Finite Group Databasebeta

← #29708820

Subgroups — #29708820

Order 15616.

1010 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839760C211yesmaximal, characteristic
2C2×#16839755C211yesmaximal, characteristic
3#21448440C211yesmaximal, characteristic, complemented
4#21448409C211yesmaximal, characteristic
5#21447241C211yesmaximal, characteristic, complemented
6#21447239C211yesmaximal, characteristic, complemented
7#21447235C211yesmaximal, characteristic, complemented
8#21447232C211yesmaximal, characteristic, complemented
9#21447231C211yesmaximal, characteristic, complemented
10#21447228C211yesmaximal, characteristic, complemented
11#21447225C211yesmaximal, characteristic, complemented
12#21445537C211yesmaximal, characteristic, complemented
13#340×D61C211yesmaximal, characteristic, complemented
14#21445514C211yesmaximal, characteristic, complemented
15C61×#2071C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C2×#14519735C2211yescharacteristic
20C2×#14519734C2211yescharacteristic
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×C4⋊C4×D61C2211yescharacteristic
23#16839760—24no—
24#16839755—24no—
25C2×#14519702C2211yescharacteristic
26C2×#14519702C2211yescharacteristic
27C2×#14519700C2211yescharacteristic
28C2×#14519700C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31#16839668C2211yescharacteristic
32#16839667C2211yescharacteristic
33#16839665C2211yescharacteristic
34#16839657—21no—
35#16839657—21no—
36#16839638—21no—
37#16839638—21no—
38#16839633—21no—
39#16839633—21no—
40#16839631C2211yescharacteristic
41#16839628C2211yescharacteristic
42#16839627C2211yescharacteristic
43#16839620—21no—
44#16839620—21no—
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839517C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C61×#390C2211yescharacteristic
57C61×#384C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C2×#11758224—22no—
62C2×#11758224—22no—
63C2×#11758224—22no—
64C2×#11758224—22no—
65C2×#11758224—22no—
66C2×#11758224D414yes—
67C22×Dic122C2311yescharacteristic
68C22×C22⋊D61—21no—
69C23×Dic61—21no—
70C22×C4×D61—21no—
71C22×C4×D61—21no—
72C22×C4×D61C2311yescharacteristic
73C2×#11758189—22no—
74C2×#11758189—22no—
75C2×#11758189—22no—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C2×C8×D61—22no—
79C2×C8×D61—22no—
80C2×C8×D61—22no—
81#14519735—22no—
82#14519735—22no—
83#14519734—22no—
84#14519734—22no—
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×#11758196—21no—
89C2×#11758196—21no—
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×#11758196D411yescharacteristic
93C2×#11758196D411yescharacteristic
94C4⋊C4×D61—22no—
95C4⋊C4×D61—22no—
96C4⋊C4×D61—22no—
97C4⋊C4×D61—22no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×#11758198—21no—
101C2×#11758198D411yescharacteristic
102C2×#11758198D411yescharacteristic
103C2×C4×Dic61—21no—
104C2×C4×Dic61C2311yescharacteristic
105#14519702—22no—
106#14519702—22no—
107#14519700—22no—
108#14519700—22no—
109#14519698—22no—
110#14519698—22no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119C22×D4×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C22×C8×C61C2311yescharacteristic
122C2×C4⋊C4×C61—21no—
123C2×C4⋊C4×C61—21no—
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C42×C61C2311yescharacteristic
130#102×C61—22no—
131#102×C61—22no—
132C24×C61—21no—
133C23×D61C2×D411yescharacteristic
134C2×D4×C61—21no—
135C2×D4×C61—21no—
136C2×D4×C61—21no—
137C2×D4×C61—21no—
138C2×D4×C61—21no—
139C2×D4×C61C2×D412yes—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2411yescharacteristic
146C2×C22⋊D61—24no—
147C2×C22⋊D61—42no—
148C2×C22⋊D61—42no—
149C22×Dic61—21no—
150C22×Dic61—24no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—21no—
154C22×Dic61—42no—
155C22×Dic61—42no—
156C22×Dic61C2×D411yescharacteristic
157C22×Dic61C2×D411yescharacteristic
158C22×Dic61C2×D411yescharacteristic
159#11758224—28no—
160#11758224—28no—
161#11758224—44no—
162#11758224—44no—
163C2×C4×D61—42no—
164C2×C4×D61—42no—
165C2×C4×D61—81no—
166C2×C4×D61—81no—
167C2×C4×D61—81no—
168C2×C4×D61—81no—
169C2×C4×D61C2×D412yes—
170C2×C4×D61#4112yes—
171C2×C4×D61#4112yes—
172C2×C4×D61#4112yes—
173C2×C4×D61#4112yes—
174C2×C4×D61#4112yes—
175C2×Dic122—21no—
176C2×Dic122—21no—
177C2×Dic122—21no—
178C2×Dic122—21no—
179C2×Dic122—21no—
180C2×Dic122C2×D412yes—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C2×C8×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—81no—
194C4⋊C4×C61—81no—
195C22⋊C4×C61—81no—
196C22⋊C4×C61—81no—
197C42×C61—21no—
198C42×C61—21no—
199C22⋊Dic61—81no—
200C22⋊Dic61—81no—
201#11758198—22no—
202#11758198—22no—
203#11758198—42no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61—21no—
207C4⋊Dic61—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61—21no—
210#11758196—22no—
211#11758196—22no—
212#11758196—42no—
213#11758196—42no—
214#11758196—81no—
215#11758196—81no—
216C4×Dic61—21no—
217C4×Dic61—21no—
218C4×Dic61—42no—
219C2×#92418—21no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418—21no—
224C2×#92418—21no—
225#11758189—44no—
226C8×D61—44no—
227C23×C61—22no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61—41no—
231C23×C61—41no—
232C23×C61—41no—
233C23×C61—41no—
234C23×C61C22×D411yescharacteristic
235C22×D61—21no—
236C22×D61—21no—
237C22×D61—21no—
238C22×D61—21no—
239C22×D61#12112yes—
240C22×D61#12312yes—
241C22×D61#12412yes—
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—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—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
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—22no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—48no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287C2×Dic61#12112yes—
288C2×Dic61#12312yes—
289C2×Dic61#12412yes—
290C4×D61—84no—
291C4×D61—84no—
292C4×D61#12314yes—
293C4×D61#12314yes—
294C4×D61#12614yes—
295C4×D61#12614yes—
296Dic122—22no—
297Dic122—22no—
298Dic122—41no—
299Dic122—41no—
300C8×C61—41no—
301C8×C61—41no—
302#92418—41no—
303#92418—41no—
304#23634—611nomaximal, Sylow
305C22×C61—42no—
306C22×C61—42no—
307C22×C61—42no—
308C22×C61—81no—
309C22×C61—81no—
310C22×C61—81no—
311C22×C61—81no—
312C22×C61C2×#12111yescharacteristic
313C22×C61C2×#12311yescharacteristic
314C22×C61C2×#12411yescharacteristic
315C22×C61#57611yescharacteristic
316C22×C61#57711yescharacteristic
317C22×C61#57711yescharacteristic
318C22×C61#57811yescharacteristic
319C2×D61—22no—
320C2×D61—22no—
321C2×D61—22no—
322C2×D61—22no—
323C2×D61—22no—
324C2×D61—22no—
325C2×D61#39714yes—
326C4×C61—41no—
327C4×C61—41no—
328C4×C61—81no—
329C4×C61—81no—
330C4×C61—81no—
331C4×C61C2×#12311yescharacteristic
332C4×C61C2×#12311yescharacteristic
333C4×C61C2×#12611yescharacteristic
334C4×C61C2×#12611yescharacteristic
335Dic61—41no—
336Dic61—41no—
337Dic61—42no—
338Dic61—81no—
339Dic61—81no—
340Dic61—81no—
341Dic61#39714yes—
342C2×#417—611no—
343C2×#416—611no—
344#2317—611no—
345#2311—611no—
346#2074—611no—
347#2074—611no—
348#2073—611no—
349#2073—611no—
350#2072—611no—
351#2072—611no—
352#2071—611no—
353#2071D6111yescharacteristic, complemented
354#1736—611no—
355C2×#340—611no—
356#1729—611no—
357C2×C61—82no—
358C2×C61C2×#39711yescharacteristic
359C2×C61#304511yescharacteristic
360C2×C61#304611yescharacteristic
361C2×C61#309811yescharacteristic
362C2×C61#309911yescharacteristic
363C2×C61#313611yescharacteristic
364C2×C61#313711yescharacteristic
365D61—24no—
366C22×#41—611no—
367C22×M16—611no—
368C23×C8—611no—
369C2×#117—611no—
370C2×#117—611no—
371C22×C4⋊C4—611no—
372C22×C4⋊C4—611no—
373#417—1224no—
374#416—1224no—
375C2×#103—611no—
376C2×#103—611no—
377C2×#103—611no—
378C2×#103—611no—
379C2×#102—611no—
380C2×#102—611no—
381C2×#102C2×D6111yescharacteristic
382C2×#102C2×D6111yescharacteristic
383#391—611no—
384#391—611no—
385#390—611no—
386#390C2×D6111yescharacteristic
387#389—1221no—
388#389—1221no—
389#386—1221no—
390#386—1221no—
391#385—1221no—
392#385—1221no—
393#384—611no—
394#384C2×D6111yescharacteristic
395#382—611no—
396#382—611no—
397#380—1221no—
398#380—1221no—
399#340—611no—
400#340—611no—
401#340—611no—
402#340—611no—
403#340—611no—
404#340—611no—
405#340C2×D6111yescharacteristic
406#340C2×D6111yescharacteristic
407#336—611no—
408#336—611no—
409#336—611no—
410#336C2×D6111yescharacteristic
411C61#2363411yescharacteristic, complemented, Sylow
412C2×#41—614no—
413C2×#41—1222no—
414C2×#41—1222no—
415C2×#41—1222no—
416C2×#41—1222no—
417C2×#41—1222no—
418C22×Q8—611no—
419C22×D4—1221no—
420C22×D4C22×D6111yescharacteristic
421C23×C4—611no—
422C23×C4—1221no—
423C23×C4—1221no—
424C23×C4—1221no—
425C2×M16—1222no—
426C2×M16—1222no—
427C2×M16—1222no—
428C22×C8—611no—
429C22×C8—611no—
430C22×C8—1222no—
431C22×C8—1222no—
432C22×C8—1222no—
433C22×C8C22×D6111yescharacteristic
434C22×C8C22×D6111yescharacteristic
435#117—1222no—
436#117—1222no—
437#117—1222no—
438#117—1222no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—611no—
442C2×C4⋊C4—611no—
443C2×C4⋊C4—611no—
444C2×C4⋊C4—611no—
445C2×C4⋊C4—611no—
446C2×C4⋊C4—1222no—
447C2×C4⋊C4—1222no—
448C2×C4⋊C4—1222no—
449C2×C4⋊C4—1222no—
450C2×C4⋊C4—1221no—
451C2×C4⋊C4—1221no—
452C2×C4⋊C4—1221no—
453C2×C4⋊C4—1221no—
454C2×C4⋊C4C22×D6111yescharacteristic
455C2×C4⋊C4C22×D6111yescharacteristic
456C2×C4⋊C4C22×D6111yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—611no—
460C2×C22⋊C4—611no—
461C2×C22⋊C4—1221no—
462C2×C22⋊C4—1221no—
463C2×C22⋊C4—1221no—
464C2×C42—611no—
465C2×C42—1221no—
466C2×C42C22×D6111yescharacteristic
467#103—1222no—
468#103—1222no—
469#103—1222no—
470#103—1222no—
471#102—22no—
472#102—22no—
473#102—1222no—
474#102—1222no—
475#95—1221no—
476#95—1221no—
477#95—1221no—
478#95—1221no—
479#95—1221no—
480#95—1221no—
481#95—1221no—
482#95—1221no—
483C24—21no—
484C24—611no—
485#41—1228no—
486#41—1228no—
487#41—2444no—
488#41—2444no—
489C2×Q8—612no—
490C2×Q8—1221no—
491C2×Q8—1221no—
492C2×Q8—1221no—
493C2×Q8—1221no—
494C2×Q8—1221no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—1224no—
501C2×D4—2442no—
502C2×D4—2442no—
503C2×D4D4×D6112yes—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—611no—
508C22×C4—612no—
509C22×C4—612no—
510C22×C4—612no—
511C22×C4—612no—
512C22×C4—612no—
513C22×C4—612no—
514C22×C4—611no—
515C22×C4—611no—
516C22×C4—1224no—
517C22×C4—1221no—
518C22×C4—1221no—
519C22×C4—1221no—
520C22×C4—1221no—
521C22×C4—4881no—
522C22×C4—4881no—
523C22×C4—4881no—
524C22×C4—4881no—
525C22×C4—2442no—
526C22×C4—2442no—
527C22×C4—2442no—
528C22×C4—2442no—
529C22×C4D4×D6111yescharacteristic
530C22×C4D4×D6111yescharacteristic
531C22×C4C23×D6111yescharacteristic
532M16—2444no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—1221no—
540C2×C8—1221no—
541C2×C8—1221no—
542C2×C8—1221no—
543C2×C8—1221no—
544C2×C8—1221no—
545C2×C8—2444no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—81no—
553C4⋊C4—81no—
554C4⋊C4—1222no—
555C4⋊C4—1222no—
556C4⋊C4—1221no—
557C4⋊C4—1221no—
558C4⋊C4—1221no—
559C4⋊C4—1221no—
560C4⋊C4—1221no—
561C4⋊C4—1221no—
562C4⋊C4—4881no—
563C4⋊C4—4881no—
564C4⋊C4—2442no—
565C4⋊C4—2442no—
566C22⋊C4—81no—
567C22⋊C4—81no—
568C22⋊C4—1222no—
569C22⋊C4—1222no—
570C22⋊C4—4881no—
571C22⋊C4—4881no—
572C22⋊C4—2442no—
573C42—21no—
574C42—21no—
575C42—1221no—
576C42—1221no—
577C42—2442no—
578C23—22no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—612no—
586C23—612no—
587C23—612no—
588C23—1221no—
589C23—1221no—
590C23—1221no—
591C23—1221no—
592C23C2×D4×D6111yescharacteristic
593Q8—1222no—
594Q8—1222no—
595Q8—2441no—
596Q8—2441no—
597D4—22no—
598D4—22no—
599D4—41no—
600D4—41no—
601D4—2448no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—612no—
618C2×C4—612no—
619C2×C4—612no—
620C2×C4—614no—
621C2×C4—614no—
622C2×C4—614no—
623C2×C4—614no—
624C2×C4—1222no—
625C2×C4—1221no—
626C2×C4—1221no—
627C2×C4—1221no—
628C2×C4—1221no—
629C2×C4—1221no—
630C2×C4—1221no—
631C2×C4—4884no—
632C2×C4—4884no—
633C2×C4—2448no—
634C2×C4—2441no—
635C2×C4—2441no—
636C2×C4—2441no—
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×C4C2×D4×D6111yescharacteristic
646C2×C4#41×D6111yescharacteristic
647C2×C4#41×D6111yescharacteristic
648C2×C4#41×D6111yescharacteristic
649C2×C4#41×D6111yescharacteristic
650C2×C4#41×D6111yescharacteristic
651C8—41no—
652C8—41no—
653C8—2441no—
654C8—2441no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22—614no—
663C22—1222no—
664C22—1222no—
665C22—1222no—
666C22—1222no—
667C22—1222no—
668C22—1222no—
669C22#121×D6111yescharacteristic
670C22#123×D6111yescharacteristic
671C22#124×D6111yescharacteristic
672C22#1684056311yescharacteristic
673C22#1684056811yescharacteristic
674C22#1684057211yescharacteristic
675C22#1684057811yescharacteristic
676C4—41no—
677C4—41no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4—614no—
682C4—4881no—
683C4—4881no—
684C4—4881no—
685C4—2442no—
686C4—2441no—
687C4—2441no—
688C4#123×D6111yescharacteristic
689C4#123×D6111yescharacteristic
690C4#126×D6111yescharacteristic
691C4#126×D6111yescharacteristic
692C2—82no—
693C2—1224no—
694C2#397×D6111yescharacteristic
695C2#2145535311yescharacteristic
696C2#2145536411yescharacteristic
697C2#2145579211yescharacteristic
698C2#2145580911yescharacteristic
699C2#2145616811yescharacteristic
700C2#2145618111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2071C2
socleC23×C61C22×D4
prime radicalC22×#11758224C22
hypercenter#2071D61
hypocenterC61#23634
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2071

Complements

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

NH ≅ G/Ntype
3. #21448440C2semidirect
5. #21447241C2semidirect
6. #21447239C2semidirect
7. #21447235C2semidirect
8. #21447232C2semidirect
9. #21447231C2semidirect
10. #21447228C2semidirect
11. #21447225C2semidirect
12. #21445537C2semidirect
13. #340×D61C2semidirect
14. #21445514C2semidirect
15. C61×#2071C2semidirect
353. #2071D61semidirect
411. C61#23634semidirect

Maximal subgroups

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

subgroupindex
C2×#168397602
C2×#168397552
#214484402
#214484092
#214472412
#214472392
#214472352
#214472322
#214472312
#214472282
#214472252
#214455372
#340×D612
#214455142
C61×#20712
#2363461