Finite Group Databasebeta

← #6467830

Subgroups — #6467830

Order 512.

1964 conjugacy classes of subgroups.

The subgroup lattice has 799 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3182C211yesmaximal, characteristic
2C2×#3170C211yesmaximal, characteristic, complemented
3#35298C211yesmaximal, characteristic
4#34225C211yesmaximal, characteristic, complemented
5#28750C211yesmaximal, characteristic, complemented
6#28717C211yesmaximal, characteristic, complemented
7#28689C211yesmaximal, characteristic, complemented
8#28656C211yesmaximal, characteristic, complemented
9#28655C211yesmaximal, characteristic, complemented
10#28616C211yesmaximal, characteristic, complemented
11#28614C211yesmaximal, characteristic, complemented
12#28590C214yesmaximal, complemented
13#28444C211yesmaximal, characteristic, complemented
14#24765C214yesmaximal, complemented
15#23695C214yesmaximal, complemented
16#21512C214yesmaximal, complemented
17#21409C211yesmaximal, characteristic, complemented
18#21401C211yesmaximal, characteristic
19C4×#424C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C2×#532C2211yescharacteristic
23#3182—28no—
24#3170—28no—
25C2×#500C2211yescharacteristic
26C2×#500C2211yescharacteristic
27C2×#494C2211yescharacteristic
28C2×#492C2211yescharacteristic
29C2×#487C2211yescharacteristic
30C2×#487C2211yescharacteristic
31C2×#487C2211yescharacteristic
32C2×#486C2211yescharacteristic
33C2×#468C2214yes—
34C2×#467C2214yes—
35C2×#464C2214yes—
36C2×#440C2214yes—
37C2×C4×Q16C2214yes—
38C2×#424C2212yes—
39C2×C4×M16C2211yescharacteristic
40C22×C4×C8C2211yescharacteristic
41#2868C2211yescharacteristic
42#2862C2211yescharacteristic
43#2858C2211yescharacteristic
44#2858C2211yescharacteristic
45#2620C2212yes—
46#2620C2212yes—
47#2566—21no—
48#2566—21no—
49#2545—21no—
50#2545—21no—
51#2500—21no—
52#2500—21no—
53#2432—21no—
54#2432—21no—
55#2370—21no—
56#2370—21no—
57#2362—21no—
58#2362—21no—
59#2356—21no—
60#2351—21no—
61#2347—21no—
62#2346—21no—
63#2326C2212yes—
64#2326C2212yes—
65#2323C2212yes—
66#2323C2212yes—
67#2320C2212yes—
68C4×C4⋊Q8C2211yescharacteristic
69C4×C4⋊Q8C2211yescharacteristic
70C4×C4⋊Q8C2211yescharacteristic
71C4×C4⋊Q8C2211yescharacteristic
72#2285C2211yescharacteristic
73#2276C2212yes—
74C4×#117C2211yescharacteristic
75#2083C2214yes—
76#2072C2214yes—
77#2068C2214yes—
78#2067C2214yes—
79#2056C2214yes—
80#2055C2214yes—
81#2042C2214yes—
82#2015C2214yes—
83#1990C2211yescharacteristic
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1983C2214yes—
88#1957C2211yescharacteristic
89#1957C2211yescharacteristic
90#1956C2211yescharacteristic
91#1956C2211yescharacteristic
92#1947C2214yes—
93#1928C2214yes—
94#1925C2214yes—
95#1894C2214yes—
96#1893C2214yes—
97#1880C2214yes—
98#1878C2214yes—
99#1803C2214yes—
100#1768C2212yes—
101#1768C2212yes—
102C4×C4⋊C8C2211yescharacteristic
103C4×C4⋊C8C2211yescharacteristic
104C4×C4⋊C8C2211yescharacteristic
105C4×C4⋊C8C2211yescharacteristic
106#1763C2214yes—
107C4×#102C2214yes—
108#1729C2212yes—
109C22×#41—21no—
110C22×Q16C2314yes—
111C22×SD16C2314yes—
112C22×M16C2312yes—
113C23×C8C2312yes—
114#533—24no—
115#533—24no—
116#533—24no—
117#533D418yes—
118#532—24no—
119#532—24no—
120C2×C4⋊Q8—21no—
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2311yescharacteristic
126C2×C4⋊Q8C2311yescharacteristic
127C2×#127C2311yescharacteristic
128C2×#125—21no—
129C2×#125—21no—
130C2×#124—21no—
131C2×#124—21no—
132C2×#124—21no—
133C2×#124C2312yes—
134C2×#124C2312yes—
135C2×C22⋊Q8—21no—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8C2312yes—
138C2×C22⋊Q8C2312yes—
139C2×#121—21no—
140C2×#121C2312yes—
141C2×C4×Q8—21no—
142C2×C4×Q8—21no—
143C2×C4×Q8—21no—
144C2×C4×Q8—21no—
145C2×C4×Q8C2312yes—
146C2×C4×Q8C2312yes—
147C2×C4×Q8C2312yes—
148C2×C4×Q8C2312yes—
149C2×C4×D4—21no—
150C2×C4×D4C2312yes—
151C2×#117—21no—
152C2×#117—21no—
153C2×#117—21no—
154C2×#117C2311yescharacteristic
155C2×#117C2311yescharacteristic
156C22×C42C2311yescharacteristic
157#500—24no—
158#500—24no—
159#494—24no—
160#492—24no—
161#487—24no—
162#487—24no—
163#487—24no—
164#486—24no—
165#468—216no—
166#467—216no—
167#464—216no—
168#440—216no—
169C4×Q16—216no—
170C2×#107C2314yes—
171C2×#107C2314yes—
172#424—28no—
173C2×C4⋊C8C2312yes—
174C2×C4⋊C8C2312yes—
175C2×C4⋊C8C2312yes—
176C2×C4⋊C8C2312yes—
177C2×#103C2314yes—
178C2×#103C2314yes—
179C2×#103C2314yes—
180C2×#103C2314yes—
181C2×#103C2314yes—
182C2×#102C2314yes—
183C2×#102C2314yes—
184C2×#102C2314yes—
185C4×M16—24no—
186C2×#97C2312yes—
187C2×C4×C8—24no—
188C2×C4×C8C2311yescharacteristic
189C2×C4×C8C2311yescharacteristic
190C2×C4×C8C2312yes—
191C2×C4×C8C2311yescharacteristic
192C2×C4×C8C2311yescharacteristic
193#396—22no—
194#396—22no—
195#396—22no—
196#396—22no—
197#394—22no—
198#394—22no—
199#394—22no—
200#394—22no—
201#391—21no—
202#391—21no—
203#391—21no—
204#391—21no—
205#391C2312yes—
206#391C2312yes—
207#391C2312yes—
208#391C2312yes—
209#390—21no—
210#390—21no—
211#390—21no—
212#390—21no—
213#390—21no—
214#390—21no—
215#390C2312yes—
216#390C2312yes—
217#389—22no—
218#389—22no—
219#389—21no—
220#389—21no—
221#389—21no—
222#389—21no—
223#389—21no—
224#389—21no—
225#389C2312yes—
226#389C2312yes—
227#388—22no—
228#388—22no—
229#388—22no—
230#388—22no—
231#388—22no—
232#388—22no—
233#388—22no—
234#388—22no—
235#387—22no—
236#387—22no—
237#387—22no—
238#387—22no—
239#385—22no—
240#385—22no—
241#385—22no—
242#385—22no—
243#384—21no—
244#384—21no—
245#384C2311yescharacteristic
246#384C2311yescharacteristic
247#384C2312yes—
248#384C2312yes—
249#383—22no—
250#382—21no—
251#382—21no—
252#382—21no—
253#382—22no—
254#380—21no—
255#380C2312yes—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4—21no—
260C4×C4⋊C4—21no—
261C4×C4⋊C4—21no—
262C4×C4⋊C4—21no—
263C4×C4⋊C4—22no—
264C4×C4⋊C4—22no—
265C4×C4⋊C4—22no—
266C4×C4⋊C4D411yescharacteristic
267C4×C4⋊C4D411yescharacteristic
268C4×C4⋊C4D411yescharacteristic
269C4×C4⋊C4D411yescharacteristic
270C4×C4⋊C4C2312yes—
271C4×C4⋊C4C2312yes—
272C4×C4⋊C4C2312yes—
273C4×C22⋊C4D411yescharacteristic
274C4×C22⋊C4D411yescharacteristic
275C4×C22⋊C4D411yescharacteristic
276C4×C22⋊C4D411yescharacteristic
277#376—22no—
278#376C2311yescharacteristic
279#376C2311yescharacteristic
280C43C2311yescharacteristic
281C43C2311yescharacteristic
282#340C2314yes—
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#336C2312yes—
287#336C2312yes—
288#336C2312yes—
289#336C2312yes—
290C2×#41—44no—
291C2×#41—82no—
292C2×#41—82no—
293C22×Q8—21no—
294C22×Q8—21no—
295C22×Q8—21no—
296C22×Q8C2412yes—
297C22×Q8C2412yes—
298C22×D4—22no—
299C22×D4—21no—
300C22×D4—21no—
301C22×D4C2412yes—
302C23×C4—22no—
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2411yescharacteristic
306C2×Q16—28no—
307C2×Q16—28no—
308C2×Q16—44no—
309C2×SD16—28no—
310C2×SD16—28no—
311C2×SD16—44no—
312C2×M16—24no—
313C2×M16—24no—
314C2×M16—42no—
315C22×C8—24no—
316C22×C8—24no—
317C22×C8—42no—
318C22×C8C2412yes—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C22×C8C2412yes—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326C4⋊Q8—22no—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330C4⋊Q8—82no—
331C4⋊Q8—82no—
332C4⋊Q8C2×D414yes—
333C4⋊Q8C2×D414yes—
334#127—22no—
335#127—22no—
336#125—28no—
337#125—44no—
338#124—28no—
339#124—44no—
340#124—44no—
341#124—82no—
342#124—82no—
343C22⋊Q8—28no—
344C22⋊Q8—24no—
345C22⋊Q8—24no—
346C22⋊Q8—24no—
347C22⋊Q8—44no—
348C22⋊Q8C2×D418yes—
349#121—24no—
350#121—24no—
351#121—44no—
352C4×Q8—28no—
353C4×Q8—24no—
354C4×Q8—24no—
355C4×Q8—24no—
356C4×Q8—28no—
357C4×Q8—44no—
358C4×Q8—44no—
359C4×Q8—82no—
360C4×Q8—82no—
361C4×Q8C2×D418yes—
362C4×D4—24no—
363C4×D4—24no—
364C4×D4—44no—
365#117—28no—
366#117—24no—
367#117—42no—
368#117—44no—
369#117—82no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4C2×D411yescharacteristic
394C2×C4⋊C4C2×D411yescharacteristic
395C2×C4⋊C4C2×D411yescharacteristic
396C2×C4⋊C4C2×D411yescharacteristic
397C2×C4⋊C4C2412yes—
398C2×C4⋊C4C2412yes—
399C2×C4⋊C4C2412yes—
400C2×C4⋊C4C2412yes—
401C2×C4⋊C4C2412yes—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4C2×D411yescharacteristic
416C2×C22⋊C4C2×D411yescharacteristic
417C2×C22⋊C4C2×D411yescharacteristic
418C2×C22⋊C4C2×D411yescharacteristic
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D414yes—
437C2×C42#4114yes—
438C2×C42C2411yescharacteristic
439C2×C42C2411yescharacteristic
440C2×C42C2411yescharacteristic
441C2×C42C2411yescharacteristic
442C2×C42C2411yescharacteristic
443C2×C42C2411yescharacteristic
444#107—28no—
445#107—28no—
446C4⋊C8—24no—
447C4⋊C8—24no—
448C4⋊C8—24no—
449C4⋊C8#4118yescomplemented
450#103—28no—
451#103—28no—
452#103—28no—
453#103—28no—
454#103—44no—
455#102—28no—
456#102—28no—
457#102—44no—
458#97—24no—
459C4×C8—24no—
460C4×C8—22no—
461C4×C8—22no—
462C4×C8—22no—
463C4×C8—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95C2×D411yescharacteristic
479#95C2×D411yescharacteristic
480#95C2×D411yescharacteristic
481#95C2×D411yescharacteristic
482#95C2×D411yescharacteristic
483#95C2×D411yescharacteristic
484#95C2×D411yescharacteristic
485#95C2×D411yescharacteristic
486C24—22no—
487C24C22×D411yescharacteristic
488#41—816no—
489C2×Q8—24no—
490C2×Q8—22no—
491C2×Q8—22no—
492C2×Q8—24no—
493C2×Q8—24no—
494C2×Q8—22no—
495C2×Q8—24no—
496C2×Q8—24no—
497C2×Q8—42no—
498C2×Q8—42no—
499C2×Q8—42no—
500C2×Q8—42no—
501C2×Q8—42no—
502C2×Q8—42no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8C22×D414yes—
506C2×D4—22no—
507C2×D4—24no—
508C2×D4—22no—
509C2×D4—24no—
510C2×D4—44no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—82no—
518C2×D4—82no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—44no—
533C22×C4—82no—
534C22×C4—82no—
535C22×C4#12114yes—
536C22×C4#12114yes—
537C22×C4C22×D411yescharacteristic
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D412yes—
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C2×#4112yes—
552C22×C4C2511yescharacteristic
553Q16—416no—
554SD16—416no—
555M16—48no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—48no—
567C2×C8C2×#4114yes—
568C2×C8C2×#4114yes—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—28no—
573C4⋊C4—28no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—24no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—24no—
583C4⋊C4—41no—
584C4⋊C4—41no—
585C4⋊C4—44no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—44no—
590C4⋊C4—44no—
591C4⋊C4—42no—
592C4⋊C4—44no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—82no—
598C4⋊C4—82no—
599C4⋊C4—82no—
600C4⋊C4—82no—
601C4⋊C4—82no—
602C4⋊C4—82no—
603C4⋊C4C22×D414yes—
604C22⋊C4—28no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—41no—
608C22⋊C4—41no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—82no—
617C22⋊C4—82no—
618C22⋊C4—82no—
619C22⋊C4—82no—
620C22⋊C4—82no—
621C42—28no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—44no—
634C42—44no—
635C42—44no—
636C42—82no—
637C42—82no—
638C42—82no—
639C42#12114yes—
640C42#12114yes—
641C42C22×D412yes—
642C42C22×D412yes—
643C42C2×#4112yes—
644C42C2×#4112yes—
645C42C2×#4114yes—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23C2×#12112yes—
660C23C23×D411yescharacteristic
661Q8—28no—
662Q8—44no—
663Q8—48no—
664Q8—44no—
665Q8—44no—
666Q8—84no—
667Q8—84no—
668D4—44no—
669D4—44no—
670D4—88no—
671D4—84no—
672D4—84no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—28no—
686C2×C4—28no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—88no—
727C2×C4C2×#12112yes—
728C2×C4C2×#12112yes—
729C2×C4C2×#12112yes—
730C2×C4C2×#12112yes—
731C2×C4C2×#12112yes—
732C2×C4#53212yes—
733C2×C4#53212yes—
734C2×C4#57612yes—
735C2×C4#57712yes—
736C2×C4#57812yes—
737C2×C4#57812yes—
738C2×C4C23×D411yescharacteristic
739C2×C4C22×#4112yes—
740C2×C4C22×#4111yescharacteristic
741C2×C4#58512yes—
742C8—24no—
743C8—24no—
744C8—42no—
745C8—42no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—82no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22C22×#12111yescharacteristic
761C22C2×#53211yescharacteristic
762C22#344911yescharacteristic
763C22C2×#57611yescharacteristic
764C22C2×#57711yescharacteristic
765C22C2×#57811yescharacteristic
766C22C2×#57811yescharacteristic
767C4—22no—
768C4—22no—
769C4—22no—
770C4—22no—
771C4—22no—
772C4—44no—
773C4—41no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—44no—
780C4—82no—
781C4—82no—
782C4—82no—
783C4—82no—
784C4—82no—
785C4#304414yes—
786C4#304514yes—
787C4D4×#4112yes—
788C4#348012yes—
789C2—42no—
790C2—162no—
791C2#3493711yescharacteristic
792C2C2×#304411yescharacteristic
793C2C2×#304511yescharacteristic
794C2#6071811yescharacteristic
795C2#6072311yescharacteristic
796C2#6100811yescharacteristic
797C2#6101411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#532C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3170C2semidirect
4. #34225C2semidirect
5. #28750C2semidirect
6. #28717C2semidirect
7. #28689C2semidirect
8. #28656C2semidirect
9. #28655C2semidirect
10. #28616C2semidirect
11. #28614C2semidirect
12. #28590C2semidirect
13. #28444C2semidirect
14. #24765C2semidirect
15. #23695C2semidirect
16. #21512C2semidirect
17. #21409C2semidirect
19. C4×#424C2semidirect
449. C4⋊C8#41semidirect

Maximal subgroups

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

subgroupindex
C2×#31822
C2×#31702
#352982
#342252
#287502
#287172
#286892
#286562
#286552
#286162
#286142
#285902
#284442
#247652
#236952
#215122
#214092
#214012
C4×#4242