Finite Group Databasebeta

← #30602971

Subgroups — #30602971

Order 15616.

974 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462298C211yesmaximal, characteristic
2#21462255C211yesmaximal, characteristic
3C2×#16840639C211yesmaximal, characteristic
4C2×#16840639C211yesmaximal, characteristic
5C2×#16840639C211yesmaximal, characteristic
6C2×#16840639C211yesmaximal, characteristic
7#342×D61C211yesmaximal, characteristic
8C22×C22⋊#6923C2211yescharacteristic
9C22×C22⋊#6923C2211yescharacteristic
10C22×C22⋊#6923C2211yescharacteristic
11C22×C22⋊#6923C2211yescharacteristic
12#16840709—22no—
13#16840709C414yescomplemented
14#16840704—22no—
15C22⋊C4×#6923—22no—
16C22⋊C4×#6923—22no—
17C4×C22⋊#6923—22no—
18#16840639—22no—
19#16840639—22no—
20#16840639—22no—
21#16840639C414yescomplemented
22C2×C22⋊C4×D61C2211yescharacteristic
23C2×C22⋊C4×D61C2211yescharacteristic
24C2×C22⋊C4×D61C2211yescharacteristic
25#16839529C411yescharacteristic, complemented
26#16839528C411yescharacteristic, complemented
27#16839528C411yescharacteristic, complemented
28C61×#342C411yescharacteristic, complemented
29C23×#6923—21no—
30C23×#6923—21no—
31C23×#6923C2×C412yes—
32C23×#6923D412yes—
33C2×C4⋊#6923—24no—
34C2×C22⋊#6923—21no—
35C2×C22⋊#6923—21no—
36C2×C22⋊#6923—21no—
37C2×C22⋊#6923—21no—
38C2×C22⋊#6923—21no—
39C2×C22⋊#6923—21no—
40C2×C22⋊#6923—21no—
41C2×C22⋊#6923—21no—
42C2×C22⋊#6923—21no—
43C2×C22⋊#6923—21no—
44C2×C22⋊#6923—21no—
45C2×C22⋊#6923—21no—
46C2×C22⋊#6923—21no—
47C2×C22⋊#6923—21no—
48C2×C22⋊#6923—21no—
49C2×C22⋊#6923—21no—
50C2×C22⋊#6923—21no—
51C2×C22⋊#6923—21no—
52C2×C22⋊#6923C2×C412yes—
53C2×C22⋊#6923C2×C412yes—
54C2×C22⋊#6923C2×C412yes—
55C2×C22⋊#6923D412yes—
56C2×C22⋊#6923D412yes—
57C2×C22⋊#6923Q812yes—
58C2×C4×#6923—24no—
59(C2×#6923)⋊C4—24no—
60(C2×#6923)⋊C4—24no—
61C24×D61C2311yescharacteristic
62C22×C4×D61—21no—
63C22×C4×D61—21no—
64C22×C4×D61—21no—
65C2×C22⋊Dic61C2×C411yescharacteristic
66C2×C22⋊Dic61C2×C411yescharacteristic
67C2×C22⋊Dic61C2×C411yescharacteristic
68C2×#11758198—21no—
69C2×#11758198—21no—
70C2×#11758198—21no—
71C22⋊C4×D61—21no—
72C22⋊C4×D61—21no—
73C22⋊C4×D61—21no—
74C22⋊C4×D61—21no—
75C22⋊C4×D61—21no—
76C22⋊C4×D61—21no—
77C22⋊C4×D61—21no—
78C22⋊C4×D61—21no—
79C22⋊C4×D61C2×C412yes—
80C22⋊C4×D61C2×C412yes—
81C22⋊C4×D61D412yes—
82C22⋊C4×D61Q812yes—
83C2×C22⋊C4×C61C2×C411yescharacteristic
84C2×C22⋊C4×C61C2×C411yescharacteristic
85C2×C22⋊C4×C61C2×C411yescharacteristic
86C24×C61C22×C411yescharacteristic
87C23×D61—82no—
88C23×D61C22×C411yescharacteristic
89C23×D61C22×C411yescharacteristic
90C23×D61C2×D411yescharacteristic
91C23×D61C2×D411yescharacteristic
92C23×D61C2×D411yescharacteristic
93C23×D61C2×D411yescharacteristic
94C23×D61C2×Q811yescharacteristic
95C23×D61C2×Q811yescharacteristic
96C23×D61#4111yescharacteristic
97C23×D61#4111yescharacteristic
98C23×D61#4111yescharacteristic
99C23×D61#4111yescharacteristic
100C23×D61#4111yescharacteristic
101C23×D61#4111yescharacteristic
102C22×#6923—22no—
103C22×#6923—22no—
104C22×#6923—22no—
105C22×#6923—22no—
106C22×#6923—22no—
107C22×#6923—22no—
108C22×#6923—22no—
109C22×#6923—22no—
110C22×#6923—22no—
111C22×#6923—41no—
112C22×#6923—41no—
113C22×#6923—82no—
114C22×#6923—82no—
115C22×#6923—82no—
116C22×#6923—82no—
117C22×#6923C22⋊C414yes—
118C22×C4×C61—21no—
119C22×C4×C61—21no—
120C22×C4×C61—21no—
121C22×Dic61—21no—
122C22×Dic61—21no—
123C22×Dic61—21no—
124C2×C4×D61—22no—
125C2×C4×D61—22no—
126C2×C4×D61—22no—
127C2×C4×D61—22no—
128C2×C4×D61—41no—
129C2×C4×D61—41no—
130C2×C4×D61—82no—
131C2×C4×D61—82no—
132C2×C4×D61—82no—
133C22⋊#6923—22no—
134C22⋊#6923—22no—
135C22⋊#6923—22no—
136C22⋊#6923—22no—
137C22⋊#6923—22no—
138C22⋊#6923—22no—
139C22⋊#6923—22no—
140C22⋊#6923—22no—
141C22⋊#6923—22no—
142C22⋊#6923—41no—
143C22⋊#6923—41no—
144C22⋊#6923—41no—
145C22⋊#6923—41no—
146C22⋊#6923—41no—
147C22⋊#6923—41no—
148C22⋊#6923C4⋊C414yescomplemented
149C4⋊#6923—84no—
150C4×#6923—84no—
151C22⋊C4×C61—21no—
152C22⋊C4×C61—21no—
153C22⋊C4×C61—21no—
154C22⋊C4×C61—21no—
155C22⋊C4×C61C4212yescomplemented
156C22⋊C4×C61C4⋊C412yescomplemented
157C22⋊Dic61—21no—
158C22⋊Dic61—21no—
159C22⋊Dic61—21no—
160C22⋊Dic61—21no—
161C22⋊Dic61C4212yescomplemented
162C22⋊Dic61C4⋊C412yescomplemented
163#11758198—22no—
164#11758198—22no—
165#11758198—22no—
166#11758198—22no—
167#11758198—41no—
168#11758198—41no—
169C23×C61—81no—
170C23×C61C2×C4211yescharacteristic
171C23×C61C2×C4⋊C411yescharacteristic
172C23×C61#11711yescharacteristic
173C23×C61C4×D411yescharacteristic
174C23×C61C4×D411yescharacteristic
175C23×C61C4×D411yescharacteristic
176C23×C61C4×Q811yescharacteristic
177C22×D61—42no—
178C22×D61—42no—
179C22×D61—42no—
180C22×D61—42no—
181C22×D61—42no—
182C22×D61—42no—
183C22×D61—42no—
184C22×D61—81no—
185C22×D61—81no—
186C22×D61—81no—
187C22×D61—81no—
188C22×D61—81no—
189C22×D61—81no—
190C22×D61—81no—
191C22×D61C2×C22⋊C411yescharacteristic
192C22×D61C2×C4⋊C411yescharacteristic
193C22×D61#11711yescharacteristic
194C22×D61#11711yescharacteristic
195C22×D61C4×D411yescharacteristic
196C22×D61C4×D411yescharacteristic
197C22×D61C4×D411yescharacteristic
198C22×D61C4×D411yescharacteristic
199C22×D61C4×D411yescharacteristic
200C22×D61C4×Q811yescharacteristic
201C22×D61C4×Q811yescharacteristic
202C22×D61C4×Q811yescharacteristic
203C22×D61#12011yescharacteristic
204C22×D61#12111yescharacteristic
205C22×D61#12111yescharacteristic
206C22×D61C22⋊Q811yescharacteristic
207C22×D61C22⋊Q811yescharacteristic
208C22×D61C22⋊Q811yescharacteristic
209C22×D61C22⋊Q811yescharacteristic
210C22×D61#12311yescharacteristic
211C22×D61#12311yescharacteristic
212C22×D61#12311yescharacteristic
213C22×D61#12411yescharacteristic
214C22×D61#12511yescharacteristic
215C22×D61#12511yescharacteristic
216C22×D61#12611yescharacteristic
217C22×D61#12611yescharacteristic
218C22×D61C4⋊Q811yescharacteristic
219C2×#6923—24no—
220C2×#6923—24no—
221C2×#6923—44no—
222C2×#6923—44no—
223C2×#6923—44no—
224C2×#6923—44no—
225C2×#6923—42no—
226C2×#6923—42no—
227C2×#6923—82no—
228C2×#6923—82no—
229C2×#6923—82no—
230C2×#6923—82no—
231C2×#6923—82no—
232C2×#6923—82no—
233C2×#6923—82no—
234C2×#6923—82no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—41no—
238C2×C4×C61—81no—
239C2×C4×C61—81no—
240C2×C4×C61—81no—
241C2×Dic61—22no—
242C2×Dic61—22no—
243C2×Dic61—41no—
244C2×Dic61—81no—
245C2×Dic61—81no—
246C2×Dic61—81no—
247C4×D61—44no—
248C4×D61—44no—
249C4×D61—82no—
250C4×D61—82no—
251C4×D61—82no—
252C4×D61—82no—
253#10915—611nomaximal, Sylow
254C22×C61—41no—
255C22×C61—41no—
256C22×C61—41no—
257C22×C61—41no—
258C22×C61—41no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61C4×C22⋊C411yescharacteristic
262C22×C61C4×C4⋊C411yescharacteristic
263C22×C61C4×C4⋊C411yescharacteristic
264C22×C61#38511yescharacteristic
265C22×C61#38711yescharacteristic
266C22×C61#38811yescharacteristic
267C22×C61#38911yescharacteristic
268C2×D61—22no—
269C2×D61—22no—
270C2×D61—22no—
271C2×D61—22no—
272C2×D61—22no—
273C2×D61—22no—
274C2×D61—22no—
275C2×D61—41no—
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—41no—
283C2×D61—41no—
284C2×D61—41no—
285C2×D61—41no—
286C2×D61—41no—
287C2×D61—41no—
288C2×D61—41no—
289C2×D61—41no—
290C2×D61—41no—
291C2×D61—41no—
292C2×D61—41no—
293C2×D61—41no—
294C2×D61—41no—
295C2×D61—41no—
296C2×D61#38511yescharacteristic
297C2×D61#38611yescharacteristic
298C2×D61#38711yescharacteristic
299C2×D61#38711yescharacteristic
300C2×D61#38711yescharacteristic
301C2×D61#38811yescharacteristic
302C2×D61#38911yescharacteristic
303C2×D61#39111yescharacteristic
304#6923—44no—
305#6923—44no—
306#6923—82no—
307#6923—82no—
308C4×C61—42no—
309C4×C61—42no—
310C4×C61—81no—
311Dic61—42no—
312Dic61—42no—
313Dic61—81no—
314#2315—611no—
315#2273—611no—
316C2×#342—611no—
317C2×#342—611no—
318C2×#342—611no—
319C2×#342—611no—
320C2×#342—611no—
321C2×C61—21no—
322C2×C61—21no—
323C2×C61—21no—
324C2×C61—21no—
325C2×C61—21no—
326C2×C61—21no—
327C2×C61—21no—
328C2×C61#143611yescharacteristic
329D61—21no—
330D61—21no—
331D61—21no—
332D61—21no—
333D61—21no—
334D61—21no—
335D61—21no—
336D61#191312yes—
337C22×C22⋊C4—611no—
338C22×C22⋊C4—611no—
339C22×C22⋊C4—611no—
340C22×C22⋊C4—611no—
341C22×C22⋊C4—611no—
342C22×C22⋊C4—611no—
343C22×C22⋊C4—611no—
344#385—614no—
345#385—1222no—
346#380—1222no—
347C4×C22⋊C4—1222no—
348C4×C22⋊C4—1222no—
349C4×C22⋊C4—1222no—
350#342—614no—
351#342—611no—
352#342—611no—
353#342—611no—
354#342—1222no—
355#342—1222no—
356#342—1222no—
357#342#692311yescharacteristic, complemented
358C61#1091511yescharacteristic, complemented, Sylow
359C25—611no—
360C23×C4—612no—
361C23×C4—612no—
362C23×C4—1221no—
363C23×C4—1221no—
364C23×C4—1221no—
365C23×C4—1221no—
366C23×C4—1221no—
367C2×C4⋊C4—1224no—
368C2×C22⋊C4—612no—
369C2×C22⋊C4—612no—
370C2×C22⋊C4—612no—
371C2×C22⋊C4—611no—
372C2×C22⋊C4—611no—
373C2×C22⋊C4—612no—
374C2×C22⋊C4—612no—
375C2×C22⋊C4—612no—
376C2×C22⋊C4—612no—
377C2×C22⋊C4—612no—
378C2×C22⋊C4—612no—
379C2×C22⋊C4—612no—
380C2×C22⋊C4—611no—
381C2×C22⋊C4—1221no—
382C2×C22⋊C4—1221no—
383C2×C22⋊C4—1221no—
384C2×C22⋊C4—1221no—
385C2×C22⋊C4—1221no—
386C2×C22⋊C4—1221no—
387C2×C22⋊C4—1221no—
388C2×C22⋊C4—1221no—
389C2×C22⋊C4—1221no—
390C2×C22⋊C4—1221no—
391C2×C22⋊C4—1221no—
392C2×C22⋊C4—1221no—
393C2×C22⋊C4—1221no—
394C2×C22⋊C4—1221no—
395C2×C22⋊C4—1221no—
396C2×C22⋊C4—1221no—
397C2×C22⋊C4—1221no—
398C2×C22⋊C4—1221no—
399C2×C22⋊C4—1221no—
400C2×C22⋊C4—1221no—
401C2×C22⋊C4—1221no—
402C2×C22⋊C4—1221no—
403C2×C22⋊C4—1221no—
404C2×C22⋊C4—1221no—
405C2×C22⋊C4—1221no—
406C2×C22⋊C4—1221no—
407C2×C22⋊C4—1221no—
408C2×C22⋊C4—1221no—
409C2×C22⋊C4—1221no—
410C2×C22⋊C4C2×#692311yescharacteristic
411C2×C22⋊C4C2×#692311yescharacteristic
412C2×C22⋊C4C2×#692311yescharacteristic
413C2×C42—1224no—
414#95—1224no—
415#95—1224no—
416C24—611no—
417C24—611no—
418C24—611no—
419C24—611no—
420C24—611no—
421C24—611no—
422C24—611no—
423C24—611no—
424C24—611no—
425C24—611no—
426C24—611no—
427C24—611no—
428C24—611no—
429C24—611no—
430C24—4882no—
431C24C22×#692311yescharacteristic
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—614no—
436C22×C4—1222no—
437C22×C4—1222no—
438C22×C4—1222no—
439C22×C4—1222no—
440C22×C4—1222no—
441C22×C4—1222no—
442C22×C4—1222no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—1222no—
446C22×C4—1222no—
447C22×C4—1222no—
448C22×C4—1222no—
449C22×C4—1222no—
450C22×C4—1221no—
451C22×C4—1222no—
452C22×C4—4882no—
453C22×C4—4882no—
454C22×C4—4882no—
455C22×C4—4882no—
456C22×C4—4882no—
457C22×C4—4882no—
458C22×C4—4882no—
459C22×C4—2441no—
460C22×C4—2441no—
461C22×C4—2441no—
462C22×C4—2441no—
463C4⋊C4—4884no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—21no—
468C22⋊C4—614no—
469C22⋊C4—612no—
470C22⋊C4—612no—
471C22⋊C4—1222no—
472C22⋊C4—1222no—
473C22⋊C4—1222no—
474C22⋊C4—1222no—
475C22⋊C4—1222no—
476C22⋊C4—1222no—
477C22⋊C4—1222no—
478C22⋊C4—1222no—
479C22⋊C4—1222no—
480C22⋊C4—1222no—
481C22⋊C4—1222no—
482C22⋊C4—1221no—
483C22⋊C4—1221no—
484C22⋊C4—1222no—
485C22⋊C4—1222no—
486C22⋊C4—1221no—
487C22⋊C4—1221no—
488C22⋊C4—2441no—
489C22⋊C4—2441no—
490C22⋊C4—2441no—
491C22⋊C4—2441no—
492C22⋊C4—2441no—
493C22⋊C4—2441no—
494C22⋊C4—2441no—
495C22⋊C4—2441no—
496C22⋊C4C4×#692312yescomplemented
497C22⋊C4C4⋊#692312yescomplemented
498C42—4884no—
499C23—81no—
500C23—611no—
501C23—611no—
502C23—611no—
503C23—611no—
504C23—611no—
505C23—611no—
506C23—611no—
507C23—611no—
508C23—611no—
509C23—611no—
510C23—611no—
511C23—611no—
512C23—611no—
513C23—611no—
514C23—611no—
515C23—611no—
516C23—611no—
517C23—611no—
518C23—611no—
519C23—611no—
520C23—611no—
521C23—611no—
522C23—611no—
523C23—611no—
524C23—611no—
525C23—611no—
526C23—611no—
527C23—611no—
528C23—4881no—
529C23—4881no—
530C23—4881no—
531C23—4881no—
532C23—4881no—
533C23—4881no—
534C23—4881no—
535C23—2442no—
536C23—2442no—
537C23—2442no—
538C23—2442no—
539C23—2442no—
540C23—2442no—
541C23—2442no—
542C23C2×C4×#692311yescharacteristic
543C23C2×C4⋊#692311yescharacteristic
544C23#1451985611yescharacteristic
545C23D4×#692311yescharacteristic
546C23D4×#692311yescharacteristic
547C23D4×#692311yescharacteristic
548C23Q8×#692311yescharacteristic
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—41no—
552C2×C4—81no—
553C2×C4—81no—
554C2×C4—81no—
555C2×C4—1224no—
556C2×C4—1224no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—4882no—
560C2×C4—4882no—
561C2×C4—4882no—
562C2×C4—4882no—
563C2×C4—4882no—
564C2×C4—4882no—
565C2×C4—4881no—
566C2×C4—4882no—
567C2×C4—4882no—
568C2×C4—4882no—
569C2×C4—4881no—
570C2×C4—4881no—
571C2×C4—4882no—
572C2×C4—4882no—
573C2×C4—4882no—
574C2×C4—2444no—
575C2×C4—2444no—
576C2×C4—2442no—
577C2×C4—2442no—
578C2×C4—2444no—
579C2×C4—2441no—
580C2×C4—2444no—
581C2×C4—2444no—
582C2×C4—2444no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—611no—
591C22—611no—
592C22—611no—
593C22—611no—
594C22—611no—
595C22—611no—
596C22—611no—
597C22—611no—
598C22—1222no—
599C22—1222no—
600C22—1222no—
601C22—1222no—
602C22—1222no—
603C22—1222no—
604C22—1222no—
605C22—2441no—
606C22—2441no—
607C22—2441no—
608C22—2441no—
609C22—2441no—
610C22—2441no—
611C22—2441no—
612C22—2441no—
613C22—2441no—
614C22—2441no—
615C22—2441no—
616C22—2441no—
617C22—2441no—
618C22—2441no—
619C22—2441no—
620C22—2441no—
621C22—2441no—
622C22—2441no—
623C22—2441no—
624C22—2441no—
625C22—2441no—
626C22C22⋊C4×#692311yescharacteristic
627C22C4×C4⋊#692311yescharacteristic
628C22C4⋊C4×#692311yescharacteristic
629C22#1684070911yescharacteristic
630C22#1684071111yescharacteristic
631C22#1684071211yescharacteristic
632C22#1684071311yescharacteristic
633C4—42no—
634C4—42no—
635C4—81no—
636C4—4881no—
637C4—4882no—
638C4—4882no—
639C4—2442no—
640C4—2442no—
641C4—2444no—
642C4—2444no—
643C2—21no—
644C2—21no—
645C2—21no—
646C2—21no—
647C2—21no—
648C2—21no—
649C2—21no—
650C2—612no—
651C2—1221no—
652C2—1221no—
653C2—1221no—
654C2—1221no—
655C2—1221no—
656C2—1221no—
657C2—1221no—
658C2#2146099911yescharacteristic
subgroupG/H
centerC2#21460999
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC61×#342C4
socleC2×C61#1436
prime radical, cosocleC24×D61C23
hypercenter#342#6923
hypocenterC61#10915
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
13. #16840709C4semidirect
21. #16840639C4semidirect
25. #16839529C4semidirect
26. #16839528C4semidirect
27. #16839528C4semidirect
28. C61×#342C4semidirect
148. C22⋊#6923C4⋊C4semidirect
155. C22⋊C4×C61C42semidirect
156. C22⋊C4×C61C4⋊C4semidirect
161. C22⋊Dic61C42semidirect
162. C22⋊Dic61C4⋊C4semidirect
357. #342#6923semidirect
358. C61#10915semidirect
496. C22⋊C4C4×#6923semidirect
497. C22⋊C4C4⋊#6923semidirect

Maximal subgroups

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

subgroupindex
#214622982
#214622552
C2×#168406392
#342×D612
#1091561