Finite Group Databasebeta

← #29647176

Subgroups — #29647176

Order 15616.

1574 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840275C211yesmaximal, characteristic
2#407×D61C211yesmaximal, characteristic, complemented
3C4×C22⋊C4×D61C211yesmaximal, characteristic, complemented
4#21444339C211yesmaximal, characteristic, complemented
5#21444336C211yesmaximal, characteristic, complemented
6#21444334C211yesmaximal, characteristic, complemented
7#21444322C214yesmaximal, complemented
8#21444309C214yesmaximal, complemented
9C61×#1508C211yesmaximal, characteristic, complemented
10C22×#11758226C411yescharacteristic, complemented
11C23×C4×D61C2211yescharacteristic
12C2×M16×D61—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×C22⋊C4×D61—21no—
30C2×C42×D61—21no—
31#16839726C2211yescharacteristic
32#16839725—21no—
33#16839724—21no—
34#16839724C2212yescomplemented
35C22⋊C8×D61—21no—
36C22⋊C8×D61C2212yescomplemented
37C22⋊C4×Dic61—21no—
38C4×#11758198—21no—
39C4×C22⋊Dic61C2211yescharacteristic
40#16839609C2212yescomplemented
41#95×D61C2212yescomplemented
42#16839499C2214yescomplemented
43#16839497C2214yescomplemented
44#16839495C2214yescomplemented
45C2×C22⋊Q8×C61C2211yescharacteristic
46C61×#407C2211yescharacteristic
47C4×C22⋊C4×C61C2211yescharacteristic
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—22no—
61C22×C4×D61—21no—
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×#11758194—21no—
76C2×#11758189—22no—
77M16×D61—44no—
78C2×C8×D61—22no—
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⋊Dic61C2×C411yescharacteristic, complemented
112C2×#11758196—21no—
113C2×C22⋊Dic61—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—22no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C22⋊C4×D61—28no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61—22no—
123C42×D61—44no—
124C22⋊#92418—21no—
125C22⋊#92418C2312yes—
126#14519689—22no—
127#14519689—22no—
128#14519684—22no—
129#14519684C2312yes—
130C22×Q8×C61C2×C411yescharacteristic, complemented
131C23×C4×C61C2311yescharacteristic
132C2×M16×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×C61C2×C411yescharacteristic, complemented
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C42×C61—21no—
142C22⋊C8×C61—21no—
143C22⋊C8×C61C2312yes—
144#95×C61C2312yes—
145C24×C61C2×D411yescharacteristic
146C23×D61—24no—
147C23×D61—21no—
148C23×D61—42no—
149C23×D61—42no—
150C23×D61C22⋊C411yescharacteristic
151C23×D61C22⋊C411yescharacteristic
152C23×D61C22⋊C411yescharacteristic
153C23×D61C22⋊C411yescharacteristic
154C23×D61C2×D411yescharacteristic
155C23×D61C2×D411yescharacteristic
156C2×Q8×C61—21no—
157C2×Q8×C61—42no—
158C2×Q8×C61C22×C412yes—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—22no—
162C22×C4×C61—42no—
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2411yescharacteristic
169C2×C22⋊D61—22no—
170C2×C22⋊D61—22no—
171C2×C22⋊D61—44no—
172C22×Dic61—21no—
173C22×Dic61—22no—
174C22×Dic61—42no—
175C22×Dic61C22⋊C411yescharacteristic
176C22×Dic61C22⋊C411yescharacteristic
177C22×Dic61C22⋊C411yescharacteristic
178C22×Dic61C22⋊C411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180C22×Dic61C2×D411yescharacteristic
181#11758226—44no—
182#11758226—44no—
183#11758226—44no—
184#11758226—44no—
185C2×D244—22no—
186C2×D244—22no—
187C2×D244—22no—
188C2×D244—22no—
189C2×D244—21no—
190C2×D244—44no—
191C2×D244—44no—
192C2×D244—42no—
193C2×D244C22×C412yes—
194C2×C4×D61—24no—
195C2×C4×D61—24no—
196C2×C4×D61—24no—
197C2×C4×D61—28no—
198C2×C4×D61—22no—
199C2×C4×D61—22no—
200C2×C4×D61—42no—
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—44no—
210C2×C4×D61—44no—
211C2×C4×D61—44no—
212C2×C4×D61C22⋊C411yescharacteristic
213C2×C4×D61C22⋊C411yescharacteristic
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×D61C2×D411yescharacteristic
225C2×C4×D61C2×D411yescharacteristic
226C2×C4×D61C2×D411yescharacteristic
227C2×C4×D61C2×D411yescharacteristic
228M16×C61—42no—
229C2×C8×C61—22no—
230C4⋊C4×C61—22no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—22no—
233C4⋊C4×C61C22×C412yes—
234C22⋊C4×C61—24no—
235C22⋊C4×C61—22no—
236C22⋊C4×C61—22no—
237C42×C61—42no—
238C22⋊Dic61—24no—
239#11758198—28no—
240#11758198—22no—
241#11758198—22no—
242#11758198—22no—
243#11758198—22no—
244#11758198—22no—
245#11758198—22no—
246#11758198—22no—
247#11758198—22no—
248C4⋊Dic61—21no—
249C4⋊Dic61C22×C412yes—
250#11758196—22no—
251#11758196—22no—
252C4×Dic61—22no—
253C4×Dic61—22no—
254C4×Dic61—44no—
255C4×Dic61—42no—
256#11758194—42no—
257C2×#92418—22no—
258#11758189—44no—
259C8×D61—44no—
260C23×C61—22no—
261C23×C61—22no—
262C23×C61—41no—
263C23×C61C2×C22⋊C411yescharacteristic
264C23×C61C2×C22⋊C411yescharacteristic
265C23×C61C22×D411yescharacteristic
266C22×D61—22no—
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—22no—
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—416no—
285C22×D61—42no—
286C22×D61—42no—
287C22×D61—42no—
288C22×D61#10414yes—
289C22×D61C2×C22⋊C411yescharacteristic
290C22×D61C2×C22⋊C411yescharacteristic
291C22×D61C2×C22⋊C411yescharacteristic
292C22×D61C2×C22⋊C411yescharacteristic
293Q8×C61—42no—
294Q8×C61—42no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—24no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61C2×C22⋊C411yescharacteristic
309C2×C4×C61C2×C22⋊C411yescharacteristic
310C2×C4×C61C23×C411yescharacteristic
311C2×C4×C61C22×D411yescharacteristic
312C22⋊D61—44no—
313C22⋊D61—44no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—24no—
318C2×Dic61—22no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61C2×C22⋊C411yescharacteristic
326C2×Dic61C2×C22⋊C411yescharacteristic
327C2×Dic61C2×C22⋊C411yescharacteristic
328C2×Dic61C2×C22⋊C411yescharacteristic
329D244—42no—
330D244—44no—
331D244—44no—
332D244—44no—
333D244—44no—
334D244—42no—
335C4×D61—22no—
336C4×D61—22no—
337C4×D61—22no—
338C4×D61—22no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—41no—
345C4×D61—41no—
346C4×D61—41no—
347C4×D61—41no—
348C4×D61—41no—
349C4×D61—41no—
350C4×D61—44no—
351C4×D61—416no—
352C4×D61—44no—
353C4×D61#9914yes—
354C8×C61—42no—
355#92418—42no—
356#17542—611nomaximal, Sylow
357C22×C61—21no—
358C22×C61—21no—
359C22×C61—21no—
360C22×C61—21no—
361C22×C61—21no—
362C22×C61—21no—
363C22×C61—21no—
364C22×C61—44no—
365C22×C61C2×#10412yes—
366C22×C61C22×C22⋊C411yescharacteristic
367C22×C61#57512yes—
368C2×D61—28no—
369C2×D61—21no—
370C2×D61—21no—
371C2×D61—21no—
372C2×D61—21no—
373C2×D61—21no—
374C2×D61—21no—
375C2×D61—21no—
376C2×D61—21no—
377C2×D61—21no—
378C2×D61—44no—
379C2×D61—44no—
380C2×D61—44no—
381C2×D61—44no—
382C2×D61—44no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—84no—
387C2×D61C2×#9912yes—
388C2×D61C2×#10412yes—
389C2×D61C2×#10412yes—
390C4×C61—21no—
391C4×C61—21no—
392C4×C61—21no—
393C4×C61—44no—
394C4×C61—42no—
395C4×C61—42no—
396C4×C61C2×#9912yes—
397Dic61—21no—
398Dic61—21no—
399Dic61—21no—
400Dic61—44no—
401Dic61—42no—
402Dic61C2×#9912yes—
403C2×#525—611no—
404C2×#407—611no—
405C2×C4×C22⋊C4—611no—
406#1508—611no—
407#1508D6111yescharacteristic, complemented
408#1507—611no—
409#1507—611no—
410#1504—614no—
411#1501—614no—
412C2×C61—22no—
413C2×C61—22no—
414C2×C61—41no—
415C2×C61C22×#9911yescharacteristic
416C2×C61#289611yescharacteristic
417C2×C61C22×#10411yescharacteristic
418D61—22no—
419D61—22no—
420D61—22no—
421D61—41no—
422D61—82no—
423C22×#41—611no—
424C24×C4—611no—
425C22×M16—1221no—
426#525—612no—
427#525—612no—
428#525—612no—
429#525—612no—
430#525—1221no—
431#525—1221no—
432#525—1221no—
433#525—1221no—
434C2×#123—1221no—
435C2×C22⋊Q8—611no—
436C2×C22⋊Q8C2×D6111yescharacteristic
437C2×#121—611no—
438C2×#121—611no—
439C2×#120—1221no—
440C2×C4×D4—1221no—
441C2×C4×D4—1221no—
442C2×#117—611no—
443C22×C22⋊C4—1221no—
444C22×C42—1221no—
445#407—611no—
446#407—612no—
447#407—1221no—
448#407—1221no—
449#407C2×D6111yescharacteristic
450C2×C22⋊C8—612no—
451C2×C22⋊C8—1221no—
452C4×C22⋊C4—611no—
453C4×C22⋊C4—612no—
454C4×C22⋊C4—1221no—
455C4×C22⋊C4—1221no—
456C4×C22⋊C4C2×D6111yescharacteristic
457C2×#95—612no—
458#328—614no—
459#328C2×D6114yescomplemented
460#327—614no—
461#327—614no—
462C61#1754211yescharacteristic, complemented, Sylow
463C25—611no—
464C2×#41—612no—
465C2×#41—612no—
466C2×#41—1221no—
467C2×#41—1221no—
468C2×#41—2444no—
469C22×Q8C4×D6111yescharacteristic, complemented
470C22×D4—611no—
471C22×D4—1221no—
472C22×D4—1221no—
473C22×D4—1221no—
474C23×C4—611no—
475C23×C4—611no—
476C23×C4—611no—
477C23×C4—611no—
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—1221no—
488C23×C4—1222no—
489C23×C4—2444no—
490C23×C4C22×D6111yescharacteristic
491C2×M16—21no—
492C2×M16—1222no—
493C2×M16—1221no—
494C2×M16—2444no—
495C22×C8—1222no—
496#123—1222no—
497#123—1222no—
498#123—1222no—
499#123—1222no—
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502C22⋊Q8—612no—
503C22⋊Q8—612no—
504C22⋊Q8—1221no—
505C22⋊Q8—1221no—
506C22⋊Q8C4×D6112yescomplemented
507C22⋊Q8C22×D6112yes—
508#121—612no—
509#121—612no—
510#121—612no—
511#121—612no—
512#121—1221no—
513#121—1221no—
514#121—1221no—
515#121—1221no—
516#120—1222no—
517#120—1222no—
518#120—1222no—
519#120—1222no—
520C4×D4—1222no—
521C4×D4—1222no—
522C4×D4—1222no—
523C4×D4—1222no—
524C4×D4—1222no—
525C4×D4—1222no—
526C4×D4—1222no—
527C4×D4—1222no—
528#117—612no—
529#117—612no—
530#117—1221no—
531#117—1221no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—611no—
534C2×C4⋊C4—1221no—
535C2×C4⋊C4C4×D6111yescharacteristic, complemented
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—1228no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1222no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C42—21no—
546C2×C42—1221no—
547C2×C42—1222no—
548C2×C42—1221no—
549C2×C42—2444no—
550C22⋊C8—21no—
551C22⋊C8—612no—
552C22⋊C8—1222no—
553C22⋊C8—1222no—
554C22⋊C8—1221no—
555C22⋊C8C22×D6112yes—
556#95—612no—
557#95—1222no—
558#95C22×D6112yes—
559C24—611no—
560C24—611no—
561C24—611no—
562C24—611no—
563C24—611no—
564C24—611no—
565C24—1224no—
566C24—1221no—
567C24—2442no—
568C24—2442no—
569C24D4×D6111yescharacteristic
570#41—2444no—
571#41—2444no—
572#41—2444no—
573#41—2444no—
574C2×Q8—21no—
575C2×Q8—42no—
576C2×Q8C2×C4×D6112yes—
577C2×D4—612no—
578C2×D4—1222no—
579C2×D4—1222no—
580C2×D4—1222no—
581C2×D4—1222no—
582C2×D4—1222no—
583C2×D4—1222no—
584C2×D4—1221no—
585C2×D4—2442no—
586C2×D4—2444no—
587C2×D4—2444no—
588C2×D4—2444no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—42no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—611no—
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—1224no—
616C22×C4—1224no—
617C22×C4—1224no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1228no—
621C22×C4—1222no—
622C22×C4—1221no—
623C22×C4—2442no—
624C22×C4—2442no—
625C22×C4—2442no—
626C22×C4—2442no—
627C22×C4—2442no—
628C22×C4—2442no—
629C22×C4—2442no—
630C22×C4—2442no—
631C22×C4—2442no—
632C22×C4—2444no—
633C22×C4—2444no—
634C22×C4—2444no—
635C22×C4—2442no—
636C22×C4C2×C4×D6111yescharacteristic
637C22×C4C2×C4×D6111yescharacteristic
638C22×C4D4×D6111yescharacteristic
639C22×C4D4×D6111yescharacteristic
640C22×C4D4×D6111yescharacteristic
641C22×C4C23×D6111yescharacteristic
642M16—42no—
643M16—2444no—
644M16—2442no—
645C2×C8—22no—
646C2×C8—1222no—
647C2×C8—2444no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—612no—
652C4⋊C4—1222no—
653C4⋊C4—1222no—
654C4⋊C4—1221no—
655C4⋊C4C2×C4×D6112yes—
656C22⋊C4—24no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—1222no—
660C22⋊C4—1222no—
661C22⋊C4—1222no—
662C22⋊C4—1222no—
663C22⋊C4—1222no—
664C22⋊C4—1222no—
665C22⋊C4—1228no—
666C22⋊C4—1224no—
667C22⋊C4—1222no—
668C22⋊C4—1222no—
669C42—42no—
670C42—1222no—
671C42—1222no—
672C42—2442no—
673C42—2444no—
674C23—22no—
675C23—22no—
676C23—41no—
677C23—611no—
678C23—611no—
679C23—611no—
680C23—614no—
681C23—611no—
682C23—1222no—
683C23—1222no—
684C23—1222no—
685C23—1222no—
686C23—1222no—
687C23—1222no—
688C23—1222no—
689C23—1222no—
690C23—1222no—
691C23—1222no—
692C23—1222no—
693C23—2441no—
694C23—2441no—
695C23—2441no—
696C23—2441no—
697C23—2441no—
698C23—2441no—
699C23—2441no—
700C23—2442no—
701C23—2442no—
702C23—24416no—
703C23—2442no—
704C23C22⋊C4×D6111yescharacteristic
705C23C22⋊C4×D6111yescharacteristic
706C23C2×D4×D6111yescharacteristic
707Q8—42no—
708Q8—42no—
709D4—2442no—
710D4—2444no—
711D4—2444no—
712D4—2444no—
713D4—2444no—
714D4—2444no—
715D4—2444no—
716D4—2442no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—611no—
731C2×C4—614no—
732C2×C4—611no—
733C2×C4—611no—
734C2×C4—611no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1224no—
748C2×C4—1222no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2444no—
756C2×C4—2444no—
757C2×C4—24416no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2442no—
762C2×C4—2442no—
763C2×C4—2442no—
764C2×C4C22⋊C4×D6111yescharacteristic
765C2×C4C22⋊C4×D6111yescharacteristic
766C2×C4C22×C4×D6111yescharacteristic
767C2×C4C2×D4×D6111yescharacteristic
768C8—42no—
769C8—2442no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—44no—
778C22—612no—
779C22—612no—
780C22—612no—
781C22—1228no—
782C22—1221no—
783C22—1221no—
784C22—1221no—
785C22—1221no—
786C22—1221no—
787C22—1221no—
788C22—1221no—
789C22—1221no—
790C22—1221no—
791C22—4884no—
792C22—2444no—
793C22—2444no—
794C22—2444no—
795C22—2444no—
796C22—2444no—
797C22—2442no—
798C22—2442no—
799C22—2442no—
800C22#104×D6112yes—
801C22C2×C22⋊C4×D6111yescharacteristic
802C22#1684056112yes—
803C4—21no—
804C4—21no—
805C4—21no—
806C4—44no—
807C4—42no—
808C4—42no—
809C4—612no—
810C4—1221no—
811C4—1221no—
812C4—1221no—
813C4—2444no—
814C4—2442no—
815C4#99×D6112yes—
816C2—22no—
817C2—22no—
818C2—41no—
819C2—1222no—
820C2—1222no—
821C2—1222no—
822C2—4882no—
823C2—2441no—
824C2C2×#99×D6111yescharacteristic
825C2#2145433711yescharacteristic
826C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1508C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840275C2
cosocleC22×C4×C61C24
hypercenter#1508D61
hypocenterC61#17542
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1508

Complements

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

NH ≅ G/Ntype
2. #407×D61C2semidirect
3. C4×C22⋊C4×D61C2semidirect
4. #21444339C2semidirect
5. #21444336C2semidirect
6. #21444334C2semidirect
7. #21444322C2semidirect
8. #21444309C2semidirect
9. C61×#1508C2semidirect
10. C22×#11758226C4semidirect
17. #16840275C4semidirect
18. #16840275C4semidirect
22. C2×#14519753C4semidirect
23. C2×#14519752C4semidirect
28. C2×#14519735C4semidirect
34. #16839724C22semidirect
36. C22⋊C8×D61C22semidirect
40. #16839609C22semidirect
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
111. C2×C4⋊Dic61C2×C4semidirect
130. C22×Q8×C61C2×C4semidirect
135. C22⋊Q8×C61C2×C4semidirect
138. C2×C4⋊C4×C61C2×C4semidirect
407. #1508D61semidirect
459. #328C2×D61semidirect
462. C61#17542semidirect
469. C22×Q8C4×D61semidirect
506. C22⋊Q8C4×D61semidirect
535. 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
#407×D612
C4×C22⋊C4×D612
#214443392
#214443362
#214443342
#214443222
#214443092
C61×#15082
#1754261