Finite Group Databasebeta

← #383584

Subgroups — #383584

Order 512.

1121 conjugacy classes of subgroups.

The subgroup lattice has 835 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3076C211yesmaximal, characteristic
2#21304C211yesmaximal, characteristic, complemented
3C2×#1945C211yesmaximal, characteristic, complemented
4C2×#1922C211yesmaximal, characteristic, complemented
5#20630C211yesmaximal, characteristic
6#11386C211yesmaximal, characteristic, complemented
7#11233C211yesmaximal, characteristic, complemented
8#11221C211yesmaximal, characteristic, complemented
9#11221C211yesmaximal, characteristic, complemented
10#11125C211yesmaximal, characteristic
11#11068C211yesmaximal, characteristic
12#10934C211yesmaximal, characteristic
13#10929C211yesmaximal, characteristic
14#10876C211yesmaximal, characteristic, complemented
15#10790C211yesmaximal, characteristic
16C2×#533C2211yescharacteristic
17C2×C4×#41C2211yescharacteristic
18#3076—24no—
19#3076—24no—
20C2×#479C411yescharacteristic, complemented
21C2×#479C411yescharacteristic, complemented
22C2×#477C411yescharacteristic, complemented
23C2×#475C411yescharacteristic, complemented
24C2×#478C411yescharacteristic, complemented
25C2×#478C411yescharacteristic, complemented
26C2×#476C411yescharacteristic, complemented
27C2×#474C411yescharacteristic, complemented
28C22×#108C2211yescharacteristic
29C2×#427C2211yescharacteristic
30C2×#427C2211yescharacteristic
31C2×#424C2211yescharacteristic
32C2×#424C2211yescharacteristic
33C2×#424C2211yescharacteristic
34C22×C4⋊C8C2211yescharacteristic
35C22×#104C2211yescharacteristic
36C22×#104C2211yescharacteristic
37C2×#416C2211yescharacteristic
38C2×#416C2211yescharacteristic
39C2×#408C2211yescharacteristic
40C2×#408C2211yescharacteristic
41C2×#405C2211yescharacteristic
42C22×C4×C8C2211yescharacteristic
43#1985—21no—
44#1985—21no—
45#1984—21no—
46#1984—21no—
47#1945—24no—
48#1922—24no—
49#1798—21no—
50#1798—21no—
51#1797—21no—
52#1797—21no—
53C2×#341C2211yescharacteristic
54C2×#341C2211yescharacteristic
55C2×#341C2211yescharacteristic
56C2×#339C2211yescharacteristic
57C2×#339C2211yescharacteristic
58C2×#339C2211yescharacteristic
59C2×#339C2211yescharacteristic
60C2×#339C2211yescharacteristic
61C2×#339C2211yescharacteristic
62#1729C2211yescharacteristic
63#1729C2211yescharacteristic
64#1728C2211yescharacteristic
65#1728C2211yescharacteristic
66C2×#336C2211yescharacteristic
67C2×#336C2211yescharacteristic
68C2×#336C2211yescharacteristic
69C2×#336C2211yescharacteristic
70C4×#95C2211yescharacteristic
71C22×#41C2311yescharacteristic
72C22×M16C2311yescharacteristic
73C22×M16C2311yescharacteristic
74C22×M16C2311yescharacteristic
75C22×M16C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80#533—22no—
81#533—22no—
82#533—41no—
83#533—41no—
84C2×C4⋊Q8C2×C411yescharacteristic
85C2×C4⋊Q8C2×C411yescharacteristic
86C2×#125C2×C411yescharacteristic
87C2×#125C2×C411yescharacteristic
88C2×C22⋊Q8—21no—
89C2×C22⋊Q8—21no—
90C4×#41—22no—
91C4×#41—22no—
92C4×#41—41no—
93C4×#41—41no—
94C2×C4×Q8—21no—
95C2×C4×Q8—21no—
96C2×C4×Q8C2×C411yescharacteristic
97C2×C4×Q8C2×C411yescharacteristic
98C2×C4×D4—21no—
99C2×C4×D4—21no—
100C2×C4×D4C2×C411yescharacteristic
101C2×C4×D4C2×C411yescharacteristic
102C2×#117—21no—
103C2×#117C2311yescharacteristic
104C2×#117C2311yescharacteristic
105C2×#117C2311yescharacteristic
106C22×C42—21no—
107C22×C42C2311yescharacteristic
108C22×C42C2311yescharacteristic
109C22×C42C2311yescharacteristic
110#479—24no—
111#479—24no—
112#478—24no—
113#478—24no—
114#477—24no—
115#476—24no—
116#475—24no—
117#474—24no—
118C2×#108—22no—
119C2×#108—41no—
120C2×#108—41no—
121#427—22no—
122#427—22no—
123#427D414yes—
124#427D414yes—
125C2×#107C2×C411yescharacteristic
126C2×#107C2×C411yescharacteristic
127C2×#107C2×C411yescharacteristic
128C2×#107C2×C411yescharacteristic
129C2×#106C2×C411yescharacteristic
130C2×#106C2×C411yescharacteristic
131C2×#106C2×C411yescharacteristic
132C2×#106C2×C411yescharacteristic
133#424—22no—
134#424—22no—
135#424—22no—
136#424—41no—
137#424—41no—
138#424—41no—
139C2×C4⋊C8—22no—
140C2×C4⋊C8—22no—
141C2×C4⋊C8—21no—
142C2×C4⋊C8—21no—
143C2×C4⋊C8—21no—
144C2×C4⋊C8—21no—
145C2×C4⋊C8—21no—
146C2×C4⋊C8—21no—
147C2×C4⋊C8C2×C411yescharacteristic
148C2×C4⋊C8C2×C411yescharacteristic
149C2×C4⋊C8C2×C411yescharacteristic
150C2×C4⋊C8C2×C411yescharacteristic
151C2×#104—22no—
152C2×#104—41no—
153C2×#104—41no—
154C2×#104—41no—
155C2×#104—41no—
156C2×#104Q814yescomplemented
157#416—22no—
158#416—22no—
159#416—22no—
160#416—22no—
161C2×#103C2×C411yescharacteristic
162C2×#103C2×C411yescharacteristic
163C2×#103C2×C411yescharacteristic
164C2×#103C2×C411yescharacteristic
165C2×#102C2×C411yescharacteristic
166C2×#102C2×C411yescharacteristic
167C2×#102C2×C411yescharacteristic
168C2×#102C2×C411yescharacteristic
169#408—22no—
170#408—22no—
171#408—41no—
172#408—41no—
173C2×C22⋊C8—21no—
174C2×C22⋊C8—21no—
175C2×C22⋊C8—21no—
176C2×C22⋊C8—21no—
177#405—22no—
178#405—41no—
179C2×#97—21no—
180C2×C4×C8—22no—
181C2×C4×C8—21no—
182C2×C4×C8—41no—
183C2×C4×C8—41no—
184C2×#95—21no—
185C2×#95—21no—
186#341—22no—
187#341—41no—
188#341—41no—
189#339—22no—
190#339—22no—
191#339—22no—
192#339—22no—
193#339—41no—
194#339—41no—
195#336—22no—
196#336—21no—
197#336—21no—
198#336—21no—
199#336—21no—
200#336—21no—
201#336—21no—
202#336—21no—
203#336—21no—
204#336—41no—
205#336—41no—
206#336D411yescharacteristic
207#336D411yescharacteristic
208#336D411yescharacteristic
209#336D411yescharacteristic
210C2×#41—21no—
211C2×#41—21no—
212C2×#41—21no—
213C2×#41—21no—
214C2×#41—21no—
215C2×#41—21no—
216C2×#41—21no—
217C2×#41—21no—
218C2×#41—21no—
219C2×#41—21no—
220C2×#41C2×Q812yes—
221C2×#41#4112yes—
222C22×Q8—21no—
223C22×Q8—21no—
224C22×Q8C22×C411yescharacteristic
225C22×D4—21no—
226C22×D4C22×C411yescharacteristic
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4#4111yescharacteristic
233C23×C4#4111yescharacteristic
234C23×C4C2411yescharacteristic
235C2×M16—21no—
236C2×M16—21no—
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—21no—
253C2×M16—21no—
254C2×M16—21no—
255C2×M16—21no—
256C2×M16—21no—
257C2×M16—21no—
258C2×M16C2×Q812yes—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8C22×C411yescharacteristic
286C22×C8C22×C411yescharacteristic
287C22×C8C22×C411yescharacteristic
288C22×C8C22×C411yescharacteristic
289C22×C8C2×D411yescharacteristic
290C22×C8C2×D411yescharacteristic
291C22×C8C2×D411yescharacteristic
292C22×C8C2×D411yescharacteristic
293C22×C8C2×D412yes—
294C22×C8C2×D412yes—
295C4⋊Q8—22no—
296C4⋊Q8—22no—
297C4⋊Q8—41no—
298C4⋊Q8—41no—
299#125—22no—
300#125—22no—
301#125—41no—
302#125—41no—
303C22⋊Q8—42no—
304C22⋊Q8—42no—
305C22⋊Q8—42no—
306C22⋊Q8—42no—
307C4×Q8—22no—
308C4×Q8—22no—
309C4×Q8—42no—
310C4×Q8—42no—
311C4×Q8—42no—
312C4×Q8—42no—
313C4×Q8—41no—
314C4×Q8—41no—
315C4×D4—22no—
316C4×D4—22no—
317C4×D4—41no—
318C4×D4—41no—
319C4×D4—42no—
320C4×D4—42no—
321C4×D4—42no—
322C4×D4—42no—
323#117—21no—
324#117—21no—
325#117—21no—
326#117—21no—
327#117—21no—
328#117—21no—
329#117—21no—
330#117—21no—
331#117—42no—
332#117—42no—
333#117C2×D412yes—
334#117C2×D412yes—
335#117C2×D412yes—
336#117C2×D412yes—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4C22×C411yescharacteristic
346C2×C4⋊C4C22×C411yescharacteristic
347C2×C4⋊C4C22×C411yescharacteristic
348C2×C4⋊C4C22×C411yescharacteristic
349C2×C4⋊C4C22×C411yescharacteristic
350C2×C4⋊C4C22×C411yescharacteristic
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—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—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—42no—
377C2×C42—42no—
378C2×C42C22×C411yescharacteristic
379C2×C42C22×C411yescharacteristic
380C2×C42C2×D411yescharacteristic
381C2×C42C2×D411yescharacteristic
382C2×C42C2×Q812yes—
383#108—44no—
384#107—22no—
385#107—22no—
386#107C22⋊C414yes—
387#107C22⋊C414yes—
388#106—22no—
389#106—22no—
390#106C22⋊C414yes—
391#106C22⋊C414yes—
392C4⋊C8—22no—
393C4⋊C8—22no—
394C4⋊C8—22no—
395C4⋊C8—22no—
396C4⋊C8—42no—
397C4⋊C8—42no—
398C4⋊C8—42no—
399C4⋊C8—42no—
400C4⋊C8—42no—
401C4⋊C8—42no—
402#104—44no—
403#104—44no—
404#103—22no—
405#103—22no—
406#103—22no—
407#103—22no—
408#102—22no—
409#102—22no—
410#102—22no—
411#102—22no—
412C22⋊C8—42no—
413C22⋊C8—42no—
414C22⋊C8—42no—
415C22⋊C8—42no—
416#97—42no—
417C4×C8—42no—
418C4×C8—44no—
419#95—24no—
420#95—42no—
421C24—21no—
422C24C2×#4111yescharacteristic
423#41—22no—
424#41—22no—
425#41—22no—
426#41—22no—
427#41—22no—
428#41—22no—
429#41—22no—
430#41—22no—
431#41—41no—
432#41—41no—
433#41—41no—
434#41—41no—
435#41—41no—
436#41—41no—
437#41—41no—
438#41—41no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—42no—
445C2×Q8—42no—
446C2×Q8—42no—
447C2×Q8—42no—
448C2×Q8—81no—
449C2×Q8—81no—
450C2×Q8C4×Q812yes—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4C4×Q812yes—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
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—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—42no—
502C22×C4—81no—
503C22×C4—81no—
504C22×C4C4×D411yescharacteristic
505C22×C4C4×D411yescharacteristic
506C22×C4C4×D411yescharacteristic
507C22×C4C4×D411yescharacteristic
508C22×C4C23×C411yescharacteristic
509C22×C4C22×D411yescharacteristic
510C22×C4C22×D411yescharacteristic
511C22×C4C22×D411yescharacteristic
512C22×C4C22×Q811yescharacteristic
513C22×C4C2×#4111yescharacteristic
514C22×C4H(5,𝔽2)11yescharacteristic
515C22×C4H(5,𝔽2)11yescharacteristic
516C22×C4H(5,𝔽2)11yescharacteristic
517C22×C4H(5,𝔽2)11yescharacteristic
518C22×C42−1+411yescharacteristic
519C22×C42−1+411yescharacteristic
520C22×C42−1+411yescharacteristic
521C22×C42−1+411yescharacteristic
522M16—22no—
523M16—22no—
524M16—41no—
525M16—41no—
526M16—41no—
527M16—41no—
528M16—41no—
529M16—41no—
530M16—41no—
531M16—41no—
532M16—41no—
533M16—41no—
534M16—41no—
535M16—41no—
536M16—41no—
537M16—41no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—22no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8C2×C22⋊C412yes—
589C2×C8C2×C22⋊C412yes—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4C2×C22⋊C412yes—
607C4⋊C4C2×C22⋊C412yes—
608C4⋊C4C2×C22⋊C412yes—
609C4⋊C4C2×C22⋊C412yes—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—41no—
617C22⋊C4—41no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—22no—
631C42—22no—
632C42—42no—
633C42—42no—
634C42—41no—
635C42—41no—
636C42—41no—
637C42—41no—
638C42—41no—
639C42—41no—
640C42—41no—
641C42—41no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—22no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23C2×C4×D411yescharacteristic
654C23#54111yescharacteristic
655C23#54211yescharacteristic
656C23#54611yescharacteristic
657C23#54611yescharacteristic
658C23#55211yescharacteristic
659C23#55411yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—41no—
663Q8—41no—
664Q8—84no—
665Q8—84no—
666D4—22no—
667D4—22no—
668D4—42no—
669D4—42no—
670D4—42no—
671D4—42no—
672D4—41no—
673D4—41no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—24no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—84no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—84no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4#44312yes—
731C2×C4C22×C22⋊C411yescharacteristic
732C2×C4C2×C4×Q811yescharacteristic
733C2×C4#51811yescharacteristic
734C2×C4#51911yescharacteristic
735C2×C4#52011yescharacteristic
736C2×C4#52011yescharacteristic
737C2×C4#53511yescharacteristic
738C2×C4#53611yescharacteristic
739C2×C4#53611yescharacteristic
740C2×C4#53711yescharacteristic
741C2×C4#53711yescharacteristic
742C2×C4#53711yescharacteristic
743C2×C4#53811yescharacteristic
744C2×C4#53911yescharacteristic
745C2×C4#54311yescharacteristic
746C2×C4#54411yescharacteristic
747C2×C4D4211yescharacteristic
748C2×C4D4211yescharacteristic
749C2×C4#54611yescharacteristic
750C2×C4#54811yescharacteristic
751C2×C4#54811yescharacteristic
752C2×C4D4×Q811yescharacteristic
753C2×C4D4×Q811yescharacteristic
754C2×C4D4×Q811yescharacteristic
755C2×C4#56211yescharacteristic
756C2×C4#56211yescharacteristic
757C2×C4#56311yescharacteristic
758C2×C4#56311yescharacteristic
759C8—22no—
760C8—22no—
761C8—41no—
762C8—41no—
763C8—41no—
764C8—41no—
765C8—41no—
766C8—41no—
767C8—42no—
768C8—81no—
769C8—81no—
770C8—81no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22#232311yescharacteristic
791C22D4×C22⋊C411yescharacteristic
792C22#236011yescharacteristic
793C22#269011yescharacteristic
794C22#269211yescharacteristic
795C22#270211yescharacteristic
796C22#270411yescharacteristic
797C22C2×#44311yescharacteristic
798C22#295511yescharacteristic
799C22#295611yescharacteristic
800C22#295711yescharacteristic
801C4—22no—
802C4—44no—
803C4—42no—
804C4—41no—
805C4—41no—
806C4—42no—
807C4—42no—
808C4—41no—
809C4—42no—
810C4—42no—
811C4—82no—
812C4—81no—
813C4—81no—
814C4#231111yescharacteristic
815C4#232911yescharacteristic
816C4Q8×C22⋊C411yescharacteristic
817C4#237811yescharacteristic
818C4#267611yescharacteristic
819C4#267711yescharacteristic
820C4#268111yescharacteristic
821C4#268311yescharacteristic
822C2—21no—
823C2—21no—
824C2—21no—
825C2—21no—
826C2—82no—
827C2#1436211yescharacteristic
828C2#2213011yescharacteristic
829C2#2213211yescharacteristic
830C2#2245311yescharacteristic
831C2#2245411yescharacteristic
832C2#2298211yescharacteristic
833C2#2298411yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C2×C4×D4
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×#336 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #21304C2semidirect
3. C2×#1945C2semidirect
4. C2×#1922C2semidirect
6. #11386C2semidirect
7. #11233C2semidirect
8. #11221C2semidirect
9. #11221C2semidirect
14. #10876C2semidirect
20. C2×#479C4semidirect
21. C2×#479C4semidirect
22. C2×#477C4semidirect
23. C2×#475C4semidirect
24. C2×#478C4semidirect
25. C2×#478C4semidirect
26. C2×#476C4semidirect
27. C2×#474C4semidirect
156. C2×#104Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#30762
#213042
C2×#19452
C2×#19222
#206302
#113862
#112332
#112212
#111252
#110682
#109342
#109292
#108762
#107902