Finite Group Databasebeta

← #29651241

Subgroups — #29651241

Order 15616.

642 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455868C211yesmaximal, characteristic
2#21454975C211yesmaximal, characteristic, complemented
3#21454856C211yesmaximal, characteristic, complemented
4#21444732C211yesmaximal, characteristic, complemented
5#21444720C211yesmaximal, characteristic, complemented
6#21444661C211yesmaximal, characteristic, complemented
7#21444654C211yesmaximal, characteristic, complemented
8#21444647C211yesmaximal, characteristic, complemented
9#21444647C211yesmaximal, characteristic, complemented
10#21444642C211yesmaximal, characteristic, complemented
11#21444630C211yesmaximal, characteristic, complemented
12#21444277C211yesmaximal, characteristic, complemented
13C2×#16839489C211yesmaximal, characteristic, complemented
14#21444112C211yesmaximal, characteristic, complemented
15C61×#1573C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18#16840098C411yescharacteristic
19#16840081C411yescharacteristic
20#16840063C411yescharacteristic
21#16840063C411yescharacteristic
22#16839978C411yescharacteristic
23#16839978C411yescharacteristic
24#16839915C411yescharacteristic
25#16839898C411yescharacteristic
26#16839889C2211yescharacteristic, complemented
27#16839886C2211yescharacteristic, complemented
28C4×#11758190C2211yescharacteristic
29C4×#11758190C2211yescharacteristic
30C4×D488C2211yescharacteristic
31C4×D488C2211yescharacteristic
32#16839839C2211yescharacteristic
33#16839839C2211yescharacteristic
34#16839839C2211yescharacteristic, complemented
35#16839835—21no—
36#16839835—21no—
37#16839833—21no—
38#16839827C2211yescharacteristic
39#16839827C2211yescharacteristic
40#16839827C2211yescharacteristic, complemented
41C8×C22⋊D61—21no—
42#16839822—21no—
43#16839815C2211yescharacteristic
44#16839787—21no—
45#16839724—21no—
46C22⋊C8×D61—21no—
47C2×C4×#92418C2211yescharacteristic
48#16839492C2211yescharacteristic, complemented
49#16839492C2211yescharacteristic, complemented
50#16839489C2211yescharacteristic
51#16839489C2211yescharacteristic
52#16839489C2211yescharacteristic
53#16839489C2211yescharacteristic
54#16839489C2211yescharacteristic, complemented
55#16839489C2211yescharacteristic, complemented
56#16839484C2211yescharacteristic, complemented
57#16839484C2211yescharacteristic, complemented
58#16839483C2211yescharacteristic, complemented
59#16839483C2211yescharacteristic, complemented
60C61×#432C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C2×C4⋊C8×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic, complemented
64C61×#335C2211yescharacteristic, complemented
65C61×#334C2211yescharacteristic, complemented
66C61×#334C2211yescharacteristic, complemented
67C22×D244C2×C411yescharacteristic
68C22×C4×D61—21no—
69C2×#11758190C2×C411yescharacteristic
70C2×#11758190C2×C411yescharacteristic
71C2×D488C2×C411yescharacteristic
72C2×D488C2×C411yescharacteristic
73C2×#11758189—21no—
74C2×#11758189—21no—
75C2×#11758189—21no—
76C22×#92418—21no—
77C2×C8×D61—21no—
78C2×C8×D61—21no—
79C2×C8×D61—21no—
80#14519771—21no—
81#14519769C2×C411yescharacteristic
82#14519765C2×C411yescharacteristic
83#14519760—21no—
84#14519756C2×C411yescharacteristic
85#14519751C2×C411yescharacteristic
86C4×Dic122C2311yescharacteristic
87C4×D244—21no—
88C4×D244—21no—
89C4×D244C2×C411yescharacteristic
90C4×D244C2×C411yescharacteristic
91C4×D244C2311yescharacteristic
92C4×D244C2311yescharacteristic
93C4×D244C2311yescharacteristic
94C4×C22⋊D61—21no—
95#14519734—21no—
96C2×C4⋊Dic61C2×C411yescharacteristic
97C2×#11758198—21no—
98#14519711C2×C411yescharacteristic
99#14519711C2×C411yescharacteristic
100#14519709C2×C411yescharacteristic
101#14519709C2×C411yescharacteristic
102C4⋊#92418D411yescharacteristic
103C4⋊#92418D411yescharacteristic
104#14519706—21no—
105#14519706—21no—
106#14519702C2×C411yescharacteristic
107#14519702C2×C411yescharacteristic
108#14519699C2×C411yescharacteristic
109#14519699C2×C411yescharacteristic
110#14519699C2×C411yescharacteristic
111#14519699C2×C411yescharacteristic
112#14519699C2×C411yescharacteristic
113#14519699C2×C411yescharacteristic
114C22⋊#92418D411yescharacteristic
115C22⋊#92418D411yescharacteristic
116#14519689—21no—
117#14519689—21no—
118#14519689—21no—
119#14519689—21no—
120#14519689—21no—
121#14519689—21no—
122#14519687—21no—
123C4×#92418—21no—
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C4×#92418C2311yescharacteristic
127C4×#92418C2311yescharacteristic
128C8×Dic61—21no—
129C22×C8×C61—21no—
130C2×C42×C61C2311yescharacteristic
131C4⋊C8×C61—21no—
132C4⋊C8×C61C2×C411yescharacteristic
133C4⋊C8×C61C2×C411yescharacteristic
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C22⋊C8×C61—21no—
139C22⋊C8×C61C2×C411yescharacteristic
140C22⋊C8×C61C2×C411yescharacteristic
141#97×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C23×D61—21no—
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61#4111yescharacteristic
148C2×C22⋊D61—21no—
149C22×Dic61—21no—
150C2×D244—22no—
151C2×D244—21no—
152C2×D244—41no—
153C2×D244C22×C411yescharacteristic
154C2×D244C22×C411yescharacteristic
155C2×D244C22×C411yescharacteristic
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—81no—
162C2×C4×D61—81no—
163C2×Dic122C22×C411yescharacteristic
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—81no—
169C2×C8×C61C22×C411yescharacteristic
170C2×C8×C61C22×C411yescharacteristic
171C2×C8×C61C22×C411yescharacteristic
172C2×C8×C61C22×C411yescharacteristic
173C42×C61C22×C411yescharacteristic
174C42×C61C2×D411yescharacteristic
175C42×C61#4111yescharacteristic
176C42×C61C2411yescharacteristic
177C22⋊Dic61—21no—
178#11758198—21no—
179#11758198—21no—
180#11758198—21no—
181#11758198—21no—
182#11758198—21no—
183#11758198—21no—
184#11758198—21no—
185#11758198—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61C22×C411yescharacteristic
188C4⋊Dic61C22×C411yescharacteristic
189C4⋊Dic61C22×C411yescharacteristic
190C4⋊Dic61C22×C411yescharacteristic
191#11758196—21no—
192#11758196—21no—
193#11758196—21no—
194#11758196—21no—
195C4×Dic61—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—42no—
199C2×#92418C2×D411yescharacteristic
200C2×#92418C2×D411yescharacteristic
201C2×#92418C2×D411yescharacteristic
202C2×#92418C2×D411yescharacteristic
203D488—22no—
204D488—41no—
205#11758190—22no—
206#11758190—41no—
207#11758189—81no—
208#11758189—81no—
209#11758189—81no—
210C8×D61—81no—
211C8×D61—81no—
212C8×D61—81no—
213C23×C61C4×D411yescharacteristic
214C22×D61—21no—
215C22×D61—21no—
216C22×D61—21no—
217C22×D61—42no—
218C22×D61—42no—
219C22×D61—81no—
220C2×C4×C61—22no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61C4×D411yescharacteristic
226C2×C4×C61C4×D411yescharacteristic
227C2×C4×C61C4×D411yescharacteristic
228C2×C4×C61C23×C411yescharacteristic
229C2×C4×C61C22×D411yescharacteristic
230C2×C4×C61C2×#4111yescharacteristic
231C22⋊D61—42no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—81no—
238D244—21no—
239D244—21no—
240D244—21no—
241D244—21no—
242D244—21no—
243D244—42no—
244D244#13112yes—
245C4×D61—41no—
246C4×D61—41no—
247C4×D61—41no—
248C4×D61—41no—
249C4×D61—41no—
250C4×D61—41no—
251C4×D61—81no—
252C4×D61—81no—
253Dic122—21no—
254Dic122—21no—
255C8×C61—21no—
256C8×C61—21no—
257C8×C61—21no—
258C8×C61—21no—
259C8×C61—41no—
260C8×C61—41no—
261C8×C61—41no—
262C8×C61—41no—
263#92418—21no—
264#92418—21no—
265#92418—21no—
266#92418—21no—
267#92418—41no—
268#92418—41no—
269#18020—611nomaximal, Sylow
270C22×C61—21no—
271C22×C61—21no—
272C22×C61#44412yes—
273C22×C61C2×C4×D411yescharacteristic
274C2×D61—22no—
275C2×D61—41no—
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—41no—
283C2×D61—84no—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—21no—
288C4×C61C2×#13111yescharacteristic
289C4×C61#56811yescharacteristic
290C4×C61#57611yescharacteristic
291C4×C61#57711yescharacteristic
292Dic61—41no—
293Dic61—41no—
294Dic61—41no—
295Dic61—41no—
296Dic61—41no—
297#3105—611no—
298#2994—611no—
299#2974—611no—
300#1594—611no—
301#1592—611no—
302#1583—611no—
303#1582—611no—
304#1581—611no—
305#1581—611no—
306#1580—611no—
307SD16⋊C8—611no—
308#1573D6111yescharacteristic, complemented
309#1494—611no—
310C2×D4⋊C8—611no—
311#1452—611no—
312C2×C61—22no—
313C2×C61#293311yescharacteristic
314C2×C61#294611yescharacteristic
315C2×C61C2×#44411yescharacteristic
316D61—42no—
317D61—81no—
318D61—81no—
319#529—611no—
320C2×C4×D4—611no—
321#484—611no—
322#481—611no—
323#478—611no—
324#478—611no—
325#463—611no—
326#463—611no—
327#450—611no—
328#447—611no—
329#446—611no—
330C8×Q8—611no—
331C4×SD16—611no—
332C4×SD16—611no—
333C4×D8—611no—
334C4×D8—611no—
335#436—611no—
336#436—611no—
337#436—611no—
338#435—1221no—
339#435—1221no—
340#435—1221no—
341C8×D4—611no—
342C8×D4—611no—
343C8×D4—611no—
344C8×D4—1221no—
345#433—1221no—
346#432C2×D6111yescharacteristic
347#431—611no—
348#431C2×D6111yescharacteristic
349#424—1221no—
350C2×C4⋊C8C2×D6111yescharacteristic
351#407—1221no—
352C2×C22⋊C8—1221no—
353C2×C4×C8—611no—
354#335C2×D6111yescharacteristic, complemented
355#335C2×D6111yescharacteristic, complemented
356#334C2×D6111yescharacteristic, complemented
357#334C2×D6111yescharacteristic, complemented
358Q8⋊C8—611no—
359Q8⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8—611no—
365D4⋊C8—611no—
366#322—611no—
367#322—611no—
368#322—611no—
369#322—611no—
370C61#1802011yescharacteristic, complemented, Sylow
371C22×D4—611no—
372C23×C4—1221no—
373C2×SD16—611no—
374C2×SD16—611no—
375C2×D8—611no—
376C2×D8—611no—
377C2×M16—1221no—
378C2×M16—1221no—
379C2×M16—1221no—
380C22×C8—21no—
381C22×C8—1221no—
382C22×C8—1221no—
383C22×C8—1221no—
384C22×C8—1221no—
385#126—1221no—
386#125—611no—
387#124—611no—
388#123—1221no—
389C22⋊Q8—611no—
390#121—611no—
391C4×Q8—611no—
392C4×D4—611no—
393C4×D4—611no—
394C4×D4—611no—
395C4×D4—611no—
396C4×D4—611no—
397C4×D4—1221no—
398C4×D4—1221no—
399C4×D4—1221no—
400#117—1221no—
401C2×C4⋊C4—611no—
402C2×C22⋊C4—1221no—
403C2×C42C22×D6111yescharacteristic
404#107—611no—
405#107—611no—
406#106—611no—
407#106—611no—
408C4⋊C8—21no—
409C4⋊C8—611no—
410C4⋊C8—611no—
411C4⋊C8—1221no—
412C4⋊C8—1221no—
413C4⋊C8C4×D6111yescharacteristic
414C4⋊C8C4×D6111yescharacteristic
415C4⋊C8C22×D6111yescharacteristic
416C4⋊C8C22×D6111yescharacteristic
417C4⋊C8C22×D6111yescharacteristic
418C4⋊C8C22×D6111yescharacteristic
419#103—611no—
420#103—611no—
421#102—611no—
422#102—611no—
423#102—611no—
424#102—611no—
425#102—611no—
426#102—611no—
427C22⋊C8—21no—
428C22⋊C8—611no—
429C22⋊C8—611no—
430C22⋊C8—1221no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436C22⋊C8C4×D6111yescharacteristic
437C22⋊C8C4×D6111yescharacteristic
438#97—21no—
439#97—1221no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—611no—
443C4×C8—611no—
444C4×C8—1221no—
445C4×C8—1221no—
446C4×C8C22×D6111yescharacteristic
447C4×C8C22×D6111yescharacteristic
448C24—1221no—
449C2×Q8—611no—
450C2×D4—611no—
451C2×D4—611no—
452C2×D4—611no—
453C2×D4—1222no—
454C2×D4—1221no—
455C2×D4—1221no—
456C2×D4—2441no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—4881no—
464C22×C4—4881no—
465C22×C4C2×C4×D6111yescharacteristic
466C22×C4D4×D6111yescharacteristic
467C22×C4#1175822611yescharacteristic
468SD16—1222no—
469SD16—2441no—
470D8—1222no—
471D8—2441no—
472M16—4881no—
473M16—4881no—
474M16—4881no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—81no—
480C2×C8—611no—
481C2×C8—611no—
482C2×C8—611no—
483C2×C8—611no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—4881no—
487C2×C8—4881no—
488C2×C8—4881no—
489C2×C8—2442no—
490C2×C8C2×C4×D6111yescharacteristic
491C2×C8C2×C4×D6111yescharacteristic
492C2×C8C2×C4×D6111yescharacteristic
493C2×C8C2×C4×D6111yescharacteristic
494C4⋊C4—611no—
495C4⋊C4—611no—
496C4⋊C4—611no—
497C4⋊C4—611no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C4⋊C4—1221no—
501C4⋊C4—1221no—
502C4⋊C4—1221no—
503C22⋊C4—1221no—
504C22⋊C4—1221no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C22⋊C4—1221no—
510C22⋊C4—1221no—
511C22⋊C4—1221no—
512C42—1221no—
513C42C2×C4×D6111yescharacteristic
514C42D4×D6111yescharacteristic
515C42#1175822611yescharacteristic
516C42C23×D6111yescharacteristic
517C23—1221no—
518C23—1221no—
519C23—1221no—
520C23—4881no—
521C23—2442no—
522C23—2442no—
523C23#1451973911yescharacteristic
524Q8—1221no—
525Q8—1221no—
526D4—612no—
527D4—1221no—
528D4—1221no—
529D4—1221no—
530D4—1221no—
531D4—1221no—
532D4—2442no—
533D4—2442no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—4881no—
545C2×C4—4881no—
546C2×C4—4881no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4#1451973911yescharacteristic
554C2×C4#1451973911yescharacteristic
555C2×C4#1451973911yescharacteristic
556C2×C4C22×C4×D6111yescharacteristic
557C2×C4C2×D4×D6111yescharacteristic
558C2×C4C2×#1175822611yescharacteristic
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—1221no—
568C8—1221no—
569C8—1221no—
570C8—1221no—
571C8—2441no—
572C8—2441no—
573C22—21no—
574C22—21no—
575C22—1222no—
576C22—4884no—
577C22—2441no—
578C22—2441no—
579C22—2441no—
580C22—2441no—
581C22—2441no—
582C22—2441no—
583C22—2441no—
584C22—2441no—
585C22#1683988312yes—
586C22C2×#1451973911yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—2441no—
592C4—2441no—
593C4—2441no—
594C4—2441no—
595C4—2441no—
596C4#131×D6111yescharacteristic
597C4#1684052711yescharacteristic
598C4#1684056611yescharacteristic
599C4#1684057111yescharacteristic
600C2—22no—
601C2—4881no—
602C2—4881no—
603C2—2442no—
604C2#2145454311yescharacteristic
605C2#2145464911yescharacteristic
606C2C2×#1683988311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1573C2
socleC22×C61C2×C4×D4
prime radical#16839898C4
cosocleC42×C61C24
hypercenter#1573D61
hypocenterC61#18020
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
2. #21454975C2semidirect
3. #21454856C2semidirect
4. #21444732C2semidirect
5. #21444720C2semidirect
6. #21444661C2semidirect
7. #21444654C2semidirect
8. #21444647C2semidirect
9. #21444647C2semidirect
10. #21444642C2semidirect
11. #21444630C2semidirect
12. #21444277C2semidirect
13. C2×#16839489C2semidirect
14. #21444112C2semidirect
15. C61×#1573C2semidirect
26. #16839889C22semidirect
27. #16839886C22semidirect
34. #16839839C22semidirect
40. #16839827C22semidirect
48. #16839492C22semidirect
49. #16839492C22semidirect
54. #16839489C22semidirect
55. #16839489C22semidirect
56. #16839484C22semidirect
57. #16839484C22semidirect
58. #16839483C22semidirect
59. #16839483C22semidirect
63. C61×#335C22semidirect
64. C61×#335C22semidirect
65. C61×#334C22semidirect
66. C61×#334C22semidirect
308. #1573D61semidirect
354. #335C2×D61semidirect
355. #335C2×D61semidirect
356. #334C2×D61semidirect
357. #334C2×D61semidirect
370. C61#18020semidirect

Maximal subgroups

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

subgroupindex
#214558682
#214549752
#214548562
#214447322
#214447202
#214446612
#214446542
#214446472
#214446422
#214446302
#214442772
C2×#168394892
#214441122
C61×#15732
#1802061