Finite Group Databasebeta

← D61×#1459 #29645808

Subgroups — D61×#1459 #29645808

Order 15616.

1826 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D61C211yesmaximal, characteristic
2C2×C22⋊C8×D61C212yesmaximal, complemented
3#21444137C211yesmaximal, characteristic, complemented
4#21444136C212yesmaximal, complemented
5#21444135C212yesmaximal, complemented
6#21444134C212yesmaximal, complemented
7#324×D61C212yesmaximal, complemented
8#323×D61C212yesmaximal, complemented
9C61×#1459C211yesmaximal, characteristic, complemented
10C22×D4×D61C411yescharacteristic
11C23×C4×D61C411yescharacteristic
12C23×C4×D61C2211yescharacteristic
13C22×C8×D61—22no—
14C2×C4×D244C411yescharacteristic
15C2×D4×Dic61C411yescharacteristic
16C2×#14519739C2211yescharacteristic
17C2×C4×C22⋊D61C411yescharacteristic
18C2×C4×C22⋊D61C2211yescharacteristic
19C2×#14519737C411yescharacteristic
20C2×#14519737C2211yescharacteristic
21C4×D4×D61—22no—
22C4×D4×D61—22no—
23C4×D4×D61—22no—
24C4×D4×D61—22no—
25C2×C4⋊C4×D61C2211yescharacteristic
26C2×C22⋊C4×D61C411yescharacteristic
27C2×C22⋊C4×D61C2211yescharacteristic
28C2×C42×D61C411yescharacteristic
29C2×C22⋊#92418C2212yescomplemented
30C2×#14519689—22no—
31C22⋊C8×D61—22no—
32C22⋊C8×D61—22no—
33C22⋊C8×D61C2214yes—
34C22⋊C8×D61C2214yescomplemented
35#16839488C2212yescomplemented
36#16839487C2214yescomplemented
37#16839486C2212yescomplemented
38#16839485C2214yescomplemented
39C2×C4×D4×C61C2211yescharacteristic
40C2×C22⋊C8×C61C2212yescomplemented
41C61×#324C2212yescomplemented
42C61×#323C2212yescomplemented
43C24×D61C2×C411yescharacteristic
44C24×D61C2×C411yescharacteristic
45C22×D244C2×C411yescharacteristic
46C22×C22⋊D61C2×C411yescharacteristic
47C22×C22⋊D61C2×C411yescharacteristic
48C2×D4×D61—22no—
49C2×D4×D61—22no—
50C2×D4×D61—24no—
51C2×D4×D61C818yescomplemented
52C23×Dic61C2×C411yescharacteristic
53C23×Dic61C2×C411yescharacteristic
54C22×C4×D61—21no—
55C22×C4×D61—21no—
56C22×C4×D61—21no—
57C22×C4×D61—21no—
58C22×C4×D61—44no—
59C22×C4×D61—44no—
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61C2×C411yescharacteristic
66C22×C4×D61C2×C411yescharacteristic
67C22×C4×D61D412yes—
68C22×C4×D61D412yes—
69C22×C4×D61D412yes—
70C22×C4×D61D412yes—
71C22×C4×D61C2311yescharacteristic
72C22×C4×D61C2311yescharacteristic
73C22×#92418—22no—
74C2×C8×D61—24no—
75C2×C8×D61—24no—
76C2×C8×D61—48no—
77C4×D244—22no—
78C4×D244—22no—
79D4×Dic61—22no—
80D4×Dic61—22no—
81#14519739—22no—
82#14519739—22no—
83C4×C22⋊D61—22no—
84C4×C22⋊D61—22no—
85C4×C22⋊D61—22no—
86C4×C22⋊D61—22no—
87#14519737—22no—
88#14519737—22no—
89#14519737—22no—
90#14519737—22no—
91C2×C4⋊Dic61C2×C411yescharacteristic
92C2×#11758196C2×C411yescharacteristic
93C2×#11758196C2311yescharacteristic
94C4⋊C4×D61—22no—
95C4⋊C4×D61—22no—
96C2×C22⋊Dic61C2×C411yescharacteristic
97C2×C22⋊Dic61C2×C411yescharacteristic
98C2×#11758198C2×C411yescharacteristic
99C2×#11758198C2×C411yescharacteristic
100C2×#11758198C2×C411yescharacteristic
101C2×#11758198C2311yescharacteristic
102C22⋊C4×D61—22no—
103C22⋊C4×D61—22no—
104C22⋊C4×D61—22no—
105C22⋊C4×D61—22no—
106C2×C4×Dic61C2×C411yescharacteristic
107C2×C4×Dic61C2×C411yescharacteristic
108C2×C4×Dic61C2×C411yescharacteristic
109C42×D61—21no—
110C42×D61—21no—
111C42×D61—21no—
112C42×D61—21no—
113C22⋊#92418—22no—
114C22⋊#92418C2314yes—
115#14519689—24no—
116#14519689—24no—
117C22×D4×C61C2×C411yescharacteristic
118C23×C4×C61C2×C411yescharacteristic
119C23×C4×C61C2311yescharacteristic
120C22×C8×C61—22no—
121C4×D4×C61—22no—
122C4×D4×C61—22no—
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C22⋊C4×C61C2×C411yescharacteristic
125C2×C22⋊C4×C61C2311yescharacteristic
126C2×C42×C61C2×C411yescharacteristic
127C22⋊C8×C61—22no—
128C22⋊C8×C61C2314yes—
129C24×C61C22×C411yescharacteristic
130C24×C61C22×C411yescharacteristic
131C23×D61—21no—
132C23×D61—21no—
133C23×D61—22no—
134C23×D61—42no—
135C23×D61—42no—
136C23×D61—42no—
137C23×D61—42no—
138C23×D61C22⋊C412yes—
139C23×D61C22⋊C412yes—
140C23×D61C2×C814yes—
141C23×D61C2×C814yescomplemented
142C23×D61M1614yes—
143C23×D61C22×C411yescharacteristic
144C23×D61C22×C411yescharacteristic
145C23×D61C22×C411yescharacteristic
146C2×D4×C61—22no—
147C2×D4×C61—22no—
148C2×D4×C61C2×C814yescomplemented
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—42no—
152C22×C4×C61—42no—
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C2×D412yes—
158C22×C4×C61C2×D412yes—
159C22×C4×C61C2411yescharacteristic
160C2×C22⋊D61—22no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—22no—
163C2×C22⋊D61—22no—
164C2×C22⋊D61C2×C814yescomplemented
165C2×C22⋊D61C2×C814yescomplemented
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—42no—
169C22×Dic61—42no—
170C22×Dic61C22⋊C412yes—
171C22×Dic61C22⋊C412yes—
172C22×Dic61C22×C411yescharacteristic
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177D4×D61—216no—
178D4×D61—216no—
179C2×D244—22no—
180C2×D244—22no—
181C2×D244C2×C814yescomplemented
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—22no—
185C2×C4×D61—24no—
186C2×C4×D61—28no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—44no—
196C2×C4×D61—42no—
197C2×C4×D61—42no—
198C2×C4×D61—44no—
199C2×C4×D61—44no—
200C2×C4×D61—42no—
201C2×C4×D61—44no—
202C2×C4×D61—44no—
203C2×C4×D61—44no—
204C2×C4×D61—44no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×C4×D61—42no—
209C2×C4×D61C22⋊C411yescharacteristic
210C2×C4×D61C22⋊C411yescharacteristic
211C2×C4×D61C22⋊C411yescharacteristic
212C2×C4×D61C22⋊C412yes—
213C2×C4×D61C22⋊C412yes—
214C2×C4×D61C22⋊C411yescharacteristic
215C2×C4×D61C2×C814yescomplemented
216C2×C4×D61C2×D412yes—
217C2×C4×D61C2×D412yes—
218C2×C4×D61C2×D412yes—
219C2×C4×D61C2×D412yes—
220C2×C8×C61—24no—
221C2×C8×C61—44no—
222C4⋊C4×C61—22no—
223C22⋊C4×C61—22no—
224C22⋊C4×C61—22no—
225C42×C61—21no—
226C42×C61—21no—
227C22⋊Dic61—22no—
228C22⋊Dic61—22no—
229#11758198—22no—
230#11758198—22no—
231#11758198—22no—
232#11758198—22no—
233C4⋊Dic61—22no—
234#11758196—22no—
235#11758196—22no—
236C4×Dic61—21no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61—21no—
240C4×Dic61—21no—
241C4×Dic61—21no—
242C2×#92418—24no—
243C2×#92418—44no—
244C8×D61—48no—
245C8×D61—48no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61C2×C22⋊C412yes—
253C23×C61C22×C812yes—
254C23×C61C22×C812yescomplemented
255C23×C61C2×M1612yes—
256C23×C61C23×C411yescharacteristic
257C22×D61—22no—
258C22×D61—24no—
259C22×D61—22no—
260C22×D61—24no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—24no—
264C22×D61—24no—
265C22×D61—48no—
266C22×D61—48no—
267C22×D61—42no—
268C22×D61—41no—
269C22×D61—42no—
270C22×D61—41no—
271C22×D61—42no—
272C22×D61—42no—
273C22×D61—48no—
274C22×D61—48no—
275C22×D61—42no—
276C22×D61—42no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61C22⋊C818yes—
280C22×D61C22⋊C818yes—
281C22×D61C2×C22⋊C412yes—
282C22×D61C2×C22⋊C411yescharacteristic
283C22×D61C2×C22⋊C411yescharacteristic
284C22×D61C22×C812yes—
285C22×D61C22×C812yes—
286C22×D61C22×C812yescomplemented
287C22×D61C2×M1612yes—
288C22×D61C2×M1612yes—
289D4×C61—28no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—24no—
293C2×C4×C61—22no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—42no—
297C2×C4×C61—41no—
298C2×C4×C61—42no—
299C2×C4×C61—42no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61C2×C22⋊C411yescharacteristic
303C2×C4×C61C2×C22⋊C411yescharacteristic
304C2×C4×C61C22×C812yescomplemented
305C2×C4×C61C22×D412yes—
306C22⋊D61—28no—
307C22⋊D61—28no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—22no—
311C2×Dic61—24no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—42no—
315C2×Dic61—41no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61C2×C22⋊C411yescharacteristic
321C2×Dic61C2×C22⋊C412yes—
322C2×Dic61C2×C22⋊C411yescharacteristic
323C2×Dic61C22×C812yescomplemented
324D244—28no—
325C4×D61—24no—
326C4×D61—24no—
327C4×D61—24no—
328C4×D61—22no—
329C4×D61—22no—
330C4×D61—24no—
331C4×D61—24no—
332C4×D61—22no—
333C4×D61—42no—
334C4×D61—42no—
335C4×D61—42no—
336C4×D61—42no—
337C4×D61—42no—
338C4×D61—42no—
339C4×D61—42no—
340C4×D61—42no—
341C4×D61—42no—
342C4×D61—42no—
343C4×D61—42no—
344C4×D61#9914yes—
345C8×C61—44no—
346#92418—44no—
347C2×#1459—611nomaximal, Sylow
348C22×C61—21no—
349C22×C61—22no—
350C22×C61—21no—
351C22×C61—22no—
352C22×C61—22no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61C2×C22⋊C814yes—
360C22×C61C22×C22⋊C411yescharacteristic
361C22×C61C23×C811yescharacteristic
362C22×C61C22×M1611yescharacteristic
363C2×D61—21no—
364C2×D61—22no—
365C2×D61—21no—
366C2×D61—22no—
367C2×D61—24no—
368C2×D61—24no—
369C2×D61—216no—
370C2×D61—22no—
371C2×D61—48no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—48no—
375C2×D61—42no—
376C2×D61—41no—
377C2×D61—41no—
378C2×D61—48no—
379C2×D61—42no—
380C2×D61C2×C22⋊C812yes—
381C2×D61C2×C22⋊C814yes—
382C2×D61C2×C22⋊C812yes—
383C2×D61C2×#9912yes—
384C2×D61#41312yes—
385C4×C61—22no—
386C4×C61—22no—
387C4×C61—21no—
388C4×C61—41no—
389C4×C61—41no—
390C4×C61C2×#9912yes—
391Dic61—22no—
392Dic61—21no—
393Dic61—22no—
394Dic61—41no—
395Dic61—41no—
396Dic61C2×#9912yes—
397C22×C4×D4—611no—
398C22×C22⋊C8—612no—
399#1459—612no—
400#1459—612no—
401#1459—612no—
402#1459—611no—
403#1459D6111yescharacteristic, direct product factor
404C2×#324—612no—
405C2×#323—612no—
406C2×C61—21no—
407C2×C61—21no—
408C2×C61—24no—
409C2×C61—42no—
410C2×C61C22×C22⋊C811yescharacteristic
411C2×C61C22×#9911yescharacteristic
412C2×C61C2×#41311yescharacteristic
413D61—22no—
414D61—24no—
415D61—42no—
416D61#145914yesdirect product factor
417C23×D4—611no—
418C24×C4—611no—
419C24×C4—611no—
420C23×C8—1222no—
421C2×C4×D4—611no—
422C2×C4×D4—611no—
423C2×C4×D4—611no—
424C2×C4×D4—611no—
425C2×C4×D4—611no—
426C2×C4×D4—611no—
427C2×C4×D4—611no—
428C2×C4×D4—1222no—
429C2×C4×D4—1222no—
430C2×C4×D4—1222no—
431C2×C4×D4—1222no—
432C2×C4×D4C2×D6111yescharacteristic
433C22×C4⋊C4—611no—
434C22×C22⋊C4—611no—
435C22×C22⋊C4—611no—
436C22×C42—611no—
437C2×C22⋊C8—612no—
438C2×C22⋊C8—614no—
439C2×C22⋊C8—614no—
440C2×C22⋊C8—1222no—
441C2×C22⋊C8—1222no—
442C2×C22⋊C8—1222no—
443C2×C22⋊C8C2×D6112yescomplemented
444#324—612no—
445#324—614no—
446#324C2×D6112yescomplemented
447#323—612no—
448#323—614no—
449#323C2×D6112yescomplemented
450C61C2×#145911yescharacteristic, complemented, Sylow
451C25—611no—
452C25—611no—
453C22×D4—611no—
454C22×D4—611no—
455C22×D4—618no—
456C22×D4—611no—
457C22×D4—1222no—
458C22×D4—1222no—
459C22×D4—1224no—
460C22×D4C4×D6111yescharacteristic
461C23×C4—611no—
462C23×C4—611no—
463C23×C4—611no—
464C23×C4—612no—
465C23×C4—611no—
466C23×C4—612no—
467C23×C4—612no—
468C23×C4—612no—
469C23×C4—611no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—611no—
473C23×C4—611no—
474C23×C4—611no—
475C23×C4—611no—
476C23×C4—1221no—
477C23×C4—1221no—
478C23×C4—1221no—
479C23×C4—1221no—
480C23×C4—2444no—
481C23×C4—2444no—
482C23×C4C4×D6111yescharacteristic
483C23×C4C22×D6111yescharacteristic
484C22×C8—22no—
485C22×C8—1224no—
486C22×C8—1224no—
487C22×C8—1222no—
488C22×C8—2448no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—1222no—
492C4×D4—1222no—
493C4×D4—1222no—
494C4×D4—1222no—
495C4×D4—1222no—
496C4×D4—1222no—
497C4×D4—1222no—
498C4×D4—1222no—
499C4×D4—1222no—
500C4×D4—1222no—
501C4×D4—1222no—
502C4×D4—1222no—
503C4×D4—1222no—
504C4×D4—1222no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—1222no—
509C2×C4⋊C4—1222no—
510C2×C4⋊C4C22×D6111yescharacteristic
511C2×C22⋊C4—611no—
512C2×C22⋊C4—611no—
513C2×C22⋊C4—611no—
514C2×C22⋊C4—611no—
515C2×C22⋊C4—611no—
516C2×C22⋊C4—611no—
517C2×C22⋊C4—1222no—
518C2×C22⋊C4—1222no—
519C2×C22⋊C4—1222no—
520C2×C22⋊C4—1222no—
521C2×C22⋊C4C4×D6111yescharacteristic
522C2×C22⋊C4C22×D6111yescharacteristic
523C2×C42—611no—
524C2×C42—611no—
525C2×C42—611no—
526C2×C42—1221no—
527C2×C42—1221no—
528C2×C42—1221no—
529C2×C42—1221no—
530C2×C42C4×D6111yescharacteristic
531C22⋊C8—22no—
532C22⋊C8—614no—
533C22⋊C8—1224no—
534C22⋊C8—1224no—
535C22⋊C8—1222no—
536C22⋊C8C22×D6114yes—
537C24—611no—
538C24—612no—
539C24—611no—
540C24—612no—
541C24—614no—
542C24—614no—
543C24—611no—
544C24—614no—
545C24—1221no—
546C24—1221no—
547C24—1222no—
548C24—2442no—
549C24—2442no—
550C24—2442no—
551C24—2442no—
552C24C2×C4×D6111yescharacteristic
553C24C2×C4×D6111yescharacteristic
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—614no—
557C2×D4—614no—
558C2×D4—614no—
559C2×D4—1222no—
560C2×D4—1222no—
561C2×D4—12216no—
562C2×D4—12216no—
563C2×D4—1222no—
564C2×D4—1222no—
565C2×D4—1222no—
566C2×D4—1222no—
567C2×D4C8×D6114yescomplemented
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—611no—
573C22×C4—611no—
574C22×C4—611no—
575C22×C4—612no—
576C22×C4—611no—
577C22×C4—612no—
578C22×C4—612no—
579C22×C4—612no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—612no—
584C22×C4—614no—
585C22×C4—612no—
586C22×C4—612no—
587C22×C4—612no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—1228no—
591C22×C4—1224no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1222no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—2444no—
606C22×C4—2442no—
607C22×C4—2442no—
608C22×C4—2444no—
609C22×C4—2444no—
610C22×C4—2442no—
611C22×C4—2444no—
612C22×C4—2442no—
613C22×C4—2444no—
614C22×C4—2444no—
615C22×C4—2444no—
616C22×C4—2442no—
617C22×C4—2442no—
618C22×C4—2442no—
619C22×C4—2442no—
620C22×C4—2442no—
621C22×C4C2×C4×D6111yescharacteristic
622C22×C4C2×C4×D6111yescharacteristic
623C22×C4C2×C4×D6111yescharacteristic
624C22×C4C2×C4×D6111yescharacteristic
625C22×C4D4×D6112yes—
626C22×C4D4×D6112yes—
627C22×C4C23×D6111yescharacteristic
628C2×C8—24no—
629C2×C8—44no—
630C2×C8—1224no—
631C2×C8—2448no—
632C2×C8—2448no—
633C2×C8—2444no—
634C4⋊C4—22no—
635C4⋊C4—1222no—
636C4⋊C4—1222no—
637C4⋊C4—1222no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—1222no—
641C22⋊C4—1222no—
642C22⋊C4—1222no—
643C22⋊C4—1222no—
644C22⋊C4—1222no—
645C22⋊C4—1222no—
646C42—21no—
647C42—21no—
648C42—1221no—
649C42—1221no—
650C42—1221no—
651C42—1221no—
652C42—1221no—
653C42—1221no—
654C23—21no—
655C23—21no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—611no—
661C23—612no—
662C23—611no—
663C23—618no—
664C23—612no—
665C23—612no—
666C23—618no—
667C23—612no—
668C23—612no—
669C23—612no—
670C23—1222no—
671C23—1224no—
672C23—1222no—
673C23—1224no—
674C23—1224no—
675C23—1224no—
676C23—1221no—
677C23—1221no—
678C23—2441no—
679C23—2442no—
680C23—2441no—
681C23—2442no—
682C23—2441no—
683C23—2441no—
684C23—2442no—
685C23—2442no—
686C23—2448no—
687C23—2448no—
688C23—2448no—
689C23—2442no—
690C23—2448no—
691C23—2442no—
692C23C22⋊C4×D6112yes—
693C23C2×C8×D6112yes—
694C23C2×C8×D6112yescomplemented
695C23M16×D6112yes—
696C23C22×C4×D6111yescharacteristic
697D4—28no—
698D4—1228no—
699D4—1228no—
700D4—1228no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—611no—
714C2×C4—614no—
715C2×C4—611no—
716C2×C4—612no—
717C2×C4—612no—
718C2×C4—1224no—
719C2×C4—1222no—
720C2×C4—1224no—
721C2×C4—1222no—
722C2×C4—1224no—
723C2×C4—1224no—
724C2×C4—1224no—
725C2×C4—1222no—
726C2×C4—1221no—
727C2×C4—1221no—
728C2×C4—1224no—
729C2×C4—1222no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—2442no—
733C2×C4—2442no—
734C2×C4—2442no—
735C2×C4—2442no—
736C2×C4—2442no—
737C2×C4—2442no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4—2442no—
743C2×C4—2441no—
744C2×C4—2442no—
745C2×C4—2442no—
746C2×C4—2442no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4C22⋊C4×D6111yescharacteristic
750C2×C4C22⋊C4×D6111yescharacteristic
751C2×C4C2×C8×D6112yescomplemented
752C2×C4C2×D4×D6112yes—
753C8—44no—
754C8—2444no—
755C22—21no—
756C22—22no—
757C22—21no—
758C22—22no—
759C22—22no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—41no—
765C22—41no—
766C22—612no—
767C22—612no—
768C22—612no—
769C22—612no—
770C22—614no—
771C22—12216no—
772C22—1224no—
773C22—1224no—
774C22—1221no—
775C22—1222no—
776C22—1221no—
777C22—1222no—
778C22—1222no—
779C22—2442no—
780C22—2442no—
781C22—2448no—
782C22—2442no—
783C22—2442no—
784C22—2448no—
785C22—2448no—
786C22—2441no—
787C22—2441no—
788C22C22⋊C8×D6114yes—
789C22C2×C22⋊C4×D6111yescharacteristic
790C22C22×C8×D6111yescharacteristic
791C22C2×M16×D6111yescharacteristic
792C4—22no—
793C4—22no—
794C4—21no—
795C4—41no—
796C4—41no—
797C4—612no—
798C4—1222no—
799C4—1222no—
800C4—1221no—
801C4—2441no—
802C4—2441no—
803C4#99×D6112yes—
804C2—21no—
805C2—21no—
806C2—24no—
807C2—42no—
808C2—614no—
809C2—1222no—
810C2—1224no—
811C2—2442no—
812C2C2×C22⋊C8×D6111yescharacteristic
813C2C2×#99×D6111yescharacteristic
814C2#413×D6111yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC22×C61C23×C8
FrattiniC22×C4C23×D61
FittingC61×#1459C2
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×D61C4
cosocleC22×C4×C61C24
hypercenter#1459D61
hypocenterC61C2×#1459
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C8×D61C2semidirect
3. #21444137C2semidirect
4. #21444136C2semidirect
5. #21444135C2semidirect
6. #21444134C2semidirect
7. #324×D61C2semidirect
8. #323×D61C2semidirect
9. C61×#1459C2semidirect
29. C2×C22⋊#92418C22semidirect
34. C22⋊C8×D61C22semidirect
35. #16839488C22semidirect
36. #16839487C22semidirect
37. #16839486C22semidirect
38. #16839485C22semidirect
40. C2×C22⋊C8×C61C22semidirect
41. C61×#324C22semidirect
42. C61×#323C22semidirect
51. C2×D4×D61C8semidirect
141. C23×D61C2×C8semidirect
148. C2×D4×C61C2×C8semidirect
164. C2×C22⋊D61C2×C8semidirect
165. C2×C22⋊D61C2×C8semidirect
181. C2×D244C2×C8semidirect
215. C2×C4×D61C2×C8semidirect
254. C23×C61C22×C8semidirect
286. C22×D61C22×C8semidirect
304. C2×C4×C61C22×C8semidirect
323. C2×Dic61C22×C8semidirect
403. #1459D61direct (N × H)
416. D61#1459direct (N × H)
443. C2×C22⋊C8C2×D61semidirect
446. #324C2×D61semidirect
449. #323C2×D61semidirect
450. C61C2×#1459semidirect
567. C2×D4C8×D61semidirect
694. C23C2×C8×D61semidirect
751. C2×C4C2×C8×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D612
C2×C22⋊C8×D612
#214441372
#214441362
#214441352
#214441342
#324×D612
#323×D612
C61×#14592
C2×#145961