Finite Group Databasebeta

← #30615706

Subgroups — #30615706

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×#16840760C212yesmaximal, complemented
3D61⋊#407C211yesmaximal, characteristic, complemented
4#21461839C214yesmaximal, complemented
5#21461837C214yesmaximal, complemented
6#21461498C212yesmaximal, complemented
7C2×#16840272C211yesmaximal, 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#16840760—28no—
18C2×#14519841C2218yescomplemented
19#16840734—21no—
20#16840733C2212yescomplemented
21#16840733C2212yescomplemented
22#16840732—21no—
23D61⋊(C22⋊C8)—21no—
24D61⋊(C22⋊C8)—21no—
25#16840632C2218yescomplemented
26C22×#11758224C2211yescharacteristic
27C23×C4×D61C2211yescharacteristic
28#16840272—21no—
29#16840272—21no—
30#16840272—21no—
31#16840272—21no—
32#16840272C412yescomplemented
33#16840272C412yescomplemented
34#16840272C2212yes—
35#16840272C2212yes—
36C2×#14519759—21no—
37C2×#14519757C411yescharacteristic, complemented
38C2×#14519756C411yescharacteristic, complemented
39C2×#14519748C411yescharacteristic, complemented
40C2×#14519745—21no—
41C2×D4×Dic61—21no—
42C2×#14519737—21no—
43C2×#14519735C2211yescharacteristic
44C2×#121×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#14519841—216no—
66#14519834—22no—
67#14519834—22no—
68C22⋊#92420—22no—
69C22⋊#92420—22no—
70C24×D61D411yescharacteristic
71C2×#11758224—24no—
72C2×#11758224—21no—
73C2×#11758224—21no—
74C2×#11758224—24no—
75C2×#11758224C2×C412yescomplemented
76C2×#11758224C2312yes—
77C22×Dic122C2×C411yescharacteristic, complemented
78C22×C22⋊D61—21no—
79C22×C22⋊D61—21no—
80C23×Dic61—21no—
81C23×Dic61D411yescharacteristic
82C22×C4×D61—24no—
83C22×C4×D61—24no—
84C22×C4×D61C2×C411yescharacteristic
85C22×C4×D61C2×C411yescharacteristic
86C22×C4×D61C2×C411yescharacteristic
87C22×C4×D61D411yescharacteristic
88C22×C4×D61D411yescharacteristic
89C22×C4×D61D411yescharacteristic
90C22×C4×D61D411yescharacteristic
91C22×C4×D61D411yescharacteristic
92C22×C4×D61D411yescharacteristic
93C22×C4×D61C2311yescharacteristic
94C22×C4×D61C2311yescharacteristic
95C22×C4×D61C2311yescharacteristic
96#14519759—22no—
97#14519759—22no—
98#14519759—22no—
99#14519759—22no—
100#14519757—21no—
101#14519757—21no—
102#14519757C2×C412yes—
103#14519757C2×C412yescomplemented
104#14519756—21no—
105#14519756—21no—
106#14519756C2×C412yes—
107#14519756C2×C412yescomplemented
108#14519748—21no—
109#14519748—21no—
110#14519748C2×C412yes—
111#14519748C2×C412yescomplemented
112#14519745—22no—
113#14519745—22no—
114#14519745—22no—
115#14519745—22no—
116D4×Dic61—22no—
117D4×Dic61—22no—
118D4×Dic61—22no—
119D4×Dic61—22no—
120#14519737—22no—
121#14519737—22no—
122#14519737—22no—
123#14519737—22no—
124#14519735—21no—
125#14519735—21no—
126#14519735C2×C412yescomplemented
127#14519735C2312yes—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61C2×C411yescharacteristic, complemented
130C2×#11758196—21no—
131C2×C22⋊Dic61—21no—
132C2×C22⋊Dic61—21no—
133C2×#11758198—21no—
134C2×#11758198—21no—
135C2×C4×Dic61—21no—
136C22×D4×C61—21no—
137C22×D4×C61C2×C411yescharacteristic, complemented
138C23×C4×C61C2×C411yescharacteristic
139#121×C61—21no—
140#121×C61—21no—
141#121×C61C2×C412yes—
142#121×C61C2×C412yescomplemented
143C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
144C2×C22⋊C4×C61—21no—
145C24×C61—21no—
146C24×C61C22⋊C411yescharacteristic
147C23×D61—22no—
148C23×D61—22no—
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×D4×C61—22no—
162C2×D4×C61—22no—
163C2×D4×C61—21no—
164C2×D4×C61—24no—
165C2×D4×C61—44no—
166C2×D4×C61C22×C412yes—
167C22×C4×C61—24no—
168C22×C4×C61—21no—
169C22×C4×C61C22⋊C411yescharacteristic
170C22×C4×C61C22⋊C411yescharacteristic
171C22×C4×C61C22⋊C411yescharacteristic
172C22×C4×C61C22×C411yescharacteristic
173C22×C4×C61C22×C411yescharacteristic
174C22×C4×C61C22×C411yescharacteristic
175C2×C22⋊D61—22no—
176C2×C22⋊D61—22no—
177C2×C22⋊D61—22no—
178C2×C22⋊D61—22no—
179C2×C22⋊D61—44no—
180C2×C22⋊D61—42no—
181C2×C22⋊D61—42no—
182C22×Dic61—24no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—44no—
188C22×Dic61C22⋊C411yescharacteristic
189C22×Dic61C22⋊C411yescharacteristic
190C22×Dic61C22⋊C411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192C22×Dic61C2×D411yescharacteristic
193C22×Dic61C2×D411yescharacteristic
194#11758224—28no—
195#11758224—24no—
196#11758224—24no—
197#11758224—42no—
198#11758224—44no—
199#11758224—42no—
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×D61C22⋊C411yescharacteristic
217C2×C4×D61C22⋊C411yescharacteristic
218C2×C4×D61C22⋊C411yescharacteristic
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×D61C2×D411yescharacteristic
226C2×C4×D61C2×D411yescharacteristic
227C2×C4×D61C2×D411yescharacteristic
228C2×C4×D61C2×D411yescharacteristic
229C2×C4×D61C2×D414yes—
230C2×C4×D61C2×D411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61#4114yes—
233C2×C4×D61C2411yescharacteristic
234C2×Dic122—24no—
235C2×Dic122—21no—
236C2×Dic122C22×C412yes—
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—21no—
250C4⋊C4×C61C22×C412yes—
251C22⋊C4×C61—22no—
252C22⋊C4×C61—22no—
253C22⋊Dic61—22no—
254C22⋊Dic61—22no—
255C22⋊Dic61—22no—
256C22⋊Dic61—22no—
257#11758198—22no—
258#11758198—22no—
259#11758198—22no—
260#11758198—22no—
261C4⋊Dic61—21no—
262C4⋊Dic61—22no—
263C4⋊Dic61—22no—
264C4⋊Dic61C22×C412yes—
265#11758196—22no—
266#11758196—22no—
267C4×Dic61—22no—
268C4×Dic61—22no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—41no—
273C23×C61—42no—
274C23×C61—42no—
275C23×C61—42no—
276C23×C61C2×C22⋊C411yescharacteristic
277C23×C61C2×C22⋊C411yescharacteristic
278C23×C61C2×C22⋊C411yescharacteristic
279C22×D61—22no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—48no—
299C22×D61—48no—
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—
310D4×C61—24no—
311D4×C61—44no—
312D4×C61—44no—
313D4×C61—42no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
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—42no—
328C22⋊D61—42no—
329C22⋊D61—44no—
330C22⋊D61—44no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61—44no—
341C2×Dic61—44no—
342C2×Dic61C2×C22⋊C411yescharacteristic
343C2×Dic61C2×C22⋊C411yescharacteristic
344C2×Dic61C2×C22⋊C411yescharacteristic
345C2×Dic61#12114yes—
346C2×Dic61C22×D411yescharacteristic
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×D61C4×D414yes—
362C4×D61#12012yes—
363C4×D61#12114yes—
364C4×D61#12312yes—
365C4×D61C22×D412yes—
366C4×D61C2×#4112yes—
367Dic122—24no—
368Dic122—42no—
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—42no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—84no—
383C22×C61#38612yes—
384C22×C61#42112yescomplemented
385C22×C61C22×C22⋊C411yescharacteristic
386C2×D61—24no—
387C2×D61—24no—
388C2×D61—21no—
389C2×D61—21no—
390C2×D61—21no—
391C2×D61—21no—
392C2×D61—21no—
393C2×D61—21no—
394C2×D61—21no—
395C2×D61—21no—
396C2×D61—21no—
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—44no—
400C2×D61—44no—
401C2×D61—44no—
402C2×D61—42no—
403C2×D61—42no—
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#38612yes—
413C4×C61C2×C4×D412yes—
414Dic61—21no—
415Dic61—21no—
416Dic61—42no—
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×C61—82no—
431C2×C61C2×#38611yescharacteristic
432C2×C61C2×#42111yescharacteristic
433C2×C61C2×#42111yescharacteristic
434D61—21no—
435D61—21no—
436D61—22no—
437D61—22no—
438D61—41no—
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—611no—
453C2×#121—611no—
454C2×#121#692311yescharacteristic, complemented
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×Q8—611no—
485C22×D4—21no—
486C22×D4—1221no—
487C22×D4—1221no—
488C22×D4C2×#692311yescharacteristic, complemented
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—612no—
517C22⋊Q8—612no—
518C22⋊Q8—612no—
519C22⋊Q8—612no—
520C22⋊Q8—1221no—
521C22⋊Q8—1221no—
522C22⋊Q8—1221no—
523C22⋊Q8—1221no—
524#121—21no—
525#121—21no—
526#121—612no—
527#121—612no—
528#121—1221no—
529#121—1221no—
530#121C2×#692312yes—
531#121C2×#692312yescomplemented
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—611no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1222no—
556C2×C4⋊C4—1222no—
557C2×C4⋊C4—1228no—
558C2×C4⋊C4—1221no—
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—21no—
578C24—611no—
579C24—611no—
580C24—611no—
581C24—611no—
582C24—611no—
583C24—611no—
584C24—1222no—
585C24—1222no—
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—612no—
596C2×Q8—1221no—
597C2×Q8—1224no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—21no—
601C2×D4—24no—
602C2×D4—44no—
603C2×D4—1222no—
604C2×D4—1222no—
605C2×D4—1222no—
606C2×D4—1222no—
607C2×D4—2442no—
608C2×D4—2442no—
609C2×D4—2444no—
610C2×D4C22×#692312yes—
611C22×C4—24no—
612C22×C4—21no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—614no—
617C22×C4—614no—
618C22×C4—611no—
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—1222no—
638C22×C4—1222no—
639C22×C4—1222no—
640C22×C4—1222no—
641C22×C4—1224no—
642C22×C4—1224no—
643C22×C4—1224no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4—1224no—
647C22×C4—1224no—
648C22×C4—1222no—
649C22×C4—1222no—
650C22×C4—1222no—
651C22×C4—1222no—
652C22×C4—1224no—
653C22×C4—1222no—
654C22×C4—1222no—
655C22×C4—1224no—
656C22×C4—1224no—
657C22×C4—1228no—
658C22×C4—1221no—
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—21no—
675C4⋊C4—612no—
676C4⋊C4—1222no—
677C4⋊C4—1222no—
678C4⋊C4—1228no—
679C4⋊C4—1228no—
680C4⋊C4—1221no—
681C4⋊C4—1222no—
682C4⋊C4—1222no—
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—22no—
704C23—41no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—611no—
709C23—611no—
710C23—611no—
711C23—612no—
712C23—612no—
713C23—611no—
714C23—1221no—
715C23—1221no—
716C23—1222no—
717C23—1221no—
718C23—1222no—
719C23—1221no—
720C23—1222no—
721C23—1222no—
722C23—1222no—
723C23—1222no—
724C23—1222no—
725C23—1222no—
726C23—2441no—
727C23—2441no—
728C23—2441no—
729C23—2441no—
730C23—2441no—
731C23—2441no—
732C23—2441no—
733C23—2448no—
734C23—2448no—
735C23C2×C22⋊#692311yescharacteristic
736C23C2×C22⋊#692311yescharacteristic
737C23C2×C22⋊#692311yescharacteristic
738Q8—1224no—
739Q8—2442no—
740D4—24no—
741D4—44no—
742D4—44no—
743D4—42no—
744D4—2444no—
745D4—2442no—
746D4—2442no—
747D4—2444no—
748D4—2444no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—42no—
756C2×C4—614no—
757C2×C4—611no—
758C2×C4—611no—
759C2×C4—612no—
760C2×C4—614no—
761C2×C4—612no—
762C2×C4—614no—
763C2×C4—612no—
764C2×C4—612no—
765C2×C4—611no—
766C2×C4—611no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1221no—
772C2×C4—1221no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1222no—
776C2×C4—1222no—
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—1228no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—2444no—
790C2×C4—2444no—
791C2×C4—2442no—
792C2×C4—24416no—
793C2×C4—2444no—
794C2×C4—2444no—
795C2×C4—2442no—
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—42no—
811C22—42no—
812C22—42no—
813C22—84no—
814C22—612no—
815C22—611no—
816C22—611no—
817C22—612no—
818C22—1224no—
819C22—1224no—
820C22—1221no—
821C22—1221no—
822C22—1221no—
823C22—1221no—
824C22—1221no—
825C22—1221no—
826C22—1221no—
827C22—1221no—
828C22—1221no—
829C22—2442no—
830C22—2442no—
831C22—2444no—
832C22—2444no—
833C22—2444no—
834C22—2442no—
835C22—2442no—
836C22#1684071012yes—
837C22#1684076012yescomplemented
838C22C22×C22⋊#692311yescharacteristic
839C4—21no—
840C4—21no—
841C4—42no—
842C4—612no—
843C4—612no—
844C4—1221no—
845C4—1221no—
846C4—2448no—
847C4—2442no—
848C4—2442no—
849C4#1684071012yes—
850C4C2×D4×#692312yes—
851C2—22no—
852C2—22no—
853C2—41no—
854C2—82no—
855C2—1221no—
856C2—1222no—
857C2—1221no—
858C2—1222no—
859C2—2441no—
860C2C2×#1684071011yescharacteristic
861C2C2×#1684076011yescharacteristic
862C2D61⋊#42111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#121×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840272C2
cosocleC2×C4×D61C24
hypercenterC2×#121#6923
hypocenterC61#20979
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#14519856C2semidirect
2. C2×#16840760C2semidirect
3. D61⋊#407C2semidirect
4. #21461839C2semidirect
5. #21461837C2semidirect
6. #21461498C2semidirect
13. C2×#14519856C22semidirect
16. C22×C4×#6923C22semidirect
18. C2×#14519841C22semidirect
20. #16840733C22semidirect
21. #16840733C22semidirect
25. #16840632C22semidirect
32. #16840272C4semidirect
33. #16840272C4semidirect
37. C2×#14519757C4semidirect
38. C2×#14519756C4semidirect
39. C2×#14519748C4semidirect
44. C2×#121×C61C4semidirect
55. #14519856D4semidirect
75. C2×#11758224C2×C4semidirect
77. C22×Dic122C2×C4semidirect
103. #14519757C2×C4semidirect
107. #14519756C2×C4semidirect
111. #14519748C2×C4semidirect
126. #14519735C2×C4semidirect
129. C2×C4⋊Dic61C2×C4semidirect
137. C22×D4×C61C2×C4semidirect
142. #121×C61C2×C4semidirect
143. C2×C4⋊C4×C61C2×C4semidirect
245. C4×#6923C2×D4semidirect
384. C22×C61#421semidirect
405. C2×D61#421semidirect
454. C2×#121#6923semidirect
476. C61#20979semidirect
488. C22×D4C2×#6923semidirect
531. #121C2×#6923semidirect
559. C2×C4⋊C4C2×#6923semidirect
837. C22#16840760semidirect

Maximal subgroups

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

subgroupindex
C22×#145198562
C2×#168407602
D61⋊#4072
#214618392
#214618372
#214614982
C2×#168402722
#2097961