Finite Group Databasebeta

← #7672430

Subgroups — #7672430

Order 512.

8444 conjugacy classes of subgroups.

The subgroup lattice has 1005 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3510C211yesmaximal, characteristic, complemented
2C22×#532C211yesmaximal, characteristic, complemented
3#59146C218yesmaximal, complemented
4#59145C218yesmaximal, complemented
5#39460C218yesmaximal, complemented
6#37699C218yesmaximal, complemented
7#36625C211yesmaximal, characteristic, complemented
8#36159C218yesmaximal, complemented
9#36141C218yesmaximal, complemented
10#35674C211yesmaximal, characteristic, complemented
11#35667C211yesmaximal, characteristic, complemented
12#35554C211yesmaximal, characteristic, complemented
13#35528C211yesmaximal, characteristic, complemented
14#35338C211yesmaximal, characteristic, complemented
15#35327C211yesmaximal, characteristic, complemented
16#35149C211yesmaximal, characteristic, complemented
17#35149C211yesmaximal, characteristic, complemented
18#34211C211yesmaximal, characteristic, complemented
19#34174C211yesmaximal, characteristic, complemented
20#34172C211yesmaximal, characteristic, complemented
21C4×#525C211yesmaximal, characteristic, complemented
22C23×#41C2211yescharacteristic
23C23×#41C2211yescharacteristic
24#3510—216no—
25C2×#559C2214yescomplemented
26C2×#556C2214yescomplemented
27C2×#551C2218yes—
28C2×#542C2214yescomplemented
29C2×#536C2211yescharacteristic
30C2×#536C2211yescharacteristic
31C2×#535C2211yescharacteristic
32C2×#535C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C2×#532—216no—
35C2×#532C2218yes—
36C2×#532C2214yes—
37C2×#532C2214yes—
38C22×C4⋊Q8C2211yescharacteristic
39C22×#127C2211yescharacteristic
40C2×#529C2214yescomplemented
41C22×#124C2211yescharacteristic
42C22×#124C2211yescharacteristic
43C2×#525C2211yescharacteristic
44C22×#121C2214yes—
45C2×#519C2211yescharacteristic
46C2×#519C2211yescharacteristic
47C2×#518C2211yescharacteristic
48C2×#518C2211yescharacteristic
49C2×C4×#41C2211yescharacteristic
50C22×C4×D4C2214yes—
51C23×C42C2211yescharacteristic
52#2861C2214yescomplemented
53#2857C2214yescomplemented
54#2855C2214yes—
55#2851C2214yescomplemented
56#2850C2214yescomplemented
57#2849C2214yes—
58#2849C2214yes—
59#2848C2214yes—
60#2703C22116yescomplemented
61#2691C22116yescomplemented
62#2681C22116yescomplemented
63#2676C22116yescomplemented
64#2640C2214yescomplemented
65#2620C2214yescomplemented
66#2613C2214yes—
67#2613C2214yes—
68#2592C2218yescomplemented
69#2561C2218yes—
70#2559C22116yescomplemented
71#2546C2214yescomplemented
72#2545C2214yescomplemented
73#2545C2214yescomplemented
74#2544C2214yescomplemented
75#2544C2214yescomplemented
76#2541C2214yescomplemented
77#2534C2218yes—
78#2484C2218yes—
79#2476C22116yescomplemented
80#2468C22116yescomplemented
81#2466C22116yescomplemented
82#2464C22116yescomplemented
83#2459C22116yescomplemented
84#2457C22116yescomplemented
85#2456C22116yescomplemented
86#2450C22116yescomplemented
87#2446C2218yescomplemented
88#2446C2218yescomplemented
89#2445C2218yescomplemented
90#2445C2218yescomplemented
91#2432C2214yescomplemented
92#2432C2214yescomplemented
93#2431C2214yescomplemented
94#2431C2214yescomplemented
95#2429C2218yescomplemented
96#2428C2218yescomplemented
97#2425C22116yescomplemented
98#2413C2218yes—
99#2410C2218yes—
100#2407C2218yescomplemented
101#2407C2218yescomplemented
102#2405C2218yes—
103#2367C2218yescomplemented
104#2364C22116yescomplemented
105#2359C22116yescomplemented
106#2342C2218yes—
107#2341C2218yescomplemented
108#2341C2218yescomplemented
109#2339C2218yescomplemented
110#2339C2218yescomplemented
111#2326C2214yescomplemented
112#2310C2211yescharacteristic
113#2310C2211yescharacteristic
114#2310C2211yescharacteristic
115#2310C2211yescharacteristic
116#2309C2211yescharacteristic
117#2309C2211yescharacteristic
118#2309C2214yes—
119#2309C2211yescharacteristic
120#2309C2211yescharacteristic
121#2308C2214yes—
122C4×#124C2214yescomplemented
123C4×C22⋊Q8C2218yescomplemented
124C4×C22⋊Q8C2214yescomplemented
125C4×#123C2214yes—
126C4×#121C2214yescomplemented
127C4×#120C2214yes—
128#2297C2211yescharacteristic
129#2296C2211yescharacteristic
130#2296C2211yescharacteristic
131#2296C2211yescharacteristic
132#2290C2214yescomplemented
133#2285C2211yescharacteristic
134#2280C2211yescharacteristic
135#2280C2211yescharacteristic
136#2280C2214yes—
137#2280C2211yescharacteristic
138C2×#381C2214yes—
139C42×D4C2214yescomplemented
140C4×#117C2211yescharacteristic
141C22×#41—28no—
142C22×#41—28no—
143C22×#41—28no—
144C22×#41—28no—
145C22×#41—44no—
146C22×#41—44no—
147C22×#41C2311yescharacteristic
148C22×#41C2314yes—
149C22×#41C2314yes—
150C22×#41C2314yes—
151C22×#41C2314yes—
152C23×Q8C2311yescharacteristic
153C23×Q8C2311yescharacteristic
154C23×D4C2311yescharacteristic
155C23×D4C2312yes—
156C23×D4C2312yes—
157C23×D4C2311yescharacteristic
158C23×D4C2314yes—
159C24×C4C2312yes—
160C24×C4C2312yes—
161C24×C4C2311yescharacteristic
162C24×C4C2312yes—
163#559—232no—
164#556—232no—
165#551—264no—
166#542—232no—
167#536—28no—
168#536—44no—
169#535—28no—
170#535—44no—
171#533—28no—
172#532—232no—
173#532—232no—
174#532—264no—
175C2×C4⋊Q8—28no—
176C2×C4⋊Q8C2312yes—
177C2×C4⋊Q8C2314yes—
178C2×C4⋊Q8C2314yes—
179C2×C4⋊Q8C2312yes—
180C2×C4⋊Q8C2312yes—
181C2×#127—28no—
182C2×#127C2314yes—
183C2×#127C2314yes—
184C2×#127C2312yes—
185C2×#127C2312yes—
186#529—232no—
187C2×#126C2318yes—
188C2×#126C2318yes—
189C2×#125C2312yes—
190C2×#124—28no—
191C2×#124D4116yescomplemented
192C2×#124C2314yes—
193C2×#124C2312yes—
194C2×#124C2312yes—
195C2×#124C2318yes—
196C2×#124C2312yes—
197C2×#124C2312yes—
198C2×#124C2312yes—
199C2×#124C2312yes—
200C2×#124C2312yes—
201C2×#124C2314yes—
202C2×#124C2312yes—
203#525—28no—
204C2×#123C2312yes—
205C2×#123C2314yes—
206C2×#123C2318yes—
207C2×#123C2318yes—
208C2×#123C2314yes—
209C2×#123C23116yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2312yes—
213C2×C22⋊Q8C2318yes—
214C2×C22⋊Q8C2318yes—
215C2×C22⋊Q8C2314yes—
216C2×#121—232no—
217C2×#121C2314yes—
218C2×#121C23116yes—
219C2×#121C23116yes—
220C2×#121C2312yes—
221C2×#121C2314yes—
222C2×#121C23116yes—
223C2×#120C2314yes—
224C2×#120C2312yes—
225C2×#120C2314yes—
226#519—28no—
227#519—44no—
228#518—28no—
229#518—44no—
230C4×#41—28no—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2314yes—
237C2×C4×D4—232no—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C23116yes—
241C2×C4×D4C2318yes—
242C2×C4×D4C23116yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2318yes—
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2314yes—
256C2×#117C2311yescharacteristic
257C2×#117C2318yes—
258C2×#117C2312yes—
259C2×#117C2314yes—
260C22×C4⋊C4C2314yes—
261C22×C22⋊C4C2314yes—
262C22×C22⋊C4C2314yes—
263C22×C22⋊C4C2314yes—
264C22×C22⋊C4C2314yes—
265C22×C42—28no—
266C22×C42C2312yes—
267C22×C42C2312yes—
268C22×C42C2312yes—
269C22×C42C2312yes—
270C22×C42C2311yescharacteristic
271C22×C42C2314yes—
272C22×C42C2311yescharacteristic
273#400C23116yes—
274#398C23116yes—
275#398C23116yes—
276#397C23116yes—
277#396C23116yes—
278#396C23116yes—
279#394C23116yes—
280#394C23116yes—
281#394C23116yes—
282#394C23116yes—
283#394C23116yes—
284#394C23116yes—
285#393C23116yes—
286#392C23116yes—
287#392C23116yes—
288#392C23116yes—
289#391C2314yes—
290#391C2314yes—
291#391C2314yes—
292#391C2314yes—
293#391C2314yes—
294#391C2314yes—
295#391C2314yes—
296#391C2314yes—
297#391C2318yes—
298#391C2312yes—
299#390C2314yes—
300#390C2314yes—
301#390C2314yes—
302#390C2314yes—
303#390C2314yes—
304#390C23116yes—
305#390C23116yes—
306#390C2314yes—
307#390C2314yes—
308#390C2314yes—
309#390C2312yes—
310#389C2314yes—
311#389C2314yes—
312#389C2318yes—
313#389C23116yes—
314#389C2314yes—
315#388C23116yes—
316#388C23116yes—
317#388C23116yes—
318#388C23116yes—
319#388C23116yes—
320#388C23116yes—
321#388C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C23116yes—
325#387C23116yes—
326#387C2318yes—
327#386C23116yes—
328#386C23116yes—
329#386C23116yes—
330#386C23116yes—
331#386C23116yes—
332#386C23116yes—
333#386C23116yes—
334#386C2314yes—
335#386C2318yes—
336#385C23116yes—
337#385C2318yes—
338#385C2318yes—
339#385C2314yes—
340#385C2314yes—
341#385C23116yes—
342#385C23116yes—
343#385C2314yes—
344#385C2318yes—
345#384C2312yes—
346#382C2312yes—
347#381C2314yes—
348#381C2314yes—
349#381C2314yes—
350#381C2314yes—
351#381C2312yes—
352#381C2312yes—
353#381C23116yes—
354#381C2312yes—
355#380C2314yes—
356#380C2318yes—
357#380C2314yes—
358#380C2314yes—
359#380C2314yes—
360#380C23116yes—
361#379C2314yes—
362#379C2314yes—
363#379C2312yes—
364#379C2312yes—
365#379C2312yes—
366#379C2314yes—
367#379C2314yes—
368C4×C4⋊C4C2314yes—
369C4×C4⋊C4C2318yes—
370C4×C4⋊C4C2314yes—
371C4×C4⋊C4C2314yes—
372C4×C4⋊C4C2314yes—
373C4×C4⋊C4C2314yes—
374C4×C22⋊C4C2314yes—
375C4×C22⋊C4C2314yes—
376C4×C22⋊C4C2314yes—
377C4×C22⋊C4C23116yes—
378C4×C22⋊C4C2314yes—
379C4×C22⋊C4C23116yes—
380C4×C22⋊C4C2318yes—
381C4×C22⋊C4C2314yes—
382C4×C22⋊C4C2318yes—
383#376C2312yes—
384C2×#95C23116yes—
385C43C2312yes—
386C25C2412yes—
387C25C2412yes—
388C25C2411yescharacteristic
389C2×#41—216no—
390C2×#41—216no—
391C2×#41—216no—
392C2×#41—216no—
393C2×#41—24no—
394C2×#41—24no—
395C2×#41—216no—
396C2×#41—216no—
397C2×#41—216no—
398C2×#41—216no—
399C2×#41—24no—
400C2×#41—48no—
401C2×#41—48no—
402C2×#41—48no—
403C2×#41—48no—
404C2×#41—464no—
405C2×#41—464no—
406C22×Q8—24no—
407C22×Q8—24no—
408C22×Q8—24no—
409C22×Q8—24no—
410C22×Q8—24no—
411C22×Q8C2×D418yes—
412C22×Q8C2411yescharacteristic
413C22×Q8C2412yes—
414C22×Q8C2412yes—
415C22×Q8C2412yes—
416C22×Q8C2412yes—
417C22×Q8C2414yes—
418C22×D4—216no—
419C22×D4—28no—
420C22×D4—28no—
421C22×D4—28no—
422C22×D4—28no—
423C22×D4—24no—
424C22×D4—24no—
425C22×D4—24no—
426C22×D4—24no—
427C22×D4—24no—
428C22×D4—416no—
429C22×D4—44no—
430C22×D4—44no—
431C22×D4C2×D418yes—
432C22×D4C2412yes—
433C22×D4C2411yescharacteristic
434C22×D4C2412yes—
435C22×D4C2412yes—
436C22×D4C24116yes—
437C22×D4C2418yes—
438C22×D4C2418yes—
439C22×D4C2412yes—
440C22×D4C2412yes—
441C22×D4C2414yes—
442C22×D4C2418yes—
443C22×D4C2418yes—
444C23×C4—24no—
445C23×C4—24no—
446C23×C4—28no—
447C23×C4—28no—
448C23×C4—28no—
449C23×C4—28no—
450C23×C4—28no—
451C23×C4—48no—
452C23×C4—44no—
453C23×C4—44no—
454C23×C4#4118yes—
455C23×C4C2412yes—
456C23×C4C2412yes—
457C23×C4C2412yes—
458C23×C4C2418yes—
459C23×C4C2418yes—
460C23×C4C2414yes—
461C23×C4C2414yes—
462C23×C4C2412yes—
463C23×C4C2412yes—
464C23×C4C2412yes—
465C23×C4C2411yescharacteristic
466C23×C4C2418yes—
467C23×C4C2414yes—
468C23×C4C2418yes—
469C23×C4C2412yes—
470C23×C4C2411yescharacteristic
471C4⋊Q8—216no—
472C4⋊Q8—216no—
473C4⋊Q8—28no—
474C4⋊Q8—28no—
475C4⋊Q8—44no—
476#127—216no—
477#127—216no—
478#127—28no—
479#127—44no—
480#126—232no—
481#126—232no—
482#125—28no—
483#124—28no—
484#124—28no—
485#124—232no—
486#124—28no—
487#124—28no—
488#124—216no—
489#124—44no—
490#124—44no—
491#124C2×D4116yes—
492#124C2×D4116yes—
493#124C2×D4132yes—
494#123—216no—
495#123—28no—
496#123—232no—
497#123—232no—
498#123—48no—
499#123—432no—
500C22⋊Q8—216no—
501C22⋊Q8—216no—
502C22⋊Q8—28no—
503C22⋊Q8—232no—
504C22⋊Q8—416no—
505C22⋊Q8—48no—
506#121—216no—
507#121—28no—
508#121—264no—
509#121—264no—
510#121—432no—
511#121—48no—
512#120—216no—
513#120—28no—
514#120—48no—
515C4×Q8—216no—
516C4×Q8—216no—
517C4×Q8—28no—
518C4×Q8—216no—
519C4×Q8—48no—
520C4×Q8—48no—
521C4×D4—216no—
522C4×D4—216no—
523C4×D4—216no—
524C4×D4—216no—
525C4×D4—264no—
526C4×D4—264no—
527C4×D4—232no—
528C4×D4—28no—
529C4×D4—48no—
530C4×D4—48no—
531C4×D4—416no—
532#117—24no—
533#117—24no—
534#117—24no—
535#117—216no—
536#117—24no—
537#117—24no—
538#117—24no—
539#117—24no—
540#117—232no—
541#117—28no—
542#117—48no—
543C2×C4⋊C4—216no—
544C2×C4⋊C4C24116yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2418yes—
565C2×C22⋊C4—216no—
566C2×C22⋊C4—216no—
567C2×C22⋊C4—48no—
568C2×C22⋊C4C2×D4132yes—
569C2×C22⋊C4C2412yes—
570C2×C22⋊C4C2412yes—
571C2×C22⋊C4C2412yes—
572C2×C22⋊C4C2412yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2412yes—
577C2×C22⋊C4C2412yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2412yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C24116yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C24116yes—
593C2×C22⋊C4C24116yes—
594C2×C22⋊C4C24116yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C42—28no—
598C2×C42—24no—
599C2×C42—28no—
600C2×C42—28no—
601C2×C42—28no—
602C2×C42—216no—
603C2×C42C2×D418yes—
604C2×C42C2412yes—
605C2×C42C2418yes—
606C2×C42C2414yes—
607C2×C42C2412yes—
608C2×C42C2412yes—
609C2×C42C2412yes—
610C2×C42C2412yes—
611C2×C42C2412yes—
612C2×C42C2412yes—
613C2×C42C2414yes—
614C2×C42C2414yes—
615C2×C42C2412yes—
616C2×C42C2412yes—
617C2×C42C2418yes—
618C2×C42C2418yes—
619C2×C42C2411yescharacteristic
620C2×C42C2412yes—
621C2×C42C2411yescharacteristic
622#95C2418yes—
623#95C2418yes—
624#95C24116yes—
625#95C24116yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630#95C2418yes—
631#95C24116yes—
632#95C2418yes—
633#95C2418yes—
634#95C24116yes—
635C24—22no—
636C24—22no—
637C24—24no—
638C24—24no—
639C24—24no—
640C24—24no—
641C24—24no—
642C24—44no—
643C24—48no—
644C24—48no—
645C24C22×D418yes—
646C24C2×#4114yes—
647C24C2514yes—
648C24C2512yes—
649C24C2514yes—
650C24C2512yes—
651C24C2511yescharacteristic
652#41—464no—
653#41—464no—
654#41—464no—
655#41—464no—
656#41—416no—
657C2×Q8—232no—
658C2×Q8—22no—
659C2×Q8—24no—
660C2×Q8—24no—
661C2×Q8—28no—
662C2×Q8—24no—
663C2×Q8—24no—
664C2×Q8—22no—
665C2×Q8—24no—
666C2×Q8—24no—
667C2×Q8—24no—
668C2×Q8—24no—
669C2×Q8—24no—
670C2×Q8—22no—
671C2×Q8—24no—
672C2×Q8—48no—
673C2×Q8—416no—
674C2×Q8C22×D418yes—
675C2×Q8C22×D418yes—
676C2×D4—24no—
677C2×D4—232no—
678C2×D4—216no—
679C2×D4—28no—
680C2×D4—24no—
681C2×D4—216no—
682C2×D4—216no—
683C2×D4—24no—
684C2×D4—216no—
685C2×D4—232no—
686C2×D4—22no—
687C2×D4—216no—
688C2×D4—24no—
689C2×D4—24no—
690C2×D4—24no—
691C2×D4—24no—
692C2×D4—22no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—22no—
699C2×D4—24no—
700C2×D4—232no—
701C2×D4—48no—
702C2×D4—416no—
703C2×D4—48no—
704C2×D4—48no—
705C2×D4—432no—
706C2×D4—464no—
707C2×D4—416no—
708C2×D4—48no—
709C2×D4—416no—
710C2×D4—432no—
711C2×D4—416no—
712C2×D4C22×D418yes—
713C2×D4C22×D418yes—
714C22×C4—24no—
715C22×C4—22no—
716C22×C4—24no—
717C22×C4—24no—
718C22×C4—22no—
719C22×C4—232no—
720C22×C4—24no—
721C22×C4—24no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—28no—
725C22×C4—24no—
726C22×C4—216no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—216no—
730C22×C4—28no—
731C22×C4—28no—
732C22×C4—24no—
733C22×C4—216no—
734C22×C4—24no—
735C22×C4—216no—
736C22×C4—216no—
737C22×C4—24no—
738C22×C4—28no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—48no—
745C22×C4—48no—
746C22×C4—432no—
747C22×C4—48no—
748C22×C4—416no—
749C22×C4—48no—
750C22×C4—416no—
751C22×C4—432no—
752C22×C4—432no—
753C22×C4C22×D418yes—
754C22×C4C22×D418yes—
755C22×C4C22×D414yes—
756C22×C4C2×#4118yes—
757C22×C4C2×#4118yes—
758C22×C4C2×#4114yes—
759C22×C4C2×#4114yes—
760C22×C4H(5,𝔽2)14yes—
761C22×C4C2514yes—
762C22×C4C2514yes—
763C22×C4C2514yes—
764C22×C4C2514yes—
765C22×C4C2514yes—
766C22×C4C2514yes—
767C22×C4C2514yes—
768C22×C4C2514yes—
769C22×C4C2512yes—
770C22×C4C2512yes—
771C22×C4C2512yes—
772C22×C4C2514yes—
773C22×C4C2512yes—
774C22×C4C2514yes—
775C22×C4C2511yescharacteristic
776C22×C4C2511yescharacteristic
777C4⋊C4—232no—
778C4⋊C4—28no—
779C4⋊C4—24no—
780C4⋊C4—24no—
781C4⋊C4—28no—
782C4⋊C4—24no—
783C4⋊C4—216no—
784C4⋊C4—216no—
785C4⋊C4—28no—
786C4⋊C4—28no—
787C4⋊C4—24no—
788C4⋊C4—28no—
789C4⋊C4—24no—
790C4⋊C4—24no—
791C4⋊C4—24no—
792C4⋊C4—216no—
793C4⋊C4—216no—
794C4⋊C4—216no—
795C4⋊C4—48no—
796C4⋊C4—48no—
797C4⋊C4—48no—
798C22⋊C4—24no—
799C22⋊C4—24no—
800C22⋊C4—216no—
801C22⋊C4—24no—
802C22⋊C4—216no—
803C22⋊C4—24no—
804C22⋊C4—28no—
805C22⋊C4—24no—
806C22⋊C4—24no—
807C22⋊C4—24no—
808C22⋊C4—216no—
809C22⋊C4—216no—
810C22⋊C4—28no—
811C22⋊C4—216no—
812C22⋊C4—28no—
813C22⋊C4—216no—
814C22⋊C4—48no—
815C22⋊C4—48no—
816C22⋊C4—48no—
817C22⋊C4—416no—
818C22⋊C4—48no—
819C22⋊C4—48no—
820C22⋊C4—48no—
821C22⋊C4—416no—
822C22⋊C4—416no—
823C22⋊C4—416no—
824C22⋊C4C22×D4132yes—
825C22⋊C4C22×D4132yes—
826C42—28no—
827C42—28no—
828C42—24no—
829C42—24no—
830C42—24no—
831C42—28no—
832C42—216no—
833C42—24no—
834C42—24no—
835C42—24no—
836C42—24no—
837C42—24no—
838C42—24no—
839C42—48no—
840C42—48no—
841C42C22×D414yes—
842C42C22×D414yes—
843C42C22×D418yes—
844C23—24no—
845C23—22no—
846C23—24no—
847C23—24no—
848C23—22no—
849C23—24no—
850C23—24no—
851C23—216no—
852C23—28no—
853C23—216no—
854C23—22no—
855C23—24no—
856C23—22no—
857C23—24no—
858C23—22no—
859C23—24no—
860C23—28no—
861C23—216no—
862C23—48no—
863C23—416no—
864C23—48no—
865C23—48no—
866C23—416no—
867C23—48no—
868C23—88no—
869C23—88no—
870C23—88no—
871C23—88no—
872C23C23×D418yes—
873C23C23×D412yes—
874C23C22×#4114yes—
875C23C22×#4112yes—
876C23C2×H(5,𝔽2)12yes—
877C23C2611yescharacteristic
878Q8—216no—
879Q8—216no—
880Q8—48no—
881Q8—48no—
882Q8—44no—
883Q8—88no—
884D4—216no—
885D4—216no—
886D4—464no—
887D4—432no—
888D4—432no—
889D4—416no—
890D4—48no—
891D4—48no—
892D4—48no—
893D4—44no—
894D4—816no—
895D4—168no—
896C2×C4—216no—
897C2×C4—24no—
898C2×C4—22no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—28no—
906C2×C4—216no—
907C2×C4—216no—
908C2×C4—216no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—22no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—22no—
921C2×C4—24no—
922C2×C4—28no—
923C2×C4—28no—
924C2×C4—28no—
925C2×C4—28no—
926C2×C4—28no—
927C2×C4—28no—
928C2×C4—28no—
929C2×C4—48no—
930C2×C4—416no—
931C2×C4—416no—
932C2×C4—432no—
933C2×C4—432no—
934C2×C4—48no—
935C2×C4—48no—
936C2×C4—88no—
937C2×C4—816no—
938C2×C4—168no—
939C2×C4#546116yes—
940C2×C4C23×D414yes—
941C2×C4C23×D414yes—
942C2×C4C23×D418yes—
943C2×C4C23×D412yes—
944C2×C4C23×D412yes—
945C2×C4C22×#4114yes—
946C2×C4C22×#4112yes—
947C2×C4C22×#4112yes—
948C2×C4C2×H(5,𝔽2)12yes—
949C2×C4C2×H(5,𝔽2)12yes—
950C2×C4#58518yes—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—216no—
955C22—24no—
956C22—24no—
957C22—24no—
958C22—28no—
959C22—416no—
960C22—44no—
961C22—48no—
962C22—48no—
963C22—44no—
964C22—44no—
965C22—48no—
966C22—44no—
967C22—48no—
968C22—44no—
969C22—48no—
970C22—44no—
971C22—42no—
972C22—816no—
973C22—816no—
974C22C2×#54614yes—
975C22C24×D411yescharacteristic
976C22C23×#4111yescharacteristic
977C22C22×H(5,𝔽2)11yescharacteristic
978C22C2×#58514yes—
979C4—28no—
980C4—24no—
981C4—24no—
982C4—24no—
983C4—28no—
984C4—44no—
985C4—44no—
986C4—44no—
987C4—44no—
988C4—44no—
989C4—44no—
990C4—44no—
991C4—44no—
992C4—42no—
993C4C2×#54614yes—
994C4C2×#54614yes—
995C2—24no—
996C2—44no—
997C2—48no—
998C2—82no—
999C2—84no—
1000C2C22×#54611yescharacteristic
1001C2#6281112yes—
1002C2#6281512yes—
1003C2#6283612yes—
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×#3510C2semidirect
2. C22×#532C2semidirect
3. #59146C2semidirect
4. #59145C2semidirect
5. #39460C2semidirect
6. #37699C2semidirect
7. #36625C2semidirect
8. #36159C2semidirect
9. #36141C2semidirect
10. #35674C2semidirect
11. #35667C2semidirect
12. #35554C2semidirect
13. #35528C2semidirect
14. #35338C2semidirect
15. #35327C2semidirect
16. #35149C2semidirect
17. #35149C2semidirect
18. #34211C2semidirect
19. #34174C2semidirect
20. #34172C2semidirect
21. C4×#525C2semidirect
25. C2×#559C22semidirect
26. C2×#556C22semidirect
28. C2×#542C22semidirect
40. C2×#529C22semidirect
52. #2861C22semidirect
53. #2857C22semidirect
55. #2851C22semidirect
56. #2850C22semidirect
60. #2703C22semidirect
61. #2691C22semidirect
62. #2681C22semidirect
63. #2676C22semidirect
64. #2640C22semidirect
65. #2620C22semidirect
68. #2592C22semidirect
70. #2559C22semidirect
71. #2546C22semidirect
72. #2545C22semidirect
73. #2545C22semidirect
74. #2544C22semidirect
75. #2544C22semidirect
76. #2541C22semidirect
79. #2476C22semidirect
80. #2468C22semidirect
81. #2466C22semidirect
82. #2464C22semidirect
83. #2459C22semidirect
84. #2457C22semidirect
85. #2456C22semidirect
86. #2450C22semidirect
87. #2446C22semidirect
88. #2446C22semidirect
89. #2445C22semidirect
90. #2445C22semidirect
91. #2432C22semidirect
92. #2432C22semidirect
93. #2431C22semidirect
94. #2431C22semidirect
95. #2429C22semidirect
96. #2428C22semidirect
97. #2425C22semidirect
100. #2407C22semidirect
101. #2407C22semidirect
103. #2367C22semidirect
104. #2364C22semidirect
105. #2359C22semidirect
107. #2341C22semidirect
108. #2341C22semidirect
109. #2339C22semidirect
110. #2339C22semidirect
111. #2326C22semidirect
122. C4×#124C22semidirect
123. C4×C22⋊Q8C22semidirect
124. C4×C22⋊Q8C22semidirect
126. C4×#121C22semidirect
132. #2290C22semidirect
139. C42×D4C22semidirect
191. C2×#124D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35102
C22×#5322
#591462
#591452
#394602
#376992
#366252
#361592
#361412
#356742
#356672
#355542
#355282
#353382
#353272
#351492
#342112
#341742
#341722
C4×#5252