Finite Group Databasebeta

← #29650073

Subgroups — #29650073

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#21455866C211yesmaximal, characteristic
2#21454970C211yesmaximal, characteristic, complemented
3#21444683C211yesmaximal, characteristic, complemented
4#21444676C211yesmaximal, characteristic, complemented
5#21444655C211yesmaximal, characteristic, complemented
6#21444648C211yesmaximal, characteristic, complemented
7#21444641C211yesmaximal, characteristic, complemented
8#21444631C211yesmaximal, characteristic, complemented
9C8×#11758200C211yesmaximal, characteristic, complemented
10C8×#11758199C211yesmaximal, characteristic, complemented
11#21444607C211yesmaximal, characteristic, complemented
12#21444244C211yesmaximal, characteristic, complemented
13#21444225C211yesmaximal, characteristic, complemented
14#21444119C211yesmaximal, characteristic, complemented
15C61×#2972C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17#16840097C411yescharacteristic
18#16840080C411yescharacteristic
19#16840062C411yescharacteristic
20#16840062C411yescharacteristic
21#16839977C411yescharacteristic
22#16839977C411yescharacteristic
23#16839913C411yescharacteristic
24#16839896C411yescharacteristic
25#16839892C2211yescharacteristic, complemented
26C8×Dic122C2211yescharacteristic, complemented
27C4×#11758200C2211yescharacteristic
28C4×#11758200C2211yescharacteristic
29C4×#11758199C2211yescharacteristic
30C4×#11758199C2211yescharacteristic
31#16839841C2211yescharacteristic, complemented
32#16839837—21no—
33#16839836—21no—
34C8×D244C2211yescharacteristic, complemented
35#16839822—21no—
36#16839815C2211yescharacteristic
37#16839815C2211yescharacteristic
38#16839787—21no—
39#16839786C2211yescharacteristic
40#16839514C2211yescharacteristic, complemented
41#16839514C2211yescharacteristic, complemented
42#16839512C2211yescharacteristic, complemented
43#16839512C2211yescharacteristic, complemented
44#16839492C2211yescharacteristic, complemented
45#16839492C2211yescharacteristic, complemented
46D4⋊#92418C2211yescharacteristic
47D4⋊#92418C2211yescharacteristic
48D4⋊#92418C2211yescharacteristic
49D4⋊#92418C2211yescharacteristic
50#16839489C2211yescharacteristic, complemented
51#16839489C2211yescharacteristic, complemented
52#16839484C2211yescharacteristic, complemented
53#16839484C2211yescharacteristic, complemented
54#16839483C2211yescharacteristic, complemented
55C8×#92418C2211yescharacteristic, complemented
56C2×C4×D4×C61C2211yescharacteristic
57C8×D4×C61—21no—
58C8×D4×C61—21no—
59C8×D4×C61C2211yescharacteristic
60C8×D4×C61C2211yescharacteristic
61C8×D4×C61C2211yescharacteristic
62C8×D4×C61C2211yescharacteristic
63C61×#431C2211yescharacteristic
64C61×#431C2211yescharacteristic
65C2×C22⋊C8×C61—21no—
66C2×C22⋊C8×C61—21no—
67C2×#11758200C2×C411yescharacteristic
68C2×#11758200C2×C411yescharacteristic
69C2×#11758199C2×C411yescharacteristic
70C2×#11758199C2×C411yescharacteristic
71C2×#11758194—21no—
72C2×#11758189—21no—
73C2×C8×D61—21no—
74#14519771—21no—
75#14519769C2×C411yescharacteristic
76#14519765C2×C411yescharacteristic
77#14519760—21no—
78#14519756C2×C411yescharacteristic
79#14519751C2×C411yescharacteristic
80C4×Dic122C2311yescharacteristic
81C4×D244C2311yescharacteristic
82C4×C22⋊D61—21no—
83#14519734—21no—
84#14519710C2×C411yescharacteristic
85#14519710C2×C411yescharacteristic
86#14519708C2×C411yescharacteristic
87#14519708C2×C411yescharacteristic
88C4⋊#92418—21no—
89C4⋊#92418—21no—
90C4⋊#92418C2×C411yescharacteristic
91C4⋊#92418C2×C411yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94#14519706—21no—
95#14519706—21no—
96#14519700C2×C411yescharacteristic
97#14519700C2×C411yescharacteristic
98#14519698C2×C411yescharacteristic
99#14519698C2×C411yescharacteristic
100#14519698C2×C411yescharacteristic
101#14519698C2×C411yescharacteristic
102#14519697C2×C411yescharacteristic
103#14519697C2×C411yescharacteristic
104C22⋊#92418—21no—
105C22⋊#92418C2×C411yescharacteristic
106C22⋊#92418C2×C411yescharacteristic
107#14519689—21no—
108#14519689—21no—
109#14519687—21no—
110C4×#92418C2311yescharacteristic
111C4×#92418C2311yescharacteristic
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C8×Dic61—21no—
115C22×D4×C61C2×C411yescharacteristic
116C23×C4×C61—21no—
117C22×C8×C61—21no—
118C22×C8×C61—21no—
119C22×C8×C61—21no—
120C22×C8×C61—21no—
121C4×D4×C61—21no—
122C4×D4×C61—21no—
123C4×D4×C61C2×C411yescharacteristic
124C4×D4×C61C2×C411yescharacteristic
125C4×D4×C61C2311yescharacteristic
126C4×D4×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2×C411yescharacteristic
128C2×C22⋊C4×C61—21no—
129C2×C42×C61C2311yescharacteristic
130C4⋊C8×C61D411yescharacteristic
131C4⋊C8×C61D411yescharacteristic
132C4⋊C8×C61C2311yescharacteristic
133C4⋊C8×C61C2311yescharacteristic
134C22⋊C8×C61—21no—
135C22⋊C8×C61—21no—
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138C22⋊C8×C61—21no—
139C22⋊C8×C61D411yescharacteristic
140C22⋊C8×C61D411yescharacteristic
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C24×C61—21no—
145C2×D4×C61—22no—
146C2×D4×C61—22no—
147C2×D4×C61—21no—
148C2×D4×C61C22×C411yescharacteristic
149C2×D4×C61C22×C411yescharacteristic
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—81no—
156C22×C4×C61—81no—
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61#4111yescharacteristic
160C2×C22⋊D61—21no—
161C2×D244C22×C411yescharacteristic
162C2×C4×D61—21no—
163C2×Dic122C22×C411yescharacteristic
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—81no—
167C2×C8×C61—81no—
168C2×C8×C61—81no—
169C2×C8×C61—81no—
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C2×C8×C61C2×D411yescharacteristic
173C2×C8×C61C2×D411yescharacteristic
174C4⋊C4×C61—21no—
175C4⋊C4×C61C22×C411yescharacteristic
176C4⋊C4×C61C22×C411yescharacteristic
177C22⋊C4×C61—21no—
178C22⋊C4×C61—21no—
179C22⋊C4×C61—21no—
180C22⋊C4×C61—21no—
181C42×C61C22×C411yescharacteristic
182C42×C61C2×D411yescharacteristic
183C42×C61#4111yescharacteristic
184C42×C61C2411yescharacteristic
185C22⋊Dic61—21no—
186#11758200—22no—
187#11758200—22no—
188#11758199—22no—
189#11758199—22no—
190#11758198—21no—
191#11758198—21no—
192#11758198—21no—
193#11758198—21no—
194C4⋊Dic61C22×C411yescharacteristic
195C4⋊Dic61C22×C411yescharacteristic
196#11758196—21no—
197#11758196—21no—
198#11758196—21no—
199#11758196—21no—
200C4×Dic61—21no—
201#11758194—81no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418C22×C411yescharacteristic
207C2×#92418C22×C411yescharacteristic
208C2×#92418C22×C411yescharacteristic
209C2×#92418C22×C411yescharacteristic
210#11758189—81no—
211C8×D61—81no—
212C23×C61—24no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—81no—
216C23×C61—81no—
217C23×C61C4×D411yescharacteristic
218C22×D61—21no—
219D4×C61—24no—
220D4×C61—21no—
221D4×C61—21no—
222D4×C61#13112yes—
223D4×C61#13112yes—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—81no—
236C2×C4×C61—81no—
237C2×C4×C61—81no—
238C2×C4×C61C4×D411yescharacteristic
239C2×C4×C61C4×D411yescharacteristic
240C2×C4×C61C4×D411yescharacteristic
241C2×C4×C61C23×C411yescharacteristic
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C22⋊D61—81no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248D244—21no—
249D244—21no—
250C4×D61—41no—
251C4×D61—41no—
252Dic122—21no—
253Dic122—21no—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—21no—
257C8×C61—21no—
258C8×C61—41no—
259C8×C61—41no—
260#92418—21no—
261#92418—21no—
262#92418—21no—
263#92418—21no—
264#92418—41no—
265#92418—41no—
266#92418—41no—
267#92418—41no—
268#17918—611nomaximal, Sylow
269C22×C61—21no—
270C22×C61—22no—
271C22×C61—22no—
272C22×C61—21no—
273C22×C61—21no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—84no—
279C22×C61C2×C4×D411yescharacteristic
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—41no—
283C4×C61—21no—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—41no—
288C4×C61—41no—
289C4×C61C2×#13111yescharacteristic
290C4×C61C2×#13111yescharacteristic
291C4×C61#57611yescharacteristic
292C4×C61#57711yescharacteristic
293Dic61—41no—
294Dic61—41no—
295Dic61—41no—
296#3105—611no—
297#2993—611no—
298#2972D6111yescharacteristic, complemented
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#1574—611no—
308#1486—611no—
309#1482—611no—
310#1454—611no—
311C2×C61—41no—
312C2×C61—42no—
313C2×C61—42no—
314C2×C61#292911yescharacteristic
315C2×C61#294611yescharacteristic
316C2×C61#295711yescharacteristic
317D61—81no—
318#529—611no—
319C2×C4×D4C2×D6111yescharacteristic
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—21no—
338C8×D4—21no—
339C8×D4—611no—
340C8×D4C2×D6111yescharacteristic
341C8×D4C2×D6111yescharacteristic
342C8×D4C2×D6111yescharacteristic
343C8×D4C2×D6111yescharacteristic
344#433—1221no—
345#431—611no—
346#431—611no—
347#431C2×D6111yescharacteristic
348#431C2×D6111yescharacteristic
349#424—1221no—
350#423—611no—
351C2×C22⋊C8—21no—
352C2×C22⋊C8—21no—
353#335—611no—
354#335—611no—
355#334—611no—
356#334—611no—
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×D4C4×D6111yescharacteristic
371C23×C4—21no—
372C2×SD16—611no—
373C2×SD16—611no—
374C2×D8—611no—
375C2×D8—611no—
376C2×M16—1221no—
377C2×M16—1221no—
378C22×C8—21no—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—21no—
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—21no—
391C4×D4—21no—
392C4×D4—611no—
393C4×D4—1221no—
394C4×D4C4×D6111yescharacteristic
395C4×D4C4×D6111yescharacteristic
396C4×D4C22×D6111yescharacteristic
397C4×D4C22×D6111yescharacteristic
398#117—1221no—
399C2×C4⋊C4C4×D6111yescharacteristic
400C2×C22⋊C4—21no—
401C2×C42C22×D6111yescharacteristic
402#107—611no—
403#107—611no—
404#106—611no—
405#106—611no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—1221no—
411C4⋊C8—1221no—
412C4⋊C8—1221no—
413C4⋊C8—1221no—
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—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—611no—
432C22⋊C8—611no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436C22⋊C8C22⋊D6111yescharacteristic
437C22⋊C8C22⋊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—21no—
448C2×Q8—611no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—611no—
453C2×D4—1221no—
454C2×D4C2×C4×D6111yescharacteristic
455C2×D4C2×C4×D6111yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—81no—
462C22×C4—81no—
463C22×C4—1221no—
464C22×C4C2×C4×D6111yescharacteristic
465C22×C4#1175822211yescharacteristic
466C22×C4C2×C22⋊D6111yescharacteristic
467SD16—1222no—
468SD16—1222no—
469D8—1222no—
470D8—1222no—
471M16—4881no—
472M16—4881no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—81no—
476C2×C8—81no—
477C2×C8—81no—
478C2×C8—81no—
479C2×C8—611no—
480C2×C8—611no—
481C2×C8—611no—
482C2×C8—611no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—4881no—
488C2×C8C2×C22⋊D6111yescharacteristic
489C2×C8C2×C22⋊D6111yescharacteristic
490C2×C8C2×C22⋊D6111yescharacteristic
491C2×C8C2×C22⋊D6111yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—611no—
494C4⋊C4—611no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4C2×C4×D6111yescharacteristic
500C4⋊C4C2×C4×D6111yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C22⋊C4—1221no—
510C42—1221no—
511C42C2×C4×D6111yescharacteristic
512C42#1175822211yescharacteristic
513C42C2×C22⋊D6111yescharacteristic
514C42C23×D6111yescharacteristic
515C23—24no—
516C23—21no—
517C23—21no—
518C23—81no—
519C23—81no—
520C23—1221no—
521C23C4×C22⋊D6111yescharacteristic
522Q8—1221no—
523Q8—1221no—
524D4—24no—
525D4—21no—
526D4—21no—
527D4—1221no—
528D4—1221no—
529D4—4881no—
530D4#1451978312yes—
531D4#1451978312yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—1221no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4C4×C22⋊D6111yescharacteristic
552C2×C4C4×C22⋊D6111yescharacteristic
553C2×C4C4×C22⋊D6111yescharacteristic
554C2×C4C22×C4×D6111yescharacteristic
555C2×C4C22×C22⋊D6111yescharacteristic
556C2×C4C2×#1175822211yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—1221no—
564C8—1221no—
565C8—1221no—
566C8—1221no—
567C8—2441no—
568C8—2441no—
569C8—2441no—
570C8—2441no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—22no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—84no—
581C22—2441no—
582C22—2441no—
583C22—2441no—
584C22C2×C4×C22⋊D6111yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—2441no—
592C4—2441no—
593C4—2441no—
594C4C2×#1451978311yescharacteristic
595C4C2×#1451978311yescharacteristic
596C4#1684056511yescharacteristic
597C4#1684057311yescharacteristic
598C2—41no—
599C2—42no—
600C2—42no—
601C2—4881no—
602C2#2145451311yescharacteristic
603C2#2145465111yescharacteristic
604C2#2145473411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2972C2
socleC22×C61C2×C4×D4
prime radical#16839896C4
cosocleC42×C61C24
hypercenter#2972D61
hypocenterC61#17918
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2972

Complements

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

NH ≅ G/Ntype
2. #21454970C2semidirect
3. #21444683C2semidirect
4. #21444676C2semidirect
5. #21444655C2semidirect
6. #21444648C2semidirect
7. #21444641C2semidirect
8. #21444631C2semidirect
9. C8×#11758200C2semidirect
10. C8×#11758199C2semidirect
11. #21444607C2semidirect
12. #21444244C2semidirect
13. #21444225C2semidirect
14. #21444119C2semidirect
15. C61×#2972C2semidirect
25. #16839892C22semidirect
26. C8×Dic122C22semidirect
31. #16839841C22semidirect
34. C8×D244C22semidirect
40. #16839514C22semidirect
41. #16839514C22semidirect
42. #16839512C22semidirect
43. #16839512C22semidirect
44. #16839492C22semidirect
45. #16839492C22semidirect
50. #16839489C22semidirect
51. #16839489C22semidirect
52. #16839484C22semidirect
53. #16839484C22semidirect
54. #16839483C22semidirect
55. C8×#92418C22semidirect
298. #2972D61semidirect
369. C61#17918semidirect

Maximal subgroups

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

subgroupindex
#214558662
#214549702
#214446832
#214446762
#214446552
#214446482
#214446412
#214446312
C8×#117582002
C8×#117581992
#214446072
#214442442
#214442252
#214441192
C61×#29722
#1791861