Finite Group Databasebeta

← #356157

Subgroups — #356157

Order 512.

1552 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34109C211yesmaximal, characteristic
2C2×#1826C211yesmaximal, characteristic
3C22⋊C4×M16C211yesmaximal, characteristic
4C2×#1733C211yesmaximal, characteristic
5#13761C211yesmaximal, characteristic
6#10886C211yesmaximal, characteristic, complemented
7#10886C211yesmaximal, characteristic, complemented
8#10879C211yesmaximal, characteristic, complemented
9#10878C211yesmaximal, characteristic, complemented
10#10808C211yesmaximal, characteristic, complemented
11#10808C211yesmaximal, characteristic, complemented
12#10732C211yesmaximal, characteristic
13#10720C211yesmaximal, characteristic
14#10701C211yesmaximal, characteristic, complemented
15C4×#339C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C22×#117C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C2×#407C2211yescharacteristic
20C2×C4×M16C2211yescharacteristic
21C2×C4×M16C2211yescharacteristic
22#2347C412yescomplemented
23#2346C412yescomplemented
24#2345C412yescomplemented
25#2344C412yescomplemented
26#2343—22no—
27#2342—22no—
28#2298—21no—
29#2298—21no—
30#2296C2211yescharacteristic
31#2296C2211yescharacteristic
32#2283—21no—
33#2280C2211yescharacteristic
34C4×#117—21no—
35C4×#117C2211yescharacteristic
36C4×#117C2211yescharacteristic
37C2×C4×C22⋊C4C2211yescharacteristic
38C2×C4×C22⋊C4C2211yescharacteristic
39C2×#376C2211yescharacteristic
40C2×C43C2211yescharacteristic
41#1826C418yescomplemented
42#1753—21no—
43#1753—21no—
44#1752—21no—
45C8×C22⋊C4—21no—
46#1733C418yescomplemented
47C2×#339C2211yescharacteristic
48C2×#339C2211yescharacteristic
49C2×#339C2211yescharacteristic
50C2×#339C2211yescharacteristic
51C2×#339C2211yescharacteristic
52C2×#339C2211yescharacteristic
53C2×#339C2211yescharacteristic
54C2×#339C2211yescharacteristic
55C2×#339C2211yescharacteristic
56C2×#339C2211yescharacteristic
57C2×#339C2211yescharacteristic
58C2×#339C2211yescharacteristic
59C2×#339C2211yescharacteristic
60C2×#339C2211yescharacteristic
61C2×#339C2211yescharacteristic
62C2×#339C2211yescharacteristic
63#1728C2211yescharacteristic
64#1728C2211yescharacteristic
65#1437—22no—
66#1436—22no—
67C4×#95C2211yescharacteristic
68C4×#95C2211yescharacteristic
69C24×C4C2311yescharacteristic
70C22×M16—21no—
71C22×M16—22no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—41no—
75C22×M16—41no—
76C22×M16C2×C414yes—
77C22×M16C2311yescharacteristic
78C22×M16C2311yescharacteristic
79C22×M16C2311yescharacteristic
80C22×M16C2311yescharacteristic
81C23×C8—21no—
82C2×#117—21no—
83C2×#117—21no—
84C2×#117—22no—
85C2×#117—22no—
86C2×#117—22no—
87C2×#117—22no—
88C2×#117—22no—
89C2×#117—22no—
90C2×#117—41no—
91C2×#117—41no—
92C2×#117C2×C414yes—
93C2×#117C2×C414yes—
94C2×#117C2×C411yescharacteristic
95C2×#117C2×C411yescharacteristic
96C2×#117C2×C414yes—
97C2×#117C2311yescharacteristic
98C2×#117C2311yescharacteristic
99C2×#117C2311yescharacteristic
100C2×#117C2311yescharacteristic
101C22×C4⋊C4—21no—
102C22×C4⋊C4C2×C411yescharacteristic
103C22×C4⋊C4C2×C411yescharacteristic
104C22×C22⋊C4—21no—
105C22×C22⋊C4—21no—
106C22×C22⋊C4—21no—
107C22×C22⋊C4D412yes—
108C22×C42—21no—
109C22×C42—22no—
110C22×C42C2311yescharacteristic
111C22×C42C2311yescharacteristic
112C22×C42C2311yescharacteristic
113C22×C42C2311yescharacteristic
114C22×C42C2311yescharacteristic
115C22×C42C2311yescharacteristic
116#407—22no—
117#407C2×C414yes—
118C2×C22⋊C8—21no—
119C2×C22⋊C8—21no—
120C4×M16—22no—
121C4×M16—22no—
122C4×M16—41no—
123C4×M16—41no—
124C2×#97—21no—
125C2×#97—21no—
126C2×C4×C8—21no—
127C2×C4×C8—21no—
128#389C2×C412yes—
129#389C2×C412yes—
130#389C2×C412yes—
131#389C2×C412yes—
132#388—22no—
133#388—22no—
134#388—22no—
135#388—22no—
136#387—22no—
137#387—22no—
138#387—22no—
139#387—22no—
140#385—22no—
141#385—22no—
142#383—22no—
143#382—22no—
144#381—21no—
145#381—22no—
146#380—22no—
147#380C2×C412yes—
148#380C2×C412yes—
149#379—21no—
150C4×C4⋊C4—21no—
151C4×C4⋊C4—21no—
152C4×C4⋊C4—21no—
153C4×C4⋊C4—21no—
154C4×C4⋊C4—22no—
155C4×C4⋊C4C2×C412yes—
156C4×C4⋊C4C2×C412yes—
157C4×C4⋊C4C2×C412yes—
158C4×C4⋊C4C2×C412yes—
159C4×C22⋊C4—22no—
160C4×C22⋊C4—22no—
161C4×C22⋊C4—21no—
162C4×C22⋊C4—21no—
163C4×C22⋊C4—22no—
164C4×C22⋊C4—22no—
165C4×C22⋊C4C2×C414yes—
166C4×C22⋊C4C2×C412yes—
167C4×C22⋊C4C2×C412yes—
168C4×C22⋊C4D411yescharacteristic
169C4×C22⋊C4D411yescharacteristic
170C4×C22⋊C4D411yescharacteristic
171C4×C22⋊C4D411yescharacteristic
172#376—21no—
173#376—21no—
174#376—22no—
175#376—22no—
176#376—41no—
177C2×#95—21no—
178C2×#95—22no—
179C2×#95—22no—
180C2×#95—22no—
181C2×#95D412yes—
182C43—21no—
183C43—21no—
184C43—22no—
185C43—41no—
186#339—22no—
187#339—22no—
188#339—22no—
189#339—22no—
190#339—41no—
191#339—41no—
192#339—41no—
193#339—41no—
194#339C2×C414yes—
195#339C2×C414yes—
196#339C2×C414yes—
197#339C2×C414yes—
198#339C2×C414yes—
199#339C2×C414yes—
200#339C2×C414yes—
201#339C2×C414yes—
202#336—21no—
203#336—21no—
204#336—21no—
205#336—21no—
206C25C2×D411yescharacteristic
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4C22×C411yescharacteristic
222C23×C4C22×C411yescharacteristic
223C23×C4C22×C412yes—
224C23×C4C22×C412yes—
225C23×C4C2×D412yes—
226C23×C4C2×D411yescharacteristic
227C23×C4C2×D411yescharacteristic
228C23×C4C2×D411yescharacteristic
229C23×C4C2×D412yes—
230C23×C4#4112yes—
231C23×C4#4112yes—
232C23×C4C2411yescharacteristic
233C2×M16—21no—
234C2×M16—21no—
235C2×M16—21no—
236C2×M16—24no—
237C2×M16—21no—
238C2×M16—21no—
239C2×M16—21no—
240C2×M16—21no—
241C2×M16—21no—
242C2×M16—21no—
243C2×M16—21no—
244C2×M16—21no—
245C2×M16—21no—
246C2×M16—21no—
247C2×M16—21no—
248C2×M16—21no—
249C2×M16—21no—
250C2×M16—21no—
251C2×M16—21no—
252C2×M16—28no—
253C2×M16—42no—
254C2×M16—42no—
255C2×M16—44no—
256C2×M16—44no—
257C2×M16—44no—
258C2×M16C22×C412yes—
259C2×M16C22×C412yes—
260C2×M16C22×C412yes—
261C2×M16C22×C412yes—
262C2×M16#4112yes—
263C2×M16#4112yes—
264C22×C8—21no—
265C22×C8—24no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—42no—
270C22×C8—42no—
271#117—22no—
272#117—22no—
273#117—24no—
274#117—24no—
275#117—24no—
276#117—24no—
277#117—21no—
278#117—21no—
279#117—21no—
280#117—21no—
281#117—28no—
282#117—21no—
283#117—21no—
284#117—21no—
285#117—21no—
286#117—21no—
287#117—21no—
288#117—21no—
289#117—21no—
290#117—44no—
291#117—44no—
292#117—44no—
293#117—48no—
294#117C4214yescomplemented
295#117C4214yescomplemented
296#117C22×C412yes—
297#117C22×C412yes—
298#117C22×C412yes—
299#117C22×C412yes—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4C4214yescomplemented
312C2×C4⋊C4C4214yescomplemented
313C2×C4⋊C4C22×C412yes—
314C2×C4⋊C4C22×C412yes—
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—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4C22⋊C412yes—
336C2×C22⋊C4C22⋊C412yes—
337C2×C22⋊C4C22⋊C412yes—
338C2×C22⋊C4C22⋊C412yes—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—24no—
342C2×C42—24no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—44no—
378C2×C42—44no—
379C2×C42—44no—
380C2×C42C22×C412yes—
381C2×C42C22×C412yes—
382C2×C42C22×C412yes—
383C2×C42C22×C412yes—
384C2×C42C22×C412yes—
385C2×C42C22×C412yes—
386C2×C42C2×D411yescharacteristic
387C2×C42C2×D411yescharacteristic
388C2×C42C2×D411yescharacteristic
389C2×C42C2×D411yescharacteristic
390C2×C42#4112yes—
391C2×C42#4112yes—
392C22⋊C8—24no—
393C22⋊C8—24no—
394#97—42no—
395#97—42no—
396C4×C8—42no—
397C4×C8—42no—
398#95—22no—
399#95—22no—
400#95—22no—
401#95—22no—
402#95—22no—
403#95—22no—
404#95—22no—
405#95—22no—
406#95—22no—
407#95—22no—
408#95—24no—
409#95—44no—
410#95—44no—
411#95—44no—
412#95C22⋊C412yes—
413#95C22⋊C412yes—
414#95C22⋊C412yes—
415#95C22⋊C412yes—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—42no—
421C24—42no—
422C24C2×C22⋊C411yescharacteristic
423C24C2×C22⋊C411yescharacteristic
424C24C4×D412yes—
425C24C4×D412yes—
426C24C22×D411yescharacteristic
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—44no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—82no—
501C22×C4C2×C4212yes—
502C22×C4C2×C4212yes—
503C22×C4C2×C22⋊C412yes—
504C22×C4C2×C22⋊C412yes—
505C22×C4C2×C22⋊C412yes—
506C22×C4C2×C22⋊C411yescharacteristic
507C22×C4C2×C22⋊C411yescharacteristic
508C22×C4C2×C22⋊C412yes—
509C22×C4#11712yes—
510C22×C4#11712yes—
511C22×C4C4×D412yes—
512C22×C4C4×D412yes—
513C22×C4C4×D412yes—
514C22×C4C4×D412yes—
515C22×C4C4×D412yes—
516C22×C4C4×D412yes—
517C22×C4C23×C411yescharacteristic
518C22×C4C23×C411yescharacteristic
519C22×C4C23×C411yescharacteristic
520C22×C4C22×D411yescharacteristic
521C22×C4C2×#4111yescharacteristic
522C22×C4C2×#4111yescharacteristic
523C22×C4C2×#4111yescharacteristic
524C22×C4C2×#4111yescharacteristic
525C22×C4C2×#4111yescharacteristic
526C22×C4C2×#4111yescharacteristic
527C22×C4H(5,𝔽2)11yescharacteristic
528C22×C4H(5,𝔽2)11yescharacteristic
529C22×C42−1+411yescharacteristic
530C22×C42−1+411yescharacteristic
531M16—22no—
532M16—22no—
533M16—22no—
534M16—22no—
535M16—22no—
536M16—22no—
537M16—22no—
538M16—22no—
539M16—22no—
540M16—48no—
541M16—41no—
542M16—41no—
543M16—41no—
544M16—41no—
545M16—41no—
546M16—41no—
547M16#11714yescomplemented
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—48no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—48no—
572C4⋊C4—44no—
573C4⋊C4—44no—
574C4⋊C4—82no—
575C4⋊C4—82no—
576C4⋊C4C2×C4212yes—
577C4⋊C4C2×C4212yes—
578C4⋊C4C2×C4212yes—
579C4⋊C4C2×C4212yes—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—24no—
585C22⋊C4—24no—
586C22⋊C4—24no—
587C22⋊C4—24no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—48no—
591C22⋊C4—48no—
592C22⋊C4—44no—
593C22⋊C4—41no—
594C22⋊C4—41no—
595C22⋊C4—41no—
596C22⋊C4—41no—
597C22⋊C4—82no—
598C42—22no—
599C42—22no—
600C42—22no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42—22no—
605C42—22no—
606C42—22no—
607C42—21no—
608C42—21no—
609C42—21no—
610C42—21no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—22no—
616C42—22no—
617C42—24no—
618C42—24no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—44no—
626C42—416no—
627C42—41no—
628C42—41no—
629C42—41no—
630C42—41no—
631C42—41no—
632C42—41no—
633C42—41no—
634C42—41no—
635C42—41no—
636C42—41no—
637C42—44no—
638C42—82no—
639C42—82no—
640C42#11714yescomplemented
641C23—22no—
642C23—22no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—82no—
660C23—82no—
661C23—82no—
662C23—82no—
663C23C4×C22⋊C412yes—
664C23C4×C22⋊C412yes—
665C23C22×C22⋊C411yescharacteristic
666C23C2×C4×D411yescharacteristic
667C23C2×C4×D411yescharacteristic
668C23#54611yescharacteristic
669C23#54611yescharacteristic
670C23#54711yescharacteristic
671C23#54711yescharacteristic
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—48no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—82no—
741C2×C4—82no—
742C2×C4—84no—
743C2×C4—82no—
744C2×C4—82no—
745C2×C4—82no—
746C2×C4—82no—
747C2×C4C4×C22⋊C412yes—
748C2×C4C4×C22⋊C412yes—
749C2×C4#42114yes—
750C2×C4C22×C4211yescharacteristic
751C2×C4C2×#11711yescharacteristic
752C2×C4C2×#11711yescharacteristic
753C2×C4C2×#11711yescharacteristic
754C2×C4C2×C4×D411yescharacteristic
755C2×C4C2×C4×D411yescharacteristic
756C2×C4C4×#4111yescharacteristic
757C2×C4C4×#4111yescharacteristic
758C2×C4C4×#4111yescharacteristic
759C2×C4C4×#4111yescharacteristic
760C2×C4#51811yescharacteristic
761C2×C4#51911yescharacteristic
762C2×C4#52011yescharacteristic
763C2×C4#52011yescharacteristic
764C2×C4#52011yescharacteristic
765C2×C4#52011yescharacteristic
766C2×C4#54611yescharacteristic
767C2×C4#54611yescharacteristic
768C2×C4#54711yescharacteristic
769C2×C4#54711yescharacteristic
770C2×C4#55111yescharacteristic
771C2×C4#55111yescharacteristic
772C2×C4#55111yescharacteristic
773C2×C4#55111yescharacteristic
774C2×C4#55211yescharacteristic
775C2×C4#55211yescharacteristic
776C2×C4#55211yescharacteristic
777C2×C4#55211yescharacteristic
778C8—24no—
779C8—42no—
780C8—42no—
781C8—42no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22C2×C4×C22⋊C411yescharacteristic
805C22#233911yescharacteristic
806C22#233911yescharacteristic
807C22#234211yescharacteristic
808C22#234411yescharacteristic
809C22#235911yescharacteristic
810C22#235911yescharacteristic
811C22C2×#42112yes—
812C22#290112yes—
813C4—22no—
814C4—22no—
815C4—24no—
816C4—44no—
817C4—44no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—82no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4C4×#11711yescharacteristic
830C4#227411yescharacteristic
831C4#234211yescharacteristic
832C4#234311yescharacteristic
833C4#234311yescharacteristic
834C4#234411yescharacteristic
835C4#235911yescharacteristic
836C4#235911yescharacteristic
837C2—21no—
838C2—21no—
839C2—21no—
840C2—21no—
841C2—42no—
842C2—42no—
843C2#1379911yescharacteristic
844C2C4×#42111yescharacteristic
845C2#2040511yescharacteristic
846C2#2250612yes—
847C2#2250712yes—
subgroupG/H
centerC22×C4C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
socleC23C22×C22⋊C4
prime radicalC25C2×D4
LCSG ▷ C2×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
6. #10886C2semidirect
7. #10886C2semidirect
8. #10879C2semidirect
9. #10878C2semidirect
10. #10808C2semidirect
11. #10808C2semidirect
14. #10701C2semidirect
15. C4×#339C2semidirect
22. #2347C4semidirect
23. #2346C4semidirect
24. #2345C4semidirect
25. #2344C4semidirect
41. #1826C4semidirect
46. #1733C4semidirect
294. #117C42semidirect
295. #117C42semidirect
311. C2×C4⋊C4C42semidirect
312. C2×C4⋊C4C42semidirect
547. M16#117semidirect
640. C42#117semidirect

Maximal subgroups

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

subgroupindex
#341092
C2×#18262
C22⋊C4×M162
C2×#17332
#137612
#108862
#108792
#108782
#108082
#107322
#107202
#107012
C4×#3392