Finite Group Databasebeta

← #29586394

Subgroups — #29586394

Order 15616.

946 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×#16839778C211yesmaximal, characteristic
2C22×#14519705C211yesmaximal, characteristic
3C2×#16839744C211yesmaximal, characteristic
4C2×#16839534C211yesmaximal, characteristic, complemented
5#21445545C211yesmaximal, characteristic, complemented
6C2×#16839522C211yesmaximal, characteristic, complemented
7C2×C4×M16×C61C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C2×#14519736C2211yescharacteristic
12#16839778—22no—
13#16839778C414yescomplemented
14C2×#14519705—22no—
15C2×#14519705—21no—
16C2×#14519705—21no—
17C2×#14519705C414yescomplemented
18C2×#14519703—22no—
19#16839744—22no—
20#16839744—22no—
21C2×#14519695C412yescomplemented
22C2×#14519693C412yescomplemented
23#16839534—22no—
24#16839526—22no—
25#16839522—22no—
26C22×M16×C61C2211yescharacteristic
27C22×M16×C61C2211yescharacteristic
28C22×C42×C61C2211yescharacteristic
29C4×M16×C61—22no—
30C4×M16×C61—22no—
31C2×#97×C61—21no—
32C2×C4×C8×C61—21no—
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×#11758194—21no—
58C2×#11758194—21no—
59C2×#11758194C2×C412yes—
60C2×#11758194C2×C412yes—
61C22×#92418—21no—
62C22×#92418—21no—
63#14519736—21no—
64#14519736—21no—
65#14519736—21no—
66#14519736C2×C412yes—
67C2×C4⋊Dic61—21no—
68C2×C22⋊Dic61—21no—
69C2×C4×Dic61—21no—
70#14519705—24no—
71#14519705—24no—
72#14519703—28no—
73#14519695—24no—
74#14519693—24no—
75C23×C4×C61—21no—
76C23×C4×C61C2311yescharacteristic
77C2×M16×C61—21no—
78C2×M16×C61—21no—
79C2×M16×C61—21no—
80C2×M16×C61—21no—
81C2×M16×C61—21no—
82C2×M16×C61—21no—
83C2×M16×C61C2×C412yes—
84C2×M16×C61C2×C412yes—
85C2×M16×C61D412yes—
86C2×M16×C61D412yes—
87C2×M16×C61D412yes—
88C2×M16×C61D412yes—
89C22×C8×C61—21no—
90C22×C8×C61—21no—
91C2×C42×C61—21no—
92C2×C42×C61—21no—
93C2×C42×C61—21no—
94C2×C42×C61C2×C412yes—
95C2×C42×C61D412yes—
96C2×C42×C61D411yescharacteristic
97C2×C42×C61D411yescharacteristic
98#97×C61—24no—
99C4×C8×C61—24no—
100C24×C61#4111yescharacteristic
101C23×D61—21no—
102C22×C4×C61—21no—
103C22×C4×C61—22no—
104C22×C4×C61—22no—
105C22×C4×C61—21no—
106C22×C4×C61—44no—
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—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—22no—
169M16×C61C22⋊C414yes—
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—
177C42×C61—22no—
178C42×C61—21no—
179C42×C61—21no—
180C42×C61—22no—
181C42×C61C22⋊C412yes—
182C42×C61C22⋊C412yes—
183C22⋊Dic61—22no—
184C22⋊Dic61—41no—
185C4⋊Dic61—22no—
186C4⋊Dic61—41no—
187C4×Dic61—22no—
188C4×Dic61—41no—
189#11758194—22no—
190#11758194—22no—
191#11758194—22no—
192#11758194—22no—
193#11758194—41no—
194#11758194—41no—
195#11758194—41no—
196#11758194—41no—
197C2×#92418—22no—
198C2×#92418—22no—
199C2×#92418—41no—
200C2×#92418—41no—
201C2×#92418—41no—
202C2×#92418—41no—
203C23×C61—42no—
204C23×C61#11711yescharacteristic
205C23×C61C4×D411yescharacteristic
206C23×C61C4×D411yescharacteristic
207C23×C61#12111yescharacteristic
208C23×C61#12311yescharacteristic
209C23×C61#12411yescharacteristic
210C23×C61#12611yescharacteristic
211C22×D61—22no—
212C22×D61—41no—
213C22×D61—41no—
214C22×D61—82no—
215C2×C4×C61—24no—
216C2×C4×C61—22no—
217C2×C4×C61—22no—
218C2×C4×C61—44no—
219C2×C4×C61—44no—
220C2×C4×C61—42no—
221C2×C4×C61C2×C4211yescharacteristic
222C2×C4×C61C2×C22⋊C411yescharacteristic
223C2×C4×C61C2×C22⋊C411yescharacteristic
224C2×C4×C61C2×C22⋊C411yescharacteristic
225C2×C4×C61#11711yescharacteristic
226C2×C4×C61#11711yescharacteristic
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×C61C4×D411yescharacteristic
236C2×C4×C61C4×D411yescharacteristic
237C2×C4×C61#12011yescharacteristic
238C2×C4×C61#12111yescharacteristic
239C2×C4×C61#12111yescharacteristic
240C2×C4×C61#12111yescharacteristic
241C2×C4×C61#12111yescharacteristic
242C2×C4×C61#12111yescharacteristic
243C2×C4×C61#12311yescharacteristic
244C2×C4×C61#12311yescharacteristic
245C2×C4×C61#12411yescharacteristic
246C2×C4×C61#12411yescharacteristic
247C2×C4×C61#12611yescharacteristic
248C2×C4×C61#12711yescharacteristic
249C22⋊D61—42no—
250C22⋊D61—42no—
251C22⋊D61—42no—
252C22⋊D61—42no—
253C2×Dic61—22no—
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—24no—
271C8×C61—24no—
272#92418—42no—
273#92418—42no—
274#10946—611nomaximal, Sylow
275C22×C61—22no—
276C22×C61—22no—
277C22×C61—22no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61C4×C22⋊C411yescharacteristic
283C22×C61#38611yescharacteristic
284C22×C61#38811yescharacteristic
285C22×C61#38811yescharacteristic
286C22×C61#38811yescharacteristic
287C22×C61#38811yescharacteristic
288C22×C61#39011yescharacteristic
289C2×D61—42no—
290C2×D61—82no—
291C2×D61—82no—
292C2×D61—82no—
293C4×C61—24no—
294C4×C61—42no—
295C4×C61C4×C22⋊C411yescharacteristic
296C4×C61C4×C22⋊C411yescharacteristic
297C4×C61#38611yescharacteristic
298C4×C61#38611yescharacteristic
299C4×C61#38811yescharacteristic
300C4×C61#38811yescharacteristic
301C4×C61#39011yescharacteristic
302C4×C61#39011yescharacteristic
303Dic61—42no—
304Dic61—82no—
305C2×#421—611no—
306C22×#104—611no—
307C2×#413—611no—
308C2×C4×M16D6111yescharacteristic, complemented
309C2×#344—611no—
310#1738—611no—
311C2×#339—611no—
312C2×C61—21no—
313C2×C61—21no—
314C2×C61—21no—
315C2×C61—21no—
316C2×C61—21no—
317C2×C61—21no—
318C2×C61#143711yescharacteristic
319C2×C61#193212yes—
320D61—82no—
321C22×#41—611no—
322C22×M16—611no—
323C22×M16—611no—
324C22×M16C2×D6111yescharacteristic
325C22×M16C2×D6111yescharacteristic
326C2×#117—611no—
327C22×C42C2×D6111yescharacteristic
328#421—614no—
329#421—1222no—
330C2×#104—614no—
331C2×#104—1222no—
332C2×#104—1222no—
333C2×#104—1221no—
334C2×#104—1221no—
335#413—1222no—
336#413—1222no—
337C2×#101—612no—
338C2×#100—612no—
339C4×M16—22no—
340C4×M16—22no—
341C2×#97—21no—
342C2×C4×C8—21no—
343#344—1222no—
344#341—1222no—
345#339—1222no—
346C61#1094611yescharacteristic, 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—21no—
363C23×C4—1221no—
364C23×C4C22×D6111yescharacteristic
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—612no—
372C2×M16—612no—
373C2×M16—1221no—
374C2×M16—1221no—
375C2×M16—1221no—
376C2×M16—1221no—
377C2×M16—1221no—
378C2×M16—1221no—
379C2×M16—1221no—
380C2×M16—1221no—
381C2×M16—1221no—
382C2×M16—1221no—
383C2×M16C4×D6112yes—
384C2×M16C4×D6112yes—
385C2×M16D24412yes—
386C2×M16D24412yes—
387C2×M16C22⋊D6112yes—
388C2×M16C22⋊D6112yes—
389C22×C8—21no—
390C22×C8—21no—
391C22×C8—1221no—
392C22×C8—1221no—
393#117—612no—
394#117—1221no—
395#117—1221no—
396#117—1221no—
397C2×C4⋊C4—1221no—
398C2×C22⋊C4—1221no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—1221no—
403C2×C42C4×D6112yes—
404C2×C42D24412yes—
405C2×C42C22⋊D6111yescharacteristic
406C2×C42C22⋊D6111yescharacteristic
407#104—1228no—
408#104—1224no—
409#104—1224no—
410#101—1224no—
411#100—1224no—
412#97—24no—
413C4×C8—24no—
414C24—1221no—
415C24#1175822211yescharacteristic
416#41—1222no—
417#41—1222no—
418#41—1222no—
419#41—1222no—
420#41—1222no—
421#41—1222no—
422#41—1222no—
423#41—1222no—
424#41—2441no—
425#41—2441no—
426#41—2441no—
427#41—2441no—
428#41—2441no—
429#41—2441no—
430#41—2441no—
431#41—2441no—
432C2×Q8—612no—
433C2×Q8—1221no—
434C2×Q8—1221no—
435C2×Q8—1221no—
436C2×Q8—1221no—
437C2×Q8—1221no—
438C2×D4—612no—
439C2×D4—1222no—
440C2×D4—1222no—
441C2×D4—1221no—
442C2×D4—1221no—
443C2×D4—1221no—
444C2×D4—1221no—
445C2×D4—1221no—
446C2×D4—2441no—
447C2×D4—2441no—
448C2×D4—2441no—
449C2×D4—2441no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—44no—
455C22×C4—1221no—
456C22×C4—1222no—
457C22×C4—1222no—
458C22×C4—2441no—
459C22×C4—2441no—
460C22×C4—2441no—
461C22×C4—2441no—
462C22×C4—2441no—
463C22×C4C2×C4×D6111yescharacteristic
464C22×C4C2×C4×D6111yescharacteristic
465C22×C4C2×C4×D6111yescharacteristic
466C22×C4C2×D24411yescharacteristic
467C22×C4C2×D24411yescharacteristic
468C22×C4C2×D24411yescharacteristic
469C22×C4#1175822211yescharacteristic
470C22×C4#1175822211yescharacteristic
471C22×C4#1175822211yescharacteristic
472C22×C4#1175822211yescharacteristic
473C22×C4#1175822211yescharacteristic
474C22×C4C2×C22⋊D6111yescharacteristic
475C22×C4C2×C22⋊D6111yescharacteristic
476C22×C4C2×C22⋊D6111yescharacteristic
477M16—22no—
478M16—22no—
479M16—22no—
480M16—22no—
481M16—22no—
482M16—22no—
483M16—1222no—
484M16—1222no—
485M16—1222no—
486M16—1222no—
487M16—2441no—
488M16—2441no—
489M16—2441no—
490M16—2441no—
491M16#1175819814yes—
492M16#1175819814yes—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—1222no—
500C2×C8—1222no—
501C2×C8—2441no—
502C2×C8—2441no—
503C2×C8—2441no—
504C2×C8—2441no—
505C4⋊C4—1222no—
506C4⋊C4—2441no—
507C22⋊C4—1222no—
508C22⋊C4—2441no—
509C42—22no—
510C42—21no—
511C42—21no—
512C42—22no—
513C42—1222no—
514C42—2441no—
515C42#1175819812yes—
516C42#1175819812yes—
517C23—42no—
518C23—1222no—
519C23—4882no—
520C23—2441no—
521C23—2441no—
522C23#1451973411yescharacteristic
523C23C4×C22⋊D6111yescharacteristic
524C23C4×D24411yescharacteristic
525C23#1451975111yescharacteristic
526C23#1451976011yescharacteristic
527C23#1451976511yescharacteristic
528C23#1451977111yescharacteristic
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—24no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—44no—
545C2×C4—44no—
546C2×C4—42no—
547C2×C4—1222no—
548C2×C4—4882no—
549C2×C4—2442no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2442no—
553C2×C4—2442no—
554C2×C4—2442no—
555C2×C4—2442no—
556C2×C4C42×D6111yescharacteristic
557C2×C4C2×#1175819811yescharacteristic
558C2×C4C2×#1175819811yescharacteristic
559C2×C4C2×#1175819811yescharacteristic
560C2×C4#1451973411yescharacteristic
561C2×C4#1451973411yescharacteristic
562C2×C4C4×C22⋊D6111yescharacteristic
563C2×C4C4×C22⋊D6111yescharacteristic
564C2×C4C4×C22⋊D6111yescharacteristic
565C2×C4C4×C22⋊D6111yescharacteristic
566C2×C4C4×C22⋊D6111yescharacteristic
567C2×C4C4×D24411yescharacteristic
568C2×C4C4×D24411yescharacteristic
569C2×C4C4×D24411yescharacteristic
570C2×C4C4×D24411yescharacteristic
571C2×C4C4×D24411yescharacteristic
572C2×C4#1451974611yescharacteristic
573C2×C4#1451975111yescharacteristic
574C2×C4#1451975111yescharacteristic
575C2×C4#1451975111yescharacteristic
576C2×C4#1451975111yescharacteristic
577C2×C4#1451975111yescharacteristic
578C2×C4#1451976011yescharacteristic
579C2×C4#1451976011yescharacteristic
580C2×C4#1451976511yescharacteristic
581C2×C4#1451976511yescharacteristic
582C2×C4#1451977111yescharacteristic
583C2×C4#1451977411yescharacteristic
584C8—24no—
585C8—24no—
586C8—2442no—
587C8—2442no—
588C22—22no—
589C22—22no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—4882no—
596C22—4882no—
597C22—4882no—
598C22—2442no—
599C22C4×#1175819811yescharacteristic
600C22#1683964111yescharacteristic
601C22#1683965311yescharacteristic
602C22#1683965311yescharacteristic
603C22#1683965311yescharacteristic
604C22#1683965311yescharacteristic
605C22#1683966411yescharacteristic
606C4—24no—
607C4—42no—
608C4—4882no—
609C4—2442no—
610C4C4×#1175819811yescharacteristic
611C4C4×#1175819811yescharacteristic
612C4#1683964111yescharacteristic
613C4#1683964111yescharacteristic
614C4#1683965311yescharacteristic
615C4#1683965311yescharacteristic
616C4#1683966411yescharacteristic
617C4#1683966411yescharacteristic
618C2—21no—
619C2—21no—
620C2—21no—
621C2—21no—
622C2—21no—
623C2—21no—
624C2—4882no—
625C2#2144405711yescharacteristic
626C2#2144648812yes—
subgroupG/H
centerC2×C4#14519751
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC2×C4×M16×C61C2
socleC22×C61#388
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenterC2×C4×M16D61
hypocenterC61#10946
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C4×M16

Complements

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

NH ≅ G/Ntype
4. C2×#16839534C2semidirect
5. #21445545C2semidirect
6. C2×#16839522C2semidirect
7. C2×C4×M16×C61C2semidirect
13. #16839778C4semidirect
17. C2×#14519705C4semidirect
21. C2×#14519695C4semidirect
22. C2×#14519693C4semidirect
308. C2×C4×M16D61semidirect
346. C61#10946semidirect

Maximal subgroups

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

subgroupindex
C2×#168397782
C22×#145197052
C2×#168397442
C2×#168395342
#214455452
C2×#168395222
C2×C4×M16×C612
#1094661