Finite Group Databasebeta

← #383365

Subgroups — #383365

Order 512.

1235 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3091C211yesmaximal, characteristic
2#21191C211yesmaximal, characteristic
3C2×#1945C211yesmaximal, characteristic, complemented
4C2×#1922C211yesmaximal, characteristic, complemented
5#20628C211yesmaximal, characteristic, complemented
6#11221C211yesmaximal, characteristic, complemented
7#11125C211yesmaximal, characteristic, complemented
8#11097C211yesmaximal, characteristic, complemented
9#11068C211yesmaximal, characteristic, complemented
10#11068C211yesmaximal, characteristic, complemented
11#10971C211yesmaximal, characteristic
12#10929C211yesmaximal, characteristic, complemented
13#10921C211yesmaximal, characteristic, complemented
14#10909C211yesmaximal, characteristic, complemented
15#10733C211yesmaximal, characteristic, complemented
16C2×#525C2211yescharacteristic
17C22×#117C2211yescharacteristic
18#3091—24no—
19#3091—24no—
20C2×#484C411yescharacteristic, complemented
21C2×#481C411yescharacteristic, complemented
22C2×#485C411yescharacteristic, complemented
23C2×#485C411yescharacteristic, complemented
24C2×#482C411yescharacteristic, complemented
25C2×#482C411yescharacteristic, complemented
26C2×#483C411yescharacteristic, complemented
27C2×#480C411yescharacteristic, complemented
28C22×#108C2211yescharacteristic
29C2×#427C2211yescharacteristic
30C2×#427C2211yescharacteristic
31C2×#424C2211yescharacteristic
32C2×#424C2211yescharacteristic
33C2×#424C2211yescharacteristic
34C22×#104C2211yescharacteristic
35C22×#104C2211yescharacteristic
36C2×#416C2211yescharacteristic
37C2×#416C2211yescharacteristic
38C2×#408C2211yescharacteristic
39C2×#408C2211yescharacteristic
40C2×#407C2211yescharacteristic
41C2×#407C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C2×#405C2211yescharacteristic
45C22×C4×C8C2211yescharacteristic
46C2×C4×C22⋊C4C2211yescharacteristic
47#1955—21no—
48#1955—21no—
49#1954—21no—
50#1954—21no—
51#1945—24no—
52#1922—24no—
53#1798—21no—
54#1798—21no—
55#1797—21no—
56#1797—21no—
57C2×#341C2211yescharacteristic
58C2×#341C2211yescharacteristic
59C2×#341C2211yescharacteristic
60C2×#339C2211yescharacteristic
61C2×#339C2211yescharacteristic
62C2×#339C2211yescharacteristic
63C2×#339C2211yescharacteristic
64C2×#339C2211yescharacteristic
65C2×#339C2211yescharacteristic
66#1729C2211yescharacteristic
67#1729C2211yescharacteristic
68C2×#336C2211yescharacteristic
69C2×#336C2211yescharacteristic
70C2×#336C2211yescharacteristic
71C22×#41C2311yescharacteristic
72C24×C4C2311yescharacteristic
73C22×M16C2311yescharacteristic
74C22×M16C2311yescharacteristic
75C22×M16C2311yescharacteristic
76C22×M16C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C23×C8C2311yescharacteristic
81#525—22no—
82#525—22no—
83#525—41no—
84#525—41no—
85C2×#123—21no—
86C2×C22⋊Q8C2×C411yescharacteristic
87C2×C22⋊Q8C2×C411yescharacteristic
88C2×#121C2×C411yescharacteristic
89C2×#121C2×C411yescharacteristic
90C2×#120—21no—
91C2×C4×D4—21no—
92C2×C4×D4—21no—
93C2×#117—21no—
94C2×#117—21no—
95C2×#117—22no—
96C2×#117—22no—
97C2×#117—41no—
98C2×#117—41no—
99C2×#117C2×C411yescharacteristic
100C2×#117C2×C411yescharacteristic
101C2×#117C2311yescharacteristic
102C2×#117C2311yescharacteristic
103C2×#117C2311yescharacteristic
104C22×C4⋊C4C2×C411yescharacteristic
105C22×C4⋊C4C2×C411yescharacteristic
106C22×C22⋊C4—21no—
107C22×C22⋊C4—21no—
108C22×C42—21no—
109C22×C42C2311yescharacteristic
110C22×C42C2311yescharacteristic
111#485—24no—
112#485—24no—
113#484—24no—
114#483—24no—
115#482—24no—
116#482—24no—
117#481—24no—
118#480—24no—
119C2×#108—22no—
120C2×#108—41no—
121C2×#108—41no—
122#427—22no—
123#427—22no—
124#427D414yes—
125#427D414yes—
126C2×#107C2×C411yescharacteristic
127C2×#107C2×C411yescharacteristic
128C2×#107C2×C411yescharacteristic
129C2×#107C2×C411yescharacteristic
130C2×#106C2×C411yescharacteristic
131C2×#106C2×C411yescharacteristic
132C2×#106C2×C411yescharacteristic
133C2×#106C2×C411yescharacteristic
134#424—22no—
135#424—22no—
136#424—22no—
137#424—41no—
138#424—41no—
139#424—41no—
140C2×C4⋊C8—21no—
141C2×C4⋊C8—21no—
142C2×C4⋊C8—21no—
143C2×C4⋊C8—21no—
144C2×C4⋊C8—21no—
145C2×C4⋊C8—21no—
146C2×#104—22no—
147C2×#104—41no—
148C2×#104—41no—
149C2×#104—41no—
150C2×#104—41no—
151C2×#104—41no—
152#416—22no—
153#416—22no—
154#416—22no—
155#416—22no—
156C2×#103C2×C411yescharacteristic
157C2×#103C2×C411yescharacteristic
158C2×#103C2×C411yescharacteristic
159C2×#103C2×C411yescharacteristic
160C2×#102C2×C411yescharacteristic
161C2×#102C2×C411yescharacteristic
162C2×#102C2×C411yescharacteristic
163C2×#102C2×C411yescharacteristic
164#408—22no—
165#408—41no—
166#408—41no—
167#408—41no—
168#407—22no—
169#407—41no—
170#407—41no—
171#407—41no—
172C2×C22⋊C8—22no—
173C2×C22⋊C8—22no—
174C2×C22⋊C8—21no—
175C2×C22⋊C8—21no—
176C2×C22⋊C8—21no—
177C2×C22⋊C8—21no—
178C2×C22⋊C8—21no—
179C2×C22⋊C8—21no—
180C2×C22⋊C8—21no—
181C2×C22⋊C8—21no—
182C2×C22⋊C8—41no—
183C2×C22⋊C8—41no—
184C2×C22⋊C8C2×C411yescharacteristic
185C2×C22⋊C8C2×C411yescharacteristic
186C2×C22⋊C8C2×C411yescharacteristic
187C2×C22⋊C8C2×C411yescharacteristic
188C2×C22⋊C8D411yescharacteristic
189C2×C22⋊C8D411yescharacteristic
190C2×C22⋊C8D411yescharacteristic
191C2×C22⋊C8D411yescharacteristic
192#405—22no—
193#405—41no—
194C2×#97—21no—
195C2×C4×C8—22no—
196C2×C4×C8—21no—
197C2×C4×C8—41no—
198C2×C4×C8—41no—
199C4×C22⋊C4—22no—
200C4×C22⋊C4—41no—
201C2×#95—21no—
202#341—22no—
203#341—22no—
204#341—41no—
205#339—22no—
206#339—22no—
207#339—22no—
208#339—22no—
209#339—41no—
210#339—41no—
211#336—21no—
212#336—21no—
213#336—21no—
214#336—21no—
215#336—22no—
216#336—22no—
217#336—41no—
218C25#4111yescharacteristic
219C2×#41—21no—
220C2×#41—21no—
221C2×#41—21no—
222C2×#41—21no—
223C2×#41—21no—
224C2×#41—21no—
225C2×#41—21no—
226C2×#41—21no—
227C2×#41—21no—
228C2×#41—21no—
229C2×#41—21no—
230C2×#41—21no—
231C22×Q8C22×C411yescharacteristic
232C22×D4—21no—
233C22×D4—21no—
234C22×D4—21no—
235C22×D4C22×C411yescharacteristic
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4C22×C411yescharacteristic
254C23×C4C22×C411yescharacteristic
255C23×C4C2×D411yescharacteristic
256C23×C4C2×D411yescharacteristic
257C23×C4#4111yescharacteristic
258C23×C4C2411yescharacteristic
259C2×M16—21no—
260C2×M16—21no—
261C2×M16—21no—
262C2×M16—21no—
263C2×M16—21no—
264C2×M16—21no—
265C2×M16—21no—
266C2×M16—21no—
267C2×M16—21no—
268C2×M16—21no—
269C2×M16—21no—
270C2×M16—21no—
271C2×M16—21no—
272C2×M16—21no—
273C2×M16—21no—
274C2×M16—21no—
275C2×M16—21no—
276C2×M16—21no—
277C2×M16—21no—
278C2×M16—21no—
279C2×M16—21no—
280C2×M16—21no—
281C2×M16—21no—
282C2×M16#4112yes—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8—21no—
295C22×C8—21no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8—21no—
301C22×C8—21no—
302C22×C8—21no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—21no—
306C22×C8—21no—
307C22×C8—21no—
308C22×C8—21no—
309C22×C8C22×C411yescharacteristic
310C22×C8C22×C411yescharacteristic
311C22×C8C22×C411yescharacteristic
312C22×C8C22×C411yescharacteristic
313C22×C8C2×D411yescharacteristic
314C22×C8C2×D411yescharacteristic
315C22×C8C2×D411yescharacteristic
316C22×C8C2×D411yescharacteristic
317C22×C8C2×D412yes—
318C22×C8C2×D412yes—
319#123—42no—
320#123—42no—
321C22⋊Q8—22no—
322C22⋊Q8—22no—
323C22⋊Q8—41no—
324C22⋊Q8—41no—
325#121—22no—
326#121—22no—
327#121—41no—
328#121—41no—
329#120—42no—
330#120—42no—
331C4×D4—42no—
332C4×D4—42no—
333C4×D4—42no—
334C4×D4—42no—
335#117—21no—
336#117—21no—
337#117—21no—
338#117—21no—
339#117—21no—
340#117—21no—
341#117—21no—
342#117—21no—
343#117—22no—
344#117—22no—
345#117—42no—
346#117—42no—
347#117—42no—
348#117—42no—
349#117—41no—
350#117—41no—
351#117C2×D412yes—
352#117C2×D412yes—
353#117C2×D412yes—
354#117C2×D412yes—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—41no—
362C2×C4⋊C4—41no—
363C2×C4⋊C4C22×C411yescharacteristic
364C2×C4⋊C4C22×C411yescharacteristic
365C2×C4⋊C4C22×C411yescharacteristic
366C2×C4⋊C4C22×C411yescharacteristic
367C2×C4⋊C4C22×C411yescharacteristic
368C2×C4⋊C4C22×C411yescharacteristic
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42#4112yes—
402#108—44no—
403#107—22no—
404#107—22no—
405#107C22⋊C414yescomplemented
406#107C22⋊C414yescomplemented
407#106—22no—
408#106—22no—
409#106C22⋊C414yescomplemented
410#106C22⋊C414yescomplemented
411C4⋊C8—42no—
412C4⋊C8—42no—
413C4⋊C8—42no—
414C4⋊C8—42no—
415C4⋊C8—42no—
416C4⋊C8—42no—
417#104—44no—
418#104—44no—
419#103—22no—
420#103—22no—
421#103—22no—
422#103—22no—
423#102—22no—
424#102—22no—
425#102—22no—
426#102—22no—
427C22⋊C8—22no—
428C22⋊C8—22no—
429C22⋊C8—22no—
430C22⋊C8—22no—
431C22⋊C8—41no—
432C22⋊C8—41no—
433C22⋊C8—41no—
434C22⋊C8—41no—
435C22⋊C8—42no—
436C22⋊C8—42no—
437C22⋊C8—42no—
438C22⋊C8—42no—
439C22⋊C8—42no—
440C22⋊C8—42no—
441C22⋊C8—42no—
442C22⋊C8—42no—
443#97—42no—
444C4×C8—42no—
445C4×C8—44no—
446#95—42no—
447C24—22no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—41no—
456C24—41no—
457C24—41no—
458C24C4×D411yescharacteristic
459C24C4×D411yescharacteristic
460C24C2×#4111yescharacteristic
461#41—41no—
462#41—41no—
463#41—41no—
464#41—41no—
465#41—41no—
466#41—41no—
467#41—41no—
468#41—41no—
469#41—41no—
470#41—41no—
471#41—41no—
472#41—41no—
473#41—41no—
474#41—41no—
475#41—41no—
476#41—41no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—41no—
493C2×D4—41no—
494C2×D4—41no—
495C2×D4—41no—
496C2×D4—41no—
497C2×D4—41no—
498C2×D4—42no—
499C2×D4—81no—
500C2×D4—81no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—42no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—42no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—81no—
579C22×C4—81no—
580C22×C4C4×D411yescharacteristic
581C22×C4C4×D411yescharacteristic
582C22×C4C23×C411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C2×#4111yescharacteristic
587C22×C4C2×#4111yescharacteristic
588C22×C4H(5,𝔽2)11yescharacteristic
589C22×C4H(5,𝔽2)11yescharacteristic
590C22×C4H(5,𝔽2)11yescharacteristic
591C22×C4H(5,𝔽2)11yescharacteristic
592C22×C4H(5,𝔽2)11yescharacteristic
593C22×C42−1+411yescharacteristic
594C22×C42−1+411yescharacteristic
595C22×C42−1+411yescharacteristic
596M16—22no—
597M16—22no—
598M16—41no—
599M16—41no—
600M16—41no—
601M16—41no—
602M16—41no—
603M16—41no—
604M16—41no—
605M16—41no—
606M16—41no—
607M16—41no—
608M16—41no—
609M16—41no—
610M16—41no—
611M16—41no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—22no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—41no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—41no—
646C2×C8—41no—
647C2×C8—41no—
648C2×C8—41no—
649C2×C8—41no—
650C2×C8—41no—
651C2×C8—41no—
652C2×C8—41no—
653C2×C8—41no—
654C2×C8—41no—
655C2×C8—41no—
656C2×C8—41no—
657C2×C8—41no—
658C2×C8—41no—
659C2×C8—41no—
660C2×C8—41no—
661C2×C8—41no—
662C2×C8C2×C22⋊C412yes—
663C2×C8C2×C22⋊C412yes—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4C2×C22⋊C412yes—
677C4⋊C4C2×C22⋊C412yes—
678C4⋊C4C2×C22⋊C412yes—
679C4⋊C4C2×C22⋊C412yes—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—48no—
691C22⋊C4—41no—
692C22⋊C4—41no—
693C42—22no—
694C42—22no—
695C42—22no—
696C42—22no—
697C42—22no—
698C42—22no—
699C42—42no—
700C42—42no—
701C42—41no—
702C42—41no—
703C42—41no—
704C42—41no—
705C42—41no—
706C42—41no—
707C42—41no—
708C42—41no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—81no—
744C23—81no—
745C23—81no—
746C23—81no—
747C23—81no—
748C23—81no—
749C23#44312yes—
750C23C2×C4×D411yescharacteristic
751C23#53911yescharacteristic
752C23#53911yescharacteristic
753C23#54611yescharacteristic
754C23#54611yescharacteristic
755C23#55111yescharacteristic
756C23#55211yescharacteristic
757Q8—41no—
758Q8—41no—
759Q8—41no—
760Q8—41no—
761D4—41no—
762D4—41no—
763D4—41no—
764D4—41no—
765D4—84no—
766D4—84no—
767D4—81no—
768D4—81no—
769D4—81no—
770D4—81no—
771C2×C4—24no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—84no—
829C2×C4—84no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4C22×C22⋊C411yescharacteristic
839C2×C4C4×#4111yescharacteristic
840C2×C4#51811yescharacteristic
841C2×C4#52011yescharacteristic
842C2×C4#52011yescharacteristic
843C2×C4#52011yescharacteristic
844C2×C4#53411yescharacteristic
845C2×C4#53511yescharacteristic
846C2×C4#53611yescharacteristic
847C2×C4#53611yescharacteristic
848C2×C4#53711yescharacteristic
849C2×C4#53711yescharacteristic
850C2×C4#53811yescharacteristic
851C2×C4#53911yescharacteristic
852C2×C4#54011yescharacteristic
853C2×C4#54211yescharacteristic
854C2×C4D4211yescharacteristic
855C2×C4D4211yescharacteristic
856C2×C4#54611yescharacteristic
857C2×C4#54711yescharacteristic
858C2×C4#54811yescharacteristic
859C2×C4#54811yescharacteristic
860C2×C4#55011yescharacteristic
861C2×C4#55011yescharacteristic
862C2×C4#56011yescharacteristic
863C2×C4#56211yescharacteristic
864C2×C4#56211yescharacteristic
865C2×C4#56311yescharacteristic
866C8—22no—
867C8—22no—
868C8—41no—
869C8—41no—
870C8—41no—
871C8—41no—
872C8—42no—
873C8—41no—
874C8—41no—
875C8—81no—
876C8—81no—
877C8—81no—
878C22—21no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—21no—
887C22—21no—
888C22—21no—
889C22—21no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—82no—
905C22—82no—
906C22—82no—
907C22—82no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22#232211yescharacteristic
916C22D4×C22⋊C411yescharacteristic
917C22#235911yescharacteristic
918C22#269411yescharacteristic
919C22#269611yescharacteristic
920C22#270511yescharacteristic
921C22#270711yescharacteristic
922C22C2×#44311yescharacteristic
923C22#295511yescharacteristic
924C22#295611yescharacteristic
925C22#295711yescharacteristic
926C4—44no—
927C4—41no—
928C4—41no—
929C4—42no—
930C4—42no—
931C4—42no—
932C4—42no—
933C4—82no—
934C4—81no—
935C4—81no—
936C4—81no—
937C4#231111yescharacteristic
938C4#233511yescharacteristic
939C4#234111yescharacteristic
940C4#237611yescharacteristic
941C4#267311yescharacteristic
942C4#267411yescharacteristic
943C4#268111yescharacteristic
944C4#268211yescharacteristic
945C2—21no—
946C2—21no—
947C2—21no—
948C2—21no—
949C2—42no—
950C2—81no—
951C2—161no—
952C2#1436011yescharacteristic
953C2#2209511yescharacteristic
954C2#2209711yescharacteristic
955C2#2245311yescharacteristic
956C2#2245411yescharacteristic
957C2#2294811yescharacteristic
958C2#2294911yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C2×C4×D4
prime radicalC2×#525C22
LCSG ▷ C22×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
3. C2×#1945C2semidirect
4. C2×#1922C2semidirect
5. #20628C2semidirect
6. #11221C2semidirect
7. #11125C2semidirect
8. #11097C2semidirect
9. #11068C2semidirect
10. #11068C2semidirect
12. #10929C2semidirect
13. #10921C2semidirect
14. #10909C2semidirect
15. #10733C2semidirect
20. C2×#484C4semidirect
21. C2×#481C4semidirect
22. C2×#485C4semidirect
23. C2×#485C4semidirect
24. C2×#482C4semidirect
25. C2×#482C4semidirect
26. C2×#483C4semidirect
27. C2×#480C4semidirect
405. #107C22⋊C4semidirect
406. #107C22⋊C4semidirect
409. #106C22⋊C4semidirect
410. #106C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#30912
#211912
C2×#19452
C2×#19222
#206282
#112212
#111252
#110972
#110682
#109712
#109292
#109212
#109092
#107332