Finite Group Databasebeta

← #29650071

Subgroups — #29650071

Order 15616.

648 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
1#21455868C211yesmaximal, characteristic
2#21454964C211yesmaximal, characteristic, complemented
3#21454842C211yesmaximal, characteristic, complemented
4#21444682C211yesmaximal, characteristic, complemented
5#21444675C211yesmaximal, characteristic, complemented
6#21444654C211yesmaximal, characteristic, complemented
7#21444647C211yesmaximal, characteristic, complemented
8#21444642C211yesmaximal, characteristic, complemented
9#21444630C211yesmaximal, characteristic, complemented
10#21444618C211yesmaximal, characteristic, complemented
11#21444613C211yesmaximal, characteristic, complemented
12#21444243C211yesmaximal, characteristic, complemented
13#21444225C211yesmaximal, characteristic, complemented
14#21444119C211yesmaximal, characteristic, complemented
15C61×#1574C211yesmaximal, 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, complemented
33#16839838—21no—
34#16839831—21no—
35C8×D244—21no—
36C8×D244—21no—
37#16839827C2211yescharacteristic
38#16839827C2211yescharacteristic
39#16839827C2211yescharacteristic
40#16839827C2211yescharacteristic
41#16839827C2211yescharacteristic, complemented
42#16839822—21no—
43#16839815C2211yescharacteristic
44#16839815C2211yescharacteristic
45#16839787—21no—
46C22⋊C8×D61—21no—
47C22⋊C8×D61—21no—
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
59C8×#92418C2211yescharacteristic, complemented
60C61×#431C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C61×#423C2211yescharacteristic
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×C8×D61—21no—
75C2×C8×D61—21no—
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78C2×C8×D61—21no—
79#14519771—21no—
80#14519769C2×C411yescharacteristic
81#14519765C2×C411yescharacteristic
82#14519760—21no—
83#14519756C2×C411yescharacteristic
84#14519751C2×C411yescharacteristic
85C4×Dic122C2311yescharacteristic
86C4×D244—21no—
87C4×D244—21no—
88C4×D244C2×C411yescharacteristic
89C4×D244C2×C411yescharacteristic
90C4×D244C2311yescharacteristic
91C4×D244C2311yescharacteristic
92C4×D244C2311yescharacteristic
93C4×C22⋊D61—21no—
94#14519734—21no—
95C2×C4⋊Dic61C2×C411yescharacteristic
96C2×#11758198—21no—
97#14519711C2×C411yescharacteristic
98#14519711C2×C411yescharacteristic
99#14519709C2×C411yescharacteristic
100#14519709C2×C411yescharacteristic
101C4⋊#92418—21no—
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⋊#92418—21no—
115C22⋊#92418D411yescharacteristic
116C22⋊#92418D411yescharacteristic
117#14519689—21no—
118#14519689—21no—
119#14519689—21no—
120#14519689—21no—
121#14519689—21no—
122#14519689—21no—
123#14519687—21no—
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C4×#92418C2311yescharacteristic
127C4×#92418C2311yescharacteristic
128C8×Dic61—21no—
129C2×M16×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
141C4×C8×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—21no—
151C2×D244—22no—
152C2×D244—22no—
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
164M16×C61—81no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
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×#92418C2×D411yescharacteristic
199C2×#92418C2×D411yescharacteristic
200C2×#92418C2×D411yescharacteristic
201C2×#92418C2×D411yescharacteristic
202D488—22no—
203D488—22no—
204#11758190—22no—
205#11758190—22no—
206#11758189—81no—
207C8×D61—81no—
208C8×D61—81no—
209C8×D61—81no—
210C8×D61—81no—
211C8×D61—81no—
212C23×C61C4×D411yescharacteristic
213C22×D61—21no—
214C22×D61—21no—
215C22×D61—24no—
216C22×D61—21no—
217C22×D61—81no—
218C22×D61—81no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—41no—
224C2×C4×C61C4×D411yescharacteristic
225C2×C4×C61C4×D411yescharacteristic
226C2×C4×C61C4×D411yescharacteristic
227C2×C4×C61C23×C411yescharacteristic
228C2×C4×C61C22×D411yescharacteristic
229C2×C4×C61C2×#4111yescharacteristic
230C22⋊D61—81no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—81no—
237D244—24no—
238D244—21no—
239D244—21no—
240D244—21no—
241D244—21no—
242D244#13112yes—
243D244#13112yes—
244C4×D61—41no—
245C4×D61—41no—
246C4×D61—41no—
247C4×D61—41no—
248C4×D61—41no—
249C4×D61—41no—
250C4×D61—81no—
251C4×D61—81no—
252Dic122—21no—
253Dic122—21no—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—21no—
257C8×C61—21no—
258C8×C61—41no—
259C8×C61—41no—
260C8×C61—41no—
261C8×C61—41no—
262#92418—21no—
263#92418—21no—
264#92418—21no—
265#92418—21no—
266#92418—41no—
267#92418—41no—
268#17918—611nomaximal, Sylow
269C22×C61—21no—
270C22×C61—21no—
271C22×C61—21no—
272C22×C61C2×C4×D411yescharacteristic
273C2×D61—22no—
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—84no—
283C4×C61—21no—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61C2×#13111yescharacteristic
288C4×C61C2×#13111yescharacteristic
289C4×C61#57611yescharacteristic
290C4×C61#57711yescharacteristic
291Dic61—41no—
292Dic61—41no—
293Dic61—41no—
294Dic61—41no—
295Dic61—41no—
296#3105—611no—
297#2993—611no—
298#2972—611no—
299#1586—611no—
300#1585—611no—
301#1582—611no—
302#1581—611no—
303#1580—611no—
304SD16⋊C8—611no—
305C8×SD16—611no—
306C8×D8—611no—
307#1574D6111yescharacteristic, complemented
308#1486—611no—
309#1482—611no—
310#1454—611no—
311C2×C61—41no—
312C2×C61#292911yescharacteristic
313C2×C61#294611yescharacteristic
314C2×C61#295711yescharacteristic
315D61—42no—
316D61—42no—
317D61—81no—
318#529—611no—
319C2×C4×D4—611no—
320#484—611no—
321#481—611no—
322#478—611no—
323#478—611no—
324#463—611no—
325#463—611no—
326#450—611no—
327#447—611no—
328#446—611no—
329C8×Q8—611no—
330C4×SD16—611no—
331C4×SD16—611no—
332C4×D8—611no—
333C4×D8—611no—
334#436—611no—
335#436—1221no—
336#435—1221no—
337C8×D4—611no—
338C8×D4—611no—
339C8×D4—611no—
340C8×D4—611no—
341C8×D4—611no—
342C8×D4—1221no—
343C8×D4—1221no—
344#433—1221no—
345#431—611no—
346#431—611no—
347#431C2×D6111yescharacteristic
348#431C2×D6111yescharacteristic
349#424—1221no—
350#423C2×D6111yescharacteristic
351C2×C22⋊C8—1221no—
352C2×C22⋊C8—1221no—
353#335C2×D6111yescharacteristic, complemented
354#335C2×D6111yescharacteristic, complemented
355#334C2×D6111yescharacteristic, complemented
356#334C2×D6111yescharacteristic, complemented
357Q8⋊C8—611no—
358Q8⋊C8—611no—
359D4⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8—611no—
365#322—611no—
366#322—611no—
367#322—611no—
368C82—611no—
369C61#1791811yescharacteristic, complemented, Sylow
370C22×D4—611no—
371C23×C4—1221no—
372C2×SD16—611no—
373C2×SD16—611no—
374C2×D8—611no—
375C2×D8—611no—
376C2×M16—21no—
377C2×M16—1221no—
378C22×C8—1221no—
379C22×C8—1221no—
380C22×C8—1221no—
381C22×C8—1221no—
382C22×C8—1221no—
383#126—1221no—
384#125—611no—
385#124—611no—
386#123—1221no—
387C22⋊Q8—611no—
388#121—611no—
389C4×Q8—611no—
390C4×D4—611no—
391C4×D4—611no—
392C4×D4—611no—
393C4×D4—611no—
394C4×D4—611no—
395C4×D4—1221no—
396C4×D4—1221no—
397C4×D4—1221no—
398#117—1221no—
399C2×C4⋊C4—611no—
400C2×C22⋊C4—1221no—
401C2×C42C22×D6111yescharacteristic
402#107—611no—
403#107—611no—
404#106—611no—
405#106—611no—
406C4⋊C8—21no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—1221no—
410C4⋊C8—1221no—
411C4⋊C8—1221no—
412C4⋊C8C4×D6111yescharacteristic
413C4⋊C8C4×D6111yescharacteristic
414C4⋊C8C22×D6111yescharacteristic
415C4⋊C8C22×D6111yescharacteristic
416C4⋊C8C22×D6111yescharacteristic
417C4⋊C8C22×D6111yescharacteristic
418#103—611no—
419#103—611no—
420#102—611no—
421#102—611no—
422#102—611no—
423#102—611no—
424#102—611no—
425#102—611no—
426C22⋊C8—21no—
427C22⋊C8—611no—
428C22⋊C8—611no—
429C22⋊C8—1221no—
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—1221no—
439C4×C8—21no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—611no—
443C4×C8—611no—
444C4×C8—1221no—
445C4×C8C22×D6111yescharacteristic
446C4×C8C22×D6111yescharacteristic
447C24—1221no—
448C2×Q8—611no—
449C2×D4—611no—
450C2×D4—611no—
451C2×D4—611no—
452C2×D4—1222no—
453C2×D4—1222no—
454C2×D4—1221no—
455C2×D4—1221no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—4881no—
463C22×C4—4881no—
464C22×C4C2×C4×D6111yescharacteristic
465C22×C4D4×D6111yescharacteristic
466C22×C4#1175822611yescharacteristic
467SD16—1222no—
468SD16—1222no—
469D8—1222no—
470D8—1222no—
471M16—81no—
472M16—4881no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—611no—
478C2×C8—611no—
479C2×C8—611no—
480C2×C8—611no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—4881no—
484C2×C8—4881no—
485C2×C8—4881no—
486C2×C8—4881no—
487C2×C8—4881no—
488C2×C8C2×C4×D6111yescharacteristic
489C2×C8C2×C4×D6111yescharacteristic
490C2×C8C2×C4×D6111yescharacteristic
491C2×C8C2×C4×D6111yescharacteristic
492C4⋊C4—611no—
493C4⋊C4—611no—
494C4⋊C4—611no—
495C4⋊C4—611no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C4⋊C4—1221no—
501C22⋊C4—1221no—
502C22⋊C4—1221no—
503C22⋊C4—1221no—
504C22⋊C4—1221no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C22⋊C4—1221no—
510C42—1221no—
511C42C2×C4×D6111yescharacteristic
512C42D4×D6111yescharacteristic
513C42#1175822611yescharacteristic
514C42C23×D6111yescharacteristic
515C23—1224no—
516C23—1221no—
517C23—1221no—
518C23—1221no—
519C23—4881no—
520C23—4881no—
521C23#1451973911yescharacteristic
522Q8—1221no—
523Q8—1221no—
524D4—612no—
525D4—612no—
526D4—1224no—
527D4—1221no—
528D4—1221no—
529D4—1221no—
530D4—1221no—
531D4—4881no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—4881no—
543C2×C4—4881no—
544C2×C4—4881no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4#1451973911yescharacteristic
552C2×C4#1451973911yescharacteristic
553C2×C4#1451973911yescharacteristic
554C2×C4C22×C4×D6111yescharacteristic
555C2×C4C2×D4×D6111yescharacteristic
556C2×C4C2×#1175822611yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—1221no—
566C8—1221no—
567C8—1221no—
568C8—1221no—
569C8—2441no—
570C8—2441no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—1222no—
575C22—1222no—
576C22—4884no—
577C22—2441no—
578C22—2441no—
579C22—2441no—
580C22—2441no—
581C22—2441no—
582C22—2441no—
583C22—2441no—
584C22C2×#1451973911yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—2441no—
590C4—2441no—
591C4—2441no—
592C4—2441no—
593C4—2441no—
594C4#131×D6111yescharacteristic
595C4#131×D6111yescharacteristic
596C4#1684056611yescharacteristic
597C4#1684057111yescharacteristic
598C2—41no—
599C2—4881no—
600C2—2442no—
601C2—2442no—
602C2#2145451211yescharacteristic
603C2#2145464911yescharacteristic
604C2#2145473511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1574C2
socleC22×C61C2×C4×D4
prime radical#16839898C4
cosocleC42×C61C24
hypercenter#1574D61
hypocenterC61#17918
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
2. #21454964C2semidirect
3. #21454842C2semidirect
4. #21444682C2semidirect
5. #21444675C2semidirect
6. #21444654C2semidirect
7. #21444647C2semidirect
8. #21444642C2semidirect
9. #21444630C2semidirect
10. #21444618C2semidirect
11. #21444613C2semidirect
12. #21444243C2semidirect
13. #21444225C2semidirect
14. #21444119C2semidirect
15. C61×#1574C2semidirect
26. #16839889C22semidirect
27. #16839886C22semidirect
32. #16839839C22semidirect
41. #16839827C22semidirect
48. #16839492C22semidirect
49. #16839492C22semidirect
54. #16839489C22semidirect
55. #16839489C22semidirect
56. #16839484C22semidirect
57. #16839484C22semidirect
58. #16839483C22semidirect
59. C8×#92418C22semidirect
63. C61×#335C22semidirect
64. C61×#335C22semidirect
65. C61×#334C22semidirect
66. C61×#334C22semidirect
307. #1574D61semidirect
353. #335C2×D61semidirect
354. #335C2×D61semidirect
355. #334C2×D61semidirect
356. #334C2×D61semidirect
369. C61#17918semidirect

Maximal subgroups

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

subgroupindex
#214558682
#214549642
#214548422
#214446822
#214446752
#214446542
#214446472
#214446422
#214446302
#214446182
#214446132
#214442432
#214442252
#214441192
C61×#15742
#1791861