Finite Group Databasebeta

← #29647537

Subgroups — #29647537

Order 15616.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459846C211yesmaximal, characteristic
2#21454853C211yesmaximal, characteristic, complemented
3#21448455C211yesmaximal, characteristic, complemented
4#21444397C211yesmaximal, characteristic, complemented
5#21444385C211yesmaximal, characteristic, complemented
6#21444372C211yesmaximal, characteristic, complemented
7#21444366C211yesmaximal, characteristic, complemented
8#21444359C211yesmaximal, characteristic, complemented
9#21444355C211yesmaximal, characteristic, complemented
10#21444346C211yesmaximal, characteristic, complemented
11#21444333C211yesmaximal, characteristic, complemented
12#21444320C211yesmaximal, characteristic, complemented
13#21444307C211yesmaximal, characteristic, complemented
14#327×D61C211yesmaximal, characteristic, complemented
15C61×#1517C211yesmaximal, characteristic, complemented
16#16840478C411yescharacteristic, complemented
17#16840473C411yescharacteristic, complemented
18#16840464—21no—
19#16840462C411yescharacteristic, complemented
20#16840462C411yescharacteristic, complemented
21#16840432C411yescharacteristic, complemented
22#16840407C411yescharacteristic, complemented
23#16840407C411yescharacteristic, complemented
24#16840400—21no—
25#16840400—21no—
26#16840397C411yescharacteristic, complemented
27#16840396—21no—
28#16840363—21no—
29#16840346—21no—
30#16840346—21no—
31#16840296C2211yescharacteristic
32#16840272C2211yescharacteristic
33#16840272C2211yescharacteristic
34#121×D61C2211yescharacteristic
35#121×D61C2211yescharacteristic
36#16840234—21no—
37C2×C4×D244C2211yescharacteristic
38#16839841—21no—
39#16839832—21no—
40#16839832—21no—
41C8×D244—21no—
42#16839819C2211yescharacteristic, complemented
43#16839724C2211yescharacteristic, complemented
44#16839724C2211yescharacteristic, complemented
45C22⋊C8×D61C2211yescharacteristic, complemented
46C22⋊C8×D61C2211yescharacteristic, complemented
47#16839652—21no—
48#16839647—21no—
49#16839640—21no—
50#16839633—21no—
51#16839630C2211yescharacteristic, complemented
52#16839624C2211yescharacteristic, complemented
53#16839621C2211yescharacteristic, complemented
54#16839609C2211yescharacteristic, complemented
55#95×D61C2211yescharacteristic, complemented
56#16839500C2211yescharacteristic, complemented
57#16839500C2211yescharacteristic, complemented
58#16839498C2211yescharacteristic, complemented
59#16839498C2211yescharacteristic, complemented
60#16839497C2211yescharacteristic
61#16839497C2211yescharacteristic
62#16839496C2211yescharacteristic, complemented
63#16839496C2211yescharacteristic, complemented
64#16839496C2211yescharacteristic, complemented
65#16839496C2211yescharacteristic, complemented
66#16839495C2211yescharacteristic
67#16839495C2211yescharacteristic
68C61×#532C2211yescharacteristic
69C61×#431C2211yescharacteristic, complemented
70C61×#382C2211yescharacteristic, complemented
71C61×#327C2211yescharacteristic, complemented
72C61×#327C2211yescharacteristic, complemented
73C61×#327C2211yescharacteristic, complemented
74C61×#327C2211yescharacteristic, complemented
75C2×#11758224C2×C411yescharacteristic
76C2×#11758224C2×C411yescharacteristic, complemented
77C22×D244D411yescharacteristic
78C2×D4×D61—21no—
79C2×D4×D61—21no—
80C2×D4×D61—21no—
81C2×D4×D61C2×C411yescharacteristic
82C2×D4×D61C2×C411yescharacteristic, complemented
83C22×C4×D61—21no—
84C22×C4×D61C2311yescharacteristic
85C22×C4×D61C2311yescharacteristic
86C2×#11758189—21no—
87C2×#11758189—21no—
88C2×C8×D61—21no—
89C2×C8×D61—21no—
90#14519773—21no—
91#14519771—21no—
92#14519770—21no—
93#14519770—21no—
94#14519769C2×C411yescharacteristic, complemented
95#14519768—21no—
96#14519766—21no—
97#14519766—21no—
98#14519765C2×C411yescharacteristic, complemented
99#14519761—21no—
100#14519761—21no—
101#14519760—21no—
102#14519760—21no—
103#14519760—21no—
104#14519759—21no—
105#14519759—21no—
106#14519757C2×C411yescharacteristic
107#14519757C2×C411yescharacteristic, complemented
108#14519756C2311yescharacteristic
109#14519753—21no—
110#14519753—21no—
111#14519752—21no—
112#14519752C2×C411yescharacteristic
113#14519752C2×C411yescharacteristic, complemented
114#14519751—21no—
115#14519751—21no—
116#14519751C2311yescharacteristic
117#14519750—21no—
118#14519750—21no—
119#14519750—21no—
120#14519750—21no—
121#14519749—21no—
122#14519749—21no—
123#14519749—21no—
124#14519749—21no—
125#14519748—21no—
126#14519748C2×C411yescharacteristic
127#14519748C2×C411yescharacteristic
128#14519748C2×C411yescharacteristic, complemented
129#14519748C2×C411yescharacteristic, complemented
130#14519747—21no—
131#14519747—21no—
132#14519745—21no—
133#14519745—21no—
134#14519745—21no—
135#14519745—21no—
136C4×Dic122C2×C411yescharacteristic, complemented
137C4×D244C2×C411yescharacteristic
138C4×D244C2×C411yescharacteristic
139C4×D244C2×C411yescharacteristic
140C4×D244C2×C411yescharacteristic
141C4×D244C2×C411yescharacteristic, complemented
142C4×D244D411yescharacteristic
143C4×D244D411yescharacteristic
144C4×D244D411yescharacteristic
145C4×D244D411yescharacteristic
146D4×Dic61—21no—
147D4×Dic61—21no—
148D4×Dic61—21no—
149#14519739—21no—
150C4×C22⋊D61—21no—
151C4×C22⋊D61—21no—
152C4×C22⋊D61—21no—
153#14519737—21no—
154#14519737—21no—
155#14519735—21no—
156#14519735C2×C411yescharacteristic
157#14519735C2×C411yescharacteristic, complemented
158#14519734—21no—
159C2×C4⋊Dic61D411yescharacteristic
160C2×#11758196—21no—
161C4⋊C4×D61C2×C411yescharacteristic
162C4⋊C4×D61C2×C411yescharacteristic, complemented
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198—21no—
166C2×#11758198—21no—
167C2×#11758198—21no—
168C2×#11758198D411yescharacteristic
169C2×#11758198D411yescharacteristic
170C22⋊C4×D61—21no—
171C22⋊C4×D61—21no—
172C2×C4×Dic61—21no—
173C4⋊#92418—21no—
174C22⋊#92418C2311yescharacteristic
175C22⋊#92418C2311yescharacteristic
176#14519689—21no—
177#14519689—21no—
178#14519689—21no—
179#14519689—21no—
180#14519688—21no—
181#14519684—21no—
182#14519684—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684C2311yescharacteristic
186#14519684C2311yescharacteristic
187C2×#41×C61—21no—
188C4⋊Q8×C61C2×C411yescharacteristic, complemented
189#127×C61C2×C411yescharacteristic, complemented
190#124×C61—21no—
191#121×C61—21no—
192#121×C61C2311yescharacteristic
193#121×C61C2311yescharacteristic
194C4×D4×C61—21no—
195C4×D4×C61C2×C411yescharacteristic, complemented
196C4×D4×C61C2×C411yescharacteristic, complemented
197C2×C4⋊C4×C61—21no—
198C2×C42×C61C2311yescharacteristic
199C4⋊C8×C61—21no—
200C22⋊C8×C61C2311yescharacteristic
201C22⋊C8×C61C2311yescharacteristic
202C4×C8×C61—21no—
203#95×C61—21no—
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C23×D61—21no—
207C23×D61—21no—
208C23×D61C2×D411yescharacteristic
209C23×D61C2×D411yescharacteristic
210#41×C61—81no—
211#41×C61—81no—
212C2×Q8×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61—21no—
216C2×D4×C61—21no—
217C2×D4×C61C22×C411yescharacteristic
218C2×D4×C61C22×C411yescharacteristic
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2411yescharacteristic
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61C2×D411yescharacteristic
240C22×Dic61C2×D411yescharacteristic
241#11758224—81no—
242#11758224—81no—
243D4×D61—44no—
244D4×D61—81no—
245D4×D61—81no—
246D4×D61—81no—
247D4×D61—81no—
248D4×D61—81no—
249D4×D61—81no—
250C2×D244—21no—
251C2×D244—21no—
252C2×D244—42no—
253C2×D244C22⋊C411yescharacteristic
254C2×D244C22⋊C411yescharacteristic
255C2×D244C22⋊C411yescharacteristic
256C2×D244C22⋊C411yescharacteristic
257C2×D244C22×C411yescharacteristic
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—42no—
262C2×C4×D61—81no—
263C2×C4×D61—81no—
264C2×C4×D61—81no—
265C2×C4×D61—81no—
266C2×C4×D61C22×C411yescharacteristic
267C2×C4×D61C22×C411yescharacteristic
268C2×C4×D61C22×C411yescharacteristic
269C2×C4×D61C22×C411yescharacteristic
270C2×C4×D61C2×D411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272C2×C4×D61C2×D411yescharacteristic
273C2×C4×D61C2×D411yescharacteristic
274C2×Dic122C22×C411yescharacteristic
275C2×C8×C61—21no—
276C2×C8×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—81no—
279C4⋊C4×C61C22×C411yescharacteristic
280C4⋊C4×C61C22×C411yescharacteristic
281C22⋊C4×C61—21no—
282C22⋊C4×C61—21no—
283C22⋊C4×C61—21no—
284C22⋊C4×C61—21no—
285C42×C61C22×C411yescharacteristic
286C42×C61C22×C411yescharacteristic
287C42×C61C2×D411yescharacteristic
288C42×C61C2×D411yescharacteristic
289C22⋊Dic61—21no—
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61—21no—
293C22⋊Dic61—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—42no—
305#11758198—81no—
306#11758198—81no—
307#11758198C22⋊C411yescharacteristic
308#11758198C22⋊C411yescharacteristic
309#11758198C22⋊C411yescharacteristic
310#11758198C22⋊C411yescharacteristic
311#11758198C22⋊C411yescharacteristic
312#11758198C22⋊C411yescharacteristic
313#11758198C22⋊C411yescharacteristic
314#11758198C22⋊C411yescharacteristic
315C4⋊Dic61—21no—
316C4⋊Dic61—21no—
317C4⋊Dic61C22⋊C411yescharacteristic
318C4⋊Dic61C22⋊C411yescharacteristic
319C4⋊Dic61C22⋊C411yescharacteristic
320C4⋊Dic61C22⋊C411yescharacteristic
321C4⋊Dic61C22×C411yescharacteristic
322C4⋊Dic61C22×C411yescharacteristic
323#11758196—21no—
324#11758196—21no—
325#11758196—21no—
326#11758196—21no—
327#11758196—21no—
328#11758196—21no—
329#11758196—81no—
330C4×Dic61—21no—
331C4×Dic61—21no—
332C4×Dic61—21no—
333C4×Dic61—81no—
334C2×#92418—21no—
335C2×#92418—21no—
336#11758189—81no—
337#11758189—81no—
338C8×D61—81no—
339C8×D61—81no—
340C23×C61—21no—
341C23×C61—21no—
342C23×C61C22×D411yescharacteristic
343C22×D61—21no—
344C22×D61—21no—
345C22×D61—21no—
346C22×D61—21no—
347C22×D61—22no—
348C22×D61—21no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—42no—
353C22×D61—42no—
354C22×D61—81no—
355C22×D61—81no—
356C22×D61—81no—
357C22×D61—81no—
358C22×D61C2×C22⋊C411yescharacteristic
359C22×D61C2×C22⋊C411yescharacteristic
360C22×D61C2×C22⋊C411yescharacteristic
361C22×D61C2×C22⋊C411yescharacteristic
362Q8×C61—81no—
363D4×C61—41no—
364D4×C61—41no—
365D4×C61—42no—
366D4×C61—41no—
367D4×C61—41no—
368D4×C61—41no—
369D4×C61—41no—
370D4×C61—81no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—81no—
384C2×C4×C61—81no—
385C2×C4×C61C2×C22⋊C411yescharacteristic
386C2×C4×C61C2×C22⋊C411yescharacteristic
387C2×C4×C61C2×C22⋊C411yescharacteristic
388C2×C4×C61C2×C22⋊C411yescharacteristic
389C2×C4×C61C23×C411yescharacteristic
390C2×C4×C61C22×D411yescharacteristic
391C22⋊D61—42no—
392C22⋊D61—41no—
393C22⋊D61—41no—
394C22⋊D61—42no—
395C22⋊D61—81no—
396C22⋊D61—81no—
397C22⋊D61—81no—
398C22⋊D61—81no—
399C22⋊D61—81no—
400C22⋊D61—81no—
401C2×Dic61—21no—
402C2×Dic61—21no—
403C2×Dic61—21no—
404C2×Dic61—41no—
405C2×Dic61—41no—
406C2×Dic61—41no—
407C2×Dic61—41no—
408C2×Dic61—41no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61—81no—
413C2×Dic61—81no—
414C2×Dic61C2×C22⋊C411yescharacteristic
415C2×Dic61C2×C22⋊C411yescharacteristic
416C2×Dic61C2×C22⋊C411yescharacteristic
417C2×Dic61C2×C22⋊C411yescharacteristic
418D244—22no—
419D244—22no—
420D244—41no—
421D244—41no—
422D244—41no—
423D244—81no—
424D244—81no—
425C4×D61—41no—
426C4×D61—41no—
427C4×D61—41no—
428C4×D61—41no—
429C4×D61—41no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61—41no—
433C4×D61—42no—
434C4×D61—81no—
435C4×D61—81no—
436C4×D61—84no—
437Dic122—41no—
438C8×C61—41no—
439C8×C61—41no—
440#92418—41no—
441#92418—41no—
442#17597—611nomaximal, Sylow
443C22×C61—21no—
444C22×C61—21no—
445C22×C61—41no—
446C22×C61—41no—
447C22×C61—41no—
448C22×C61—41no—
449C22×C61—41no—
450C22×C61—41no—
451C22×C61C22×C22⋊C411yescharacteristic
452C22×C61#57611yescharacteristic
453C22×C61#57711yescharacteristic
454C2×D61—21no—
455C2×D61—21no—
456C2×D61—21no—
457C2×D61—21no—
458C2×D61—21no—
459C2×D61—21no—
460C2×D61—21no—
461C2×D61—21no—
462C2×D61—21no—
463C2×D61—21no—
464C2×D61—21no—
465C2×D61—42no—
466C2×D61—42no—
467C2×D61—41no—
468C2×D61—41no—
469C2×D61—41no—
470C2×D61—81no—
471C2×D61—81no—
472C2×D61—162no—
473C2×D61—162no—
474C2×D61#42112yes—
475C4×C61—21no—
476C4×C61—21no—
477C4×C61—21no—
478C4×C61—21no—
479C4×C61—21no—
480C4×C61—21no—
481C4×C61—41no—
482C4×C61—41no—
483C4×C61—81no—
484C4×C61—81no—
485Dic61—21no—
486Dic61—21no—
487Dic61—21no—
488Dic61—21no—
489Dic61—41no—
490Dic61—41no—
491Dic61—41no—
492Dic61—81no—
493Dic61—81no—
494#3519—611no—
495#2974—611no—
496#2318—611no—
497#1521—611no—
498#1519—611no—
499#1517D6111yescharacteristic, complemented
500#1516—611no—
501#1514—611no—
502#1513—611no—
503#1512—611no—
504#1510—611no—
505#1507—611no—
506#1504—611no—
507#1501—611no—
508C2×#327—611no—
509C2×C61—21no—
510C2×C61—21no—
511C2×C61—81no—
512C2×C61—81no—
513C2×C61#288311yescharacteristic
514C2×C61#289711yescharacteristic
515C2×C61C2×#42111yescharacteristic
516D61—22no—
517D61—41no—
518D61—41no—
519D61—41no—
520D61—81no—
521#555—611no—
522#554—611no—
523#553—611no—
524#553—611no—
525#553—1221no—
526#550—611no—
527#546—611no—
528#546—611no—
529#546—1221no—
530#546—1221no—
531D42—611no—
532D42—1221no—
533#540—1221no—
534#538—1221no—
535#538—1221no—
536#532C2×D6111yescharacteristic
537#529—611no—
538#525—611no—
539#525—611no—
540C2×#121—611no—
541C2×#121—611no—
542#518—1221no—
543C2×C4×D4—611no—
544#436—1221no—
545#435—1221no—
546#435—1221no—
547C8×D4—1221no—
548#432—611no—
549#431C2×D6111yescharacteristic, complemented
550#407—611no—
551#407—611no—
552C2×C22⋊C8—611no—
553C2×C22⋊C8—611no—
554#388—1221no—
555#387—1221no—
556#386—1221no—
557#385—1221no—
558#383—611no—
559#382C2×D6111yescharacteristic, complemented
560#381—611no—
561#380—611no—
562C4×C22⋊C4—611no—
563C2×#95—611no—
564#328—611no—
565#328—611no—
566#328—611no—
567#328—611no—
568#327—611no—
569#327—611no—
570#327—611no—
571#327—611no—
572#327—611no—
573#327—611no—
574#327—611no—
575#327—611no—
576#327C2×D6111yescharacteristic, complemented
577#327C2×D6111yescharacteristic, complemented
578#327C2×D6111yescharacteristic, complemented
579#327C2×D6111yescharacteristic, complemented
580C61#1759711yescharacteristic, complemented, Sylow
581C2×#41—21no—
582C2×#41—611no—
583C2×#41—611no—
584C22×D4—611no—
585C22×D4—611no—
586C22×D4—611no—
587C22×D4—1221no—
588C22×D4—1221no—
589C22×D4—1221no—
590C23×C4—611no—
591C23×C4—611no—
592C23×C4—1221no—
593C2×M16—1221no—
594C2×M16—1221no—
595C22×C8—1221no—
596C22×C8—1221no—
597C4⋊Q8C4×D6111yescharacteristic, complemented
598#127—1221no—
599#127C4×D6111yescharacteristic, complemented
600#126—1221no—
601#126—1221no—
602#126—1221no—
603#125—611no—
604#125—1221no—
605#124—21no—
606#124—611no—
607#124—1221no—
608#124—1221no—
609#123—1221no—
610#123—1221no—
611#123—1221no—
612#123—1221no—
613#123—1221no—
614#123—1221no—
615#123—1221no—
616C22⋊Q8—611no—
617C22⋊Q8—611no—
618C22⋊Q8—611no—
619C22⋊Q8—1221no—
620C22⋊Q8—1221no—
621#121—21no—
622#121—611no—
623#121—611no—
624#121—611no—
625#121—611no—
626#121—611no—
627#121—611no—
628#121—611no—
629#121—1221no—
630#121—1221no—
631#121—1221no—
632#121—1221no—
633#121—1221no—
634#121—1221no—
635#121—1221no—
636#121—1221no—
637#121—1221no—
638#121—1221no—
639#121—1221no—
640#121—1221no—
641#121C22×D6111yescharacteristic
642#121C22×D6111yescharacteristic
643#120—1221no—
644#120—1221no—
645#120—1221no—
646#120—1221no—
647#120—1221no—
648#120—1221no—
649C4×Q8—611no—
650C4×D4—21no—
651C4×D4—611no—
652C4×D4—611no—
653C4×D4—611no—
654C4×D4—611no—
655C4×D4—611no—
656C4×D4—611no—
657C4×D4—611no—
658C4×D4—611no—
659C4×D4—611no—
660C4×D4—1221no—
661C4×D4—1221no—
662C4×D4—1221no—
663C4×D4—1221no—
664C4×D4—1221no—
665C4×D4—1221no—
666C4×D4—1221no—
667C4×D4—1221no—
668C4×D4—1221no—
669C4×D4C4×D6111yescharacteristic, complemented
670C4×D4C4×D6111yescharacteristic, complemented
671#117—611no—
672#117—611no—
673#117—1221no—
674#117—1221no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—611no—
677C2×C4⋊C4—611no—
678C2×C4⋊C4—611no—
679C2×C4⋊C4—1221no—
680C2×C22⋊C4—611no—
681C2×C22⋊C4—611no—
682C2×C22⋊C4—1221no—
683C2×C22⋊C4—1221no—
684C2×C22⋊C4—1221no—
685C2×C22⋊C4—1221no—
686C2×C22⋊C4—1221no—
687C2×C22⋊C4—1221no—
688C2×C22⋊C4—1221no—
689C2×C42—1221no—
690C2×C42C22×D6111yescharacteristic
691C4⋊C8—21no—
692C4⋊C8—1221no—
693C22⋊C8—611no—
694C22⋊C8—611no—
695C22⋊C8—1221no—
696C22⋊C8—1221no—
697C22⋊C8—1221no—
698C22⋊C8—1221no—
699C22⋊C8C22×D6111yescharacteristic
700C22⋊C8C22×D6111yescharacteristic
701#97—1221no—
702C4×C8—21no—
703#95—21no—
704#95—611no—
705#95—611no—
706#95—1221no—
707#95—1221no—
708#95—1221no—
709#95—1221no—
710#95C22×D6111yescharacteristic
711#95C22×D6111yescharacteristic
712C24—611no—
713C24—611no—
714C24—1221no—
715C24—1221no—
716#41—81no—
717#41—81no—
718#41—4881no—
719#41—4881no—
720C2×Q8—21no—
721C2×Q8—611no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—611no—
727C2×D4—611no—
728C2×D4—611no—
729C2×D4—611no—
730C2×D4—611no—
731C2×D4—1221no—
732C2×D4—1221no—
733C2×D4—1221no—
734C2×D4—1221no—
735C2×D4—1221no—
736C2×D4—1221no—
737C2×D4—1221no—
738C2×D4—1221no—
739C2×D4—1221no—
740C2×D4—1221no—
741C2×D4—1221no—
742C2×D4—4881no—
743C2×D4—4881no—
744C2×D4—4881no—
745C2×D4—4881no—
746C2×D4—4881no—
747C2×D4—4881no—
748C2×D4—2442no—
749C2×D4—2444no—
750C2×D4C2×C4×D6111yescharacteristic
751C2×D4C2×C4×D6111yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—611no—
757C22×C4—611no—
758C22×C4—611no—
759C22×C4—611no—
760C22×C4—611no—
761C22×C4—611no—
762C22×C4—611no—
763C22×C4—611no—
764C22×C4—611no—
765C22×C4—611no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—4881no—
774C22×C4—4881no—
775C22×C4—4881no—
776C22×C4—4881no—
777C22×C4—2442no—
778C22×C4D4×D6111yescharacteristic
779C22×C4D4×D6111yescharacteristic
780C22×C4C23×D6111yescharacteristic
781M16—4881no—
782M16—4881no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—1221no—
786C2×C8—1221no—
787C2×C8—4881no—
788C2×C8—4881no—
789C4⋊C4—21no—
790C4⋊C4—81no—
791C4⋊C4—611no—
792C4⋊C4—611no—
793C4⋊C4—611no—
794C4⋊C4—611no—
795C4⋊C4—611no—
796C4⋊C4—611no—
797C4⋊C4—1221no—
798C4⋊C4—1221no—
799C4⋊C4—1221no—
800C4⋊C4—1221no—
801C4⋊C4—1221no—
802C4⋊C4—1221no—
803C4⋊C4—1221no—
804C4⋊C4—1221no—
805C4⋊C4—4881no—
806C4⋊C4C2×C4×D6111yescharacteristic
807C4⋊C4C2×C4×D6111yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—611no—
813C22⋊C4—611no—
814C22⋊C4—611no—
815C22⋊C4—611no—
816C22⋊C4—611no—
817C22⋊C4—611no—
818C22⋊C4—611no—
819C22⋊C4—611no—
820C22⋊C4—1221no—
821C22⋊C4—1221no—
822C22⋊C4—1221no—
823C22⋊C4—1221no—
824C22⋊C4—1221no—
825C22⋊C4—1221no—
826C22⋊C4—1221no—
827C22⋊C4—1221no—
828C22⋊C4—1221no—
829C22⋊C4—1221no—
830C22⋊C4—1221no—
831C22⋊C4—1221no—
832C22⋊C4—1221no—
833C22⋊C4—1221no—
834C22⋊C4—1221no—
835C22⋊C4—4881no—
836C22⋊C4—4881no—
837C22⋊C4—2442no—
838C42—1221no—
839C42—1221no—
840C42—1221no—
841C42—4881no—
842C42C2×C4×D6111yescharacteristic
843C42C2×C4×D6111yescharacteristic
844C42D4×D6111yescharacteristic
845C42D4×D6111yescharacteristic
846C23—21no—
847C23—21no—
848C23—611no—
849C23—611no—
850C23—611no—
851C23—611no—
852C23—1222no—
853C23—1221no—
854C23—1221no—
855C23—1221no—
856C23—1221no—
857C23—1221no—
858C23—4881no—
859C23—4881no—
860C23—4881no—
861C23—4881no—
862C23—2441no—
863C23—2441no—
864C23—2441no—
865C23—2442no—
866C23—2442no—
867C23C2×D4×D6111yescharacteristic
868Q8—81no—
869Q8—2441no—
870D4—41no—
871D4—41no—
872D4—42no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—81no—
878D4—1222no—
879D4—1222no—
880D4—4881no—
881D4—4881no—
882D4—4881no—
883D4—4881no—
884D4—4881no—
885D4—4881no—
886D4—4881no—
887D4—4881no—
888D4—2441no—
889D4—2441no—
890D4—2441no—
891D4—2442no—
892D4—2442no—
893D4—2441no—
894D4—2441no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—81no—
908C2×C4—81no—
909C2×C4—611no—
910C2×C4—611no—
911C2×C4—611no—
912C2×C4—611no—
913C2×C4—1221no—
914C2×C4—1221no—
915C2×C4—1221no—
916C2×C4—4881no—
917C2×C4—4881no—
918C2×C4—4884no—
919C2×C4—4881no—
920C2×C4—4881no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4—2441no—
924C2×C4—2441no—
925C2×C4—2441no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2442no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4C22⋊C4×D6111yescharacteristic
939C2×C4C22⋊C4×D6111yescharacteristic
940C2×C4C22⋊C4×D6111yescharacteristic
941C2×C4C22⋊C4×D6111yescharacteristic
942C2×C4C22×C4×D6111yescharacteristic
943C2×C4C2×D4×D6111yescharacteristic
944C8—41no—
945C8—41no—
946C8—2441no—
947C8—2441no—
948C22—21no—
949C22—21no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—41no—
956C22—612no—
957C22—1221no—
958C22—1221no—
959C22—1221no—
960C22—1221no—
961C22—1221no—
962C22—1221no—
963C22—1221no—
964C22—1221no—
965C22—1221no—
966C22—1221no—
967C22—1221no—
968C22—9762no—
969C22—9762no—
970C22—4881no—
971C22—4881no—
972C22—2442no—
973C22—2442no—
974C22—2441no—
975C22—2441no—
976C22—2441no—
977C22C2×C22⋊C4×D6111yescharacteristic
978C22#1684056311yescharacteristic
979C22#1684056811yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—41no—
987C4—41no—
988C4—81no—
989C4—81no—
990C4—1221no—
991C4—1221no—
992C4—1221no—
993C4—1221no—
994C4—4881no—
995C4—4881no—
996C4—2441no—
997C4—2441no—
998C4—2441no—
999C2—21no—
1000C2—21no—
1001C2—81no—
1002C2—81no—
1003C2—1222no—
1004C2—4881no—
1005C2—2441no—
1006C2—2441no—
1007C2—2441no—
1008C2#2145427811yescharacteristic
1009C2#2145434011yescharacteristic
1010C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1517C2
socleC22×C61C22×C22⋊C4
prime radical#21459846C2
cosocleC22×C4×C61C24
hypercenter#1517D61
hypocenterC61#17597
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1517

Complements

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

NH ≅ G/Ntype
2. #21454853C2semidirect
3. #21448455C2semidirect
4. #21444397C2semidirect
5. #21444385C2semidirect
6. #21444372C2semidirect
7. #21444366C2semidirect
8. #21444359C2semidirect
9. #21444355C2semidirect
10. #21444346C2semidirect
11. #21444333C2semidirect
12. #21444320C2semidirect
13. #21444307C2semidirect
14. #327×D61C2semidirect
15. C61×#1517C2semidirect
16. #16840478C4semidirect
17. #16840473C4semidirect
19. #16840462C4semidirect
20. #16840462C4semidirect
21. #16840432C4semidirect
22. #16840407C4semidirect
23. #16840407C4semidirect
26. #16840397C4semidirect
42. #16839819C22semidirect
43. #16839724C22semidirect
44. #16839724C22semidirect
45. C22⋊C8×D61C22semidirect
46. C22⋊C8×D61C22semidirect
51. #16839630C22semidirect
52. #16839624C22semidirect
53. #16839621C22semidirect
54. #16839609C22semidirect
55. #95×D61C22semidirect
56. #16839500C22semidirect
57. #16839500C22semidirect
58. #16839498C22semidirect
59. #16839498C22semidirect
62. #16839496C22semidirect
63. #16839496C22semidirect
64. #16839496C22semidirect
65. #16839496C22semidirect
69. C61×#431C22semidirect
70. C61×#382C22semidirect
71. C61×#327C22semidirect
72. C61×#327C22semidirect
73. C61×#327C22semidirect
74. C61×#327C22semidirect
76. C2×#11758224C2×C4semidirect
82. C2×D4×D61C2×C4semidirect
94. #14519769C2×C4semidirect
98. #14519765C2×C4semidirect
107. #14519757C2×C4semidirect
113. #14519752C2×C4semidirect
128. #14519748C2×C4semidirect
129. #14519748C2×C4semidirect
136. C4×Dic122C2×C4semidirect
141. C4×D244C2×C4semidirect
157. #14519735C2×C4semidirect
162. C4⋊C4×D61C2×C4semidirect
188. C4⋊Q8×C61C2×C4semidirect
189. #127×C61C2×C4semidirect
195. C4×D4×C61C2×C4semidirect
196. C4×D4×C61C2×C4semidirect
499. #1517D61semidirect
549. #431C2×D61semidirect
559. #382C2×D61semidirect
576. #327C2×D61semidirect
577. #327C2×D61semidirect
578. #327C2×D61semidirect
579. #327C2×D61semidirect
580. C61#17597semidirect
597. C4⋊Q8C4×D61semidirect
599. #127C4×D61semidirect
669. C4×D4C4×D61semidirect
670. C4×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214598462
#214548532
#214484552
#214443972
#214443852
#214443722
#214443662
#214443592
#214443552
#214443462
#214443332
#214443202
#214443072
#327×D612
C61×#15172
#1759761