Finite Group Databasebeta

← #7672441

Subgroups — #7672441

Order 512.

11358 conjugacy classes of subgroups.

The subgroup lattice has 1268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3500C211yesmaximal, characteristic, complemented
2C2×#3487C211yesmaximal, characteristic, complemented
3C2×#3485C211yesmaximal, characteristic, complemented
4C22×#532C211yesmaximal, characteristic, complemented
5#59129C218yesmaximal, complemented
6#59128C218yesmaximal, complemented
7#39332C218yesmaximal, complemented
8#37681C214yesmaximal, complemented
9#37680C214yesmaximal, complemented
10#36624C211yesmaximal, characteristic, complemented
11#36125C214yesmaximal, complemented
12#36124C214yesmaximal, complemented
13#36099C218yesmaximal, complemented
14#35667C211yesmaximal, characteristic, complemented
15#35666C211yesmaximal, characteristic, complemented
16#35528C211yesmaximal, characteristic, complemented
17#35527C211yesmaximal, characteristic, complemented
18#35329C211yesmaximal, characteristic, complemented
19#35327C211yesmaximal, characteristic, complemented
20#35149C211yesmaximal, characteristic, complemented
21#35149C211yesmaximal, characteristic, complemented
22#34211C211yesmaximal, characteristic, complemented
23C4×#525C211yesmaximal, characteristic, complemented
24C22×2−1+4C2211yescharacteristic
25C22×H(5,𝔽2)C2211yescharacteristic
26C23×#41C2211yescharacteristic
27C23×#41C2211yescharacteristic, complemented
28#3500—216no—
29#3487—216no—
30#3485—216no—
31C2×#550C2214yescomplemented
32C2×#550C2214yescomplemented
33C2×#548C2214yescomplemented
34C2×#548C2214yescomplemented
35C2×#548C2214yescomplemented
36C2×#547C2214yescomplemented
37C2×#547C2214yescomplemented
38C2×#546C2218yes—
39C2×#546C2214yescomplemented
40C2×#546C2214yescomplemented
41C2×#546C2214yescomplemented
42C2×#536C2211yescharacteristic
43C2×#536C2211yescharacteristic
44C2×#536C2211yescharacteristic
45C2×#536C2212yescomplemented
46C2×#536C2211yescharacteristic, complemented
47C2×#535C2211yescharacteristic
48C2×#535C2211yescharacteristic
49C2×#535C2211yescharacteristic
50C2×#535C2211yescharacteristic, complemented
51C2×#535C2212yescomplemented
52C2×#535C2214yescomplemented
53C2×#534C2214yes—
54C2×#532—216no—
55C2×#532C2211yescharacteristic
56C2×#532C2214yescomplemented
57C2×#532C2212yescomplemented
58C2×#532C2214yescomplemented
59C2×#532C2218yescomplemented
60C22×C4⋊Q8C2211yescharacteristic, complemented
61C22×#127C2211yescharacteristic
62C22×#124C2211yescharacteristic
63C22×#124C2211yescharacteristic, complemented
64C22×#124C2212yescomplemented
65C2×#525C2211yescharacteristic
66C2×#525C2211yescharacteristic
67C2×#525C2214yescomplemented
68C2×#525C2211yescharacteristic, complemented
69C22×#123C2214yes—
70C22×#121C2214yescomplemented
71C2×#519C2211yescharacteristic, complemented
72C2×#518C2211yescharacteristic
73C2×C4×#41C2211yescharacteristic
74C22×C4×D4C2214yescomplemented
75C23×C42C2211yescharacteristic, complemented
76#2858C2212yescomplemented
77#2858C2212yescomplemented
78#2857C2212yescomplemented
79#2856C2212yescomplemented
80#2854C2214yescomplemented
81#2850C2212yescomplemented
82#2850C2212yescomplemented
83#2850C2214yescomplemented
84#2849C2214yescomplemented
85#2849C2214yescomplemented
86#2847C2214yescomplemented
87#2675C22116yescomplemented
88#2672C22116yescomplemented
89#2671C22116yescomplemented
90#2669C22116yescomplemented
91#2658C2212yescomplemented
92#2657C2212yescomplemented
93#2620C2214yescomplemented
94#2613C2214yescomplemented
95#2613C2214yescomplemented
96#2555C22116yescomplemented
97#2546C2214yescomplemented
98#2545C2214yescomplemented
99#2545C2214yescomplemented
100#2544C2214yescomplemented
101#2544C2214yescomplemented
102#2541C2214yescomplemented
103#2540C2218yescomplemented
104#2539C2218yescomplemented
105#2534C2218yescomplemented
106#2464C22116yescomplemented
107#2464C22116yescomplemented
108#2461C22116yescomplemented
109#2456C22116yescomplemented
110#2455C22116yescomplemented
111#2449C22116yescomplemented
112#2434C2214yescomplemented
113#2434C2214yescomplemented
114#2433C2214yescomplemented
115#2433C2214yescomplemented
116#2432C2214yescomplemented
117#2432C2214yescomplemented
118#2432C2214yescomplemented
119#2432C2214yescomplemented
120#2431C2214yescomplemented
121#2431C2214yescomplemented
122#2431C2214yescomplemented
123#2431C2214yescomplemented
124#2429C2218yescomplemented
125#2428C22116yescomplemented
126#2428C2218yescomplemented
127#2424C22116yescomplemented
128#2424C22116yescomplemented
129#2413C2218yescomplemented
130#2410C2218yescomplemented
131#2407C2218yescomplemented
132#2407C2218yescomplemented
133#2406C2218yescomplemented
134#2403C2218yes—
135#2367C2218yescomplemented
136#2361C22116yescomplemented
137#2358C22116yescomplemented
138#2342C2218yescomplemented
139#2326C2214yescomplemented
140#2310C2211yescharacteristic, complemented
141#2310C2211yescharacteristic, complemented
142#2309C2211yescharacteristic
143#2309C2211yescharacteristic, complemented
144C4×#124C2214yescomplemented
145C4×C22⋊Q8C2214yescomplemented
146C4×#123C2214yescomplemented
147C4×#121C2218yescomplemented
148C4×#121C2214yescomplemented
149C4×#120C2214yescomplemented
150#2297C2211yescharacteristic
151#2297C2211yescharacteristic
152#2297C2211yescharacteristic, complemented
153#2296C2211yescharacteristic, complemented
154#2290C2214yescomplemented
155#2285C2211yescharacteristic, complemented
156#2280C2211yescharacteristic, complemented
157C42×D4C2214yescomplemented
158C4×#117C2211yescharacteristic, complemented
159C2×2−1+4—28no—
160C2×2−1+4—28no—
161C2×2−1+4—44no—
162C2×H(5,𝔽2)—28no—
163C2×H(5,𝔽2)—28no—
164C2×H(5,𝔽2)—44no—
165C22×#41—28no—
166C22×#41—28no—
167C22×#41—28no—
168C22×#41—28no—
169C22×#41—44no—
170C22×#41—44no—
171C22×#41C2311yescharacteristic
172C22×#41C2311yescharacteristic
173C22×#41C2314yes—
174C22×#41C2314yes—
175C22×#41C2314yes—
176C22×#41C2314yes—
177C22×#41C2312yes—
178C22×#41C2312yes—
179C22×#41C2314yes—
180C22×#41C2312yes—
181C22×#41C2312yes—
182C22×#41C2311yescharacteristic
183C23×Q8C2311yescharacteristic
184C23×Q8C2312yes—
185C23×Q8C2312yes—
186C23×Q8C2311yescharacteristic
187C23×D4C2311yescharacteristic
188C23×D4C2312yes—
189C23×D4C2312yes—
190C23×D4C2314yes—
191C23×D4C2312yes—
192C23×D4C2312yes—
193C23×D4C2311yescharacteristic
194C23×D4C2314yes—
195C24×C4C2312yes—
196C24×C4C2312yes—
197C24×C4C2311yescharacteristic
198C24×C4C2312yes—
199#550—232no—
200#550—232no—
201#548—232no—
202#548—232no—
203#548—232no—
204#547—232no—
205#547—232no—
206#546—232no—
207#546—232no—
208#546—232no—
209#546—264no—
210#536—28no—
211#536—28no—
212#536—216no—
213#536—28no—
214#536—44no—
215#535—28no—
216#535—28no—
217#535—216no—
218#535—232no—
219#535—28no—
220#535—44no—
221#534—232no—
222#532—232no—
223#532—232no—
224#532—264no—
225#532—216no—
226#532—28no—
227C2×C4⋊Q8—28no—
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2314yes—
231C2×C4⋊Q8C2314yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2312yes—
235C2×#127—28no—
236C2×#127C2311yescharacteristic
237C2×#127C2312yes—
238C2×#127C2318yes—
239C2×#127C2314yes—
240C2×#127C2314yes—
241C2×#127C2312yes—
242C2×#127C2312yes—
243C2×#127C2312yes—
244C2×#124—216no—
245C2×#124—28no—
246C2×#124D4116yescomplemented
247C2×#124C2311yescharacteristic
248C2×#124C2312yes—
249C2×#124C2311yescharacteristic
250C2×#124C2312yes—
251C2×#124C2312yes—
252C2×#124C2312yes—
253C2×#124C2314yes—
254C2×#124C2312yes—
255C2×#124C2312yes—
256C2×#124C2318yes—
257C2×#124C2318yes—
258C2×#124C2312yes—
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#124C2312yes—
262C2×#124C2312yes—
263C2×#124C2314yes—
264C2×#124C2312yes—
265#525—28no—
266#525—28no—
267#525—232no—
268#525D4116yescomplemented
269C2×#123—232no—
270C2×#123C2312yes—
271C2×#123C2312yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×#123C2318yes—
276C2×#123C2318yes—
277C2×#123C2318yes—
278C2×#123C2318yes—
279C2×#123C2314yes—
280C2×#123C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2318yes—
286C2×C22⋊Q8C2318yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2312yes—
290C2×#121—232no—
291C2×#121C2314yes—
292C2×#121C2312yes—
293C2×#121C2312yes—
294C2×#121C2314yes—
295C2×#121C2314yes—
296C2×#121C23116yes—
297C2×#121C23116yes—
298C2×#121C2318yes—
299C2×#121C2318yes—
300C2×#121C2318yes—
301C2×#121C2318yes—
302C2×#121C2318yes—
303C2×#121C2318yes—
304C2×#121C2318yes—
305C2×#121C2314yes—
306C2×#121C2318yes—
307C2×#121C23116yes—
308C2×#121C2314yes—
309C2×#121C2312yes—
310C2×#120C2312yes—
311C2×#120C2312yes—
312C2×#120C2314yes—
313C2×#120C2314yes—
314C2×#120C2314yes—
315C2×#120C2318yes—
316C2×#120C2318yes—
317C2×#120C2314yes—
318C2×#120C23116yes—
319C2×#120C2312yes—
320#519—28no—
321#518—28no—
322C4×#41—28no—
323C2×C4×Q8C2314yes—
324C2×C4×Q8C2314yes—
325C2×C4×Q8C2312yes—
326C2×C4×D4—232no—
327C2×C4×D4C2314yes—
328C2×C4×D4C2318yes—
329C2×C4×D4C23116yes—
330C2×C4×D4C2318yes—
331C2×C4×D4C2318yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C23116yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2314yes—
339C2×C4×D4C2318yes—
340C2×C4×D4C2314yes—
341C2×#117C2311yescharacteristic
342C2×#117C2311yescharacteristic
343C2×#117C2311yescharacteristic
344C2×#117C2311yescharacteristic
345C2×#117C2314yes—
346C2×#117C2312yes—
347C2×#117C2311yescharacteristic
348C22×C4⋊C4C2318yes—
349C22×C4⋊C4C2314yes—
350C22×C22⋊C4C2314yes—
351C22×C22⋊C4C2318yes—
352C22×C22⋊C4C2318yes—
353C22×C22⋊C4C2314yes—
354C22×C22⋊C4C2314yes—
355C22×C42—28no—
356C22×C42C2312yes—
357C22×C42C2312yes—
358C22×C42C2312yes—
359C22×C42C2312yes—
360C22×C42C2311yescharacteristic
361C22×C42C2314yes—
362C22×C42C2311yescharacteristic
363#399C23116yes—
364#398C23116yes—
365#396C23116yes—
366#396C23116yes—
367#395C23116yes—
368#394C23116yes—
369#394C23116yes—
370#394C23116yes—
371#394C23116yes—
372#394C23116yes—
373#392C23116yes—
374#392C23116yes—
375#392C23116yes—
376#392C23116yes—
377#392C23116yes—
378#392C23116yes—
379#391C2314yes—
380#391C2314yes—
381#391C2314yes—
382#391C2314yes—
383#391C2312yes—
384#391C2312yes—
385#391C2312yes—
386#390C2314yes—
387#390C2314yes—
388#390C2314yes—
389#390C2314yes—
390#390C2312yes—
391#390C2312yes—
392#390C2318yes—
393#390C23116yes—
394#390C23116yes—
395#390C2312yes—
396#389C2318yes—
397#389C23116yes—
398#389C2314yes—
399#388C23116yes—
400#388C2318yes—
401#388C2318yes—
402#388C23116yes—
403#388C23116yes—
404#388C23116yes—
405#388C2318yes—
406#387C2318yes—
407#386C2318yes—
408#386C2318yes—
409#386C2314yes—
410#386C2314yes—
411#386C23116yes—
412#386C23116yes—
413#386C23116yes—
414#386C23116yes—
415#386C23116yes—
416#386C2314yes—
417#386C2318yes—
418#385C23116yes—
419#385C23116yes—
420#385C23116yes—
421#385C23116yes—
422#385C23116yes—
423#385C2314yes—
424#385C2318yes—
425#384C2312yes—
426#382C2312yes—
427#381C2314yes—
428#381C2314yes—
429#381C2312yes—
430#380C2314yes—
431#380C2318yes—
432#380C2314yes—
433#379C2314yes—
434#379C2314yes—
435#379C2312yes—
436C4×C4⋊C4C2318yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2314yes—
440C4×C22⋊C4C2314yes—
441C4×C22⋊C4C23116yes—
442C4×C22⋊C4C2318yes—
443C4×C22⋊C4C2314yes—
444C4×C22⋊C4C2314yes—
445C4×C22⋊C4C2314yes—
446C4×C22⋊C4C2314yes—
447C4×C22⋊C4C2318yes—
448#376C2312yes—
449C43C2312yes—
450C25C2412yes—
451C25C2414yes—
452C25C2412yes—
453C25C2411yescharacteristic
4542−1+4—464no—
455H(5,𝔽2)—464no—
456C2×#41—216no—
457C2×#41—216no—
458C2×#41—28no—
459C2×#41—28no—
460C2×#41—28no—
461C2×#41—216no—
462C2×#41—216no—
463C2×#41—216no—
464C2×#41—28no—
465C2×#41—28no—
466C2×#41—28no—
467C2×#41—24no—
468C2×#41—24no—
469C2×#41—24no—
470C2×#41—24no—
471C2×#41—24no—
472C2×#41—216no—
473C2×#41—216no—
474C2×#41—216no—
475C2×#41—28no—
476C2×#41—216no—
477C2×#41—216no—
478C2×#41—28no—
479C2×#41—24no—
480C2×#41—24no—
481C2×#41—24no—
482C2×#41—48no—
483C2×#41—48no—
484C2×#41—48no—
485C2×#41—48no—
486C2×#41—48no—
487C2×#41—44no—
488C2×#41—44no—
489C2×#41—44no—
490C2×#41—44no—
491C2×#41—464no—
492C2×#41—464no—
493C2×#41C2×D418yes—
494C22×Q8—28no—
495C22×Q8—28no—
496C22×Q8—28no—
497C22×Q8—24no—
498C22×Q8—24no—
499C22×Q8—24no—
500C22×Q8—28no—
501C22×Q8—24no—
502C22×Q8—24no—
503C22×Q8—44no—
504C22×Q8—44no—
505C22×Q8C2×D418yes—
506C22×Q8C2412yes—
507C22×Q8C2411yescharacteristic
508C22×Q8C2412yes—
509C22×Q8C2411yescharacteristic
510C22×Q8C2414yes—
511C22×Q8C2412yes—
512C22×Q8C2411yescharacteristic
513C22×Q8C2412yes—
514C22×D4—216no—
515C22×D4—28no—
516C22×D4—28no—
517C22×D4—28no—
518C22×D4—216no—
519C22×D4—216no—
520C22×D4—28no—
521C22×D4—28no—
522C22×D4—28no—
523C22×D4—24no—
524C22×D4—28no—
525C22×D4—24no—
526C22×D4—24no—
527C22×D4—28no—
528C22×D4—24no—
529C22×D4—24no—
530C22×D4—416no—
531C22×D4—44no—
532C22×D4—44no—
533C22×D4—44no—
534C22×D4—44no—
535C22×D4—48no—
536C22×D4C2×D418yes—
537C22×D4C2412yes—
538C22×D4C2412yes—
539C22×D4C2412yes—
540C22×D4C2411yescharacteristic
541C22×D4C2412yes—
542C22×D4C2411yescharacteristic
543C22×D4C24116yes—
544C22×D4C2414yes—
545C22×D4C2418yes—
546C22×D4C2418yes—
547C22×D4C2414yes—
548C22×D4C2414yes—
549C22×D4C2412yes—
550C22×D4C2412yes—
551C22×D4C2411yescharacteristic
552C22×D4C2412yes—
553C22×D4C2414yes—
554C22×D4C2418yes—
555C22×D4C2418yes—
556C22×D4C2414yes—
557C22×D4C2414yes—
558C22×D4C2418yes—
559C22×D4C2418yes—
560C22×D4C2414yes—
561C23×C4—24no—
562C23×C4—24no—
563C23×C4—28no—
564C23×C4—28no—
565C23×C4—28no—
566C23×C4—28no—
567C23×C4—28no—
568C23×C4—48no—
569C23×C4—44no—
570C23×C4—44no—
571C23×C4C2×D418yes—
572C23×C4C2412yes—
573C23×C4C2412yes—
574C23×C4C2412yes—
575C23×C4C2412yes—
576C23×C4C2414yes—
577C23×C4C2418yes—
578C23×C4C2414yes—
579C23×C4C2418yes—
580C23×C4C2414yes—
581C23×C4C2414yes—
582C23×C4C2414yes—
583C23×C4C2412yes—
584C23×C4C2412yes—
585C23×C4C2412yes—
586C23×C4C2412yes—
587C23×C4C2411yescharacteristic
588C23×C4C2418yes—
589C23×C4C2414yes—
590C23×C4C2412yes—
591C23×C4C2411yescharacteristic
592C4⋊Q8—216no—
593C4⋊Q8—216no—
594C4⋊Q8—28no—
595C4⋊Q8—28no—
596C4⋊Q8—24no—
597C4⋊Q8—28no—
598C4⋊Q8—44no—
599#127—216no—
600#127—216no—
601#127—28no—
602#127—232no—
603#127—28no—
604#127—24no—
605#127—28no—
606#127—44no—
607#124—28no—
608#124—28no—
609#124—28no—
610#124—28no—
611#124—232no—
612#124—232no—
613#124—24no—
614#124—28no—
615#124—28no—
616#124—216no—
617#124—24no—
618#124—28no—
619#124—28no—
620#124—44no—
621#124—44no—
622#124C2×D4116yes—
623#124C2×D4116yes—
624#124C2×D4132yes—
625#123—216no—
626#123—28no—
627#123—28no—
628#123—216no—
629#123—232no—
630#123—216no—
631#123—232no—
632#123—232no—
633#123—232no—
634#123—48no—
635#123C2×D4116yes—
636C22⋊Q8—216no—
637C22⋊Q8—28no—
638C22⋊Q8—28no—
639C22⋊Q8—216no—
640C22⋊Q8—232no—
641C22⋊Q8—216no—
642C22⋊Q8—232no—
643C22⋊Q8—48no—
644C22⋊Q8C2×D4116yescomplemented
645#121—232no—
646#121—216no—
647#121—232no—
648#121—28no—
649#121—28no—
650#121—216no—
651#121—216no—
652#121—216no—
653#121—264no—
654#121—264no—
655#121—232no—
656#121—232no—
657#121—232no—
658#121—232no—
659#121—232no—
660#121—416no—
661#121—432no—
662#121—48no—
663#121C2×D4116yescomplemented
664#120—28no—
665#120—28no—
666#120—216no—
667#120—216no—
668#120—232no—
669#120—216no—
670#120—232no—
671#120—432no—
672#120—48no—
673#120C2×D4116yes—
674C4×Q8—216no—
675C4×Q8—28no—
676C4×Q8—216no—
677C4×D4—216no—
678C4×D4—216no—
679C4×D4—216no—
680C4×D4—216no—
681C4×D4—232no—
682C4×D4—264no—
683C4×D4—264no—
684C4×D4—232no—
685C4×D4—232no—
686C4×D4—28no—
687C4×D4—216no—
688C4×D4—216no—
689C4×D4—416no—
690C4×D4C2×D4132yescomplemented
691#117—24no—
692#117—24no—
693#117—24no—
694#117—24no—
695#117—216no—
696#117—28no—
697#117C2×D418yes—
698C2×C4⋊C4—216no—
699C2×C4⋊C4—232no—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C24116yes—
702C2×C4⋊C4C2418yes—
703C2×C4⋊C4C2418yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2418yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2418yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2418yes—
714C2×C4⋊C4C2418yes—
715C2×C4⋊C4C2418yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2412yes—
718C2×C22⋊C4—216no—
719C2×C22⋊C4—216no—
720C2×C22⋊C4—232no—
721C2×C22⋊C4—232no—
722C2×C22⋊C4C2×D4132yes—
723C2×C22⋊C4C2412yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2418yes—
727C2×C22⋊C4C2418yes—
728C2×C22⋊C4C2418yes—
729C2×C22⋊C4C2418yes—
730C2×C22⋊C4C2418yes—
731C2×C22⋊C4C2418yes—
732C2×C22⋊C4C2418yes—
733C2×C22⋊C4C2412yes—
734C2×C22⋊C4C2412yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2412yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2418yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2418yes—
743C2×C22⋊C4C2418yes—
744C2×C22⋊C4C2418yes—
745C2×C22⋊C4C2418yes—
746C2×C22⋊C4C2418yes—
747C2×C22⋊C4C2418yes—
748C2×C22⋊C4C24116yes—
749C2×C22⋊C4C24116yes—
750C2×C22⋊C4C2418yes—
751C2×C22⋊C4C2412yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2418yes—
754C2×C22⋊C4C2418yes—
755C2×C22⋊C4C2414yes—
756C2×C42—28no—
757C2×C42—24no—
758C2×C42—28no—
759C2×C42—28no—
760C2×C42—28no—
761C2×C42—216no—
762C2×C42C2×D418yes—
763C2×C42C2412yes—
764C2×C42C2412yes—
765C2×C42C2412yes—
766C2×C42C2418yes—
767C2×C42C2412yes—
768C2×C42C2414yes—
769C2×C42C2414yes—
770C2×C42C2414yes—
771C2×C42C2412yes—
772C2×C42C2412yes—
773C2×C42C2418yes—
774C2×C42C2411yescharacteristic
775C2×C42C2412yes—
776C2×C42C2412yes—
777C2×C42C2411yescharacteristic
778#95C2418yes—
779#95C2418yes—
780#95C2418yes—
781#95C2418yes—
782#95C2418yes—
783#95C2418yes—
784#95C2418yes—
785#95C24116yes—
786#95C24116yes—
787C24—22no—
788C24—22no—
789C24—24no—
790C24—24no—
791C24—24no—
792C24—28no—
793C24—28no—
794C24—24no—
795C24—24no—
796C24—44no—
797C24—48no—
798C24—48no—
799C24—44no—
800C24—416no—
801C24C22×D418yes—
802C24C22×D414yes—
803C24C2512yes—
804C24C2514yes—
805C24C2512yes—
806C24C2512yes—
807C24C2514yes—
808C24C2512yes—
809C24C2511yescharacteristic
810#41—232no—
811#41—464no—
812#41—464no—
813#41—432no—
814#41—464no—
815#41—464no—
816#41—464no—
817#41—432no—
818#41—432no—
819#41—432no—
820#41—416no—
821#41—416no—
822C2×Q8—232no—
823C2×Q8—24no—
824C2×Q8—22no—
825C2×Q8—24no—
826C2×Q8—28no—
827C2×Q8—28no—
828C2×Q8—22no—
829C2×Q8—24no—
830C2×Q8—24no—
831C2×Q8—22no—
832C2×Q8—22no—
833C2×Q8—24no—
834C2×Q8—24no—
835C2×Q8—22no—
836C2×Q8—24no—
837C2×Q8—24no—
838C2×Q8—22no—
839C2×Q8—24no—
840C2×Q8—22no—
841C2×Q8—24no—
842C2×Q8—22no—
843C2×Q8—44no—
844C2×Q8—432no—
845C2×Q8—432no—
846C2×Q8—416no—
847C2×Q8C22×D418yes—
848C2×Q8C22×D414yes—
849C2×Q8C22×D418yes—
850C2×D4—24no—
851C2×D4—24no—
852C2×D4—232no—
853C2×D4—24no—
854C2×D4—24no—
855C2×D4—216no—
856C2×D4—24no—
857C2×D4—216no—
858C2×D4—28no—
859C2×D4—28no—
860C2×D4—24no—
861C2×D4—28no—
862C2×D4—216no—
863C2×D4—28no—
864C2×D4—24no—
865C2×D4—24no—
866C2×D4—28no—
867C2×D4—216no—
868C2×D4—216no—
869C2×D4—28no—
870C2×D4—232no—
871C2×D4—24no—
872C2×D4—22no—
873C2×D4—24no—
874C2×D4—28no—
875C2×D4—216no—
876C2×D4—28no—
877C2×D4—22no—
878C2×D4—24no—
879C2×D4—24no—
880C2×D4—22no—
881C2×D4—22no—
882C2×D4—24no—
883C2×D4—24no—
884C2×D4—22no—
885C2×D4—28no—
886C2×D4—216no—
887C2×D4—24no—
888C2×D4—24no—
889C2×D4—22no—
890C2×D4—24no—
891C2×D4—22no—
892C2×D4—24no—
893C2×D4—22no—
894C2×D4—232no—
895C2×D4—432no—
896C2×D4—48no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—416no—
900C2×D4—48no—
901C2×D4—48no—
902C2×D4—44no—
903C2×D4—432no—
904C2×D4—464no—
905C2×D4—416no—
906C2×D4—416no—
907C2×D4—48no—
908C2×D4—48no—
909C2×D4—48no—
910C2×D4—416no—
911C2×D4—48no—
912C2×D4—416no—
913C2×D4—432no—
914C2×D4—464no—
915C2×D4—432no—
916C2×D4—416no—
917C2×D4C22×D418yes—
918C2×D4C22×D418yes—
919C2×D4C22×D414yes—
920C2×D4C22×D418yes—
921C2×D4C22×D4116yes—
922C22×C4—24no—
923C22×C4—22no—
924C22×C4—24no—
925C22×C4—22no—
926C22×C4—24no—
927C22×C4—232no—
928C22×C4—24no—
929C22×C4—24no—
930C22×C4—24no—
931C22×C4—24no—
932C22×C4—24no—
933C22×C4—24no—
934C22×C4—28no—
935C22×C4—24no—
936C22×C4—216no—
937C22×C4—28no—
938C22×C4—28no—
939C22×C4—24no—
940C22×C4—24no—
941C22×C4—28no—
942C22×C4—28no—
943C22×C4—28no—
944C22×C4—216no—
945C22×C4—28no—
946C22×C4—216no—
947C22×C4—28no—
948C22×C4—28no—
949C22×C4—24no—
950C22×C4—24no—
951C22×C4—216no—
952C22×C4—24no—
953C22×C4—24no—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—28no—
957C22×C4—28no—
958C22×C4—28no—
959C22×C4—216no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—48no—
964C22×C4—48no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—432no—
969C22×C4—48no—
970C22×C4—416no—
971C22×C4—432no—
972C22×C4—432no—
973C22×C4C22×D418yes—
974C22×C4C22×D418yes—
975C22×C4C22×D418yes—
976C22×C4C22×D418yes—
977C22×C4C22×D414yes—
978C22×C4C22×D418yes—
979C22×C4C22×D414yes—
980C22×C4C22×D414yes—
981C22×C4H(5,𝔽2)14yes—
982C22×C4C2514yes—
983C22×C4C2514yes—
984C22×C4C2514yes—
985C22×C4C2514yes—
986C22×C4C2512yes—
987C22×C4C2514yes—
988C22×C4C2512yes—
989C22×C4C2512yes—
990C22×C4C2514yes—
991C22×C4C2512yes—
992C22×C4C2512yes—
993C22×C4C2512yes—
994C22×C4C2514yes—
995C22×C4C2514yes—
996C22×C4C2511yescharacteristic
997C22×C4C2511yescharacteristic
998C4⋊C4—28no—
999C4⋊C4—232no—
1000C4⋊C4—216no—
1001C4⋊C4—216no—
1002C4⋊C4—24no—
1003C4⋊C4—28no—
1004C4⋊C4—24no—
1005C4⋊C4—216no—
1006C4⋊C4—24no—
1007C4⋊C4—28no—
1008C4⋊C4—216no—
1009C4⋊C4—28no—
1010C4⋊C4—24no—
1011C4⋊C4—216no—
1012C4⋊C4—48no—
1013C4⋊C4—48no—
1014C4⋊C4C22×D4116yes—
1015C4⋊C4C22×D418yes—
1016C22⋊C4—24no—
1017C22⋊C4—216no—
1018C22⋊C4—216no—
1019C22⋊C4—24no—
1020C22⋊C4—24no—
1021C22⋊C4—28no—
1022C22⋊C4—28no—
1023C22⋊C4—24no—
1024C22⋊C4—28no—
1025C22⋊C4—28no—
1026C22⋊C4—216no—
1027C22⋊C4—216no—
1028C22⋊C4—216no—
1029C22⋊C4—216no—
1030C22⋊C4—216no—
1031C22⋊C4—28no—
1032C22⋊C4—28no—
1033C22⋊C4—28no—
1034C22⋊C4—216no—
1035C22⋊C4—216no—
1036C22⋊C4—216no—
1037C22⋊C4—216no—
1038C22⋊C4—216no—
1039C22⋊C4—48no—
1040C22⋊C4—416no—
1041C22⋊C4—48no—
1042C22⋊C4—416no—
1043C22⋊C4—48no—
1044C22⋊C4C22×D418yes—
1045C22⋊C4C22×D4116yes—
1046C22⋊C4C22×D4132yes—
1047C22⋊C4C22×D4132yes—
1048C22⋊C4C22×D4116yes—
1049C42—28no—
1050C42—28no—
1051C42—24no—
1052C42—24no—
1053C42—24no—
1054C42—28no—
1055C42—24no—
1056C42—216no—
1057C42—24no—
1058C42—24no—
1059C42—48no—
1060C42C22×D414yes—
1061C42C22×D414yes—
1062C42C22×D418yes—
1063C42C22×D418yes—
1064C23—24no—
1065C23—22no—
1066C23—24no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—24no—
1071C23—28no—
1072C23—24no—
1073C23—216no—
1074C23—24no—
1075C23—28no—
1076C23—216no—
1077C23—22no—
1078C23—22no—
1079C23—24no—
1080C23—24no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—24no—
1085C23—22no—
1086C23—28no—
1087C23—28no—
1088C23—216no—
1089C23—48no—
1090C23—416no—
1091C23—416no—
1092C23—48no—
1093C23—48no—
1094C23—416no—
1095C23—48no—
1096C23—88no—
1097C23—88no—
1098C23—88no—
1099C23—88no—
1100C23—816no—
1101C23—816no—
1102C23—168no—
1103C23C23×D414yes—
1104C23C23×D414yes—
1105C23C23×D418yes—
1106C23C23×D412yes—
1107C23C23×D412yes—
1108C23C2×H(5,𝔽2)12yes—
1109C23C2611yescharacteristic
1110Q8—216no—
1111Q8—216no—
1112Q8—28no—
1113Q8—416no—
1114Q8—44no—
1115Q8—48no—
1116Q8—48no—
1117Q8—44no—
1118D4—216no—
1119D4—216no—
1120D4—216no—
1121D4—28no—
1122D4—416no—
1123D4—464no—
1124D4—416no—
1125D4—432no—
1126D4—416no—
1127D4—416no—
1128D4—432no—
1129D4—48no—
1130D4—48no—
1131D4—44no—
1132D4—48no—
1133D4—48no—
1134D4—44no—
1135D4—88no—
1136D4—816no—
1137D4—816no—
1138D4—88no—
1139D4—816no—
1140D4—88no—
1141D4—168no—
1142C2×C4—216no—
1143C2×C4—24no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—24no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—28no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—28no—
1155C2×C4—216no—
1156C2×C4—216no—
1157C2×C4—216no—
1158C2×C4—216no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—24no—
1169C2×C4—22no—
1170C2×C4—24no—
1171C2×C4—22no—
1172C2×C4—28no—
1173C2×C4—28no—
1174C2×C4—28no—
1175C2×C4—28no—
1176C2×C4—48no—
1177C2×C4—416no—
1178C2×C4—416no—
1179C2×C4—432no—
1180C2×C4—416no—
1181C2×C4—432no—
1182C2×C4—416no—
1183C2×C4—416no—
1184C2×C4—48no—
1185C2×C4—48no—
1186C2×C4—48no—
1187C2×C4—88no—
1188C2×C4—816no—
1189C2×C4D42116yes—
1190C2×C4C23×D414yes—
1191C2×C4C23×D414yes—
1192C2×C4C23×D418yes—
1193C2×C4C23×D414yes—
1194C2×C4C23×D414yes—
1195C2×C4C23×D418yes—
1196C2×C4C23×D412yes—
1197C2×C4C23×D412yes—
1198C2×C4C23×D412yes—
1199C2×C4C23×D412yes—
1200C2×C4C2×H(5,𝔽2)12yes—
1201C2×C4C2×H(5,𝔽2)12yes—
1202C2×C4#58518yes—
1203C22—24no—
1204C22—24no—
1205C22—24no—
1206C22—216no—
1207C22—24no—
1208C22—28no—
1209C22—24no—
1210C22—24no—
1211C22—24no—
1212C22—28no—
1213C22—416no—
1214C22—44no—
1215C22—44no—
1216C22—48no—
1217C22—44no—
1218C22—48no—
1219C22—44no—
1220C22—48no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—48no—
1225C22—44no—
1226C22—44no—
1227C22—48no—
1228C22—44no—
1229C22—42no—
1230C22—44no—
1231C22—42no—
1232C22—816no—
1233C22—816no—
1234C22—1616no—
1235C22C2×D4214yes—
1236C22C24×D411yescharacteristic
1237C22C24×D411yescharacteristic
1238C22C22×H(5,𝔽2)11yescharacteristic
1239C22C2×#58514yes—
1240C4—28no—
1241C4—24no—
1242C4—24no—
1243C4—28no—
1244C4—24no—
1245C4—24no—
1246C4—28no—
1247C4—44no—
1248C4—44no—
1249C4—44no—
1250C4—44no—
1251C4—42no—
1252C4—44no—
1253C4—42no—
1254C4C2×D4214yes—
1255C4C2×D4214yes—
1256C2—24no—
1257C2—44no—
1258C2—48no—
1259C2—44no—
1260C2—82no—
1261C2—84no—
1262C2—82no—
1263C2C22×D4211yescharacteristic
1264C2#6281112yes—
1265C2#6281212yes—
1266C2#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×#3500C2semidirect
2. C2×#3487C2semidirect
3. C2×#3485C2semidirect
4. C22×#532C2semidirect
5. #59129C2semidirect
6. #59128C2semidirect
7. #39332C2semidirect
8. #37681C2semidirect
9. #37680C2semidirect
10. #36624C2semidirect
11. #36125C2semidirect
12. #36124C2semidirect
13. #36099C2semidirect
14. #35667C2semidirect
15. #35666C2semidirect
16. #35528C2semidirect
17. #35527C2semidirect
18. #35329C2semidirect
19. #35327C2semidirect
20. #35149C2semidirect
21. #35149C2semidirect
22. #34211C2semidirect
23. C4×#525C2semidirect
27. C23×#41C22semidirect
31. C2×#550C22semidirect
32. C2×#550C22semidirect
33. C2×#548C22semidirect
34. C2×#548C22semidirect
35. C2×#548C22semidirect
36. C2×#547C22semidirect
37. C2×#547C22semidirect
39. C2×#546C22semidirect
40. C2×#546C22semidirect
41. C2×#546C22semidirect
45. C2×#536C22semidirect
46. C2×#536C22semidirect
50. C2×#535C22semidirect
51. C2×#535C22semidirect
52. C2×#535C22semidirect
56. C2×#532C22semidirect
57. C2×#532C22semidirect
58. C2×#532C22semidirect
59. C2×#532C22semidirect
60. C22×C4⋊Q8C22semidirect
63. C22×#124C22semidirect
64. C22×#124C22semidirect
67. C2×#525C22semidirect
68. C2×#525C22semidirect
70. C22×#121C22semidirect
71. C2×#519C22semidirect
74. C22×C4×D4C22semidirect
75. C23×C42C22semidirect
76. #2858C22semidirect
77. #2858C22semidirect
78. #2857C22semidirect
79. #2856C22semidirect
80. #2854C22semidirect
81. #2850C22semidirect
82. #2850C22semidirect
83. #2850C22semidirect
84. #2849C22semidirect
85. #2849C22semidirect
86. #2847C22semidirect
87. #2675C22semidirect
88. #2672C22semidirect
89. #2671C22semidirect
90. #2669C22semidirect
91. #2658C22semidirect
92. #2657C22semidirect
93. #2620C22semidirect
94. #2613C22semidirect
95. #2613C22semidirect
96. #2555C22semidirect
97. #2546C22semidirect
98. #2545C22semidirect
99. #2545C22semidirect
100. #2544C22semidirect
101. #2544C22semidirect
102. #2541C22semidirect
103. #2540C22semidirect
104. #2539C22semidirect
105. #2534C22semidirect
106. #2464C22semidirect
107. #2464C22semidirect
108. #2461C22semidirect
109. #2456C22semidirect
110. #2455C22semidirect
111. #2449C22semidirect
112. #2434C22semidirect
113. #2434C22semidirect
114. #2433C22semidirect
115. #2433C22semidirect
116. #2432C22semidirect
117. #2432C22semidirect
118. #2432C22semidirect
119. #2432C22semidirect
120. #2431C22semidirect
121. #2431C22semidirect
122. #2431C22semidirect
123. #2431C22semidirect
124. #2429C22semidirect
125. #2428C22semidirect
126. #2428C22semidirect
127. #2424C22semidirect
128. #2424C22semidirect
129. #2413C22semidirect
130. #2410C22semidirect
131. #2407C22semidirect
132. #2407C22semidirect
133. #2406C22semidirect
135. #2367C22semidirect
136. #2361C22semidirect
137. #2358C22semidirect
138. #2342C22semidirect
139. #2326C22semidirect
140. #2310C22semidirect
141. #2310C22semidirect
143. #2309C22semidirect
144. C4×#124C22semidirect
145. C4×C22⋊Q8C22semidirect
146. C4×#123C22semidirect
147. C4×#121C22semidirect
148. C4×#121C22semidirect
149. C4×#120C22semidirect
152. #2297C22semidirect
153. #2296C22semidirect
154. #2290C22semidirect
155. #2285C22semidirect
156. #2280C22semidirect
157. C42×D4C22semidirect
158. C4×#117C22semidirect
246. C2×#124D4semidirect
268. #525D4semidirect
644. C22⋊Q8C2×D4semidirect
663. #121C2×D4semidirect
690. C4×D4C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35002
C2×#34872
C2×#34852
C22×#5322
#591292
#591282
#393322
#376812
#376802
#366242
#361252
#361242
#360992
#356672
#356662
#355282
#355272
#353292
#353272
#351492
#342112
C4×#5252