Finite Group Databasebeta

← #7643522

Subgroups — #7643522

Order 512.

8294 conjugacy classes of subgroups.

The subgroup lattice has 1103 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3510C211yesmaximal, characteristic, complemented
2C2×#3500C211yesmaximal, characteristic, complemented
3#39954C218yesmaximal, complemented
4#39953C218yesmaximal, complemented
5#38420C2116yesmaximal, complemented
6#37391C214yesmaximal, complemented
7#37305C214yesmaximal, complemented
8#36639C211yesmaximal, characteristic, complemented
9C2×#2858C211yesmaximal, characteristic, complemented
10#35677C211yesmaximal, characteristic, complemented
11#35676C211yesmaximal, characteristic, complemented
12#35667C211yesmaximal, characteristic, complemented
13#35666C211yesmaximal, characteristic, complemented
14#35617C211yesmaximal, characteristic, complemented
15#35616C211yesmaximal, characteristic, complemented
16#35528C211yesmaximal, characteristic, complemented
17#35527C211yesmaximal, characteristic, complemented
18#35338C211yesmaximal, characteristic, complemented
19#35329C211yesmaximal, characteristic, complemented
20#35191C214yesmaximal, complemented
21#35131C214yesmaximal, complemented
22#34026C211yesmaximal, characteristic, complemented
23C22×2−1+4C2211yescharacteristic
24C22×H(5,𝔽2)C2211yescharacteristic
25#3510—216no—
26#3500—216no—
27C2×#559C2214yescomplemented
28C2×#556C2214yescomplemented
29C2×#551C2218yescomplemented
30C2×#548C2214yescomplemented
31C2×#546C2218yes—
32C2×#546C2214yescomplemented
33C2×#542C2214yescomplemented
34C2×#536C2211yescharacteristic
35C2×#536C2211yescharacteristic
36C2×#536C2211yescharacteristic
37C2×#536C2212yescomplemented
38C2×#536C2211yescharacteristic, complemented
39C2×#535C2211yescharacteristic
40C2×#535C2211yescharacteristic
41C2×#535C2211yescharacteristic
42C2×#535C2212yescomplemented
43C2×#535C2211yescharacteristic, complemented
44C2×#533C2211yescharacteristic, complemented
45C2×#532C2211yescharacteristic
46C2×#532C2212yescomplemented
47C22×C4⋊Q8C2211yescharacteristic, complemented
48C22×#127C2211yescharacteristic
49C2×#529C2214yescomplemented
50C22×#124C2211yescharacteristic
51C22×#124C2211yescharacteristic
52C22×#124C2211yescharacteristic, complemented
53C22×#124C2212yescomplemented
54C22×#124C2211yescharacteristic, complemented
55C2×#519C2211yescharacteristic, complemented
56C2×#518C2211yescharacteristic, complemented
57C2×C4×#41C2211yescharacteristic
58#2862C2212yescomplemented
59#2861C2214yescomplemented
60#2861C2212yescomplemented
61#2861C2212yescomplemented
62#2858C2212yescomplemented
63#2858C2212yescomplemented
64#2858C2214yescomplemented
65#2858C2218yescomplemented
66#2858C2214yescomplemented
67#2858C2212yescomplemented
68#2850C2218yescomplemented
69#2723C22116yescomplemented
70#2714C22116yescomplemented
71#2710C22116yescomplemented
72#2706C22116yescomplemented
73#2692C22116yescomplemented
74#2678C22116yescomplemented
75#2676C22116yescomplemented
76#2670C22116yescomplemented
77#2662C22116yescomplemented
78#2661C22116yescomplemented
79#2658C2212yescomplemented
80#2657C2212yescomplemented
81#2640C2214yescomplemented
82#2610C22116yescomplemented
83#2603C22116yescomplemented
84#2592C2218yescomplemented
85#2561C2218yescomplemented
86#2548C2214yescomplemented
87#2547C2214yescomplemented
88#2546C2214yescomplemented
89#2545C2214yescomplemented
90#2545C2214yescomplemented
91#2544C2214yescomplemented
92#2544C2214yescomplemented
93#2541C2214yescomplemented
94#2540C2218yescomplemented
95#2539C2218yescomplemented
96#2436C2214yescomplemented
97#2436C2214yescomplemented
98#2435C2214yescomplemented
99#2435C2214yescomplemented
100#2434C2214yescomplemented
101#2434C2214yescomplemented
102#2433C2214yes—
103#2433C2214yes—
104#2432C2214yescomplemented
105#2432C2214yescomplemented
106#2432C2214yescomplemented
107#2432C2214yescomplemented
108#2431C2214yes—
109#2431C2214yes—
110#2431C2214yescomplemented
111#2431C2214yescomplemented
112#2429C2218yescomplemented
113#2428C2218yescomplemented
114#2427C2218yescomplemented
115#2426C2218yescomplemented
116#2414C22116yescomplemented
117#2413C2218yescomplemented
118#2412C2218yescomplemented
119#2411C22116yescomplemented
120#2411C2218yescomplemented
121#2410C2218yescomplemented
122#2406C2218yescomplemented
123#2405C2218yes—
124#2404C2218yescomplemented
125#2403C2218yes—
126#2324C22116yescomplemented
127#2321C22116yescomplemented
128#2310C2211yescharacteristic, complemented
129#2310C2211yescharacteristic, complemented
130#2309C2211yescharacteristic
131#2309C2211yescharacteristic
132C4×#124C2218yescomplemented
133#2298C2214yescomplemented
134#2297C2211yescharacteristic
135#2297C2211yescharacteristic
136#2297C2211yescharacteristic
137#2297C2211yescharacteristic
138#2297C2211yescharacteristic, complemented
139#2297C2211yescharacteristic, complemented
140#2296C2211yescharacteristic, complemented
141#2296C2211yescharacteristic, complemented
142#2295C2214yescomplemented
143#2293C2214yescomplemented
144C2×#390C2218yescomplemented
145#2290C2218yescomplemented
146C4×#117C2211yescharacteristic, complemented
147C4×#117C2214yescomplemented
148C2×C43C2211yescharacteristic, complemented
149C2×2−1+4—28no—
150C2×2−1+4—44no—
151C2×2−1+4—44no—
152C2×H(5,𝔽2)—28no—
153C2×H(5,𝔽2)—44no—
154C2×H(5,𝔽2)—44no—
155C22×#41C2311yescharacteristic
156C22×#41C2311yescharacteristic
157C22×#41C2311yescharacteristic
158C22×#41C2312yes—
159C22×#41C2312yes—
160C22×#41C2314yes—
161C22×#41C2312yes—
162C22×#41C2312yes—
163C23×Q8C2311yescharacteristic
164C23×Q8C2311yescharacteristic
165C23×Q8C2312yes—
166C23×Q8C2312yes—
167C23×D4C2311yescharacteristic
168C23×D4C2311yescharacteristic
169C23×D4C2314yes—
170C23×D4C2312yes—
171C23×D4C2312yes—
172C23×D4C2314yes—
173#559—232no—
174#556—232no—
175#551—264no—
176#548—232no—
177#546—264no—
178#546—232no—
179#542—232no—
180#536—28no—
181#536—28no—
182#536—216no—
183#536—44no—
184#536—44no—
185#535—28no—
186#535—28no—
187#535—216no—
188#535—44no—
189#535—44no—
190#533—28no—
191#532—28no—
192#532—216no—
193C2×C4⋊Q8—44no—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2311yescharacteristic
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2314yes—
199C2×C4⋊Q8C2314yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2312yes—
202C2×#127—44no—
203C2×#127C2311yescharacteristic
204C2×#127C2312yes—
205C2×#127C2312yes—
206C2×#127C2314yes—
207C2×#127C2314yes—
208C2×#127C2312yes—
209C2×#127C2312yes—
210#529—232no—
211C2×#126C2318yes—
212C2×#126C2318yes—
213C2×#125C2312yes—
214C2×#124—28no—
215C2×#124—28no—
216C2×#124—216no—
217C2×#124—44no—
218C2×#124—44no—
219C2×#124C2314yes—
220C2×#124C2312yes—
221C2×#124C2312yes—
222C2×#124C2311yescharacteristic
223C2×#124C2311yescharacteristic
224C2×#124C2312yes—
225C2×#124C2312yes—
226C2×#124C2314yes—
227C2×#124C2318yes—
228C2×#124C2312yes—
229C2×#124C2312yes—
230C2×#124C2318yes—
231C2×#124C2312yes—
232C2×#124C2312yes—
233C2×#124C2318yes—
234C2×#124C2314yes—
235C2×#124C2314yes—
236C2×#124C2314yes—
237C2×#124C2314yes—
238C2×#124C2312yes—
239C2×#124C2312yes—
240C2×#124C2312yes—
241C2×#124C2312yes—
242C2×#123C2314yes—
243C2×#123C2318yes—
244C2×#123C2314yes—
245C2×#123C2318yes—
246C2×#123C2318yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2318yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2318yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×#121C2314yes—
257C2×#121C2318yes—
258C2×#121C2314yes—
259C2×#121C2318yes—
260C2×#121C2314yes—
261C2×#121C23116yes—
262C2×#121C2314yes—
263C2×#121C2314yes—
264C2×#120C2314yes—
265C2×#120C2314yes—
266C2×#120C2318yes—
267C2×#120C23116yes—
268C2×#120C2314yes—
269C2×#120C2314yes—
270#519—28no—
271#518—28no—
272C4×#41D4116yescomplemented
273C2×C4×Q8C2314yes—
274C2×C4×Q8C2314yes—
275C2×C4×Q8C2314yes—
276C2×C4×Q8C2312yes—
277C2×C4×D4C2318yes—
278C2×C4×D4C2318yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2312yes—
284C2×#117C2311yescharacteristic
285C2×#117C2311yescharacteristic
286C2×#117C2311yescharacteristic
287C2×#117C2311yescharacteristic
288C2×#117C2318yes—
289C2×#117C2314yes—
290C2×#117C2318yes—
291C2×#117C2311yescharacteristic
292C2×#117C2312yes—
293C22×C4⋊C4C2314yes—
294C22×C22⋊C4C2314yes—
295C22×C22⋊C4C2318yes—
296C22×C22⋊C4C2314yes—
297C22×C22⋊C4C2314yes—
298C22×C22⋊C4C2314yes—
299C22×C22⋊C4C2314yes—
300C22×C42C2311yescharacteristic
301C22×C42C2311yescharacteristic
302C22×C42C2314yes—
303C22×C42C2311yescharacteristic
304C22×C42C2312yes—
305#399C23116yes—
306#398C23116yes—
307#397C23116yes—
308#397C23116yes—
309#396C23116yes—
310#396C23116yes—
311#395C23116yes—
312#394C23116yes—
313#394C23116yes—
314#394C23116yes—
315#394C23116yes—
316#394C23116yes—
317#394C23116yes—
318#393C23116yes—
319#393C23116yes—
320#392C23116yes—
321#392C23116yes—
322#392C23116yes—
323#392C23116yes—
324#392C23116yes—
325#391C2314yes—
326#391C2314yes—
327#391C2314yes—
328#391C2314yes—
329#391C2318yes—
330#391C2312yes—
331#391C2312yes—
332#391C2312yes—
333#391C2312yes—
334#391C2312yes—
335#391C2312yes—
336#390C2314yes—
337#390C2314yes—
338#390C2314yes—
339#390C2314yes—
340#390C23116yes—
341#390C23116yes—
342#390C23116yes—
343#390C23116yes—
344#390C2318yes—
345#390C23116yes—
346#390C23116yes—
347#390C23116yes—
348#390C2312yes—
349#390C2312yes—
350#390C2312yes—
351#390C2312yes—
352#390C2312yes—
353#390C2312yes—
354#389C23116yes—
355#389C2314yes—
356#389C2314yes—
357#388C23116yes—
358#388C23116yes—
359#388C2318yes—
360#388C23116yes—
361#388C23116yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#387C2318yes—
368#387C2318yes—
369#386C23116yes—
370#386C23116yes—
371#386C23116yes—
372#386C23116yes—
373#386C23116yes—
374#386C2314yes—
375#386C2314yes—
376#386C2314yes—
377#386C2314yes—
378#386C2314yes—
379#386C2314yes—
380#385C23116yes—
381#385C23116yes—
382#385C23116yes—
383#385C2314yes—
384#385C2314yes—
385#382C2318yes—
386#381C2314yes—
387#381C2314yes—
388#380C23116yes—
389#379C2314yes—
390#379C2314yes—
391#379C23116yes—
392C4×C4⋊C4C2318yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2314yes—
395C4×C4⋊C4C2314yes—
396C4×C22⋊C4C2314yes—
397C4×C22⋊C4C2318yes—
398C4×C22⋊C4C2314yes—
399C4×C22⋊C4C2314yes—
400C4×C22⋊C4C2314yes—
401C4×C22⋊C4C2314yes—
402C4×C22⋊C4C2314yes—
403C4×C22⋊C4C2314yes—
404#376C2318yes—
405#376C2312yes—
406C43C2312yes—
407C43C2312yes—
408C43C2312yes—
409C43C2314yes—
410C25C2412yes—
411C25C2412yes—
412C25C2414yes—
4132−1+4—464no—
414H(5,𝔽2)—464no—
415C2×#41—28no—
416C2×#41—216no—
417C2×#41—28no—
418C2×#41—28no—
419C2×#41—24no—
420C2×#41—28no—
421C2×#41—24no—
422C2×#41—24no—
423C2×#41—24no—
424C2×#41—24no—
425C2×#41—24no—
426C2×#41—24no—
427C2×#41—24no—
428C2×#41—48no—
429C2×#41—48no—
430C2×#41—44no—
431C2×#41—44no—
432C2×#41—44no—
433C2×#41—44no—
434C2×#41—44no—
435C2×#41—44no—
436C2×#41—44no—
437C2×#41—44no—
438C2×#41C2×D418yes—
439C22×Q8—28no—
440C22×Q8—24no—
441C22×Q8—28no—
442C22×Q8—24no—
443C22×Q8—24no—
444C22×Q8—24no—
445C22×Q8—24no—
446C22×Q8—24no—
447C22×Q8—44no—
448C22×Q8—44no—
449C22×Q8—44no—
450C22×Q8—44no—
451C22×Q8C2412yes—
452C22×Q8C2412yes—
453C22×Q8C2412yes—
454C22×Q8C2412yes—
455C22×Q8C2411yescharacteristic
456C22×Q8C2411yescharacteristic
457C22×Q8C2411yescharacteristic
458C22×Q8C2414yes—
459C22×Q8C2414yes—
460C22×D4—216no—
461C22×D4—28no—
462C22×D4—24no—
463C22×D4—28no—
464C22×D4—24no—
465C22×D4—24no—
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—24no—
469C22×D4—44no—
470C22×D4—44no—
471C22×D4—44no—
472C22×D4—44no—
473C22×D4—416no—
474C22×D4—48no—
475C22×D4—48no—
476C22×D4—48no—
477C22×D4C2412yes—
478C22×D4C2412yes—
479C22×D4C2412yes—
480C22×D4C2412yes—
481C22×D4C2412yes—
482C22×D4C2412yes—
483C22×D4C2411yescharacteristic
484C22×D4C2411yescharacteristic
485C22×D4C2412yes—
486C22×D4C2411yescharacteristic
487C22×D4C2418yes—
488C22×D4C2418yes—
489C22×D4C2414yes—
490C22×D4C2414yes—
491C22×D4C24116yes—
492C22×D4C2414yes—
493C22×D4C2414yes—
494C22×D4C2418yes—
495C22×D4C2418yes—
496C23×C4C2412yes—
497C23×C4C2412yes—
498C23×C4C2412yes—
499C23×C4C2412yes—
500C23×C4C2412yes—
501C23×C4C2412yes—
502C23×C4C2412yes—
503C23×C4C2414yes—
504C23×C4C2418yes—
505C23×C4C2414yes—
506C23×C4C2414yes—
507C23×C4C2412yes—
508C23×C4C2414yes—
509C23×C4C2411yescharacteristic
510C4⋊Q8—28no—
511C4⋊Q8—24no—
512C4⋊Q8—28no—
513C4⋊Q8—28no—
514C4⋊Q8—48no—
515C4⋊Q8—48no—
516C4⋊Q8—44no—
517C4⋊Q8—44no—
518#127—28no—
519#127—24no—
520#127—28no—
521#127—48no—
522#127—48no—
523#127—44no—
524#127—44no—
525#126—232no—
526#126—232no—
527#125—28no—
528#124—28no—
529#124—28no—
530#124—232no—
531#124—28no—
532#124—24no—
533#124—28no—
534#124—28no—
535#124—28no—
536#124—28no—
537#124—28no—
538#124—216no—
539#124—232no—
540#124—216no—
541#124—24no—
542#124—416no—
543#124—48no—
544#124—48no—
545#124—48no—
546#124—48no—
547#124—44no—
548#124—44no—
549#124—44no—
550#124—44no—
551#123—216no—
552#123—232no—
553#123—216no—
554#123—232no—
555#123—232no—
556#123—48no—
557#123—48no—
558C22⋊Q8—216no—
559C22⋊Q8—216no—
560C22⋊Q8—216no—
561C22⋊Q8—232no—
562C22⋊Q8—232no—
563C22⋊Q8—48no—
564C22⋊Q8—48no—
565#121—216no—
566#121—216no—
567#121—232no—
568#121—216no—
569#121—232no—
570#121—432no—
571#121—48no—
572#121—48no—
573#120—216no—
574#120—216no—
575#120—232no—
576#120—432no—
577#120—48no—
578#120—48no—
579C4×Q8—216no—
580C4×Q8—216no—
581C4×Q8—216no—
582C4×Q8C2×D4116yescomplemented
583C4×D4—232no—
584C4×D4—216no—
585C4×D4—216no—
586C4×D4—216no—
587C4×D4—232no—
588C4×D4C2×D4132yes—
589C4×D4C2×D4116yescomplemented
590#117—24no—
591#117—24no—
592#117—24no—
593#117—24no—
594#117—216no—
595#117—232no—
596#117—416no—
597#117C2×D418yes—
598#117C2×D4116yescomplemented
599C2×C4⋊C4—48no—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C24116yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C22⋊C4—216no—
619C2×C22⋊C4—232no—
620C2×C22⋊C4—216no—
621C2×C22⋊C4—216no—
622C2×C22⋊C4—48no—
623C2×C22⋊C4—48no—
624C2×C22⋊C4C2412yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2412yes—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2412yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C24116yes—
643C2×C22⋊C4C24116yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C24116yes—
648C2×C22⋊C4C24116yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2414yes—
655C2×C42—24no—
656C2×C42—24no—
657C2×C42—48no—
658C2×C42C2×D418yes—
659C2×C42C2×D4116yescomplemented
660C2×C42C2418yes—
661C2×C42C2414yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2412yes—
665C2×C42C2412yes—
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2414yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2418yes—
672C2×C42C2414yes—
673C2×C42C2414yes—
674C2×C42C2414yes—
675C2×C42C2412yes—
676C2×C42C2411yescharacteristic
677C2×C42C2412yes—
678C2×C42C2411yescharacteristic
679#95C2418yes—
680#95C2418yes—
681#95C2418yes—
682#95C2418yes—
683#95C2418yes—
684#95C2418yes—
685#95C2418yes—
686#95C2418yes—
687#95C2418yes—
688#95C24116yes—
689#95C24116yes—
690C24—24no—
691C24—28no—
692C24—24no—
693C24—24no—
694C24—24no—
695C24—24no—
696C24—24no—
697C24—44no—
698C24—44no—
699C24—48no—
700C24—48no—
701C24—416no—
702C24C2512yes—
703C24C2514yes—
704C24C2514yes—
705C24C2512yes—
706C24C2512yes—
707C24C2511yescharacteristic
708#41—232no—
709#41—432no—
710#41—432no—
711#41—464no—
712#41—432no—
713#41—432no—
714#41—416no—
715#41—416no—
716C2×Q8—24no—
717C2×Q8—24no—
718C2×Q8—28no—
719C2×Q8—24no—
720C2×Q8—24no—
721C2×Q8—22no—
722C2×Q8—22no—
723C2×Q8—28no—
724C2×Q8—22no—
725C2×Q8—22no—
726C2×Q8—24no—
727C2×Q8—24no—
728C2×Q8—24no—
729C2×Q8—24no—
730C2×Q8—24no—
731C2×Q8—22no—
732C2×Q8—22no—
733C2×Q8—24no—
734C2×Q8—24no—
735C2×Q8—24no—
736C2×Q8—22no—
737C2×Q8—22no—
738C2×Q8—44no—
739C2×Q8—44no—
740C2×Q8—48no—
741C2×Q8—432no—
742C2×Q8—432no—
743C2×Q8—416no—
744C2×Q8—416no—
745C2×Q8C22×D414yes—
746C2×D4—24no—
747C2×D4—24no—
748C2×D4—28no—
749C2×D4—24no—
750C2×D4—28no—
751C2×D4—24no—
752C2×D4—24no—
753C2×D4—24no—
754C2×D4—24no—
755C2×D4—24no—
756C2×D4—216no—
757C2×D4—24no—
758C2×D4—24no—
759C2×D4—28no—
760C2×D4—24no—
761C2×D4—24no—
762C2×D4—22no—
763C2×D4—22no—
764C2×D4—216no—
765C2×D4—28no—
766C2×D4—22no—
767C2×D4—22no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—24no—
772C2×D4—24no—
773C2×D4—22no—
774C2×D4—22no—
775C2×D4—24no—
776C2×D4—24no—
777C2×D4—24no—
778C2×D4—22no—
779C2×D4—22no—
780C2×D4—232no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—432no—
788C2×D4—416no—
789C2×D4—416no—
790C2×D4—48no—
791C2×D4—416no—
792C2×D4—416no—
793C2×D4—48no—
794C2×D4—48no—
795C2×D4—416no—
796C2×D4—416no—
797C2×D4—464no—
798C2×D4—432no—
799C2×D4—416no—
800C2×D4—416no—
801C2×D4—832no—
802C2×D4C22×D418yes—
803C2×D4C22×D414yes—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—28no—
808C22×C4—24no—
809C22×C4—28no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—28no—
817C22×C4—24no—
818C22×C4—28no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—216no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—48no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—416no—
835C22×C4C22×D418yes—
836C22×C4C22×D418yes—
837C22×C4C22×D4116yes—
838C22×C4C22×D414yes—
839C22×C4H(5,𝔽2)14yes—
840C22×C4H(5,𝔽2)14yes—
841C22×C4C2514yes—
842C22×C4C2514yes—
843C22×C4C2514yes—
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2512yes—
847C22×C4C2514yes—
848C22×C4C2512yes—
849C22×C4C2514yes—
850C22×C4C2512yes—
851C22×C4C2512yes—
852C22×C4C2514yes—
853C22×C4C2512yes—
854C22×C4C2514yes—
855C22×C4C2511yescharacteristic
856C22×C4C2511yescharacteristic
857C4⋊C4—28no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—216no—
861C4⋊C4—216no—
862C4⋊C4—28no—
863C4⋊C4—216no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—216no—
869C4⋊C4—416no—
870C4⋊C4—48no—
871C4⋊C4—48no—
872C4⋊C4—48no—
873C4⋊C4C22×D418yes—
874C4⋊C4C22×D4116yes—
875C22⋊C4—24no—
876C22⋊C4—24no—
877C22⋊C4—216no—
878C22⋊C4—24no—
879C22⋊C4—24no—
880C22⋊C4—216no—
881C22⋊C4—28no—
882C22⋊C4—216no—
883C22⋊C4—216no—
884C22⋊C4—216no—
885C22⋊C4—216no—
886C22⋊C4—216no—
887C22⋊C4—216no—
888C22⋊C4—216no—
889C22⋊C4—28no—
890C22⋊C4—216no—
891C22⋊C4—216no—
892C22⋊C4—216no—
893C22⋊C4—416no—
894C22⋊C4—416no—
895C22⋊C4—48no—
896C22⋊C4—416no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—416no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4C22×D418yes—
905C22⋊C4C22×D4116yes—
906C42—216no—
907C42—24no—
908C42—24no—
909C42—24no—
910C42—24no—
911C42—24no—
912C42—24no—
913C42—24no—
914C42—24no—
915C42—28no—
916C42—28no—
917C42—44no—
918C42—44no—
919C42—48no—
920C42C22×D414yes—
921C42C22×D414yes—
922C42C22×D418yes—
923C42C22×D4116yes—
924C42C22×D418yes—
925C23—24no—
926C23—22no—
927C23—22no—
928C23—28no—
929C23—24no—
930C23—22no—
931C23—24no—
932C23—22no—
933C23—24no—
934C23—22no—
935C23—22no—
936C23—24no—
937C23—24no—
938C23—22no—
939C23—22no—
940C23—24no—
941C23—28no—
942C23—28no—
943C23—216no—
944C23—216no—
945C23—416no—
946C23—48no—
947C23—48no—
948C23—88no—
949C23—88no—
950C23—88no—
951C23—88no—
952C23—88no—
953C23—88no—
954C23—816no—
955C23—168no—
956C23—168no—
957C23C23×D414yes—
958C23C23×D412yes—
959C23C2×H(5,𝔽2)12yes—
960C23C2×H(5,𝔽2)12yes—
961C23C2611yescharacteristic
962Q8—28no—
963Q8—416no—
964Q8—48no—
965Q8—48no—
966Q8—48no—
967Q8—44no—
968Q8—48no—
969Q8—44no—
970Q8—88no—
971D4—216no—
972D4—28no—
973D4—416no—
974D4—416no—
975D4—416no—
976D4—48no—
977D4—48no—
978D4—48no—
979D4—48no—
980D4—48no—
981D4—44no—
982D4—48no—
983D4—44no—
984D4—816no—
985D4—88no—
986D4—832no—
987D4—816no—
988D4—168no—
989D4—168no—
990C2×C4—216no—
991C2×C4—24no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—28no—
998C2×C4—216no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—28no—
1019C2×C4—28no—
1020C2×C4—28no—
1021C2×C4—28no—
1022C2×C4—416no—
1023C2×C4—48no—
1024C2×C4—416no—
1025C2×C4—416no—
1026C2×C4—48no—
1027C2×C4—416no—
1028C2×C4—48no—
1029C2×C4—48no—
1030C2×C4—48no—
1031C2×C4—48no—
1032C2×C4—816no—
1033C2×C4#535116yes—
1034C2×C4C23×D418yes—
1035C2×C4C23×D414yes—
1036C2×C4C23×D414yes—
1037C2×C4C23×D414yes—
1038C2×C4C23×D412yes—
1039C2×C4C23×D412yes—
1040C2×C4C2×H(5,𝔽2)12yes—
1041C2×C4C2×H(5,𝔽2)12yes—
1042C2×C4C2×H(5,𝔽2)12yes—
1043C2×C4C2×H(5,𝔽2)12yes—
1044C2×C4#58518yes—
1045C22—24no—
1046C22—24no—
1047C22—24no—
1048C22—28no—
1049C22—24no—
1050C22—44no—
1051C22—44no—
1052C22—48no—
1053C22—44no—
1054C22—44no—
1055C22—48no—
1056C22—48no—
1057C22—48no—
1058C22—44no—
1059C22—44no—
1060C22—44no—
1061C22—48no—
1062C22—44no—
1063C22—48no—
1064C22—42no—
1065C22—44no—
1066C22—42no—
1067C22—44no—
1068C22—168no—
1069C22—168no—
1070C22—1616no—
1071C22C2×#53514yes—
1072C22C24×D411yescharacteristic
1073C22C22×H(5,𝔽2)11yescharacteristic
1074C22C22×H(5,𝔽2)11yescharacteristic
1075C22C2×#58514yes—
1076C4—24no—
1077C4—28no—
1078C4—24no—
1079C4—28no—
1080C4—24no—
1081C4—44no—
1082C4—44no—
1083C4—44no—
1084C4—44no—
1085C4—44no—
1086C4—42no—
1087C4—42no—
1088C4—44no—
1089C4—44no—
1090C4C2×#53514yes—
1091C4C2×#53514yes—
1092C2—24no—
1093C2—44no—
1094C2—82no—
1095C2—84no—
1096C2—84no—
1097C2—82no—
1098C2C22×#53511yescharacteristic
1099C2#6281212yes—
1100C2#6282412yes—
1101C2#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. C2×#3500C2semidirect
3. #39954C2semidirect
4. #39953C2semidirect
5. #38420C2semidirect
6. #37391C2semidirect
7. #37305C2semidirect
8. #36639C2semidirect
9. C2×#2858C2semidirect
10. #35677C2semidirect
11. #35676C2semidirect
12. #35667C2semidirect
13. #35666C2semidirect
14. #35617C2semidirect
15. #35616C2semidirect
16. #35528C2semidirect
17. #35527C2semidirect
18. #35338C2semidirect
19. #35329C2semidirect
20. #35191C2semidirect
21. #35131C2semidirect
22. #34026C2semidirect
27. C2×#559C22semidirect
28. C2×#556C22semidirect
29. C2×#551C22semidirect
30. C2×#548C22semidirect
32. C2×#546C22semidirect
33. C2×#542C22semidirect
37. C2×#536C22semidirect
38. C2×#536C22semidirect
42. C2×#535C22semidirect
43. C2×#535C22semidirect
44. C2×#533C22semidirect
46. C2×#532C22semidirect
47. C22×C4⋊Q8C22semidirect
49. C2×#529C22semidirect
52. C22×#124C22semidirect
53. C22×#124C22semidirect
54. C22×#124C22semidirect
55. C2×#519C22semidirect
56. C2×#518C22semidirect
58. #2862C22semidirect
59. #2861C22semidirect
60. #2861C22semidirect
61. #2861C22semidirect
62. #2858C22semidirect
63. #2858C22semidirect
64. #2858C22semidirect
65. #2858C22semidirect
66. #2858C22semidirect
67. #2858C22semidirect
68. #2850C22semidirect
69. #2723C22semidirect
70. #2714C22semidirect
71. #2710C22semidirect
72. #2706C22semidirect
73. #2692C22semidirect
74. #2678C22semidirect
75. #2676C22semidirect
76. #2670C22semidirect
77. #2662C22semidirect
78. #2661C22semidirect
79. #2658C22semidirect
80. #2657C22semidirect
81. #2640C22semidirect
82. #2610C22semidirect
83. #2603C22semidirect
84. #2592C22semidirect
85. #2561C22semidirect
86. #2548C22semidirect
87. #2547C22semidirect
88. #2546C22semidirect
89. #2545C22semidirect
90. #2545C22semidirect
91. #2544C22semidirect
92. #2544C22semidirect
93. #2541C22semidirect
94. #2540C22semidirect
95. #2539C22semidirect
96. #2436C22semidirect
97. #2436C22semidirect
98. #2435C22semidirect
99. #2435C22semidirect
100. #2434C22semidirect
101. #2434C22semidirect
104. #2432C22semidirect
105. #2432C22semidirect
106. #2432C22semidirect
107. #2432C22semidirect
110. #2431C22semidirect
111. #2431C22semidirect
112. #2429C22semidirect
113. #2428C22semidirect
114. #2427C22semidirect
115. #2426C22semidirect
116. #2414C22semidirect
117. #2413C22semidirect
118. #2412C22semidirect
119. #2411C22semidirect
120. #2411C22semidirect
121. #2410C22semidirect
122. #2406C22semidirect
124. #2404C22semidirect
126. #2324C22semidirect
127. #2321C22semidirect
128. #2310C22semidirect
129. #2310C22semidirect
132. C4×#124C22semidirect
133. #2298C22semidirect
138. #2297C22semidirect
139. #2297C22semidirect
140. #2296C22semidirect
141. #2296C22semidirect
142. #2295C22semidirect
143. #2293C22semidirect
144. C2×#390C22semidirect
145. #2290C22semidirect
146. C4×#117C22semidirect
147. C4×#117C22semidirect
148. C2×C43C22semidirect
272. C4×#41D4semidirect
582. C4×Q8C2×D4semidirect
589. C4×D4C2×D4semidirect
598. #117C2×D4semidirect
659. C2×C42C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35102
C2×#35002
#399542
#399532
#384202
#373912
#373052
#366392
C2×#28582
#356772
#356762
#356672
#356662
#356172
#356162
#355282
#355272
#353382
#353292
#351912
#351312
#340262