Finite Group Databasebeta

← #29685658

Subgroups — #29685658

Order 15616.

1952 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D61C211yesmaximal, characteristic, complemented
2C2×#16839897C211yesmaximal, characteristic
3C2×#16839875C211yesmaximal, characteristic, complemented
4C2×#16839872C211yesmaximal, characteristic, complemented
5C4×#14519752C211yesmaximal, characteristic, complemented
6#21446168C211yesmaximal, characteristic, complemented
7#21446165C211yesmaximal, characteristic, complemented
8#21446135C211yesmaximal, characteristic, complemented
9#21446082C211yesmaximal, characteristic, complemented
10#21446081C211yesmaximal, characteristic, complemented
11#21446013C211yesmaximal, characteristic, complemented
12#21445748C211yesmaximal, characteristic, complemented
13#21445647C211yesmaximal, characteristic, complemented
14#21445582C211yesmaximal, characteristic, complemented
15C61×#1762C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C23×C4×D61—21no—
18C22×D488C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20C2×#14519752C2211yescharacteristic
21C2×C4×D244—21no—
22C2×C4×D244C2211yescharacteristic
23C2×C4×D244C2211yescharacteristic, complemented
24C2×D4×Dic61C2211yescharacteristic
25C2×#14519739C2211yescharacteristic
26C2×C4×C22⋊D61—21no—
27C2×#14519737—21no—
28C4×D4×D61—24no—
29C4×D4×D61—24no—
30C2×C4⋊C4×D61C2211yescharacteristic
31C2×C22⋊C4×D61—21no—
32C2×C42×D61C2211yescharacteristic
33#16839897C418yescomplemented
34#16839875—24no—
35#16839872—24no—
36C2×#14519709C2211yescharacteristic, complemented
37C2×#14519708C2211yescharacteristic, complemented
38C2×#14519699C2211yescharacteristic
39C2×#14519699C2211yescharacteristic, complemented
40C2×#14519698C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic, complemented
44C2×#14519689C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46C2×#14519688C2211yescharacteristic, complemented
47#16839663C2211yescharacteristic, complemented
48#16839661C2211yescharacteristic, complemented
49#16839654—21no—
50#16839640—21no—
51#16839619C2211yescharacteristic
52C4×#11758198—21no—
53#16839524C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839516C2211yescharacteristic, complemented
56#16839516C2211yescharacteristic, complemented
57C2×C4×D4×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#97×C61C2211yescharacteristic, complemented
61C4×C4⋊C4×C61C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C24×D61—21no—
65C22×D244—21no—
66C22×D244C2311yescharacteristic
67C22×D244C2311yescharacteristic
68C22×C22⋊D61—21no—
69C2×D4×D61—22no—
70C2×D4×D61—22no—
71C2×D4×D61—22no—
72C2×D4×D61—22no—
73C2×D4×D61—22no—
74C2×D4×D61C2×C414yescomplemented
75C23×Dic61—21no—
76C22×C4×D61—28no—
77C22×C4×D61—21no—
78C22×C4×D61—21no—
79C22×C4×D61—21no—
80C22×C4×D61—21no—
81C22×C4×D61—44no—
82C22×C4×D61—44no—
83C22×C4×D61D411yescharacteristic
84C22×C4×D61D411yescharacteristic
85C22×C4×D61C2311yescharacteristic
86C2×D488—22no—
87C2×D488—22no—
88C2×D488C2×C414yescomplemented
89C2×#11758199—22no—
90C2×#11758199—22no—
91C2×#11758199C2×C414yescomplemented
92C22×#92418C2311yescharacteristic
93C22×#92418C2311yescharacteristic
94#14519752—22no—
95#14519752C2×C414yescomplemented
96C4×D244—22no—
97C4×D244—22no—
98C4×D244—22no—
99C4×D244—44no—
100C4×D244D414yescomplemented
101D4×Dic61—22no—
102D4×Dic61—22no—
103#14519739—22no—
104#14519739—22no—
105C4×C22⋊D61—28no—
106#14519737—28no—
107C2×C4⋊Dic61—21no—
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C4⋊Dic61C2311yescharacteristic
110C2×#11758196—21no—
111C4⋊C4×D61—22no—
112C4⋊C4×D61—22no—
113C2×C22⋊Dic61—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C22⋊C4×D61—28no—
122C2×C4×Dic61D411yescharacteristic
123C2×C4×Dic61D411yescharacteristic
124C2×C4×Dic61C2311yescharacteristic
125C42×D61—22no—
126C42×D61—22no—
127#14519709—22no—
128#14519708—22no—
129#14519699—22no—
130#14519699—22no—
131#14519698—22no—
132#14519697—22no—
133#14519697—22no—
134#14519697C2×C414yescomplemented
135#14519689—22no—
136#14519689C2×C414yescomplemented
137#14519688—22no—
138#14519684—21no—
139#14519684—21no—
140C22×D4×C61C2311yescharacteristic
141C23×C4×C61—21no—
142C22×C8×C61C2311yescharacteristic
143C22×C8×C61C2311yescharacteristic
144C4×D4×C61—22no—
145C4×D4×C61D414yescomplemented
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C22⋊C4×C61—21no—
150C2×C42×C61—21no—
151C2×C42×C61C2311yescharacteristic
152#102×C61—22no—
153#102×C61C2×C414yescomplemented
154#97×C61—22no—
155#95×C61—21no—
156C24×C61—21no—
157C23×D61—24no—
158C23×D61—24no—
159C23×D61—21no—
160C23×D61—24no—
161C23×D61—21no—
162C23×D61—42no—
163C23×D61—42no—
164C23×D61—42no—
165C23×D61—42no—
166C23×D61C2×D411yescharacteristic
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61C22×C412yes—
171C2×D4×C61C2×D412yes—
172C2×D4×C61#4112yes—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—24no—
176C22×C4×C61—21no—
177C22×C4×C61—42no—
178C22×C4×C61—42no—
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2411yescharacteristic
182C2×C22⋊D61—24no—
183C2×C22⋊D61—24no—
184C2×C22⋊D61—24no—
185C22×Dic61—24no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—42no—
189C22×Dic61—42no—
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192C22×Dic61C2×D411yescharacteristic
193D4×D61—28no—
194D4×D61—28no—
195D4×D61—28no—
196D4×D61—28no—
197C2×D244—21no—
198C2×D244—21no—
199C2×D244—21no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—24no—
205C2×D244—21no—
206C2×D244—42no—
207C2×D244—42no—
208C2×D244C22×C412yes—
209C2×D244C22×C412yescomplemented
210C2×D244C2×D412yes—
211C2×D244#4112yes—
212C2×C4×D61—22no—
213C2×C4×D61—22no—
214C2×C4×D61—21no—
215C2×C4×D61—21no—
216C2×C4×D61—21no—
217C2×C4×D61—21no—
218C2×C4×D61—22no—
219C2×C4×D61—24no—
220C2×C4×D61—24no—
221C2×C4×D61—22no—
222C2×C4×D61—24no—
223C2×C4×D61—22no—
224C2×C4×D61—432no—
225C2×C4×D61—41no—
226C2×C4×D61—42no—
227C2×C4×D61—42no—
228C2×C4×D61—42no—
229C2×C4×D61—42no—
230C2×C4×D61—42no—
231C2×C4×D61—42no—
232C2×C4×D61—42no—
233C2×C4×D61—42no—
234C2×C4×D61—42no—
235C2×C4×D61C22×C412yes—
236C2×C4×D61#4112yes—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61C22×C412yescomplemented
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61C22×C412yescomplemented
248C4⋊C4×C61C2×D412yes—
249C22⋊C4×C61—24no—
250C42×C61—42no—
251C42×C61C2×D412yes—
252C42×C61C2×D412yes—
253C22⋊Dic61—24no—
254#11758199—28no—
255#11758198—24no—
256#11758198—24no—
257#11758198—24no—
258#11758198—42no—
259#11758198—42no—
260#11758198—42no—
261#11758198—42no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—42no—
266C4⋊Dic61C2×D412yes—
267#11758196—24no—
268C4×Dic61—22no—
269C4×Dic61—22no—
270C4×Dic61—21no—
271C4×Dic61—21no—
272C2×#92418—21no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418C22×C412yescomplemented
278D488—28no—
279C23×C61—22no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61C22×D411yescharacteristic
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—216no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—48no—
297C22×D61—48no—
298C22×D61—48no—
299C22×D61—48no—
300C22×D61—48no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—48no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61C4×D412yes—
313C22×D61AGL(1,ℤ/8)12yes—
314C22×D61AGL(1,ℤ/8)12yes—
315D4×C61—22no—
316D4×C61—22no—
317D4×C61—22no—
318D4×C61C4×D414yescomplemented
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—48no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61#12012yes—
334C2×C4×C61#12012yes—
335C2×C4×C61C23×C411yescharacteristic
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C2×#4111yescharacteristic
339C2×C4×C61C2×#4111yescharacteristic
340C2×C4×C61C2×#4111yescharacteristic
341C22⋊D61—216no—
342C2×Dic61—21no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—22no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—48no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61C4×D412yes—
357C2×Dic61AGL(1,ℤ/8)12yes—
358D244—22no—
359D244—22no—
360D244—22no—
361D244—22no—
362D244—22no—
363D244—48no—
364D244—41no—
365D244—41no—
366D244C4×D414yescomplemented
367C4×D61—28no—
368C4×D61—22no—
369C4×D61—22no—
370C4×D61—22no—
371C4×D61—22no—
372C4×D61—48no—
373C4×D61—44no—
374C4×D61—48no—
375C4×D61—48no—
376C4×D61—84no—
377C8×C61—22no—
378C8×C61—41no—
379#92418—22no—
380#92418—41no—
381#21452—611nomaximal, Sylow
382C22×C61—24no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—42no—
387C22×C61—42no—
388C22×C61—42no—
389C22×C61C2×C4×D411yescharacteristic
390C22×C61C2×#12011yescharacteristic
391C22×C61#52511yescharacteristic
392C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
393C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
394C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
395C22×C61#57511yescharacteristic
396C2×D61—22no—
397C2×D61—22no—
398C2×D61—22no—
399C2×D61—22no—
400C2×D61—22no—
401C2×D61—22no—
402C2×D61—24no—
403C2×D61—432no—
404C2×D61—42no—
405C2×D61—42no—
406C2×D61—42no—
407C2×D61—42no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—42no—
412C2×D61—42no—
413C2×D61—81no—
414C2×D61—81no—
415C2×D61—81no—
416C2×D61—81no—
417C2×D61#44214yescomplemented
418C4×C61—22no—
419C4×C61—22no—
420C4×C61—42no—
421C4×C61—42no—
422C4×C61—81no—
423C4×C61C2×C4×D411yescharacteristic
424C4×C61C2×C4×D411yescharacteristic
425C4×C61#52511yescharacteristic
426C4×C61#52511yescharacteristic
427Dic61—22no—
428Dic61—22no—
429Dic61—42no—
430Dic61—41no—
431Dic61—81no—
432C22×C4×D4—611no—
433C2×#447—611no—
434C2×#442—611no—
435C2×#442—611no—
436C4×#121—611no—
437#1879—611no—
438#1879—611no—
439#1874—611no—
440#1864—611no—
441#1864—611no—
442#1853—611no—
443#1786—611no—
444#1762—611no—
445#1762D6111yescharacteristic, complemented
446#1749—611no—
447C2×C61—44no—
448C2×C61C4×#12011yescharacteristic
449C2×C61C2×#44211yescharacteristic
450C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
451C2×C61#300311yescharacteristic
452C2×C61#300611yescharacteristic
453C2×C61#310911yescharacteristic
454C2×C61#311411yescharacteristic
455D61—24no—
456D61—44no—
457D61—82no—
458C23×D4—611no—
459C24×C4—1221no—
460C22×D8—611no—
461C22×D8—611no—
462C2×#121—611no—
463C2×C4×D4—611no—
464C2×C4×D4—611no—
465C2×C4×D4—611no—
466C2×C4×D4—611no—
467C2×C4×D4—1221no—
468C2×C4×D4—1221no—
469C2×C4×D4—1221no—
470C2×C4×D4—1224no—
471C2×C4×D4—1224no—
472C2×C4×D4C2×D6111yescharacteristic
473C22×C4⋊C4—611no—
474C22×C22⋊C4—1221no—
475C22×C42—611no—
476#447—618no—
477#442—1224no—
478#442—1224no—
479C2×#106—611no—
480C2×#106—611no—
481C2×#102—611no—
482C2×#102—611no—
483C2×#102—611no—
484C2×#102—611no—
485C2×#102—611no—
486C2×#102—611no—
487C2×#102C2×D6111yescharacteristic
488C2×#102C2×D6111yescharacteristic
489C2×C22⋊C8—611no—
490C2×C22⋊C8—611no—
491C2×#97—611no—
492C2×#97C2×D6111yescharacteristic, complemented
493#390—611no—
494#389—611no—
495#388—1221no—
496#386—1221no—
497#380—611no—
498C4×C4⋊C4C2×D6111yescharacteristic, complemented
499C4×C22⋊C4—1221no—
500#340—611no—
501#340—611no—
502#340C2×D6111yescharacteristic, complemented
503#340C2×D6111yescharacteristic, complemented
504#336—611no—
505#336—611no—
506C61#2145211yescharacteristic, complemented, Sylow
507C25—1221no—
508C22×D4—614no—
509C22×D4—611no—
510C22×D4—611no—
511C22×D4—1221no—
512C22×D4—1222no—
513C22×D4—1221no—
514C22×D4—1222no—
515C22×D4—1222no—
516C22×D4—1222no—
517C22×D4—1222no—
518C22×D4C22×D6111yescharacteristic
519C23×C4—21no—
520C23×C4—611no—
521C23×C4—611no—
522C23×C4—611no—
523C23×C4—1221no—
524C23×C4—1221no—
525C23×C4—1228no—
526C23×C4—1221no—
527C23×C4—1221no—
528C23×C4—1221no—
529C23×C4—2444no—
530C23×C4—2444no—
531C2×D8—614no—
532C2×D8—614no—
533C2×D8—1222no—
534C2×D8—1222no—
535C2×D8—1222no—
536C2×D8—1222no—
537C22×C8—611no—
538C22×C8—611no—
539C22×C8C22×D6111yescharacteristic
540C22×C8C22×D6111yescharacteristic
541#121—614no—
542#121—1222no—
543C4×D4—22no—
544C4×D4—614no—
545C4×D4—1228no—
546C4×D4—1222no—
547C4×D4—1222no—
548C4×D4—1228no—
549C4×D4—1222no—
550C4×D4—1222no—
551C4×D4—1222no—
552C4×D4—1222no—
553C4×D4—1222no—
554C4×D4—2444no—
555C4×D4D24414yescomplemented
556C2×C4⋊C4—611no—
557C2×C4⋊C4—611no—
558C2×C4⋊C4—1222no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4—1222no—
561C2×C4⋊C4—1221no—
562C2×C4⋊C4C22×D6111yescharacteristic
563C2×C4⋊C4C22×D6111yescharacteristic
564C2×C4⋊C4C22×D6111yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—1228no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C42—21no—
576C2×C42—611no—
577C2×C42—611no—
578C2×C42—611no—
579C2×C42—1222no—
580C2×C42—1222no—
581C2×C42C22×D6111yescharacteristic
582#106—1222no—
583#106—1222no—
584#102—22no—
585#102—614no—
586#102—1222no—
587#102—1222no—
588#102—1222no—
589#102—1222no—
590#102—1222no—
591#102C4×D6114yescomplemented
592C22⋊C8—614no—
593C22⋊C8—1222no—
594#97—22no—
595#97—1222no—
596#95—21no—
597#95—1221no—
598#95—1221no—
599C24—21no—
600C24—611no—
601C24—1224no—
602C24—1224no—
603C24—1224no—
604C24—1221no—
605C24—1221no—
606C24—2442no—
607C24—2442no—
608C24—2442no—
609C24—2442no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—612no—
614C2×D4—612no—
615C2×D4—612no—
616C2×D4—612no—
617C2×D4—1224no—
618C2×D4—1224no—
619C2×D4—1228no—
620C2×D4—1228no—
621C2×D4—1228no—
622C2×D4—1224no—
623C2×D4—1224no—
624C2×D4—1228no—
625C2×D4—1221no—
626C2×D4—1221no—
627C2×D4—1221no—
628C2×D4—1221no—
629C2×D4—1221no—
630C2×D4—1221no—
631C2×D4—1221no—
632C2×D4—1221no—
633C2×D4—2442no—
634C2×D4—2442no—
635C2×D4C2×C4×D6112yes—
636C2×D4C2×D24412yes—
637C2×D4#1175822212yes—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—21no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—611no—
645C22×C4—611no—
646C22×C4—612no—
647C22×C4—612no—
648C22×C4—611no—
649C22×C4—1222no—
650C22×C4—1222no—
651C22×C4—1222no—
652C22×C4—1224no—
653C22×C4—1224no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1222no—
659C22×C4—1224no—
660C22×C4—1221no—
661C22×C4—1222no—
662C22×C4—1224no—
663C22×C4—1221no—
664C22×C4—2441no—
665C22×C4—2442no—
666C22×C4—2442no—
667C22×C4—2442no—
668C22×C4—2442no—
669C22×C4—2442no—
670C22×C4—24432no—
671C22×C4—2442no—
672C22×C4—2442no—
673C22×C4—2442no—
674C22×C4—2442no—
675C22×C4—2442no—
676C22×C4—2442no—
677C22×C4D4×D6111yescharacteristic
678C22×C4D4×D6111yescharacteristic
679C22×C4C23×D6111yescharacteristic
680D8—1228no—
681D8—1228no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—612no—
688C2×C8—1221no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8C2×C4×D6112yescomplemented
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—612no—
699C4⋊C4—1224no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—2442no—
704C4⋊C4C2×C4×D6112yescomplemented
705C4⋊C4C2×D24412yes—
706C22⋊C4—24no—
707C22⋊C4—1224no—
708C22⋊C4—1224no—
709C22⋊C4—1224no—
710C22⋊C4—1224no—
711C22⋊C4—2442no—
712C22⋊C4—2442no—
713C22⋊C4—2442no—
714C22⋊C4—2442no—
715C42—42no—
716C42—1221no—
717C42—1221no—
718C42—1222no—
719C42—1222no—
720C42C2×D24412yes—
721C42D4×D6112yes—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—612no—
730C23—612no—
731C23—612no—
732C23—12216no—
733C23—1221no—
734C23—1221no—
735C23—1221no—
736C23—1221no—
737C23—1222no—
738C23—1222no—
739C23—1222no—
740C23—1222no—
741C23—2448no—
742C23—2448no—
743C23—2448no—
744C23—2448no—
745C23—2448no—
746C23—2448no—
747C23—2441no—
748C23—2441no—
749C23—2441no—
750C23—2441no—
751C23—2441no—
752C23—2441no—
753C23—2441no—
754C23—2441no—
755C23—2441no—
756C23—2441no—
757C23C2×D4×D6111yescharacteristic
758D4—22no—
759D4—22no—
760D4—22no—
761D4—614no—
762D4—12216no—
763D4—1222no—
764D4—1222no—
765D4—1222no—
766D4—1222no—
767D4—1222no—
768D4—2448no—
769D4—2441no—
770D4—2441no—
771D4C4×D24414yescomplemented
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—48no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—612no—
787C2×C4—612no—
788C2×C4—1228no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—1222no—
794C2×C4—1222no—
795C2×C4—1222no—
796C2×C4—1222no—
797C2×C4—1221no—
798C2×C4—1222no—
799C2×C4—1221no—
800C2×C4—1221no—
801C2×C4—4884no—
802C2×C4—2444no—
803C2×C4—2448no—
804C2×C4—2448no—
805C2×C4—2448no—
806C2×C4—2448no—
807C2×C4—2441no—
808C2×C4—2441no—
809C2×C4—2441no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4#1451974712yes—
813C2×C4#1451974712yes—
814C2×C4C22×C4×D6111yescharacteristic
815C2×C4C2×D4×D6111yescharacteristic
816C2×C4C22×D24411yescharacteristic
817C2×C4#41×D6111yescharacteristic
818C2×C4#41×D6111yescharacteristic
819C2×C4C2×#1175822211yescharacteristic
820C8—22no—
821C8—41no—
822C8—1222no—
823C8—2441no—
824C22—24no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—614no—
832C22—1222no—
833C22—1222no—
834C22—1222no—
835C22—1222no—
836C22—1222no—
837C22—1222no—
838C22—1224no—
839C22—4881no—
840C22—4881no—
841C22—4881no—
842C22—4881no—
843C22—24432no—
844C22—2442no—
845C22—2442no—
846C22—2442no—
847C22—2442no—
848C22—2442no—
849C22—2442no—
850C22—2442no—
851C22—2442no—
852C22—2442no—
853C22C4×D4×D6111yescharacteristic
854C22C2×#1451974711yescharacteristic
855C22#1684027111yescharacteristic
856C22AGL(1,ℤ/8)×D6111yescharacteristic
857C22AGL(1,ℤ/8)×D6111yescharacteristic
858C22AGL(1,ℤ/8)×D6111yescharacteristic
859C22#1684056111yescharacteristic
860C4—22no—
861C4—22no—
862C4—42no—
863C4—42no—
864C4—81no—
865C4—1222no—
866C4—1222no—
867C4—4881no—
868C4—2442no—
869C4—2441no—
870C4C4×D4×D6111yescharacteristic
871C4C2×C4×D24411yescharacteristic
872C4#1684027111yescharacteristic
873C4#1684027411yescharacteristic
874C2—44no—
875C2—1224no—
876C2—4882no—
877C2—2444no—
878C2C4×#1451974711yescharacteristic
879C2#442×D6111yescharacteristic
880C2#2145462411yescharacteristic
881C2#2145504811yescharacteristic
882C2#2145507211yescharacteristic
883C2#2145590811yescharacteristic
884C2#2145596111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1762C2
socleC23×C61C22×D4
prime radicalC2×#16839897C2
cosocleC22×C4×C61C24
hypercenter#1762D61
hypocenterC61#21452
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
1. C2×C4×D4×D61C2semidirect
3. C2×#16839875C2semidirect
4. C2×#16839872C2semidirect
5. C4×#14519752C2semidirect
6. #21446168C2semidirect
7. #21446165C2semidirect
8. #21446135C2semidirect
9. #21446082C2semidirect
10. #21446081C2semidirect
11. #21446013C2semidirect
12. #21445748C2semidirect
13. #21445647C2semidirect
14. #21445582C2semidirect
15. C61×#1762C2semidirect
23. C2×C4×D244C22semidirect
33. #16839897C4semidirect
36. C2×#14519709C22semidirect
37. C2×#14519708C22semidirect
39. C2×#14519699C22semidirect
43. C2×#14519697C22semidirect
46. C2×#14519688C22semidirect
47. #16839663C22semidirect
48. #16839661C22semidirect
53. #16839524C22semidirect
54. #16839524C22semidirect
55. #16839516C22semidirect
56. #16839516C22semidirect
60. C2×#97×C61C22semidirect
61. C4×C4⋊C4×C61C22semidirect
62. C61×#340C22semidirect
63. C61×#340C22semidirect
74. C2×D4×D61C2×C4semidirect
88. C2×D488C2×C4semidirect
91. C2×#11758199C2×C4semidirect
95. #14519752C2×C4semidirect
100. C4×D244D4semidirect
134. #14519697C2×C4semidirect
136. #14519689C2×C4semidirect
145. C4×D4×C61D4semidirect
153. #102×C61C2×C4semidirect
209. C2×D244C22×C4semidirect
242. C2×C8×C61C22×C4semidirect
247. C4⋊C4×C61C22×C4semidirect
277. C2×#92418C22×C4semidirect
318. D4×C61C4×D4semidirect
366. D244C4×D4semidirect
417. C2×D61#442semidirect
445. #1762D61semidirect
492. C2×#97C2×D61semidirect
498. C4×C4⋊C4C2×D61semidirect
502. #340C2×D61semidirect
503. #340C2×D61semidirect
506. C61#21452semidirect
555. C4×D4D244semidirect
591. #102C4×D61semidirect
693. C2×C8C2×C4×D61semidirect
704. C4⋊C4C2×C4×D61semidirect
771. D4C4×D244semidirect

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×#168398972
C2×#168398752
C2×#168398722
C4×#145197522
#214461682
#214461652
#214461352
#214460822
#214460812
#214460132
#214457482
#214456472
#214455822
C61×#17622
#2145261