Finite Group Databasebeta

← #29680141

Subgroups — #29680141

Order 15616.

1336 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#41×D61C211yesmaximal, characteristic
2#21454450C211yesmaximal, characteristic, complemented
3#21448211C211yesmaximal, characteristic, complemented
4#21445917C212yesmaximal, complemented
5#21445838C212yesmaximal, complemented
6#21445837C212yesmaximal, complemented
7#21445761C212yesmaximal
8#21445632C211yesmaximal, characteristic, complemented
9#21445630C211yesmaximal, characteristic, complemented
10#21445629C211yesmaximal, characteristic, complemented
11C61×#1759C211yesmaximal, characteristic, complemented
12C2×#41×D61C2211yescharacteristic
13#41×Dic61C2211yescharacteristic
14C4×#11758226C411yescharacteristic, complemented
15C4×#11758226C411yescharacteristic, complemented
16C4×#11758222—21no—
17C4×#11758222C2211yescharacteristic
18#16840230—21no—
19#16840230C2211yescharacteristic
20C4×#11758224—21no—
21C4×#11758224—21no—
22C4×#11758224C411yescharacteristic, complemented
23C4×#11758224C411yescharacteristic, complemented
24C4×Q8×D61C411yescharacteristic, complemented
25C4×Q8×D61C411yescharacteristic, complemented
26C4×D4×D61—21no—
27C4×D4×D61—21no—
28C4×D4×D61C411yescharacteristic, complemented
29C4×D4×D61C411yescharacteristic, complemented
30#117×D61—21no—
31#117×D61C2211yescharacteristic
32C2×C42×D61—21no—
33C2×C42×D61C2211yescharacteristic
34#16839817—21no—
35#16839817—21no—
36#16839813—21no—
37#16839813—21no—
38#16839785C2212yescomplemented
39C2×#14519705C2212yes—
40C2×#14519704C2212yes—
41C2×#14519703C2212yes—
42#16839725C2212yes—
43C4×#11758194C2211yescharacteristic, complemented
44#16839629—21no—
45#16839626—21no—
46#16839624—21no—
47#16839621—21no—
48C4×#11758196C2212yescomplemented
49C4×#11758198C2212yes—
50#16839608C2211yescharacteristic, complemented
51#16839523C2212yescomplemented
52#16839522C2212yescomplemented
53#16839521C2212yescomplemented
54C4×#41×C61C2211yescharacteristic
55C2×#104×C61C2212yes—
56C4×M16×C61C2211yescharacteristic, complemented
57C61×#376C2211yescharacteristic, complemented
58C61×#339C2212yescomplemented
59C2×#11758226C2×C411yescharacteristic
60C2×#11758222—21no—
61C2×#11758222C2311yescharacteristic
62C2×#11758224—21no—
63C2×#11758224C2×C411yescharacteristic
64#41×D61—24no—
65#41×D61—24no—
66C2×Q8×D61C2×C411yescharacteristic
67C2×D4×D61—21no—
68C2×D4×D61C2×C411yescharacteristic
69C22×C4×D61—21no—
70C22×C4×D61—21no—
71C22×C4×D61—21no—
72C22×C4×D61D411yescharacteristic
73C22×C4×D61D411yescharacteristic
74C22×C4×D61C2311yescharacteristic
75C2×#11758194C2312yes—
76Q8×Dic61C2×C411yescharacteristic
77Q8×Dic61C2×C411yescharacteristic
78C4×Dic122—21no—
79C4×Dic122—21no—
80C4×Dic122C2×C411yescharacteristic
81C4×Dic122C2×C411yescharacteristic
82#14519742—21no—
83#14519742—21no—
84#14519742C2×C411yescharacteristic
85#14519742C2×C411yescharacteristic
86C4×D244—21no—
87C4×D244—21no—
88C4×D244C2×C411yescharacteristic
89C4×D244C2×C411yescharacteristic
90D4×Dic61—21no—
91D4×Dic61—21no—
92D4×Dic61C2×C411yescharacteristic
93D4×Dic61C2×C411yescharacteristic
94#14519739—21no—
95#14519739—21no—
96#14519739C2×C411yescharacteristic
97#14519739C2×C411yescharacteristic
98C4×C22⋊D61—21no—
99C4×C22⋊D61—21no—
100C4×C22⋊D61—21no—
101C4×C22⋊D61—21no—
102C4×C22⋊D61—21no—
103C4×C22⋊D61—21no—
104#14519737—21no—
105#14519737—21no—
106#14519737—21no—
107#14519737—21no—
108#14519737—21no—
109#14519737—21no—
110#14519736—21no—
111#14519736C2311yescharacteristic
112#14519735—21no—
113#14519735—21no—
114#14519735C2×C411yescharacteristic
115#14519735C2×C411yescharacteristic
116#14519734—21no—
117#14519734—21no—
118#14519734—21no—
119#14519733—21no—
120#14519733—21no—
121#14519733—21no—
122C2×#11758196—22no—
123C4⋊C4×D61—21no—
124C4⋊C4×D61—21no—
125C4⋊C4×D61C2×C411yescharacteristic
126C4⋊C4×D61C2×C411yescharacteristic
127C2×#11758198—22no—
128C22⋊C4×D61—21no—
129C22⋊C4×D61—21no—
130C22⋊C4×D61—21no—
131C2×C4×Dic61—21no—
132C2×C4×Dic61—21no—
133C2×C4×Dic61—21no—
134C2×C4×Dic61D411yescharacteristic
135C2×C4×Dic61D411yescharacteristic
136C2×C4×Dic61C2312yes—
137C2×C4×Dic61C2311yescharacteristic
138C42×D61—21no—
139C42×D61—21no—
140C42×D61—21no—
141C42×D61—21no—
142C42×D61—21no—
143C42×D61—21no—
144C42×D61—21no—
145C42×D61C2×C411yescharacteristic
146C42×D61C2×C411yescharacteristic
147C42×D61C2×C411yescharacteristic
148C42×D61C2×C411yescharacteristic
149C42×D61D411yescharacteristic
150C42×D61D411yescharacteristic
151C42×D61D411yescharacteristic
152C42×D61D411yescharacteristic
153#14519706—22no—
154#14519706—22no—
155#14519705—24no—
156#14519704—24no—
157#14519703—24no—
158#14519689—22no—
159#14519689—22no—
160#14519688—21no—
161C4×#92418—21no—
162#14519684—21no—
163#14519684—21no—
164#14519684—22no—
165#14519684—22no—
166C2×#41×C61C2311yescharacteristic
167C2×M16×C61C2312yes—
168C4×Q8×C61C2×C411yescharacteristic
169C4×Q8×C61C2×C411yescharacteristic
170C4×D4×C61—21no—
171C4×D4×C61—21no—
172C4×D4×C61C2×C411yescharacteristic
173C4×D4×C61C2×C411yescharacteristic
174#117×C61—21no—
175#117×C61C2311yescharacteristic
176C2×C42×C61—21no—
177C2×C42×C61C2312yes—
178C2×C42×C61C2311yescharacteristic
179#104×C61—24no—
180#97×C61—21no—
181C4×C8×C61—21no—
182#95×C61—21no—
183#95×C61—21no—
184C23×D61—21no—
185C23×D61C2×D411yescharacteristic
186#41×C61—22no—
187#41×C61#4114yes—
188C2×Q8×C61C22×C411yescharacteristic
189C2×D4×C61—21no—
190C2×D4×C61C22×C411yescharacteristic
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—22no—
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2411yescharacteristic
198C2×C22⋊D61—21no—
199C2×C22⋊D61—21no—
200C2×C22⋊D61—21no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—22no—
205C22×Dic61C2×D411yescharacteristic
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208#11758226—22no—
209#11758226—22no—
210Q8×D61—22no—
211Q8×D61—22no—
212#11758224—28no—
213#11758224—22no—
214#11758224—22no—
215D4×D61—28no—
216D4×D61—22no—
217D4×D61—22no—
218#11758222—28no—
219#11758222—22no—
220#11758222#4114yes—
221C2×D244—21no—
222C2×D244C22×C411yescharacteristic
223C2×C4×D61—28no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—22no—
227C2×C4×D61—22no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—42no—
236C2×C4×D61—42no—
237C2×C4×D61—44no—
238C2×C4×D61—44no—
239C2×C4×D61C22⋊C411yescharacteristic
240C2×C4×D61C22⋊C411yescharacteristic
241C2×C4×D61C22⋊C411yescharacteristic
242C2×C4×D61C22⋊C411yescharacteristic
243C2×C4×D61C22⋊C411yescharacteristic
244C2×C4×D61C22⋊C411yescharacteristic
245C2×C4×D61C22⋊C411yescharacteristic
246C2×C4×D61C22⋊C411yescharacteristic
247C2×C4×D61C22×C411yescharacteristic
248C2×C4×D61C22×C411yescharacteristic
249C2×C4×D61C2×D411yescharacteristic
250C2×C4×D61C2×D411yescharacteristic
251C2×Dic122—21no—
252C2×Dic122C22×C411yescharacteristic
253M16×C61—22no—
254M16×C61—22no—
255C2×C8×C61—22no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61C22×C411yescharacteristic
259C4⋊C4×C61C22×C411yescharacteristic
260C22⋊C4×C61—21no—
261C22⋊C4×C61—21no—
262C22⋊C4×C61—21no—
263C42×C61—21no—
264C42×C61—21no—
265C42×C61—21no—
266C42×C61—22no—
267C42×C61—22no—
268C42×C61C22×C411yescharacteristic
269C42×C61C22×C411yescharacteristic
270C42×C61C2×D411yescharacteristic
271C42×C61C2×D411yescharacteristic
272C22⋊Dic61—21no—
273C22⋊Dic61—21no—
274C22⋊Dic61—21no—
275#11758198—21no—
276#11758198—21no—
277#11758198—21no—
278#11758198—21no—
279#11758198—21no—
280#11758198—21no—
281#11758198—44no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61C22×C411yescharacteristic
285C4⋊Dic61C22×C411yescharacteristic
286#11758196—21no—
287#11758196—21no—
288#11758196—21no—
289#11758196—21no—
290#11758196—21no—
291#11758196—21no—
292#11758196—44no—
293C4×Dic61—21no—
294C4×Dic61—21no—
295C4×Dic61—21no—
296C4×Dic61—21no—
297C4×Dic61—21no—
298C4×Dic61—21no—
299C4×Dic61—21no—
300C4×Dic61—21no—
301C4×Dic61—21no—
302C4×Dic61—22no—
303C4×Dic61—22no—
304C4×Dic61C22⋊C411yescharacteristic
305C4×Dic61C22⋊C411yescharacteristic
306C4×Dic61C22⋊C411yescharacteristic
307C4×Dic61C22⋊C411yescharacteristic
308C4×Dic61C22⋊C411yescharacteristic
309C4×Dic61C22⋊C411yescharacteristic
310C4×Dic61C22⋊C411yescharacteristic
311C4×Dic61C22⋊C411yescharacteristic
312C4×Dic61C22×C411yescharacteristic
313C4×Dic61C22×C411yescharacteristic
314C4×Dic61C2×D411yescharacteristic
315C4×Dic61C2×D411yescharacteristic
316#11758194—22no—
317#11758194—22no—
318C2×#92418—22no—
319C23×C61—21no—
320C23×C61C22×D411yescharacteristic
321C22×D61—24no—
322C22×D61—21no—
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—41no—
326C22×D61—42no—
327C22×D61—42no—
328C22×D61C2×C22⋊C411yescharacteristic
329C22×D61C2×C22⋊C411yescharacteristic
330Q8×C61—21no—
331Q8×C61#11712yes—
332D4×C61—24no—
333D4×C61—21no—
334D4×C61#11712yes—
335C2×C4×C61—21no—
336C2×C4×C61—24no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—42no—
342C2×C4×C61—42no—
343C2×C4×C61—42no—
344C2×C4×C61—42no—
345C2×C4×C61—42no—
346C2×C4×C61C2×C22⋊C411yescharacteristic
347C2×C4×C61C2×C22⋊C411yescharacteristic
348C2×C4×C61C2×C22⋊C411yescharacteristic
349C2×C4×C61C2×C22⋊C411yescharacteristic
350C2×C4×C61C23×C411yescharacteristic
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61C2×#4112yes—
353C2×C4×C61C2×#4112yes—
354C22⋊D61—24no—
355C22⋊D61—24no—
356C22⋊D61—24no—
357C2×Dic61—24no—
358C2×Dic61—21no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—41no—
364C2×Dic61—42no—
365C2×Dic61—42no—
366C2×Dic61—42no—
367C2×Dic61—42no—
368C2×Dic61—42no—
369C2×Dic61C2×C22⋊C411yescharacteristic
370C2×Dic61C2×C22⋊C411yescharacteristic
371C2×Dic61C2×C22⋊C411yescharacteristic
372C2×Dic61C2×C22⋊C411yescharacteristic
373C2×Dic61C2×C22⋊C411yescharacteristic
374C2×Dic61C2×C22⋊C411yescharacteristic
375D244—24no—
376D244—21no—
377D244#11712yes—
378C4×D61—24no—
379C4×D61—24no—
380C4×D61—22no—
381C4×D61—22no—
382C4×D61—21no—
383C4×D61—21no—
384C4×D61—21no—
385C4×D61—21no—
386C4×D61—22no—
387C4×D61—24no—
388C4×D61—22no—
389C4×D61—22no—
390C4×D61—22no—
391C4×D61—41no—
392C4×D61—41no—
393C4×D61—41no—
394C4×D61—41no—
395C4×D61—42no—
396C4×D61—42no—
397C4×D61—42no—
398C4×D61—42no—
399C4×D61—42no—
400C4×D61—42no—
401Dic122—24no—
402Dic122—21no—
403Dic122#11712yes—
404C8×C61—42no—
405#92418—42no—
406#20748—611nomaximal, Sylow
407C22×C61—21no—
408C22×C61—21no—
409C22×C61—22no—
410C22×C61—41no—
411C22×C61—41no—
412C22×C61C22×C22⋊C411yescharacteristic
413C22×C61#52512yes—
414C2×D61—21no—
415C2×D61—21no—
416C2×D61—21no—
417C2×D61—21no—
418C2×D61—21no—
419C2×D61—22no—
420C2×D61—44no—
421C2×D61—48no—
422C2×D61—41no—
423C2×D61—41no—
424C2×D61#42112yes—
425C4×C61—21no—
426C4×C61—21no—
427C4×C61—21no—
428C4×C61—21no—
429C4×C61—22no—
430C4×C61—41no—
431C4×C61—41no—
432C4×C61—82no—
433C4×C61C2×#11711yescharacteristic
434C4×C61C2×#11711yescharacteristic
435C4×C61#52512yes—
436Dic61—21no—
437Dic61—21no—
438Dic61—21no—
439Dic61—21no—
440Dic61—22no—
441Dic61—21no—
442Dic61—41no—
443Dic61—41no—
444Dic61—82no—
445Dic61#42112yes—
446C2×C4×#41—611no—
447#2920—611no—
448#2283—611no—
449#1826—612no—
450#1806—612no—
451#1806—612no—
452#1789—612no—
453#1759—611no—
454#1759—611no—
455#1759—611no—
456#1759D6111yescharacteristic, complemented
457C2×C61—22no—
458C2×C61—42no—
459C2×C61#228011yescharacteristic
460C2×C61C2×#42111yescharacteristic
461C2×C61C2×#42111yescharacteristic
462D61—22no—
463D61—41no—
464D61—42no—
465C22×#41—611no—
466C4×#41—611no—
467C4×#41—611no—
468C4×#41—611no—
469C4×#41—611no—
470C4×#41—611no—
471C4×#41—611no—
472C4×#41—611no—
473C4×#41—1221no—
474C4×#41—1221no—
475C4×#41—1221no—
476C4×#41—1221no—
477C4×#41C2×D6111yescharacteristic
478C2×C4×Q8—611no—
479C2×C4×Q8—611no—
480C2×C4×D4—611no—
481C2×C4×D4—611no—
482C2×C4×D4—1221no—
483C2×C4×D4—1221no—
484C2×#117—611no—
485C2×#117—1221no—
486C22×C42—611no—
487C22×C42—1221no—
488#432—1221no—
489#432—1221no—
490#431—1221no—
491#431—1221no—
492#423—612no—
493C2×#104—612no—
494C2×#104—612no—
495C2×#104—612no—
496C2×#104C2×D6112yes—
497#407—612no—
498C4×M16—611no—
499C4×M16C2×D6111yescharacteristic, complemented
500#383—1221no—
501#382—1221no—
502#381—1221no—
503#380—1221no—
504C4×C4⋊C4—612no—
505C4×C22⋊C4—612no—
506#376—611no—
507#376C2×D6111yescharacteristic, complemented
508#339—612no—
509#339—612no—
510#339—612no—
511#339C2×D6112yescomplemented
512C61#2074811yescharacteristic, complemented, Sylow
513C2×#41—611no—
514C2×#41—611no—
515C2×#41—611no—
516C2×#41—1221no—
517C2×#41—1221no—
518C2×#41—1224no—
519C2×#41—1224no—
520C2×#41C22×D6111yescharacteristic
521C22×Q8—611no—
522C22×D4—611no—
523C22×D4—1221no—
524C23×C4—611no—
525C23×C4—611no—
526C23×C4—611no—
527C23×C4—1221no—
528C23×C4—1221no—
529C23×C4—1221no—
530C2×M16—612no—
531C2×M16C22×D6112yes—
532C4×Q8—611no—
533C4×Q8—611no—
534C4×Q8—611no—
535C4×Q8—611no—
536C4×Q8—611no—
537C4×Q8—611no—
538C4×Q8—1221no—
539C4×Q8—1221no—
540C4×Q8—1221no—
541C4×Q8—1221no—
542C4×Q8C4×D6111yescharacteristic
543C4×Q8C4×D6111yescharacteristic
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—611no—
547C4×D4—611no—
548C4×D4—611no—
549C4×D4—611no—
550C4×D4—611no—
551C4×D4—611no—
552C4×D4—1221no—
553C4×D4—1221no—
554C4×D4—1221no—
555C4×D4—1221no—
556C4×D4—1221no—
557C4×D4—1221no—
558C4×D4—1221no—
559C4×D4—1221no—
560C4×D4—1221no—
561C4×D4—1221no—
562C4×D4—1221no—
563C4×D4—1221no—
564C4×D4—1221no—
565C4×D4—1221no—
566C4×D4—1221no—
567C4×D4—1221no—
568C4×D4—1221no—
569C4×D4—1221no—
570C4×D4C4×D6111yescharacteristic
571C4×D4C4×D6111yescharacteristic
572#117—21no—
573#117—611no—
574#117—611no—
575#117—611no—
576#117—1221no—
577#117—1221no—
578#117—1221no—
579#117—1221no—
580#117—1221no—
581#117—1221no—
582#117—1221no—
583#117—1221no—
584#117—1221no—
585#117C22×D6111yescharacteristic
586C2×C4⋊C4—611no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—1221no—
589C2×C4⋊C4—1221no—
590C2×C4⋊C4—1222no—
591C2×C22⋊C4—1221no—
592C2×C22⋊C4—1221no—
593C2×C22⋊C4—1221no—
594C2×C22⋊C4—1222no—
595C2×C42—21no—
596C2×C42—611no—
597C2×C42—611no—
598C2×C42—611no—
599C2×C42—611no—
600C2×C42—611no—
601C2×C42—611no—
602C2×C42—611no—
603C2×C42—611no—
604C2×C42—611no—
605C2×C42—611no—
606C2×C42—611no—
607C2×C42—612no—
608C2×C42—1221no—
609C2×C42—1221no—
610C2×C42—1221no—
611C2×C42—1221no—
612C2×C42—1221no—
613C2×C42—1221no—
614C2×C42—1221no—
615C2×C42—1221no—
616C2×C42—1221no—
617C2×C42—1221no—
618C2×C42C22×D6112yes—
619C2×C42C22×D6111yescharacteristic
620C4⋊C8—1222no—
621C4⋊C8—1222no—
622#104—24no—
623#104—1224no—
624#104—1224no—
625#104—1224no—
626C22⋊C8—1222no—
627C22⋊C8—1222no—
628#97—21no—
629#97—1221no—
630C4×C8—21no—
631C4×C8—1221no—
632#95—21no—
633#95—21no—
634#95—1222no—
635#95—1222no—
636#95—1221no—
637#95—1221no—
638C24—611no—
639C24—1221no—
640#41—22no—
641#41—614no—
642#41—1228no—
643#41—1222no—
644#41—1228no—
645#41—1222no—
646#41—1222no—
647#41—1222no—
648#41—1222no—
649#41#1175822214yes—
650C2×Q8—611no—
651C2×Q8—1221no—
652C2×Q8—1222no—
653C2×Q8—1222no—
654C2×Q8C2×C4×D6111yescharacteristic
655C2×D4—21no—
656C2×D4—611no—
657C2×D4—1221no—
658C2×D4—1221no—
659C2×D4—1222no—
660C2×D4—1228no—
661C2×D4—1221no—
662C2×D4—1221no—
663C2×D4—1222no—
664C2×D4C2×C4×D6111yescharacteristic
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—22no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—611no—
674C22×C4—611no—
675C22×C4—611no—
676C22×C4—611no—
677C22×C4—611no—
678C22×C4—611no—
679C22×C4—611no—
680C22×C4—611no—
681C22×C4—611no—
682C22×C4—611no—
683C22×C4—611no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1228no—
689C22×C4—1221no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4—1221no—
695C22×C4—1222no—
696C22×C4—1222no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1222no—
700C22×C4—2442no—
701C22×C4—2442no—
702C22×C4—2444no—
703C22×C4—2444no—
704C22×C4D4×D6111yescharacteristic
705C22×C4D4×D6111yescharacteristic
706C22×C4C23×D6111yescharacteristic
707M16—22no—
708M16—22no—
709M16—1222no—
710M16—1222no—
711C2×C8—22no—
712C2×C8—1222no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—611no—
716C4⋊C4—611no—
717C4⋊C4—1221no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4—2444no—
726C4⋊C4C2×C4×D6111yescharacteristic
727C4⋊C4C2×C4×D6111yescharacteristic
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—1221no—
732C22⋊C4—1221no—
733C22⋊C4—1221no—
734C22⋊C4—1221no—
735C22⋊C4—1221no—
736C22⋊C4—1221no—
737C22⋊C4—1221no—
738C22⋊C4—1221no—
739C22⋊C4—1221no—
740C22⋊C4—2444no—
741C42—21no—
742C42—21no—
743C42—21no—
744C42—22no—
745C42—22no—
746C42—611no—
747C42—611no—
748C42—611no—
749C42—611no—
750C42—611no—
751C42—611no—
752C42—611no—
753C42—611no—
754C42—611no—
755C42—611no—
756C42—611no—
757C42—611no—
758C42—1221no—
759C42—1221no—
760C42—1221no—
761C42—1221no—
762C42—1221no—
763C42—1221no—
764C42—1221no—
765C42—1221no—
766C42—1221no—
767C42—1222no—
768C42—1222no—
769C42C2×C4×D6111yescharacteristic
770C42C2×C4×D6111yescharacteristic
771C42D4×D6111yescharacteristic
772C42D4×D6111yescharacteristic
773C23—21no—
774C23—611no—
775C23—611no—
776C23—1222no—
777C23—1224no—
778C23—1221no—
779C23—1222no—
780C23—2441no—
781C23—2442no—
782C23—2442no—
783C23C2×D4×D6111yescharacteristic
784Q8—21no—
785Q8—612no—
786Q8—1224no—
787Q8—1221no—
788Q8#1451973412yes—
789D4—24no—
790D4—21no—
791D4—612no—
792D4—1224no—
793D4—1224no—
794D4—1224no—
795D4—1224no—
796D4—1221no—
797D4#1451973412yes—
798C2×C4—21no—
799C2×C4—24no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—611no—
810C2×C4—611no—
811C2×C4—611no—
812C2×C4—611no—
813C2×C4—611no—
814C2×C4—611no—
815C2×C4—1222no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—1222no—
819C2×C4—1224no—
820C2×C4—1224no—
821C2×C4—1222no—
822C2×C4—1224no—
823C2×C4—1221no—
824C2×C4—1222no—
825C2×C4—1221no—
826C2×C4—1221no—
827C2×C4—1221no—
828C2×C4—1221no—
829C2×C4—1222no—
830C2×C4—1222no—
831C2×C4—1224no—
832C2×C4—1221no—
833C2×C4—1221no—
834C2×C4—2441no—
835C2×C4—2441no—
836C2×C4—2441no—
837C2×C4—2441no—
838C2×C4—2442no—
839C2×C4—2442no—
840C2×C4—2442no—
841C2×C4—2442no—
842C2×C4—2442no—
843C2×C4—2442no—
844C2×C4—2442no—
845C2×C4—2441no—
846C2×C4—2442no—
847C2×C4—2442no—
848C2×C4—2442no—
849C2×C4—2442no—
850C2×C4C22⋊C4×D6111yescharacteristic
851C2×C4C22⋊C4×D6111yescharacteristic
852C2×C4C22⋊C4×D6111yescharacteristic
853C2×C4C22⋊C4×D6111yescharacteristic
854C2×C4C22×C4×D6111yescharacteristic
855C2×C4C2×D4×D6111yescharacteristic
856C2×C4#41×D6112yes—
857C2×C4C2×#1175822212yes—
858C8—42no—
859C8—2442no—
860C22—21no—
861C22—21no—
862C22—22no—
863C22—41no—
864C22—41no—
865C22—612no—
866C22—1221no—
867C22—1221no—
868C22—1222no—
869C22—1221no—
870C22—1221no—
871C22—1221no—
872C22—2444no—
873C22—2448no—
874C22—2441no—
875C22—2441no—
876C22C2×C22⋊C4×D6111yescharacteristic
877C22#1684027112yes—
878C4—22no—
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—41no—
884C4—41no—
885C4—82no—
886C4—612no—
887C4—1221no—
888C4—1221no—
889C4—1222no—
890C4—1221no—
891C4—1221no—
892C4—1221no—
893C4—4882no—
894C4—2441no—
895C4—2441no—
896C4#117×D6111yescharacteristic
897C4C2×#1451973411yescharacteristic
898C4#1684027112yes—
899C2—22no—
900C2—42no—
901C2—1222no—
902C2—2441no—
903C2—2442no—
904C2#2144820011yescharacteristic
905C2#421×D6111yescharacteristic
906C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1759C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#41×D61C22
cosocleC22×C4×C61C24
hypercenter#1759D61
hypocenterC61#20748
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1759

Complements

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

NH ≅ G/Ntype
2. #21454450C2semidirect
3. #21448211C2semidirect
4. #21445917C2semidirect
5. #21445838C2semidirect
6. #21445837C2semidirect
8. #21445632C2semidirect
9. #21445630C2semidirect
10. #21445629C2semidirect
11. C61×#1759C2semidirect
14. C4×#11758226C4semidirect
15. C4×#11758226C4semidirect
22. C4×#11758224C4semidirect
23. C4×#11758224C4semidirect
24. C4×Q8×D61C4semidirect
25. C4×Q8×D61C4semidirect
28. C4×D4×D61C4semidirect
29. C4×D4×D61C4semidirect
38. #16839785C22semidirect
43. C4×#11758194C22semidirect
48. C4×#11758196C22semidirect
50. #16839608C22semidirect
51. #16839523C22semidirect
52. #16839522C22semidirect
53. #16839521C22semidirect
56. C4×M16×C61C22semidirect
57. C61×#376C22semidirect
58. C61×#339C22semidirect
456. #1759D61semidirect
499. C4×M16C2×D61semidirect
507. #376C2×D61semidirect
511. #339C2×D61semidirect
512. C61#20748semidirect

Maximal subgroups

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

subgroupindex
C4×#41×D612
#214544502
#214482112
#214459172
#214458382
#214458372
#214457612
#214456322
#214456302
#214456292
C61×#17592
#2074861