Finite Group Databasebeta

← #29779382

Subgroups — #29779382

Order 15616.

716 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450416C211yesmaximal, characteristic, complemented
2#21449691C211yesmaximal, characteristic, complemented
3#21447307C211yesmaximal, characteristic, complemented
4#21447234C211yesmaximal, characteristic, complemented
5#21447130C211yesmaximal, characteristic
6#21446966C211yesmaximal, characteristic, complemented
7#21446784C211yesmaximal, characteristic, complemented
8#21446685C211yesmaximal, characteristic
9#21446516C211yesmaximal, characteristic, complemented
10#21446516C211yesmaximal, characteristic, complemented
11#21446516C211yesmaximal, characteristic, complemented
12#21446391C211yesmaximal, characteristic, complemented
13#21446166C211yesmaximal, characteristic
14#21445645C211yesmaximal, characteristic, complemented
15C61×#1771C211yesmaximal, characteristic, complemented
16C22×D488C2211yescharacteristic
17C2×#14519769C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×#14519711C2211yescharacteristic
20C2×#14519699C2211yescharacteristic
21C2×#14519699C2211yescharacteristic
22C2×#14519699C2211yescharacteristic
23C2×#14519699C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26#16839697—21no—
27#16839691—21no—
28#16839688—21no—
29#16839686—21no—
30#16839664C2211yescharacteristic
31#16839664C2211yescharacteristic
32#16839664C2211yescharacteristic
33#16839664C2211yescharacteristic
34#16839664C2211yescharacteristic
35#16839660C2211yescharacteristic
36#16839660C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839652—21no—
39#16839651—21no—
40#16839633—21no—
41#16839628C2211yescharacteristic
42#16839621—21no—
43C4×C4⋊Dic61C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52C2×C4⋊C8×C61C2211yescharacteristic
53C2×#97×C61C2211yescharacteristic
54C2×#97×C61C2211yescharacteristic
55C2×C4×C8×C61C2211yescharacteristic
56C4×C4⋊C4×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×D244C2311yescharacteristic
60C22×D244C2311yescharacteristic
61C22×C4×D61—21no—
62C2×D488—22no—
63C2×D488—22no—
64C2×D488—41no—
65#14519769—22no—
66#14519769—41no—
67C4×D244—22no—
68C4×D244—41no—
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×C4×Dic61—21no—
92#14519711—22no—
93#14519699—22no—
94#14519699—22no—
95#14519699—22no—
96#14519699—22no—
97#14519699—22no—
98#14519699—41no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105C22×C8×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C22×C8×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C2×C4⋊C4×C61D411yescharacteristic
110C2×C4⋊C4×C61D411yescharacteristic
111C2×C42×C61C2311yescharacteristic
112C2×C42×C61C2311yescharacteristic
113C2×C42×C61C2311yescharacteristic
114C4⋊C8×C61—22no—
115#97×C61—22no—
116#97×C61—41no—
117C4×C8×C61—41no—
118#95×C61D411yescharacteristic
119#95×C61D411yescharacteristic
120C23×D61—21no—
121C23×D61—21no—
122C22×C4×C61C2×D411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2411yescharacteristic
129C22×Dic61—21no—
130C22×Dic61—21no—
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61—21no—
135C2×D244—21no—
136C2×D244—21no—
137C2×D244—21no—
138C2×D244—21no—
139C2×D244—21no—
140C2×D244—21no—
141C2×D244—21no—
142C2×D244—21no—
143C2×D244—21no—
144C2×D244—21no—
145C2×D244—21no—
146C2×D244#4112yes—
147C2×C4×D61—42no—
148C2×C4×D61—42no—
149C2×C4×D61—81no—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61—21no—
154C2×C8×C61—21no—
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61#4112yes—
161C2×C8×C61#4112yes—
162C4⋊C4×C61—41no—
163C4⋊C4×C61—41no—
164C42×C61—21no—
165C42×C61—21no—
166C42×C61—21no—
167C42×C61—21no—
168C42×C61—21no—
169C42×C61—21no—
170#11758198—42no—
171#11758198—42no—
172#11758198—42no—
173#11758198—42no—
174#11758198—81no—
175#11758198—81no—
176#11758198—81no—
177#11758198—81no—
178#11758198—81no—
179#11758198—81no—
180#11758198—81no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61#4112yes—
193#11758196—42no—
194#11758196—42no—
195#11758196—81no—
196#11758196—81no—
197#11758196—81no—
198C4×Dic61—81no—
199D488—44no—
200C23×C61C22×D411yescharacteristic
201C22×D61—22no—
202C22×D61—41no—
203C22×D61—41no—
204C22×D61—41no—
205C22×D61—41no—
206C22×D61—41no—
207C22×D61—41no—
208C22×D61—41no—
209C22×D61—41no—
210C22×D61—41no—
211C22×D61—41no—
212C22×D61—41no—
213C22×D61—41no—
214C22×D61—41no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61C2×#4111yescharacteristic
234C2×C4×C61C2×#4111yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C2×C4×C61C2×#4111yescharacteristic
237C2×C4×C61H(5,𝔽2)11yescharacteristic
238C2×C4×C612−1+411yescharacteristic
239C2×Dic61—22no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257D244—22no—
258D244—22no—
259D244—41no—
260D244—41no—
261D244—41no—
262D244—41no—
263D244—41no—
264D244—41no—
265C4×D61—84no—
266C8×C61—22no—
267C8×C61—22no—
268C8×C61—41no—
269C8×C61—41no—
270#29096—611nomaximal, Sylow
271C22×C61#53211yescharacteristic
272C22×C61#54611yescharacteristic
273C22×C61#54811yescharacteristic
274C22×C61#57511yescharacteristic
275C22×C61#57511yescharacteristic
276C22×C61#57611yescharacteristic
277C22×C61#57611yescharacteristic
278C2×D61—42no—
279C2×D61—42no—
280C2×D61—42no—
281C2×D61—81no—
282C2×D61—81no—
283C2×D61—81no—
284C2×D61—81no—
285C2×D61—81no—
286C2×D61—81no—
287C2×D61—81no—
288C2×D61—81no—
289C2×D61—81no—
290C2×D61—81no—
291C2×D61—81no—
292C4×C61—41no—
293C4×C61—41no—
294C4×C61—41no—
295C4×C61—41no—
296C4×C61—41no—
297C4×C61—41no—
298C4×C61#52911yescharacteristic
299C4×C61#53911yescharacteristic
300C4×C61#55111yescharacteristic
301C4×C61#55611yescharacteristic
302Dic61—42no—
303Dic61—81no—
304Dic61—81no—
305Dic61—81no—
306Dic61—81no—
307Dic61—81no—
308#2513—611no—
309#2454—611no—
310#2086—611no—
311#2073—611no—
312#2054—611no—
313#2025—611no—
314#1991—611no—
315#1970—611no—
316#1936—611no—
317#1936—611no—
318#1936—611no—
319#1918—611no—
320#1879—611no—
321#1771D6111yescharacteristic, complemented
322#1762—611no—
323C2×C61#256011yescharacteristic
324C2×C61#317611yescharacteristic
325C2×C61#318311yescharacteristic
326C2×C61#330911yescharacteristic
327C2×C61#331911yescharacteristic
328C2×C61#337011yescharacteristic
329C2×C61#337011yescharacteristic
330D61—82no—
331D61—161no—
332C22×D8—611no—
333C2×#125—611no—
334C2×C4×D4—611no—
335C2×#107—611no—
336C2×C4⋊C8C2×D6111yescharacteristic
337C2×#102—611no—
338C2×#102—611no—
339C2×#102—611no—
340C2×#102—611no—
341C2×#102—611no—
342C2×#102—611no—
343C2×#97C2×D6111yescharacteristic
344C2×#97C2×D6111yescharacteristic
345C2×C4×C8C2×D6111yescharacteristic
346#399—1221no—
347#397—1221no—
348#397—1221no—
349#396—1221no—
350#390—611no—
351#390—611no—
352#390—611no—
353#390—611no—
354#390—611no—
355#389—611no—
356#389—611no—
357#389—611no—
358#388—1221no—
359#388—1221no—
360#385—1221no—
361#382—611no—
362#380—1221no—
363C4×C4⋊C4—611no—
364C4×C4⋊C4C2×D6111yescharacteristic
365#340—611no—
366#340—611no—
367#340—611no—
368#340—611no—
369#340—611no—
370#340—611no—
371#340—611no—
372#340—611no—
373#336C2×D6111yescharacteristic
374#336C2×D6111yescharacteristic
375C61#2909611yescharacteristic, complemented, Sylow
376C22×D4—611no—
377C22×D4—611no—
378C23×C4—1221no—
379C2×D8—1222no—
380C2×D8—1222no—
381C2×D8—2441no—
382C22×C8C22×D6111yescharacteristic
383C22×C8C22×D6111yescharacteristic
384C22×C8C22×D6111yescharacteristic
385C22×C8C22×D6111yescharacteristic
386#125—1222no—
387#125—2441no—
388C4×D4—1222no—
389C4×D4—2441no—
390C2×C4⋊C4—611no—
391C2×C4⋊C4—611no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—611no—
394C2×C4⋊C4—611no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—1221no—
397C2×C4⋊C4—1221no—
398C2×C4⋊C4—1221no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4D24411yescharacteristic
402C2×C4⋊C4D24411yescharacteristic
403C2×C22⋊C4—1221no—
404C2×C22⋊C4—1221no—
405C2×C22⋊C4—1221no—
406C2×C22⋊C4—1221no—
407C2×C22⋊C4—1221no—
408C2×C22⋊C4—1221no—
409C2×C22⋊C4—1221no—
410C2×C22⋊C4—1221no—
411C2×C22⋊C4—1221no—
412C2×C22⋊C4—1221no—
413C2×C22⋊C4—1221no—
414C2×C42—1221no—
415C2×C42C22×D6111yescharacteristic
416C2×C42C22×D6111yescharacteristic
417C2×C42C22×D6111yescharacteristic
418#107—1222no—
419C4⋊C8—22no—
420#102—1222no—
421#102—1222no—
422#102—1222no—
423#102—1222no—
424#102—1222no—
425#102—2441no—
426#97—22no—
427#97—41no—
428C4×C8—41no—
429#95—1221no—
430#95—1221no—
431#95—1221no—
432#95—1221no—
433#95—1221no—
434#95—1221no—
435#95D24411yescharacteristic
436#95D24411yescharacteristic
437C24—1221no—
438C24—1221no—
439C2×D4—612no—
440C2×D4—1221no—
441C2×D4—1221no—
442C2×D4—1221no—
443C2×D4—1221no—
444C2×D4—1221no—
445C2×D4—1221no—
446C2×D4—1221no—
447C2×D4—1221no—
448C2×D4—1221no—
449C2×D4—1221no—
450C2×D4—1221no—
451C22×C4—1221no—
452C22×C4—1221no—
453C22×C4—1221no—
454C22×C4—1221no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4—4881no—
458C22×C4—2442no—
459C22×C4—2442no—
460C22×C4C2×D24411yescharacteristic
461C22×C4C2×D24411yescharacteristic
462C22×C4C2×D24411yescharacteristic
463C22×C4C2×D24411yescharacteristic
464C22×C4C2×D24411yescharacteristic
465C22×C4C2×D24411yescharacteristic
466C22×C4C23×D6111yescharacteristic
467D8—2444no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8#1175822212yes—
479C2×C8#1175822212yes—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—612no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4—1221no—
494C4⋊C4—4881no—
495C4⋊C4—4881no—
496C4⋊C4—4881no—
497C4⋊C4—2442no—
498C4⋊C4—2442no—
499C22⋊C4—4881no—
500C22⋊C4—4881no—
501C22⋊C4—4881no—
502C22⋊C4—4881no—
503C22⋊C4—4881no—
504C22⋊C4—4881no—
505C22⋊C4—4881no—
506C22⋊C4—2442no—
507C22⋊C4—2442no—
508C22⋊C4—2442no—
509C22⋊C4—2442no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—4881no—
517C23—1222no—
518C23—2441no—
519C23—2441no—
520C23—2441no—
521C23—2441no—
522C23—2441no—
523C23—2441no—
524C23—2441no—
525C23—2441no—
526C23—2441no—
527C23—2441no—
528C23—2441no—
529C23—2441no—
530C23—2441no—
531C23C22×D24411yescharacteristic
532D4—1222no—
533D4—1222no—
534D4—2441no—
535D4—2441no—
536D4—2441no—
537D4—2441no—
538D4—2441no—
539D4—2441no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—1222no—
559C2×C4—4884no—
560C2×C4—2441no—
561C2×C4—2441no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4#41×D6111yescharacteristic
578C2×C4#41×D6111yescharacteristic
579C2×C4C2×#1175822211yescharacteristic
580C2×C4C2×#1175822211yescharacteristic
581C2×C4#1451982211yescharacteristic
582C2×C4#1451982511yescharacteristic
583C8—22no—
584C8—22no—
585C8—41no—
586C8—41no—
587C22—4881no—
588C22—4881no—
589C22—4881no—
590C22—4881no—
591C22—4881no—
592C22—4881no—
593C22—4881no—
594C22—4881no—
595C22—4881no—
596C22—4881no—
597C22—4881no—
598C22—2442no—
599C22—2442no—
600C22—2442no—
601C22#1684031211yescharacteristic
602C22#1684040711yescharacteristic
603C22#1684042411yescharacteristic
604C22#1684056211yescharacteristic
605C22#1684056211yescharacteristic
606C22#1684056711yescharacteristic
607C22#1684056711yescharacteristic
608C4—41no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—4881no—
615C4—4881no—
616C4—4881no—
617C4—4881no—
618C4—4881no—
619C4—2442no—
620C4#1684029011yescharacteristic
621C4#1684035911yescharacteristic
622C4#1684044111yescharacteristic
623C4#1684048411yescharacteristic
624C2—9761no—
625C2—4882no—
626C2#2145095711yescharacteristic
627C2#2145646911yescharacteristic
628C2#2145654811yescharacteristic
629C2#2145782711yescharacteristic
630C2#2145797711yescharacteristic
631C2#2145857411yescharacteristic
632C2#2145857411yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1771C2
socleC23×C61C22×D4
prime radicalC22×D488C22
hypercenter#1771D61
hypocenterC61#29096
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
1. #21450416C2semidirect
2. #21449691C2semidirect
3. #21447307C2semidirect
4. #21447234C2semidirect
6. #21446966C2semidirect
7. #21446784C2semidirect
9. #21446516C2semidirect
10. #21446516C2semidirect
11. #21446516C2semidirect
12. #21446391C2semidirect
14. #21445645C2semidirect
15. C61×#1771C2semidirect
321. #1771D61semidirect
375. C61#29096semidirect

Maximal subgroups

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

subgroupindex
#214504162
#214496912
#214473072
#214472342
#214471302
#214469662
#214467842
#214466852
#214465162
#214463912
#214461662
#214456452
C61×#17712
#2909661