Finite Group Databasebeta

← #29586328

Subgroups — #29586328

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×#14519705C211yesmaximal, characteristic
2C2×#16839759C211yesmaximal, characteristic
3C2×#16839728C211yesmaximal, characteristic
4C2×#16839717C211yesmaximal, characteristic, complemented
5C2×#16839527C211yesmaximal, characteristic, complemented
6C2×#16839522C211yesmaximal, characteristic, complemented
7C2×C61×#336C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C2×#14519736C2211yescharacteristic
12C2×#14519705—22no—
13C2×#14519705—22no—
14C2×#14519705C414yescomplemented
15#16839759—22no—
16#16839759—22no—
17C2×#14519702C412yescomplemented
18C2×#14519699C412yescomplemented
19#16839728—22no—
20#16839728C414yescomplemented
21C2×#14519689—21no—
22C2×#14519689—21no—
23#16839717—22no—
24#16839717—22no—
25C2×#14519687—21no—
26C2×C8×Dic61—21no—
27#16839527—22no—
28#16839522—22no—
29C23×C8×C61C2211yescharacteristic
30C23×C8×C61C2211yescharacteristic
31C22×C42×C61C2211yescharacteristic
32C61×#336—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×#11758194—21no—
53C2×#11758194—21no—
54C2×#11758194—21no—
55C2×#11758194—21no—
56C2×#11758194—21no—
57C2×#11758194C2×C412yes—
58C2×#11758194C2×C412yes—
59C2×#11758194D412yes—
60C2×#11758194D412yes—
61C22×#92418—21no—
62C22×#92418—21no—
63#14519736—21no—
64#14519736—21no—
65#14519736D412yes—
66#14519736D412yes—
67C2×C4⋊Dic61C2×C412yes—
68C2×C22⋊Dic61—21no—
69C2×C4×Dic61—21no—
70#14519705—28no—
71#14519702—24no—
72#14519699—24no—
73#14519689—24no—
74#14519689—24no—
75#14519687—24no—
76C8×Dic61—24no—
77C23×C4×C61—21no—
78C23×C4×C61C2311yescharacteristic
79C22×C8×C61—21no—
80C22×C8×C61—21no—
81C22×C8×C61—21no—
82C22×C8×C61—21no—
83C22×C8×C61—21no—
84C22×C8×C61—21no—
85C22×C8×C61—21no—
86C22×C8×C61—21no—
87C22×C8×C61—21no—
88C22×C8×C61—21no—
89C22×C8×C61C2×C412yes—
90C22×C8×C61C2×C412yes—
91C22×C8×C61D411yescharacteristic
92C22×C8×C61D411yescharacteristic
93C22×C8×C61D412yes—
94C2×C42×C61—21no—
95C2×C42×C61—21no—
96C2×C42×C61—21no—
97C2×C42×C61—21no—
98C2×C42×C61—21no—
99C2×C42×C61C2×C412yes—
100C24×C61#4111yescharacteristic
101C23×D61—21no—
102C22×C4×C61—24no—
103C22×C4×C61—22no—
104C22×C4×C61—42no—
105C22×C4×C61—41no—
106C22×C4×C61—41no—
107C22×C4×C61C22×C411yescharacteristic
108C22×C4×C61C22×C411yescharacteristic
109C22×C4×C61C22×C411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61#4111yescharacteristic
117C22×C4×C61#4111yescharacteristic
118C22×C4×C61#4111yescharacteristic
119C22×C4×C61#4111yescharacteristic
120C22×C4×C61#4111yescharacteristic
121C2×C22⋊D61—22no—
122C2×C22⋊D61—22no—
123C2×C22⋊D61—41no—
124C2×C22⋊D61—41no—
125C2×C22⋊D61—41no—
126C2×C22⋊D61—41no—
127C22×Dic61—21no—
128C22×Dic61—22no—
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—
163C2×C8×C61—22no—
164C2×C8×C61—22no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—22no—
168C2×C8×C61—22no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—22no—
172C2×C8×C61—22no—
173C2×C8×C61—22no—
174C2×C8×C61—41no—
175C2×C8×C61—41no—
176C2×C8×C61—41no—
177C2×C8×C61—41no—
178C2×C8×C61C22⋊C412yes—
179C2×C8×C61C22⋊C412yes—
180C42×C61—22no—
181C42×C61—22no—
182C42×C61—41no—
183C42×C61—41no—
184C22⋊Dic61—22no—
185C22⋊Dic61—22no—
186C4⋊Dic61—22no—
187C4⋊Dic61C22⋊C414yes—
188C4×Dic61—22no—
189C4×Dic61—22no—
190#11758194—22no—
191#11758194—22no—
192#11758194—22no—
193#11758194—22no—
194#11758194—22no—
195#11758194—41no—
196#11758194—41no—
197#11758194C22⋊C414yes—
198C2×#92418—22no—
199C2×#92418—22no—
200C2×#92418—22no—
201C2×#92418—22no—
202C2×#92418—41no—
203C2×#92418—41no—
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×C61—24no—
219C2×C4×C61—44no—
220C2×C4×C61—44no—
221C2×C4×C61—42no—
222C2×C4×C61—42no—
223C2×C4×C61C2×C4211yescharacteristic
224C2×C4×C61C2×C22⋊C411yescharacteristic
225C2×C4×C61C2×C22⋊C411yescharacteristic
226C2×C4×C61C2×C22⋊C411yescharacteristic
227C2×C4×C61#11711yescharacteristic
228C2×C4×C61#11711yescharacteristic
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×C61C4×D411yescharacteristic
236C2×C4×C61C4×D411yescharacteristic
237C2×C4×C61C4×D411yescharacteristic
238C2×C4×C61C4×D411yescharacteristic
239C2×C4×C61#12011yescharacteristic
240C2×C4×C61#12111yescharacteristic
241C2×C4×C61#12111yescharacteristic
242C2×C4×C61#12111yescharacteristic
243C2×C4×C61#12111yescharacteristic
244C2×C4×C61#12111yescharacteristic
245C2×C4×C61#12311yescharacteristic
246C2×C4×C61#12311yescharacteristic
247C2×C4×C61#12411yescharacteristic
248C2×C4×C61#12411yescharacteristic
249C2×C4×C61#12611yescharacteristic
250C2×C4×C61#12711yescharacteristic
251C22⋊D61—42no—
252C22⋊D61—42no—
253C22⋊D61—42no—
254C22⋊D61—42no—
255C2×Dic61—22no—
256C2×Dic61—24no—
257C2×Dic61—41no—
258C2×Dic61—41no—
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—22no—
274C8×C61—22no—
275C8×C61—42no—
276#92418—24no—
277#92418—42no—
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×C61—44no—
302C4×C61C4×C22⋊C411yescharacteristic
303C4×C61C4×C22⋊C411yescharacteristic
304C4×C61#38611yescharacteristic
305C4×C61#38611yescharacteristic
306C4×C61#38811yescharacteristic
307C4×C61#38811yescharacteristic
308C4×C61#39011yescharacteristic
309C4×C61#39011yescharacteristic
310Dic61—44no—
311Dic61—42no—
312C22×#104—611no—
313C2×#416—611no—
314C2×#408—611no—
315C2×#405—611no—
316C2×#341—611no—
317C2×#339—611no—
318C2×#336D6111yescharacteristic, complemented
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×M16—611no—
331C22×M16—611no—
332C23×C8C2×D6111yescharacteristic
333C23×C8C2×D6111yescharacteristic
334C2×#117—611no—
335C22×C42C2×D6111yescharacteristic
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—1222no—
352#339—1222no—
353#336—22no—
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—21no—
371C23×C4—1221no—
372C23×C4C22×D6111yescharacteristic
373C2×M16—612no—
374C2×M16—612no—
375C2×M16—612no—
376C2×M16—612no—
377C2×M16—1221no—
378C2×M16—1221no—
379C2×M16—1221no—
380C2×M16—1221no—
381C2×M16—1221no—
382C2×M16—1221no—
383C2×M16—1221no—
384C2×M16—1221no—
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—21no—
394C22×C8—21no—
395C22×C8—1221no—
396C22×C8—1221no—
397C22×C8C4×D6112yes—
398C22×C8C4×D6112yes—
399C22×C8D24411yescharacteristic
400C22×C8D24411yescharacteristic
401C22×C8C22⋊D6112yes—
402#117—612no—
403#117—612no—
404#117—1221no—
405#117—1221no—
406C2×C4⋊C4—612no—
407C2×C22⋊C4—1221no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—1221no—
414C2×C42C4×D6112yes—
415#104—1228no—
416#103—1224no—
417#102—1224no—
418C22⋊C8—1224no—
419C22⋊C8—1224no—
420#97—1224no—
421C4×C8—1224no—
422C24—1221no—
423C24#1175822211yescharacteristic
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—24no—
459C22×C4—22no—
460C22×C4—42no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—1222no—
464C22×C4—1221no—
465C22×C4—1222no—
466C22×C4—1222no—
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×C4D4×D6111yescharacteristic
477C22×C4D4×D6111yescharacteristic
478C22×C4D4×D6111yescharacteristic
479C22×C4D4×D6111yescharacteristic
480C22×C4#1175822411yescharacteristic
481C22×C4#1175822411yescharacteristic
482C22×C4#1175822611yescharacteristic
483C22×C4#1175822611yescharacteristic
484C22×C4C2×C22⋊D6111yescharacteristic
485M16—614no—
486M16—1222no—
487M16—1222no—
488M16—1222no—
489M16—1222no—
490M16—1222no—
491M16—2441no—
492M16—2441no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—1222no—
509C2×C8—1222no—
510C2×C8—1222no—
511C2×C8—1222no—
512C2×C8—2441no—
513C2×C8—2441no—
514C2×C8#1175819812yes—
515C2×C8#1175819812yes—
516C4⋊C4—614no—
517C4⋊C4—1222no—
518C22⋊C4—1222no—
519C22⋊C4—1222no—
520C42—22no—
521C42—22no—
522C42—41no—
523C42—41no—
524C42—1222no—
525C42—1222no—
526C23—22no—
527C23—22no—
528C23—1222no—
529C23—2442no—
530C23—2442no—
531C23—2441no—
532C23—2441no—
533C23#1451973411yescharacteristic
534C23C4×C22⋊D6111yescharacteristic
535C23C4×D24411yescharacteristic
536C23#1451975011yescharacteristic
537C23#1451976211yescharacteristic
538C23#1451976311yescharacteristic
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—24no—
553C2×C4—44no—
554C2×C4—42no—
555C2×C4—44no—
556C2×C4—42no—
557C2×C4—1222no—
558C2×C4—1224no—
559C2×C4—2442no—
560C2×C4—2442no—
561C2×C4—2441no—
562C2×C4—2441no—
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#1451973511yescharacteristic
572C2×C4#1451973511yescharacteristic
573C2×C4#1451973711yescharacteristic
574C2×C4#1451973711yescharacteristic
575C2×C4#1451973711yescharacteristic
576C2×C4#1451973711yescharacteristic
577C2×C4C4×C22⋊D6111yescharacteristic
578C2×C4#1451973911yescharacteristic
579C2×C4#1451973911yescharacteristic
580C2×C4#1451973911yescharacteristic
581C2×C4#1451973911yescharacteristic
582C2×C4C4×D24411yescharacteristic
583C2×C4#1451974711yescharacteristic
584C2×C4#1451974911yescharacteristic
585C2×C4#1451974911yescharacteristic
586C2×C4#1451975011yescharacteristic
587C2×C4#1451975211yescharacteristic
588C2×C4#1451975211yescharacteristic
589C2×C4#1451976111yescharacteristic
590C2×C4#1451976211yescharacteristic
591C2×C4#1451976311yescharacteristic
592C2×C4#1451976611yescharacteristic
593C2×C4#1451977211yescharacteristic
594C2×C4#1451977311yescharacteristic
595C8—22no—
596C8—22no—
597C8—42no—
598C8—1224no—
599C8—2442no—
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—
613C22C4×#1175819811yescharacteristic
614C22#1683964011yescharacteristic
615C22#1683965111yescharacteristic
616C22#1683965111yescharacteristic
617C22#1683965211yescharacteristic
618C22#1683965411yescharacteristic
619C22#1683966211yescharacteristic
620C22#1683988012yes—
621C22#1683988512yes—
622C4—44no—
623C4—2444no—
624C4—2442no—
625C4#1683960911yescharacteristic
626C4#1683960911yescharacteristic
627C4#1683963911yescharacteristic
628C4#1683964011yescharacteristic
629C4#1683965211yescharacteristic
630C4#1683965411yescharacteristic
631C4#1683966211yescharacteristic
632C4#1683966311yescharacteristic
633C2—21no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—4882no—
638C2#2144405511yescharacteristic
639C2#2144565611yescharacteristic
640C2#2144566311yescharacteristic
641C2#2144614512yes—
642C2#2144646812yes—
subgroupG/H
centerC22×C4C2×D244
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC2×C61×#336C2
socleC23×C61C4×D4
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenterC2×#336D61
hypocenterC61#10934
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
4. C2×#16839717C2semidirect
5. C2×#16839527C2semidirect
6. C2×#16839522C2semidirect
7. C2×C61×#336C2semidirect
14. C2×#14519705C4semidirect
17. C2×#14519702C4semidirect
18. C2×#14519699C4semidirect
20. #16839728C4semidirect
318. C2×#336D61semidirect
354. C61#10934semidirect

Maximal subgroups

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

subgroupindex
C22×#145197052
C2×#168397592
C2×#168397282
C2×#168397172
C2×#168395272
C2×#168395222
C2×C61×#3362
#1093461