Finite Group Databasebeta

← #360875

Subgroups — #360875

Order 512.

1508 conjugacy classes of subgroups.

The subgroup lattice has 1043 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4⋊C4×#41C211yesmaximal, characteristic
2#21023C211yesmaximal, characteristic, complemented
3C2×#1806C211yesmaximal, characteristic
4C2×C4×#104C211yesmaximal, characteristic
5C4×#387C211yesmaximal, characteristic, complemented
6#11370C211yesmaximal, characteristic, complemented
7#11359C211yesmaximal, characteristic, complemented
8#11226C211yesmaximal, characteristic, complemented
9#11209C211yesmaximal, characteristic, complemented
10#10886C211yesmaximal, characteristic, complemented
11#10878C211yesmaximal, characteristic, complemented
12#10790C211yesmaximal, characteristic
13#10790C211yesmaximal, characteristic
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
25#2351C411yescharacteristic, complemented
26#2351C411yescharacteristic, complemented
27Q8×C4⋊C4C411yescharacteristic, complemented
28Q8×C4⋊C4C411yescharacteristic, complemented
29#2349—21no—
30#2349—21no—
31#2349C411yescharacteristic, complemented
32#2349C411yescharacteristic, complemented
33D4×C4⋊C4—21no—
34D4×C4⋊C4—21no—
35D4×C4⋊C4C411yescharacteristic, complemented
36D4×C4⋊C4C411yescharacteristic, complemented
37#2296—21no—
38#2296—21no—
39#2296C2211yescharacteristic
40#2296C2211yescharacteristic
41C2×#387—21no—
42#2285—21no—
43#2285C2211yescharacteristic
44C2×C4×C4⋊C4—21no—
45C2×C4×C4⋊C4C2211yescharacteristic
46C2×C4×C4⋊C4C2211yescharacteristic
47C2×C43C2211yescharacteristic
48#1917—21no—
49#1917—21no—
50#1916—21no—
51#1916—21no—
52#1806—24no—
53C4×#104—24no—
54C2×#339C2211yescharacteristic
55C2×#339C2211yescharacteristic
56C2×#339C2211yescharacteristic
57C2×#339C2211yescharacteristic
58C2×#339C2211yescharacteristic
59C2×#339C2211yescharacteristic
60C2×#339C2211yescharacteristic
61C2×#339C2211yescharacteristic
62C2×#339C2211yescharacteristic
63C2×#339C2211yescharacteristic
64C2×#339C2211yescharacteristic
65C2×#339C2211yescharacteristic
66#1728C2211yescharacteristic
67#1728C2211yescharacteristic
68#1728C2211yescharacteristic
69#1728C2211yescharacteristic
70#1436—21no—
71#1436—21no—
72#1434—21no—
73C4×#95C2211yescharacteristic
74C4×#95C2211yescharacteristic
75C4×#95C2211yescharacteristic
76C4×#95C2211yescharacteristic
77C22×#41C2311yescharacteristic
78C22×M16C2311yescharacteristic
79C22×M16C2311yescharacteristic
80C22×M16C2311yescharacteristic
81C22×M16C2311yescharacteristic
82C4×#41—22no—
83C4×#41—22no—
84C4×#41—22no—
85C4×#41—22no—
86C4×#41—22no—
87C4×#41—22no—
88C4×#41—22no—
89C4×#41—22no—
90C4×#41—41no—
91C4×#41—41no—
92C4×#41—41no—
93C4×#41—41no—
94C2×C4×Q8C2×C411yescharacteristic
95C2×C4×Q8C2×C411yescharacteristic
96C2×C4×Q8C2×C411yescharacteristic
97C2×C4×Q8C2×C411yescharacteristic
98C2×C4×Q8C2×C411yescharacteristic
99C2×C4×Q8C2×C411yescharacteristic
100C2×C4×D4—21no—
101C2×C4×D4—21no—
102C2×C4×D4—21no—
103C2×C4×D4—21no—
104C2×C4×D4—21no—
105C2×C4×D4—21no—
106C2×C4×D4C2×C411yescharacteristic
107C2×C4×D4C2×C411yescharacteristic
108C2×C4×D4C2×C411yescharacteristic
109C2×C4×D4C2×C411yescharacteristic
110C2×C4×D4C2×C411yescharacteristic
111C2×C4×D4C2×C411yescharacteristic
112C2×#117—21no—
113C2×#117—21no—
114C2×#117—21no—
115C2×#117C2311yescharacteristic
116C2×#117C2311yescharacteristic
117C2×#117C2311yescharacteristic
118C22×C4⋊C4—21no—
119C22×C4⋊C4—21no—
120C22×C4⋊C4—21no—
121C22×C4⋊C4D411yescharacteristic
122C22×C4⋊C4D411yescharacteristic
123C22×C42—21no—
124C22×C42—21no—
125C22×C42—21no—
126C22×C42—21no—
127C22×C42—21no—
128C22×C42C2311yescharacteristic
129C22×C42C2311yescharacteristic
130C22×C42C2311yescharacteristic
131C22×C42C2311yescharacteristic
132C22×C42C2311yescharacteristic
133C22×C42C2311yescharacteristic
134C22×C42C2311yescharacteristic
135#423—22no—
136#423—41no—
137C2×C4⋊C8—21no—
138C2×C4⋊C8—21no—
139C2×#104—22no—
140C2×#104—22no—
141C2×#104—22no—
142C2×#104—22no—
143C2×#104—22no—
144C2×#104—22no—
145C2×#104—22no—
146C2×#104—22no—
147C2×#104—22no—
148C2×#104—22no—
149C2×#104D414yes—
150C2×#104Q814yes—
151C4×M16—22no—
152C4×M16—41no—
153C2×#97—21no—
154C2×C4×C8—21no—
155#389—21no—
156#389—21no—
157#389—21no—
158#389—21no—
159#389—21no—
160#389—21no—
161#389—21no—
162#389—21no—
163#389C2×C411yescharacteristic
164#389C2×C411yescharacteristic
165#389C2×C411yescharacteristic
166#389C2×C411yescharacteristic
167#389C2×C411yescharacteristic
168#389C2×C411yescharacteristic
169#389C2×C411yescharacteristic
170#389C2×C411yescharacteristic
171#387—28no—
172#385—21no—
173#385—21no—
174#385—21no—
175#385—21no—
176#385—21no—
177#385—21no—
178#385—21no—
179#385—21no—
180#385—21no—
181#385—21no—
182#385—21no—
183#385—21no—
184#384—21no—
185#384—21no—
186#384C2×C411yescharacteristic
187#384C2×C411yescharacteristic
188#382—21no—
189#382—21no—
190#382C2×C411yescharacteristic
191#382C2×C411yescharacteristic
192#380—21no—
193#380—21no—
194#380—21no—
195#380—21no—
196#380—21no—
197#380—21no—
198C4×C4⋊C4—21no—
199C4×C4⋊C4—21no—
200C4×C4⋊C4—21no—
201C4×C4⋊C4—21no—
202C4×C4⋊C4—21no—
203C4×C4⋊C4—21no—
204C4×C4⋊C4—21no—
205C4×C4⋊C4—21no—
206C4×C4⋊C4—21no—
207C4×C4⋊C4—21no—
208C4×C4⋊C4—22no—
209C4×C4⋊C4—41no—
210C4×C4⋊C4C2×C411yescharacteristic
211C4×C4⋊C4C2×C411yescharacteristic
212C4×C4⋊C4C2×C411yescharacteristic
213C4×C4⋊C4C2×C411yescharacteristic
214C4×C4⋊C4D411yescharacteristic
215C4×C4⋊C4D411yescharacteristic
216C4×C4⋊C4D411yescharacteristic
217C4×C4⋊C4D411yescharacteristic
218C2×#95—21no—
219C2×#95—21no—
220C2×#95—21no—
221C2×#95—21no—
222C2×#95—21no—
223C2×#95—21no—
224C2×#95—21no—
225C2×#95—21no—
226C2×#95—21no—
227C2×#95—21no—
228C2×#95—21no—
229C2×#95D411yescharacteristic
230C2×#95D411yescharacteristic
231C43—22no—
232C43—41no—
233#339—22no—
234#339—22no—
235#339—22no—
236#339—22no—
237#339—22no—
238#339—22no—
239#339—22no—
240#339—22no—
241#339—41no—
242#339—41no—
243#339—41no—
244#339—41no—
245#336—21no—
246#336—21no—
247#336—21no—
248#336—21no—
249#336—21no—
250#336—21no—
251#336—21no—
252#336—21no—
253C2×#41—21no—
254C2×#41—21no—
255C2×#41—21no—
256C2×#41—21no—
257C2×#41—21no—
258C2×#41—21no—
259C2×#41C2×D412yes—
260C2×#41C2×Q812yes—
261C2×#41#4112yes—
262C2×#41#4112yes—
263C2×#41#4112yes—
264C2×#41#4112yes—
265C22×Q8C22×C411yescharacteristic
266C22×D4—21no—
267C22×D4C22×C411yescharacteristic
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
285C23×C4C2411yescharacteristic
286C2×M16—21no—
287C2×M16—21no—
288C2×M16—21no—
289C2×M16—21no—
290C2×M16—21no—
291C2×M16—21no—
292C2×M16—21no—
293C2×M16—21no—
294C2×M16—21no—
295C2×M16—21no—
296C2×M16—21no—
297C2×M16—21no—
298C2×M16—21no—
299C2×M16—21no—
300C2×M16—21no—
301C2×M16—21no—
302C2×M16—21no—
303C2×M16—21no—
304C2×M16—21no—
305C2×M16—21no—
306C2×M16—21no—
307C2×M16—21no—
308C2×M16C2×D412yes—
309C2×M16C2×Q812yes—
310C22×C8—21no—
311C22×C8—21no—
312C22×C8—21no—
313C22×C8—21no—
314C4×Q8—22no—
315C4×Q8—22no—
316C4×Q8—22no—
317C4×Q8—22no—
318C4×Q8—22no—
319C4×Q8—22no—
320C4×Q8—22no—
321C4×Q8—22no—
322C4×Q8—41no—
323C4×Q8—41no—
324C4×Q8—41no—
325C4×Q8—41no—
326C4×D4—24no—
327C4×D4—24no—
328C4×D4—24no—
329C4×D4—24no—
330C4×D4—22no—
331C4×D4—22no—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4—22no—
335C4×D4—22no—
336C4×D4—22no—
337C4×D4—22no—
338C4×D4—41no—
339C4×D4—41no—
340C4×D4—41no—
341C4×D4—41no—
342C4×D4—42no—
343C4×D4—42no—
344C4×D4—42no—
345C4×D4—42no—
346C4×D4—42no—
347C4×D4—42no—
348C4×D4—42no—
349C4×D4—42no—
350#117—24no—
351#117—24no—
352#117—21no—
353#117—21no—
354#117—21no—
355#117—21no—
356#117—21no—
357#117—21no—
358#117—21no—
359#117—21no—
360#117—21no—
361#117—21no—
362#117—42no—
363#117—42no—
364#117—42no—
365#117—42no—
366#117#4112yes—
367#117#4112yes—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4—44no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4—42no—
392C2×C4⋊C4—44no—
393C2×C4⋊C4C22⋊C411yescharacteristic
394C2×C4⋊C4C22⋊C411yescharacteristic
395C2×C4⋊C4C22⋊C411yescharacteristic
396C2×C4⋊C4C22⋊C411yescharacteristic
397C2×C4⋊C4C22⋊C411yescharacteristic
398C2×C4⋊C4C22⋊C411yescharacteristic
399C2×C4⋊C4C22⋊C411yescharacteristic
400C2×C4⋊C4C22⋊C411yescharacteristic
401C2×C4⋊C4C22×C411yescharacteristic
402C2×C4⋊C4C22×C411yescharacteristic
403C2×C4⋊C4C22×C411yescharacteristic
404C2×C4⋊C4C22×C411yescharacteristic
405C2×C4⋊C4C22×C411yescharacteristic
406C2×C4⋊C4C22×C411yescharacteristic
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C42—24no—
417C2×C42—24no—
418C2×C42—21no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42—21no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—21no—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—21no—
432C2×C42—21no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42—24no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—21no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—21no—
453C2×C42—21no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—42no—
463C2×C42—42no—
464C2×C42—42no—
465C2×C42—42no—
466C2×C42—42no—
467C2×C42—42no—
468C2×C42—42no—
469C2×C42—42no—
470C2×C42—42no—
471C2×C42C22×C411yescharacteristic
472C2×C42C22×C411yescharacteristic
473C2×C42C22×C411yescharacteristic
474C2×C42C22×C411yescharacteristic
475C2×C42C22×C411yescharacteristic
476C2×C42C22×C411yescharacteristic
477C2×C42C2×D412yes—
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D411yescharacteristic
480C2×C42C2×D411yescharacteristic
481C2×C42C2×D411yescharacteristic
482C2×C42C2×D411yescharacteristic
483C2×C42C2×D411yescharacteristic
484C2×C42C2×Q812yes—
485C4⋊C8—42no—
486C4⋊C8—42no—
487#104—28no—
488#104—28no—
489#104—44no—
490#104—44no—
491#97—42no—
492C4×C8—42no—
493#95—24no—
494#95—24no—
495#95—24no—
496#95—24no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—42no—
510#95—42no—
511#95—42no—
512#95—42no—
513#95—42no—
514#95C22⋊C411yescharacteristic
515#95C22⋊C411yescharacteristic
516#95C22⋊C411yescharacteristic
517#95C22⋊C411yescharacteristic
518#95C22⋊C411yescharacteristic
519#95C22⋊C411yescharacteristic
520#95C22⋊C411yescharacteristic
521#95C22⋊C411yescharacteristic
522C24—21no—
523C24C22×D411yescharacteristic
524#41—22no—
525#41—22no—
526#41—22no—
527#41—22no—
528#41—22no—
529#41—22no—
530#41—22no—
531#41—22no—
532#41—22no—
533#41—22no—
534#41—22no—
535#41—22no—
536#41C22⋊Q814yes—
537#41#12314yes—
538#41#12514yes—
539#41#12614yes—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8#11712yes—
544C2×Q8C4×D412yes—
545C2×Q8C4×Q812yes—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4#11712yes—
556C2×D4C4×D412yes—
557C2×D4C4×Q812yes—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—42no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—81no—
636C22×C4—81no—
637C22×C4—81no—
638C22×C4—81no—
639C22×C4—81no—
640C22×C4—81no—
641C22×C4C2×C22⋊C411yescharacteristic
642C22×C4C2×C22⋊C411yescharacteristic
643C22×C4C2×C22⋊C411yescharacteristic
644C22×C4C2×C22⋊C411yescharacteristic
645C22×C4C2×C22⋊C411yescharacteristic
646C22×C4C2×C22⋊C411yescharacteristic
647C22×C4C2×C22⋊C411yescharacteristic
648C22×C4C2×C22⋊C411yescharacteristic
649C22×C4C2×C22⋊C411yescharacteristic
650C22×C4C2×C22⋊C411yescharacteristic
651C22×C4C2×C22⋊C411yescharacteristic
652C22×C4C2×C22⋊C411yescharacteristic
653C22×C4C23×C411yescharacteristic
654C22×C4C22×D411yescharacteristic
655C22×C4C22×D411yescharacteristic
656C22×C4C22×Q811yescharacteristic
657C22×C4C2×#4111yescharacteristic
658C22×C4C2×#4111yescharacteristic
659C22×C4C2×#4111yescharacteristic
660C22×C4C2×#4111yescharacteristic
661C22×C4C2×#4111yescharacteristic
662C22×C4C2×#4111yescharacteristic
663C22×C4H(5,𝔽2)11yescharacteristic
664C22×C4H(5,𝔽2)11yescharacteristic
665C22×C42−1+411yescharacteristic
666C22×C42−1+411yescharacteristic
667M16—22no—
668M16—22no—
669M16—22no—
670M16—22no—
671M16—41no—
672M16—41no—
673M16—41no—
674M16—41no—
675M16—41no—
676M16—41no—
677M16—41no—
678M16—41no—
679M16—41no—
680M16—41no—
681M16—41no—
682M16—41no—
683C2×C8—22no—
684C2×C8—22no—
685C2×C8—41no—
686C2×C8—41no—
687C2×C8—41no—
688C2×C8—41no—
689C2×C8—41no—
690C2×C8—41no—
691C2×C8—41no—
692C2×C8—41no—
693C2×C8—41no—
694C2×C8—41no—
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—22no—
703C4⋊C4—22no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—41no—
713C4⋊C4—41no—
714C4⋊C4—42no—
715C4⋊C4—42no—
716C4⋊C4—42no—
717C4⋊C4—42no—
718C4⋊C4—42no—
719C4⋊C4—48no—
720C4⋊C4—42no—
721C4⋊C4—42no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—81no—
726C4⋊C4—81no—
727C4⋊C4—81no—
728C4⋊C4—81no—
729C4⋊C4—81no—
730C4⋊C4—81no—
731C4⋊C4#10414yescomplemented
732C4⋊C4#11712yes—
733C4⋊C4#11712yes—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—41no—
743C22⋊C4—41no—
744C22⋊C4—41no—
745C22⋊C4—41no—
746C42—24no—
747C42—24no—
748C42—21no—
749C42—21no—
750C42—21no—
751C42—21no—
752C42—21no—
753C42—21no—
754C42—21no—
755C42—21no—
756C42—21no—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—21no—
761C42—21no—
762C42—22no—
763C42—22no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42—21no—
769C42—21no—
770C42—21no—
771C42—21no—
772C42—21no—
773C42—21no—
774C42—22no—
775C42—22no—
776C42—22no—
777C42—22no—
778C42—42no—
779C42—42no—
780C42—42no—
781C42—42no—
782C42—48no—
783C42—48no—
784C42—41no—
785C42—41no—
786C42—41no—
787C42—41no—
788C42—41no—
789C42—41no—
790C42—41no—
791C42—41no—
792C42—41no—
793C42—41no—
794C42—41no—
795C42—41no—
796C42—41no—
797C42—41no—
798C42—41no—
799C42—41no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23C22×C22⋊C411yescharacteristic
812C23#52511yescharacteristic
813C23#52511yescharacteristic
814C23D4211yescharacteristic
815C23#54611yescharacteristic
816C23#54811yescharacteristic
817C23D4×Q811yescharacteristic
818Q8—22no—
819Q8—22no—
820Q8—22no—
821Q8#38714yescomplemented
822D4—24no—
823D4—24no—
824D4—24no—
825D4—24no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4#38714yescomplemented
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—48no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—42no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—84no—
917C2×C4—84no—
918C2×C4—84no—
919C2×C4—81no—
920C2×C4—81no—
921C2×C4—81no—
922C2×C4—81no—
923C2×C4—84no—
924C2×C4—84no—
925C2×C4—81no—
926C2×C4—81no—
927C2×C4—81no—
928C2×C4—81no—
929C2×C4—81no—
930C2×C4—81no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4C2×#10412yes—
934C2×C4C2×#10412yes—
935C2×C4C2×#10412yes—
936C2×C4#42112yes—
937C2×C4C2×#11711yescharacteristic
938C2×C4C2×#11711yescharacteristic
939C2×C4C2×C4×D411yescharacteristic
940C2×C4C2×C4×Q811yescharacteristic
941C2×C4#51811yescharacteristic
942C2×C4#51911yescharacteristic
943C2×C4C2×C22⋊Q811yescharacteristic
944C2×C4C2×#12311yescharacteristic
945C2×C4#52511yescharacteristic
946C2×C4#52511yescharacteristic
947C2×C4C2×#12511yescharacteristic
948C2×C4C2×#12611yescharacteristic
949C2×C4#53911yescharacteristic
950C2×C4#53911yescharacteristic
951C2×C4#53911yescharacteristic
952C2×C4#53911yescharacteristic
953C2×C4D4211yescharacteristic
954C2×C4#54611yescharacteristic
955C2×C4#54711yescharacteristic
956C2×C4#54711yescharacteristic
957C2×C4#54811yescharacteristic
958C2×C4D4×Q811yescharacteristic
959C2×C4#55211yescharacteristic
960C2×C4#55211yescharacteristic
961C2×C4#55311yescharacteristic
962C2×C4#55311yescharacteristic
963C2×C4#55411yescharacteristic
964C2×C4#55411yescharacteristic
965C8—42no—
966C8—42no—
967C8—81no—
968C8—81no—
969C22—21no—
970C22—21no—
971C22—21no—
972C22—21no—
973C22—21no—
974C22—21no—
975C22—21no—
976C22—21no—
977C22—21no—
978C22—21no—
979C22—21no—
980C22—21no—
981C22—24no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22#228011yescharacteristic
989C22D4×C22⋊C411yescharacteristic
990C22Q8×C22⋊C411yescharacteristic
991C22#244311yescharacteristic
992C22#244911yescharacteristic
993C22#247311yescharacteristic
994C22#248111yescharacteristic
995C22C22×#10411yescharacteristic
996C22C2×#42111yescharacteristic
997C22#290111yescharacteristic
998C22#290111yescharacteristic
999C4—22no—
1000C4—24no—
1001C4—22no—
1002C4—22no—
1003C4—22no—
1004C4—44no—
1005C4—44no—
1006C4—41no—
1007C4—42no—
1008C4—41no—
1009C4—41no—
1010C4—42no—
1011C4—41no—
1012C4—41no—
1013C4—41no—
1014C4—41no—
1015C4—41no—
1016C4—82no—
1017C4—82no—
1018C4—81no—
1019C4—81no—
1020C4—81no—
1021C4—81no—
1022C4C2×#38711yescharacteristic
1023C4#231311yescharacteristic
1024C4#234411yescharacteristic
1025C4#234511yescharacteristic
1026C4#244311yescharacteristic
1027C4#244911yescharacteristic
1028C4#247311yescharacteristic
1029C4#248111yescharacteristic
1030C2—21no—
1031C2—21no—
1032C2—21no—
1033C2—21no—
1034C2—44no—
1035C2#1388211yescharacteristic
1036C2#2074711yescharacteristic
1037C2#2074911yescharacteristic
1038C2D4×#10411yescharacteristic
1039C2#2243411yescharacteristic
1040C2Q8×#10411yescharacteristic
1041C2#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. #21023C2semidirect
5. C4×#387C2semidirect
6. #11370C2semidirect
7. #11359C2semidirect
8. #11226C2semidirect
9. #11209C2semidirect
10. #10886C2semidirect
11. #10878C2semidirect
25. #2351C4semidirect
26. #2351C4semidirect
27. Q8×C4⋊C4C4semidirect
28. Q8×C4⋊C4C4semidirect
31. #2349C4semidirect
32. #2349C4semidirect
35. D4×C4⋊C4C4semidirect
36. D4×C4⋊C4C4semidirect
731. C4⋊C4#104semidirect
821. Q8#387semidirect
829. D4#387semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×#412
#210232
C2×#18062
C2×C4×#1042
C4×#3872
#113702
#113592
#112262
#112092
#108862
#108782
#107902