Finite Group Databasebeta

← #29685659

Subgroups — #29685659

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×#16839894C211yesmaximal, characteristic
3C2×#16839874C211yesmaximal, characteristic, complemented
4C2×#16839871C211yesmaximal, characteristic, complemented
5#21448335C211yesmaximal, characteristic, complemented
6#21446170C211yesmaximal, characteristic, complemented
7#21446133C211yesmaximal, characteristic, complemented
8#21446083C211yesmaximal, characteristic, complemented
9#21446080C211yesmaximal, characteristic, complemented
10#21446013C211yesmaximal, characteristic, complemented
11#21445748C211yesmaximal, characteristic, complemented
12#21445646C211yesmaximal, characteristic, complemented
13#21445643C211yesmaximal, characteristic, complemented
14#21445580C211yesmaximal, characteristic, complemented
15C61×#1879C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C23×C4×D61—21no—
18C22×#11758199C2211yescharacteristic
19C2×#14519748C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×D4×Dic61C2211yescharacteristic
22C2×D4×Dic61C2211yescharacteristic, complemented
23C2×#14519739C2211yescharacteristic
24C2×C4×C22⋊D61—21no—
25C2×#14519737—21no—
26C2×#14519737—21no—
27C4×D4×D61—24no—
28C4×D4×D61—24no—
29C2×C4⋊C4×D61C2211yescharacteristic
30C2×C22⋊C4×D61—21no—
31C2×C42×D61C2211yescharacteristic
32#16839894C418yescomplemented
33#16839874—24no—
34#16839871—24no—
35C2×#14519709C2211yescharacteristic, complemented
36C2×#14519708C2211yescharacteristic, complemented
37C2×#14519699C2211yescharacteristic
38C2×#14519699C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×#14519698C2211yescharacteristic, complemented
42C2×#14519697C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519687C2211yescharacteristic, complemented
46C2×#14519687C2211yescharacteristic, complemented
47#16839660C2211yescharacteristic, complemented
48#16839656—21no—
49#16839638—21no—
50#16839619C2211yescharacteristic
51C4⋊C4×Dic61C2211yescharacteristic, complemented
52C22⋊C4×Dic61—21no—
53#16839525C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839517C2211yescharacteristic, complemented
57C22×D8×C61C2211yescharacteristic
58C2×C4×D4×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic, complemented
61C61×#390C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#336C2211yescharacteristic, complemented
64C24×D61—21no—
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C2×D4×D61—22no—
69C2×D4×D61—22no—
70C2×D4×D61—22no—
71C2×D4×D61—22no—
72C2×D4×D61—22no—
73C2×D4×D61C2×C414yescomplemented
74C23×Dic61—21no—
75C23×Dic61—21no—
76C22×C4×D61—28no—
77C22×C4×D61—21no—
78C22×C4×D61—21no—
79C22×C4×D61—21no—
80C22×C4×D61—44no—
81C22×C4×D61—44no—
82C22×C4×D61D411yescharacteristic
83C22×C4×D61D411yescharacteristic
84C22×C4×D61C2311yescharacteristic
85C2×#11758199—22no—
86C2×#11758199—22no—
87C2×#11758199C2×C414yescomplemented
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90#14519748—22no—
91#14519748C2×C414yescomplemented
92C4×D244—22no—
93C4×D244—22no—
94D4×Dic61—22no—
95D4×Dic61—22no—
96D4×Dic61—22no—
97D4×Dic61D414yescomplemented
98#14519739—22no—
99#14519739D414yescomplemented
100C4×C22⋊D61—28no—
101#14519737—28no—
102#14519737—44no—
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×#11758196—21no—
107C2×#11758196—21no—
108C4⋊C4×D61—22no—
109C4⋊C4×D61—22no—
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C22⋊C4×D61—28no—
117C2×C4×Dic61—21no—
118C2×C4×Dic61D411yescharacteristic
119C2×C4×Dic61D411yescharacteristic
120C2×C4×Dic61C2311yescharacteristic
121C42×D61—22no—
122C42×D61—22no—
123#14519709—22no—
124#14519708—22no—
125#14519699—22no—
126#14519699C2×C414yescomplemented
127#14519698—22no—
128#14519698—22no—
129#14519698C2×C414yescomplemented
130#14519697—22no—
131#14519689—22no—
132#14519689C2×C414yescomplemented
133#14519687—22no—
134#14519687—22no—
135#14519684—21no—
136#14519684—21no—
137#14519684—21no—
138C22×D4×C61C2311yescharacteristic
139C22×D4×C61C2311yescharacteristic
140C23×C4×C61—21no—
141C2×D8×C61—22no—
142C2×D8×C61—22no—
143C2×D8×C61C2×C414yescomplemented
144C22×C8×C61C2311yescharacteristic
145C22×C8×C61C2311yescharacteristic
146C4×D4×C61—22no—
147C4×D4×C61—22no—
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C22⋊C4×C61—21no—
151C2×C22⋊C4×C61—21no—
152C2×C22⋊C4×C61—21no—
153C2×C42×C61C2311yescharacteristic
154#102×C61—22no—
155#102×C61—22no—
156C24×C61—21no—
157C24×C61—21no—
158C23×D61—24no—
159C23×D61—24no—
160C23×D61—21no—
161C23×D61—24no—
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×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61C22×C412yes—
176C2×D4×C61C22×C412yescomplemented
177C2×D4×C61C2×D412yes—
178C2×D4×C61#4112yes—
179C22×C4×C61—24no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—42no—
183C22×C4×C61—42no—
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2411yescharacteristic
187C2×C22⋊D61—24no—
188C2×C22⋊D61—24no—
189C2×C22⋊D61—24no—
190C2×C22⋊D61—24no—
191C2×C22⋊D61—42no—
192C2×C22⋊D61—42no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—24no—
196C22×Dic61—21no—
197C22×Dic61—42no—
198C22×Dic61—42no—
199C22×Dic61—42no—
200C22×Dic61—42no—
201C22×Dic61—42no—
202C22×Dic61C2×D411yescharacteristic
203C22×Dic61C2×D411yescharacteristic
204C22×Dic61C2×D411yescharacteristic
205D4×D61—28no—
206D4×D61—28no—
207D4×D61—28no—
208D4×D61—28no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244—21no—
212C2×D244C22×C412yes—
213C2×D244C2×D412yes—
214C2×D244#4112yes—
215C2×C4×D61—22no—
216C2×C4×D61—22no—
217C2×C4×D61—21no—
218C2×C4×D61—21no—
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61—22no—
222C2×C4×D61—24no—
223C2×C4×D61—24no—
224C2×C4×D61—22no—
225C2×C4×D61—24no—
226C2×C4×D61—22no—
227C2×C4×D61—432no—
228C2×C4×D61—41no—
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—
237D8×C61—28no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61C22×C412yescomplemented
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61C2×D412yes—
248C22⋊C4×C61—24no—
249C22⋊C4×C61—42no—
250C22⋊C4×C61—42no—
251C42×C61—21no—
252C42×C61—21no—
253C22⋊Dic61—24no—
254C22⋊Dic61—24no—
255C22⋊Dic61—42no—
256#11758199—28no—
257#11758198—24no—
258#11758198—24no—
259#11758198—42no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61C22×C412yescomplemented
265C4⋊Dic61C2×D412yes—
266#11758196—24no—
267#11758196—42no—
268C4×Dic61—22no—
269C4×Dic61—22no—
270C4×Dic61—42no—
271C4×Dic61C2×D412yes—
272C4×Dic61C2×D412yes—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418C22×C412yescomplemented
279C23×C61—22no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—22no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61C22×D411yescharacteristic
294C22×D61—21no—
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—216no—
299C22×D61—22no—
300C22×D61—22no—
301C22×D61—22no—
302C22×D61—48no—
303C22×D61—48no—
304C22×D61—48no—
305C22×D61—48no—
306C22×D61—48no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—48no—
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×C61—22no—
319D4×C61—22no—
320D4×C61—41no—
321D4×C61—41no—
322D4×C61C4×D414yescomplemented
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—22no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—48no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61AGL(1,ℤ/8)12yes—
336C2×C4×C61C23×C411yescharacteristic
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C2×#4111yescharacteristic
340C2×C4×C61C2×#4111yescharacteristic
341C2×C4×C61C2×#4111yescharacteristic
342C22⋊D61—216no—
343C22⋊D61—48no—
344C2×Dic61—21no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—48no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—84no—
361C2×Dic61C4×D412yes—
362C2×Dic61#12012yes—
363C2×Dic61#12012yes—
364D244—22no—
365D244—22no—
366D244—22no—
367D244C4×D414yescomplemented
368C4×D61—28no—
369C4×D61—22no—
370C4×D61—22no—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—44no—
374C4×D61—48no—
375C4×D61—48no—
376C4×D61—48no—
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×C61—42no—
390C22×C61—42no—
391C22×C61—42no—
392C22×C61—81no—
393C22×C61—81no—
394C22×C61—81no—
395C22×C61—81no—
396C22×C61C2×C4×D411yescharacteristic
397C22×C61C2×#12011yescharacteristic
398C22×C61#52511yescharacteristic
399C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
400C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
402C22×C61#57511yescharacteristic
403C2×D61—22no—
404C2×D61—22no—
405C2×D61—22no—
406C2×D61—22no—
407C2×D61—22no—
408C2×D61—22no—
409C2×D61—24no—
410C2×D61—432no—
411C2×D61—42no—
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—42no—
416C2×D61—42no—
417C2×D61#44214yescomplemented
418C4×C61—22no—
419C4×C61—42no—
420C4×C61—41no—
421C4×C61—81no—
422C4×C61C2×C4×D411yescharacteristic
423C4×C61C2×C4×D411yescharacteristic
424C4×C61#52511yescharacteristic
425C4×C61#52511yescharacteristic
426Dic61—22no—
427Dic61—22no—
428Dic61—22no—
429Dic61—42no—
430Dic61—42no—
431Dic61—81no—
432C22×C4×D4—611no—
433C2×#447—611no—
434C2×#442—611no—
435C2×#442—611no—
436C4×#121—611no—
437#1879—611no—
438#1879D6111yescharacteristic, complemented
439#1874—611no—
440#1864—611no—
441#1864—611no—
442#1853—611no—
443#1786—611no—
444#1762—611no—
445#1762—611no—
446#1749—611no—
447C2×C61—44no—
448C2×C61—82no—
449C2×C61C4×#12011yescharacteristic
450C2×C61C2×#44211yescharacteristic
451C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
452C2×C61#300311yescharacteristic
453C2×C61#300611yescharacteristic
454C2×C61#310911yescharacteristic
455C2×C61#311411yescharacteristic
456D61—24no—
457D61—44no—
458C23×D4—611no—
459C24×C4—1221no—
460C22×D8—611no—
461C22×D8C2×D6111yescharacteristic
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, complemented
489C2×C22⋊C8—611no—
490C2×C22⋊C8—611no—
491C2×#97—611no—
492C2×#97—611no—
493#390C2×D6111yescharacteristic, complemented
494#389—611no—
495#388—1221no—
496#386—1221no—
497#380—611no—
498C4×C4⋊C4—611no—
499C4×C22⋊C4—1221no—
500#340—611no—
501#340—611no—
502#340—611no—
503#340C2×D6111yescharacteristic, complemented
504#336—611no—
505#336C2×D6111yescharacteristic, complemented
506C61#2145211yescharacteristic, complemented, Sylow
507C25—1221no—
508C22×D4—614no—
509C22×D4—611no—
510C22×D4—1222no—
511C22×D4—1221no—
512C22×D4—1222no—
513C22×D4—1222no—
514C22×D4—1222no—
515C22×D4—1222no—
516C22×D4—1221no—
517C22×D4C22×D6111yescharacteristic
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—22no—
532C2×D8—22no—
533C2×D8—614no—
534C2×D8—1222no—
535C2×D8—1222no—
536C2×D8C4×D6114yescomplemented
537C22×C8—611no—
538C22×C8—611no—
539C22×C8C22×D6111yescharacteristic
540C22×C8C22×D6111yescharacteristic
541#121—614no—
542#121—1222no—
543C4×D4—22no—
544C4×D4—22no—
545C4×D4—614no—
546C4×D4—614no—
547C4×D4—1222no—
548C4×D4—1222no—
549C4×D4—1222no—
550C4×D4—1222no—
551C4×D4—1222no—
552C4×D4—1222no—
553C4×D4—1228no—
554C4×D4—1228no—
555C4×D4—2444no—
556C2×C4⋊C4—611no—
557C2×C4⋊C4—611no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—1222no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4—1222no—
562C2×C4⋊C4—1221no—
563C2×C4⋊C4C22×D6111yescharacteristic
564C2×C4⋊C4C22×D6111yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—1228no—
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—611no—
576C2×C42—611no—
577C2×C42—611no—
578C2×C42—1222no—
579C2×C42—1222no—
580C2×C42—1221no—
581C2×C42C22×D6111yescharacteristic
582#106—1222no—
583#106—1222no—
584#102—22no—
585#102—22no—
586#102—614no—
587#102—614no—
588#102—1222no—
589#102—1222no—
590#102—1222no—
591#102—1222no—
592C22⋊C8—614no—
593C22⋊C8—1222no—
594#97—1222no—
595#97—1222no—
596#95—1221no—
597#95—1221no—
598#95—1221no—
599C24—21no—
600C24—21no—
601C24—611no—
602C24—1224no—
603C24—1224no—
604C24—1224no—
605C24—1221no—
606C24—2442no—
607C24—2442no—
608C24—2442no—
609C24—2442no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—612no—
619C2×D4—612no—
620C2×D4—612no—
621C2×D4—1224no—
622C2×D4—1228no—
623C2×D4—1228no—
624C2×D4—1228no—
625C2×D4—1224no—
626C2×D4—1224no—
627C2×D4—1228no—
628C2×D4—1224no—
629C2×D4—1221no—
630C2×D4—1221no—
631C2×D4—1221no—
632C2×D4—2442no—
633C2×D4—2442no—
634C2×D4C2×C4×D6112yes—
635C2×D4C2×C4×D6112yescomplemented
636C2×D4D4×D6112yes—
637C2×D4#1175822412yes—
638C22×C4—24no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—611no—
644C22×C4—611no—
645C22×C4—611no—
646C22×C4—612no—
647C22×C4—612no—
648C22×C4—1222no—
649C22×C4—1222no—
650C22×C4—1224no—
651C22×C4—1222no—
652C22×C4—1222no—
653C22×C4—1224no—
654C22×C4—1224no—
655C22×C4—1224no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1222no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—2441no—
665C22×C4—2442no—
666C22×C4—24432no—
667C22×C4—2442no—
668C22×C4—2442no—
669C22×C4—2442no—
670C22×C4—2442no—
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—28no—
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—612no—
698C4⋊C4—612no—
699C4⋊C4—1224no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—2442no—
705C4⋊C4D4×D6112yes—
706C22⋊C4—24no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—1224no—
710C22⋊C4—1224no—
711C22⋊C4—1224no—
712C22⋊C4—1224no—
713C22⋊C4—2442no—
714C22⋊C4—2442no—
715C42—21no—
716C42—21no—
717C42—612no—
718C42—612no—
719C42—1222no—
720C42—1222no—
721C42—2442no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—612no—
737C23—612no—
738C23—612no—
739C23—12216no—
740C23—1221no—
741C23—1221no—
742C23—1221no—
743C23—1221no—
744C23—1222no—
745C23—1222no—
746C23—1222no—
747C23—2448no—
748C23—2448no—
749C23—2448no—
750C23—2448no—
751C23—2448no—
752C23—2448no—
753C23—2441no—
754C23—2441no—
755C23—2441no—
756C23—2441no—
757C23C2×D4×D6111yescharacteristic
758D4—22no—
759D4—22no—
760D4—22no—
761D4—22no—
762D4—22no—
763D4—41no—
764D4—41no—
765D4—614no—
766D4—12216no—
767D4—1222no—
768D4—1222no—
769D4—1222no—
770D4—2448no—
771D4#1451973714yescomplemented
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—48no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—612no—
785C2×C4—612no—
786C2×C4—612no—
787C2×C4—1228no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—1221no—
794C2×C4—1222no—
795C2×C4—1222no—
796C2×C4—1222no—
797C2×C4—1222no—
798C2×C4—1222no—
799C2×C4—1222no—
800C2×C4—4884no—
801C2×C4—2448no—
802C2×C4—2444no—
803C2×C4—2448no—
804C2×C4—2448no—
805C2×C4—2448no—
806C2×C4—2441no—
807C2×C4—2441no—
808C2×C4—2441no—
809C2×C4—2441no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4—2441no—
813C2×C4#1451980112yes—
814C2×C4C22×C4×D6111yescharacteristic
815C2×C4C2×D4×D6111yescharacteristic
816C2×C4C2×D4×D6111yescharacteristic
817C2×C4#41×D6111yescharacteristic
818C2×C4#41×D6111yescharacteristic
819C2×C4C2×#1175822411yescharacteristic
820C8—22no—
821C8—41no—
822C8—1222no—
823C8—2441no—
824C22—24no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—614no—
839C22—1222no—
840C22—1222no—
841C22—1222no—
842C22—1222no—
843C22—1222no—
844C22—1222no—
845C22—1224no—
846C22—24432no—
847C22—2442no—
848C22—2442no—
849C22—2442no—
850C22—2442no—
851C22—2442no—
852C22—2442no—
853C22C4×D4×D6111yescharacteristic
854C22#120×D6111yescharacteristic
855C22#1684027211yescharacteristic
856C22AGL(1,ℤ/8)×D6111yescharacteristic
857C22AGL(1,ℤ/8)×D6111yescharacteristic
858C22C2×#1451980111yescharacteristic
859C22#1684055911yescharacteristic
860C4—22no—
861C4—42no—
862C4—41no—
863C4—81no—
864C4—1222no—
865C4—1222no—
866C4—1222no—
867C4—4881no—
868C4—2442no—
869C4—2442no—
870C4C4×D4×D6111yescharacteristic
871C4C2×#1451973711yescharacteristic
872C4#1684027011yescharacteristic
873C4#1684027211yescharacteristic
874C2—44no—
875C2—82no—
876C2—1224no—
877C2—2444no—
878C2#2144832411yescharacteristic
879C2#442×D6111yescharacteristic
880C2C4×#1451980111yescharacteristic
881C2#2145504311yescharacteristic
882C2#2145506811yescharacteristic
883C2#2145590911yescharacteristic
884C2#2145595611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1879C2
socleC23×C61C22×D4
prime radicalC2×#16839894C2
cosocleC22×C4×C61C24
hypercenter#1879D61
hypocenterC61#21452
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
1. C2×C4×D4×D61C2semidirect
3. C2×#16839874C2semidirect
4. C2×#16839871C2semidirect
5. #21448335C2semidirect
6. #21446170C2semidirect
7. #21446133C2semidirect
8. #21446083C2semidirect
9. #21446080C2semidirect
10. #21446013C2semidirect
11. #21445748C2semidirect
12. #21445646C2semidirect
13. #21445643C2semidirect
14. #21445580C2semidirect
15. C61×#1879C2semidirect
22. C2×D4×Dic61C22semidirect
32. #16839894C4semidirect
35. C2×#14519709C22semidirect
36. C2×#14519708C22semidirect
41. C2×#14519698C22semidirect
45. C2×#14519687C22semidirect
46. C2×#14519687C22semidirect
47. #16839660C22semidirect
51. C4⋊C4×Dic61C22semidirect
53. #16839525C22semidirect
54. #16839524C22semidirect
55. #16839524C22semidirect
56. #16839517C22semidirect
60. C2×#102×C61C22semidirect
61. C61×#390C22semidirect
62. C61×#340C22semidirect
63. C61×#336C22semidirect
73. C2×D4×D61C2×C4semidirect
87. C2×#11758199C2×C4semidirect
91. #14519748C2×C4semidirect
97. D4×Dic61D4semidirect
99. #14519739D4semidirect
126. #14519699C2×C4semidirect
129. #14519698C2×C4semidirect
132. #14519689C2×C4semidirect
143. C2×D8×C61C2×C4semidirect
176. C2×D4×C61C22×C4semidirect
243. C2×C8×C61C22×C4semidirect
264. C4⋊Dic61C22×C4semidirect
278. C2×#92418C22×C4semidirect
322. D4×C61C4×D4semidirect
367. D244C4×D4semidirect
417. C2×D61#442semidirect
438. #1879D61semidirect
488. C2×#102C2×D61semidirect
493. #390C2×D61semidirect
503. #340C2×D61semidirect
505. #336C2×D61semidirect
506. C61#21452semidirect
536. C2×D8C4×D61semidirect
635. C2×D4C2×C4×D61semidirect
693. C2×C8C2×C4×D61semidirect
771. D4#14519737semidirect

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×#168398942
C2×#168398742
C2×#168398712
#214483352
#214461702
#214461332
#214460832
#214460802
#214460132
#214457482
#214456462
#214456432
#214455802
C61×#18792
#2145261