Finite Group Databasebeta

← #35422739

Subgroups — #35422739

Order 21248.

1086 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127813C211yesmaximal, characteristic
2C2×D8×Dic83C211yesmaximal, characteristic
3#24910373C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic83C211yesmaximal, characteristic, complemented
5#24908207C211yesmaximal, characteristic, complemented
6#24908192C211yesmaximal, characteristic, complemented
7#24907726C211yesmaximal, characteristic, complemented
8#24907726C211yesmaximal, characteristic, complemented
9#24907712C211yesmaximal, characteristic, complemented
10#24907712C211yesmaximal, characteristic, complemented
11#24907631C211yesmaximal, characteristic, complemented
12#24907473C211yesmaximal, characteristic, complemented
13#24907463C211yesmaximal, characteristic, complemented
14#24907335C211yesmaximal, characteristic, complemented
15C2×#442×C83C211yesmaximal, characteristic
16C2×D4×Dic83C2211yescharacteristic
17C2×D4×Dic83C2211yescharacteristic
18C2×D4×Dic83C2211yescharacteristic
19C2×D4×Dic83C2211yescharacteristic
20C22×C4⋊Dic83—21no—
21#19127813—24no—
22D8×Dic83—24no—
23C2×#14581726C2211yescharacteristic
24C2×#14581726C2211yescharacteristic
25C2×#14581724C2211yescharacteristic
26C2×#14581724C2211yescharacteristic
27C2×C4⋊(C83⋊C8)C2211yescharacteristic
28C2×#14581713C2211yescharacteristic
29C2×#14581713C2211yescharacteristic
30C2×#14581713C2211yescharacteristic
31C2×#14581713C2211yescharacteristic
32C2×#14581702C2211yescharacteristic
33C2×C8×Dic83C2211yescharacteristic
34#19127600C2211yescharacteristic
35#19127600C2211yescharacteristic
36#19127600C2211yescharacteristic
37#19127600C2211yescharacteristic
38#19127576—21no—
39#19127576—21no—
40#19127576—21no—
41#19127576—21no—
42#19127571C2211yescharacteristic
43#19127567C2211yescharacteristic
44#19127561—21no—
45#19127561—21no—
46C4×C4⋊Dic83C2211yescharacteristic
47C2×C83⋊#95—21no—
48#19127463C2211yescharacteristic
49#19127463C2211yescharacteristic
50#19127463C2211yescharacteristic
51#19127463C2211yescharacteristic
52#19127455C2211yescharacteristic
53#19127455C2211yescharacteristic
54C22×D8×C83C2211yescharacteristic
55C2×C4×D4×C83C2211yescharacteristic
56C2×C4×D4×C83C2211yescharacteristic
57#442×C83C418yescomplemented
58C2×#106×C83C2211yescharacteristic
59C2×#102×C83C2211yescharacteristic
60C2×#102×C83C2211yescharacteristic
61C2×#97×C83C2211yescharacteristic
62C23×Dic83—21no—
63C23×Dic83—21no—
64C23×Dic83—21no—
65C23×Dic83—21no—
66C22×C83⋊C8C2311yescharacteristic
67C22×C83⋊C8C2311yescharacteristic
68D4×Dic83—22no—
69D4×Dic83—22no—
70D4×Dic83—22no—
71D4×Dic83—22no—
72D4×Dic83—41no—
73D4×Dic83—41no—
74D4×Dic83—41no—
75D4×Dic83—41no—
76C2×C4⋊Dic83—21no—
77C2×C4⋊Dic83—21no—
78C2×C4⋊Dic83—21no—
79C2×C4⋊Dic83—21no—
80C2×C4⋊Dic83—21no—
81C2×C4⋊Dic83—21no—
82C2×C4⋊Dic83—44no—
83C2×C4⋊Dic83D411yescharacteristic
84C2×C4⋊Dic83D411yescharacteristic
85C2×C4⋊Dic83C2311yescharacteristic
86C2×C4⋊Dic83C2311yescharacteristic
87C2×C4⋊Dic83C2311yescharacteristic
88C2×C4⋊Dic83C2311yescharacteristic
89C2×C22⋊Dic83—21no—
90C2×C22⋊Dic83—21no—
91C2×C22⋊Dic83—21no—
92C2×C22⋊Dic83—21no—
93C2×C4×Dic83C2311yescharacteristic
94C2×C4×Dic83C2311yescharacteristic
95#14581726—22no—
96#14581726—41no—
97#14581724—22no—
98#14581724—41no—
99C4⋊(C83⋊C8)—22no—
100#14581713—22no—
101#14581713—22no—
102#14581713—22no—
103#14581713—22no—
104#14581702—22no—
105C8×Dic83—22no—
106C83⋊#95—21no—
107C83⋊#95—21no—
108C83⋊#95—21no—
109C83⋊#95—21no—
110C83⋊#95—21no—
111C83⋊#95—21no—
112C83⋊#95D411yescharacteristic
113C83⋊#95D411yescharacteristic
114C22×D4×C83C2311yescharacteristic
115C22×D4×C83C2311yescharacteristic
116C23×C4×C83—21no—
117C23×C4×C83—21no—
118C2×D8×C83C2×C414yes—
119C2×D8×C83D414yes—
120C2×D8×C83Q814yes—
121C22×C8×C83C2311yescharacteristic
122C22×C8×C83C2311yescharacteristic
123C4×D4×C83—22no—
124C4×D4×C83—22no—
125C4×D4×C83C2×C414yescomplemented
126C4×D4×C83C2×C414yescomplemented
127C2×C4⋊C4×C83C2311yescharacteristic
128C2×C4⋊C4×C83C2311yescharacteristic
129C2×C22⋊C4×C83—21no—
130C2×C22⋊C4×C83—21no—
131C2×C42×C83C2311yescharacteristic
132#106×C83C2×C414yescomplemented
133#102×C83C2×C414yescomplemented
134#102×C83C2×C414yescomplemented
135#97×C83C2×C414yescomplemented
136C22×Dic83—21no—
137C22×Dic83—21no—
138C22×Dic83—21no—
139C22×Dic83—21no—
140C22×Dic83—42no—
141C22×Dic83—42no—
142C22×Dic83—42no—
143C22×Dic83—42no—
144C22×Dic83—42no—
145C22×Dic83—42no—
146C22×Dic83—42no—
147C22×Dic83—42no—
148C22×Dic83—81no—
149C22×Dic83—81no—
150C22×Dic83—81no—
151C22×Dic83—81no—
152C22×Dic83C2×D411yescharacteristic
153C22×Dic83C2×D411yescharacteristic
154C22×Dic83C2×D411yescharacteristic
155C22×Dic83C2×D411yescharacteristic
156C2×C83⋊C8—21no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8—21no—
160C2×C83⋊C8—21no—
161C2×C83⋊C8—21no—
162C4⋊Dic83—22no—
163C4⋊Dic83—21no—
164C4⋊Dic83—21no—
165C4⋊Dic83—21no—
166C4⋊Dic83—21no—
167C4⋊Dic83—21no—
168C4⋊Dic83—21no—
169C4⋊Dic83—21no—
170C4⋊Dic83—21no—
171C4⋊Dic83—41no—
172C4⋊Dic83—42no—
173C4⋊Dic83—42no—
174C4⋊Dic83—42no—
175C4⋊Dic83—81no—
176C4⋊Dic83—81no—
177C4⋊Dic83—81no—
178C22⋊Dic83—42no—
179C22⋊Dic83—42no—
180C22⋊Dic83—42no—
181C22⋊Dic83—42no—
182C4×Dic83—21no—
183C4×Dic83—21no—
184C4×Dic83—21no—
185C4×Dic83—21no—
186C24×C83—21no—
187C24×C83—21no—
188C2×D4×C83—21no—
189C2×D4×C83—21no—
190C2×D4×C83—21no—
191C2×D4×C83—21no—
192C2×D4×C83—21no—
193C2×D4×C83—21no—
194C2×D4×C83C22×C412yes—
195C2×D4×C83C22×C412yes—
196C2×D4×C83C2×D412yes—
197C2×D4×C83C2×D412yes—
198C2×D4×C83C2×Q812yes—
199C2×D4×C83C2×Q812yes—
200C22×C4×C83—21no—
201C22×C4×C83—21no—
202C22×C4×C83—24no—
203C22×C4×C83—24no—
204C22×C4×C83—42no—
205C22×C4×C83—42no—
206C22×C4×C83—81no—
207C22×C4×C83—81no—
208C22×C4×C83C2×D411yescharacteristic
209C22×C4×C83C2×D411yescharacteristic
210C22×C4×C83C2411yescharacteristic
211D8×C83C4⋊C4116yescomplemented
212C2×C8×C83—21no—
213C2×C8×C83—21no—
214C2×C8×C83C22×C412yes—
215C2×C8×C83C22×C412yes—
216C2×C8×C83C2×D412yes—
217C2×C8×C83C2×Q812yes—
218C4⋊C4×C83—21no—
219C4⋊C4×C83—21no—
220C4⋊C4×C83C22×C412yes—
221C4⋊C4×C83C22×C412yes—
222C22⋊C4×C83—24no—
223C22⋊C4×C83—24no—
224C42×C83C22×C412yes—
225C42×C83#4112yes—
226C23×C83—22no—
227C23×C83—22no—
228C23×C83—22no—
229C23×C83—22no—
230C23×C83—22no—
231C23×C83—22no—
232C23×C83—41no—
233C23×C83—41no—
234C23×C83—41no—
235C23×C83—41no—
236C23×C83—41no—
237C23×C83—41no—
238C23×C83—41no—
239C23×C83—41no—
240C23×C83C22×D411yescharacteristic
241D4×C83—22no—
242D4×C83—22no—
243D4×C83—22no—
244D4×C83—22no—
245D4×C83—22no—
246D4×C83—22no—
247D4×C83C2×C4⋊C414yes—
248D4×C83C2×C4⋊C414yescomplemented
249C2×C4×C83—21no—
250C2×C4×C83—21no—
251C2×C4×C83—21no—
252C2×C4×C83—21no—
253C2×C4×C83—22no—
254C2×C4×C83—22no—
255C2×C4×C83—48no—
256C2×C4×C83—41no—
257C2×C4×C83—41no—
258C2×C4×C83—41no—
259C2×C4×C83—41no—
260C2×C4×C83—84no—
261C2×C4×C83C4×D412yes—
262C2×C4×C83C4×D412yes—
263C2×C4×C83C23×C411yescharacteristic
264C2×C4×C83C22×D411yescharacteristic
265C2×C4×C83C22×Q811yescharacteristic
266C2×C4×C83C2×#4111yescharacteristic
267C2×C4×C83H(5,𝔽2)11yescharacteristic
268C2×C4×C832−1+411yescharacteristic
269C2×Dic83—21no—
270C2×Dic83—21no—
271C2×Dic83—21no—
272C2×Dic83—21no—
273C2×Dic83—21no—
274C2×Dic83—21no—
275C2×Dic83—21no—
276C2×Dic83—21no—
277C2×Dic83—21no—
278C2×Dic83—21no—
279C2×Dic83—21no—
280C2×Dic83—41no—
281C2×Dic83—41no—
282C2×Dic83—41no—
283C2×Dic83—41no—
284C2×Dic83—41no—
285C2×Dic83—41no—
286C2×Dic83—41no—
287C2×Dic83—41no—
288C2×Dic83—41no—
289C2×Dic83—41no—
290C2×Dic83—41no—
291C2×Dic83—41no—
292C2×Dic83—84no—
293C2×Dic83—84no—
294C2×Dic83—84no—
295C2×Dic83—84no—
296C2×Dic83AGL(1,ℤ/8)12yes—
297C8×C83—22no—
298C8×C83C2×C4⋊C414yescomplemented
299C83⋊C8—41no—
300C83⋊C8—41no—
301C22×C83—24no—
302C22×C83—24no—
303C22×C83—42no—
304C22×C83—42no—
305C22×C83—42no—
306C22×C83—42no—
307C22×C83—42no—
308C22×C83—42no—
309C22×C83—42no—
310C22×C83—42no—
311C22×C83—42no—
312C22×C83—42no—
313C22×C83—42no—
314C22×C83—42no—
315C22×C83C2×C4×D411yescharacteristic
316C22×C83D4211yescharacteristic
317C22×C83D4×Q811yescharacteristic
318C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
319C22×C83#57511yescharacteristic
320C22×C83#57611yescharacteristic
321C22×C83#57711yescharacteristic
322C4×C83—22no—
323C4×C83—22no—
324C4×C83—42no—
325C4×C83—42no—
326C4×C83C22×C4⋊C411yescharacteristic
327C4×C83#52011yescharacteristic
328C4×C83#54711yescharacteristic
329C4×C83#55411yescharacteristic
330Dic83—22no—
331Dic83—41no—
332Dic83—41no—
333Dic83—41no—
334Dic83—81no—
335Dic83—81no—
336Dic83—81no—
337Dic83—81no—
338#22676—831nomaximal, Sylow
339C2×C83—44no—
340C2×C83—44no—
341C2×C83D4×C4⋊C411yescharacteristic
342C2×C83C4×AGL(1,ℤ/8)11yescharacteristic
343C2×C83#294611yescharacteristic
344C2×C83#326411yescharacteristic
345C2×C83#326711yescharacteristic
346C2×C83#338411yescharacteristic
347C2×C83#338911yescharacteristic
348C2×#442—831no—
349C2×#442D8311yescharacteristic
350C2×C4×D8—831no—
351#2349—831no—
352D4×C4⋊C4—831no—
353#1944—831no—
354#1941—831no—
355#1864—831no—
356#1864—831no—
357#1862—831no—
358#1862—831no—
359#1847—831no—
360#1804—831no—
361#1802—831no—
362#1771—831no—
363C83#2267611yescharacteristic, complemented, Sylow
364C22×D8C2×D8311yescharacteristic
365C2×C4×D4—831no—
366C2×C4×D4—831no—
367C2×C4×D4—831no—
368C2×C4×D4—831no—
369C2×C4×D4C2×D8311yescharacteristic
370C2×C4×D4C2×D8311yescharacteristic
371C22×C4⋊C4—1661no—
372#442—1664no—
373#442Dic8318yescomplemented
374C4×D8—1664no—
375C2×#107—831no—
376C2×#107—831no—
377C2×#106—831no—
378C2×#106—831no—
379C2×#106C2×D8311yescharacteristic
380C2×C4⋊C8—831no—
381C2×#102—831no—
382C2×#102—831no—
383C2×#102—831no—
384C2×#102—831no—
385C2×#102C2×D8311yescharacteristic
386C2×#102C2×D8311yescharacteristic
387C2×#97—831no—
388C2×#97C2×D8311yescharacteristic
389C2×C4×C8—831no—
390#389—831no—
391#389—831no—
392#389—831no—
393#389—831no—
394#385—1661no—
395#385—1661no—
396#385—1661no—
397#385—1661no—
398#384—831no—
399#382—831no—
400#380—1661no—
401#380—1661no—
402C4×C4⋊C4—831no—
403C2×#95—1661no—
404#340—831no—
405#340—831no—
406#340—831no—
407#340—831no—
408#336—831no—
409#336—831no—
410C22×D4C22×D8311yescharacteristic
411C22×D4C22×D8311yescharacteristic
412C23×C4—21no—
413C23×C4—21no—
414C23×C4—1661no—
415C23×C4—1661no—
416C23×C4—1661no—
417C23×C4—1661no—
418C2×D8Dic16614yes—
419C2×D8D33214yes—
420C2×D8C2×Dic8314yes—
421C22×C8—831no—
422C22×C8—831no—
423C22×C8C22×D8311yescharacteristic
424C22×C8C22×D8311yescharacteristic
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—3321no—
428C4×D4—3321no—
429C4×D4—3321no—
430C4×D4—3321no—
431C4×D4—1662no—
432C4×D4—1662no—
433C4×D4—1662no—
434C4×D4—1662no—
435C4×D4C2×Dic8314yescomplemented
436C4×D4C2×Dic8314yescomplemented
437C2×C4⋊C4—3324no—
438C2×C4⋊C4—831no—
439C2×C4⋊C4—831no—
440C2×C4⋊C4—831no—
441C2×C4⋊C4—831no—
442C2×C4⋊C4—831no—
443C2×C4⋊C4—831no—
444C2×C4⋊C4—1661no—
445C2×C4⋊C4—1661no—
446C2×C4⋊C4—1661no—
447C2×C4⋊C4—1661no—
448C2×C4⋊C4—1661no—
449C2×C4⋊C4—1661no—
450C2×C4⋊C4C22×D8311yescharacteristic
451C2×C4⋊C4C22×D8311yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—1661no—
455C2×C22⋊C4—1661no—
456C2×C22⋊C4—1661no—
457C2×C22⋊C4—1661no—
458C2×C42—831no—
459C2×C42—831no—
460C2×C42C22×D8311yescharacteristic
461#107—3321no—
462#107—1662no—
463#106—3321no—
464#106—1662no—
465#106C2×Dic8314yescomplemented
466C4⋊C8—1662no—
467#102—1662no—
468#102—1662no—
469#102—1662no—
470#102—1662no—
471#102C2×Dic8314yescomplemented
472#102C2×Dic8314yescomplemented
473#97—1662no—
474#97C2×Dic8314yescomplemented
475C4×C8—1662no—
476#95—831no—
477#95—831no—
478#95—1661no—
479#95—1661no—
480#95—1661no—
481#95—1661no—
482#95—1661no—
483#95—1661no—
484C24—21no—
485C24—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4C22×Dic8312yes—
493C2×D4C22×Dic8312yes—
494C2×D4C2×D33212yes—
495C2×D4C2×D33212yes—
496C2×D4C2×Dic16612yes—
497C2×D4C2×Dic16612yes—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—81no—
505C22×C4—81no—
506C22×C4—3322no—
507C22×C4—3322no—
508C22×C4—3322no—
509C22×C4—3322no—
510C22×C4—3322no—
511C22×C4—3322no—
512C22×C4—3322no—
513C22×C4—3322no—
514C22×C4—831no—
515C22×C4—831no—
516C22×C4—831no—
517C22×C4—831no—
518C22×C4—6641no—
519C22×C4—6641no—
520C22×C4—6641no—
521C22×C4—6641no—
522C22×C4—1661no—
523C22×C4—1661no—
524C22×C4—1661no—
525C22×C4—1661no—
526C22×C4D4×D8311yescharacteristic
527C22×C4D4×D8311yescharacteristic
528C22×C4C23×D8311yescharacteristic
529D8C4⋊Dic83116yescomplemented
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—1661no—
533C2×C8—1661no—
534C2×C8—1661no—
535C2×C8—1661no—
536C2×C8—1661no—
537C2×C8—1661no—
538C2×C8C22×Dic8312yes—
539C2×C8C22×Dic8312yes—
540C2×C8C2×D33212yes—
541C2×C8C2×Dic16612yes—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—3322no—
545C4⋊C4—3321no—
546C4⋊C4—3322no—
547C4⋊C4—3322no—
548C4⋊C4—6641no—
549C4⋊C4—6641no—
550C4⋊C4—6641no—
551C4⋊C4—1662no—
552C4⋊C4—1661no—
553C4⋊C4—1661no—
554C4⋊C4—1661no—
555C4⋊C4—1661no—
556C4⋊C4—1661no—
557C4⋊C4—1661no—
558C4⋊C4—1661no—
559C4⋊C4—1661no—
560C4⋊C4C22×Dic8312yes—
561C4⋊C4C22×Dic8312yes—
562C22⋊C4—24no—
563C22⋊C4—24no—
564C22⋊C4—3322no—
565C22⋊C4—3322no—
566C22⋊C4—3322no—
567C22⋊C4—3322no—
568C42—1661no—
569C42—1661no—
570C42—1661no—
571C42—1661no—
572C42C22×Dic8312yes—
573C42#1305058912yes—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23C2×D4×D8311yescharacteristic
589D4—22no—
590D4—22no—
591D4—22no—
592D4—22no—
593D4—22no—
594D4—22no—
595D4C2×C4⋊Dic8314yes—
596D4C2×C4⋊Dic8314yescomplemented
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—48no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—84no—
609C2×C4—3321no—
610C2×C4—3321no—
611C2×C4—3321no—
612C2×C4—3321no—
613C2×C4—3321no—
614C2×C4—3321no—
615C2×C4—3321no—
616C2×C4—3321no—
617C2×C4—3321no—
618C2×C4—3321no—
619C2×C4—3321no—
620C2×C4—3321no—
621C2×C4—832no—
622C2×C4—6644no—
623C2×C4—6644no—
624C2×C4—6644no—
625C2×C4—6644no—
626C2×C4—1661no—
627C2×C4—1661no—
628C2×C4—1661no—
629C2×C4—1661no—
630C2×C4—1661no—
631C2×C4—1661no—
632C2×C4—1661no—
633C2×C4—1661no—
634C2×C4—1661no—
635C2×C4—1661no—
636C2×C4—1661no—
637C2×C4D4×Dic8312yes—
638C2×C4D4×Dic8312yes—
639C2×C4C23×Dic8311yescharacteristic
640C2×C4C22×D33211yescharacteristic
641C2×C4C22×Dic16611yescharacteristic
642C2×C4C2×#1305058911yescharacteristic
643C2×C4#1458183811yescharacteristic
644C2×C4#1458183911yescharacteristic
645C8—22no—
646C8—3321no—
647C8—3321no—
648C8C2×C4⋊Dic8314yescomplemented
649C22—24no—
650C22—24no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—42no—
660C22—42no—
661C22—42no—
662C22—42no—
663C22C2×D4×Dic8311yescharacteristic
664C22D4×D33211yescharacteristic
665C22D4×Dic16611yescharacteristic
666C22AGL(1,ℤ/8)×D8311yescharacteristic
667C22#1912849711yescharacteristic
668C22#1912850511yescharacteristic
669C22#1912851111yescharacteristic
670C4—22no—
671C4—22no—
672C4—42no—
673C4—42no—
674C4—3321no—
675C4—3321no—
676C4—3321no—
677C4—6641no—
678C4—6641no—
679C4—6641no—
680C4—6641no—
681C4—1662no—
682C4C22×C4⋊Dic8311yescharacteristic
683C4#1912818411yescharacteristic
684C4#1912835511yescharacteristic
685C4#1912840811yescharacteristic
686C2—44no—
687C2—44no—
688C2D4×C4⋊Dic8311yescharacteristic
689C2AGL(1,ℤ/8)×Dic8311yescharacteristic
690C2#2491629611yescharacteristic
691C2#2491894511yescharacteristic
692C2#2491899011yescharacteristic
693C2#2492036311yescharacteristic
694C2#2492042211yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC2×#442×C83C2
socleC23×C83C22×D4
prime radicalC22×D8×C83C22
cosocleC22×C4×C83C24
hypercenterC2×#442D83
hypocenterC83#22676
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
3. #24910373C2semidirect
4. D4×C4⋊Dic83C2semidirect
5. #24908207C2semidirect
6. #24908192C2semidirect
7. #24907726C2semidirect
8. #24907726C2semidirect
9. #24907712C2semidirect
10. #24907712C2semidirect
11. #24907631C2semidirect
12. #24907473C2semidirect
13. #24907463C2semidirect
14. #24907335C2semidirect
57. #442×C83C4semidirect
125. C4×D4×C83C2×C4semidirect
126. C4×D4×C83C2×C4semidirect
132. #106×C83C2×C4semidirect
133. #102×C83C2×C4semidirect
134. #102×C83C2×C4semidirect
135. #97×C83C2×C4semidirect
211. D8×C83C4⋊C4semidirect
248. D4×C83C2×C4⋊C4semidirect
298. C8×C83C2×C4⋊C4semidirect
363. C83#22676semidirect
373. #442Dic83semidirect
435. C4×D4C2×Dic83semidirect
436. C4×D4C2×Dic83semidirect
465. #106C2×Dic83semidirect
471. #102C2×Dic83semidirect
472. #102C2×Dic83semidirect
474. #97C2×Dic83semidirect
529. D8C4⋊Dic83semidirect
596. D4C2×C4⋊Dic83semidirect
648. C8C2×C4⋊Dic83semidirect

Maximal subgroups

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

subgroupindex
C2×#191278132
C2×D8×Dic832
#249103732
D4×C4⋊Dic832
#249082072
#249081922
#249077262
#249077122
#249076312
#249074732
#249074632
#249073352
C2×#442×C832
#2267683