Finite Group Databasebeta

← #29709521

Subgroups — #29709521

Order 15616.

820 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758202C211yesmaximal, characteristic, complemented
2C2×#16839824C211yesmaximal, characteristic
3#21448502C211yesmaximal, characteristic
4#21448495C211yesmaximal, characteristic
5#21447316C211yesmaximal, characteristic, complemented
6#21447251C211yesmaximal, characteristic
7#21447201C211yesmaximal, characteristic, complemented
8#21447196C211yesmaximal, characteristic, complemented
9#21447140C211yesmaximal, characteristic, complemented
10#21447018C211yesmaximal, characteristic
11#21447013C211yesmaximal, characteristic
12#21446828C211yesmaximal, characteristic
13C4×#14519708C211yesmaximal, characteristic, complemented
14#21445650C211yesmaximal, characteristic, complemented
15C61×#1763C211yesmaximal, characteristic, complemented
16C22×#11758202C2211yescharacteristic
17C2×#14519757C2211yescharacteristic
18C2×#14519753C2211yescharacteristic
19C2×C4×Dic122C2211yescharacteristic
20C2×#14519734C2211yescharacteristic
21C4×#11758202—24no—
22#16839824—24no—
23C2×#14519710C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519702C2211yescharacteristic
29C2×#14519702C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×C4×#92418C2211yescharacteristic
35#16839669C2211yescharacteristic
36#16839667C2211yescharacteristic
37#16839661C2211yescharacteristic
38#16839660—21no—
39#16839658C2211yescharacteristic
40#16839657—21no—
41#16839654—21no—
42#16839653—21no—
43#16839653—21no—
44#16839652—21no—
45#16839647—21no—
46#16839646—21no—
47#16839619C2211yescharacteristic
48#16839619C2211yescharacteristic
49C4×C4⋊Dic61C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54C2×C4×Q8×C61C2211yescharacteristic
55C2×#103×C61C2211yescharacteristic
56C2×#103×C61C2211yescharacteristic
57C2×#97×C61C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×Dic122C2311yescharacteristic
62C22×C4×D61C2311yescharacteristic
63C2×#11758202—22no—
64C2×#11758202—22no—
65C2×#11758202—22no—
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68#14519757—22no—
69#14519757—22no—
70#14519753—22no—
71#14519753—22no—
72C4×Dic122—22no—
73C4×Dic122—22no—
74#14519734—22no—
75#14519734—22no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196D411yescharacteristic
85C2×#11758196D411yescharacteristic
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198D411yescharacteristic
91C2×#11758198D411yescharacteristic
92C2×C4×Dic61—21no—
93C2×C4×Dic61—21no—
94C2×C4×Dic61C2311yescharacteristic
95#14519710—22no—
96#14519708—22no—
97#14519708—22no—
98#14519706—22no—
99#14519706—22no—
100#14519702—22no—
101#14519702—22no—
102#14519701—22no—
103#14519700—22no—
104#14519689—22no—
105#14519689—22no—
106C4×#92418D414yes—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116C22×Q8×C61C2311yescharacteristic
117C22×C8×C61C2311yescharacteristic
118C22×C8×C61C2311yescharacteristic
119C4×Q8×C61—22no—
120C4×Q8×C61—22no—
121C2×C4⋊C4×C61—21no—
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C42×C61—21no—
126C2×C42×C61—21no—
127C2×C42×C61C2311yescharacteristic
128#103×C61—22no—
129#103×C61—22no—
130#97×C61—22no—
131#95×C61—21no—
132C23×D61C2×D411yescharacteristic
133C2×Q8×C61—21no—
134C2×Q8×C61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61#4112yes—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2411yescharacteristic
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61C2×D411yescharacteristic
151C22×Dic61C2×D411yescharacteristic
152C22×Dic61C2×D411yescharacteristic
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—21no—
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122#4112yes—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—42no—
177C4⋊C4×C61#4112yes—
178C42×C61—42no—
179C42×C61—81no—
180C42×C61C2×D412yes—
181C42×C61#4112yes—
182#11758202—28no—
183#11758198—24no—
184#11758198—24no—
185#11758198—22no—
186#11758198—22no—
187#11758198—81no—
188#11758198—81no—
189C4⋊Dic61—24no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—81no—
196C4⋊Dic61#4112yes—
197#11758196—24no—
198#11758196—22no—
199#11758196—22no—
200#11758196—42no—
201#11758196—81no—
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61—42no—
205C4×Dic61—81no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418C2×D412yes—
211C2×#92418C2×D412yes—
212C23×C61C22×D411yescharacteristic
213C22×D61—21no—
214C22×D61—21no—
215C22×D61—21no—
216C22×D61—21no—
217C22×D61—21no—
218C22×D61—21no—
219C22×D61—21no—
220Q8×C61—22no—
221Q8×C61—22no—
222Q8×C61—41no—
223Q8×C61—41no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61#12112yes—
241C2×C4×C61#12112yes—
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—22no—
253C2×Dic61—21no—
254C2×Dic61—22no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C4×D61—41no—
270C4×D61—41no—
271C4×D61—41no—
272C4×D61—41no—
273Dic122—22no—
274Dic122—22no—
275Dic122—41no—
276Dic122—41no—
277C8×C61—41no—
278C8×C61—41no—
279#92418—22no—
280#92418—22no—
281#23704—611nomaximal, Sylow
282C22×C61C2×#12111yescharacteristic
283C22×C61#52511yescharacteristic
284C22×C61#52511yescharacteristic
285C22×C61#57711yescharacteristic
286C22×C61#57711yescharacteristic
287C22×C61#57811yescharacteristic
288C22×C61#57811yescharacteristic
289C2×D61—41no—
290C2×D61—41no—
291C2×D61—41no—
292C2×D61—41no—
293C2×D61—41no—
294C2×D61—41no—
295C2×D61—41no—
296C4×C61—22no—
297C4×C61—22no—
298C4×C61—42no—
299C4×C61—42no—
300C4×C61—81no—
301C4×C61—81no—
302C4×C61#52511yescharacteristic
303C4×C61#52911yescharacteristic
304C4×C61#52911yescharacteristic
305C4×C61#53211yescharacteristic
306Dic61—42no—
307Dic61—42no—
308Dic61—41no—
309Dic61—41no—
310Dic61—41no—
311Dic61—81no—
312Dic61—81no—
313C2×C4×Q16—611no—
314C2×#433—611no—
315#2323—611no—
316#2323—611no—
317#2087—611no—
318#2076—611no—
319#2066—611no—
320#2066—611no—
321#2056—611no—
322#2035—611no—
323#2035—611no—
324#2001—611no—
325C4×#106—611no—
326#1763—611no—
327#1763D6111yescharacteristic, complemented
328C2×C61#239211yescharacteristic
329C2×C61#305911yescharacteristic
330C2×C61#306011yescharacteristic
331C2×C61#312011yescharacteristic
332C2×C61#312011yescharacteristic
333C2×C61#312111yescharacteristic
334C2×C61#312111yescharacteristic
335D61—81no—
336C22×Q16—611no—
337C2×C22⋊Q8—611no—
338C2×C22⋊Q8—611no—
339C2×C4×Q8—611no—
340C2×C4×Q8C2×D6111yescharacteristic
341C2×#117—611no—
342C4×Q16—1224no—
343#433—1224no—
344C2×#107—611no—
345C2×#106—611no—
346C2×#106—611no—
347C2×C4⋊C8—611no—
348C2×C4⋊C8—611no—
349C2×#103—611no—
350C2×#103—611no—
351C2×#103—611no—
352C2×#103—611no—
353C2×#103C2×D6111yescharacteristic
354C2×#103C2×D6111yescharacteristic
355C2×C22⋊C8—611no—
356C2×C22⋊C8—611no—
357C2×#97C2×D6111yescharacteristic
358C2×C4×C8—611no—
359#391—611no—
360#391—611no—
361#389—611no—
362#389—611no—
363#389—1221no—
364#389—1221no—
365#388—1221no—
366#388—1221no—
367#388—1221no—
368#388—1221no—
369#387—1221no—
370#387—1221no—
371#380—611no—
372#380—611no—
373C4×C4⋊C4—611no—
374C4×C4⋊C4C2×D6111yescharacteristic
375#340—611no—
376#340—611no—
377#340—611no—
378#340—611no—
379#340C2×D6111yescharacteristic
380#340C2×D6111yescharacteristic
381C61#2370411yescharacteristic, complemented, Sylow
382C22×Q8—611no—
383C22×Q8C22×D6111yescharacteristic
384C23×C4—611no—
385C2×Q16—1222no—
386C2×Q16—1222no—
387C2×Q16—1222no—
388C22×C8—611no—
389C22×C8—611no—
390C22×C8C22×D6111yescharacteristic
391C22×C8C22×D6111yescharacteristic
392C22⋊Q8—1222no—
393C22⋊Q8—1222no—
394C22⋊Q8—1222no—
395C22⋊Q8—1222no—
396C4×Q8—22no—
397C4×Q8—22no—
398C4×Q8—1222no—
399C4×Q8—1222no—
400#117—1222no—
401#117—1222no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4—611no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4—611no—
407C2×C4⋊C4—611no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4C22×D6111yescharacteristic
414C2×C4⋊C4C22×D6111yescharacteristic
415C2×C4⋊C4C22×D6111yescharacteristic
416C2×C22⋊C4—611no—
417C2×C22⋊C4—611no—
418C2×C22⋊C4—1221no—
419C2×C22⋊C4—1221no—
420C2×C22⋊C4—1221no—
421C2×C22⋊C4—1221no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42—611no—
425C2×C42—1221no—
426C2×C42—1221no—
427C2×C42C22×D6111yescharacteristic
428#107—1222no—
429#106—1222no—
430#106—1222no—
431C4⋊C8—1222no—
432C4⋊C8—1222no—
433#103—22no—
434#103—22no—
435#103—1222no—
436#103—1222no—
437#103—1222no—
438#103—1222no—
439C22⋊C8—1222no—
440C22⋊C8—1222no—
441#97—22no—
442C4×C8—614no—
443#95—21no—
444#95—1221no—
445#95—1221no—
446#95—1221no—
447#95—1221no—
448#95—1221no—
449#95—1221no—
450#95—1221no—
451#95—1221no—
452#95—1221no—
453C24—611no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—612no—
460C2×Q8—1221no—
461C2×Q8—1221no—
462C2×Q8—1221no—
463C2×Q8—1221no—
464C2×Q8—1221no—
465C2×Q8#1175822212yes—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4D4×D6111yescharacteristic
484C22×C4D4×D6111yescharacteristic
485C22×C4C23×D6111yescharacteristic
486Q16—1228no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—612no—
494C2×C8—612no—
495C2×C8—1221no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—1221no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—42no—
505C4⋊C4—612no—
506C4⋊C4—1224no—
507C4⋊C4—1224no—
508C4⋊C4—1221no—
509C4⋊C4—1222no—
510C4⋊C4—1222no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—4881no—
516C4⋊C4—4881no—
517C4⋊C4—2442no—
518C4⋊C4#1175822212yes—
519C22⋊C4—1224no—
520C22⋊C4—1224no—
521C22⋊C4—1222no—
522C22⋊C4—1222no—
523C22⋊C4—4881no—
524C22⋊C4—4881no—
525C42—42no—
526C42—81no—
527C42—1221no—
528C42—1221no—
529C42—4881no—
530C42—2442no—
531C42#1175822212yes—
532C42D4×D6112yes—
533C23—1221no—
534C23—1221no—
535C23—1221no—
536C23—1221no—
537C23—1221no—
538C23—1221no—
539C23—1221no—
540C23C2×D4×D6111yescharacteristic
541Q8—22no—
542Q8—22no—
543Q8—41no—
544Q8—41no—
545Q8—1222no—
546Q8—1222no—
547Q8—2441no—
548Q8—2441no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—1221no—
568C2×C4—1222no—
569C2×C4—1222no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—1221no—
575C2×C4—1221no—
576C2×C4—2441no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4#1451975012yes—
591C2×C4#1451975012yes—
592C2×C4C2×D4×D6111yescharacteristic
593C2×C4#41×D6111yescharacteristic
594C2×C4#41×D6111yescharacteristic
595C2×C4C2×#1175822211yescharacteristic
596C2×C4C2×#1175822211yescharacteristic
597C2×C4C2×#1175822211yescharacteristic
598C8—41no—
599C8—41no—
600C8—1222no—
601C8—1222no—
602C22—2441no—
603C22—2441no—
604C22—2441no—
605C22—2441no—
606C22—2441no—
607C22—2441no—
608C22—2441no—
609C22C2×#1451975011yescharacteristic
610C22#1684027111yescharacteristic
611C22#1684027111yescharacteristic
612C22#1684057111yescharacteristic
613C22#1684057211yescharacteristic
614C22#1684057811yescharacteristic
615C22#1684057811yescharacteristic
616C4—22no—
617C4—22no—
618C4—42no—
619C4—42no—
620C4—81no—
621C4—81no—
622C4—4881no—
623C4—4881no—
624C4—2441no—
625C4—2442no—
626C4—2441no—
627C4—2441no—
628C4—2442no—
629C4#1684027111yescharacteristic
630C4#1684029011yescharacteristic
631C4#1684029611yescharacteristic
632C4#1684030911yescharacteristic
633C2—4881no—
634C2#2144906311yescharacteristic
635C2#2145547311yescharacteristic
636C2#2145548011yescharacteristic
637C2#2145603111yescharacteristic
638C2#2145603711yescharacteristic
639C2#2145604611yescharacteristic
640C2#2145605211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1763C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenter#1763D61
hypocenterC61#23704
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
1. C2×C4×#11758202C2semidirect
5. #21447316C2semidirect
7. #21447201C2semidirect
8. #21447196C2semidirect
9. #21447140C2semidirect
13. C4×#14519708C2semidirect
14. #21445650C2semidirect
15. C61×#1763C2semidirect
327. #1763D61semidirect
381. C61#23704semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582022
C2×#168398242
#214485022
#214484952
#214473162
#214472512
#214472012
#214471962
#214471402
#214470182
#214470132
#214468282
C4×#145197082
#214456502
C61×#17632
#2370461