Finite Group Databasebeta

← #29700117

Subgroups — #29700117

Order 15616.

754 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448260C211yesmaximal, characteristic
2#21446617C211yesmaximal, characteristic
3#21446612C211yesmaximal, characteristic
4#21446432C211yesmaximal, characteristic, complemented
5#21446430C211yesmaximal, characteristic, complemented
6#21446430C211yesmaximal, characteristic, complemented
7#21446425C211yesmaximal, characteristic, complemented
8#21445938C211yesmaximal, characteristic, complemented
9#21445889C211yesmaximal, characteristic, complemented
10#21445886C211yesmaximal, characteristic, complemented
11#21445688C211yesmaximal, characteristic, complemented
12#21445679C211yesmaximal, characteristic, complemented
13#21445586C211yesmaximal, characteristic, complemented
14#21445582C211yesmaximal, characteristic, complemented
15C61×#1771C211yesmaximal, characteristic, complemented
16C2×C4×D244C2211yescharacteristic
17C2×#14519734C2211yescharacteristic
18C2×C42×D61C2211yescharacteristic
19C2×C4⋊#92418C2211yescharacteristic
20C2×#14519706C2211yescharacteristic
21C2×#14519706C2211yescharacteristic
22C2×#14519689C2211yescharacteristic
23C2×#14519689C2211yescharacteristic
24C2×#14519689C2211yescharacteristic
25C2×#14519689C2211yescharacteristic
26C2×#14519689C2211yescharacteristic
27C2×#14519689C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30C2×#14519688C2211yescharacteristic
31C2×#14519688C2211yescharacteristic
32C2×C4×#92418C2211yescharacteristic
33#16839652C411yescharacteristic
34#16839652C411yescharacteristic
35#16839645C411yescharacteristic
36#16839645C411yescharacteristic
37#16839640C411yescharacteristic
38#16839640C411yescharacteristic
39#16839633C411yescharacteristic
40#16839633C411yescharacteristic
41C4×#11758198C2211yescharacteristic
42C4×#11758198C2211yescharacteristic
43#16839608C2211yescharacteristic
44#16839517C2211yescharacteristic
45#16839517C2211yescharacteristic
46#16839516C2211yescharacteristic
47#16839516C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×C4⋊C8×C61C2211yescharacteristic
53C2×#97×C61C2211yescharacteristic
54C2×#97×C61C2211yescharacteristic
55C2×C4×C8×C61C2211yescharacteristic
56C4×C4⋊C4×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×D244C2×C411yescharacteristic
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61C2311yescharacteristic
63C22×C4×D61C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C4×D244—22no—
69C4×D244—22no—
70#14519734—41no—
71#14519734—41no—
72C2×C4⋊Dic61C2×C411yescharacteristic
73C2×#11758196C2×C411yescharacteristic
74C2×#11758196C2×C411yescharacteristic
75C2×#11758198C2×C411yescharacteristic
76C2×#11758198C2×C411yescharacteristic
77C2×#11758198C2×C411yescharacteristic
78C2×#11758198C2×C411yescharacteristic
79C2×#11758198C2×C411yescharacteristic
80C2×#11758198C2×C411yescharacteristic
81C2×#11758198C2×C411yescharacteristic
82C2×#11758198C2×C411yescharacteristic
83C2×C4×Dic61C2×C411yescharacteristic
84C2×C4×Dic61C2×C411yescharacteristic
85C2×C4×Dic61C2311yescharacteristic
86C2×C4×Dic61C2311yescharacteristic
87C42×D61—41no—
88C42×D61—41no—
89C4⋊#92418—22no—
90#14519706—22no—
91#14519706—22no—
92#14519689—22no—
93#14519689—22no—
94#14519689—22no—
95#14519689—22no—
96#14519689—41no—
97#14519689—41no—
98#14519689—41no—
99#14519689—41no—
100#14519688—41no—
101#14519688—41no—
102C4×#92418—22no—
103#14519684C2×C411yescharacteristic
104#14519684C2×C411yescharacteristic
105#14519684C2×C411yescharacteristic
106#14519684C2×C411yescharacteristic
107#14519684C2×C411yescharacteristic
108#14519684C2×C411yescharacteristic
109#14519684C2×C411yescharacteristic
110#14519684C2×C411yescharacteristic
111C22×C8×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2×C411yescharacteristic
116C2×C4⋊C4×C61C2×C411yescharacteristic
117C2×C42×C61C2311yescharacteristic
118C2×C42×C61C2311yescharacteristic
119C2×C42×C61C2311yescharacteristic
120C4⋊C8×C61—22no—
121#97×C61—22no—
122#97×C61—41no—
123C4×C8×C61—41no—
124#95×C61C2×C411yescharacteristic
125#95×C61C2×C411yescharacteristic
126C23×D61C22×C411yescharacteristic
127C23×D61C22×C411yescharacteristic
128C22×C4×C61C22×C411yescharacteristic
129C22×C4×C61C22×C411yescharacteristic
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C2411yescharacteristic
135C22×Dic61C22×C411yescharacteristic
136C22×Dic61C22×C411yescharacteristic
137C22×Dic61C22×C411yescharacteristic
138C22×Dic61C22×C411yescharacteristic
139C22×Dic61C22×C411yescharacteristic
140C22×Dic61C22×C411yescharacteristic
141C2×D244—22no—
142C2×D244—22no—
143C2×D244—41no—
144C2×C4×D61—22no—
145C2×C4×D61—21no—
146C2×C4×D61—21no—
147C2×C4×D61—21no—
148C2×C4×D61—21no—
149C2×C4×D61—21no—
150C2×C4×D61—21no—
151C2×C4×D61—21no—
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—41no—
158C2×C4×D61—41no—
159C2×C4×D61—41no—
160C2×C4×D61—41no—
161C2×C4×D61—41no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61#4112yes—
174C4⋊C4×C61—41no—
175C4⋊C4×C61—41no—
176C42×C61—21no—
177C42×C61—21no—
178C42×C61—21no—
179C42×C61—21no—
180C42×C61#4112yes—
181C42×C61#4112yes—
182#11758198—22no—
183#11758198—22no—
184#11758198—22no—
185#11758198—41no—
186#11758198—41no—
187#11758198—41no—
188#11758198—41no—
189#11758198—41no—
190C4⋊Dic61—22no—
191#11758196—41no—
192#11758196—41no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61—21no—
197C4×Dic61—41no—
198C4×Dic61—41no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418#4112yes—
211C23×C61C23×C411yescharacteristic
212C22×D61—21no—
213C22×D61—21no—
214C22×D61—21no—
215C22×D61—21no—
216C22×D61—21no—
217C22×D61—21no—
218C22×D61—21no—
219C22×D61—21no—
220C22×D61—21no—
221C22×D61—21no—
222C22×D61—21no—
223C22×D61—21no—
224C22×D61—21no—
225C22×D61#13112yes—
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—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61#11712yes—
243C2×C4×C61#11712yes—
244C2×C4×C61C2×#4111yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61H(5,𝔽2)11yescharacteristic
249C2×C4×C61H(5,𝔽2)11yescharacteristic
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268D244—44no—
269C4×D61—44no—
270C4×D61—44no—
271C4×D61—41no—
272C4×D61—41no—
273C4×D61—41no—
274C4×D61—41no—
275C4×D61—41no—
276C4×D61—41no—
277C4×D61—41no—
278C4×D61—41no—
279C8×C61—22no—
280C8×C61—41no—
281C8×C61—41no—
282C8×C61—41no—
283#92418—22no—
284#92418—41no—
285#92418—41no—
286#92418—41no—
287#22841—611nomaximal, Sylow
288C22×C61C2×#11711yescharacteristic
289C22×C61C4×#4111yescharacteristic
290C22×C61#51811yescharacteristic
291C22×C61C2×#13111yescharacteristic
292C22×C61#56811yescharacteristic
293C22×C61#56811yescharacteristic
294C22×C61#56811yescharacteristic
295C2×D61—22no—
296C2×D61—22no—
297C2×D61—22no—
298C2×D61—41no—
299C2×D61—41no—
300C2×D61—41no—
301C2×D61—41no—
302C2×D61—41no—
303C2×D61—41no—
304C2×D61—41no—
305C2×D61—41no—
306C2×D61—41no—
307C2×D61—41no—
308C2×D61—41no—
309C4×C61—22no—
310C4×C61—22no—
311C4×C61—41no—
312C4×C61—41no—
313C4×C61—41no—
314C4×C61—41no—
315C4×C61#55311yescharacteristic
316C4×C61#55311yescharacteristic
317C4×C61#55911yescharacteristic
318C4×C61#55911yescharacteristic
319Dic61—41no—
320Dic61—41no—
321Dic61—41no—
322Dic61—41no—
323Dic61—41no—
324Dic61—41no—
325#2290—611no—
326#1955—611no—
327#1954—611no—
328#1924—611no—
329#1924—611no—
330#1924—611no—
331#1923—611no—
332#1832—611no—
333#1818—611no—
334#1817—611no—
335#1771D6111yescharacteristic, complemented
336#1770—611no—
337#1768—611no—
338#1750—611no—
339#1749—611no—
340C2×C61#235711yescharacteristic
341C2×C61#292311yescharacteristic
342C2×C61#292411yescharacteristic
343C2×C61#296711yescharacteristic
344C2×C61#296811yescharacteristic
345C2×C61#297611yescharacteristic
346C2×C61#297811yescharacteristic
347D61—42no—
348D61—81no—
349C2×C4×D4—611no—
350C2×#117—611no—
351C22×C42—611no—
352C2×C4⋊C8—611no—
353C2×C4⋊C8—611no—
354C2×C4⋊C8—611no—
355C2×C4⋊C8C2×D6111yescharacteristic
356C2×C22⋊C8—611no—
357C2×C22⋊C8—611no—
358C2×C22⋊C8—611no—
359C2×C22⋊C8—611no—
360C2×C22⋊C8—611no—
361C2×C22⋊C8—611no—
362C2×C22⋊C8—611no—
363C2×C22⋊C8—611no—
364C2×#97—611no—
365C2×#97—611no—
366C2×#97C2×D6111yescharacteristic
367C2×#97C2×D6111yescharacteristic
368C2×C4×C8—611no—
369C2×C4×C8C2×D6111yescharacteristic
370#388—611no—
371#388—611no—
372#387—611no—
373#387—611no—
374#386—611no—
375#386—611no—
376#385—611no—
377#385—611no—
378C4×C4⋊C4C2×D6111yescharacteristic
379C4×C22⋊C4—611no—
380C4×C22⋊C4—611no—
381#376—611no—
382#336—611no—
383#336—611no—
384#336—611no—
385#336—611no—
386#336—611no—
387#336—611no—
388#336—611no—
389#336—611no—
390#336C2×D6111yescharacteristic
391#336C2×D6111yescharacteristic
392C61#2284111yescharacteristic, complemented, Sylow
393C22×D4—611no—
394C23×C4—611no—
395C23×C4—611no—
396C23×C4—611no—
397C23×C4—611no—
398C22×C8—611no—
399C22×C8—611no—
400C22×C8—611no—
401C22×C8—611no—
402C22×C8C22×D6111yescharacteristic
403C22×C8C22×D6111yescharacteristic
404C22×C8C22×D6111yescharacteristic
405C22×C8C22×D6111yescharacteristic
406C4×D4—1222no—
407C4×D4—1222no—
408#117—2441no—
409#117—2441no—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—611no—
412C2×C4⋊C4—611no—
413C2×C4⋊C4C4×D6111yescharacteristic
414C2×C4⋊C4C4×D6111yescharacteristic
415C2×C22⋊C4—611no—
416C2×C22⋊C4—611no—
417C2×C22⋊C4—611no—
418C2×C22⋊C4—611no—
419C2×C22⋊C4—611no—
420C2×C22⋊C4—611no—
421C2×C22⋊C4—611no—
422C2×C22⋊C4—611no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—611no—
426C2×C42—611no—
427C2×C42—2441no—
428C2×C42—2441no—
429C2×C42C22×D6111yescharacteristic
430C2×C42C22×D6111yescharacteristic
431C2×C42C22×D6111yescharacteristic
432C4⋊C8—22no—
433C4⋊C8—1222no—
434C4⋊C8—1222no—
435C4⋊C8—1222no—
436C22⋊C8—1222no—
437C22⋊C8—1222no—
438C22⋊C8—1222no—
439C22⋊C8—1222no—
440C22⋊C8—2441no—
441C22⋊C8—2441no—
442C22⋊C8—2441no—
443C22⋊C8—2441no—
444#97—22no—
445#97—41no—
446#97—2441no—
447#97—2441no—
448C4×C8—41no—
449C4×C8—1222no—
450#95—611no—
451#95—611no—
452#95—611no—
453#95—611no—
454#95—611no—
455#95—611no—
456#95—611no—
457#95—611no—
458#95C4×D6111yescharacteristic
459#95C4×D6111yescharacteristic
460C24—611no—
461C24—611no—
462C2×D4—1222no—
463C2×D4—1222no—
464C2×D4—2441no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—1222no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4—2441no—
485C22×C4—2441no—
486C22×C4—2441no—
487C22×C4—2441no—
488C22×C4—2441no—
489C22×C4C2×C4×D6111yescharacteristic
490C22×C4C2×C4×D6111yescharacteristic
491C22×C4C2×C4×D6111yescharacteristic
492C22×C4C2×C4×D6111yescharacteristic
493C22×C4C2×C4×D6111yescharacteristic
494C22×C4C2×C4×D6111yescharacteristic
495C22×C4C23×D6111yescharacteristic
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—612no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—1221no—
511C2×C8—1221no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—1221no—
519C2×C8#1175822612yes—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—1222no—
523C4⋊C4—2441no—
524C4⋊C4—2441no—
525C22⋊C4—1222no—
526C22⋊C4—1222no—
527C22⋊C4—1222no—
528C22⋊C4—2441no—
529C22⋊C4—2441no—
530C22⋊C4—2441no—
531C22⋊C4—2441no—
532C22⋊C4—2441no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—1221no—
538C42—1221no—
539C42—1221no—
540C42—1221no—
541C42—2441no—
542C42—2441no—
543C42#1175822212yes—
544C42#1175822212yes—
545C23—612no—
546C23—1221no—
547C23—1221no—
548C23—1221no—
549C23—1221no—
550C23—1221no—
551C23—1221no—
552C23—1221no—
553C23—1221no—
554C23—1221no—
555C23—1221no—
556C23—1221no—
557C23—1221no—
558C23—1221no—
559C23C22×C4×D6111yescharacteristic
560D4—2444no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—1221no—
581C2×C4—1221no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1221no—
590C2×C4—1221no—
591C2×C4—1221no—
592C2×C4—1221no—
593C2×C4—1221no—
594C2×C4—1221no—
595C2×C4—2444no—
596C2×C4—2444no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4#1451973412yes—
606C2×C4#1451973412yes—
607C2×C4#41×D6111yescharacteristic
608C2×C4C2×#1175822211yescharacteristic
609C2×C4C2×#1175822211yescharacteristic
610C2×C4C2×#1175822611yescharacteristic
611C2×C4#1451982211yescharacteristic
612C2×C4#1451982311yescharacteristic
613C8—22no—
614C8—41no—
615C8—41no—
616C8—41no—
617C8—1222no—
618C8—2441no—
619C8—2441no—
620C8—2441no—
621C22—1222no—
622C22—1222no—
623C22—1222no—
624C22—2441no—
625C22—2441no—
626C22—2441no—
627C22—2441no—
628C22—2441no—
629C22—2441no—
630C22—2441no—
631C22—2441no—
632C22—2441no—
633C22—2441no—
634C22—2441no—
635C22C2×#1451973411yescharacteristic
636C22C4×#1175822611yescharacteristic
637C22#1684023411yescharacteristic
638C22#131×D6111yescharacteristic
639C22#1684052711yescharacteristic
640C22#1684052811yescharacteristic
641C22#1684052811yescharacteristic
642C4—22no—
643C4—22no—
644C4—41no—
645C4—41no—
646C4—41no—
647C4—41no—
648C4—2441no—
649C4—2441no—
650C4—2441no—
651C4—2441no—
652C4—2441no—
653C4—2441no—
654C4#1684045611yescharacteristic
655C4#1684046011yescharacteristic
656C4#1684049511yescharacteristic
657C4#1684049711yescharacteristic
658C2—4881no—
659C2—2442no—
660C2#2144878811yescharacteristic
661C2#2145447111yescharacteristic
662C2#2145447411yescharacteristic
663C2#2145480311yescharacteristic
664C2#2145481211yescharacteristic
665C2#2145486611yescharacteristic
666C2#2145487811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1771C2
prime radicalC22×D244C2×C4
cosocleC22×C4×C61C24
hypercenter#1771D61
hypocenterC61#22841
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
4. #21446432C2semidirect
5. #21446430C2semidirect
6. #21446430C2semidirect
7. #21446425C2semidirect
8. #21445938C2semidirect
9. #21445889C2semidirect
10. #21445886C2semidirect
11. #21445688C2semidirect
12. #21445679C2semidirect
13. #21445586C2semidirect
14. #21445582C2semidirect
15. C61×#1771C2semidirect
335. #1771D61semidirect
392. C61#22841semidirect

Maximal subgroups

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

subgroupindex
#214482602
#214466172
#214466122
#214464322
#214464302
#214464252
#214459382
#214458892
#214458862
#214456882
#214456792
#214455862
#214455822
C61×#17712
#2284161