Finite Group Databasebeta

← #29845871

Subgroups — #29845871

Order 15616.

2016 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840512C211yesmaximal, characteristic
2#21448986C212yesmaximal, complemented
3#21448969C211yesmaximal, characteristic
4#21448954C211yesmaximal, characteristic
5#21448937C212yesmaximal, complemented
6#21448934C212yesmaximal, complemented
7#21448931C211yesmaximal, characteristic
8#21448924C212yesmaximal, complemented
9#21448873C212yesmaximal, complemented
10#21448819C212yesmaximal, complemented
11#21448595C212yesmaximal, complemented
12#21448592C212yesmaximal, complemented
13#21448569C212yesmaximal, complemented
14#21448562C212yesmaximal, complemented
15#21448558C212yesmaximal, complemented
16#21448484C211yesmaximal, characteristic
17#21448351C212yesmaximal, complemented
18C4×#14519758C211yesmaximal, characteristic
19C61×#2326C211yesmaximal, characteristic
20#16840512C4116yescomplemented
21C2×#14519775C2212yes—
22C2×#14519770C2212yes—
23C2×#14519770C2212yes—
24C2×#14519769C2212yes—
25C2×#14519758C2211yescharacteristic
26C2×#14519758C2211yescharacteristic
27C2×#14519754C2212yes—
28C2×#14519754C2212yes—
29C2×#14519742C2212yes—
30C22×#11758196C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32#16839669C2212yes—
33#16839668C2212yes—
34#16839666C2212yes—
35#16839666C2212yes—
36#16839659C2212yes—
37#16839658C2212yes—
38#16839658C2212yes—
39#16839657C2212yes—
40#16839657C2212yes—
41#16839657C2212yes—
42#16839657C2212yes—
43#16839657C2212yes—
44#16839656C2212yes—
45#16839656C2212yes—
46#16839656C2212yes—
47#16839656C2212yes—
48#16839655C2212yes—
49#16839655C2212yes—
50#16839650C2212yes—
51#16839650C2212yes—
52#16839649C2212yes—
53#16839647C2212yes—
54#16839647C2212yes—
55#16839646C2212yes—
56#16839646C2212yes—
57#16839646C2212yes—
58#16839645C2212yes—
59#16839645C2212yes—
60#16839644C2212yes—
61#16839644C2212yes—
62#16839644C2212yes—
63#16839643C2212yes—
64#16839643C2212yes—
65#16839643C2212yes—
66#16839643C2212yes—
67#16839643C2212yes—
68#16839642C2211yescharacteristic
69#16839642C2211yescharacteristic
70#16839635C2212yes—
71#16839634C2212yes—
72#16839634C2211yescharacteristic
73#16839634C2211yescharacteristic
74#16839626C2212yes—
75#16839623C2211yescharacteristic
76#16839623C2211yescharacteristic
77#16839620C2212yes—
78C4⋊C4×Dic61C2212yes—
79C4⋊C4×Dic61C2212yes—
80C4⋊C4×Dic61C2212yes—
81C4×#11758196C2212yes—
82C4×#11758196C2212yes—
83C4×#11758196C2212yes—
84C4×#11758196C2212yes—
85#16839613C2212yes—
86#16839613C2212yes—
87#16839613C2212yes—
88C22⋊C4×Dic61C2212yes—
89C22⋊C4×Dic61C2212yes—
90C22⋊C4×Dic61C2212yes—
91C22⋊C4×Dic61C2212yes—
92C4×C22⋊Dic61C2211yescharacteristic
93C4×C22⋊Dic61C2212yes—
94C4×C22⋊Dic61C2211yescharacteristic
95#16839608C2212yes—
96#16839607C2212yes—
97C2×#124×C61C2211yescharacteristic
98C2×C4×Q8×C61C2211yescharacteristic
99C2×C4×D4×C61C2211yescharacteristic
100C61×#391C2211yescharacteristic
101C61×#390C2211yescharacteristic
102C61×#388C2212yes—
103C61×#388C2212yes—
104C61×#385C2212yes—
105C61×#385C2212yes—
106C61×#384C2211yescharacteristic
107C61×#376C2211yescharacteristic
108C22×Dic122C2312yes—
109C23×Dic61C2311yescharacteristic
110C23×Dic61C2311yescharacteristic
111C23×Dic61C2311yescharacteristic
112C23×Dic61C2311yescharacteristic
113#14519775C2×C4116yescomplemented
114#14519770C2×C4116yescomplemented
115#14519770C2×C4116yescomplemented
116#14519769C2×C4116yescomplemented
117#14519758C2×C418yes—
118#14519758C2×C418yes—
119#14519754C2×C4116yescomplemented
120#14519754C2×C4116yescomplemented
121#14519742—44no—
122C2×C4⋊Dic61C2312yes—
123C2×C4⋊Dic61C2312yes—
124C2×C4⋊Dic61C2312yes—
125C2×#11758196—42no—
126C2×#11758196C2312yes—
127C2×#11758196C2312yes—
128C2×#11758196C2312yes—
129C2×#11758196C2312yes—
130C2×#11758196C2312yes—
131C2×#11758196C2312yes—
132C2×#11758196C2312yes—
133C2×#11758196C2312yes—
134C2×#11758196C2312yes—
135C2×#11758196C2312yes—
136C2×#11758196C2312yes—
137C2×#11758196C2312yes—
138C2×#11758196C2312yes—
139C2×#11758196C2312yes—
140C2×C22⋊Dic61C2312yes—
141C2×C22⋊Dic61C2311yescharacteristic
142C2×C22⋊Dic61C2311yescharacteristic
143C2×C22⋊Dic61C2312yes—
144C2×C22⋊Dic61C2312yes—
145C2×C22⋊Dic61C2312yes—
146C2×C22⋊Dic61C2311yescharacteristic
147C2×C22⋊Dic61C2311yescharacteristic
148C2×C4×Dic61—42no—
149C2×C4×Dic61C2312yes—
150C2×C4×Dic61C2312yes—
151C2×C4×Dic61C2312yes—
152C2×C4×Dic61C2312yes—
153C2×C4×Dic61C2312yes—
154C2×C4×Dic61C2312yes—
155C2×C4×Dic61C2312yes—
156C2×C4×Dic61C2312yes—
157C2×C4×Dic61C2312yes—
158C2×C4×Dic61C2312yes—
159C2×C4×Dic61C2312yes—
160C2×C4×Dic61C2312yes—
161#14519684C2312yes—
162#14519684C2312yes—
163#14519684C2312yes—
164#14519684C2312yes—
165#14519684C2312yes—
166#14519684C2312yes—
167#14519684C2312yes—
168#14519684C2312yes—
169#14519684C2312yes—
170#14519684C2312yes—
171#14519684C2312yes—
172#14519684C2312yes—
173#14519684C2312yes—
174#14519684C2312yes—
175#14519684C2312yes—
176#14519684C2312yes—
177#14519684C2312yes—
178#14519684C2312yes—
179#14519684C2312yes—
180#14519684C2312yes—
181#14519684C2312yes—
182#14519684C2312yes—
183C22×Q8×C61C2311yescharacteristic
184C22×D4×C61C2311yescharacteristic
185C23×C4×C61C2311yescharacteristic
186C23×C4×C61C2311yescharacteristic
187#124×C61C2×C418yes—
188C4×Q8×C61—42no—
189C4×D4×C61—42no—
190C2×C4⋊C4×C61C2312yes—
191C2×C4⋊C4×C61C2312yes—
192C2×C4⋊C4×C61C2312yes—
193C2×C4⋊C4×C61C2311yescharacteristic
194C2×C4⋊C4×C61C2311yescharacteristic
195C2×C22⋊C4×C61C2312yes—
196C2×C22⋊C4×C61C2312yes—
197C2×C22⋊C4×C61C2311yescharacteristic
198C2×C22⋊C4×C61C2311yescharacteristic
199C2×C22⋊C4×C61C2312yes—
200C2×C22⋊C4×C61C2312yes—
201C2×C42×C61C2311yescharacteristic
202C2×C42×C61C2311yescharacteristic
203C2×C42×C61C2312yes—
204C2×C42×C61C2311yescharacteristic
205#95×C61C2312yes—
206#95×C61C2312yes—
207#95×C61C2312yes—
208#95×C61C2312yes—
209C24×C61C2411yescharacteristic
210C24×C61C2411yescharacteristic
211C2×Q8×C61—41no—
212C2×Q8×C61—41no—
213C2×Q8×C61C22×C414yes—
214C2×D4×C61—41no—
215C2×D4×C61—41no—
216C2×D4×C61C22×C414yes—
217C22×C4×C61—22no—
218C22×C4×C61—22no—
219C22×C4×C61—42no—
220C22×C4×C61—42no—
221C22×C4×C61C2412yes—
222C22×C4×C61C2411yescharacteristic
223C22×C4×C61C2411yescharacteristic
224C22×C4×C61C2411yescharacteristic
225C22×C4×C61C2412yes—
226C22×C4×C61C2412yes—
227C22×C4×C61C2412yes—
228C22×C4×C61C2411yescharacteristic
229C22×C4×C61C2411yescharacteristic
230C22×Dic61—24no—
231C22×Dic61—41no—
232C22×Dic61—41no—
233C22×Dic61—41no—
234C22×Dic61—41no—
235C22×Dic61—41no—
236C22×Dic61—42no—
237C22×Dic61—41no—
238C22×Dic61C22×C414yes—
239C22×Dic61C22×C414yes—
240C22×Dic61C2412yes—
241C22×Dic61C2412yes—
242C22×Dic61C2412yes—
243C22×Dic61C2412yes—
244C22×Dic61C2412yes—
245C22×Dic61C2412yes—
246C22×Dic61C2412yes—
247C22×Dic61C2412yes—
248C2×Dic122—42no—
249C2×Dic122—42no—
250C2×Dic122C22×C418yes—
251C4⋊C4×C61—24no—
252C4⋊C4×C61—42no—
253C4⋊C4×C61—42no—
254C4⋊C4×C61—41no—
255C4⋊C4×C61—41no—
256C22⋊C4×C61—42no—
257C22⋊C4×C61—42no—
258C22⋊C4×C61—41no—
259C22⋊C4×C61—41no—
260C22⋊C4×C61C22×C418yes—
261C22⋊C4×C61C22×C418yes—
262C42×C61—22no—
263C42×C61—41no—
264C42×C61—42no—
265C42×C61C22×C414yes—
266C22⋊Dic61—24no—
267C22⋊Dic61—42no—
268C22⋊Dic61—41no—
269C22⋊Dic61—41no—
270C22⋊Dic61C22×C418yes—
271C22⋊Dic61C22×C418yes—
272C22⋊Dic61C22×C414yes—
273C22⋊Dic61C22×C414yes—
274C4⋊Dic61—42no—
275C4⋊Dic61C22×C418yes—
276C4⋊Dic61C22×C418yes—
277#11758196—24no—
278#11758196—24no—
279#11758196—42no—
280#11758196—42no—
281#11758196—42no—
282#11758196—42no—
283#11758196—42no—
284#11758196—42no—
285#11758196C22×C418yes—
286#11758196C22×C418yes—
287#11758196C22×C418yes—
288#11758196C22×C418yes—
289#11758196C22×C418yes—
290#11758196C22×C418yes—
291C4×Dic61—24no—
292C4×Dic61—24no—
293C4×Dic61—24no—
294C4×Dic61—42no—
295C4×Dic61—42no—
296C4×Dic61—42no—
297C4×Dic61—42no—
298C4×Dic61—42no—
299C4×Dic61—42no—
300C4×Dic61—42no—
301C4×Dic61—42no—
302C4×Dic61C22×C418yes—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—22no—
311C23×C61C23×C412yes—
312C23×C61C23×C412yes—
313C23×C61C2511yescharacteristic
314Q8×C61—44no—
315D4×C61—44no—
316C2×C4×C61—22no—
317C2×C4×C61—21no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—22no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—44no—
336C2×C4×C61—82no—
337C2×C4×C61C23×C414yes—
338C2×C4×C61C23×C412yes—
339C2×C4×C61C23×C414yes—
340C2×C4×C61H(5,𝔽2)12yes—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—44no—
361C2×Dic61—44no—
362C2×Dic61—44no—
363C2×Dic61—82no—
364C2×Dic61C23×C414yes—
365C2×Dic61C23×C414yes—
366C2×Dic61C23×C414yes—
367C2×Dic61C23×C414yes—
368C2×Dic612−1+414yes—
369Dic122—48no—
370#34514—611nomaximal, Sylow
371C22×C61—22no—
372C22×C61—22no—
373C22×C61—24no—
374C22×C61—24no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—42no—
380C22×C61—42no—
381C22×C61C24×C411yescharacteristic
382C22×C61C2×H(5,𝔽2)11yescharacteristic
383C22×C61C2×2−1+412yes—
384C22×C61#58512yes—
385C22×C61#58511yescharacteristic
386C4×C61—24no—
387C4×C61—22no—
388C4×C61—24no—
389C4×C61—22no—
390C4×C61—42no—
391C4×C61—41no—
392C4×C61—41no—
393C4×C61—41no—
394C4×C61—42no—
395Dic61—24no—
396Dic61—24no—
397Dic61—24no—
398Dic61—24no—
399Dic61—24no—
400Dic61—42no—
401Dic61—42no—
402Dic61—42no—
403C2×#563—611no—
404#2378—612no—
405#2376—611no—
406#2374—611no—
407#2373—612no—
408#2373—612no—
409#2372—611no—
410#2371—612no—
411#2365—612no—
412#2360—612no—
413#2334—612no—
414#2334—612no—
415#2332—612no—
416#2331—612no—
417#2330—612no—
418#2326D6111yescharacteristic
419#2322—611no—
420C4×C22⋊Q8—612no—
421C4×#123—611no—
422C2×C61—42no—
423C2×C61—42no—
424C2×C61C4×H(5,𝔽2)11yescharacteristic
425C2×C61C4×2−1+412yes—
426C2×C61#353311yescharacteristic
427C2×C61#353811yescharacteristic
428C2×C61#356512yes—
429#563—6116no—
430C2×C4⋊Q8—612no—
431C2×#126—612no—
432C2×#126—612no—
433C2×#125—612no—
434C2×#124C2×D6111yescharacteristic
435C2×#123—611no—
436C2×#123—611no—
437C2×C22⋊Q8—612no—
438C2×C22⋊Q8—612no—
439C2×C4×Q8—612no—
440C2×C4×Q8C2×D6111yescharacteristic
441C2×C4×D4C2×D6111yescharacteristic
442C22×C4⋊C4—611no—
443C22×C42—611no—
444#391—612no—
445#391—612no—
446#391—612no—
447#391—612no—
448#391C2×D6111yescharacteristic
449#390C2×D6111yescharacteristic
450#389—612no—
451#389—612no—
452#389—612no—
453#389—612no—
454#389—612no—
455#389—612no—
456#389—612no—
457#389—612no—
458#388—612no—
459#388—612no—
460#388—612no—
461#388—612no—
462#388—612no—
463#388—612no—
464#388—612no—
465#388—612no—
466#388C2×D6112yes—
467#388C2×D6112yes—
468#387—612no—
469#387—612no—
470#387—612no—
471#387—612no—
472#387—612no—
473#387—612no—
474#387—612no—
475#387—612no—
476#387—612no—
477#387—612no—
478#387—612no—
479#387—612no—
480#387—612no—
481#387—612no—
482#387—612no—
483#387—612no—
484#386—611no—
485#386—611no—
486#385—612no—
487#385—611no—
488#385—612no—
489#385—611no—
490#385C2×D6112yes—
491#385C2×D6112yes—
492#384C2×D6111yescharacteristic
493#382—612no—
494#381—611no—
495#381—611no—
496#380—612no—
497C4×C4⋊C4—612no—
498C4×C4⋊C4—612no—
499C4×C4⋊C4—612no—
500C4×C4⋊C4—612no—
501C4×C4⋊C4—612no—
502C4×C4⋊C4—612no—
503C4×C4⋊C4—612no—
504C4×C4⋊C4—612no—
505C4×C4⋊C4—612no—
506C4×C4⋊C4—612no—
507C4×C22⋊C4—611no—
508C4×C22⋊C4—611no—
509C4×C22⋊C4—612no—
510C4×C22⋊C4—612no—
511C4×C22⋊C4—612no—
512C4×C22⋊C4—612no—
513C4×C22⋊C4—612no—
514#376—612no—
515#376—612no—
516#376C2×D6111yescharacteristic
517C61#3451411yescharacteristic, complemented, Sylow
518C22×Q8—612no—
519C22×Q8C22×D6111yescharacteristic
520C22×D4C22×D6111yescharacteristic
521C23×C4—611no—
522C23×C4—611no—
523C23×C4—611no—
524C23×C4—611no—
525C23×C4C22×D6111yescharacteristic
526C23×C4C22×D6111yescharacteristic
527C4⋊Q8—6116no—
528#126—6116no—
529#126—6116no—
530#125—6116no—
531#124C4×D6118yes—
532#123—618no—
533#123—618no—
534C22⋊Q8—6116no—
535C22⋊Q8—6116no—
536C4×Q8—42no—
537C4×Q8—2444no—
538C4×D4—42no—
539C2×C4⋊C4—612no—
540C2×C4⋊C4—612no—
541C2×C4⋊C4—612no—
542C2×C4⋊C4—612no—
543C2×C4⋊C4—612no—
544C2×C4⋊C4—612no—
545C2×C4⋊C4—612no—
546C2×C4⋊C4—612no—
547C2×C4⋊C4—612no—
548C2×C4⋊C4—612no—
549C2×C4⋊C4—612no—
550C2×C4⋊C4—612no—
551C2×C4⋊C4—612no—
552C2×C4⋊C4—612no—
553C2×C4⋊C4—612no—
554C2×C4⋊C4—612no—
555C2×C4⋊C4—612no—
556C2×C4⋊C4—2442no—
557C2×C4⋊C4C22×D6112yes—
558C2×C4⋊C4C22×D6111yescharacteristic
559C2×C4⋊C4C22×D6111yescharacteristic
560C2×C4⋊C4C22×D6112yes—
561C2×C4⋊C4C22×D6112yes—
562C2×C22⋊C4—612no—
563C2×C22⋊C4—612no—
564C2×C22⋊C4—611no—
565C2×C22⋊C4—611no—
566C2×C22⋊C4—612no—
567C2×C22⋊C4—612no—
568C2×C22⋊C4—611no—
569C2×C22⋊C4—611no—
570C2×C22⋊C4C22×D6111yescharacteristic
571C2×C22⋊C4C22×D6111yescharacteristic
572C2×C22⋊C4C22×D6112yes—
573C2×C22⋊C4C22×D6112yes—
574C2×C22⋊C4C22×D6112yes—
575C2×C22⋊C4C22×D6112yes—
576C2×C42—612no—
577C2×C42—612no—
578C2×C42—612no—
579C2×C42—612no—
580C2×C42—612no—
581C2×C42—612no—
582C2×C42—612no—
583C2×C42—612no—
584C2×C42—612no—
585C2×C42—612no—
586C2×C42—612no—
587C2×C42—612no—
588C2×C42—2442no—
589C2×C42C22×D6111yescharacteristic
590C2×C42C22×D6112yes—
591C2×C42C22×D6111yescharacteristic
592C2×C42C22×D6111yescharacteristic
593#95—612no—
594#95—612no—
595#95—612no—
596#95—612no—
597#95—612no—
598#95—612no—
599#95—612no—
600#95—612no—
601#95—612no—
602#95—612no—
603#95—612no—
604#95—612no—
605#95—612no—
606#95—612no—
607#95—612no—
608#95—612no—
609#95—612no—
610#95—612no—
611#95—612no—
612#95—612no—
613#95—612no—
614#95—612no—
615#95C22×D6112yes—
616#95C22×D6112yes—
617#95C22×D6112yes—
618#95C22×D6112yes—
619C24C23×D6111yescharacteristic
620C24C23×D6111yescharacteristic
621C2×Q8—41no—
622C2×Q8—41no—
623C2×Q8—618no—
624C2×Q8—2442no—
625C2×Q8—2442no—
626C2×Q8C2×C4×D6114yes—
627C2×D4—41no—
628C2×D4—41no—
629C2×D4C2×C4×D6114yes—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—612no—
635C22×C4—612no—
636C22×C4—612no—
637C22×C4—612no—
638C22×C4—612no—
639C22×C4—614no—
640C22×C4—614no—
641C22×C4—612no—
642C22×C4—612no—
643C22×C4—612no—
644C22×C4—1224no—
645C22×C4—2441no—
646C22×C4—2442no—
647C22×C4—2441no—
648C22×C4—2441no—
649C22×C4—2441no—
650C22×C4—2441no—
651C22×C4—2441no—
652C22×C4C23×D6111yescharacteristic
653C22×C4C23×D6112yes—
654C22×C4C23×D6111yescharacteristic
655C22×C4C23×D6111yescharacteristic
656C22×C4C23×D6112yes—
657C22×C4C23×D6111yescharacteristic
658C22×C4C23×D6112yes—
659C22×C4C23×D6112yes—
660C22×C4C23×D6111yescharacteristic
661C4⋊C4—24no—
662C4⋊C4—41no—
663C4⋊C4—41no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—618no—
667C4⋊C4—618no—
668C4⋊C4—618no—
669C4⋊C4—618no—
670C4⋊C4—618no—
671C4⋊C4—618no—
672C4⋊C4—618no—
673C4⋊C4—618no—
674C4⋊C4—1224no—
675C4⋊C4—1224no—
676C4⋊C4—2442no—
677C4⋊C4—2442no—
678C4⋊C4—2442no—
679C4⋊C4—2442no—
680C4⋊C4—2442no—
681C4⋊C4—2442no—
682C4⋊C4—2442no—
683C22⋊C4—41no—
684C22⋊C4—41no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—618no—
688C22⋊C4—618no—
689C22⋊C4—614no—
690C22⋊C4—614no—
691C22⋊C4—1224no—
692C22⋊C4—2442no—
693C22⋊C4—2441no—
694C22⋊C4—2441no—
695C22⋊C4C2×C4×D6118yes—
696C22⋊C4C2×C4×D6118yes—
697C42—22no—
698C42—42no—
699C42—41no—
700C42—618no—
701C42—1224no—
702C42—1224no—
703C42—1224no—
704C42—2442no—
705C42—2442no—
706C42—2442no—
707C42—2442no—
708C42—2442no—
709C42—2442no—
710C42—2442no—
711C42—2442no—
712C42C2×C4×D6114yes—
713C23—21no—
714C23—21no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—21no—
720C23—21no—
721C23C22×C4×D6112yes—
722C23C22×C4×D6112yes—
723C23C24×D6111yescharacteristic
724Q8—44no—
725Q8—2448no—
726D4—44no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—44no—
747C2×C4—82no—
748C2×C4—614no—
749C2×C4—614no—
750C2×C4—614no—
751C2×C4—614no—
752C2×C4—614no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—4882no—
773C2×C4—2444no—
774C2×C4—2444no—
775C2×C4—2444no—
776C2×C4C22×C4×D6114yes—
777C2×C4C22×C4×D6114yes—
778C2×C4C22×C4×D6112yes—
779C2×C4#1451982212yes—
780C22—22no—
781C22—22no—
782C22—24no—
783C22—24no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—42no—
789C22—42no—
790C22C23×C4×D6111yescharacteristic
791C22C2×#1451982211yescharacteristic
792C222−1+4×D6112yes—
793C22#1684059712yes—
794C22#1684059811yescharacteristic
795C4—22no—
796C4—22no—
797C4—24no—
798C4—24no—
799C4—42no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—42no—
804C4—1224no—
805C4—1224no—
806C4—1224no—
807C4—1224no—
808C4—1224no—
809C4—2442no—
810C4—2442no—
811C4—2442no—
812C2—42no—
813C2—42no—
814C2C4×#1451982211yescharacteristic
815C2#2145903012yes—
816C2#2145999211yescharacteristic
817C2#2146006211yescharacteristic
818C2#2146045512yes—
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingC61×#2326C2
socle, cosocleC23×C61C25
prime radicalC22×D4×C61C23
hypercenter#2326D61
hypocenterC61#34514
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2326

Complements

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

NH ≅ G/Ntype
2. #21448986C2semidirect
5. #21448937C2semidirect
6. #21448934C2semidirect
8. #21448924C2semidirect
9. #21448873C2semidirect
10. #21448819C2semidirect
11. #21448595C2semidirect
12. #21448592C2semidirect
13. #21448569C2semidirect
14. #21448562C2semidirect
15. #21448558C2semidirect
17. #21448351C2semidirect
20. #16840512C4semidirect
113. #14519775C2×C4semidirect
114. #14519770C2×C4semidirect
115. #14519770C2×C4semidirect
116. #14519769C2×C4semidirect
119. #14519754C2×C4semidirect
120. #14519754C2×C4semidirect
517. C61#34514semidirect

Maximal subgroups

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

subgroupindex
C2×#168405122
#214489862
#214489692
#214489542
#214489372
#214489342
#214489312
#214489242
#214488732
#214488192
#214485952
#214485922
#214485692
#214485622
#214485582
#214484842
#214483512
C4×#145197582
C61×#23262
#3451461