Finite Group Databasebeta

← #29647502

Subgroups — #29647502

Order 15616.

1510 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840275C211yesmaximal, characteristic
2C2×#16839724C211yesmaximal, characteristic, complemented
3#380×D61C211yesmaximal, characteristic, complemented
4#21444391C211yesmaximal, characteristic, complemented
5#21444388C211yesmaximal, characteristic, complemented
6#21444386C211yesmaximal, characteristic, complemented
7#21444361C214yesmaximal, complemented
8#21444322C214yesmaximal, complemented
9C61×#1520C211yesmaximal, characteristic, complemented
10C22×#11758226C411yescharacteristic, complemented
11C23×C4×D61C2211yescharacteristic
12C22×#11758189—21no—
13#16840275—21no—
14#16840275—21no—
15#16840275—21no—
16#16840275—21no—
17#16840275C412yescomplemented
18#16840275C412yescomplemented
19#16840275C2212yes—
20#16840275C2212yes—
21C2×#14519762—21no—
22C2×#14519753C411yescharacteristic, complemented
23C2×#14519752C411yescharacteristic, complemented
24C2×#14519751C2211yescharacteristic
25C2×#14519747—21no—
26C2×#14519739—21no—
27C2×#14519737—21no—
28C2×#14519735C411yescharacteristic, complemented
29C2×C4⋊C4×D61—21no—
30C2×C22⋊C4×D61—21no—
31#16839724—21no—
32#16839724—21no—
33#16839724C2212yescomplemented
34#16839724C2212yescomplemented
35C2×C22⋊#92418C2211yescharacteristic
36C2×#14519689—21no—
37#16839622C2211yescharacteristic
38#16839621C2212yescomplemented
39#16839620—21no—
40#16839619—21no—
41#95×D61C2212yescomplemented
42#16839499C2214yescomplemented
43#16839497C2214yescomplemented
44#16839495C2214yescomplemented
45C2×C22⋊Q8×C61C2211yescharacteristic
46C2×C22⋊C8×C61C2211yescharacteristic
47C61×#380C2211yescharacteristic
48C61×#328C2214yescomplemented
49C24×D61D411yescharacteristic
50C2×#11758226—21no—
51C2×#11758226—21no—
52C2×#11758226—44no—
53C2×#11758226C2×C412yes—
54C2×#11758226C2×C412yescomplemented
55C22×D244—21no—
56C22×D244—21no—
57C22×D244C2×C411yescharacteristic, complemented
58C22×C22⋊D61—21no—
59C23×Dic61D411yescharacteristic
60C22×C4×D61—21no—
61C22×C4×D61—22no—
62C22×C4×D61—44no—
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61C2×C411yescharacteristic
66C22×C4×D61C2×C411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D411yescharacteristic
73C22×C4×D61C2311yescharacteristic
74C22×C4×D61C2311yescharacteristic
75C2×#11758189—22no—
76C2×#11758189—22no—
77C2×#11758189—44no—
78C22×#92418—21no—
79#14519762—22no—
80#14519762—22no—
81#14519762—22no—
82#14519762—22no—
83#14519753—21no—
84#14519753—21no—
85#14519753C2×C412yes—
86#14519753C2×C412yescomplemented
87#14519752—21no—
88#14519752—21no—
89#14519752C2×C412yes—
90#14519752C2×C412yescomplemented
91#14519751—21no—
92#14519751—21no—
93#14519751C2×C412yescomplemented
94#14519751C2312yes—
95#14519747—22no—
96#14519747—22no—
97#14519747—22no—
98#14519747—22no—
99#14519739—22no—
100#14519739—22no—
101#14519739—22no—
102#14519739—22no—
103#14519737—22no—
104#14519737—22no—
105#14519737—22no—
106#14519737—22no—
107#14519735—21no—
108#14519735—21no—
109#14519735C2×C412yes—
110#14519735C2×C412yescomplemented
111C2×C4⋊Dic61—21no—
112C2×C4⋊Dic61C2×C411yescharacteristic, complemented
113C2×#11758196—21no—
114C2×#11758196—22no—
115C4⋊C4×D61—44no—
116C2×C22⋊Dic61—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198—22no—
122C22⋊C4×D61—44no—
123C2×C4×Dic61—21no—
124C22⋊#92418—21no—
125C22⋊#92418C2312yes—
126#14519689—22no—
127#14519689—22no—
128#14519684—22no—
129#14519684C2312yes—
130C22×Q8×C61C2×C411yescharacteristic, complemented
131C23×C4×C61C2311yescharacteristic
132C22×C8×C61—21no—
133C22⋊Q8×C61—21no—
134C22⋊Q8×C61—21no—
135C22⋊Q8×C61C2×C412yescomplemented
136C22⋊Q8×C61C2312yes—
137C2×C4⋊C4×C61—21no—
138C2×C4⋊C4×C61—21no—
139C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C22⋊C8×C61—21no—
143C22⋊C8×C61C2312yes—
144#95×C61C2312yes—
145C24×C61C2×D411yescharacteristic
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×D61C22⋊C411yescharacteristic
155C23×D61C2×D411yescharacteristic
156C23×D61C2×D411yescharacteristic
157C2×Q8×C61—21no—
158C2×Q8×C61—42no—
159C2×Q8×C61C22×C412yes—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—22no—
163C22×C4×C61—42no—
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C22×C411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2411yescharacteristic
170C2×C22⋊D61—22no—
171C2×C22⋊D61—22no—
172C2×C22⋊D61—42no—
173C2×C22⋊D61—42no—
174C22×Dic61—21no—
175C22×Dic61—22no—
176C22×Dic61—42no—
177C22×Dic61C22⋊C411yescharacteristic
178C22×Dic61C22⋊C411yescharacteristic
179C22×Dic61C22⋊C411yescharacteristic
180C22×Dic61C22⋊C411yescharacteristic
181C22×Dic61C2×D411yescharacteristic
182C22×Dic61C2×D411yescharacteristic
183#11758226—44no—
184#11758226—44no—
185#11758226—44no—
186#11758226—44no—
187C2×D244—22no—
188C2×D244—22no—
189C2×D244—22no—
190C2×D244—22no—
191C2×D244—21no—
192C2×D244—44no—
193C2×D244—44no—
194C2×D244—42no—
195C2×D244C22×C412yes—
196C2×C4×D61—24no—
197C2×C4×D61—24no—
198C2×C4×D61—24no—
199C2×C4×D61—22no—
200C2×C4×D61—22no—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×C4×D61—42no—
209C2×C4×D61—42no—
210C2×C4×D61—44no—
211C2×C4×D61—44no—
212C2×C4×D61—44no—
213C2×C4×D61—44no—
214C2×C4×D61C22⋊C411yescharacteristic
215C2×C4×D61C22⋊C411yescharacteristic
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×D61C22×C411yescharacteristic
226C2×C4×D61C2×D411yescharacteristic
227C2×C4×D61C2×D411yescharacteristic
228C2×C4×D61C2×D411yescharacteristic
229C2×C4×D61C2×D411yescharacteristic
230C2×C8×C61—22no—
231C2×C8×C61—42no—
232C4⋊C4×C61—22no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—22no—
235C4⋊C4×C61—42no—
236C4⋊C4×C61C22×C412yes—
237C22⋊C4×C61—22no—
238C22⋊C4×C61—22no—
239C22⋊C4×C61—42no—
240C22⋊Dic61—42no—
241#11758198—22no—
242#11758198—22no—
243#11758198—22no—
244#11758198—22no—
245#11758198—22no—
246#11758198—22no—
247#11758198—22no—
248#11758198—22no—
249#11758198—44no—
250C4⋊Dic61—21no—
251C4⋊Dic61—42no—
252C4⋊Dic61C22×C412yes—
253#11758196—22no—
254#11758196—22no—
255#11758196—44no—
256C4×Dic61—22no—
257C4×Dic61—22no—
258C2×#92418—22no—
259C2×#92418—42no—
260#11758189—44no—
261#11758189—44no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61C2×C22⋊C411yescharacteristic
265C23×C61C2×C22⋊C411yescharacteristic
266C23×C61AGL(1,ℤ/8)12yes—
267C23×C61#13712yes—
268C23×C61C22×D411yescharacteristic
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61—48no—
291C22×D61—48no—
292C22×D61—42no—
293C22×D61—42no—
294C22×D61—42no—
295C22×D61C2×C22⋊C411yescharacteristic
296C22×D61C2×C22⋊C411yescharacteristic
297C22×D61C2×C22⋊C411yescharacteristic
298C22×D61C2×C22⋊C411yescharacteristic
299Q8×C61—42no—
300Q8×C61—42no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—42no—
310C2×C4×C61—42no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61C2×C22⋊C411yescharacteristic
315C2×C4×C61C2×C22⋊C411yescharacteristic
316C2×C4×C61C23×C411yescharacteristic
317C2×C4×C61C22×D411yescharacteristic
318C22⋊D61—42no—
319C22⋊D61—42no—
320C22⋊D61—44no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61—42no—
332C2×Dic61C2×C22⋊C411yescharacteristic
333C2×Dic61C2×C22⋊C411yescharacteristic
334C2×Dic61C2×C22⋊C411yescharacteristic
335C2×Dic61C2×C22⋊C411yescharacteristic
336D244—42no—
337D244—44no—
338D244—44no—
339D244—44no—
340D244—44no—
341D244—42no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—41no—
352C4×D61—41no—
353C4×D61—41no—
354C4×D61—41no—
355C4×D61—41no—
356C4×D61—41no—
357C4×D61—44no—
358C4×D61—44no—
359C4×D61—88no—
360C4×D61#9914yes—
361C8×C61—42no—
362#92418—42no—
363#17592—611nomaximal, Sylow
364C22×C61—21no—
365C22×C61—21no—
366C22×C61—21no—
367C22×C61—21no—
368C22×C61—21no—
369C22×C61—21no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61#41712yes—
373C22×C61#41712yes—
374C22×C61C22×C22⋊C411yescharacteristic
375C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
376C22×C61C2×#13711yescharacteristic
377C2×D61—24no—
378C2×D61—24no—
379C2×D61—21no—
380C2×D61—21no—
381C2×D61—21no—
382C2×D61—21no—
383C2×D61—21no—
384C2×D61—21no—
385C2×D61—21no—
386C2×D61—21no—
387C2×D61—21no—
388C2×D61—21no—
389C2×D61—44no—
390C2×D61—44no—
391C2×D61—44no—
392C2×D61—44no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—42no—
397C2×D61—42no—
398C2×D61—84no—
399C2×D61C2×#9912yes—
400C2×D61#42112yes—
401C4×C61—21no—
402C4×C61—21no—
403C4×C61—21no—
404C4×C61—42no—
405C4×C61—42no—
406C4×C61—82no—
407C4×C61C2×#9912yes—
408Dic61—21no—
409Dic61—21no—
410Dic61—21no—
411Dic61—42no—
412Dic61—82no—
413Dic61C2×#9912yes—
414C2×#525—611no—
415C2×#407—611no—
416C2×#380—611no—
417#1520—611no—
418#1520D6111yescharacteristic, complemented
419#1519—611no—
420#1519—611no—
421#1513—614no—
422#1504—614no—
423C2×C61—21no—
424C2×C61—21no—
425C2×C61—22no—
426C2×C61—22no—
427C2×C61C22×#9911yescharacteristic
428C2×C61C2×#41711yescharacteristic
429C2×C61C2×#42111yescharacteristic
430D61—22no—
431D61—22no—
432D61—41no—
433D61—41no—
434D61—82no—
435C22×#41—611no—
436C24×C4—611no—
437C22×M16—1221no—
438#525—612no—
439#525—612no—
440#525—612no—
441#525—612no—
442#525—1221no—
443#525—1221no—
444#525—1221no—
445#525—1221no—
446C2×#123—1221no—
447C2×C22⋊Q8—611no—
448C2×C22⋊Q8C2×D6111yescharacteristic
449C2×#121—611no—
450C2×#121—611no—
451C2×#120—1221no—
452C2×C4×D4—1221no—
453C2×C4×D4—1221no—
454C2×#117—611no—
455C22×C4⋊C4—1221no—
456C22×C22⋊C4—1221no—
457#407—612no—
458#407—612no—
459#407—1221no—
460#407—1221no—
461C2×C22⋊C8—611no—
462C2×C22⋊C8—1221no—
463C2×C22⋊C8C2×D6111yescharacteristic
464#380—611no—
465#380—612no—
466#380—1221no—
467#380—1221no—
468#380C2×D6111yescharacteristic
469C2×#95—612no—
470#328—614no—
471#328C2×D6114yescomplemented
472#327—614no—
473#327—614no—
474C61#1759211yescharacteristic, complemented, Sylow
475C25—611no—
476C2×#41—612no—
477C2×#41—612no—
478C2×#41—1221no—
479C2×#41—1221no—
480C2×#41—2444no—
481C22×Q8C4×D6111yescharacteristic, complemented
482C22×D4—611no—
483C22×D4—1221no—
484C22×D4—1221no—
485C22×D4—1221no—
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—611no—
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—1221no—
500C23×C4—1222no—
501C23×C4—2444no—
502C23×C4C22×D6111yescharacteristic
503C2×M16—1222no—
504C2×M16—1222no—
505C2×M16—2444no—
506C22×C8—21no—
507C22×C8—1221no—
508#123—1222no—
509#123—1222no—
510#123—1222no—
511#123—1222no—
512C22⋊Q8—21no—
513C22⋊Q8—21no—
514C22⋊Q8—612no—
515C22⋊Q8—612no—
516C22⋊Q8—1221no—
517C22⋊Q8—1221no—
518C22⋊Q8C4×D6112yescomplemented
519C22⋊Q8C22×D6112yes—
520#121—612no—
521#121—612no—
522#121—612no—
523#121—612no—
524#121—1221no—
525#121—1221no—
526#121—1221no—
527#121—1221no—
528#120—1222no—
529#120—1222no—
530#120—1222no—
531#120—1222no—
532C4×D4—1222no—
533C4×D4—1222no—
534C4×D4—1222no—
535C4×D4—1222no—
536C4×D4—1222no—
537C4×D4—1222no—
538C4×D4—1222no—
539C4×D4—1222no—
540#117—612no—
541#117—612no—
542#117—1221no—
543#117—1221no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—611no—
547C2×C4⋊C4—1221no—
548C2×C4⋊C4—1222no—
549C2×C4⋊C4—1221no—
550C2×C4⋊C4—2444no—
551C2×C4⋊C4C4×D6111yescharacteristic, complemented
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1221no—
557C2×C22⋊C4—1221no—
558C2×C22⋊C4—1222no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—2444no—
561C2×C42—1221no—
562C22⋊C8—21no—
563C22⋊C8—612no—
564C22⋊C8—1222no—
565C22⋊C8—1222no—
566C22⋊C8—1221no—
567C22⋊C8C22×D6112yes—
568#95—612no—
569#95—1222no—
570#95C22×D6112yes—
571C24—611no—
572C24—611no—
573C24—611no—
574C24—611no—
575C24—611no—
576C24—611no—
577C24—1222no—
578C24—1222no—
579C24—1221no—
580C24—2442no—
581C24—2442no—
582C24D4×D6111yescharacteristic
583#41—2444no—
584#41—2444no—
585#41—2444no—
586#41—2444no—
587C2×Q8—21no—
588C2×Q8—42no—
589C2×Q8C2×C4×D6112yes—
590C2×D4—612no—
591C2×D4—1222no—
592C2×D4—1222no—
593C2×D4—1222no—
594C2×D4—1222no—
595C2×D4—1222no—
596C2×D4—1222no—
597C2×D4—1221no—
598C2×D4—2442no—
599C2×D4—2444no—
600C2×D4—2444no—
601C2×D4—2442no—
602C2×D4—2442no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—42no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—611no—
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—1224no—
630C22×C4—1224no—
631C22×C4—1224no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1221no—
635C22×C4—1222no—
636C22×C4—2442no—
637C22×C4—2442no—
638C22×C4—2442no—
639C22×C4—2442no—
640C22×C4—2442no—
641C22×C4—2442no—
642C22×C4—2442no—
643C22×C4—2442no—
644C22×C4—2442no—
645C22×C4—2444no—
646C22×C4—2444no—
647C22×C4—2444no—
648C22×C4—2444no—
649C22×C4—2442no—
650C22×C4C2×C4×D6111yescharacteristic
651C22×C4C2×C4×D6111yescharacteristic
652C22×C4D4×D6111yescharacteristic
653C22×C4D4×D6111yescharacteristic
654C22×C4D4×D6111yescharacteristic
655C22×C4C23×D6111yescharacteristic
656M16—2444no—
657M16—2444no—
658C2×C8—22no—
659C2×C8—42no—
660C2×C8—1222no—
661C2×C8—2442no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—42no—
666C4⋊C4—612no—
667C4⋊C4—1222no—
668C4⋊C4—1222no—
669C4⋊C4—1221no—
670C4⋊C4—2442no—
671C4⋊C4—2444no—
672C4⋊C4C2×C4×D6112yes—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—42no—
676C22⋊C4—1222no—
677C22⋊C4—1222no—
678C22⋊C4—1222no—
679C22⋊C4—1222no—
680C22⋊C4—1222no—
681C22⋊C4—1222no—
682C22⋊C4—1222no—
683C22⋊C4—1222no—
684C22⋊C4—2444no—
685C22⋊C4—2442no—
686C42—1222no—
687C42—1222no—
688C23—41no—
689C23—41no—
690C23—611no—
691C23—611no—
692C23—611no—
693C23—611no—
694C23—1222no—
695C23—1222no—
696C23—1222no—
697C23—1222no—
698C23—1222no—
699C23—1222no—
700C23—1221no—
701C23—1221no—
702C23—1222no—
703C23—1222no—
704C23—1222no—
705C23—1222no—
706C23—1221no—
707C23—1221no—
708C23—1222no—
709C23—2441no—
710C23—2441no—
711C23—2441no—
712C23—2441no—
713C23—2441no—
714C23—2441no—
715C23—2442no—
716C23—2442no—
717C23—2448no—
718C23—2448no—
719C23—2442no—
720C23C22⋊C4×D6111yescharacteristic
721C23C22⋊C4×D6111yescharacteristic
722C23#1451980412yes—
723C23#1451980912yes—
724C23C2×D4×D6111yescharacteristic
725Q8—42no—
726Q8—42no—
727D4—2442no—
728D4—2444no—
729D4—2444no—
730D4—2444no—
731D4—2444no—
732D4—2444no—
733D4—2442no—
734D4—2442no—
735D4—2442no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—611no—
750C2×C4—614no—
751C2×C4—611no—
752C2×C4—611no—
753C2×C4—611no—
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—4888no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4—2444no—
775C2×C4—2444no—
776C2×C4—2441no—
777C2×C4—2441no—
778C2×C4—2441no—
779C2×C4—2442no—
780C2×C4—2442no—
781C2×C4—2442no—
782C2×C4—2442no—
783C2×C4C22⋊C4×D6111yescharacteristic
784C2×C4C22⋊C4×D6111yescharacteristic
785C2×C4C22×C4×D6111yescharacteristic
786C2×C4C2×D4×D6111yescharacteristic
787C8—42no—
788C8—2442no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—42no—
796C22—42no—
797C22—612no—
798C22—612no—
799C22—1224no—
800C22—1224no—
801C22—1221no—
802C22—1221no—
803C22—1221no—
804C22—1221no—
805C22—1221no—
806C22—1221no—
807C22—1221no—
808C22—1221no—
809C22—1221no—
810C22—1221no—
811C22—4884no—
812C22—2444no—
813C22—2444no—
814C22—2444no—
815C22—2444no—
816C22—2442no—
817C22—2442no—
818C22—2442no—
819C22—2442no—
820C22—2442no—
821C22#1683976212yes—
822C22#1683976212yes—
823C22C2×C22⋊C4×D6111yescharacteristic
824C22C2×#1451980411yescharacteristic
825C22C2×#1451980911yescharacteristic
826C4—21no—
827C4—21no—
828C4—21no—
829C4—42no—
830C4—42no—
831C4—82no—
832C4—612no—
833C4—1221no—
834C4—1221no—
835C4—1221no—
836C4—4882no—
837C4—2442no—
838C4#99×D6112yes—
839C2—21no—
840C2—21no—
841C2—22no—
842C2—22no—
843C2—1222no—
844C2—1222no—
845C2—4882no—
846C2—2441no—
847C2—2441no—
848C2C2×#99×D6111yescharacteristic
849C2C2×#1683976211yescharacteristic
850C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1520C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840275C2
cosocleC22×C4×C61C24
hypercenter#1520D61
hypocenterC61#17592
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
2. C2×#16839724C2semidirect
3. #380×D61C2semidirect
4. #21444391C2semidirect
5. #21444388C2semidirect
6. #21444386C2semidirect
7. #21444361C2semidirect
8. #21444322C2semidirect
9. C61×#1520C2semidirect
10. C22×#11758226C4semidirect
17. #16840275C4semidirect
18. #16840275C4semidirect
22. C2×#14519753C4semidirect
23. C2×#14519752C4semidirect
28. C2×#14519735C4semidirect
33. #16839724C22semidirect
34. #16839724C22semidirect
38. #16839621C22semidirect
41. #95×D61C22semidirect
42. #16839499C22semidirect
43. #16839497C22semidirect
44. #16839495C22semidirect
48. C61×#328C22semidirect
54. C2×#11758226C2×C4semidirect
57. C22×D244C2×C4semidirect
86. #14519753C2×C4semidirect
90. #14519752C2×C4semidirect
93. #14519751C2×C4semidirect
110. #14519735C2×C4semidirect
112. C2×C4⋊Dic61C2×C4semidirect
130. C22×Q8×C61C2×C4semidirect
135. C22⋊Q8×C61C2×C4semidirect
139. C2×C4⋊C4×C61C2×C4semidirect
418. #1520D61semidirect
471. #328C2×D61semidirect
474. C61#17592semidirect
481. C22×Q8C4×D61semidirect
518. C22⋊Q8C4×D61semidirect
551. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402752
C2×#168397242
#380×D612
#214443912
#214443882
#214443862
#214443612
#214443222
C61×#15202
#1759261