Finite Group Databasebeta

← #7563473

Subgroups — #7563473

Order 512.

1790 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3381C211yesmaximal, characteristic, complemented
2C2×#3160C211yesmaximal, characteristic, complemented
3#59067C211yesmaximal, characteristic, complemented
4#59052C211yesmaximal, characteristic
5#30960C212yesmaximal, complemented
6#30951C212yesmaximal, complemented
7#28811C212yesmaximal, complemented
8#28677C211yesmaximal, characteristic, complemented
9#28530C211yesmaximal, characteristic, complemented
10#26481C212yesmaximal, complemented
11#26351C212yesmaximal, complemented
12#26345C212yesmaximal
13#26063C212yesmaximal, complemented
14#25840C211yesmaximal, characteristic, complemented
15#25839C211yesmaximal, characteristic, complemented
16#25455C211yesmaximal, characteristic, complemented
17#25449C211yesmaximal, characteristic, complemented
18#24303C211yesmaximal, characteristic, complemented
19#24300C211yesmaximal, characteristic
20#23156C211yesmaximal, characteristic, complemented
21#23023C212yesmaximal
22C8×C22⋊Q8C211yesmaximal, characteristic, complemented
23C4×#465C211yesmaximal, characteristic
24C2×#557C2211yescharacteristic
25C2×#554C2211yescharacteristic
26C2×#533C2211yescharacteristic
27C2×#533C2211yescharacteristic
28#3381—28no—
29#3160—28no—
30C2×#500C2211yescharacteristic
31C2×#500C2211yescharacteristic
32C2×#499C2212yes—
33C2×#499C2212yes—
34C2×#499C2212yes—
35C2×#498C2211yescharacteristic
36C2×#498C2211yescharacteristic
37C2×#479C2212yes—
38C2×#477C2211yescharacteristic
39C2×#475C2211yescharacteristic
40C2×#478C2212yes—
41C2×#476C2211yescharacteristic
42C2×#474C2211yescharacteristic
43C2×#465C2211yescharacteristic
44C2×C8×Q8C2211yescharacteristic
45C2×C4×SD16C2211yescharacteristic
46C2×C4×SD16C2212yes—
47C2×#427C2212yes—
48C2×#427C2212yes—
49C22×C4×C8C2211yescharacteristic
50#2732—22no—
51#2720—22no—
52#2567C2211yescharacteristic
53#2567C2211yescharacteristic
54#2552C2212yes—
55#2552C2212yes—
56#2546C2211yescharacteristic
57#2542—21no—
58#2542C2211yescharacteristic
59#2462—22no—
60#2454C2212yes—
61#2453C2212yes—
62#2446—21no—
63#2441C2212yes—
64#2441C2212yes—
65#2429—21no—
66#2429—21no—
67#2423—22no—
68#2423—21no—
69#2417—21no—
70#2369C2211yescharacteristic
71#2365C2211yescharacteristic
72#2363C2212yes—
73#2362C2212yes—
74#2360—21no—
75Q8×C4⋊C4—21no—
76C4×C22⋊Q8C2211yescharacteristic
77C4×C22⋊Q8C2211yescharacteristic
78C4×#121C2211yescharacteristic
79#2096C2212yes—
80#2094C2212yes—
81#2088C2212yes—
82#2088C2212yes—
83#2083C2212yes—
84#2083C2212yes—
85#2068C2212yes—
86#2067C2212yes—
87#2059C2212yes—
88#2059C2212yes—
89#2059C2212yes—
90#2059C2212yes—
91#2059C2212yes—
92#2059C2212yes—
93#2026C2212yes—
94#2025C2212yes—
95#1988C2211yescharacteristic
96#1988C2211yescharacteristic
97#1987C2211yescharacteristic
98#1987C2211yescharacteristic
99#1984C2211yescharacteristic
100#1968C2211yescharacteristic
101#1968C2212yes—
102#1947C2212yes—
103#1947C2212yes—
104#1941C2212yes—
105#1941C2212yes—
106#1941C2211yescharacteristic
107#1941C2212yes—
108#1939C2211yescharacteristic
109#1934C2211yescharacteristic
110#1933C2211yescharacteristic
111#1928C2212yes—
112#1925C2212yes—
113#1920C2212yes—
114#1919C2212yes—
115#1916C2212yes—
116#1893C2211yescharacteristic
117#1892C2211yescharacteristic
118#1875C2212yes—
119#1873C2212yes—
120#1863C2212yes—
121#1863C2212yes—
122#1862C2212yes—
123#1862C2212yes—
124#1854C2212yes—
125#1854C2212yes—
126#1850C2212yes—
127#1844C2212yes—
128#1807C2211yescharacteristic
129#1797C2211yescharacteristic
130C4×#106C2211yescharacteristic
131C4×#106C2212yes—
132C8×C4⋊C4C2212yes—
133C8×C4⋊C4C2211yescharacteristic
134C4×#103C2211yescharacteristic
135C4×#102C2211yescharacteristic
136C8×C22⋊C4C2212yes—
137C22×SD16C2311yescharacteristic
138C23×C8C2311yescharacteristic
139C23×C8C2311yescharacteristic
140#557—24no—
141#557—42no—
142#554—24no—
143#554—42no—
144#533—24no—
145#533—24no—
146#533—42no—
147#533—42no—
148C2×C4⋊Q8—21no—
149C2×C4⋊Q8—21no—
150C2×C4⋊Q8C2311yescharacteristic
151C2×C4⋊Q8C2311yescharacteristic
152C2×C4⋊Q8C2311yescharacteristic
153C2×C4⋊Q8C2311yescharacteristic
154C2×#125—22no—
155C2×#125C2312yes—
156C2×#125C2312yes—
157C2×#125C2312yes—
158C2×#125C2312yes—
159C2×C22⋊Q8—21no—
160C2×C22⋊Q8—21no—
161C2×C22⋊Q8—21no—
162C2×C22⋊Q8—21no—
163C2×C22⋊Q8—21no—
164C2×C22⋊Q8—21no—
165C2×C22⋊Q8—22no—
166C2×C22⋊Q8—21no—
167C2×C22⋊Q8D411yescharacteristic
168C2×C22⋊Q8C2311yescharacteristic
169C2×#121C2311yescharacteristic
170C2×C4×Q8—21no—
171C2×C4×Q8—21no—
172C2×C4×Q8—21no—
173C2×C4×Q8—21no—
174C2×C4×Q8—21no—
175C2×C4×Q8—21no—
176C2×C4×Q8C2311yescharacteristic
177C2×C4×Q8C2312yes—
178C2×C4×Q8C2311yescharacteristic
179C2×C4×D4—21no—
180C2×C4×D4C2311yescharacteristic
181C2×C4×D4C2312yes—
182C2×#117C2312yes—
183C2×#117C2312yes—
184C22×C4⋊C4—21no—
185C22×C42C2311yescharacteristic
186#500—24no—
187#500—24no—
188#499—28no—
189#499—28no—
190#499—28no—
191#498—24no—
192#498D418yescomplemented
193#479—28no—
194#478—28no—
195#477—24no—
196#476—42no—
197#475—42no—
198#474—24no—
199#465Q818yescomplemented
200C8×Q8—24no—
201C4×SD16—28no—
202C4×SD16—24no—
203#427—28no—
204#427—28no—
205C2×#107C2312yes—
206C2×#107C2312yes—
207C2×#107C2312yes—
208C2×#107C2312yes—
209C2×#107C2312yes—
210C2×#107C2312yes—
211C2×#106C2311yescharacteristic
212C2×#106C2311yescharacteristic
213C2×#106C2312yes—
214C2×#106C2312yes—
215C2×#106C2312yes—
216C2×#106C2312yes—
217C2×#106C2312yes—
218C2×#106C2312yes—
219C2×#106C2311yescharacteristic
220C2×C4⋊C8C2312yes—
221C2×C4⋊C8C2311yescharacteristic
222C2×C4⋊C8C2311yescharacteristic
223C2×C4⋊C8C2312yes—
224C2×#103C2312yes—
225C2×#103C2311yescharacteristic
226C2×#103C2311yescharacteristic
227C2×#103C2312yes—
228C2×#103C2311yescharacteristic
229C2×#102C2311yescharacteristic
230C2×#102C2312yes—
231C2×#102C2311yescharacteristic
232C2×#102C2312yes—
233C2×#102C2311yescharacteristic
234C2×C22⋊C8C2312yes—
235C2×C4×C8—24no—
236C2×C4×C8C2312yes—
237C2×C4×C8C2311yescharacteristic
238C2×C4×C8C2311yescharacteristic
239C2×C4×C8C2311yescharacteristic
240C2×C4×C8C2312yes—
241C2×C4×C8C2311yescharacteristic
242#400—22no—
243#399—22no—
244#399—22no—
245#399—22no—
246#399—22no—
247#398—22no—
248#398—22no—
249#398—22no—
250#398—22no—
251#398—22no—
252#398—22no—
253#396—22no—
254#396—22no—
255#396—22no—
256#395—22no—
257#395—22no—
258#391—21no—
259#391—21no—
260#391—21no—
261#391—22no—
262#391D411yescharacteristic
263#391C2312yes—
264#391C2311yescharacteristic
265#390—22no—
266#390C2312yes—
267#390C2311yescharacteristic
268#389—21no—
269#389—21no—
270#389—22no—
271#389—22no—
272#389—21no—
273#389—22no—
274#389—22no—
275#389—22no—
276#389D411yescharacteristic
277#389C2312yes—
278#389C2312yes—
279#389C2311yescharacteristic
280#389C2311yescharacteristic
281#389C2312yes—
282#389C2312yes—
283#389C2312yes—
284#389C2312yes—
285#388—22no—
286#388—22no—
287#388—21no—
288#388—22no—
289#387—21no—
290#387—22no—
291#387—22no—
292#387—22no—
293#387—22no—
294#387—22no—
295#387D412yes—
296#386—21no—
297#386—22no—
298#385—21no—
299#385—22no—
300#385D412yes—
301#384—21no—
302#384—22no—
303#384—22no—
304#384C2312yes—
305#384C2312yes—
306#380—22no—
307#380D411yescharacteristic
308#380C2311yescharacteristic
309#380C2311yescharacteristic
310C4×C4⋊C4—21no—
311C4×C4⋊C4—21no—
312C4×C4⋊C4—22no—
313C4×C4⋊C4C2311yescharacteristic
314C4×C4⋊C4C2312yes—
315C4×C4⋊C4C2312yes—
316C4×C4⋊C4C2311yescharacteristic
317C4×C4⋊C4C2311yescharacteristic
318C4×C4⋊C4C2312yes—
319C4×C22⋊C4—21no—
320C4×C22⋊C4—21no—
321C4×C22⋊C4—22no—
322C4×C22⋊C4C2312yes—
323#340C2311yescharacteristic
324#340C2311yescharacteristic
325#340C2312yes—
326#340C2312yes—
327#340C2311yescharacteristic
328#340C2311yescharacteristic
329#340C2312yes—
330#340C2312yes—
331#340C2312yes—
332#340C2312yes—
333#340C2312yes—
334#340C2312yes—
335#340C2311yescharacteristic
336#340C2311yescharacteristic
337#336C2312yes—
338#336C2312yes—
339#336C2312yes—
340#336C2312yes—
341#336C2312yes—
342C22×Q8—21no—
343C22×Q8—21no—
344C22×Q8—21no—
345C22×Q8—21no—
346C22×Q8C2×D411yescharacteristic
347C22×Q8C2411yescharacteristic
348C22×D4—21no—
349C22×D4C2411yescharacteristic
350C23×C4—21no—
351C23×C4—22no—
352C23×C4C2×D411yescharacteristic
353C23×C4C2×D411yescharacteristic
354C23×C4C2411yescharacteristic
355C2×SD16—22no—
356C2×SD16—22no—
357C2×SD16C2×Q814yes—
358C22×C8—22no—
359C22×C8—22no—
360C22×C8—22no—
361C22×C8—22no—
362C22×C8—22no—
363C22×C8C2×Q814yes—
364C22×C8C2412yes—
365C22×C8C2412yes—
366C22×C8C2411yescharacteristic
367C22×C8C2411yescharacteristic
368C22×C8C2411yescharacteristic
369C22×C8C2411yescharacteristic
370C4⋊Q8—22no—
371C4⋊Q8—22no—
372C4⋊Q8—22no—
373C4⋊Q8—22no—
374C4⋊Q8—22no—
375C4⋊Q8—22no—
376C4⋊Q8—44no—
377C4⋊Q8—82no—
378C4⋊Q8C2×D414yes—
379C4⋊Q8C2×D414yes—
380#125—24no—
381#125—24no—
382#125—24no—
383#125—24no—
384#125—42no—
385#125—42no—
386#125—42no—
387#125—42no—
388#125—48no—
389C22⋊Q8—22no—
390C22⋊Q8—24no—
391C22⋊Q8—44no—
392C22⋊Q8—44no—
393C22⋊Q8—44no—
394C22⋊Q8—48no—
395C22⋊Q8—44no—
396C22⋊Q8—44no—
397C22⋊Q8—44no—
398C22⋊Q8—82no—
399C22⋊Q8C2×Q814yes—
400#121—22no—
401#121C2×Q814yes—
402C4×Q8—22no—
403C4×Q8—22no—
404C4×Q8—24no—
405C4×Q8—22no—
406C4×Q8—22no—
407C4×Q8—42no—
408C4×Q8—44no—
409C4×Q8—44no—
410C4×Q8—44no—
411C4×Q8—44no—
412C4×Q8—44no—
413C4×Q8—44no—
414C4×D4—24no—
415C4×D4—22no—
416C4×D4—22no—
417C4×D4—42no—
418C4×D4—82no—
419#117—24no—
420#117—24no—
421#117—42no—
422#117—42no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—44no—
451C2×C4⋊C4C2×D411yescharacteristic
452C2×C4⋊C4C2×D412yes—
453C2×C4⋊C4C2×D411yescharacteristic
454C2×C4⋊C4C2×D412yes—
455C2×C4⋊C4C2×D412yes—
456C2×C4⋊C4C2×D411yescharacteristic
457C2×C4⋊C4C2412yes—
458C2×C4⋊C4C2412yes—
459C2×C4⋊C4C2411yescharacteristic
460C2×C4⋊C4C2411yescharacteristic
461C2×C4⋊C4C2411yescharacteristic
462C2×C4⋊C4C2411yescharacteristic
463C2×C4⋊C4C2412yes—
464C2×C4⋊C4C2412yes—
465C2×C4⋊C4C2411yescharacteristic
466C2×C4⋊C4C2411yescharacteristic
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4C2×D412yes—
480C2×C22⋊C4C2×D412yes—
481C2×C42—22no—
482C2×C42—22no—
483C2×C42—22no—
484C2×C42—22no—
485C2×C42—21no—
486C2×C42—22no—
487C2×C42—21no—
488C2×C42—21no—
489C2×C42—22no—
490C2×C42—22no—
491C2×C42C2×D411yescharacteristic
492C2×C42C2×D411yescharacteristic
493C2×C42C2412yes—
494C2×C42C2411yescharacteristic
495C2×C42C2412yes—
496C2×C42C2411yescharacteristic
497#107—24no—
498#107—24no—
499#107—24no—
500#107—24no—
501#107—24no—
502#107—24no—
503#106—24no—
504#106—24no—
505#106—22no—
506#106—22no—
507#106—42no—
508#106—42no—
509#106C2×D418yes—
510#106C2×D418yes—
511#106C2×Q814yes—
512C4⋊C8—24no—
513C4⋊C8—24no—
514C4⋊C8—22no—
515C4⋊C8—22no—
516#103—22no—
517#103—22no—
518#103—24no—
519#103—42no—
520#103C2×Q814yes—
521#102—22no—
522#102—22no—
523#102—24no—
524#102—42no—
525#102C2×Q814yes—
526C22⋊C8—24no—
527C4×C8—22no—
528C4×C8—22no—
529C4×C8—24no—
530C4×C8—24no—
531C4×C8—22no—
532C4×C8C2×D414yes—
533#95—21no—
534#95—21no—
535#95—22no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—22no—
540#95—21no—
541#95—22no—
542#95—21no—
543#95—22no—
544#95—21no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95C2×D412yes—
552#95C2×D412yes—
553#95C2×D412yes—
554#95C2×D412yes—
555#95C2×D412yes—
556C24—21no—
557C24C22×D411yescharacteristic
558C2×Q8—22no—
559C2×Q8—24no—
560C2×Q8—24no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—42no—
569C2×Q8—42no—
570C2×Q8—42no—
571C2×Q8—42no—
572C2×Q8—42no—
573C2×Q8—42no—
574C2×Q8—81no—
575C2×Q8—81no—
576C2×Q8—81no—
577C2×Q8—81no—
578C2×Q8C22×Q812yes—
579C2×D4—24no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4C22×Q812yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—44no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—82no—
614C22×C4—82no—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D412yes—
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D412yes—
623C22×C4C22×D411yescharacteristic
624C22×C4C22×Q812yes—
625C22×C42−1+412yes—
626C22×C4C2511yescharacteristic
627SD16—28no—
628C2×C8—28no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—28no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8C22×D412yes—
643C2×C8C22×D412yes—
644C2×C8C22×Q812yes—
645C2×C8C22×Q812yes—
646C2×C82−1+412yes—
647C2×C82−1+412yes—
648C4⋊C4—24no—
649C4⋊C4—24no—
650C4⋊C4—22no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—42no—
672C4⋊C4—44no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4—44no—
685C4⋊C4—44no—
686C4⋊C4—82no—
687C4⋊C4—82no—
688C4⋊C4—82no—
689C4⋊C4—82no—
690C4⋊C4—81no—
691C4⋊C4—82no—
692C4⋊C4—81no—
693C4⋊C4—82no—
694C4⋊C4—82no—
695C4⋊C4—82no—
696C4⋊C4#13514yes—
697C4⋊C4C22×D414yes—
698C4⋊C4C22×D414yes—
699C4⋊C4C22×Q812yes—
700C4⋊C4C22×Q812yes—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—42no—
705C22⋊C4—44no—
706C22⋊C4—44no—
707C22⋊C4—44no—
708C22⋊C4—42no—
709C22⋊C4—44no—
710C22⋊C4—81no—
711C22⋊C4—81no—
712C22⋊C4—82no—
713C22⋊C4—81no—
714C22⋊C4—81no—
715C42—22no—
716C42—22no—
717C42—21no—
718C42—22no—
719C42—21no—
720C42—22no—
721C42—22no—
722C42—22no—
723C42—44no—
724C42—44no—
725C42—44no—
726C42—42no—
727C42—44no—
728C42—42no—
729C42—42no—
730C42—82no—
731C42C22×D412yes—
732C42H(5,𝔽2)12yes—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—22no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23D4×Q812yes—
747C23C23×D411yescharacteristic
748Q8—22no—
749Q8—22no—
750Q8—41no—
751Q8—44no—
752Q8—48no—
753Q8—41no—
754Q8—84no—
755Q8—84no—
756Q8—84no—
757D4—22no—
758D4—22no—
759D4—41no—
760D4—41no—
761D4—84no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—21no—
789C2×C4—22no—
790C2×C4—21no—
791C2×C4—22no—
792C2×C4—44no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—84no—
823C2×C4—164no—
824C2×C4D4212yes—
825C2×C4D4212yes—
826C2×C4D4×Q812yes—
827C2×C4C2×#13514yes—
828C2×C4C2×#13512yes—
829C2×C4#57712yes—
830C2×C4C23×D411yescharacteristic
831C2×C4C23×Q811yescharacteristic
832C2×C4C2×H(5,𝔽2)11yescharacteristic
833C2×C4C2×2−1+411yescharacteristic
834C2×C4C2×2−1+411yescharacteristic
835C2×C4C2×2−1+411yescharacteristic
836C8—22no—
837C8—22no—
838C8—22no—
839C8—42no—
840C8—42no—
841C8D4×Q814yes—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22C2×D4211yescharacteristic
857C22C2×D4×Q811yescharacteristic
858C22#349911yescharacteristic
859C22C22×#13511yescharacteristic
860C22C2×#57711yescharacteristic
861C22#358411yescharacteristic
862C22#358411yescharacteristic
863C4—24no—
864C4—22no—
865C4—22no—
866C4—42no—
867C4—41no—
868C4—42no—
869C4—44no—
870C4—41no—
871C4—42no—
872C4—44no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—81no—
877C4—81no—
878C4—81no—
879C4—82no—
880C4—81no—
881C4—82no—
882C4#328414yes—
883C4C2×D4×Q811yescharacteristic
884C4#348611yescharacteristic
885C4#350311yescharacteristic
886C4#355211yescharacteristic
887C2—42no—
888C2—82no—
889C2#5912711yescharacteristic
890C2C2×#328411yescharacteristic
891C2#6105211yescharacteristic
892C2Q8×#13511yescharacteristic
893C2#6137111yescharacteristic
894C2#6247511yescharacteristic
895C2#6249411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3381C2semidirect
2. C2×#3160C2semidirect
3. #59067C2semidirect
5. #30960C2semidirect
6. #30951C2semidirect
7. #28811C2semidirect
8. #28677C2semidirect
9. #28530C2semidirect
10. #26481C2semidirect
11. #26351C2semidirect
13. #26063C2semidirect
14. #25840C2semidirect
15. #25839C2semidirect
16. #25455C2semidirect
17. #25449C2semidirect
18. #24303C2semidirect
20. #23156C2semidirect
22. C8×C22⋊Q8C2semidirect
192. #498D4semidirect
199. #465Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#33812
C2×#31602
#590672
#590522
#309602
#309512
#288112
#286772
#285302
#264812
#263512
#263452
#260632
#258402
#258392
#254552
#254492
#243032
#243002
#231562
#230232
C8×C22⋊Q82
C4×#4652