Finite Group Databasebeta

← #29779386

Subgroups — #29779386

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#21449691C211yesmaximal, characteristic, complemented
2#21447310C211yesmaximal, characteristic, complemented
3#21447233C211yesmaximal, characteristic, complemented
4#21447129C211yesmaximal, characteristic
5#21446965C211yesmaximal, characteristic, complemented
6#21446783C211yesmaximal, characteristic, complemented
7#21446684C211yesmaximal, characteristic
8#21446519C211yesmaximal, characteristic, complemented
9#21446519C211yesmaximal, characteristic, complemented
10#21446515C211yesmaximal, characteristic, complemented
11#21446390C211yesmaximal, characteristic, complemented
12#21446170C211yesmaximal, characteristic
13#21445694C211yesmaximal, characteristic, complemented
14#21445647C211yesmaximal, characteristic, complemented
15C61×#2513C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C2×#14519769C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×#14519710C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21C2×#14519698C2211yescharacteristic
22C2×#14519698C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519697C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519688C2211yescharacteristic
28C2×#14519688C2211yescharacteristic
29C2×C4×#92418C2211yescharacteristic
30#16839697—21no—
31#16839686—21no—
32#16839664C2211yescharacteristic
33#16839664C2211yescharacteristic
34#16839660C2211yescharacteristic
35#16839660C2211yescharacteristic
36#16839633—21no—
37#16839621—21no—
38#16839524C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C61×#397—21no—
49C61×#397—21no—
50C61×#390C2211yescharacteristic
51C61×#390C2211yescharacteristic
52C61×#390C2211yescharacteristic
53C61×#389C2211yescharacteristic
54C61×#388—21no—
55C61×#388—21no—
56C61×#382C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C22×D244C2311yescharacteristic
60C22×C4×D61—21no—
61C2×#11758199—22no—
62C2×#11758199—22no—
63C2×#11758199—41no—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68#14519769—22no—
69#14519769—41no—
70C4×D244—22no—
71C4×D244—41no—
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84#14519710—22no—
85C4⋊#92418—22no—
86#14519698—22no—
87#14519698—22no—
88#14519698—41no—
89#14519697—22no—
90#14519697—22no—
91#14519697—22no—
92#14519688—22no—
93#14519688—41no—
94C4×#92418—41no—
95#14519684—21no—
96#14519684—21no—
97C22×D4×C61C2311yescharacteristic
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61D411yescharacteristic
100C2×C4⋊C4×C61D411yescharacteristic
101C2×C4⋊C4×C61C2311yescharacteristic
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C4⋊C4×C61C2311yescharacteristic
104C2×C22⋊C4×C61—21no—
105C2×C22⋊C4×C61—21no—
106C2×C22⋊C4×C61—21no—
107C2×C22⋊C4×C61—21no—
108C2×C22⋊C4×C61—21no—
109C2×C22⋊C4×C61—21no—
110C2×C42×C61—21no—
111C2×C42×C61C2311yescharacteristic
112C2×C42×C61C2311yescharacteristic
113C2×C42×C61C2311yescharacteristic
114#95×C61—21no—
115#95×C61—21no—
116#95×C61—21no—
117#95×C61—21no—
118#95×C61D411yescharacteristic
119#95×C61D411yescharacteristic
120C24×C61—21no—
121C23×D61—21no—
122C2×D4×C61—21no—
123C2×D4×C61—21no—
124C2×D4×C61—21no—
125C2×D4×C61—21no—
126C2×D4×C61—21no—
127C2×D4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2411yescharacteristic
138C22×Dic61—21no—
139C22×Dic61—21no—
140C22×Dic61—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—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61—41no—
157C4⋊C4×C61—41no—
158C4⋊C4×C61—81no—
159C22⋊C4×C61—42no—
160C22⋊C4×C61—42no—
161C22⋊C4×C61—81no—
162C22⋊C4×C61—81no—
163C22⋊C4×C61—81no—
164C22⋊C4×C61—81no—
165C42×C61—21no—
166C42×C61—21no—
167C42×C61—21no—
168C42×C61—21no—
169C42×C61—21no—
170C42×C61—21no—
171C42×C61—81no—
172#11758199—44no—
173#11758198—42no—
174#11758198—42no—
175#11758198—81no—
176#11758198—81no—
177#11758198—81no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61#4112yes—
184#11758196—42no—
185#11758196—42no—
186#11758196—81no—
187#11758196—81no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418#4112yes—
199C2×#92418#4112yes—
200C23×C61—41no—
201C23×C61—41no—
202C23×C61—41no—
203C23×C61—41no—
204C23×C61—41no—
205C23×C61—41no—
206C23×C61—41no—
207C23×C61C22×D411yescharacteristic
208C22×D61—22no—
209C22×D61—41no—
210C22×D61—41no—
211C22×D61—41no—
212C22×D61—41no—
213C22×D61—41no—
214C22×D61—41no—
215D4×C61—41no—
216D4×C61—41no—
217D4×C61—41no—
218D4×C61—41no—
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×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
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—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61C2×#4111yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C2×C4×C61C2×#4111yescharacteristic
250C2×C4×C61H(5,𝔽2)11yescharacteristic
251C2×C4×C612−1+411yescharacteristic
252C2×Dic61—22no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261D244—22no—
262D244—22no—
263D244—41no—
264D244—41no—
265C4×D61—84no—
266#92418—22no—
267#92418—22no—
268#92418—41no—
269#92418—41no—
270#29096—611nomaximal, Sylow
271C22×C61—81no—
272C22×C61—81no—
273C22×C61—81no—
274C22×C61—81no—
275C22×C61—81no—
276C22×C61—81no—
277C22×C61—81no—
278C22×C61#53211yescharacteristic
279C22×C61#54611yescharacteristic
280C22×C61#54811yescharacteristic
281C22×C61#57511yescharacteristic
282C22×C61#57511yescharacteristic
283C22×C61#57611yescharacteristic
284C22×C61#57611yescharacteristic
285C2×D61—42no—
286C2×D61—42no—
287C2×D61—42no—
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—81no—
299C4×C61—81no—
300C4×C61—81no—
301C4×C61#52911yescharacteristic
302C4×C61#53911yescharacteristic
303C4×C61#55111yescharacteristic
304C4×C61#55611yescharacteristic
305Dic61—42no—
306Dic61—81no—
307Dic61—81no—
308#2513D6111yescharacteristic, complemented
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#1771—611no—
322#1762—611no—
323C2×C61—161no—
324C2×C61#256011yescharacteristic
325C2×C61#317611yescharacteristic
326C2×C61#318311yescharacteristic
327C2×C61#330911yescharacteristic
328C2×C61#331911yescharacteristic
329C2×C61#337011yescharacteristic
330C2×C61#337011yescharacteristic
331D61—82no—
332C22×D8—611no—
333C2×#125—611no—
334C2×C4×D4—611no—
335C2×#107—611no—
336C2×C4⋊C8—611no—
337C2×#102—611no—
338C2×#102—611no—
339C2×#102—611no—
340C2×#102—611no—
341C2×#102—611no—
342C2×#102—611no—
343C2×#97—611no—
344C2×#97—611no—
345C2×C4×C8—611no—
346#399—1221no—
347#397—21no—
348#397—21no—
349#396—1221no—
350#390—611no—
351#390—611no—
352#390C2×D6111yescharacteristic
353#390C2×D6111yescharacteristic
354#390C2×D6111yescharacteristic
355#389—611no—
356#389—611no—
357#389C2×D6111yescharacteristic
358#388—21no—
359#388—21no—
360#385—1221no—
361#382C2×D6111yescharacteristic
362#380—1221no—
363C4×C4⋊C4C2×D6111yescharacteristic
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#336—611no—
374#336—611no—
375C61#2909611yescharacteristic, complemented, Sylow
376C22×D4—611no—
377C22×D4C22×D6111yescharacteristic
378C23×C4—1221no—
379C2×D8—1222no—
380C2×D8—1222no—
381C2×D8—2441no—
382C22×C8—611no—
383C22×C8—611no—
384C22×C8—611no—
385C22×C8—611no—
386#125—1222no—
387#125—2441no—
388C4×D4—1222no—
389C4×D4—2441no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—611no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—611no—
394C2×C4⋊C4—1221no—
395C2×C4⋊C4—1221no—
396C2×C4⋊C4—1221no—
397C2×C4⋊C4—1221no—
398C2×C4⋊C4C22⋊D6111yescharacteristic
399C2×C4⋊C4C22⋊D6111yescharacteristic
400C2×C4⋊C4C22×D6111yescharacteristic
401C2×C4⋊C4C22×D6111yescharacteristic
402C2×C4⋊C4C22×D6111yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—1221no—
410C2×C22⋊C4—1221no—
411C2×C22⋊C4—1221no—
412C2×C22⋊C4—1221no—
413C2×C22⋊C4—1221no—
414C2×C42—21no—
415C2×C42C22×D6111yescharacteristic
416C2×C42C22×D6111yescharacteristic
417C2×C42C22×D6111yescharacteristic
418#107—1222no—
419C4⋊C8—1222no—
420#102—1222no—
421#102—1222no—
422#102—1222no—
423#102—1222no—
424#102—1222no—
425#102—2441no—
426#97—1222no—
427#97—2441no—
428C4×C8—2441no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—1221no—
434#95—1221no—
435#95C22⋊D6111yescharacteristic
436#95C22⋊D6111yescharacteristic
437C24—21no—
438C24—1221no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—612no—
446C2×D4—1221no—
447C2×D4—1221no—
448C2×D4—1221no—
449C2×D4—1221no—
450C2×D4—1221no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—1221no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4—4881no—
458C22×C4—2442no—
459C22×C4—2442no—
460C22×C4C2×C22⋊D6111yescharacteristic
461C22×C4C2×C22⋊D6111yescharacteristic
462C22×C4C2×C22⋊D6111yescharacteristic
463C22×C4C2×C22⋊D6111yescharacteristic
464C22×C4C2×C22⋊D6111yescharacteristic
465C22×C4C2×C22⋊D6111yescharacteristic
466C22×C4C23×D6111yescharacteristic
467D8—2444no—
468C2×C8—612no—
469C2×C8—612no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—81no—
489C4⋊C4—612no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C4⋊C4—4881no—
496C4⋊C4—4881no—
497C4⋊C4—2442no—
498C4⋊C4—2442no—
499C22⋊C4—42no—
500C22⋊C4—42no—
501C22⋊C4—81no—
502C22⋊C4—81no—
503C22⋊C4—81no—
504C22⋊C4—81no—
505C22⋊C4—4881no—
506C22⋊C4—4881no—
507C22⋊C4—4881no—
508C22⋊C4—2442no—
509C22⋊C4—2442no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—81no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—1222no—
525C23—2441no—
526C23—2441no—
527C23—2441no—
528C23—2441no—
529C23—2441no—
530C23—2441no—
531C23C22×C22⋊D6111yescharacteristic
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—1222no—
537D4—1222no—
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—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—1222no—
568C2×C4—4884no—
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×C4#41×D6111yescharacteristic
580C2×C4#41×D6111yescharacteristic
581C2×C4#1451982311yescharacteristic
582C2×C4#1451982411yescharacteristic
583C8—1222no—
584C8—1222no—
585C8—2441no—
586C8—2441no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—4881no—
595C22—4881no—
596C22—4881no—
597C22—4881no—
598C22—2442no—
599C22—2442no—
600C22—2442no—
601C22#1684030811yescharacteristic
602C22#1684040011yescharacteristic
603C22#1684041911yescharacteristic
604C22#1684056011yescharacteristic
605C22#1684056011yescharacteristic
606C22#1684056511yescharacteristic
607C22#1684056511yescharacteristic
608C4—41no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—81no—
615C4—81no—
616C4—81no—
617C4—4881no—
618C4—4881no—
619C4—2442no—
620C4#1684029511yescharacteristic
621C4#1684035311yescharacteristic
622C4#1684043711yescharacteristic
623C4#1684047911yescharacteristic
624C2—161no—
625C2—4882no—
626C2#2145096111yescharacteristic
627C2#2145646311yescharacteristic
628C2#2145654211yescharacteristic
629C2#2145781911yescharacteristic
630C2#2145796911yescharacteristic
631C2#2145856611yescharacteristic
632C2#2145856611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2513C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
hypercenter#2513D61
hypocenterC61#29096
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2513

Complements

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

NH ≅ G/Ntype
1. #21449691C2semidirect
2. #21447310C2semidirect
3. #21447233C2semidirect
5. #21446965C2semidirect
6. #21446783C2semidirect
8. #21446519C2semidirect
9. #21446519C2semidirect
10. #21446515C2semidirect
11. #21446390C2semidirect
13. #21445694C2semidirect
14. #21445647C2semidirect
15. C61×#2513C2semidirect
308. #2513D61semidirect
375. C61#29096semidirect

Maximal subgroups

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

subgroupindex
#214496912
#214473102
#214472332
#214471292
#214469652
#214467832
#214466842
#214465192
#214465152
#214463902
#214461702
#214456942
#214456472
C61×#25132
#2909661