Finite Group Databasebeta

← #7563486

Subgroups — #7563486

Order 512.

1810 conjugacy classes of subgroups.

The subgroup lattice has 899 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3386C211yesmaximal, characteristic, complemented
2C2×#3160C211yesmaximal, characteristic, complemented
3#59067C211yesmaximal, characteristic, complemented
4#59036C211yesmaximal, characteristic
5#30961C212yesmaximal, complemented
6#30959C212yesmaximal, complemented
7#28822C212yesmaximal, complemented
8#28682C211yesmaximal, characteristic, complemented
9#28539C211yesmaximal, characteristic, complemented
10#26494C212yesmaximal, complemented
11#26347C212yesmaximal
12#26339C212yesmaximal, complemented
13#26070C212yesmaximal, complemented
14#25836C211yesmaximal, characteristic, complemented
15#25834C211yesmaximal, characteristic, complemented
16#25453C211yesmaximal, characteristic, complemented
17#25452C211yesmaximal, characteristic, complemented
18#24303C211yesmaximal, characteristic, complemented
19#24300C211yesmaximal, characteristic
20#23161C211yesmaximal, characteristic, complemented
21#23033C212yesmaximal
22#21597C211yesmaximal, characteristic, complemented
23C4×#465C211yesmaximal, characteristic
24C2×#557C2211yescharacteristic
25C2×D4×Q8C2211yescharacteristic
26C2×#533C2211yescharacteristic
27C2×#533C2211yescharacteristic
28#3386—28no—
29C2×#501C2212yes—
30#3160—28no—
31C2×#500C2211yescharacteristic
32C2×#500C2211yescharacteristic
33C2×#499C2212yes—
34C2×#499C2212yes—
35C2×#498C2211yescharacteristic
36C2×#498C2211yescharacteristic
37C2×#477C2212yes—
38C2×#477C2211yescharacteristic
39C2×#475C2211yescharacteristic
40C2×#478C2212yes—
41C2×#476C2211yescharacteristic
42C2×#474C2211yescharacteristic
43C2×#465C2211yescharacteristic
44C2×#446C2211yescharacteristic
45C2×#440C2212yes—
46C2×C4×SD16C2211yescharacteristic
47C2×#427C2212yes—
48C2×#427C2212yes—
49C22×C4×C8C2211yescharacteristic
50#2720—22no—
51#2692—22no—
52#2567C2211yescharacteristic
53#2567C2211yescharacteristic
54#2567C2211yescharacteristic
55#2563C2211yescharacteristic
56#2552C2212yes—
57#2550C2212yes—
58#2538—21no—
59#2465—22no—
60#2462—22no—
61#2454C2212yes—
62#2453C2212yes—
63#2446—21no—
64#2441C2212yes—
65#2439C2212yes—
66#2429—21no—
67#2423—21no—
68#2423—21no—
69#2409—21no—
70#2365C2211yescharacteristic
71#2365C2211yescharacteristic
72#2363C2212yes—
73#2362C2212yes—
74Q8×C4⋊C4—21no—
75Q8×C22⋊C4—21no—
76C4×C22⋊Q8C2211yescharacteristic
77C4×C22⋊Q8C2211yescharacteristic
78C4×#121C2211yescharacteristic
79#2097C2212yes—
80#2093C2212yes—
81#2086C2212yes—
82#2086C2212yes—
83#2085C2212yes—
84#2084C2212yes—
85#2066C2212yes—
86#2065C2212yes—
87#2059C2212yes—
88#2059C2212yes—
89#2059C2212yes—
90#2059C2212yes—
91#2058C2212yes—
92#2058C2212yes—
93#2026C2212yes—
94#2025C2212yes—
95#1988C2211yescharacteristic
96#1988C2211yescharacteristic
97#1987C2211yescharacteristic
98#1987C2211yescharacteristic
99#1984C2211yescharacteristic
100#1973C2212yes—
101#1968C2211yescharacteristic
102#1949C2212yes—
103#1948C2212yes—
104#1944C2212yes—
105#1944C2212yes—
106#1943C2212yes—
107#1941C2211yescharacteristic
108#1939C2211yescharacteristic
109#1934C2211yescharacteristic
110#1933C2211yescharacteristic
111#1927C2212yes—
112#1926C2212yes—
113#1921C2212yes—
114#1921C2212yes—
115#1916C2212yes—
116#1893C2211yescharacteristic
117#1892C2211yescharacteristic
118#1875C2212yes—
119#1873C2212yes—
120#1865C2212yes—
121#1865C2212yes—
122#1864C2212yes—
123#1864C2212yes—
124#1854C2212yes—
125#1854C2212yes—
126#1850C2212yes—
127#1847C2212yes—
128#1807C2211yescharacteristic
129#1797C2211yescharacteristic
130#1776C2212yes—
131C4×#106C2211yescharacteristic
132#1771C2212yes—
133#1770C2211yescharacteristic
134C4×#103C2211yescharacteristic
135C4×#102C2211yescharacteristic
136#1752C2212yes—
137C23×Q8—21no—
138C22×SD16C2311yescharacteristic
139C23×C8C2311yescharacteristic
140C23×C8C2311yescharacteristic
141#557—24no—
142#557—42no—
143D4×Q8—24no—
144D4×Q8—42no—
145#533—24no—
146#533—24no—
147#533—42no—
148#533—42no—
149C2×C4⋊Q8—21no—
150C2×C4⋊Q8C2311yescharacteristic
151C2×C4⋊Q8C2311yescharacteristic
152C2×C4⋊Q8C2312yes—
153C2×C4⋊Q8C2311yescharacteristic
154C2×C4⋊Q8C2311yescharacteristic
155C2×#125—22no—
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—22no—
165C2×C22⋊Q8D411yescharacteristic
166C2×C22⋊Q8C2311yescharacteristic
167C2×#121C2311yescharacteristic
168C2×C4×Q8—21no—
169C2×C4×Q8—21no—
170C2×C4×Q8—21no—
171C2×C4×Q8—21no—
172C2×C4×Q8—21no—
173C2×C4×Q8—21no—
174C2×C4×Q8—21no—
175C2×C4×Q8C2311yescharacteristic
176C2×C4×Q8C2312yes—
177C2×C4×Q8C2311yescharacteristic
178C2×C4×D4—21no—
179C2×C4×D4C2311yescharacteristic
180C2×C4×D4C2312yes—
181C2×#117C2312yes—
182C2×#117C2312yes—
183C22×C42C2311yescharacteristic
184#501—28no—
185#500—24no—
186#500D418yescomplemented
187#499—28no—
188#499—28no—
189#498—24no—
190#498—24no—
191#478—28no—
192#477—28no—
193#477—42no—
194#476—42no—
195#475—24no—
196#474—24no—
197#465Q818yescomplemented
198#446—24no—
199#440—28no—
200C4×SD16—24no—
201#427—28no—
202#427—28no—
203C2×#107C2312yes—
204C2×#107C2312yes—
205C2×#107C2312yes—
206C2×#107C2312yes—
207C2×#107C2312yes—
208C2×#107C2312yes—
209C2×#106C2312yes—
210C2×#106C2312yes—
211C2×#106C2312yes—
212C2×#106C2312yes—
213C2×#106C2312yes—
214C2×#106C2311yescharacteristic
215C2×#106C2311yescharacteristic
216C2×#106C2312yes—
217C2×#106C2311yescharacteristic
218C2×C4⋊C8C2312yes—
219C2×C4⋊C8C2311yescharacteristic
220C2×C4⋊C8C2311yescharacteristic
221C2×C4⋊C8C2312yes—
222C2×#103C2312yes—
223C2×#103C2311yescharacteristic
224C2×#103C2311yescharacteristic
225C2×#103C2312yes—
226C2×#103C2311yescharacteristic
227C2×#102C2311yescharacteristic
228C2×#102C2312yes—
229C2×#102C2311yescharacteristic
230C2×#102C2312yes—
231C2×#102C2311yescharacteristic
232C2×C22⋊C8C2312yes—
233C2×#97C2312yes—
234C2×#97C2312yes—
235C2×C4×C8—24no—
236C2×C4×C8C2311yescharacteristic
237C2×C4×C8C2311yescharacteristic
238C2×C4×C8C2311yescharacteristic
239C2×C4×C8C2311yescharacteristic
240#400—22no—
241#399—22no—
242#399—22no—
243#398—22no—
244#398—22no—
245#398—22no—
246#398—22no—
247#396—22no—
248#396—22no—
249#396—22no—
250#395—22no—
251#395—22no—
252#395—22no—
253#395—22no—
254#393—22no—
255#393—22no—
256#391—21no—
257#391—21no—
258#391—21no—
259#391—21no—
260#391—22no—
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—22no—
273#389—22no—
274#389D411yescharacteristic
275#389C2312yes—
276#389C2312yes—
277#389C2312yes—
278#389C2312yes—
279#389C2311yescharacteristic
280#389C2311yescharacteristic
281#389C2312yes—
282#389C2312yes—
283#388—22no—
284#388—22no—
285#388—21no—
286#388—22no—
287#387—21no—
288#387—22no—
289#387—22no—
290#387—22no—
291#387—22no—
292#387—22no—
293#387—22no—
294#387D412yes—
295#386—21no—
296#386—22no—
297#385—21no—
298#385—22no—
299#385D412yes—
300#384—21no—
301#384—21no—
302#384—22no—
303#384C2312yes—
304#382C2312yes—
305#380—21no—
306#380—21no—
307#380—22no—
308#380D411yescharacteristic
309#380C2311yescharacteristic
310#380C2311yescharacteristic
311C4×C4⋊C4—21no—
312C4×C4⋊C4—22no—
313C4×C4⋊C4C2311yescharacteristic
314C4×C4⋊C4C2311yescharacteristic
315C4×C4⋊C4C2312yes—
316C4×C4⋊C4C2312yes—
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#340C2312yes—
329#340C2311yescharacteristic
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—22no—
345C22×Q8—21no—
346C22×Q8—21no—
347C22×Q8—44no—
348C22×Q8—44no—
349C22×Q8—82no—
350C22×Q8C2×D411yescharacteristic
351C22×Q8C2411yescharacteristic
352C22×D4—21no—
353C22×D4C2411yescharacteristic
354C23×C4—21no—
355C23×C4—22no—
356C23×C4C2×D411yescharacteristic
357C23×C4C2×D411yescharacteristic
358C23×C4C2411yescharacteristic
359C2×SD16—22no—
360C2×SD16—22no—
361C2×SD16C2×Q814yes—
362C22×C8—22no—
363C22×C8—22no—
364C22×C8—22no—
365C22×C8—22no—
366C22×C8—22no—
367C22×C8C2×Q814yescomplemented
368C22×C8C2412yes—
369C22×C8C2412yes—
370C22×C8C2411yescharacteristic
371C22×C8C2411yescharacteristic
372C22×C8C2411yescharacteristic
373C22×C8C2411yescharacteristic
374C4⋊Q8—24no—
375C4⋊Q8—22no—
376C4⋊Q8—22no—
377C4⋊Q8—22no—
378C4⋊Q8—22no—
379C4⋊Q8—22no—
380C4⋊Q8—22no—
381C4⋊Q8—42no—
382C4⋊Q8—44no—
383C4⋊Q8C2×D414yes—
384C4⋊Q8C2×D414yes—
385#125—24no—
386#125—24no—
387#125—24no—
388#125—42no—
389#125—42no—
390#125—42no—
391#125—48no—
392C22⋊Q8—22no—
393C22⋊Q8—48no—
394C22⋊Q8—42no—
395C22⋊Q8—44no—
396C22⋊Q8—44no—
397C22⋊Q8—44no—
398C22⋊Q8—44no—
399C22⋊Q8—44no—
400C22⋊Q8C2×Q814yescomplemented
401#121—22no—
402#121C2×Q814yes—
403C4×Q8—22no—
404C4×Q8—22no—
405C4×Q8—24no—
406C4×Q8—22no—
407C4×Q8—22no—
408C4×Q8—42no—
409C4×Q8—44no—
410C4×Q8—44no—
411C4×Q8—44no—
412C4×Q8—44no—
413C4×Q8—44no—
414C4×Q8—44no—
415C4×Q8—82no—
416C4×D4—24no—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—42no—
420C4×D4—82no—
421#117—24no—
422#117—24no—
423#117—42no—
424#117—42no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4C2×D411yescharacteristic
450C2×C4⋊C4C2×D411yescharacteristic
451C2×C4⋊C4C2×D411yescharacteristic
452C2×C4⋊C4C2×D412yes—
453C2×C4⋊C4C2×D412yes—
454C2×C4⋊C4C2×D412yes—
455C2×C4⋊C4C2412yes—
456C2×C4⋊C4C2412yes—
457C2×C4⋊C4C2411yescharacteristic
458C2×C4⋊C4C2411yescharacteristic
459C2×C4⋊C4C2411yescharacteristic
460C2×C4⋊C4C2411yescharacteristic
461C2×C4⋊C4C2412yes—
462C2×C4⋊C4C2412yes—
463C2×C4⋊C4C2411yescharacteristic
464C2×C4⋊C4C2411yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4C2×D412yes—
478C2×C22⋊C4C2×D412yes—
479C2×C42—22no—
480C2×C42—22no—
481C2×C42—22no—
482C2×C42—22no—
483C2×C42—21no—
484C2×C42—22no—
485C2×C42—21no—
486C2×C42—21no—
487C2×C42—22no—
488C2×C42—22no—
489C2×C42C2×D411yescharacteristic
490C2×C42C2×D411yescharacteristic
491C2×C42C2412yes—
492C2×C42C2411yescharacteristic
493C2×C42C2412yes—
494C2×C42C2411yescharacteristic
495#107—24no—
496#107—24no—
497#107—24no—
498#107—42no—
499#107C2×D418yes—
500#107C2×D418yes—
501#106—22no—
502#106—22no—
503#106—24no—
504#106—24no—
505#106—24no—
506#106—24no—
507#106—24no—
508#106—42no—
509#106C2×Q814yescomplemented
510C4⋊C8—24no—
511C4⋊C8—24no—
512C4⋊C8—22no—
513C4⋊C8—22no—
514#103—22no—
515#103—22no—
516#103—24no—
517#103—42no—
518#103C2×Q814yescomplemented
519#102—22no—
520#102—22no—
521#102—24no—
522#102—42no—
523#102C2×Q814yes—
524C22⋊C8—24no—
525#97—24no—
526#97—24no—
527C4×C8—22no—
528C4×C8—22no—
529C4×C8—22no—
530C4×C8C2×D414yes—
531#95—21no—
532#95—22no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—22no—
539#95—21no—
540#95—21no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
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—44no—
569C2×Q8—44no—
570C2×Q8—42no—
571C2×Q8—42no—
572C2×Q8—42no—
573C2×Q8—42no—
574C2×Q8—42no—
575C2×Q8—42no—
576C2×Q8—81no—
577C2×Q8—81no—
578C2×Q8—81no—
579C2×Q8—81no—
580C2×Q8—82no—
581C2×Q8—816no—
582C2×Q8C22×Q812yes—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4C22×Q812yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—21no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—82no—
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D412yes—
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×Q812yes—
629C22×C42−1+412yes—
630C22×C4C2511yescharacteristic
631SD16—28no—
632C2×C8—28no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—28no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8C22×D412yes—
647C2×C8C22×D412yes—
648C2×C8C22×Q812yes—
649C2×C8C22×Q812yes—
650C2×C82−1+412yes—
651C2×C82−1+412yes—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—22no—
655C4⋊C4—24no—
656C4⋊C4—24no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C4⋊C4—44no—
682C4⋊C4—44no—
683C4⋊C4—44no—
684C4⋊C4—44no—
685C4⋊C4—44no—
686C4⋊C4—42no—
687C4⋊C4—42no—
688C4⋊C4—42no—
689C4⋊C4—82no—
690C4⋊C4—82no—
691C4⋊C4—82no—
692C4⋊C4—82no—
693C4⋊C4—81no—
694C4⋊C4—82no—
695C4⋊C4—82no—
696C4⋊C4—81no—
697C4⋊C4—82no—
698C4⋊C4C22×D414yes—
699C4⋊C4C22×D414yes—
700C4⋊C4C22×Q812yes—
701C4⋊C4C22×Q812yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—44no—
707C22⋊C4—44no—
708C22⋊C4—44no—
709C22⋊C4—42no—
710C22⋊C4—82no—
711C22⋊C4—82no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C22⋊C4—81no—
715C22⋊C4—81no—
716C42—22no—
717C42—22no—
718C42—21no—
719C42—22no—
720C42—21no—
721C42—22no—
722C42—22no—
723C42—22no—
724C42—44no—
725C42—44no—
726C42—44no—
727C42—44no—
728C42—42no—
729C42—42no—
730C42—42no—
731C42—82no—
732C42C22×D412yes—
733C42H(5,𝔽2)12yes—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—22no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23D4×Q812yes—
748C23C23×D411yescharacteristic
749Q8—22no—
750Q8—22no—
751Q8—41no—
752Q8—44no—
753Q8—48no—
754Q8—48no—
755Q8—41no—
756Q8—84no—
757Q8—84no—
758Q8—88no—
759D4—22no—
760D4—22no—
761D4—41no—
762D4—41no—
763D4—84no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—22no—
795C2×C4—44no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—44no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—88no—
826C2×C4—84no—
827C2×C4D4212yes—
828C2×C4D4212yes—
829C2×C4D4×Q812yes—
830C2×C4#57512yes—
831C2×C4#57712yes—
832C2×C4C23×D411yescharacteristic
833C2×C4C23×Q811yescharacteristic
834C2×C4C2×H(5,𝔽2)11yescharacteristic
835C2×C4C2×2−1+411yescharacteristic
836C2×C4C2×2−1+411yescharacteristic
837C2×C4C2×2−1+411yescharacteristic
838C8—22no—
839C8—22no—
840C8—22no—
841C8—42no—
842C8—42no—
843C8D4×Q814yes—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22C2×D4211yescharacteristic
859C22C2×D4×Q811yescharacteristic
860C22#349911yescharacteristic
861C22C2×#57511yescharacteristic
862C22C2×#57711yescharacteristic
863C22#358411yescharacteristic
864C22#358411yescharacteristic
865C4—22no—
866C4—22no—
867C4—42no—
868C4—42no—
869C4—41no—
870C4—42no—
871C4—44no—
872C4—44no—
873C4—42no—
874C4—41no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—81no—
879C4—81no—
880C4—81no—
881C4—81no—
882C4—82no—
883C4—82no—
884C4#326714yes—
885C4C2×D4×Q811yescharacteristic
886C4#348611yescharacteristic
887C4#350311yescharacteristic
888C4#355211yescharacteristic
889C2—42no—
890C2—82no—
891C2#5912711yescharacteristic
892C2C2×#326711yescharacteristic
893C2#6105411yescharacteristic
894C2#6136511yescharacteristic
895C2#6137111yescharacteristic
896C2#6248511yescharacteristic
897C2#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×#3386C2semidirect
2. C2×#3160C2semidirect
3. #59067C2semidirect
5. #30961C2semidirect
6. #30959C2semidirect
7. #28822C2semidirect
8. #28682C2semidirect
9. #28539C2semidirect
10. #26494C2semidirect
12. #26339C2semidirect
13. #26070C2semidirect
14. #25836C2semidirect
15. #25834C2semidirect
16. #25453C2semidirect
17. #25452C2semidirect
18. #24303C2semidirect
20. #23161C2semidirect
22. #21597C2semidirect
186. #500D4semidirect
197. #465Q8semidirect
367. C22×C8C2×Q8semidirect
400. C22⋊Q8C2×Q8semidirect
509. #106C2×Q8semidirect
518. #103C2×Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#33862
C2×#31602
#590672
#590362
#309612
#309592
#288222
#286822
#285392
#264942
#263472
#263392
#260702
#258362
#258342
#254532
#254522
#243032
#243002
#231612
#230332
#215972
C4×#4652