Finite Group Databasebeta

← #29709472

Subgroups — #29709472

Order 15616.

978 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839853C211yesmaximal, characteristic, complemented
2C2×#16839814C211yesmaximal, characteristic, complemented
3#21448349C211yesmaximal, characteristic, complemented
4#21448335C211yesmaximal, characteristic
5#21447321C211yesmaximal, characteristic, complemented
6#21447258C211yesmaximal, characteristic, complemented
7#21447199C211yesmaximal, characteristic, complemented
8#21447136C211yesmaximal, characteristic, complemented
9#21447017C211yesmaximal, characteristic, complemented
10#21447007C211yesmaximal, characteristic
11#21446823C211yesmaximal, characteristic
12#106×Dic61C211yesmaximal, characteristic, complemented
13#21445638C211yesmaximal, characteristic, complemented
14#102×Dic61C211yesmaximal, characteristic, complemented
15C61×#2065C211yesmaximal, characteristic, complemented
16C22×#11758200C2211yescharacteristic
17C2×#14519757C2211yescharacteristic
18C2×#14519748C2211yescharacteristic
19C2×#14519742C2211yescharacteristic
20C2×D4×Dic61C2211yescharacteristic
21C2×#14519737—21no—
22C2×C42×D61C2211yescharacteristic
23#16839853—24no—
24#16839814—24no—
25C2×#14519709C2211yescharacteristic
26C2×#14519708C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×#14519702C2211yescharacteristic
29C2×#14519702C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×C8×Dic61C2211yescharacteristic
35C2×C8×Dic61C2211yescharacteristic
36#16839668C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839656—21no—
39#16839645—21no—
40#16839638—21no—
41#16839633—21no—
42#16839619C2211yescharacteristic
43#16839619C2211yescharacteristic
44C4⋊C4×Dic61—21no—
45C4⋊C4×Dic61C2211yescharacteristic
46C4⋊C4×Dic61C2211yescharacteristic
47C22⋊C4×Dic61—21no—
48#16839609—21no—
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54C2×#106×C61C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C61×#390C2211yescharacteristic
59C61×#389C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×Dic122C2311yescharacteristic
62C22×C22⋊D61—21no—
63C23×Dic61—21no—
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C2×#11758200—22no—
68C2×#11758200—22no—
69C2×#11758200—22no—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72#14519757—22no—
73#14519757—22no—
74#14519748—22no—
75#14519748—22no—
76#14519742—22no—
77#14519742—22no—
78D4×Dic61—22no—
79D4×Dic61—22no—
80#14519737—44no—
81C2×C4⋊Dic61—21no—
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×C4×Dic61—21no—
93C2×C4×Dic61—21no—
94C2×C4×Dic61—21no—
95C2×C4×Dic61D411yescharacteristic
96C2×C4×Dic61D411yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98C42×D61—22no—
99C42×D61—22no—
100#14519709—22no—
101#14519708—22no—
102C4⋊#92418—22no—
103#14519702—22no—
104#14519702—22no—
105#14519700—22no—
106#14519698—22no—
107#14519689—22no—
108#14519689—22no—
109C8×Dic61—22no—
110C8×Dic61D414yescomplemented
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118C22×D4×C61C2311yescharacteristic
119C22×C8×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C2×C4⋊C4×C61—21no—
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C42×C61C2311yescharacteristic
128#106×C61—22no—
129C4⋊C8×C61—22no—
130#102×C61—22no—
131#102×C61—22no—
132#95×C61—21no—
133C24×C61—21no—
134C23×D61C2×D411yescharacteristic
135C2×D4×C61—21no—
136C2×D4×C61—21no—
137C2×D4×C61—21no—
138C2×D4×C61—21no—
139C2×D4×C61—21no—
140C2×D4×C61#4112yes—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2411yescharacteristic
147C2×C22⋊D61—24no—
148C2×C22⋊D61—42no—
149C2×C22⋊D61—42no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—21no—
154C22×Dic61—42no—
155C22×Dic61—42no—
156C22×Dic61—42no—
157C22×Dic61C2×D411yescharacteristic
158C22×Dic61C2×D411yescharacteristic
159C22×Dic61C2×D411yescharacteristic
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—22no—
169C2×C4×D61—41no—
170C2×C4×D61—41no—
171C2×C4×D61SD1614yescomplemented
172C2×Dic122—21no—
173C2×Dic122—21no—
174C2×Dic122—21no—
175C2×Dic122—21no—
176C2×Dic122—21no—
177C2×Dic122#4112yes—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61C2×D412yes—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—42no—
190C4⋊C4×C61#4112yes—
191C22⋊C4×C61—42no—
192C22⋊C4×C61—42no—
193C42×C61—21no—
194C42×C61—21no—
195C22⋊Dic61—24no—
196C22⋊Dic61—42no—
197#11758200—28no—
198#11758198—24no—
199#11758198—42no—
200#11758198—42no—
201C4⋊Dic61—24no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61—21no—
207C4⋊Dic61#4112yes—
208#11758196—42no—
209#11758196—42no—
210C4×Dic61—22no—
211C4×Dic61—22no—
212C4×Dic61—42no—
213C4×Dic61—42no—
214C4×Dic61—42no—
215C4×Dic61C2×D412yes—
216C4×Dic61#4112yes—
217C2×#92418—21no—
218C2×#92418—21no—
219C2×#92418—21no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418C2×D412yes—
223C23×C61—22no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61—41no—
227C23×C61—41no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61C22×D411yescharacteristic
231C22×D61—21no—
232C22×D61—21no—
233C22×D61—21no—
234C22×D61—21no—
235C22×D61—21no—
236C22×D61—21no—
237C22×D61C2×SD1612yes—
238D4×C61—22no—
239D4×C61—22no—
240D4×C61—41no—
241D4×C61—41no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—22no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61C2×SD1612yes—
257C2×C4×C61C22×D411yescharacteristic
258C2×C4×C61C2×#4111yescharacteristic
259C2×C4×C61C2×#4111yescharacteristic
260C2×C4×C61C2×#4111yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C22⋊D61—48no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—22no—
269C2×Dic61—22no—
270C2×Dic61—21no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—84no—
282C2×Dic61#12112yes—
283C2×Dic61#12112yes—
284C2×Dic61C2×SD1612yes—
285C2×Dic61#13512yes—
286C4×D61—28no—
287C4×D61—44no—
288C4×D61—41no—
289C4×D61—41no—
290C4×D61—41no—
291C4×D61—41no—
292Dic122—22no—
293Dic122—22no—
294Dic122—41no—
295Dic122—41no—
296C8×C61—22no—
297C8×C61—41no—
298#92418—22no—
299#92418—41no—
300#23700—611nomaximal, Sylow
301C22×C61—42no—
302C22×C61—42no—
303C22×C61—42no—
304C22×C61—81no—
305C22×C61—81no—
306C22×C61—81no—
307C22×C61—81no—
308C22×C61C2×#12111yescharacteristic
309C22×C61#52511yescharacteristic
310C22×C61#52511yescharacteristic
311C22×C61C22×SD1611yescharacteristic
312C22×C61C2×#13511yescharacteristic
313C22×C61#57511yescharacteristic
314C22×C61#57511yescharacteristic
315C2×D61—22no—
316C2×D61—22no—
317C2×D61—22no—
318C2×D61—41no—
319C2×D61—41no—
320C2×D61—41no—
321C2×D61—41no—
322C4×C61—22no—
323C4×C61—42no—
324C4×C61—41no—
325C4×C61—81no—
326C4×C61—81no—
327C4×C61#52511yescharacteristic
328C4×C61#52911yescharacteristic
329C4×C61#52911yescharacteristic
330C4×C61#53211yescharacteristic
331Dic61—22no—
332Dic61—42no—
333Dic61—42no—
334Dic61—41no—
335Dic61—81no—
336Dic61—81no—
337Dic61#46514yes—
338C2×C4×SD16—611no—
339C2×#431—611no—
340C4×C22⋊Q8—611no—
341C4×#121—611no—
342#2088—611no—
343#2077—611no—
344#2066—611no—
345#2065D6111yescharacteristic, complemented
346#2055—611no—
347#2035—611no—
348#2034—611no—
349#2000—611no—
350C4×#106—611no—
351C4×#103—611no—
352C4×#102—611no—
353C2×C61—82no—
354C2×C61#239211yescharacteristic
355C2×C61C2×#46511yescharacteristic
356C2×C61#305411yescharacteristic
357C2×C61#310111yescharacteristic
358C2×C61#310211yescharacteristic
359C2×C61#310211yescharacteristic
360C2×C61#310311yescharacteristic
361D61—42no—
362C22×SD16—611no—
363C2×C22⋊Q8—611no—
364C2×#121—611no—
365C2×C4×Q8—611no—
366C2×C4×D4—611no—
367C2×C4×D4—1221no—
368C22×C42—611no—
369C4×SD16—1224no—
370#431—1224no—
371C2×#106—611no—
372C2×#106—611no—
373C2×#106C2×D6111yescharacteristic
374C2×C4⋊C8—611no—
375C2×C4⋊C8C2×D6111yescharacteristic
376C2×#103—611no—
377C2×#103—611no—
378C2×#103—611no—
379C2×#102—611no—
380C2×#102C2×D6111yescharacteristic
381C2×#102C2×D6111yescharacteristic
382C2×C22⋊C8—611no—
383C2×C22⋊C8—611no—
384C2×C4×C8—611no—
385C2×C4×C8—611no—
386#391—611no—
387#390C2×D6111yescharacteristic
388#389—611no—
389#389C2×D6111yescharacteristic
390#388—1221no—
391#387—1221no—
392#386—1221no—
393#385—1221no—
394#380—611no—
395#380—611no—
396C4×C4⋊C4—611no—
397C4×C4⋊C4—611no—
398C4×C4⋊C4—1221no—
399C4×C22⋊C4—1221no—
400C4×C22⋊C4—1221no—
401#340—611no—
402#340—611no—
403#340—611no—
404#340—611no—
405#340—611no—
406#340C2×D6111yescharacteristic
407C61#2370011yescharacteristic, complemented, Sylow
408C22×Q8—611no—
409C22×D4—1221no—
410C22×D4C22×D6111yescharacteristic
411C23×C4—611no—
412C23×C4—611no—
413C23×C4—611no—
414C23×C4—1221no—
415C2×SD16—1222no—
416C2×SD16—1222no—
417C2×SD16—1222no—
418C22×C8—611no—
419C22×C8—611no—
420C22×C8C22×D6111yescharacteristic
421C22×C8C22×D6111yescharacteristic
422C22⋊Q8—1222no—
423C22⋊Q8—1222no—
424#121—1222no—
425#121—1222no—
426C4×Q8—1222no—
427C4×Q8—1222no—
428C4×D4—1222no—
429C4×D4—1222no—
430C4×D4—2444no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—611no—
433C2×C4⋊C4—611no—
434C2×C4⋊C4—611no—
435C2×C4⋊C4—1221no—
436C2×C4⋊C4—1221no—
437C2×C4⋊C4—1221no—
438C2×C4⋊C4C22×D6111yescharacteristic
439C2×C4⋊C4C22×D6111yescharacteristic
440C2×C4⋊C4C22×D6111yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—1221no—
444C2×C22⋊C4—1221no—
445C2×C22⋊C4—1221no—
446C2×C22⋊C4—1221no—
447C2×C22⋊C4—1221no—
448C2×C42—611no—
449C2×C42—611no—
450C2×C42—611no—
451C2×C42—1222no—
452C2×C42—1222no—
453C2×C42—1221no—
454C2×C42—1221no—
455C2×C42—1221no—
456C2×C42C22×D6111yescharacteristic
457#106—22no—
458#106—1222no—
459#106—1222no—
460C4⋊C8—22no—
461C4⋊C8—1222no—
462#103—1222no—
463#103—1222no—
464#103—1222no—
465#102—22no—
466#102—22no—
467#102—1222no—
468C22⋊C8—1222no—
469C22⋊C8—1222no—
470C4×C8—614no—
471C4×C8—1222no—
472#95—21no—
473#95—1221no—
474#95—1221no—
475#95—1221no—
476#95—1221no—
477#95—1221no—
478#95—1221no—
479#95—1221no—
480C24—21no—
481C24—611no—
482C2×Q8—612no—
483C2×Q8—1221no—
484C2×Q8—1221no—
485C2×Q8—1221no—
486C2×Q8—1221no—
487C2×Q8—1221no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—1224no—
494C2×D4—2442no—
495C2×D4—2442no—
496C2×D4#1175822612yes—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—611no—
501C22×C4—611no—
502C22×C4—614no—
503C22×C4—611no—
504C22×C4—1222no—
505C22×C4—1222no—
506C22×C4—1222no—
507C22×C4—1221no—
508C22×C4—1221no—
509C22×C4—1221no—
510C22×C4—1221no—
511C22×C4—1221no—
512C22×C4—1221no—
513C22×C4—1221no—
514C22×C4—1221no—
515C22×C4—1221no—
516C22×C4—1221no—
517C22×C4—2441no—
518C22×C4—2441no—
519C22×C4—2442no—
520C22×C4—2442no—
521C22×C4—2442no—
522C22×C4D4×D6111yescharacteristic
523C22×C4D4×D6111yescharacteristic
524C22×C4C23×D6111yescharacteristic
525SD16—1228no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—612no—
532C2×C8—1221no—
533C2×C8—1221no—
534C2×C8—1221no—
535C2×C8—1221no—
536C2×C8—1221no—
537C2×C8D4×D6112yes—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—42no—
544C4⋊C4—612no—
545C4⋊C4—1224no—
546C4⋊C4—1221no—
547C4⋊C4—1221no—
548C4⋊C4—1221no—
549C4⋊C4—1221no—
550C4⋊C4—1221no—
551C4⋊C4—2442no—
552C4⋊C4—2442no—
553C4⋊C4#1175822412yes—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—1224no—
557C22⋊C4—1224no—
558C22⋊C4—2442no—
559C22⋊C4—2442no—
560C22⋊C4—2442no—
561C42—21no—
562C42—21no—
563C42—612no—
564C42—612no—
565C42—1222no—
566C42—1222no—
567C42—2442no—
568C42—2442no—
569C42—2442no—
570C23—22no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—612no—
578C23—1221no—
579C23—1221no—
580C23—1221no—
581C23—1221no—
582C23—1221no—
583C23—1221no—
584C23C2×D4×D6111yescharacteristic
585Q8—1222no—
586Q8—1222no—
587Q8—2441no—
588Q8—2441no—
589D4—22no—
590D4—22no—
591D4—41no—
592D4—41no—
593D4—2448no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—612no—
609C2×C4—612no—
610C2×C4—612no—
611C2×C4—612no—
612C2×C4—1228no—
613C2×C4—1221no—
614C2×C4—1221no—
615C2×C4—1221no—
616C2×C4—1222no—
617C2×C4—1221no—
618C2×C4—1221no—
619C2×C4—1222no—
620C2×C4—4884no—
621C2×C4—2444no—
622C2×C4—2441no—
623C2×C4—2441no—
624C2×C4—2441no—
625C2×C4—2441no—
626C2×C4—2441no—
627C2×C4—2441no—
628C2×C4—2441no—
629C2×C4—2441no—
630C2×C4—2441no—
631C2×C4—2441no—
632C2×C4—2441no—
633C2×C4—2441no—
634C2×C4—2441no—
635C2×C4—2441no—
636C2×C4SD16×D6112yes—
637C2×C4C2×D4×D6111yescharacteristic
638C2×C4#41×D6111yescharacteristic
639C2×C4#41×D6111yescharacteristic
640C2×C4#41×D6111yescharacteristic
641C2×C4C2×#1175822411yescharacteristic
642C2×C4C2×#1175822611yescharacteristic
643C8—22no—
644C8—41no—
645C8—1222no—
646C8—2441no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—1222no—
655C22—1222no—
656C22—1222no—
657C22—2441no—
658C22—2441no—
659C22—2441no—
660C22—2441no—
661C22#121×D6111yescharacteristic
662C22#1684027211yescharacteristic
663C22#1684027511yescharacteristic
664C22C2×SD16×D6111yescharacteristic
665C22#135×D6111yescharacteristic
666C22#1684055811yescharacteristic
667C22#1684055811yescharacteristic
668C4—22no—
669C4—41no—
670C4—42no—
671C4—81no—
672C4—81no—
673C4—614no—
674C4—1222no—
675C4—4881no—
676C4—4881no—
677C4—2441no—
678C4—2442no—
679C4—2442no—
680C4#1684027511yescharacteristic
681C4#1684029511yescharacteristic
682C4#1684029811yescharacteristic
683C4#1684030711yescharacteristic
684C2—82no—
685C2—2442no—
686C2#2144906411yescharacteristic
687C2#465×D6111yescharacteristic
688C2#2145542611yescharacteristic
689C2#2145582911yescharacteristic
690C2#2145583411yescharacteristic
691C2#2145584211yescharacteristic
692C2#2145584911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2065C2
socleC23×C61C22×D4
prime radicalC2×#14519748C22
hypercenter#2065D61
hypocenterC61#23700
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2065

Complements

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

NH ≅ G/Ntype
1. C2×#16839853C2semidirect
2. C2×#16839814C2semidirect
3. #21448349C2semidirect
5. #21447321C2semidirect
6. #21447258C2semidirect
7. #21447199C2semidirect
8. #21447136C2semidirect
9. #21447017C2semidirect
12. #106×Dic61C2semidirect
13. #21445638C2semidirect
14. #102×Dic61C2semidirect
15. C61×#2065C2semidirect
110. C8×Dic61D4semidirect
171. C2×C4×D61SD16semidirect
345. #2065D61semidirect
407. C61#23700semidirect

Maximal subgroups

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

subgroupindex
C2×#168398532
C2×#168398142
#214483492
#214483352
#214473212
#214472582
#214471992
#214471362
#214470172
#214470072
#214468232
#106×Dic612
#214456382
#102×Dic612
C61×#20652
#2370061