Finite Group Databasebeta

← #356644

Subgroups — #356644

Order 512.

1606 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2933C211yesmaximal, characteristic
2#20989C211yesmaximal, characteristic
3#20983C211yesmaximal, characteristic
4C2×#1757C211yesmaximal, characteristic, complemented
5#20389C211yesmaximal, characteristic, complemented
6#20379C211yesmaximal, characteristic, complemented
7C22×#344C211yesmaximal, characteristic, complemented
8#10961C211yesmaximal, characteristic, complemented
9#10961C211yesmaximal, characteristic, complemented
10#10914C211yesmaximal, characteristic, complemented
11#10914C211yesmaximal, characteristic, complemented
12#10803C211yesmaximal, characteristic, complemented
13#10764C211yesmaximal, characteristic, complemented
14#10729C211yesmaximal, characteristic, complemented
15#10711C211yesmaximal, characteristic, complemented
16C22×#131C2211yescharacteristic
17C23×M16C2211yescharacteristic
18C23×M16C2211yescharacteristic
19C2×#525C2211yescharacteristic
20C22×#117C2211yescharacteristic
21#2933—21no—
22#2933—21no—
23#2933—21no—
24#2933—21no—
25#2933—21no—
26#2933—21no—
27#2933—21no—
28#2933—21no—
29C2×#436C412yescomplemented
30C2×#435C412yescomplemented
31C2×#435C412yescomplemented
32C2×C8×D4C412yescomplemented
33C2×#424C2211yescharacteristic
34C2×#413C2211yescharacteristic
35C2×#413C2211yescharacteristic
36C2×#410C2211yescharacteristic
37C2×#410C2211yescharacteristic
38C2×#408C2211yescharacteristic
39C2×#407C2211yescharacteristic
40C22×C22⋊C8C2211yescharacteristic
41C2×#405C2211yescharacteristic
42C2×#405C2211yescharacteristic
43C2×#405C2211yescharacteristic
44C2×#405C2211yescharacteristic
45C2×#405C2211yescharacteristic
46#2280C2211yescharacteristic
47#1901C412yescomplemented
48#1901C412yescomplemented
49#1900C412yescomplemented
50#1900C412yescomplemented
51#1899C414yes—
52#1898C414yes—
53#1757—24no—
54#1753—21no—
55#1753—21no—
56#1752—21no—
57C8×C22⋊C4—21no—
58#1750—21no—
59#1750—21no—
60#1749—21no—
61C4×C22⋊C8—21no—
62C2×#344—24no—
63C2×#344C2211yescharacteristic
64C2×#344C2211yescharacteristic
65C2×#344C2211yescharacteristic
66C2×#344C2211yescharacteristic
67C2×#344C2211yescharacteristic
68C2×#344C2211yescharacteristic
69C2×#344C2211yescharacteristic
70C2×#344C2211yescharacteristic
71#1742C2211yescharacteristic
72#1742C2211yescharacteristic
73#1740C2211yescharacteristic
74#1740C2211yescharacteristic
75#1729C2211yescharacteristic
76#1729C2211yescharacteristic
77#1729C2211yescharacteristic
78#1729C2211yescharacteristic
79C22×#41C2311yescharacteristic
80C24×C4C2311yescharacteristic
81C2×#131—22no—
82C2×#131—22no—
83C2×#131—21no—
84C2×#131—21no—
85C2×#131—21no—
86C2×#131—21no—
87C2×#131—41no—
88C2×#131—41no—
89C22×M16—21no—
90C22×M16—21no—
91C22×M16—21no—
92C22×M16—21no—
93C22×M16—21no—
94C22×M16—21no—
95C22×M16—21no—
96C22×M16—22no—
97C22×M16—22no—
98C22×M16—22no—
99C22×M16—22no—
100C22×M16—41no—
101C22×M16—41no—
102C22×M16—41no—
103C22×M16—41no—
104C22×M16C2×C412yes—
105C22×M16C2×C412yes—
106C22×M16C2×C412yes—
107C22×M16C2×C412yescomplemented
108C22×M16C2311yescharacteristic
109C22×M16C2311yescharacteristic
110C22×M16C2311yescharacteristic
111C22×M16C2311yescharacteristic
112C22×M16C2311yescharacteristic
113C22×M16C2311yescharacteristic
114C23×C8—21no—
115C23×C8C2×C412yes—
116C23×C8C2×C412yescomplemented
117C23×C8C2311yescharacteristic
118C23×C8C2311yescharacteristic
119#525—21no—
120#525—21no—
121#525—21no—
122#525—21no—
123#525—21no—
124#525—21no—
125#525—21no—
126#525—21no—
127C2×#123C2×C412yes—
128C2×C22⋊Q8C2×C411yescharacteristic
129C2×C22⋊Q8C2×C411yescharacteristic
130C2×#121C2×C411yescharacteristic
131C2×#121C2×C411yescharacteristic
132C2×#120C2×C412yes—
133C2×C4×D4C2×C412yes—
134C2×C4×D4C2×C412yes—
135C2×#117—21no—
136C2×#117—21no—
137C2×#117—22no—
138C2×#117—22no—
139C2×#117—41no—
140C2×#117—41no—
141C2×#117C2×C412yes—
142C2×#117C2311yescharacteristic
143C2×#117C2311yescharacteristic
144C2×#117C2311yescharacteristic
145C2×#117C2311yescharacteristic
146C2×#117C2311yescharacteristic
147C22×C4⋊C4—21no—
148C22×C22⋊C4C2×C412yes—
149C22×C42—21no—
150#436—22no—
151#436—22no—
152#436—22no—
153#436—22no—
154#435—22no—
155#435—22no—
156#435—22no—
157#435—22no—
158#435—22no—
159#435—22no—
160#435—22no—
161#435—22no—
162C8×D4—22no—
163C8×D4—22no—
164C8×D4—22no—
165C8×D4—22no—
166#424—21no—
167#424—21no—
168#424—21no—
169#424—21no—
170C2×C4⋊C8C2×C412yescomplemented
171C2×C4⋊C8C2×C412yescomplemented
172#413—22no—
173#413—22no—
174#413—41no—
175#413—41no—
176C2×#101C2×C412yescomplemented
177C2×#101C2×C412yescomplemented
178C2×#100C2×C412yescomplemented
179C2×#100C2×C412yescomplemented
180#410—22no—
181#410—22no—
182#410—41no—
183#410—41no—
184C2×#99C2×C414yes—
185C2×#99C2×C414yes—
186#408—21no—
187#408—21no—
188#408—21no—
189#408—21no—
190#407—21no—
191#407—21no—
192#407C2×C412yes—
193#407C2×C412yes—
194C2×C22⋊C8—21no—
195C2×C22⋊C8—21no—
196C2×C22⋊C8C2×C411yescharacteristic
197C2×C22⋊C8C2×C411yescharacteristic
198C2×C22⋊C8C2×C411yescharacteristic
199C2×C22⋊C8C2×C411yescharacteristic
200C2×C22⋊C8C2×C412yescomplemented
201C2×C22⋊C8C2×C412yescomplemented
202C2×C22⋊C8D411yescharacteristic
203C2×C22⋊C8D411yescharacteristic
204C2×C22⋊C8D411yescharacteristic
205C2×C22⋊C8D411yescharacteristic
206C2×C22⋊C8D411yescharacteristic
207C2×C22⋊C8D411yescharacteristic
208C2×C22⋊C8D411yescharacteristic
209C2×C22⋊C8D411yescharacteristic
210#405—21no—
211#405—21no—
212#405—21no—
213#405—21no—
214#405—22no—
215#405—22no—
216#405—22no—
217#405—22no—
218#405—41no—
219#405—41no—
220#405—41no—
221#405—41no—
222C2×#97—21no—
223C2×#97—21no—
224C2×#97—21no—
225C2×#97—21no—
226C2×#97C2×C412yescomplemented
227C2×C4×C8—21no—
228C2×C4×C8—21no—
229C2×C4×C8—21no—
230C2×C4×C8—21no—
231C2×C4×C8C2×C412yescomplemented
232#381C2×C412yes—
233#380—21no—
234#380—21no—
235#379C2×C412yes—
236C4×C22⋊C4—21no—
237C4×C22⋊C4—21no—
238#344—22no—
239#344—22no—
240#344—22no—
241#344—22no—
242#344—22no—
243#344—41no—
244#344—41no—
245#344D414yescomplemented
246#343C2×C412yescomplemented
247#343C2×C412yescomplemented
248#343C2×C412yescomplemented
249#343C2×C412yescomplemented
250#342C2×C414yes—
251#342C2×C414yes—
252#336—21no—
253#336—21no—
254#336—21no—
255#336—21no—
256#336—21no—
257#336—21no—
258#336—21no—
259#336—21no—
260C25C22×C411yescharacteristic
261C2×#41—21no—
262C2×#41—21no—
263C2×#41—21no—
264C2×#41—21no—
265C2×#41—21no—
266C2×#41—21no—
267C2×#41—21no—
268C2×#41—21no—
269C2×#41—21no—
270C2×#41—21no—
271C2×#41—21no—
272C2×#41—21no—
273C22×Q8C22×C411yescharacteristic
274C22×D4C4212yes—
275C22×D4C4212yes—
276C22×D4C22×C412yes—
277C22×D4C22×C411yescharacteristic
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—22no—
287C23×C4C22×C412yes—
288C23×C4C22×C411yescharacteristic
289C23×C4C22×C411yescharacteristic
290C23×C4C22×C411yescharacteristic
291C23×C4C22×C411yescharacteristic
292C23×C4C22×C411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4#4111yescharacteristic
298C23×C4#4111yescharacteristic
299C23×C4#4111yescharacteristic
300C23×C4#4111yescharacteristic
301C23×C4C2411yescharacteristic
302#131—42no—
303#131—42no—
304#131—42no—
305#131—42no—
306#131—42no—
307#131—42no—
308#131—42no—
309#131—42no—
310C2×M16—21no—
311C2×M16—21no—
312C2×M16—21no—
313C2×M16—21no—
314C2×M16—21no—
315C2×M16—21no—
316C2×M16—21no—
317C2×M16—22no—
318C2×M16—22no—
319C2×M16—22no—
320C2×M16—22no—
321C2×M16—21no—
322C2×M16—21no—
323C2×M16—21no—
324C2×M16—21no—
325C2×M16—21no—
326C2×M16—21no—
327C2×M16—21no—
328C2×M16—21no—
329C2×M16—21no—
330C2×M16—22no—
331C2×M16—22no—
332C2×M16—24no—
333C2×M16—24no—
334C2×M16—21no—
335C2×M16—21no—
336C2×M16—21no—
337C2×M16—21no—
338C2×M16—21no—
339C2×M16—21no—
340C2×M16—21no—
341C2×M16—21no—
342C2×M16—21no—
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—24no—
347C2×M16—24no—
348C2×M16—42no—
349C2×M16—42no—
350C2×M16—42no—
351C2×M16—42no—
352C2×M16—42no—
353C2×M16—42no—
354C2×M16—42no—
355C2×M16—42no—
356C2×M16—42no—
357C2×M16—42no—
358C2×M16—42no—
359C2×M16—42no—
360C2×M16—42no—
361C2×M16—42no—
362C2×M16—42no—
363C2×M16—42no—
364C2×M16—42no—
365C2×M16—42no—
366C2×M16C22×C412yes—
367C2×M16C22×C412yes—
368C2×M16C22×C412yes—
369C2×M16C22×C412yes—
370C2×M16C2×D412yes—
371C2×M16C2×D412yes—
372C2×M16#4112yes—
373C2×M16#4112yes—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—21no—
382C22×C8—21no—
383C22×C8—22no—
384C22×C8—22no—
385C22×C8—22no—
386C22×C8—22no—
387C22×C8—21no—
388C22×C8—21no—
389C22×C8—21no—
390C22×C8—22no—
391C22×C8—22no—
392C22×C8—24no—
393C22×C8—24no—
394C22×C8—42no—
395C22×C8—42no—
396C22×C8—42no—
397C22×C8—42no—
398C22×C8C22×C412yes—
399C22×C8C22×C411yescharacteristic
400C22×C8C22×C411yescharacteristic
401C22×C8C22×C411yescharacteristic
402C22×C8C22×C411yescharacteristic
403C22×C8C22×C412yes—
404C22×C8C2×D411yescharacteristic
405C22×C8C2×D411yescharacteristic
406C22×C8C2×D411yescharacteristic
407C22×C8C2×D411yescharacteristic
408C22×C8C2×D411yescharacteristic
409C22×C8C2×D411yescharacteristic
410C22×C8C2×D411yescharacteristic
411C22×C8C2×D411yescharacteristic
412#123—22no—
413#123—22no—
414#123—22no—
415#123—22no—
416C22⋊Q8—21no—
417C22⋊Q8—21no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—21no—
421C22⋊Q8—21no—
422C22⋊Q8—21no—
423C22⋊Q8—21no—
424#121—21no—
425#121—21no—
426#121—21no—
427#121—21no—
428#121—21no—
429#121—21no—
430#121—21no—
431#121—21no—
432#120—22no—
433#120—22no—
434#120—22no—
435#120—22no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—22no—
441C4×D4—22no—
442C4×D4—22no—
443C4×D4—22no—
444#117—21no—
445#117—21no—
446#117—21no—
447#117—21no—
448#117—21no—
449#117—21no—
450#117—21no—
451#117—21no—
452#117—21no—
453#117—21no—
454#117—21no—
455#117—21no—
456#117—21no—
457#117—21no—
458#117—21no—
459#117—21no—
460#117—21no—
461#117—21no—
462#117—24no—
463#117—42no—
464#117—42no—
465#117—42no—
466#117—42no—
467#117—42no—
468#117C2×D412yes—
469#117#4112yes—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—42no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4C4212yes—
478C2×C4⋊C4C4212yes—
479C2×C4⋊C4C22×C411yescharacteristic
480C2×C4⋊C4C22×C411yescharacteristic
481C2×C22⋊C4—24no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4C4212yes—
487C2×C22⋊C4C4212yes—
488C2×C22⋊C4C4212yes—
489C2×C22⋊C4C4212yes—
490C2×C22⋊C4C22×C412yes—
491C2×C22⋊C4C22×C412yes—
492C2×C22⋊C4C22×C412yes—
493C2×C22⋊C4C22×C412yes—
494C2×C22⋊C4C22×C412yes—
495C2×C42—21no—
496C2×C42—22no—
497C2×C42—21no—
498C2×C42—21no—
499C2×C42—21no—
500C2×C42—42no—
501C2×C42—42no—
502C2×C42C22×C412yes—
503C4⋊C8—22no—
504C4⋊C8—22no—
505C4⋊C8—22no—
506C4⋊C8—22no—
507#101—24no—
508#101—42no—
509#100—24no—
510#100—42no—
511#99—28no—
512#99—44no—
513C22⋊C8—22no—
514C22⋊C8—22no—
515C22⋊C8—22no—
516C22⋊C8—22no—
517C22⋊C8—22no—
518C22⋊C8—22no—
519C22⋊C8—22no—
520C22⋊C8—22no—
521C22⋊C8C22⋊C411yescharacteristic
522C22⋊C8C22⋊C411yescharacteristic
523C22⋊C8C22⋊C411yescharacteristic
524C22⋊C8C22⋊C411yescharacteristic
525C22⋊C8C22⋊C411yescharacteristic
526C22⋊C8C22⋊C411yescharacteristic
527C22⋊C8C22⋊C411yescharacteristic
528C22⋊C8C22⋊C411yescharacteristic
529C22⋊C8C22⋊C411yescharacteristic
530C22⋊C8C22⋊C411yescharacteristic
531C22⋊C8C22⋊C411yescharacteristic
532C22⋊C8C22⋊C411yescharacteristic
533C22⋊C8C22⋊C411yescharacteristic
534C22⋊C8C22⋊C411yescharacteristic
535C22⋊C8C22⋊C411yescharacteristic
536C22⋊C8C22⋊C411yescharacteristic
537#97—22no—
538#97—22no—
539#97—42no—
540#97—42no—
541#97—42no—
542#97—42no—
543C4×C8—22no—
544C4×C8—22no—
545C4×C8—42no—
546C4×C8—42no—
547C4×C8—42no—
548C4×C8—42no—
549#95—22no—
550#95—22no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24—21no—
555C24—42no—
556C24—81no—
557C24C2×C4211yescharacteristic
558C24C2×C4212yes—
559C24C2×C4211yescharacteristic
560C24C4×D411yescharacteristic
561C24C4×D411yescharacteristic
562C24C4×D411yescharacteristic
563C24C4×D411yescharacteristic
564C24C23×C411yescharacteristic
565#41—41no—
566#41—41no—
567#41—41no—
568#41—41no—
569#41—41no—
570#41—41no—
571#41—41no—
572#41—41no—
573#41—41no—
574#41—41no—
575#41—41no—
576#41—41no—
577#41—41no—
578#41—41no—
579#41—41no—
580#41—41no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—44no—
604C2×D4—82no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—82no—
670C22×C4C2×C4212yes—
671C22×C4C2×C4211yescharacteristic
672C22×C4C2×C4211yescharacteristic
673C22×C4C2×C4212yes—
674C22×C4C2×C4212yes—
675C22×C4C2×C22⋊C411yescharacteristic
676C22×C4C2×C22⋊C411yescharacteristic
677C22×C4C2×C22⋊C411yescharacteristic
678C22×C4C2×C22⋊C411yescharacteristic
679C22×C4#11711yescharacteristic
680C22×C4#11711yescharacteristic
681C22×C4#11711yescharacteristic
682C22×C4#11711yescharacteristic
683C22×C4C4×D411yescharacteristic
684C22×C4C4×D411yescharacteristic
685C22×C4C4×D411yescharacteristic
686C22×C4C4×D411yescharacteristic
687C22×C4C4×D411yescharacteristic
688C22×C4C4×D411yescharacteristic
689C22×C4C4×D411yescharacteristic
690C22×C4C4×D411yescharacteristic
691C22×C4C4×D411yescharacteristic
692C22×C4C4×D411yescharacteristic
693C22×C4C4×D411yescharacteristic
694C22×C4C4×D411yescharacteristic
695C22×C4C23×C411yescharacteristic
696C22×C4C23×C411yescharacteristic
697C22×C4C22×D411yescharacteristic
698C22×C4C22×D411yescharacteristic
699C22×C4C22×D411yescharacteristic
700C22×C4C2×#4111yescharacteristic
701C22×C4C2×#4111yescharacteristic
702C22×C4C2×#4111yescharacteristic
703C22×C4C2×#4111yescharacteristic
704C22×C4C2×#4111yescharacteristic
705C22×C4H(5,𝔽2)11yescharacteristic
706C22×C4H(5,𝔽2)11yescharacteristic
707C22×C4H(5,𝔽2)11yescharacteristic
708C22×C42−1+411yescharacteristic
709M16—22no—
710M16—22no—
711M16—22no—
712M16—22no—
713M16—22no—
714M16—22no—
715M16—22no—
716M16—22no—
717M16—22no—
718M16—22no—
719M16—22no—
720M16—22no—
721M16—22no—
722M16—44no—
723M16—44no—
724M16—44no—
725M16—44no—
726M16—44no—
727M16—44no—
728M16—41no—
729M16—41no—
730M16—41no—
731M16—41no—
732M16—41no—
733M16—41no—
734M16—41no—
735M16—41no—
736M16—41no—
737M16—41no—
738M16C4×D414yes—
739C2×C8—22no—
740C2×C8—21no—
741C2×C8—22no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—22no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—22no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—22no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—22no—
769C2×C8—22no—
770C2×C8—22no—
771C2×C8—22no—
772C2×C8—22no—
773C2×C8—22no—
774C2×C8—44no—
775C2×C8—44no—
776C2×C8—44no—
777C2×C8—44no—
778C2×C8—44no—
779C2×C8—44no—
780C2×C8—41no—
781C2×C8—41no—
782C2×C8—41no—
783C2×C8—41no—
784C2×C8—41no—
785C2×C8—41no—
786C2×C8C2×C22⋊C411yescharacteristic
787C2×C8C2×C22⋊C411yescharacteristic
788C2×C8C2×C22⋊C411yescharacteristic
789C2×C8C2×C22⋊C411yescharacteristic
790C2×C8C2×C22⋊C411yescharacteristic
791C2×C8C2×C22⋊C411yescharacteristic
792C2×C8C2×C22⋊C411yescharacteristic
793C2×C8C2×C22⋊C411yescharacteristic
794C2×C8C4×D414yes—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—22no—
800C4⋊C4—22no—
801C4⋊C4—22no—
802C4⋊C4—22no—
803C4⋊C4—22no—
804C4⋊C4—22no—
805C4⋊C4—44no—
806C4⋊C4—41no—
807C4⋊C4—41no—
808C4⋊C4—41no—
809C4⋊C4—41no—
810C4⋊C4—41no—
811C4⋊C4—41no—
812C22⋊C4—22no—
813C22⋊C4—22no—
814C22⋊C4—22no—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—22no—
818C22⋊C4—22no—
819C22⋊C4—22no—
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—22no—
826C22⋊C4—22no—
827C22⋊C4—22no—
828C22⋊C4—22no—
829C22⋊C4—44no—
830C22⋊C4—44no—
831C22⋊C4—82no—
832C22⋊C4C4×D414yes—
833C42—22no—
834C42—22no—
835C42—22no—
836C42—22no—
837C42—44no—
838C42—41no—
839C42—41no—
840C42—41no—
841C42—41no—
842C42—41no—
843C42—41no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—21no—
855C23—21no—
856C23—21no—
857C23—21no—
858C23—21no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—42no—
874C23—42no—
875C23—82no—
876C23—82no—
877C23—82no—
878C23—82no—
879C23C4×C22⋊C411yescharacteristic
880C23C4×C22⋊C411yescharacteristic
881C23C4×C22⋊C411yescharacteristic
882C23C4×C22⋊C411yescharacteristic
883C23C22×C4211yescharacteristic
884C23C2×C4×D411yescharacteristic
885C23C2×C4×D411yescharacteristic
886C23C2×C4×D411yescharacteristic
887C23C4×#4111yescharacteristic
888C23#51811yescharacteristic
889C23#52011yescharacteristic
890Q8—41no—
891Q8—41no—
892Q8—41no—
893Q8—41no—
894D4—44no—
895D4—42no—
896D4—42no—
897D4—42no—
898D4—42no—
899D4—44no—
900D4—41no—
901D4—41no—
902D4—41no—
903D4—41no—
904D4—82no—
905D4—82no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—88no—
974C2×C4C4×C22⋊C411yescharacteristic
975C2×C4C4×C22⋊C411yescharacteristic
976C2×C4C4×C22⋊C411yescharacteristic
977C2×C4C4×C22⋊C411yescharacteristic
978C2×C4C22×C22⋊C411yescharacteristic
979C2×C4C2×#11711yescharacteristic
980C2×C4C2×C4×D411yescharacteristic
981C2×C4C2×C4×D411yescharacteristic
982C2×C4C2×C4×D411yescharacteristic
983C2×C4C2×C4×D411yescharacteristic
984C2×C4C4×#4111yescharacteristic
985C2×C4C4×#4111yescharacteristic
986C2×C4#51811yescharacteristic
987C2×C4#51811yescharacteristic
988C2×C4#52011yescharacteristic
989C2×C4#52011yescharacteristic
990C2×C4D4211yescharacteristic
991C2×C4D4211yescharacteristic
992C2×C4#54611yescharacteristic
993C2×C4#54611yescharacteristic
994C2×C4#54611yescharacteristic
995C2×C4#54611yescharacteristic
996C2×C4#54611yescharacteristic
997C2×C4#54711yescharacteristic
998C2×C4#54711yescharacteristic
999C2×C4#54811yescharacteristic
1000C2×C4#55111yescharacteristic
1001C2×C4#55111yescharacteristic
1002C2×C4#55211yescharacteristic
1003C2×C4#55311yescharacteristic
1004C2×C4#55311yescharacteristic
1005C2×C4#55311yescharacteristic
1006C8—21no—
1007C8—21no—
1008C8—21no—
1009C8—21no—
1010C8—24no—
1011C8—21no—
1012C8—21no—
1013C8—21no—
1014C8—21no—
1015C8—24no—
1016C8—42no—
1017C8—42no—
1018C8—42no—
1019C8—42no—
1020C22—21no—
1021C22—21no—
1022C22—21no—
1023C22—21no—
1024C22—21no—
1025C22—21no—
1026C22—21no—
1027C22—21no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—21no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—21no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—81no—
1051C22—81no—
1052C22—81no—
1053C22—81no—
1054C22—81no—
1055C22—81no—
1056C22—82no—
1057C22—82no—
1058C22#175712yescomplemented
1059C22C2×C4×C22⋊C411yescharacteristic
1060C22C42×D411yescharacteristic
1061C22#227511yescharacteristic
1062C22#235811yescharacteristic
1063C22#235911yescharacteristic
1064C22#236111yescharacteristic
1065C22#236411yescharacteristic
1066C4—21no—
1067C4—21no—
1068C4—21no—
1069C4—21no—
1070C4—44no—
1071C4—42no—
1072C4—42no—
1073C4—42no—
1074C4—82no—
1075C4—82no—
1076C4—82no—
1077C4D4×C22⋊C411yescharacteristic
1078C4#233911yescharacteristic
1079C4#235211yescharacteristic
1080C4#235311yescharacteristic
1081C4#235811yescharacteristic
1082C4#235911yescharacteristic
1083C4#236111yescharacteristic
1084C4#236411yescharacteristic
1085C2—21no—
1086C2—21no—
1087C2—21no—
1088C2—22no—
1089C2—21no—
1090C2—21no—
1091C2—21no—
1092C2—41no—
1093C2—41no—
1094C2—41no—
1095C2—82no—
1096C2#1381311yescharacteristic
1097C2C2×#175711yescharacteristic
1098C2#2040111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊C4
commutatorC23C22×C42
Frattini, cosocleC23×C4C24
socleC22C2×C4×C22⋊C4
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×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×#1757C2semidirect
5. #20389C2semidirect
6. #20379C2semidirect
7. C22×#344C2semidirect
8. #10961C2semidirect
9. #10961C2semidirect
10. #10914C2semidirect
11. #10914C2semidirect
12. #10803C2semidirect
13. #10764C2semidirect
14. #10729C2semidirect
15. #10711C2semidirect
29. C2×#436C4semidirect
30. C2×#435C4semidirect
31. C2×#435C4semidirect
32. C2×C8×D4C4semidirect
47. #1901C4semidirect
48. #1901C4semidirect
49. #1900C4semidirect
50. #1900C4semidirect
107. C22×M16C2×C4semidirect
116. C23×C8C2×C4semidirect
170. C2×C4⋊C8C2×C4semidirect
171. C2×C4⋊C8C2×C4semidirect
176. C2×#101C2×C4semidirect
177. C2×#101C2×C4semidirect
178. C2×#100C2×C4semidirect
179. C2×#100C2×C4semidirect
200. C2×C22⋊C8C2×C4semidirect
201. C2×C22⋊C8C2×C4semidirect
226. C2×#97C2×C4semidirect
231. C2×C4×C8C2×C4semidirect
245. #344D4semidirect
246. #343C2×C4semidirect
247. #343C2×C4semidirect
248. #343C2×C4semidirect
249. #343C2×C4semidirect
1058. C22#1757semidirect

Maximal subgroups

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

subgroupindex
C2×#29332
#209892
#209832
C2×#17572
#203892
#203792
C22×#3442
#109612
#109142
#108032
#107642
#107292
#107112