Finite Group Databasebeta

← #29650067

Subgroups — #29650067

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#21454964C211yesmaximal, characteristic, complemented
3#21454843C211yesmaximal, characteristic, complemented
4#21444680C211yesmaximal, characteristic, complemented
5#21444673C211yesmaximal, characteristic, complemented
6#21444652C211yesmaximal, characteristic, complemented
7#21444645C211yesmaximal, characteristic, complemented
8#21444640C211yesmaximal, characteristic, complemented
9#21444628C211yesmaximal, characteristic, complemented
10#21444622C211yesmaximal, characteristic, complemented
11#21444611C211yesmaximal, characteristic, complemented
12#21444610C211yesmaximal, characteristic, complemented
13#21444228C211yesmaximal, characteristic, complemented
14#21444119C211yesmaximal, characteristic, complemented
15C61×#1486C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17#16840097C411yescharacteristic
18#16840080C411yescharacteristic
19#16840062C411yescharacteristic
20#16840062C411yescharacteristic
21#16839977C411yescharacteristic
22#16839977C411yescharacteristic
23#16839913C411yescharacteristic
24#16839896C411yescharacteristic
25#16839889C2211yescharacteristic, complemented
26#16839886C2211yescharacteristic, complemented
27C4×#11758200C2211yescharacteristic
28C4×#11758200C2211yescharacteristic
29C4×#11758199C2211yescharacteristic
30C4×#11758199C2211yescharacteristic
31#16839839C2211yescharacteristic, complemented
32#16839838—21no—
33#16839831—21no—
34D4×#92418—21no—
35D4×#92418—21no—
36D4×#92418C2211yescharacteristic
37D4×#92418C2211yescharacteristic
38D4×#92418C2211yescharacteristic
39D4×#92418C2211yescharacteristic
40#16839827C2211yescharacteristic, complemented
41#16839822—21no—
42#16839815C2211yescharacteristic
43#16839815C2211yescharacteristic
44#16839815C2211yescharacteristic
45#16839787—21no—
46C2×C22⋊#92418—21no—
47C2×C22⋊#92418—21no—
48#16839514C2211yescharacteristic, complemented
49#16839514C2211yescharacteristic, complemented
50#16839512C2211yescharacteristic, complemented
51#16839512C2211yescharacteristic, complemented
52#16839494C2211yescharacteristic, complemented
53#16839494C2211yescharacteristic, complemented
54#16839491C2211yescharacteristic, complemented
55#16839491C2211yescharacteristic, complemented
56#16839484C2211yescharacteristic, complemented
57#16839484C2211yescharacteristic, complemented
58#16839483C2211yescharacteristic, complemented
59C8×#92418C2211yescharacteristic, complemented
60C2×C4×D4×C61C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C61×#423C2211yescharacteristic
63C61×D4⋊C8C2211yescharacteristic
64C61×D4⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×D4⋊C8C2211yescharacteristic
67C2×#11758200C2×C411yescharacteristic
68C2×#11758200C2×C411yescharacteristic
69C2×#11758199C2×C411yescharacteristic
70C2×#11758199C2×C411yescharacteristic
71C2×#11758189—21no—
72C22×#92418—21no—
73C22×#92418—21no—
74C22×#92418—21no—
75C22×#92418—21no—
76C2×C8×D61—21no—
77#14519771—21no—
78#14519769C2×C411yescharacteristic
79#14519765C2×C411yescharacteristic
80#14519760—21no—
81#14519756C2×C411yescharacteristic
82#14519751C2×C411yescharacteristic
83C4×Dic122C2311yescharacteristic
84C4×D244C2311yescharacteristic
85C4×C22⋊D61—21no—
86#14519734—21no—
87#14519710C2×C411yescharacteristic
88#14519710C2×C411yescharacteristic
89#14519708C2×C411yescharacteristic
90#14519708C2×C411yescharacteristic
91C4⋊#92418C2×C411yescharacteristic
92C4⋊#92418C2×C411yescharacteristic
93C4⋊#92418D411yescharacteristic
94C4⋊#92418D411yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519706—21no—
98#14519706—21no—
99#14519700C2×C411yescharacteristic
100#14519700C2×C411yescharacteristic
101#14519698C2×C411yescharacteristic
102#14519698C2×C411yescharacteristic
103#14519698C2×C411yescharacteristic
104#14519698C2×C411yescharacteristic
105#14519697C2×C411yescharacteristic
106#14519697C2×C411yescharacteristic
107C22⋊#92418—21no—
108C22⋊#92418—21no—
109C22⋊#92418—21no—
110C22⋊#92418—21no—
111C22⋊#92418—21no—
112C22⋊#92418C2×C411yescharacteristic
113C22⋊#92418C2×C411yescharacteristic
114C22⋊#92418D411yescharacteristic
115C22⋊#92418D411yescharacteristic
116#14519689—21no—
117#14519689—21no—
118#14519687—21no—
119C4×#92418—21no—
120C4×#92418C2311yescharacteristic
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C8×Dic61—21no—
125C22×D4×C61C2×C411yescharacteristic
126C23×C4×C61—21no—
127C2×M16×C61—21no—
128C4×D4×C61—21no—
129C4×D4×C61—21no—
130C4×D4×C61C2×C411yescharacteristic
131C4×D4×C61C2×C411yescharacteristic
132C4×D4×C61C2311yescharacteristic
133C4×D4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61—21no—
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61—21no—
138C4⋊C8×C61—21no—
139C4⋊C8×C61C2311yescharacteristic
140C4⋊C8×C61C2311yescharacteristic
141C22⋊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
164M16×C61—81no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61C22×C411yescharacteristic
171C4⋊C4×C61C22×C411yescharacteristic
172C22⋊C4×C61—21no—
173C22⋊C4×C61—21no—
174C22⋊C4×C61—21no—
175C22⋊C4×C61—21no—
176C42×C61C22×C411yescharacteristic
177C42×C61C2×D411yescharacteristic
178C42×C61#4111yescharacteristic
179C42×C61C2411yescharacteristic
180C22⋊Dic61—21no—
181#11758200—22no—
182#11758200—22no—
183#11758199—22no—
184#11758199—22no—
185#11758198—21no—
186#11758198—21no—
187#11758198—21no—
188#11758198—21no—
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—81no—
199C2×#92418—81no—
200C2×#92418—81no—
201C2×#92418—81no—
202C2×#92418C22×C411yescharacteristic
203C2×#92418C22×C411yescharacteristic
204C2×#92418C22×C411yescharacteristic
205C2×#92418C22×C411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207C2×#92418C2×D411yescharacteristic
208C2×#92418C2×D411yescharacteristic
209C2×#92418C2×D411yescharacteristic
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—41no—
255C8×C61—41no—
256C8×C61—41no—
257C8×C61—41no—
258#92418—21no—
259#92418—21no—
260#92418—21no—
261#92418—21no—
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—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#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#1574—611no—
308#1486D6111yescharacteristic, complemented
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—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#431—611no—
348#431C2×D6111yescharacteristic
349#424—1221no—
350#423C2×D6111yescharacteristic
351C2×C22⋊C8—1221no—
352C2×C22⋊C8—1221no—
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⋊C8C2×D6111yescharacteristic
362D4⋊C8C2×D6111yescharacteristic
363D4⋊C8C2×D6111yescharacteristic
364D4⋊C8C2×D6111yescharacteristic
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—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—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—21no—
407C4⋊C8—21no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—1221no—
415C4⋊C8—1221no—
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—611no—
430C22⋊C8—611no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436C22⋊C8—1221no—
437C22⋊C8—1221no—
438#97—1221no—
439C4×C8—611no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—611no—
443C4×C8—1221no—
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×C4D4×D6111yescharacteristic
466C22×C4#1175822411yescharacteristic
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—611no—
482C2×C8—611no—
483C2×C8—611no—
484C2×C8—611no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—4881no—
488C2×C8—4881no—
489C2×C8—4881no—
490C2×C8—4881no—
491C2×C8—4881no—
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
512C42D4×D6111yescharacteristic
513C42#1175822411yescharacteristic
514C42C23×D6111yescharacteristic
515C23—24no—
516C23—21no—
517C23—21no—
518C23—81no—
519C23—81no—
520C23—1221no—
521C23#1451973711yescharacteristic
522Q8—1221no—
523Q8—1221no—
524D4—24no—
525D4—21no—
526D4—21no—
527D4—1221no—
528D4—1221no—
529D4—4881no—
530D4#1451978512yes—
531D4#1451978512yes—
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×C4#1451973711yescharacteristic
552C2×C4#1451973711yescharacteristic
553C2×C4#1451973711yescharacteristic
554C2×C4C22×C4×D6111yescharacteristic
555C2×C4C2×D4×D6111yescharacteristic
556C2×C4C2×#1175822411yescharacteristic
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—1221no—
562C8—1221no—
563C8—1221no—
564C8—1221no—
565C8—1221no—
566C8—1221no—
567C8—1221no—
568C8—1221no—
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×#1451973711yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—2441no—
592C4—2441no—
593C4—2441no—
594C4C2×#1451978511yescharacteristic
595C4C2×#1451978511yescharacteristic
596C4#1684056311yescharacteristic
597C4#1684056811yescharacteristic
598C2—41no—
599C2—42no—
600C2—42no—
601C2—4881no—
602C2#2145450911yescharacteristic
603C2#2145464511yescharacteristic
604C2#2145473211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1486C2
socleC22×C61C2×C4×D4
prime radical#16839896C4
cosocleC42×C61C24
hypercenter#1486D61
hypocenterC61#17918
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #21454964C2semidirect
3. #21454843C2semidirect
4. #21444680C2semidirect
5. #21444673C2semidirect
6. #21444652C2semidirect
7. #21444645C2semidirect
8. #21444640C2semidirect
9. #21444628C2semidirect
10. #21444622C2semidirect
11. #21444611C2semidirect
12. #21444610C2semidirect
13. #21444228C2semidirect
14. #21444119C2semidirect
15. C61×#1486C2semidirect
25. #16839889C22semidirect
26. #16839886C22semidirect
31. #16839839C22semidirect
40. #16839827C22semidirect
48. #16839514C22semidirect
49. #16839514C22semidirect
50. #16839512C22semidirect
51. #16839512C22semidirect
52. #16839494C22semidirect
53. #16839494C22semidirect
54. #16839491C22semidirect
55. #16839491C22semidirect
56. #16839484C22semidirect
57. #16839484C22semidirect
58. #16839483C22semidirect
59. C8×#92418C22semidirect
308. #1486D61semidirect
369. C61#17918semidirect

Maximal subgroups

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

subgroupindex
#214558662
#214549642
#214548432
#214446802
#214446732
#214446522
#214446452
#214446402
#214446282
#214446222
#214446112
#214446102
#214442282
#214441192
C61×#14862
#1791861