Finite Group Databasebeta

← #29742997

Subgroups — #29742997

Order 15616.

896 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840065C211yesmaximal, characteristic, complemented
2C2×#16839842C211yesmaximal, characteristic
3#21449694C211yesmaximal, characteristic, complemented
4#21448727C211yesmaximal, characteristic, complemented
5#21447301C211yesmaximal, characteristic, complemented
6#21447205C211yesmaximal, characteristic, complemented
7#21447159C211yesmaximal, characteristic, complemented
8#21446550C211yesmaximal, characteristic, complemented
9#21446377C211yesmaximal, characteristic, complemented
10#21446170C211yesmaximal, characteristic
11#21446164C211yesmaximal, characteristic
12#21446078C211yesmaximal, characteristic, complemented
13#21446077C211yesmaximal, characteristic, complemented
14#21446069C211yesmaximal, characteristic, complemented
15C61×#2092C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C2×#14519768C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20C2×#14519739C2211yescharacteristic
21C2×#14519739C2211yescharacteristic
22#16840065—24no—
23#16839842—24no—
24C2×#14519711C2211yescharacteristic
25C2×#14519710C2211yescharacteristic
26C2×#14519708C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519699C2211yescharacteristic
29C2×#14519699C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×C8×Dic61C2211yescharacteristic
33#16839698—21no—
34#16839685—21no—
35#16839665C2211yescharacteristic
36#16839660C2211yescharacteristic
37#16839658C2211yescharacteristic
38#16839658C2211yescharacteristic
39#16839658C2211yescharacteristic
40#16839637—21no—
41#16839636—21no—
42#16839636—21no—
43#16839621—21no—
44#16839620—21no—
45C4×C4⋊Dic61C2211yescharacteristic
46#95×D61—21no—
47#16839525C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839517C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C2×#107×C61C2211yescharacteristic
55C2×#106×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C61×#390C2211yescharacteristic
59C61×#382C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×D244C2311yescharacteristic
62C23×Dic61—21no—
63C22×C4×D61—21no—
64C22×C4×D61—21no—
65C22×C4×D61—21no—
66C2×#11758199—22no—
67C2×#11758199—22no—
68C2×#11758199Q814yes—
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71#14519768—22no—
72#14519768—41no—
73C4×D244—22no—
74C4×D244—22no—
75D4×Dic61—22no—
76D4×Dic61—41no—
77#14519739—22no—
78#14519739—22no—
79#14519739—41no—
80#14519739—41no—
81C2×C4⋊Dic61—21no—
82C2×C4⋊Dic61D411yescharacteristic
83C2×C4⋊Dic61D411yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×#11758196—21no—
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×C4×Dic61C2311yescharacteristic
99C2×C4×Dic61C2311yescharacteristic
100#14519711—22no—
101#14519710—22no—
102#14519708—22no—
103#14519706—22no—
104#14519699—22no—
105#14519699D414yes—
106#14519698—22no—
107#14519697—22no—
108C8×Dic61—22no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684D411yescharacteristic
114#14519684D411yescharacteristic
115C22×D4×C61C2311yescharacteristic
116C22×C8×C61C2311yescharacteristic
117C22×C8×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C22⋊C4×C61—21no—
122C2×C22⋊C4×C61—21no—
123C2×C42×C61C2311yescharacteristic
124#107×C61—22no—
125#106×C61—41no—
126#102×C61—22no—
127#102×C61—41no—
128#95×C61—21no—
129#95×C61—21no—
130C24×C61—21no—
131C23×D61—21no—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61—21no—
136C2×D4×C61—21no—
137C2×D4×C61C2×Q812yes—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2411yescharacteristic
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—42no—
148C22×Dic61—42no—
149C22×Dic61—81no—
150C22×Dic61C2×D411yescharacteristic
151C22×Dic61C2×D411yescharacteristic
152C22×Dic61C2×D411yescharacteristic
153C22×Dic61C2×D411yescharacteristic
154C2×D244—21no—
155C2×D244—21no—
156C2×D244—21no—
157C2×D244C2×D412yes—
158C2×D244C2×Q812yes—
159C2×D244#4112yes—
160C2×C4×D61—24no—
161C2×C4×D61—42no—
162C2×C4×D61—42no—
163C2×C4×D61—42no—
164C2×C4×D61—42no—
165C2×C4×D61—81no—
166C2×C4×D61—81no—
167C2×C4×D61—81no—
168C2×C4×D61—81no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61C2×D412yes—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C22⋊C4×C61—42no—
182C22⋊C4×C61—81no—
183C42×C61—21no—
184C42×C61—21no—
185C22⋊Dic61—42no—
186C22⋊Dic61—81no—
187C22⋊Dic61—81no—
188#11758199—28no—
189#11758198—24no—
190#11758198—42no—
191#11758198—42no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—22no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—41no—
198C4⋊Dic61—42no—
199C4⋊Dic61C2×D412yes—
200C4⋊Dic61#4112yes—
201#11758196—42no—
202#11758196—81no—
203#11758196—81no—
204#11758196—81no—
205#11758196—81no—
206C4×Dic61—21no—
207C4×Dic61—21no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418C2×Q812yes—
216C23×C61—22no—
217C23×C61—41no—
218C23×C61—41no—
219C23×C61—41no—
220C23×C61—41no—
221C23×C61—41no—
222C23×C61—41no—
223C23×C61C22×D411yescharacteristic
224C22×D61—22no—
225C22×D61—22no—
226C22×D61—22no—
227C22×D61—41no—
228C22×D61—41no—
229C22×D61—41no—
230C22×D61—41no—
231D4×C61—22no—
232D4×C61—22no—
233D4×C61—41no—
234D4×C61—41no—
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—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61C22×D411yescharacteristic
251C2×C4×C61C22×Q811yescharacteristic
252C2×C4×C61C2×#4111yescharacteristic
253C2×C4×C61C2×#4111yescharacteristic
254C2×C4×C61H(5,𝔽2)11yescharacteristic
255C2×C4×C612−1+411yescharacteristic
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—22no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—22no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—84no—
277C2×Dic61#13512yes—
278D244—22no—
279D244—22no—
280D244—22no—
281D244C22⋊Q814yes—
282C4×D61—84no—
283C4×D61—84no—
284C4×D61—84no—
285C8×C61—22no—
286C8×C61—41no—
287#92418—22no—
288#92418—41no—
289#26370—611nomaximal, Sylow
290C22×C61—42no—
291C22×C61—42no—
292C22×C61—42no—
293C22×C61—81no—
294C22×C61—81no—
295C22×C61—81no—
296C22×C61—81no—
297C22×C61#52511yescharacteristic
298C22×C61D4211yescharacteristic
299C22×C61D4×Q811yescharacteristic
300C22×C61C2×#13511yescharacteristic
301C22×C61#57511yescharacteristic
302C22×C61#57611yescharacteristic
303C22×C61#57611yescharacteristic
304C2×D61—24no—
305C2×D61—42no—
306C2×D61—42no—
307C2×D61—42no—
308C2×D61—42no—
309C2×D61—42no—
310C2×D61—42no—
311C4×C61—41no—
312C4×C61—41no—
313C4×C61—81no—
314C4×C61—81no—
315C4×C61—81no—
316C4×C61C2×C22⋊Q811yescharacteristic
317C4×C61#53911yescharacteristic
318C4×C61#54711yescharacteristic
319C4×C61#55411yescharacteristic
320Dic61—22no—
321Dic61—42no—
322Dic61—41no—
323Dic61—41no—
324Dic61—41no—
325Dic61—42no—
326Dic61—81no—
327C2×#478—611no—
328C2×C4×D8—611no—
329#2454—611no—
330#2349—611no—
331#2092D6111yescharacteristic, complemented
332#2085—611no—
333#2067—611no—
334#2059—611no—
335#1942—611no—
336#1916—611no—
337#1879—611no—
338#1879—611no—
339#1864—611no—
340#1864—611no—
341#1862—611no—
342C2×C61—82no—
343C2×C61#244911yescharacteristic
344C2×C61#310211yescharacteristic
345C2×C61#312211yescharacteristic
346C2×C61#326811yescharacteristic
347C2×C61#328011yescharacteristic
348C2×C61#338011yescharacteristic
349C2×C61#338911yescharacteristic
350D61—44no—
351C22×D8—611no—
352C2×#125—611no—
353C2×C4×D4—611no—
354C2×C4×D4—611no—
355C2×C4×D4—611no—
356C2×C4×D4—611no—
357#478—1224no—
358C4×D8—1224no—
359C2×#107—611no—
360C2×#107—611no—
361C2×#107C2×D6111yescharacteristic
362C2×#106—611no—
363C2×#106C2×D6111yescharacteristic
364C2×C4⋊C8—611no—
365C2×#102—611no—
366C2×#102—611no—
367C2×#102—611no—
368C2×#102—611no—
369C2×#102C2×D6111yescharacteristic
370C2×#102C2×D6111yescharacteristic
371C2×C4×C8—611no—
372#399—1221no—
373#396—1221no—
374#390—611no—
375#390C2×D6111yescharacteristic
376#389—611no—
377#389—611no—
378#389—611no—
379#389—611no—
380#385—1221no—
381#385—1221no—
382#385—1221no—
383#382C2×D6111yescharacteristic
384#380—1221no—
385#380—1221no—
386C4×C4⋊C4—611no—
387C2×#95—1221no—
388#340—611no—
389#340—611no—
390#340—611no—
391#340—611no—
392#336—611no—
393#336—611no—
394#336—611no—
395#336C2×D6111yescharacteristic
396C61#2637011yescharacteristic, complemented, Sylow
397C22×D4—611no—
398C22×D4C22×D6111yescharacteristic
399C23×C4—1221no—
400C23×C4—1221no—
401C23×C4—1221no—
402C23×C4—1221no—
403C2×D8—614no—
404C2×D8—1222no—
405C2×D8—1222no—
406C22×C8—611no—
407C22×C8—611no—
408C22×C8C22×D6111yescharacteristic
409C22×C8C22×D6111yescharacteristic
410#125—1222no—
411#125—2441no—
412C4×D4—1222no—
413C4×D4—1222no—
414C4×D4—1222no—
415C4×D4—1222no—
416C4×D4—1222no—
417C4×D4—2441no—
418C4×D4—2441no—
419C4×D4—2441no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—611no—
423C2×C4⋊C4—611no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—1221no—
426C2×C4⋊C4—1221no—
427C2×C4⋊C4—1221no—
428C2×C4⋊C4—1221no—
429C2×C4⋊C4—1221no—
430C2×C4⋊C4—1221no—
431C2×C4⋊C4C22×D6111yescharacteristic
432C2×C4⋊C4C22×D6111yescharacteristic
433C2×C4⋊C4C22×D6111yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—1221no—
437C2×C22⋊C4—1221no—
438C2×C22⋊C4—1221no—
439C2×C22⋊C4—1221no—
440C2×C22⋊C4—1221no—
441C2×C22⋊C4—1221no—
442C2×C42—611no—
443C2×C42—611no—
444C2×C42C22×D6111yescharacteristic
445#107—22no—
446#107—1222no—
447#107—1222no—
448#106—41no—
449#106—1222no—
450C4⋊C8—1222no—
451#102—22no—
452#102—41no—
453#102—614no—
454#102—1222no—
455#102—1222no—
456#102—1222no—
457C4×C8—1222no—
458#95—21no—
459#95—21no—
460#95—611no—
461#95—611no—
462#95—1221no—
463#95—1221no—
464#95—1221no—
465#95—1221no—
466C24—21no—
467C24—1221no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—612no—
474C2×D4—612no—
475C2×D4—612no—
476C2×D4—1221no—
477C2×D4—1221no—
478C2×D4—1221no—
479C2×D4Q8×D6112yes—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—1224no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—4881no—
492C22×C4—4881no—
493C22×C4—4881no—
494C22×C4—4881no—
495C22×C4—4881no—
496C22×C4—2442no—
497C22×C4—2442no—
498C22×C4—2442no—
499C22×C4—2442no—
500C22×C4—2442no—
501C22×C4—2442no—
502C22×C4D4×D6111yescharacteristic
503C22×C4D4×D6111yescharacteristic
504C22×C4C23×D6111yescharacteristic
505D8—1228no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—612no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8D4×D6112yes—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—612no—
525C4⋊C4—612no—
526C4⋊C4—1222no—
527C4⋊C4—1221no—
528C4⋊C4—1221no—
529C4⋊C4—1221no—
530C4⋊C4—1221no—
531C4⋊C4—4881no—
532C4⋊C4—4881no—
533C4⋊C4—4881no—
534C4⋊C4—4881no—
535C4⋊C4—2441no—
536C4⋊C4—2442no—
537C4⋊C4—2442no—
538C22⋊C4—42no—
539C22⋊C4—81no—
540C22⋊C4—1224no—
541C22⋊C4—4881no—
542C22⋊C4—4881no—
543C22⋊C4—2442no—
544C22⋊C4—2442no—
545C22⋊C4—2442no—
546C42—21no—
547C42—21no—
548C42—1221no—
549C42—1221no—
550C42—1221no—
551C42—1221no—
552C23—22no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—1222no—
560C23—1222no—
561C23—1222no—
562C23—2441no—
563C23—2441no—
564C23—2441no—
565C23—2441no—
566C23C2×D4×D6111yescharacteristic
567D4—22no—
568D4—22no—
569D4—41no—
570D4—41no—
571D4—614no—
572D4—1222no—
573D4—1222no—
574D4—1222no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—612no—
591C2×C4—1221no—
592C2×C4—1221no—
593C2×C4—1222no—
594C2×C4—1221no—
595C2×C4—1221no—
596C2×C4—1221no—
597C2×C4—1221no—
598C2×C4—1221no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—1222no—
604C2×C4—4884no—
605C2×C4—4884no—
606C2×C4—4884no—
607C2×C4—4884no—
608C2×C4—2441no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4—2441no—
612C2×C4—2441no—
613C2×C4—2441no—
614C2×C4—2441no—
615C2×C4C2×D4×D6111yescharacteristic
616C2×C4C2×Q8×D6111yescharacteristic
617C2×C4#41×D6111yescharacteristic
618C2×C4#41×D6111yescharacteristic
619C2×C4#1451982211yescharacteristic
620C2×C4#1451982411yescharacteristic
621C8—22no—
622C8—41no—
623C8—1222no—
624C8—2441no—
625C22—42no—
626C22—42no—
627C22—42no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—1224no—
633C22—2442no—
634C22—2442no—
635C22—2442no—
636C22—2442no—
637C22—2442no—
638C22—2442no—
639C22#1684027011yescharacteristic
640C22#1684039711yescharacteristic
641C22#1684042511yescharacteristic
642C22#135×D6111yescharacteristic
643C22#1684055811yescharacteristic
644C22#1684056411yescharacteristic
645C22#1684056611yescharacteristic
646C4—41no—
647C4—41no—
648C4—81no—
649C4—81no—
650C4—81no—
651C4—1222no—
652C4—4881no—
653C4—2441no—
654C4—2442no—
655C4—2442no—
656C4—2441no—
657C4—2441no—
658C4C22⋊Q8×D6111yescharacteristic
659C4#1684035511yescharacteristic
660C4#1684041011yescharacteristic
661C4#1684046611yescharacteristic
662C2—82no—
663C2—2444no—
664C2#2144963111yescharacteristic
665C2#2145583211yescharacteristic
666C2#2145605811yescharacteristic
667C2#2145735811yescharacteristic
668C2#2145750311yescharacteristic
669C2#2145868111yescharacteristic
670C2#2145877611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2092C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
hypercenter#2092D61
hypocenterC61#26370
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2092

Complements

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

NH ≅ G/Ntype
1. C2×#16840065C2semidirect
3. #21449694C2semidirect
4. #21448727C2semidirect
5. #21447301C2semidirect
6. #21447205C2semidirect
7. #21447159C2semidirect
8. #21446550C2semidirect
9. #21446377C2semidirect
12. #21446078C2semidirect
13. #21446077C2semidirect
14. #21446069C2semidirect
15. C61×#2092C2semidirect
331. #2092D61semidirect
396. C61#26370semidirect

Maximal subgroups

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

subgroupindex
C2×#168400652
C2×#168398422
#214496942
#214487272
#214473012
#214472052
#214471592
#214465502
#214463772
#214461702
#214461642
#214460782
#214460772
#214460692
C61×#20922
#2637061