Finite Group Databasebeta

← #362114

Subgroups — #362114

Order 512.

1604 conjugacy classes of subgroups.

The subgroup lattice has 793 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4⋊C4×#41C211yesmaximal, characteristic
2#21146C211yesmaximal, characteristic, complemented
3C2×#1806C212yesmaximal
4C2×#1806C211yesmaximal, characteristic
5C2×C4×#104C211yesmaximal, characteristic
6C4×#389C211yesmaximal, characteristic, complemented
7#11226C212yesmaximal, complemented
8#11209C212yesmaximal, complemented
9#10851C211yesmaximal, characteristic, complemented
10#10839C211yesmaximal, characteristic, complemented
11#10790C212yesmaximal
12C2×C4×#41C2212yes—
13C2×C4×#41C2211yescharacteristic
14C2×#423C2211yescharacteristic
15C2×#423C2212yes—
16C22×#104C2212yes—
17C22×#104C2211yescharacteristic
18C22×#104C2211yescharacteristic
19C2×C4×M16C2211yescharacteristic
20#2351C412yescomplemented
21Q8×C4⋊C4C411yescharacteristic, complemented
22Q8×C4⋊C4C411yescharacteristic, complemented
23#2349—22no—
24#2349C412yescomplemented
25D4×C4⋊C4—21no—
26D4×C4⋊C4—21no—
27D4×C4⋊C4C411yescharacteristic, complemented
28D4×C4⋊C4C411yescharacteristic, complemented
29#2296—22no—
30#2296C2212yes—
31C2×#389—21no—
32#2285—21no—
33#2285C2211yescharacteristic
34C2×C4×C4⋊C4—21no—
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C4×C4⋊C4C2212yes—
37C2×C4×C4⋊C4C2211yescharacteristic
38C2×C43C2211yescharacteristic
39#1940—22no—
40#1939—21no—
41#1939—21no—
42#1806—28no—
43#1806—24no—
44C4×#104—24no—
45C2×#339C2212yes—
46C2×#339C2212yes—
47C2×#339C2212yes—
48C2×#339C2211yescharacteristic
49C2×#339C2211yescharacteristic
50C2×#339C2212yes—
51C2×#339C2212yes—
52#1728C2212yes—
53#1436—22no—
54C4⋊#95—21no—
55C4×#95C2212yes—
56C22×#41C2311yescharacteristic
57C22×M16C2312yes—
58C22×M16C2311yescharacteristic
59C22×M16C2311yescharacteristic
60C4×#41—22no—
61C4×#41—22no—
62C4×#41—24no—
63C4×#41—24no—
64C4×#41—42no—
65C4×#41—42no—
66C4×#41D414yes—
67C4×#41Q814yes—
68C2×C4×Q8C2×C412yes—
69C2×C4×Q8C2×C412yes—
70C2×C4×Q8C2×C411yescharacteristic
71C2×C4×Q8C2×C411yescharacteristic
72C2×C4×D4—21no—
73C2×C4×D4—21no—
74C2×C4×D4—22no—
75C2×C4×D4—22no—
76C2×C4×D4C2×C412yes—
77C2×C4×D4C2×C412yes—
78C2×C4×D4C2×C411yescharacteristic
79C2×C4×D4C2×C411yescharacteristic
80C2×#117—21no—
81C2×#117—22no—
82C2×#117C2312yes—
83C2×#117C2311yescharacteristic
84C22×C4⋊C4—21no—
85C22×C4⋊C4—22no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4D411yescharacteristic
89C22×C4⋊C4D411yescharacteristic
90C22×C42—21no—
91C22×C42—21no—
92C22×C42—22no—
93C22×C42—21no—
94C22×C42C2312yes—
95C22×C42C2311yescharacteristic
96C22×C42C2311yescharacteristic
97C22×C42C2312yes—
98C22×C42C2311yescharacteristic
99#423—24no—
100#423—22no—
101#423—22no—
102#423—42no—
103C2×C4⋊C8—21no—
104C2×C4⋊C8—22no—
105C2×C4⋊C8—22no—
106C2×C4⋊C8—21no—
107C2×#104—22no—
108C2×#104—22no—
109C2×#104—22no—
110C2×#104—22no—
111C2×#104—24no—
112C2×#104—24no—
113C2×#104—24no—
114C2×#104D414yes—
115C2×#104Q814yes—
116C4×M16—22no—
117C4×M16—22no—
118C2×#97—21no—
119C2×C4×C8—21no—
120#389—28no—
121#389—22no—
122#389—22no—
123#389—22no—
124#389—22no—
125#389C2×C412yes—
126#389C2×C412yes—
127#389C2×C412yes—
128#389C2×C412yes—
129#385—22no—
130#385—22no—
131#385—22no—
132#385—22no—
133#385—22no—
134#385—22no—
135#384—21no—
136#384—21no—
137#384C2×C411yescharacteristic
138#384C2×C411yescharacteristic
139#382—22no—
140#382C2×C412yes—
141#380—21no—
142#380—21no—
143#380—21no—
144#380—21no—
145#380—22no—
146C4×C4⋊C4—21no—
147C4×C4⋊C4—21no—
148C4×C4⋊C4—21no—
149C4×C4⋊C4—22no—
150C4×C4⋊C4—22no—
151C4×C4⋊C4—21no—
152C4×C4⋊C4—22no—
153C4×C4⋊C4—24no—
154C4×C4⋊C4—22no—
155C4×C4⋊C4—22no—
156C4×C4⋊C4—42no—
157C4×C4⋊C4C2×C411yescharacteristic
158C4×C4⋊C4C2×C411yescharacteristic
159C4×C4⋊C4C2×C412yes—
160C4×C4⋊C4D411yescharacteristic
161C4×C4⋊C4D411yescharacteristic
162C4×C4⋊C4D412yes—
163C2×#95—22no—
164C2×#95—22no—
165C2×#95—22no—
166C2×#95—22no—
167C2×#95—21no—
168C2×#95D412yes—
169C43—22no—
170C43—22no—
171#339—24no—
172#339—24no—
173#339—22no—
174#339—22no—
175#339—24no—
176#339—42no—
177#339—42no—
178#336—22no—
179#336—22no—
180C2×#41—21no—
181C2×#41—21no—
182C2×#41—21no—
183C2×#41—21no—
184C2×#41—21no—
185C2×#41—21no—
186C2×#41C2×D412yes—
187C2×#41C2×D412yes—
188C2×#41C2×Q812yes—
189C2×#41C2×Q812yes—
190C2×#41#4112yes—
191C2×#41#4112yes—
192C22×Q8C22×C411yescharacteristic
193C22×D4—21no—
194C22×D4C22×C411yescharacteristic
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4C2×D412yes—
204C23×C4C2×D411yescharacteristic
205C23×C4C2×D412yes—
206C23×C4C2×D411yescharacteristic
207C23×C4C2411yescharacteristic
208C2×M16—21no—
209C2×M16—21no—
210C2×M16—21no—
211C2×M16—21no—
212C2×M16—21no—
213C2×M16—21no—
214C2×M16—21no—
215C2×M16—21no—
216C2×M16—21no—
217C2×M16—21no—
218C2×M16—22no—
219C2×M16—22no—
220C2×M16—22no—
221C2×M16—22no—
222C2×M16—22no—
223C2×M16—22no—
224C2×M16C2×D412yes—
225C2×M16C2×Q812yes—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—22no—
229C4×Q8—22no—
230C4×Q8—22no—
231C4×Q8—24no—
232C4×Q8—24no—
233C4×Q8—42no—
234C4×Q8—42no—
235C4×Q8C4⋊C414yescomplemented
236C4×Q8C4⋊C414yescomplemented
237C4×D4—24no—
238C4×D4—24no—
239C4×D4—24no—
240C4×D4—24no—
241C4×D4—24no—
242C4×D4—24no—
243C4×D4—22no—
244C4×D4—22no—
245C4×D4—42no—
246C4×D4—42no—
247C4×D4—44no—
248C4×D4—44no—
249C4×D4—44no—
250C4×D4—44no—
251C4×D4C4⋊C414yescomplemented
252C4×D4C4⋊C414yescomplemented
253#117—21no—
254#117—21no—
255#117—24no—
256#117—24no—
257#117—22no—
258#117—22no—
259#117—22no—
260#117—22no—
261#117—44no—
262#117—44no—
263#117C2×D412yes—
264#117C2×Q812yes—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—28no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—44no—
282C2×C4⋊C4—44no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—44no—
287C2×C4⋊C4C22⋊C411yescharacteristic
288C2×C4⋊C4C22⋊C411yescharacteristic
289C2×C4⋊C4C22⋊C411yescharacteristic
290C2×C4⋊C4C22⋊C412yes—
291C2×C4⋊C4C22⋊C412yes—
292C2×C4⋊C4C22⋊C411yescharacteristic
293C2×C4⋊C4C22×C412yes—
294C2×C4⋊C4C22×C412yes—
295C2×C4⋊C4C22×C411yescharacteristic
296C2×C4⋊C4C22×C411yescharacteristic
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C42—21no—
304C2×C42—21no—
305C2×C42—22no—
306C2×C42—21no—
307C2×C42—22no—
308C2×C42—22no—
309C2×C42—22no—
310C2×C42—24no—
311C2×C42—24no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—24no—
321C2×C42—22no—
322C2×C42—22no—
323C2×C42—22no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—22no—
327C2×C42—22no—
328C2×C42—22no—
329C2×C42—22no—
330C2×C42—22no—
331C2×C42—22no—
332C2×C42—44no—
333C2×C42—44no—
334C2×C42—42no—
335C2×C42—42no—
336C2×C42—42no—
337C2×C42—42no—
338C2×C42—42no—
339C2×C42C22×C412yes—
340C2×C42C22×C412yes—
341C2×C42C22×C411yescharacteristic
342C2×C42C22×C411yescharacteristic
343C2×C42C2×D412yes—
344C2×C42C2×D412yes—
345C2×C42C2×D412yes—
346C2×C42C2×D412yes—
347C2×C42C2×D411yescharacteristic
348C2×C42C2×D411yescharacteristic
349C2×C42C2×Q812yes—
350C2×C42C2×Q812yes—
351C2×C42#4112yes—
352C2×C42#4112yes—
353C4⋊C8—44no—
354C4⋊C8—44no—
355C4⋊C8—42no—
356C4⋊C8—42no—
357#104—28no—
358#104—28no—
359#104—48no—
360#97—42no—
361C4×C8—42no—
362#95—28no—
363#95—22no—
364#95—22no—
365#95—22no—
366#95—22no—
367#95—22no—
368#95—22no—
369#95—44no—
370#95—44no—
371#95—42no—
372#95C22⋊C412yes—
373#95C22⋊C412yes—
374#95C22⋊C412yes—
375#95C22⋊C412yes—
376C24—21no—
377C24C22×D411yescharacteristic
378#41—22no—
379#41—22no—
380#41—22no—
381#41—22no—
382#41—22no—
383#41—22no—
384#41—22no—
385#41—22no—
386#41—22no—
387#41—22no—
388#41—22no—
389#41—22no—
390#41#12114yes—
391#41C22⋊Q814yes—
392#41#12514yes—
393#41C4⋊Q814yes—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8C2×C4⋊C412yes—
398C2×Q8C4×D412yes—
399C2×Q8C4×Q812yes—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4C2×C4⋊C412yes—
410C2×D4C4×D412yes—
411C2×D4C4×Q812yes—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—44no—
445C22×C4—44no—
446C22×C4—44no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—44no—
464C22×C4—81no—
465C22×C4—81no—
466C22×C4—82no—
467C22×C4—82no—
468C22×C4C2×C22⋊C412yes—
469C22×C4C2×C22⋊C412yes—
470C22×C4C2×C22⋊C412yes—
471C22×C4C2×C22⋊C411yescharacteristic
472C22×C4C2×C22⋊C411yescharacteristic
473C22×C4C2×C22⋊C411yescharacteristic
474C22×C4C2×C22⋊C412yes—
475C22×C4C2×C22⋊C411yescharacteristic
476C22×C4#12112yes—
477C22×C4#12112yes—
478C22×C4C22⋊Q812yes—
479C22×C4C22⋊Q812yes—
480C22×C4C23×C411yescharacteristic
481C22×C4C22×D411yescharacteristic
482C22×C4C22×D411yescharacteristic
483C22×C4C22×D411yescharacteristic
484C22×C4C22×Q811yescharacteristic
485C22×C4C22×Q811yescharacteristic
486C22×C4C2×#4111yescharacteristic
487C22×C4C2×#4111yescharacteristic
488C22×C4C2×#4111yescharacteristic
489C22×C4C2×#4111yescharacteristic
490C22×C4H(5,𝔽2)11yescharacteristic
491C22×C4H(5,𝔽2)11yescharacteristic
492C22×C42−1+411yescharacteristic
493C22×C42−1+411yescharacteristic
494M16—22no—
495M16—22no—
496M16—22no—
497M16—22no—
498M16—41no—
499M16—41no—
500M16—41no—
501M16—41no—
502M16—42no—
503M16—42no—
504M16—42no—
505M16—42no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—42no—
513C2×C8—42no—
514C2×C8—42no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—24no—
518C4⋊C4—24no—
519C4⋊C4—24no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—42no—
528C4⋊C4—44no—
529C4⋊C4—44no—
530C4⋊C4—48no—
531C4⋊C4—416no—
532C4⋊C4—44no—
533C4⋊C4—44no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—81no—
537C4⋊C4—81no—
538C4⋊C4—82no—
539C4⋊C4—82no—
540C4⋊C4#10414yescomplemented
541C4⋊C4C2×C4⋊C412yes—
542C4⋊C4C2×C4⋊C412yes—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—24no—
546C22⋊C4—24no—
547C22⋊C4—44no—
548C22⋊C4—44no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C42—22no—
552C42—22no—
553C42—22no—
554C42—22no—
555C42—22no—
556C42—22no—
557C42—22no—
558C42—22no—
559C42—22no—
560C42—22no—
561C42—24no—
562C42—24no—
563C42—22no—
564C42—22no—
565C42—22no—
566C42—22no—
567C42—44no—
568C42—44no—
569C42—48no—
570C42—48no—
571C42—41no—
572C42—41no—
573C42—42no—
574C42—42no—
575C42—41no—
576C42—41no—
577C42—42no—
578C42—42no—
579C42—42no—
580C42—42no—
581C42C2×C4⋊C412yes—
582C42C2×C4⋊C412yes—
583C42#11712yes—
584C42#11712yes—
585C42#12112yes—
586C42#12112yes—
587C42C22⋊Q812yes—
588C42C22⋊Q812yes—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23C22×C22⋊C411yescharacteristic
601C23C2×#12111yescharacteristic
602C23C2×C22⋊Q811yescharacteristic
603C23D4211yescharacteristic
604C23#54611yescharacteristic
605C23#54811yescharacteristic
606C23D4×Q811yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—22no—
610Q8#38914yescomplemented
611D4—24no—
612D4—24no—
613D4—24no—
614D4—24no—
615D4—22no—
616D4—22no—
617D4—22no—
618D4#38914yescomplemented
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—44no—
652C2×C4—44no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—48no—
670C2×C4—44no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—84no—
680C2×C4—88no—
681C2×C4—82no—
682C2×C4—82no—
683C2×C4—88no—
684C2×C4—82no—
685C2×C4—82no—
686C2×C4—82no—
687C2×C4—82no—
688C2×C4#38012yes—
689C2×C4#38012yes—
690C2×C4#38012yes—
691C2×C4#38012yes—
692C2×C4C2×#10414yes—
693C2×C4C2×#10412yes—
694C2×C4#42112yes—
695C2×C4C22×C4⋊C411yescharacteristic
696C2×C4C2×#11711yescharacteristic
697C2×C4C2×C4×D411yescharacteristic
698C2×C4C2×C4×Q811yescharacteristic
699C2×C4#51811yescharacteristic
700C2×C4#51911yescharacteristic
701C2×C4C2×#12111yescharacteristic
702C2×C4C2×#12111yescharacteristic
703C2×C4C2×C22⋊Q811yescharacteristic
704C2×C4C2×C22⋊Q811yescharacteristic
705C2×C4C2×#12511yescharacteristic
706C2×C4C2×C4⋊Q811yescharacteristic
707C2×C4#53711yescharacteristic
708C2×C4#53711yescharacteristic
709C2×C4#54411yescharacteristic
710C2×C4#54411yescharacteristic
711C2×C4D4211yescharacteristic
712C2×C4#54611yescharacteristic
713C2×C4#54711yescharacteristic
714C2×C4#54711yescharacteristic
715C2×C4#54811yescharacteristic
716C2×C4D4×Q811yescharacteristic
717C2×C4#55211yescharacteristic
718C2×C4#55211yescharacteristic
719C2×C4#55311yescharacteristic
720C2×C4#55311yescharacteristic
721C2×C4#55411yescharacteristic
722C2×C4#55411yescharacteristic
723C8—42no—
724C8—42no—
725C8—82no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—24no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22C2×#38011yescharacteristic
746C22D4×C22⋊C411yescharacteristic
747C22Q8×C22⋊C411yescharacteristic
748C22#241611yescharacteristic
749C22#241711yescharacteristic
750C22#244011yescharacteristic
751C22#244211yescharacteristic
752C22C22×#10411yescharacteristic
753C22C2×#42111yescharacteristic
754C22#290111yescharacteristic
755C22#290111yescharacteristic
756C4—24no—
757C4—24no—
758C4—22no—
759C4—22no—
760C4—22no—
761C4—44no—
762C4—44no—
763C4—42no—
764C4—42no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—84no—
769C4—82no—
770C4—82no—
771C4#180614yescomplemented
772C4C2×#38911yescharacteristic
773C4#231611yescharacteristic
774C4#234411yescharacteristic
775C4#234511yescharacteristic
776C4#241611yescharacteristic
777C4#241711yescharacteristic
778C4#244011yescharacteristic
779C4#244211yescharacteristic
780C2—21no—
781C2—21no—
782C2—21no—
783C2—21no—
784C2—44no—
785C2#1390711yescharacteristic
786C2C2×#180611yescharacteristic
787C2#2065511yescharacteristic
788C2D4×#10411yescharacteristic
789C2#2243511yescharacteristic
790C2Q8×#10411yescharacteristic
791C2#2252911yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C22×C22⋊C4
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #21146C2semidirect
6. C4×#389C2semidirect
7. #11226C2semidirect
8. #11209C2semidirect
9. #10851C2semidirect
10. #10839C2semidirect
20. #2351C4semidirect
21. Q8×C4⋊C4C4semidirect
22. Q8×C4⋊C4C4semidirect
24. #2349C4semidirect
27. D4×C4⋊C4C4semidirect
28. D4×C4⋊C4C4semidirect
235. C4×Q8C4⋊C4semidirect
236. C4×Q8C4⋊C4semidirect
251. C4×D4C4⋊C4semidirect
252. C4×D4C4⋊C4semidirect
540. C4⋊C4#104semidirect
610. Q8#389semidirect
618. D4#389semidirect
771. C4#1806semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×#412
#211462
C2×#18062
C2×C4×#1042
C4×#3892
#112262
#112092
#108512
#108392
#107902