Finite Group Databasebeta

← #29736989

Subgroups — #29736989

Order 15616.

1054 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×Dic122C211yesmaximal, characteristic, complemented
2C2×#16840120C211yesmaximal, characteristic
3C2×#16839982C211yesmaximal, characteristic
4#21451304C211yesmaximal, characteristic
5#21446961C211yesmaximal, characteristic, complemented
6#21446959C211yesmaximal, characteristic, complemented
7#21446955C211yesmaximal, characteristic
8#21446953C211yesmaximal, characteristic
9#21446769C211yesmaximal, characteristic, complemented
10#21446757C211yesmaximal, characteristic, complemented
11#21446176C211yesmaximal, characteristic
12#21446160C211yesmaximal, characteristic, complemented
13#21446158C211yesmaximal, characteristic, complemented
14#21445651C211yesmaximal, characteristic, complemented
15C61×#1880C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17Q8×Dic122—24no—
18Q8×Dic122—24no—
19C2×#14519777—21no—
20C2×#14519777C2211yescharacteristic
21C2×#14519776—21no—
22C2×#14519776—21no—
23C2×#14519776C2211yescharacteristic
24C2×#14519776C2211yescharacteristic
25C2×#14519764C2211yescharacteristic
26C2×Q8×Dic61C2211yescharacteristic
27C2×Q8×Dic61C2211yescharacteristic
28C2×C4×Dic122—21no—
29C2×C4×Dic122C2211yescharacteristic
30#16840120—24no—
31#16839982—24no—
32C2×#14519706C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519687C2211yescharacteristic
40#16839690—21no—
41#16839674—21no—
42#16839668C2211yescharacteristic
43#16839667C2211yescharacteristic
44#16839665C2211yescharacteristic
45#16839655—21no—
46#16839650—21no—
47C4⋊C4×Dic61C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839517C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C22×SD16×C61C2211yescharacteristic
57C2×C4×Q8×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C61×#390C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122—21no—
65C22×Dic122—21no—
66C22×Dic122D411yescharacteristic
67C22×Dic122C2311yescharacteristic
68C2×#11758202—22no—
69C2×#11758202—22no—
70C2×#11758202—22no—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73#14519777—28no—
74#14519777—22no—
75#14519777—22no—
76#14519776—28no—
77#14519776—28no—
78#14519776—22no—
79#14519776—22no—
80#14519776—22no—
81#14519776D414yes—
82#14519764—22no—
83#14519764—22no—
84Q8×Dic61—22no—
85Q8×Dic61—22no—
86Q8×Dic61—22no—
87Q8×Dic61D414yes—
88C4×Dic122—28no—
89C4×Dic122—22no—
90C4×Dic122—22no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61—21no—
94C2×C4⋊Dic61D411yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196D411yescharacteristic
101C2×#11758196D411yescharacteristic
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—21no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—21no—
109C2×C4×Dic61C2311yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111#14519706—22no—
112#14519702—22no—
113#14519702—22no—
114#14519701—22no—
115#14519700—22no—
116#14519698—22no—
117#14519698—22no—
118#14519687—22no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124C22×Q8×C61C2311yescharacteristic
125C22×D4×C61C2311yescharacteristic
126C2×SD16×C61—22no—
127C2×SD16×C61—22no—
128C2×SD16×C61—22no—
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C4×Q8×C61—22no—
132C4×Q8×C61—22no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C42×C61—21no—
139C2×C42×C61C2311yescharacteristic
140#103×C61—22no—
141#102×C61—22no—
142C24×C61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61C2×D412yes—
147C2×Q8×C61#4112yes—
148C2×Q8×C61#4112yes—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2411yescharacteristic
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61C2×D411yescharacteristic
166C22×Dic61C2×D411yescharacteristic
167C22×Dic61C2×D411yescharacteristic
168C22×Dic61C2×D411yescharacteristic
169C2×Dic122—22no—
170C2×Dic122—22no—
171C2×Dic122—22no—
172C2×Dic122—21no—
173C2×Dic122—21no—
174C2×Dic122—21no—
175C2×Dic122—21no—
176C2×Dic122—21no—
177C2×Dic122—21no—
178C2×Dic122—24no—
179C2×Dic122—24no—
180C2×Dic122—24no—
181C2×Dic122—81no—
182C2×Dic122—81no—
183C2×Dic122—81no—
184C2×Dic122—81no—
185C2×Dic122—81no—
186C2×Dic122—81no—
187SD16×C61—44no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C4⋊C4×C61—24no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61C2×D412yes—
199C22⋊C4×C61—42no—
200C22⋊C4×C61—81no—
201C42×C61—24no—
202C42×C61—21no—
203C42×C61—21no—
204C22⋊Dic61—42no—
205C22⋊Dic61—42no—
206C22⋊Dic61—42no—
207C22⋊Dic61—81no—
208#11758202—44no—
209C4⋊Dic61—24no—
210C4⋊Dic61—24no—
211C4⋊Dic61—21no—
212C4⋊Dic61—21no—
213C4⋊Dic61—24no—
214C4⋊Dic61—22no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61C2×D412yes—
218C4⋊Dic61C2×D412yes—
219#11758196—24no—
220#11758196—24no—
221#11758196—22no—
222#11758196—22no—
223C4×Dic61—24no—
224C4×Dic61—21no—
225C4×Dic61—21no—
226C4×Dic61—24no—
227C4×Dic61—81no—
228C4×Dic61C2×D412yes—
229C4×Dic61C2×D412yes—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61C22×D411yescharacteristic
244Q8×C61—22no—
245Q8×C61—22no—
246Q8×C61—22no—
247Q8×C61#12414yes—
248D4×C61—41no—
249D4×C61—41no—
250D4×C61—41no—
251D4×C61—41no—
252C2×C4×C61—22no—
253C2×C4×C61—21no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—22no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61#13712yes—
267C2×C4×C61C22×D411yescharacteristic
268C2×C4×C61C22×D411yescharacteristic
269C2×C4×C61C2×#4111yescharacteristic
270C2×C4×C61C2×#4111yescharacteristic
271C2×C4×C612−1+411yescharacteristic
272C2×C4×C612−1+411yescharacteristic
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—22no—
281C2×Dic61—22no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61—41no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61#12012yes—
295C2×Dic61#12012yes—
296C2×Dic61#13712yes—
297Dic122—28no—
298Dic122—41no—
299Dic122—41no—
300Dic122—41no—
301Dic122—41no—
302Dic122—84no—
303Dic122—84no—
304Dic122—84no—
305C8×C61—41no—
306C8×C61—41no—
307#92418—41no—
308#92418—41no—
309#25942—611nomaximal, Sylow
310C22×C61—81no—
311C22×C61—81no—
312C22×C61—81no—
313C22×C61—81no—
314C22×C61—81no—
315C22×C61—81no—
316C22×C61—81no—
317C22×C61C2×#12011yescharacteristic
318C22×C61#54811yescharacteristic
319C22×C61#54811yescharacteristic
320C22×C61C2×#13711yescharacteristic
321C22×C61C2×#13711yescharacteristic
322C22×C61#57611yescharacteristic
323C22×C61#57711yescharacteristic
324C4×C61—24no—
325C4×C61—22no—
326C4×C61—41no—
327C4×C61—42no—
328C4×C61—81no—
329C4×C61C2×#12411yescharacteristic
330C4×C61#53611yescharacteristic
331C4×C61#54811yescharacteristic
332C4×C61#54811yescharacteristic
333Dic61—22no—
334Dic61—22no—
335Dic61—22no—
336Dic61—41no—
337Dic61—42no—
338Dic61—42no—
339Dic61—81no—
340Dic61—81no—
341C2×Q82—611no—
342C2×#489—611no—
343C2×#464—611no—
344#2592—611no—
345#2024—611no—
346#2024—611no—
347#2023—611no—
348#2023—611no—
349#1988—611no—
350#1985—611no—
351#1880—611no—
352#1880D6111yescharacteristic
353#1878—611no—
354#1878—611no—
355#1763—611no—
356C2×C61—161no—
357C2×C61#243611yescharacteristic
358C2×C61#300411yescharacteristic
359C2×C61#301211yescharacteristic
360C2×C61#336911yescharacteristic
361C2×C61#336911yescharacteristic
362C2×C61#337511yescharacteristic
363C2×C61#337511yescharacteristic
364C22×Q16—611no—
365C22×SD16C2×D6111yescharacteristic
366Q82—1224no—
367Q82—1224no—
368C2×C4⋊Q8—611no—
369C2×C4⋊Q8—611no—
370C2×C4⋊Q8—611no—
371C2×C4⋊Q8—1221no—
372C2×C4⋊Q8—1221no—
373C2×C4⋊Q8—1221no—
374C2×#124—611no—
375C2×C4×Q8—611no—
376C2×C4×Q8—611no—
377C2×C4×Q8—611no—
378C2×C4×Q8—1221no—
379C2×C4×Q8C2×D6111yescharacteristic
380#489—1224no—
381#464—1224no—
382C2×C4⋊C8—611no—
383C2×#103—611no—
384C2×#103—611no—
385C2×#103—611no—
386C2×#103—611no—
387C2×#103C2×D6111yescharacteristic
388C2×#102—611no—
389C2×#102—611no—
390C2×#102C2×D6111yescharacteristic
391C2×#97—611no—
392#397—1221no—
393#393—1221no—
394#391—611no—
395#391—611no—
396#390—611no—
397#390C2×D6111yescharacteristic
398#388—1221no—
399#388—1221no—
400C4×C4⋊C4—611no—
401#340—611no—
402#340—611no—
403#340—611no—
404#340—611no—
405#340—611no—
406#340C2×D6111yescharacteristic
407#336—611no—
408#336—611no—
409#336—611no—
410#336C2×D6111yescharacteristic
411C61#2594211yescharacteristic, complemented, Sylow
412C22×Q8—611no—
413C22×Q8—611no—
414C22×Q8—1221no—
415C22×Q8—1221no—
416C22×Q8—1221no—
417C22×Q8C22×D6111yescharacteristic
418C22×D4C22×D6111yescharacteristic
419C2×Q16—1222no—
420C2×Q16—1222no—
421C2×Q16—1222no—
422C2×SD16—22no—
423C2×SD16—22no—
424C2×SD16—22no—
425C22×C8—611no—
426C22×C8—611no—
427C22×C8C22×D6111yescharacteristic
428C22×C8C22×D6111yescharacteristic
429C4⋊Q8—614no—
430C4⋊Q8—1222no—
431C4⋊Q8—1222no—
432C4⋊Q8—1228no—
433C4⋊Q8—1222no—
434C4⋊Q8—1222no—
435C4⋊Q8—1228no—
436C4⋊Q8—1228no—
437C4⋊Q8—1222no—
438#124—1222no—
439#124—1222no—
440C4×Q8—22no—
441C4×Q8—22no—
442C4×Q8—614no—
443C4×Q8—1222no—
444C4×Q8—1222no—
445C4×Q8—1228no—
446C4×Q8—1222no—
447C4×Q8—1222no—
448C4×Q8—1222no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—611no—
451C2×C4⋊C4—611no—
452C2×C4⋊C4—611no—
453C2×C4⋊C4—611no—
454C2×C4⋊C4—611no—
455C2×C4⋊C4—611no—
456C2×C4⋊C4—1221no—
457C2×C4⋊C4—1221no—
458C2×C4⋊C4—1221no—
459C2×C4⋊C4—1221no—
460C2×C4⋊C4—1221no—
461C2×C4⋊C4C22×D6111yescharacteristic
462C2×C4⋊C4C22×D6111yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—1221no—
466C2×C22⋊C4—1221no—
467C2×C22⋊C4—1221no—
468C2×C22⋊C4—1221no—
469C2×C42—21no—
470C2×C42—611no—
471C2×C42—611no—
472C2×C42—1221no—
473C2×C42—1221no—
474C2×C42—1221no—
475C2×C42C22×D6111yescharacteristic
476C4⋊C8—1222no—
477#103—22no—
478#103—1222no—
479#103—1222no—
480#103—1222no—
481#103—1222no—
482#102—22no—
483#102—1222no—
484#102—1222no—
485#97—1222no—
486#95—1221no—
487#95—1221no—
488#95—1221no—
489#95—1221no—
490#95—1221no—
491C24—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—1222no—
496C2×Q8—1222no—
497C2×Q8—1224no—
498C2×Q8—1224no—
499C2×Q8—1224no—
500C2×Q8—1222no—
501C2×Q8—1221no—
502C2×Q8—1221no—
503C2×Q8—1221no—
504C2×Q8—1221no—
505C2×Q8—1221no—
506C2×Q8—1221no—
507C2×Q8—4881no—
508C2×Q8—4881no—
509C2×Q8—4881no—
510C2×Q8—4881no—
511C2×Q8—4881no—
512C2×Q8—4881no—
513C2×Q8#1175822212yes—
514C2×Q8D4×D6112yes—
515C2×Q8#1175822412yes—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—611no—
526C22×C4—611no—
527C22×C4—611no—
528C22×C4—611no—
529C22×C4—1221no—
530C22×C4—1221no—
531C22×C4—1221no—
532C22×C4—1221no—
533C22×C4D4×D6111yescharacteristic
534C22×C4D4×D6111yescharacteristic
535C22×C4C23×D6111yescharacteristic
536Q16—2444no—
537SD16—44no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—1221no—
545C2×C8—1221no—
546C2×C8—1221no—
547C2×C8—1221no—
548C2×C8—1221no—
549C2×C8—1221no—
550C4⋊C4—24no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—612no—
555C4⋊C4—612no—
556C4⋊C4—1222no—
557C4⋊C4—1222no—
558C4⋊C4—1222no—
559C4⋊C4—1224no—
560C4⋊C4—1224no—
561C4⋊C4—1224no—
562C4⋊C4—1224no—
563C4⋊C4—1224no—
564C4⋊C4—1221no—
565C4⋊C4—1221no—
566C4⋊C4—1221no—
567C4⋊C4—1221no—
568C4⋊C4D4×D6112yes—
569C22⋊C4—42no—
570C22⋊C4—81no—
571C22⋊C4—4881no—
572C22⋊C4—2442no—
573C22⋊C4—2442no—
574C22⋊C4—2442no—
575C42—24no—
576C42—21no—
577C42—21no—
578C42—612no—
579C42—612no—
580C42—1224no—
581C42—1224no—
582C42—1221no—
583C42—1221no—
584C42—4881no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23C2×D4×D6111yescharacteristic
593Q8—22no—
594Q8—22no—
595Q8—22no—
596Q8—1228no—
597Q8—4884no—
598Q8—4884no—
599Q8—4884no—
600Q8—2441no—
601Q8—2441no—
602Q8—2441no—
603Q8—2441no—
604Q8#1451976314yes—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—41no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—612no—
624C2×C4—612no—
625C2×C4—612no—
626C2×C4—1221no—
627C2×C4—1221no—
628C2×C4—1221no—
629C2×C4—1221no—
630C2×C4—1221no—
631C2×C4—1221no—
632C2×C4—1222no—
633C2×C4—1222no—
634C2×C4—1221no—
635C2×C4—1221no—
636C2×C4—1221no—
637C2×C4—2441no—
638C2×C4—2441no—
639C2×C4—2441no—
640C2×C4—2441no—
641C2×C4—2441no—
642C2×C4—2441no—
643C2×C4—2441no—
644C2×C4—2441no—
645C2×C4—2441no—
646C2×C4—2441no—
647C2×C4#1451980612yes—
648C2×C4C2×D4×D6111yescharacteristic
649C2×C4C2×D4×D6111yescharacteristic
650C2×C4C2×#1175822411yescharacteristic
651C2×C4C2×#1175822211yescharacteristic
652C2×C4#1451982411yescharacteristic
653C2×C4#1451982411yescharacteristic
654C8—41no—
655C8—41no—
656C8—2441no—
657C8—2441no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22#120×D6111yescharacteristic
666C22#1684041811yescharacteristic
667C22#1684042111yescharacteristic
668C22#137×D6111yescharacteristic
669C22C2×#1451980611yescharacteristic
670C22#1684056611yescharacteristic
671C22#1684056911yescharacteristic
672C4—24no—
673C4—22no—
674C4—41no—
675C4—42no—
676C4—81no—
677C4—1222no—
678C4—1222no—
679C4—1222no—
680C4—4881no—
681C4—4881no—
682C4—2441no—
683C4—2442no—
684C4—2442no—
685C4C2×#1451976311yescharacteristic
686C4#1684033411yescharacteristic
687C4#1684041811yescharacteristic
688C4#1684042111yescharacteristic
689C2—161no—
690C2#2144947511yescharacteristic
691C2#2145505011yescharacteristic
692C2#2145512111yescharacteristic
693C2#2145855411yescharacteristic
694C2#2145855711yescharacteristic
695C2#2145863411yescharacteristic
696C2#2145863711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1880C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
hypercenter#1880D61
hypocenterC61#25942
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic122C2semidirect
5. #21446961C2semidirect
6. #21446959C2semidirect
9. #21446769C2semidirect
10. #21446757C2semidirect
12. #21446160C2semidirect
13. #21446158C2semidirect
14. #21445651C2semidirect
411. C61#25942semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic1222
C2×#168401202
C2×#168399822
#214513042
#214469612
#214469592
#214469552
#214469532
#214467692
#214467572
#214461762
#214461602
#214461582
#214456512
C61×#18802
#2594261