Finite Group Databasebeta

← #29709155

Subgroups — #29709155

Order 15616.

1092 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758199C211yesmaximal, characteristic, complemented
2C4×#14519773C211yesmaximal, characteristic, complemented
3#21448284C211yesmaximal, characteristic, complemented
4#21447293C211yesmaximal, characteristic, complemented
5#21447225C211yesmaximal, characteristic, complemented
6#21447203C211yesmaximal, characteristic, complemented
7#21447202C211yesmaximal, characteristic, complemented
8#21447128C211yesmaximal, characteristic, complemented
9#21447127C211yesmaximal, characteristic, complemented
10#21447052C211yesmaximal, characteristic, complemented
11#21446888C211yesmaximal, characteristic
12C4×#14519706C211yesmaximal, characteristic, complemented
13C4×#14519699C211yesmaximal, characteristic, complemented
14C4×#14519698C211yesmaximal, characteristic, complemented
15C2×C4×D8×C61C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C2×#14519773C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×C4×C22⋊D61—21no—
20C2×C4×C22⋊D61—21no—
21C2×#14519736—21no—
22C4×#11758199—24no—
23C2×#14519710C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27C2×#14519699C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×C4×#92418C2211yescharacteristic
33#16839665C2211yescharacteristic
34#16839665C2211yescharacteristic
35#16839665C2211yescharacteristic
36#16839663C2211yescharacteristic
37#16839662—21no—
38#16839662—21no—
39#16839661C2211yescharacteristic
40#16839661C2211yescharacteristic
41#16839655—21no—
42#16839655—21no—
43#16839631C2211yescharacteristic
44C4×C4⋊Dic61C2211yescharacteristic
45C4×C22⋊Dic61—21no—
46C42×Dic61C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53C22×D8×C61C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C4×D8×C61—24no—
57C2×#107×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×C4×C8×C61C2211yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C22×C22⋊D61—21no—
64C22×C4×D61—21no—
65C2×#11758199—22no—
66C2×#11758199—22no—
67C2×#11758199—22no—
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70#14519773—22no—
71#14519773—22no—
72C4×D244—22no—
73C4×D244—22no—
74C4×C22⋊D61—44no—
75C4×C22⋊D61—44no—
76#14519736—44no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×C4×Dic61—21no—
94C2×C4×Dic61D411yescharacteristic
95C2×C4×Dic61D411yescharacteristic
96C2×C4×Dic61D411yescharacteristic
97C2×C4×Dic61D411yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99C2×C4×Dic61C2311yescharacteristic
100#14519710—22no—
101#14519706—22no—
102#14519706—22no—
103#14519699—22no—
104#14519699—22no—
105#14519698—22no—
106#14519698—22no—
107#14519698—22no—
108#14519697—22no—
109C4×#92418—22no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113C22×D4×C61C2311yescharacteristic
114C22×D4×C61C2311yescharacteristic
115C23×C4×C61—21no—
116C23×C4×C61—21no—
117C2×D8×C61—22no—
118C2×D8×C61—22no—
119C2×D8×C61—22no—
120C22×C8×C61C2311yescharacteristic
121C22×C8×C61C2311yescharacteristic
122C4×D4×C61—22no—
123C4×D4×C61—22no—
124C4×D4×C61—22no—
125C4×D4×C61D414yescomplemented
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C42×C61C2311yescharacteristic
131#107×C61—22no—
132#102×C61—22no—
133#102×C61—22no—
134C4×C8×C61—22no—
135C24×C61—21no—
136C24×C61—21no—
137C23×D61—21no—
138C2×D4×C61—21no—
139C2×D4×C61—21no—
140C2×D4×C61—21no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61C2×D412yes—
149C2×D4×C61#4112yes—
150C22×C4×C61—21no—
151C22×C4×C61—24no—
152C22×C4×C61—21no—
153C22×C4×C61—42no—
154C22×C4×C61—42no—
155C22×C4×C61—42no—
156C22×C4×C61—42no—
157C22×C4×C61—42no—
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2411yescharacteristic
161C2×C22⋊D61—24no—
162C2×C22⋊D61—24no—
163C2×C22⋊D61—42no—
164C2×C22⋊D61—42no—
165C2×C22⋊D61—42no—
166C2×C22⋊D61—42no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61C2×D411yescharacteristic
171C22×Dic61C2×D411yescharacteristic
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244#4112yes—
180C2×C4×D61—42no—
181C2×C4×D61—42no—
182C2×C4×D61—42no—
183D8×C61—28no—
184C2×C8×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61#4112yes—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61C2×D412yes—
194C22⋊C4×C61—24no—
195C22⋊C4×C61—42no—
196C42×C61C2×D412yes—
197C42×C61#4112yes—
198C22⋊Dic61—42no—
199C22⋊Dic61—42no—
200C22⋊Dic61—42no—
201C22⋊Dic61—42no—
202C22⋊Dic61—42no—
203C22⋊Dic61—42no—
204#11758199—28no—
205#11758198—42no—
206#11758198—42no—
207#11758198—42no—
208C4⋊Dic61—21no—
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61—21no—
213C4⋊Dic61—21no—
214C4⋊Dic61—42no—
215C4⋊Dic61—42no—
216#11758196—42no—
217#11758196—42no—
218C4×Dic61—22no—
219C4×Dic61—21no—
220C4×Dic61—21no—
221C4×Dic61—21no—
222C4×Dic61—21no—
223C4×Dic61—22no—
224C4×Dic61—41no—
225C4×Dic61—42no—
226C4×Dic61D814yescomplemented
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418#4112yes—
233C23×C61—22no—
234C23×C61—22no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61C22×D411yescharacteristic
248C22×D61—22no—
249C22×D61—41no—
250C22×D61—41no—
251C22×D61—41no—
252C22×D61—41no—
253C22×D61—41no—
254C22×D61—41no—
255D4×C61—22no—
256D4×C61—22no—
257D4×C61—22no—
258D4×C61—22no—
259D4×C61—41no—
260D4×C61—41no—
261D4×C61—41no—
262D4×C61—41no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—22no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—48no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—84no—
273C2×C4×C61#12112yes—
274C2×C4×C61#12112yes—
275C2×C4×C61C2×D812yes—
276C2×C4×C61AGL(1,ℤ/8)12yes—
277C2×C4×C61C22×D411yescharacteristic
278C2×C4×C61C2×#4111yescharacteristic
279C2×C4×C61C2×#4111yescharacteristic
280C2×C4×C61C2×#4111yescharacteristic
281C2×C4×C61C2×#4111yescharacteristic
282C2×C4×C61C2×#4111yescharacteristic
283C22⋊D61—48no—
284C22⋊D61—48no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61C2×D812yes—
304C2×Dic61C2×D812yes—
305C2×Dic61#13512yes—
306D244—22no—
307D244—22no—
308D244—41no—
309D244—41no—
310C4×D61—84no—
311C8×C61—22no—
312C8×C61—41no—
313#92418—22no—
314#92418—41no—
315#23676—611nomaximal, Sylow
316C22×C61—42no—
317C22×C61—42no—
318C22×C61—42no—
319C22×C61—42no—
320C22×C61—42no—
321C22×C61—42no—
322C22×C61—81no—
323C22×C61—81no—
324C22×C61—81no—
325C22×C61—81no—
326C22×C61—81no—
327C22×C61—81no—
328C22×C61—81no—
329C22×C61—81no—
330C22×C61C2×#12111yescharacteristic
331C22×C61#52511yescharacteristic
332C22×C61#53211yescharacteristic
333C22×C61C22×D811yescharacteristic
334C22×C61C2×#13511yescharacteristic
335C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
336C22×C61#57511yescharacteristic
337C2×D61—42no—
338C2×D61—42no—
339C2×D61—42no—
340C2×D61—81no—
341C2×D61—81no—
342C2×D61—81no—
343C2×D61—81no—
344C4×C61—22no—
345C4×C61—42no—
346C4×C61—81no—
347C4×C61#45914yes—
348C4×C61#52511yescharacteristic
349C4×C61#52511yescharacteristic
350C4×C61#52911yescharacteristic
351C4×C61#52911yescharacteristic
352Dic61—22no—
353Dic61—22no—
354Dic61—22no—
355Dic61—41no—
356Dic61—81no—
357Dic61—81no—
358Dic61—81no—
359C2×C4×D8—611no—
360C2×C4×D8D6111yescharacteristic, complemented
361C4×#127—611no—
362#2293—611no—
363#2083—611no—
364#2071—611no—
365#2067—611no—
366#2067—611no—
367#2054—611no—
368#2054—611no—
369#2041—611no—
370#2011—611no—
371C4×C4⋊C8—611no—
372C4×#102—611no—
373C4×#102—611no—
374C2×C61—82no—
375C2×C61—82no—
376C2×C61#239211yescharacteristic
377C2×C61C2×#45911yescharacteristic
378C2×C61#303511yescharacteristic
379C2×C61#310011yescharacteristic
380C2×C61#310511yescharacteristic
381C2×C61#316911yescharacteristic
382C2×C61#317111yescharacteristic
383D61—82no—
384C22×D8—611no—
385C22×D8C2×D6111yescharacteristic
386C2×#127—611no—
387C2×C4×D4—611no—
388C2×C4×D4—1221no—
389C2×C4×D4—1221no—
390C2×C4×D4C2×D6111yescharacteristic
391C2×C4×D4C2×D6111yescharacteristic
392C2×#117—1221no—
393C4×D8—24no—
394C4×D8—1224no—
395C2×#107—611no—
396C2×#107C2×D6111yescharacteristic
397C2×C4⋊C8—611no—
398C2×C4⋊C8—611no—
399C2×#102—611no—
400C2×#102—611no—
401C2×#102—611no—
402C2×#102—611no—
403C2×#102—611no—
404C2×#102—611no—
405C2×#102C2×D6111yescharacteristic
406C2×#102C2×D6111yescharacteristic
407C2×C4×C8—611no—
408C2×C4×C8C2×D6111yescharacteristic
409#390—611no—
410#390—611no—
411#390—611no—
412#390—611no—
413#390—1221no—
414#390—1221no—
415#389—611no—
416#389—611no—
417#388—1221no—
418#388—1221no—
419#384—611no—
420C4×C4⋊C4—611no—
421C4×C22⋊C4—1221no—
422C43—611no—
423#340—611no—
424#340—611no—
425#340—611no—
426#340—611no—
427#336—611no—
428#336—611no—
429C61#2367611yescharacteristic, complemented, Sylow
430C22×D4—611no—
431C22×D4—1221no—
432C22×D4—1221no—
433C22×D4C22×D6111yescharacteristic
434C22×D4C22×D6111yescharacteristic
435C23×C4—21no—
436C23×C4—21no—
437C23×C4—1221no—
438C2×D8—22no—
439C2×D8—22no—
440C2×D8—22no—
441C2×D8—1222no—
442C2×D8—1222no—
443C2×D8—1222no—
444C22×C8—611no—
445C22×C8—611no—
446C22×C8C22×D6111yescharacteristic
447C22×C8C22×D6111yescharacteristic
448#127—1222no—
449#127—1222no—
450C4×D4—22no—
451C4×D4—22no—
452C4×D4—22no—
453C4×D4—1222no—
454C4×D4—1222no—
455C4×D4—2444no—
456C4×D4—2444no—
457C4×D4C22⋊D6114yescomplemented
458#117—2444no—
459C2×C4⋊C4—611no—
460C2×C4⋊C4—611no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4—1221no—
463C2×C4⋊C4—1221no—
464C2×C4⋊C4—1221no—
465C2×C4⋊C4—1221no—
466C2×C4⋊C4C22×D6111yescharacteristic
467C2×C4⋊C4C22×D6111yescharacteristic
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—1221no—
471C2×C22⋊C4—1221no—
472C2×C22⋊C4—1221no—
473C2×C22⋊C4—1221no—
474C2×C22⋊C4—1221no—
475C2×C22⋊C4—1221no—
476C2×C22⋊C4—1221no—
477C2×C22⋊C4—1221no—
478C2×C22⋊C4—1221no—
479C2×C42—611no—
480C2×C42—611no—
481C2×C42—611no—
482C2×C42—611no—
483C2×C42—611no—
484C2×C42—611no—
485C2×C42—1221no—
486C2×C42C22×D6111yescharacteristic
487#107—22no—
488#107—1222no—
489C4⋊C8—1222no—
490C4⋊C8—1222no—
491#102—22no—
492#102—22no—
493#102—1222no—
494#102—1222no—
495#102—1222no—
496#102—1222no—
497#102—1222no—
498#102—1222no—
499C4×C8—22no—
500C4×C8—1222no—
501#95—1221no—
502#95—1221no—
503#95—1221no—
504C24—21no—
505C24—21no—
506C24—1221no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—612no—
518C2×D4—1224no—
519C2×D4—1224no—
520C2×D4—1221no—
521C2×D4—1221no—
522C2×D4—1221no—
523C2×D4—1221no—
524C2×D4—1221no—
525C2×D4—2442no—
526C2×D4—2442no—
527C2×D4—2442no—
528C2×D4—2442no—
529C2×D4#1175822212yes—
530C2×D4C2×C22⋊D6112yes—
531C22×C4—21no—
532C22×C4—24no—
533C22×C4—21no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—611no—
540C22×C4—611no—
541C22×C4—611no—
542C22×C4—611no—
543C22×C4—1221no—
544C22×C4—1221no—
545C22×C4—1221no—
546C22×C4—2442no—
547C22×C4—2442no—
548C22×C4—2442no—
549C22×C4D4×D6111yescharacteristic
550C22×C4D4×D6111yescharacteristic
551C22×C4C23×D6111yescharacteristic
552D8—28no—
553D8—1228no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—612no—
560C2×C8—1221no—
561C2×C8—1221no—
562C2×C8—1221no—
563C2×C8—1221no—
564C2×C8—1221no—
565C2×C8#1175822212yes—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—1221no—
570C4⋊C4—1221no—
571C4⋊C4—1221no—
572C4⋊C4—1221no—
573C4⋊C4—1221no—
574C4⋊C4—1221no—
575C4⋊C4—2442no—
576C4⋊C4—2442no—
577C4⋊C4—2442no—
578C4⋊C4—2442no—
579C4⋊C4C2×C22⋊D6112yes—
580C22⋊C4—24no—
581C22⋊C4—42no—
582C22⋊C4—2442no—
583C22⋊C4—2442no—
584C22⋊C4—2442no—
585C22⋊C4—2442no—
586C22⋊C4—2442no—
587C22⋊C4—2442no—
588C22⋊C4—2442no—
589C22⋊C4—2442no—
590C22⋊C4—2442no—
591C42—614no—
592C42—1222no—
593C42—1221no—
594C42—1221no—
595C42—1221no—
596C42—1221no—
597C42—1222no—
598C42—2441no—
599C42—2442no—
600C42#1175822412yes—
601C42C2×C22⋊D6112yes—
602C23—22no—
603C23—22no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—1222no—
617C23—2441no—
618C23—2441no—
619C23—2441no—
620C23—2441no—
621C23—2441no—
622C23—2441no—
623C23C2×D4×D6111yescharacteristic
624D4—22no—
625D4—22no—
626D4—22no—
627D4—22no—
628D4—41no—
629D4—41no—
630D4—41no—
631D4—41no—
632D4—1222no—
633D4—1222no—
634D4—2448no—
635D4—2448no—
636D4—2441no—
637D4—2441no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—22no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—48no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—84no—
648C2×C4—612no—
649C2×C4—612no—
650C2×C4—612no—
651C2×C4—1221no—
652C2×C4—1221no—
653C2×C4—1221no—
654C2×C4—1221no—
655C2×C4—1221no—
656C2×C4—1221no—
657C2×C4—1221no—
658C2×C4—1221no—
659C2×C4—1221no—
660C2×C4—4884no—
661C2×C4—2441no—
662C2×C4—2441no—
663C2×C4—2441no—
664C2×C4—2441no—
665C2×C4—2441no—
666C2×C4—2441no—
667C2×C4—2441no—
668C2×C4—2441no—
669C2×C4—2441no—
670C2×C4#1451974912yes—
671C2×C4#1451974912yes—
672C2×C4D8×D6112yes—
673C2×C4#1451980112yes—
674C2×C4C22×C22⋊D6111yescharacteristic
675C2×C4#41×D6111yescharacteristic
676C2×C4#41×D6111yescharacteristic
677C2×C4C2×#1175822411yescharacteristic
678C2×C4C2×#1175822211yescharacteristic
679C2×C4C2×#1175822211yescharacteristic
680C8—22no—
681C8—41no—
682C8—1222no—
683C8—2441no—
684C22—42no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—42no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22—4881no—
699C22—4881no—
700C22—4881no—
701C22—4881no—
702C22—2442no—
703C22—2442no—
704C22—2442no—
705C22C2×#1451974911yescharacteristic
706C22#1684027111yescharacteristic
707C22#1684030911yescharacteristic
708C22C2×D8×D6111yescharacteristic
709C22#135×D6111yescharacteristic
710C22C2×#1451980111yescharacteristic
711C22#1684055911yescharacteristic
712C4—22no—
713C4—42no—
714C4—81no—
715C4—1222no—
716C4—1222no—
717C4—1222no—
718C4—4881no—
719C4—4881no—
720C4—4881no—
721C4—2441no—
722C4#1683995514yes—
723C4#1684026911yescharacteristic
724C4#1684027311yescharacteristic
725C4#1684029211yescharacteristic
726C4#1684029411yescharacteristic
727C2—82no—
728C2—82no—
729C2—4882no—
730C2#2144906111yescharacteristic
731C2C2×#1683995511yescharacteristic
732C2#2145527011yescharacteristic
733C2#2145581711yescharacteristic
734C2#2145586411yescharacteristic
735C2#2145639511yescharacteristic
736C2#2145641211yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C4×D8×C61C2
socleC23×C61C22×D4
prime radical#21446888C2
hypercenterC2×C4×D8D61
hypocenterC61#23676
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×C4×#11758199C2semidirect
2. C4×#14519773C2semidirect
3. #21448284C2semidirect
4. #21447293C2semidirect
5. #21447225C2semidirect
6. #21447203C2semidirect
7. #21447202C2semidirect
8. #21447128C2semidirect
9. #21447127C2semidirect
10. #21447052C2semidirect
12. C4×#14519706C2semidirect
13. C4×#14519699C2semidirect
14. C4×#14519698C2semidirect
15. C2×C4×D8×C61C2semidirect
125. C4×D4×C61D4semidirect
226. C4×Dic61D8semidirect
360. C2×C4×D8D61semidirect
429. C61#23676semidirect
457. C4×D4C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117581992
C4×#145197732
#214482842
#214472932
#214472252
#214472032
#214472022
#214471282
#214471272
#214470522
#214468882
C4×#145197062
C4×#145196992
C4×#145196982
C2×C4×D8×C612
#2367661