Finite Group Databasebeta

← #29709479

Subgroups — #29709479

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×SD16×Dic61C211yesmaximal, characteristic, complemented
2C2×#16839814C211yesmaximal, characteristic, complemented
3#21448357C211yesmaximal, characteristic, complemented
4#21448335C211yesmaximal, characteristic
5#21447317C211yesmaximal, characteristic, complemented
6#21447254C211yesmaximal, characteristic, complemented
7#21447214C211yesmaximal, characteristic, complemented
8#21447207C211yesmaximal, characteristic, complemented
9#21447020C211yesmaximal, characteristic, complemented
10#21446999C211yesmaximal, characteristic
11#21446819C211yesmaximal, characteristic
12#21445711C211yesmaximal, characteristic, complemented
13#103×Dic61C211yesmaximal, characteristic, complemented
14#102×Dic61C211yesmaximal, characteristic, complemented
15C61×#2055C211yesmaximal, characteristic, complemented
16C2×#14519753C2211yescharacteristic
17C2×#14519748C2211yescharacteristic
18C2×Q8×Dic61C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20C2×#14519737—21no—
21C2×C42×D61C2211yescharacteristic
22SD16×Dic61—24no—
23#16839814—24no—
24C2×#14519710C2211yescharacteristic
25C2×#14519710C2211yescharacteristic
26C2×#14519709C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×C8×Dic61C2211yescharacteristic
35C2×C8×Dic61C2211yescharacteristic
36#16839660C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839656—21no—
39#16839649—21no—
40#16839638—21no—
41#16839636—21no—
42#16839619C2211yescharacteristic
43#16839619C2211yescharacteristic
44C4⋊C4×Dic61C2211yescharacteristic
45C4⋊C4×Dic61C2211yescharacteristic
46#16839613—21no—
47C22⋊C4×Dic61—21no—
48#16839609—21no—
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54C22×SD16×C61C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×#103×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C61×#391C2211yescharacteristic
59C61×#390C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×C22⋊D61—21no—
62C23×Dic61—21no—
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68#14519753—22no—
69#14519753—22no—
70#14519748—22no—
71#14519748—22no—
72Q8×Dic61—22no—
73Q8×Dic61—22no—
74D4×Dic61—22no—
75D4×Dic61—22no—
76#14519737—44no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×C4×Dic61—21no—
91C2×C4×Dic61—21no—
92C2×C4×Dic61—21no—
93C2×C4×Dic61D411yescharacteristic
94C2×C4×Dic61D411yescharacteristic
95C2×C4×Dic61C2311yescharacteristic
96C42×D61—22no—
97C42×D61—22no—
98#14519710—22no—
99#14519710—22no—
100#14519709—22no—
101C4⋊#92418—22no—
102#14519701—22no—
103#14519701—22no—
104#14519698—22no—
105#14519698—22no—
106#14519689—22no—
107#14519689—22no—
108C8×Dic61—22no—
109C8×Dic61D414yescomplemented
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116C22×Q8×C61C2311yescharacteristic
117C22×D4×C61C2311yescharacteristic
118C2×SD16×C61—22no—
119C2×SD16×C61—22no—
120C2×SD16×C61—22no—
121C22×C8×C61C2311yescharacteristic
122C22×C8×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C42×C61C2311yescharacteristic
128C4⋊C8×C61—22no—
129#103×C61—22no—
130#102×C61—22no—
131#95×C61—21no—
132#95×C61—21no—
133C24×C61—21no—
134C23×D61C2×D411yescharacteristic
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61—21no—
139C2×Q8×C61—21no—
140C2×Q8×C61#4112yes—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61#4112yes—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2411yescharacteristic
153C2×C22⋊D61—24no—
154C2×C22⋊D61—42no—
155C2×C22⋊D61—42no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—42no—
161C22×Dic61—42no—
162C22×Dic61—42no—
163C22×Dic61C2×D411yescharacteristic
164C22×Dic61C2×D411yescharacteristic
165C22×Dic61C2×D411yescharacteristic
166C2×C4×D61—22no—
167C2×C4×D61—22no—
168C2×C4×D61—22no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—22no—
178SD16×C61—28no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C2×C8×C61C2×D412yes—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C22⋊C4×C61—42no—
190C22⋊C4×C61—42no—
191C42×C61—21no—
192C42×C61—21no—
193C22⋊Dic61—24no—
194C22⋊Dic61—42no—
195#11758198—24no—
196#11758198—42no—
197#11758198—42no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—42no—
205C4⋊Dic61#4112yes—
206C4⋊Dic61#4112yes—
207#11758196—24no—
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×D61#13512yes—
238Q8×C61—22no—
239Q8×C61—22no—
240Q8×C61—41no—
241Q8×C61—41no—
242D4×C61—22no—
243D4×C61—22no—
244D4×C61—41no—
245D4×C61—41no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—22no—
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—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61#13512yes—
261C2×C4×C61C22×D411yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C2×C4×C61C2×#4111yescharacteristic
264C2×C4×C61C2×#4111yescharacteristic
265C2×C4×C61C2×#4111yescharacteristic
266C2×C4×C61C2×#4111yescharacteristic
267C22⋊D61—48no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—22no—
273C2×Dic61—22no—
274C2×Dic61—21no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—84no—
286C2×Dic61#12112yes—
287C2×Dic61#12112yes—
288C2×Dic61AGL(1,ℤ/8)12yes—
289C2×Dic61#13712yes—
290C4×D61—28no—
291C4×D61—41no—
292C4×D61—41no—
293C4×D61—41no—
294C4×D61—41no—
295C4×D61—44no—
296C8×C61—22no—
297C8×C61—41no—
298#92418—22no—
299#92418—41no—
300#23701—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×C61C2×#13511yescharacteristic
312C22×C61C2×#13511yescharacteristic
313C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
314C22×C61C2×#13711yescharacteristic
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#46814yes—
338C2×C4×SD16—611no—
339C2×#431—611no—
340C4×C22⋊Q8—611no—
341C4×#121—611no—
342#2088—611no—
343#2077—611no—
344#2068—611no—
345#2067—611no—
346#2055D6111yescharacteristic, complemented
347#2036—611no—
348#2033—611no—
349#2000—611no—
350C4×#107—611no—
351C4×#103—611no—
352C4×#102—611no—
353C2×C61—82no—
354C2×C61#239211yescharacteristic
355C2×C61#305011yescharacteristic
356C2×C61C2×#46811yescharacteristic
357C2×C61#310511yescharacteristic
358C2×C61#310611yescharacteristic
359C2×C61#310711yescharacteristic
360C2×C61#310811yescharacteristic
361D61—42no—
362C22×SD16C2×D6111yescharacteristic
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×#107—611no—
372C2×#107—611no—
373C2×#106—611no—
374C2×C4⋊C8—611no—
375C2×C4⋊C8C2×D6111yescharacteristic
376C2×#103—611no—
377C2×#103—611no—
378C2×#103C2×D6111yescharacteristic
379C2×#102—611no—
380C2×#102—611no—
381C2×#102C2×D6111yescharacteristic
382C2×C22⋊C8—611no—
383C2×C22⋊C8—611no—
384C2×C4×C8—611no—
385C2×C4×C8—611no—
386#391C2×D6111yescharacteristic
387#390C2×D6111yescharacteristic
388#389—611no—
389#389—611no—
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#2370111yescharacteristic, complemented, Sylow
408C22×Q8C22×D6111yescharacteristic
409C22×D4—1221no—
410C22×D4C22×D6111yescharacteristic
411C23×C4—611no—
412C23×C4—611no—
413C23×C4—611no—
414C23×C4—1221no—
415C2×SD16—22no—
416C2×SD16—22no—
417C2×SD16—22no—
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—611no—
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⋊C4—1221no—
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#107—1222no—
458#107—1222no—
459#106—1222no—
460C4⋊C8—22no—
461C4⋊C8—1222no—
462#103—22no—
463#103—1222no—
464#103—1222no—
465#102—22no—
466#102—1222no—
467#102—1222no—
468C22⋊C8—1222no—
469C22⋊C8—1222no—
470C4×C8—614no—
471C4×C8—1222no—
472#95—21no—
473#95—21no—
474#95—1221no—
475#95—1221no—
476#95—1221no—
477#95—1221no—
478#95—1221no—
479#95—1221no—
480C24—21no—
481C24—611no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8#1175822412yes—
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#1175822412yes—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—611no—
501C22×C4—611no—
502C22×C4—611no—
503C22×C4—1222no—
504C22×C4—1222no—
505C22×C4—1222no—
506C22×C4—1222no—
507C22×C4—1222no—
508C22×C4—1222no—
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—1221no—
518C22×C4—1221no—
519C22×C4—2442no—
520C22×C4—2442no—
521C22×C4—2442no—
522C22×C4D4×D6111yescharacteristic
523C22×C4D4×D6111yescharacteristic
524C22×C4C23×D6111yescharacteristic
525SD16—28no—
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—612no—
543C4⋊C4—612no—
544C4⋊C4—1224no—
545C4⋊C4—1221no—
546C4⋊C4—1221no—
547C4⋊C4—1221no—
548C4⋊C4—1221no—
549C4⋊C4—1221no—
550C4⋊C4—1221no—
551C4⋊C4—2442no—
552C4⋊C4—2442no—
553C4⋊C4—2442no—
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—22no—
586Q8—22no—
587Q8—41no—
588Q8—41no—
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—1221no—
617C2×C4—1222no—
618C2×C4—1222no—
619C2×C4—1221no—
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×C4#1451979812yes—
637C2×C4C2×D4×D6111yescharacteristic
638C2×C4#41×D6111yescharacteristic
639C2×C4#41×D6111yescharacteristic
640C2×C4#41×D6111yescharacteristic
641C2×C4C2×#1175822411yescharacteristic
642C2×C4C2×#1175822411yescharacteristic
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#1684027211yescharacteristic
664C22#135×D6111yescharacteristic
665C22C2×#1451979811yescharacteristic
666C22AGL(1,ℤ/8)×D6111yescharacteristic
667C22#137×D6111yescharacteristic
668C4—22no—
669C4—41no—
670C4—42no—
671C4—81no—
672C4—81no—
673C4—614no—
674C4—1222no—
675C4—4881no—
676C4—4881no—
677C4—2442no—
678C4—2441no—
679C4—2442no—
680C4#1684026811yescharacteristic
681C4#1684028911yescharacteristic
682C4#1684028911yescharacteristic
683C4#1684031111yescharacteristic
684C2—82no—
685C2—2442no—
686C2#2144905811yescharacteristic
687C2#2145539511yescharacteristic
688C2#468×D6111yescharacteristic
689C2#2145586511yescharacteristic
690C2#2145587811yescharacteristic
691C2#2145588711yescharacteristic
692C2#2145589811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2055C2
socleC23×C61C22×D4
prime radicalC2×#14519748C22
hypercenter#2055D61
hypocenterC61#23701
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2055

Complements

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

NH ≅ G/Ntype
1. C2×SD16×Dic61C2semidirect
2. C2×#16839814C2semidirect
3. #21448357C2semidirect
5. #21447317C2semidirect
6. #21447254C2semidirect
7. #21447214C2semidirect
8. #21447207C2semidirect
9. #21447020C2semidirect
12. #21445711C2semidirect
13. #103×Dic61C2semidirect
14. #102×Dic61C2semidirect
15. C61×#2055C2semidirect
109. C8×Dic61D4semidirect
346. #2055D61semidirect
407. C61#23701semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic612
C2×#168398142
#214483572
#214483352
#214473172
#214472542
#214472142
#214472072
#214470202
#214469992
#214468192
#214457112
#103×Dic612
#102×Dic612
C61×#20552
#2370161