Finite Group Databasebeta

← #29683138

Subgroups — #29683138

Order 15616.

862 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448462C211yesmaximal, characteristic
2#21448184C211yesmaximal, characteristic, complemented
3#21446448C211yesmaximal, characteristic
4#21446441C211yesmaximal, characteristic
5#21446413C211yesmaximal, characteristic, complemented
6#21446392C211yesmaximal, characteristic, complemented
7#21446176C211yesmaximal, characteristic
8#21446176C211yesmaximal, characteristic
9#21446089C211yesmaximal, characteristic, complemented
10#21446075C211yesmaximal, characteristic, complemented
11#21445716C211yesmaximal, characteristic, complemented
12C4×#14519701C211yesmaximal, characteristic, complemented
13C4×#14519698C211yesmaximal, characteristic
14#21445572C211yesmaximal, characteristic, complemented
15C2×C61×#440C211yesmaximal, characteristic
16C2×Q8×Dic61C2211yescharacteristic
17C2×Q8×Dic61C2211yescharacteristic
18C2×#14519711C2211yescharacteristic
19C2×#14519709C2211yescharacteristic
20C2×#14519701C2211yescharacteristic
21C2×#14519701C2211yescharacteristic
22C2×#14519698C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×C4×#92418C2211yescharacteristic
25#16839665C2211yescharacteristic
26#16839665C2211yescharacteristic
27#16839661C2211yescharacteristic
28#16839661C2211yescharacteristic
29#16839655—21no—
30#16839655—21no—
31#16839625—21no—
32#16839622—21no—
33C4⋊C4×Dic61—21no—
34C4⋊C4×Dic61—21no—
35C4⋊C4×Dic61C2211yescharacteristic
36C4⋊C4×Dic61C2211yescharacteristic
37C4×C4⋊Dic61—21no—
38C4×C4⋊Dic61C2211yescharacteristic
39C4×C4⋊Dic61C2211yescharacteristic
40#16839608—21no—
41#16839608C2211yescharacteristic
42#16839525C2211yescharacteristic
43#16839525C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C22×SD16×C61C2211yescharacteristic
53C2×C4×Q8×C61C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C61×#440C418yescomplemented
56C2×#107×C61C2211yescharacteristic
57C2×#103×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#97×C61C2211yescharacteristic
60C22×#92418C2311yescharacteristic
61C22×#92418C2311yescharacteristic
62Q8×Dic61—22no—
63Q8×Dic61—22no—
64Q8×Dic61—22no—
65Q8×Dic61—22no—
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C22⋊Dic61—21no—
75C2×C22⋊Dic61—21no—
76C2×C22⋊Dic61—21no—
77C2×C22⋊Dic61—21no—
78C2×C4×Dic61—21no—
79C2×C4×Dic61—21no—
80C2×C4×Dic61—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61C2311yescharacteristic
85C2×C4×Dic61C2311yescharacteristic
86#14519711—22no—
87#14519709—22no—
88#14519701—22no—
89#14519701—22no—
90#14519698—22no—
91#14519698—22no—
92C4×#92418—22no—
93#14519684—21no—
94#14519684—21no—
95#14519684—21no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684D411yescharacteristic
100#14519684D411yescharacteristic
101#14519684D411yescharacteristic
102#14519684D411yescharacteristic
103C22×Q8×C61C2311yescharacteristic
104C22×D4×C61C2311yescharacteristic
105C23×C4×C61—21no—
106C2×SD16×C61—22no—
107C2×SD16×C61—22no—
108C2×SD16×C61C2×C414yes—
109C22×C8×C61C2311yescharacteristic
110C22×C8×C61C2311yescharacteristic
111C4×Q8×C61—22no—
112C4×Q8×C61C2×C414yes—
113C4×D4×C61—22no—
114C4×D4×C61C2×C414yes—
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C22⋊C4×C61—21no—
119C2×C42×C61—21no—
120C2×C42×C61C2311yescharacteristic
121#107×C61C2×C414yes—
122#103×C61C2×C414yes—
123#102×C61C2×C414yes—
124#97×C61C2×C414yes—
125C24×C61—21no—
126C2×Q8×C61—21no—
127C2×Q8×C61—21no—
128C2×Q8×C61—21no—
129C2×Q8×C61C22×C412yes—
130C2×Q8×C61#4112yes—
131C2×Q8×C61#4112yes—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61—21no—
136C2×D4×C61—21no—
137C2×D4×C61C22×C412yes—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—24no—
142C22×C4×C61—81no—
143C22×C4×C61—81no—
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2411yescharacteristic
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61C2×D411yescharacteristic
152C22×Dic61C2×D411yescharacteristic
153C22×Dic61C2×D411yescharacteristic
154C22×Dic61C2×D411yescharacteristic
155SD16×C61—28no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61C22×C412yes—
161C2×C8×C61C22×C412yes—
162C4⋊C4×C61—24no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61C22×C412yes—
166C4⋊C4×C61C22×C412yes—
167C22⋊C4×C61—24no—
168C42×C61—24no—
169C42×C61C22×C412yes—
170C42×C61#4112yes—
171C22⋊Dic61—81no—
172C22⋊Dic61—81no—
173C22⋊Dic61—81no—
174C22⋊Dic61—81no—
175C4⋊Dic61—24no—
176C4⋊Dic61—24no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—81no—
184C4⋊Dic61—81no—
185C4⋊Dic61#4112yes—
186C4⋊Dic61#4112yes—
187C4×Dic61—24no—
188C4×Dic61—24no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—81no—
194C4×Dic61—81no—
195C4×Dic61—81no—
196C4×Dic61—81no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C23×C61—22no—
204C23×C61—41no—
205C23×C61—41no—
206C23×C61—41no—
207C23×C61—41no—
208C23×C61—41no—
209C23×C61—41no—
210C23×C61C22×D411yescharacteristic
211Q8×C61—22no—
212Q8×C61—22no—
213Q8×C61—22no—
214Q8×C61#11714yes—
215D4×C61—22no—
216D4×C61—22no—
217D4×C61—41no—
218D4×C61—41no—
219C2×C4×C61—22no—
220C2×C4×C61—22no—
221C2×C4×C61—22no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—22no—
227C2×C4×C61—22no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—84no—
233C2×C4×C61C4×D412yes—
234C2×C4×C61C4×D412yes—
235C2×C4×C61C23×C411yescharacteristic
236C2×C4×C61C2×#4111yescharacteristic
237C2×C4×C61C2×#4111yescharacteristic
238C2×C4×C61C2×#4111yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C8×C61—22no—
266C8×C61—22no—
267#92418—41no—
268#92418—41no—
269#21128—611nomaximal, Sylow
270C22×C61—42no—
271C22×C61—42no—
272C22×C61—42no—
273C22×C61—81no—
274C22×C61—81no—
275C22×C61—81no—
276C22×C61—81no—
277C22×C61C2×C4×D411yescharacteristic
278C22×C61#52511yescharacteristic
279C22×C61#52511yescharacteristic
280C22×C61#57611yescharacteristic
281C22×C61#57711yescharacteristic
282C22×C61#57711yescharacteristic
283C22×C61#57811yescharacteristic
284C4×C61—22no—
285C4×C61—22no—
286C4×C61—24no—
287C4×C61—42no—
288C4×C61—42no—
289C4×C61C2×#11711yescharacteristic
290C4×C61C4×#4111yescharacteristic
291C4×C61#52911yescharacteristic
292C4×C61#52911yescharacteristic
293Dic61—41no—
294Dic61—42no—
295Dic61—41no—
296Dic61—41no—
297Dic61—42no—
298Dic61—41no—
299Dic61—81no—
300Dic61—81no—
301C2×#440D6111yescharacteristic
302#2319—611no—
303#2276—611no—
304#1926—611no—
305#1925—611no—
306#1921—611no—
307#1918—611no—
308#1880—611no—
309#1880—611no—
310#1865—611no—
311#1863—611no—
312#1776—611no—
313C4×#103—611no—
314C4×#102—611no—
315#1746—611no—
316C2×C61—82no—
317C2×C61#229011yescharacteristic
318C2×C61#294611yescharacteristic
319C2×C61#294711yescharacteristic
320C2×C61#311911yescharacteristic
321C2×C61#312111yescharacteristic
322C2×C61#312411yescharacteristic
323C2×C61#312611yescharacteristic
324C22×SD16C2×D6111yescharacteristic
325C2×C4×Q8—611no—
326C2×C4×Q8—611no—
327C2×C4×Q8C2×D6111yescharacteristic
328C2×C4×D4C2×D6111yescharacteristic
329#440Dic6118yescomplemented
330C2×#107—611no—
331C2×#107C2×D6111yescharacteristic
332C2×#106—611no—
333C2×#103—611no—
334C2×#103—611no—
335C2×#103C2×D6111yescharacteristic
336C2×#102—611no—
337C2×#102—611no—
338C2×#102C2×D6111yescharacteristic
339C2×#97C2×D6111yescharacteristic
340C2×C4×C8—611no—
341#390—611no—
342#390—611no—
343#389—611no—
344#389—611no—
345#388—1221no—
346#388—1221no—
347#381—1221no—
348#380—1221no—
349C4×C4⋊C4—611no—
350C4×C4⋊C4—611no—
351C4×C4⋊C4—611no—
352C4×C4⋊C4—611no—
353C4×C4⋊C4—1221no—
354C4×C4⋊C4—1221no—
355C4×C4⋊C4—1221no—
356#376—611no—
357#376—1221no—
358#340—611no—
359#340—611no—
360#340—611no—
361#340—611no—
362#340—611no—
363#340—611no—
364#336—611no—
365#336—611no—
366#336—611no—
367#336—611no—
368C61#2112811yescharacteristic, complemented, Sylow
369C22×Q8C22×D6111yescharacteristic
370C22×D4C22×D6111yescharacteristic
371C23×C4—21no—
372C2×SD16—22no—
373C2×SD16—22no—
374C2×SD16C2×Dic6114yes—
375C22×C8—611no—
376C22×C8—611no—
377C22×C8C22×D6111yescharacteristic
378C22×C8C22×D6111yescharacteristic
379C4×Q8—22no—
380C4×Q8—1222no—
381C4×Q8—1222no—
382C4×Q8—1222no—
383C4×Q8—1222no—
384C4×Q8C2×Dic6114yes—
385C4×D4—22no—
386C4×D4C2×Dic6114yes—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—611no—
390C2×C4⋊C4—611no—
391C2×C4⋊C4—611no—
392C2×C4⋊C4—1221no—
393C2×C4⋊C4—1221no—
394C2×C4⋊C4—1221no—
395C2×C4⋊C4—1221no—
396C2×C4⋊C4C22×D6111yescharacteristic
397C2×C4⋊C4C22×D6111yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—1221no—
400C2×C22⋊C4—1221no—
401C2×C22⋊C4—1221no—
402C2×C22⋊C4—1221no—
403C2×C42—21no—
404C2×C42—611no—
405C2×C42—611no—
406C2×C42—1221no—
407C2×C42—1221no—
408C2×C42—1221no—
409C2×C42—1221no—
410C2×C42—1221no—
411C2×C42—1221no—
412C2×C42C22×D6111yescharacteristic
413#107—1222no—
414#107C2×Dic6114yes—
415#106—1222no—
416#103—1222no—
417#103—1222no—
418#103C2×Dic6114yes—
419#102—1222no—
420#102—1222no—
421#102C2×Dic6114yes—
422#97C2×Dic6114yes—
423C4×C8—1222no—
424#95—611no—
425#95—611no—
426#95—611no—
427#95—611no—
428#95—1221no—
429#95—1221no—
430#95—1221no—
431#95—1221no—
432#95—1221no—
433#95—1221no—
434C24—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8#1175822212yes—
439C2×Q8#1175822212yes—
440C2×Q8C22×Dic6112yes—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4C22×Dic6112yes—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—24no—
451C22×C4—81no—
452C22×C4—81no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4D4×D6111yescharacteristic
462C22×C4D4×D6111yescharacteristic
463C22×C4C23×D6111yescharacteristic
464SD16—28no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8C22×Dic6112yes—
476C2×C8C22×Dic6112yes—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—24no—
480C4⋊C4—612no—
481C4⋊C4—612no—
482C4⋊C4—1224no—
483C4⋊C4—1224no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—4881no—
491C4⋊C4—4881no—
492C4⋊C4C22×Dic6112yes—
493C4⋊C4C22×Dic6112yes—
494C22⋊C4—24no—
495C22⋊C4—4881no—
496C22⋊C4—4881no—
497C22⋊C4—4881no—
498C22⋊C4—4881no—
499C42—24no—
500C42—1224no—
501C42—1224no—
502C42—1221no—
503C42—1221no—
504C42—1221no—
505C42—1221no—
506C42—4881no—
507C42—4881no—
508C42—4881no—
509C42—4881no—
510C42#1175822412yes—
511C42C22×Dic6112yes—
512C23—22no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23C2×D4×D6111yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—22no—
523Q8#1451973614yes—
524D4—22no—
525D4—22no—
526D4—41no—
527D4—41no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—84no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—1222no—
545C2×C4—1222no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1221no—
555C2×C4—1221no—
556C2×C4—2441no—
557C2×C4—2441no—
558C2×C4—2441no—
559C2×C4—2441no—
560C2×C4—2441no—
561C2×C4—2441no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4D4×Dic6112yes—
567C2×C4D4×Dic6112yes—
568C2×C4C23×Dic6111yescharacteristic
569C2×C4#41×D6111yescharacteristic
570C2×C4#41×D6111yescharacteristic
571C2×C4C2×#1175822411yescharacteristic
572C2×C4C2×#1175822211yescharacteristic
573C2×C4C2×#1175822211yescharacteristic
574C8—22no—
575C8—22no—
576C8—2441no—
577C8—2441no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22C2×D4×Dic6111yescharacteristic
586C22#1684027111yescharacteristic
587C22#1684027111yescharacteristic
588C22#1684056611yescharacteristic
589C22#1684057111yescharacteristic
590C22#1684057211yescharacteristic
591C22#1684057811yescharacteristic
592C4—22no—
593C4—22no—
594C4—24no—
595C4—42no—
596C4—42no—
597C4—4881no—
598C4—4881no—
599C4—2441no—
600C4—2442no—
601C4—2441no—
602C4—2441no—
603C4—2442no—
604C4—2441no—
605C4C2×#1451973611yescharacteristic
606C4#41×Dic6111yescharacteristic
607C4#1684029211yescharacteristic
608C4#1684029211yescharacteristic
609C2—82no—
610C2#2144826411yescharacteristic
611C2#2145465211yescharacteristic
612C2#2145466311yescharacteristic
613C2#2145601611yescharacteristic
614C2#2145604611yescharacteristic
615C2#2145607911yescharacteristic
616C2#2145610911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#440C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
cosocleC22×C4×C61C24
hypercenterC2×#440D61
hypocenterC61#21128
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. #21448184C2semidirect
5. #21446413C2semidirect
6. #21446392C2semidirect
9. #21446089C2semidirect
10. #21446075C2semidirect
11. #21445716C2semidirect
12. C4×#14519701C2semidirect
14. #21445572C2semidirect
55. C61×#440C4semidirect
329. #440Dic61semidirect
368. C61#21128semidirect

Maximal subgroups

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

subgroupindex
#214484622
#214481842
#214464482
#214464412
#214464132
#214463922
#214461762
#214460892
#214460752
#214457162
C4×#145197012
C4×#145196982
#214455722
C2×C61×#4402
#2112861