Finite Group Databasebeta

← #29647794

Subgroups — #29647794

Order 15616.

1074 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459647C211yesmaximal, characteristic
2#21454846C211yesmaximal, characteristic, complemented
3#21448723C211yesmaximal, characteristic, complemented
4#21444389C211yesmaximal, characteristic, complemented
5#21444385C211yesmaximal, characteristic, complemented
6#21444360C211yesmaximal, characteristic, complemented
7#21444356C211yesmaximal, characteristic, complemented
8#21444354C211yesmaximal, characteristic, complemented
9#21444343C211yesmaximal, characteristic, complemented
10#21444341C211yesmaximal, characteristic, complemented
11#21444324C211yesmaximal, characteristic, complemented
12#21444323C211yesmaximal, characteristic, complemented
13#328×D61C211yesmaximal, characteristic, complemented
14#327×D61C211yesmaximal, characteristic, complemented
15C61×#1513C211yesmaximal, characteristic, complemented
16#16840462—21no—
17#16840459C411yescharacteristic, complemented
18#16840457—21no—
19#16840456C411yescharacteristic, complemented
20#16840451C411yescharacteristic, complemented
21#16840446C411yescharacteristic, complemented
22#16840441—21no—
23#16840440—21no—
24#16840422C411yescharacteristic, complemented
25#16840419C411yescharacteristic, complemented
26#16840409C411yescharacteristic, complemented
27#16840400C411yescharacteristic, complemented
28#16840354—21no—
29#16840347—21no—
30#16840322—21no—
31#16840298C2211yescharacteristic
32#16840293C2211yescharacteristic
33#16840273C2211yescharacteristic
34C22⋊Q8×D61C2211yescharacteristic
35#121×D61C2211yescharacteristic
36#16840234—21no—
37C2×C4×C22⋊D61C2211yescharacteristic
38C2×#14519737—21no—
39#16839836—21no—
40#16839836—21no—
41#16839831—21no—
42#16839831—21no—
43#16839816C2211yescharacteristic, complemented
44#16839816C2211yescharacteristic, complemented
45#16839726C2211yescharacteristic, complemented
46C22⋊C8×D61C2211yescharacteristic
47C22⋊C8×D61C2211yescharacteristic
48#16839657—21no—
49#16839634—21no—
50#16839633—21no—
51#16839626C2211yescharacteristic, complemented
52#16839621C2211yescharacteristic
53#16839613C2211yescharacteristic, complemented
54C2×#14519684C2211yescharacteristic, complemented
55#95×D61C2211yescharacteristic
56#16839500C2211yescharacteristic, complemented
57#16839500C2211yescharacteristic, complemented
58#16839499C2211yescharacteristic, complemented
59#16839499C2211yescharacteristic, complemented
60#16839498C2211yescharacteristic, complemented
61#16839498C2211yescharacteristic, complemented
62#16839497C2211yescharacteristic
63#16839497C2211yescharacteristic
64#16839496C2211yescharacteristic
65#16839496C2211yescharacteristic
66#16839495C2211yescharacteristic
67#16839495C2211yescharacteristic
68C61×#525C2211yescharacteristic
69C61×#407C2211yescharacteristic, complemented
70C61×#380C2211yescharacteristic, complemented
71C61×#328C2211yescharacteristic, complemented
72C61×#328C2211yescharacteristic, complemented
73C61×#327C2211yescharacteristic
74C61×#327C2211yescharacteristic
75C2×#11758222C2×C411yescharacteristic, complemented
76C2×Q8×D61C2×C411yescharacteristic, complemented
77C22×C22⋊D61D411yescharacteristic
78C2×D4×D61—21no—
79C2×D4×D61C2×C411yescharacteristic, complemented
80C23×Dic61—21no—
81C22×C4×D61—21no—
82C22×C4×D61C2311yescharacteristic
83C2×#11758194—21no—
84C2×C8×D61—21no—
85C2×C8×D61—21no—
86#14519772—21no—
87#14519771—21no—
88#14519770—21no—
89#14519770—21no—
90#14519770—21no—
91#14519770—21no—
92#14519769—21no—
93#14519768C2×C411yescharacteristic, complemented
94#14519768C2×C411yescharacteristic, complemented
95#14519767—21no—
96#14519766C2×C411yescharacteristic, complemented
97#14519764—21no—
98#14519764C2×C411yescharacteristic, complemented
99#14519763—21no—
100#14519761—21no—
101#14519760—21no—
102#14519760—21no—
103#14519759—21no—
104#14519759—21no—
105#14519759—21no—
106#14519759—21no—
107#14519758—21no—
108#14519758—21no—
109#14519757C2×C411yescharacteristic, complemented
110#14519756—21no—
111#14519756C2×C411yescharacteristic, complemented
112#14519756C2311yescharacteristic
113#14519755—21no—
114#14519755—21no—
115#14519754—21no—
116#14519753C2×C411yescharacteristic, complemented
117#14519752C2×C411yescharacteristic, complemented
118#14519751C2×C411yescharacteristic, complemented
119#14519751C2311yescharacteristic
120#14519750—21no—
121#14519750—21no—
122#14519750—21no—
123#14519749—21no—
124#14519749—21no—
125#14519748—21no—
126#14519748—21no—
127#14519748—21no—
128#14519748C2×C411yescharacteristic, complemented
129#14519746—21no—
130#14519745—21no—
131#14519745—21no—
132Q8×Dic61C2×C411yescharacteristic, complemented
133#14519742C2×C411yescharacteristic, complemented
134C4×D244—21no—
135D4×Dic61—21no—
136D4×Dic61C2×C411yescharacteristic, complemented
137#14519739—21no—
138#14519739C2×C411yescharacteristic, complemented
139C4×C22⋊D61—21no—
140C4×C22⋊D61—21no—
141C4×C22⋊D61—21no—
142C4×C22⋊D61C2×C411yescharacteristic
143C4×C22⋊D61C2×C411yescharacteristic
144C4×C22⋊D61C2×C411yescharacteristic
145C4×C22⋊D61C2×C411yescharacteristic
146C4×C22⋊D61D411yescharacteristic
147C4×C22⋊D61D411yescharacteristic
148C4×C22⋊D61D411yescharacteristic
149C4×C22⋊D61D411yescharacteristic
150#14519737—21no—
151#14519737—21no—
152#14519737—44no—
153#14519736C2×C411yescharacteristic, complemented
154#14519735—21no—
155#14519735—21no—
156#14519734—21no—
157#14519733—21no—
158C2×#11758196—21no—
159C2×#11758196—21no—
160C2×#11758196—21no—
161C2×#11758196D411yescharacteristic
162C4⋊C4×D61—21no—
163C4⋊C4×D61C2×C411yescharacteristic, complemented
164C4⋊C4×D61C2×C411yescharacteristic, complemented
165C2×C22⋊Dic61D411yescharacteristic
166C2×#11758198—21no—
167C2×#11758198—21no—
168C2×#11758198D411yescharacteristic
169C22⋊C4×D61—21no—
170C22⋊C4×D61—21no—
171C22⋊C4×D61—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—
182#14519687—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684—21no—
186#14519684C2311yescharacteristic
187#14519684C2311yescharacteristic
188C2×#41×C61C2×C411yescharacteristic, complemented
189C23×C4×C61C2311yescharacteristic
190C2×M16×C61—21no—
191#123×C61—21no—
192C22⋊Q8×C61C2×C411yescharacteristic, complemented
193C22⋊Q8×C61C2311yescharacteristic
194#121×C61C2×C411yescharacteristic, complemented
195#121×C61C2311yescharacteristic
196#120×C61—21no—
197C4×D4×C61—21no—
198C4×D4×C61—21no—
199#117×C61C2×C411yescharacteristic, complemented
200C2×C4⋊C4×C61—21no—
201C2×C22⋊C4×C61—21no—
202C22⋊C8×C61—21no—
203C22⋊C8×C61C2311yescharacteristic
204C22⋊C8×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206#95×C61C2311yescharacteristic
207C24×C61C2×D411yescharacteristic
208C23×D61—21no—
209C23×D61C2×D411yescharacteristic
210#41×C61—81no—
211C2×Q8×C61C22×C411yescharacteristic
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61C22×C411yescharacteristic
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—81no—
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C22×C411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2411yescharacteristic
226C2×C22⋊D61—22no—
227C2×C22⋊D61—22no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61C22⋊C411yescharacteristic
234C2×C22⋊D61C22⋊C411yescharacteristic
235C2×C22⋊D61C22⋊C411yescharacteristic
236C2×C22⋊D61C22⋊C411yescharacteristic
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—42no—
241C22×Dic61—42no—
242C22×Dic61—81no—
243C22×Dic61C2×D411yescharacteristic
244C22×Dic61C2×D411yescharacteristic
245C22×Dic61C2×D411yescharacteristic
246Q8×D61—81no—
247D4×D61—42no—
248D4×D61—42no—
249D4×D61—81no—
250#11758222—81no—
251C2×D244—21no—
252C2×D244C22×C411yescharacteristic
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—42no—
259C2×C4×D61—42no—
260C2×C4×D61—81no—
261C2×C4×D61—81no—
262C2×C4×D61C22×C411yescharacteristic
263C2×C4×D61C22×C411yescharacteristic
264C2×C4×D61C2×D411yescharacteristic
265C2×C4×D61C2×D411yescharacteristic
266C2×Dic122—21no—
267C2×Dic122C22×C411yescharacteristic
268M16×C61—81no—
269C2×C8×C61—21no—
270C2×C8×C61—21no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61—81no—
274C4⋊C4×C61C22×C411yescharacteristic
275C4⋊C4×C61C22×C411yescharacteristic
276C22⋊C4×C61—21no—
277C22⋊C4×C61—21no—
278C22⋊C4×C61—21no—
279C22⋊C4×C61—21no—
280C22⋊C4×C61—21no—
281C22⋊C4×C61—42no—
282C42×C61—21no—
283C22⋊Dic61—21no—
284C22⋊Dic61—21no—
285C22⋊Dic61—21no—
286C22⋊Dic61—21no—
287C22⋊Dic61—21no—
288C22⋊Dic61—21no—
289C22⋊Dic61—21no—
290C22⋊Dic61C22⋊C411yescharacteristic
291C22⋊Dic61C22⋊C411yescharacteristic
292C22⋊Dic61C22⋊C411yescharacteristic
293C22⋊Dic61C22⋊C411yescharacteristic
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—42no—
303#11758198C22⋊C411yescharacteristic
304#11758198C22⋊C411yescharacteristic
305#11758198C22⋊C411yescharacteristic
306#11758198C22⋊C411yescharacteristic
307C4⋊Dic61—21no—
308C4⋊Dic61—21no—
309C4⋊Dic61—21no—
310C4⋊Dic61—21no—
311C4⋊Dic61C22×C411yescharacteristic
312C4⋊Dic61C22×C411yescharacteristic
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—42no—
322#11758196—42no—
323#11758196—81no—
324#11758196C22⋊C411yescharacteristic
325#11758196C22⋊C411yescharacteristic
326#11758196C22⋊C411yescharacteristic
327#11758196C22⋊C411yescharacteristic
328C4×Dic61—21no—
329C4×Dic61—21no—
330C4×Dic61—21no—
331C4×Dic61—42no—
332C4×Dic61C22×C411yescharacteristic
333C4×Dic61C22×C411yescharacteristic
334C4×Dic61C2×D411yescharacteristic
335C4×Dic61C2×D411yescharacteristic
336#11758194—81no—
337C2×#92418—21no—
338C2×#92418—21no—
339C8×D61—81no—
340C8×D61—81no—
341C23×C61—21no—
342C23×C61—21no—
343C23×C61—21no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61C2×C22⋊C411yescharacteristic
347C23×C61C2×C22⋊C411yescharacteristic
348C23×C61C22×D411yescharacteristic
349C22×D61—21no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—42no—
353C22×D61—81no—
354C22×D61—81no—
355C22×D61C2×C22⋊C411yescharacteristic
356C22×D61C2×C22⋊C411yescharacteristic
357C22×D61AGL(1,ℤ/8)12yes—
358C22×D61#13712yes—
359Q8×C61—41no—
360D4×C61—41no—
361D4×C61—41no—
362D4×C61—41no—
363D4×C61—81no—
364D4×C61—81no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
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—81no—
381C2×C4×C61C2×C22⋊C411yescharacteristic
382C2×C4×C61C2×C22⋊C411yescharacteristic
383C2×C4×C61C23×C411yescharacteristic
384C2×C4×C61C22×D411yescharacteristic
385C22⋊D61—22no—
386C22⋊D61—22no—
387C22⋊D61—22no—
388C22⋊D61—22no—
389C22⋊D61—41no—
390C22⋊D61—41no—
391C22⋊D61—42no—
392C22⋊D61—81no—
393C22⋊D61—81no—
394C22⋊D61—81no—
395C2×Dic61—21no—
396C2×Dic61—21no—
397C2×Dic61—22no—
398C2×Dic61—21no—
399C2×Dic61—21no—
400C2×Dic61—21no—
401C2×Dic61—41no—
402C2×Dic61—41no—
403C2×Dic61—41no—
404C2×Dic61—41no—
405C2×Dic61—41no—
406C2×Dic61—41no—
407C2×Dic61—41no—
408C2×Dic61—81no—
409C2×Dic61—84no—
410C2×Dic61C2×C22⋊C411yescharacteristic
411C2×Dic61C2×C22⋊C411yescharacteristic
412C2×Dic61C2×C22⋊C411yescharacteristic
413C2×Dic61C2×C22⋊C411yescharacteristic
414C2×Dic61C2×C22⋊C411yescharacteristic
415C2×Dic61C2×C22⋊C411yescharacteristic
416D244—41no—
417D244—42no—
418C4×D61—41no—
419C4×D61—41no—
420C4×D61—41no—
421C4×D61—41no—
422C4×D61—42no—
423C4×D61—81no—
424C4×D61—81no—
425C4×D61—81no—
426C4×D61—81no—
427C4×D61—84no—
428Dic122—41no—
429Dic122—81no—
430C8×C61—41no—
431C8×C61—41no—
432#92418—41no—
433#92418—41no—
434#17622—611nomaximal, Sylow
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—41no—
446C22×C61—41no—
447C22×C61—41no—
448C22×C61C22×C22⋊C411yescharacteristic
449C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
450C22×C61C2×#13711yescharacteristic
451C2×D61—21no—
452C2×D61—21no—
453C2×D61—21no—
454C2×D61—21no—
455C2×D61—42no—
456C2×D61—42no—
457C2×D61—41no—
458C2×D61—41no—
459C2×D61—41no—
460C2×D61—162no—
461C2×D61#41712yes—
462C2×D61#41712yes—
463C4×C61—21no—
464C4×C61—21no—
465C4×C61—21no—
466C4×C61—21no—
467C4×C61—41no—
468C4×C61—41no—
469C4×C61—41no—
470C4×C61—81no—
471C4×C61—81no—
472Dic61—21no—
473Dic61—21no—
474Dic61—21no—
475Dic61—21no—
476Dic61—21no—
477Dic61—21no—
478Dic61—42no—
479Dic61—41no—
480Dic61—41no—
481Dic61—41no—
482Dic61—81no—
483#3505—611no—
484#2973—611no—
485#2349—611no—
486#1520—611no—
487#1519—611no—
488#1513—611no—
489#1513D6111yescharacteristic, complemented
490#1512—611no—
491#1512—611no—
492#1509—611no—
493#1509—611no—
494#1504—611no—
495#1504—611no—
496C2×#328—611no—
497C2×#327—611no—
498C2×C61—21no—
499C2×C61—21no—
500C2×C61—41no—
501C2×C61—41no—
502C2×C61—81no—
503C2×C61#288311yescharacteristic
504C2×C61C2×#41711yescharacteristic
505C2×C61#290111yescharacteristic
506D61—22no—
507D61—22no—
508D61—81no—
509#553—611no—
510#553—611no—
511#553—1221no—
512#553—1221no—
513#552—611no—
514#552—611no—
515#551—1221no—
516#551—1221no—
517#548—611no—
518#548—611no—
519#546—611no—
520#546—611no—
521#539—1221no—
522#538—1221no—
523#534—1221no—
524#529—611no—
525#529—611no—
526#525—611no—
527#525C2×D6111yescharacteristic
528C2×C22⋊Q8—611no—
529C2×#121—611no—
530#518—1221no—
531C2×C4×D4—611no—
532C2×C4×D4—1221no—
533#435—1221no—
534#435—1221no—
535#435—1221no—
536#435—1221no—
537#432—611no—
538#432—611no—
539#407—611no—
540#407C2×D6111yescharacteristic, complemented
541C2×C22⋊C8—611no—
542C2×C22⋊C8—611no—
543#389—1221no—
544#385—1221no—
545#385—1221no—
546#382—611no—
547#380—611no—
548#380C2×D6111yescharacteristic, complemented
549C4×C4⋊C4—611no—
550C2×#95—611no—
551C2×#95—611no—
552#328—611no—
553#328—611no—
554#328—611no—
555#328—611no—
556#328—611no—
557#328—611no—
558#328C2×D6111yescharacteristic, complemented
559#328C2×D6111yescharacteristic, complemented
560#327—611no—
561#327—611no—
562#327—611no—
563#327—611no—
564#327—611no—
565#327—611no—
566#327C2×D6111yescharacteristic
567#327C2×D6111yescharacteristic
568C61#1762211yescharacteristic, complemented, Sylow
569C2×#41—611no—
570C2×#41C4×D6111yescharacteristic, complemented
571C22×Q8—611no—
572C22×D4—611no—
573C22×D4—611no—
574C22×D4—1221no—
575C23×C4—611no—
576C23×C4—1221no—
577C23×C4—1221no—
578C23×C4C22×D6111yescharacteristic
579C2×M16—21no—
580C2×M16—1221no—
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#125—611no—
590#125—611no—
591#125—1221no—
592#125—1221no—
593#124—611no—
594#124—611no—
595#124—1221no—
596#124—1221no—
597#123—21no—
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—611no—
608C22⋊Q8—611no—
609C22⋊Q8—611no—
610C22⋊Q8—611no—
611C22⋊Q8—1221no—
612C22⋊Q8—1221no—
613C22⋊Q8—1221no—
614C22⋊Q8—1221no—
615C22⋊Q8C4×D6111yescharacteristic, complemented
616C22⋊Q8C22×D6111yescharacteristic
617#121—611no—
618#121—611no—
619#121—611no—
620#121—611no—
621#121—1221no—
622#121—1221no—
623#121—1221no—
624#121—1221no—
625#121—1221no—
626#121—1221no—
627#121—1221no—
628#121—1221no—
629#121C4×D6111yescharacteristic, complemented
630#121C22×D6111yescharacteristic
631#120—21no—
632#120—1221no—
633#120—1221no—
634#120—1221no—
635C4×Q8—611no—
636C4×Q8—611no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—611no—
640C4×D4—611no—
641C4×D4—611no—
642C4×D4—611no—
643C4×D4—611no—
644C4×D4—611no—
645C4×D4—611no—
646C4×D4—611no—
647C4×D4—611no—
648C4×D4—611no—
649C4×D4—1221no—
650C4×D4—1221no—
651C4×D4—1221no—
652C4×D4—1221no—
653C4×D4—1221no—
654C4×D4—1221no—
655C4×D4—1221no—
656C4×D4—1221no—
657C4×D4—2444no—
658#117—611no—
659#117—1221no—
660#117—1221no—
661#117—1221no—
662#117—1221no—
663#117C4×D6111yescharacteristic, complemented
664C2×C4⋊C4—21no—
665C2×C4⋊C4—611no—
666C2×C4⋊C4—611no—
667C2×C4⋊C4—611no—
668C2×C4⋊C4—1221no—
669C2×C4⋊C4—1221no—
670C2×C4⋊C4—1221no—
671C2×C4⋊C4—1221no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—611no—
674C2×C22⋊C4—611no—
675C2×C22⋊C4—1221no—
676C2×C22⋊C4—1221no—
677C2×C22⋊C4—1221no—
678C2×C22⋊C4—1221no—
679C2×C22⋊C4—1221no—
680C2×C42—611no—
681C2×C42—1221no—
682C4⋊C8—1221no—
683C4⋊C8—1221no—
684C22⋊C8—21no—
685C22⋊C8—611no—
686C22⋊C8—611no—
687C22⋊C8—1221no—
688C22⋊C8—1221no—
689C22⋊C8—1221no—
690C22⋊C8C22×D6111yescharacteristic
691C22⋊C8C22×D6111yescharacteristic
692#97—1221no—
693#97—1221no—
694#95—611no—
695#95—611no—
696#95—1221no—
697#95—1221no—
698#95—1221no—
699#95C22×D6111yescharacteristic
700#95C22×D6111yescharacteristic
701C24—611no—
702C24—1221no—
703C24D4×D6111yescharacteristic
704#41—81no—
705#41—4881no—
706C2×Q8—611no—
707C2×Q8—1221no—
708C2×Q8—4881no—
709C2×Q8C2×C4×D6111yescharacteristic
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—611no—
714C2×D4—611no—
715C2×D4—611no—
716C2×D4—611no—
717C2×D4—611no—
718C2×D4—1221no—
719C2×D4—1221no—
720C2×D4—1222no—
721C2×D4—1222no—
722C2×D4—1221no—
723C2×D4—1221no—
724C2×D4—1221no—
725C2×D4—1221no—
726C2×D4—4881no—
727C2×D4—2442no—
728C2×D4—2442no—
729C2×D4C2×C4×D6111yescharacteristic
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—81no—
734C22×C4—611no—
735C22×C4—611no—
736C22×C4—611no—
737C22×C4—611no—
738C22×C4—611no—
739C22×C4—611no—
740C22×C4—611no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—4881no—
750C22×C4—4881no—
751C22×C4—4881no—
752C22×C4—2442no—
753C22×C4—2442no—
754C22×C4—2442no—
755C22×C4—2442no—
756C22×C4C2×C4×D6111yescharacteristic
757C22×C4C2×C4×D6111yescharacteristic
758C22×C4D4×D6111yescharacteristic
759C22×C4D4×D6111yescharacteristic
760C22×C4D4×D6111yescharacteristic
761C22×C4C23×D6111yescharacteristic
762M16—81no—
763M16—4881no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—1221no—
767C2×C8—1221no—
768C2×C8—4881no—
769C2×C8—4881no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—81no—
773C4⋊C4—611no—
774C4⋊C4—611no—
775C4⋊C4—611no—
776C4⋊C4—611no—
777C4⋊C4—611no—
778C4⋊C4—611no—
779C4⋊C4—1221no—
780C4⋊C4—1221no—
781C4⋊C4—1221no—
782C4⋊C4—1221no—
783C4⋊C4—1221no—
784C4⋊C4—1221no—
785C4⋊C4—1221no—
786C4⋊C4—1221no—
787C4⋊C4—1221no—
788C4⋊C4—1221no—
789C4⋊C4—1221no—
790C4⋊C4—1221no—
791C4⋊C4—4881no—
792C4⋊C4—2442no—
793C4⋊C4—2442no—
794C4⋊C4C2×C4×D6111yescharacteristic
795C4⋊C4C2×C4×D6111yescharacteristic
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—611no—
803C22⋊C4—611no—
804C22⋊C4—611no—
805C22⋊C4—611no—
806C22⋊C4—611no—
807C22⋊C4—611no—
808C22⋊C4—611no—
809C22⋊C4—611no—
810C22⋊C4—1221no—
811C22⋊C4—1221no—
812C22⋊C4—1221no—
813C22⋊C4—1221no—
814C22⋊C4—1221no—
815C22⋊C4—1221no—
816C22⋊C4—1221no—
817C22⋊C4—1221no—
818C22⋊C4—1221no—
819C22⋊C4—1221no—
820C22⋊C4—1221no—
821C22⋊C4—1221no—
822C22⋊C4—1221no—
823C22⋊C4—1221no—
824C22⋊C4—1221no—
825C22⋊C4—2442no—
826C42—21no—
827C42—611no—
828C42—611no—
829C42—611no—
830C42—611no—
831C42—1221no—
832C42—1221no—
833C42—1221no—
834C42—2442no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—41no—
839C23—41no—
840C23—611no—
841C23—611no—
842C23—612no—
843C23—612no—
844C23—1221no—
845C23—4881no—
846C23—4881no—
847C23—2441no—
848C23—2441no—
849C23—2442no—
850C23C22⋊C4×D6111yescharacteristic
851C23C22⋊C4×D6111yescharacteristic
852C23C2×D4×D6111yescharacteristic
853Q8—41no—
854Q8—4881no—
855Q8—2441no—
856D4—41no—
857D4—41no—
858D4—41no—
859D4—81no—
860D4—81no—
861D4—1222no—
862D4—1222no—
863D4—1222no—
864D4—1222no—
865D4—4881no—
866D4—4881no—
867D4—4881no—
868D4—2441no—
869D4—2442no—
870D4—2442no—
871D4—2441no—
872D4—2441no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—81no—
889C2×C4—611no—
890C2×C4—611no—
891C2×C4—611no—
892C2×C4—611no—
893C2×C4—611no—
894C2×C4—611no—
895C2×C4—1221no—
896C2×C4—1221no—
897C2×C4—1222no—
898C2×C4—1221no—
899C2×C4—1221no—
900C2×C4—1221no—
901C2×C4—4881no—
902C2×C4—4881no—
903C2×C4—4881no—
904C2×C4—4881no—
905C2×C4—4884no—
906C2×C4—4881no—
907C2×C4—4884no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2442no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4C22⋊C4×D6111yescharacteristic
921C2×C4C22⋊C4×D6111yescharacteristic
922C2×C4C22×C4×D6111yescharacteristic
923C2×C4C2×D4×D6111yescharacteristic
924C8—41no—
925C8—41no—
926C8—2441no—
927C8—2441no—
928C22—21no—
929C22—21no—
930C22—21no—
931C22—21no—
932C22—21no—
933C22—21no—
934C22—21no—
935C22—21no—
936C22—42no—
937C22—42no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—612no—
942C22—612no—
943C22—1221no—
944C22—1221no—
945C22—1221no—
946C22—1221no—
947C22—9762no—
948C22—2442no—
949C22—2442no—
950C22—2441no—
951C22—2441no—
952C22—2441no—
953C22C2×C22⋊C4×D6111yescharacteristic
954C22AGL(1,ℤ/8)×D6111yescharacteristic
955C22#137×D6111yescharacteristic
956C4—21no—
957C4—21no—
958C4—21no—
959C4—21no—
960C4—41no—
961C4—41no—
962C4—41no—
963C4—81no—
964C4—81no—
965C4—1221no—
966C4—1221no—
967C4—1221no—
968C4—1221no—
969C4—1221no—
970C4—1221no—
971C4—4881no—
972C4—2442no—
973C4—2441no—
974C4—2441no—
975C4—2441no—
976C2—21no—
977C2—21no—
978C2—41no—
979C2—41no—
980C2—81no—
981C2—1222no—
982C2—1222no—
983C2—4881no—
984C2#2145427711yescharacteristic
985C2#417×D6111yescharacteristic
986C2#2145436511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1513C2
socleC22×C61C22×C22⋊C4
prime radical#21459647C2
cosocleC22×C4×C61C24
hypercenter#1513D61
hypocenterC61#17622
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1513

Complements

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

NH ≅ G/Ntype
2. #21454846C2semidirect
3. #21448723C2semidirect
4. #21444389C2semidirect
5. #21444385C2semidirect
6. #21444360C2semidirect
7. #21444356C2semidirect
8. #21444354C2semidirect
9. #21444343C2semidirect
10. #21444341C2semidirect
11. #21444324C2semidirect
12. #21444323C2semidirect
13. #328×D61C2semidirect
14. #327×D61C2semidirect
15. C61×#1513C2semidirect
17. #16840459C4semidirect
19. #16840456C4semidirect
20. #16840451C4semidirect
21. #16840446C4semidirect
24. #16840422C4semidirect
25. #16840419C4semidirect
26. #16840409C4semidirect
27. #16840400C4semidirect
43. #16839816C22semidirect
44. #16839816C22semidirect
45. #16839726C22semidirect
51. #16839626C22semidirect
53. #16839613C22semidirect
54. C2×#14519684C22semidirect
56. #16839500C22semidirect
57. #16839500C22semidirect
58. #16839499C22semidirect
59. #16839499C22semidirect
60. #16839498C22semidirect
61. #16839498C22semidirect
69. C61×#407C22semidirect
70. C61×#380C22semidirect
71. C61×#328C22semidirect
72. C61×#328C22semidirect
75. C2×#11758222C2×C4semidirect
76. C2×Q8×D61C2×C4semidirect
79. C2×D4×D61C2×C4semidirect
93. #14519768C2×C4semidirect
94. #14519768C2×C4semidirect
96. #14519766C2×C4semidirect
98. #14519764C2×C4semidirect
109. #14519757C2×C4semidirect
111. #14519756C2×C4semidirect
116. #14519753C2×C4semidirect
117. #14519752C2×C4semidirect
118. #14519751C2×C4semidirect
128. #14519748C2×C4semidirect
132. Q8×Dic61C2×C4semidirect
133. #14519742C2×C4semidirect
136. D4×Dic61C2×C4semidirect
138. #14519739C2×C4semidirect
153. #14519736C2×C4semidirect
163. C4⋊C4×D61C2×C4semidirect
164. C4⋊C4×D61C2×C4semidirect
188. C2×#41×C61C2×C4semidirect
192. C22⋊Q8×C61C2×C4semidirect
194. #121×C61C2×C4semidirect
199. #117×C61C2×C4semidirect
489. #1513D61semidirect
540. #407C2×D61semidirect
548. #380C2×D61semidirect
558. #328C2×D61semidirect
559. #328C2×D61semidirect
568. C61#17622semidirect
570. C2×#41C4×D61semidirect
615. C22⋊Q8C4×D61semidirect
629. #121C4×D61semidirect
663. #117C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214596472
#214548462
#214487232
#214443892
#214443852
#214443602
#214443562
#214443542
#214443432
#214443412
#214443242
#214443232
#328×D612
#327×D612
C61×#15132
#1762261