Finite Group Databasebeta

← #29650894

Subgroups — #29650894

Order 15616.

748 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455817C211yesmaximal, characteristic
2#21454558C211yesmaximal, characteristic, complemented
3D4×#11758189C211yesmaximal, characteristic, complemented
4#21444705C211yesmaximal, characteristic, complemented
5#21444701C211yesmaximal, characteristic, complemented
6#21444649C211yesmaximal, characteristic, complemented
7#21444648C211yesmaximal, characteristic, complemented
8#21444648C211yesmaximal, characteristic, complemented
9#21444647C211yesmaximal, characteristic, complemented
10#21444611C211yesmaximal, characteristic, complemented
11#21444592C211yesmaximal, characteristic, complemented
12#21444268C211yesmaximal, characteristic, complemented
13D4⋊C8×D61C211yesmaximal, characteristic, complemented
14C8×#11758189C211yesmaximal, characteristic, complemented
15C8×D8×C61C211yesmaximal, characteristic, complemented
16C2×#14519783—21no—
17C22×#11758189—21no—
18#16840309C2211yescharacteristic
19C4×D4×D61C2211yescharacteristic
20#16840077C411yescharacteristic
21#16840074C411yescharacteristic
22#16840041C411yescharacteristic
23#16840040C411yescharacteristic
24#16839956C411yescharacteristic
25#16839955C411yescharacteristic
26#16839897C411yescharacteristic
27#16839894C411yescharacteristic
28C4×D488C2211yescharacteristic
29C4×#11758199C2211yescharacteristic
30C4×#11758199C2211yescharacteristic
31#16839841C2211yescharacteristic
32#16839841C2211yescharacteristic, complemented
33#16839840C2211yescharacteristic, complemented
34#16839839C2211yescharacteristic
35#16839836—21no—
36#16839833—21no—
37#16839833—21no—
38#16839830—21no—
39D4×#92418C2211yescharacteristic
40#16839827C2211yescharacteristic, complemented
41#16839813C2211yescharacteristic
42#16839784C2211yescharacteristic
43C4⋊C8×D61C2211yescharacteristic
44#16839727—21no—
45#16839724—21no—
46C4×#11758189C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839515C2211yescharacteristic, complemented
49#16839514C2211yescharacteristic, complemented
50#16839514C2211yescharacteristic, complemented
51#16839491C2211yescharacteristic
52#16839491C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic, complemented
55#16839489C2211yescharacteristic
56#16839489C2211yescharacteristic, complemented
57#16839484C2211yescharacteristic, complemented
58#16839483C2211yescharacteristic, complemented
59C8×#92418C2211yescharacteristic, complemented
60C4×D8×C61C2211yescharacteristic
61C8×D4×C61C2211yescharacteristic
62C8×D4×C61C2211yescharacteristic, complemented
63C61×#335C2211yescharacteristic, complemented
64C61×D4⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic, complemented
66C82×C61C2211yescharacteristic, complemented
67C2×#11758222—21no—
68C2×D4×D61C2×C411yescharacteristic
69C22×C4×D61—21no—
70C2×D488C2×C411yescharacteristic
71C2×#11758199C2×C411yescharacteristic
72C2×#11758199C2×C411yescharacteristic
73#14519783—44no—
74C2×#11758194—21no—
75C2×#11758189—21no—
76C2×#11758189—21no—
77C2×#11758189—21no—
78C2×#11758189—21no—
79C2×#11758189—44no—
80C2×#11758189D411yescharacteristic
81C2×#11758189D411yescharacteristic
82C22×#92418—21no—
83C2×C8×D61—21no—
84C2×C8×D61—21no—
85C2×C8×D61—21no—
86#14519776C2×C411yescharacteristic
87#14519773C2×C411yescharacteristic
88#14519763—21no—
89#14519752C2×C411yescharacteristic
90#14519750—21no—
91#14519748C2×C411yescharacteristic
92C4×D244C2311yescharacteristic
93C4×D244C2311yescharacteristic
94D4×Dic61C2×C411yescharacteristic
95#14519739C2×C411yescharacteristic
96C4×C22⋊D61—21no—
97C4×C22⋊D61—21no—
98#14519737—21no—
99C4⋊C4×D61C2×C411yescharacteristic
100C22⋊C4×D61—21no—
101C42×D61C2311yescharacteristic
102#14519711C2×C411yescharacteristic
103#14519710C2×C411yescharacteristic
104#14519710C2×C411yescharacteristic
105C4⋊#92418C2311yescharacteristic
106C4⋊#92418C2311yescharacteristic
107#14519706—21no—
108#14519706—21no—
109#14519706C2×C411yescharacteristic
110#14519706C2×C411yescharacteristic
111#14519699C2×C411yescharacteristic
112#14519699C2×C411yescharacteristic
113#14519698C2×C411yescharacteristic
114#14519698C2×C411yescharacteristic
115#14519697C2×C411yescharacteristic
116#14519697C2×C411yescharacteristic
117C22⋊#92418—21no—
118C22⋊#92418—21no—
119#14519689—21no—
120#14519689—21no—
121#14519689—21no—
122#14519689—21no—
123#14519689C2×C411yescharacteristic
124#14519689C2×C411yescharacteristic
125#14519687D411yescharacteristic
126#14519687D411yescharacteristic
127C4×#92418C2311yescharacteristic
128C4×#92418C2311yescharacteristic
129C4×#92418C2311yescharacteristic
130C8×Dic61—21no—
131C2×D8×C61C2×C411yescharacteristic
132C22×C8×C61—21no—
133C22×C8×C61—21no—
134C4×D4×C61C2311yescharacteristic
135C4×D4×C61C2311yescharacteristic
136#107×C61C2×C411yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139#102×C61C2×C411yescharacteristic
140#102×C61C2×C411yescharacteristic
141C22⋊C8×C61—21no—
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C4×C8×C61C2311yescharacteristic
145C4×C8×C61C2311yescharacteristic
146C23×D61—21no—
147C2×D4×C61C22×C411yescharacteristic
148C2×D4×C61C22×C411yescharacteristic
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C2×C22⋊D61—21no—
152C2×C22⋊D61—21no—
153C2×C22⋊D61—21no—
154C2×C22⋊D61—21no—
155C22×Dic61—21no—
156D4×D61—22no—
157D4×D61—41no—
158#11758222—42no—
159#11758222—42no—
160C2×D244—21no—
161C2×D244C22×C411yescharacteristic
162C2×D244C22×C411yescharacteristic
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—42no—
168C2×C4×D61—42no—
169C2×C4×D61C22×C411yescharacteristic
170C2×C4×D61C2×D411yescharacteristic
171C2×C4×D61#4111yescharacteristic
172C2×Dic122—21no—
173D8×C61—22no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—42no—
178C2×C8×C61—42no—
179C2×C8×C61C22×C411yescharacteristic
180C2×C8×C61C22×C411yescharacteristic
181C2×C8×C61C2×D411yescharacteristic
182C2×C8×C61C2×D411yescharacteristic
183C4⋊C4×C61C22×C411yescharacteristic
184C4⋊C4×C61C22×C411yescharacteristic
185C22⋊C4×C61—21no—
186C22⋊C4×C61—21no—
187C42×C61C2411yescharacteristic
188C22⋊Dic61—21no—
189C22⋊Dic61—21no—
190#11758199—22no—
191#11758199—41no—
192#11758198—21no—
193#11758198—21no—
194#11758198—21no—
195#11758198—21no—
196C4⋊Dic61C22×C411yescharacteristic
197C4⋊Dic61C22×C411yescharacteristic
198#11758196—21no—
199#11758196—21no—
200C4×Dic61C22×C411yescharacteristic
201C4×Dic61C2×D411yescharacteristic
202C4×Dic61#4111yescharacteristic
203#11758194—42no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—42no—
208C2×#92418C22×C411yescharacteristic
209C2×#92418C22×C411yescharacteristic
210C2×#92418C2×D411yescharacteristic
211C2×#92418C2×D411yescharacteristic
212D488—41no—
213#11758189—22no—
214#11758189—42no—
215#11758189—42no—
216#11758189—42no—
217#11758189—42no—
218#11758189D814yescomplemented
219C8×D61—42no—
220C8×D61—42no—
221C8×D61—42no—
222C23×C61—21no—
223C23×C61—21no—
224C22×D61—21no—
225C22×D61—21no—
226C22×D61—42no—
227C22×D61—42no—
228C22×D61—81no—
229C22×D61C4×D411yescharacteristic
230D4×C61—21no—
231D4×C61—21no—
232D4×C61—21no—
233D4×C61#13112yescomplemented
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61C23×C411yescharacteristic
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C22⋊D61—42no—
244C22⋊D61—42no—
245C22⋊D61—42no—
246C22⋊D61—81no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—42no—
250C2×Dic61C4×D411yescharacteristic
251C2×Dic61C4×D411yescharacteristic
252C2×Dic61C4×D411yescharacteristic
253D244—21no—
254D244—21no—
255D244—21no—
256D244—21no—
257D244—42no—
258C4×D61—21no—
259C4×D61—21no—
260C4×D61—41no—
261C4×D61—42no—
262C4×D61—41no—
263C4×D61—41no—
264C4×D61—41no—
265C4×D61—41no—
266C4×D61—42no—
267C4×D61C2×D812yes—
268C4×D61#13512yes—
269Dic122—42no—
270C8×C61—22no—
271C8×C61—21no—
272C8×C61—21no—
273C8×C61—21no—
274C8×C61—41no—
275C8×C61—41no—
276C8×C61C2×D812yes—
277#92418—21no—
278#92418—21no—
279#92418—21no—
280#92418—41no—
281#92418—41no—
282#92418—41no—
283#92418C2×D812yes—
284#17994—611nomaximal, Sylow
285C22×C61—22no—
286C22×C61—41no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61—41no—
290C22×C61—41no—
291C22×C61C2×C4×D411yescharacteristic
292C2×D61—21no—
293C2×D61—21no—
294C2×D61—41no—
295C2×D61—41no—
296C2×D61—41no—
297C2×D61—41no—
298C2×D61—41no—
299C2×D61—41no—
300C2×D61—84no—
301C2×D61C4×D812yes—
302C4×C61—21no—
303C4×C61—41no—
304C4×C61—41no—
305C4×C61C2×#13111yescharacteristic
306C4×C61#56811yescharacteristic
307C4×C61C22×D811yescharacteristic
308C4×C61C2×#13511yescharacteristic
309Dic61—21no—
310Dic61—21no—
311Dic61—41no—
312Dic61—41no—
313Dic61C4×D812yes—
314#3100—611no—
315#2935—611no—
316D4×M16—611no—
317#1589—611no—
318#1589—611no—
319#1581—611no—
320#1581—611no—
321#1581—611no—
322#1581—611no—
323C8×D8—611no—
324C8×D8D6111yescharacteristic, complemented
325#1571—611no—
326#1492—611no—
327C2×D4⋊C8—611no—
328C8×M16—611no—
329C2×C61—42no—
330C2×C61—81no—
331C2×C61#293311yescharacteristic
332C2×C61C2×C4×D811yescharacteristic
333C2×C61#295611yescharacteristic
334D61—22no—
335D61—81no—
336D61—81no—
337C2×#131—1221no—
338C22×M16—1221no—
339#532—611no—
340C2×C4×D4—611no—
341#480—611no—
342#480—611no—
343#474—611no—
344#474—611no—
345#459—611no—
346#459—611no—
347#447—611no—
348#447—611no—
349C4×D8—611no—
350C4×D8—611no—
351C4×D8—611no—
352C4×D8C2×D6111yescharacteristic
353#436—611no—
354#436—611no—
355#436—611no—
356#436—611no—
357#435—1221no—
358#435—1221no—
359#435—1221no—
360#435—1221no—
361C8×D4—611no—
362C8×D4—611no—
363C8×D4C2×D6111yescharacteristic
364C8×D4C2×D6111yescharacteristic, complemented
365#431—611no—
366#423—611no—
367C2×C4⋊C8—611no—
368#408—1221no—
369#407—1221no—
370C4×M16—611no—
371C2×C4×C8—611no—
372#335—611no—
373#335—611no—
374#335—611no—
375#335C2×D6111yescharacteristic, complemented
376D4⋊C8—611no—
377D4⋊C8—611no—
378D4⋊C8—611no—
379D4⋊C8—611no—
380D4⋊C8—611no—
381D4⋊C8—611no—
382D4⋊C8C2×D6111yescharacteristic
383D4⋊C8C2×D6111yescharacteristic, complemented
384#322—611no—
385#322—611no—
386C82—611no—
387C82C2×D6111yescharacteristic, complemented
388C61#1799411yescharacteristic, complemented, Sylow
389C2×#41—1221no—
390C22×D4—611no—
391C23×C4—1221no—
392C2×D8—611no—
393C2×D8—611no—
394C2×D8—611no—
395C2×D8C4×D6111yescharacteristic
396#131—2444no—
397C2×M16—611no—
398C2×M16—611no—
399C2×M16—1221no—
400C2×M16—1221no—
401C2×M16—1221no—
402C2×M16—1221no—
403C2×M16—1221no—
404C2×M16—2444no—
405C22×C8—21no—
406C22×C8—21no—
407C22×C8—1221no—
408C22×C8—1221no—
409C22×C8—1221no—
410C22×C8—1221no—
411C4⋊Q8—611no—
412#127—611no—
413#124—1221no—
414#121—611no—
415#121—611no—
416#121—1221no—
417C4×D4—611no—
418C4×D4—611no—
419C4×D4—611no—
420C4×D4—611no—
421C4×D4—1221no—
422C4×D4—1221no—
423C4×D4—1221no—
424C4×D4C22×D6111yescharacteristic
425C4×D4C22×D6111yescharacteristic
426C2×C4⋊C4—611no—
427C2×C22⋊C4—1221no—
428C2×C42—611no—
429#107—611no—
430#107—611no—
431#107—611no—
432#107C4×D6111yescharacteristic
433C4⋊C8—611no—
434C4⋊C8—611no—
435C4⋊C8—611no—
436C4⋊C8—611no—
437C4⋊C8—1221no—
438C4⋊C8—1221no—
439C4⋊C8C22×D6111yescharacteristic
440C4⋊C8C22×D6111yescharacteristic
441#102—611no—
442#102—611no—
443#102—611no—
444#102—611no—
445#102—611no—
446#102—611no—
447#102C4×D6111yescharacteristic
448#102C4×D6111yescharacteristic
449C22⋊C8—21no—
450C22⋊C8—21no—
451C22⋊C8—611no—
452C22⋊C8—611no—
453C22⋊C8—1221no—
454C22⋊C8—1221no—
455C22⋊C8—1221no—
456C22⋊C8—1221no—
457C22⋊C8—1221no—
458C22⋊C8—1221no—
459#97—611no—
460#97—611no—
461C4×C8—611no—
462C4×C8—611no—
463C4×C8—611no—
464C4×C8—1221no—
465C4×C8C22×D6111yescharacteristic
466C4×C8C22×D6111yescharacteristic
467C4×C8C22×D6111yescharacteristic
468C24—1221no—
469#41—2442no—
470#41—2442no—
471C2×Q8—1221no—
472C2×D4—611no—
473C2×D4—611no—
474C2×D4—1221no—
475C2×D4—1221no—
476C2×D4—1221no—
477C2×D4—1221no—
478C2×D4—1222no—
479C2×D4—1221no—
480C2×D4—2441no—
481C2×D4C2×C4×D6111yescharacteristic
482C2×D4C2×C4×D6111yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4—2442no—
494C22×C4—2442no—
495D8—22no—
496D8—1222no—
497D8—2441no—
498D8—2441no—
499M16—614no—
500M16—1222no—
501M16—2442no—
502M16—2442no—
503M16—2442no—
504M16—2442no—
505M16—2442no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—42no—
510C2×C8—42no—
511C2×C8—611no—
512C2×C8—611no—
513C2×C8—611no—
514C2×C8—611no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—2442no—
519C2×C8—2442no—
520C2×C8—2442no—
521C2×C8—2442no—
522C2×C8C2×C4×D6111yescharacteristic
523C2×C8C2×C4×D6111yescharacteristic
524C2×C8D4×D6111yescharacteristic
525C2×C8D4×D6111yescharacteristic
526C4⋊C4—611no—
527C4⋊C4—611no—
528C4⋊C4—1221no—
529C4⋊C4—1221no—
530C4⋊C4C2×C4×D6111yescharacteristic
531C4⋊C4C2×C4×D6111yescharacteristic
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—1221no—
535C22⋊C4—1221no—
536C22⋊C4—1221no—
537C22⋊C4—1221no—
538C22⋊C4—1221no—
539C22⋊C4—1221no—
540C42—611no—
541C42—611no—
542C42—611no—
543C42C23×D6111yescharacteristic
544C23—21no—
545C23—21no—
546C23—611no—
547C23—1221no—
548C23—1221no—
549C23—4881no—
550C23—2442no—
551C23—2442no—
552Q8—2442no—
553D4—21no—
554D4—21no—
555D4—21no—
556D4—1221no—
557D4—1221no—
558D4—1221no—
559D4—1221no—
560D4—4881no—
561D4—2442no—
562D4—2442no—
563D4—2442no—
564D4—2442no—
565D4#1451978312yescomplemented
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—611no—
573C2×C4—612no—
574C2×C4—612no—
575C2×C4—611no—
576C2×C4—611no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—1221no—
581C2×C4—2441no—
582C2×C4—2442no—
583C2×C4—2442no—
584C2×C4—2442no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4C22×C4×D6111yescharacteristic
590C2×C4C2×D4×D6111yescharacteristic
591C2×C4#41×D6111yescharacteristic
592C8—22no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—41no—
597C8—41no—
598C8—612no—
599C8—1221no—
600C8—1221no—
601C8—1221no—
602C8—2441no—
603C8—2441no—
604C8—2441no—
605C8D8×D6112yes—
606C22—22no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—612no—
613C22—1221no—
614C22—1221no—
615C22—4884no—
616C22—2441no—
617C22—2441no—
618C22—2441no—
619C22—2441no—
620C22—2441no—
621C22—2441no—
622C22C4×D4×D6111yescharacteristic
623C4—21no—
624C4—41no—
625C4—41no—
626C4—612no—
627C4—1221no—
628C4—1221no—
629C4—2441no—
630C4—2441no—
631C4C2×#1451978311yescharacteristic
632C4#1684052711yescharacteristic
633C4C2×D8×D6111yescharacteristic
634C4#135×D6111yescharacteristic
635C2—42no—
636C2—81no—
637C2—1222no—
638C2—4881no—
639C2—4881no—
640C2#2145453911yescharacteristic
641C2C4×D8×D6111yescharacteristic
642C2#2145472411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC8×D8×C61C2
socleC22×C61C2×C4×D4
prime radical#21455817C2
cosocleC42×C61C24
hypercenterC8×D8D61
hypocenterC61#17994
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×D8

Complements

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

NH ≅ G/Ntype
2. #21454558C2semidirect
3. D4×#11758189C2semidirect
4. #21444705C2semidirect
5. #21444701C2semidirect
6. #21444649C2semidirect
7. #21444648C2semidirect
8. #21444648C2semidirect
9. #21444647C2semidirect
10. #21444611C2semidirect
11. #21444592C2semidirect
12. #21444268C2semidirect
13. D4⋊C8×D61C2semidirect
14. C8×#11758189C2semidirect
15. C8×D8×C61C2semidirect
32. #16839841C22semidirect
33. #16839840C22semidirect
40. #16839827C22semidirect
48. #16839515C22semidirect
49. #16839514C22semidirect
50. #16839514C22semidirect
52. #16839491C22semidirect
54. D4⋊#92418C22semidirect
56. #16839489C22semidirect
57. #16839484C22semidirect
58. #16839483C22semidirect
59. C8×#92418C22semidirect
62. C8×D4×C61C22semidirect
63. C61×#335C22semidirect
65. C61×D4⋊C8C22semidirect
66. C82×C61C22semidirect
218. #11758189D8semidirect
233. D4×C61#131semidirect
324. C8×D8D61semidirect
364. C8×D4C2×D61semidirect
375. #335C2×D61semidirect
383. D4⋊C8C2×D61semidirect
387. C82C2×D61semidirect
388. C61#17994semidirect
565. D4#14519783semidirect

Maximal subgroups

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

subgroupindex
#214558172
#214545582
D4×#117581892
#214447052
#214447012
#214446492
#214446482
#214446472
#214446112
#214445922
#214442682
D4⋊C8×D612
C8×#117581892
C8×D8×C612
#1799461