Finite Group Databasebeta

← #196783

Subgroups — #196783

Order 512.

1219 conjugacy classes of subgroups.

The subgroup lattice has 789 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2990C211yesmaximal, characteristic
2#35280C211yesmaximal, characteristic
3#21851C211yesmaximal, characteristic
4C2×#1552C211yesmaximal, characteristic, complemented
5C2×#1552C211yesmaximal, characteristic, complemented
6#9140C211yesmaximal, characteristic, complemented
7#9139C211yesmaximal, characteristic, complemented
8#9138C211yesmaximal, characteristic, complemented
9#9137C211yesmaximal, characteristic, complemented
10#9132C211yesmaximal, characteristic, complemented
11#9131C211yesmaximal, characteristic, complemented
12#9130C211yesmaximal, characteristic, complemented
13#9129C211yesmaximal, characteristic, complemented
14#8040C211yesmaximal, characteristic, complemented
15C2×#1296C211yesmaximal, characteristic, complemented
16C2×#533C2211yescharacteristic
17C2×C4×#41C2211yescharacteristic
18#2990—24no—
19#2990—24no—
20C2×#446—21no—
21C2×#435—21no—
22C2×#435—21no—
23C2×C8×D4—21no—
24C2×#432C2211yescharacteristic
25C2×#432C2211yescharacteristic
26C2×#432C2211yescharacteristic
27C2×#431C2211yescharacteristic
28C2×#423C2211yescharacteristic
29C22×C4⋊C8C2211yescharacteristic
30C22×C4⋊C8C2211yescharacteristic
31C22×C4⋊C8C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2629C412yes—
37#2629C412yes—
38#2582—21no—
39#2582—21no—
40#2538—21no—
41#2538—21no—
42#2417—21no—
43#2417—21no—
44#2417—21no—
45#2417—21no—
46#2316C412yes—
47#2311C412yes—
48C2×#384C2211yescharacteristic
49#1985—21no—
50#1955—21no—
51#1869—21no—
52#1869—21no—
53#1797C2211yescharacteristic
54#1797C2211yescharacteristic
55#1797C2211yescharacteristic
56#1797C2211yescharacteristic
57#1552—24no—
58#1552—24no—
59C2×#332C2211yescharacteristic
60C2×#332C2211yescharacteristic
61C2×#332C2211yescharacteristic
62C2×#332C2211yescharacteristic
63C2×#332C2211yescharacteristic
64C2×#332C2211yescharacteristic
65C2×#332C2211yescharacteristic
66C2×#332C2211yescharacteristic
67#1296C2211yescharacteristic
68#1296C2211yescharacteristic
69#1296C2211yescharacteristic
70#1296C2211yescharacteristic
71#1296C2211yescharacteristic
72#1296C2211yescharacteristic
73#1296C2211yescharacteristic
74#1296C2211yescharacteristic
75C22×#41C2×C411yescharacteristic
76C22×M16—21no—
77C23×C8—21no—
78C23×C8—21no—
79C23×C8—21no—
80#533—22no—
81#533—22no—
82#533—22no—
83#533—22no—
84C2×C4⋊Q8C2311yescharacteristic
85C2×C4⋊Q8C2311yescharacteristic
86C2×#125C2×C412yes—
87C2×C22⋊Q8—21no—
88C2×C22⋊Q8—21no—
89C2×C22⋊Q8—21no—
90C2×C22⋊Q8—21no—
91C2×C22⋊Q8—21no—
92C2×C22⋊Q8—21no—
93C4×#41—22no—
94C4×#41—22no—
95C4×#41—22no—
96C4×#41—22no—
97C2×C4×Q8—21no—
98C2×C4×Q8—21no—
99C2×C4×Q8D411yescharacteristic
100C2×C4×Q8D411yescharacteristic
101C2×C4×D4D411yescharacteristic
102C2×C4×D4D411yescharacteristic
103C2×C4×D4D411yescharacteristic
104C2×C4×D4D411yescharacteristic
105C2×C4×D4D411yescharacteristic
106C2×C4×D4D411yescharacteristic
107C2×#117C2×C412yes—
108C2×#117C2×C411yescharacteristic
109C2×#117C2×C411yescharacteristic
110C2×#117C2×C411yescharacteristic
111C22×C4⋊C4—21no—
112C22×C4⋊C4—21no—
113C22×C4⋊C4C2×C412yes—
114C22×C42C2311yescharacteristic
115C22×C42C2311yescharacteristic
116C22×C42C2311yescharacteristic
117#446—28no—
118#435—28no—
119#435—28no—
120C8×D4—28no—
121#432—22no—
122#432—22no—
123#432—22no—
124#432—22no—
125#432—22no—
126#432D414yes—
127#431—22no—
128#431—22no—
129#423—22no—
130#423—22no—
131C2×C4⋊C8—21no—
132C2×C4⋊C8—21no—
133C2×C4⋊C8—22no—
134C2×C4⋊C8—21no—
135C2×C4⋊C8—22no—
136C2×C4⋊C8—22no—
137C2×C4⋊C8—22no—
138C2×C4⋊C8—22no—
139C2×C4⋊C8—21no—
140C2×C4⋊C8D414yes—
141C2×C4⋊C8C2311yescharacteristic
142C2×C4⋊C8C2311yescharacteristic
143C2×C4⋊C8C2311yescharacteristic
144C2×C4⋊C8C2311yescharacteristic
145C2×C4⋊C8C2311yescharacteristic
146C2×C4⋊C8C2311yescharacteristic
147C2×C4⋊C8C2311yescharacteristic
148C2×C4⋊C8C2311yescharacteristic
149C2×C22⋊C8—21no—
150C2×C22⋊C8—21no—
151C2×C22⋊C8—21no—
152C2×C22⋊C8—21no—
153C2×C22⋊C8—21no—
154C2×C22⋊C8—21no—
155C2×C22⋊C8—21no—
156C2×C22⋊C8—21no—
157C2×#97—21no—
158C2×#97—21no—
159C2×#97—21no—
160C2×C4×C8—21no—
161#398—22no—
162#398—22no—
163#398—22no—
164#398—22no—
165#396—22no—
166#396—22no—
167#396—22no—
168#396—22no—
169#391—22no—
170#391—21no—
171#391—21no—
172#391—21no—
173#391—21no—
174#390—22no—
175#389—22no—
176#389—22no—
177#389—21no—
178#389—21no—
179#389—21no—
180#389—21no—
181#389C2×C412yes—
182#389C2×C412yes—
183#389C2×C412yes—
184#389C2×C412yes—
185#386—22no—
186#386—22no—
187#384—21no—
188#384—21no—
189#384C2×C412yes—
190#384C2311yescharacteristic
191#384C2311yescharacteristic
192#380—21no—
193#380—21no—
194#380—21no—
195#380—21no—
196#380—22no—
197#380—22no—
198#380C2×C412yes—
199#380C2×C412yes—
200#380C2×C412yes—
201#380C2×C412yes—
202#336—21no—
203#336—21no—
204#336—21no—
205#336—21no—
206#332—22no—
207#332—22no—
208#332—22no—
209#332—22no—
210#332—22no—
211#332—22no—
212#332—22no—
213#332—22no—
214C2×#41—24no—
215C2×#41—22no—
216C2×#41—22no—
217C2×#41—42no—
218C22×Q8—21no—
219C22×Q8—21no—
220C22×Q8C22⋊C411yescharacteristic
221C22×D4C22⋊C411yescharacteristic
222C22×D4C22⋊C411yescharacteristic
223C22×D4C22⋊C411yescharacteristic
224C23×C4—22no—
225C23×C4C22×C411yescharacteristic
226C23×C4C22×C411yescharacteristic
227C23×C4C22×C411yescharacteristic
228C23×C4C2×D411yescharacteristic
229C23×C4C2×D411yescharacteristic
230C23×C4C2×D411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C2×M16—24no—
235C2×M16—81no—
236C2×M16—81no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—24no—
242C22×C8—24no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—42no—
248C22×C8—81no—
249C22×C8—81no—
250C22×C8—81no—
251C22×C8—81no—
252C22×C8—81no—
253C22×C8—81no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8—21no—
262#125—24no—
263#125—24no—
264C22⋊Q8—42no—
265C22⋊Q8—42no—
266C22⋊Q8—42no—
267C22⋊Q8—42no—
268C22⋊Q8—81no—
269C22⋊Q8—81no—
270C22⋊Q8—81no—
271C22⋊Q8—81no—
272C22⋊Q8—81no—
273C22⋊Q8—81no—
274C22⋊Q8—81no—
275C22⋊Q8—81no—
276C4×Q8—22no—
277C4×Q8—22no—
278C4×Q8—22no—
279C4×Q8—22no—
280C4×Q8—42no—
281C4×Q8—42no—
282C4×Q8—42no—
283C4×Q8—42no—
284C4×D4—22no—
285C4×D4—22no—
286C4×D4—22no—
287C4×D4—22no—
288C4×D4—22no—
289C4×D4—22no—
290C4×D4—22no—
291C4×D4—22no—
292C4×D4—22no—
293C4×D4—22no—
294C4×D4—22no—
295C4×D4—22no—
296#117—22no—
297#117—22no—
298#117—22no—
299#117—22no—
300#117—22no—
301#117—22no—
302#117—24no—
303#117—24no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—81no—
321C2×C4⋊C4—81no—
322C2×C4⋊C4—81no—
323C2×C4⋊C4—81no—
324C2×C4⋊C4C22⋊C411yescharacteristic
325C2×C4⋊C4C22⋊C411yescharacteristic
326C2×C4⋊C4C22⋊C411yescharacteristic
327C2×C4⋊C4C22⋊C411yescharacteristic
328C2×C4⋊C4C22⋊C411yescharacteristic
329C2×C4⋊C4C22⋊C411yescharacteristic
330C2×C4⋊C4C22×C412yes—
331C2×C4⋊C4C22×C412yes—
332C2×C4⋊C4C22×C412yes—
333C2×C4⋊C4C22×C412yes—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4C22⋊C411yescharacteristic
340C2×C22⋊C4C22⋊C411yescharacteristic
341C2×C22⋊C4C22⋊C411yescharacteristic
342C2×C22⋊C4C22⋊C411yescharacteristic
343C2×C22⋊C4C22⋊C411yescharacteristic
344C2×C22⋊C4C22⋊C411yescharacteristic
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—22no—
354C2×C42C22×C411yescharacteristic
355C2×C42C22×C411yescharacteristic
356C2×C42C22×C411yescharacteristic
357C2×C42C2×D411yescharacteristic
358C2×C42C2×D411yescharacteristic
359C2×C42C2×D411yescharacteristic
360C2×C42C2×D411yescharacteristic
361C2×C42C2×D412yes—
362C2×C42C2×D412yes—
363C2×C42C2×D411yescharacteristic
364C2×C42C2×D411yescharacteristic
365C2×C42#4112yes—
366C2×C42#4112yes—
367C2×C42C2411yescharacteristic
368C4⋊C8—24no—
369C4⋊C8—24no—
370C4⋊C8—24no—
371C4⋊C8—21no—
372C4⋊C8—21no—
373C4⋊C8—21no—
374C4⋊C8—21no—
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8—21no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—42no—
384C4⋊C8C2×D412yes—
385C4⋊C8C2×D412yes—
386C4⋊C8C2×D412yes—
387C4⋊C8C2×D412yes—
388C22⋊C8—24no—
389C22⋊C8—24no—
390C22⋊C8—24no—
391C22⋊C8—42no—
392C22⋊C8—81no—
393C22⋊C8—81no—
394C22⋊C8—81no—
395C22⋊C8—81no—
396#97—24no—
397#97—24no—
398#97—42no—
399C4×C8—24no—
400#95—22no—
401#95—22no—
402#95—22no—
403#95—22no—
404#95—22no—
405#95—22no—
406#95—22no—
407#95—22no—
408C24C2×C22⋊C411yescharacteristic
409C24C2×C22⋊C411yescharacteristic
410C24C2×C22⋊C411yescharacteristic
411#41—48no—
412#41—48no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—41no—
416C2×Q8—41no—
417C2×Q8—41no—
418C2×Q8—41no—
419C2×Q8—41no—
420C2×Q8—41no—
421C2×Q8—41no—
422C2×Q8—41no—
423C2×Q8—41no—
424C2×Q8—41no—
425C2×Q8—41no—
426C2×Q8—41no—
427C2×Q8—41no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—41no—
436C2×D4#10114yes—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—44no—
484C22×C4—82no—
485C22×C4—82no—
486C22×C4C2×C22⋊C411yescharacteristic
487C22×C4C2×C22⋊C411yescharacteristic
488C22×C4C2×C22⋊C411yescharacteristic
489C22×C4C2×C22⋊C411yescharacteristic
490C22×C4C2×C22⋊C411yescharacteristic
491C22×C4C2×C22⋊C411yescharacteristic
492C22×C4C2×C22⋊C411yescharacteristic
493C22×C4C2×C22⋊C411yescharacteristic
494C22×C4C2×C22⋊C411yescharacteristic
495C22×C4C4×D412yes—
496C22×C4C4×D412yes—
497C22×C4#12012yes—
498C22×C4#12112yes—
499C22×C4#12112yes—
500C22×C4#12312yes—
501C22×C4C23×C411yescharacteristic
502C22×C4C22×D411yescharacteristic
503C22×C4C22×D411yescharacteristic
504M16—84no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C2×C8—41no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—84no—
530C2×C8—84no—
531C2×C8—84no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—44no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—41no—
548C4⋊C4—41no—
549C4⋊C4—41no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—41no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—44no—
558C4⋊C4—44no—
559C4⋊C4—82no—
560C4⋊C4—82no—
561C4⋊C4—82no—
562C4⋊C4—82no—
563C4⋊C4—82no—
564C4⋊C4—82no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—44no—
572C22⋊C4—82no—
573C22⋊C4—82no—
574C22⋊C4—82no—
575C22⋊C4—82no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—44no—
589C42C4×D412yes—
590C42C4×D412yes—
591C42#12012yes—
592C42#12112yes—
593C42#12112yes—
594C42#12312yes—
595C42C22×D411yescharacteristic
596C42C22×D411yescharacteristic
597C42C2×#4111yescharacteristic
598C42C2×#4111yescharacteristic
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23#38612yes—
617C23C2×#10112yes—
618C23C2×#10112yes—
619C23#41312yes—
620C23C22×C22⋊C411yescharacteristic
621Q8—44no—
622Q8—81no—
623Q8—81no—
624Q8—81no—
625Q8—81no—
626Q8—81no—
627Q8—81no—
628Q8—81no—
629Q8—81no—
630D4—28no—
631D4—44no—
632D4—44no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—164no—
701C2×C4#38612yes—
702C2×C4#38612yes—
703C2×C4#38612yes—
704C2×C4C2×#10112yes—
705C2×C4C2×C4×D411yescharacteristic
706C2×C4C2×C4×D411yescharacteristic
707C2×C4C2×#12011yescharacteristic
708C2×C4C2×#12111yescharacteristic
709C2×C4C2×#12111yescharacteristic
710C2×C4C2×#12311yescharacteristic
711C2×C4#57611yescharacteristic
712C2×C4#57611yescharacteristic
713C2×C4#57711yescharacteristic
714C2×C4#57711yescharacteristic
715C2×C4#57711yescharacteristic
716C2×C4#57711yescharacteristic
717C2×C4#57811yescharacteristic
718C2×C4#57811yescharacteristic
719C8—42no—
720C8—42no—
721C8—42no—
722C8—42no—
723C8—81no—
724C8—81no—
725C8—81no—
726C8—81no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22#190114yes—
748C22C2×#38611yescharacteristic
749C22C22×#10111yescharacteristic
750C22C2×#41311yescharacteristic
751C22#289711yescharacteristic
752C22#289711yescharacteristic
753C22#289811yescharacteristic
754C22#289811yescharacteristic
755C4—22no—
756C4—22no—
757C4—21no—
758C4—21no—
759C4—22no—
760C4—22no—
761C4—41no—
762C4—41no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—82no—
767C4—82no—
768C4—82no—
769C4—82no—
770C4#301211yescharacteristic
771C4#301311yescharacteristic
772C4#306011yescharacteristic
773C4#306111yescharacteristic
774C4#306211yescharacteristic
775C4#306311yescharacteristic
776C4#309811yescharacteristic
777C4#309911yescharacteristic
778C2—24no—
779C2—42no—
780C2—81no—
781C2#1777111yescharacteristic
782C2#1777411yescharacteristic
783C2#1777411yescharacteristic
784C2#1778011yescharacteristic
785C2#2091511yescharacteristic
786C2#2097611yescharacteristic
787C2C2×#190111yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radicalC22×#41C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1552C2semidirect
5. C2×#1552C2semidirect
6. #9140C2semidirect
7. #9139C2semidirect
8. #9138C2semidirect
9. #9137C2semidirect
10. #9132C2semidirect
11. #9131C2semidirect
12. #9130C2semidirect
13. #9129C2semidirect
14. #8040C2semidirect
15. C2×#1296C2semidirect

Maximal subgroups

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

subgroupindex
C2×#29902
#352802
#218512
C2×#15522
#91402
#91392
#91382
#91372
#91322
#91312
#91302
#91292
#80402
C2×#12962