Finite Group Databasebeta

← #29647211

Subgroups — #29647211

Order 15616.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459845C211yesmaximal, characteristic
2#21454855C211yesmaximal, characteristic, complemented
3#21448178C211yesmaximal, characteristic, complemented
4#21444341C211yesmaximal, characteristic, complemented
5#21444333C211yesmaximal, characteristic, complemented
6#21444325C211yesmaximal, characteristic, complemented
7#21444324C211yesmaximal, characteristic, complemented
8#21444320C211yesmaximal, characteristic, complemented
9#21444312C211yesmaximal, characteristic, complemented
10#21444308C211yesmaximal, characteristic, complemented
11#21444307C211yesmaximal, characteristic, complemented
12#21444302C211yesmaximal, characteristic, complemented
13C2×#16839496C211yesmaximal, characteristic, complemented
14#327×D61C211yesmaximal, characteristic, complemented
15C61×#1507C211yesmaximal, characteristic, complemented
16#16840476C411yescharacteristic, complemented
17#16840467C411yescharacteristic, complemented
18#16840460C411yescharacteristic, complemented
19#16840459C411yescharacteristic, complemented
20#16840455—21no—
21#16840430C411yescharacteristic, complemented
22#16840409C411yescharacteristic, complemented
23#16840406—21no—
24#16840406C411yescharacteristic, complemented
25#16840401—21no—
26D4×C22⋊D61—21no—
27D4×C22⋊D61C411yescharacteristic, complemented
28#16840362—21no—
29#16840350—21no—
30#16840344—21no—
31#16840307C2211yescharacteristic
32#16840293C2211yescharacteristic
33#16840273C2211yescharacteristic
34#16840272C2211yescharacteristic
35#121×D61C2211yescharacteristic
36#16840235—21no—
37C2×C4×C22⋊D61C2211yescharacteristic
38C2×#14519737—21no—
39#16839838—21no—
40#16839831—21no—
41#16839830—21no—
42#16839825—21no—
43#16839816C2211yescharacteristic, complemented
44#16839812C2211yescharacteristic, complemented
45#16839724C2211yescharacteristic, complemented
46C2×C22⋊#92418C2211yescharacteristic, complemented
47C22⋊C8×D61C2211yescharacteristic, complemented
48C4×#11758196—21no—
49#16839613C2211yescharacteristic, complemented
50C22⋊C4×Dic61—21no—
51C4×#11758198—21no—
52#16839609C2211yescharacteristic, complemented
53#16839607C2211yescharacteristic, complemented
54C2×#14519684C2211yescharacteristic, complemented
55#95×D61C2211yescharacteristic, complemented
56#16839500C2211yescharacteristic, complemented
57#16839500C2211yescharacteristic, complemented
58#16839498C2211yescharacteristic, complemented
59#16839498C2211yescharacteristic, complemented
60#16839497C2211yescharacteristic, complemented
61#16839497C2211yescharacteristic, complemented
62#16839496C2211yescharacteristic
63#16839496C2211yescharacteristic
64#16839496C2211yescharacteristic, complemented
65#16839496C2211yescharacteristic, complemented
66#16839495C2211yescharacteristic, complemented
67#16839495C2211yescharacteristic, complemented
68C2×#121×C61C2211yescharacteristic
69C61×#407C2211yescharacteristic, complemented
70C4×C22⋊C4×C61C2211yescharacteristic, complemented
71C61×#327C2211yescharacteristic
72C61×#327C2211yescharacteristic
73C61×#327C2211yescharacteristic, complemented
74C61×#327C2211yescharacteristic, complemented
75C2×#11758222C2×C411yescharacteristic, complemented
76C2×#11758224—21no—
77C2×#11758224C2×C411yescharacteristic, complemented
78C22×C22⋊D61—21no—
79C22×C22⋊D61D411yescharacteristic
80C2×D4×D61—21no—
81C2×D4×D61C2×C411yescharacteristic, complemented
82C23×Dic61—21no—
83C22×C4×D61—21no—
84C22×C4×D61C2311yescharacteristic
85C2×#11758189—21no—
86C22×#92418—21no—
87C2×C8×D61—21no—
88#14519776C2×C411yescharacteristic, complemented
89#14519773—21no—
90#14519773C2×C411yescharacteristic, complemented
91#14519772—21no—
92#14519770—21no—
93#14519770—21no—
94#14519768C2×C411yescharacteristic, complemented
95#14519767—21no—
96#14519764—21no—
97#14519764C2×C411yescharacteristic, complemented
98#14519763—21no—
99#14519763—21no—
100#14519762—21no—
101#14519760—21no—
102#14519759—21no—
103#14519759—21no—
104#14519758—21no—
105#14519758—21no—
106#14519758—21no—
107#14519757C2×C411yescharacteristic, complemented
108#14519756—21no—
109#14519756C2×C411yescharacteristic, complemented
110#14519756C2311yescharacteristic
111#14519755—21no—
112#14519752C2×C411yescharacteristic, complemented
113#14519751—21no—
114#14519751C2×C411yescharacteristic, complemented
115#14519751C2311yescharacteristic
116#14519750—21no—
117#14519750—21no—
118#14519749—21no—
119#14519749—21no—
120#14519749—21no—
121#14519749—21no—
122#14519749—21no—
123#14519749—21no—
124#14519748—21no—
125#14519748—21no—
126#14519748C2×C411yescharacteristic, complemented
127#14519748C2×C411yescharacteristic, complemented
128#14519746—21no—
129#14519746—21no—
130#14519746—21no—
131#14519745—21no—
132#14519745—21no—
133#14519745—21no—
134#14519742C2×C411yescharacteristic, complemented
135D4×Dic61—21no—
136D4×Dic61—21no—
137D4×Dic61C2×C411yescharacteristic, complemented
138D4×Dic61C2×C411yescharacteristic, complemented
139#14519739C2×C411yescharacteristic, complemented
140C4×C22⋊D61—21no—
141C4×C22⋊D61—21no—
142C4×C22⋊D61—21no—
143C4×C22⋊D61—21no—
144C4×C22⋊D61C2×C411yescharacteristic
145C4×C22⋊D61C2×C411yescharacteristic
146C4×C22⋊D61C2×C411yescharacteristic
147C4×C22⋊D61C2×C411yescharacteristic
148C4×C22⋊D61D411yescharacteristic
149C4×C22⋊D61D411yescharacteristic
150C4×C22⋊D61D411yescharacteristic
151C4×C22⋊D61D411yescharacteristic
152#14519737—28no—
153#14519737—21no—
154#14519737—21no—
155#14519737—21no—
156#14519737—21no—
157#14519736C2×C411yescharacteristic, complemented
158#14519735C2×C411yescharacteristic, complemented
159#14519733—21no—
160#14519733—21no—
161C2×#11758196—21no—
162C2×#11758196D411yescharacteristic
163C4⋊C4×D61C2×C411yescharacteristic, complemented
164C2×C22⋊Dic61—21no—
165C2×C22⋊Dic61D411yescharacteristic
166C2×#11758198—21no—
167C2×#11758198D411yescharacteristic
168C22⋊C4×D61—21no—
169C22⋊C4×D61—21no—
170C2×C4×Dic61—21no—
171C2×C4×Dic61—21no—
172C2×C4×Dic61—21no—
173C2×C4×Dic61C2311yescharacteristic
174#14519706—21no—
175#14519706—21no—
176C22⋊#92418—21no—
177C22⋊#92418C2311yescharacteristic
178C22⋊#92418C2311yescharacteristic
179#14519689—21no—
180#14519689—21no—
181#14519687—21no—
182C8×Dic61—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684—21no—
186#14519684C2311yescharacteristic
187#14519684C2311yescharacteristic
188C22×D4×C61—21no—
189C22×D4×C61C2×C411yescharacteristic, complemented
190C23×C4×C61C2311yescharacteristic
191C2×M16×C61—21no—
192#121×C61—21no—
193#121×C61—21no—
194#121×C61C2×C411yescharacteristic, complemented
195#121×C61C2×C411yescharacteristic, complemented
196#121×C61C2311yescharacteristic
197#121×C61C2311yescharacteristic
198C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
199C2×C22⋊C4×C61—21no—
200C2×C22⋊C4×C61—21no—
201C2×C42×C61—21no—
202C22⋊C8×C61—21no—
203C22⋊C8×C61C2311yescharacteristic
204C22⋊C8×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206#95×C61C2311yescharacteristic
207C24×C61—21no—
208C24×C61C2×D411yescharacteristic
209C23×D61—21no—
210C23×D61C2×D411yescharacteristic
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61—21no—
216C2×D4×C61—81no—
217C2×D4×C61—81no—
218C2×D4×C61—81no—
219C2×D4×C61C22×C411yescharacteristic
220C2×D4×C61C22×C411yescharacteristic
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—81no—
225C22×C4×C61C22×C411yescharacteristic
226C22×C4×C61C22×C411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2411yescharacteristic
231C2×C22⋊D61—24no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C2×C22⋊D61—21no—
236C2×C22⋊D61—21no—
237C2×C22⋊D61—21no—
238C2×C22⋊D61—21no—
239C2×C22⋊D61—21no—
240C2×C22⋊D61—21no—
241C2×C22⋊D61—44no—
242C2×C22⋊D61C22⋊C411yescharacteristic
243C2×C22⋊D61C22⋊C411yescharacteristic
244C2×C22⋊D61C22⋊C411yescharacteristic
245C2×C22⋊D61C22⋊C411yescharacteristic
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—24no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—81no—
253C22×Dic61—81no—
254C22×Dic61C2×D411yescharacteristic
255C22×Dic61C2×D411yescharacteristic
256C22×Dic61C2×D411yescharacteristic
257#11758224—81no—
258#11758224—81no—
259#11758224—81no—
260D4×D61—81no—
261D4×D61—81no—
262D4×D61—81no—
263#11758222—81no—
264C2×D244—21no—
265C2×D244C22×C411yescharacteristic
266C2×C4×D61—24no—
267C2×C4×D61—21no—
268C2×C4×D61—21no—
269C2×C4×D61—21no—
270C2×C4×D61—81no—
271C2×C4×D61—81no—
272C2×C4×D61—81no—
273C2×C4×D61C22×C411yescharacteristic
274C2×C4×D61C22×C411yescharacteristic
275C2×C4×D61C2×D411yescharacteristic
276C2×C4×D61C2×D411yescharacteristic
277C2×Dic122—21no—
278C2×Dic122C22×C411yescharacteristic
279M16×C61—81no—
280C2×C8×C61—21no—
281C2×C8×C61—21no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61C22×C411yescharacteristic
284C4⋊C4×C61C22×C411yescharacteristic
285C22⋊C4×C61—24no—
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—21no—
289C22⋊C4×C61—21no—
290C42×C61—81no—
291C22⋊Dic61—21no—
292C22⋊Dic61—21no—
293C22⋊Dic61—21no—
294C22⋊Dic61—21no—
295C22⋊Dic61—21no—
296C22⋊Dic61—21no—
297C22⋊Dic61—21no—
298C22⋊Dic61—21no—
299C22⋊Dic61—21no—
300C22⋊Dic61C22⋊C411yescharacteristic
301C22⋊Dic61C22⋊C411yescharacteristic
302C22⋊Dic61C22⋊C411yescharacteristic
303C22⋊Dic61C22⋊C411yescharacteristic
304#11758198—24no—
305#11758198—21no—
306#11758198—21no—
307#11758198—21no—
308#11758198—21no—
309#11758198—21no—
310#11758198—21no—
311#11758198C22⋊C411yescharacteristic
312#11758198C22⋊C411yescharacteristic
313#11758198C22⋊C411yescharacteristic
314#11758198C22⋊C411yescharacteristic
315C4⋊Dic61—21no—
316C4⋊Dic61—21no—
317C4⋊Dic61C22×C411yescharacteristic
318C4⋊Dic61C22×C411yescharacteristic
319#11758196—24no—
320#11758196—21no—
321#11758196—21no—
322#11758196—21no—
323#11758196—21no—
324#11758196—21no—
325#11758196—21no—
326#11758196C22⋊C411yescharacteristic
327#11758196C22⋊C411yescharacteristic
328#11758196C22⋊C411yescharacteristic
329#11758196C22⋊C411yescharacteristic
330C4×Dic61—24no—
331C4×Dic61—21no—
332C4×Dic61—21no—
333C4×Dic61—21no—
334C4×Dic61—81no—
335C4×Dic61—81no—
336C4×Dic61C22×C411yescharacteristic
337C4×Dic61C22×C411yescharacteristic
338C4×Dic61C2×D411yescharacteristic
339C4×Dic61C2×D411yescharacteristic
340C2×#92418—21no—
341C2×#92418—21no—
342C2×#92418—81no—
343#11758189—81no—
344C8×D61—81no—
345C23×C61—21no—
346C23×C61—21no—
347C23×C61—22no—
348C23×C61—21no—
349C23×C61—21no—
350C23×C61—41no—
351C23×C61—42no—
352C23×C61—81no—
353C23×C61—81no—
354C23×C61C2×C22⋊C411yescharacteristic
355C23×C61C2×C22⋊C411yescharacteristic
356C23×C61C22×D411yescharacteristic
357C22×D61—21no—
358C22×D61—21no—
359C22×D61—22no—
360C22×D61—21no—
361C22×D61—41no—
362C22×D61—42no—
363C22×D61—81no—
364C22×D61—81no—
365C22×D61C2×C22⋊C411yescharacteristic
366C22×D61C2×C22⋊C411yescharacteristic
367D4×C61—41no—
368D4×C61—41no—
369D4×C61—41no—
370D4×C61—41no—
371D4×C61—41no—
372D4×C61—41no—
373D4×C61—81no—
374D4×C61—81no—
375D4×C61—81no—
376C2×C4×C61—22no—
377C2×C4×C61—22no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—81no—
391C2×C4×C61C2×C22⋊C411yescharacteristic
392C2×C4×C61C2×C22⋊C411yescharacteristic
393C2×C4×C61C23×C411yescharacteristic
394C2×C4×C61C22×D411yescharacteristic
395C22⋊D61—22no—
396C22⋊D61—22no—
397C22⋊D61—22no—
398C22⋊D61—41no—
399C22⋊D61—41no—
400C22⋊D61—42no—
401C22⋊D61—42no—
402C22⋊D61—42no—
403C22⋊D61—81no—
404C22⋊D61—81no—
405C22⋊D61—81no—
406C22⋊D61—81no—
407C22⋊D61—81no—
408C22⋊D61#10414yes—
409C2×Dic61—21no—
410C2×Dic61—21no—
411C2×Dic61—22no—
412C2×Dic61—22no—
413C2×Dic61—22no—
414C2×Dic61—21no—
415C2×Dic61—21no—
416C2×Dic61—21no—
417C2×Dic61—41no—
418C2×Dic61—41no—
419C2×Dic61—41no—
420C2×Dic61—41no—
421C2×Dic61—41no—
422C2×Dic61—42no—
423C2×Dic61—81no—
424C2×Dic61—81no—
425C2×Dic61—84no—
426C2×Dic61C2×C22⋊C411yescharacteristic
427C2×Dic61C2×C22⋊C411yescharacteristic
428C2×Dic61C2×C22⋊C411yescharacteristic
429C2×Dic61C2×C22⋊C411yescharacteristic
430C2×Dic61C2×C22⋊C411yescharacteristic
431C2×Dic61C2×C22⋊C411yescharacteristic
432D244—41no—
433D244—81no—
434C4×D61—41no—
435C4×D61—41no—
436C4×D61—41no—
437C4×D61—41no—
438C4×D61—81no—
439C4×D61—81no—
440C4×D61—81no—
441C4×D61—84no—
442Dic122—41no—
443Dic122—81no—
444C8×C61—41no—
445C8×C61—41no—
446#92418—41no—
447#92418—41no—
448#17547—611nomaximal, Sylow
449C22×C61—21no—
450C22×C61—21no—
451C22×C61—21no—
452C22×C61—21no—
453C22×C61—21no—
454C22×C61—21no—
455C22×C61—21no—
456C22×C61—42no—
457C22×C61—42no—
458C22×C61—41no—
459C22×C61—41no—
460C22×C61—41no—
461C22×C61—41no—
462C22×C61—41no—
463C22×C61—41no—
464C22×C61—162no—
465C22×C61C2×#10412yes—
466C22×C61C22×C22⋊C411yescharacteristic
467C22×C61#57611yescharacteristic
468C22×C61#57711yescharacteristic
469C2×D61—21no—
470C2×D61—21no—
471C2×D61—21no—
472C2×D61—21no—
473C2×D61—21no—
474C2×D61—42no—
475C2×D61—42no—
476C2×D61—41no—
477C2×D61—41no—
478C2×D61—41no—
479C2×D61—162no—
480C2×D61C2×#10412yes—
481C4×C61—21no—
482C4×C61—21no—
483C4×C61—21no—
484C4×C61—21no—
485C4×C61—42no—
486C4×C61—42no—
487C4×C61—41no—
488C4×C61—41no—
489Dic61—21no—
490Dic61—21no—
491Dic61—21no—
492Dic61—21no—
493Dic61—21no—
494Dic61—42no—
495Dic61—42no—
496Dic61—41no—
497Dic61—41no—
498Dic61—41no—
499Dic61C2×#10412yes—
500#3519—611no—
501#2974—611no—
502#2275—611no—
503#1509—611no—
504#1507—611no—
505#1507D6111yescharacteristic, complemented
506#1505—611no—
507#1504—611no—
508#1504—611no—
509#1502—611no—
510#1501—611no—
511#1501—611no—
512#1500—611no—
513C2×#327—611no—
514C2×#327—611no—
515C2×C61—21no—
516C2×C61—21no—
517C2×C61—22no—
518C2×C61—41no—
519C2×C61—81no—
520C2×C61—81no—
521C2×C61#288311yescharacteristic
522C2×C61#289711yescharacteristic
523C2×C61C22×#10411yescharacteristic
524D61—22no—
525D61—41no—
526D61—81no—
527#555—611no—
528#554—611no—
529#553—611no—
530#553—611no—
531#553—1221no—
532#550—611no—
533#546—611no—
534#546—611no—
535#546—1221no—
536#546—1221no—
537D42—611no—
538D42—1221no—
539#540—1221no—
540#538—1221no—
541#538—1221no—
542#532—611no—
543#529—611no—
544#525—611no—
545#525—611no—
546C2×#121—611no—
547C2×#121C2×D6111yescharacteristic
548#518—1221no—
549C2×C4×D4—611no—
550C2×C4×D4—1221no—
551#436—1221no—
552#435—1221no—
553#435—1221no—
554C8×D4—1221no—
555#432—611no—
556#431—611no—
557#407—611no—
558#407C2×D6111yescharacteristic, complemented
559C2×C22⋊C8—611no—
560C2×C22⋊C8—611no—
561C4×C4⋊C4—611no—
562C4×C4⋊C4—1221no—
563C4×C22⋊C4—611no—
564C4×C22⋊C4—1221no—
565C4×C22⋊C4—1221no—
566C4×C22⋊C4C2×D6111yescharacteristic, complemented
567#376—611no—
568C2×#95—611no—
569C2×#95—611no—
570#328—611no—
571#328—611no—
572#328—611no—
573#328—611no—
574#327—611no—
575#327—611no—
576#327—611no—
577#327—611no—
578#327—611no—
579#327—611no—
580#327—611no—
581#327—611no—
582#327C2×D6111yescharacteristic
583#327C2×D6111yescharacteristic
584#327C2×D6111yescharacteristic, complemented
585#327C2×D6111yescharacteristic, complemented
586C61#1754711yescharacteristic, complemented, Sylow
587C2×#41—611no—
588C2×#41—611no—
589C2×#41—1221no—
590C22×D4—21no—
591C22×D4—611no—
592C22×D4—611no—
593C22×D4—1221no—
594C22×D4—1221no—
595C22×D4C4×D6111yescharacteristic, complemented
596C23×C4—611no—
597C23×C4—1221no—
598C23×C4—1221no—
599C23×C4C22×D6111yescharacteristic
600C2×M16—21no—
601C2×M16—1221no—
602C22×C8—1221no—
603C22×C8—1221no—
604C4⋊Q8—611no—
605#127—611no—
606#127—1221no—
607#126—1221no—
608#126—1221no—
609#126—1221no—
610#125—611no—
611#125—1221no—
612#124—611no—
613#124—1221no—
614#124—1221no—
615#124—1221no—
616#123—1221no—
617#123—1221no—
618#123—1221no—
619#123—1221no—
620#123—1221no—
621#123—1221no—
622#123—1221no—
623C22⋊Q8—611no—
624C22⋊Q8—611no—
625C22⋊Q8—611no—
626C22⋊Q8—1221no—
627C22⋊Q8—1221no—
628#121—21no—
629#121—21no—
630#121—611no—
631#121—611no—
632#121—611no—
633#121—611no—
634#121—611no—
635#121—1221no—
636#121—1221no—
637#121—1221no—
638#121—1221no—
639#121—1221no—
640#121—1221no—
641#121—1221no—
642#121—1221no—
643#121—1221no—
644#121—1221no—
645#121—1221no—
646#121C4×D6111yescharacteristic, complemented
647#121C4×D6111yescharacteristic, complemented
648#121C22×D6111yescharacteristic
649#121C22×D6111yescharacteristic
650#120—1221no—
651#120—1221no—
652#120—1221no—
653#120—1221no—
654#120—1221no—
655#120—1221no—
656C4×Q8—611no—
657C4×D4—611no—
658C4×D4—611no—
659C4×D4—611no—
660C4×D4—611no—
661C4×D4—611no—
662C4×D4—611no—
663C4×D4—611no—
664C4×D4—611no—
665C4×D4—611no—
666C4×D4—611no—
667C4×D4—611no—
668C4×D4—1221no—
669C4×D4—1221no—
670C4×D4—1221no—
671C4×D4—1221no—
672C4×D4—1228no—
673C4×D4—1221no—
674C4×D4—1221no—
675C4×D4—1221no—
676C4×D4—1221no—
677C4×D4—1221no—
678C4×D4—1221no—
679#117—611no—
680#117—611no—
681#117—1221no—
682#117—1221no—
683C2×C4⋊C4—611no—
684C2×C4⋊C4—611no—
685C2×C4⋊C4—1221no—
686C2×C4⋊C4C4×D6111yescharacteristic, complemented
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—611no—
690C2×C22⋊C4—611no—
691C2×C22⋊C4—1221no—
692C2×C22⋊C4—1221no—
693C2×C22⋊C4—1221no—
694C2×C22⋊C4—1221no—
695C2×C42—21no—
696C2×C42—611no—
697C2×C42—1221no—
698C2×C42—1221no—
699C2×C42—1221no—
700C4⋊C8—1221no—
701C4⋊C8—1221no—
702C22⋊C8—21no—
703C22⋊C8—611no—
704C22⋊C8—611no—
705C22⋊C8—1221no—
706C22⋊C8—1221no—
707C22⋊C8—1221no—
708C22⋊C8C22×D6111yescharacteristic
709C22⋊C8C22×D6111yescharacteristic
710#97—1221no—
711C4×C8—1221no—
712#95—611no—
713#95—611no—
714#95—1221no—
715#95—1221no—
716#95—1221no—
717#95C22×D6111yescharacteristic
718#95C22×D6111yescharacteristic
719C24—21no—
720C24—611no—
721C24—1221no—
722C24D4×D6111yescharacteristic
723#41—4881no—
724#41—4881no—
725#41—4881no—
726#41—4881no—
727C2×Q8—611no—
728C2×Q8—1221no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—81no—
735C2×D4—81no—
736C2×D4—81no—
737C2×D4—611no—
738C2×D4—611no—
739C2×D4—611no—
740C2×D4—611no—
741C2×D4—611no—
742C2×D4—1221no—
743C2×D4—1221no—
744C2×D4—1221no—
745C2×D4—1221no—
746C2×D4—1224no—
747C2×D4—1221no—
748C2×D4—1221no—
749C2×D4—1221no—
750C2×D4—1221no—
751C2×D4—1221no—
752C2×D4—1221no—
753C2×D4—4881no—
754C2×D4—4881no—
755C2×D4—4881no—
756C2×D4—2444no—
757C2×D4C2×C4×D6111yescharacteristic
758C2×D4C2×C4×D6111yescharacteristic
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—81no—
763C22×C4—611no—
764C22×C4—611no—
765C22×C4—611no—
766C22×C4—611no—
767C22×C4—611no—
768C22×C4—611no—
769C22×C4—611no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1224no—
773C22×C4—1221no—
774C22×C4—1221no—
775C22×C4—1221no—
776C22×C4—1224no—
777C22×C4—1221no—
778C22×C4—1221no—
779C22×C4—1221no—
780C22×C4—4881no—
781C22×C4—4881no—
782C22×C4—4881no—
783C22×C4—4881no—
784C22×C4—4881no—
785C22×C4C2×C4×D6111yescharacteristic
786C22×C4C2×C4×D6111yescharacteristic
787C22×C4D4×D6111yescharacteristic
788C22×C4D4×D6111yescharacteristic
789C22×C4D4×D6111yescharacteristic
790C22×C4C23×D6111yescharacteristic
791M16—81no—
792M16—4881no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—1221no—
796C2×C8—1221no—
797C2×C8—4881no—
798C2×C8—4881no—
799C4⋊C4—21no—
800C4⋊C4—611no—
801C4⋊C4—611no—
802C4⋊C4—611no—
803C4⋊C4—611no—
804C4⋊C4—611no—
805C4⋊C4—611no—
806C4⋊C4—1221no—
807C4⋊C4—1221no—
808C4⋊C4—1221no—
809C4⋊C4—1221no—
810C4⋊C4—1221no—
811C4⋊C4—1221no—
812C4⋊C4—1224no—
813C4⋊C4—1221no—
814C4⋊C4—1221no—
815C4⋊C4C2×C4×D6111yescharacteristic
816C4⋊C4C2×C4×D6111yescharacteristic
817C22⋊C4—24no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—611no—
823C22⋊C4—611no—
824C22⋊C4—611no—
825C22⋊C4—611no—
826C22⋊C4—611no—
827C22⋊C4—611no—
828C22⋊C4—611no—
829C22⋊C4—611no—
830C22⋊C4—1221no—
831C22⋊C4—1221no—
832C22⋊C4—1221no—
833C22⋊C4—1221no—
834C22⋊C4—1224no—
835C22⋊C4—1221no—
836C22⋊C4—1221no—
837C22⋊C4—1221no—
838C22⋊C4—1221no—
839C22⋊C4—1221no—
840C22⋊C4—1221no—
841C22⋊C4—1221no—
842C22⋊C4—1221no—
843C22⋊C4—1221no—
844C22⋊C4—1221no—
845C22⋊C4—1221no—
846C42—81no—
847C42—611no—
848C42—611no—
849C42—611no—
850C42—611no—
851C42—1221no—
852C42—1221no—
853C42—1224no—
854C42—1221no—
855C42—4881no—
856C42—4881no—
857C23—22no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—41no—
863C23—42no—
864C23—81no—
865C23—81no—
866C23—611no—
867C23—611no—
868C23—1222no—
869C23—1221no—
870C23—1221no—
871C23—1221no—
872C23—4881no—
873C23—4881no—
874C23—2441no—
875C23—2442no—
876C23C22⋊C4×D6111yescharacteristic
877C23C22⋊C4×D6111yescharacteristic
878C23C2×D4×D6111yescharacteristic
879Q8—4881no—
880Q8—2441no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—81no—
888D4—81no—
889D4—81no—
890D4—614no—
891D4—1222no—
892D4—1222no—
893D4—1222no—
894D4—4881no—
895D4—4881no—
896D4—4881no—
897D4—4881no—
898D4—4881no—
899D4—4881no—
900D4—2441no—
901D4—2442no—
902D4—2442no—
903D4—2442no—
904D4—2441no—
905D4—2441no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—81no—
921C2×C4—611no—
922C2×C4—611no—
923C2×C4—611no—
924C2×C4—611no—
925C2×C4—611no—
926C2×C4—611no—
927C2×C4—1222no—
928C2×C4—1221no—
929C2×C4—1221no—
930C2×C4—1222no—
931C2×C4—1222no—
932C2×C4—1221no—
933C2×C4—1221no—
934C2×C4—1221no—
935C2×C4—4881no—
936C2×C4—4881no—
937C2×C4—4881no—
938C2×C4—4884no—
939C2×C4—4881no—
940C2×C4—4881no—
941C2×C4—4884no—
942C2×C4—2441no—
943C2×C4—2441no—
944C2×C4—2441no—
945C2×C4—2441no—
946C2×C4—2442no—
947C2×C4—2441no—
948C2×C4—2441no—
949C2×C4—2441no—
950C2×C4—2441no—
951C2×C4—2441no—
952C2×C4C22⋊C4×D6111yescharacteristic
953C2×C4C22⋊C4×D6111yescharacteristic
954C2×C4C22×C4×D6111yescharacteristic
955C2×C4C2×D4×D6111yescharacteristic
956C8—41no—
957C8—41no—
958C8—2441no—
959C8—2441no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—42no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—41no—
973C22—41no—
974C22—41no—
975C22—162no—
976C22—612no—
977C22—1221no—
978C22—1221no—
979C22—1221no—
980C22—1221no—
981C22—1221no—
982C22—9762no—
983C22—2442no—
984C22—2442no—
985C22—2441no—
986C22—2441no—
987C22—2441no—
988C22#104×D6112yes—
989C22C2×C22⋊C4×D6111yescharacteristic
990C22#1684056611yescharacteristic
991C22#1684057211yescharacteristic
992C4—21no—
993C4—21no—
994C4—21no—
995C4—21no—
996C4—42no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—612no—
1001C4—1221no—
1002C4—1221no—
1003C4—1221no—
1004C4—1221no—
1005C4—1221no—
1006C4—2442no—
1007C4—2442no—
1008C4—2441no—
1009C4—2441no—
1010C4—2441no—
1011C2—21no—
1012C2—21no—
1013C2—22no—
1014C2—41no—
1015C2—81no—
1016C2—81no—
1017C2—1222no—
1018C2—4881no—
1019C2—2441no—
1020C2#2145427711yescharacteristic
1021C2#2145434411yescharacteristic
1022C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1507C2
socleC22×C61C22×C22⋊C4
prime radical#21459845C2
cosocleC22×C4×C61C24
hypercenter#1507D61
hypocenterC61#17547
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
2. #21454855C2semidirect
3. #21448178C2semidirect
4. #21444341C2semidirect
5. #21444333C2semidirect
6. #21444325C2semidirect
7. #21444324C2semidirect
8. #21444320C2semidirect
9. #21444312C2semidirect
10. #21444308C2semidirect
11. #21444307C2semidirect
12. #21444302C2semidirect
13. C2×#16839496C2semidirect
14. #327×D61C2semidirect
15. C61×#1507C2semidirect
16. #16840476C4semidirect
17. #16840467C4semidirect
18. #16840460C4semidirect
19. #16840459C4semidirect
21. #16840430C4semidirect
22. #16840409C4semidirect
24. #16840406C4semidirect
27. D4×C22⋊D61C4semidirect
43. #16839816C22semidirect
44. #16839812C22semidirect
45. #16839724C22semidirect
46. C2×C22⋊#92418C22semidirect
47. C22⋊C8×D61C22semidirect
49. #16839613C22semidirect
52. #16839609C22semidirect
53. #16839607C22semidirect
54. C2×#14519684C22semidirect
55. #95×D61C22semidirect
56. #16839500C22semidirect
57. #16839500C22semidirect
58. #16839498C22semidirect
59. #16839498C22semidirect
60. #16839497C22semidirect
61. #16839497C22semidirect
64. #16839496C22semidirect
65. #16839496C22semidirect
66. #16839495C22semidirect
67. #16839495C22semidirect
69. C61×#407C22semidirect
70. C4×C22⋊C4×C61C22semidirect
73. C61×#327C22semidirect
74. C61×#327C22semidirect
75. C2×#11758222C2×C4semidirect
77. C2×#11758224C2×C4semidirect
81. C2×D4×D61C2×C4semidirect
88. #14519776C2×C4semidirect
90. #14519773C2×C4semidirect
94. #14519768C2×C4semidirect
97. #14519764C2×C4semidirect
107. #14519757C2×C4semidirect
109. #14519756C2×C4semidirect
112. #14519752C2×C4semidirect
114. #14519751C2×C4semidirect
126. #14519748C2×C4semidirect
127. #14519748C2×C4semidirect
134. #14519742C2×C4semidirect
137. D4×Dic61C2×C4semidirect
138. D4×Dic61C2×C4semidirect
139. #14519739C2×C4semidirect
157. #14519736C2×C4semidirect
158. #14519735C2×C4semidirect
163. C4⋊C4×D61C2×C4semidirect
189. C22×D4×C61C2×C4semidirect
194. #121×C61C2×C4semidirect
195. #121×C61C2×C4semidirect
198. C2×C4⋊C4×C61C2×C4semidirect
505. #1507D61semidirect
558. #407C2×D61semidirect
566. C4×C22⋊C4C2×D61semidirect
584. #327C2×D61semidirect
585. #327C2×D61semidirect
586. C61#17547semidirect
595. C22×D4C4×D61semidirect
646. #121C4×D61semidirect
647. #121C4×D61semidirect
686. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214598452
#214548552
#214481782
#214443412
#214443332
#214443252
#214443242
#214443202
#214443122
#214443082
#214443072
#214443022
C2×#168394962
#327×D612
C61×#15072
#1754761