Finite Group Databasebeta

← #29701852

Subgroups — #29701852

Order 15616.

846 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840059C211yesmaximal, characteristic
2#21448730C211yesmaximal, characteristic
3#21446785C211yesmaximal, characteristic, complemented
4#21446587C211yesmaximal, characteristic, complemented
5#21446549C211yesmaximal, characteristic, complemented
6#21446544C211yesmaximal, characteristic, complemented
7#21446411C211yesmaximal, characteristic, complemented
8#21446404C211yesmaximal, characteristic, complemented
9#21446079C211yesmaximal, characteristic
10#21446065C211yesmaximal, characteristic
11C4⋊C4×#92418C211yesmaximal, characteristic, complemented
12C4×#14519697C211yesmaximal, characteristic
13C4×#14519697C211yesmaximal, characteristic
14C4×#14519697C211yesmaximal, characteristic
15C61×#2370C211yesmaximal, characteristic, complemented
16C2×C4×D244C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19#16840059C418yescomplemented
20C2×#14519710C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×C4×#92418C2211yescharacteristic
30C2×C4×#92418C2211yescharacteristic
31C2×C4×#92418C2211yescharacteristic
32#16839660C2211yescharacteristic
33#16839660C2211yescharacteristic
34#16839633—21no—
35#16839633—21no—
36#16839628C2211yescharacteristic
37#16839621—21no—
38#95×D61—21no—
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839517C2211yescharacteristic
48#16839517C2211yescharacteristic
49C2×#125×C61C2211yescharacteristic
50C61×#389—21no—
51C61×#389C2211yescharacteristic
52C61×#389C2211yescharacteristic
53C61×#387—21no—
54C61×#387—21no—
55C4×C4⋊C4×C61—21no—
56C4×C4⋊C4×C61C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C4×C4⋊C4×C61C2211yescharacteristic
60C22×D244C2311yescharacteristic
61C22×C4×D61—21no—
62C22×C4×D61—21no—
63C22×C4×D61—21no—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C4×D244—22no—
69C4×D244—22no—
70C4×D244—22no—
71C4×D244—41no—
72C4×D244—41no—
73C4×D244C2×C414yes—
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82#14519710—41no—
83#14519710C2×C414yescomplemented
84#14519708—41no—
85#14519708C2×C414yescomplemented
86C4⋊#92418C2×C414yescomplemented
87#14519697—22no—
88#14519697C2×C414yes—
89#14519697C2×C414yes—
90#14519697Q814yes—
91C4×#92418—22no—
92C4×#92418—41no—
93C4×#92418—41no—
94#14519684—21no—
95#14519684—21no—
96#14519684—21no—
97#14519684—21no—
98#125×C61—22no—
99#125×C61C2×C414yescomplemented
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61—21no—
102C2×C4⋊C4×C61—21no—
103C2×C4⋊C4×C61—21no—
104C2×C4⋊C4×C61D411yescharacteristic
105C2×C4⋊C4×C61D411yescharacteristic
106C2×C4⋊C4×C61C2311yescharacteristic
107C2×C4⋊C4×C61C2311yescharacteristic
108C2×C4⋊C4×C61C2311yescharacteristic
109C2×C4⋊C4×C61C2311yescharacteristic
110C2×C42×C61—21no—
111C2×C42×C61—21no—
112C2×C42×C61—21no—
113C2×C42×C61C2311yescharacteristic
114C2×C42×C61C2311yescharacteristic
115C2×C42×C61C2311yescharacteristic
116#95×C61—21no—
117#95×C61—21no—
118#95×C61—21no—
119#95×C61—21no—
120#95×C61—21no—
121#95×C61D411yescharacteristic
122#95×C61D411yescharacteristic
123C23×D61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2411yescharacteristic
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61—21no—
138C2×D244—21no—
139C2×D244—21no—
140C2×D244—21no—
141C2×D244C22×C412yes—
142C2×D244C2×Q812yes—
143C2×D244#4112yes—
144C2×C4×D61—24no—
145C2×C4×D61—42no—
146C2×C4×D61—42no—
147C2×C4×D61—42no—
148C2×C4×D61—42no—
149C2×C4×D61—81no—
150C2×C4×D61—81no—
151C2×C4×D61—81no—
152C2×C4×D61—81no—
153C4⋊C4×C61—24no—
154C4⋊C4×C61—24no—
155C4⋊C4×C61—22no—
156C4⋊C4×C61—22no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—42no—
163C4⋊C4×C61—81no—
164C4⋊C4×C61C22×C412yes—
165C4⋊C4×C61C22×C412yes—
166C4⋊C4×C61C2×Q812yes—
167C42×C61—21no—
168C42×C61—21no—
169C42×C61—21no—
170C42×C61—21no—
171C42×C61—42no—
172C42×C61—81no—
173C42×C61—81no—
174C42×C61C22×C412yes—
175C42×C61#4112yes—
176#11758198—24no—
177#11758198—42no—
178#11758198—42no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61C22×C412yes—
185#11758196—81no—
186#11758196—81no—
187C2×#92418—21no—
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×#92418C22×C412yes—
197C2×#92418C22×C412yes—
198C2×#92418C2×Q812yes—
199C23×C61C22×D411yescharacteristic
200C22×D61—22no—
201C22×D61—22no—
202C22×D61—22no—
203C22×D61—41no—
204C22×D61—41no—
205C22×D61—41no—
206C22×D61—41no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—22no—
216C2×C4×C61—22no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—22no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61C4×D412yes—
234C2×C4×C61C4×D412yes—
235C2×C4×C61#13512yes—
236C2×C4×C61#13512yes—
237C2×C4×C61C23×C411yescharacteristic
238C2×C4×C61C22×Q811yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C2×C4×C61H(5,𝔽2)11yescharacteristic
242C2×C4×C612−1+411yescharacteristic
243C2×Dic61—22no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252D244—22no—
253D244—22no—
254D244—22no—
255D244C4×Q814yes—
256C4×D61—84no—
257C4×D61—84no—
258C4×D61—84no—
259#92418—22no—
260#92418—22no—
261#92418—22no—
262#92418—41no—
263#22966—611nomaximal, Sylow
264C22×C61C2×C4×D411yescharacteristic
265C22×C61#54611yescharacteristic
266C22×C61D4×Q811yescharacteristic
267C22×C61C2×#13511yescharacteristic
268C22×C61C2×#13511yescharacteristic
269C22×C61#57611yescharacteristic
270C22×C61#57711yescharacteristic
271C2×D61—24no—
272C2×D61—42no—
273C2×D61—42no—
274C2×D61—42no—
275C2×D61—42no—
276C2×D61—42no—
277C2×D61—42no—
278C4×C61—22no—
279C4×C61—22no—
280C4×C61—22no—
281C4×C61—22no—
282C4×C61—42no—
283C4×C61—42no—
284C4×C61—42no—
285C4×C61—41no—
286C4×C61—41no—
287C4×C61—81no—
288C4×C61C2×C4×Q811yescharacteristic
289C4×C61#52011yescharacteristic
290C4×C61#55211yescharacteristic
291C4×C61#55411yescharacteristic
292Dic61—42no—
293Dic61—81no—
294Dic61—81no—
295C2×#478—611no—
296#2370D6111yescharacteristic, complemented
297#2349—611no—
298#1991—611no—
299#1949—611no—
300#1942—611no—
301#1941—611no—
302#1921—611no—
303#1920—611no—
304#1864—611no—
305#1862—611no—
306C8×C4⋊C4—611no—
307C4×#102—611no—
308C4×#102—611no—
309C4×#102—611no—
310C2×C61#236011yescharacteristic
311C2×C61C4×#13511yescharacteristic
312C2×C61#294611yescharacteristic
313C2×C61#329611yescharacteristic
314C2×C61#329711yescharacteristic
315C2×C61#338011yescharacteristic
316C2×C61#338111yescharacteristic
317D61—44no—
318C2×#125C2×D6111yescharacteristic
319C2×C4×D4—611no—
320C2×C4×D4—611no—
321C2×C4×D4—611no—
322#478—618no—
323C2×#107—611no—
324C2×#107—611no—
325C2×#106—611no—
326C2×#106—611no—
327C2×C4⋊C8—611no—
328C2×#102—611no—
329C2×#102—611no—
330C2×#102—611no—
331C2×#102—611no—
332C2×C4×C8—611no—
333C2×C4×C8—611no—
334C2×C4×C8—611no—
335#389—21no—
336#389—611no—
337#389—611no—
338#389C2×D6111yescharacteristic
339#389C2×D6111yescharacteristic
340#387—21no—
341#387—21no—
342#385—1221no—
343#385—1221no—
344#382—611no—
345#380—1221no—
346C4×C4⋊C4—21no—
347C4×C4⋊C4C2×D6111yescharacteristic
348C4×C4⋊C4C2×D6111yescharacteristic
349C4×C4⋊C4C2×D6111yescharacteristic
350C4×C4⋊C4C2×D6111yescharacteristic
351C2×#95—1221no—
352#340—611no—
353#340—611no—
354#340—611no—
355#340—611no—
356#340—611no—
357#340—611no—
358#340—611no—
359#340—611no—
360#336—611no—
361#336—611no—
362C61#2296611yescharacteristic, complemented, Sylow
363C22×D4—611no—
364C23×C4—1221no—
365C23×C4—1221no—
366C23×C4—1221no—
367C22×C8—611no—
368C22×C8—611no—
369C22×C8—611no—
370C22×C8—611no—
371#125—22no—
372#125C4×D6114yescomplemented
373C4×D4—614no—
374C4×D4—1222no—
375C4×D4—1222no—
376C4×D4—1222no—
377C4×D4—2441no—
378C4×D4—2441no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—611no—
384C2×C4⋊C4—611no—
385C2×C4⋊C4—611no—
386C2×C4⋊C4—1221no—
387C2×C4⋊C4—1221no—
388C2×C4⋊C4C22⋊D6111yescharacteristic
389C2×C4⋊C4C22⋊D6111yescharacteristic
390C2×C4⋊C4C22×D6111yescharacteristic
391C2×C4⋊C4C22×D6111yescharacteristic
392C2×C4⋊C4C22×D6111yescharacteristic
393C2×C4⋊C4C22×D6111yescharacteristic
394C2×C22⋊C4—1221no—
395C2×C22⋊C4—1221no—
396C2×C22⋊C4—1221no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42C22×D6111yescharacteristic
401C2×C42C22×D6111yescharacteristic
402C2×C42C22×D6111yescharacteristic
403#107—614no—
404#107—2441no—
405#106—614no—
406#106—2441no—
407C4⋊C8—614no—
408#102—614no—
409#102—614no—
410#102—614no—
411#102—1222no—
412C4×C8—1222no—
413C4×C8—2441no—
414C4×C8—2441no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—1221no—
421#95—1221no—
422#95—1221no—
423#95—1221no—
424#95C22⋊D6111yescharacteristic
425#95C22⋊D6111yescharacteristic
426C24—1221no—
427C2×D4—612no—
428C2×D4—612no—
429C2×D4—612no—
430C2×D4—1221no—
431C2×D4—1221no—
432C2×D4—1221no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—1221no—
438C22×C4—1224no—
439C22×C4—1221no—
440C22×C4—1221no—
441C22×C4—4881no—
442C22×C4—4881no—
443C22×C4—4881no—
444C22×C4—4881no—
445C22×C4—2442no—
446C22×C4—2442no—
447C22×C4—2442no—
448C22×C4—2442no—
449C22×C4C2×C22⋊D6111yescharacteristic
450C22×C4C2×C22⋊D6111yescharacteristic
451C22×C4C2×C22⋊D6111yescharacteristic
452C22×C4C2×C22⋊D6111yescharacteristic
453C22×C4C2×C22⋊D6111yescharacteristic
454C22×C4C2×C22⋊D6111yescharacteristic
455C22×C4C23×D6111yescharacteristic
456C2×C8—612no—
457C2×C8—612no—
458C2×C8—612no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—24no—
472C4⋊C4—24no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—42no—
478C4⋊C4—81no—
479C4⋊C4—612no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—4881no—
486C4⋊C4—4881no—
487C4⋊C4C2×C4×D6112yes—
488C4⋊C4C2×C4×D6112yes—
489C4⋊C4Q8×D6112yes—
490C22⋊C4—1224no—
491C22⋊C4—2442no—
492C22⋊C4—2442no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—42no—
498C42—81no—
499C42—81no—
500C42C2×C4×D6112yes—
501C42#1175822212yes—
502C23—1222no—
503C23—1222no—
504C23—1222no—
505C23—2441no—
506C23—2441no—
507C23—2441no—
508C23—2441no—
509C23C22×C22⋊D6111yescharacteristic
510D4—614no—
511D4—1222no—
512D4—1222no—
513D4—1222no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—1222no—
541C2×C4—4884no—
542C2×C4—4884no—
543C2×C4—4884no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4C4×C22⋊D6112yes—
553C2×C4C4×C22⋊D6112yes—
554C2×C4#1451979712yes—
555C2×C4#1451979712yes—
556C2×C4C22×C4×D6111yescharacteristic
557C2×C4C2×Q8×D6111yescharacteristic
558C2×C4#41×D6111yescharacteristic
559C2×C4C2×#1175822211yescharacteristic
560C2×C4#1451982311yescharacteristic
561C2×C4#1451982511yescharacteristic
562C8—1222no—
563C8—1222no—
564C8—1222no—
565C8—2441no—
566C22—1224no—
567C22—2442no—
568C22—2442no—
569C22—2442no—
570C22—2442no—
571C22—2442no—
572C22—2442no—
573C22C2×C4×C22⋊D6111yescharacteristic
574C22#1684040011yescharacteristic
575C22Q8×C22⋊D6111yescharacteristic
576C22C2×#1451979711yescharacteristic
577C22C2×#1451979711yescharacteristic
578C22#1684056511yescharacteristic
579C22#1684057011yescharacteristic
580C4—22no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—42no—
585C4—41no—
586C4—42no—
587C4—42no—
588C4—41no—
589C4—81no—
590C4—4881no—
591C4—4881no—
592C4—2442no—
593C4C4×Q8×D6111yescharacteristic
594C4#1684024411yescharacteristic
595C4#1684045311yescharacteristic
596C4#1684047211yescharacteristic
597C2—2444no—
598C2#2144882011yescharacteristic
599C2C4×#1451979711yescharacteristic
600C2#2145464711yescharacteristic
601C2#2145764811yescharacteristic
602C2#2145766311yescharacteristic
603C2#2145868211yescharacteristic
604C2#2145869011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2370C2
socleC23×C61C22×D4
prime radicalC22×D244C23
cosocleC22×C4×C61C24
hypercenter#2370D61
hypocenterC61#22966
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2370

Complements

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

NH ≅ G/Ntype
3. #21446785C2semidirect
4. #21446587C2semidirect
5. #21446549C2semidirect
6. #21446544C2semidirect
7. #21446411C2semidirect
8. #21446404C2semidirect
11. C4⋊C4×#92418C2semidirect
15. C61×#2370C2semidirect
19. #16840059C4semidirect
83. #14519710C2×C4semidirect
85. #14519708C2×C4semidirect
86. C4⋊#92418C2×C4semidirect
99. #125×C61C2×C4semidirect
296. #2370D61semidirect
362. C61#22966semidirect
372. #125C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168400592
#214487302
#214467852
#214465872
#214465492
#214465442
#214464112
#214464042
#214460792
#214460652
C4⋊C4×#924182
C4×#145196972
C61×#23702
#2296661