—
291C4×D61—22no—
292C4×D61—22no—
293C4×D61—22no—
294C4×D61—22no—
295C4×D61—22no—
296C4×D61—22no—
297C4×D61—41no—
298C4×D61—41no—
299C4×D61—44no—
300C4×D61—44no—
301C4×D61H(5,𝔽2)14yes—
302Dic122—24no—
303Dic122—42no—
304#92420—44no—
305#21815—611nomaximal, Sylow
306C22×C61—21no—
307C22×C61—21no—
308C22×C61—42no—
309C22×C61—42no—
310C22×C61—42no—
311C22×C61—84no—
312C22×C61C2×#10412yes—
313C22×C61C22×C22⋊C411yescharacteristic
314C2×D61—21no—
315C2×D61—21no—
316C2×D61—21no—
317C2×D61—21no—
318C2×D61—21no—
319C2×D61—44no—
320C2×D61—42no—
321C2×D61—42no—
322C2×D61—42no—
323C2×D61—84no—
324C2×D61#53512yes—
325#6923—48no—
326C4×C61—21no—
327C4×C61—21no—
328C4×C61—21no—
329C4×C61—21no—
330C4×C61—21no—
331C4×C61—42no—
332C4×C61#51812yes—
333Dic61—21no—
334Dic61—21no—
335Dic61—42no—
336Dic61C2×#10412yes—
337Dic61C2×#10412yes—
338Dic61#42112yes—
339Dic61#53512yes—
340C2×#532—611no—
341#2920—611no—
342C4×#117—611no—
343#1980—614no—
344#1962—614no—
345#1789—612no—
346#1789—612no—
347C2×C61—22no—
348C2×C61—82no—
349C2×C61#230911yescharacteristic
350C2×C61C22×#10411yescharacteristic
351C2×C61C2×#42111yescharacteristic
352D61—22no—
353D61—41no—
354D61—82no—
355C22×#41—611no—
356C22×#41—611no—
357#532—612no—
358#532—612no—
359#532—612no—
360#532—612no—
361#532—1221no—
362#532—1221no—
363#532—1221no—
364#532—1221no—
365C2×C4⋊Q8—611no—
366C2×#127—611no—
367C2×#124—611no—
368C2×#124#692311yescharacteristic, complemented
369C2×#121—1221no—
370C2×#121—1221no—
371C2×C4×D4—1221no—
372C2×C4×D4—1221no—
373C2×#117—1221no—
374C22×C42—611no—
375#432—1221no—
376#432—1221no—
377#431—1221no—
378#431—1221no—
379#423—612no—
380C2×#104—618no—
381C2×#104—618no—
382#407—612no—
383C4×M16—612no—
384C4×C4⋊C4—612no—
385C4×C4⋊C4—1221no—
386C4×C22⋊C4—612no—
387C4×C22⋊C4—1221no—
388#376—1221no—
389C43—612no—
390C61#2181511yescharacteristic, complemented, Sylow
391C2×#41—612no—
392C2×#41—612no—
393C2×#41—612no—
394C2×#41—612no—
395C2×#41—1221no—
396C2×#41—1221no—
397C2×#41—1221no—
398C2×#41—1221no—
399C2×#41—2444no—
400C2×#41—2444no—
401C22×Q8—611no—
402C22×Q8C2×#692311yescharacteristic
403C22×D4—611no—
404C22×D4—1221no—
405C22×D4—1221no—
406C22×D4—1221no—
407C22×D4—1221no—
408C22×D4C2×#692311yescharacteristic
409C23×C4—611no—
410C23×C4—611no—
411C23×C4—611no—
412C23×C4—1221no—
413C23×C4—1221no—
414C2×M16—614no—
415C4⋊Q8—612no—
416C4⋊Q8—612no—
417C4⋊Q8—1221no—
418C4⋊Q8—1221no—
419#127—612no—
420#127—612no—
421#127—1221no—
422#127—1221no—
423#124—21no—
424#124—21no—
425#124—612no—
426#124—612no—
427#124—1221no—
428#124—1221no—
429#124C2×#692312yes—
430#124C2×#692312yes—
431#121—1222no—
432#121—1222no—
433#121—1222no—
434#121—1222no—
435#121—1222no—
436#121—1222no—
437#121—1222no—
438#121—1222no—
439C4×D4—1222no—
440C4×D4—1222no—
441C4×D4—1222no—
442C4×D4—1222no—
443C4×D4—1222no—
444C4×D4—1222no—
445C4×D4—1222no—
446C4×D4—1222no—
447#117—1228no—
448C2×C4⋊C4—1221no—
449C2×C4⋊C4—1221no—
450C2×C4⋊C4—1222no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—1222no—
454C2×C22⋊C4—1221no—
455C2×C22⋊C4—1221no—
456C2×C42—611no—
457C2×C42—611no—
458C2×C42—611no—
459C2×C42—611no—
460C2×C42—611no—
461C2×C42—611no—
462C2×C42—611no—
463C2×C42—611no—
464C2×C42—611no—
465C2×C42—611no—
466C2×C42—611no—
467C2×C42—614no—
468C2×C42—1222no—
469C2×C42—1222no—
470C2×C42C2×#692311yescharacteristic
471C4⋊C8—1222no—
472C4⋊C8—1222no—
473#104—2448no—
474#104—2448no—
475C22⋊C8—1222no—
476C22⋊C8—1222no—
477#97—1222no—
478C4×C8—1222no—
479#95—1222no—
480#95—1222no—
481C24—21no—
482C24—611no—
483C24—1221no—
484#41—1228no—
485#41—1228no—
486#41—2444no—
487#41—2444no—
488#41—2444no—
489#41—2444no—
490#41—2444no—
491#41—2444no—
492C2×Q8—21no—
493C2×Q8—42no—
494C2×Q8—612no—
495C2×Q8—1221no—
496C2×Q8—2442no—
497C2×Q8C22×#692312yes—
498C2×D4—21no—
499C2×D4—42no—
500C2×D4—612no—
501C2×D4—1222no—
502C2×D4—1222no—
503C2×D4—1222no—
504C2×D4—1222no—
505C2×D4—1222no—
506C2×D4—1222no—
507C2×D4—1222no—
508C2×D4—1222no—
509C2×D4—1221no—
510C2×D4—2442no—
511C2×D4—2444no—
512C2×D4—2444no—
513C2×D4—2444no—
514C2×D4—2444no—
515C2×D4C22×#692312yes—
516C22×C4—21no—
517C22×C4—611no—
518C22×C4—611no—
519C22×C4—611no—
520C22×C4—611no—
521C22×C4—611no—
522C22×C4—611no—
523C22×C4—611no—
524C22×C4—611no—
525C22×C4—611no—
526C22×C4—611no—
527C22×C4—611no—
528C22×C4—611no—
529C22×C4—611no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—1224no—
533C22×C4—1224no—
534C22×C4—1222no—
535C22×C4—1222no—
536C22×C4—1222no—
537C22×C4—1222no—
538C22×C4—1224no—
539C22×C4—1221no—
540C22×C4—2442no—
541C22×C4—2444no—
542C22×C4—2444no—
543C22×C4C22⋊#692311yescharacteristic
544C22×C4C22⋊#692311yescharacteristic
545C22×C4C22×#692311yescharacteristic
546M16—1228no—
547C2×C8—1224no—
548C4⋊C4—1222no—
549C4⋊C4—1222no—
550C4⋊C4—1222no—
551C4⋊C4—1222no—
552C4⋊C4—1228no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—1228no—
558C22⋊C4—1222no—
559C22⋊C4—1222no—
560C22⋊C4—1222no—
561C22⋊C4—1222no—
562C42—611no—
563C42—611no—
564C42—611no—
565C42—611no—
566C42—611no—
567C42—611no—
568C42—611no—
569C42—611no—
570C42—611no—
571C42—611no—
572C42—611no—
573C42—611no—
574C42—1228no—
575C42—1228no—
576C42—2444no—
577C42C22⋊#692311yescharacteristic
578C42C22⋊#692311yescharacteristic
579C42C22×#692311yescharacteristic
580C42C22×#692311yescharacteristic
581C23—22no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—611no—
586C23—611no—
587C23—1222no—
588C23—1222no—
589C23—1222no—
590C23—2441no—
591C23—2442no—
592C23—2442no—
593C23—2442no—
594C23C2×C22⋊#692311yescharacteristic
595Q8—24no—
596Q8—42no—
597Q8—1224no—
598Q8—2442no—
599D4—24no—
600D4—42no—
601D4—1224no—
602D4—2442no—
603D4—2444no—
604D4—2444no—
605D4—2444no—
606D4—2444no—
607D4—2444no—
608D4—2444no—
609D4—2444no—
610D4—2444no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—614no—
617C2×C4—611no—
618C2×C4—611no—
619C2×C4—611no—
620C2×C4—611no—
621C2×C4—614no—
622C2×C4—611no—
623C2×C4—611no—
624C2×C4—1222no—
625C2×C4—1222no—
626C2×C4—1222no—
627C2×C4—1222no—
628C2×C4—1222no—
629C2×C4—1222no—
630C2×C4—1222no—
631C2×C4—1222no—
632C2×C4—1222no—
633C2×C4—1222no—
634C2×C4—1222no—
635C2×C4—1228no—
636C2×C4—1222no—
637C2×C4—2441no—
638C2×C4—2441no—
639C2×C4—2444no—
640C2×C4—2444no—
641C2×C4—2444no—
642C2×C4—2444no—
643C2×C4—2442no—
644C2×C4—2444no—
645C2×C4—2444no—
646C2×C4C2×C22⋊#692311yescharacteristic
647C2×C4C2×C22⋊#692311yescharacteristic
648C2×C4C2×C22⋊#692311yescharacteristic
649C2×C4C2×C22⋊#692311yescharacteristic
650C2×C4C2×C22⋊#692311yescharacteristic
651C2×C4C23×#692311yescharacteristic
652C8—2444no—
653C22—21no—
654C22—21no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—84no—
659C22—612no—
660C22—1221no—
661C22—1221no—
662C22—1221no—
663C22—1221no—
664C22—1221no—
665C22—4884no—
666C22—2444no—
667C22—2442no—
668C22—2442no—
669C22—2442no—
670C22D61⋊#10412yes—
671C22C22×C22⋊#692311yescharacteristic
672C4—21no—
673C4—21no—
674C4—21no—
675C4—21no—
676C4—21no—
677C4—42no—
678C4—612no—
679C4—612no—
680C4—612no—
681C4—612no—
682C4—1221no—
683C4—1221no—
684C4—2448no—
685C4—2442no—
686C4#1684082912yes—
687C2—22no—
688C2—82no—
689C2—1222no—
690C2—4882no—
691C2—2441no—
692C2#2146229211yescharacteristic
693C2C2×D61⋊#10411yescharacteristic
694C2D61⋊#42111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#124×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840311C2
cosocleC2×C4×D61C24
hypercenterC2×#124#6923
hypocenterC61#21815
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #21462498C2semidirect
2. C4×#14519856C2semidirect
3. #21461984C2semidirect
4. #21461954C2semidirect
5. #21461662C2semidirect
6. #21461660C2semidirect
13. #16840767C22semidirect
14. C2×#14519842C22semidirect
15. C2×#14519841C22semidirect
17. C4×#11758213C22semidirect
19. C4×C4⋊#6923C22semidirect
23. C42×#6923C22semidirect
30. #16840311C4semidirect
31. #16840311C4semidirect
34. C2×#14519775C4semidirect
35. C2×#14519773C4semidirect
36. C2×#14519765C4semidirect
42. C2×#124×C61C4semidirect
277. C2×Dic61#104semidirect
368. C2×#124#6923semidirect
390. C61#21815semidirect

Maximal subgroups

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

subgroupindex
#214624982
C4×#145198562
#214619842
#214619542
#214616622
#214616602
C2×#168403112
#2181561