Finite Group Databasebeta

← #29646284

Subgroups — #29646284

Order 15616.

1060 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840441C211yesmaximal, characteristic
2#21454854C211yesmaximal, characteristic, complemented
3#21444189C211yesmaximal, characteristic, complemented
4#21444186C211yesmaximal, characteristic, complemented
5#21444184C211yesmaximal, characteristic, complemented
6#21444182C211yesmaximal, characteristic, complemented
7#21444168C211yesmaximal, characteristic, complemented
8#21444165C211yesmaximal, characteristic, complemented
9#21444155C211yesmaximal, characteristic, complemented
10#21444151C211yesmaximal, characteristic, complemented
11#21444145C211yesmaximal, characteristic, complemented
12#21444135C211yesmaximal, characteristic, complemented
13#21444131C211yesmaximal, characteristic, complemented
14C2×#16839485C211yesmaximal, characteristic, complemented
15C61×#2974C211yesmaximal, characteristic, complemented
16#16840441—21no—
17#16840441—21no—
18#16840441—21no—
19#16840441—21no—
20#16840441—21no—
21#16840441—21no—
22#16840441—21no—
23#16840441—21no—
24C2×#14519772C411yescharacteristic
25C2×#14519771C2211yescharacteristic
26C2×#14519763C411yescharacteristic
27C2×#14519760C2211yescharacteristic
28C2×#14519759C411yescharacteristic
29C2×#14519758C411yescharacteristic
30C2×#14519756C2211yescharacteristic
31C2×#14519755C411yescharacteristic
32C2×#14519745C411yescharacteristic
33C2×C4×C22⋊D61C2211yescharacteristic
34C2×#14519734C2211yescharacteristic
35C2×#14519733C411yescharacteristic
36C22×#11758198C2211yescharacteristic
37C2×C22⋊C4×D61C411yescharacteristic
38#16839840—21no—
39#16839834—21no—
40#16839834—21no—
41D4×#92418—21no—
42#16839819C2211yescharacteristic, complemented
43#16839815C2211yescharacteristic, complemented
44#16839726C2211yescharacteristic
45#16839726C2211yescharacteristic, complemented
46C2×C22⋊#92418C2211yescharacteristic
47C2×C22⋊#92418C2211yescharacteristic, complemented
48#16839487C2211yescharacteristic, complemented
49#16839487C2211yescharacteristic, complemented
50#16839487C2211yescharacteristic, complemented
51#16839487C2211yescharacteristic, complemented
52#16839487C2211yescharacteristic, complemented
53#16839487C2211yescharacteristic, complemented
54#16839487C2211yescharacteristic, complemented
55#16839487C2211yescharacteristic, complemented
56#16839485C2211yescharacteristic
57#16839485C2211yescharacteristic
58#16839485C2211yescharacteristic
59#16839485C2211yescharacteristic
60#16839485C2211yescharacteristic
61#16839485C2211yescharacteristic
62#16839485C2211yescharacteristic
63#16839485C2211yescharacteristic
64C2×C4×D4×C61C2211yescharacteristic
65C61×#436—21no—
66C61×#435—21no—
67C61×#435—21no—
68C8×D4×C61—21no—
69C61×#432C2211yescharacteristic, complemented
70C61×#431C2211yescharacteristic, complemented
71C61×#407C2211yescharacteristic
72C61×#407C2211yescharacteristic, complemented
73C2×C22⋊C8×C61C2211yescharacteristic
74C2×C22⋊C8×C61C2211yescharacteristic, complemented
75C24×D61C2×C411yescharacteristic
76C22×Dic122C2×C411yescharacteristic
77C22×C22⋊D61C2×C411yescharacteristic
78C22×C22⋊D61C2×C411yescharacteristic
79C23×Dic61C2×C411yescharacteristic
80C22×C4×D61C2×C411yescharacteristic
81C22×C4×D61C2×C411yescharacteristic
82C2×#11758194—21no—
83C2×#11758194—21no—
84C22×#92418—21no—
85C22×#92418—21no—
86#14519772—21no—
87#14519772—21no—
88#14519772—21no—
89#14519772—21no—
90#14519771—21no—
91#14519771—21no—
92#14519771—21no—
93#14519771—21no—
94#14519763—21no—
95#14519763—21no—
96#14519763—21no—
97#14519763—21no—
98#14519760—21no—
99#14519760—21no—
100#14519760—21no—
101#14519760—21no—
102#14519759—21no—
103#14519759—21no—
104#14519759—21no—
105#14519759—21no—
106#14519758—21no—
107#14519758—21no—
108#14519758—21no—
109#14519758—21no—
110#14519756—21no—
111#14519756—21no—
112#14519756—21no—
113#14519756—21no—
114#14519755—21no—
115#14519755—21no—
116#14519755—21no—
117#14519755—21no—
118#14519745—21no—
119#14519745—21no—
120#14519745—21no—
121#14519745—21no—
122C4×C22⋊D61—21no—
123C4×C22⋊D61—21no—
124C4×C22⋊D61—21no—
125C4×C22⋊D61—21no—
126#14519734—21no—
127#14519734—21no—
128#14519734—21no—
129#14519734—21no—
130#14519733—21no—
131#14519733—21no—
132#14519733—21no—
133#14519733—21no—
134C2×C4⋊Dic61C2×C411yescharacteristic
135C2×#11758196C2×C411yescharacteristic
136C2×#11758196C2×C411yescharacteristic
137C2×#11758196C2×C411yescharacteristic
138C2×#11758196C2×C411yescharacteristic
139C2×#11758196C2311yescharacteristic
140C2×#11758196C2311yescharacteristic
141C2×C22⋊Dic61C2×C411yescharacteristic
142C2×C22⋊Dic61C2×C411yescharacteristic
143C2×C22⋊Dic61C2×C411yescharacteristic
144C2×C22⋊Dic61C2×C411yescharacteristic
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198C2×C411yescharacteristic
150C2×#11758198C2×C411yescharacteristic
151C2×#11758198C2×C411yescharacteristic
152C2×#11758198C2×C411yescharacteristic
153C2×#11758198C2×C411yescharacteristic
154C2×#11758198C2×C411yescharacteristic
155C2×#11758198C2311yescharacteristic
156C2×#11758198C2311yescharacteristic
157C22⋊C4×D61—21no—
158C22⋊C4×D61—21no—
159C22⋊C4×D61—21no—
160C22⋊C4×D61—21no—
161C2×C4×Dic61C2×C411yescharacteristic
162C2×C4×Dic61C2×C411yescharacteristic
163C4⋊#92418—21no—
164C4⋊#92418—21no—
165C22⋊#92418—21no—
166C22⋊#92418—21no—
167C22⋊#92418—21no—
168C22⋊#92418—21no—
169C22⋊#92418C2311yescharacteristic
170C22⋊#92418C2311yescharacteristic
171C22⋊#92418C2311yescharacteristic
172C22⋊#92418C2311yescharacteristic
173#14519688—21no—
174C4×#92418—21no—
175C22×D4×C61C2×C411yescharacteristic
176C23×C4×C61C2311yescharacteristic
177C23×C4×C61C2311yescharacteristic
178C2×M16×C61—21no—
179C2×M16×C61—21no—
180C22×C8×C61—21no—
181C22×C8×C61—21no—
182C4×D4×C61D411yescharacteristic
183C4×D4×C61D411yescharacteristic
184C4×D4×C61D411yescharacteristic
185C4×D4×C61D411yescharacteristic
186C4×D4×C61D411yescharacteristic
187C4×D4×C61D411yescharacteristic
188C4×D4×C61D411yescharacteristic
189C4×D4×C61D411yescharacteristic
190C2×C4⋊C4×C61C2×C411yescharacteristic
191C2×C22⋊C4×C61C2×C411yescharacteristic
192C2×C22⋊C4×C61C2×C411yescharacteristic
193C2×C42×C61C2311yescharacteristic
194C4⋊C8×C61—21no—
195C4⋊C8×C61—21no—
196C22⋊C8×C61—21no—
197C22⋊C8×C61—21no—
198C22⋊C8×C61—21no—
199C22⋊C8×C61—21no—
200C22⋊C8×C61C2311yescharacteristic
201C22⋊C8×C61C2311yescharacteristic
202C22⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61C2311yescharacteristic
204#97×C61—21no—
205C4×C8×C61—21no—
206C24×C61C22×C411yescharacteristic
207C24×C61C22×C411yescharacteristic
208C23×D61—21no—
209C23×D61—21no—
210C23×D61—22no—
211C23×D61—41no—
212C23×D61—42no—
213C23×D61—81no—
214C23×D61C22×C411yescharacteristic
215C23×D61C22×C411yescharacteristic
216C2×D4×C61—42no—
217C2×D4×C61C22⋊C411yescharacteristic
218C2×D4×C61C22⋊C411yescharacteristic
219C2×D4×C61C22⋊C411yescharacteristic
220C2×D4×C61C22⋊C411yescharacteristic
221C22×C4×C61—81no—
222C22×C4×C61—81no—
223C22×C4×C61C22×C411yescharacteristic
224C22×C4×C61C22×C411yescharacteristic
225C22×C4×C61C22×C411yescharacteristic
226C22×C4×C61C22×C411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61C2411yescharacteristic
236C2×C22⋊D61—21no—
237C2×C22⋊D61—21no—
238C2×C22⋊D61—22no—
239C2×C22⋊D61—21no—
240C2×C22⋊D61—21no—
241C2×C22⋊D61—41no—
242C2×C22⋊D61—81no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—42no—
246C22×Dic61C22×C411yescharacteristic
247C22×Dic61C22×C411yescharacteristic
248C22×Dic61C22×C411yescharacteristic
249C22×Dic61C22×C411yescharacteristic
250C22×Dic61C22×C411yescharacteristic
251C22×Dic61C22×C411yescharacteristic
252C2×C4×D61—22no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—41no—
258C2×C4×D61—81no—
259C2×Dic122—21no—
260C2×Dic122—21no—
261C2×Dic122—81no—
262M16×C61—81no—
263M16×C61—81no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C2×C8×C61—81no—
269C2×C8×C61—81no—
270C4⋊C4×C61C22⋊C411yescharacteristic
271C4⋊C4×C61C22⋊C411yescharacteristic
272C4⋊C4×C61C22⋊C411yescharacteristic
273C4⋊C4×C61C22⋊C411yescharacteristic
274C22⋊C4×C61C22⋊C411yescharacteristic
275C22⋊C4×C61C22⋊C411yescharacteristic
276C22⋊C4×C61C22⋊C411yescharacteristic
277C22⋊C4×C61C22⋊C411yescharacteristic
278C22⋊C4×C61C22⋊C411yescharacteristic
279C22⋊C4×C61C22⋊C411yescharacteristic
280C22⋊C4×C61C22⋊C411yescharacteristic
281C22⋊C4×C61C22⋊C411yescharacteristic
282C42×C61C2×D411yescharacteristic
283C42×C61C2×D411yescharacteristic
284C42×C61C2×D411yescharacteristic
285C42×C61C2×D411yescharacteristic
286C22⋊Dic61—21no—
287C22⋊Dic61—21no—
288C22⋊Dic61—21no—
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—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198—21no—
308#11758198—21no—
309#11758198—21no—
310C4⋊Dic61—21no—
311C4⋊Dic61—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196—21no—
323#11758196—21no—
324C4×Dic61—21no—
325C4×Dic61—21no—
326C4×Dic61—21no—
327C4×Dic61—21no—
328#11758194—81no—
329#11758194—81no—
330C2×#92418—21no—
331C2×#92418—21no—
332C2×#92418—21no—
333C2×#92418—21no—
334C2×#92418—81no—
335C2×#92418—81no—
336C23×C61—21no—
337C23×C61—21no—
338C23×C61—22no—
339C23×C61—21no—
340C23×C61—21no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61C2×C22⋊C411yescharacteristic
345C23×C61C2×C22⋊C411yescharacteristic
346C23×C61C2×C22⋊C411yescharacteristic
347C23×C61C2×C22⋊C411yescharacteristic
348C23×C61C23×C411yescharacteristic
349C22×D61—21no—
350C22×D61—21no—
351C22×D61—21no—
352C22×D61—21no—
353C22×D61—21no—
354C22×D61—42no—
355C22×D61—42no—
356C22×D61—41no—
357C22×D61—41no—
358C22×D61—42no—
359C22×D61—42no—
360C22×D61—41no—
361C22×D61—41no—
362C22×D61—81no—
363C22×D61—81no—
364C22×D61—84no—
365C22×D61—84no—
366C22×D61#13112yes—
367D4×C61—22no—
368D4×C61—22no—
369D4×C61—41no—
370D4×C61—41no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
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—41no—
384C2×C4×C61—41no—
385C2×C4×C61C2×C22⋊C411yescharacteristic
386C2×C4×C61C2×C22⋊C411yescharacteristic
387C2×C4×C61C2×C22⋊C411yescharacteristic
388C2×C4×C61C2×C22⋊C411yescharacteristic
389C2×C4×C61C2×C22⋊C411yescharacteristic
390C2×C4×C61C2×C22⋊C411yescharacteristic
391C2×C4×C61C2×C22⋊C411yescharacteristic
392C2×C4×C61C2×C22⋊C411yescharacteristic
393C2×C4×C61C22×D411yescharacteristic
394C2×C4×C61C22×D411yescharacteristic
395C22⋊D61—42no—
396C22⋊D61—42no—
397C22⋊D61—81no—
398C22⋊D61—81no—
399C2×Dic61—21no—
400C2×Dic61—21no—
401C2×Dic61—21no—
402C2×Dic61—21no—
403C2×Dic61—21no—
404C2×Dic61—21no—
405C2×Dic61—21no—
406C2×Dic61—21no—
407C2×Dic61—21no—
408C2×Dic61—21no—
409C2×Dic61—42no—
410C2×Dic61—42no—
411C2×Dic61—41no—
412C2×Dic61—41no—
413C2×Dic61—41no—
414C2×Dic61—41no—
415C4×D61—42no—
416C4×D61—42no—
417C4×D61—81no—
418C4×D61—81no—
419Dic122—81no—
420Dic122—81no—
421C8×C61—41no—
422C8×C61—41no—
423C8×C61—41no—
424C8×C61—41no—
425#92418—41no—
426#92418—41no—
427#92418—41no—
428#92418—41no—
429#17422—611nomaximal, Sylow
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—21no—
436C22×C61—21no—
437C22×C61—21no—
438C22×C61—21no—
439C22×C61—21no—
440C22×C61—21no—
441C22×C61—21no—
442C22×C61—21no—
443C22×C61—42no—
444C22×C61—42no—
445C22×C61—81no—
446C22×C61—81no—
447C22×C61#41312yes—
448C22×C61C22×C22⋊C411yescharacteristic
449C22×C61C2×#13111yescharacteristic
450C22×C61#56811yescharacteristic
451C2×D61—22no—
452C2×D61—42no—
453C2×D61—41no—
454C2×D61—41no—
455C2×D61—42no—
456C2×D61—41no—
457C2×D61—41no—
458C2×D61—41no—
459C2×D61—84no—
460C2×D61—84no—
461C2×D61—81no—
462C2×D61—81no—
463C4×C61—21no—
464C4×C61—21no—
465C4×C61—21no—
466C4×C61—21no—
467C4×C61—21no—
468C4×C61—21no—
469C4×C61—21no—
470C4×C61—21no—
471C4×C61—21no—
472C4×C61—21no—
473Dic61—41no—
474Dic61—41no—
475Dic61—41no—
476Dic61—41no—
477Dic61—41no—
478Dic61—41no—
479C2×#551—611no—
480#2974—611no—
481#2974D6111yescharacteristic, complemented
482#1473—611no—
483#1473—611no—
484#1472—611no—
485#1472—611no—
486#1468—611no—
487#1468—611no—
488#1465—611no—
489#1464—611no—
490#1462—611no—
491#1459—611no—
492#1458—611no—
493C2×#323—611no—
494C2×C61—21no—
495C2×C61—21no—
496C2×C61—22no—
497C2×C61—41no—
498C2×C61—41no—
499C2×C61—41no—
500C2×C61#288011yescharacteristic
501C2×C61#288311yescharacteristic
502C2×C61C2×#41311yescharacteristic
503D61—42no—
504D61—81no—
505#551—1221no—
506#551—1221no—
507#551—1221no—
508#551—1221no—
509#551—1221no—
510#551—1221no—
511#551—1221no—
512#551—1221no—
513C2×#126—611no—
514C2×#126—611no—
515C2×#124—611no—
516C2×#123—611no—
517C2×#123—611no—
518C2×#123—611no—
519C2×C22⋊Q8—611no—
520C2×C22⋊Q8—611no—
521C2×#120—611no—
522C2×C4×D4—611no—
523C2×C4×D4C2×D6111yescharacteristic
524C2×#117—611no—
525C2×#117—611no—
526C22×C22⋊C4—611no—
527C22×C22⋊C4—611no—
528#436—21no—
529#436—1221no—
530#435—21no—
531#435—21no—
532#435—1221no—
533#435—1221no—
534C8×D4—21no—
535C8×D4—1221no—
536#432—611no—
537#432C2×D6111yescharacteristic, complemented
538#431—611no—
539#431C2×D6111yescharacteristic, complemented
540#407—611no—
541#407—611no—
542#407C2×D6111yescharacteristic
543#407C2×D6111yescharacteristic, complemented
544C2×C22⋊C8—611no—
545C2×C22⋊C8—611no—
546C2×C22⋊C8C2×D6111yescharacteristic
547C2×C22⋊C8C2×D6111yescharacteristic, complemented
548#324—611no—
549#324—611no—
550#324—611no—
551#324—611no—
552#324—611no—
553#324—611no—
554#324—611no—
555#324—611no—
556#323—611no—
557#323—611no—
558#323—611no—
559#323—611no—
560#323—611no—
561#323—611no—
562#323—611no—
563#323—611no—
564C61#1742211yescharacteristic, complemented, Sylow
565C25—611no—
566C22×Q8—611no—
567C22×D4—611no—
568C22×D4—611no—
569C22×D4C4×D6111yescharacteristic
570C23×C4—611no—
571C23×C4—611no—
572C23×C4—611no—
573C23×C4C22×D6111yescharacteristic
574C23×C4C22×D6111yescharacteristic
575C2×M16—21no—
576C2×M16—21no—
577C2×M16—1221no—
578C2×M16—1221no—
579C22×C8—21no—
580C22×C8—21no—
581C22×C8—1221no—
582C22×C8—1221no—
583#126—1221no—
584#126—1221no—
585#126—1221no—
586#126—1221no—
587#126—1221no—
588#126—1221no—
589#126—1221no—
590#126—1221no—
591#124—1221no—
592#124—1221no—
593#124—1221no—
594#124—1221no—
595#123—1221no—
596#123—1221no—
597#123—1221no—
598#123—1221no—
599#123—1221no—
600#123—1221no—
601#123—1221no—
602#123—1221no—
603#123—1221no—
604#123—1221no—
605#123—1221no—
606#123—1221no—
607C22⋊Q8—1221no—
608C22⋊Q8—1221no—
609C22⋊Q8—1221no—
610C22⋊Q8—1221no—
611C22⋊Q8—1221no—
612C22⋊Q8—1221no—
613C22⋊Q8—1221no—
614C22⋊Q8—1221no—
615#120—1221no—
616#120—1221no—
617#120—1221no—
618#120—1221no—
619C4×D4—1221no—
620C4×D4—1221no—
621C4×D4—1221no—
622C4×D4—1221no—
623C4×D4D24411yescharacteristic
624C4×D4D24411yescharacteristic
625C4×D4D24411yescharacteristic
626C4×D4D24411yescharacteristic
627C4×D4C22⋊D6111yescharacteristic
628C4×D4C22⋊D6111yescharacteristic
629C4×D4C22⋊D6111yescharacteristic
630C4×D4C22⋊D6111yescharacteristic
631#117—1221no—
632#117—1221no—
633#117—1221no—
634#117—1221no—
635#117—1221no—
636#117—1221no—
637#117—1221no—
638#117—1221no—
639C2×C4⋊C4—611no—
640C2×C4⋊C4—611no—
641C2×C4⋊C4—611no—
642C2×C4⋊C4—611no—
643C2×C4⋊C4—611no—
644C2×C4⋊C4—611no—
645C2×C4⋊C4—611no—
646C2×C4⋊C4C4×D6111yescharacteristic
647C2×C22⋊C4—611no—
648C2×C22⋊C4—611no—
649C2×C22⋊C4—611no—
650C2×C22⋊C4—611no—
651C2×C22⋊C4—611no—
652C2×C22⋊C4—611no—
653C2×C22⋊C4—611no—
654C2×C22⋊C4—611no—
655C2×C22⋊C4—611no—
656C2×C22⋊C4—611no—
657C2×C22⋊C4—611no—
658C2×C22⋊C4—611no—
659C2×C22⋊C4—1221no—
660C2×C22⋊C4—1221no—
661C2×C22⋊C4—1221no—
662C2×C22⋊C4—1221no—
663C2×C22⋊C4—1221no—
664C2×C22⋊C4—1221no—
665C2×C22⋊C4—1221no—
666C2×C22⋊C4—1221no—
667C2×C22⋊C4C4×D6111yescharacteristic
668C2×C22⋊C4C4×D6111yescharacteristic
669C2×C42—611no—
670C2×C42—611no—
671C2×C42C22×D6111yescharacteristic
672C4⋊C8—21no—
673C4⋊C8—21no—
674C4⋊C8—1221no—
675C4⋊C8—1221no—
676C22⋊C8—21no—
677C22⋊C8—21no—
678C22⋊C8—21no—
679C22⋊C8—21no—
680C22⋊C8—611no—
681C22⋊C8—611no—
682C22⋊C8—611no—
683C22⋊C8—611no—
684C22⋊C8—1221no—
685C22⋊C8—1221no—
686C22⋊C8—1221no—
687C22⋊C8—1221no—
688C22⋊C8C22×D6111yescharacteristic
689C22⋊C8C22×D6111yescharacteristic
690C22⋊C8C22×D6111yescharacteristic
691C22⋊C8C22×D6111yescharacteristic
692#97—21no—
693#97—1221no—
694C4×C8—21no—
695C4×C8—1221no—
696C24—611no—
697C24—611no—
698C24—1222no—
699C24—1221no—
700C24—1221no—
701C24—4881no—
702C24—2441no—
703C24—2442no—
704C24C2×C4×D6111yescharacteristic
705C24C2×C4×D6111yescharacteristic
706C2×Q8—1221no—
707C2×Q8—1221no—
708C2×Q8—4881no—
709C2×D4—42no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4—1222no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—4881no—
716C2×D4—2441no—
717C2×D4#1175819811yescharacteristic
718C2×D4#1175819811yescharacteristic
719C2×D4#1175819811yescharacteristic
720C2×D4#1175819811yescharacteristic
721C22×C4—81no—
722C22×C4—81no—
723C22×C4—611no—
724C22×C4—611no—
725C22×C4—611no—
726C22×C4—611no—
727C22×C4—611no—
728C22×C4—611no—
729C22×C4—1222no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—4881no—
737C22×C4—2441no—
738C22×C4—2442no—
739C22×C4C2×C4×D6111yescharacteristic
740C22×C4C2×C4×D6111yescharacteristic
741C22×C4C2×C4×D6111yescharacteristic
742C22×C4C2×C4×D6111yescharacteristic
743C22×C4C2×D24411yescharacteristic
744C22×C4C2×D24411yescharacteristic
745C22×C4C2×D24411yescharacteristic
746C22×C4C2×D24411yescharacteristic
747C22×C4C2×C22⋊D6111yescharacteristic
748C22×C4C2×C22⋊D6111yescharacteristic
749C22×C4C2×C22⋊D6111yescharacteristic
750C22×C4C2×C22⋊D6111yescharacteristic
751C22×C4C23×D6111yescharacteristic
752M16—81no—
753M16—81no—
754M16—4881no—
755M16—4881no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C2×C8—81no—
762C2×C8—1221no—
763C2×C8—1221no—
764C2×C8—1221no—
765C2×C8—1221no—
766C2×C8—4881no—
767C2×C8—4881no—
768C4⋊C4—1221no—
769C4⋊C4—1221no—
770C4⋊C4—1221no—
771C4⋊C4—1221no—
772C4⋊C4—1221no—
773C4⋊C4—1221no—
774C4⋊C4—1221no—
775C4⋊C4—1221no—
776C4⋊C4—1221no—
777C4⋊C4—1221no—
778C4⋊C4—1221no—
779C4⋊C4—1221no—
780C4⋊C4—1221no—
781C4⋊C4—1221no—
782C4⋊C4#1175819811yescharacteristic
783C4⋊C4#1175819811yescharacteristic
784C4⋊C4#1175819811yescharacteristic
785C4⋊C4#1175819811yescharacteristic
786C22⋊C4—1221no—
787C22⋊C4—1221no—
788C22⋊C4—1221no—
789C22⋊C4—1221no—
790C22⋊C4—1221no—
791C22⋊C4—1221no—
792C22⋊C4—1221no—
793C22⋊C4—1221no—
794C22⋊C4—1221no—
795C22⋊C4—1221no—
796C22⋊C4—1221no—
797C22⋊C4—1221no—
798C22⋊C4—1221no—
799C22⋊C4—1221no—
800C22⋊C4—1221no—
801C22⋊C4—1221no—
802C22⋊C4—1221no—
803C22⋊C4—1221no—
804C22⋊C4—1221no—
805C22⋊C4—1221no—
806C22⋊C4—1221no—
807C22⋊C4—1221no—
808C22⋊C4—1221no—
809C22⋊C4—1221no—
810C22⋊C4#1175819811yescharacteristic
811C22⋊C4#1175819811yescharacteristic
812C22⋊C4#1175819811yescharacteristic
813C22⋊C4#1175819811yescharacteristic
814C22⋊C4#1175819811yescharacteristic
815C22⋊C4#1175819811yescharacteristic
816C22⋊C4#1175819811yescharacteristic
817C22⋊C4#1175819811yescharacteristic
818C42—1221no—
819C42—1221no—
820C42—1221no—
821C42—1221no—
822C42C2×D24411yescharacteristic
823C42C2×D24411yescharacteristic
824C42C2×C22⋊D6111yescharacteristic
825C42C2×C22⋊D6111yescharacteristic
826C23—22no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—612no—
835C23—1221no—
836C23—1221no—
837C23—1221no—
838C23—1221no—
839C23—1221no—
840C23—4881no—
841C23—4881no—
842C23—4884no—
843C23—4884no—
844C23—2442no—
845C23—2442no—
846C23—2441no—
847C23—2441no—
848C23—2442no—
849C23—2441no—
850C23—2441no—
851C23—2442no—
852C23C2×#1175819811yescharacteristic
853C23C2×#1175819811yescharacteristic
854C23C2×#1175819811yescharacteristic
855C23C2×#1175819811yescharacteristic
856C23C22×C4×D6111yescharacteristic
857Q8—4881no—
858Q8—4881no—
859D4—22no—
860D4—22no—
861D4—41no—
862D4—41no—
863D4—4881no—
864D4—4881no—
865D4—2442no—
866D4—2442no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—1221no—
882C2×C4—1221no—
883C2×C4—1221no—
884C2×C4—1221no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—1221no—
888C2×C4—1221no—
889C2×C4—1221no—
890C2×C4—1221no—
891C2×C4—4881no—
892C2×C4—4881no—
893C2×C4—2442no—
894C2×C4—2442no—
895C2×C4—2442no—
896C2×C4—2442no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2441no—
900C2×C4—2441no—
901C2×C4C2×#1175819811yescharacteristic
902C2×C4C2×#1175819811yescharacteristic
903C2×C4C2×#1175819811yescharacteristic
904C2×C4C2×#1175819811yescharacteristic
905C2×C4C2×#1175819811yescharacteristic
906C2×C4C2×#1175819811yescharacteristic
907C2×C4C2×#1175819811yescharacteristic
908C2×C4C2×#1175819811yescharacteristic
909C2×C4C22×C22⋊D6111yescharacteristic
910C2×C4C22×D24411yescharacteristic
911C8—41no—
912C8—41no—
913C8—41no—
914C8—41no—
915C8—2441no—
916C8—2441no—
917C8—2441no—
918C8—2441no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—21no—
926C22—21no—
927C22—21no—
928C22—21no—
929C22—21no—
930C22—21no—
931C22—21no—
932C22—42no—
933C22—42no—
934C22—81no—
935C22—81no—
936C22—1222no—
937C22—4881no—
938C22—4881no—
939C22—4884no—
940C22—4884no—
941C22—2442no—
942C22—2442no—
943C22—2441no—
944C22—2441no—
945C22—2441no—
946C22—2441no—
947C22—2441no—
948C22#1683974412yes—
949C22C22×#1175819811yescharacteristic
950C22#131×D6111yescharacteristic
951C22#1684052711yescharacteristic
952C4—21no—
953C4—21no—
954C4—21no—
955C4—21no—
956C4—21no—
957C4—21no—
958C4—21no—
959C4—21no—
960C4—21no—
961C4—21no—
962C4—2441no—
963C4—2441no—
964C4—2441no—
965C4—2441no—
966C4—2441no—
967C4—2441no—
968C2—21no—
969C2—21no—
970C2—22no—
971C2—41no—
972C2—41no—
973C2—41no—
974C2—4881no—
975C2—2442no—
976C2#2145426611yescharacteristic
977C2#2145427911yescharacteristic
978C2C2×#1683974411yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2974C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519745C4
cosocleC22×C4×C61C24
hypercenter#2974D61
hypocenterC61#17422
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #21454854C2semidirect
3. #21444189C2semidirect
4. #21444186C2semidirect
5. #21444184C2semidirect
6. #21444182C2semidirect
7. #21444168C2semidirect
8. #21444165C2semidirect
9. #21444155C2semidirect
10. #21444151C2semidirect
11. #21444145C2semidirect
12. #21444135C2semidirect
13. #21444131C2semidirect
14. C2×#16839485C2semidirect
15. C61×#2974C2semidirect
42. #16839819C22semidirect
43. #16839815C22semidirect
45. #16839726C22semidirect
47. C2×C22⋊#92418C22semidirect
48. #16839487C22semidirect
49. #16839487C22semidirect
50. #16839487C22semidirect
51. #16839487C22semidirect
52. #16839487C22semidirect
53. #16839487C22semidirect
54. #16839487C22semidirect
55. #16839487C22semidirect
69. C61×#432C22semidirect
70. C61×#431C22semidirect
72. C61×#407C22semidirect
74. C2×C22⋊C8×C61C22semidirect
481. #2974D61semidirect
537. #432C2×D61semidirect
539. #431C2×D61semidirect
543. #407C2×D61semidirect
547. C2×C22⋊C8C2×D61semidirect
564. C61#17422semidirect

Maximal subgroups

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

subgroupindex
C2×#168404412
#214548542
#214441892
#214441862
#214441842
#214441822
#214441682
#214441652
#214441552
#214441512
#214441452
#214441352
#214441312
C2×#168394852
C61×#29742
#1742261