Finite Group Databasebeta

← #7674608

Subgroups — #7674608

Order 512.

8596 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3512C211yesmaximal, characteristic, complemented
2C2×#3498C211yesmaximal, characteristic, complemented
3#43102C2116yesmaximal, complemented
4#38093C214yesmaximal, complemented
5#38089C214yesmaximal, complemented
6#38084C214yesmaximal, complemented
7#38080C214yesmaximal, complemented
8#37751C218yesmaximal, complemented
9#37701C214yesmaximal, complemented
10#37694C214yesmaximal, complemented
11#35531C212yesmaximal, complemented
12#35513C212yesmaximal, complemented
13#35333C211yesmaximal, characteristic, complemented
14#35272C211yesmaximal, characteristic, complemented
15#35256C212yesmaximal, complemented
16C2×#2641C211yesmaximal, characteristic, complemented
17#34258C212yesmaximal, complemented
18#34070C211yesmaximal, characteristic, complemented
19#34070C211yesmaximal, characteristic, complemented
20C22×H(5,𝔽2)C2212yes—
21#3512—216no—
22#3498—216no—
23C2×#553C2218yescomplemented
24C2×#553C2214yescomplemented
25C2×#552C2214yescomplemented
26C2×#550C2214yes—
27C2×D42C2218yes—
28C2×D42C2214yes—
29C2×#541C2212yescomplemented
30C2×#540C2212yescomplemented
31C2×#537C2212yescomplemented
32C2×#535C2214yes—
33C2×#535C2212yes—
34C2×#535C2212yescomplemented
35C2×#532C2211yescharacteristic
36C2×#532C2212yes—
37C2×#532C2211yescharacteristic
38C22×#127C2211yescharacteristic
39C22×#127C2212yes—
40C2×#529C2214yescomplemented
41C22×#125C2211yescharacteristic, complemented
42C2×#520C2212yescomplemented
43C2×C4×#41C2211yescharacteristic
44C2×C4×#41C2211yescharacteristic, complemented
45C2×C4×#41C2212yescomplemented
46#2856C2214yescomplemented
47#2856C2214yescomplemented
48#2851C2214yescomplemented
49#2850C2214yescomplemented
50#2714C22116yescomplemented
51#2711C22116yescomplemented
52#2709C22116yescomplemented
53#2691C22116yescomplemented
54#2685C22116yescomplemented
55#2678C22116yescomplemented
56#2673C22116yescomplemented
57#2671C22116yescomplemented
58#2641C2214yescomplemented
59#2641C2214yescomplemented
60#2641C2214yescomplemented
61#2641C2214yescomplemented
62#2629C2214yescomplemented
63#2620C2214yescomplemented
64#2619C2214yescomplemented
65#2619C2214yescomplemented
66#2579C2218yescomplemented
67#2566C2214yescomplemented
68#2565C2214yescomplemented
69#2548C2214yescomplemented
70#2541C2214yescomplemented
71#2504C2214yescomplemented
72#2501C2214yescomplemented
73#2500C2214yescomplemented
74#2500C2214yescomplemented
75#2476C22116yescomplemented
76#2467C22116yescomplemented
77#2464C22116yescomplemented
78#2460C22116yescomplemented
79#2448C2218yescomplemented
80#2445C2218yescomplemented
81#2435C2214yescomplemented
82#2433C2214yescomplemented
83#2432C2214yescomplemented
84#2431C2214yescomplemented
85#2428C2218yescomplemented
86#2426C2218yescomplemented
87#2424C22116yescomplemented
88#2424C22116yescomplemented
89#2418C22116yescomplemented
90#2411C22116yescomplemented
91#2410C22116yescomplemented
92#2410C22116yescomplemented
93#2408C2218yescomplemented
94#2408C2218yescomplemented
95#2407C2218yescomplemented
96#2405C22116yescomplemented
97C2×#394C2218yescomplemented
98#2341C2218yescomplemented
99D4×C22⋊C4C2218yescomplemented
100D4×C22⋊C4C22116yescomplemented
101#2328C2212yescomplemented
102#2328C2212yescomplemented
103#2327C2212yescomplemented
104#2327C2212yescomplemented
105#2326C2214yescomplemented
106#2326C2212yescomplemented
107#2326C2212yescomplemented
108#2325C2218yescomplemented
109#2325C2218yescomplemented
110#2317C2212yescomplemented
111#2311C2212yes—
112#2311C2214yescomplemented
113#2309C2214yescomplemented
114#2309C2212yescomplemented
115#2297C2211yescharacteristic
116#2297C2211yescharacteristic, complemented
117#2297C2212yescomplemented
118#2297C2214yescomplemented
119C2×#390C2212yescomplemented
120C2×#390C2212yescomplemented
121C2×#390C2214yescomplemented
122#2290C2214yescomplemented
123#2290C2214yescomplemented
124#2290C2214yescomplemented
125#2290C2214yescomplemented
126#2285C2211yescharacteristic, complemented
127#2285C2211yescharacteristic, complemented
128C2×#376C2211yescharacteristic, complemented
129C2×H(5,𝔽2)—216no—
130C2×H(5,𝔽2)—216no—
131C2×H(5,𝔽2)—48no—
132C22×#41C2311yescharacteristic
133C22×#41C2314yes—
134C22×#41C2314yes—
135C22×#41C2312yes—
136C22×#41C2311yescharacteristic
137C23×D4C2312yes—
138C23×D4C2314yes—
139C23×D4C2314yes—
140C23×D4C2318yes—
141C23×D4C2314yes—
142C23×D4C2318yes—
143#553—264no—
144#553—232no—
145#552—232no—
146#550—232no—
147D42—264no—
148D42—232no—
149#541—216no—
150#540—216no—
151#537—216no—
152#535—216no—
153#535—232no—
154#535—48no—
155#532—28no—
156#532—216no—
157#532D4116yescomplemented
158C2×C4⋊Q8C2311yescharacteristic
159C2×C4⋊Q8C2311yescharacteristic
160C2×#127—216no—
161C2×#127—28no—
162C2×#127C2311yescharacteristic
163C2×#127C2312yes—
164C2×#127C2312yes—
165C2×#127C2314yes—
166C2×#127C2318yes—
167C2×#127C2314yes—
168C2×#127C2314yes—
169C2×#127C2311yescharacteristic
170#529—232no—
171C2×#126C2318yes—
172C2×#126C2318yes—
173C2×#125—28no—
174C2×#125C2314yes—
175C2×#125C2312yes—
176C2×#125C2312yes—
177C2×#125C2318yes—
178C2×#124C2311yescharacteristic
179C2×#124C2311yescharacteristic
180C2×#124C2314yes—
181C2×#124C2314yes—
182C2×#124C2312yes—
183C2×#123C2318yes—
184C2×#123C2318yes—
185C2×#123C23116yes—
186C2×C22⋊Q8C2314yes—
187C2×C22⋊Q8C2314yes—
188C2×#121C2314yes—
189C2×#121C2314yes—
190C2×#121C2314yes—
191C2×#121C2314yes—
192C2×#121C2314yes—
193C2×#121C2318yes—
194C2×#121C2318yes—
195C2×#121C2318yes—
196C2×#121C2318yes—
197C2×#121C2318yes—
198C2×#121C2318yes—
199C2×#121C23116yes—
200C2×#121C23116yes—
201C2×#121C2314yes—
202C2×#120C2318yes—
203C2×#120C2318yes—
204C2×#120C2318yes—
205C2×#120C2318yes—
206C2×#120C23116yes—
207#520—216no—
208C4×#41—28no—
209C4×#41—28no—
210C4×#41—48no—
211C2×C4×Q8C2312yes—
212C2×C4×Q8C2312yes—
213C2×C4×Q8C2314yes—
214C2×C4×Q8C2314yes—
215C2×C4×D4C2312yes—
216C2×C4×D4C2314yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2312yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C2318yes—
221C2×C4×D4C2314yes—
222C2×C4×D4C2318yes—
223C2×C4×D4C2318yes—
224C2×C4×D4C2318yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C2314yes—
227C2×#117C2311yescharacteristic
228C2×#117C2312yes—
229C2×#117C2314yes—
230C2×#117C2311yescharacteristic
231C2×#117C2312yes—
232C2×#117C2312yes—
233C2×#117C2318yes—
234C2×#117C2314yes—
235C22×C4⋊C4C2312yes—
236C22×C4⋊C4C2314yes—
237C22×C4⋊C4C2314yes—
238C22×C22⋊C4C2318yes—
239C22×C22⋊C4C23116yes—
240C22×C22⋊C4C2318yes—
241C22×C42C2312yes—
242C22×C42C2312yes—
243C22×C42C2311yescharacteristic
244C22×C42C2311yescharacteristic
245C22×C42C2314yes—
246C22×C42C2311yescharacteristic
247#399C23116yes—
248#398C23116yes—
249#397C23116yes—
250#396C23116yes—
251#396C23116yes—
252#394C23116yes—
253#394C23116yes—
254#394C23116yes—
255#394C23116yes—
256#394C23116yes—
257#394C23116yes—
258#394C23116yes—
259#394C23116yes—
260#394C23116yes—
261#394C23116yes—
262#394C23116yes—
263#392C23116yes—
264#392C23116yes—
265#392C23116yes—
266#392C23116yes—
267#391C2314yes—
268#391C2312yes—
269#391C2312yes—
270#391C2314yes—
271#390C2312yes—
272#390C2314yes—
273#390C2314yes—
274#390C2314yes—
275#390C2314yes—
276#390C2318yes—
277#390C23116yes—
278#390C2312yes—
279#390C2314yes—
280#390C2318yes—
281#390C23116yes—
282#390C23116yes—
283#390C23116yes—
284#390C2314yes—
285#390C2318yes—
286#390C2314yes—
287#390C2314yes—
288#389C2318yes—
289#388C2318yes—
290#388C2318yes—
291#388C2318yes—
292#388C2318yes—
293#388C23116yes—
294#388C23116yes—
295#388C23116yes—
296#387C23116yes—
297#387C2318yes—
298#387C2318yes—
299#387C2318yes—
300#387C2318yes—
301#386C2318yes—
302#386C23116yes—
303#386C2314yes—
304#386C2318yes—
305#386C2314yes—
306#386C2318yes—
307#386C2318yes—
308#386C2318yes—
309#386C2318yes—
310#386C23116yes—
311#386C23116yes—
312#386C23116yes—
313#386C23116yes—
314#385C23116yes—
315#385C2318yes—
316#385C2318yes—
317#385C2318yes—
318#385C2318yes—
319#385C2318yes—
320#385C23116yes—
321#384C2314yes—
322#384C2312yes—
323#384C2312yes—
324#382C2314yes—
325#382C2312yes—
326#382C2312yes—
327#380C2318yes—
328#380C23116yes—
329#380C2314yes—
330#380C2314yes—
331#379C23116yes—
332#379C2318yes—
333#379C23116yes—
334C4×C4⋊C4C2314yes—
335C4×C4⋊C4C2314yes—
336C4×C22⋊C4C2314yes—
337C4×C22⋊C4C23116yes—
338C4×C22⋊C4C2314yes—
339C4×C22⋊C4C2314yes—
340C4×C22⋊C4C2314yes—
341#376C2312yes—
342#376C2312yes—
343#376C2312yes—
344#376C2312yes—
345C2×#95C2314yes—
346C25C2414yes—
347C25C2418yes—
348H(5,𝔽2)—4128no—
349C2×#41—216no—
350C2×#41—216no—
351C2×#41—24no—
352C2×#41—24no—
353C2×#41—216no—
354C2×#41—28no—
355C2×#41—24no—
356C2×#41—216no—
357C2×#41—28no—
358C2×#41—24no—
359C2×#41—24no—
360C2×#41—48no—
361C2×#41—48no—
362C2×#41C2×D4116yes—
363C2×#41#4118yes—
364C22×Q8C2411yescharacteristic
365C22×Q8C2412yes—
366C22×Q8C2411yescharacteristic
367C22×D4—216no—
368C22×D4—232no—
369C22×D4—216no—
370C22×D4—232no—
371C22×D4—232no—
372C22×D4—28no—
373C22×D4—216no—
374C22×D4—216no—
375C22×D4—216no—
376C22×D4—28no—
377C22×D4—28no—
378C22×D4—48no—
379C22×D4—48no—
380C22×D4—416no—
381C22×D4—88no—
382C22×D4—816no—
383C22×D4C2412yes—
384C22×D4C2411yescharacteristic
385C22×D4C2414yes—
386C22×D4C2414yes—
387C22×D4C2418yes—
388C22×D4C2418yes—
389C22×D4C2414yes—
390C22×D4C2412yes—
391C22×D4C2412yes—
392C22×D4C2411yescharacteristic
393C22×D4C2414yes—
394C22×D4C2418yes—
395C22×D4C2418yes—
396C22×D4C2418yes—
397C22×D4C2418yes—
398C22×D4C2418yes—
399C22×D4C24116yes—
400C22×D4C2414yes—
401C23×C4C2412yes—
402C23×C4C2418yes—
403C23×C4C2414yes—
404C23×C4C2412yes—
405C23×C4C2414yes—
406C23×C4C2412yes—
407C23×C4C2412yes—
408C23×C4C2418yes—
409C23×C4C2414yes—
410C23×C4C2414yes—
411C23×C4C2418yes—
412C23×C4C2412yes—
413C23×C4C2411yescharacteristic
414C4⋊Q8—24no—
415C4⋊Q8C2×D418yes—
416#127—216no—
417#127—232no—
418#127—24no—
419#127—28no—
420#127—28no—
421#127—216no—
422#127—48no—
423#127C2×D418yes—
424#126—232no—
425#126—232no—
426#125—232no—
427#125—28no—
428#125—28no—
429#125—216no—
430#124—216no—
431#124—24no—
432#124—24no—
433#124—48no—
434#124C2×D4116yes—
435#123—232no—
436#123—232no—
437#123—816no—
438C22⋊Q8—216no—
439C22⋊Q8—216no—
440#121—216no—
441#121—232no—
442#121—232no—
443#121—216no—
444#121—216no—
445#121—216no—
446#121—216no—
447#121—232no—
448#121—232no—
449#121—232no—
450#121—416no—
451#121—816no—
452#121—816no—
453#121C2×D4132yes—
454#120—232no—
455#120—232no—
456#120—232no—
457#120—416no—
458#120—816no—
459C4×Q8—216no—
460C4×Q8—28no—
461C4×Q8—28no—
462C4×Q8—48no—
463C4×D4—216no—
464C4×D4—232no—
465C4×D4—216no—
466C4×D4—216no—
467C4×D4—216no—
468C4×D4—232no—
469C4×D4—232no—
470C4×D4—28no—
471C4×D4—28no—
472C4×D4—48no—
473C4×D4—416no—
474C4×D4C2×D4132yes—
475#117—24no—
476#117—24no—
477#117—216no—
478#117—28no—
479#117—232no—
480#117—28no—
481#117—28no—
482#117—48no—
483C2×C4⋊C4—28no—
484C2×C4⋊C4—216no—
485C2×C4⋊C4—216no—
486C2×C4⋊C4C2412yes—
487C2×C4⋊C4C2414yes—
488C2×C4⋊C4C2418yes—
489C2×C4⋊C4C2414yes—
490C2×C4⋊C4C2418yes—
491C2×C4⋊C4C2418yes—
492C2×C4⋊C4C2412yes—
493C2×C4⋊C4C2414yes—
494C2×C4⋊C4C2414yes—
495C2×C4⋊C4C2414yes—
496C2×C4⋊C4C2418yes—
497C2×C4⋊C4C2414yes—
498C2×C4⋊C4C2418yes—
499C2×C4⋊C4C2418yes—
500C2×C4⋊C4C24116yes—
501C2×C4⋊C4C2418yes—
502C2×C4⋊C4C2414yes—
503C2×C22⋊C4—816no—
504C2×C22⋊C4—88no—
505C2×C22⋊C4—88no—
506C2×C22⋊C4C2412yes—
507C2×C22⋊C4C2412yes—
508C2×C22⋊C4C2414yes—
509C2×C22⋊C4C2414yes—
510C2×C22⋊C4C2414yes—
511C2×C22⋊C4C2418yes—
512C2×C22⋊C4C2418yes—
513C2×C22⋊C4C2418yes—
514C2×C22⋊C4C2418yes—
515C2×C22⋊C4C2418yes—
516C2×C22⋊C4C2414yes—
517C2×C22⋊C4C2414yes—
518C2×C22⋊C4C2418yes—
519C2×C22⋊C4C24116yes—
520C2×C22⋊C4C24116yes—
521C2×C22⋊C4C24116yes—
522C2×C22⋊C4C24116yes—
523C2×C22⋊C4C24116yes—
524C2×C22⋊C4C24116yes—
525C2×C22⋊C4C2418yes—
526C2×C22⋊C4C2418yes—
527C2×C22⋊C4C24116yes—
528C2×C22⋊C4C2418yes—
529C2×C22⋊C4C24116yes—
530C2×C22⋊C4C2418yes—
531C2×C22⋊C4C2414yes—
532C2×C22⋊C4C2414yes—
533C2×C42—24no—
534C2×C42—24no—
535C2×C42—28no—
536C2×C42—28no—
537C2×C42—48no—
538C2×C42C2×D418yes—
539C2×C42C2412yes—
540C2×C42C2418yes—
541C2×C42C2414yes—
542C2×C42C2412yes—
543C2×C42C2414yes—
544C2×C42C2412yes—
545C2×C42C2414yes—
546C2×C42C2412yes—
547C2×C42C2412yes—
548C2×C42C2411yescharacteristic
549C2×C42C2411yescharacteristic
550C2×C42C2418yes—
551C2×C42C2411yescharacteristic
552C2×C42C2411yescharacteristic
553C2×C42C2412yes—
554#95C2414yes—
555#95C2414yes—
556#95C2414yes—
557#95C2414yes—
558#95C2418yes—
559#95C24116yes—
560#95C2418yes—
561#95C2418yes—
562#95C2418yes—
563#95C2418yes—
564#95C2418yes—
565#95C24116yes—
566C24—216no—
567C24—28no—
568C24—216no—
569C24—28no—
570C24—28no—
571C24—48no—
572C24—48no—
573C24—48no—
574C24—416no—
575C24—416no—
576C24C2518yes—
577C24C2512yes—
578C24C2514yes—
579C24C2512yes—
580C24C2511yescharacteristic
581#41—264no—
582#41—232no—
583#41—464no—
584#41—464no—
585#41—416no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—24no—
589C2×Q8—22no—
590C2×Q8—24no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8C22×D418yes—
594C2×Q8C2×#4114yes—
595C2×D4—24no—
596C2×D4—28no—
597C2×D4—28no—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—216no—
601C2×D4—24no—
602C2×D4—216no—
603C2×D4—24no—
604C2×D4—216no—
605C2×D4—216no—
606C2×D4—216no—
607C2×D4—28no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—216no—
611C2×D4—216no—
612C2×D4—28no—
613C2×D4—28no—
614C2×D4—216no—
615C2×D4—24no—
616C2×D4—22no—
617C2×D4—216no—
618C2×D4—28no—
619C2×D4—28no—
620C2×D4—24no—
621C2×D4—22no—
622C2×D4—28no—
623C2×D4—28no—
624C2×D4—22no—
625C2×D4—464no—
626C2×D4—464no—
627C2×D4—48no—
628C2×D4—48no—
629C2×D4—48no—
630C2×D4—416no—
631C2×D4—48no—
632C2×D4—416no—
633C2×D4—416no—
634C2×D4—416no—
635C2×D4—416no—
636C2×D4—416no—
637C2×D4—416no—
638C2×D4—416no—
639C2×D4—4128no—
640C2×D4—432no—
641C2×D4—832no—
642C2×D4—864no—
643C2×D4C22×D4116yes—
644C2×D4C22×D418yes—
645C2×D4C22×D4116yes—
646C2×D4C2×#4118yes—
647C2×D4C2×#4114yes—
648C22×C4—24no—
649C22×C4—28no—
650C22×C4—28no—
651C22×C4—24no—
652C22×C4—28no—
653C22×C4—216no—
654C22×C4—24no—
655C22×C4—24no—
656C22×C4—24no—
657C22×C4—28no—
658C22×C4—216no—
659C22×C4—24no—
660C22×C4—216no—
661C22×C4—24no—
662C22×C4—28no—
663C22×C4—48no—
664C22×C4—44no—
665C22×C4—48no—
666C22×C4—48no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—48no—
670C22×C4—48no—
671C22×C4—416no—
672C22×C4—48no—
673C22×C4—48no—
674C22×C4C22×D4116yes—
675C22×C4C22×D418yes—
676C22×C4C22×D414yes—
677C22×C4C2×#4118yes—
678C22×C4C2×#4114yes—
679C22×C4H(5,𝔽2)14yes—
680C22×C4C2512yes—
681C22×C4C2514yes—
682C22×C4C2512yes—
683C22×C4C2518yes—
684C22×C4C2514yes—
685C22×C4C2514yes—
686C22×C4C2512yes—
687C22×C4C2518yes—
688C22×C4C2512yes—
689C22×C4C2514yes—
690C22×C4C2512yes—
691C22×C4C2512yes—
692C22×C4C2511yescharacteristic
693C22×C4C2511yescharacteristic
694C4⋊C4—24no—
695C4⋊C4—28no—
696C4⋊C4—216no—
697C4⋊C4—28no—
698C4⋊C4—216no—
699C4⋊C4—216no—
700C4⋊C4—28no—
701C4⋊C4—24no—
702C4⋊C4—28no—
703C4⋊C4—216no—
704C4⋊C4—28no—
705C4⋊C4—28no—
706C4⋊C4—48no—
707C4⋊C4—48no—
708C4⋊C4—416no—
709C4⋊C4—48no—
710C4⋊C4C22×D4116yes—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—216no—
714C22⋊C4—216no—
715C22⋊C4—28no—
716C22⋊C4—28no—
717C22⋊C4—28no—
718C22⋊C4—28no—
719C22⋊C4—216no—
720C22⋊C4—216no—
721C22⋊C4—216no—
722C22⋊C4—28no—
723C22⋊C4—48no—
724C22⋊C4—416no—
725C22⋊C4—416no—
726C22⋊C4—416no—
727C22⋊C4—416no—
728C22⋊C4—416no—
729C22⋊C4—416no—
730C22⋊C4—48no—
731C22⋊C4—416no—
732C22⋊C4—48no—
733C22⋊C4—48no—
734C22⋊C4—416no—
735C22⋊C4—48no—
736C22⋊C4C22×D4116yes—
737C22⋊C4C22×D4116yes—
738C42—24no—
739C42—28no—
740C42—24no—
741C42—28no—
742C42—216no—
743C42—24no—
744C42—22no—
745C42—22no—
746C42—24no—
747C42—24no—
748C42—28no—
749C42—48no—
750C42C22×D414yes—
751C42C22×D414yes—
752C42C22×D418yes—
753C23—24no—
754C23—22no—
755C23—24no—
756C23—24no—
757C23—22no—
758C23—28no—
759C23—28no—
760C23—28no—
761C23—22no—
762C23—28no—
763C23—22no—
764C23—28no—
765C23—28no—
766C23—22no—
767C23—216no—
768C23—216no—
769C23—28no—
770C23—432no—
771C23—416no—
772C23—88no—
773C23—88no—
774C23—816no—
775C23—816no—
776C23—816no—
777C23—816no—
778C23—832no—
779C23—1616no—
780C23C23×D418yes—
781C23C23×D412yes—
782C23C22×#4114yes—
783C23C22×#4112yes—
784C23C2×H(5,𝔽2)12yes—
785C23C2611yescharacteristic
786Q8—216no—
787Q8—28no—
788Q8—44no—
789D4—216no—
790D4—232no—
791D4—28no—
792D4—216no—
793D4—416no—
794D4—432no—
795D4—432no—
796D4—432no—
797D4—48no—
798D4—416no—
799D4—416no—
800D4—44no—
801D4—816no—
802D4—816no—
803D4—88no—
804D4—816no—
805D4—816no—
806D4—1616no—
807C2×C4—22no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—232no—
814C2×C4—216no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—22no—
818C2×C4—28no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—28no—
824C2×C4—22no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—28no—
830C2×C4—216no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—48no—
835C2×C4—432no—
836C2×C4—416no—
837C2×C4—48no—
838C2×C4—88no—
839C2×C4—816no—
840C2×C4—88no—
841C2×C4—84no—
842C2×C4—84no—
843C2×C4—816no—
844C2×C4#546116yes—
845C2×C4C23×D414yes—
846C2×C4C23×D414yes—
847C2×C4C23×D418yes—
848C2×C4C23×D412yes—
849C2×C4C23×D412yes—
850C2×C4C22×#4114yes—
851C2×C4C22×#4112yes—
852C2×C4C22×#4112yes—
853C2×C4C2×H(5,𝔽2)12yes—
854C2×C4C2×H(5,𝔽2)12yes—
855C22—24no—
856C22—24no—
857C22—24no—
858C22—28no—
859C22—28no—
860C22—28no—
861C22—24no—
862C22—28no—
863C22—44no—
864C22—48no—
865C22—48no—
866C22—44no—
867C22—44no—
868C22—48no—
869C22—48no—
870C22—44no—
871C22—416no—
872C22—44no—
873C22—416no—
874C22—48no—
875C22—42no—
876C22—1616no—
877C22—1632no—
878C22C2×#54614yes—
879C22C24×D411yescharacteristic
880C22C23×#4111yescharacteristic
881C22C22×H(5,𝔽2)11yescharacteristic
882C22H(7,𝔽2)14yes—
883C4—24no—
884C4—24no—
885C4—24no—
886C4—28no—
887C4—44no—
888C4—44no—
889C4—48no—
890C4—42no—
891C4—42no—
892C4—44no—
893C4—48no—
894C4—42no—
895C4C2×#54614yes—
896C4C2×#54614yes—
897C2—24no—
898C2—48no—
899C2—44no—
900C2—82no—
901C2—88no—
902C2C22×#54611yescharacteristic
903C2#6285212yes—
904C2#6285812yes—
905C2#6288012yes—
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×#3512C2semidirect
2. C2×#3498C2semidirect
3. #43102C2semidirect
4. #38093C2semidirect
5. #38089C2semidirect
6. #38084C2semidirect
7. #38080C2semidirect
8. #37751C2semidirect
9. #37701C2semidirect
10. #37694C2semidirect
11. #35531C2semidirect
12. #35513C2semidirect
13. #35333C2semidirect
14. #35272C2semidirect
15. #35256C2semidirect
16. C2×#2641C2semidirect
17. #34258C2semidirect
18. #34070C2semidirect
19. #34070C2semidirect
23. C2×#553C22semidirect
24. C2×#553C22semidirect
25. C2×#552C22semidirect
29. C2×#541C22semidirect
30. C2×#540C22semidirect
31. C2×#537C22semidirect
34. C2×#535C22semidirect
40. C2×#529C22semidirect
41. C22×#125C22semidirect
42. C2×#520C22semidirect
44. C2×C4×#41C22semidirect
45. C2×C4×#41C22semidirect
46. #2856C22semidirect
47. #2856C22semidirect
48. #2851C22semidirect
49. #2850C22semidirect
50. #2714C22semidirect
51. #2711C22semidirect
52. #2709C22semidirect
53. #2691C22semidirect
54. #2685C22semidirect
55. #2678C22semidirect
56. #2673C22semidirect
57. #2671C22semidirect
58. #2641C22semidirect
59. #2641C22semidirect
60. #2641C22semidirect
61. #2641C22semidirect
62. #2629C22semidirect
63. #2620C22semidirect
64. #2619C22semidirect
65. #2619C22semidirect
66. #2579C22semidirect
67. #2566C22semidirect
68. #2565C22semidirect
69. #2548C22semidirect
70. #2541C22semidirect
71. #2504C22semidirect
72. #2501C22semidirect
73. #2500C22semidirect
74. #2500C22semidirect
75. #2476C22semidirect
76. #2467C22semidirect
77. #2464C22semidirect
78. #2460C22semidirect
79. #2448C22semidirect
80. #2445C22semidirect
81. #2435C22semidirect
82. #2433C22semidirect
83. #2432C22semidirect
84. #2431C22semidirect
85. #2428C22semidirect
86. #2426C22semidirect
87. #2424C22semidirect
88. #2424C22semidirect
89. #2418C22semidirect
90. #2411C22semidirect
91. #2410C22semidirect
92. #2410C22semidirect
93. #2408C22semidirect
94. #2408C22semidirect
95. #2407C22semidirect
96. #2405C22semidirect
97. C2×#394C22semidirect
98. #2341C22semidirect
99. D4×C22⋊C4C22semidirect
100. D4×C22⋊C4C22semidirect
101. #2328C22semidirect
102. #2328C22semidirect
103. #2327C22semidirect
104. #2327C22semidirect
105. #2326C22semidirect
106. #2326C22semidirect
107. #2326C22semidirect
108. #2325C22semidirect
109. #2325C22semidirect
110. #2317C22semidirect
112. #2311C22semidirect
113. #2309C22semidirect
114. #2309C22semidirect
116. #2297C22semidirect
117. #2297C22semidirect
118. #2297C22semidirect
119. C2×#390C22semidirect
120. C2×#390C22semidirect
121. C2×#390C22semidirect
122. #2290C22semidirect
123. #2290C22semidirect
124. #2290C22semidirect
125. #2290C22semidirect
126. #2285C22semidirect
127. #2285C22semidirect
128. C2×#376C22semidirect
157. #532D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35122
C2×#34982
#431022
#380932
#380892
#380842
#380802
#377512
#377012
#376942
#355312
#355132
#353332
#352722
#352562
C2×#26412
#342582
#340702