Finite Group Databasebeta

← #29699228

Subgroups — #29699228

Order 15616.

906 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839842C211yesmaximal, characteristic
2#21448788C211yesmaximal, characteristic, complemented
3#21448724C211yesmaximal, characteristic, complemented
4#21446516C211yesmaximal, characteristic, complemented
5#21446514C211yesmaximal, characteristic, complemented
6#21446390C211yesmaximal, characteristic, complemented
7#21446388C211yesmaximal, characteristic, complemented
8#21446167C211yesmaximal, characteristic
9#21446165C211yesmaximal, characteristic
10#21445948C211yesmaximal, characteristic, complemented
11#21445828C211yesmaximal, characteristic, complemented
12#21445827C211yesmaximal, characteristic, complemented
13#21445687C211yesmaximal, characteristic, complemented
14#21445646C211yesmaximal, characteristic, complemented
15C61×#1762C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C2×D4×Dic61C2211yescharacteristic
18C2×D4×Dic61C2211yescharacteristic
19C2×#14519739C2211yescharacteristic
20#16839842C418yescomplemented
21C2×#14519710C2211yescharacteristic
22C2×#14519706C2211yescharacteristic
23C2×#14519699C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519687C2211yescharacteristic
28C2×C8×Dic61C2211yescharacteristic
29#16839664C2211yescharacteristic
30#16839663C2211yescharacteristic
31#16839660C2211yescharacteristic
32#16839658C2211yescharacteristic
33#16839653—21no—
34#16839651—21no—
35#16839635—21no—
36#16839634—21no—
37#16839627C2211yescharacteristic
38#16839627C2211yescharacteristic
39#16839624—21no—
40#16839620—21no—
41C4⋊C4×Dic61C2211yescharacteristic
42C4×#11758196C2211yescharacteristic
43C4×#11758198—21no—
44C2×#14519684—21no—
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839517C2211yescharacteristic
52#16839516C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C2×#97×C61C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C22×D244C2311yescharacteristic
61C23×Dic61—21no—
62C23×Dic61—21no—
63C22×C4×D61—21no—
64C2×#11758199—22no—
65C2×#11758199—22no—
66C2×#11758199C2×C414yes—
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69D4×Dic61—22no—
70D4×Dic61—22no—
71D4×Dic61—41no—
72D4×Dic61C2×C414yes—
73#14519739—22no—
74#14519739C2×C414yescomplemented
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758196D411yescharacteristic
81C2×#11758196D411yescharacteristic
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×C4×Dic61—21no—
90C2×C4×Dic61C2311yescharacteristic
91C2×C4×Dic61C2311yescharacteristic
92#14519710C2×C414yescomplemented
93#14519706—22no—
94#14519699—41no—
95#14519699C2×C414yescomplemented
96#14519698—22no—
97#14519697—41no—
98#14519687—41no—
99C8×Dic61C2×C414yescomplemented
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684D411yescharacteristic
108#14519684D411yescharacteristic
109C22×D4×C61C2311yescharacteristic
110C23×C4×C61—21no—
111C22×C8×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113C4×D4×C61—22no—
114C4×D4×C61—41no—
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C22⋊C4×C61—21no—
119C2×C42×C61—21no—
120C2×C42×C61C2311yescharacteristic
121#102×C61—22no—
122#102×C61C2×C414yes—
123#97×C61—41no—
124#95×C61—21no—
125C24×C61—21no—
126C23×D61—21no—
127C2×D4×C61—21no—
128C2×D4×C61—21no—
129C2×D4×C61—21no—
130C2×D4×C61C22×C412yes—
131C2×D4×C61#4112yes—
132C2×D4×C61#4112yes—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—42no—
137C22×C4×C61—42no—
138C22×C4×C61—81no—
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2411yescharacteristic
142C22×Dic61—21no—
143C22×Dic61—24no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—42no—
147C22×Dic61—42no—
148C22×Dic61—81no—
149C22×Dic61—81no—
150C22×Dic61—81no—
151C22×Dic61C2×D411yescharacteristic
152C22×Dic61C2×D411yescharacteristic
153C22×Dic61C2×D411yescharacteristic
154C22×Dic61C2×D411yescharacteristic
155C2×D244—21no—
156C2×D244—21no—
157C2×D244—21no—
158C2×D244—21no—
159C2×D244—21no—
160C2×D244C22×C412yes—
161C2×C4×D61—24no—
162C2×C4×D61—81no—
163C2×C4×D61—81no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61C22×C412yes—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61C22×C412yes—
176C22⋊C4×C61—42no—
177C42×C61—21no—
178C42×C61—21no—
179C42×C61—81no—
180C22⋊Dic61—24no—
181C22⋊Dic61—42no—
182#11758199—28no—
183#11758198—24no—
184#11758198—42no—
185#11758198—42no—
186#11758198—81no—
187#11758198—81no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61C22×C412yes—
194#11758196—41no—
195#11758196—41no—
196#11758196—81no—
197#11758196—81no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—81no—
201C4×Dic61C22×C412yes—
202C4×Dic61#4112yes—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418C22×C412yes—
209C23×C61—22no—
210C23×C61—22no—
211C23×C61—22no—
212C23×C61—41no—
213C23×C61—41no—
214C23×C61—41no—
215C23×C61—41no—
216C23×C61C22×D411yescharacteristic
217C22×D61—22no—
218C22×D61—41no—
219C22×D61—41no—
220C22×D61—41no—
221C22×D61—41no—
222C22×D61—41no—
223C22×D61—41no—
224D4×C61—22no—
225D4×C61—22no—
226D4×C61—22no—
227D4×C61#11714yes—
228C2×C4×C61—22no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—84no—
244C2×C4×C61C23×C411yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61H(5,𝔽2)11yescharacteristic
249C2×C4×C612−1+411yescharacteristic
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—22no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
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×Dic61—84no—
270C2×Dic61—84no—
271C2×Dic61C4×D412yes—
272C2×Dic61C4×D412yes—
273D244—22no—
274D244—22no—
275D244—41no—
276D244—41no—
277C4×D61—84no—
278C8×C61—22no—
279C8×C61—41no—
280#92418—22no—
281#92418—41no—
282#22764—611nomaximal, Sylow
283C22×C61—24no—
284C22×C61—42no—
285C22×C61—42no—
286C22×C61—42no—
287C22×C61—42no—
288C22×C61—42no—
289C22×C61—42no—
290C22×C61C2×C4×D411yescharacteristic
291C22×C61#54611yescharacteristic
292C22×C61#54811yescharacteristic
293C22×C61#57511yescharacteristic
294C22×C61#57511yescharacteristic
295C22×C61#57611yescharacteristic
296C22×C61#57611yescharacteristic
297C2×D61—42no—
298C2×D61—42no—
299C2×D61—42no—
300C2×D61—81no—
301C2×D61—81no—
302C2×D61—81no—
303C2×D61—81no—
304C4×C61—42no—
305C4×C61—41no—
306C4×C61—41no—
307C4×C61—81no—
308C4×C61—81no—
309C4×C61C2×#11711yescharacteristic
310C4×C61#52011yescharacteristic
311C4×C61#55211yescharacteristic
312C4×C61#55311yescharacteristic
313Dic61—22no—
314Dic61—22no—
315Dic61—42no—
316Dic61—41no—
317Dic61—41no—
318Dic61—81no—
319Dic61—81no—
320C2×C4×D8—611no—
321#2357—611no—
322#2349—611no—
323#1936—611no—
324#1936—611no—
325#1918—611no—
326#1918—611no—
327#1879—611no—
328#1879—611no—
329#1835—611no—
330#1804—611no—
331#1804—611no—
332#1770—611no—
333#1762—611no—
334#1762D6111yescharacteristic, complemented
335C2×C61—44no—
336C2×C61#235211yescharacteristic
337C2×C61#294311yescharacteristic
338C2×C61#294811yescharacteristic
339C2×C61#332211yescharacteristic
340C2×C61#332211yescharacteristic
341C2×C61#337011yescharacteristic
342C2×C61#337011yescharacteristic
343D61—82no—
344C22×D8—611no—
345C2×C4×D4—611no—
346C2×C4×D4—611no—
347C2×C4×D4—611no—
348C2×C4×D4C2×D6111yescharacteristic
349C4×D8—618no—
350C2×#107—611no—
351C2×C4⋊C8—611no—
352C2×#102—611no—
353C2×#102—611no—
354C2×#102—611no—
355C2×#102—611no—
356C2×#102C2×D6111yescharacteristic
357C2×#102C2×D6111yescharacteristic
358C2×#97—611no—
359C2×#97C2×D6111yescharacteristic
360C2×C4×C8—611no—
361#390—611no—
362#390—611no—
363#389—611no—
364#389—611no—
365#388—1221no—
366#388—1221no—
367#385—1221no—
368#385—1221no—
369#382—611no—
370#382—611no—
371#381—1221no—
372#380—1221no—
373C4×C4⋊C4—611no—
374C4×C4⋊C4—611no—
375C4×C4⋊C4C2×D6111yescharacteristic
376C4×C22⋊C4—1221no—
377C2×#95—1221no—
378#340—611no—
379#340—611no—
380#340—611no—
381#340—611no—
382#340—611no—
383#340—611no—
384#340C2×D6111yescharacteristic
385#340C2×D6111yescharacteristic
386#336—611no—
387#336—611no—
388C61#2276411yescharacteristic, complemented, Sylow
389C22×D4—611no—
390C22×D4C22×D6111yescharacteristic
391C23×C4—21no—
392C23×C4—1221no—
393C23×C4—1221no—
394C23×C4—1221no—
395C2×D8—614no—
396C2×D8—1222no—
397C2×D8—1222no—
398C22×C8—611no—
399C22×C8—611no—
400C22×C8C22×D6111yescharacteristic
401C22×C8C22×D6111yescharacteristic
402C4×D4—22no—
403C4×D4—41no—
404C4×D4—614no—
405C4×D4—614no—
406C4×D4—1222no—
407C4×D4—1222no—
408C4×D4—1222no—
409C4×D4—2441no—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—611no—
412C2×C4⋊C4—611no—
413C2×C4⋊C4—611no—
414C2×C4⋊C4—611no—
415C2×C4⋊C4—1221no—
416C2×C4⋊C4—1221no—
417C2×C4⋊C4C22×D6111yescharacteristic
418C2×C4⋊C4C22×D6111yescharacteristic
419C2×C4⋊C4C22×D6111yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—1221no—
422C2×C22⋊C4—1221no—
423C2×C22⋊C4—1221no—
424C2×C22⋊C4—1221no—
425C2×C22⋊C4—1221no—
426C2×C22⋊C4—1221no—
427C2×C22⋊C4—1221no—
428C2×C42—21no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—1221no—
432C2×C42C22×D6111yescharacteristic
433#107—614no—
434C4⋊C8—1222no—
435#102—22no—
436#102—614no—
437#102—1222no—
438#102—2441no—
439#102—2441no—
440#102C4×D6114yes—
441#97—41no—
442#97—2441no—
443C4×C8—614no—
444#95—21no—
445#95—611no—
446#95—611no—
447#95—1221no—
448#95—1221no—
449#95—1221no—
450#95—1221no—
451#95—1221no—
452#95—1221no—
453#95—1221no—
454C24—21no—
455C24—1221no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—612no—
460C2×D4—1221no—
461C2×D4—1221no—
462C2×D4—1221no—
463C2×D4—1221no—
464C2×D4—1221no—
465C2×D4C2×C4×D6112yes—
466C2×D4#1175822212yes—
467C2×D4#1175822212yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—81no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—1224no—
479C22×C4—1224no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—4881no—
484C22×C4—4881no—
485C22×C4—4881no—
486C22×C4—4881no—
487C22×C4—4881no—
488C22×C4—2442no—
489C22×C4—2442no—
490C22×C4D4×D6111yescharacteristic
491C22×C4D4×D6111yescharacteristic
492C22×C4C23×D6111yescharacteristic
493D8—1228no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—612no—
500C2×C8—1221no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8C2×C4×D6112yes—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—612no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4—1221no—
517C4⋊C4—4881no—
518C4⋊C4—4881no—
519C4⋊C4—2441no—
520C4⋊C4—2441no—
521C4⋊C4C2×C4×D6112yes—
522C22⋊C4—42no—
523C22⋊C4—1224no—
524C22⋊C4—1224no—
525C22⋊C4—4881no—
526C22⋊C4—4881no—
527C22⋊C4—2442no—
528C22⋊C4—2442no—
529C22⋊C4—2442no—
530C42—21no—
531C42—21no—
532C42—81no—
533C42—612no—
534C42—612no—
535C42—1221no—
536C42—1221no—
537C42—4881no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—1222no—
546C23—2441no—
547C23—2441no—
548C23—2441no—
549C23—2441no—
550C23—2441no—
551C23—2441no—
552C23C2×D4×D6111yescharacteristic
553D4—22no—
554D4—22no—
555D4—22no—
556D4—1222no—
557D4—1222no—
558D4—2441no—
559D4—2441no—
560D4#1451973414yes—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—84no—
577C2×C4—612no—
578C2×C4—612no—
579C2×C4—1221no—
580C2×C4—1221no—
581C2×C4—1221no—
582C2×C4—1221no—
583C2×C4—1222no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1221no—
590C2×C4—4884no—
591C2×C4—4884no—
592C2×C4—4884no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4—2441no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4C22×C4×D6111yescharacteristic
602C2×C4#41×D6111yescharacteristic
603C2×C4C2×#1175822211yescharacteristic
604C2×C4C2×#1175822211yescharacteristic
605C2×C4#1451982211yescharacteristic
606C2×C4#1451982411yescharacteristic
607C8—22no—
608C8—41no—
609C8—1222no—
610C8—2441no—
611C22—24no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—4881no—
619C22—4881no—
620C22—4881no—
621C22—4881no—
622C22—2442no—
623C22—2442no—
624C22—2442no—
625C22C4×D4×D6111yescharacteristic
626C22#1684040211yescharacteristic
627C22#1684042111yescharacteristic
628C22#1684055811yescharacteristic
629C22#1684056111yescharacteristic
630C22#1684056611yescharacteristic
631C22#1684056611yescharacteristic
632C4—42no—
633C4—41no—
634C4—41no—
635C4—81no—
636C4—81no—
637C4—1222no—
638C4—1222no—
639C4—4881no—
640C4—4881no—
641C4—2442no—
642C4—2441no—
643C4—2441no—
644C4C2×#1451973411yescharacteristic
645C4#1684024111yescharacteristic
646C4#1684044511yescharacteristic
647C4#1684046111yescharacteristic
648C2—44no—
649C2—4882no—
650C2#2144874211yescharacteristic
651C2#2145461411yescharacteristic
652C2#2145466811yescharacteristic
653C2#2145801611yescharacteristic
654C2#2145802111yescharacteristic
655C2#2145857311yescharacteristic
656C2#2145857711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1762C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
cosocleC22×C4×C61C24
hypercenter#1762D61
hypocenterC61#22764
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. #21448788C2semidirect
3. #21448724C2semidirect
4. #21446516C2semidirect
5. #21446514C2semidirect
6. #21446390C2semidirect
7. #21446388C2semidirect
10. #21445948C2semidirect
11. #21445828C2semidirect
12. #21445827C2semidirect
13. #21445687C2semidirect
14. #21445646C2semidirect
15. C61×#1762C2semidirect
20. #16839842C4semidirect
74. #14519739C2×C4semidirect
92. #14519710C2×C4semidirect
95. #14519699C2×C4semidirect
99. C8×Dic61C2×C4semidirect
334. #1762D61semidirect
388. C61#22764semidirect

Maximal subgroups

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

subgroupindex
C2×#168398422
#214487882
#214487242
#214465162
#214465142
#214463902
#214463882
#214461672
#214461652
#214459482
#214458282
#214458272
#214456872
#214456462
C61×#17622
#2276461