Finite Group Databasebeta

← #30615704

Subgroups — #30615704

Order 15616.

1954 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519856C211yesmaximal, characteristic, complemented
2C2×#16840761C212yesmaximal, complemented
3D61⋊#407C211yesmaximal, characteristic, complemented
4#21461838C214yesmaximal, complemented
5#21461836C214yesmaximal, complemented
6#21461498C212yesmaximal, complemented
7C2×#16840275C211yesmaximal, characteristic
8C2×D61⋊M16C2212yes—
9C2×#14519856—28no—
10C2×#14519856—21no—
11C2×#14519856—21no—
12C2×#14519856C2212yes—
13C2×#14519856C2212yescomplemented
14C22×C4⋊#6923—21no—
15C22×C22⋊#6923—21no—
16C22×C4×#6923C2212yescomplemented
17#16840761—28no—
18C2×#14519842C2218yescomplemented
19#16840734—21no—
20#16840733C2212yescomplemented
21#16840733C2212yescomplemented
22#16840732—21no—
23D61⋊(C22⋊C8)—21no—
24D61⋊(C22⋊C8)—21no—
25#16840632C2218yescomplemented
26C22×#11758226C2211yescharacteristic
27C23×C4×D61C2211yescharacteristic
28#16840275—21no—
29#16840275—21no—
30#16840275—21no—
31#16840275—21no—
32#16840275C412yescomplemented
33#16840275C412yescomplemented
34#16840275C2212yes—
35#16840275C2212yes—
36C2×#14519762—21no—
37C2×#14519753C411yescharacteristic, complemented
38C2×#14519752C411yescharacteristic, complemented
39C2×#14519751C411yescharacteristic, complemented
40C2×#14519747—21no—
41C2×#14519739—21no—
42C2×#14519737—21no—
43C2×#14519735C2211yescharacteristic
44C2×C22⋊Q8×C61C411yescharacteristic, complemented
45C23×#6923—22no—
46C2×#11758213C2314yes—
47D61⋊M16—24no—
48D61⋊M16—24no—
49C2×#11758217—22no—
50C2×D61⋊C8—22no—
51#14519856—28no—
52#14519856—28no—
53#14519856—24no—
54#14519856—28no—
55#14519856D418yescomplemented
56C2×C4⋊#6923—28no—
57C2×C4⋊#6923—22no—
58C2×C4⋊#6923—22no—
59C2×C22⋊#6923—28no—
60C2×C22⋊#6923—22no—
61C2×C22⋊#6923—22no—
62C2×C4×#6923—22no—
63C2×C4×#6923—28no—
64C2×C4×#6923C2314yes—
65#14519842—216no—
66#14519834—22no—
67#14519834—22no—
68C22⋊#92420—22no—
69C22⋊#92420—22no—
70C24×D61D411yescharacteristic
71C2×#11758226—21no—
72C2×#11758226—21no—
73C2×#11758226—24no—
74C2×#11758226—24no—
75C2×#11758226C2×C412yescomplemented
76C2×#11758226C2312yes—
77C22×D244—21no—
78C22×D244—21no—
79C22×D244C2×C411yescharacteristic, complemented
80C22×C22⋊D61—21no—
81C23×Dic61D411yescharacteristic
82C22×C4×D61—24no—
83C22×C4×D61—24no—
84C22×C4×D61—21no—
85C22×C4×D61C2×C411yescharacteristic
86C22×C4×D61C2×C411yescharacteristic
87C22×C4×D61C2×C411yescharacteristic
88C22×C4×D61D411yescharacteristic
89C22×C4×D61D411yescharacteristic
90C22×C4×D61D411yescharacteristic
91C22×C4×D61D411yescharacteristic
92C22×C4×D61D411yescharacteristic
93C22×C4×D61D411yescharacteristic
94C22×C4×D61C2311yescharacteristic
95C22×C4×D61C2311yescharacteristic
96C22×C4×D61C2311yescharacteristic
97#14519762—22no—
98#14519762—22no—
99#14519762—22no—
100#14519762—22no—
101#14519753—21no—
102#14519753—21no—
103#14519753C2×C412yes—
104#14519753C2×C412yescomplemented
105#14519752—21no—
106#14519752—21no—
107#14519752C2×C412yes—
108#14519752C2×C412yescomplemented
109#14519751—21no—
110#14519751—21no—
111#14519751C2×C412yes—
112#14519751C2×C412yescomplemented
113#14519747—22no—
114#14519747—22no—
115#14519747—22no—
116#14519747—22no—
117#14519739—22no—
118#14519739—22no—
119#14519739—22no—
120#14519739—22no—
121#14519737—22no—
122#14519737—22no—
123#14519737—22no—
124#14519737—22no—
125#14519735—21no—
126#14519735—21no—
127#14519735C2×C412yescomplemented
128#14519735C2312yes—
129C2×C4⋊Dic61C2×C411yescharacteristic, complemented
130C2×#11758196—21no—
131C2×#11758198—21no—
132C2×#11758198—21no—
133C2×#11758198—21no—
134C2×#11758198—21no—
135C2×C4×Dic61—21no—
136C22×Q8×C61C2×C411yescharacteristic, complemented
137C23×C4×C61C2×C411yescharacteristic
138C22⋊Q8×C61—21no—
139C22⋊Q8×C61—21no—
140C22⋊Q8×C61C2×C412yes—
141C22⋊Q8×C61C2×C412yescomplemented
142C2×C4⋊C4×C61—21no—
143C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
144C2×C22⋊C4×C61—21no—
145C24×C61C22⋊C411yescharacteristic
146C23×D61—22no—
147C23×D61—22no—
148C23×D61—21no—
149C23×D61—42no—
150C23×D61—42no—
151C23×D61C22⋊C411yescharacteristic
152C23×D61C22⋊C411yescharacteristic
153C23×D61C22⋊C411yescharacteristic
154C23×D61C2×D411yescharacteristic
155C23×D61C2×D411yescharacteristic
156C23×D61C2×D411yescharacteristic
157C22×#6923—28no—
158C22×#6923—24no—
159C22×#6923—44no—
160C22×#6923—44no—
161C2×Q8×C61—21no—
162C2×Q8×C61—24no—
163C2×Q8×C61C22×C412yes—
164C22×C4×C61—24no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61C22⋊C411yescharacteristic
168C22×C4×C61C22⋊C411yescharacteristic
169C22×C4×C61C22⋊C411yescharacteristic
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C22×C411yescharacteristic
173C2×C22⋊D61—22no—
174C2×C22⋊D61—22no—
175C2×C22⋊D61—44no—
176C22×Dic61—24no—
177C22×Dic61—21no—
178C22×Dic61C22⋊C411yescharacteristic
179C22×Dic61C22⋊C411yescharacteristic
180C22×Dic61C22⋊C411yescharacteristic
181C22×Dic61C2×D411yescharacteristic
182C22×Dic61C2×D411yescharacteristic
183C22×Dic61C2×D411yescharacteristic
184#11758226—28no—
185#11758226—24no—
186#11758226—24no—
187#11758226—42no—
188#11758226—44no—
189#11758226—42no—
190C2×D244—24no—
191C2×D244—22no—
192C2×D244—22no—
193C2×D244—22no—
194C2×D244—22no—
195C2×D244—21no—
196C2×D244—44no—
197C2×D244—42no—
198C2×D244—42no—
199C2×D244C22×C412yes—
200C2×C4×D61—22no—
201C2×C4×D61—22no—
202C2×C4×D61—24no—
203C2×C4×D61—24no—
204C2×C4×D61—24no—
205C2×C4×D61—24no—
206C2×C4×D61—22no—
207C2×C4×D61—22no—
208C2×C4×D61—24no—
209C2×C4×D61—24no—
210C2×C4×D61—22no—
211C2×C4×D61—22no—
212C2×C4×D61—22no—
213C2×C4×D61—22no—
214C2×C4×D61—22no—
215C2×C4×D61—22no—
216C2×C4×D61—22no—
217C2×C4×D61—22no—
218C2×C4×D61—44no—
219C2×C4×D61C22⋊C411yescharacteristic
220C2×C4×D61C22⋊C411yescharacteristic
221C2×C4×D61C22⋊C411yescharacteristic
222C2×C4×D61C22⋊C411yescharacteristic
223C2×C4×D61C22⋊C411yescharacteristic
224C2×C4×D61C22⋊C411yescharacteristic
225C2×C4×D61C22×C411yescharacteristic
226C2×C4×D61C22×C411yescharacteristic
227C2×C4×D61C22×C411yescharacteristic
228C2×C4×D61C2×D411yescharacteristic
229C2×C4×D61C2×D411yescharacteristic
230C2×C4×D61C2×D411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61C2×D414yes—
233C2×C4×D61C2×D411yescharacteristic
234C2×C4×D61C2×D411yescharacteristic
235C2×C4×D61#4114yes—
236C2×C4×D61C2411yescharacteristic
237C22⋊#6923—28no—
238C22⋊#6923—28no—
239#11758217—44no—
240C2×#92420—24no—
241C4⋊#6923—28no—
242C4⋊#6923—28no—
243C4×#6923—28no—
244C4×#6923—24no—
245C4×#6923C2×D418yescomplemented
246#11758213—24no—
247#11758213—24no—
248D61⋊C8—44no—
249C4⋊C4×C61—22no—
250C4⋊C4×C61—22no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61C22×C412yes—
253C22⋊C4×C61—22no—
254C22⋊C4×C61—22no—
255#11758198—22no—
256#11758198—22no—
257#11758198—22no—
258#11758198—22no—
259#11758198—22no—
260#11758198—22no—
261#11758198—22no—
262#11758198—22no—
263C4⋊Dic61—21no—
264C4⋊Dic61C22×C412yes—
265#11758196—22no—
266#11758196—22no—
267C4×Dic61—22no—
268C4×Dic61—22no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—41no—
272C23×C61C2×C22⋊C411yescharacteristic
273C23×C61C2×C22⋊C411yescharacteristic
274C23×C61C2×C22⋊C411yescharacteristic
275C22×D61—22no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—22no—
287C22×D61—22no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—48no—
296C22×D61—48no—
297C22×D61—42no—
298C22×D61—42no—
299C22×D61—42no—
300C22×D61C2×C22⋊C411yescharacteristic
301C22×D61C2×C22⋊C411yescharacteristic
302C22×D61C2×C22⋊C411yescharacteristic
303C22×D61#12012yes—
304C22×D61#12312yes—
305C22×D61C22×D411yescharacteristic
306C2×#6923—28no—
307C2×#6923—416no—
308C2×#6923—44no—
309C2×#6923—44no—
310Q8×C61—24no—
311Q8×C61—42no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—42no—
320C2×C4×C61—42no—
321C2×C4×C61C2×C22⋊C411yescharacteristic
322C2×C4×C61C2×C22⋊C411yescharacteristic
323C2×C4×C61C2×C22⋊C411yescharacteristic
324C2×C4×C61C4×D414yes—
325C2×C4×C61C23×C411yescharacteristic
326C22⋊D61—44no—
327C22⋊D61—44no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—42no—
335C2×Dic61C2×C22⋊C411yescharacteristic
336C2×Dic61C2×C22⋊C411yescharacteristic
337C2×Dic61C2×C22⋊C411yescharacteristic
338C2×Dic61#12114yes—
339C2×Dic61C22×D411yescharacteristic
340D244—24no—
341D244—44no—
342D244—42no—
343D244—42no—
344D244—44no—
345D244—44no—
346D244—42no—
347C4×D61—21no—
348C4×D61—21no—
349C4×D61—21no—
350C4×D61—21no—
351C4×D61—22no—
352C4×D61—22no—
353C4×D61—22no—
354C4×D61—22no—
355C4×D61—22no—
356C4×D61—22no—
357C4×D61—22no—
358C4×D61—22no—
359C4×D61—22no—
360C4×D61—22no—
361C4×D61—44no—
362C4×D61—44no—
363C4×D61C4×D414yes—
364C4×D61#12012yes—
365C4×D61#12114yes—
366C4×D61#12312yes—
367C4×D61C22×D412yes—
368C4×D61C2×#4112yes—
369#92420—44no—
370#20979—611nomaximal, Sylow
371C22×C61—21no—
372C22×C61—21no—
373C22×C61—21no—
374C22×C61—21no—
375C22×C61—21no—
376C22×C61—21no—
377C22×C61—21no—
378C22×C61—44no—
379C22×C61#38612yes—
380C22×C61#42112yescomplemented
381C22×C61C22×C22⋊C411yescharacteristic
382C2×D61—24no—
383C2×D61—24no—
384C2×D61—21no—
385C2×D61—21no—
386C2×D61—21no—
387C2×D61—21no—
388C2×D61—21no—
389C2×D61—21no—
390C2×D61—21no—
391C2×D61—21no—
392C2×D61—21no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—44no—
396C2×D61—44no—
397C2×D61—44no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—42no—
401C2×D61—42no—
402C2×D61—42no—
403C2×D61—84no—
404C2×D61#38612yes—
405C2×D61#42112yescomplemented
406C2×D61C2×#12011yescharacteristic
407C2×D61C2×#12311yescharacteristic
408#6923—48no—
409C4×C61—21no—
410C4×C61—21no—
411C4×C61—42no—
412C4×C61—42no—
413C4×C61#38612yes—
414C4×C61C2×C4×D412yes—
415Dic61—21no—
416Dic61—21no—
417Dic61—42no—
418Dic61#38612yes—
419Dic61C2×#12112yes—
420C2×#525—611no—
421C22×#117—611no—
422C2×#421—612no—
423C2×#407—611no—
424#1897—614no—
425#1896—614no—
426#1733—612no—
427C2×C61—22no—
428C2×C61—22no—
429C2×C61—41no—
430C2×C61C2×#38611yescharacteristic
431C2×C61C2×#42111yescharacteristic
432C2×C61C2×#42111yescharacteristic
433D61—21no—
434D61—21no—
435D61—22no—
436D61—22no—
437D61—41no—
438D61—82no—
439C22×#41—611no—
440C24×C4—611no—
441C22×M16—612no—
442#525—612no—
443#525—612no—
444#525—612no—
445#525—612no—
446#525—1221no—
447#525—1221no—
448#525—1221no—
449#525—1221no—
450C2×#123—1221no—
451C2×C22⋊Q8—611no—
452C2×C22⋊Q8#692311yescharacteristic, complemented
453C2×#121—611no—
454C2×#121—611no—
455C2×#120—1221no—
456C2×C4×D4—1221no—
457C2×C4×D4—1221no—
458C2×#117—612no—
459C2×#117—612no—
460C2×#117—611no—
461C2×#117—1228no—
462C2×#117—1221no—
463C2×#117—1221no—
464C22×C4⋊C4—1221no—
465C22×C22⋊C4—1221no—
466C22×C42—612no—
467#421—1228no—
468C2×#104—618no—
469#407—612no—
470#407—612no—
471#407—1221no—
472#407—1221no—
473C2×C22⋊C8—1221no—
474C2×C22⋊C8—1221no—
475#339—618no—
476C61#2097911yescharacteristic, complemented, Sylow
477C25—611no—
478C2×#41—612no—
479C2×#41—612no—
480C2×#41—1221no—
481C2×#41—1221no—
482C2×#41—1224no—
483C2×#41—1224no—
484C22×Q8C2×#692311yescharacteristic, complemented
485C22×D4—611no—
486C22×D4—1221no—
487C22×D4—1221no—
488C22×D4—1221no—
489C23×C4—611no—
490C23×C4—611no—
491C23×C4—611no—
492C23×C4—611no—
493C23×C4—611no—
494C23×C4—611no—
495C23×C4—611no—
496C23×C4—611no—
497C23×C4—611no—
498C23×C4—611no—
499C23×C4—611no—
500C23×C4—611no—
501C23×C4—611no—
502C23×C4—1224no—
503C23×C4—1224no—
504C23×C4—1221no—
505C23×C4—1222no—
506C23×C4C2×#692311yescharacteristic
507C2×M16—614no—
508C2×M16—1222no—
509C2×M16—1224no—
510C2×M16—1224no—
511C22×C8—1222no—
512#123—1222no—
513#123—1222no—
514#123—1222no—
515#123—1222no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—612no—
519C22⋊Q8—612no—
520C22⋊Q8—1221no—
521C22⋊Q8—1221no—
522C22⋊Q8C2×#692312yes—
523C22⋊Q8C2×#692312yescomplemented
524#121—612no—
525#121—612no—
526#121—612no—
527#121—612no—
528#121—1221no—
529#121—1221no—
530#121—1221no—
531#121—1221no—
532#120—1222no—
533#120—1222no—
534#120—1222no—
535#120—1222no—
536C4×D4—1222no—
537C4×D4—1222no—
538C4×D4—1222no—
539C4×D4—1222no—
540C4×D4—1222no—
541C4×D4—1222no—
542C4×D4—1222no—
543C4×D4—1222no—
544#117—618no—
545#117—612no—
546#117—612no—
547#117—1228no—
548#117—1221no—
549#117—1221no—
550#117—1224no—
551#117—1228no—
552#117—1228no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—1222no—
557C2×C4⋊C4—1222no—
558C2×C4⋊C4—1228no—
559C2×C4⋊C4C2×#692311yescharacteristic, complemented
560C2×C22⋊C4—21no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1222no—
565C2×C22⋊C4—1222no—
566C2×C22⋊C4—1228no—
567C2×C22⋊C4—1221no—
568C2×C42—614no—
569C2×C42—1228no—
570C2×C42—1221no—
571C2×C42—1222no—
572#104—12216no—
573C22⋊C8—1222no—
574C22⋊C8—1222no—
575C22⋊C8—1222no—
576C22⋊C8—1222no—
577C24—611no—
578C24—611no—
579C24—611no—
580C24—611no—
581C24—611no—
582C24—611no—
583C24—1222no—
584C24—1222no—
585C24—1221no—
586C24—2442no—
587C24—2442no—
588C24C22⋊#692311yescharacteristic
589#41—1224no—
590#41—1228no—
591#41—1224no—
592#41—2442no—
593#41—2444no—
594#41—2442no—
595C2×Q8—21no—
596C2×Q8—24no—
597C2×Q8C22×#692312yes—
598C2×D4—612no—
599C2×D4—1222no—
600C2×D4—1222no—
601C2×D4—1222no—
602C2×D4—1222no—
603C2×D4—1222no—
604C2×D4—1222no—
605C2×D4—1221no—
606C2×D4—1224no—
607C2×D4—2442no—
608C2×D4—2442no—
609C2×D4—2444no—
610C2×D4—2444no—
611C22×C4—24no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—614no—
618C22×C4—614no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—1222no—
639C22×C4—1222no—
640C22×C4—1222no—
641C22×C4—1222no—
642C22×C4—1224no—
643C22×C4—1224no—
644C22×C4—1224no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—1224no—
648C22×C4—1224no—
649C22×C4—1222no—
650C22×C4—1222no—
651C22×C4—1222no—
652C22×C4—1222no—
653C22×C4—1222no—
654C22×C4—1222no—
655C22×C4—1224no—
656C22×C4—1224no—
657C22×C4—1224no—
658C22×C4—1228no—
659C22×C4—1221no—
660C22×C4—2444no—
661C22×C4—2444no—
662C22×C4—2444no—
663C22×C4C22⋊#692311yescharacteristic
664C22×C4C22⋊#692311yescharacteristic
665C22×C4C22⋊#692311yescharacteristic
666C22×C4C22×#692311yescharacteristic
667C22×C4C22×#692311yescharacteristic
668C22×C4C22×#692311yescharacteristic
669M16—1224no—
670M16—1224no—
671M16—2444no—
672C2×C8—1224no—
673C2×C8—2444no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—21no—
677C4⋊C4—612no—
678C4⋊C4—1222no—
679C4⋊C4—1222no—
680C4⋊C4—1228no—
681C4⋊C4—1228no—
682C4⋊C4—1221no—
683C4⋊C4C22×#692312yes—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—1222no—
687C22⋊C4—1222no—
688C22⋊C4—1222no—
689C22⋊C4—1222no—
690C22⋊C4—1222no—
691C22⋊C4—1222no—
692C22⋊C4—1228no—
693C22⋊C4—1228no—
694C22⋊C4—1222no—
695C22⋊C4—1222no—
696C42—618no—
697C42—1222no—
698C42—1222no—
699C42—1224no—
700C42—1228no—
701C23—22no—
702C23—22no—
703C23—41no—
704C23—611no—
705C23—611no—
706C23—611no—
707C23—612no—
708C23—612no—
709C23—611no—
710C23—1221no—
711C23—1221no—
712C23—1222no—
713C23—1221no—
714C23—1222no—
715C23—1221no—
716C23—1222no—
717C23—1222no—
718C23—1222no—
719C23—1222no—
720C23—1222no—
721C23—1222no—
722C23—1222no—
723C23—2441no—
724C23—2441no—
725C23—2441no—
726C23—2441no—
727C23—2441no—
728C23—2441no—
729C23—2441no—
730C23—2442no—
731C23—2442no—
732C23—2448no—
733C23—2448no—
734C23—2442no—
735C23C2×C22⋊#692311yescharacteristic
736C23C2×C22⋊#692311yescharacteristic
737C23C2×C22⋊#692311yescharacteristic
738Q8—24no—
739Q8—42no—
740D4—1224no—
741D4—2444no—
742D4—2442no—
743D4—2442no—
744D4—2444no—
745D4—2444no—
746D4—2444no—
747D4—2444no—
748D4—2442no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—614no—
759C2×C4—611no—
760C2×C4—611no—
761C2×C4—612no—
762C2×C4—614no—
763C2×C4—612no—
764C2×C4—614no—
765C2×C4—612no—
766C2×C4—612no—
767C2×C4—611no—
768C2×C4—611no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—1222no—
782C2×C4—1222no—
783C2×C4—1222no—
784C2×C4—1222no—
785C2×C4—1222no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—1228no—
789C2×C4—1222no—
790C2×C4—2444no—
791C2×C4—2444no—
792C2×C4—2442no—
793C2×C4—24416no—
794C2×C4—2444no—
795C2×C4—2444no—
796C2×C4C2×C22⋊#692311yescharacteristic
797C2×C4C2×C22⋊#692311yescharacteristic
798C2×C4C2×C22⋊#692311yescharacteristic
799C2×C4D4×#692314yes—
800C2×C4C23×#692311yescharacteristic
801C8—2444no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—44no—
810C22—612no—
811C22—611no—
812C22—611no—
813C22—612no—
814C22—1224no—
815C22—1224no—
816C22—1221no—
817C22—1221no—
818C22—1221no—
819C22—1221no—
820C22—1221no—
821C22—1221no—
822C22—1221no—
823C22—1221no—
824C22—1221no—
825C22—4884no—
826C22—2442no—
827C22—2442no—
828C22—2444no—
829C22—2444no—
830C22—2444no—
831C22—2442no—
832C22—2442no—
833C22—2442no—
834C22—2442no—
835C22—2442no—
836C22#1684071012yes—
837C22#1684076112yescomplemented
838C22C22×C22⋊#692311yescharacteristic
839C4—21no—
840C4—21no—
841C4—42no—
842C4—42no—
843C4—612no—
844C4—612no—
845C4—1221no—
846C4—1221no—
847C4—2448no—
848C4—2442no—
849C4#1684071012yes—
850C4C2×D4×#692312yes—
851C2—22no—
852C2—22no—
853C2—41no—
854C2—1221no—
855C2—1222no—
856C2—1221no—
857C2—1222no—
858C2—4882no—
859C2—2441no—
860C2C2×#1684071011yescharacteristic
861C2D61⋊#42111yescharacteristic
862C2C2×#1684076111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C22⋊Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840275C2
cosocleC2×C4×D61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61#20979
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14519856C2semidirect
2. C2×#16840761C2semidirect
3. D61⋊#407C2semidirect
4. #21461838C2semidirect
5. #21461836C2semidirect
6. #21461498C2semidirect
13. C2×#14519856C22semidirect
16. C22×C4×#6923C22semidirect
18. C2×#14519842C22semidirect
20. #16840733C22semidirect
21. #16840733C22semidirect
25. #16840632C22semidirect
32. #16840275C4semidirect
33. #16840275C4semidirect
37. C2×#14519753C4semidirect
38. C2×#14519752C4semidirect
39. C2×#14519751C4semidirect
44. C2×C22⋊Q8×C61C4semidirect
55. #14519856D4semidirect
75. C2×#11758226C2×C4semidirect
79. C22×D244C2×C4semidirect
104. #14519753C2×C4semidirect
108. #14519752C2×C4semidirect
112. #14519751C2×C4semidirect
127. #14519735C2×C4semidirect
129. C2×C4⋊Dic61C2×C4semidirect
136. C22×Q8×C61C2×C4semidirect
141. C22⋊Q8×C61C2×C4semidirect
143. C2×C4⋊C4×C61C2×C4semidirect
245. C4×#6923C2×D4semidirect
380. C22×C61#421semidirect
405. C2×D61#421semidirect
452. C2×C22⋊Q8#6923semidirect
476. C61#20979semidirect
484. C22×Q8C2×#6923semidirect
523. C22⋊Q8C2×#6923semidirect
559. C2×C4⋊C4C2×#6923semidirect
837. C22#16840761semidirect

Maximal subgroups

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

subgroupindex
C22×#145198562
C2×#168407612
D61⋊#4072
#214618382
#214618362
#214614982
C2×#168402752
#2097961