Finite Group Databasebeta

← #30603327

Subgroups — #30603327

Order 15616.

930 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519848C211yesmaximal, characteristic, complemented
2C22×#14519841C211yesmaximal, characteristic
3C2×#16840736C211yesmaximal, characteristic
4C2×#16840632C211yesmaximal, characteristic, complemented
5#21461486C211yesmaximal, characteristic, complemented
6C2×(C2×#6923)⋊C8C211yesmaximal, characteristic, complemented
7C2×#16839755C211yesmaximal, characteristic
8C22×#11758213C2211yescharacteristic
9C22×#11758213C2211yescharacteristic
10C22×D61⋊C8C2211yescharacteristic
11C22×C4×#6923C2211yescharacteristic
12C2×#14519848—22no—
13C2×#14519848—22no—
14C2×#14519848—22no—
15C2×#14519841—22no—
16C2×#14519841—22no—
17C2×#14519841—22no—
18#16840736—22no—
19#16840736—22no—
20C2×C22⋊#92420—22no—
21#16840632—22no—
22#16840628—22no—
23(C2×#6923)⋊C8—22no—
24C22×#11758224C2211yescharacteristic
25C22×C8×D61C2211yescharacteristic
26C2×#14519735C2211yescharacteristic
27#16839755—22no—
28#16839755—22no—
29C2×#14519702C411yescharacteristic, complemented
30C2×#14519700C411yescharacteristic, complemented
31C2×#14519698C411yescharacteristic, complemented
32C2×#102×C61C411yescharacteristic, complemented
33C23×#6923—21no—
34C2×#11758213—21no—
35C2×#11758213—21no—
36C2×#11758213—21no—
37C2×#11758213—21no—
38C2×#11758213—21no—
39C2×#11758213—21no—
40C2×#11758213—21no—
41C2×#11758213—21no—
42C2×#11758213—21no—
43C2×#11758213—21no—
44C2×#11758213D412yes—
45C2×#11758213D412yes—
46C2×D61⋊C8—21no—
47C2×D61⋊C8—21no—
48C2×D61⋊C8—21no—
49C2×D61⋊C8—21no—
50C2×D61⋊C8—21no—
51C2×D61⋊C8—21no—
52C22×#92420—21no—
53C22×#92420—21no—
54C22×#92420D412yes—
55C2×C4×#6923—21no—
56C2×C4×#6923—21no—
57C2×C4×#6923—21no—
58C2×C4×#6923—21no—
59C2×C4×#6923—21no—
60C2×C4×#6923D412yes—
61#14519848—28no—
62#14519841—28no—
63C22⋊#92420—28no—
64C2×#11758224—21no—
65C2×#11758224—21no—
66C2×#11758224—21no—
67C2×#11758224—21no—
68C2×#11758224—21no—
69C2×#11758224—21no—
70C2×#11758224—21no—
71C2×#11758224—21no—
72C2×#11758224—21no—
73C2×#11758224—21no—
74C2×#11758224D412yes—
75C2×#11758224Q812yes—
76C22×Dic122C2×C411yescharacteristic
77C22×C22⋊D61—21no—
78C23×Dic61—21no—
79C22×C4×D61C2311yescharacteristic
80C22×#92418C2×C411yescharacteristic
81C2×C8×D61—21no—
82C2×C8×D61—21no—
83C2×C8×D61—21no—
84C2×C8×D61—21no—
85C2×C8×D61D412yes—
86C2×C8×D61D412yes—
87#14519735—21no—
88#14519735—21no—
89#14519735—21no—
90#14519735—21no—
91C2×C4⋊Dic61C2×C411yescharacteristic
92C2×#11758198—21no—
93C2×C4×Dic61—21no—
94#14519702—22no—
95#14519700—22no—
96#14519698—22no—
97C22×D4×C61C2×C411yescharacteristic
98C22×C8×C61C2×C411yescharacteristic
99C2×C4⋊C4×C61C2×C411yescharacteristic
100#102×C61—22no—
101C24×C61—21no—
102C23×D61#4111yescharacteristic
103C22×#6923—24no—
104C22×#6923—22no—
105C22×#6923—42no—
106C22×#6923—41no—
107C22×#6923—41no—
108C2×D4×C61—21no—
109C2×D4×C61—21no—
110C2×D4×C61—21no—
111C2×D4×C61—21no—
112C2×D4×C61—21no—
113C2×D4×C61C4⋊C412yes—
114C22×C4×C61—21no—
115C22×C4×C61C22×C411yescharacteristic
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—21no—
123C22×Dic61—22no—
124C22×Dic61—22no—
125C22×Dic61—21no—
126C22×Dic61—41no—
127C22×Dic61—41no—
128C22×Dic61—41no—
129C22×Dic61—41no—
130C22×Dic61C2×D411yescharacteristic
131#11758224—22no—
132#11758224—22no—
133#11758224—22no—
134#11758224—22no—
135#11758224—22no—
136#11758224—22no—
137#11758224—22no—
138#11758224—22no—
139#11758224—41no—
140#11758224—41no—
141#11758224—41no—
142#11758224—41no—
143#11758224—41no—
144#11758224—41no—
145#11758224—41no—
146#11758224—41no—
147C2×C4×D61C2×D411yescharacteristic
148C2×C4×D61C2×D411yescharacteristic
149C2×C4×D61C2×D411yescharacteristic
150C2×C4×D61C2×D411yescharacteristic
151C2×C4×D61C2×D411yescharacteristic
152C2×C4×D61C2×D411yescharacteristic
153C2×C4×D61C2×Q811yescharacteristic
154C2×C4×D61#4111yescharacteristic
155C2×C4×D61#4111yescharacteristic
156C2×C4×D61#4111yescharacteristic
157C2×C4×D61#4111yescharacteristic
158C2×C4×D61#4111yescharacteristic
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—21no—
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122C4⋊C412yes—
165C2×#92420—22no—
166C2×#92420—22no—
167C2×#92420—22no—
168C2×#92420—22no—
169C2×#92420—22no—
170C2×#92420—41no—
171C2×#92420—41no—
172C2×#92420—41no—
173C2×#92420—41no—
174C4×#6923—22no—
175C4×#6923—22no—
176C4×#6923—41no—
177C4×#6923—41no—
178#11758213—22no—
179#11758213—22no—
180#11758213—22no—
181#11758213—22no—
182#11758213—41no—
183#11758213—41no—
184#11758213—41no—
185#11758213—41no—
186D61⋊C8—41no—
187D61⋊C8—41no—
188D61⋊C8—41no—
189D61⋊C8—41no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61C22⋊C412yes—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195#11758198—41no—
196#11758198—41no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4×Dic61—41no—
200C4×Dic61—41no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418C22⋊C412yes—
204C8×D61—22no—
205C8×D61—22no—
206C8×D61—22no—
207C8×D61—22no—
208C23×C61—22no—
209C23×C61—41no—
210C23×C61—41no—
211C23×C61—42no—
212C23×C61—42no—
213C23×C61C4×D411yescharacteristic
214C22×D61—22no—
215C22×D61—22no—
216C22×D61#12111yescharacteristic
217C22×D61C22⋊Q811yescharacteristic
218C22×D61#12311yescharacteristic
219C22×D61#12411yescharacteristic
220C22×D61#12411yescharacteristic
221C22×D61#12611yescharacteristic
222C2×#6923—24no—
223C2×#6923—44no—
224C2×#6923—44no—
225C2×#6923—42no—
226C2×#6923—42no—
227D4×C61—22no—
228D4×C61—22no—
229D4×C61—41no—
230D4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—42no—
233C2×C4×C61C2×C22⋊C411yescharacteristic
234C2×C4×C61C2×C4⋊C411yescharacteristic
235C2×C4×C61#11711yescharacteristic
236C2×C4×C61C4×D411yescharacteristic
237C2×C4×C61C4×D411yescharacteristic
238C2×C4×C61C4×D411yescharacteristic
239C22⋊D61—42no—
240C22⋊D61—42no—
241C22⋊D61—42no—
242C22⋊D61—42no—
243C2×Dic61—22no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—42no—
247C2×Dic61—42no—
248C2×Dic61—42no—
249C2×Dic61—42no—
250C2×Dic61—41no—
251C2×Dic61—42no—
252C2×Dic61#12011yescharacteristic
253C2×Dic61#12111yescharacteristic
254C2×Dic61#12111yescharacteristic
255C2×Dic61C22⋊Q811yescharacteristic
256C2×Dic61#12311yescharacteristic
257C2×Dic61#12711yescharacteristic
258C4×D61#12011yescharacteristic
259C4×D61#12011yescharacteristic
260C4×D61#12111yescharacteristic
261C4×D61#12111yescharacteristic
262C4×D61#12111yescharacteristic
263C4×D61#12111yescharacteristic
264C4×D61#12111yescharacteristic
265C4×D61C22⋊Q811yescharacteristic
266C4×D61C22⋊Q811yescharacteristic
267C4×D61C22⋊Q811yescharacteristic
268C4×D61C22⋊Q811yescharacteristic
269C4×D61#12311yescharacteristic
270C4×D61#12311yescharacteristic
271C4×D61#12311yescharacteristic
272C4×D61#12411yescharacteristic
273C4×D61#12611yescharacteristic
274Dic122—22no—
275Dic122—22no—
276Dic122—41no—
277Dic122—41no—
278#92420—42no—
279#92420—42no—
280#92420—42no—
281C8×C61—22no—
282#92418—22no—
283#11125—611nomaximal, Sylow
284C22×C61—44no—
285C22×C61—42no—
286C22×C61—82no—
287C22×C61—81no—
288C22×C61—81no—
289C22×C61#38511yescharacteristic
290C22×C61#38811yescharacteristic
291C22×C61#39011yescharacteristic
292C22×C61#44312yes—
293C22×C61#44412yes—
294C2×D61—22no—
295C2×D61—22no—
296C2×D61—22no—
297C2×D61—22no—
298C2×D61—21no—
299C2×D61—21no—
300C2×D61—21no—
301C2×D61—21no—
302C2×D61#39311yescharacteristic
303C2×D61#39411yescharacteristic
304C2×D61#39611yescharacteristic
305C2×D61#39711yescharacteristic
306#6923—44no—
307C4×C61—81no—
308C4×C61#38011yescharacteristic
309C4×C61#38511yescharacteristic
310C4×C61#38611yescharacteristic
311C4×C61#38811yescharacteristic
312Dic61—42no—
313Dic61—81no—
314Dic61#39211yescharacteristic
315Dic61#39411yescharacteristic
316Dic61#39611yescharacteristic
317Dic61#39911yescharacteristic
318C22×#108—611no—
319C22×#104—611no—
320C2×#416—611no—
321C2×#408—611no—
322C2×#339—611no—
323#1729—611no—
324C2×#336—611no—
325C2×C61—82no—
326C2×C61#143911yescharacteristic
327C2×C61#186612yes—
328C2×C61#192912yes—
329C2×C61#197411yescharacteristic
330C2×C61#197511yescharacteristic
331D61—21no—
332D61—21no—
333D61—21no—
334D61—21no—
335C22×#41—611no—
336C22×M16—611no—
337C22×M16—611no—
338C23×C8—611no—
339C23×C8—611no—
340C2×#117—611no—
341C22×C42—611no—
342C2×#108—1222no—
343C2×#108—1222no—
344C2×#108—1222no—
345C2×#104—1222no—
346C2×#104—1222no—
347C2×#104—1222no—
348#416—1222no—
349#416—1222no—
350C2×#103—611no—
351C2×#103—611no—
352C2×#102—611no—
353C2×#102#692311yescharacteristic, complemented
354#408—1222no—
355#408—1222no—
356C2×C22⋊C8—1222no—
357#339—1222no—
358#336—1222no—
359#336—1222no—
360C61#1112511yescharacteristic, complemented, Sylow
361C2×#41—612no—
362C2×#41—612no—
363C2×#41—1221no—
364C2×#41—1221no—
365C2×#41—1221no—
366C2×#41—1221no—
367C2×#41—1221no—
368C2×#41—1221no—
369C2×#41—1221no—
370C2×#41—1221no—
371C2×#41—1221no—
372C2×#41—1221no—
373C22×Q8—611no—
374C22×D4—1221no—
375C22×D4C2×#692311yescharacteristic
376C23×C4—611no—
377C23×C4—1221no—
378C23×C4—1221no—
379C2×M16—612no—
380C2×M16—612no—
381C2×M16—1221no—
382C2×M16—1221no—
383C2×M16—1221no—
384C2×M16—1221no—
385C2×M16—1221no—
386C2×M16—1221no—
387C2×M16—1221no—
388C2×M16—1221no—
389C2×M16—1221no—
390C2×M16—1221no—
391C22×C8—611no—
392C22×C8—612no—
393C22×C8—612no—
394C22×C8—612no—
395C22×C8—1221no—
396C22×C8—1221no—
397C22×C8—1221no—
398C22×C8—1221no—
399C22×C8—1221no—
400C22×C8—1221no—
401C22×C8—1221no—
402C22×C8—1221no—
403C22×C8—1221no—
404C22×C8—1221no—
405C22×C8—1221no—
406C22×C8—1221no—
407C22×C8C2×#692311yescharacteristic
408#117—1221no—
409#117—1221no—
410#117—1221no—
411#117—1221no—
412C2×C4⋊C4—611no—
413C2×C4⋊C4C2×#692311yescharacteristic
414C2×C22⋊C4—1221no—
415C2×C42—612no—
416C2×C42—1221no—
417C2×C42—1221no—
418C2×C42—1221no—
419C2×C42—1221no—
420C2×C42—1221no—
421C2×C42—1221no—
422#108—1228no—
423#104—1228no—
424#103—1222no—
425#103—1222no—
426#102—22no—
427#102—1222no—
428C22⋊C8—1228no—
429C24—21no—
430C24—611no—
431#41—1222no—
432#41—1222no—
433#41—1222no—
434#41—1222no—
435#41—1222no—
436#41—1222no—
437#41—1222no—
438#41—1222no—
439#41—2441no—
440#41—2441no—
441#41—2441no—
442#41—2441no—
443#41—2441no—
444#41—2441no—
445#41—2441no—
446#41—2441no—
447C2×Q8—612no—
448C2×Q8—1221no—
449C2×Q8—1221no—
450C2×Q8—1221no—
451C2×Q8—1221no—
452C2×Q8—1221no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—1222no—
459C2×D4—1222no—
460C2×D4—2441no—
461C2×D4—2441no—
462C2×D4—2441no—
463C2×D4—2441no—
464C2×D4C4⋊#692312yes—
465C22×C4—21no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—1222no—
480C22×C4—1222no—
481C22×C4—1222no—
482C22×C4—1224no—
483C22×C4—1221no—
484C22×C4—1221no—
485C22×C4—2441no—
486C22×C4—2441no—
487C22×C4—2441no—
488C22×C4—2441no—
489C22×C4—2441no—
490C22×C4—2441no—
491C22×C4—2442no—
492C22×C4C22×#692311yescharacteristic
493M16—1222no—
494M16—1222no—
495M16—1222no—
496M16—1222no—
497M16—2441no—
498M16—2441no—
499M16—2441no—
500M16—2441no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—612no—
504C2×C8—1222no—
505C2×C8—1222no—
506C2×C8—1222no—
507C2×C8—1222no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—1222no—
511C2×C8—1222no—
512C2×C8—1222no—
513C2×C8—1222no—
514C2×C8—1222no—
515C2×C8—2441no—
516C2×C8—2441no—
517C2×C8—2441no—
518C2×C8—2441no—
519C2×C8—2441no—
520C2×C8—2441no—
521C2×C8—2441no—
522C2×C8—2441no—
523C2×C8C22⋊#692312yes—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—1221no—
527C4⋊C4—1221no—
528C22⋊C4—2441no—
529C22⋊C4—2441no—
530C42—1222no—
531C42—1222no—
532C42—2441no—
533C42—2441no—
534C42—2441no—
535C42—2441no—
536C23—22no—
537C23—41no—
538C23—41no—
539C23—42no—
540C23—42no—
541C23—611no—
542C23—611no—
543C23—611no—
544C23—611no—
545C23—611no—
546C23—611no—
547C23—1222no—
548C23—1222no—
549C23D4×#692311yescharacteristic
550Q8—1222no—
551Q8—1222no—
552Q8—2441no—
553Q8—2441no—
554D4—22no—
555D4—22no—
556D4—41no—
557D4—41no—
558D4—2442no—
559D4—2442no—
560D4—2442no—
561D4—2442no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—611no—
565C2×C4—611no—
566C2×C4—611no—
567C2×C4—611no—
568C2×C4—611no—
569C2×C4—611no—
570C2×C4—611no—
571C2×C4—611no—
572C2×C4—611no—
573C2×C4—611no—
574C2×C4—611no—
575C2×C4—611no—
576C2×C4—611no—
577C2×C4—611no—
578C2×C4—611no—
579C2×C4—611no—
580C2×C4—611no—
581C2×C4—611no—
582C2×C4—611no—
583C2×C4—611no—
584C2×C4—611no—
585C2×C4—611no—
586C2×C4—1224no—
587C2×C4—1222no—
588C2×C4—2442no—
589C2×C4—2442no—
590C2×C4—2442no—
591C2×C4—2442no—
592C2×C4—2441no—
593C2×C4—2442no—
594C2×C4—2442no—
595C2×C4—2444no—
596C2×C4—2444no—
597C2×C4—2442no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4C2×C22⋊#692311yescharacteristic
601C2×C4C2×C4⋊#692311yescharacteristic
602C2×C4#1451985611yescharacteristic
603C2×C4D4×#692311yescharacteristic
604C2×C4D4×#692311yescharacteristic
605C2×C4D4×#692311yescharacteristic
606C8—22no—
607C8—1222no—
608C8—2442no—
609C8—2442no—
610C8—2442no—
611C22—42no—
612C22—44no—
613C22—82no—
614C22—81no—
615C22—81no—
616C22—611no—
617C22—611no—
618C22—611no—
619C22—611no—
620C22—1222no—
621C22—1222no—
622C22—1222no—
623C22—1222no—
624C22—1221no—
625C22—1221no—
626C22—1221no—
627C22—1221no—
628C22#1684070911yescharacteristic
629C22#1684071211yescharacteristic
630C22#1684071411yescharacteristic
631C22#1684080412yes—
632C22#1684080712yes—
633C4—81no—
634C4—611no—
635C4—611no—
636C4—611no—
637C4—611no—
638C4—4881no—
639C4—2444no—
640C4—2442no—
641C4#1684070411yescharacteristic
642C4#1684070911yescharacteristic
643C4#1684071011yescharacteristic
644C4#1684071211yescharacteristic
645C2—82no—
646C2—1221no—
647C2—1221no—
648C2—1221no—
649C2—1221no—
650C2#2146100211yescharacteristic
651C2#2146178612yes—
652C2#2146190012yes—
653C2#2146197211yescharacteristic
654C2#2146197511yescharacteristic
subgroupG/H
centerC23D4×#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#102×C61C4
socleC23×C61C4×D4
prime radicalC22×#11758224C22
cosocleC22×C4×D61C23
hypercenterC2×#102#6923
hypocenterC61#11125
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×#14519848C2semidirect
4. C2×#16840632C2semidirect
5. #21461486C2semidirect
6. C2×(C2×#6923)⋊C8C2semidirect
29. C2×#14519702C4semidirect
30. C2×#14519700C4semidirect
31. C2×#14519698C4semidirect
32. C2×#102×C61C4semidirect
353. C2×#102#6923semidirect
360. C61#11125semidirect

Maximal subgroups

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

subgroupindex
C22×#145198482
C22×#145198412
C2×#168407362
C2×#168406322
#214614862
C2×(C2×#6923)⋊C82
C2×#168397552
#1112561