Finite Group Databasebeta

← #7563485

Subgroups — #7563485

Order 512.

1868 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3387C211yesmaximal, characteristic, complemented
2C22×#498C211yesmaximal, characteristic
3#59151C211yesmaximal, characteristic
4#59144C211yesmaximal, characteristic
5#30956C212yesmaximal, complemented
6#30949C212yesmaximal, complemented
7#28819C212yesmaximal, complemented
8#28684C211yesmaximal, characteristic, complemented
9#28542C211yesmaximal, characteristic, complemented
10#26491C212yesmaximal, complemented
11#26346C212yesmaximal
12#26340C212yesmaximal
13#26068C212yesmaximal
14#25837C211yesmaximal, characteristic, complemented
15#25836C211yesmaximal, characteristic, complemented
16#25454C211yesmaximal, characteristic, complemented
17#25453C211yesmaximal, characteristic, complemented
18#24302C211yesmaximal, characteristic
19#24301C211yesmaximal, characteristic
20#23163C211yesmaximal, characteristic, complemented
21#23028C212yesmaximal
22#21597C211yesmaximal, characteristic
23C4×#467C211yesmaximal, characteristic
24C2×Q82C2211yescharacteristic
25C2×#557C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C22×C4⋊Q8C2211yescharacteristic
28#3387—28no—
29C2×#501C2212yes—
30C2×#498—28no—
31C2×#498C2211yescharacteristic
32C2×#498C2211yescharacteristic
33C2×#498C2211yescharacteristic
34C2×#498C2212yes—
35C2×#498C2212yes—
36C2×#498C2211yescharacteristic
37C2×#479C2212yes—
38C2×#477C2211yescharacteristic
39C2×#477C2211yescharacteristic
40C2×#475C2211yescharacteristic
41C2×#475C2212yes—
42C2×#475C2211yescharacteristic
43C2×#467C2211yescharacteristic
44C2×#446C2211yescharacteristic
45C2×#441C2212yes—
46C2×C4×Q16C2211yescharacteristic
47C22×#106C2212yes—
48C22×#106C2212yes—
49C22×C4×C8C2211yescharacteristic
50#2734—22no—
51#2713—22no—
52#2568C2211yescharacteristic
53#2567C2211yescharacteristic
54#2567C2211yescharacteristic
55#2551—21no—
56#2551C2212yes—
57#2550C2212yes—
58#2546—21no—
59#2546C2211yescharacteristic
60#2473—22no—
61#2451—21no—
62#2451C2212yes—
63#2451C2212yes—
64#2446—21no—
65#2442C2212yes—
66#2440—21no—
67#2440C2212yes—
68#2434—22no—
69#2434—21no—
70#2369C2211yescharacteristic
71#2365C2211yescharacteristic
72#2360—21no—
73#2360C2212yes—
74#2360C2212yes—
75Q8×C22⋊C4—21no—
76C4×C22⋊Q8C2211yescharacteristic
77C4×C22⋊Q8C2211yescharacteristic
78C4×C22⋊Q8C2211yescharacteristic
79#2097C2212yes—
80#2096C2212yes—
81#2088C2212yes—
82#2088C2212yes—
83#2085C2212yes—
84#2084C2212yes—
85#2066C2212yes—
86#2066C2212yes—
87#2059C2212yes—
88#2059C2212yes—
89#2058C2212yes—
90#2058C2212yes—
91#2058C2212yes—
92#2057C2212yes—
93#2024C2212yes—
94#2024C2212yes—
95#1988C2211yescharacteristic
96#1988C2211yescharacteristic
97#1987C2211yescharacteristic
98#1987C2211yescharacteristic
99#1984C2211yescharacteristic
100#1971C2212yes—
101#1969C2211yescharacteristic
102#1949C2212yes—
103#1948C2212yes—
104#1944C2212yes—
105#1943C2212yes—
106#1943C2212yes—
107#1942C2211yescharacteristic
108#1939C2211yescharacteristic
109#1933C2211yescharacteristic
110#1933C2211yescharacteristic
111#1927C2212yes—
112#1927C2212yes—
113#1920C2212yes—
114#1919C2212yes—
115#1916C2212yes—
116#1892C2211yescharacteristic
117#1892C2211yescharacteristic
118#1872C2212yes—
119#1872C2212yes—
120#1865C2212yes—
121#1865C2212yes—
122#1865C2212yes—
123#1865C2212yes—
124#1853C2212yes—
125#1852C2212yes—
126#1850C2212yes—
127#1847C2212yes—
128#1808C2211yescharacteristic
129#1797C2211yescharacteristic
130#1776C2212yes—
131C4×#107C2211yescharacteristic
132#1771C2212yes—
133#1770C2211yescharacteristic
134C4×#103C2211yescharacteristic
135C4×#103C2211yescharacteristic
136#1752C2212yes—
137C23×Q8—21no—
138C23×Q8—21no—
139C22×Q16C2311yescharacteristic
140C23×C8C2311yescharacteristic
141C23×C8C2311yescharacteristic
142Q82—24no—
143Q82—42no—
144#557—24no—
145#557—42no—
146C2×C4⋊Q8—21no—
147C2×C4⋊Q8—21no—
148C2×C4⋊Q8—22no—
149C2×C4⋊Q8—21no—
150C2×C4⋊Q8—22no—
151C2×C4⋊Q8—24no—
152C2×C4⋊Q8—24no—
153C2×C4⋊Q8—21no—
154C2×C4⋊Q8—21no—
155C2×C4⋊Q8—21no—
156C2×C4⋊Q8—21no—
157C2×C4⋊Q8—42no—
158C2×C4⋊Q8—42no—
159C2×C4⋊Q8C2311yescharacteristic
160C2×C4⋊Q8C2311yescharacteristic
161C2×C4⋊Q8C2312yes—
162C2×C4⋊Q8C2312yes—
163C2×C4⋊Q8C2312yes—
164C2×C4⋊Q8C2311yescharacteristic
165C2×C4⋊Q8C2311yescharacteristic
166C2×#125—22no—
167C2×#125C2312yes—
168C2×C22⋊Q8—22no—
169C2×C22⋊Q8D411yescharacteristic
170C2×C22⋊Q8C2311yescharacteristic
171C2×C22⋊Q8C2311yescharacteristic
172C2×C4×Q8—21no—
173C2×C4×Q8—21no—
174C2×C4×Q8—21no—
175C2×C4×Q8C2311yescharacteristic
176C2×C4×Q8C2311yescharacteristic
177C2×C4×Q8C2312yes—
178C2×C4×Q8C2312yes—
179C2×C4×Q8C2311yescharacteristic
180C22×C4⋊C4—21no—
181C22×C4⋊C4—21no—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2312yes—
184C22×C42C2311yescharacteristic
185#501—28no—
186#498—24no—
187#498—24no—
188#498—28no—
189#498—28no—
190#498—24no—
191#498D418yes—
192#479—28no—
193#477—24no—
194#477—42no—
195#475—24no—
196#475—28no—
197#475—42no—
198#467Q818yescomplemented
199#446—24no—
200#441—28no—
201C4×Q16—24no—
202C2×#107C2312yes—
203C2×#107C2311yescharacteristic
204C2×#107C2311yescharacteristic
205C2×#107C2312yes—
206C2×#107C2311yescharacteristic
207C2×#106—28no—
208C2×#106—28no—
209C2×#106C2312yes—
210C2×#106C2312yes—
211C2×#106C2312yes—
212C2×#106C2312yes—
213C2×#106C2312yes—
214C2×#106C2312yes—
215C2×#106C2312yes—
216C2×#106C2312yes—
217C2×#106C2312yes—
218C2×#106C2312yes—
219C2×C4⋊C8C2311yescharacteristic
220C2×C4⋊C8C2311yescharacteristic
221C2×C4⋊C8C2312yes—
222C2×C4⋊C8C2312yes—
223C2×#103C2311yescharacteristic
224C2×#103C2312yes—
225C2×#103C2312yes—
226C2×#103C2311yescharacteristic
227C2×#103C2311yescharacteristic
228C2×#103C2311yescharacteristic
229C2×#103C2312yes—
230C2×#103C2312yes—
231C2×#103C2311yescharacteristic
232C2×#103C2311yescharacteristic
233C2×C22⋊C8C2312yes—
234C2×#97C2312yes—
235C2×#97C2312yes—
236C2×C4×C8—24no—
237C2×C4×C8C2311yescharacteristic
238C2×C4×C8C2311yescharacteristic
239C2×C4×C8C2311yescharacteristic
240C2×C4×C8C2311yescharacteristic
241#400—22no—
242#400—22no—
243#398—22no—
244#398—22no—
245#398—22no—
246#398—22no—
247#398—22no—
248#398—22no—
249#395—22no—
250#395—22no—
251#395—22no—
252#395—22no—
253#395—22no—
254#395—22no—
255#395—22no—
256#395—22no—
257#391—21no—
258#391—21no—
259#391—21no—
260#391—21no—
261#391—21no—
262#391—22no—
263#391—22no—
264#391—22no—
265#391—22no—
266#391D411yescharacteristic
267#391C2312yes—
268#391C2312yes—
269#391C2311yescharacteristic
270#391C2311yescharacteristic
271#389—21no—
272#389—21no—
273#389—22no—
274#389—21no—
275#389—22no—
276#389—22no—
277#389—22no—
278#389D411yescharacteristic
279#389C2312yes—
280#389C2312yes—
281#389C2311yescharacteristic
282#389C2311yescharacteristic
283#389C2312yes—
284#389C2312yes—
285#389C2312yes—
286#389C2312yes—
287#387—22no—
288#387—22no—
289#387—21no—
290#387—21no—
291#387—22no—
292#387—22no—
293#387—22no—
294#387D412yes—
295#385—21no—
296#385—21no—
297#385—22no—
298#385—22no—
299#385—22no—
300#385—22no—
301#385D412yes—
302#384—21no—
303#384C2312yes—
304#382C2312yes—
305#380—22no—
306#380D411yescharacteristic
307#380C2311yescharacteristic
308#380C2311yescharacteristic
309C4×C4⋊C4—21no—
310C4×C4⋊C4—21no—
311C4×C4⋊C4—21no—
312C4×C4⋊C4C2311yescharacteristic
313C4×C4⋊C4C2312yes—
314C4×C4⋊C4C2312yes—
315C4×C4⋊C4C2311yescharacteristic
316C4×C4⋊C4C2311yescharacteristic
317C4×C4⋊C4C2312yes—
318C4×C22⋊C4—21no—
319C4×C22⋊C4—21no—
320C4×C22⋊C4—22no—
321C4×C22⋊C4—22no—
322C4×C22⋊C4C2312yes—
323#340C2312yes—
324#340C2312yes—
325#340C2311yescharacteristic
326#340C2311yescharacteristic
327#340C2312yes—
328#340C2312yes—
329#340C2312yes—
330#340C2311yescharacteristic
331#340C2311yescharacteristic
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—22no—
346C22×Q8—22no—
347C22×Q8—22no—
348C22×Q8—21no—
349C22×Q8—44no—
350C22×Q8—44no—
351C22×Q8—44no—
352C22×Q8—82no—
353C22×Q8—82no—
354C22×Q8—82no—
355C22×Q8C2×D411yescharacteristic
356C22×Q8C2411yescharacteristic
357C22×Q8C2411yescharacteristic
358C23×C4—22no—
359C23×C4—22no—
360C23×C4C2×D411yescharacteristic
361C23×C4C2×D411yescharacteristic
362C23×C4C2411yescharacteristic
363C2×Q16—22no—
364C2×Q16—22no—
365C2×Q16C2×Q814yescomplemented
366C22×C8—22no—
367C22×C8—22no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8—22no—
371C22×C8C2×Q814yes—
372C22×C8C2412yes—
373C22×C8C2412yes—
374C22×C8C2411yescharacteristic
375C22×C8C2411yescharacteristic
376C22×C8C2411yescharacteristic
377C22×C8C2411yescharacteristic
378C4⋊Q8—24no—
379C4⋊Q8—24no—
380C4⋊Q8—24no—
381C4⋊Q8—22no—
382C4⋊Q8—22no—
383C4⋊Q8—22no—
384C4⋊Q8—22no—
385C4⋊Q8—22no—
386C4⋊Q8—22no—
387C4⋊Q8—42no—
388C4⋊Q8—42no—
389C4⋊Q8—42no—
390C4⋊Q8—44no—
391C4⋊Q8—44no—
392C4⋊Q8—44no—
393C4⋊Q8—44no—
394C4⋊Q8—44no—
395C4⋊Q8—48no—
396C4⋊Q8—44no—
397C4⋊Q8—82no—
398C4⋊Q8—84no—
399C4⋊Q8C2×D414yes—
400C4⋊Q8C2×D414yes—
401#125—24no—
402#125—42no—
403#125—48no—
404C22⋊Q8—24no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—84no—
408C22⋊Q8C2×Q814yes—
409C22⋊Q8C2×Q814yes—
410C4×Q8—22no—
411C4×Q8—22no—
412C4×Q8—24no—
413C4×Q8—24no—
414C4×Q8—22no—
415C4×Q8—22no—
416C4×Q8—22no—
417C4×Q8—22no—
418C4×Q8—42no—
419C4×Q8—42no—
420C4×Q8—44no—
421C4×Q8—44no—
422C4×Q8—82no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—44no—
455C2×C4⋊C4—44no—
456C2×C4⋊C4C2×D411yescharacteristic
457C2×C4⋊C4C2×D411yescharacteristic
458C2×C4⋊C4C2×D412yes—
459C2×C4⋊C4C2×D411yescharacteristic
460C2×C4⋊C4C2×D412yes—
461C2×C4⋊C4C2×D412yes—
462C2×C4⋊C4C2412yes—
463C2×C4⋊C4C2412yes—
464C2×C4⋊C4C2411yescharacteristic
465C2×C4⋊C4C2411yescharacteristic
466C2×C4⋊C4C2411yescharacteristic
467C2×C4⋊C4C2411yescharacteristic
468C2×C4⋊C4C2412yes—
469C2×C4⋊C4C2412yes—
470C2×C4⋊C4C2411yescharacteristic
471C2×C4⋊C4C2411yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4C2×D412yes—
477C2×C22⋊C4C2×D412yes—
478C2×C42—22no—
479C2×C42—22no—
480C2×C42—22no—
481C2×C42—21no—
482C2×C42—21no—
483C2×C42—22no—
484C2×C42—21no—
485C2×C42—21no—
486C2×C42—22no—
487C2×C42—22no—
488C2×C42C2×D411yescharacteristic
489C2×C42C2×D411yescharacteristic
490C2×C42C2412yes—
491C2×C42C2411yescharacteristic
492C2×C42C2412yes—
493C2×C42C2411yescharacteristic
494#107—22no—
495#107—22no—
496#107—24no—
497#107—42no—
498#107C2×Q814yescomplemented
499#106—24no—
500#106—24no—
501#106—24no—
502#106—24no—
503#106—24no—
504#106—24no—
505#106—24no—
506#106—42no—
507#106C2×D418yes—
508#106C2×D418yes—
509C4⋊C8—24no—
510C4⋊C8—24no—
511C4⋊C8—22no—
512C4⋊C8—22no—
513#103—22no—
514#103—22no—
515#103—22no—
516#103—22no—
517#103—24no—
518#103—24no—
519#103—42no—
520#103—42no—
521#103C2×Q814yescomplemented
522#103C2×Q814yescomplemented
523C22⋊C8—24no—
524#97—24no—
525#97—24no—
526C4×C8—22no—
527C4×C8—22no—
528C4×C8—22no—
529C4×C8C2×D414yes—
530#95—21no—
531#95—21no—
532#95—22no—
533#95—22no—
534#95—21no—
535#95—22no—
536#95—21no—
537#95—22no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—22no—
542#95—21no—
543#95—21no—
544#95—22no—
545#95—22no—
546#95—21no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—22no—
552#95—22no—
553#95—22no—
554#95C2×D412yes—
555#95C2×D412yes—
556#95C2×D412yes—
557#95C2×D412yes—
558#95C2×D412yes—
559C24C22×D411yescharacteristic
560C2×Q8—22no—
561C2×Q8—24no—
562C2×Q8—24no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—44no—
576C2×Q8—44no—
577C2×Q8—44no—
578C2×Q8—42no—
579C2×Q8—42no—
580C2×Q8—42no—
581C2×Q8—44no—
582C2×Q8—42no—
583C2×Q8—42no—
584C2×Q8—44no—
585C2×Q8—42no—
586C2×Q8—82no—
587C2×Q8—81no—
588C2×Q8—81no—
589C2×Q8—82no—
590C2×Q8—81no—
591C2×Q8—81no—
592C2×Q8—82no—
593C2×Q8—82no—
594C2×Q8—816no—
595C2×Q8—816no—
596C2×Q8C22×Q812yes—
597C2×Q8C22×Q812yes—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—21no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—82no—
624C22×C4—82no—
625C22×C4#13714yes—
626C22×C4C22×D412yes—
627C22×C4C22×D412yes—
628C22×C4C22×D412yes—
629C22×C4C22×D412yes—
630C22×C4C22×D411yescharacteristic
631C22×C4C22×D411yescharacteristic
632C22×C4C22×D411yescharacteristic
633C22×C4C22×D411yescharacteristic
634C22×C4C22×D411yescharacteristic
635C22×C4C22×Q812yes—
636C22×C42−1+412yes—
637C22×C4C2511yescharacteristic
638Q16—28no—
639C2×C8—28no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—28no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8C22×D412yes—
654C2×C8C22×D412yes—
655C2×C8C22×Q812yes—
656C2×C8C22×Q812yes—
657C2×C82−1+412yes—
658C2×C82−1+412yes—
659C4⋊C4—24no—
660C4⋊C4—24no—
661C4⋊C4—22no—
662C4⋊C4—24no—
663C4⋊C4—24no—
664C4⋊C4—24no—
665C4⋊C4—22no—
666C4⋊C4—24no—
667C4⋊C4—22no—
668C4⋊C4—24no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—44no—
686C4⋊C4—44no—
687C4⋊C4—44no—
688C4⋊C4—44no—
689C4⋊C4—44no—
690C4⋊C4—44no—
691C4⋊C4—44no—
692C4⋊C4—44no—
693C4⋊C4—44no—
694C4⋊C4—42no—
695C4⋊C4—42no—
696C4⋊C4—42no—
697C4⋊C4—42no—
698C4⋊C4—42no—
699C4⋊C4—42no—
700C4⋊C4—82no—
701C4⋊C4—82no—
702C4⋊C4—82no—
703C4⋊C4—82no—
704C4⋊C4—82no—
705C4⋊C4—82no—
706C4⋊C4—82no—
707C4⋊C4—82no—
708C4⋊C4C22×D414yes—
709C4⋊C4C22×D414yes—
710C4⋊C4C22×Q812yes—
711C4⋊C4C22×Q812yes—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C42—22no—
719C42—22no—
720C42—21no—
721C42—22no—
722C42—21no—
723C42—22no—
724C42—22no—
725C42—22no—
726C42—44no—
727C42—44no—
728C42—42no—
729C42—42no—
730C42—42no—
731C42—42no—
732C42—82no—
733C42—82no—
734C42C22×D412yes—
735C42H(5,𝔽2)12yes—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23D4×Q812yes—
741C23C2×#13712yes—
742C23#57712yes—
743C23C23×D411yescharacteristic
744Q8—22no—
745Q8—22no—
746Q8—22no—
747Q8—22no—
748Q8—41no—
749Q8—41no—
750Q8—44no—
751Q8—48no—
752Q8—41no—
753Q8—41no—
754Q8—84no—
755Q8—88no—
756Q8—88no—
757Q8—84no—
758Q8—84no—
759Q8—164no—
760C2×C4—28no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—28no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—88no—
823C2×C4—88no—
824C2×C4D4212yes—
825C2×C4D4212yes—
826C2×C4D4×Q812yes—
827C2×C4C2×#13712yes—
828C2×C4C2×#13712yes—
829C2×C4#57712yes—
830C2×C4#57712yes—
831C2×C4C23×D411yescharacteristic
832C2×C4C23×Q811yescharacteristic
833C2×C4C2×H(5,𝔽2)11yescharacteristic
834C2×C4C2×2−1+411yescharacteristic
835C2×C4C2×2−1+411yescharacteristic
836C2×C4C2×2−1+411yescharacteristic
837C8—22no—
838C8—22no—
839C8—22no—
840C8—42no—
841C8—42no—
842C8D4×Q814yes—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22#338714yescomplemented
850C22C2×D4211yescharacteristic
851C22C2×D4×Q811yescharacteristic
852C22#349911yescharacteristic
853C22C22×#13711yescharacteristic
854C22C2×#57711yescharacteristic
855C22C2×#57711yescharacteristic
856C22C2×#57711yescharacteristic
857C4—22no—
858C4—22no—
859C4—22no—
860C4—22no—
861C4—42no—
862C4—42no—
863C4—42no—
864C4—44no—
865C4—42no—
866C4—44no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4—81no—
872C4—81no—
873C4—82no—
874C4—81no—
875C4—82no—
876C4—81no—
877C4#326614yes—
878C4C2×D4×Q811yescharacteristic
879C4#348611yescharacteristic
880C4#350311yescharacteristic
881C4#355211yescharacteristic
882C2—24no—
883C2#5912711yescharacteristic
884C2C2×#326611yescharacteristic
885C2#6105011yescharacteristic
886C2C2×#338711yescharacteristic
887C2#6137411yescharacteristic
888C2#6247811yescharacteristic
889C2#6248611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
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×#3387C2semidirect
5. #30956C2semidirect
6. #30949C2semidirect
7. #28819C2semidirect
8. #28684C2semidirect
9. #28542C2semidirect
10. #26491C2semidirect
14. #25837C2semidirect
15. #25836C2semidirect
16. #25454C2semidirect
17. #25453C2semidirect
20. #23163C2semidirect
198. #467Q8semidirect
365. C2×Q16C2×Q8semidirect
498. #107C2×Q8semidirect
521. #103C2×Q8semidirect
522. #103C2×Q8semidirect
849. C22#3387semidirect

Maximal subgroups

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

subgroupindex
C2×#33872
C22×#4982
#591512
#591442
#309562
#309492
#288192
#286842
#285422
#264912
#263462
#263402
#260682
#258372
#258362
#254542
#254532
#243022
#243012
#231632
#230282
#215972
C4×#4672