Finite Group Databasebeta

← #30610347

Subgroups — #30610347

Order 15616.

996 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462678C212yesmaximal
2#21461099C212yesmaximal, complemented
3#21461098C212yesmaximal, complemented
4#21461091C212yesmaximal, complemented
5#21461083C211yesmaximal, characteristic, complemented
6#21461069C211yesmaximal, characteristic, complemented
7#21461068C211yesmaximal, characteristic, complemented
8#21461063C211yesmaximal, characteristic, complemented
9C2×#16840608C211yesmaximal, characteristic, complemented
10D61⋊#324C211yesmaximal, characteristic, complemented
11C2×#16840466C211yesmaximal, characteristic
12#16840795—22no—
13#16840794—22no—
14#16840791—22no—
15#16840789—22no—
16#16840782C2212yes—
17#16840778C2212yes—
18#16840733C2212yes—
19#16840732C2212yes—
20D61⋊(C22⋊C8)C2212yes—
21C2×C22⋊#92420C2212yes—
22#16840608C2211yescharacteristic
23#16840608C2211yescharacteristic
24#16840608C2211yescharacteristic
25#16840608C2212yes—
26#16840608C2211yescharacteristic
27#16840608C2212yes—
28#16840608C2212yes—
29#16840608C2212yes—
30#16840607C2212yes—
31#16840607C2212yes—
32#16840466—22no—
33#16840466—22no—
34#16840466—22no—
35#16840466—22no—
36C2×#14519775C411yescharacteristic
37C2×#14519767C411yescharacteristic
38C2×#14519767C2211yescharacteristic
39C2×#14519755C411yescharacteristic
40C2×#14519755C411yescharacteristic
41C2×#14519754C411yescharacteristic
42C2×#14519754C2211yescharacteristic
43C2×#14519753C2211yescharacteristic
44C2×#14519742C2211yescharacteristic
45C2×C4×C22⋊D61C411yescharacteristic
46C2×#14519737C411yescharacteristic
47C2×#14519737C2211yescharacteristic
48C22×#11758196C2211yescharacteristic
49C2×C4⋊C4×D61C2211yescharacteristic
50C2×C22⋊Q8×C61C411yescharacteristic
51C2×#11758213—22no—
52C2×#11758217—22no—
53C2×D61⋊C8—22no—
54C22×#92420—22no—
55#14519844—22no—
56C4⋊#92420—22no—
57#14519834—22no—
58#14519834—22no—
59C22⋊#92420—22no—
60C22⋊#92420—22no—
61C22⋊#92420C2312yes—
62C22⋊#92420C2312yes—
63C22⋊#92420C2312yes—
64C22⋊#92420C2312yes—
65#14519832—22no—
66C4×#92420—22no—
67C22×Dic122C2×C411yescharacteristic
68C22×Dic122C2×C411yescharacteristic
69C22×C22⋊D61C2×C411yescharacteristic
70C23×Dic61C2×C411yescharacteristic
71C23×Dic61C2311yescharacteristic
72C22×C4×D61C2×C411yescharacteristic
73C22×C4×D61C2×C411yescharacteristic
74C22×C4×D61C2311yescharacteristic
75#14519775—22no—
76#14519775—22no—
77#14519767—22no—
78#14519767—22no—
79#14519767—22no—
80#14519767—22no—
81#14519755—22no—
82#14519755—22no—
83#14519755—22no—
84#14519755—22no—
85#14519754—22no—
86#14519754—22no—
87#14519754—22no—
88#14519754—22no—
89#14519753—22no—
90#14519753—22no—
91#14519742—22no—
92#14519742—22no—
93C4×C22⋊D61—21no—
94C4×C22⋊D61—21no—
95C4×C22⋊D61—21no—
96C4×C22⋊D61—21no—
97#14519737—21no—
98#14519737—21no—
99#14519737—21no—
100#14519737—21no—
101#14519737D412yes—
102#14519737D412yes—
103#14519737D412yes—
104#14519737D412yes—
105C2×C4⋊Dic61C2×C411yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—22no—
108C2×#11758196—22no—
109C2×#11758196C2×C411yescharacteristic
110C2×#11758196C2×C411yescharacteristic
111C2×#11758196C2×C411yescharacteristic
112C2×#11758196C2×C411yescharacteristic
113C2×#11758196C2×C411yescharacteristic
114C2×#11758196C2×C411yescharacteristic
115C2×#11758196C2×C411yescharacteristic
116C2×#11758196C2×C411yescharacteristic
117C2×#11758196C2311yescharacteristic
118C2×#11758196C2311yescharacteristic
119C2×#11758196C2311yescharacteristic
120C4⋊C4×D61—22no—
121C4⋊C4×D61—22no—
122C2×C22⋊Dic61C2×C411yescharacteristic
123C2×#11758198C2×C411yescharacteristic
124C2×#11758198C2×C411yescharacteristic
125C2×#11758198C2×C411yescharacteristic
126C2×C4×Dic61C2×C411yescharacteristic
127C2×C4×Dic61C2×C411yescharacteristic
128C2×C4×Dic61C2311yescharacteristic
129C22×Q8×C61C2×C411yescharacteristic
130C23×C4×C61C2×C411yescharacteristic
131C22⋊Q8×C61—22no—
132C22⋊Q8×C61—22no—
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C4⋊C4×C61C2×C411yescharacteristic
135C2×C4⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2×C411yescharacteristic
137C2×C22⋊C4×C61C2×C411yescharacteristic
138C24×C61C22×C411yescharacteristic
139C23×D61C22×C411yescharacteristic
140C2×Q8×C61—22no—
141C2×Q8×C61—81no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—81no—
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C2×C22⋊D61—24no—
152C2×C22⋊D61C22⋊C411yescharacteristic
153C2×C22⋊D61C22⋊C411yescharacteristic
154C2×C22⋊D61C22⋊C411yescharacteristic
155C2×C22⋊D61C22⋊C411yescharacteristic
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—22no—
159C22×Dic61—41no—
160C22×Dic61—81no—
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C411yescharacteristic
163C22×Dic61C22×C411yescharacteristic
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C2×D412yes—
168C22×Dic61C2×D412yes—
169C22×Dic61C2411yescharacteristic
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—22no—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—41no—
176C2×C4×D61—81no—
177C2×C4×D61—81no—
178C2×C4×D61C2×D412yes—
179C2×C4×D61C2×D412yes—
180C2×Dic122—22no—
181C2×Dic122—22no—
182C2×Dic122—22no—
183C2×Dic122—41no—
184C2×Dic122—81no—
185#11758217—82no—
186C2×#92420—22no—
187C2×#92420—22no—
188C2×#92420—22no—
189C2×#92420—22no—
190C2×#92420—82no—
191#11758213—82no—
192D61⋊C8—82no—
193C4⋊C4×C61—22no—
194C4⋊C4×C61—22no—
195C4⋊C4×C61—22no—
196C22⋊C4×C61—21no—
197C22⋊C4×C61—21no—
198C22⋊C4×C61C22⋊C412yes—
199C22⋊C4×C61C22⋊C412yes—
200C22⋊Dic61—21no—
201C22⋊Dic61—21no—
202#11758198—21no—
203#11758198—21no—
204#11758198—21no—
205#11758198—21no—
206#11758198C22⋊C412yes—
207#11758198C22⋊C412yes—
208C4⋊Dic61—22no—
209C4⋊Dic61—22no—
210#11758196—22no—
211#11758196—22no—
212#11758196—22no—
213#11758196—22no—
214#11758196—21no—
215#11758196—21no—
216#11758196—21no—
217#11758196—21no—
218#11758196—22no—
219#11758196—22no—
220#11758196—22no—
221#11758196—22no—
222#11758196C22⋊C412yes—
223#11758196C22⋊C412yes—
224C4×Dic61—21no—
225C4×Dic61—21no—
226C4×Dic61—21no—
227C4×Dic61—21no—
228C4×Dic61C2×D412yes—
229C4×Dic61C2×D412yes—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—22no—
233C23×C61—41no—
234C23×C61C2×C22⋊C411yescharacteristic
235C23×C61C2×C22⋊C411yescharacteristic
236C23×C61C23×C411yescharacteristic
237C22×D61—21no—
238C22×D61—21no—
239C22×D61—22no—
240C22×D61—41no—
241C22×D61C2×C22⋊C411yescharacteristic
242C22×D61C2×C22⋊C411yescharacteristic
243Q8×C61—82no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—81no—
257C2×C4×C61—81no—
258C2×C4×C61C2×C22⋊C412yes—
259C2×C4×C61C2×C22⋊C412yes—
260C22⋊D61—22no—
261C22⋊D61—22no—
262C22⋊D61—22no—
263C22⋊D61#10114yes—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—22no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—42no—
275C2×Dic61—42no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—42no—
279C2×Dic61—42no—
280C2×Dic61—41no—
281C2×Dic61C2×C22⋊C411yescharacteristic
282C2×Dic61C2×C22⋊C412yes—
283C2×Dic61C2×C22⋊C411yescharacteristic
284C2×Dic61#13112yes—
285C2×Dic61C22×D412yes—
286C4×D61—42no—
287C4×D61—42no—
288C4×D61—42no—
289C4×D61—42no—
290C4×D61—81no—
291C4×D61—81no—
292Dic122—44no—
293Dic122—82no—
294#92420—42no—
295#92420—42no—
296#92420—42no—
297#92420—42no—
298#17426—611nomaximal, Sylow
299C22×C61—21no—
300C22×C61—21no—
301C22×C61—21no—
302C22×C61—21no—
303C22×C61—21no—
304C22×C61—21no—
305C22×C61—21no—
306C22×C61—42no—
307C22×C61—42no—
308C22×C61C2×#10112yes—
309C22×C61C22×C22⋊C411yescharacteristic
310C22×C61C2×#13111yescharacteristic
311C22×C61#56811yescharacteristic
312C2×D61—21no—
313C2×D61—21no—
314C2×D61—21no—
315C2×D61—21no—
316C2×D61—21no—
317C2×D61—42no—
318C2×D61—42no—
319C2×D61C2×#10112yes—
320C4×C61—22no—
321C4×C61—22no—
322C4×C61—41no—
323C4×C61—41no—
324C4×C61—41no—
325C4×C61—41no—
326Dic61—22no—
327Dic61—22no—
328Dic61—22no—
329Dic61—21no—
330Dic61—41no—
331Dic61—41no—
332Dic61—41no—
333Dic61C2×#10112yes—
334C2×#554—611no—
335#2974—612no—
336#1472—612no—
337#1472—612no—
338#1470—612no—
339#1467—611no—
340#1463—611no—
341#1463—611no—
342#1461—611no—
343C2×#324—611no—
344C2×#324—611no—
345C2×C61—21no—
346C2×C61—21no—
347C2×C61—22no—
348C2×C61—41no—
349C2×C61#288011yescharacteristic
350C2×C61#288311yescharacteristic
351C2×C61C22×#10111yescharacteristic
352D61—22no—
353D61—41no—
354#554—1222no—
355#554—1222no—
356#554—1222no—
357#554—1222no—
358C2×C4⋊Q8—611no—
359C2×#125—611no—
360C2×#125—611no—
361C2×C22⋊Q8—611no—
362C2×C22⋊Q8—611no—
363C2×C22⋊Q8—611no—
364C2×C22⋊Q8—611no—
365C2×C22⋊Q8—611no—
366C2×C22⋊Q8#692311yescharacteristic
367C2×C4×Q8—611no—
368C2×C4×D4—611no—
369C2×C4×D4—611no—
370C2×C4×D4—611no—
371C22×C4⋊C4—611no—
372C22×C4⋊C4—611no—
373#436—1222no—
374#435—1222no—
375#435—1222no—
376C8×D4—1222no—
377#432—612no—
378#431—612no—
379#407—612no—
380#407—612no—
381C2×C22⋊C8—612no—
382C2×C22⋊C8—612no—
383#324—612no—
384#324—612no—
385#324—611no—
386#324—611no—
387#324—611no—
388#324—612no—
389#324—611no—
390#324—612no—
391#324—612no—
392#324—612no—
393C61#1742611yescharacteristic, complemented, Sylow
394C22×Q8—611no—
395C22×Q8—611no—
396C22×Q8C2×#692311yescharacteristic
397C22×D4—611no—
398C23×C4—611no—
399C23×C4—611no—
400C23×C4—611no—
401C23×C4—611no—
402C23×C4—611no—
403C23×C4C2×#692311yescharacteristic
404C2×M16—1222no—
405C2×M16—1222no—
406C22×C8—1222no—
407C22×C8—1222no—
408C4⋊Q8—1222no—
409C4⋊Q8—1222no—
410#125—1222no—
411#125—1222no—
412#125—1222no—
413#125—1222no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—1222no—
417C22⋊Q8—1222no—
418C22⋊Q8—1222no—
419C22⋊Q8—1222no—
420C22⋊Q8—1222no—
421C22⋊Q8—1222no—
422C22⋊Q8—1222no—
423C22⋊Q8—1222no—
424C22⋊Q8—1222no—
425C22⋊Q8—1222no—
426C4×Q8—1222no—
427C4×Q8—1222no—
428C4×D4—612no—
429C4×D4—612no—
430C4×D4—612no—
431C4×D4—612no—
432C4×D4—1221no—
433C4×D4—1221no—
434C4×D4—1221no—
435C4×D4—1221no—
436C4×D4—1221no—
437C4×D4—1221no—
438C4×D4—1221no—
439C4×D4—1221no—
440C2×C4⋊C4—611no—
441C2×C4⋊C4—611no—
442C2×C4⋊C4—611no—
443C2×C4⋊C4—611no—
444C2×C4⋊C4—611no—
445C2×C4⋊C4—611no—
446C2×C4⋊C4—611no—
447C2×C4⋊C4—611no—
448C2×C4⋊C4—611no—
449C2×C4⋊C4—611no—
450C2×C4⋊C4—611no—
451C2×C4⋊C4—611no—
452C2×C4⋊C4—611no—
453C2×C4⋊C4—1222no—
454C2×C4⋊C4—1222no—
455C2×C4⋊C4—1222no—
456C2×C4⋊C4—1222no—
457C2×C4⋊C4C2×#692311yescharacteristic
458C2×C4⋊C4C2×#692311yescharacteristic
459C2×C4⋊C4C2×#692311yescharacteristic
460C2×C22⋊C4—611no—
461C2×C22⋊C4—611no—
462C2×C22⋊C4—611no—
463C2×C22⋊C4—611no—
464C2×C22⋊C4C2×#692311yescharacteristic
465C2×C22⋊C4C2×#692311yescharacteristic
466C2×C42—611no—
467C2×C42—611no—
468C2×C42—611no—
469C4⋊C8—1222no—
470C4⋊C8—1222no—
471C22⋊C8—612no—
472C22⋊C8—612no—
473C22⋊C8—612no—
474C22⋊C8—612no—
475C22⋊C8—1222no—
476C22⋊C8—1222no—
477C22⋊C8—1222no—
478C22⋊C8—1222no—
479#97—1222no—
480C4×C8—1222no—
481C24—611no—
482C24C22×#692311yescharacteristic
483C2×Q8—22no—
484C2×Q8—81no—
485C2×Q8—1222no—
486C2×Q8—1222no—
487C2×Q8—1222no—
488C2×Q8—4881no—
489C2×Q8—2441no—
490C2×D4—611no—
491C2×D4—611no—
492C2×D4—611no—
493C2×D4—611no—
494C2×D4—1224no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—81no—
498C22×C4—611no—
499C22×C4—611no—
500C22×C4—612no—
501C22×C4—612no—
502C22×C4—611no—
503C22×C4—611no—
504C22×C4—612no—
505C22×C4—612no—
506C22×C4—611no—
507C22×C4—611no—
508C22×C4—611no—
509C22×C4—1222no—
510C22×C4—1221no—
511C22×C4—1221no—
512C22×C4—1221no—
513C22×C4—1221no—
514C22×C4—1222no—
515C22×C4—1221no—
516C22×C4—1221no—
517C22×C4—4881no—
518C22×C4—4881no—
519C22×C4—4881no—
520C22×C4—2441no—
521C22×C4—2441no—
522C22×C4C22×#692311yescharacteristic
523C22×C4C22×#692311yescharacteristic
524C22×C4C22×#692311yescharacteristic
525C22×C4C22×#692311yescharacteristic
526C22×C4C22×#692311yescharacteristic
527C22×C4C22×#692311yescharacteristic
528M16—4882no—
529M16—4882no—
530C2×C8—1222no—
531C2×C8—1222no—
532C2×C8—1222no—
533C2×C8—1222no—
534C2×C8—4882no—
535C2×C8—4882no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—612no—
540C4⋊C4—612no—
541C4⋊C4—1222no—
542C4⋊C4—1222no—
543C4⋊C4—1222no—
544C4⋊C4—1222no—
545C4⋊C4—1222no—
546C4⋊C4—1221no—
547C4⋊C4—1221no—
548C4⋊C4—1221no—
549C4⋊C4—1221no—
550C4⋊C4—1222no—
551C4⋊C4—1222no—
552C4⋊C4—1222no—
553C4⋊C4—1222no—
554C4⋊C4—1222no—
555C22⋊C4—21no—
556C22⋊C4—21no—
557C22⋊C4—612no—
558C22⋊C4—612no—
559C22⋊C4—1221no—
560C22⋊C4—1221no—
561C22⋊C4—1221no—
562C22⋊C4—1221no—
563C22⋊C4—1221no—
564C22⋊C4—1221no—
565C22⋊C4C22⋊#692312yes—
566C22⋊C4C22⋊#692312yes—
567C42—612no—
568C42—612no—
569C42—1221no—
570C42—1221no—
571C42—1221no—
572C42—1221no—
573C23—22no—
574C23—21no—
575C23—21no—
576C23—41no—
577C23—611no—
578C23—611no—
579C23—1222no—
580C23—1221no—
581C23—1221no—
582C23—2441no—
583C23C2×C22⋊#692311yescharacteristic
584C23C2×C22⋊#692311yescharacteristic
585C23C23×#692311yescharacteristic
586Q8—82no—
587Q8—4882no—
588Q8—2444no—
589D4—614no—
590D4—1222no—
591D4—1222no—
592D4—1222no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—81no—
606C2×C4—81no—
607C2×C4—611no—
608C2×C4—611no—
609C2×C4—612no—
610C2×C4—612no—
611C2×C4—612no—
612C2×C4—1222no—
613C2×C4—1221no—
614C2×C4—1221no—
615C2×C4—1221no—
616C2×C4—1221no—
617C2×C4—1221no—
618C2×C4—1221no—
619C2×C4—1221no—
620C2×C4—1221no—
621C2×C4—1221no—
622C2×C4—4881no—
623C2×C4—4881no—
624C2×C4—2442no—
625C2×C4—2442no—
626C2×C4—2442no—
627C2×C4—2442no—
628C2×C4—2442no—
629C2×C4—2442no—
630C2×C4—2441no—
631C2×C4—2441no—
632C2×C4—2442no—
633C2×C4—2442no—
634C2×C4—2441no—
635C2×C4C2×C22⋊#692312yes—
636C2×C4C2×C22⋊#692312yes—
637C8—2442no—
638C8—2442no—
639C8—2442no—
640C8—2442no—
641C22—21no—
642C22—21no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—21no—
647C22—21no—
648C22—42no—
649C22—42no—
650C22—612no—
651C22—1221no—
652C22—1221no—
653C22—1221no—
654C22—1221no—
655C22—1221no—
656C22—2442no—
657C22—2442no—
658C22D61⋊#10112yes—
659C22C22×C22⋊#692311yescharacteristic
660C22D61⋊#13111yescharacteristic
661C22#1684084111yescharacteristic
662C4—22no—
663C4—22no—
664C4—41no—
665C4—41no—
666C4—41no—
667C4—41no—
668C4—612no—
669C4—1222no—
670C4—1222no—
671C4—1222no—
672C4—1221no—
673C4—2441no—
674C4—2441no—
675C4—2441no—
676C2—21no—
677C2—21no—
678C2—22no—
679C2—41no—
680C2—1222no—
681C2—2441no—
682C2#2146240911yescharacteristic
683C2#2146241811yescharacteristic
684C2C2×D61⋊#10111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C22⋊Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×C22⋊D61C2×C4
cosocleC22×Dic61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61#17426
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #21461099C2semidirect
3. #21461098C2semidirect
4. #21461091C2semidirect
5. #21461083C2semidirect
6. #21461069C2semidirect
7. #21461068C2semidirect
8. #21461063C2semidirect
9. C2×#16840608C2semidirect
10. D61⋊#324C2semidirect
393. C61#17426semidirect

Maximal subgroups

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

subgroupindex
#214626782
#214610992
#214610982
#214610912
#214610832
#214610692
#214610682
#214610632
C2×#168406082
D61⋊#3242
C2×#168404662
#1742661