Finite Group Databasebeta

← #370520

Subgroups — #370520

Order 512.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1091 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34739C211yesmaximal, characteristic
2C2×#1986C211yesmaximal, characteristic, complemented
3C22⋊C4×M16C211yesmaximal, characteristic
4C22×#339C211yesmaximal, characteristic
5C4×#385C211yesmaximal, characteristic
6#11386C211yesmaximal, characteristic, complemented
7#11370C211yesmaximal, characteristic, complemented
8#11226C211yesmaximal, characteristic, complemented
9#11226C211yesmaximal, characteristic, complemented
10#10886C211yesmaximal, characteristic, complemented
11#10886C211yesmaximal, characteristic, complemented
12#10851C211yesmaximal, characteristic, complemented
13#10733C211yesmaximal, characteristic
14#10732C211yesmaximal, characteristic
15#10719C211yesmaximal, characteristic
16C23×M16C2211yescharacteristic
17C2×#533C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C23×C42C2211yescharacteristic
20C2×#407C2211yescharacteristic
21C2×C4×M16C2211yescharacteristic
22C2×C4×M16C2211yescharacteristic
23#2442C411yescharacteristic, complemented
24#2442C411yescharacteristic, complemented
25#2441C411yescharacteristic, complemented
26#2441C411yescharacteristic, complemented
27#2440C411yescharacteristic, complemented
28#2440C411yescharacteristic, complemented
29#2439C411yescharacteristic, complemented
30#2439C411yescharacteristic, complemented
31#2438—21no—
32#2438—21no—
33#2437—21no—
34#2437—21no—
35#2396—21no—
36#2396—21no—
37C4×C22⋊Q8—21no—
38C4×C22⋊Q8—21no—
39#2296C2211yescharacteristic
40#2296C2211yescharacteristic
41C2×#385—21no—
42#2285C2211yescharacteristic
43#2280C2211yescharacteristic
44C2×C4×C4⋊C4C2211yescharacteristic
45C2×C4×C4⋊C4C2211yescharacteristic
46C2×C4×C22⋊C4C2211yescharacteristic
47C2×C4×C22⋊C4C2211yescharacteristic
48#1986—24no—
49#1753—21no—
50#1753—21no—
51#1752—21no—
52C8×C22⋊C4—21no—
53C2×#339—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
66C2×#339C2211yescharacteristic
67C2×#339C2211yescharacteristic
68C2×#339C2211yescharacteristic
69C2×#339C2211yescharacteristic
70#1728C2211yescharacteristic
71#1728C2211yescharacteristic
72#1436—21no—
73#1436—21no—
74C22⋊#95—21no—
75C4×#95C2211yescharacteristic
76C4×#95C2211yescharacteristic
77C24×C4—21no—
78C24×C4C2311yescharacteristic
79C22×M16—21no—
80C22×M16—22no—
81C22×M16—22no—
82C22×M16—22no—
83C22×M16—41no—
84C22×M16—41no—
85C22×M16Q814yescomplemented
86C22×M16C2311yescharacteristic
87C22×M16C2311yescharacteristic
88C22×M16C2311yescharacteristic
89C22×M16C2311yescharacteristic
90C23×C8—21no—
91#533—22no—
92#533—22no—
93#533—41no—
94#533—41no—
95C2×C4⋊Q8C2×C411yescharacteristic, complemented
96C2×C4⋊Q8C2×C411yescharacteristic, complemented
97C2×#125C2×C411yescharacteristic, complemented
98C2×#125C2×C411yescharacteristic, complemented
99C2×C22⋊Q8—21no—
100C2×C22⋊Q8—21no—
101C2×C22⋊Q8—21no—
102C2×C22⋊Q8—21no—
103C2×C4×Q8—21no—
104C2×C4×Q8—21no—
105C2×#117—21no—
106C2×#117—21no—
107C2×#117—22no—
108C2×#117—22no—
109C2×#117—41no—
110C2×#117—41no—
111C2×#117C2×C411yescharacteristic
112C2×#117C2×C411yescharacteristic
113C2×#117C2311yescharacteristic
114C2×#117C2311yescharacteristic
115C2×#117C2311yescharacteristic
116C2×#117C2311yescharacteristic
117C22×C4⋊C4—21no—
118C22×C4⋊C4—21no—
119C22×C4⋊C4C2×C411yescharacteristic
120C22×C4⋊C4C2×C411yescharacteristic
121C22×C22⋊C4—21no—
122C22×C22⋊C4—21no—
123C22×C22⋊C4D411yescharacteristic
124C22×C22⋊C4D411yescharacteristic
125C22×C42—22no—
126C22×C42—22no—
127C22×C42—22no—
128C22×C42—21no—
129C22×C42—22no—
130C22×C42—21no—
131C22×C42—41no—
132C22×C42—41no—
133C22×C42C2311yescharacteristic
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136C22×C42C2311yescharacteristic
137C22×C42C2311yescharacteristic
138C22×C42C2311yescharacteristic
139#407—22no—
140#407Q814yescomplemented
141C2×C22⋊C8—21no—
142C2×C22⋊C8—21no—
143C4×M16—22no—
144C4×M16—22no—
145C4×M16—41no—
146C4×M16—41no—
147C2×#97—21no—
148C2×#97—21no—
149C2×C4×C8—21no—
150C2×C4×C8—21no—
151#400—21no—
152#400—21no—
153#399—21no—
154#399—21no—
155#398—21no—
156#398—21no—
157#398—21no—
158#398—21no—
159#396—21no—
160#396—21no—
161#396—21no—
162#396—21no—
163#395—21no—
164#395—21no—
165#393—21no—
166#393—21no—
167#391—21no—
168#391—21no—
169#389—21no—
170#389—21no—
171#389C2×C411yescharacteristic, complemented
172#389C2×C411yescharacteristic, complemented
173#389C2×C411yescharacteristic, complemented
174#389C2×C411yescharacteristic, complemented
175#389C2×C411yescharacteristic, complemented
176#389C2×C411yescharacteristic, complemented
177#389C2×C411yescharacteristic, complemented
178#389C2×C411yescharacteristic, complemented
179#387—21no—
180#387—21no—
181#387—21no—
182#387—21no—
183#385—28no—
184#385—21no—
185#385—21no—
186#385—21no—
187#385—21no—
188#385—21no—
189#385—21no—
190#385—21no—
191#385—21no—
192#384C2×C411yescharacteristic, complemented
193#384C2×C411yescharacteristic, complemented
194#382C2×C411yescharacteristic, complemented
195#382C2×C411yescharacteristic, complemented
196#381—21no—
197#380—21no—
198#380—21no—
199#380—21no—
200#380—21no—
201#380C2×C411yescharacteristic
202#380C2×C411yescharacteristic
203#380C2×C411yescharacteristic
204#380C2×C411yescharacteristic
205#379—21no—
206C4×C4⋊C4—21no—
207C4×C4⋊C4—21no—
208C4×C4⋊C4—21no—
209C4×C4⋊C4—21no—
210C4×C4⋊C4—21no—
211C4×C4⋊C4—21no—
212C4×C4⋊C4—22no—
213C4×C4⋊C4—22no—
214C4×C4⋊C4—41no—
215C4×C4⋊C4—41no—
216C4×C22⋊C4—21no—
217C4×C22⋊C4—21no—
218C4×C22⋊C4—22no—
219C4×C22⋊C4—22no—
220C4×C22⋊C4C2×C411yescharacteristic
221C4×C22⋊C4C2×C411yescharacteristic
222C4×C22⋊C4C2×C411yescharacteristic
223C4×C22⋊C4C2×C411yescharacteristic
224C4×C22⋊C4D411yescharacteristic
225C4×C22⋊C4D411yescharacteristic
226C4×C22⋊C4D411yescharacteristic
227C4×C22⋊C4D411yescharacteristic
228C2×#95—21no—
229C2×#95—21no—
230C2×#95—21no—
231C2×#95—21no—
232C2×#95—21no—
233C2×#95—21no—
234C2×#95—21no—
235C2×#95D411yescharacteristic
236C2×#95D411yescharacteristic
237#339—22no—
238#339—22no—
239#339—22no—
240#339—22no—
241#339—22no—
242#339—22no—
243#339—22no—
244#339—22no—
245#339—22no—
246#339—41no—
247#339—41no—
248#339—41no—
249#339—41no—
250#339—41no—
251#339—41no—
252#339D414yes—
253#336—21no—
254#336—21no—
255#336—21no—
256#336—21no—
257C25C2×D411yescharacteristic
258C22×Q8—21no—
259C22×Q8—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—24no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4C22×C411yescharacteristic
282C23×C4C22×C411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×Q812yes—
291C23×C4C2×Q812yes—
292C23×C4#4112yes—
293C23×C4#4112yes—
294C23×C4C2411yescharacteristic
295C2×M16—21no—
296C2×M16—21no—
297C2×M16—21no—
298C2×M16—24no—
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×M16—21no—
309C2×M16—21no—
310C2×M16—21no—
311C2×M16—21no—
312C2×M16—21no—
313C2×M16—21no—
314C2×M16—28no—
315C2×M16—42no—
316C2×M16—42no—
317C2×M16—44no—
318C2×M16—44no—
319C2×M16—44no—
320C2×M16C2×D412yes—
321C2×M16C2×Q812yes—
322C2×M16C2×Q812yes—
323C2×M16C2×Q812yes—
324C2×M16C2×Q812yes—
325C2×M16#4112yes—
326C22×C8—21no—
327C22×C8—24no—
328C22×C8—21no—
329C22×C8—21no—
330C22×C8—21no—
331C22×C8—42no—
332C22×C8—42no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—41no—
336C4⋊Q8—41no—
337#125—22no—
338#125—22no—
339#125—41no—
340#125—41no—
341C22⋊Q8—42no—
342C22⋊Q8—42no—
343C22⋊Q8—42no—
344C22⋊Q8—42no—
345C22⋊Q8—44no—
346C22⋊Q8—44no—
347C4×Q8—42no—
348C4×Q8—42no—
349C4×Q8—42no—
350C4×Q8—42no—
351#117—21no—
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—21no—
363#117—21no—
364#117—21no—
365#117—22no—
366#117—22no—
367#117—42no—
368#117—42no—
369#117—42no—
370#117—42no—
371#117—41no—
372#117—41no—
373#117C2×D412yes—
374#117#4112yes—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—24no—
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—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—41no—
400C2×C4⋊C4—41no—
401C2×C4⋊C4—42no—
402C2×C4⋊C4—42no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4—42no—
405C2×C4⋊C4C22×C411yescharacteristic
406C2×C4⋊C4C22×C411yescharacteristic
407C2×C4⋊C4C22×C411yescharacteristic
408C2×C4⋊C4C22×C411yescharacteristic
409C2×C4⋊C4C22×C411yescharacteristic
410C2×C4⋊C4C22×C411yescharacteristic
411C2×C4⋊C4C22×C411yescharacteristic
412C2×C4⋊C4C22×C411yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—42no—
426C2×C22⋊C4—42no—
427C2×C22⋊C4—42no—
428C2×C22⋊C4—42no—
429C2×C22⋊C4—42no—
430C2×C22⋊C4C22⋊C411yescharacteristic
431C2×C22⋊C4C22⋊C411yescharacteristic
432C2×C22⋊C4C22⋊C411yescharacteristic
433C2×C22⋊C4C22⋊C411yescharacteristic
434C2×C22⋊C4C22⋊C411yescharacteristic
435C2×C22⋊C4C22⋊C411yescharacteristic
436C2×C22⋊C4C22⋊C411yescharacteristic
437C2×C22⋊C4C22⋊C411yescharacteristic
438C2×C42—21no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—21no—
446C2×C42—21no—
447C2×C42—28no—
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—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—42no—
476C2×C42—42no—
477C2×C42—44no—
478C2×C42—44no—
479C2×C42—42no—
480C2×C42—42no—
481C2×C42—44no—
482C2×C42—42no—
483C2×C42C22×C411yescharacteristic
484C2×C42C22×C411yescharacteristic
485C2×C42C22×C411yescharacteristic
486C2×C42C22×C411yescharacteristic
487C2×C42C2×D412yes—
488C2×C42C2×D411yescharacteristic
489C2×C42C2×D411yescharacteristic
490C2×C42C2×D411yescharacteristic
491C2×C42C2×D411yescharacteristic
492C2×C42#4112yes—
493C22⋊C8—24no—
494C22⋊C8—24no—
495#97—42no—
496#97—42no—
497C4×C8—42no—
498C4×C8—42no—
499#95—24no—
500#95—24no—
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—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—42no—
518#95—42no—
519#95—42no—
520#95—42no—
521#95—42no—
522#95C22⋊C411yescharacteristic
523#95C22⋊C411yescharacteristic
524#95C22⋊C411yescharacteristic
525#95C22⋊C411yescharacteristic
526#95C22⋊C411yescharacteristic
527#95C22⋊C411yescharacteristic
528#95C22⋊C411yescharacteristic
529#95C22⋊C411yescharacteristic
530C24—21no—
531C24—21no—
532C24—21no—
533C24—21no—
534C24—22no—
535C24—22no—
536C24—41no—
537C24—41no—
538C24C2×C22⋊C411yescharacteristic
539C24C2×C22⋊C411yescharacteristic
540C24#12412yes—
541C24C4⋊Q812yes—
542C24C22×D411yescharacteristic
543C2×Q8—42no—
544C2×Q8—42no—
545C2×Q8—42no—
546C2×Q8—42no—
547C2×Q8—81no—
548C2×Q8—81no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
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—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—48no—
618C22×C4—48no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—48no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—48no—
627C22×C4—48no—
628C22×C4—48no—
629C22×C4—48no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—41no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—81no—
649C22×C4—81no—
650C22×C4C2×C22⋊C411yescharacteristic
651C22×C4C2×C22⋊C411yescharacteristic
652C22×C4C2×C22⋊C411yescharacteristic
653C22×C4C2×C22⋊C411yescharacteristic
654C22×C4C2×C22⋊C411yescharacteristic
655C22×C4C2×C22⋊C411yescharacteristic
656C22×C4C2×C22⋊C411yescharacteristic
657C22×C4C2×C22⋊C411yescharacteristic
658C22×C4C2×C22⋊C411yescharacteristic
659C22×C4C2×C22⋊C411yescharacteristic
660C22×C4C4×Q812yes—
661C22×C4C4×Q812yes—
662C22×C4C4×Q812yes—
663C22×C4C4×Q812yes—
664C22×C4C22⋊Q812yes—
665C22×C4C22⋊Q812yes—
666C22×C4C22⋊Q812yes—
667C22×C4C22⋊Q812yes—
668C22×C4#12412yes—
669C22×C4C4⋊Q812yes—
670C22×C4C23×C411yescharacteristic
671C22×C4C22×D411yescharacteristic
672C22×C4C22×D411yescharacteristic
673C22×C4C22×Q811yescharacteristic
674C22×C4C22×Q811yescharacteristic
675C22×C4C2×#4111yescharacteristic
676C22×C4C2×#4111yescharacteristic
677C22×C4C2×#4111yescharacteristic
678C22×C4C2×#4111yescharacteristic
679C22×C4C2×#4111yescharacteristic
680C22×C4H(5,𝔽2)11yescharacteristic
681C22×C4H(5,𝔽2)11yescharacteristic
682C22×C4H(5,𝔽2)11yescharacteristic
683C22×C42−1+411yescharacteristic
684M16—22no—
685M16—22no—
686M16—22no—
687M16—22no—
688M16—22no—
689M16—22no—
690M16—22no—
691M16—22no—
692M16—22no—
693M16—48no—
694M16—41no—
695M16—41no—
696M16—41no—
697M16—41no—
698M16—41no—
699M16—41no—
700M16C22⋊Q814yescomplemented
701C2×C8—22no—
702C2×C8—22no—
703C2×C8—22no—
704C2×C8—22no—
705C2×C8—22no—
706C2×C8—22no—
707C2×C8—48no—
708C2×C8—41no—
709C2×C8—41no—
710C2×C8—41no—
711C2×C8—41no—
712C2×C8—41no—
713C2×C8—41no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—42no—
729C4⋊C4—42no—
730C4⋊C4—42no—
731C4⋊C4—42no—
732C4⋊C4—42no—
733C4⋊C4—42no—
734C4⋊C4—42no—
735C4⋊C4—42no—
736C4⋊C4—48no—
737C4⋊C4—48no—
738C4⋊C4—42no—
739C4⋊C4—42no—
740C4⋊C4—42no—
741C4⋊C4—42no—
742C4⋊C4—42no—
743C4⋊C4—42no—
744C4⋊C4—81no—
745C4⋊C4—81no—
746C4⋊C4—81no—
747C4⋊C4—81no—
748C4⋊C4—81no—
749C4⋊C4—81no—
750C4⋊C4C4×D412yes—
751C4⋊C4C4×D412yes—
752C22⋊C4—22no—
753C22⋊C4—22no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—22no—
757C22⋊C4—22no—
758C22⋊C4—22no—
759C22⋊C4—41no—
760C22⋊C4—41no—
761C22⋊C4—42no—
762C22⋊C4—42no—
763C22⋊C4—48no—
764C22⋊C4—41no—
765C22⋊C4—41no—
766C22⋊C4—41no—
767C22⋊C4—41no—
768C22⋊C4—41no—
769C22⋊C4—41no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C22⋊C4—81no—
773C22⋊C4—81no—
774C22⋊C4#10414yes—
775C42—21no—
776C42—21no—
777C42—21no—
778C42—21no—
779C42—21no—
780C42—21no—
781C42—21no—
782C42—21no—
783C42—21no—
784C42—21no—
785C42—22no—
786C42—21no—
787C42—21no—
788C42—21no—
789C42—21no—
790C42—22no—
791C42—21no—
792C42—21no—
793C42—22no—
794C42—22no—
795C42—22no—
796C42—22no—
797C42—42no—
798C42—42no—
799C42—48no—
800C42—41no—
801C42—41no—
802C42—41no—
803C42—41no—
804C42—41no—
805C42—41no—
806C42—41no—
807C42—41no—
808C42—41no—
809C42—41no—
810C42—41no—
811C42—41no—
812C42—41no—
813C42—41no—
814C42—41no—
815C42—41no—
816C42—41no—
817C42—41no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—24no—
836C23—24no—
837C23—22no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23#39112yes—
849C23#39112yes—
850C23C2×#10412yes—
851C23#42112yes—
852C23C22×C22⋊C411yescharacteristic
853C23C2×#12411yescharacteristic
854C23C2×C4⋊Q811yescharacteristic
855C23D4211yescharacteristic
856C23#54611yescharacteristic
857C23#54611yescharacteristic
858C23#54711yescharacteristic
859Q8—84no—
860Q8—84no—
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—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—42no—
925C2×C4—432no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—42no—
937C2×C4—42no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—81no—
957C2×C4—81no—
958C2×C4—81no—
959C2×C4—81no—
960C2×C4—84no—
961C2×C4—84no—
962C2×C4—81no—
963C2×C4—81no—
964C2×C4—81no—
965C2×C4—81no—
966C2×C4—81no—
967C2×C4—81no—
968C2×C4—81no—
969C2×C4—81no—
970C2×C4#39112yes—
971C2×C4#39112yes—
972C2×C4C2×#10412yes—
973C2×C4C2×#10412yes—
974C2×C4C2×C4×D411yescharacteristic
975C2×C4C2×C4×Q811yescharacteristic
976C2×C4C2×C4×Q811yescharacteristic
977C2×C4C4×#4111yescharacteristic
978C2×C4#51811yescharacteristic
979C2×C4#52011yescharacteristic
980C2×C4C2×C22⋊Q811yescharacteristic
981C2×C4C2×C22⋊Q811yescharacteristic
982C2×C4C2×C22⋊Q811yescharacteristic
983C2×C4#52511yescharacteristic
984C2×C4#52911yescharacteristic
985C2×C4#53311yescharacteristic
986C2×C4#53811yescharacteristic
987C2×C4#53911yescharacteristic
988C2×C4#54311yescharacteristic
989C2×C4#54411yescharacteristic
990C2×C4D4211yescharacteristic
991C2×C4#54611yescharacteristic
992C2×C4#54611yescharacteristic
993C2×C4#54611yescharacteristic
994C2×C4#54711yescharacteristic
995C2×C4D4×Q811yescharacteristic
996C2×C4#55111yescharacteristic
997C2×C4#55111yescharacteristic
998C2×C4#55211yescharacteristic
999C2×C4#55411yescharacteristic
1000C2×C4#55411yescharacteristic
1001C2×C4#55411yescharacteristic
1002C8—24no—
1003C8—42no—
1004C8—42no—
1005C8—42no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—22no—
1011C22—21no—
1012C22—21no—
1013C22—22no—
1014C22—21no—
1015C22—21no—
1016C22—22no—
1017C22—22no—
1018C22—21no—
1019C22—21no—
1020C22—22no—
1021C22—21no—
1022C22—21no—
1023C22—22no—
1024C22—22no—
1025C22—22no—
1026C22—22no—
1027C22—44no—
1028C22—44no—
1029C22—44no—
1030C22—44no—
1031C22—41no—
1032C22—41no—
1033C22—41no—
1034C22—41no—
1035C22#198614yescomplemented
1036C22C2×#39111yescharacteristic
1037C22D4×C22⋊C411yescharacteristic
1038C22#233911yescharacteristic
1039C22#244011yescharacteristic
1040C22#247211yescharacteristic
1041C22#248811yescharacteristic
1042C22#254911yescharacteristic
1043C22C22×#10411yescharacteristic
1044C22C2×#42111yescharacteristic
1045C22#290111yescharacteristic
1046C22#290111yescharacteristic
1047C4—22no—
1048C4—22no—
1049C4—22no—
1050C4—22no—
1051C4—44no—
1052C4—44no—
1053C4—41no—
1054C4—42no—
1055C4—41no—
1056C4—41no—
1057C4—42no—
1058C4—41no—
1059C4—41no—
1060C4—41no—
1061C4—82no—
1062C4—82no—
1063C4—81no—
1064C4—81no—
1065C4—81no—
1066C4—81no—
1067C4—81no—
1068C4—81no—
1069C4C4×C22⋊Q811yescharacteristic
1070C4#232911yescharacteristic
1071C4#236011yescharacteristic
1072C4#236811yescharacteristic
1073C4#243711yescharacteristic
1074C4#243811yescharacteristic
1075C4#244911yescharacteristic
1076C4#245011yescharacteristic
1077C2—21no—
1078C2—21no—
1079C2—21no—
1080C2—24no—
1081C2—21no—
1082C2—42no—
1083C2#1405211yescharacteristic
1084C2C2×#198611yescharacteristic
1085C2#2130711yescharacteristic
1086C2D4×#10411yescharacteristic
1087C2#2243411yescharacteristic
1088C2#2250511yescharacteristic
1089C2#2250611yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C22×C22⋊C4
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1986C2semidirect
6. #11386C2semidirect
7. #11370C2semidirect
8. #11226C2semidirect
9. #11226C2semidirect
10. #10886C2semidirect
11. #10886C2semidirect
12. #10851C2semidirect
23. #2442C4semidirect
24. #2442C4semidirect
25. #2441C4semidirect
26. #2441C4semidirect
27. #2440C4semidirect
28. #2440C4semidirect
29. #2439C4semidirect
30. #2439C4semidirect
85. C22×M16Q8semidirect
95. C2×C4⋊Q8C2×C4semidirect
96. C2×C4⋊Q8C2×C4semidirect
97. C2×#125C2×C4semidirect
98. C2×#125C2×C4semidirect
140. #407Q8semidirect
171. #389C2×C4semidirect
172. #389C2×C4semidirect
173. #389C2×C4semidirect
174. #389C2×C4semidirect
175. #389C2×C4semidirect
176. #389C2×C4semidirect
177. #389C2×C4semidirect
178. #389C2×C4semidirect
192. #384C2×C4semidirect
193. #384C2×C4semidirect
194. #382C2×C4semidirect
195. #382C2×C4semidirect
700. M16C22⋊Q8semidirect
1035. C22#1986semidirect

Maximal subgroups

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

subgroupindex
#347392
C2×#19862
C22⋊C4×M162
C22×#3392
C4×#3852
#113862
#113702
#112262
#108862
#108512
#107332
#107322
#107192