Finite Group Databasebeta

← #356099

Subgroups — #356099

Order 512.

2350 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#421C211yesmaximal, characteristic
2C2×#2880C211yesmaximal, characteristic
3#20597C211yesmaximal, characteristic
4C2×#1765C211yesmaximal, characteristic, complemented
5C2×#1764C211yesmaximal, characteristic, complemented
6#20389C211yesmaximal, characteristic, complemented
7C2×#1750C211yesmaximal, characteristic, complemented
8#10934C211yesmaximal, characteristic, complemented
9#10934C211yesmaximal, characteristic, complemented
10#10930C211yesmaximal, characteristic, complemented
11#10929C211yesmaximal, characteristic, complemented
12#10791C211yesmaximal, characteristic, complemented
13#10791C211yesmaximal, characteristic, complemented
14#10734C211yesmaximal, characteristic, complemented
15#10720C211yesmaximal, characteristic, complemented
16C23×#41C2211yescharacteristic
17C22×#131C2211yescharacteristic
18C22×#131C2211yescharacteristic
19C23×M16C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C2×#421—24no—
22C2×#421—24no—
23C2×#421C418yescomplemented
24C22×#104C2211yescharacteristic
25C22×#104C2211yescharacteristic
26C22×#104C2211yescharacteristic
27C22×#104C2211yescharacteristic
28C2×#416C2211yescharacteristic
29C2×#416C2211yescharacteristic
30C2×#416C2211yescharacteristic
31C2×#416C2211yescharacteristic
32#2880—24no—
33#2880C418yescomplemented
34C2×#408—21no—
35C2×#408—21no—
36C2×#408C2211yescharacteristic
37C2×#408C2211yescharacteristic
38C2×#407—21no—
39C2×#407C2211yescharacteristic
40C22×C22⋊C8—21no—
41C22×C22⋊C8C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C2×#405C2211yescharacteristic, complemented
44C2×#405C2211yescharacteristic, complemented
45C22×#97C2211yescharacteristic, complemented
46C22×C4×C8C2211yescharacteristic, complemented
47#2280C2211yescharacteristic
48#1788C412yescomplemented
49#1788C412yescomplemented
50#1787C412yescomplemented
51#1786C412yescomplemented
52#1765—24no—
53#1764—24no—
54#1753—21no—
55#1753—21no—
56#1752—21no—
57C8×C22⋊C4—21no—
58#1750—24no—
59C2×#341C2211yescharacteristic, complemented
60C2×#341C2211yescharacteristic, complemented
61C2×#341C2211yescharacteristic, complemented
62C2×#341C2211yescharacteristic, complemented
63C2×#339C2211yescharacteristic, complemented
64C2×#339C2211yescharacteristic, complemented
65C2×#339C2211yescharacteristic, complemented
66C2×#339C2211yescharacteristic, complemented
67#1729C2211yescharacteristic, complemented
68#1729C2211yescharacteristic, complemented
69C2×#336C2211yescharacteristic, complemented
70C2×#336C2211yescharacteristic, complemented
71C22×#41—21no—
72C22×#41—22no—
73C22×#41—21no—
74C22×#41—22no—
75C22×#41—22no—
76C22×#41—22no—
77C22×#41—22no—
78C22×#41—22no—
79C22×#41—41no—
80C22×#41—41no—
81C22×#41—41no—
82C22×#41—41no—
83C22×#41C2×C414yes—
84C22×#41C2×C414yes—
85C22×#41C2×C411yescharacteristic
86C22×#41C2×C411yescharacteristic
87C22×#41C2311yescharacteristic
88C22×#41C2311yescharacteristic
89C23×Q8C2×C411yescharacteristic
90C23×D4—21no—
91C23×D4C2×C411yescharacteristic
92C24×C4—21no—
93C24×C4C2311yescharacteristic
94C2×#131—22no—
95C2×#131—22no—
96C2×#131—22no—
97C2×#131—22no—
98C2×#131—22no—
99C2×#131—22no—
100C2×#131—41no—
101C2×#131—41no—
102C2×#131—41no—
103C2×#131—41no—
104C2×#131C2×C414yes—
105C2×#131C2×C414yes—
106C22×M16—21no—
107C22×M16—22no—
108C22×M16—21no—
109C22×M16—21no—
110C22×M16—22no—
111C22×M16—22no—
112C22×M16—41no—
113C22×M16—41no—
114C22×M16C2×C414yes—
115C22×M16C2311yescharacteristic
116C22×M16C2311yescharacteristic
117C22×M16C2311yescharacteristic
118C22×M16C2311yescharacteristic
119C23×C8—21no—
120C23×C8—21no—
121C23×C8—21no—
122C23×C8C2311yescharacteristic
123C23×C8C2311yescharacteristic
124C23×C8C2311yescharacteristic
125C23×C8C2311yescharacteristic
126C2×#117—22no—
127C2×#117—22no—
128C2×#117—22no—
129C2×#117—41no—
130C2×#117—41no—
131C2×#117C2×C414yes—
132C2×#117C2311yescharacteristic
133C2×#117C2311yescharacteristic
134C22×C4⋊C4—21no—
135C22×C22⋊C4—21no—
136C22×C42C2311yescharacteristic
137C22×C42C2311yescharacteristic
138#421—232no—
139C2×#104—22no—
140C2×#104—22no—
141C2×#104—22no—
142C2×#104—22no—
143C2×#104—22no—
144C2×#104—22no—
145C2×#104C2×C414yes—
146C2×#104C2×C414yes—
147C2×#104C2×C414yes—
148C2×#104C2×C414yes—
149C2×#104D414yes—
150C2×#104D414yes—
151#416—22no—
152#416—22no—
153#416—22no—
154#416—22no—
155#416—41no—
156#416—41no—
157#416—41no—
158#416—41no—
159C2×#103C2×C412yes—
160C2×#103C2×C412yes—
161C2×#103C2×C412yes—
162C2×#103C2×C412yes—
163C2×#102C2×C412yes—
164C2×#102C2×C412yes—
165C2×#102C2×C412yes—
166C2×#102C2×C412yes—
167#408—22no—
168#408—22no—
169#408—28no—
170#408—28no—
171#408C2×C414yes—
172#408C2×C414yes—
173#407—22no—
174#407—28no—
175#407C2×C414yes—
176C2×C22⋊C8—21no—
177C2×C22⋊C8—22no—
178C2×C22⋊C8—21no—
179C2×C22⋊C8—22no—
180C2×C22⋊C8—21no—
181C2×C22⋊C8—21no—
182C2×C22⋊C8—21no—
183C2×C22⋊C8—21no—
184C2×C22⋊C8—28no—
185C2×C22⋊C8C2×C412yes—
186C2×C22⋊C8C2×C412yes—
187C2×C22⋊C8C2×C414yes—
188C2×C22⋊C8D411yescharacteristic
189C2×C22⋊C8D411yescharacteristic
190C2×C22⋊C8D411yescharacteristic
191C2×C22⋊C8D411yescharacteristic
192C2×C22⋊C8D414yes—
193#405—22no—
194#405—22no—
195#405—41no—
196#405—41no—
197C2×#97—22no—
198C2×#97—21no—
199C2×#97—21no—
200C2×#97—22no—
201C2×#97—41no—
202C2×C4×C8—22no—
203C2×C4×C8—21no—
204C2×C4×C8—21no—
205C2×C4×C8—22no—
206C2×C4×C8—41no—
207#381—21no—
208#380C2×C412yes—
209#380C2×C412yes—
210#379—21no—
211C4×C22⋊C4—21no—
212C4×C22⋊C4—21no—
213#341—22no—
214#341—22no—
215#341—41no—
216#341—41no—
217#339—22no—
218#339—22no—
219#339—41no—
220#339—41no—
221#336—22no—
222#336—22no—
223#336—21no—
224#336—21no—
225#336—21no—
226#336—21no—
227C25—21no—
228C25#4111yescharacteristic
229C2×#41—24no—
230C2×#41—24no—
231C2×#41—24no—
232C2×#41—22no—
233C2×#41—22no—
234C2×#41—24no—
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—28no—
244C2×#41—28no—
245C2×#41—28no—
246C2×#41—28no—
247C2×#41—22no—
248C2×#41—22no—
249C2×#41—22no—
250C2×#41—22no—
251C2×#41—21no—
252C2×#41—21no—
253C2×#41—21no—
254C2×#41—21no—
255C2×#41—21no—
256C2×#41—21no—
257C2×#41—21no—
258C2×#41—21no—
259C2×#41—42no—
260C2×#41—42no—
261C2×#41—42no—
262C2×#41—42no—
263C2×#41—41no—
264C2×#41—41no—
265C2×#41—41no—
266C2×#41—41no—
267C2×#41—42no—
268C2×#41—42no—
269C2×#41—42no—
270C2×#41—42no—
271C2×#41—44no—
272C2×#41—44no—
273C2×#41—44no—
274C2×#41—44no—
275C2×#41—44no—
276C2×#41—44no—
277C2×#41—44no—
278C2×#41—44no—
279C2×#41—44no—
280C2×#41—44no—
281C2×#41—44no—
282C2×#41—44no—
283C2×#41C4214yes—
284C2×#41C4214yes—
285C2×#41C22×C412yes—
286C2×#41C22×C412yes—
287C2×#41C22×C412yes—
288C2×#41C22×C412yes—
289C2×#41C2×D412yes—
290C2×#41C2×D412yes—
291C2×#41#4112yes—
292C2×#41#4112yes—
293C22×Q8—21no—
294C22×Q8—22no—
295C22×Q8—22no—
296C22×Q8—22no—
297C22×Q8—41no—
298C22×Q8—41no—
299C22×Q8C4214yes—
300C22×Q8C22×C411yescharacteristic
301C22×Q8C22×C411yescharacteristic
302C22×D4—21no—
303C22×D4—22no—
304C22×D4—22no—
305C22×D4—24no—
306C22×D4—21no—
307C22×D4—21no—
308C22×D4—24no—
309C22×D4—21no—
310C22×D4—22no—
311C22×D4—21no—
312C22×D4—41no—
313C22×D4—41no—
314C22×D4—42no—
315C22×D4—42no—
316C22×D4—42no—
317C22×D4—42no—
318C22×D4C4214yes—
319C22×D4C22×C411yescharacteristic
320C22×D4C22×C411yescharacteristic
321C23×C4—21no—
322C23×C4—21no—
323C23×C4—21no—
324C23×C4—21no—
325C23×C4—21no—
326C23×C4—21no—
327C23×C4—21no—
328C23×C4—21no—
329C23×C4—21no—
330C23×C4—21no—
331C23×C4—21no—
332C23×C4—24no—
333C23×C4—21no—
334C23×C4—24no—
335C23×C4—21no—
336C23×C4—21no—
337C23×C4—21no—
338C23×C4—42no—
339C23×C4—42no—
340C23×C4—42no—
341C23×C4—42no—
342C23×C4C22×C412yes—
343C23×C4C22×C412yes—
344C23×C4C22×C411yescharacteristic
345C23×C4C22×C411yescharacteristic
346C23×C4C2×D412yes—
347C23×C4C2×D411yescharacteristic
348C23×C4C2×D411yescharacteristic
349C23×C4#4111yescharacteristic
350C23×C4#4112yes—
351C23×C4C2411yescharacteristic
352#131—28no—
353#131—28no—
354#131—44no—
355#131—44no—
356#131—44no—
357#131—44no—
358#131—44no—
359#131—44no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—24no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—24no—
368C2×M16—24no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—28no—
382C2×M16—42no—
383C2×M16—42no—
384C2×M16—42no—
385C2×M16—42no—
386C2×M16—42no—
387C2×M16—42no—
388C2×M16—44no—
389C2×M16—44no—
390C2×M16—44no—
391C2×M16C22×C412yes—
392C2×M16C22×C412yes—
393C2×M16C22×C412yes—
394C2×M16C22×C412yes—
395C2×M16C2×D412yes—
396C2×M16C2×D412yes—
397C22×C8—21no—
398C22×C8—21no—
399C22×C8—21no—
400C22×C8—21no—
401C22×C8—21no—
402C22×C8—21no—
403C22×C8—21no—
404C22×C8—21no—
405C22×C8—21no—
406C22×C8—24no—
407C22×C8—21no—
408C22×C8—21no—
409C22×C8—21no—
410C22×C8—21no—
411C22×C8—21no—
412C22×C8—21no—
413C22×C8—21no—
414C22×C8—21no—
415C22×C8—21no—
416C22×C8—21no—
417C22×C8—21no—
418C22×C8—21no—
419C22×C8—21no—
420C22×C8—21no—
421C22×C8—21no—
422C22×C8—24no—
423C22×C8—24no—
424C22×C8—42no—
425C22×C8—42no—
426C22×C8—42no—
427C22×C8—42no—
428C22×C8—42no—
429C22×C8—42no—
430C22×C8C22×C412yes—
431C22×C8C22×C412yes—
432C22×C8C22×C412yes—
433C22×C8C22×C412yes—
434C22×C8C2×D412yes—
435C22×C8C2×D412yes—
436C22×C8C2×D411yescharacteristic
437C22×C8C2×D411yescharacteristic
438C22×C8C2×D411yescharacteristic
439C22×C8C2×D411yescharacteristic
440#117—28no—
441#117—21no—
442#117—21no—
443#117—21no—
444#117—21no—
445#117—21no—
446#117—21no—
447#117—21no—
448#117—21no—
449#117—44no—
450#117—44no—
451#117—44no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4C22×C412yes—
456C2×C4⋊C4C22×C412yes—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—42no—
463C2×C22⋊C4—42no—
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×C42C22×C412yes—
475C2×C42C22×C412yes—
476C2×C42C2×D412yes—
477C2×C42C2×D412yes—
478#104—28no—
479#104—28no—
480#104—28no—
481#104C22⋊C4116yescomplemented
482#103—24no—
483#103—24no—
484#103—42no—
485#103—42no—
486#102—24no—
487#102—24no—
488#102—42no—
489#102—42no—
490C22⋊C8—24no—
491C22⋊C8—24no—
492C22⋊C8—24no—
493C22⋊C8—24no—
494C22⋊C8—24no—
495C22⋊C8—24no—
496C22⋊C8—24no—
497C22⋊C8—24no—
498C22⋊C8C22⋊C414yes—
499C22⋊C8C22⋊C414yes—
500C22⋊C8C22⋊C414yes—
501C22⋊C8C22⋊C414yes—
502#97—44no—
503#97—42no—
504#97—42no—
505C4×C8—44no—
506C4×C8—42no—
507C4×C8—42no—
508#95—22no—
509#95—22no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—24no—
517C24—42no—
518C24—42no—
519C24—42no—
520C24—42no—
521C24—44no—
522C24—82no—
523C24#11712yes—
524C24C4×D411yescharacteristic
525C24C4×D411yescharacteristic
526C24C4×D412yes—
527C24C2×#4111yescharacteristic
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#41—22no—
537#41—22no—
538#41—22no—
539#41—22no—
540#41—28no—
541#41—28no—
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—48no—
551#41—48no—
552#41—48no—
553#41—48no—
554#41—44no—
555#41—44no—
556#41—48no—
557#41—48no—
558#41—48no—
559#41—48no—
560#41—44no—
561#41—44no—
562#41—44no—
563#41—44no—
564#41—41no—
565#41—41no—
566#41—41no—
567#41—41no—
568#41—41no—
569#41—41no—
570#41—41no—
571#41—41no—
572#41C2×C22⋊C414yes—
573#41#11714yes—
574#41C4×D414yes—
575#41C4×D414yes—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—24no—
581C2×Q8—28no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—42no—
587C2×Q8—42no—
588C2×Q8—44no—
589C2×Q8—44no—
590C2×Q8—44no—
591C2×Q8C2×C4212yes—
592C2×Q8C2×C4212yes—
593C2×Q8C4×D412yes—
594C2×Q8C4×D412yes—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—28no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—24no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—42no—
622C2×D4—48no—
623C2×D4—48no—
624C2×D4—48no—
625C2×D4—48no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—41no—
632C2×D4C2×C4212yes—
633C2×D4C2×C4212yes—
634C2×D4C4×D412yes—
635C2×D4C4×D412yes—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—21no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—24no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—24no—
687C22×C4—24no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—48no—
694C22×C4—48no—
695C22×C4—48no—
696C22×C4—48no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—41no—
704C22×C4—41no—
705C22×C4—41no—
706C22×C4—41no—
707C22×C4—42no—
708C22×C4—42no—
709C22×C4—41no—
710C22×C4—41no—
711C22×C4C2×C4212yes—
712C22×C4C2×C4212yes—
713C22×C4C2×C22⋊C412yes—
714C22×C4C2×C22⋊C412yes—
715C22×C4#11712yes—
716C22×C4C4×D412yes—
717C22×C4C4×D412yes—
718C22×C4C4×D412yes—
719C22×C4C4×D412yes—
720C22×C4C4×D411yescharacteristic
721C22×C4C4×D411yescharacteristic
722C22×C4C4×D412yes—
723C22×C4C23×C411yescharacteristic
724C22×C4C23×C411yescharacteristic
725C22×C4C23×C411yescharacteristic
726C22×C4C22×D411yescharacteristic
727C22×C4C22×D411yescharacteristic
728C22×C4C22×D411yescharacteristic
729C22×C4C22×D411yescharacteristic
730C22×C4C2×#4111yescharacteristic
731C22×C4C2×#4111yescharacteristic
732C22×C4C2×#4111yescharacteristic
733C22×C4H(5,𝔽2)11yescharacteristic
734C22×C4H(5,𝔽2)11yescharacteristic
735C22×C4H(5,𝔽2)11yescharacteristic
736C22×C4H(5,𝔽2)11yescharacteristic
737M16—22no—
738M16—22no—
739M16—22no—
740M16—22no—
741M16—22no—
742M16—22no—
743M16—22no—
744M16—22no—
745M16—22no—
746M16—48no—
747M16—48no—
748M16—48no—
749M16—41no—
750M16—41no—
751M16—41no—
752M16—41no—
753M16—41no—
754M16—41no—
755M16C2×C22⋊C414yes—
756C2×C8—22no—
757C2×C8—22no—
758C2×C8—22no—
759C2×C8—22no—
760C2×C8—22no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8—22no—
764C2×C8—22no—
765C2×C8—22no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—22no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—22no—
774C2×C8—22no—
775C2×C8—22no—
776C2×C8—22no—
777C2×C8—22no—
778C2×C8—22no—
779C2×C8—22no—
780C2×C8—22no—
781C2×C8—22no—
782C2×C8—22no—
783C2×C8—22no—
784C2×C8—48no—
785C2×C8—48no—
786C2×C8—48no—
787C2×C8—41no—
788C2×C8—41no—
789C2×C8—41no—
790C2×C8—41no—
791C2×C8—41no—
792C2×C8—41no—
793C2×C8—41no—
794C2×C8—41no—
795C2×C8—41no—
796C2×C8—41no—
797C2×C8—41no—
798C2×C8—41no—
799C2×C8—41no—
800C2×C8—41no—
801C2×C8C2×C22⋊C412yes—
802C2×C8C2×C22⋊C412yes—
803C2×C8C2×C22⋊C412yes—
804C2×C8C2×C22⋊C412yes—
805C4⋊C4—22no—
806C4⋊C4—22no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—48no—
810C22⋊C4—48no—
811C22⋊C4—44no—
812C22⋊C4—41no—
813C22⋊C4—41no—
814C22⋊C4—41no—
815C22⋊C4—41no—
816C22⋊C4—82no—
817C42—22no—
818C42—22no—
819C42—22no—
820C42—22no—
821C42—22no—
822C42—41no—
823C42—41no—
824C42—41no—
825C42—41no—
826C42—41no—
827C42—41no—
828C42C2×C22⋊C414yes—
829C23—22no—
830C23—22no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—48no—
852C23—48no—
853C23—42no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—82no—
860C23—82no—
861C23—82no—
862C23—82no—
863C23—84no—
864C23—88no—
865C23—88no—
866C23C4×C22⋊C412yes—
867C23C4×C22⋊C412yes—
868C23C2×#11711yescharacteristic
869C23C2×C4×D411yescharacteristic
870C23C2×C4×D411yescharacteristic
871C23#54611yescharacteristic
872C23#54611yescharacteristic
873C23#55111yescharacteristic
874C23#55111yescharacteristic
875Q8—22no—
876Q8—22no—
877Q8—22no—
878Q8—22no—
879Q8—22no—
880Q8—48no—
881Q8—41no—
882Q8—41no—
883Q8C4×C22⋊C414yes—
884D4—24no—
885D4—24no—
886D4—24no—
887D4—24no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—22no—
892D4—22no—
893D4—48no—
894D4—48no—
895D4—48no—
896D4—42no—
897D4—42no—
898D4—42no—
899D4—42no—
900D4—41no—
901D4—41no—
902D4C4×C22⋊C414yes—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—24no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—24no—
935C2×C4—22no—
936C2×C4—48no—
937C2×C4—48no—
938C2×C4—48no—
939C2×C4—44no—
940C2×C4—44no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—82no—
959C2×C4—82no—
960C2×C4C4×C22⋊C412yes—
961C2×C4C4×C22⋊C412yes—
962C2×C4C22×C4211yescharacteristic
963C2×C4C22×C22⋊C411yescharacteristic
964C2×C4C22×C22⋊C411yescharacteristic
965C2×C4C2×#11711yescharacteristic
966C2×C4C2×C4×D411yescharacteristic
967C2×C4C2×C4×D411yescharacteristic
968C2×C4C2×C4×D411yescharacteristic
969C2×C4C2×C4×D411yescharacteristic
970C2×C4C2×C4×D411yescharacteristic
971C2×C4C2×C4×D411yescharacteristic
972C2×C4#51811yescharacteristic
973C2×C4#51811yescharacteristic
974C2×C4#51811yescharacteristic
975C2×C4#51811yescharacteristic
976C2×C4#51811yescharacteristic
977C2×C4#51811yescharacteristic
978C2×C4D4211yescharacteristic
979C2×C4D4211yescharacteristic
980C2×C4D4211yescharacteristic
981C2×C4D4211yescharacteristic
982C2×C4#54611yescharacteristic
983C2×C4#54611yescharacteristic
984C2×C4#54611yescharacteristic
985C2×C4#54611yescharacteristic
986C2×C4#54611yescharacteristic
987C2×C4#54611yescharacteristic
988C2×C4#55111yescharacteristic
989C2×C4#55111yescharacteristic
990C8—22no—
991C8—22no—
992C8—22no—
993C8—22no—
994C8—24no—
995C8—42no—
996C8—42no—
997C8—42no—
998C8—42no—
999C8—42no—
1000C22—22no—
1001C22—22no—
1002C22—22no—
1003C22—22no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—22no—
1009C22—22no—
1010C22—22no—
1011C22—22no—
1012C22—22no—
1013C22—22no—
1014C22—24no—
1015C22—42no—
1016C22—42no—
1017C22—44no—
1018C22—42no—
1019C22—42no—
1020C22—44no—
1021C22—42no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—82no—
1027C22—82no—
1028C22—82no—
1029C22—82no—
1030C22—816no—
1031C22—82no—
1032C22—82no—
1033C22C2×C4×C22⋊C411yescharacteristic
1034C22D4×C22⋊C411yescharacteristic
1035C22#234211yescharacteristic
1036C22#234211yescharacteristic
1037C22#234211yescharacteristic
1038C22#235811yescharacteristic
1039C22#235811yescharacteristic
1040C22#295512yes—
1041C22#295712yes—
1042C4—22no—
1043C4—22no—
1044C4—24no—
1045C4—44no—
1046C4—42no—
1047C4—82no—
1048C4—82no—
1049C4—82no—
1050C4C2×C4×C22⋊C411yescharacteristic
1051C4#227311yescharacteristic
1052C4D4×C22⋊C411yescharacteristic
1053C4D4×C22⋊C411yescharacteristic
1054C4D4×C22⋊C411yescharacteristic
1055C4#234211yescharacteristic
1056C4#235811yescharacteristic
1057C4#235811yescharacteristic
1058C2—21no—
1059C2—21no—
1060C2—21no—
1061C2—21no—
1062C2—42no—
1063C2—42no—
1064C2—44no—
1065C2—82no—
1066C2C22⋊C4211yescharacteristic
1067C2#2042011yescharacteristic
1068C2#2042211yescharacteristic
1069C2#2288712yes—
1070C2#2288912yes—
subgroupG/H
centerC22×C4C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
socleC23C2×C4×D4
prime radicalC23×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C22⋊C8 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1765C2semidirect
5. C2×#1764C2semidirect
6. #20389C2semidirect
7. C2×#1750C2semidirect
8. #10934C2semidirect
9. #10934C2semidirect
10. #10930C2semidirect
11. #10929C2semidirect
12. #10791C2semidirect
13. #10791C2semidirect
14. #10734C2semidirect
15. #10720C2semidirect
23. C2×#421C4semidirect
33. #2880C4semidirect
43. C2×#405C22semidirect
44. C2×#405C22semidirect
45. C22×#97C22semidirect
46. C22×C4×C8C22semidirect
48. #1788C4semidirect
49. #1788C4semidirect
50. #1787C4semidirect
51. #1786C4semidirect
59. C2×#341C22semidirect
60. C2×#341C22semidirect
61. C2×#341C22semidirect
62. C2×#341C22semidirect
63. C2×#339C22semidirect
64. C2×#339C22semidirect
65. C2×#339C22semidirect
66. C2×#339C22semidirect
67. #1729C22semidirect
68. #1729C22semidirect
69. C2×#336C22semidirect
70. C2×#336C22semidirect
481. #104C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4212
C2×#28802
#205972
C2×#17652
C2×#17642
#203892
C2×#17502
#109342
#109302
#109292
#107912
#107342
#107202