Finite Group Databasebeta

← #29586382

Subgroups — #29586382

Order 15616.

930 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839780C211yesmaximal, characteristic
2C2×#16839759C211yesmaximal, characteristic
3C2×#16839735C211yesmaximal, characteristic
4C2×#16839717C211yesmaximal, characteristic, complemented
5#21445551C211yesmaximal, characteristic, complemented
6#21445529C211yesmaximal, characteristic, complemented
7C61×#1735C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C2×#14519736C2211yescharacteristic
11C2×#14519736C2211yescharacteristic
12#16839780—22no—
13#16839780C414yescomplemented
14C2×#14519705—22no—
15#16839759—21no—
16#16839759—21no—
17#16839759—22no—
18C2×#14519702C412yescomplemented
19C2×#14519699C412yescomplemented
20#16839735—22no—
21#16839735C414yescomplemented
22C2×#14519691—22no—
23#16839717—22no—
24#16839717—22no—
25C2×#14519687—21no—
26C2×C8×Dic61—21no—
27#16839528—22no—
28#16839522—22no—
29C23×C8×C61C2211yescharacteristic
30C2×#117×C61C2211yescharacteristic
31C2×#117×C61C2211yescharacteristic
32C61×#340—22no—
33C2×#11758222—21no—
34C2×#11758222—21no—
35C2×#11758222—21no—
36C2×#11758222—21no—
37C2×#11758222—21no—
38C2×#11758222—21no—
39C2×#11758222—21no—
40C2×#11758222—21no—
41C2×#11758222—21no—
42C2×#11758222—21no—
43C2×#11758222C2×C412yes—
44C2×#11758222C2×C412yes—
45C22×Dic122C2×C411yescharacteristic
46C22×D244C2×C411yescharacteristic
47C22×C22⋊D61—21no—
48C22×C4×D61—21no—
49C2×#11758194—21no—
50C2×#11758194—21no—
51C2×#11758194—21no—
52C2×#11758194C2×C412yes—
53C2×#11758194D412yes—
54C2×#11758194D412yes—
55C22×#92418—21no—
56#14519736—21no—
57#14519736—21no—
58#14519736—21no—
59#14519736—21no—
60#14519736—21no—
61#14519736—21no—
62#14519736C2×C412yes—
63#14519736D412yes—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61C2×C412yes—
66C2×C22⋊Dic61—21no—
67C2×C22⋊Dic61D412yes—
68C2×C4×Dic61—21no—
69C2×C4×Dic61—21no—
70#14519705—28no—
71#14519702—22no—
72#14519702—22no—
73#14519699—22no—
74#14519699—22no—
75#14519691—28no—
76#14519687—24no—
77C8×Dic61—24no—
78C23×C4×C61C2311yescharacteristic
79C22×C8×C61—21no—
80C22×C8×C61—21no—
81C22×C8×C61—21no—
82C22×C8×C61—21no—
83C22×C8×C61C2×C412yes—
84C22×C8×C61D411yescharacteristic
85C22×C8×C61D411yescharacteristic
86C22×C8×C61D412yes—
87#117×C61—21no—
88#117×C61—21no—
89#117×C61—21no—
90#117×C61—21no—
91#117×C61—21no—
92#117×C61—21no—
93#117×C61C2×C412yes—
94#117×C61C2×C412yes—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61—21no—
97C2×C22⋊C4×C61—21no—
98C2×C22⋊C4×C61—21no—
99C2×C42×C61—21no—
100C2×C42×C61—21no—
101C24×C61C2×D411yescharacteristic
102C23×D61—21no—
103C22×C4×C61—41no—
104C22×C4×C61—41no—
105C22×C4×C61C22×C411yescharacteristic
106C22×C4×C61C22×C411yescharacteristic
107C22×C4×C61C22×C411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61#4111yescharacteristic
114C22×C4×C61#4111yescharacteristic
115C22×C4×C61#4111yescharacteristic
116C22×C4×C61#4111yescharacteristic
117C22×C4×C61#4111yescharacteristic
118C22×C4×C61#4111yescharacteristic
119C2×C22⋊D61—22no—
120C2×C22⋊D61—22no—
121C2×C22⋊D61—41no—
122C2×C22⋊D61—41no—
123C2×C22⋊D61—41no—
124C2×C22⋊D61—41no—
125C22×Dic61—21no—
126C22×Dic61—22no—
127C22×Dic61—22no—
128#11758222—22no—
129#11758222—22no—
130#11758222—22no—
131#11758222—22no—
132#11758222—22no—
133#11758222—22no—
134#11758222—22no—
135#11758222—22no—
136#11758222—41no—
137#11758222—41no—
138#11758222—41no—
139#11758222—41no—
140#11758222—41no—
141#11758222—41no—
142#11758222—41no—
143#11758222—41no—
144C2×D244—21no—
145C2×D244—21no—
146C2×D244—21no—
147C2×D244—21no—
148C2×D244—21no—
149C2×D244C4212yes—
150C2×C4×D61—22no—
151C2×C4×D61—22no—
152C2×C4×D61—41no—
153C2×C4×D61—41no—
154C2×C4×D61—41no—
155C2×C4×D61—41no—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122C4212yes—
162C2×C8×C61—22no—
163C2×C8×C61—22no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—22no—
167C2×C8×C61—22no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61C22⋊C412yes—
171C2×C8×C61C22⋊C412yes—
172C4⋊C4×C61—22no—
173C4⋊C4×C61—22no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61—41no—
176C22⋊C4×C61—22no—
177C22⋊C4×C61—22no—
178C22⋊C4×C61—41no—
179C22⋊C4×C61—41no—
180C42×C61—22no—
181C42×C61—22no—
182C42×C61—41no—
183C42×C61—41no—
184C22⋊Dic61—22no—
185C22⋊Dic61—41no—
186C22⋊Dic61—41no—
187C22⋊Dic61C22⋊C414yes—
188C4⋊Dic61—22no—
189C4⋊Dic61—22no—
190C4⋊Dic61—22no—
191C4⋊Dic61—22no—
192C4×Dic61—22no—
193C4×Dic61—22no—
194C4×Dic61—41no—
195C4×Dic61—41no—
196#11758194—22no—
197#11758194—22no—
198#11758194—22no—
199#11758194C22⋊C414yes—
200C2×#92418—22no—
201C2×#92418—22no—
202C2×#92418—22no—
203C23×C61—42no—
204C23×C61C2×C22⋊C411yescharacteristic
205C23×C61C4×D411yescharacteristic
206C23×C61C4×D411yescharacteristic
207C23×C61#12111yescharacteristic
208C23×C61#12111yescharacteristic
209C23×C61#12411yescharacteristic
210C23×C61#12711yescharacteristic
211C22×D61—22no—
212C22×D61—41no—
213C22×D61—41no—
214C22×D61—82no—
215C2×C4×C61—42no—
216C2×C4×C61—42no—
217C2×C4×C61—82no—
218C2×C4×C61—82no—
219C2×C4×C61C2×C4211yescharacteristic
220C2×C4×C61C2×C22⋊C411yescharacteristic
221C2×C4×C61C2×C22⋊C411yescharacteristic
222C2×C4×C61#11711yescharacteristic
223C2×C4×C61#11711yescharacteristic
224C2×C4×C61#11711yescharacteristic
225C2×C4×C61C4×D411yescharacteristic
226C2×C4×C61C4×D411yescharacteristic
227C2×C4×C61C4×D411yescharacteristic
228C2×C4×C61C4×D411yescharacteristic
229C2×C4×C61C4×D411yescharacteristic
230C2×C4×C61C4×D411yescharacteristic
231C2×C4×C61C4×D411yescharacteristic
232C2×C4×C61C4×D411yescharacteristic
233C2×C4×C61C4×D411yescharacteristic
234C2×C4×C61C4×D411yescharacteristic
235C2×C4×C61#12011yescharacteristic
236C2×C4×C61#12111yescharacteristic
237C2×C4×C61#12111yescharacteristic
238C2×C4×C61#12111yescharacteristic
239C2×C4×C61#12111yescharacteristic
240C2×C4×C61#12311yescharacteristic
241C2×C4×C61#12311yescharacteristic
242C2×C4×C61#12311yescharacteristic
243C2×C4×C61#12411yescharacteristic
244C2×C4×C61#12411yescharacteristic
245C2×C4×C61#12611yescharacteristic
246C2×C4×C61#12611yescharacteristic
247C22⋊D61—42no—
248C22⋊D61—42no—
249C22⋊D61—42no—
250C22⋊D61—42no—
251C2×Dic61—22no—
252C2×Dic61—24no—
253C2×Dic61—44no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—42no—
257C2×Dic61—82no—
258D244—22no—
259D244—22no—
260D244—41no—
261D244—41no—
262C4×D61—42no—
263C4×D61—42no—
264C4×D61—42no—
265C4×D61—42no—
266Dic122—22no—
267Dic122—22no—
268Dic122—41no—
269Dic122—41no—
270C8×C61—22no—
271C8×C61—22no—
272#92418—24no—
273#10944—611nomaximal, Sylow
274C22×C61—22no—
275C22×C61—22no—
276C22×C61—22no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61C4×C22⋊C411yescharacteristic
282C22×C61#38611yescharacteristic
283C22×C61#38811yescharacteristic
284C22×C61#38811yescharacteristic
285C22×C61#39011yescharacteristic
286C22×C61#39011yescharacteristic
287C22×C61#39011yescharacteristic
288C2×D61—42no—
289C2×D61—82no—
290C2×D61—82no—
291C2×D61—82no—
292C4×C61—82no—
293C4×C61—82no—
294C4×C61C4×C22⋊C411yescharacteristic
295C4×C61C4×C22⋊C411yescharacteristic
296C4×C61#38611yescharacteristic
297C4×C61#38611yescharacteristic
298C4×C61#38811yescharacteristic
299C4×C61#38811yescharacteristic
300C4×C61#38811yescharacteristic
301C4×C61#38811yescharacteristic
302Dic61—44no—
303Dic61—42no—
304Dic61—82no—
305C2×#421—611no—
306C2×#416—611no—
307C2×#410—611no—
308C2×#405—611no—
309#1740—611no—
310#1735D6111yescharacteristic, complemented
311#1733—611no—
312C2×C61—21no—
313C2×C61—21no—
314C2×C61—21no—
315C2×C61—21no—
316C2×C61—21no—
317C2×C61—21no—
318C2×C61#143711yescharacteristic
319C2×C61#197612yes—
320D61—82no—
321C22×#41—611no—
322C22×M16—611no—
323C23×C8C2×D6111yescharacteristic
324C2×#117—611no—
325C2×#117—611no—
326C2×#117C2×D6111yescharacteristic
327C2×#117C2×D6111yescharacteristic
328#421—614no—
329#421—1222no—
330C2×#104—1222no—
331#416—1221no—
332#416—1221no—
333#416—1222no—
334C2×#103—612no—
335C2×#102—612no—
336#410—614no—
337#410—1222no—
338C2×#99—1222no—
339#405—1222no—
340#405—1222no—
341C2×#97—1221no—
342C2×C4×C8—1221no—
343#342—1222no—
344#340—22no—
345#339—1222no—
346C61#1094411yescharacteristic, complemented, Sylow
347C2×#41—612no—
348C2×#41—612no—
349C2×#41—1221no—
350C2×#41—1221no—
351C2×#41—1221no—
352C2×#41—1221no—
353C2×#41—1221no—
354C2×#41—1221no—
355C2×#41—1221no—
356C2×#41—1221no—
357C2×#41—1221no—
358C2×#41—1221no—
359C22×Q8—611no—
360C22×D4—611no—
361C22×D4—1221no—
362C23×C4—1221no—
363C23×C4C22×D6111yescharacteristic
364C2×M16—612no—
365C2×M16—612no—
366C2×M16—612no—
367C2×M16—1221no—
368C2×M16—1221no—
369C2×M16—1221no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—1221no—
375C22×C8C4×D6112yes—
376C22×C8D24411yescharacteristic
377C22×C8D24411yescharacteristic
378C22×C8C22⋊D6112yes—
379#117—21no—
380#117—21no—
381#117—21no—
382#117—21no—
383#117—21no—
384#117—21no—
385#117—612no—
386#117—612no—
387#117—1221no—
388#117—1221no—
389#117—1221no—
390#117—1221no—
391#117—1221no—
392#117—1221no—
393#117C4×D6112yes—
394#117C4×D6112yes—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—612no—
398C2×C4⋊C4—1221no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—612no—
402C2×C22⋊C4—1221no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—1221no—
406C2×C42—1221no—
407#104—1228no—
408#103—1222no—
409#103—1222no—
410#102—1222no—
411#102—1222no—
412#99—1228no—
413#97—1224no—
414C4×C8—1224no—
415C24—1221no—
416C24D4×D6111yescharacteristic
417#41—1222no—
418#41—1222no—
419#41—1222no—
420#41—1222no—
421#41—1222no—
422#41—1222no—
423#41—1222no—
424#41—1222no—
425#41—2441no—
426#41—2441no—
427#41—2441no—
428#41—2441no—
429#41—2441no—
430#41—2441no—
431#41—2441no—
432#41—2441no—
433C2×Q8—612no—
434C2×Q8—1221no—
435C2×Q8—1221no—
436C2×Q8—1221no—
437C2×Q8—1221no—
438C2×Q8—1221no—
439C2×D4—612no—
440C2×D4—1222no—
441C2×D4—1222no—
442C2×D4—1221no—
443C2×D4—1221no—
444C2×D4—1221no—
445C2×D4—1221no—
446C2×D4—1221no—
447C2×D4—2441no—
448C2×D4—2441no—
449C2×D4—2441no—
450C2×D4—2441no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—1221no—
454C22×C4—1222no—
455C22×C4—1222no—
456C22×C4—1222no—
457C22×C4—1222no—
458C22×C4—2441no—
459C22×C4—2441no—
460C22×C4—2441no—
461C22×C4—2441no—
462C22×C4C2×C4×D6111yescharacteristic
463C22×C4C2×C4×D6111yescharacteristic
464C22×C4C2×C4×D6111yescharacteristic
465C22×C4C2×D24411yescharacteristic
466C22×C4#1175822211yescharacteristic
467C22×C4#1175822211yescharacteristic
468C22×C4D4×D6111yescharacteristic
469C22×C4D4×D6111yescharacteristic
470C22×C4D4×D6111yescharacteristic
471C22×C4#1175822411yescharacteristic
472C22×C4#1175822411yescharacteristic
473C22×C4#1175822611yescharacteristic
474C22×C4#1175822611yescharacteristic
475C22×C4C2×C22⋊D6111yescharacteristic
476M16—614no—
477M16—1222no—
478M16—1222no—
479M16—1222no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—1222no—
489C2×C8—1222no—
490C2×C8—1222no—
491C2×C8#1175819812yes—
492C2×C8#1175819812yes—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—1222no—
498C4⋊C4—1222no—
499C4⋊C4—1222no—
500C4⋊C4—1222no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—614no—
506C22⋊C4—1222no—
507C22⋊C4—2441no—
508C22⋊C4—2441no—
509C42—22no—
510C42—22no—
511C42—41no—
512C42—41no—
513C42—1222no—
514C42—1222no—
515C42—2441no—
516C42—2441no—
517C23—42no—
518C23—1222no—
519C23—4882no—
520C23—2441no—
521C23—2441no—
522C23C22⋊C4×D6111yescharacteristic
523C23#1451973711yescharacteristic
524C23#1451973911yescharacteristic
525C23#1451975011yescharacteristic
526C23#1451975211yescharacteristic
527C23#1451976311yescharacteristic
528C23#1451977311yescharacteristic
529Q8—1222no—
530Q8—1222no—
531Q8—2441no—
532Q8—2441no—
533D4—1222no—
534D4—1222no—
535D4—2442no—
536D4—2442no—
537D4—2442no—
538D4—2442no—
539D4—2441no—
540D4—2441no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—82no—
544C2×C4—82no—
545C2×C4—1222no—
546C2×C4—1224no—
547C2×C4—4882no—
548C2×C4—2442no—
549C2×C4—2444no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2442no—
553C2×C4—2442no—
554C2×C4—2442no—
555C2×C4—2442no—
556C2×C4C42×D6111yescharacteristic
557C2×C4C22⋊C4×D6111yescharacteristic
558C2×C4C2×#1175819811yescharacteristic
559C2×C4#1451973411yescharacteristic
560C2×C4#1451973511yescharacteristic
561C2×C4#1451973511yescharacteristic
562C2×C4#1451973711yescharacteristic
563C2×C4#1451973711yescharacteristic
564C2×C4#1451973711yescharacteristic
565C2×C4C4×C22⋊D6111yescharacteristic
566C2×C4C4×C22⋊D6111yescharacteristic
567C2×C4#1451973911yescharacteristic
568C2×C4#1451973911yescharacteristic
569C2×C4#1451973911yescharacteristic
570C2×C4C4×D24411yescharacteristic
571C2×C4C4×D24411yescharacteristic
572C2×C4#1451974711yescharacteristic
573C2×C4#1451974911yescharacteristic
574C2×C4#1451974911yescharacteristic
575C2×C4#1451975011yescharacteristic
576C2×C4#1451975211yescharacteristic
577C2×C4#1451976111yescharacteristic
578C2×C4#1451976211yescharacteristic
579C2×C4#1451976211yescharacteristic
580C2×C4#1451976311yescharacteristic
581C2×C4#1451976611yescharacteristic
582C2×C4#1451977211yescharacteristic
583C2×C4#1451977211yescharacteristic
584C8—22no—
585C8—22no—
586C8—1224no—
587C22—22no—
588C22—22no—
589C22—22no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—4882no—
595C22—4882no—
596C22—4882no—
597C22—2442no—
598C22#1683960911yescharacteristic
599C22#1683964011yescharacteristic
600C22#1683965111yescharacteristic
601C22#1683965411yescharacteristic
602C22#1683966211yescharacteristic
603C22#1683966211yescharacteristic
604C22#1683966311yescharacteristic
605C4—82no—
606C4—82no—
607C4—4882no—
608C4—2444no—
609C4—2442no—
610C4#1683960911yescharacteristic
611C4C4×#1175819811yescharacteristic
612C4#1683963911yescharacteristic
613C4#1683964011yescharacteristic
614C4#1683965111yescharacteristic
615C4#1683965211yescharacteristic
616C4#1683965211yescharacteristic
617C4#1683965411yescharacteristic
618C2—21no—
619C2—21no—
620C2—21no—
621C2—21no—
622C2—21no—
623C2—21no—
624C2—4882no—
625C2#2144405511yescharacteristic
626C2#2144671512yes—
subgroupG/H
centerC2×C4#14519752
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC61×#1735C2
socleC22×C61#390
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenter#1735D61
hypocenterC61#10944
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1735

Complements

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

NH ≅ G/Ntype
4. C2×#16839717C2semidirect
5. #21445551C2semidirect
6. #21445529C2semidirect
7. C61×#1735C2semidirect
13. #16839780C4semidirect
18. C2×#14519702C4semidirect
19. C2×#14519699C4semidirect
21. #16839735C4semidirect
310. #1735D61semidirect
346. C61#10944semidirect

Maximal subgroups

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

subgroupindex
C2×#168397802
C2×#168397592
C2×#168397352
C2×#168397172
#214455512
#214455292
C61×#17352
#1094461