Finite Group Databasebeta

← #29605362

Subgroups — #29605362

Order 15616.

2422 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D244C211yesmaximal, characteristic
2C2×#16839679C211yesmaximal, characteristic
3C2×#16839653C212yesmaximal, complemented
4C2×#16839633C212yesmaximal, complemented
5#21444083C211yesmaximal, characteristic, complemented
6#21444072C211yesmaximal, characteristic, complemented
7#21444059C211yesmaximal, characteristic
8#21444057C212yesmaximal, complemented
9#21444046C211yesmaximal, characteristic, complemented
10#21444040C212yesmaximal, complemented
11C2×C4×C4⋊C4×C61C211yesmaximal, characteristic, complemented
12C23×D244C2211yescharacteristic
13C23×C4×D61C2212yes—
14C2×C4×D244—28no—
15C2×C4×D244—24no—
16C22×C4⋊Dic61C2211yescharacteristic
17C22×#11758196C2212yes—
18C22×#11758198C2212yes—
19C22×#11758198C2212yes—
20C22×#11758198C2212yes—
21C22×#11758198C2212yes—
22C22×#11758198C2212yes—
23#16839679C418yescomplemented
24#16839653—28no—
25#16839633—28no—
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2211yescharacteristic
31C2×#14519684C2212yes—
32C2×#14519684C2211yescharacteristic
33C22×C4⋊C4×C61C2211yescharacteristic
34C22×C4⋊C4×C61C2211yescharacteristic
35C22×C42×C61C2211yescharacteristic
36C22×C42×C61C2211yescharacteristic
37C22×C42×C61C2211yescharacteristic
38C4×C4⋊C4×C61—24no—
39C2×#95×C61C2211yescharacteristic
40C2×#95×C61C2211yescharacteristic
41C24×D61C2312yes—
42C22×D244—24no—
43C22×D244—24no—
44C22×D244—22no—
45C22×D244—22no—
46C22×D244C2×C414yes—
47C23×Dic61C2312yes—
48C23×Dic61C2312yes—
49C23×Dic61C2312yes—
50C22×C4×D61—24no—
51C22×C4×D61—24no—
52C22×C4×D61—24no—
53C22×C4×D61—24no—
54C22×C4×D61—24no—
55C22×C4×D61—42no—
56C22×C4×D61—42no—
57C4×D244—232no—
58C2×C4⋊Dic61—22no—
59C2×C4⋊Dic61—24no—
60C2×#11758196—24no—
61C2×#11758196—24no—
62C2×#11758196—42no—
63C2×#11758198—24no—
64C2×#11758198—24no—
65C2×#11758198—24no—
66C2×#11758198—24no—
67C2×#11758198—24no—
68C2×#11758198—24no—
69C2×#11758198—24no—
70C2×#11758198—24no—
71C2×#11758198—24no—
72C2×#11758198—24no—
73C2×#11758198—42no—
74C2×#11758198—42no—
75C2×#11758198C2×C418yescomplemented
76C2×#11758198C2×C418yescomplemented
77C2×#11758198D418yes—
78#14519684—24no—
79#14519684—24no—
80#14519684—24no—
81#14519684—22no—
82#14519684—24no—
83#14519684—42no—
84#14519684C2×C414yescomplemented
85C23×C4×C61C2311yescharacteristic
86C23×C4×C61C2311yescharacteristic
87C23×C4×C61C2311yescharacteristic
88C23×C4×C61C2311yescharacteristic
89C23×C4×C61C2311yescharacteristic
90C23×C4×C61C2311yescharacteristic
91C23×C4×C61C2311yescharacteristic
92C2×C4⋊C4×C61—22no—
93C2×C4⋊C4×C61—22no—
94C2×C4⋊C4×C61—22no—
95C2×C4⋊C4×C61—22no—
96C2×C4⋊C4×C61C2×C414yescomplemented
97C2×C4⋊C4×C61D414yescomplemented
98C2×C42×C61—24no—
99C2×C42×C61—22no—
100C2×C42×C61—22no—
101C2×C42×C61—22no—
102C2×C42×C61—22no—
103C2×C42×C61—24no—
104C2×C42×C61D414yes—
105#95×C61—22no—
106#95×C61—22no—
107C24×C61C2411yescharacteristic
108C23×D61—22no—
109C23×D61—22no—
110C23×D61—22no—
111C23×D61—22no—
112C23×D61—22no—
113C23×D61—22no—
114C23×D61—22no—
115C23×D61—22no—
116C23×D61—22no—
117C23×D61—22no—
118C23×D61—22no—
119C23×D61—22no—
120C23×D61C22×C414yes—
121C23×D61C2×D414yes—
122C23×D61#4114yes—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—21no—
126C22×C4×C61—22no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61C22×C412yes—
147C22×C4×C61C22×C412yes—
148C22×C4×C61C22×C412yes—
149C22×C4×C61C2×D412yes—
150C22×C4×C61C2×D412yes—
151C22×C4×C61C2×D412yes—
152C22×C4×C61C2×D414yes—
153C22×C4×C61C2×D412yes—
154C22×C4×C61C2×D412yes—
155C22×C4×C61C2×D412yes—
156C22×C4×C61#4112yes—
157C22×C4×C61#4112yes—
158C22×C4×C61#4112yes—
159C22×C4×C61#4112yes—
160C22×Dic61—22no—
161C22×Dic61—22no—
162C22×Dic61—22no—
163C22×Dic61—22no—
164C22×Dic61—22no—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61C22×C414yes—
180C22×Dic61C2×D414yes—
181C2×D244—28no—
182C2×D244—216no—
183C2×D244—28no—
184C2×D244—216no—
185C2×D244—28no—
186C2×C4×D61—216no—
187C2×C4×D61—48no—
188C2×C4×D61—48no—
189C2×C4×D61—48no—
190C2×C4×D61—48no—
191C2×C4×D61—48no—
192C2×C4×D61—48no—
193C4⋊C4×C61—28no—
194C4⋊C4×C61—28no—
195C42×C61—28no—
196C42×C61—28no—
197C42×C61—44no—
198#11758198—216no—
199#11758198—216no—
200#11758198—216no—
201#11758198—48no—
202#11758198—48no—
203C4⋊Dic61—28no—
204#11758196—48no—
205C23×C61C23×C411yescharacteristic
206C23×C61C22×D411yescharacteristic
207C23×C61C22×D412yes—
208C23×C61C22×D411yescharacteristic
209C23×C61C2×#4111yescharacteristic
210C23×C61C2×#4112yes—
211C23×C61C2×#4111yescharacteristic
212C23×C61C2×#4111yescharacteristic
213C23×C61C2×#4111yescharacteristic
214C23×C61H(5,𝔽2)12yes—
215C23×C612−1+412yes—
216C22×D61—24no—
217C22×D61—24no—
218C22×D61—24no—
219C22×D61—24no—
220C22×D61—24no—
221C22×D61—24no—
222C22×D61—24no—
223C22×D61—24no—
224C22×D61—24no—
225C22×D61—24no—
226C22×D61—24no—
227C22×D61—24no—
228C22×D61—24no—
229C22×D61—24no—
230C22×D61—24no—
231C22×D61—24no—
232C22×D61—24no—
233C22×D61—24no—
234C22×D61—42no—
235C22×D61—42no—
236C22×D61—42no—
237C22×D61—42no—
238C22×D61—42no—
239C22×D61—42no—
240C22×D61—42no—
241C22×D61—42no—
242C22×D61—42no—
243C22×D61—42no—
244C22×D61—42no—
245C22×D61—42no—
246C22×D61—42no—
247C22×D61—42no—
248C22×D61—42no—
249C22×D61—42no—
250C22×D61C4×D418yes—
251C2×C4×C61—22no—
252C2×C4×C61—24no—
253C2×C4×C61—22no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
256C2×C4×C61—22no—
257C2×C4×C61—22no—
258C2×C4×C61—22no—
259C2×C4×C61—22no—
260C2×C4×C61—24no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—24no—
266C2×C4×C61—24no—
267C2×C4×C61—24no—
268C2×C4×C61—24no—
269C2×C4×C61—24no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—24no—
274C2×C4×C61—24no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—42no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—42no—
283C2×C4×C61—42no—
284C2×C4×C61C4×D414yes—
285C2×C4×C61C4×D414yescomplemented
286C2×C4×C61#12014yes—
287C2×C4×C61#12114yes—
288C2×Dic61—24no—
289C2×Dic61—24no—
290C2×Dic61—24no—
291C2×Dic61—24no—
292C2×Dic61—24no—
293C2×Dic61—24no—
294C2×Dic61—42no—
295C2×Dic61—42no—
296C2×Dic61—42no—
297C2×Dic61—42no—
298C2×Dic61—42no—
299C2×Dic61—42no—
300C2×Dic61—42no—
301C2×Dic61—42no—
302C2×Dic61—42no—
303C2×Dic61—42no—
304C2×Dic61—42no—
305C2×Dic61—42no—
306C2×Dic61—42no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309D244—232no—
310C4×D61—432no—
311#14176—611nomaximal, Sylow
312C22×C61C2×C4×D412yes—
313C22×C61C2×C4×D411yescharacteristic
314C22×C61C2×C4×D411yescharacteristic
315C22×C61C4×#4111yescharacteristic
316C22×C61#52012yes—
317C22×C61C2×#12011yescharacteristic
318C22×C61C2×#12111yescharacteristic
319C22×C61#52511yescharacteristic
320C22×C61#52512yes—
321C22×C61#52511yescharacteristic
322C22×C61#52911yescharacteristic
323C22×C61#53211yescharacteristic
324C22×C61#53511yescharacteristic
325C22×C61#53611yescharacteristic
326C22×C61#54212yes—
327C22×C61D4212yes—
328C22×C61#54612yes—
329C22×C61#54712yes—
330C22×C61#54712yes—
331C22×C61#54812yes—
332C22×C61#55112yes—
333C22×C61#55212yes—
334C22×C61#55312yes—
335C2×D61—28no—
336C2×D61—28no—
337C2×D61—28no—
338C2×D61—44no—
339C2×D61—44no—
340C2×D61—44no—
341C2×D61—44no—
342C2×D61—44no—
343C2×D61—44no—
344C2×D61—44no—
345C2×D61—44no—
346C2×D61—44no—
347C2×D61—44no—
348C2×D61—44no—
349C2×D61—44no—
350C4×C61—24no—
351C4×C61—24no—
352C4×C61—24no—
353C4×C61—24no—
354C4×C61—42no—
355C4×C61—42no—
356C4×C61—42no—
357Dic61—44no—
358Dic61—44no—
359Dic61—82no—
360C22×C4×D4—611no—
361C2×#394—611no—
362C2×#388—612no—
363C2×#385—612no—
364C2×C4×C4⋊C4D6111yescharacteristic, complemented
365#1444—611no—
366#1441—611no—
367#1438—611no—
368#1437—612no—
369#1434—611no—
370C22⋊#95—612no—
371C2×C61C4×#12011yescharacteristic
372C2×C61C4×#12111yescharacteristic
373C2×C61#232611yescharacteristic
374C2×C61#235912yes—
375C2×C61#236112yes—
376C2×C61#240611yescharacteristic
377C2×C61#240811yescharacteristic
378C2×C61#246112yes—
379C2×C61#246812yes—
380C2×C61#253611yescharacteristic
381C2×C61#259811yescharacteristic
382D61—48no—
383C23×D4—611no—
384C24×C4—612no—
385C2×C4×D4—1228no—
386C2×C4×D4—1224no—
387C22×C4⋊C4—611no—
388C22×C4⋊C4—612no—
389C22×C4⋊C4C2×D6111yescharacteristic
390C22×C4⋊C4C2×D6111yescharacteristic
391C22×C22⋊C4—612no—
392C22×C22⋊C4—612no—
393C22×C22⋊C4—612no—
394C22×C22⋊C4—612no—
395C22×C22⋊C4—612no—
396C22×C42C2×D6111yescharacteristic
397C22×C42C2×D6111yescharacteristic
398C22×C42C2×D6111yescharacteristic
399#394—618no—
400#388—1228no—
401#385—1228no—
402C4×C4⋊C4—24no—
403C2×#95—611no—
404C2×#95—612no—
405C2×#95—612no—
406C2×#95—612no—
407C2×#95—611no—
408C2×#95—612no—
409C2×#95—612no—
410C2×#95C2×D6111yescharacteristic
411C2×#95C2×D6111yescharacteristic
412C61#1417611yescharacteristic, complemented, Sylow
413C25—612no—
414C22×D4—614no—
415C22×D4—1224no—
416C22×D4—1224no—
417C22×D4—1222no—
418C22×D4—1222no—
419C23×C4—612no—
420C23×C4—612no—
421C23×C4—612no—
422C23×C4—1224no—
423C23×C4—1224no—
424C23×C4—1224no—
425C23×C4—1224no—
426C23×C4—1224no—
427C23×C4—2442no—
428C23×C4—2442no—
429C23×C4C22×D6111yescharacteristic
430C23×C4C22×D6111yescharacteristic
431C23×C4C22×D6111yescharacteristic
432C23×C4C22×D6111yescharacteristic
433C23×C4C22×D6111yescharacteristic
434C23×C4C22×D6111yescharacteristic
435C23×C4C22×D6111yescharacteristic
436C4×D4—12232no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—1224no—
442C2×C4⋊C4—1222no—
443C2×C4⋊C4—1224no—
444C2×C4⋊C4—1224no—
445C2×C4⋊C4—2442no—
446C2×C4⋊C4C4×D6114yescomplemented
447C2×C4⋊C4D24414yescomplemented
448C2×C22⋊C4—618no—
449C2×C22⋊C4—618no—
450C2×C22⋊C4—618no—
451C2×C22⋊C4—1224no—
452C2×C22⋊C4—1224no—
453C2×C22⋊C4—1224no—
454C2×C22⋊C4—1224no—
455C2×C22⋊C4—1224no—
456C2×C22⋊C4—1224no—
457C2×C22⋊C4—1224no—
458C2×C22⋊C4—1224no—
459C2×C22⋊C4—1224no—
460C2×C22⋊C4—1224no—
461C2×C22⋊C4—2442no—
462C2×C22⋊C4—2442no—
463C2×C42—22no—
464C2×C42—22no—
465C2×C42—24no—
466C2×C42—22no—
467C2×C42—24no—
468C2×C42—22no—
469C2×C42C22⋊D6114yes—
470#95—22no—
471#95—22no—
472#95—614no—
473#95—1224no—
474#95—1224no—
475#95—1224no—
476#95—1222no—
477#95—1224no—
478#95—2442no—
479C24—614no—
480C24—614no—
481C24—614no—
482C24—1222no—
483C24—1222no—
484C24—1222no—
485C24—1222no—
486C24—1222no—
487C24—1222no—
488C24—1222no—
489C24—1222no—
490C24—1222no—
491C24—1222no—
492C24—1222no—
493C24—1222no—
494C24C23×D6111yescharacteristic
495C2×D4—12216no—
496C2×D4—1228no—
497C2×D4—1228no—
498C2×D4—12216no—
499C2×D4—1228no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—614no—
524C22×C4—614no—
525C22×C4—12216no—
526C22×C4—1222no—
527C22×C4—1222no—
528C22×C4—1222no—
529C22×C4—1222no—
530C22×C4—1222no—
531C22×C4—1222no—
532C22×C4—1222no—
533C22×C4—1222no—
534C22×C4—1222no—
535C22×C4—1222no—
536C22×C4—1222no—
537C22×C4—1222no—
538C22×C4—1222no—
539C22×C4—1222no—
540C22×C4—1222no—
541C22×C4—1222no—
542C22×C4—1222no—
543C22×C4—1222no—
544C22×C4—1222no—
545C22×C4—2448no—
546C22×C4—2448no—
547C22×C4—2448no—
548C22×C4—2448no—
549C22×C4—2448no—
550C22×C4—2448no—
551C22×C4C2×C4×D6112yes—
552C22×C4C2×C4×D6112yes—
553C22×C4C2×C4×D6112yes—
554C22×C4C2×D24412yes—
555C22×C4C2×D24412yes—
556C22×C4C2×D24412yes—
557C22×C4#1175822212yes—
558C22×C4#1175822212yes—
559C22×C4#1175822212yes—
560C22×C4#1175822212yes—
561C22×C4D4×D6114yes—
562C22×C4C2×C22⋊D6112yes—
563C22×C4C2×C22⋊D6112yes—
564C22×C4C2×C22⋊D6112yes—
565C4⋊C4—28no—
566C4⋊C4—28no—
567C4⋊C4—1228no—
568C4⋊C4—2448no—
569C22⋊C4—12216no—
570C22⋊C4—12216no—
571C22⋊C4—12216no—
572C22⋊C4—2448no—
573C22⋊C4—2448no—
574C42—28no—
575C42—28no—
576C42—44no—
577C23—618no—
578C23—1224no—
579C23—1224no—
580C23—1224no—
581C23—1224no—
582C23—1224no—
583C23—1224no—
584C23—1224no—
585C23—1224no—
586C23—1224no—
587C23—1224no—
588C23—1224no—
589C23—1224no—
590C23—1224no—
591C23—1224no—
592C23—1224no—
593C23—1224no—
594C23—1224no—
595C23—1224no—
596C23—2442no—
597C23—2442no—
598C23—2442no—
599C23—2442no—
600C23—2442no—
601C23—2442no—
602C23—2442no—
603C23—2442no—
604C23—2442no—
605C23—2442no—
606C23—2442no—
607C23—2442no—
608C23—2442no—
609C23—2442no—
610C23—2442no—
611C23—2442no—
612C23C22×C4×D6111yescharacteristic
613C23C2×D4×D6112yes—
614C23C22×C22⋊D6111yescharacteristic
615C23C22×D24411yescharacteristic
616C23#41×D6112yes—
617C23C2×#1175822211yescharacteristic
618C23C2×#1175822211yescharacteristic
619C23C2×#1175822211yescharacteristic
620C23C2×#1175822211yescharacteristic
621C23#1451982312yes—
622C23#1451982512yes—
623D4—12232no—
624C2×C4—24no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—24no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—42no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—42no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—42no—
657C2×C4—1224no—
658C2×C4—1224no—
659C2×C4—1224no—
660C2×C4—1224no—
661C2×C4—1224no—
662C2×C4—1224no—
663C2×C4—24432no—
664C2×C4—2442no—
665C2×C4—2442no—
666C2×C4—2442no—
667C2×C4—2442no—
668C2×C4—2442no—
669C2×C4—2442no—
670C2×C4—2442no—
671C2×C4—2442no—
672C2×C4—2442no—
673C2×C4—2442no—
674C2×C4—2442no—
675C2×C4—2442no—
676C2×C4—2442no—
677C2×C4—2442no—
678C2×C4—2442no—
679C2×C4C4×C22⋊D6114yes—
680C2×C4C4×D24414yescomplemented
681C2×C4#1451974514yes—
682C2×C4#1451975114yes—
683C22—1228no—
684C22—1228no—
685C22—1228no—
686C22—2444no—
687C22—2444no—
688C22—2444no—
689C22—2444no—
690C22—2444no—
691C22—2444no—
692C22—2444no—
693C22—2444no—
694C22—2444no—
695C22—2444no—
696C22—2444no—
697C22—2444no—
698C22C4×D4×D6112yes—
699C22C2×C4×C22⋊D6111yescharacteristic
700C22C2×C4×D24411yescharacteristic
701C22C4×#1175822211yescharacteristic
702C22#1684024412yes—
703C22C2×#1451974511yescharacteristic
704C22C2×#1451975111yescharacteristic
705C22#1684026911yescharacteristic
706C22#1684027112yes—
707C22#1684027311yescharacteristic
708C22#1684029611yescharacteristic
709C22#1684031211yescharacteristic
710C22#1684032611yescharacteristic
711C22#1684033611yescharacteristic
712C22#1684038412yes—
713C22D4×D24412yes—
714C22#1684040812yes—
715C22#1684041312yes—
716C22#1684041312yes—
717C22#1684042412yes—
718C22#1684043612yes—
719C22#1684045312yes—
720C22#1684045612yes—
721C4—24no—
722C4—24no—
723C4—24no—
724C4—24no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—4882no—
729C4—2444no—
730C4—2444no—
731C2—2448no—
732C2C4×#1451974511yescharacteristic
733C2C4×#1451975111yescharacteristic
734C2#2144852611yescharacteristic
735C2#2144881612yes—
736C2#2144883712yes—
737C2#2144915411yescharacteristic
738C2#2144917511yescharacteristic
739C2#2144978612yes—
740C2#2144988512yes—
741C2#2145072411yescharacteristic
742C2#2145138511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C4×C4⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenterC2×C4×C4⋊C4D61
hypocenterC61#14176
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#16839653C2semidirect
4. C2×#16839633C2semidirect
5. #21444083C2semidirect
6. #21444072C2semidirect
8. #21444057C2semidirect
9. #21444046C2semidirect
10. #21444040C2semidirect
11. C2×C4×C4⋊C4×C61C2semidirect
23. #16839679C4semidirect
75. C2×#11758198C2×C4semidirect
76. C2×#11758198C2×C4semidirect
84. #14519684C2×C4semidirect
96. C2×C4⋊C4×C61C2×C4semidirect
97. C2×C4⋊C4×C61D4semidirect
285. C2×C4×C61C4×D4semidirect
364. C2×C4×C4⋊C4D61semidirect
412. C61#14176semidirect
446. C2×C4⋊C4C4×D61semidirect
447. C2×C4⋊C4D244semidirect
680. C2×C4C4×D244semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D2442
C2×#168396792
C2×#168396532
C2×#168396332
#214440832
#214440722
#214440592
#214440572
#214440462
#214440402
C2×C4×C4⋊C4×C612
#1417661