Finite Group Databasebeta

← #30603412

Subgroups — #30603412

Order 15616.

886 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519841C211yesmaximal, characteristic
2C2×#16840736C211yesmaximal, characteristic
3C2×#16840638C211yesmaximal, characteristic, complemented
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×#14519841—22no—
13C2×#14519841—22no—
14C2×#14519841—22no—
15#16840736—22no—
16#16840736—22no—
17C2×C22⋊#92420—22no—
18#16840638—22no—
19#16840632—22no—
20#16840628—22no—
21(C2×#6923)⋊C8—22no—
22C22×#11758224C2211yescharacteristic
23C22×C8×D61C2211yescharacteristic
24C2×#14519735C2211yescharacteristic
25#16839755—22no—
26#16839755—22no—
27C2×#14519702C411yescharacteristic, complemented
28C2×#14519700C411yescharacteristic, complemented
29C2×#14519698C411yescharacteristic, complemented
30C2×#102×C61C411yescharacteristic, complemented
31C23×#6923—21no—
32C2×#11758213—21no—
33C2×#11758213—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×#11758213D412yes—
43C2×#11758213D412yes—
44C2×D61⋊C8—21no—
45C2×D61⋊C8—21no—
46C2×D61⋊C8—21no—
47C2×D61⋊C8—21no—
48C2×D61⋊C8—21no—
49C2×D61⋊C8—21no—
50C22×#92420—21no—
51C22×#92420—21no—
52C22×#92420D412yes—
53C2×C4×#6923—21no—
54C2×C4×#6923—21no—
55C2×C4×#6923—21no—
56C2×C4×#6923—21no—
57C2×C4×#6923—21no—
58C2×C4×#6923D412yes—
59#14519841—28no—
60C22⋊#92420—28no—
61C2×#11758224—21no—
62C2×#11758224—21no—
63C2×#11758224—21no—
64C2×#11758224—21no—
65C2×#11758224—21no—
66C2×#11758224—21no—
67C2×#11758224—21no—
68C2×#11758224—21no—
69C2×#11758224—21no—
70C2×#11758224—21no—
71C2×#11758224D412yes—
72C2×#11758224D412yes—
73C22×Dic122C2×C411yescharacteristic
74C22×C22⋊D61—21no—
75C23×Dic61—21no—
76C22×C4×D61C2311yescharacteristic
77C22×#92418C2×C411yescharacteristic
78C2×C8×D61—21no—
79C2×C8×D61—21no—
80C2×C8×D61—21no—
81C2×C8×D61—21no—
82C2×C8×D61—21no—
83C2×C8×D61—21no—
84#14519735—21no—
85#14519735—21no—
86#14519735—21no—
87#14519735—21no—
88C2×C4⋊Dic61C2×C411yescharacteristic
89C2×#11758198—21no—
90C2×C4×Dic61—21no—
91#14519702—22no—
92#14519700—22no—
93#14519698—22no—
94C22×D4×C61C2×C411yescharacteristic
95C22×C8×C61C2×C411yescharacteristic
96C2×C4⋊C4×C61C2×C411yescharacteristic
97#102×C61—22no—
98C24×C61—21no—
99C23×D61#4111yescharacteristic
100C22×#6923—22no—
101C22×#6923—22no—
102C22×#6923—22no—
103C22×#6923—41no—
104C22×#6923—41no—
105C22×#6923—41no—
106C22×#6923—41no—
107C2×D4×C61—21no—
108C2×D4×C61—21no—
109C2×D4×C61—21no—
110C2×D4×C61—21no—
111C2×D4×C61—21no—
112C2×D4×C61C22⋊C412yes—
113C22×C4×C61—21no—
114C22×C4×C61C22×C411yescharacteristic
115C2×C22⋊D61—22no—
116C2×C22⋊D61—22no—
117C2×C22⋊D61—41no—
118C2×C22⋊D61—41no—
119C2×C22⋊D61—41no—
120C2×C22⋊D61—41no—
121C22×Dic61—21no—
122C22×Dic61—22no—
123C22×Dic61—22no—
124C22×Dic61—21no—
125C22×Dic61—41no—
126C22×Dic61—41no—
127C22×Dic61—41no—
128C22×Dic61—41no—
129C22×Dic61C2×D411yescharacteristic
130#11758224—22no—
131#11758224—22no—
132#11758224—22no—
133#11758224—22no—
134#11758224—22no—
135#11758224—22no—
136#11758224—22no—
137#11758224—22no—
138#11758224—41no—
139#11758224—41no—
140#11758224—41no—
141#11758224—41no—
142#11758224—41no—
143#11758224—41no—
144#11758224—41no—
145#11758224—41no—
146C2×C4×D61C2×D411yescharacteristic
147C2×C4×D61C2×D411yescharacteristic
148C2×C4×D61C2×D411yescharacteristic
149C2×C4×D61C2×D411yescharacteristic
150C2×C4×D61C2×D411yescharacteristic
151C2×C4×D61#4111yescharacteristic
152C2×C4×D61#4111yescharacteristic
153C2×C4×D61#4111yescharacteristic
154C2×C4×D61#4111yescharacteristic
155C2×C4×D61#4111yescharacteristic
156C2×C4×D61#4111yescharacteristic
157C2×C4×D61#4111yescharacteristic
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—21no—
162C2×Dic122—21no—
163C2×Dic122C22⋊C412yes—
164C2×#92420—22no—
165C2×#92420—22no—
166C2×#92420—22no—
167C2×#92420—22no—
168C2×#92420—22no—
169C2×#92420—41no—
170C2×#92420—41no—
171C2×#92420—41no—
172C2×#92420—41no—
173C4×#6923—22no—
174C4×#6923—22no—
175C4×#6923—41no—
176C4×#6923—41no—
177#11758213—22no—
178#11758213—22no—
179#11758213—22no—
180#11758213—22no—
181#11758213—41no—
182#11758213—41no—
183#11758213—41no—
184#11758213—41no—
185D61⋊C8—41no—
186D61⋊C8—41no—
187D61⋊C8—41no—
188D61⋊C8—41no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—21no—
194#11758198—41no—
195#11758198—41no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4×Dic61—41no—
199C4×Dic61—41no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C8×D61—41no—
204C8×D61—41no—
205C8×D61—41no—
206C8×D61—41no—
207C23×C61—22no—
208C23×C61—41no—
209C23×C61—41no—
210C23×C61—41no—
211C23×C61—41no—
212C23×C61—41no—
213C23×C61—41no—
214C23×C61C4×D411yescharacteristic
215C22×D61—21no—
216C22×D61—21no—
217C22×D61—21no—
218C22×D61—21no—
219C22×D61#12111yescharacteristic
220C22×D61#12311yescharacteristic
221C22×D61#12311yescharacteristic
222C22×D61#12411yescharacteristic
223C22×D61#12611yescharacteristic
224C22×D61#12611yescharacteristic
225C2×#6923—24no—
226C2×#6923—42no—
227C2×#6923—42no—
228C2×#6923—42no—
229C2×#6923—42no—
230C2×#6923—42no—
231C2×#6923—42no—
232D4×C61—22no—
233D4×C61—22no—
234D4×C61—41no—
235D4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61C2×C22⋊C411yescharacteristic
240C2×C4×C61#11711yescharacteristic
241C2×C4×C61#11711yescharacteristic
242C2×C4×C61C4×D411yescharacteristic
243C2×C4×C61C4×D411yescharacteristic
244C2×C4×C61C4×D411yescharacteristic
245C22⋊D61—42no—
246C22⋊D61—42no—
247C22⋊D61—42no—
248C22⋊D61—42no—
249C2×Dic61—22no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—42no—
253C2×Dic61—42no—
254C2×Dic61—42no—
255C2×Dic61—42no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61#12011yescharacteristic
260C2×Dic61#12111yescharacteristic
261C2×Dic61#12111yescharacteristic
262C2×Dic61#12111yescharacteristic
263C2×Dic61#12311yescharacteristic
264C2×Dic61#12411yescharacteristic
265C4×D61#12011yescharacteristic
266C4×D61#12111yescharacteristic
267C4×D61#12111yescharacteristic
268C4×D61#12111yescharacteristic
269C4×D61#12111yescharacteristic
270C4×D61#12311yescharacteristic
271C4×D61#12311yescharacteristic
272C4×D61#12311yescharacteristic
273C4×D61#12311yescharacteristic
274C4×D61#12311yescharacteristic
275C4×D61#12311yescharacteristic
276C4×D61#12311yescharacteristic
277C4×D61#12411yescharacteristic
278C4×D61#12411yescharacteristic
279C4×D61#12611yescharacteristic
280C4×D61#12611yescharacteristic
281Dic122—22no—
282Dic122—22no—
283Dic122—41no—
284Dic122—41no—
285#92420—42no—
286#92420—42no—
287#92420—42no—
288C8×C61—41no—
289#92418—41no—
290#11191—611nomaximal, Sylow
291C22×C61—42no—
292C22×C61—42no—
293C22×C61—42no—
294C22×C61—81no—
295C22×C61—81no—
296C22×C61—81no—
297C22×C61—81no—
298C22×C61#38611yescharacteristic
299C22×C61#38811yescharacteristic
300C22×C61#38811yescharacteristic
301C22×C61#44311yescharacteristic
302C22×C61#44311yescharacteristic
303C22×C61#44411yescharacteristic
304C22×C61#44411yescharacteristic
305C2×D61—21no—
306C2×D61—21no—
307C2×D61—21no—
308C2×D61—21no—
309C2×D61—21no—
310C2×D61—21no—
311C2×D61—21no—
312C2×D61—21no—
313C2×D61—21no—
314C2×D61—21no—
315C2×D61—21no—
316C2×D61—21no—
317C2×D61#39411yescharacteristic
318C2×D61#39711yescharacteristic
319C2×D61#39711yescharacteristic
320C2×D61#39711yescharacteristic
321#6923—44no—
322C4×C61—81no—
323C4×C61#38111yescharacteristic
324C4×C61#38611yescharacteristic
325C4×C61#38811yescharacteristic
326C4×C61#38811yescharacteristic
327Dic61—42no—
328Dic61—81no—
329Dic61#39411yescharacteristic
330Dic61#39411yescharacteristic
331Dic61#39411yescharacteristic
332Dic61#39711yescharacteristic
333C22×#104—611no—
334C2×#416—611no—
335C2×#408—611no—
336C2×#341—611no—
337C2×#339—611no—
338#1729—611no—
339C2×#336—611no—
340C2×C61—82no—
341C2×C61#144011yescharacteristic
342C2×C61#187611yescharacteristic
343C2×C61#187611yescharacteristic
344C2×C61#192911yescharacteristic
345C2×C61#192911yescharacteristic
346C2×C61#193711yescharacteristic
347C2×C61#193811yescharacteristic
348D61—21no—
349D61—21no—
350D61—21no—
351D61—21no—
352C22×#41—611no—
353C22×M16—611no—
354C22×M16—611no—
355C23×C8—611no—
356C23×C8—611no—
357C2×#117—611no—
358C22×C42—611no—
359C2×#104—1222no—
360C2×#104—1222no—
361C2×#104—1222no—
362#416—1222no—
363#416—1222no—
364C2×#103—611no—
365C2×#103—611no—
366C2×#102—611no—
367C2×#102#692311yescharacteristic, complemented
368#408—1222no—
369#408—1222no—
370C2×C22⋊C8—1222no—
371#341—1222no—
372#339—1222no—
373#336—1222no—
374#336—1222no—
375C61#1119111yescharacteristic, complemented, Sylow
376C2×#41—612no—
377C2×#41—612no—
378C2×#41—1221no—
379C2×#41—1221no—
380C2×#41—1221no—
381C2×#41—1221no—
382C2×#41—1221no—
383C2×#41—1221no—
384C2×#41—1221no—
385C2×#41—1221no—
386C2×#41—1221no—
387C2×#41—1221no—
388C22×Q8—611no—
389C22×D4—1221no—
390C22×D4C2×#692311yescharacteristic
391C23×C4—611no—
392C23×C4—1221no—
393C23×C4—1221no—
394C2×M16—612no—
395C2×M16—612no—
396C2×M16—1221no—
397C2×M16—1221no—
398C2×M16—1221no—
399C2×M16—1221no—
400C2×M16—1221no—
401C2×M16—1221no—
402C2×M16—1221no—
403C2×M16—1221no—
404C2×M16—1221no—
405C2×M16—1221no—
406C22×C8—612no—
407C22×C8—611no—
408C22×C8—1221no—
409C22×C8—1221no—
410C22×C8—1221no—
411C22×C8—1221no—
412C22×C8—1221no—
413C22×C8—1221no—
414C22×C8—1221no—
415C22×C8—1221no—
416C22×C8—1221no—
417C22×C8—1221no—
418C22×C8—1221no—
419C22×C8—1221no—
420C22×C8—1221no—
421C22×C8—1221no—
422C22×C8C2×#692311yescharacteristic
423#117—1221no—
424#117—1221no—
425#117—1221no—
426#117—1221no—
427C2×C4⋊C4—611no—
428C2×C4⋊C4C2×#692311yescharacteristic
429C2×C22⋊C4—1221no—
430C2×C42—612no—
431C2×C42—1221no—
432C2×C42—1221no—
433C2×C42—1221no—
434C2×C42—1221no—
435C2×C42—1221no—
436C2×C42—1221no—
437#104—1228no—
438#103—1222no—
439#103—1222no—
440#102—22no—
441#102—1222no—
442C22⋊C8—1228no—
443C24—21no—
444C24—611no—
445#41—1222no—
446#41—1222no—
447#41—1222no—
448#41—1222no—
449#41—1222no—
450#41—1222no—
451#41—1222no—
452#41—1222no—
453#41—2441no—
454#41—2441no—
455#41—2441no—
456#41—2441no—
457#41—2441no—
458#41—2441no—
459#41—2441no—
460#41—2441no—
461C2×Q8—612no—
462C2×Q8—1221no—
463C2×Q8—1221no—
464C2×Q8—1221no—
465C2×Q8—1221no—
466C2×Q8—1221no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—1222no—
473C2×D4—1222no—
474C2×D4—2441no—
475C2×D4—2441no—
476C2×D4—2441no—
477C2×D4—2441no—
478C2×D4C22⋊#692312yes—
479C22×C4—21no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—611no—
490C22×C4—611no—
491C22×C4—611no—
492C22×C4—611no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—1221no—
499C22×C4—1221no—
500C22×C4—2441no—
501C22×C4—2441no—
502C22×C4—2441no—
503C22×C4—2441no—
504C22×C4—2441no—
505C22×C4—2441no—
506C22×C4—2441no—
507C22×C4—2441no—
508C22×C4C22×#692311yescharacteristic
509M16—1222no—
510M16—1222no—
511M16—1222no—
512M16—1222no—
513M16—2441no—
514M16—2441no—
515M16—2441no—
516M16—2441no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—1222no—
521C2×C8—1222no—
522C2×C8—1222no—
523C2×C8—1222no—
524C2×C8—1222no—
525C2×C8—1221no—
526C2×C8—1221no—
527C2×C8—1221no—
528C2×C8—2441no—
529C2×C8—2441no—
530C2×C8—2441no—
531C2×C8—2441no—
532C2×C8—2441no—
533C2×C8—2441no—
534C2×C8—2441no—
535C2×C8—2441no—
536C2×C8—2441no—
537C2×C8—2441no—
538C2×C8—2441no—
539C2×C8—2441no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—1221no—
543C4⋊C4—1221no—
544C22⋊C4—2441no—
545C22⋊C4—2441no—
546C42—1222no—
547C42—1222no—
548C42—2441no—
549C42—2441no—
550C42—2441no—
551C42—2441no—
552C23—22no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—611no—
560C23—611no—
561C23—611no—
562C23—611no—
563C23—611no—
564C23—611no—
565C23—1221no—
566C23—1221no—
567C23—1221no—
568C23—1221no—
569C23D4×#692311yescharacteristic
570Q8—1222no—
571Q8—1222no—
572Q8—2441no—
573Q8—2441no—
574D4—22no—
575D4—22no—
576D4—41no—
577D4—41no—
578D4—2442no—
579D4—2442no—
580D4—2442no—
581D4—2442no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—611no—
586C2×C4—611no—
587C2×C4—611no—
588C2×C4—611no—
589C2×C4—611no—
590C2×C4—611no—
591C2×C4—611no—
592C2×C4—611no—
593C2×C4—611no—
594C2×C4—611no—
595C2×C4—611no—
596C2×C4—611no—
597C2×C4—611no—
598C2×C4—611no—
599C2×C4—611no—
600C2×C4—611no—
601C2×C4—611no—
602C2×C4—611no—
603C2×C4—611no—
604C2×C4—611no—
605C2×C4—611no—
606C2×C4—611no—
607C2×C4—1224no—
608C2×C4—1222no—
609C2×C4—2442no—
610C2×C4—2442no—
611C2×C4—2442no—
612C2×C4—2442no—
613C2×C4—2441no—
614C2×C4—2441no—
615C2×C4—2441no—
616C2×C4—2442no—
617C2×C4—2442no—
618C2×C4—2442no—
619C2×C4—2442no—
620C2×C4—2442no—
621C2×C4—2442no—
622C2×C4—2441no—
623C2×C4—2441no—
624C2×C4C2×C22⋊#692311yescharacteristic
625C2×C4#1451985611yescharacteristic
626C2×C4#1451985611yescharacteristic
627C2×C4D4×#692311yescharacteristic
628C2×C4D4×#692311yescharacteristic
629C2×C4D4×#692311yescharacteristic
630C8—41no—
631C8—2442no—
632C8—2442no—
633C8—2442no—
634C8—2441no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—611no—
643C22—611no—
644C22—611no—
645C22—611no—
646C22—1221no—
647C22—1221no—
648C22—1221no—
649C22—1221no—
650C22—1221no—
651C22—1221no—
652C22—1221no—
653C22—1221no—
654C22—1221no—
655C22—1221no—
656C22—1221no—
657C22—1221no—
658C22#1684071011yescharacteristic
659C22#1684071211yescharacteristic
660C22#1684071211yescharacteristic
661C22#1684080411yescharacteristic
662C22#1684080511yescharacteristic
663C22#1684080711yescharacteristic
664C22#1684080911yescharacteristic
665C4—81no—
666C4—611no—
667C4—611no—
668C4—611no—
669C4—611no—
670C4—4881no—
671C4—2444no—
672C4—2442no—
673C4#1684070511yescharacteristic
674C4#1684071011yescharacteristic
675C4#1684071211yescharacteristic
676C4#1684071211yescharacteristic
677C2—82no—
678C2—1221no—
679C2—1221no—
680C2—1221no—
681C2—1221no—
682C2#2146100311yescharacteristic
683C2#2146180811yescharacteristic
684C2#2146181011yescharacteristic
685C2#2146190011yescharacteristic
686C2#2146190111yescharacteristic
687C2#2146191311yescharacteristic
688C2#2146191511yescharacteristic
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#11191
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
3. C2×#16840638C2semidirect
4. C2×#16840632C2semidirect
5. #21461486C2semidirect
6. C2×(C2×#6923)⋊C8C2semidirect
27. C2×#14519702C4semidirect
28. C2×#14519700C4semidirect
29. C2×#14519698C4semidirect
30. C2×#102×C61C4semidirect
367. C2×#102#6923semidirect
375. C61#11191semidirect

Maximal subgroups

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

subgroupindex
C22×#145198412
C2×#168407362
C2×#168406382
C2×#168406322
#214614862
C2×(C2×#6923)⋊C82
C2×#168397552
#1119161