Finite Group Databasebeta

← #29701865

Subgroups — #29701865

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×#16840061C211yesmaximal, characteristic
2#21448917C211yesmaximal, characteristic, complemented
3#21448728C211yesmaximal, characteristic
4#21446782C211yesmaximal, characteristic, complemented
5#21446586C211yesmaximal, characteristic, complemented
6#21446549C211yesmaximal, characteristic, complemented
7#21446548C211yesmaximal, characteristic, complemented
8#21446414C211yesmaximal, characteristic, complemented
9#21446083C211yesmaximal, characteristic
10#21446067C211yesmaximal, characteristic
11#21445680C211yesmaximal, characteristic, complemented
12C4×#14519697C211yesmaximal, characteristic
13#21445633C211yesmaximal, characteristic
14#21445633C211yesmaximal, characteristic
15C61×#1920C211yesmaximal, characteristic, complemented
16C2×#14519768C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18C2×#14519739C2211yescharacteristic
19C2×#14519739C2211yescharacteristic
20#16840061C418yescomplemented
21C2×#14519710C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519709C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×C4×#92418C2211yescharacteristic
30C2×C8×Dic61C2211yescharacteristic
31C2×C8×Dic61C2211yescharacteristic
32#16839661C2211yescharacteristic
33#16839661C2211yescharacteristic
34#16839660C2211yescharacteristic
35#16839659—21no—
36#16839646—21no—
37#16839645—21no—
38#16839636—21no—
39#16839633—21no—
40#16839627C2211yescharacteristic
41#16839619—21no—
42C4⋊C4×Dic61C2211yescharacteristic
43C4⋊C4×Dic61C2211yescharacteristic
44C4×#11758196C2211yescharacteristic
45C4×C4⋊Dic61—21no—
46#95×D61—21no—
47#16839525C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53C2×#106×C61C2211yescharacteristic
54C61×#389C2211yescharacteristic
55C4×C4⋊C4×C61C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C22×D244C2311yescharacteristic
61C22×C4×D61—21no—
62C22×C4×D61—21no—
63C22×C4×D61—21no—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66#14519768—22no—
67#14519768C2×C414yescomplemented
68C4×D244—22no—
69C4×D244—41no—
70#14519739—22no—
71#14519739—22no—
72#14519739—41no—
73#14519739C2×C414yes—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196D411yescharacteristic
83C2×#11758196D411yescharacteristic
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61—21no—
89C2×C4×Dic61C2311yescharacteristic
90C2×C4×Dic61C2311yescharacteristic
91#14519710—41no—
92#14519710C2×C414yescomplemented
93#14519709—41no—
94#14519706C2×C414yescomplemented
95#14519699—22no—
96#14519699C2×C414yes—
97#14519697C2×C414yes—
98#14519697Q814yes—
99C4×#92418—41no—
100C8×Dic61—22no—
101C8×Dic61—41no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684D411yescharacteristic
110#14519684D411yescharacteristic
111C22×C8×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113C2×C4⋊C4×C61—21no—
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C42×C61—21no—
119C2×C42×C61C2311yescharacteristic
120#106×C61C2×C414yescomplemented
121#95×C61—21no—
122#95×C61—21no—
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×C61C2411yescharacteristic
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61C2×D411yescharacteristic
135C22×Dic61C2×D411yescharacteristic
136C22×Dic61C2×D411yescharacteristic
137C22×Dic61C2×D411yescharacteristic
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—
153C2×C8×C61—21no—
154C2×C8×C61—21no—
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61C22×C412yes—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—81no—
165C4⋊C4×C61C22×C412yes—
166C4⋊C4×C61C22×C412yes—
167C4⋊C4×C61C2×Q812yes—
168C42×C61—21no—
169C42×C61—21no—
170C42×C61—42no—
171#11758198—24no—
172#11758198—42no—
173#11758198—42no—
174C4⋊Dic61—21no—
175C4⋊Dic61—24no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—42no—
181C4⋊Dic61—81no—
182C4⋊Dic61C22×C412yes—
183#11758196—22no—
184#11758196—24no—
185#11758196—22no—
186#11758196—81no—
187C4×Dic61—21no—
188C4×Dic61—21no—
189C4×Dic61—81no—
190C4×Dic61—81no—
191C4×Dic61C22×C412yes—
192C4×Dic61#4112yes—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
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—22no—
210C2×C4×C61—22no—
211C2×C4×C61—21no—
212C2×C4×C61—22no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61#13512yes—
225C2×C4×C61C23×C411yescharacteristic
226C2×C4×C61C22×Q811yescharacteristic
227C2×C4×C61C2×#4111yescharacteristic
228C2×C4×C61C2×#4111yescharacteristic
229C2×C4×C61H(5,𝔽2)11yescharacteristic
230C2×C4×C612−1+411yescharacteristic
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—22no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61C4×D412yes—
250C2×Dic61C4×D412yes—
251C2×Dic61#13512yes—
252D244—22no—
253D244—22no—
254D244—22no—
255D244C4×Q814yes—
256C4×D61—84no—
257C4×D61—84no—
258C4×D61—84no—
259C8×C61—22no—
260C8×C61—41no—
261#92418—22no—
262#92418—22no—
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—42no—
280C4×C61—42no—
281C4×C61—42no—
282C4×C61—41no—
283C4×C61—81no—
284C4×C61C2×C4×Q811yescharacteristic
285C4×C61#52011yescharacteristic
286C4×C61#55211yescharacteristic
287C4×C61#55411yescharacteristic
288Dic61—22no—
289Dic61—22no—
290Dic61—22no—
291Dic61—42no—
292Dic61—41no—
293Dic61—81no—
294Dic61—81no—
295C2×#478—611no—
296#2370—611no—
297#2349—611no—
298#1991—611no—
299#1949—611no—
300#1942—611no—
301#1941—611no—
302#1921—611no—
303#1920D6111yescharacteristic, complemented
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×#125—611no—
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×#106C2×D6111yescharacteristic
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—611no—
336#389—611no—
337#389—611no—
338#389—1221no—
339#389C2×D6111yescharacteristic
340#387—1221no—
341#387—1221no—
342#385—1221no—
343#385—1221no—
344#382—611no—
345#380—1221no—
346C4×C4⋊C4—611no—
347C4×C4⋊C4—611no—
348C4×C4⋊C4—611no—
349C4×C4⋊C4—1221no—
350C4×C4⋊C4C2×D6111yescharacteristic
351C2×#95—1221no—
352#340—611no—
353#340—611no—
354#340—611no—
355#340—611no—
356#340—611no—
357#340C2×D6111yescharacteristic
358#340C2×D6111yescharacteristic
359#340C2×D6111yescharacteristic
360#336—611no—
361#336C2×D6111yescharacteristic
362C61#2296611yescharacteristic, complemented, Sylow
363C22×D4—611no—
364C23×C4—1221no—
365C23×C4—1221no—
366C23×C4—1221no—
367C22×C8—611no—
368C22×C8—611no—
369C22×C8C22×D6111yescharacteristic
370C22×C8C22×D6111yescharacteristic
371#125—614no—
372#125—1222no—
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—611no—
381C2×C4⋊C4—611no—
382C2×C4⋊C4—611no—
383C2×C4⋊C4—611no—
384C2×C4⋊C4—611no—
385C2×C4⋊C4—1221no—
386C2×C4⋊C4—1221no—
387C2×C4⋊C4—1221no—
388C2×C4⋊C4—1221no—
389C2×C4⋊C4—1221no—
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—611no—
399C2×C42—611no—
400C2×C42—1221no—
401C2×C42—1221no—
402C2×C42C22×D6111yescharacteristic
403#107—614no—
404#107—2441no—
405#106—2441no—
406#106C4×D6114yescomplemented
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—611no—
418#95—611no—
419#95—1221no—
420#95—1221no—
421#95—1221no—
422#95—1221no—
423#95—1221no—
424#95—1221no—
425#95—1221no—
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—611no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—611no—
441C22×C4—1224no—
442C22×C4—1221no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—4881no—
446C22×C4—4881no—
447C22×C4—4881no—
448C22×C4—4881no—
449C22×C4—2442no—
450C22×C4—2442no—
451C22×C4—2442no—
452C22×C4—2442no—
453C22×C4D4×D6111yescharacteristic
454C22×C4D4×D6111yescharacteristic
455C22×C4C23×D6111yescharacteristic
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—612no—
462C2×C8—612no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8C2×C4×D6112yes—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—81no—
474C4⋊C4—612no—
475C4⋊C4—1222no—
476C4⋊C4—1224no—
477C4⋊C4—1224no—
478C4⋊C4—1221no—
479C4⋊C4—1222no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—4881no—
485C4⋊C4—4881no—
486C4⋊C4—2442no—
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—42no—
496C42—612no—
497C42—612no—
498C42—1221no—
499C42—1221no—
500C42—4881no—
501C42—4881no—
502C23—1222no—
503C23—1222no—
504C23—1222no—
505C23—2441no—
506C23—2441no—
507C23—2441no—
508C23—2441no—
509C23C2×D4×D6111yescharacteristic
510D4—614no—
511D4—1222no—
512D4—1222no—
513D4—1222no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—612no—
532C2×C4—612no—
533C2×C4—612no—
534C2×C4—1221no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1222no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—4884no—
545C2×C4—4884no—
546C2×C4—4884no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4#1451979812yes—
556C2×C4C22×C4×D6111yescharacteristic
557C2×C4C2×Q8×D6111yescharacteristic
558C2×C4#41×D6111yescharacteristic
559C2×C4#41×D6111yescharacteristic
560C2×C4#1451982311yescharacteristic
561C2×C4#1451982411yescharacteristic
562C8—22no—
563C8—41no—
564C8—1222no—
565C8—1222no—
566C22—1224no—
567C22—2442no—
568C22—2442no—
569C22—2442no—
570C22—2442no—
571C22—2442no—
572C22—2442no—
573C22C4×D4×D6111yescharacteristic
574C22#1684040411yescharacteristic
575C22#1684042511yescharacteristic
576C22#135×D6111yescharacteristic
577C22C2×#1451979811yescharacteristic
578C22#1684056611yescharacteristic
579C22#1684057111yescharacteristic
580C4—22no—
581C4—41no—
582C4—42no—
583C4—42no—
584C4—42no—
585C4—81no—
586C4—1222no—
587C4—1222no—
588C4—1222no—
589C4—4881no—
590C4—4881no—
591C4—2442no—
592C4—2441no—
593C4C4×Q8×D6111yescharacteristic
594C4#1684024211yescharacteristic
595C4#1684044811yescharacteristic
596C4#1684046811yescharacteristic
597C2—2444no—
598C2#2144882711yescharacteristic
599C2C4×#1451979811yescharacteristic
600C2#2145465011yescharacteristic
601C2#2145765211yescharacteristic
602C2#2145767211yescharacteristic
603C2#2145868511yescharacteristic
604C2#2145869711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1920C2
socleC23×C61C22×D4
prime radicalC22×D244C23
cosocleC22×C4×C61C24
hypercenter#1920D61
hypocenterC61#22966
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1920

Complements

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

NH ≅ G/Ntype
2. #21448917C2semidirect
4. #21446782C2semidirect
5. #21446586C2semidirect
6. #21446549C2semidirect
7. #21446548C2semidirect
8. #21446414C2semidirect
11. #21445680C2semidirect
15. C61×#1920C2semidirect
20. #16840061C4semidirect
67. #14519768C2×C4semidirect
92. #14519710C2×C4semidirect
94. #14519706C2×C4semidirect
120. #106×C61C2×C4semidirect
303. #1920D61semidirect
362. C61#22966semidirect
406. #106C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168400612
#214489172
#214487282
#214467822
#214465862
#214465492
#214465482
#214464142
#214460832
#214460672
#214456802
C4×#145196972
#214456332
C61×#19202
#2296661