Finite Group Databasebeta

← #356207

Subgroups — #356207

Order 512.

1640 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4⋊C4×#41C211yesmaximal, characteristic
2C2×#1806C211yesmaximal, characteristic
3C4⋊C4×M16C211yesmaximal, characteristic, complemented
4C2×#1759C211yesmaximal, characteristic
5C2×#1759C211yesmaximal, characteristic
6C2×C4×#104C211yesmaximal, characteristic
7#13759C211yesmaximal, characteristic, complemented
8#10886C211yesmaximal, characteristic, complemented
9#10886C211yesmaximal, characteristic, complemented
10#10879C211yesmaximal, characteristic, complemented
11#10878C211yesmaximal, characteristic, complemented
12#10851C211yesmaximal, characteristic, complemented
13#10840C211yesmaximal, characteristic, complemented
14#10790C211yesmaximal, characteristic
15#10790C211yesmaximal, characteristic
16C2×C4×#41C2211yescharacteristic
17C2×C4×#41C2211yescharacteristic
18C2×C4×#41C2211yescharacteristic
19C2×#423C2211yescharacteristic
20C22×#104C2211yescharacteristic
21C22×#104C2211yescharacteristic
22C22×#104C2211yescharacteristic
23C22×#104C2211yescharacteristic
24C2×C4×M16C2211yescharacteristic
25C2×C4×M16C2211yescharacteristic
26C2×C4×M16C2211yescharacteristic
27#2351C412yescomplemented
28Q8×C4⋊C4C412yescomplemented
29#2349—22no—
30#2349C412yescomplemented
31D4×C4⋊C4—22no—
32D4×C4⋊C4C412yescomplemented
33#2296—21no—
34#2296—21no—
35#2296C2211yescharacteristic
36#2296C2211yescharacteristic
37#2285—21no—
38#2285C2211yescharacteristic
39C2×C4×C4⋊C4—21no—
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×#376C2211yescharacteristic
43C2×#376C2211yescharacteristic
44C2×C43C2211yescharacteristic
45#1806C418yescomplemented
46#1771—21no—
47#1771—21no—
48#1770—21no—
49C8×C4⋊C4—21no—
50#1759—24no—
51#1759C418yescomplemented
52C4×#104—24no—
53C2×#339C2211yescharacteristic
54C2×#339C2211yescharacteristic
55C2×#339C2211yescharacteristic
56C2×#339C2211yescharacteristic
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×M16C2311yescharacteristic
73C22×M16C2311yescharacteristic
74C22×M16C2311yescharacteristic
75C22×M16C2311yescharacteristic
76C4×#41—22no—
77C4×#41—22no—
78C4×#41—22no—
79C4×#41—22no—
80C4×#41—22no—
81C4×#41—22no—
82C4×#41—41no—
83C4×#41—41no—
84C4×#41—41no—
85C4×#41—41no—
86C4×#41C2×C414yes—
87C4×#41C2×C414yes—
88C2×C4×Q8C2×C412yes—
89C2×C4×Q8C2×C412yes—
90C2×C4×Q8C2×C411yescharacteristic
91C2×C4×Q8C2×C411yescharacteristic
92C2×C4×D4—21no—
93C2×C4×D4—21no—
94C2×C4×D4—22no—
95C2×C4×D4—22no—
96C2×C4×D4C2×C412yes—
97C2×C4×D4C2×C412yes—
98C2×C4×D4C2×C411yescharacteristic
99C2×C4×D4C2×C411yescharacteristic
100C2×#117—21no—
101C2×#117—21no—
102C2×#117—21no—
103C2×#117C2311yescharacteristic
104C2×#117C2311yescharacteristic
105C2×#117C2311yescharacteristic
106C22×C4⋊C4—21no—
107C22×C4⋊C4—22no—
108C22×C4⋊C4D412yes—
109C22×C42—21no—
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×#104C2×C414yes—
131C2×#104C2×C414yes—
132C2×#104C2×C414yes—
133C2×#104C2×C414yes—
134C2×#104D414yes—
135C2×#104Q814yes—
136C4×M16—22no—
137C4×M16—22no—
138C4×M16—22no—
139C4×M16—41no—
140C4×M16—41no—
141C4×M16C2×C414yescomplemented
142C2×#97—21no—
143C2×#97—21no—
144C2×#97—21no—
145C2×C4×C8—21no—
146C2×C4×C8—21no—
147C2×C4×C8—21no—
148#389—22no—
149#389—22no—
150#389—22no—
151#389—22no—
152#389C2×C412yes—
153#389C2×C412yes—
154#389C2×C412yes—
155#389C2×C412yes—
156#385—22no—
157#385—22no—
158#385—22no—
159#385—22no—
160#385—22no—
161#385—22no—
162#384—22no—
163#384C2×C412yes—
164#382—22no—
165#382C2×C412yes—
166#380—21no—
167#380—21no—
168#380—22no—
169#380—22no—
170C4×C4⋊C4—22no—
171C4×C4⋊C4—21no—
172C4×C4⋊C4—21no—
173C4×C4⋊C4—21no—
174C4×C4⋊C4—21no—
175C4×C4⋊C4—21no—
176C4×C4⋊C4—21no—
177C4×C4⋊C4—22no—
178C4×C4⋊C4—22no—
179C4×C4⋊C4C2×C412yes—
180C4×C4⋊C4C2×C412yes—
181C4×C4⋊C4C2×C414yescomplemented
182C4×C4⋊C4D411yescharacteristic
183C4×C4⋊C4D411yescharacteristic
184C4×C4⋊C4D411yescharacteristic
185C4×C4⋊C4D411yescharacteristic
186#376—22no—
187#376—22no—
188#376—41no—
189#376C2×C414yescomplemented
190C2×#95—21no—
191C2×#95—21no—
192C2×#95—21no—
193C2×#95—22no—
194C2×#95—22no—
195C2×#95—22no—
196C2×#95—22no—
197C2×#95D412yes—
198C43—22no—
199C43—41no—
200#339—22no—
201#339—22no—
202#339—22no—
203#339—22no—
204#339—41no—
205#339—41no—
206#339—41no—
207#339—41no—
208#339C2×C414yescomplemented
209#339C2×C414yescomplemented
210#339C2×C414yescomplemented
211#339C2×C414yescomplemented
212#336—21no—
213#336—21no—
214#336—21no—
215#336—21no—
216C2×#41—21no—
217C2×#41—21no—
218C2×#41—21no—
219C2×#41—21no—
220C2×#41—21no—
221C2×#41—21no—
222C2×#41C22×C412yes—
223C2×#41C22×C412yes—
224C2×#41C2×D412yes—
225C2×#41C2×Q812yes—
226C2×#41#4112yes—
227C2×#41#4112yes—
228C22×Q8C22×C411yescharacteristic
229C22×D4—21no—
230C22×D4C22×C411yescharacteristic
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4C2×D412yes—
241C23×C4C2×D412yes—
242C23×C4C2×D411yescharacteristic
243C23×C4C2×D411yescharacteristic
244C23×C4C2411yescharacteristic
245C2×M16—21no—
246C2×M16—21no—
247C2×M16—21no—
248C2×M16—21no—
249C2×M16—21no—
250C2×M16—21no—
251C2×M16—21no—
252C2×M16—21no—
253C2×M16—21no—
254C2×M16—21no—
255C2×M16—21no—
256C2×M16—21no—
257C2×M16—21no—
258C2×M16—21no—
259C2×M16—21no—
260C2×M16—21no—
261C2×M16—21no—
262C2×M16—21no—
263C2×M16C22×C412yes—
264C2×M16C22×C412yes—
265C2×M16C22×C412yes—
266C2×M16C22×C412yes—
267C2×M16C2×D412yes—
268C2×M16C2×Q812yes—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C4×Q8—22no—
274C4×Q8—22no—
275C4×Q8—24no—
276C4×Q8—24no—
277C4×Q8—42no—
278C4×Q8—42no—
279C4×Q8C4214yescomplemented
280C4×Q8C4214yescomplemented
281C4×D4—24no—
282C4×D4—24no—
283C4×D4—24no—
284C4×D4—24no—
285C4×D4—24no—
286C4×D4—24no—
287C4×D4—22no—
288C4×D4—22no—
289C4×D4—42no—
290C4×D4—42no—
291C4×D4—44no—
292C4×D4—44no—
293C4×D4—44no—
294C4×D4—44no—
295C4×D4C4214yescomplemented
296C4×D4C4214yescomplemented
297#117—21no—
298#117—21no—
299#117—24no—
300#117—24no—
301#117—21no—
302#117—21no—
303#117—21no—
304#117—21no—
305#117—21no—
306#117—21no—
307#117—21no—
308#117—21no—
309#117—42no—
310#117—42no—
311#117—42no—
312#117—42no—
313#117C22×C412yes—
314#117C22×C412yes—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—48no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4C22⋊C412yes—
330C2×C4⋊C4C22⋊C412yes—
331C2×C4⋊C4C22⋊C412yes—
332C2×C4⋊C4C22⋊C412yes—
333C2×C4⋊C4C22×C412yes—
334C2×C4⋊C4C22×C412yes—
335C2×C4⋊C4C22×C411yescharacteristic
336C2×C4⋊C4C22×C411yescharacteristic
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C42—21no—
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—21no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
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—22no—
373C2×C42—22no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—42no—
380C2×C42—42no—
381C2×C42—42no—
382C2×C42—42no—
383C2×C42—44no—
384C2×C42—44no—
385C2×C42—44no—
386C2×C42C22×C412yes—
387C2×C42C22×C412yes—
388C2×C42C22×C412yes—
389C2×C42C22×C412yes—
390C2×C42C22×C412yes—
391C2×C42C22×C412yes—
392C2×C42C22×C411yescharacteristic
393C2×C42C22×C411yescharacteristic
394C2×C42C22×C412yes—
395C2×C42C22×C412yes—
396C2×C42C2×D411yescharacteristic
397C2×C42C2×D411yescharacteristic
398C2×C42C2×D411yescharacteristic
399C2×C42C2×D411yescharacteristic
400C2×C42C2×D412yes—
401C2×C42C2×D411yescharacteristic
402C2×C42C2×D411yescharacteristic
403C2×C42C2×Q812yes—
404C2×C42#4112yes—
405C2×C42#4112yes—
406C4⋊C8—24no—
407C4⋊C8—24no—
408#104—28no—
409#104—28no—
410#104—28no—
411#104C4⋊C4116yescomplemented
412#97—24no—
413#97—42no—
414#97—42no—
415C4×C8—24no—
416C4×C8—42no—
417C4×C8—42no—
418#95—22no—
419#95—22no—
420#95—22no—
421#95—22no—
422#95—22no—
423#95—22no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—44no—
428#95—44no—
429#95—44no—
430#95C22⋊C412yes—
431#95C22⋊C412yes—
432#95C22⋊C412yes—
433#95C22⋊C412yes—
434C24—21no—
435C24C22×D411yescharacteristic
436#41—22no—
437#41—22no—
438#41—22no—
439#41—22no—
440#41—22no—
441#41—22no—
442#41—22no—
443#41—22no—
444#41—22no—
445#41—22no—
446#41—22no—
447#41—22no—
448#41C2×C4⋊C414yes—
449#41#11714yes—
450#41C4×D414yes—
451#41C4×Q814yes—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8C2×C4212yes—
456C2×Q8C4×D412yes—
457C2×Q8C4×Q812yes—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4C2×C4212yes—
468C2×D4C4×D412yes—
469C2×D4C4×Q812yes—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—44no—
518C22×C4—82no—
519C22×C4—82no—
520C22×C4—82no—
521C22×C4C2×C22⋊C412yes—
522C22×C4C2×C22⋊C412yes—
523C22×C4C2×C22⋊C412yes—
524C22×C4C2×C22⋊C411yescharacteristic
525C22×C4C2×C22⋊C411yescharacteristic
526C22×C4C2×C22⋊C411yescharacteristic
527C22×C4C2×C22⋊C411yescharacteristic
528C22×C4C2×C22⋊C412yes—
529C22×C4C4×D412yes—
530C22×C4C4×D412yes—
531C22×C4C4×D412yes—
532C22×C4C4×D412yes—
533C22×C4C23×C411yescharacteristic
534C22×C4C23×C411yescharacteristic
535C22×C4C23×C411yescharacteristic
536C22×C4C22×D411yescharacteristic
537C22×C4C22×D411yescharacteristic
538C22×C4C22×Q811yescharacteristic
539C22×C4C2×#4111yescharacteristic
540C22×C4C2×#4111yescharacteristic
541C22×C4C2×#4111yescharacteristic
542C22×C4C2×#4111yescharacteristic
543C22×C4H(5,𝔽2)11yescharacteristic
544C22×C4H(5,𝔽2)11yescharacteristic
545C22×C42−1+411yescharacteristic
546C22×C42−1+411yescharacteristic
547M16—22no—
548M16—22no—
549M16—22no—
550M16—22no—
551M16—22no—
552M16—22no—
553M16—22no—
554M16—22no—
555M16—22no—
556M16—41no—
557M16—41no—
558M16—41no—
559M16—41no—
560M16—41no—
561M16—41no—
562M16C2×C4⋊C414yescomplemented
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—41no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—44no—
588C4⋊C4—44no—
589C4⋊C4—44no—
590C4⋊C4—48no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—82no—
594C4⋊C4—82no—
595C4⋊C4—82no—
596C4⋊C4C2×C4212yes—
597C4⋊C4C2×C4212yes—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—41no—
605C22⋊C4—41no—
606C22⋊C4—41no—
607C22⋊C4—41no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—22no—
624C42—22no—
625C42—24no—
626C42—24no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—44no—
634C42—44no—
635C42—416no—
636C42—41no—
637C42—41no—
638C42—41no—
639C42—41no—
640C42—41no—
641C42—41no—
642C42—41no—
643C42—41no—
644C42—41no—
645C42—41no—
646C42C2×C4212yes—
647C42C2×C4212yes—
648C42C2×C4⋊C414yescomplemented
649C42#11712yes—
650C42#11712yes—
651C42C4×D412yes—
652C42C4×D412yes—
653C42C4×D412yes—
654C42C4×D412yes—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23C22×C22⋊C411yescharacteristic
663C23C2×C4×D411yescharacteristic
664C23C2×C4×D411yescharacteristic
665C23D4211yescharacteristic
666C23#54611yescharacteristic
667C23#54811yescharacteristic
668C23D4×Q811yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8C4×C4⋊C414yes—
673D4—24no—
674D4—24no—
675D4—24no—
676D4—24no—
677D4—22no—
678D4—22no—
679D4—22no—
680D4C4×C4⋊C414yes—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—48no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—84no—
737C2×C4—88no—
738C2×C4—82no—
739C2×C4—82no—
740C2×C4—88no—
741C2×C4—82no—
742C2×C4—82no—
743C2×C4—82no—
744C2×C4—82no—
745C2×C4C4×C22⋊C412yes—
746C2×C4C4×C22⋊C412yes—
747C2×C4C4×C22⋊C412yes—
748C2×C4C4×C22⋊C412yes—
749C2×C4#42114yes—
750C2×C4C22×C4211yescharacteristic
751C2×C4C22×C4⋊C411yescharacteristic
752C2×C4C2×#11711yescharacteristic
753C2×C4C2×#11711yescharacteristic
754C2×C4C2×C4×D411yescharacteristic
755C2×C4C2×C4×D411yescharacteristic
756C2×C4C2×C4×D411yescharacteristic
757C2×C4C2×C4×D411yescharacteristic
758C2×C4C2×C4×Q811yescharacteristic
759C2×C4C2×C4×Q811yescharacteristic
760C2×C4#51811yescharacteristic
761C2×C4#51911yescharacteristic
762C2×C4#52011yescharacteristic
763C2×C4#52011yescharacteristic
764C2×C4#52011yescharacteristic
765C2×C4#52011yescharacteristic
766C2×C4D4211yescharacteristic
767C2×C4#54611yescharacteristic
768C2×C4#54711yescharacteristic
769C2×C4#54711yescharacteristic
770C2×C4#54811yescharacteristic
771C2×C4D4×Q811yescharacteristic
772C2×C4#55211yescharacteristic
773C2×C4#55211yescharacteristic
774C2×C4#55311yescharacteristic
775C2×C4#55311yescharacteristic
776C2×C4#55411yescharacteristic
777C2×C4#55411yescharacteristic
778C8—24no—
779C8—42no—
780C8—42no—
781C8—42no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—24no—
791C22—44no—
792C22—44no—
793C22—42no—
794C22—42no—
795C22C2×C4×C22⋊C411yescharacteristic
796C22D4×C22⋊C411yescharacteristic
797C22Q8×C22⋊C411yescharacteristic
798C22D4×C4⋊C411yescharacteristic
799C22#235211yescharacteristic
800C22#236011yescharacteristic
801C22#236111yescharacteristic
802C22C2×#42112yes—
803C22#290112yes—
804C4—24no—
805C4—22no—
806C4—22no—
807C4—22no—
808C4—22no—
809C4—24no—
810C4—44no—
811C4—44no—
812C4—42no—
813C4—42no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—82no—
818C4—82no—
819C4—82no—
820C4—82no—
821C4C2×C4×C4⋊C411yescharacteristic
822C4#227411yescharacteristic
823C4#234411yescharacteristic
824C4#234511yescharacteristic
825C4D4×C4⋊C411yescharacteristic
826C4#235211yescharacteristic
827C4#236011yescharacteristic
828C4#236111yescharacteristic
829C2—21no—
830C2—21no—
831C2—21no—
832C2—21no—
833C2—44no—
834C2C22⋊C4×C4⋊C411yescharacteristic
835C2C4×#42111yescharacteristic
836C2#2040511yescharacteristic
837C2#2243412yes—
838C2#2252912yes—
subgroupG/H
centerC22×C4C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
socleC23C22×C22⋊C4
prime radicalC22×#41C23
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
3. C4⋊C4×M16C2semidirect
7. #13759C2semidirect
8. #10886C2semidirect
9. #10886C2semidirect
10. #10879C2semidirect
11. #10878C2semidirect
12. #10851C2semidirect
13. #10840C2semidirect
27. #2351C4semidirect
28. Q8×C4⋊C4C4semidirect
30. #2349C4semidirect
32. D4×C4⋊C4C4semidirect
45. #1806C4semidirect
51. #1759C4semidirect
121. #423C2×C4semidirect
141. C4×M16C2×C4semidirect
181. C4×C4⋊C4C2×C4semidirect
189. #376C2×C4semidirect
208. #339C2×C4semidirect
209. #339C2×C4semidirect
210. #339C2×C4semidirect
211. #339C2×C4semidirect
279. C4×Q8C42semidirect
280. C4×Q8C42semidirect
295. C4×D4C42semidirect
296. C4×D4C42semidirect
411. #104C4⋊C4semidirect
562. M16C2×C4⋊C4semidirect
648. C42C2×C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×#412
C2×#18062
C4⋊C4×M162
C2×#17592
C2×C4×#1042
#137592
#108862
#108792
#108782
#108512
#108402
#107902