Finite Group Databasebeta

← #7644117

Subgroups — #7644117

Order 512.

7512 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3506C211yesmaximal, characteristic, complemented
2C22×#540C211yesmaximal, characteristic, complemented
3#42646C214yesmaximal, complemented
4#42645C214yesmaximal, complemented
5#42445C218yesmaximal, complemented
6#42444C218yesmaximal, complemented
7#42425C214yesmaximal, complemented
8#42424C214yesmaximal, complemented
9#37452C214yesmaximal, complemented
10#37439C214yesmaximal, complemented
11#36709C214yesmaximal, complemented
12#36706C214yesmaximal, complemented
13#35639C212yesmaximal, complemented
14#35563C212yesmaximal, complemented
15#35528C212yesmaximal, complemented
16#35514C212yesmaximal, complemented
17#35172C211yesmaximal, characteristic, complemented
18#35165C211yesmaximal, characteristic, complemented
19#34634C211yesmaximal, characteristic, complemented
20#34633C211yesmaximal, characteristic, complemented
21#34181C211yesmaximal, characteristic, complemented
22#3506—216no—
23C2×#559C2214yescomplemented
24C2×#556C2212yescomplemented
25C2×#555C2212yescomplemented
26C2×#553C2214yescomplemented
27C2×#550C2212yescomplemented
28C2×#547C2212yescomplemented
29C2×#540—216no—
30C2×#540C2214yes—
31C2×#540C2214yes—
32C2×#540C2214yes—
33C2×#540C2214yes—
34C2×#538C2214yes—
35C2×#535C2212yes—
36C2×#535C2212yes—
37C2×#533C2211yescharacteristic
38C2×#532C2211yescharacteristic
39C22×#127C2211yescharacteristic
40C22×#125C2211yescharacteristic
41C2×#525C2214yes—
42C2×#525C2212yes—
43C22×#123C2212yes—
44C22×#123C2212yes—
45C22×#121C2212yes—
46C22×#121C2212yes—
47C22×#121C2211yescharacteristic
48C22×#121C2211yescharacteristic
49C2×#520C2212yes—
50C2×#518C2212yes—
51C22×C4×D4C2211yescharacteristic
52C22×C4×D4C2211yescharacteristic
53C22×#117C2211yescharacteristic
54#2848C2214yes—
55#2847C2214yes—
56#2814C2218yescomplemented
57#2813C22116yescomplemented
58#2813C2218yescomplemented
59#2695C22116yescomplemented
60#2693C22116yescomplemented
61#2691C22116yescomplemented
62#2676C22116yescomplemented
63#2675C22116yescomplemented
64#2672C22116yescomplemented
65#2671C22116yescomplemented
66#2671C22116yescomplemented
67#2656C2218yescomplemented
68#2639C2218yescomplemented
69#2630C22116yescomplemented
70#2629C2214yescomplemented
71#2628C2212yescomplemented
72#2628C2212yescomplemented
73#2627C2212yes—
74#2627C2212yes—
75#2626C2212yes—
76#2626C2214yes—
77#2626C2212yes—
78#2624C2218yescomplemented
79#2621C2212yescomplemented
80#2620C2214yescomplemented
81#2619C2212yescomplemented
82#2618C2212yes—
83#2618C2212yes—
84#2618C22116yescomplemented
85#2617C2212yes—
86#2617C2214yes—
87#2617C2212yes—
88#2615C2218yescomplemented
89#2580C2214yescomplemented
90#2579C2218yes—
91#2566C2214yescomplemented
92#2563C2212yescomplemented
93#2547C2212yescomplemented
94#2544C2214yescomplemented
95#2544C2218yescomplemented
96#2542C2212yescomplemented
97#2541C2212yescomplemented
98#2541C2218yescomplemented
99#2538C2214yescomplemented
100#2537C2214yescomplemented
101#2537C2218yescomplemented
102#2535C2214yescomplemented
103#2535C2218yescomplemented
104#2534C2218yes—
105#2498C2218yescomplemented
106#2487C2218yes—
107#2454C2218yescomplemented
108#2453C2218yescomplemented
109#2442C2218yescomplemented
110#2441C2218yescomplemented
111#2430C2218yescomplemented
112#2428C2218yescomplemented
113#2428C2218yescomplemented
114#2428C2218yescomplemented
115#2428C2218yescomplemented
116#2427C2218yescomplemented
117#2426C2218yescomplemented
118#2416C22116yescomplemented
119#2416C2218yescomplemented
120#2414C2218yescomplemented
121#2412C2218yes—
122#2410C2218yes—
123#2410C2218yes—
124#2410C2218yes—
125#2408C2218yes—
126#2396C2214yescomplemented
127#2396C2214yescomplemented
128#2392C2214yescomplemented
129#2392C2214yescomplemented
130#2349C2214yescomplemented
131#2349C2214yescomplemented
132D4×C4⋊C4C2214yescomplemented
133D4×C4⋊C4C2214yescomplemented
134#2317C2212yes—
135#2316C2212yes—
136#2315C2214yes—
137#2311C2212yes—
138#2309C2212yes—
139#2297C2212yes—
140#2296C2212yes—
141#2285C2211yescharacteristic
142#2285C2211yescharacteristic
143#2280C2212yes—
144C2×#380C2214yes—
145C22×#41C2312yes—
146C22×#41C2314yes—
147C23×D4C2311yescharacteristic
148C23×D4C2311yescharacteristic
149C23×D4C2312yes—
150C23×D4C2312yes—
151C23×D4C2312yes—
152C23×D4C2312yes—
153C24×C4C2311yescharacteristic
154C24×C4C2312yes—
155C24×C4C2312yes—
156#559—232no—
157#556—216no—
158#555—216no—
159#553—232no—
160#550—216no—
161#547—216no—
162#540—232no—
163#540—232no—
164#540—232no—
165#540—232no—
166#538—232no—
167#535—216no—
168#535—48no—
169#533—28no—
170#532—28no—
171C2×C4⋊Q8C2311yescharacteristic
172C2×C4⋊Q8C2311yescharacteristic
173C2×C4⋊Q8C2311yescharacteristic
174C2×#127—28no—
175C2×#127C2311yescharacteristic
176C2×#127C2314yes—
177C2×#127C2314yes—
178C2×#127C2314yes—
179C2×#127C2314yes—
180C2×#126C2318yes—
181C2×#125—28no—
182C2×#125C2312yes—
183C2×#125C2314yes—
184C2×#125C2314yes—
185C2×#124C2312yes—
186C2×#124C2318yes—
187C2×#124C2314yes—
188C2×#124C2314yes—
189#525—232no—
190#525—48no—
191C2×#123—216no—
192C2×#123—216no—
193C2×#123C2318yes—
194C2×#123C2318yes—
195C2×#123C2318yes—
196C2×#123C2318yes—
197C2×#123C2318yes—
198C2×#123C2318yes—
199C2×#123C2314yes—
200C2×C22⋊Q8C2312yes—
201C2×C22⋊Q8C2312yes—
202C2×C22⋊Q8C2314yes—
203C2×C22⋊Q8C2314yes—
204C2×C22⋊Q8C2318yes—
205C2×#121—28no—
206C2×#121—216no—
207C2×#121—28no—
208C2×#121—216no—
209C2×#121C2312yes—
210C2×#121C2318yes—
211C2×#121C2312yes—
212C2×#121C2314yes—
213C2×#121C2314yes—
214C2×#121C2318yes—
215C2×#121C2318yes—
216C2×#121C2318yes—
217C2×#121C2314yes—
218C2×#121C2314yes—
219C2×#121C2314yes—
220C2×#121C2318yes—
221C2×#121C2314yes—
222C2×#121C2314yes—
223C2×#121C2314yes—
224C2×#121C2318yes—
225C2×#121C2318yes—
226C2×#121C23116yes—
227C2×#121C23116yes—
228C2×#121C23116yes—
229C2×#121C23116yes—
230C2×#120C2318yes—
231C2×#120C2318yes—
232C2×#120C2314yes—
233#520—216no—
234#518—48no—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2314yes—
238C2×C4×D4—28no—
239C2×C4×D4D4116yescomplemented
240C2×C4×D4C2312yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2318yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2318yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2318yes—
250C2×C4×D4C2318yes—
251C2×C4×D4C2318yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2312yes—
256C2×#117—28no—
257C2×#117C2312yes—
258C2×#117C2312yes—
259C2×#117C2312yes—
260C2×#117C2312yes—
261C2×#117C2312yes—
262C2×#117C2314yes—
263C2×#117C2312yes—
264C2×#117C2312yes—
265C2×#117C2314yes—
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2311yescharacteristic
270C22×C4⋊C4C2314yes—
271C22×C4⋊C4C2312yes—
272C22×C4⋊C4C2318yes—
273C22×C4⋊C4C2311yescharacteristic
274C22×C22⋊C4C2311yescharacteristic
275C22×C22⋊C4C2311yescharacteristic
276C22×C22⋊C4C2312yes—
277C22×C22⋊C4C2312yes—
278C22×C22⋊C4C2312yes—
279C22×C22⋊C4C2318yes—
280C22×C22⋊C4C2312yes—
281C22×C42C2311yescharacteristic
282C22×C42C2311yescharacteristic
283#400C2314yes—
284#400C2314yes—
285#400C23116yes—
286#399C2318yes—
287#399C2314yes—
288#399C2314yes—
289#399C23116yes—
290#398C23116yes—
291#398C2314yes—
292#398C2314yes—
293#398C2318yes—
294#398C2318yes—
295#397C2314yes—
296#397C2314yes—
297#397C2318yes—
298#397C23116yes—
299#396C23116yes—
300#396C23116yes—
301#396C2318yes—
302#396C2318yes—
303#396C23116yes—
304#396C2318yes—
305#396C2318yes—
306#395C2314yes—
307#395C2314yes—
308#394C23116yes—
309#394C2318yes—
310#394C2318yes—
311#394C2314yes—
312#394C2314yes—
313#394C23116yes—
314#394C23116yes—
315#394C23116yes—
316#394C23116yes—
317#394C23116yes—
318#394C23116yes—
319#393C2318yes—
320#393C2314yes—
321#393C2314yes—
322#392C2314yes—
323#392C2318yes—
324#392C23116yes—
325#392C23116yes—
326#392C2314yes—
327#392C23116yes—
328#392C23116yes—
329#391C2314yes—
330#391C2314yes—
331#390C2314yes—
332#390C2314yes—
333#390C2318yes—
334#390C2314yes—
335#390C2314yes—
336#390C23116yes—
337#389C2318yes—
338#389C2318yes—
339#389C2318yes—
340#389C23116yes—
341#389C2314yes—
342#389C2314yes—
343#388C23116yes—
344#387C23116yes—
345#386C2318yes—
346#386C2314yes—
347#386C23116yes—
348#386C2314yes—
349#386C23116yes—
350#386C23116yes—
351#386C23116yes—
352#386C23116yes—
353#386C23116yes—
354#385C23116yes—
355#385C23116yes—
356#385C23116yes—
357#385C2318yes—
358#385C2314yes—
359#385C23116yes—
360#385C2314yes—
361#384C2314yes—
362#384C2312yes—
363#384C2312yes—
364#382C2314yes—
365#382C2312yes—
366#382C2312yes—
367#381C2314yes—
368#380C2318yes—
369#380C2318yes—
370#380C2312yes—
371#380C2312yes—
372#380C2318yes—
373#380C2318yes—
374#380C2318yes—
375#380C2318yes—
376#380C23116yes—
377#380C2312yes—
378#380C2312yes—
379#380C23116yes—
380#380C2314yes—
381#380C2314yes—
382#379C2318yes—
383#379C2314yes—
384C4×C4⋊C4C2312yes—
385C4×C4⋊C4C2312yes—
386C4×C4⋊C4C2312yes—
387C4×C4⋊C4C2312yes—
388C4×C4⋊C4C2318yes—
389C4×C22⋊C4C2318yes—
390C4×C22⋊C4C2318yes—
391C2×#95C2318yes—
392C25C2411yescharacteristic
393C25C2412yes—
394C25C2412yes—
395C2×#41—28no—
396C2×#41—216no—
397C2×#41—28no—
398C2×#41—28no—
399C2×#41—88no—
400C22×Q8C2412yes—
401C22×Q8C2412yes—
402C22×Q8C2412yes—
403C22×D4—28no—
404C22×D4—28no—
405C22×D4—28no—
406C22×D4—24no—
407C22×D4—28no—
408C22×D4—24no—
409C22×D4—24no—
410C22×D4—24no—
411C22×D4—24no—
412C22×D4—84no—
413C22×D4—84no—
414C22×D4—84no—
415C22×D4—84no—
416C22×D4C2×D418yes—
417C22×D4C2414yes—
418C22×D4C2412yes—
419C22×D4C2412yes—
420C22×D4C2412yes—
421C22×D4C2412yes—
422C22×D4C2412yes—
423C22×D4C2418yes—
424C22×D4C2412yes—
425C22×D4C2412yes—
426C22×D4C2418yes—
427C22×D4C2418yes—
428C22×D4C2418yes—
429C22×D4C2418yes—
430C22×D4C2418yes—
431C22×D4C2418yes—
432C22×D4C24116yes—
433C23×C4—24no—
434C23×C4—24no—
435C23×C4—24no—
436C23×C4—28no—
437C23×C4—84no—
438C23×C4—84no—
439C23×C4C2×D4116yes—
440C23×C4C2411yescharacteristic
441C23×C4C2414yes—
442C23×C4C2412yes—
443C23×C4C2412yes—
444C23×C4C2412yes—
445C23×C4C2411yescharacteristic
446C23×C4C2411yescharacteristic
447C23×C4C2418yes—
448C23×C4C2414yes—
449C23×C4C2414yes—
450C23×C4C24116yes—
451C23×C4C2411yescharacteristic
452C23×C4C2411yescharacteristic
453C23×C4C2412yes—
454C23×C4C2414yes—
455C23×C4C2414yes—
456C23×C4C2411yescharacteristic
457C4⋊Q8—24no—
458C4⋊Q8—24no—
459C4⋊Q8—24no—
460#127—216no—
461#127—216no—
462#127—216no—
463#127—24no—
464#127—48no—
465#126—232no—
466#125—216no—
467#125—216no—
468#125—28no—
469#124—216no—
470#124—232no—
471#124—28no—
472#124—48no—
473#123—232no—
474#123—232no—
475#123—232no—
476#123—232no—
477#123—232no—
478#123—232no—
479#123—48no—
480C22⋊Q8—28no—
481C22⋊Q8—216no—
482C22⋊Q8—28no—
483C22⋊Q8—48no—
484C22⋊Q8—88no—
485#121—216no—
486#121—216no—
487#121—216no—
488#121—216no—
489#121—232no—
490#121—232no—
491#121—28no—
492#121—216no—
493#121—28no—
494#121—216no—
495#121—216no—
496#121—232no—
497#121—232no—
498#121—232no—
499#121—48no—
500#121—416no—
501#121—816no—
502#121—88no—
503#121—816no—
504#121—816no—
505#121—816no—
506#120—232no—
507#120—48no—
508#120—416no—
509C4×Q8—216no—
510C4×Q8—28no—
511C4×Q8—28no—
512C4×D4—232no—
513C4×D4—232no—
514C4×D4—216no—
515C4×D4—28no—
516C4×D4—28no—
517C4×D4—28no—
518C4×D4—28no—
519C4×D4—28no—
520C4×D4—28no—
521C4×D4—416no—
522C4×D4—416no—
523C4×D4—416no—
524C4×D4C2×D4116yes—
525C4×D4C2×D4116yes—
526C4×D4C2×D4116yes—
527C4×D4C2×D4116yes—
528#117—28no—
529#117—216no—
530#117—28no—
531#117—28no—
532#117—216no—
533#117—28no—
534#117—28no—
535#117—28no—
536#117—28no—
537C2×C4⋊C4—24no—
538C2×C4⋊C4—24no—
539C2×C4⋊C4—24no—
540C2×C4⋊C4—28no—
541C2×C4⋊C4—28no—
542C2×C4⋊C4—216no—
543C2×C4⋊C4—88no—
544C2×C4⋊C4C2×D418yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C24116yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C24116yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2412yes—
575C2×C22⋊C4—28no—
576C2×C22⋊C4—24no—
577C2×C22⋊C4—24no—
578C2×C22⋊C4—28no—
579C2×C22⋊C4—28no—
580C2×C22⋊C4—416no—
581C2×C22⋊C4C2×D4116yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2412yes—
585C2×C22⋊C4C2412yes—
586C2×C22⋊C4C2412yes—
587C2×C22⋊C4C2412yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C24116yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C24116yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C24116yes—
607C2×C22⋊C4C24116yes—
608C2×C22⋊C4C24116yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C42—24no—
612C2×C42C2×D418yes—
613C2×C42C2418yes—
614C2×C42C2412yes—
615C2×C42C2412yes—
616C2×C42C2414yes—
617C2×C42C2414yes—
618C2×C42C2414yes—
619C2×C42C2411yescharacteristic
620C2×C42C2411yescharacteristic
621C2×C42C2411yescharacteristic
622C2×C42C2411yescharacteristic
623#95C2414yes—
624#95C2414yes—
625#95C24116yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630#95C2418yes—
631#95C2414yes—
632#95C2414yes—
633#95C2418yes—
634#95C24116yes—
635#95C24116yes—
636C24—24no—
637C24—24no—
638C24—24no—
639C24—22no—
640C24—22no—
641C24—24no—
642C24—22no—
643C24—24no—
644C24—44no—
645C24—44no—
646C24—44no—
647C24—42no—
648C24—44no—
649C24—42no—
650C24C22×D418yes—
651C24C2512yes—
652C24C2514yes—
653C24C2514yes—
654C24C2514yes—
655C24C2511yescharacteristic
656#41—432no—
657#41—832no—
658C2×Q8—24no—
659C2×Q8—24no—
660C2×Q8—24no—
661C2×Q8—24no—
662C2×Q8—24no—
663C2×Q8—44no—
664C2×Q8—44no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—216no—
669C2×D4—216no—
670C2×D4—216no—
671C2×D4—216no—
672C2×D4—216no—
673C2×D4—232no—
674C2×D4—24no—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—24no—
679C2×D4—216no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—24no—
683C2×D4—24no—
684C2×D4—24no—
685C2×D4—24no—
686C2×D4—24no—
687C2×D4—24no—
688C2×D4—24no—
689C2×D4—24no—
690C2×D4—44no—
691C2×D4—48no—
692C2×D4—44no—
693C2×D4—48no—
694C2×D4—48no—
695C2×D4—416no—
696C2×D4—416no—
697C2×D4—416no—
698C2×D4—416no—
699C2×D4—416no—
700C2×D4—416no—
701C2×D4—416no—
702C2×D4—416no—
703C2×D4—416no—
704C2×D4—416no—
705C2×D4—816no—
706C2×D4—816no—
707C2×D4—816no—
708C2×D4—816no—
709C2×D4C22×D418yes—
710C2×D4C22×D418yes—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—24no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—28no—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—24no—
721C22×C4—28no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—24no—
725C22×C4—28no—
726C22×C4—216no—
727C22×C4—28no—
728C22×C4—28no—
729C22×C4—48no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—48no—
735C22×C4—42no—
736C22×C4—42no—
737C22×C4—48no—
738C22×C4—416no—
739C22×C4—48no—
740C22×C4—416no—
741C22×C4—416no—
742C22×C4—416no—
743C22×C4—416no—
744C22×C4—816no—
745C22×C4—816no—
746C22×C4C22×D414yes—
747C22×C4C22×D414yes—
748C22×C4C22×D418yes—
749C22×C4C22×D4116yes—
750C22×C4C22×D4116yes—
751C22×C4C22×D414yes—
752C22×C4H(5,𝔽2)14yes—
753C22×C42−1+414yes—
754C22×C4C2518yes—
755C22×C4C2514yes—
756C22×C4C2512yes—
757C22×C4C2512yes—
758C22×C4C2518yes—
759C22×C4C2514yes—
760C22×C4C2512yes—
761C22×C4C2514yes—
762C22×C4C2514yes—
763C22×C4C2511yescharacteristic
764C22×C4C2511yescharacteristic
765C22×C4C2514yes—
766C22×C4C2511yescharacteristic
767C22×C4C2511yescharacteristic
768C22×C4C2511yescharacteristic
769C22×C4C2511yescharacteristic
770C4⋊C4—24no—
771C4⋊C4—24no—
772C4⋊C4—24no—
773C4⋊C4—24no—
774C4⋊C4—24no—
775C4⋊C4—24no—
776C4⋊C4—24no—
777C4⋊C4—216no—
778C4⋊C4—216no—
779C4⋊C4—216no—
780C4⋊C4—24no—
781C4⋊C4—24no—
782C4⋊C4—24no—
783C4⋊C4—28no—
784C4⋊C4—24no—
785C4⋊C4—28no—
786C4⋊C4—24no—
787C4⋊C4—28no—
788C4⋊C4—28no—
789C4⋊C4—44no—
790C4⋊C4—44no—
791C4⋊C4—416no—
792C4⋊C4—48no—
793C4⋊C4—44no—
794C4⋊C4—48no—
795C4⋊C4—48no—
796C4⋊C4—416no—
797C4⋊C4—44no—
798C4⋊C4C22×D418yes—
799C4⋊C4C22×D418yes—
800C22⋊C4—216no—
801C22⋊C4—28no—
802C22⋊C4—216no—
803C22⋊C4—216no—
804C22⋊C4—28no—
805C22⋊C4—28no—
806C22⋊C4—24no—
807C22⋊C4—24no—
808C22⋊C4—24no—
809C22⋊C4—24no—
810C22⋊C4—28no—
811C22⋊C4—28no—
812C22⋊C4—216no—
813C22⋊C4—216no—
814C22⋊C4—28no—
815C22⋊C4—28no—
816C22⋊C4—416no—
817C22⋊C4—48no—
818C22⋊C4—48no—
819C22⋊C4—416no—
820C22⋊C4—416no—
821C22⋊C4—48no—
822C22⋊C4—48no—
823C22⋊C4—48no—
824C22⋊C4—416no—
825C22⋊C4—48no—
826C22⋊C4—416no—
827C22⋊C4C22×D4116yes—
828C22⋊C4C22×D4116yes—
829C42—24no—
830C42—24no—
831C42—216no—
832C42—28no—
833C42—28no—
834C42—28no—
835C42C22×D414yes—
836C42C22×D414yes—
837C42C22×D414yes—
838C42C22×D414yes—
839C23—22no—
840C23—22no—
841C23—24no—
842C23—24no—
843C23—28no—
844C23—28no—
845C23—216no—
846C23—24no—
847C23—24no—
848C23—22no—
849C23—22no—
850C23—24no—
851C23—24no—
852C23—22no—
853C23—24no—
854C23—24no—
855C23—28no—
856C23—28no—
857C23—24no—
858C23—28no—
859C23—24no—
860C23—28no—
861C23—48no—
862C23—48no—
863C23—48no—
864C23—44no—
865C23—48no—
866C23—44no—
867C23—44no—
868C23—48no—
869C23—88no—
870C23—84no—
871C23—88no—
872C23—88no—
873C23—84no—
874C23—88no—
875C23C23×D418yes—
876C23C23×D412yes—
877C23C2×H(5,𝔽2)12yes—
878C23C2×2−1+412yes—
879C23C2611yescharacteristic
880Q8—48no—
881Q8—48no—
882Q8—84no—
883D4—216no—
884D4—216no—
885D4—48no—
886D4—416no—
887D4—48no—
888D4—48no—
889D4—48no—
890D4—84no—
891D4—816no—
892D4—816no—
893D4—816no—
894D4—816no—
895D4—816no—
896D4—816no—
897D4—816no—
898D4—1616no—
899C2×C4—22no—
900C2×C4—28no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—24no—
909C2×C4—22no—
910C2×C4—24no—
911C2×C4—28no—
912C2×C4—28no—
913C2×C4—24no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—24no—
917C2×C4—28no—
918C2×C4—28no—
919C2×C4—28no—
920C2×C4—28no—
921C2×C4—28no—
922C2×C4—28no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—28no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—416no—
929C2×C4—48no—
930C2×C4—416no—
931C2×C4—48no—
932C2×C4—44no—
933C2×C4—44no—
934C2×C4—44no—
935C2×C4—48no—
936C2×C4—48no—
937C2×C4—416no—
938C2×C4—88no—
939C2×C4—88no—
940C2×C4—816no—
941C2×C4—1616no—
942C2×C4#537116yes—
943C2×C4C23×D418yes—
944C2×C4C23×D412yes—
945C2×C4C23×D412yes—
946C2×C4C23×D412yes—
947C2×C4C23×D412yes—
948C2×C4C23×D412yes—
949C2×C4C23×D412yes—
950C2×C4C2×H(5,𝔽2)12yes—
951C2×C4C2×H(5,𝔽2)12yes—
952C2×C4C2×2−1+412yes—
953C2×C4C2×2−1+412yes—
954C22—22no—
955C22—22no—
956C22—24no—
957C22—24no—
958C22—28no—
959C22—28no—
960C22—28no—
961C22—48no—
962C22—48no—
963C22—44no—
964C22—42no—
965C22—44no—
966C22—44no—
967C22—42no—
968C22—44no—
969C22—44no—
970C22—48no—
971C22—48no—
972C22—48no—
973C22—44no—
974C22—48no—
975C22—42no—
976C22—44no—
977C22—44no—
978C22—816no—
979C22—816no—
980C22—88no—
981C22C2×#53714yes—
982C22C24×D411yescharacteristic
983C22C22×H(5,𝔽2)11yescharacteristic
984C22C22×2−1+411yescharacteristic
985C22H(7,𝔽2)12yes—
986C22H(7,𝔽2)12yes—
987C4—22no—
988C4—22no—
989C4—28no—
990C4—22no—
991C4—22no—
992C4—42no—
993C4—44no—
994C4—44no—
995C4—42no—
996C4—44no—
997C4—48no—
998C4—48no—
999C4—42no—
1000C4—44no—
1001C4C2×#53714yes—
1002C4C2×#53714yes—
1003C2—24no—
1004C2—48no—
1005C2—84no—
1006C2—84no—
1007C2—82no—
1008C2C22×#53711yescharacteristic
1009C2#6284211yescharacteristic
1010C2#6285211yescharacteristic
1011C2#6288012yes—
1012C2#6288112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3506C2semidirect
2. C22×#540C2semidirect
3. #42646C2semidirect
4. #42645C2semidirect
5. #42445C2semidirect
6. #42444C2semidirect
7. #42425C2semidirect
8. #42424C2semidirect
9. #37452C2semidirect
10. #37439C2semidirect
11. #36709C2semidirect
12. #36706C2semidirect
13. #35639C2semidirect
14. #35563C2semidirect
15. #35528C2semidirect
16. #35514C2semidirect
17. #35172C2semidirect
18. #35165C2semidirect
19. #34634C2semidirect
20. #34633C2semidirect
21. #34181C2semidirect
23. C2×#559C22semidirect
24. C2×#556C22semidirect
25. C2×#555C22semidirect
26. C2×#553C22semidirect
27. C2×#550C22semidirect
28. C2×#547C22semidirect
56. #2814C22semidirect
57. #2813C22semidirect
58. #2813C22semidirect
59. #2695C22semidirect
60. #2693C22semidirect
61. #2691C22semidirect
62. #2676C22semidirect
63. #2675C22semidirect
64. #2672C22semidirect
65. #2671C22semidirect
66. #2671C22semidirect
67. #2656C22semidirect
68. #2639C22semidirect
69. #2630C22semidirect
70. #2629C22semidirect
71. #2628C22semidirect
72. #2628C22semidirect
78. #2624C22semidirect
79. #2621C22semidirect
80. #2620C22semidirect
81. #2619C22semidirect
84. #2618C22semidirect
88. #2615C22semidirect
89. #2580C22semidirect
91. #2566C22semidirect
92. #2563C22semidirect
93. #2547C22semidirect
94. #2544C22semidirect
95. #2544C22semidirect
96. #2542C22semidirect
97. #2541C22semidirect
98. #2541C22semidirect
99. #2538C22semidirect
100. #2537C22semidirect
101. #2537C22semidirect
102. #2535C22semidirect
103. #2535C22semidirect
105. #2498C22semidirect
107. #2454C22semidirect
108. #2453C22semidirect
109. #2442C22semidirect
110. #2441C22semidirect
111. #2430C22semidirect
112. #2428C22semidirect
113. #2428C22semidirect
114. #2428C22semidirect
115. #2428C22semidirect
116. #2427C22semidirect
117. #2426C22semidirect
118. #2416C22semidirect
119. #2416C22semidirect
120. #2414C22semidirect
126. #2396C22semidirect
127. #2396C22semidirect
128. #2392C22semidirect
129. #2392C22semidirect
130. #2349C22semidirect
131. #2349C22semidirect
132. D4×C4⋊C4C22semidirect
133. D4×C4⋊C4C22semidirect
239. C2×C4×D4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35062
C22×#5402
#426462
#426452
#424452
#424442
#424252
#424242
#374522
#374392
#367092
#367062
#356392
#355632
#355282
#355142
#351722
#351652
#346342
#346332
#341812