Finite Group Databasebeta

← #29646193

Subgroups — #29646193

Order 15616.

1424 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840402C211yesmaximal, characteristic
2#21454265C212yesmaximal, complemented
3#21444177C212yesmaximal, complemented
4#21444165C212yesmaximal, complemented
5#21444164C212yesmaximal, complemented
6#21444154C211yesmaximal, characteristic, complemented
7#21444146C211yesmaximal, characteristic, complemented
8#21444144C211yesmaximal, characteristic, complemented
9#21444134C211yesmaximal, characteristic, complemented
10#323×D61C211yesmaximal, characteristic, complemented
11C2×C61×#323C211yesmaximal, characteristic, complemented
12C22×#11758222C2211yescharacteristic
13C23×C22⋊D61C411yescharacteristic
14C2×#14519783—22no—
15#16840402—22no—
16#16840402—22no—
17#16840402—22no—
18#16840402—22no—
19C2×#14519763C411yescharacteristic
20C2×#14519760C2211yescharacteristic
21C2×#14519759C2211yescharacteristic
22C2×#14519754C411yescharacteristic
23C2×#14519751C411yescharacteristic
24C2×#14519750C411yescharacteristic
25C2×#14519750C2211yescharacteristic
26C2×#14519747C411yescharacteristic
27C2×#14519746C411yescharacteristic
28C2×C4×C22⋊D61C411yescharacteristic
29C2×#14519737C2211yescharacteristic
30C2×C22⋊C4×D61C2211yescharacteristic
31#16839728—22no—
32#16839727—22no—
33#16839727—22no—
34#16839726C2212yescomplemented
35#16839724C2212yescomplemented
36#16839724C2212yescomplemented
37C22⋊C8×D61C2212yescomplemented
38C22⋊C8×D61C2212yescomplemented
39#16839487C2212yescomplemented
40#16839487C2212yescomplemented
41#16839486C2211yescharacteristic
42#16839486C2211yescharacteristic
43#16839486C2212yescomplemented
44#16839485C2212yescomplemented
45#16839485C2212yescomplemented
46C22×C22⋊C4×C61C2211yescharacteristic
47C2×C22⋊C8×C61C2212yescomplemented
48C61×#323C2211yescharacteristic
49C61×#323C2211yescharacteristic
50C61×#323C2212yescomplemented
51C24×D61C2×C411yescharacteristic
52C2×#11758222—44no—
53C2×#11758222D412yes—
54C2×#11758222D412yes—
55C2×#11758222D412yes—
56C2×#11758222D412yes—
57C22×Dic122C2×C411yescharacteristic
58C22×D244C2×C411yescharacteristic
59C22×D244C2×C411yescharacteristic
60C22×C22⋊D61—21no—
61C22×C22⋊D61—21no—
62C22×C22⋊D61—21no—
63C22×C22⋊D61—21no—
64C22×C22⋊D61—44no—
65C22×C22⋊D61C2×C411yescharacteristic
66C22×C22⋊D61C2×C411yescharacteristic
67C22×C22⋊D61C2×C411yescharacteristic
68C22×C22⋊D61C2×C411yescharacteristic
69C22×C22⋊D61C2×C411yescharacteristic
70C22×C22⋊D61C2×C411yescharacteristic
71C22×C22⋊D61C2×C411yescharacteristic
72C23×Dic61C2×C411yescharacteristic
73C22×C4×D61C2×C411yescharacteristic
74C22×C4×D61C2311yescharacteristic
75C22×C4×D61C2311yescharacteristic
76#14519783—48no—
77C2×#11758194—22no—
78C2×#11758189—22no—
79C2×#11758189—22no—
80C2×C8×D61—22no—
81C2×C8×D61—22no—
82#14519763—22no—
83#14519763—22no—
84#14519760—22no—
85#14519760—22no—
86#14519759—22no—
87#14519759—22no—
88#14519754—22no—
89#14519754—22no—
90#14519751—22no—
91#14519751—22no—
92#14519750—22no—
93#14519750—22no—
94#14519750—22no—
95#14519750—22no—
96#14519747—22no—
97#14519747—22no—
98#14519746—22no—
99#14519746—22no—
100C4×C22⋊D61—21no—
101C4×C22⋊D61—21no—
102C4×C22⋊D61—21no—
103C4×C22⋊D61—21no—
104#14519737—22no—
105#14519737—22no—
106C2×C4⋊Dic61C2×C411yescharacteristic
107C2×#11758196C2×C411yescharacteristic
108C2×#11758196C2×C411yescharacteristic
109C2×#11758196C2311yescharacteristic
110C2×C22⋊Dic61C2×C411yescharacteristic
111C2×C22⋊Dic61C2×C411yescharacteristic
112C2×C22⋊Dic61C2×C411yescharacteristic
113C2×#11758198C2×C411yescharacteristic
114C2×#11758198C2×C411yescharacteristic
115C2×#11758198C2×C411yescharacteristic
116C2×#11758198C2×C411yescharacteristic
117C2×#11758198C2311yescharacteristic
118C22⋊C4×D61—22no—
119C22⋊C4×D61—22no—
120C2×C4×Dic61C2×C411yescharacteristic
121C22⋊#92418—22no—
122C22⋊#92418C2312yes—
123C22⋊#92418C2312yes—
124#14519689—22no—
125#14519689—22no—
126#14519689—22no—
127#14519689—22no—
128C25×C61C2×C411yescharacteristic
129C23×C4×C61C2×C411yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C22×C8×C61—22no—
132C2×C22⋊C4×C61—22no—
133C2×C22⋊C4×C61—22no—
134C2×C22⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61C2311yescharacteristic
138C22⋊C8×C61—22no—
139C22⋊C8×C61C2312yes—
140C22⋊C8×C61C2312yes—
141C24×C61—21no—
142C24×C61—21no—
143C24×C61—22no—
144C24×C61—41no—
145C24×C61—42no—
146C24×C61—81no—
147C24×C61C22×C411yescharacteristic
148C24×C61C22×C411yescharacteristic
149C24×C61C22×C411yescharacteristic
150C23×D61—22no—
151C23×D61—21no—
152C23×D61—21no—
153C23×D61—41no—
154C23×D61—42no—
155C23×D61—81no—
156C23×D61C22×C411yescharacteristic
157C23×D61C22×C411yescharacteristic
158C23×D61C22×C411yescharacteristic
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—42no—
162C22×C4×C61—81no—
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C22×C411yescharacteristic
166C22×C4×C61C2×D412yes—
167C22×C4×C61C2×D412yes—
168C22×C4×C61C2411yescharacteristic
169C2×C22⋊D61—24no—
170C2×C22⋊D61—21no—
171C2×C22⋊D61—21no—
172C2×C22⋊D61—22no—
173C2×C22⋊D61—21no—
174C2×C22⋊D61—21no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61—22no—
177C2×C22⋊D61—21no—
178C2×C22⋊D61—21no—
179C2×C22⋊D61—41no—
180C2×C22⋊D61—42no—
181C2×C22⋊D61—42no—
182C2×C22⋊D61—44no—
183C2×C22⋊D61—44no—
184C2×C22⋊D61—44no—
185C2×C22⋊D61—44no—
186C2×C22⋊D61—42no—
187C2×C22⋊D61—42no—
188C2×C22⋊D61—81no—
189C2×C22⋊D61C22⋊C411yescharacteristic
190C2×C22⋊D61C22⋊C411yescharacteristic
191C2×C22⋊D61C22⋊C411yescharacteristic
192C2×C22⋊D61C22⋊C412yes—
193C2×C22⋊D61C22⋊C412yes—
194C2×C22⋊D61C22⋊C411yescharacteristic
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—42no—
198C22×Dic61C22×C411yescharacteristic
199C22×Dic61C22×C411yescharacteristic
200C22×Dic61C22×C411yescharacteristic
201C22×Dic61C22×C411yescharacteristic
202C22×Dic61C22×C411yescharacteristic
203#11758222—28no—
204#11758222—44no—
205#11758222—44no—
206#11758222—44no—
207C2×D244—22no—
208C2×D244—42no—
209C2×D244—81no—
210C2×D244C22⋊C412yes—
211C2×D244C22⋊C412yes—
212C2×C4×D61—21no—
213C2×C4×D61—21no—
214C2×C4×D61—42no—
215C2×C4×D61—42no—
216C2×C4×D61—81no—
217C2×C4×D61C2×D412yes—
218C2×C4×D61C2×D412yes—
219C2×C4×D61C2×D412yes—
220C2×C4×D61C2×D412yes—
221C2×Dic122—42no—
222C2×Dic122C22⋊C412yes—
223C2×Dic122C22⋊C412yes—
224C2×C8×C61—22no—
225C2×C8×C61—22no—
226C2×C8×C61—44no—
227C22⋊C4×C61—22no—
228C22⋊C4×C61—22no—
229C22⋊C4×C61—22no—
230C22⋊C4×C61—22no—
231C22⋊Dic61—21no—
232C22⋊Dic61—21no—
233C22⋊Dic61—22no—
234C22⋊Dic61—22no—
235#11758198—22no—
236#11758198—21no—
237#11758198—21no—
238#11758198—22no—
239#11758198—22no—
240#11758198—22no—
241C4⋊Dic61—22no—
242#11758196—22no—
243#11758196—22no—
244#11758196—21no—
245#11758196—21no—
246C4×Dic61—21no—
247C4×Dic61—21no—
248#11758194—44no—
249C2×#92418—22no—
250C2×#92418—22no—
251#11758189—44no—
252#11758189—44no—
253C8×D61—44no—
254C8×D61—44no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—22no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—41no—
264C23×C61—42no—
265C23×C61—42no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—42no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—42no—
272C23×C61—81no—
273C23×C61—81no—
274C23×C61—84no—
275C23×C61—84no—
276C23×C61C2×C22⋊C411yescharacteristic
277C23×C61C2×C22⋊C411yescharacteristic
278C23×C61#13112yescomplemented
279C23×C61C23×C411yescharacteristic
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—22no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61—42no—
292C22×D61—42no—
293C22×D61—42no—
294C22×D61—42no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—81no—
298C22×D61—81no—
299C22×D61—84no—
300C22×D61—84no—
301C22×D61C2×C22⋊C411yescharacteristic
302C22×D61C2×C22⋊C412yes—
303C22×D61C2×C22⋊C411yescharacteristic
304C2×C4×C61—24no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—42no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—81no—
313C2×C4×C61—81no—
314C2×C4×C61C2×C22⋊C412yes—
315C2×C4×C61C22×D412yes—
316C22⋊D61—24no—
317C22⋊D61—22no—
318C22⋊D61—22no—
319C22⋊D61—22no—
320C22⋊D61—42no—
321C22⋊D61—42no—
322C22⋊D61—44no—
323C22⋊D61—42no—
324C22⋊D61—42no—
325C22⋊D61—42no—
326C22⋊D61—42no—
327C22⋊D61—42no—
328C22⋊D61—82no—
329C22⋊D61#9914yes—
330C2×Dic61—22no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—41no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61C2×C22⋊C411yescharacteristic
342C2×Dic61C2×C22⋊C412yes—
343C2×Dic61C2×C22⋊C411yescharacteristic
344D244—24no—
345D244—42no—
346D244—82no—
347C4×D61—24no—
348C4×D61—24no—
349C4×D61—42no—
350C4×D61—42no—
351C4×D61—81no—
352C4×D61—81no—
353Dic122—24no—
354Dic122—42no—
355C8×C61—42no—
356C8×C61—42no—
357#92418—42no—
358#92418—42no—
359#17411—611nomaximal, Sylow
360C22×C61—21no—
361C22×C61—21no—
362C22×C61—21no—
363C22×C61—21no—
364C22×C61—22no—
365C22×C61—21no—
366C22×C61—21no—
367C22×C61—21no—
368C22×C61—42no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—84no—
378C22×C61—81no—
379C22×C61—81no—
380C22×C61—84no—
381C22×C61C2×#9912yes—
382C22×C61C22×C22⋊C411yescharacteristic
383C22×C61C2×#13111yescharacteristic
384C22×C61#56811yescharacteristic
385C2×D61—21no—
386C2×D61—21no—
387C2×D61—22no—
388C2×D61—21no—
389C2×D61—22no—
390C2×D61—21no—
391C2×D61—21no—
392C2×D61—22no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—41no—
396C2×D61—41no—
397C2×D61—41no—
398C2×D61—84no—
399C2×D61—81no—
400C2×D61—81no—
401C2×D61—84no—
402C2×D61—81no—
403C2×D61—81no—
404C2×D61C2×#9912yes—
405C4×C61—22no—
406C4×C61—22no—
407C4×C61—41no—
408C4×C61—41no—
409Dic61—22no—
410Dic61—21no—
411Dic61—41no—
412Dic61—41no—
413Dic61—41no—
414Dic61C2×#9912yes—
415C2×#546—611no—
416#2880—612no—
417#1471—612no—
418#1468—612no—
419#1468—612no—
420#1465—611no—
421#1462—611no—
422#1462—611no—
423#1459—611no—
424C2×#323—611no—
425C2×#323D6111yescharacteristic, complemented
426C2×C61—21no—
427C2×C61—21no—
428C2×C61—22no—
429C2×C61—42no—
430C2×C61—41no—
431C2×C61—81no—
432C2×C61#288011yescharacteristic
433C2×C61C22×#9911yescharacteristic
434C2×C61#288811yescharacteristic
435D61—22no—
436D61—41no—
437D61—42no—
438D61—81no—
439C22×#41—611no—
440C23×D4—611no—
441C2×#131—1222no—
442#546—1222no—
443#546—1222no—
444#546—1222no—
445#546—1222no—
446C2×#124—611no—
447C2×#123—611no—
448C2×#123—611no—
449C2×C22⋊Q8—611no—
450C2×#121—611no—
451C2×#121—611no—
452C2×#121—611no—
453C2×#120—611no—
454C2×#120—611no—
455C2×C4×D4—611no—
456C2×C4×D4—611no—
457C22×C22⋊C4—611no—
458C22×C22⋊C4C2×D6111yescharacteristic
459#408—1222no—
460#408—1222no—
461#408—1222no—
462#407—612no—
463#407—612no—
464#407—612no—
465C2×C22⋊C8—612no—
466C2×C22⋊C8—612no—
467C2×C22⋊C8C2×D6112yescomplemented
468#324—612no—
469#324—612no—
470#323—611no—
471#323—611no—
472#323—612no—
473#323—612no—
474#323—612no—
475#323C2×D6111yescharacteristic
476#323C2×D6111yescharacteristic
477#323C2×D6112yescomplemented
478C61#1741111yescharacteristic, complemented, Sylow
479C25—611no—
480C25C4×D6111yescharacteristic
481C2×#41—612no—
482C2×#41—612no—
483C2×#41—612no—
484C2×#41—612no—
485C2×#41—2444no—
486C22×Q8—611no—
487C22×D4—611no—
488C22×D4—611no—
489C22×D4—611no—
490C22×D4—611no—
491C22×D4—611no—
492C22×D4—611no—
493C22×D4—611no—
494C22×D4—611no—
495C22×D4—611no—
496C22×D4—1221no—
497C22×D4—1221no—
498C22×D4—1221no—
499C22×D4—1221no—
500C22×D4—2444no—
501C23×C4—611no—
502C23×C4—611no—
503C23×C4—611no—
504C23×C4—611no—
505C23×C4C4×D6111yescharacteristic
506C23×C4C22×D6111yescharacteristic
507#131—2448no—
508C2×M16—1222no—
509C2×M16—1222no—
510C2×M16—1222no—
511C22×C8—22no—
512C22×C8—1222no—
513C22×C8—1222no—
514#124—1222no—
515#124—1222no—
516#123—1222no—
517#123—1222no—
518#123—1222no—
519#123—1222no—
520C22⋊Q8—1222no—
521C22⋊Q8—1222no—
522#121—1222no—
523#121—1222no—
524#121—1222no—
525#121—1222no—
526#121—1222no—
527#121—1222no—
528#120—1222no—
529#120—1222no—
530#120—1222no—
531#120—1222no—
532C4×D4—1222no—
533C4×D4—1222no—
534C4×D4—1221no—
535C4×D4—1221no—
536C4×D4—1221no—
537C4×D4—1221no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—611no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—611no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—611no—
545C2×C22⋊C4—611no—
546C2×C22⋊C4—611no—
547C2×C22⋊C4—611no—
548C2×C22⋊C4—611no—
549C2×C22⋊C4—611no—
550C2×C22⋊C4—611no—
551C2×C22⋊C4—611no—
552C2×C22⋊C4—1222no—
553C2×C22⋊C4—1222no—
554C2×C22⋊C4C4×D6111yescharacteristic
555C2×C22⋊C4C4×D6111yescharacteristic
556C2×C22⋊C4C22×D6111yescharacteristic
557C2×C22⋊C4C22×D6111yescharacteristic
558C2×C42—611no—
559C22⋊C8—22no—
560C22⋊C8—612no—
561C22⋊C8—612no—
562C22⋊C8—1222no—
563C22⋊C8—1222no—
564C22⋊C8—1222no—
565C22⋊C8—1222no—
566C22⋊C8—1222no—
567C22⋊C8C22×D6112yes—
568C22⋊C8C22×D6112yes—
569C24—21no—
570C24—21no—
571C24—22no—
572C24—41no—
573C24—42no—
574C24—81no—
575C24—611no—
576C24—611no—
577C24—611no—
578C24—1221no—
579C24—1221no—
580C24—1222no—
581C24—4881no—
582C24—2441no—
583C24—2442no—
584C24C2×C4×D6111yescharacteristic
585C24C2×C4×D6111yescharacteristic
586C24C2×C4×D6111yescharacteristic
587#41—1228no—
588#41—2444no—
589#41—2444no—
590#41—2444no—
591C2×Q8—612no—
592C2×Q8—612no—
593C2×Q8—2442no—
594C2×D4—611no—
595C2×D4—611no—
596C2×D4—611no—
597C2×D4—611no—
598C2×D4—612no—
599C2×D4—612no—
600C2×D4—612no—
601C2×D4—612no—
602C2×D4—1222no—
603C2×D4—1221no—
604C2×D4—1221no—
605C2×D4—1224no—
606C2×D4—1222no—
607C2×D4—1222no—
608C2×D4—1221no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—1222no—
613C2×D4—4881no—
614C2×D4—4881no—
615C2×D4—2442no—
616C2×D4—2441no—
617C2×D4—2442no—
618C2×D4—2444no—
619C2×D4—2442no—
620C2×D4—2444no—
621C2×D4—2444no—
622C2×D4—2444no—
623C2×D4—2442no—
624C2×D4—2442no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—42no—
628C22×C4—81no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—612no—
632C22×C4—612no—
633C22×C4—612no—
634C22×C4—612no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—1221no—
642C22×C4—4881no—
643C22×C4—2442no—
644C22×C4—2442no—
645C22×C4—2442no—
646C22×C4C2×C4×D6111yescharacteristic
647C22×C4C2×C4×D6111yescharacteristic
648C22×C4C2×C4×D6111yescharacteristic
649C22×C4D4×D6112yes—
650C22×C4D4×D6112yes—
651C22×C4C23×D6111yescharacteristic
652M16—2444no—
653M16—2444no—
654M16—2444no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—44no—
658C2×C8—1222no—
659C2×C8—1222no—
660C2×C8—2444no—
661C2×C8—2444no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C4⋊C4—1222no—
665C4⋊C4—1222no—
666C4⋊C4—1222no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—1222no—
672C22⋊C4—1221no—
673C22⋊C4—1221no—
674C22⋊C4—1222no—
675C22⋊C4—1222no—
676C22⋊C4—1222no—
677C22⋊C4—1221no—
678C22⋊C4—1221no—
679C22⋊C4—1222no—
680C22⋊C4—1222no—
681C42—1221no—
682C42—1221no—
683C23—21no—
684C23—22no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—41no—
692C23—42no—
693C23—42no—
694C23—41no—
695C23—41no—
696C23—42no—
697C23—41no—
698C23—41no—
699C23—42no—
700C23—81no—
701C23—81no—
702C23—84no—
703C23—84no—
704C23—611no—
705C23—611no—
706C23—612no—
707C23—1222no—
708C23—1221no—
709C23—1221no—
710C23—1221no—
711C23—1221no—
712C23—1221no—
713C23—1221no—
714C23—1221no—
715C23—4881no—
716C23—4881no—
717C23—4884no—
718C23—4884no—
719C23—2441no—
720C23—2441no—
721C23—2441no—
722C23—2442no—
723C23—2442no—
724C23—2441no—
725C23—2441no—
726C23—2442no—
727C23—2442no—
728C23C22⋊C4×D6111yescharacteristic
729C23C22⋊C4×D6111yescharacteristic
730C23#1451978312yescomplemented
731C23C22×C4×D6111yescharacteristic
732Q8—1224no—
733Q8—2442no—
734D4—614no—
735D4—1224no—
736D4—1222no—
737D4—1222no—
738D4—1222no—
739D4—1224no—
740D4—4882no—
741D4—4882no—
742D4—2442no—
743D4—2442no—
744D4—2442no—
745D4—2442no—
746D4—2444no—
747D4—2442no—
748D4—2442no—
749D4—2442no—
750D4—2442no—
751C2×C4—24no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—611no—
762C2×C4—611no—
763C2×C4—612no—
764C2×C4—1224no—
765C2×C4—1224no—
766C2×C4—1222no—
767C2×C4—1221no—
768C2×C4—1221no—
769C2×C4—1221no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—4881no—
773C2×C4—4881no—
774C2×C4—2442no—
775C2×C4—2442no—
776C2×C4—2442no—
777C2×C4—2441no—
778C2×C4—2442no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4C22⋊C4×D6112yes—
782C2×C4C2×D4×D6112yes—
783C8—42no—
784C8—42no—
785C8—2442no—
786C8—2442no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—22no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—84no—
805C22—81no—
806C22—81no—
807C22—84no—
808C22—612no—
809C22—1221no—
810C22—1221no—
811C22—1222no—
812C22—1221no—
813C22—1222no—
814C22—1221no—
815C22—1221no—
816C22—1222no—
817C22—4881no—
818C22—4881no—
819C22—4881no—
820C22—4881no—
821C22—4884no—
822C22—4884no—
823C22—2442no—
824C22—2442no—
825C22—2441no—
826C22—2441no—
827C22—2441no—
828C22#99×D6112yes—
829C22C2×C22⋊C4×D6111yescharacteristic
830C22C2×#1451978311yescharacteristic
831C22#1684052811yescharacteristic
832C4—22no—
833C4—22no—
834C4—41no—
835C4—41no—
836C4—612no—
837C4—1221no—
838C4—1222no—
839C4—2441no—
840C4—2441no—
841C4—2441no—
842C2—21no—
843C2—21no—
844C2—22no—
845C2—41no—
846C2—42no—
847C2—81no—
848C2—1222no—
849C2—4881no—
850C2—2441no—
851C2—2442no—
852C2#2145426511yescharacteristic
853C2C2×#99×D6111yescharacteristic
854C2#2145429511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#323C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840402C2
cosocleC22×C4×C61C24
hypercenterC2×#323D61
hypocenterC61#17411
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. #21454265C2semidirect
3. #21444177C2semidirect
4. #21444165C2semidirect
5. #21444164C2semidirect
6. #21444154C2semidirect
7. #21444146C2semidirect
8. #21444144C2semidirect
9. #21444134C2semidirect
10. #323×D61C2semidirect
11. C2×C61×#323C2semidirect
34. #16839726C22semidirect
35. #16839724C22semidirect
36. #16839724C22semidirect
37. C22⋊C8×D61C22semidirect
38. C22⋊C8×D61C22semidirect
39. #16839487C22semidirect
40. #16839487C22semidirect
43. #16839486C22semidirect
44. #16839485C22semidirect
45. #16839485C22semidirect
47. C2×C22⋊C8×C61C22semidirect
50. C61×#323C22semidirect
278. C23×C61#131semidirect
425. C2×#323D61semidirect
467. C2×C22⋊C8C2×D61semidirect
477. #323C2×D61semidirect
478. C61#17411semidirect
730. C23#14519783semidirect

Maximal subgroups

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

subgroupindex
C2×#168404022
#214542652
#214441772
#214441652
#214441642
#214441542
#214441462
#214441442
#214441342
#323×D612
C2×C61×#3232
#1741161