Finite Group Databasebeta

← #30603423

Subgroups — #30603423

Order 15616.

1186 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊(C22⋊C8)C211yesmaximal, characteristic
2C2×#16840704C211yesmaximal, characteristic
3C2×#16840635C212yesmaximal, complemented
4C2×#16840635C212yesmaximal, complemented
5#380×D61C211yesmaximal, characteristic
6C22×D61⋊C8C2212yes—
7C22×C4⋊#6923C2212yes—
8C22×C22⋊#6923—21no—
9C2×#14519834—21no—
10D61⋊(C22⋊C8)—24no—
11C2×C22⋊#92420—21no—
12#16840704—24no—
13C2×(C2×#6923)⋊C4—21no—
14#16840635—24no—
15#16840635—24no—
16C23×C4×D61C2211yescharacteristic
17C2×C4⋊C4×D61C2211yescharacteristic
18C2×C4⋊C4×D61C2211yescharacteristic
19C2×C22⋊C4×D61—21no—
20#16839622C411yescharacteristic, complemented
21#16839621—21no—
22#16839620—21no—
23#16839619C411yescharacteristic, complemented
24#16839619C411yescharacteristic, complemented
25#95×D61—21no—
26C61×#380C411yescharacteristic, complemented
27C23×#6923—22no—
28C2×D61⋊C8—22no—
29C2×D61⋊C8—22no—
30C2×D61⋊C8—22no—
31C2×D61⋊C8—22no—
32C2×D61⋊C8—22no—
33C2×D61⋊C8D414yes—
34C22×#92420—22no—
35C2×C4⋊#6923—22no—
36C2×C4⋊#6923—22no—
37C2×C4⋊#6923—22no—
38C2×C4⋊#6923—22no—
39C2×C4⋊#6923—22no—
40C2×C4⋊#6923D414yes—
41C2×C22⋊#6923—24no—
42C2×C22⋊#6923—42no—
43C2×C22⋊#6923—42no—
44#14519834—24no—
45C22⋊#92420—24no—
46(C2×#6923)⋊C4—24no—
47C24×D61D411yescharacteristic
48C23×Dic61D411yescharacteristic
49C22×C4×D61—22no—
50C22×C4×D61—22no—
51C22×C4×D61—22no—
52C22×C4×D61—22no—
53C22×C4×D61—22no—
54C22×C4×D61—22no—
55C22×C4×D61—21no—
56C22×C4×D61—21no—
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61D411yescharacteristic
59C22×C4×D61D411yescharacteristic
60C22×C4×D61C2311yescharacteristic
61C2×C4⋊Dic61C2×C411yescharacteristic
62C2×C4⋊Dic61C2×C411yescharacteristic
63C2×#11758196—21no—
64C2×#11758196—21no—
65C4⋊C4×D61—22no—
66C4⋊C4×D61—22no—
67C4⋊C4×D61—22no—
68C4⋊C4×D61—22no—
69C2×C22⋊Dic61—21no—
70C2×#11758198—21no—
71C2×#11758198—21no—
72C22⋊C4×D61—44no—
73#14519684—21no—
74#14519684—21no—
75#14519684—21no—
76C23×C4×C61C2×C411yescharacteristic
77C2×C4⋊C4×C61C2×C411yescharacteristic
78C2×C4⋊C4×C61C2×C411yescharacteristic
79C2×C22⋊C4×C61—21no—
80#95×C61—21no—
81C24×C61C22⋊C411yescharacteristic
82C23×D61—21no—
83C23×D61—22no—
84C23×D61—22no—
85C23×D61—21no—
86C23×D61—22no—
87C23×D61—21no—
88C23×D61—22no—
89C23×D61—21no—
90C23×D61C22⋊C411yescharacteristic
91C23×D61SD1612yes—
92C23×D61Q1612yes—
93C23×D61C2×D411yescharacteristic
94C22×#6923—24no—
95C22×#6923—42no—
96C22×#6923—42no—
97C22×#6923—42no—
98C22×#6923—42no—
99C22×#6923—42no—
100C22×#6923—42no—
101C22×C4×C61—21no—
102C22×C4×C61—21no—
103C22×C4×C61—22no—
104C22×C4×C61—22no—
105C22×C4×C61—21no—
106C22×C4×C61—21no—
107C22×C4×C61C22⋊C411yescharacteristic
108C22×C4×C61C22×C411yescharacteristic
109C22×Dic61—21no—
110C22×Dic61—22no—
111C22×Dic61—22no—
112C22×Dic61—21no—
113C22×Dic61—21no—
114C22×Dic61—21no—
115C22×Dic61C22⋊C411yescharacteristic
116C22×Dic61C2×D411yescharacteristic
117C2×C4×D61—21no—
118C2×C4×D61—22no—
119C2×C4×D61—22no—
120C2×C4×D61—21no—
121C2×C4×D61—21no—
122C2×C4×D61—21no—
123C2×C4×D61—22no—
124C2×C4×D61—22no—
125C2×C4×D61—21no—
126C2×C4×D61—22no—
127C2×C4×D61—22no—
128C2×C4×D61—21no—
129C2×C4×D61—42no—
130C2×C4×D61—42no—
131C2×C4×D61—42no—
132C2×C4×D61—42no—
133C2×C4×D61—42no—
134C2×C4×D61—42no—
135C2×C4×D61—42no—
136C2×C4×D61—42no—
137C2×C4×D61—41no—
138C2×C4×D61—42no—
139C2×C4×D61—41no—
140C2×C4×D61—42no—
141C2×C4×D61—41no—
142C2×C4×D61—42no—
143C2×C4×D61—42no—
144C2×C4×D61—41no—
145C2×C4×D61C2×D412yes—
146C2×C4×D61C2×D412yes—
147C2×C4×D61#4112yes—
148C2×C4×D61#4112yes—
149C2×C4×D61#4112yes—
150C2×C4×D61#4112yes—
151C22⋊#6923—48no—
152C2×#92420—24no—
153C2×#92420—42no—
154C2×#92420—42no—
155C4⋊#6923—24no—
156C4⋊#6923—24no—
157C4⋊#6923—42no—
158C4⋊#6923—42no—
159D61⋊C8—24no—
160D61⋊C8—24no—
161D61⋊C8—42no—
162D61⋊C8—42no—
163C4⋊C4×C61—22no—
164C4⋊C4×C61—22no—
165C22⋊C4×C61—42no—
166C22⋊Dic61—42no—
167#11758198—42no—
168#11758198—42no—
169C4⋊Dic61—22no—
170C4⋊Dic61—22no—
171#11758196—41no—
172#11758196—42no—
173#11758196—41no—
174C23×C61—21no—
175C23×C61—21no—
176C23×C61—21no—
177C23×C61—21no—
178C23×C61—21no—
179C23×C61—21no—
180C23×C61#10312yes—
181C23×C61C2×C22⋊C411yescharacteristic
182C22×D61—21no—
183C22×D61—21no—
184C22×D61—21no—
185C22×D61—21no—
186C22×D61—21no—
187C22×D61—21no—
188C22×D61—22no—
189C22×D61—22no—
190C22×D61—24no—
191C22×D61—24no—
192C22×D61—24no—
193C22×D61—22no—
194C22×D61—24no—
195C22×D61—22no—
196C22×D61—42no—
197C22×D61—42no—
198C22×D61—42no—
199C22×D61—42no—
200C22×D61—42no—
201C22×D61—42no—
202C22×D61—42no—
203C22×D61—42no—
204C22×D61#10312yes—
205C22×D61#12011yescharacteristic
206C22×D61#12112yes—
207C22×D61#12312yes—
208C22×D61#12311yescharacteristic
209C22×D61C2×SD1611yescharacteristic
210C22×D61C2×Q1611yescharacteristic
211C22×D61#13512yes—
212C22×D61AGL(1,ℤ/8)12yes—
213C22×D61AGL(1,ℤ/8)11yescharacteristic
214C22×D61#13711yescharacteristic
215C2×#6923—44no—
216C2×#6923—44no—
217C2×#6923—44no—
218C2×#6923—82no—
219C2×#6923—82no—
220C2×#6923—82no—
221C2×#6923—82no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61#11711yescharacteristic
234C2×C4×C61#11711yescharacteristic
235C2×C4×C61C4×D412yes—
236C2×C4×C61C4×D412yes—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—42no—
241C2×Dic61—42no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61#12011yescharacteristic
249C2×Dic61#12112yes—
250C2×Dic61#12312yes—
251C2×Dic61#12311yescharacteristic
252C4×D61—42no—
253C4×D61—42no—
254C4×D61—42no—
255C4×D61—42no—
256C4×D61—42no—
257C4×D61—42no—
258C4×D61—82no—
259C4×D61—82no—
260C4×D61—82no—
261C4×D61—82no—
262C4×D61#12112yes—
263C4×D61#12112yes—
264C4×D61#12312yes—
265C4×D61#12312yes—
266C4×D61#12412yes—
267C4×D61#12412yes—
268C4×D61#12612yes—
269C4×D61#12612yes—
270#92420—44no—
271#11200—611nomaximal, Sylow
272C22×C61—22no—
273C22×C61—22no—
274C22×C61—22no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61#38111yescharacteristic
280C22×C61#38611yescharacteristic
281C22×C61#38611yescharacteristic
282C22×C61C2×#10311yescharacteristic
283C22×C61#41611yescharacteristic
284C22×C61#41711yescharacteristic
285C22×C61#41811yescharacteristic
286C2×D61—22no—
287C2×D61—22no—
288C2×D61—22no—
289C2×D61—41no—
290C2×D61—41no—
291C2×D61—41no—
292C2×D61—41no—
293C2×D61—44no—
294C2×D61—44no—
295C2×D61—44no—
296C2×D61—44no—
297C2×D61#39412yes—
298C2×D61#39712yes—
299C2×D61#44912yes—
300C2×D61#45011yescharacteristic
301C2×D61#45111yescharacteristic
302C2×D61#46512yes—
303C2×D61#46712yes—
304C2×D61#46812yes—
305C2×D61#46912yes—
306C2×D61#48112yes—
307C2×D61#48212yes—
308C2×D61#48212yes—
309C2×D61#48311yescharacteristic
310C2×D61#48411yescharacteristic
311C2×D61#48412yes—
312C2×D61#48512yes—
313#6923—84no—
314C4×C61—41no—
315C4×C61—81no—
316C4×C61—81no—
317C4×C61#38812yes—
318C4×C61#38812yes—
319Dic61—41no—
320Dic61—81no—
321Dic61—81no—
322Dic61#39412yes—
323Dic61#39712yes—
324C22×C22⋊C8—611no—
325C2×#380—611no—
326C2×#380—611no—
327C2×#340—612no—
328C2×#340—612no—
329C2×C61—42no—
330C2×C61#144011yescharacteristic
331C2×C61#182411yescharacteristic
332C2×C61#182511yescharacteristic
333C2×C61#187211yescharacteristic
334C2×C61#187511yescharacteristic
335C2×C61#189211yescharacteristic
336C2×C61#189511yescharacteristic
337D61—42no—
338D61#203412yes—
339D61#203612yes—
340D61#207612yes—
341D61#207712yes—
342C24×C4—611no—
343C23×C8—612no—
344C22×C4⋊C4—612no—
345C22×C4⋊C4—611no—
346C22×C4⋊C4—611no—
347C22×C22⋊C4—1221no—
348C22×C22⋊C4—1221no—
349C2×C22⋊C8—1224no—
350C2×C22⋊C8—1221no—
351C2×C22⋊C8—1221no—
352#380—611no—
353#380—611no—
354#380—611no—
355#380—1221no—
356#380—1221no—
357#380—1224no—
358#380#692311yescharacteristic, complemented
359C2×#95—1221no—
360C2×#95—1221no—
361#340—1224no—
362#340—1224no—
363C61#1120011yescharacteristic, complemented, Sylow
364C25—611no—
365C23×C4—611no—
366C23×C4—611no—
367C23×C4—611no—
368C23×C4—611no—
369C23×C4—611no—
370C23×C4—1222no—
371C23×C4—1222no—
372C23×C4—1222no—
373C23×C4—1222no—
374C23×C4—1222no—
375C23×C4—1222no—
376C23×C4—1221no—
377C23×C4—1221no—
378C23×C4—1222no—
379C23×C4C2×#692311yescharacteristic
380C22×C8—614no—
381C22×C8—1222no—
382C22×C8—1222no—
383C22×C8—1222no—
384C22×C8—1222no—
385C22×C8—1222no—
386C22×C8—1222no—
387C2×C4⋊C4—614no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—611no—
390C2×C4⋊C4—1222no—
391C2×C4⋊C4—1222no—
392C2×C4⋊C4—1222no—
393C2×C4⋊C4—1222no—
394C2×C4⋊C4—1222no—
395C2×C4⋊C4—1222no—
396C2×C4⋊C4—1222no—
397C2×C4⋊C4—1222no—
398C2×C4⋊C4—1221no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1222no—
401C2×C4⋊C4C2×#692311yescharacteristic
402C2×C4⋊C4C2×#692311yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—1221no—
405C2×C22⋊C4—1221no—
406C2×C22⋊C4—1224no—
407C2×C22⋊C4—1221no—
408C2×C22⋊C4—2444no—
409C2×C22⋊C4—2442no—
410C2×C22⋊C4—2442no—
411C22⋊C8—1224no—
412C22⋊C8—1224no—
413#95—21no—
414#95—1221no—
415#95—1221no—
416#95—1224no—
417#95—1221no—
418C24—611no—
419C24—612no—
420C24—612no—
421C24—611no—
422C24—1221no—
423C24—1221no—
424C24—1222no—
425C24—1222no—
426C24—1222no—
427C24—1221no—
428C24—1222no—
429C24—1221no—
430C24C22⋊#692311yescharacteristic
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—611no—
438C22×C4—612no—
439C22×C4—612no—
440C22×C4—612no—
441C22×C4—612no—
442C22×C4—612no—
443C22×C4—612no—
444C22×C4—611no—
445C22×C4—1221no—
446C22×C4—1222no—
447C22×C4—1222no—
448C22×C4—1221no—
449C22×C4—1221no—
450C22×C4—1222no—
451C22×C4—1222no—
452C22×C4—1221no—
453C22×C4—1221no—
454C22×C4—1222no—
455C22×C4—1222no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1222no—
460C22×C4—1222no—
461C22×C4—1224no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—2442no—
465C22×C4—2442no—
466C22×C4—2442no—
467C22×C4—2442no—
468C22×C4—2442no—
469C22×C4—2442no—
470C22×C4—2442no—
471C22×C4—2442no—
472C22×C4—2442no—
473C22×C4—2442no—
474C22×C4—2441no—
475C22×C4—2442no—
476C22×C4—2441no—
477C22×C4—2442no—
478C22×C4—2441no—
479C22×C4—2441no—
480C22×C4—2442no—
481C22×C4—2442no—
482C22×C4—2442no—
483C22×C4—2442no—
484C22×C4—2442no—
485C22×C4—2442no—
486C22×C4C22⋊#692311yescharacteristic
487C22×C4C22×#692311yescharacteristic
488C2×C8—1224no—
489C2×C8—1224no—
490C2×C8—1224no—
491C2×C8—2442no—
492C2×C8—2442no—
493C2×C8—2442no—
494C2×C8—2442no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—1224no—
498C4⋊C4—1224no—
499C4⋊C4—1222no—
500C4⋊C4—1222no—
501C4⋊C4—2441no—
502C4⋊C4—2442no—
503C4⋊C4—2441no—
504C4⋊C4—2442no—
505C4⋊C4—2442no—
506C22⋊C4—42no—
507C22⋊C4—2442no—
508C22⋊C4—2442no—
509C22⋊C4—2442no—
510C22⋊C4—2448no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—612no—
518C23—611no—
519C23—612no—
520C23—611no—
521C23—611no—
522C23—611no—
523C23—612no—
524C23—611no—
525C23—611no—
526C23—612no—
527C23—612no—
528C23—1222no—
529C23—1222no—
530C23—1222no—
531C23—1222no—
532C23—1224no—
533C23—1224no—
534C23—1224no—
535C23—1224no—
536C23—1221no—
537C23—1221no—
538C23—1221no—
539C23—1221no—
540C23—1221no—
541C23—1221no—
542C23—2442no—
543C23—2442no—
544C23—2442no—
545C23—2442no—
546C23—2442no—
547C23—2442no—
548C23—2442no—
549C23—2442no—
550C23#1451984012yes—
551C23C2×C22⋊#692311yescharacteristic
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—612no—
564C2×C4—611no—
565C2×C4—612no—
566C2×C4—611no—
567C2×C4—612no—
568C2×C4—612no—
569C2×C4—612no—
570C2×C4—612no—
571C2×C4—612no—
572C2×C4—612no—
573C2×C4—612no—
574C2×C4—612no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—4882no—
579C2×C4—4882no—
580C2×C4—4882no—
581C2×C4—4882no—
582C2×C4—4882no—
583C2×C4—4882no—
584C2×C4—4882no—
585C2×C4—4882no—
586C2×C4—2442no—
587C2×C4—2442no—
588C2×C4—2442no—
589C2×C4—2442no—
590C2×C4—2442no—
591C2×C4—2442no—
592C2×C4—2444no—
593C2×C4—2444no—
594C2×C4—2444no—
595C2×C4—2441no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2442no—
602C2×C4—2442no—
603C2×C4#1451985611yescharacteristic
604C2×C4#1451985611yescharacteristic
605C2×C4D4×#692312yes—
606C2×C4D4×#692312yes—
607C8—2444no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—612no—
616C22—612no—
617C22—611no—
618C22—611no—
619C22—611no—
620C22—611no—
621C22—612no—
622C22—612no—
623C22—612no—
624C22—612no—
625C22—612no—
626C22—612no—
627C22—612no—
628C22—612no—
629C22—612no—
630C22—612no—
631C22—1222no—
632C22—1222no—
633C22—1222no—
634C22—2444no—
635C22—2444no—
636C22—2444no—
637C22—2444no—
638C22—2441no—
639C22—2441no—
640C22—2441no—
641C22—2441no—
642C22#1684070511yescharacteristic
643C22#1684071011yescharacteristic
644C22#1684071011yescharacteristic
645C22C2×#1451984011yescharacteristic
646C22#1684075211yescharacteristic
647C22#1684075311yescharacteristic
648C22#1684075411yescharacteristic
649C4—41no—
650C4—81no—
651C4—81no—
652C4—612no—
653C4—612no—
654C4—4884no—
655C4—4881no—
656C4—4881no—
657C4—2441no—
658C4#1684071212yes—
659C4#1684071212yes—
660C2—42no—
661C2—612no—
662C2—612no—
663C2—612no—
664C2—612no—
665C2—2442no—
666C2#2146100311yescharacteristic
667C2#2146172311yescharacteristic
668C2#2146172411yescharacteristic
669C2#2146180411yescharacteristic
670C2#2146180711yescharacteristic
671C2#2146183211yescharacteristic
672C2#2146183511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC23×C61C2×C22⋊C4
prime radicalC24×D61D4
cosocleC22×C4×D61C23
hypercenter#380#6923
hypocenterC61#11200
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. C2×#16840635C2semidirect
4. C2×#16840635C2semidirect
20. #16839622C4semidirect
23. #16839619C4semidirect
24. #16839619C4semidirect
26. C61×#380C4semidirect
358. #380#6923semidirect
363. C61#11200semidirect

Maximal subgroups

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

subgroupindex
C2×D61⋊(C22⋊C8)2
C2×#168407042
C2×#168406352
#380×D612
#1120061