Finite Group Databasebeta

← D61×#1468 #29645953

Subgroups — D61×#1468 #29645953

Order 15616.

1490 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#123×D61C211yesmaximal, characteristic
2#407×D61C211yesmaximal, characteristic, complemented
3C2×C22⋊C8×D61C211yesmaximal, characteristic, complemented
4#21444168C211yesmaximal, characteristic, complemented
5#21444167C211yesmaximal, characteristic, complemented
6#21444166C212yesmaximal, complemented
7#21444165C211yesmaximal, characteristic, complemented
8#21444164C212yesmaximal, complemented
9#324×D61C212yesmaximal, complemented
10#323×D61C212yesmaximal, complemented
11C61×#1468C211yesmaximal, characteristic, complemented
12C22×D4×D61C411yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C2×M16×D61—21no—
15C22×C8×D61—21no—
16C2×#14519762C411yescharacteristic
17C2×#14519762C2211yescharacteristic
18C2×#14519761C411yescharacteristic
19C2×#14519760C2211yescharacteristic
20C2×#14519759C411yescharacteristic
21C2×#14519759C2211yescharacteristic
22C2×#14519758C411yescharacteristic
23#123×D61—21no—
24#123×D61—21no—
25#123×D61—21no—
26#123×D61—21no—
27#123×D61—21no—
28#123×D61—21no—
29#123×D61—21no—
30#123×D61—21no—
31C2×C4⋊C4×D61C411yescharacteristic
32C2×C4⋊C4×D61C2211yescharacteristic
33C2×C22⋊C4×D61C411yescharacteristic
34C2×C22⋊C4×D61C411yescharacteristic
35C2×C22⋊C4×D61C2211yescharacteristic
36#16839726C2211yescharacteristic, complemented
37#16839725—21no—
38#16839724—21no—
39#16839724C2212yescomplemented
40C2×C22⋊#92418C2211yescharacteristic, complemented
41C2×#14519689—21no—
42C22⋊C8×D61—21no—
43C22⋊C8×D61—21no—
44C22⋊C8×D61—21no—
45C22⋊C8×D61C2212yes—
46C22⋊C8×D61C2212yes—
47C22⋊C8×D61C2212yescomplemented
48#16839488C2212yescomplemented
49#16839487C2212yescomplemented
50#16839487C2212yescomplemented
51#16839486C2212yescomplemented
52#16839485C2212yescomplemented
53#16839485C2212yescomplemented
54C2×#123×C61C2211yescharacteristic
55C61×#407C2211yescharacteristic, complemented
56C2×C22⋊C8×C61C2211yescharacteristic, complemented
57C61×#324C2212yescomplemented
58C61×#323C2212yescomplemented
59C24×D61C2×C411yescharacteristic
60C24×D61C2×C411yescharacteristic
61C22×D244C2×C411yescharacteristic
62C22×C22⋊D61C2×C411yescharacteristic
63C22×C22⋊D61C2×C411yescharacteristic
64C2×D4×D61—21no—
65C2×D4×D61—21no—
66C2×D4×D61—21no—
67C2×D4×D61—21no—
68C2×D4×D61—44no—
69C23×Dic61C2×C411yescharacteristic
70C22×C4×D61—44no—
71C22×C4×D61C2×C411yescharacteristic
72C22×C4×D61C2×C411yescharacteristic
73C22×C4×D61C2×C411yescharacteristic
74C22×C4×D61C2×C411yescharacteristic
75C22×C4×D61C2×C411yescharacteristic
76C22×C4×D61D411yescharacteristic
77C22×C4×D61D411yescharacteristic
78C22×C4×D61D411yescharacteristic
79C22×C4×D61D411yescharacteristic
80C22×C4×D61D411yescharacteristic
81C22×C4×D61D411yescharacteristic
82C22×C4×D61D411yescharacteristic
83C22×C4×D61D411yescharacteristic
84C22×C4×D61C2311yescharacteristic
85C22×C4×D61C2311yescharacteristic
86C2×#11758194—21no—
87C2×#11758189—22no—
88M16×D61—44no—
89C22×#92418—21no—
90C2×C8×D61—22no—
91C2×C8×D61—22no—
92C2×C8×D61—22no—
93C2×C8×D61—44no—
94#14519762—21no—
95#14519762—21no—
96#14519762—21no—
97#14519762—21no—
98#14519762—21no—
99#14519762—21no—
100#14519762—21no—
101#14519762—21no—
102#14519761—21no—
103#14519761—21no—
104#14519761—21no—
105#14519761—21no—
106#14519760—21no—
107#14519760—21no—
108#14519760—21no—
109#14519760—21no—
110#14519759—21no—
111#14519759—21no—
112#14519759—21no—
113#14519759—21no—
114#14519759—21no—
115#14519759—21no—
116#14519759—21no—
117#14519759—21no—
118#14519758—21no—
119#14519758—21no—
120#14519758—21no—
121#14519758—21no—
122C2×C4⋊Dic61C2×C411yescharacteristic
123C2×C4⋊Dic61C2×C411yescharacteristic
124C2×#11758196C2×C411yescharacteristic
125C2×#11758196C2×C411yescharacteristic
126C2×#11758196C2×C411yescharacteristic
127C2×#11758196C2311yescharacteristic
128C4⋊C4×D61—21no—
129C4⋊C4×D61—21no—
130C4⋊C4×D61—21no—
131C4⋊C4×D61—21no—
132C4⋊C4×D61—21no—
133C4⋊C4×D61—21no—
134C4⋊C4×D61—21no—
135C4⋊C4×D61—21no—
136C2×C22⋊Dic61C2×C411yescharacteristic
137C2×C22⋊Dic61C2×C411yescharacteristic
138C2×C22⋊Dic61C2×C411yescharacteristic
139C2×#11758198C2×C411yescharacteristic
140C2×#11758198C2×C411yescharacteristic
141C2×#11758198C2×C411yescharacteristic
142C2×#11758198C2×C411yescharacteristic
143C2×#11758198C2×C411yescharacteristic
144C2×#11758198C2311yescharacteristic
145C22⋊C4×D61—21no—
146C22⋊C4×D61—21no—
147C22⋊C4×D61—21no—
148C22⋊C4×D61—21no—
149C22⋊C4×D61—21no—
150C22⋊C4×D61—21no—
151C22⋊C4×D61—21no—
152C22⋊C4×D61—21no—
153C22⋊C4×D61—21no—
154C22⋊C4×D61—21no—
155C22⋊C4×D61—21no—
156C22⋊C4×D61—21no—
157C22⋊#92418—21no—
158C22⋊#92418—21no—
159C22⋊#92418C2312yes—
160C22⋊#92418C2312yes—
161#14519689—22no—
162#14519689—22no—
163#14519689—22no—
164#14519689—22no—
165C22×D4×C61C2×C411yescharacteristic
166C23×C4×C61C2311yescharacteristic
167C2×M16×C61—21no—
168C22×C8×C61—21no—
169#123×C61—21no—
170#123×C61—21no—
171#123×C61—21no—
172#123×C61—21no—
173C2×C4⋊C4×C61C2×C411yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61C2×C411yescharacteristic
176C2×C22⋊C4×C61C2×C411yescharacteristic
177C2×C22⋊C4×C61C2311yescharacteristic
178C22⋊C8×C61—21no—
179C22⋊C8×C61—21no—
180C22⋊C8×C61C2312yes—
181C22⋊C8×C61C2312yes—
182C24×C61C22×C411yescharacteristic
183C24×C61C22×C411yescharacteristic
184C23×D61—24no—
185C23×D61—24no—
186C23×D61—21no—
187C23×D61—21no—
188C23×D61—24no—
189C23×D61—42no—
190C23×D61—42no—
191C23×D61—42no—
192C23×D61C22⋊C411yescharacteristic
193C23×D61C22⋊C411yescharacteristic
194C23×D61C22⋊C411yescharacteristic
195C23×D61C22⋊C411yescharacteristic
196C23×D61C22×C411yescharacteristic
197C23×D61C22×C411yescharacteristic
198C23×D61C22×C411yescharacteristic
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—42no—
202C22×C4×C61—42no—
203C22×C4×C61C22×C411yescharacteristic
204C22×C4×C61C22×C411yescharacteristic
205C22×C4×C61C22×C411yescharacteristic
206C22×C4×C61C22×C411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2411yescharacteristic
212C2×C22⋊D61—21no—
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61—42no—
217C2×C22⋊D61—42no—
218C22×Dic61—42no—
219C22×Dic61C22⋊C411yescharacteristic
220C22×Dic61C22⋊C411yescharacteristic
221C22×Dic61C22⋊C411yescharacteristic
222C22×Dic61C22⋊C411yescharacteristic
223C22×Dic61C22×C411yescharacteristic
224C22×Dic61C22×C411yescharacteristic
225C22×Dic61C22×C411yescharacteristic
226C22×Dic61C22×C411yescharacteristic
227C22×Dic61C22×C411yescharacteristic
228D4×D61—44no—
229D4×D61—44no—
230D4×D61—44no—
231D4×D61—44no—
232C2×D244—21no—
233C2×D244—21no—
234C2×D244—42no—
235C2×C4×D61—24no—
236C2×C4×D61—24no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—24no—
244C2×C4×D61—42no—
245C2×C4×D61—42no—
246C2×C4×D61—42no—
247C2×C4×D61—42no—
248C2×C4×D61—42no—
249C2×C4×D61—42no—
250C2×C4×D61—42no—
251C2×C4×D61—42no—
252C2×C4×D61—42no—
253C2×C4×D61—42no—
254C2×C4×D61—42no—
255C2×C4×D61—42no—
256C2×C4×D61C22⋊C411yescharacteristic
257C2×C4×D61C22⋊C411yescharacteristic
258C2×C4×D61C22⋊C411yescharacteristic
259C2×C4×D61C22⋊C411yescharacteristic
260C2×C4×D61C22⋊C411yescharacteristic
261C2×C4×D61C22⋊C411yescharacteristic
262C2×C4×D61C22⋊C411yescharacteristic
263C2×C4×D61C22⋊C411yescharacteristic
264C2×C4×D61C2×D411yescharacteristic
265C2×C4×D61C2×D411yescharacteristic
266C2×C4×D61C2×D411yescharacteristic
267C2×C4×D61C2×D411yescharacteristic
268C2×C4×D61C2×D411yescharacteristic
269C2×C4×D61C2×D411yescharacteristic
270C2×C4×D61C2×D411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272M16×C61—42no—
273C2×C8×C61—22no—
274C2×C8×C61—22no—
275C2×C8×C61—42no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C22⋊C4×C61—21no—
281C22⋊C4×C61—21no—
282C22⋊C4×C61—21no—
283C22⋊C4×C61—21no—
284C22⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C22⋊Dic61—21no—
287C22⋊Dic61—21no—
288C22⋊Dic61—21no—
289C22⋊Dic61—21no—
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304C4⋊Dic61—21no—
305C4⋊Dic61—21no—
306C4⋊Dic61—21no—
307C4⋊Dic61—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758194—42no—
317C2×#92418—22no—
318C2×#92418—22no—
319C2×#92418—42no—
320#11758189—44no—
321C8×D61—44no—
322C8×D61—44no—
323C8×D61—44no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—21no—
327C23×C61—22no—
328C23×C61—41no—
329C23×C61—41no—
330C23×C61—41no—
331C23×C61C2×C22⋊C411yescharacteristic
332C23×C61C2×C22⋊C411yescharacteristic
333C23×C61C23×C411yescharacteristic
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—22no—
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—22no—
346C22×D61—22no—
347C22×D61—21no—
348C22×D61—22no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—416no—
353C22×D61—42no—
354C22×D61—42no—
355C22×D61—42no—
356C22×D61—42no—
357C22×D61—42no—
358C22×D61—42no—
359C22×D61—41no—
360C22×D61—41no—
361C22×D61—88no—
362C22×D61#9914yes—
363C22×D61C2×C22⋊C411yescharacteristic
364C22×D61C2×C22⋊C411yescharacteristic
365C22×D61C2×C22⋊C411yescharacteristic
366C22×D61C2×C22⋊C411yescharacteristic
367C22×D61#13114yes—
368D4×C61—42no—
369D4×C61—42no—
370C2×C4×C61—22no—
371C2×C4×C61—22no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—22no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61C2×C22⋊C411yescharacteristic
383C2×C4×C61C2×C22⋊C411yescharacteristic
384C2×C4×C61C22×D411yescharacteristic
385C2×C4×C61C22×D411yescharacteristic
386C22⋊D61—42no—
387C22⋊D61—42no—
388C22⋊D61—42no—
389C22⋊D61—42no—
390C2×Dic61—22no—
391C2×Dic61—22no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—22no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61C2×C22⋊C411yescharacteristic
403C2×Dic61C2×C22⋊C411yescharacteristic
404C2×Dic61C2×C22⋊C411yescharacteristic
405C2×Dic61C2×C22⋊C411yescharacteristic
406D244—42no—
407D244—42no—
408C4×D61—22no—
409C4×D61—22no—
410C4×D61—22no—
411C4×D61—22no—
412C4×D61—22no—
413C4×D61—22no—
414C4×D61—22no—
415C4×D61—22no—
416C4×D61—41no—
417C4×D61—41no—
418C4×D61—41no—
419C4×D61—41no—
420C4×D61—41no—
421C4×D61—41no—
422C4×D61—41no—
423C4×D61—41no—
424C4×D61—42no—
425C4×D61—42no—
426C4×D61—42no—
427C4×D61—42no—
428C4×D61—42no—
429C4×D61—42no—
430C8×C61—42no—
431C8×C61—42no—
432#92418—42no—
433#92418—42no—
434C2×#1468—611nomaximal, Sylow
435C22×C61—21no—
436C22×C61—21no—
437C22×C61—21no—
438C22×C61—21no—
439C22×C61—21no—
440C22×C61—21no—
441C22×C61—21no—
442C22×C61—44no—
443C22×C61—41no—
444C22×C61—41no—
445C22×C61—41no—
446C22×C61—82no—
447C22×C61C2×#9912yes—
448C22×C61C22×C22⋊C411yescharacteristic
449C22×C61C2×#13112yes—
450C2×D61—21no—
451C2×D61—21no—
452C2×D61—21no—
453C2×D61—21no—
454C2×D61—28no—
455C2×D61—28no—
456C2×D61—21no—
457C2×D61—21no—
458C2×D61—21no—
459C2×D61—44no—
460C2×D61—44no—
461C2×D61—44no—
462C2×D61—44no—
463C2×D61—41no—
464C2×D61—41no—
465C2×D61—41no—
466C2×D61—84no—
467C2×D61—84no—
468C2×D61—82no—
469C2×D61#40812yes—
470C2×D61#40812yes—
471C2×D61C2×#9912yes—
472C2×D61C2×#9912yes—
473C2×D61#41312yes—
474C4×C61—21no—
475C4×C61—21no—
476C4×C61—21no—
477C4×C61—21no—
478C4×C61—41no—
479C4×C61—41no—
480C4×C61—41no—
481Dic61—21no—
482Dic61—21no—
483Dic61—21no—
484Dic61—21no—
485Dic61—41no—
486Dic61—41no—
487Dic61—41no—
488C22×#123—611no—
489C2×#407—611no—
490C22×C22⋊C8—611no—
491#1468—611no—
492#1468—611no—
493#1468—612no—
494#1468—612no—
495#1468—611no—
496#1468D6111yescharacteristic, direct product factor
497C2×#324—612no—
498C2×#323—612no—
499C2×C61—22no—
500C2×C61—22no—
501C2×C61—41no—
502C2×C61—81no—
503C2×C61C2×#40811yescharacteristic
504C2×C61C22×#9911yescharacteristic
505C2×C61C2×#41311yescharacteristic
506D61—22no—
507D61—22no—
508D61—41no—
509D61—81no—
510D61#146814yesdirect product factor
511C23×D4—611no—
512C24×C4—611no—
513C22×M16—1221no—
514C23×C8—1221no—
515C2×#123—611no—
516C2×#123—611no—
517C2×#123—611no—
518C2×#123—611no—
519C2×#123—611no—
520C2×#123—611no—
521C2×#123—611no—
522C2×#123—1221no—
523C2×#123—1221no—
524C2×#123—1221no—
525C2×#123—1221no—
526C2×#123—1221no—
527C2×#123—1221no—
528C2×#123—1221no—
529C2×#123—1221no—
530C2×#123C2×D6111yescharacteristic
531C22×C4⋊C4—611no—
532C22×C4⋊C4—611no—
533C22×C22⋊C4—611no—
534C22×C22⋊C4—611no—
535C22×C22⋊C4—611no—
536#407—611no—
537#407—612no—
538#407—1221no—
539#407—1221no—
540#407C2×D6111yescharacteristic, complemented
541C2×C22⋊C8—611no—
542C2×C22⋊C8—612no—
543C2×C22⋊C8—612no—
544C2×C22⋊C8—612no—
545C2×C22⋊C8—1221no—
546C2×C22⋊C8—1221no—
547C2×C22⋊C8—1221no—
548C2×C22⋊C8—1221no—
549C2×C22⋊C8C2×D6111yescharacteristic, complemented
550#324—612no—
551#324—612no—
552#324—612no—
553#324C2×D6112yescomplemented
554#323—612no—
555#323—612no—
556#323—612no—
557#323C2×D6112yescomplemented
558C61C2×#146811yescharacteristic, complemented, Sylow
559C25—611no—
560C25—611no—
561C22×D4—611no—
562C22×D4—611no—
563C22×D4—611no—
564C22×D4—1221no—
565C22×D4—1221no—
566C22×D4—1221no—
567C22×D4—1221no—
568C22×D4—2444no—
569C22×D4C4×D6111yescharacteristic
570C23×C4—611no—
571C23×C4—611no—
572C23×C4—611no—
573C23×C4—611no—
574C23×C4—611no—
575C23×C4—611no—
576C23×C4—611no—
577C23×C4—611no—
578C23×C4—611no—
579C23×C4—611no—
580C23×C4—611no—
581C23×C4—611no—
582C23×C4—611no—
583C23×C4—611no—
584C23×C4—611no—
585C23×C4—611no—
586C23×C4—2444no—
587C23×C4C22×D6111yescharacteristic
588C2×M16—21no—
589C2×M16—1222no—
590C2×M16—1221no—
591C2×M16—2444no—
592C22×C8—21no—
593C22×C8—1222no—
594C22×C8—1222no—
595C22×C8—1222no—
596C22×C8—1221no—
597C22×C8—2444no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—1221no—
603#123—1221no—
604#123—1221no—
605#123—1221no—
606#123—1221no—
607#123—1221no—
608#123—1221no—
609#123—1221no—
610#123—1221no—
611#123—1221no—
612#123—1221no—
613#123—1221no—
614#123—1221no—
615#123—1221no—
616#123—1221no—
617#123—1221no—
618#123—1221no—
619#123—1221no—
620#123—1221no—
621#123—1221no—
622#123—1221no—
623#123—1221no—
624#123—1221no—
625#123—1221no—
626#123—1221no—
627#123—1221no—
628#123—1221no—
629#123—1221no—
630C2×C4⋊C4—611no—
631C2×C4⋊C4—611no—
632C2×C4⋊C4—611no—
633C2×C4⋊C4—611no—
634C2×C4⋊C4—611no—
635C2×C4⋊C4—611no—
636C2×C4⋊C4—1221no—
637C2×C4⋊C4—1221no—
638C2×C4⋊C4—1221no—
639C2×C4⋊C4—1221no—
640C2×C4⋊C4—1221no—
641C2×C4⋊C4—1221no—
642C2×C4⋊C4—1221no—
643C2×C4⋊C4—1221no—
644C2×C4⋊C4C4×D6111yescharacteristic
645C2×C4⋊C4C22×D6111yescharacteristic
646C2×C22⋊C4—611no—
647C2×C22⋊C4—611no—
648C2×C22⋊C4—611no—
649C2×C22⋊C4—611no—
650C2×C22⋊C4—611no—
651C2×C22⋊C4—611no—
652C2×C22⋊C4—611no—
653C2×C22⋊C4—611no—
654C2×C22⋊C4—611no—
655C2×C22⋊C4—1221no—
656C2×C22⋊C4—1221no—
657C2×C22⋊C4—1221no—
658C2×C22⋊C4—1221no—
659C2×C22⋊C4—1221no—
660C2×C22⋊C4—1221no—
661C2×C22⋊C4—1221no—
662C2×C22⋊C4—1221no—
663C2×C22⋊C4—1221no—
664C2×C22⋊C4—1221no—
665C2×C22⋊C4—1221no—
666C2×C22⋊C4—1221no—
667C2×C22⋊C4C4×D6111yescharacteristic
668C2×C22⋊C4C4×D6111yescharacteristic
669C2×C22⋊C4C22×D6111yescharacteristic
670C22⋊C8—21no—
671C22⋊C8—21no—
672C22⋊C8—612no—
673C22⋊C8—612no—
674C22⋊C8—1222no—
675C22⋊C8—1222no—
676C22⋊C8—1222no—
677C22⋊C8—1222no—
678C22⋊C8—1221no—
679C22⋊C8—1221no—
680C22⋊C8C22×D6112yes—
681C22⋊C8C22×D6112yes—
682C24—611no—
683C24—611no—
684C24—611no—
685C24—611no—
686C24—611no—
687C24—611no—
688C24—611no—
689C24—1224no—
690C24—1224no—
691C24—1224no—
692C24—1221no—
693C24—1221no—
694C24—2442no—
695C24—2442no—
696C24—2442no—
697C24C2×C4×D6111yescharacteristic
698C24C2×C4×D6111yescharacteristic
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—42no—
702C2×D4—1221no—
703C2×D4—1221no—
704C2×D4—1221no—
705C2×D4—1221no—
706C2×D4—1221no—
707C2×D4—1221no—
708C2×D4—2442no—
709C2×D4—2444no—
710C2×D4—2444no—
711C2×D4—2444no—
712C2×D4—2444no—
713C2×D4—2442no—
714C2×D4—2442no—
715C22×C4—42no—
716C22×C4—611no—
717C22×C4—611no—
718C22×C4—611no—
719C22×C4—611no—
720C22×C4—611no—
721C22×C4—611no—
722C22×C4—611no—
723C22×C4—611no—
724C22×C4—611no—
725C22×C4—611no—
726C22×C4—611no—
727C22×C4—611no—
728C22×C4—611no—
729C22×C4—611no—
730C22×C4—611no—
731C22×C4—611no—
732C22×C4—611no—
733C22×C4—611no—
734C22×C4—611no—
735C22×C4—611no—
736C22×C4—611no—
737C22×C4—611no—
738C22×C4—611no—
739C22×C4—611no—
740C22×C4—611no—
741C22×C4—1224no—
742C22×C4—1224no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1224no—
750C22×C4—2442no—
751C22×C4—2442no—
752C22×C4—2442no—
753C22×C4—2442no—
754C22×C4—2442no—
755C22×C4—2442no—
756C22×C4—2442no—
757C22×C4—2442no—
758C22×C4—2442no—
759C22×C4—2442no—
760C22×C4—2442no—
761C22×C4—2442no—
762C22×C4—2442no—
763C22×C4C2×C4×D6111yescharacteristic
764C22×C4C2×C4×D6111yescharacteristic
765C22×C4C2×C4×D6111yescharacteristic
766C22×C4C2×C4×D6111yescharacteristic
767C22×C4D4×D6111yescharacteristic
768C22×C4D4×D6111yescharacteristic
769C22×C4D4×D6111yescharacteristic
770C22×C4D4×D6111yescharacteristic
771C22×C4C23×D6111yescharacteristic
772M16—42no—
773M16—2444no—
774M16—2442no—
775C2×C8—22no—
776C2×C8—22no—
777C2×C8—42no—
778C2×C8—1222no—
779C2×C8—1222no—
780C2×C8—2444no—
781C2×C8—2444no—
782C2×C8—2444no—
783C2×C8—2442no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—1221no—
789C4⋊C4—1221no—
790C4⋊C4—1221no—
791C4⋊C4—1221no—
792C4⋊C4—1221no—
793C4⋊C4—1221no—
794C4⋊C4—1221no—
795C4⋊C4—1221no—
796C4⋊C4—1221no—
797C4⋊C4—1221no—
798C4⋊C4—1221no—
799C4⋊C4—1221no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—1221no—
807C22⋊C4—1221no—
808C22⋊C4—1221no—
809C22⋊C4—1221no—
810C22⋊C4—1221no—
811C22⋊C4—1221no—
812C22⋊C4—1221no—
813C22⋊C4—1221no—
814C22⋊C4—1221no—
815C22⋊C4—1221no—
816C22⋊C4—1221no—
817C22⋊C4—1221no—
818C22⋊C4—1221no—
819C22⋊C4—1221no—
820C22⋊C4—1221no—
821C22⋊C4—1221no—
822C22⋊C4—1221no—
823C22⋊C4—1221no—
824C23—22no—
825C23—22no—
826C23—21no—
827C23—22no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—611no—
832C23—611no—
833C23—611no—
834C23—614no—
835C23—614no—
836C23—611no—
837C23—1222no—
838C23—1222no—
839C23—1222no—
840C23—1222no—
841C23—1222no—
842C23—1222no—
843C23—1222no—
844C23—1222no—
845C23—1222no—
846C23—1222no—
847C23—1222no—
848C23—1222no—
849C23—1222no—
850C23—1222no—
851C23—1221no—
852C23—4888no—
853C23—2441no—
854C23—2441no—
855C23—2441no—
856C23—2441no—
857C23—2441no—
858C23—2442no—
859C23—2442no—
860C23—2442no—
861C23—2442no—
862C23—24416no—
863C23—2442no—
864C23—2442no—
865C23C22⋊C4×D6111yescharacteristic
866C23C22⋊C4×D6111yescharacteristic
867C23C22×C4×D6111yescharacteristic
868D4—42no—
869D4—42no—
870D4—2442no—
871D4—2442no—
872D4—2442no—
873D4—2442no—
874D4—2442no—
875D4—2442no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—22no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—611no—
889C2×C4—611no—
890C2×C4—611no—
891C2×C4—611no—
892C2×C4—1222no—
893C2×C4—1222no—
894C2×C4—1222no—
895C2×C4—1222no—
896C2×C4—1222no—
897C2×C4—1222no—
898C2×C4—1222no—
899C2×C4—1222no—
900C2×C4—1222no—
901C2×C4—1222no—
902C2×C4—1221no—
903C2×C4—1221no—
904C2×C4—1221no—
905C2×C4—1222no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2442no—
915C2×C4—2442no—
916C2×C4—2442no—
917C2×C4—2442no—
918C2×C4—2442no—
919C2×C4—2442no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4—2441no—
924C2×C4—2441no—
925C2×C4—2441no—
926C2×C4C22⋊C4×D6111yescharacteristic
927C2×C4C22⋊C4×D6111yescharacteristic
928C2×C4C2×D4×D6111yescharacteristic
929C2×C4C2×D4×D6111yescharacteristic
930C8—42no—
931C8—42no—
932C8—2442no—
933C8—2442no—
934C22—21no—
935C22—21no—
936C22—21no—
937C22—21no—
938C22—21no—
939C22—21no—
940C22—21no—
941C22—44no—
942C22—41no—
943C22—41no—
944C22—41no—
945C22—82no—
946C22—612no—
947C22—612no—
948C22—612no—
949C22—612no—
950C22—612no—
951C22—1228no—
952C22—1228no—
953C22—1221no—
954C22—1221no—
955C22—1221no—
956C22—1221no—
957C22—1221no—
958C22—1221no—
959C22—1221no—
960C22—4882no—
961C22—4884no—
962C22—4884no—
963C22—2444no—
964C22—2444no—
965C22—2444no—
966C22—2444no—
967C22—2441no—
968C22—2441no—
969C22—2441no—
970C22#99×D6112yes—
971C22C2×C22⋊C4×D6111yescharacteristic
972C22#131×D6112yes—
973C4—21no—
974C4—21no—
975C4—21no—
976C4—21no—
977C4—41no—
978C4—41no—
979C4—41no—
980C4—1221no—
981C4—1221no—
982C4—1221no—
983C4—1221no—
984C4—2441no—
985C4—2441no—
986C4—2441no—
987C2—22no—
988C2—22no—
989C2—41no—
990C2—81no—
991C2—614no—
992C2—1222no—
993C2—1222no—
994C2—4881no—
995C2—2441no—
996C2#408×D6111yescharacteristic
997C2C2×#99×D6111yescharacteristic
998C2#413×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1468C2
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×D61C4
cosocleC22×C4×C61C24
hypercenter#1468D61
hypocenterC61C2×#1468
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1468

Complements

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

NH ≅ G/Ntype
2. #407×D61C2semidirect
3. C2×C22⋊C8×D61C2semidirect
4. #21444168C2semidirect
5. #21444167C2semidirect
6. #21444166C2semidirect
7. #21444165C2semidirect
8. #21444164C2semidirect
9. #324×D61C2semidirect
10. #323×D61C2semidirect
11. C61×#1468C2semidirect
36. #16839726C22semidirect
39. #16839724C22semidirect
40. C2×C22⋊#92418C22semidirect
47. C22⋊C8×D61C22semidirect
48. #16839488C22semidirect
49. #16839487C22semidirect
50. #16839487C22semidirect
51. #16839486C22semidirect
52. #16839485C22semidirect
53. #16839485C22semidirect
55. C61×#407C22semidirect
56. C2×C22⋊C8×C61C22semidirect
57. C61×#324C22semidirect
58. C61×#323C22semidirect
496. #1468D61direct (N × H)
510. D61#1468direct (N × H)
540. #407C2×D61semidirect
549. C2×C22⋊C8C2×D61semidirect
553. #324C2×D61semidirect
557. #323C2×D61semidirect
558. C61C2×#1468semidirect

Maximal subgroups

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

subgroupindex
C2×#123×D612
#407×D612
C2×C22⋊C8×D612
#214441682
#214441672
#214441662
#214441652
#214441642
#324×D612
#323×D612
C61×#14682
C2×#146861