Finite Group Databasebeta

← #357011

Subgroups — #357011

Order 512.

1688 conjugacy classes of subgroups.

The subgroup lattice has 917 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34141C211yesmaximal, characteristic
2C2×#1980C211yesmaximal, characteristic
3C2×#1963C211yesmaximal, characteristic
4C4⋊C4×M16C211yesmaximal, characteristic, complemented
5C2×#1759C211yesmaximal, characteristic, complemented
6C2×C4×#104C211yesmaximal, characteristic, complemented
7#13759C211yesmaximal, characteristic, complemented
8#10933C211yesmaximal, characteristic, complemented
9#10933C211yesmaximal, characteristic, complemented
10#10924C211yesmaximal, characteristic, complemented
11#10923C211yesmaximal, characteristic, complemented
12#10852C211yesmaximal, characteristic, complemented
13#10790C211yesmaximal, characteristic, complemented
14#10790C211yesmaximal, characteristic, complemented
15#10701C211yesmaximal, characteristic, complemented
16C2×#532C2211yescharacteristic
17C2×C4×#41C2211yescharacteristic
18C2×C4×#41C2211yescharacteristic
19C2×#423C2211yescharacteristic
20C22×#104C2211yescharacteristic
21C22×#104C2211yescharacteristic
22C22×#104C2211yescharacteristic
23C22×#104C2211yescharacteristic
24C22×#104C2211yescharacteristic
25C22×#104C2211yescharacteristic
26C22×#104C2211yescharacteristic
27C22×#104C2211yescharacteristic
28C2×C4×M16C2211yescharacteristic
29C2×C4×M16C2211yescharacteristic
30C2×C4×M16C2211yescharacteristic
31#2367C412yescomplemented
32#2367C412yescomplemented
33#2366C412yescomplemented
34#2365C412yescomplemented
35#2364—22no—
36#2361—22no—
37#2297C2211yescharacteristic
38#2297C2211yescharacteristic
39#2293—21no—
40#2290—21no—
41#2290—21no—
42C42×D4—21no—
43C4×#117C2211yescharacteristic
44C2×C4×C4⋊C4C2211yescharacteristic
45C2×C4×C4⋊C4C2211yescharacteristic
46C2×#376C2211yescharacteristic
47C2×#376C2211yescharacteristic
48C2×C43C2211yescharacteristic
49#1980C418yescomplemented
50#1963C418yescomplemented
51#1771—21no—
52#1771—21no—
53#1770—21no—
54C8×C4⋊C4—21no—
55#1759—24no—
56C4×#104—24no—
57C2×#339C2211yescharacteristic
58C2×#339C2211yescharacteristic
59C2×#339C2211yescharacteristic
60C2×#339C2211yescharacteristic
61C2×#339C2211yescharacteristic
62C2×#339C2211yescharacteristic
63C2×#339C2211yescharacteristic
64C2×#339C2211yescharacteristic
65#1728C2211yescharacteristic
66#1728C2211yescharacteristic
67#1436—22no—
68#1436—22no—
69C4×#95C2211yescharacteristic
70C4×#95C2211yescharacteristic
71C22×#41C2311yescharacteristic
72C22×#41C2311yescharacteristic
73C22×M16C2311yescharacteristic
74C22×M16C2311yescharacteristic
75C22×M16C2311yescharacteristic
76C22×M16C2311yescharacteristic
77#532—22no—
78#532—22no—
79#532C2×C414yes—
80#532C2×C414yes—
81C2×C4⋊Q8C2×C411yescharacteristic
82C2×#127C2×C411yescharacteristic
83C2×#124C2×C411yescharacteristic
84C2×#124C2×C411yescharacteristic
85C2×#121—21no—
86C2×#121—21no—
87C4×#41—22no—
88C4×#41—22no—
89C4×#41—22no—
90C4×#41—22no—
91C4×#41—41no—
92C4×#41—41no—
93C4×#41—41no—
94C4×#41—41no—
95C2×C4×Q8C2×C412yes—
96C2×C4×Q8C2×C412yes—
97C2×C4×D4—22no—
98C2×C4×D4—22no—
99C2×C4×D4—22no—
100C2×C4×D4—21no—
101C2×C4×D4—21no—
102C2×C4×D4C2×C412yes—
103C2×C4×D4C2×C412yes—
104C2×#117—21no—
105C2×#117—21no—
106C2×#117C2311yescharacteristic
107C2×#117C2311yescharacteristic
108C22×C4⋊C4—21no—
109C22×C4⋊C4D412yes—
110C22×C42—21no—
111C22×C42—21no—
112C22×C42—22no—
113C22×C42C2311yescharacteristic
114C22×C42C2311yescharacteristic
115C22×C42C2311yescharacteristic
116C22×C42C2311yescharacteristic
117C22×C42C2311yescharacteristic
118C22×C42C2311yescharacteristic
119C22×C42C2311yescharacteristic
120#423—22no—
121#423C2×C414yescomplemented
122C2×C4⋊C8—21no—
123C2×C4⋊C8—21no—
124C2×#104—22no—
125C2×#104—22no—
126C2×#104—22no—
127C2×#104—22no—
128C2×#104—22no—
129C2×#104—22no—
130C2×#104—22no—
131C2×#104—22no—
132C2×#104—41no—
133C2×#104—41no—
134C2×#104—41no—
135C2×#104—41no—
136C2×#104—41no—
137C2×#104—41no—
138C2×#104—41no—
139C2×#104—41no—
140C2×#104C2×C414yescomplemented
141C2×#104C2×C414yescomplemented
142C2×#104C2×C414yescomplemented
143C2×#104C2×C414yescomplemented
144C2×#104C2×C414yescomplemented
145C2×#104C2×C414yescomplemented
146C2×#104C2×C414yescomplemented
147C2×#104C2×C414yescomplemented
148C4×M16—22no—
149C4×M16—22no—
150C4×M16—22no—
151C4×M16—41no—
152C4×M16—41no—
153C4×M16C2×C414yescomplemented
154C2×#97—21no—
155C2×#97—21no—
156C2×#97—21no—
157C2×C4×C8—21no—
158C2×C4×C8—21no—
159C2×C4×C8—21no—
160#391C2×C412yes—
161#391C2×C412yes—
162#390—22no—
163#390C2×C412yes—
164#390C2×C412yes—
165#389—22no—
166#388—22no—
167#388—22no—
168#388—22no—
169#388—22no—
170#387—22no—
171#387—22no—
172#386—22no—
173#386—22no—
174#386—22no—
175#386—22no—
176#385—22no—
177#385—22no—
178C4×C4⋊C4—22no—
179C4×C4⋊C4—22no—
180C4×C4⋊C4C2×C412yes—
181C4×C4⋊C4C2×C412yes—
182C4×C4⋊C4C2×C412yes—
183C4×C4⋊C4C2×C412yes—
184C4×C4⋊C4C2×C414yescomplemented
185C4×C4⋊C4D411yescharacteristic
186C4×C4⋊C4D411yescharacteristic
187C4×C4⋊C4D411yescharacteristic
188C4×C4⋊C4D411yescharacteristic
189C4×C22⋊C4—21no—
190C4×C22⋊C4—21no—
191C4×C22⋊C4—21no—
192C4×C22⋊C4—21no—
193C4×C22⋊C4—21no—
194C4×C22⋊C4—21no—
195C4×C22⋊C4—22no—
196C4×C22⋊C4—22no—
197#376—21no—
198#376—22no—
199#376—22no—
200#376—41no—
201#376C2×C414yescomplemented
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—22no—
206C2×#95—22no—
207C2×#95—22no—
208C2×#95D412yes—
209C43—21no—
210C43—22no—
211C43—41no—
212#339—22no—
213#339—22no—
214#339—22no—
215#339—22no—
216#339—22no—
217#339—41no—
218#339—41no—
219#339D414yescomplemented
220#336—21no—
221#336—21no—
222#336—21no—
223#336—21no—
224C2×#41—21no—
225C2×#41—21no—
226C2×#41—21no—
227C2×#41—21no—
228C2×#41—21no—
229C2×#41—21no—
230C2×#41—21no—
231C2×#41—21no—
232C2×#41—21no—
233C2×#41—21no—
234C2×#41—21no—
235C2×#41—21no—
236C2×#41—21no—
237C2×#41—21no—
238C2×#41—21no—
239C2×#41—21no—
240C2×#41—21no—
241C2×#41—21no—
242C2×#41—21no—
243C2×#41—21no—
244C2×#41C22×C412yes—
245C2×#41C22×C412yes—
246C2×#41C22×C412yes—
247C2×#41C22×C412yes—
248C22×Q8C22×C411yescharacteristic
249C22×Q8C22×C411yescharacteristic
250C22×D4—21no—
251C22×D4—21no—
252C22×D4—21no—
253C22×D4—21no—
254C22×D4C22×C411yescharacteristic
255C22×D4C22×C411yescharacteristic
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4C2×D412yes—
265C23×C4C2×D412yes—
266C23×C4C2×D411yescharacteristic
267C23×C4C2×D411yescharacteristic
268C23×C4C2411yescharacteristic
269C2×M16—21no—
270C2×M16—21no—
271C2×M16—21no—
272C2×M16—21no—
273C2×M16—21no—
274C2×M16—21no—
275C2×M16—21no—
276C2×M16—21no—
277C2×M16—21no—
278C2×M16—21no—
279C2×M16—21no—
280C2×M16—21no—
281C2×M16—21no—
282C2×M16—21no—
283C2×M16—21no—
284C2×M16—21no—
285C2×M16—21no—
286C2×M16—21no—
287C2×M16C22×C412yes—
288C2×M16C22×C412yes—
289C2×M16C22×C412yes—
290C2×M16C22×C412yes—
291C2×M16C2×D412yes—
292C2×M16#4112yes—
293C22×C8—21no—
294C22×C8—21no—
295C22×C8—21no—
296C22×C8—21no—
297C4⋊Q8—22no—
298C4⋊Q8C4214yescomplemented
299#127—22no—
300#127C4214yescomplemented
301#124—22no—
302#124—22no—
303#124C4214yescomplemented
304#124C4214yescomplemented
305#121—24no—
306#121—24no—
307#121—24no—
308#121—24no—
309C4×Q8—24no—
310C4×Q8—24no—
311C4×Q8—42no—
312C4×Q8—42no—
313C4×D4—24no—
314C4×D4—24no—
315C4×D4—24no—
316C4×D4—24no—
317C4×D4—24no—
318C4×D4—24no—
319C4×D4—42no—
320C4×D4—42no—
321C4×D4—44no—
322C4×D4—44no—
323C4×D4—44no—
324C4×D4—44no—
325C4×D4—48no—
326#117—21no—
327#117—21no—
328#117—21no—
329#117—21no—
330#117—21no—
331#117—21no—
332#117—42no—
333#117—42no—
334#117—42no—
335#117—42no—
336#117C2×D412yes—
337#117#4112yes—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4C22⋊C412yes—
346C2×C4⋊C4C22⋊C412yes—
347C2×C4⋊C4C22⋊C412yes—
348C2×C4⋊C4C22⋊C412yes—
349C2×C4⋊C4C22×C412yes—
350C2×C4⋊C4C22×C412yes—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—22no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—44no—
400C2×C42—44no—
401C2×C42—44no—
402C2×C42C22×C412yes—
403C2×C42C22×C412yes—
404C2×C42C22×C412yes—
405C2×C42C22×C412yes—
406C2×C42C22×C412yes—
407C2×C42C22×C412yes—
408C2×C42C22×C411yescharacteristic
409C2×C42C22×C411yescharacteristic
410C2×C42C22×C412yes—
411C2×C42C22×C412yes—
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D412yes—
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42#4112yes—
420C2×C42#4112yes—
421C2×C42#4112yes—
422C4⋊C8—24no—
423C4⋊C8—24no—
424#104—28no—
425#104—28no—
426#104—28no—
427#104—28no—
428#104—44no—
429#104—44no—
430#104—44no—
431#104—44no—
432#97—24no—
433#97—42no—
434#97—42no—
435C4×C8—24no—
436C4×C8—42no—
437C4×C8—42no—
438#95—22no—
439#95—22no—
440#95—22no—
441#95—22no—
442#95—22no—
443#95—22no—
444#95—24no—
445#95—24no—
446#95—24no—
447#95—44no—
448#95—44no—
449#95—44no—
450#95C22⋊C412yes—
451#95C22⋊C412yes—
452#95C22⋊C412yes—
453#95C22⋊C412yes—
454C24—21no—
455C24—21no—
456C24C22×D411yescharacteristic
457#41—22no—
458#41—22no—
459#41—22no—
460#41—22no—
461#41—22no—
462#41—22no—
463#41—22no—
464#41—22no—
465#41—22no—
466#41—22no—
467#41—22no—
468#41—22no—
469#41—22no—
470#41—22no—
471#41—22no—
472#41—22no—
473#41—41no—
474#41—41no—
475#41—41no—
476#41—41no—
477#41—41no—
478#41—41no—
479#41—41no—
480#41—41no—
481#41—41no—
482#41—41no—
483#41—41no—
484#41—41no—
485#41—41no—
486#41—41no—
487#41—41no—
488#41—41no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C2×C4212yes—
500C2×Q8C2×C4212yes—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—21no—
506C2×D4—21no—
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—24no—
516C2×D4—24no—
517C2×D4—44no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4—41no—
523C2×D4—41no—
524C2×D4—41no—
525C2×D4—41no—
526C2×D4—82no—
527C2×D4C2×C4212yes—
528C2×D4C2×C4212yes—
529C22×C4—24no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—44no—
579C22×C4—82no—
580C22×C4—82no—
581C22×C4C2×C22⋊C412yes—
582C22×C4C2×C22⋊C412yes—
583C22×C4C2×C22⋊C412yes—
584C22×C4C2×C22⋊C411yescharacteristic
585C22×C4C2×C22⋊C411yescharacteristic
586C22×C4C2×C22⋊C411yescharacteristic
587C22×C4C2×C22⋊C411yescharacteristic
588C22×C4C2×C22⋊C412yes—
589C22×C4C4×D412yes—
590C22×C4C4×D412yes—
591C22×C4C4×D412yes—
592C22×C4C4×D412yes—
593C22×C4C23×C411yescharacteristic
594C22×C4C23×C411yescharacteristic
595C22×C4C23×C411yescharacteristic
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C2×#4111yescharacteristic
599C22×C4C2×#4111yescharacteristic
600C22×C4C2×#4111yescharacteristic
601C22×C4C2×#4111yescharacteristic
602C22×C4C2×#4111yescharacteristic
603C22×C4H(5,𝔽2)11yescharacteristic
604C22×C4H(5,𝔽2)11yescharacteristic
605C22×C4H(5,𝔽2)11yescharacteristic
606C22×C42−1+411yescharacteristic
607M16—22no—
608M16—22no—
609M16—22no—
610M16—22no—
611M16—22no—
612M16—22no—
613M16—22no—
614M16—22no—
615M16—22no—
616M16—41no—
617M16—41no—
618M16—41no—
619M16—41no—
620M16—41no—
621M16—41no—
622M16C4×D414yescomplemented
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—41no—
630C2×C8—41no—
631C2×C8—41no—
632C2×C8—41no—
633C2×C8—41no—
634C2×C8—41no—
635C4⋊C4—22no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—24no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4—44no—
645C4⋊C4—44no—
646C4⋊C4—48no—
647C4⋊C4C4×D414yes—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—41no—
658C22⋊C4—41no—
659C22⋊C4—44no—
660C22⋊C4—82no—
661C22⋊C4—82no—
662C42—22no—
663C42—22no—
664C42—22no—
665C42—22no—
666C42—22no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—22no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—22no—
677C42—22no—
678C42—22no—
679C42—22no—
680C42—22no—
681C42—22no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—44no—
686C42—44no—
687C42—44no—
688C42—416no—
689C42—41no—
690C42—41no—
691C42—41no—
692C42—41no—
693C42—41no—
694C42—41no—
695C42—41no—
696C42—41no—
697C42—82no—
698C42C2×C4212yes—
699C42C2×C4212yes—
700C42#11712yes—
701C42#11712yes—
702C42C4×D412yes—
703C42C4×D412yes—
704C42C4×D412yes—
705C42C4×D412yes—
706C42C4×D414yescomplemented
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23C22×C22⋊C411yescharacteristic
720C23C2×C4×D411yescharacteristic
721C23C2×C4×D411yescharacteristic
722C23D4211yescharacteristic
723C23#54611yescharacteristic
724C23#54811yescharacteristic
725C23#55011yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—22no—
729Q8—22no—
730Q8—41no—
731Q8—41no—
732Q8—41no—
733Q8—41no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—48no—
739D4—42no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—42no—
744D4—42no—
745D4—42no—
746D4—42no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—84no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—88no—
810C2×C4—82no—
811C2×C4—82no—
812C2×C4—88no—
813C2×C4—82no—
814C2×C4—82no—
815C2×C4—82no—
816C2×C4—82no—
817C2×C4C4×C22⋊C412yes—
818C2×C4C4×C22⋊C412yes—
819C2×C4C4×C22⋊C412yes—
820C2×C4C4×C22⋊C412yes—
821C2×C4#42114yes—
822C2×C4C22×C4211yescharacteristic
823C2×C4C2×#11711yescharacteristic
824C2×C4C2×C4×D411yescharacteristic
825C2×C4C2×C4×D411yescharacteristic
826C2×C4C2×C4×D411yescharacteristic
827C2×C4C2×C4×D411yescharacteristic
828C2×C4C2×C4×D411yescharacteristic
829C2×C4C4×#4111yescharacteristic
830C2×C4C4×#4111yescharacteristic
831C2×C4C4×#4111yescharacteristic
832C2×C4#51811yescharacteristic
833C2×C4#51811yescharacteristic
834C2×C4#51811yescharacteristic
835C2×C4#52011yescharacteristic
836C2×C4#52011yescharacteristic
837C2×C4#52011yescharacteristic
838C2×C4D4211yescharacteristic
839C2×C4#54611yescharacteristic
840C2×C4#54711yescharacteristic
841C2×C4#54811yescharacteristic
842C2×C4#55011yescharacteristic
843C2×C4#55011yescharacteristic
844C2×C4#55311yescharacteristic
845C2×C4#55311yescharacteristic
846C2×C4#55511yescharacteristic
847C2×C4#55611yescharacteristic
848C2×C4#55911yescharacteristic
849C2×C4#55911yescharacteristic
850C8—24no—
851C8—42no—
852C8—42no—
853C8—42no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—82no—
869C22—82no—
870C22—82no—
871C22—82no—
872C22C2×C4×C22⋊C411yescharacteristic
873C22D4×C22⋊C411yescharacteristic
874C22#234111yescharacteristic
875C22#236111yescharacteristic
876C22#236311yescharacteristic
877C22#236611yescharacteristic
878C22#236711yescharacteristic
879C22C2×#42112yes—
880C22#290112yes—
881C4—24no—
882C4—22no—
883C4—22no—
884C4—22no—
885C4—22no—
886C4—44no—
887C4—44no—
888C4—42no—
889C4—42no—
890C4—42no—
891C4—44no—
892C4—42no—
893C4—42no—
894C4—82no—
895C4—82no—
896C4—82no—
897C4C42×D411yescharacteristic
898C4#227511yescharacteristic
899C4#235411yescharacteristic
900C4#235711yescharacteristic
901C4#236111yescharacteristic
902C4#236311yescharacteristic
903C4#236611yescharacteristic
904C4#236711yescharacteristic
905C2—21no—
906C2—21no—
907C2—21no—
908C2—21no—
909C2—82no—
910C2—82no—
911C2#1382011yescharacteristic
912C2C4×#42111yescharacteristic
913C2#2040511yescharacteristic
914C2#2243412yes—
915C2#2255112yes—
subgroupG/H
centerC22×C4C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
socleC23C22×C22⋊C4
prime radicalC2×#532C22
LCSG ▷ C2×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
4. C4⋊C4×M16C2semidirect
5. C2×#1759C2semidirect
6. C2×C4×#104C2semidirect
7. #13759C2semidirect
8. #10933C2semidirect
9. #10933C2semidirect
10. #10924C2semidirect
11. #10923C2semidirect
12. #10852C2semidirect
13. #10790C2semidirect
14. #10790C2semidirect
15. #10701C2semidirect
31. #2367C4semidirect
32. #2367C4semidirect
33. #2366C4semidirect
34. #2365C4semidirect
49. #1980C4semidirect
50. #1963C4semidirect
121. #423C2×C4semidirect
140. C2×#104C2×C4semidirect
141. C2×#104C2×C4semidirect
142. C2×#104C2×C4semidirect
143. C2×#104C2×C4semidirect
144. C2×#104C2×C4semidirect
145. C2×#104C2×C4semidirect
146. C2×#104C2×C4semidirect
147. C2×#104C2×C4semidirect
153. C4×M16C2×C4semidirect
184. C4×C4⋊C4C2×C4semidirect
201. #376C2×C4semidirect
219. #339D4semidirect
298. C4⋊Q8C42semidirect
300. #127C42semidirect
303. #124C42semidirect
304. #124C42semidirect
622. M16C4×D4semidirect
706. C42C4×D4semidirect

Maximal subgroups

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

subgroupindex
#341412
C2×#19802
C2×#19632
C4⋊C4×M162
C2×#17592
C2×C4×#1042
#137592
#109332
#109242
#109232
#108522
#107902
#107012