Finite Group Databasebeta

← #29647205

Subgroups — #29647205

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#21454850C211yesmaximal, characteristic, complemented
3#21448177C211yesmaximal, characteristic, complemented
4#21444341C211yesmaximal, characteristic, complemented
5#21444335C211yesmaximal, characteristic, complemented
6#21444333C211yesmaximal, characteristic, complemented
7#21444325C211yesmaximal, characteristic, complemented
8#21444321C211yesmaximal, characteristic, complemented
9#21444320C211yesmaximal, characteristic, complemented
10#21444312C211yesmaximal, characteristic, complemented
11#21444311C211yesmaximal, characteristic, complemented
12#21444307C211yesmaximal, characteristic, complemented
13#21444302C211yesmaximal, characteristic, complemented
14#327×D61C211yesmaximal, characteristic, complemented
15C2×C61×#327C211yesmaximal, 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⋊D61—21no—
38C2×C4×C22⋊D61C2211yescharacteristic
39#16839837—21no—
40#16839836—21no—
41#16839833—21no—
42C8×C22⋊D61—21no—
43#16839816C2211yescharacteristic, complemented
44#16839812C2211yescharacteristic, complemented
45#16839726C2211yescharacteristic, complemented
46#16839724C2211yescharacteristic, complemented
47C22⋊C8×D61C2211yescharacteristic, complemented
48#16839613—21no—
49#16839613C2211yescharacteristic, complemented
50C4×C22⋊Dic61—21no—
51C4×C22⋊Dic61C2211yescharacteristic, complemented
52#16839609—21no—
53#16839609C2211yescharacteristic, complemented
54#16839607C2211yescharacteristic, 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
69C2×C22⋊C8×C61C2211yescharacteristic, complemented
70C2×#95×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
82C22×C4×D61—21no—
83C22×C4×D61C2311yescharacteristic
84C2×#11758194—21no—
85C2×#11758189—21no—
86C2×C8×D61—21no—
87#14519776C2×C411yescharacteristic, complemented
88#14519773—21no—
89#14519773C2×C411yescharacteristic, complemented
90#14519772—21no—
91#14519770—21no—
92#14519770—21no—
93#14519768C2×C411yescharacteristic, complemented
94#14519767—21no—
95#14519764—21no—
96#14519764C2×C411yescharacteristic, complemented
97#14519763—21no—
98#14519763—21no—
99#14519762—21no—
100#14519760—21no—
101#14519759—21no—
102#14519759—21no—
103#14519758—21no—
104#14519758—21no—
105#14519758—21no—
106#14519757C2×C411yescharacteristic, complemented
107#14519756—21no—
108#14519756C2×C411yescharacteristic, complemented
109#14519756C2311yescharacteristic
110#14519755—21no—
111#14519752C2×C411yescharacteristic, complemented
112#14519751—21no—
113#14519751C2×C411yescharacteristic, complemented
114#14519751C2311yescharacteristic
115#14519750—21no—
116#14519750—21no—
117#14519749—21no—
118#14519749—21no—
119#14519749—21no—
120#14519749—21no—
121#14519749—21no—
122#14519749—21no—
123#14519748—21no—
124#14519748—21no—
125#14519748C2×C411yescharacteristic, complemented
126#14519748C2×C411yescharacteristic, complemented
127#14519746—21no—
128#14519746—21no—
129#14519746—21no—
130#14519745—21no—
131#14519745—21no—
132#14519745—21no—
133#14519742C2×C411yescharacteristic, complemented
134D4×Dic61—21no—
135D4×Dic61—21no—
136D4×Dic61C2×C411yescharacteristic, complemented
137D4×Dic61C2×C411yescharacteristic, complemented
138#14519739C2×C411yescharacteristic, complemented
139C4×C22⋊D61—28no—
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—21no—
153#14519737—21no—
154#14519737—21no—
155#14519737—21no—
156#14519736C2×C411yescharacteristic, complemented
157#14519735C2×C411yescharacteristic, complemented
158#14519733—21no—
159#14519733—21no—
160C2×#11758196—21no—
161C2×#11758196D411yescharacteristic
162C4⋊C4×D61C2×C411yescharacteristic, complemented
163C2×C22⋊Dic61—21no—
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×Dic61—21no—
174C2×C4×Dic61C2311yescharacteristic
175#14519706—21no—
176#14519706—21no—
177C22⋊#92418—21no—
178C22⋊#92418C2311yescharacteristic
179C22⋊#92418C2311yescharacteristic
180#14519689—21no—
181#14519689—21no—
182#14519687—21no—
183C8×Dic61—21no—
184#14519684—21no—
185#14519684—21no—
186#14519684C2311yescharacteristic
187#14519684C2311yescharacteristic
188C22×D4×C61—21no—
189C22×D4×C61C2×C411yescharacteristic, complemented
190C23×C4×C61—21no—
191C23×C4×C61C2311yescharacteristic
192C22×C8×C61—21no—
193#121×C61—21no—
194#121×C61—21no—
195#121×C61C2×C411yescharacteristic, complemented
196#121×C61C2×C411yescharacteristic, complemented
197#121×C61C2311yescharacteristic
198#121×C61C2311yescharacteristic
199C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
200C2×C22⋊C4×C61—21no—
201C22⋊C8×C61—21no—
202C22⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61C2311yescharacteristic
204#95×C61—21no—
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—24no—
224C22×C4×C61—21no—
225C22×C4×C61—81no—
226C22×C4×C61—81no—
227C22×C4×C61—81no—
228C22×C4×C61C22×C411yescharacteristic
229C22×C4×C61C22×C411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2411yescharacteristic
234C2×C22⋊D61—24no—
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—21no—
242C2×C22⋊D61—21no—
243C2×C22⋊D61—21no—
244C2×C22⋊D61—44no—
245C2×C22⋊D61C22⋊C411yescharacteristic
246C2×C22⋊D61C22⋊C411yescharacteristic
247C2×C22⋊D61C22⋊C411yescharacteristic
248C2×C22⋊D61C22⋊C411yescharacteristic
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253C22×Dic61—21no—
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
279C2×C8×C61—21no—
280C2×C8×C61—21no—
281C2×C8×C61—81no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61C22×C411yescharacteristic
284C4⋊C4×C61C22×C411yescharacteristic
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—21no—
289C22⋊Dic61—24no—
290C22⋊Dic61—21no—
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⋊Dic61C22⋊C411yescharacteristic
300C22⋊Dic61C22⋊C411yescharacteristic
301C22⋊Dic61C22⋊C411yescharacteristic
302C22⋊Dic61C22⋊C411yescharacteristic
303#11758198—24no—
304#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198—21no—
308#11758198—21no—
309#11758198—21no—
310#11758198C22⋊C411yescharacteristic
311#11758198C22⋊C411yescharacteristic
312#11758198C22⋊C411yescharacteristic
313#11758198C22⋊C411yescharacteristic
314C4⋊Dic61—21no—
315C4⋊Dic61—21no—
316C4⋊Dic61C22×C411yescharacteristic
317C4⋊Dic61C22×C411yescharacteristic
318#11758196—24no—
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196—21no—
323#11758196—21no—
324#11758196—21no—
325#11758196C22⋊C411yescharacteristic
326#11758196C22⋊C411yescharacteristic
327#11758196C22⋊C411yescharacteristic
328#11758196C22⋊C411yescharacteristic
329C4×Dic61—24no—
330C4×Dic61—21no—
331C4×Dic61—21no—
332C4×Dic61—21no—
333C4×Dic61—81no—
334C4×Dic61—81no—
335C4×Dic61—81no—
336C4×Dic61C22×C411yescharacteristic
337C4×Dic61C22×C411yescharacteristic
338C4×Dic61C2×D411yescharacteristic
339C4×Dic61C2×D411yescharacteristic
340#11758194—81no—
341C2×#92418—21no—
342C2×#92418—21no—
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×C61—84no—
392C2×C4×C61C2×C22⋊C411yescharacteristic
393C2×C4×C61C2×C22⋊C411yescharacteristic
394C2×C4×C61C23×C411yescharacteristic
395C2×C4×C61C22×D411yescharacteristic
396C22⋊D61—22no—
397C22⋊D61—22no—
398C22⋊D61—22no—
399C22⋊D61—41no—
400C22⋊D61—41no—
401C22⋊D61—42no—
402C22⋊D61—42no—
403C22⋊D61—42no—
404C22⋊D61—81no—
405C22⋊D61—81no—
406C22⋊D61—81no—
407C22⋊D61—81no—
408C22⋊D61—81no—
409C22⋊D61#10414yes—
410C2×Dic61—21no—
411C2×Dic61—21no—
412C2×Dic61—22no—
413C2×Dic61—22no—
414C2×Dic61—22no—
415C2×Dic61—21no—
416C2×Dic61—21no—
417C2×Dic61—21no—
418C2×Dic61—41no—
419C2×Dic61—41no—
420C2×Dic61—41no—
421C2×Dic61—41no—
422C2×Dic61—41no—
423C2×Dic61—42no—
424C2×Dic61—81no—
425C2×Dic61—81no—
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#1507—611no—
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×#327D6111yescharacteristic, complemented
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#407—611no—
559C2×C22⋊C8—611no—
560C2×C22⋊C8C2×D6111yescharacteristic, complemented
561C4×C4⋊C4—611no—
562C4×C4⋊C4—1221no—
563C4×C22⋊C4—611no—
564C4×C22⋊C4—611no—
565C4×C22⋊C4—1221no—
566C4×C22⋊C4—1221no—
567#376—611no—
568C2×#95—611no—
569C2×#95C2×D6111yescharacteristic, complemented
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—21no—
597C23×C4—611no—
598C23×C4—1221no—
599C23×C4C22×D6111yescharacteristic
600C2×M16—1221no—
601C2×M16—1221no—
602C22×C8—21no—
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—1221no—
673C4×D4—1221no—
674C4×D4—1228no—
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—611no—
689C2×C22⋊C4—611no—
690C2×C22⋊C4—1221no—
691C2×C22⋊C4—1221no—
692C2×C22⋊C4—1221no—
693C2×C22⋊C4—1221no—
694C2×C22⋊C4—1221no—
695C2×C42—611no—
696C2×C42—1221no—
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—21no—
713#95—611no—
714#95—611no—
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—24no—
762C22×C4—21no—
763C22×C4—81no—
764C22×C4—81no—
765C22×C4—81no—
766C22×C4—611no—
767C22×C4—611no—
768C22×C4—611no—
769C22×C4—611no—
770C22×C4—611no—
771C22×C4—611no—
772C22×C4—611no—
773C22×C4—1221no—
774C22×C4—1221no—
775C22×C4—1224no—
776C22×C4—1221no—
777C22×C4—1221no—
778C22×C4—1221no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—1221no—
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—4881no—
792M16—4881no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—81no—
796C2×C8—1221no—
797C2×C8—1221no—
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—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—611no—
822C22⋊C4—611no—
823C22⋊C4—611no—
824C22⋊C4—611no—
825C22⋊C4—611no—
826C22⋊C4—611no—
827C22⋊C4—611no—
828C22⋊C4—611no—
829C22⋊C4—1221no—
830C22⋊C4—1221no—
831C22⋊C4—1221no—
832C22⋊C4—1221no—
833C22⋊C4—1224no—
834C22⋊C4—1221no—
835C22⋊C4—1221no—
836C22⋊C4—1221no—
837C22⋊C4—1221no—
838C22⋊C4—1221no—
839C22⋊C4—1221no—
840C22⋊C4—1224no—
841C22⋊C4—1221no—
842C22⋊C4—1221no—
843C22⋊C4—1221no—
844C22⋊C4—1221no—
845C22⋊C4—1221no—
846C42—611no—
847C42—611no—
848C42—611no—
849C42—611no—
850C42—1221no—
851C42—1221no—
852C42—1224no—
853C42—1221no—
854C42—4881no—
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—84no—
922C2×C4—611no—
923C2×C4—611no—
924C2×C4—611no—
925C2×C4—611no—
926C2×C4—611no—
927C2×C4—611no—
928C2×C4—1222no—
929C2×C4—1221no—
930C2×C4—1221no—
931C2×C4—1222no—
932C2×C4—1222no—
933C2×C4—1221no—
934C2×C4—1221no—
935C2×C4—1221no—
936C2×C4—4881no—
937C2×C4—4881no—
938C2×C4—4881no—
939C2×C4—4884no—
940C2×C4—4881no—
941C2×C4—4881no—
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#1684056311yescharacteristic
991C22#1684056811yescharacteristic
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#2145434011yescharacteristic
1022C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#327C2
socleC22×C61C22×C22⋊C4
prime radical#21459845C2
cosocleC22×C4×C61C24
hypercenterC2×#327D61
hypocenterC61#17547
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. #21454850C2semidirect
3. #21448177C2semidirect
4. #21444341C2semidirect
5. #21444335C2semidirect
6. #21444333C2semidirect
7. #21444325C2semidirect
8. #21444321C2semidirect
9. #21444320C2semidirect
10. #21444312C2semidirect
11. #21444311C2semidirect
12. #21444307C2semidirect
13. #21444302C2semidirect
14. #327×D61C2semidirect
15. C2×C61×#327C2semidirect
16. #16840476C4semidirect
17. #16840467C4semidirect
18. #16840460C4semidirect
19. #16840459C4semidirect
21. #16840430C4semidirect
22. #16840409C4semidirect
24. #16840406C4semidirect
27. D4×C22⋊D61C4semidirect
43. #16839816C22semidirect
44. #16839812C22semidirect
45. #16839726C22semidirect
46. #16839724C22semidirect
47. C22⋊C8×D61C22semidirect
49. #16839613C22semidirect
51. C4×C22⋊Dic61C22semidirect
53. #16839609C22semidirect
54. #16839607C22semidirect
55. #95×D61C22semidirect
56. #16839500C22semidirect
57. #16839500C22semidirect
58. #16839498C22semidirect
59. #16839498C22semidirect
60. #16839497C22semidirect
61. #16839497C22semidirect
64. #16839496C22semidirect
65. #16839496C22semidirect
66. #16839495C22semidirect
67. #16839495C22semidirect
69. C2×C22⋊C8×C61C22semidirect
70. C2×#95×C61C22semidirect
73. C61×#327C22semidirect
74. C61×#327C22semidirect
75. C2×#11758222C2×C4semidirect
77. C2×#11758224C2×C4semidirect
81. C2×D4×D61C2×C4semidirect
87. #14519776C2×C4semidirect
89. #14519773C2×C4semidirect
93. #14519768C2×C4semidirect
96. #14519764C2×C4semidirect
106. #14519757C2×C4semidirect
108. #14519756C2×C4semidirect
111. #14519752C2×C4semidirect
113. #14519751C2×C4semidirect
125. #14519748C2×C4semidirect
126. #14519748C2×C4semidirect
133. #14519742C2×C4semidirect
136. D4×Dic61C2×C4semidirect
137. D4×Dic61C2×C4semidirect
138. #14519739C2×C4semidirect
156. #14519736C2×C4semidirect
157. #14519735C2×C4semidirect
162. C4⋊C4×D61C2×C4semidirect
189. C22×D4×C61C2×C4semidirect
195. #121×C61C2×C4semidirect
196. #121×C61C2×C4semidirect
199. C2×C4⋊C4×C61C2×C4semidirect
514. C2×#327D61semidirect
560. C2×C22⋊C8C2×D61semidirect
569. C2×#95C2×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
#214548502
#214481772
#214443412
#214443352
#214443332
#214443252
#214443212
#214443202
#214443122
#214443112
#214443072
#214443022
#327×D612
C2×C61×#3272
#1754761