Finite Group Databasebeta

← #163933

Subgroups — #163933

Order 512.

1142 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34267C211yesmaximal, characteristic
2#22471C211yesmaximal, characteristic, complemented
3#22471C211yesmaximal, characteristic, complemented
4#7648C211yesmaximal, characteristic, complemented
5#7647C211yesmaximal, characteristic, complemented
6#7634C211yesmaximal, characteristic, complemented
7#7633C211yesmaximal, characteristic, complemented
8#7623C211yesmaximal, characteristic, complemented
9#7620C211yesmaximal, characteristic, complemented
10#7617C211yesmaximal, characteristic, complemented
11#7616C211yesmaximal, characteristic, complemented
12#7593C211yesmaximal, characteristic, complemented
13#7578C211yesmaximal, characteristic, complemented
14#7578C211yesmaximal, characteristic, complemented
15C2×#1271C211yesmaximal, characteristic, complemented
16C2×#537C411yescharacteristic
17C2×#520C411yescharacteristic
18C2×C4×#41C2211yescharacteristic
19C2×#435—21no—
20C2×#435—21no—
21#2364—21no—
22#2364—21no—
23#2363—21no—
24#2362—21no—
25#2361—21no—
26#2361—21no—
27#2361—21no—
28#2360—21no—
29#2324C411yescharacteristic
30#2324C411yescharacteristic
31#2323C411yescharacteristic
32#2323C411yescharacteristic
33#2311C411yescharacteristic
34C4×C22⋊Q8C2211yescharacteristic
35C4×C22⋊Q8C2211yescharacteristic
36C4×#121C2211yescharacteristic
37C4×#121C2211yescharacteristic
38#2297C2211yescharacteristic
39C2×#389C2211yescharacteristic
40#2274C411yescharacteristic
41#1985—21no—
42#1985—21no—
43#1870—21no—
44#1870—21no—
45#1869—21no—
46#1869—21no—
47#1817C2211yescharacteristic
48#1817C2211yescharacteristic
49#1817C2211yescharacteristic
50#1817C2211yescharacteristic
51#1797C2211yescharacteristic
52#1797C2211yescharacteristic
53#1749C2211yescharacteristic
54#1749C2211yescharacteristic
55#1728C2211yescharacteristic
56#1728C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59#1272C2211yescharacteristic
60#1272C2211yescharacteristic
61#1272C2211yescharacteristic
62#1272C2211yescharacteristic
63#1271C2211yescharacteristic
64#1271C2211yescharacteristic
65#1271C2211yescharacteristic
66#1271C2211yescharacteristic
67#1271C2211yescharacteristic
68#1271C2211yescharacteristic
69#1271C2211yescharacteristic
70#1271C2211yescharacteristic
71#1270C2211yescharacteristic
72#1270C2211yescharacteristic
73#1270C2211yescharacteristic
74#1270C2211yescharacteristic
75C22×#41C2×C411yescharacteristic
76C22×#41C2×C411yescharacteristic
77C22×M16—21no—
78C22×M16—21no—
79C23×C8—21no—
80C23×C8—21no—
81#537—24no—
82#537—24no—
83C2×C22⋊Q8—21no—
84C2×C22⋊Q8C2×C411yescharacteristic
85C2×C22⋊Q8C2×C411yescharacteristic
86C2×#121—21no—
87C2×#121—21no—
88C2×#121—21no—
89C2×#121C2×C411yescharacteristic
90C2×#121C2×C411yescharacteristic
91#520—44no—
92C4×#41—44no—
93C2×C4×Q8C2×C411yescharacteristic
94C2×C4×Q8C2×C411yescharacteristic
95C2×C4×Q8D411yescharacteristic
96C2×C4×Q8D411yescharacteristic
97C2×C4×D4—21no—
98C2×C4×D4—21no—
99C2×C4×D4—21no—
100C2×C4×D4—21no—
101C2×C4×D4C2×C411yescharacteristic
102C2×C4×D4C2×C411yescharacteristic
103C2×C4×D4D411yescharacteristic
104C2×C4×D4D411yescharacteristic
105C2×C4×D4D411yescharacteristic
106C2×C4×D4D411yescharacteristic
107C2×C4×D4D411yescharacteristic
108C2×C4×D4D411yescharacteristic
109C2×#117—21no—
110C2×#117C2×C411yescharacteristic
111C2×#117C2×C411yescharacteristic
112C2×#117C2×C411yescharacteristic
113C2×#117C2×C411yescharacteristic
114C22×C4⋊C4—21no—
115C22×C4⋊C4—21no—
116C22×C4⋊C4C2×C411yescharacteristic
117C22×C4⋊C4C2×C411yescharacteristic
118C22×C42C2311yescharacteristic
119C22×C42C2311yescharacteristic
120C22×C42C2311yescharacteristic
121#435—44no—
122#435—44no—
123C2×C4⋊C8—21no—
124C2×C4⋊C8—21no—
125C2×C22⋊C8—21no—
126C2×C22⋊C8—21no—
127C2×C22⋊C8—21no—
128C2×C22⋊C8—21no—
129C2×C22⋊C8—21no—
130C2×C22⋊C8—21no—
131C2×C22⋊C8—21no—
132C2×C22⋊C8—21no—
133C2×#97—21no—
134C2×#97—21no—
135#391—21no—
136#391C2×C411yescharacteristic
137#391C2311yescharacteristic
138#390—21no—
139#390—21no—
140#390—21no—
141#390C2×C411yescharacteristic
142#390C2311yescharacteristic
143#389—21no—
144#389—21no—
145#389—21no—
146#389—21no—
147#389C2×C411yescharacteristic
148#389C2×C411yescharacteristic
149#389C2311yescharacteristic
150#389C2311yescharacteristic
151#388—21no—
152#388—21no—
153#388—21no—
154#388—21no—
155#388—21no—
156#388—21no—
157#388—21no—
158#388—21no—
159#387—21no—
160#387—21no—
161#387—21no—
162#387—21no—
163#386—21no—
164#386—21no—
165#386—21no—
166#386—21no—
167#386—21no—
168#386—21no—
169#386—21no—
170#386—21no—
171#385—21no—
172#385—21no—
173#385—21no—
174#385—21no—
175#380C2×C411yescharacteristic
176#380C2×C411yescharacteristic
177#380C2×C411yescharacteristic
178#380C2×C411yescharacteristic
179C4×C4⋊C4—21no—
180C4×C4⋊C4—21no—
181C4×C4⋊C4—21no—
182C4×C4⋊C4—21no—
183C4×C4⋊C4C2×C411yescharacteristic
184C4×C4⋊C4C2×C411yescharacteristic
185C4×C4⋊C4C2×C411yescharacteristic
186C4×C4⋊C4C2×C411yescharacteristic
187C4×C22⋊C4—21no—
188C4×C22⋊C4—21no—
189C4×C22⋊C4—21no—
190C4×C22⋊C4—21no—
191C4×C22⋊C4—21no—
192C4×C22⋊C4—21no—
193C4×C22⋊C4—21no—
194C4×C22⋊C4—21no—
195C2×#95—21no—
196#336—21no—
197#336—21no—
198#336—21no—
199#336—21no—
200#336—21no—
201#336—21no—
202#336—21no—
203#336—21no—
204#336C2311yescharacteristic
205#336C2311yescharacteristic
206#336C2311yescharacteristic
207#336C2311yescharacteristic
208#336C2311yescharacteristic
209#336C2311yescharacteristic
210#336C2311yescharacteristic
211#336C2311yescharacteristic
212C2×#41—22no—
213C2×#41—22no—
214C2×#41—22no—
215C2×#41—42no—
216C2×#41—42no—
217C2×#41—42no—
218C2×#41—42no—
219C2×#41M1614yescomplemented
220C22×Q8C22⋊C411yescharacteristic
221C22×Q8C22×C411yescharacteristic
222C22×D4—21no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4C22⋊C411yescharacteristic
226C22×D4C22⋊C411yescharacteristic
227C22×D4C22⋊C411yescharacteristic
228C22×D4C22×C411yescharacteristic
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4C22×C411yescharacteristic
235C23×C4C22×C411yescharacteristic
236C23×C4C22×C411yescharacteristic
237C23×C4C2×D411yescharacteristic
238C23×C4C2×D411yescharacteristic
239C23×C4C2×D411yescharacteristic
240C23×C4C2×D411yescharacteristic
241C23×C4C2×D411yescharacteristic
242C23×C4C2×D411yescharacteristic
243C2×M16—42no—
244C2×M16—42no—
245C2×M16—42no—
246C2×M16—42no—
247C2×M16—81no—
248C2×M16—81no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—42no—
258C22×C8—42no—
259C22×C8—42no—
260C22×C8—42no—
261C22×C8—81no—
262C22×C8—81no—
263C22⋊Q8—28no—
264C22⋊Q8—22no—
265C22⋊Q8—22no—
266C22⋊Q8—22no—
267C22⋊Q8—22no—
268#121—28no—
269#121—28no—
270#121—28no—
271#121—22no—
272#121—22no—
273#121—22no—
274#121—22no—
275C4×Q8—42no—
276C4×Q8—42no—
277C4×Q8—42no—
278C4×Q8—42no—
279C4×D4—24no—
280C4×D4—24no—
281C4×D4—42no—
282C4×D4—42no—
283C4×D4—42no—
284C4×D4—42no—
285C4×D4—42no—
286C4×D4—42no—
287C4×D4—44no—
288C4×D4—44no—
289C4×D4—81no—
290C4×D4—81no—
291C4×D4—81no—
292C4×D4—81no—
293#117—24no—
294#117—42no—
295#117—42no—
296#117—44no—
297#117—42no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—81no—
312C2×C4⋊C4—81no—
313C2×C4⋊C4C22⋊C411yescharacteristic
314C2×C4⋊C4C22⋊C411yescharacteristic
315C2×C4⋊C4C22⋊C411yescharacteristic
316C2×C4⋊C4C22⋊C411yescharacteristic
317C2×C4⋊C4C22⋊C411yescharacteristic
318C2×C4⋊C4C22⋊C411yescharacteristic
319C2×C4⋊C4M1614yescomplemented
320C2×C4⋊C4C22×C411yescharacteristic
321C2×C4⋊C4C22×C411yescharacteristic
322C2×C4⋊C4C22×C411yescharacteristic
323C2×C4⋊C4C22×C411yescharacteristic
324C2×C4⋊C4C22×C411yescharacteristic
325C2×C4⋊C4C22×C411yescharacteristic
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4C22⋊C411yescharacteristic
342C2×C22⋊C4C22⋊C411yescharacteristic
343C2×C22⋊C4C22⋊C411yescharacteristic
344C2×C22⋊C4C22⋊C411yescharacteristic
345C2×C22⋊C4C22⋊C411yescharacteristic
346C2×C22⋊C4C22⋊C411yescharacteristic
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—42no—
355C2×C42—42no—
356C2×C42—42no—
357C2×C42C22×C411yescharacteristic
358C2×C42C22×C411yescharacteristic
359C2×C42C22×C411yescharacteristic
360C2×C42C2×D411yescharacteristic
361C2×C42C2×D411yescharacteristic
362C2×C42C2×D411yescharacteristic
363C2×C42C2×D411yescharacteristic
364C2×C42C2×D411yescharacteristic
365C2×C42C2×D411yescharacteristic
366C2×C42C2411yescharacteristic
367C4⋊C8—42no—
368C4⋊C8—42no—
369C22⋊C8—42no—
370C22⋊C8—42no—
371C22⋊C8—42no—
372C22⋊C8—42no—
373C22⋊C8—42no—
374C22⋊C8—42no—
375C22⋊C8—81no—
376C22⋊C8—81no—
377#97—42no—
378#97—42no—
379#95—21no—
380#95—21no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395C24—21no—
396C24C2×C22⋊C411yescharacteristic
397C24C2×C22⋊C411yescharacteristic
398C24C2×C22⋊C411yescharacteristic
399#41—48no—
400#41—48no—
401#41—48no—
402#41—48no—
403C2×Q8—21no—
404C2×Q8—22no—
405C2×Q8—41no—
406C2×Q8—41no—
407C2×Q8—41no—
408C2×Q8—41no—
409C2×Q8C2×M1612yes—
410C2×D4—24no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—24no—
418C2×D4—24no—
419C2×D4—21no—
420C2×D4—22no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4—81no—
428C2×D4—81no—
429C2×D4—81no—
430C2×D4—81no—
431C2×D4C2×M1612yes—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—24no—
453C22×C4—22no—
454C22×C4—22no—
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—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—81no—
481C22×C4—81no—
482C22×C4—81no—
483C22×C4—81no—
484C22×C4—81no—
485C22×C4—81no—
486C22×C4—81no—
487C22×C4—81no—
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×C4C2×C22⋊C411yescharacteristic
496C22×C4C2×C22⋊C411yescharacteristic
497C22×C4C2×M1612yes—
498C22×C4C2×M1612yes—
499C22×C4C23×C411yescharacteristic
500C22×C4C22×D411yescharacteristic
501C22×C4C22×D411yescharacteristic
502M16—84no—
503M16—84no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
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—84no—
529C2×C8—84no—
530C4⋊C4—24no—
531C4⋊C4—24no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—24no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—41no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—41no—
543C4⋊C4—41no—
544C4⋊C4—41no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—41no—
548C4⋊C4—41no—
549C4⋊C4—41no—
550C4⋊C4—41no—
551C4⋊C4—42no—
552C4⋊C4—81no—
553C4⋊C4—81no—
554C4⋊C4C2×M1612yes—
555C4⋊C4C2×M1612yes—
556C22⋊C4—24no—
557C22⋊C4—24no—
558C22⋊C4—24no—
559C22⋊C4—24no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—41no—
564C22⋊C4—41no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—41no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C22⋊C4—41no—
571C22⋊C4—42no—
572C22⋊C4—81no—
573C22⋊C4—81no—
574C22⋊C4—81no—
575C22⋊C4—81no—
576C22⋊C4—81no—
577C22⋊C4—81no—
578C22⋊C4#9914yes—
579C42—22no—
580C42—22no—
581C42—22no—
582C42—22no—
583C42—41no—
584C42—41no—
585C42—41no—
586C42—41no—
587C42—41no—
588C42—41no—
589C42—42no—
590C42—42no—
591C42—42no—
592C42—81no—
593C42—81no—
594C42—81no—
595C42—81no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—22no—
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—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23#40712yes—
622C23C2×#9912yes—
623C23#41312yes—
624C23C22×C22⋊C411yescharacteristic
625Q8—42no—
626Q8—42no—
627Q8—44no—
628D4—42no—
629D4—42no—
630D4—44no—
631D4—44no—
632D4—44no—
633D4—48no—
634D4—84no—
635D4—84no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—24no—
649C2×C4—24no—
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—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—48no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—81no—
705C2×C4—81no—
706C2×C4—84no—
707C2×C4—162no—
708C2×C4—162no—
709C2×C4—162no—
710C2×C4#40712yes—
711C2×C4C2×#9912yes—
712C2×C4C2×#9912yes—
713C2×C4C22×M1611yescharacteristic
714C2×C4C22×M1611yescharacteristic
715C2×C4#57611yescharacteristic
716C2×C4#57711yescharacteristic
717C2×C4#57711yescharacteristic
718C2×C4#57811yescharacteristic
719C8—42no—
720C8—42no—
721C8—81no—
722C8—81no—
723C8—81no—
724C8—81no—
725C8—81no—
726C8—81no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—42no—
738C22—41no—
739C22—41no—
740C22—42no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22#146514yes—
755C22C2×#40711yescharacteristic
756C22C22×#9911yescharacteristic
757C22C2×#41311yescharacteristic
758C22#289711yescharacteristic
759C22#289811yescharacteristic
760C22#290111yescharacteristic
761C22#290111yescharacteristic
762C4—21no—
763C4—21no—
764C4—22no—
765C4—21no—
766C4—21no—
767C4—22no—
768C4—21no—
769C4—21no—
770C4—22no—
771C4—42no—
772C4—42no—
773C4—41no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—42no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C2—24no—
785C2—81no—
786C2—81no—
787C2—82no—
788C2C2×#146511yescharacteristic
789C2#1745311yescharacteristic
790C2#1745411yescharacteristic
791C2#1760311yescharacteristic
792C2#1760811yescharacteristic
793C2#1769011yescharacteristic
794C2#1777511yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radicalC2×#537C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22471C2semidirect
3. #22471C2semidirect
4. #7648C2semidirect
5. #7647C2semidirect
6. #7634C2semidirect
7. #7633C2semidirect
8. #7623C2semidirect
9. #7620C2semidirect
10. #7617C2semidirect
11. #7616C2semidirect
12. #7593C2semidirect
13. #7578C2semidirect
14. #7578C2semidirect
15. C2×#1271C2semidirect
219. C2×#41M16semidirect
319. C2×C4⋊C4M16semidirect

Maximal subgroups

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

subgroupindex
#342672
#224712
#76482
#76472
#76342
#76332
#76232
#76202
#76172
#76162
#75932
#75782
C2×#12712