Finite Group Databasebeta

← #29586325

Subgroups — #29586325

Order 15616.

982 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519703C211yesmaximal, characteristic
2C2×#16839759C211yesmaximal, characteristic
3C2×#16839730C211yesmaximal, characteristic
4C2×#16839720C211yesmaximal, characteristic, complemented
5C2×#16839523C211yesmaximal, characteristic, complemented
6C2×#16839516C211yesmaximal, characteristic, complemented
7C2×C61×#341C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C23×#92418C2211yescharacteristic
10C2×#14519736C2211yescharacteristic
11C22×C4×Dic61C2211yescharacteristic
12C2×#14519703—22no—
13C2×#14519703—22no—
14C2×#14519703C414yescomplemented
15#16839759—22no—
16#16839759—22no—
17C2×#14519702C412yescomplemented
18C2×#14519699C412yescomplemented
19#16839730—22no—
20#16839730C414yescomplemented
21C2×#14519689—21no—
22C2×#14519689—21no—
23#16839720—22no—
24#16839720—22no—
25C2×#14519687—21no—
26C2×C8×Dic61—21no—
27#16839523—22no—
28#16839516—22no—
29C22×M16×C61C2211yescharacteristic
30C22×M16×C61C2211yescharacteristic
31C23×C8×C61C2211yescharacteristic
32C61×#341—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—
48C23×Dic61—21no—
49C22×C4×D61—21no—
50C22×#92418—21no—
51C22×#92418—21no—
52C22×#92418—21no—
53C22×#92418—21no—
54C22×#92418C2×C412yes—
55C22×#92418D411yescharacteristic
56C22×#92418D411yescharacteristic
57C22×#92418D412yes—
58#14519736—21no—
59#14519736—21no—
60#14519736D412yes—
61#14519736D412yes—
62C2×C4⋊Dic61C2×C412yes—
63C2×C22⋊Dic61—21no—
64C2×C4×Dic61—21no—
65C2×C4×Dic61—21no—
66C2×C4×Dic61—21no—
67C2×C4×Dic61—21no—
68C2×C4×Dic61—21no—
69C2×C4×Dic61—21no—
70C2×C4×Dic61C2×C412yes—
71#14519703—28no—
72#14519702—24no—
73#14519699—24no—
74#14519689—24no—
75#14519689—24no—
76#14519687—24no—
77C8×Dic61—24no—
78C23×C4×C61C2311yescharacteristic
79C2×M16×C61—21no—
80C2×M16×C61—21no—
81C2×M16×C61—21no—
82C2×M16×C61—21no—
83C2×M16×C61—21no—
84C2×M16×C61—21no—
85C2×M16×C61—21no—
86C2×M16×C61—21no—
87C2×M16×C61C2×C412yes—
88C2×M16×C61C2×C412yes—
89C2×M16×C61D412yes—
90C2×M16×C61D412yes—
91C22×C8×C61—21no—
92C22×C8×C61—21no—
93C22×C8×C61—21no—
94C22×C8×C61—21no—
95C22×C8×C61—21no—
96C22×C8×C61—21no—
97C22×C8×C61—21no—
98C22×C8×C61—21no—
99C22×C8×C61C2×C412yes—
100C24×C61#4111yescharacteristic
101C23×D61—21no—
102C22×C4×C61C22×C411yescharacteristic
103C22×C4×C61C22×C411yescharacteristic
104C22×C4×C61C22×C411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61#4111yescharacteristic
112C22×C4×C61#4111yescharacteristic
113C22×C4×C61#4111yescharacteristic
114C22×C4×C61#4111yescharacteristic
115C22×C4×C61#4111yescharacteristic
116C2×C22⋊D61—22no—
117C2×C22⋊D61—22no—
118C2×C22⋊D61—41no—
119C2×C22⋊D61—41no—
120C2×C22⋊D61—41no—
121C2×C22⋊D61—41no—
122C22×Dic61—24no—
123C22×Dic61—21no—
124C22×Dic61—22no—
125C22×Dic61—22no—
126C22×Dic61—42no—
127C22×Dic61—41no—
128C22×Dic61—41no—
129#11758222—22no—
130#11758222—22no—
131#11758222—22no—
132#11758222—22no—
133#11758222—22no—
134#11758222—22no—
135#11758222—22no—
136#11758222—22no—
137#11758222—41no—
138#11758222—41no—
139#11758222—41no—
140#11758222—41no—
141#11758222—41no—
142#11758222—41no—
143#11758222—41no—
144#11758222—41no—
145C2×D244—21no—
146C2×D244—21no—
147C2×D244—21no—
148C2×D244—21no—
149C2×D244—21no—
150C2×D244C4212yes—
151C2×C4×D61—22no—
152C2×C4×D61—22no—
153C2×C4×D61—41no—
154C2×C4×D61—41no—
155C2×C4×D61—41no—
156C2×C4×D61—41no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—21no—
162C2×Dic122C4212yes—
163M16×C61—22no—
164M16×C61—22no—
165M16×C61—22no—
166M16×C61—22no—
167M16×C61—22no—
168M16×C61—41no—
169M16×C61—41no—
170M16×C61C22⋊C414yes—
171C2×C8×C61—22no—
172C2×C8×C61—22no—
173C2×C8×C61—22no—
174C2×C8×C61—22no—
175C2×C8×C61—22no—
176C2×C8×C61—22no—
177C2×C8×C61—22no—
178C2×C8×C61—41no—
179C2×C8×C61—41no—
180C2×C8×C61—41no—
181C2×C8×C61—41no—
182C2×C8×C61—41no—
183C2×C8×C61—41no—
184C22⋊Dic61—22no—
185C22⋊Dic61—22no—
186C4⋊Dic61—22no—
187C4⋊Dic61C22⋊C414yes—
188C4×Dic61—22no—
189C4×Dic61—22no—
190C4×Dic61—22no—
191C4×Dic61—22no—
192C4×Dic61—41no—
193C4×Dic61—41no—
194C2×#92418—22no—
195C2×#92418—22no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—22no—
199C2×#92418—22no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418C22⋊C412yes—
203C2×#92418C22⋊C412yes—
204C23×C61—22no—
205C23×C61—22no—
206C23×C61#11711yescharacteristic
207C23×C61C4×D411yescharacteristic
208C23×C61C4×D411yescharacteristic
209C23×C61#12111yescharacteristic
210C23×C61#12311yescharacteristic
211C23×C61#12411yescharacteristic
212C23×C61#12611yescharacteristic
213C22×D61—22no—
214C22×D61—41no—
215C22×D61—41no—
216C22×D61—42no—
217C22×D61—42no—
218C2×C4×C61C2×C4211yescharacteristic
219C2×C4×C61C2×C22⋊C411yescharacteristic
220C2×C4×C61C2×C22⋊C411yescharacteristic
221C2×C4×C61C2×C22⋊C411yescharacteristic
222C2×C4×C61#11711yescharacteristic
223C2×C4×C61#11711yescharacteristic
224C2×C4×C61C4×D411yescharacteristic
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×C61#12011yescharacteristic
235C2×C4×C61#12111yescharacteristic
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#12411yescharacteristic
243C2×C4×C61#12411yescharacteristic
244C2×C4×C61#12611yescharacteristic
245C2×C4×C61#12711yescharacteristic
246C22⋊D61—42no—
247C22⋊D61—42no—
248C22⋊D61—42no—
249C22⋊D61—42no—
250C2×Dic61—24no—
251C2×Dic61—22no—
252C2×Dic61—24no—
253C2×Dic61—44no—
254C2×Dic61—44no—
255C2×Dic61—42no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—42no—
259C2×Dic61—42no—
260C2×Dic61—42no—
261D244—22no—
262D244—22no—
263D244—41no—
264D244—41no—
265C4×D61—42no—
266C4×D61—42no—
267C4×D61—42no—
268C4×D61—42no—
269Dic122—22no—
270Dic122—22no—
271Dic122—41no—
272Dic122—41no—
273C8×C61—24no—
274C8×C61—42no—
275C8×C61—42no—
276#92418—22no—
277#92418—22no—
278#10934—611nomaximal, Sylow
279C22×C61—22no—
280C22×C61—22no—
281C22×C61—22no—
282C22×C61—22no—
283C22×C61—21no—
284C22×C61—21no—
285C22×C61—21no—
286C22×C61—21no—
287C22×C61C4×C22⋊C411yescharacteristic
288C22×C61#38611yescharacteristic
289C22×C61#38811yescharacteristic
290C22×C61#38811yescharacteristic
291C22×C61#38811yescharacteristic
292C22×C61#38811yescharacteristic
293C22×C61#39011yescharacteristic
294C22×C61#44312yes—
295C22×C61#44412yes—
296C2×D61—42no—
297C2×D61—42no—
298C2×D61—42no—
299C2×D61—82no—
300C2×D61—82no—
301C4×C61C4×C22⋊C411yescharacteristic
302C4×C61C4×C22⋊C411yescharacteristic
303C4×C61#38611yescharacteristic
304C4×C61#38611yescharacteristic
305C4×C61#38811yescharacteristic
306C4×C61#38811yescharacteristic
307C4×C61#39011yescharacteristic
308C4×C61#39011yescharacteristic
309Dic61—44no—
310Dic61—44no—
311Dic61—42no—
312C22×#104—611no—
313C2×#416—611no—
314C2×#408—611no—
315C2×#405—611no—
316C2×#341D6111yescharacteristic, complemented
317C2×#339—611no—
318C2×#336—611no—
319C2×C61—21no—
320C2×C61—21no—
321C2×C61—21no—
322C2×C61—21no—
323C2×C61#143711yescharacteristic
324C2×C61#176411yescharacteristic
325C2×C61#176511yescharacteristic
326C2×C61#187612yes—
327C2×C61#192912yes—
328D61—82no—
329C22×#41—611no—
330C22×M16C2×D6111yescharacteristic
331C22×M16C2×D6111yescharacteristic
332C23×C8—611no—
333C23×C8C2×D6111yescharacteristic
334C2×#117—611no—
335C22×C42—611no—
336C2×#104—614no—
337C2×#104—1222no—
338C2×#104—1222no—
339#416—1222no—
340#416—1222no—
341C2×#103—612no—
342C2×#102—612no—
343#408—614no—
344#408—1222no—
345C2×C22⋊C8—1221no—
346C2×C22⋊C8—1221no—
347#405—1222no—
348#405—1222no—
349C2×#97—1221no—
350C2×C4×C8—1221no—
351#341—22no—
352#339—1222no—
353#336—1222no—
354C61#1093411yescharacteristic, complemented, Sylow
355C2×#41—612no—
356C2×#41—612no—
357C2×#41—1221no—
358C2×#41—1221no—
359C2×#41—1221no—
360C2×#41—1221no—
361C2×#41—1221no—
362C2×#41—1221no—
363C2×#41—1221no—
364C2×#41—1221no—
365C2×#41—1221no—
366C2×#41—1221no—
367C22×Q8—611no—
368C22×D4—611no—
369C22×D4—1221no—
370C23×C4—1221no—
371C23×C4—1221no—
372C23×C4C22×D6111yescharacteristic
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16C4×D6112yes—
382C2×M16C4×D6112yes—
383C2×M16D24412yes—
384C2×M16C22⋊D6112yes—
385C22×C8—21no—
386C22×C8—21no—
387C22×C8—21no—
388C22×C8—21no—
389C22×C8—21no—
390C22×C8—21no—
391C22×C8—21no—
392C22×C8—21no—
393C22×C8—612no—
394C22×C8—612no—
395C22×C8—611no—
396C22×C8—611no—
397C22×C8—1221no—
398C22×C8—1221no—
399C22×C8—1221no—
400C22×C8—1221no—
401C22×C8C4×D6112yes—
402#117—612no—
403#117—612no—
404#117—1221no—
405#117—1221no—
406C2×C4⋊C4—612no—
407C2×C22⋊C4—1221no—
408C2×C42—612no—
409C2×C42—1221no—
410C2×C42—1221no—
411C2×C42—1221no—
412C2×C42—1221no—
413C2×C42—1221no—
414C2×C42—1221no—
415#104—1228no—
416#103—1224no—
417#102—1224no—
418C22⋊C8—1224no—
419C22⋊C8—1224no—
420#97—1224no—
421C4×C8—1224no—
422C24—1221no—
423C24#1175822611yescharacteristic
424#41—1222no—
425#41—1222no—
426#41—1222no—
427#41—1222no—
428#41—1222no—
429#41—1222no—
430#41—1222no—
431#41—1222no—
432#41—2441no—
433#41—2441no—
434#41—2441no—
435#41—2441no—
436#41—2441no—
437#41—2441no—
438#41—2441no—
439#41—2441no—
440C2×Q8—612no—
441C2×Q8—1221no—
442C2×Q8—1221no—
443C2×Q8—1221no—
444C2×Q8—1221no—
445C2×Q8—1221no—
446C2×D4—612no—
447C2×D4—1222no—
448C2×D4—1222no—
449C2×D4—1221no—
450C2×D4—1221no—
451C2×D4—1221no—
452C2×D4—1221no—
453C2×D4—1221no—
454C2×D4—2441no—
455C2×D4—2441no—
456C2×D4—2441no—
457C2×D4—2441no—
458C22×C4—1224no—
459C22×C4—1222no—
460C22×C4—1222no—
461C22×C4—1221no—
462C22×C4—1222no—
463C22×C4—1222no—
464C22×C4—2442no—
465C22×C4—2441no—
466C22×C4—2441no—
467C22×C4—2441no—
468C22×C4—2441no—
469C22×C4—2441no—
470C22×C4—2441no—
471C22×C4C2×C4×D6111yescharacteristic
472C22×C4C2×C4×D6111yescharacteristic
473C22×C4C2×C4×D6111yescharacteristic
474C22×C4C2×D24411yescharacteristic
475C22×C4#1175822211yescharacteristic
476C22×C4#1175822211yescharacteristic
477C22×C4D4×D6111yescharacteristic
478C22×C4D4×D6111yescharacteristic
479C22×C4D4×D6111yescharacteristic
480C22×C4D4×D6111yescharacteristic
481C22×C4#1175822411yescharacteristic
482C22×C4#1175822411yescharacteristic
483C22×C4#1175822611yescharacteristic
484C22×C4C2×C22⋊D6111yescharacteristic
485M16—22no—
486M16—22no—
487M16—22no—
488M16—22no—
489M16—22no—
490M16—41no—
491M16—41no—
492M16#1175819814yes—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—612no—
507C2×C8—612no—
508C2×C8—1222no—
509C2×C8—1222no—
510C2×C8—1221no—
511C2×C8—1221no—
512C2×C8—1222no—
513C2×C8—1222no—
514C2×C8—1221no—
515C2×C8—1221no—
516C4⋊C4—614no—
517C4⋊C4—1222no—
518C22⋊C4—1222no—
519C22⋊C4—1222no—
520C42—1222no—
521C42—1222no—
522C42—1222no—
523C42—1222no—
524C42—2441no—
525C42—2441no—
526C23—22no—
527C23—22no—
528C23—1222no—
529C23—2442no—
530C23—2442no—
531C23—2441no—
532C23—2441no—
533C23#1451973511yescharacteristic
534C23#1451973911yescharacteristic
535C23#1451973911yescharacteristic
536C23#1451975211yescharacteristic
537C23#1451976211yescharacteristic
538C23#1451976611yescharacteristic
539C23#1451977211yescharacteristic
540Q8—1222no—
541Q8—1222no—
542Q8—2441no—
543Q8—2441no—
544D4—1222no—
545D4—1222no—
546D4—2442no—
547D4—2442no—
548D4—2442no—
549D4—2442no—
550D4—2441no—
551D4—2441no—
552C2×C4—1224no—
553C2×C4—1222no—
554C2×C4—1224no—
555C2×C4—2444no—
556C2×C4—2442no—
557C2×C4—2444no—
558C2×C4—2442no—
559C2×C4—2442no—
560C2×C4—2441no—
561C2×C4—2441no—
562C2×C4—2442no—
563C2×C4—2442no—
564C2×C4—2442no—
565C2×C4—2442no—
566C2×C4—2442no—
567C2×C4C42×D6111yescharacteristic
568C2×C4C22⋊C4×D6111yescharacteristic
569C2×C4C22⋊C4×D6111yescharacteristic
570C2×C4C2×#1175819811yescharacteristic
571C2×C4#1451973411yescharacteristic
572C2×C4#1451973511yescharacteristic
573C2×C4#1451973711yescharacteristic
574C2×C4#1451973711yescharacteristic
575C2×C4#1451973711yescharacteristic
576C2×C4#1451973711yescharacteristic
577C2×C4C4×C22⋊D6111yescharacteristic
578C2×C4C4×C22⋊D6111yescharacteristic
579C2×C4#1451973911yescharacteristic
580C2×C4#1451973911yescharacteristic
581C2×C4C4×D24411yescharacteristic
582C2×C4C4×D24411yescharacteristic
583C2×C4#1451974711yescharacteristic
584C2×C4#1451974911yescharacteristic
585C2×C4#1451974911yescharacteristic
586C2×C4#1451975011yescharacteristic
587C2×C4#1451975011yescharacteristic
588C2×C4#1451975211yescharacteristic
589C2×C4#1451976111yescharacteristic
590C2×C4#1451976211yescharacteristic
591C2×C4#1451976311yescharacteristic
592C2×C4#1451976311yescharacteristic
593C2×C4#1451977211yescharacteristic
594C2×C4#1451977311yescharacteristic
595C8—24no—
596C8—42no—
597C8—42no—
598C8—1222no—
599C8—1222no—
600C22—22no—
601C22—22no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—22no—
607C22—22no—
608C22—4882no—
609C22—4882no—
610C22—2442no—
611C22—2442no—
612C22—2442no—
613C22#1683960911yescharacteristic
614C22#1683964011yescharacteristic
615C22#1683965111yescharacteristic
616C22#1683965211yescharacteristic
617C22#1683965211yescharacteristic
618C22#1683965411yescharacteristic
619C22#1683966311yescharacteristic
620C22#1683987812yes—
621C22#1683988312yes—
622C4—2444no—
623C4—2444no—
624C4—2442no—
625C4#1683960911yescharacteristic
626C4C4×#1175819811yescharacteristic
627C4#1683963911yescharacteristic
628C4#1683964011yescharacteristic
629C4#1683965111yescharacteristic
630C4#1683965411yescharacteristic
631C4#1683966211yescharacteristic
632C4#1683966211yescharacteristic
633C2—21no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—4882no—
638C2#2144405511yescharacteristic
639C2#2144565511yescharacteristic
640C2#2144566211yescharacteristic
641C2#2144614712yes—
642C2#2144646612yes—
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC2×C61×#341C2
socleC23×C61C4×D4
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenterC2×#341D61
hypocenterC61#10934
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#341

Complements

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

NH ≅ G/Ntype
4. C2×#16839720C2semidirect
5. C2×#16839523C2semidirect
6. C2×#16839516C2semidirect
7. C2×C61×#341C2semidirect
14. C2×#14519703C4semidirect
17. C2×#14519702C4semidirect
18. C2×#14519699C4semidirect
20. #16839730C4semidirect
316. C2×#341D61semidirect
354. C61#10934semidirect

Maximal subgroups

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

subgroupindex
C22×#145197032
C2×#168397592
C2×#168397302
C2×#168397202
C2×#168395232
C2×#168395162
C2×C61×#3412
#1093461