Finite Group Databasebeta

← #222216

Subgroups — #222216

Order 512.

1205 conjugacy classes of subgroups.

The subgroup lattice has 815 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3100C211yesmaximal, characteristic
2#22402C211yesmaximal, characteristic, complemented
3#22401C211yesmaximal, characteristic, complemented
4C2×#1589C211yesmaximal, characteristic, complemented
5C2×#1581C211yesmaximal, characteristic, complemented
6#9663C211yesmaximal, characteristic, complemented
7#9657C211yesmaximal, characteristic, complemented
8#8951C211yesmaximal, characteristic, complemented
9#8951C211yesmaximal, characteristic, complemented
10#8951C211yesmaximal, characteristic, complemented
11#8947C211yesmaximal, characteristic, complemented
12#8599C211yesmaximal, characteristic, complemented
13#8313C211yesmaximal, characteristic, complemented
14#8310C211yesmaximal, characteristic, complemented
15#8148C211yesmaximal, characteristic, complemented
16C2×#532C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18#3100—24no—
19#3100—24no—
20C2×#480C411yescharacteristic
21C2×#480C411yescharacteristic
22C2×#474C411yescharacteristic
23C2×#474C411yescharacteristic
24C2×#459C411yescharacteristic
25C2×#459C411yescharacteristic
26C2×#447C411yescharacteristic
27C2×#447C411yescharacteristic
28C2×C4×D8C2211yescharacteristic
29C2×C4×D8C2211yescharacteristic
30C2×C4×D8C2211yescharacteristic
31C2×C4×D8C2211yescharacteristic
32C2×#436C2211yescharacteristic
33C2×#436C2211yescharacteristic
34C2×#436C2211yescharacteristic, complemented
35C2×C8×D4C2211yescharacteristic, complemented
36C2×#431C2211yescharacteristic
37C2×#408—21no—
38C2×#407—21no—
39#1954C2211yescharacteristic
40#1954C2211yescharacteristic
41#1954C2211yescharacteristic, complemented
42#1954C2211yescharacteristic, complemented
43#1870—21no—
44#1870—21no—
45#1870—21no—
46#1869—21no—
47#1797C2211yescharacteristic
48#1797C2211yescharacteristic
49#1780—21no—
50#1779—21no—
51C4×C22⋊C8C2211yescharacteristic
52C4×C22⋊C8C2211yescharacteristic
53#1589—24no—
54#1581—24no—
55C2×#335C2211yescharacteristic, complemented
56C2×#335C2211yescharacteristic, complemented
57C2×D4⋊C8C2211yescharacteristic
58C2×D4⋊C8C2211yescharacteristic
59C2×D4⋊C8C2211yescharacteristic
60C2×D4⋊C8C2211yescharacteristic
61C2×D4⋊C8C2211yescharacteristic, complemented
62C2×D4⋊C8C2211yescharacteristic, complemented
63C2×D4⋊C8C2211yescharacteristic, complemented
64C2×D4⋊C8C2211yescharacteristic, complemented
65C2×#322C2211yescharacteristic, complemented
66C2×C82C2211yescharacteristic, complemented
67#1277C2211yescharacteristic, complemented
68#1277C2211yescharacteristic, complemented
69#1273C2211yescharacteristic, complemented
70#1273C2211yescharacteristic, complemented
71C22×#41—21no—
72C23×D4C2×C411yescharacteristic
73C24×C4—21no—
74C22×D8C2×C411yescharacteristic
75C22×D8C2×C411yescharacteristic
76C22×D8C2×C411yescharacteristic
77C22×D8C2×C411yescharacteristic
78C22×M16—21no—
79C22×M16—21no—
80C22×M16—21no—
81C23×C8—21no—
82#532—22no—
83#532—22no—
84#532—41no—
85#532—41no—
86C2×C4⋊Q8C2×C411yescharacteristic
87C2×#127C2×C411yescharacteristic
88C2×#124—21no—
89C2×#121—21no—
90C2×#121C2×C411yescharacteristic
91C2×#121C2×C411yescharacteristic
92C2×C4×D4—22no—
93C2×C4×D4—22no—
94C2×C4×D4—21no—
95C2×C4×D4—21no—
96C2×C4×D4—21no—
97C2×C4×D4—41no—
98C2×C4×D4—41no—
99C2×C4×D4C2×C411yescharacteristic
100C2×C4×D4C2×C411yescharacteristic
101C2×C4×D4C2311yescharacteristic
102C2×C4×D4C2311yescharacteristic
103C2×C4×D4C2311yescharacteristic
104C2×C4×D4C2311yescharacteristic
105C22×C4⋊C4C2×C411yescharacteristic
106C22×C22⋊C4—21no—
107C22×C42C2311yescharacteristic
108#480—24no—
109#480—24no—
110#474—24no—
111#474—24no—
112#459—24no—
113#459—24no—
114#447—24no—
115#447—24no—
116C4×D8—22no—
117C4×D8—22no—
118C4×D8—22no—
119C4×D8—22no—
120C4×D8—22no—
121C4×D8—22no—
122C4×D8D414yes—
123C4×D8D414yes—
124#436—22no—
125#436—22no—
126#436—22no—
127#436—41no—
128#436—41no—
129#436—41no—
130C8×D4—22no—
131C8×D4—41no—
132#431—22no—
133#431—22no—
134C2×#107C2×C411yescharacteristic
135C2×#107C2×C411yescharacteristic
136C2×#107C2×C411yescharacteristic
137C2×#107C2×C411yescharacteristic
138C2×C4⋊C8C2×C411yescharacteristic
139C2×C4⋊C8C2×C411yescharacteristic
140C2×C4⋊C8C2311yescharacteristic
141C2×C4⋊C8C2311yescharacteristic
142C2×C4⋊C8C2311yescharacteristic
143C2×C4⋊C8C2311yescharacteristic
144C2×#102C2×C411yescharacteristic
145C2×#102C2×C411yescharacteristic
146C2×#102C2×C411yescharacteristic
147C2×#102C2×C411yescharacteristic
148C2×#102C2×C411yescharacteristic
149C2×#102C2×C411yescharacteristic
150C2×#102C2×C411yescharacteristic
151C2×#102C2×C411yescharacteristic
152#408—44no—
153#407—44no—
154C2×C22⋊C8—21no—
155C2×C22⋊C8—21no—
156C2×C22⋊C8—21no—
157C2×C22⋊C8—21no—
158C2×C22⋊C8—21no—
159C2×C22⋊C8—21no—
160C2×C22⋊C8—21no—
161C2×C22⋊C8—21no—
162C2×C22⋊C8—21no—
163C2×C22⋊C8—21no—
164C2×C22⋊C8—21no—
165C2×C22⋊C8—21no—
166C2×C22⋊C8—21no—
167C2×C22⋊C8—21no—
168C2×C22⋊C8—21no—
169C2×C22⋊C8C2×C411yescharacteristic
170C2×C22⋊C8C2×C411yescharacteristic
171C2×C22⋊C8D411yescharacteristic
172C2×C22⋊C8D411yescharacteristic
173C2×C4×C8C2311yescharacteristic
174C2×C4×C8C2311yescharacteristic
175C2×C4×C8C2311yescharacteristic
176C2×C4×C8C2311yescharacteristic
177C2×C4×C8C2311yescharacteristic
178C2×C4×C8C2311yescharacteristic
179#336—21no—
180#336—21no—
181#336—21no—
182#336D411yescharacteristic
183#336D411yescharacteristic
184#335—22no—
185#335—22no—
186D4⋊C8—22no—
187D4⋊C8—22no—
188D4⋊C8—22no—
189D4⋊C8—22no—
190D4⋊C8—41no—
191D4⋊C8—41no—
192D4⋊C8—41no—
193D4⋊C8—41no—
194#322—22no—
195C82—22no—
196C25—21no—
197C2×#41—42no—
198C2×#41—42no—
199C2×#41—42no—
200C2×#41—42no—
201C2×#41—81no—
202C2×#41—81no—
203C22×Q8—21no—
204C22×D4—22no—
205C22×D4—22no—
206C22×D4—21no—
207C22×D4—21no—
208C22×D4—21no—
209C22×D4—21no—
210C22×D4—21no—
211C22×D4—41no—
212C22×D4—41no—
213C22×D4—41no—
214C22×D4—41no—
215C22×D4C22×C411yescharacteristic
216C22×D4C22×C411yescharacteristic
217C22×D4C22×C411yescharacteristic
218C22×D4C22×C411yescharacteristic
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—81no—
231C23×C4—81no—
232C23×C4C22×C411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C23×C4#4111yescharacteristic
235C2×D8—22no—
236C2×D8—22no—
237C2×D8—22no—
238C2×D8—22no—
239C2×D8—22no—
240C2×D8—41no—
241C2×D8—41no—
242C2×D8—41no—
243C2×D8—41no—
244C2×D8—41no—
245C2×D8—41no—
246C2×D8C22⋊C414yes—
247C2×M16—42no—
248C2×M16—42no—
249C2×M16—42no—
250C2×M16—42no—
251C2×M16—42no—
252C2×M16—42no—
253C2×M16—81no—
254C2×M16—81no—
255C2×M16—81no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—42no—
263C22×C8—42no—
264C22×C8—81no—
265C22×C8C22×C411yescharacteristic
266C22×C8C22×C411yescharacteristic
267C22×C8C22×C411yescharacteristic
268C22×C8C22×C411yescharacteristic
269C22×C8C2×D411yescharacteristic
270C22×C8C2×D411yescharacteristic
271C22×C8C2×D411yescharacteristic
272C22×C8C2×D411yescharacteristic
273C4⋊Q8—22no—
274C4⋊Q8—41no—
275#127—22no—
276#127—41no—
277#124—42no—
278#124—42no—
279#121—22no—
280#121—22no—
281#121—42no—
282#121—42no—
283#121—41no—
284#121—41no—
285C4×D4—22no—
286C4×D4—22no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4—21no—
290C4×D4—21no—
291C4×D4—21no—
292C4×D4—21no—
293C4×D4—21no—
294C4×D4—21no—
295C4×D4—21no—
296C4×D4—21no—
297C4×D4—21no—
298C4×D4—21no—
299C4×D4—42no—
300C4×D4—42no—
301C4×D4—41no—
302C4×D4—41no—
303C4×D4—42no—
304C4×D4—42no—
305C4×D4—42no—
306C4×D4—42no—
307C4×D4C2×D412yes—
308C4×D4C2×D412yes—
309C4×D4C2×D412yes—
310C4×D4C2×D412yes—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—41no—
315C2×C4⋊C4C22×C411yescharacteristic
316C2×C4⋊C4C22×C411yescharacteristic
317C2×C4⋊C4C22×C411yescharacteristic
318C2×C4⋊C4C22×C411yescharacteristic
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42C22×C411yescharacteristic
334C2×C42C2×D411yescharacteristic
335C2×C42#4111yescharacteristic
336C2×C42C2411yescharacteristic
337#107—22no—
338#107—22no—
339#107—22no—
340#107C22⋊C414yes—
341C4⋊C8—22no—
342C4⋊C8—22no—
343C4⋊C8—21no—
344C4⋊C8—21no—
345C4⋊C8—21no—
346C4⋊C8—21no—
347C4⋊C8—21no—
348C4⋊C8—21no—
349C4⋊C8—21no—
350C4⋊C8—21no—
351#102—22no—
352#102—22no—
353#102—22no—
354#102—22no—
355#102—22no—
356#102—22no—
357#102C22⋊C414yes—
358#102C22⋊C414yes—
359C22⋊C8—22no—
360C22⋊C8—22no—
361C22⋊C8—22no—
362C22⋊C8—42no—
363C22⋊C8—42no—
364C22⋊C8—42no—
365C22⋊C8—42no—
366C22⋊C8—42no—
367C22⋊C8—42no—
368C22⋊C8—42no—
369C22⋊C8—42no—
370C22⋊C8—42no—
371C22⋊C8—42no—
372C22⋊C8—42no—
373C22⋊C8—81no—
374C22⋊C8—81no—
375C22⋊C8—81no—
376C22⋊C8—81no—
377C22⋊C8D814yescomplemented
378C4×C8—21no—
379C4×C8—21no—
380C4×C8—21no—
381C4×C8—21no—
382C4×C8—21no—
383C4×C8—21no—
384C4×C8—21no—
385C4×C8—21no—
386C4×C8—21no—
387C4×C8—21no—
388C4×C8C2×D412yes—
389C4×C8C2×D412yes—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—42no—
395C24—42no—
396C24—42no—
397C24—42no—
398C24—42no—
399C24—81no—
400C24—81no—
401C24C4×D411yescharacteristic
402#41—84no—
403#41—84no—
404#41—84no—
405#41—84no—
406C2×Q8—42no—
407C2×Q8—42no—
408C2×Q8—81no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—42no—
431C2×D4—42no—
432C2×D4—42no—
433C2×D4—42no—
434C2×D4—42no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—44no—
438C2×D4—44no—
439C2×D4—44no—
440C2×D4—44no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—42no—
444C2×D4—42no—
445C2×D4—81no—
446C2×D4—81no—
447C2×D4—81no—
448C2×D4—81no—
449C2×D4C2×C22⋊C412yes—
450C2×D4C2×C22⋊C412yes—
451C2×D4#13112yes—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—42no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—81no—
501C22×C4—81no—
502C22×C4—84no—
503C22×C4—84no—
504C22×C4—84no—
505C22×C4—84no—
506C22×C4—81no—
507C22×C4C4×D411yescharacteristic
508C22×C4C4×D411yescharacteristic
509C22×C4C4×D411yescharacteristic
510C22×C4C2×D812yes—
511C22×C4#13512yes—
512C22×C4C23×C411yescharacteristic
513C22×C4C22×D411yescharacteristic
514C22×C4C2×#4111yescharacteristic
515D8—44no—
516D8—44no—
517D8—44no—
518D8—44no—
519M16—84no—
520M16—84no—
521M16—84no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—22no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8—41no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—84no—
561C2×C8C2×C22⋊C412yes—
562C2×C8C2×C22⋊C412yes—
563C2×C8C2×D812yes—
564C2×C8C2×D812yes—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4C2×C22⋊C412yes—
574C4⋊C4C2×C22⋊C412yes—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—22no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—41no—
584C22⋊C4—41no—
585C22⋊C4—41no—
586C22⋊C4—41no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42C22×D411yescharacteristic
594C42C22×D411yescharacteristic
595C42H(5,𝔽2)11yescharacteristic
596C42H(5,𝔽2)11yescharacteristic
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—48no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—84no—
633C23—84no—
634C23—84no—
635C23—84no—
636C23—84no—
637C23—84no—
638C23C4×D812yes—
639C23C2×C4×D411yescharacteristic
640Q8—84no—
641D4—22no—
642D4—22no—
643D4—22no—
644D4—22no—
645D4—22no—
646D4—22no—
647D4—48no—
648D4—41no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—41no—
658D4—84no—
659D4—84no—
660D4—84no—
661D4—84no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—81no—
701C2×C4—81no—
702C2×C4—84no—
703C2×C4—84no—
704C2×C4—84no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4C4×D812yes—
714C2×C4C22×C22⋊C411yescharacteristic
715C2×C4#51811yescharacteristic
716C2×C4D4211yescharacteristic
717C2×C4D4211yescharacteristic
718C2×C4#54611yescharacteristic
719C2×C4#54611yescharacteristic
720C2×C4C2×#13111yescharacteristic
721C2×C4#56811yescharacteristic
722C2×C4#56811yescharacteristic
723C2×C4#56811yescharacteristic
724C2×C4C22×D811yescharacteristic
725C2×C4C2×#13511yescharacteristic
726C2×C4#57611yescharacteristic
727C2×C4#57611yescharacteristic
728C8—22no—
729C8—22no—
730C8—22no—
731C8—22no—
732C8—42no—
733C8—41no—
734C8—41no—
735C8—41no—
736C8—41no—
737C8—81no—
738C8—81no—
739C8—81no—
740C8—81no—
741C8—81no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—816no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22D4×C22⋊C411yescharacteristic
779C22#293011yescharacteristic
780C22#293311yescharacteristic
781C22C2×C4×D811yescharacteristic
782C22#294811yescharacteristic
783C22#295511yescharacteristic
784C22#295611yescharacteristic
785C4—22no—
786C4—21no—
787C4—21no—
788C4—41no—
789C4—42no—
790C4—42no—
791C4—41no—
792C4—81no—
793C4—81no—
794C4#287911yescharacteristic
795C4#288011yescharacteristic
796C4#297611yescharacteristic
797C4#297811yescharacteristic
798C4D4×D811yescharacteristic
799C4D4×D811yescharacteristic
800C4#328011yescharacteristic
801C4#328011yescharacteristic
802C2—42no—
803C2—82no—
804C2—82no—
805C2—82no—
806C2—161no—
807C2#1792811yescharacteristic
808C2#1795011yescharacteristic
809C2#1799411yescharacteristic
810C2#1802611yescharacteristic
811C2#2240011yescharacteristic
812C2C22⋊C4×D811yescharacteristic
813C2#2245311yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23C2×C4×D4
prime radicalC2×#3100C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C8 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22402C2semidirect
3. #22401C2semidirect
4. C2×#1589C2semidirect
5. C2×#1581C2semidirect
6. #9663C2semidirect
7. #9657C2semidirect
8. #8951C2semidirect
9. #8951C2semidirect
10. #8951C2semidirect
11. #8947C2semidirect
12. #8599C2semidirect
13. #8313C2semidirect
14. #8310C2semidirect
15. #8148C2semidirect
34. C2×#436C22semidirect
35. C2×C8×D4C22semidirect
41. #1954C22semidirect
42. #1954C22semidirect
55. C2×#335C22semidirect
56. C2×#335C22semidirect
61. C2×D4⋊C8C22semidirect
62. C2×D4⋊C8C22semidirect
63. C2×D4⋊C8C22semidirect
64. C2×D4⋊C8C22semidirect
65. C2×#322C22semidirect
66. C2×C82C22semidirect
67. #1277C22semidirect
68. #1277C22semidirect
69. #1273C22semidirect
70. #1273C22semidirect
377. C22⋊C8D8semidirect

Maximal subgroups

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

subgroupindex
C2×#31002
#224022
#224012
C2×#15892
C2×#15812
#96632
#96572
#89512
#89472
#85992
#83132
#83102
#81482