Finite Group Databasebeta

← #29710005

Subgroups — #29710005

Order 15616.

880 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519748C211yesmaximal, characteristic
2#21448223C211yesmaximal, characteristic, complemented
3#21447379C211yesmaximal, characteristic, complemented
4#21447345C211yesmaximal, characteristic, complemented
5#21447294C211yesmaximal, characteristic, complemented
6#21447246C211yesmaximal, characteristic, complemented
7#21447244C211yesmaximal, characteristic, complemented
8#21447225C211yesmaximal, characteristic, complemented
9#21447000C211yesmaximal, characteristic
10#21446999C211yesmaximal, characteristic
11C4×#14519710C211yesmaximal, characteristic, complemented
12C4×#14519711C211yesmaximal, characteristic, complemented
13C4×#14519698C211yesmaximal, characteristic, complemented
14C4×#14519689C211yesmaximal, characteristic, complemented
15C4×#102×C61C211yesmaximal, characteristic, complemented
16C2×#14519748C2211yescharacteristic
17C2×C4×C22⋊D61—21no—
18C2×#14519734—21no—
19C2×C42×D61C2211yescharacteristic
20C2×#14519711C2211yescharacteristic
21C2×#14519711C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519710C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519689C2211yescharacteristic
27C2×#14519689C2211yescharacteristic
28C2×C4×#92418C2211yescharacteristic
29#16839665C2211yescharacteristic
30#16839658C2211yescharacteristic
31#16839650—21no—
32#16839638—21no—
33#16839631C2211yescharacteristic
34#16839631C2211yescharacteristic
35#16839626—21no—
36#16839621—21no—
37#16839619C2211yescharacteristic
38#16839619C2211yescharacteristic
39#16839619C2211yescharacteristic
40C4×#11758196—21no—
41C4×C4⋊Dic61C2211yescharacteristic
42C4×C4⋊Dic61C2211yescharacteristic
43C4×C22⋊Dic61—21no—
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C2×#102×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×C4×C8×C61C2211yescharacteristic
56C4×C4⋊C4×C61C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C22×C22⋊D61—21no—
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65#14519748—22no—
66#14519748—22no—
67C4×C22⋊D61—44no—
68#14519734—44no—
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61D411yescharacteristic
87C2×C4×Dic61D411yescharacteristic
88C2×C4×Dic61C2311yescharacteristic
89C42×D61—22no—
90C42×D61—22no—
91#14519711—22no—
92#14519711—22no—
93#14519710—22no—
94#14519710—22no—
95#14519698—22no—
96#14519698—22no—
97#14519689—22no—
98#14519689—22no—
99C4×#92418—22no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106C22×D4×C61C2311yescharacteristic
107C23×C4×C61—21no—
108C22×C8×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110C4×D4×C61—22no—
111C4×D4×C61—22no—
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C22⋊C4×C61—21no—
116C2×C42×C61—21no—
117C2×C42×C61C2311yescharacteristic
118#102×C61—22no—
119#102×C61—22no—
120C4×C8×C61—22no—
121#95×C61—21no—
122C24×C61—21no—
123C23×D61C2×D411yescharacteristic
124C2×D4×C61—21no—
125C2×D4×C61—21no—
126C2×D4×C61—21no—
127C2×D4×C61—21no—
128C2×D4×C61—21no—
129C2×D4×C61#4112yes—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—42no—
134C22×C4×C61—42no—
135C22×C4×C61—42no—
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2411yescharacteristic
139C2×C22⋊D61—24no—
140C2×C22⋊D61—42no—
141C2×C22⋊D61—42no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61C2×D411yescharacteristic
147C22×Dic61C2×D411yescharacteristic
148C22×Dic61C2×D411yescharacteristic
149C2×C4×D61—22no—
150C2×C4×D61—22no—
151C2×C4×D61—22no—
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—22no—
159C2×C4×D61—41no—
160C2×C4×D61D814yes—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61#4112yes—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C22⋊C4×C61—42no—
174C42×C61—42no—
175C42×C61#4112yes—
176C42×C61#4112yes—
177C22⋊Dic61—24no—
178C22⋊Dic61—42no—
179C22⋊Dic61—42no—
180#11758198—42no—
181#11758198—42no—
182#11758198—42no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61#4112yes—
191#11758196—42no—
192#11758196—42no—
193#11758196—42no—
194#11758196—42no—
195#11758196—42no—
196C4×Dic61—22no—
197C4×Dic61—22no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—42no—
201C4×Dic61—42no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418#4112yes—
208C23×C61—22no—
209C23×C61—41no—
210C23×C61—41no—
211C23×C61—41no—
212C23×C61—41no—
213C23×C61—41no—
214C23×C61—41no—
215C23×C61C22×D411yescharacteristic
216C22×D61—21no—
217C22×D61—21no—
218C22×D61—21no—
219C22×D61—21no—
220C22×D61—21no—
221C22×D61—21no—
222C22×D61C2×D812yes—
223D4×C61—22no—
224D4×C61—22no—
225D4×C61—41no—
226D4×C61—41no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—41no—
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—84no—
239C2×C4×C61#12312yes—
240C2×C4×C61#12312yes—
241C2×C4×C61C2×D812yes—
242C2×C4×C61#13712yes—
243C2×C4×C61C2×#4111yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C22⋊D61—48no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—22no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—41no—
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—
269C2×Dic61C2×D812yes—
270C2×Dic61#13512yes—
271C4×D61—28no—
272C4×D61—44no—
273C4×D61—41no—
274C4×D61—41no—
275C4×D61—41no—
276C4×D61—41no—
277C8×C61—22no—
278C8×C61—41no—
279#92418—22no—
280#92418—41no—
281#23754—611nomaximal, Sylow
282C22×C61—42no—
283C22×C61—42no—
284C22×C61—42no—
285C22×C61—81no—
286C22×C61—81no—
287C22×C61—81no—
288C22×C61—81no—
289C22×C61C2×#12311yescharacteristic
290C22×C61#52511yescharacteristic
291C22×C61#53211yescharacteristic
292C22×C61C22×D811yescharacteristic
293C22×C61C2×#13511yescharacteristic
294C22×C61C2×#13711yescharacteristic
295C22×C61#57511yescharacteristic
296C2×D61—22no—
297C2×D61—22no—
298C2×D61—22no—
299C2×D61—41no—
300C2×D61—41no—
301C2×D61—41no—
302C2×D61—41no—
303C4×C61—22no—
304C4×C61—81no—
305C4×C61—81no—
306C4×C61—81no—
307C4×C61#48014yes—
308C4×C61#52911yescharacteristic
309C4×C61#52911yescharacteristic
310C4×C61#52911yescharacteristic
311C4×C61#52911yescharacteristic
312Dic61—22no—
313Dic61—22no—
314Dic61—42no—
315Dic61—41no—
316Dic61—81no—
317Dic61—81no—
318Dic61—81no—
319C4×#121—611no—
320#2285—611no—
321#2099—611no—
322#2093—611no—
323#2083—611no—
324#2075—611no—
325#2075—611no—
326#2071—611no—
327#2033—611no—
328#2033—611no—
329C4×#107—611no—
330C4×#107—611no—
331C4×#102—611no—
332C4×#102D6111yescharacteristic, complemented
333C4×C22⋊C8—611no—
334C2×C61—82no—
335C2×C61#239511yescharacteristic
336C2×C61C2×#48011yescharacteristic
337C2×C61#309111yescharacteristic
338C2×C61#310011yescharacteristic
339C2×C61#310711yescharacteristic
340C2×C61#316911yescharacteristic
341C2×C61#317211yescharacteristic
342D61—42no—
343C2×#121—611no—
344C2×C4×D4—1221no—
345C2×C4×D4C2×D6111yescharacteristic
346C2×#117—1221no—
347C22×C42—611no—
348C2×#107—611no—
349C2×#107—611no—
350C2×#107—611no—
351C2×#107—611no—
352C2×#102—611no—
353C2×#102—611no—
354C2×#102C2×D6111yescharacteristic
355C2×#102C2×D6111yescharacteristic
356C2×C22⋊C8—611no—
357C2×C22⋊C8—611no—
358C2×C4×C8—611no—
359C2×C4×C8C2×D6111yescharacteristic
360#390—611no—
361#389—611no—
362#388—1221no—
363#386—1221no—
364#384—611no—
365#384—611no—
366#382—1221no—
367#380—611no—
368#380—611no—
369#380—611no—
370#380—1221no—
371C4×C4⋊C4—611no—
372C4×C4⋊C4—611no—
373C4×C4⋊C4—1221no—
374C4×C4⋊C4C2×D6111yescharacteristic
375C4×C22⋊C4—1221no—
376#340—611no—
377#340—611no—
378#340—611no—
379#340—611no—
380#340—611no—
381#340—611no—
382#340C2×D6111yescharacteristic
383#340C2×D6111yescharacteristic
384#336—611no—
385#336—611no—
386C61#2375411yescharacteristic, complemented, Sylow
387C22×D4—1221no—
388C22×D4C22×D6111yescharacteristic
389C23×C4—21no—
390C23×C4—611no—
391C23×C4—611no—
392C23×C4—611no—
393C22×C8—611no—
394C22×C8—611no—
395C22×C8C22×D6111yescharacteristic
396C22×C8C22×D6111yescharacteristic
397#121—1222no—
398#121—1222no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—2444no—
402#117—2444no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4—611no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4—611no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4C22×D6111yescharacteristic
413C2×C4⋊C4C22×D6111yescharacteristic
414C2×C4⋊C4C22×D6111yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—1221no—
417C2×C22⋊C4—1221no—
418C2×C22⋊C4—1221no—
419C2×C22⋊C4—1221no—
420C2×C22⋊C4—1221no—
421C2×C22⋊C4—1221no—
422C2×C42—21no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—611no—
426C2×C42—1222no—
427C2×C42—1222no—
428C2×C42—1221no—
429C2×C42—1221no—
430C2×C42C22×D6111yescharacteristic
431#107—1222no—
432#107—1222no—
433#107—1222no—
434#107—1222no—
435#102—22no—
436#102—22no—
437#102—1222no—
438#102—1222no—
439C22⋊C8—1222no—
440C22⋊C8—1222no—
441C4×C8—22no—
442C4×C8—1222no—
443#95—21no—
444#95—1221no—
445#95—1221no—
446#95—1221no—
447#95—1221no—
448#95—1221no—
449#95—1221no—
450C24—21no—
451C24—611no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—1224no—
458C2×D4—2442no—
459C2×D4—2442no—
460C2×D4#1175822212yes—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—614no—
470C22×C4—611no—
471C22×C4—1222no—
472C22×C4—1222no—
473C22×C4—1222no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1222no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4—1221no—
485C22×C4—2441no—
486C22×C4D4×D6111yescharacteristic
487C22×C4D4×D6111yescharacteristic
488C22×C4C23×D6111yescharacteristic
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—612no—
495C2×C8—1221no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8#1175822212yes—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—612no—
508C4⋊C4—1221no—
509C4⋊C4—1221no—
510C4⋊C4—1221no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—2442no—
516C4⋊C4—2442no—
517C4⋊C4—2442no—
518C4⋊C4—2442no—
519C4⋊C4—2442no—
520C22⋊C4—42no—
521C22⋊C4—1224no—
522C22⋊C4—2442no—
523C22⋊C4—2442no—
524C22⋊C4—2442no—
525C22⋊C4—2442no—
526C22⋊C4—2442no—
527C42—42no—
528C42—1221no—
529C42—1221no—
530C42—1222no—
531C42—1222no—
532C42—2442no—
533C42—2442no—
534C42#1175822212yes—
535C42#1175822412yes—
536C23—22no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—612no—
544C23—1221no—
545C23—1221no—
546C23—1221no—
547C23—1221no—
548C23—1221no—
549C23—1221no—
550C23C2×D4×D6111yescharacteristic
551D4—22no—
552D4—22no—
553D4—41no—
554D4—41no—
555D4—2448no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—84no—
568C2×C4—612no—
569C2×C4—612no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—1228no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—1222no—
578C2×C4—1221no—
579C2×C4—2444no—
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—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4#1451975912yes—
596C2×C4#1451975912yes—
597C2×C4D8×D6112yes—
598C2×C4#1451980612yes—
599C2×C4#41×D6111yescharacteristic
600C2×C4#41×D6111yescharacteristic
601C2×C4C2×#1175822411yescharacteristic
602C2×C4C2×#1175822211yescharacteristic
603C2×C4C2×#1175822211yescharacteristic
604C2×C4C2×#1175822211yescharacteristic
605C8—22no—
606C8—41no—
607C8—1222no—
608C8—2441no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—1222no—
617C22—1222no—
618C22—1222no—
619C22—2441no—
620C22—2441no—
621C22—2441no—
622C22—2441no—
623C22C2×#1451975911yescharacteristic
624C22#1684027111yescharacteristic
625C22#1684030911yescharacteristic
626C22C2×D8×D6111yescharacteristic
627C22#135×D6111yescharacteristic
628C22C2×#1451980611yescharacteristic
629C22#1684055911yescharacteristic
630C4—22no—
631C4—81no—
632C4—81no—
633C4—81no—
634C4—1222no—
635C4—1222no—
636C4—4881no—
637C4—4881no—
638C4—4881no—
639C4—2441no—
640C4—2442no—
641C4#1684007414yes—
642C4#1684029011yescharacteristic
643C4#1684029211yescharacteristic
644C4#1684029211yescharacteristic
645C4#1684029611yescharacteristic
646C2—82no—
647C2—2442no—
648C2#2144908011yescharacteristic
649C2C2×#1684007411yescharacteristic
650C2#2145573011yescharacteristic
651C2#2145581711yescharacteristic
652C2#2145588611yescharacteristic
653C2#2145639511yescharacteristic
654C2#2145642111yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC4×#102×C61C2
socleC23×C61C22×D4
prime radicalC2×#14519748C22
hypercenterC4×#102D61
hypocenterC61#23754
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. #21448223C2semidirect
3. #21447379C2semidirect
4. #21447345C2semidirect
5. #21447294C2semidirect
6. #21447246C2semidirect
7. #21447244C2semidirect
8. #21447225C2semidirect
11. C4×#14519710C2semidirect
12. C4×#14519711C2semidirect
13. C4×#14519698C2semidirect
14. C4×#14519689C2semidirect
15. C4×#102×C61C2semidirect
332. C4×#102D61semidirect
386. C61#23754semidirect

Maximal subgroups

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

subgroupindex
C4×#145197482
#214482232
#214473792
#214473452
#214472942
#214472462
#214472442
#214472252
#214470002
#214469992
C4×#145197102
C4×#145197112
C4×#145196982
C4×#145196892
C4×#102×C612
#2375461