Finite Group Databasebeta

← #29740601

Subgroups — #29740601

Order 15616.

844 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448748C211yesmaximal, characteristic, complemented
2#21447387C211yesmaximal, characteristic, complemented
3#21447256C211yesmaximal, characteristic, complemented
4#21447232C211yesmaximal, characteristic, complemented
5#21446998C211yesmaximal, characteristic, complemented
6#21446443C211yesmaximal, characteristic, complemented
7#21446387C211yesmaximal, characteristic, complemented
8#21446248C211yesmaximal, characteristic, complemented
9#21446142C211yesmaximal, characteristic, complemented
10#21446137C211yesmaximal, characteristic, complemented
11#21446112C211yesmaximal, characteristic, complemented
12#21446018C211yesmaximal, characteristic, complemented
13#21445907C211yesmaximal, characteristic, complemented
14#21445535C211yesmaximal, characteristic, complemented
15C61×#2414C211yesmaximal, characteristic
16C23×#92418C2211yescharacteristic
17C2×#14519736C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C2×#14519710C2211yescharacteristic
20C2×#14519708C2211yescharacteristic
21C2×#14519698C2211yescharacteristic
22C2×#14519698C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×C22⋊#92418C2211yescharacteristic
26C2×C22⋊#92418C2211yescharacteristic
27C2×C22⋊#92418C2211yescharacteristic
28#16839655—21no—
29#16839648—21no—
30#16839642—21no—
31#16839628C2211yescharacteristic
32#16839622C2211yescharacteristic
33#16839622C2211yescharacteristic
34C4×C4⋊Dic61C2211yescharacteristic
35C22⋊C4×Dic61—21no—
36#16839524C2211yescharacteristic
37#16839524C2211yescharacteristic
38#16839524C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C2×#121×C61C2211yescharacteristic
49C2×#121×C61C2211yescharacteristic
50C2×C4×D4×C61C2211yescharacteristic
51C2×#117×C61C2211yescharacteristic
52C61×#394—21no—
53C61×#392—21no—
54C61×#390—21no—
55C61×#390C2211yescharacteristic
56C61×#389C2211yescharacteristic
57C61×#388—21no—
58C61×#380C2211yescharacteristic
59C23×Dic61—21no—
60C22×#92418—22no—
61C22×#92418—41no—
62C22×#92418—41no—
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67#14519736—22no—
68#14519736—41no—
69C2×C4⋊Dic61—22no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—41no—
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C22⋊Dic61—21no—
77C2×C22⋊Dic61—21no—
78C2×C22⋊Dic61—21no—
79C2×C4×Dic61—21no—
80C2×C4×Dic61—21no—
81#14519710—22no—
82#14519708—41no—
83#14519698—22no—
84#14519698—41no—
85#14519698—41no—
86#14519698—41no—
87C22⋊#92418—22no—
88C22⋊#92418—41no—
89C22⋊#92418—41no—
90#14519684—21no—
91#14519684—21no—
92#14519684—21no—
93#14519684—21no—
94#14519684—21no—
95C22×D4×C61—21no—
96C22×D4×C61—21no—
97C22×D4×C61D411yescharacteristic
98C22×D4×C61C2311yescharacteristic
99C23×C4×C61C2311yescharacteristic
100C23×C4×C61C2311yescharacteristic
101#121×C61—22no—
102#121×C61—22no—
103#121×C61—22no—
104#121×C61—41no—
105C4×D4×C61—22no—
106C4×D4×C61—22no—
107#117×C61—22no—
108#117×C61—41no—
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61D411yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C22⋊C4×C61—21no—
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61—21no—
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61D411yescharacteristic
121C2×C22⋊C4×C61D411yescharacteristic
122C2×C42×C61—21no—
123C2×C42×C61C2311yescharacteristic
124#95×C61—21no—
125#95×C61—21no—
126C24×C61—21no—
127C24×C61C2×D411yescharacteristic
128C24×C61C2×D411yescharacteristic
129C2×D4×C61—22no—
130C2×D4×C61—22no—
131C2×D4×C61—21no—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61—21no—
136C2×D4×C61—21no—
137C2×D4×C61—41no—
138C2×D4×C61—42no—
139C2×D4×C61—42no—
140C2×D4×C61—42no—
141C2×D4×C61—81no—
142C2×D4×C61—81no—
143C2×D4×C61—81no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61#4112yes—
162C22×C4×C61#4112yes—
163C22×C4×C61C2411yescharacteristic
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—42no—
169C22×Dic61—42no—
170C22×Dic61—81no—
171C4⋊C4×C61—22no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—81no—
178C4⋊C4×C61#4112yes—
179C22⋊C4×C61—22no—
180C22⋊C4×C61—22no—
181C22⋊C4×C61—42no—
182C22⋊C4×C61—42no—
183C22⋊C4×C61—42no—
184C22⋊C4×C61—42no—
185C22⋊C4×C61—81no—
186C22⋊C4×C61—81no—
187C42×C61—21no—
188C42×C61—21no—
189C42×C61—42no—
190C22⋊Dic61—42no—
191C22⋊Dic61—42no—
192C22⋊Dic61—81no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—42no—
201C4⋊Dic61#4112yes—
202C4×Dic61—42no—
203C4×Dic61—81no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—44no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61—21no—
227C23×C61—21no—
228C23×C61—21no—
229C23×C61—41no—
230C23×C61—41no—
231C23×C61—41no—
232C23×C61—41no—
233C23×C61—41no—
234C23×C61—41no—
235C23×C61—41no—
236C23×C61#12312yes—
237C23×C61#13512yes—
238C23×C61C22×D411yescharacteristic
239D4×C61—44no—
240D4×C61—41no—
241D4×C61—41no—
242D4×C61—41no—
243D4×C61—41no—
244D4×C61—84no—
245D4×C61—84no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—22no—
249C2×C4×C61—22no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—22no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61#12312yes—
275C2×C4×C61C2×#4111yescharacteristic
276C2×C4×C61C2×#4111yescharacteristic
277C2×C4×C61C2×#4111yescharacteristic
278C2×C4×C61C2×#4111yescharacteristic
279C2×C4×C61H(5,𝔽2)11yescharacteristic
280C2×C4×C61H(5,𝔽2)11yescharacteristic
281C2×Dic61—22no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61—41no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—84no—
294#92418—41no—
295#92418—41no—
296#92418—41no—
297#92418—41no—
298#26199—611nomaximal, Sylow
299C22×C61—22no—
300C22×C61—22no—
301C22×C61—22no—
302C22×C61—22no—
303C22×C61—22no—
304C22×C61—22no—
305C22×C61—41no—
306C22×C61—41no—
307C22×C61—41no—
308C22×C61—41no—
309C22×C61—41no—
310C22×C61—41no—
311C22×C61—41no—
312C22×C61—41no—
313C22×C61—81no—
314C22×C61—81no—
315C22×C61—81no—
316C22×C61—81no—
317C22×C61—81no—
318C22×C61—81no—
319C22×C61—81no—
320C22×C61C2×#12311yescharacteristic
321C22×C61#54611yescharacteristic
322C22×C61#54611yescharacteristic
323C22×C61C2×#13511yescharacteristic
324C22×C61#57511yescharacteristic
325C22×C61#57611yescharacteristic
326C22×C61#57711yescharacteristic
327C4×C61—22no—
328C4×C61—41no—
329C4×C61—41no—
330C4×C61—41no—
331C4×C61—42no—
332C4×C61—81no—
333C4×C61—81no—
334C4×C61#52911yescharacteristic
335C4×C61#53811yescharacteristic
336C4×C61#55311yescharacteristic
337C4×C61#55311yescharacteristic
338Dic61—42no—
339Dic61—81no—
340Dic61—81no—
341Dic61—81no—
342#2414D6111yescharacteristic
343#2352—611no—
344#2101—611no—
345#2077—611no—
346#2073—611no—
347#2033—611no—
348#1926—611no—
349#1918—611no—
350#1893—611no—
351#1875—611no—
352#1874—611no—
353#1869—611no—
354#1854—611no—
355#1824—611no—
356#1735—611no—
357C2×C61—42no—
358C2×C61—42no—
359C2×C61—161no—
360C2×C61#244411yescharacteristic
361C2×C61#309111yescharacteristic
362C2×C61#309611yescharacteristic
363C2×C61#329711yescharacteristic
364C2×C61#330111yescharacteristic
365C2×C61#331711yescharacteristic
366C2×C61#331911yescharacteristic
367C23×C8—611no—
368C2×#121C2×D6111yescharacteristic
369C2×#121C2×D6111yescharacteristic
370C2×C4×D4C2×D6111yescharacteristic
371C2×#117—611no—
372C2×#117C2×D6111yescharacteristic
373C22×C4⋊C4—611no—
374C2×#107—611no—
375C2×#106—611no—
376C2×#102—611no—
377C2×#102—611no—
378C2×#102—611no—
379C2×#102—611no—
380C2×C22⋊C8—611no—
381C2×C22⋊C8—611no—
382C2×C22⋊C8—611no—
383#394—21no—
384#392—21no—
385#390—21no—
386#390C2×D6111yescharacteristic
387#389C2×D6111yescharacteristic
388#388—21no—
389#388—1221no—
390#387—1221no—
391#386—1221no—
392#382—611no—
393#380—611no—
394#380—611no—
395#380C2×D6111yescharacteristic
396C4×C4⋊C4—611no—
397C4×C22⋊C4—1221no—
398#340—611no—
399#340—611no—
400#340—611no—
401#340—611no—
402#340—611no—
403#340—611no—
404#340—611no—
405#340—611no—
406#340—611no—
407#340—611no—
408#336—611no—
409#336—611no—
410C61#2619911yescharacteristic, complemented, Sylow
411C22×D4—21no—
412C22×D4—21no—
413C22×D4C22⋊D6111yescharacteristic
414C22×D4C22×D6111yescharacteristic
415C23×C4—1221no—
416C23×C4C22×D6111yescharacteristic
417C23×C4C22×D6111yescharacteristic
418C22×C8—611no—
419C22×C8—611no—
420C22×C8—611no—
421C22×C8—611no—
422C22×C8—1222no—
423C22×C8—2441no—
424C22×C8—2441no—
425#121—22no—
426#121—22no—
427#121—22no—
428#121—41no—
429C4×D4—22no—
430C4×D4—22no—
431#117—22no—
432#117—41no—
433#117—1222no—
434#117—2441no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—611no—
437C2×C4⋊C4—611no—
438C2×C4⋊C4—611no—
439C2×C4⋊C4—611no—
440C2×C4⋊C4—1222no—
441C2×C4⋊C4—1221no—
442C2×C4⋊C4—2441no—
443C2×C4⋊C4C22⋊D6111yescharacteristic
444C2×C4⋊C4C22×D6111yescharacteristic
445C2×C4⋊C4C22×D6111yescharacteristic
446C2×C4⋊C4C22×D6111yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—1221no—
454C2×C22⋊C4—1221no—
455C2×C22⋊C4—1221no—
456C2×C22⋊C4C22⋊D6111yescharacteristic
457C2×C22⋊C4C22⋊D6111yescharacteristic
458C2×C42—21no—
459C2×C42—1221no—
460C2×C42—1221no—
461C2×C42C22×D6111yescharacteristic
462#107—1222no—
463#106—2441no—
464#102—1222no—
465#102—2441no—
466#102—2441no—
467#102—2441no—
468C22⋊C8—1222no—
469C22⋊C8—2441no—
470C22⋊C8—2441no—
471#95—21no—
472#95—21no—
473#95—1221no—
474#95—1221no—
475#95—1221no—
476#95—1221no—
477#95—1221no—
478C24—21no—
479C24C2×C22⋊D6111yescharacteristic
480C24C2×C22⋊D6111yescharacteristic
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—41no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—81no—
494C2×D4—81no—
495C2×D4—81no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—1221no—
510C22×C4—1221no—
511C22×C4—1221no—
512C22×C4—1221no—
513C22×C4—4881no—
514C22×C4—2442no—
515C22×C4—2442no—
516C22×C4#1175822412yes—
517C22×C4#1175822412yes—
518C22×C4C2×C22⋊D6111yescharacteristic
519C22×C4C2×C22⋊D6111yescharacteristic
520C22×C4C2×C22⋊D6111yescharacteristic
521C22×C4C2×C22⋊D6111yescharacteristic
522C22×C4C23×D6111yescharacteristic
523C2×C8—1221no—
524C2×C8—1221no—
525C2×C8—1221no—
526C2×C8—1221no—
527C2×C8—1221no—
528C2×C8—1221no—
529C2×C8—1221no—
530C2×C8—1221no—
531C2×C8—1221no—
532C2×C8—1221no—
533C2×C8—1221no—
534C2×C8—1221no—
535C2×C8—2444no—
536C4⋊C4—21no—
537C4⋊C4—22no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—81no—
543C4⋊C4—612no—
544C4⋊C4—1221no—
545C4⋊C4—1221no—
546C4⋊C4—1221no—
547C4⋊C4—1221no—
548C4⋊C4—1221no—
549C4⋊C4—1221no—
550C4⋊C4—1221no—
551C4⋊C4—2442no—
552C4⋊C4#1175822412yes—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—81no—
560C22⋊C4—81no—
561C22⋊C4—4881no—
562C22⋊C4—2442no—
563C22⋊C4—2442no—
564C42—21no—
565C42—21no—
566C42—42no—
567C42—4881no—
568C42—2442no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23#1451975812yes—
589C23#1451979712yes—
590C23C22×C22⋊D6111yescharacteristic
591D4—44no—
592D4—41no—
593D4—41no—
594D4—41no—
595D4—41no—
596D4—84no—
597D4—84no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—1222no—
627C2×C4—4884no—
628C2×C4—2441no—
629C2×C4—2441no—
630C2×C4—2441no—
631C2×C4—2441no—
632C2×C4—2441no—
633C2×C4—2441no—
634C2×C4—2441no—
635C2×C4—2441no—
636C2×C4—2441no—
637C2×C4—2441no—
638C2×C4—2441no—
639C2×C4#1451975812yes—
640C2×C4#41×D6111yescharacteristic
641C2×C4C2×#1175822411yescharacteristic
642C2×C4C2×#1175822411yescharacteristic
643C2×C4C2×#1175822411yescharacteristic
644C2×C4#1451982211yescharacteristic
645C2×C4#1451982311yescharacteristic
646C8—2441no—
647C8—2441no—
648C8—2441no—
649C8—2441no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22C2×#1451975811yescharacteristic
672C22#1684040011yescharacteristic
673C22#1684040611yescharacteristic
674C22C2×#1451979711yescharacteristic
675C22#1684056011yescharacteristic
676C22#1684056511yescharacteristic
677C22#1684057311yescharacteristic
678C4—22no—
679C4—42no—
680C4—41no—
681C4—41no—
682C4—41no—
683C4—81no—
684C4—81no—
685C4—4881no—
686C4—4881no—
687C4—4881no—
688C4—2442no—
689C4#1684029311yescharacteristic
690C4#1684034911yescharacteristic
691C4#1684045511yescharacteristic
692C4#1684046411yescharacteristic
693C2—42no—
694C2—42no—
695C2—161no—
696C2#2144956511yescharacteristic
697C2#2145572811yescharacteristic
698C2#2145577111yescharacteristic
699C2#2145766911yescharacteristic
700C2#2145771511yescharacteristic
701C2#2145794511yescharacteristic
702C2#2145796911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#2414C2
socleC23×C61C22×D4
hypercenter#2414D61
hypocenterC61#26199
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2414

Complements

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

NH ≅ G/Ntype
1. #21448748C2semidirect
2. #21447387C2semidirect
3. #21447256C2semidirect
4. #21447232C2semidirect
5. #21446998C2semidirect
6. #21446443C2semidirect
7. #21446387C2semidirect
8. #21446248C2semidirect
9. #21446142C2semidirect
10. #21446137C2semidirect
11. #21446112C2semidirect
12. #21446018C2semidirect
13. #21445907C2semidirect
14. #21445535C2semidirect
410. C61#26199semidirect

Maximal subgroups

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

subgroupindex
#214487482
#214473872
#214472562
#214472322
#214469982
#214464432
#214463872
#214462482
#214461422
#214461372
#214461122
#214460182
#214459072
#214455352
C61×#24142
#2619961