Finite Group Databasebeta

← #6618307

Subgroups — #6618307

Order 512.

1899 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3387C211yesmaximal, characteristic, complemented
2C2×#3368C211yesmaximal, characteristic
3#36457C211yesmaximal, characteristic
4C4×#557C211yesmaximal, characteristic, complemented
5#33031C211yesmaximal, characteristic, complemented
6#33025C212yesmaximal, complemented
7#28661C212yesmaximal, complemented
8#28654C211yesmaximal, characteristic, complemented
9#28208C212yesmaximal, complemented
10#28203C211yesmaximal, characteristic, complemented
11#25466C212yesmaximal, complemented
12#25452C211yesmaximal, characteristic, complemented
13#25291C212yesmaximal, complemented
14#25279C211yesmaximal, characteristic, complemented
15#24828C212yesmaximal, complemented
16#24814C211yesmaximal, characteristic, complemented
17#24747C212yesmaximal, complemented
18#24733C211yesmaximal, characteristic, complemented
19#22736C211yesmaximal, characteristic, complemented
20#22545C211yesmaximal, characteristic
21#22525C211yesmaximal, characteristic, complemented
22#21508C212yesmaximal, complemented
23C4×#464C211yesmaximal, characteristic, complemented
24C2×Q82C2211yescharacteristic
25C2×#557C2211yescharacteristic
26C2×#550C2211yescharacteristic
27#3387—28no—
28#3368—28no—
29C2×#501C2212yes—
30C2×#498C2211yescharacteristic
31C2×#490C2212yes—
32C2×#486C2211yescharacteristic
33C2×#479C2212yes—
34C2×#477C2211yescharacteristic
35C2×#475C2212yes—
36C2×#475C2211yescharacteristic
37C2×#478C2212yes—
38C2×#474C2211yescharacteristic
39C2×#464C2212yes—
40C2×#464C2211yescharacteristic
41C2×#460C2212yes—
42C2×#460C2211yescharacteristic
43C2×#446C2211yescharacteristic
44C2×#446C2211yescharacteristic
45C2×#441C2212yes—
46C2×#440C2212yes—
47C2×C4×Q16C2211yescharacteristic
48C2×C4×SD16C2211yescharacteristic
49#2858C2212yes—
50#2858C2211yescharacteristic
51#2563C2211yescharacteristic
52#2563C2212yes—
53#2548C2211yescharacteristic
54#2548C2212yes—
55#2491—22no—
56#2491—21no—
57#2491—22no—
58#2491—21no—
59#2370—22no—
60#2370C2212yes—
61#2365—21no—
62#2365C2211yescharacteristic
63#2355—21no—
64#2355C2211yescharacteristic
65#2351C2212yes—
66Q8×C4⋊C4C2211yescharacteristic
67#2341—21no—
68#2341—21no—
69C4×C4⋊Q8—21no—
70C4×C4⋊Q8C2211yescharacteristic
71C4×#125—22no—
72C4×#125C2212yes—
73C4×#124C2212yes—
74C4×#124C2211yescharacteristic
75C42×Q8—21no—
76C42×Q8C2212yes—
77C42×Q8C2211yescharacteristic
78C42×Q8C2211yescharacteristic
79#2085C2212yes—
80#2085C2212yes—
81#2085C2212yes—
82#2067C2212yes—
83#2067C2212yes—
84#2065C2212yes—
85#2065C2212yes—
86#2065C2212yes—
87#2065C2212yes—
88#2042C2212yes—
89#2042C2212yes—
90#2042C2212yes—
91#1993C2212yes—
92#1990C2211yescharacteristic
93#1988C2212yes—
94#1987C2211yescharacteristic
95#1983C2212yes—
96#1983C2211yescharacteristic
97#1982C2212yes—
98#1982C2211yescharacteristic
99#1961C2212yes—
100#1957C2211yescharacteristic
101#1949C2212yes—
102#1949C2211yescharacteristic
103#1940C2212yes—
104#1940C2212yes—
105#1939C2211yescharacteristic
106#1939C2211yescharacteristic
107#1928C2212yes—
108#1927C2211yescharacteristic
109#1926C2212yes—
110#1926C2212yes—
111#1926C2212yes—
112#1926C2212yes—
113#1926C2212yes—
114#1925C2212yes—
115#1925C2212yes—
116#1925C2211yescharacteristic
117#1880C2211yescharacteristic
118#1880C2212yes—
119#1880C2212yes—
120#1880C2212yes—
121#1880C2212yes—
122#1878C2211yescharacteristic
123#1831C2212yes—
124#1831C2211yescharacteristic
125#1805C2212yes—
126#1805C2212yes—
127#1805C2211yescharacteristic
128#1804C2212yes—
129#1803C2211yescharacteristic
130#1802C2211yescharacteristic
131#1767C2212yes—
132C4×C4⋊C8C2211yescharacteristic
133#1763C2212yes—
134#1762C2212yes—
135C4×#103C2211yescharacteristic
136C4×#102C2211yescharacteristic
137C22×#41—21no—
138C22×Q16C2311yescharacteristic
139C22×SD16C2311yescharacteristic
140C22×SD16C2312yes—
141Q82—24no—
142Q82—24no—
143#557—24no—
144#557D418yes—
145#550—24no—
146#550—24no—
147C2×C4⋊Q8—21no—
148C2×C4⋊Q8—21no—
149C2×C4⋊Q8—22no—
150C2×C4⋊Q8C2312yes—
151C2×C4⋊Q8C2311yescharacteristic
152C2×C4⋊Q8C2311yescharacteristic
153C2×#127C2311yescharacteristic
154C2×#127C2312yes—
155C2×#125—22no—
156C2×#125C2312yes—
157C2×#124—22no—
158C2×#124—21no—
159C2×#124—22no—
160C2×#124—21no—
161C2×#124C2312yes—
162C2×#124C2311yescharacteristic
163C2×#121—21no—
164C2×#121—22no—
165C2×C4×Q8—21no—
166C2×C4×Q8—21no—
167C2×C4×Q8—21no—
168C2×C4×Q8—21no—
169C2×C4×Q8D411yescharacteristic
170C2×C4×Q8D411yescharacteristic
171C2×C4×Q8C2311yescharacteristic
172C2×C4×Q8C2312yes—
173C2×C4×Q8C2311yescharacteristic
174C2×C4×Q8C2312yes—
175C2×C4×Q8C2311yescharacteristic
176C2×C4×Q8C2312yes—
177C2×C4×Q8C2311yescharacteristic
178C2×C4×Q8C2311yescharacteristic
179C2×C4×D4C2312yes—
180C2×C4×D4C2311yescharacteristic
181#501—28no—
182#498—24no—
183#490—28no—
184#486—24no—
185#479—28no—
186#478—28no—
187#477—24no—
188#475—24no—
189#475—28no—
190#474—24no—
191#464—28no—
192#464—24no—
193#460—28no—
194#460—24no—
195#446—24no—
196#446—24no—
197#441—28no—
198#440—28no—
199C4×Q16—24no—
200C4×SD16—24no—
201C2×#107C2312yes—
202C2×#107C2312yes—
203C2×#107C2311yescharacteristic
204C2×#106C2311yescharacteristic
205C2×#106C2312yes—
206C2×#106C2312yes—
207C2×#106C2312yes—
208C2×C4⋊C8C2312yes—
209C2×C4⋊C8C2311yescharacteristic
210C2×C4⋊C8C2312yes—
211C2×C4⋊C8C2311yescharacteristic
212C2×C4⋊C8C2311yescharacteristic
213C2×C4⋊C8C2312yes—
214C2×C4⋊C8C2311yescharacteristic
215C2×C4⋊C8C2312yes—
216C2×#103C2311yescharacteristic
217C2×#103C2312yes—
218C2×#103C2312yes—
219C2×#103C2311yescharacteristic
220C2×#103C2312yes—
221C2×#103C2311yescharacteristic
222C2×#103C2311yescharacteristic
223C2×#103C2311yescharacteristic
224C2×#102C2312yes—
225C2×#102C2312yes—
226C2×#102C2312yes—
227C2×#102C2311yescharacteristic
228C2×#102C2312yes—
229C2×#102C2312yes—
230C2×#102C2311yescharacteristic
231C2×#102C2312yes—
232C2×#102C2311yescharacteristic
233C2×#102C2312yes—
234C2×#102C2312yes—
235C2×#102C2312yes—
236C2×#97C2312yes—
237C2×#97C2312yes—
238C2×C4×C8C2311yescharacteristic
239C2×C4×C8C2311yescharacteristic
240#394—22no—
241#394—22no—
242#394—22no—
243#393—22no—
244#393—22no—
245#393—22no—
246#391—21no—
247#391—21no—
248#391—21no—
249#391C2311yescharacteristic
250#390—21no—
251#390—21no—
252#390—22no—
253#390—22no—
254#390—21no—
255#390—21no—
256#390—22no—
257#390—22no—
258#390C2312yes—
259#390C2312yes—
260#390C2312yes—
261#390C2311yescharacteristic
262#390C2312yes—
263#389—22no—
264#389—22no—
265#389—22no—
266#389—21no—
267#389—22no—
268#389C2312yes—
269#389C2312yes—
270#389C2312yes—
271#388—22no—
272#388—21no—
273#388—22no—
274#388—21no—
275#387—22no—
276#387—22no—
277#387—22no—
278#387—22no—
279#387—22no—
280#387—22no—
281#384—21no—
282#384C2311yescharacteristic
283#382—22no—
284#382C2312yes—
285#382C2312yes—
286#382C2311yescharacteristic
287#380—21no—
288#380—21no—
289#380—22no—
290#380—22no—
291C4×C4⋊C4—21no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4—21no—
295C4×C4⋊C4—22no—
296C4×C4⋊C4—22no—
297C4×C4⋊C4—22no—
298C4×C4⋊C4—21no—
299C4×C4⋊C4—22no—
300C4×C4⋊C4—22no—
301C4×C4⋊C4—21no—
302C4×C4⋊C4—22no—
303C4×C4⋊C4—22no—
304C4×C4⋊C4D412yes—
305C4×C4⋊C4D411yescharacteristic
306C4×C4⋊C4D412yes—
307C4×C4⋊C4D411yescharacteristic
308C4×C4⋊C4C2311yescharacteristic
309C4×C4⋊C4C2312yes—
310C4×C4⋊C4C2311yescharacteristic
311C4×C4⋊C4C2312yes—
312C4×C4⋊C4C2312yes—
313C4×C4⋊C4C2311yescharacteristic
314C4×C4⋊C4C2311yescharacteristic
315C4×C4⋊C4C2312yes—
316C4×C22⋊C4—21no—
317C4×C22⋊C4—21no—
318C4×C22⋊C4—22no—
319C4×C22⋊C4—22no—
320C43—22no—
321C43—21no—
322C43C2312yes—
323C43C2311yescharacteristic
324#340C2312yes—
325#340C2312yes—
326#340C2311yescharacteristic
327#340C2311yescharacteristic
328#340C2312yes—
329#340C2312yes—
330#340C2312yes—
331#340C2311yescharacteristic
332#340C2312yes—
333#340C2311yescharacteristic
334#336C2312yes—
335#336C2312yes—
336#336C2312yes—
337#336C2312yes—
338#336C2311yescharacteristic
339#336C2311yescharacteristic
340C2×#41—44no—
341C2×#41—44no—
342C2×#41—44no—
343C22×Q8—21no—
344C22×Q8—22no—
345C22×Q8—21no—
346C22×Q8C2×D411yescharacteristic
347C22×Q8C2411yescharacteristic
348C22×Q8C2411yescharacteristic
349C22×D4—22no—
350C22×D4—21no—
351C22×D4—22no—
352C22×D4—21no—
353C22×D4C2412yes—
354C22×D4C2411yescharacteristic
355C23×C4—22no—
356C23×C4—21no—
357C2×Q16—22no—
358C2×Q16—22no—
359C2×Q16#4114yescomplemented
360C2×SD16—22no—
361C2×SD16—24no—
362C2×SD16—22no—
363C2×SD16—24no—
364C2×SD16—22no—
365C2×SD16—24no—
366C22×C8C2411yescharacteristic
367C22×C8C2412yes—
368C22×C8C2411yescharacteristic
369C22×C8C2412yes—
370C22×C8C2411yescharacteristic
371C22×C8C2411yescharacteristic
372C4⋊Q8—28no—
373C4⋊Q8—24no—
374C4⋊Q8—22no—
375C4⋊Q8—22no—
376C4⋊Q8—24no—
377C4⋊Q8—22no—
378C4⋊Q8—44no—
379C4⋊Q8—48no—
380C4⋊Q8C2×D414yes—
381#127—22no—
382#127—24no—
383#127—24no—
384#127—22no—
385#125—216no—
386#125—24no—
387#125C2×D418yes—
388#124—24no—
389#124—22no—
390#124—42no—
391#124—41no—
392#124—84no—
393#124—82no—
394#124—84no—
395#124—82no—
396#121—44no—
397#121—48no—
398C4×Q8—22no—
399C4×Q8—28no—
400C4×Q8—22no—
401C4×Q8—24no—
402C4×Q8—22no—
403C4×Q8—24no—
404C4×Q8—22no—
405C4×Q8—22no—
406C4×Q8—24no—
407C4×Q8—24no—
408C4×Q8—22no—
409C4×Q8—42no—
410C4×Q8—42no—
411C4×Q8—42no—
412C4×Q8—41no—
413C4×Q8—44no—
414C4×Q8—44no—
415C4×Q8—44no—
416C4×Q8C2×D414yes—
417C4×Q8C2×D418yes—
418C4×Q8C2×D414yes—
419C4×Q8#4114yes—
420C4×D4—22no—
421C4×D4—24no—
422C4×D4—24no—
423C4×D4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
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—22no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4C2×D411yescharacteristic
442C2×C4⋊C4C2×D411yescharacteristic
443C2×C4⋊C4C2×D412yes—
444C2×C4⋊C4C2×D412yes—
445C2×C4⋊C4C2×D411yescharacteristic
446C2×C4⋊C4C2×D412yes—
447C2×C4⋊C4C2411yescharacteristic
448C2×C4⋊C4C2411yescharacteristic
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2411yescharacteristic
451C2×C4⋊C4C2412yes—
452C2×C4⋊C4C2411yescharacteristic
453C2×C4⋊C4C2412yes—
454C2×C4⋊C4C2411yescharacteristic
455C2×C22⋊C4—22no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C42—22no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—22no—
475C2×C42—21no—
476C2×C42—22no—
477C2×C42—22no—
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—22no—
481C2×C42—21no—
482C2×C42—22no—
483C2×C42—21no—
484C2×C42C2×D411yescharacteristic
485C2×C42C2×D411yescharacteristic
486C2×C42C2×D412yes—
487C2×C42C2×D411yescharacteristic
488C2×C42C2×D412yes—
489C2×C42C2×D412yes—
490C2×C42C2×D412yes—
491C2×C42C2×D411yescharacteristic
492C2×C42C2411yescharacteristic
493C2×C42C2412yes—
494C2×C42C2411yescharacteristic
495C2×C42C2412yes—
496C2×C42C2411yescharacteristic
497#107—22no—
498#107—24no—
499#107—24no—
500#106—22no—
501#106—24no—
502#106—24no—
503#106—24no—
504C4⋊C8—22no—
505C4⋊C8—24no—
506C4⋊C8—22no—
507C4⋊C8—24no—
508C4⋊C8—22no—
509C4⋊C8—24no—
510C4⋊C8—41no—
511C4⋊C8—42no—
512#103—22no—
513#103—22no—
514#103—24no—
515#103—24no—
516#103—22no—
517#103—22no—
518#103—24no—
519#103—22no—
520#102—22no—
521#102—24no—
522#102—22no—
523#102—24no—
524#102—24no—
525#102—24no—
526#102—24no—
527#102—24no—
528#102—22no—
529#102—42no—
530#102—42no—
531#102—42no—
532#97—24no—
533#97—24no—
534C4×C8—22no—
535C4×C8—22no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—22no—
540#95—22no—
541#95—21no—
542#95—22no—
543#95—22no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—22no—
552#95—22no—
553#95C2×D412yes—
554#95C2×D412yes—
555#95C2×D412yes—
556C24—22no—
557C24—21no—
558#41—816no—
559C2×Q8—24no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—44no—
571C2×Q8—42no—
572C2×Q8—42no—
573C2×Q8—42no—
574C2×Q8—82no—
575C2×Q8—81no—
576C2×Q8—82no—
577C2×Q8—81no—
578C2×Q8#12114yes—
579C2×Q8C22×D412yes—
580C2×Q8C2×#4112yes—
581C2×Q8C2×#4112yes—
582C2×Q82−1+412yes—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—22no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—22no—
593C2×D4—21no—
594C2×D4—22no—
595C2×D4—44no—
596C2×D4—44no—
597C2×D4—44no—
598C2×D4—42no—
599C2×D4—44no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—82no—
604C2×D4—81no—
605C2×D4—82no—
606C2×D4—81no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—22no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D412yes—
626C22×C4C22×D412yes—
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D412yes—
629C22×C4C22×D412yes—
630C22×C4C22×D411yescharacteristic
631C22×C4C22×D411yescharacteristic
632C22×C4C22×D411yescharacteristic
633C22×C4C2511yescharacteristic
634Q16—28no—
635SD16—44no—
636SD16—48no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—21no—
645C2×C8—22no—
646C2×C8—21no—
647C2×C8—22no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—22no—
651C2×C8—21no—
652C2×C8—22no—
653C2×C8—21no—
654C2×C8C2×#4112yes—
655C4⋊C4—24no—
656C4⋊C4—28no—
657C4⋊C4—24no—
658C4⋊C4—28no—
659C4⋊C4—24no—
660C4⋊C4—28no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—22no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—22no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—22no—
674C4⋊C4—21no—
675C4⋊C4—22no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C4⋊C4—44no—
682C4⋊C4—44no—
683C4⋊C4—42no—
684C4⋊C4—44no—
685C4⋊C4—42no—
686C4⋊C4—42no—
687C4⋊C4—81no—
688C4⋊C4—82no—
689C4⋊C4#12114yes—
690C4⋊C4#12118yes—
691C4⋊C4C22×D414yes—
692C4⋊C4C22×D412yes—
693C4⋊C42−1+412yes—
694C22⋊C4—44no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—44no—
698C22⋊C4—44no—
699C22⋊C4—42no—
700C22⋊C4—44no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—44no—
704C22⋊C4—82no—
705C22⋊C4—82no—
706C22⋊C4—82no—
707C22⋊C4—82no—
708C22⋊C4—82no—
709C22⋊C4—82no—
710C42—24no—
711C42—28no—
712C42—24no—
713C42—22no—
714C42—22no—
715C42—24no—
716C42—22no—
717C42—22no—
718C42—21no—
719C42—21no—
720C42—21no—
721C42—22no—
722C42—21no—
723C42—42no—
724C42—42no—
725C42—42no—
726C42—41no—
727C42—44no—
728C42—42no—
729C42—44no—
730C42—44no—
731C42—44no—
732C42—42no—
733C42—42no—
734C42—42no—
735C42—82no—
736C42—81no—
737C42C22×D412yes—
738C42C22×D414yes—
739C42C2×#4114yes—
740C42C2×#4112yes—
741C23—42no—
742C23—41no—
743C23—42no—
744C23—41no—
745C23—42no—
746C23—41no—
747C23—42no—
748C23—41no—
749C23—42no—
750C23—41no—
751C23—42no—
752C23—41no—
753C23—42no—
754C23—41no—
755C23C23×D411yescharacteristic
756Q8—22no—
757Q8—22no—
758Q8—22no—
759Q8—28no—
760Q8—22no—
761Q8—22no—
762Q8—41no—
763Q8—41no—
764Q8—48no—
765Q8—164no—
766Q8—162no—
767Q8#54814yes—
768D4—41no—
769D4—42no—
770D4—41no—
771D4—42no—
772D4—41no—
773D4—42no—
774D4—42no—
775D4—41no—
776D4—88no—
777D4—84no—
778D4—164no—
779D4—162no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—24no—
796C2×C4—22no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—88no—
834C2×C4—84no—
835C2×C4C2×#12114yes—
836C2×C4C2×#12114yes—
837C2×C4C2×#12112yes—
838C2×C4C2×#12112yes—
839C2×C4#57512yes—
840C2×C4#57512yes—
841C2×C4#57712yes—
842C2×C4C23×D411yescharacteristic
843C2×C4C22×#4111yescharacteristic
844C2×C4C22×#4111yescharacteristic
845C2×C4C2×2−1+411yescharacteristic
846C2×C4C2×2−1+411yescharacteristic
847C2×C4#58511yescharacteristic
848C8—22no—
849C8—41no—
850C8—42no—
851C8—41no—
852C8—41no—
853C8—42no—
854C22—82no—
855C22—81no—
856C22—82no—
857C22—81no—
858C22—82no—
859C22—81no—
860C22—82no—
861C22—81no—
862C22—82no—
863C22—81no—
864C22—82no—
865C22—81no—
866C22—82no—
867C22—81no—
868C22C22×#12111yescharacteristic
869C22D4×#4111yescharacteristic
870C22#348611yescharacteristic
871C22C2×#57511yescharacteristic
872C22C2×#57511yescharacteristic
873C22C2×#57711yescharacteristic
874C22#358511yescharacteristic
875C4—24no—
876C4—22no—
877C4—24no—
878C4—22no—
879C4—24no—
880C4—42no—
881C4—41no—
882C4—42no—
883C4—41no—
884C4—42no—
885C4—42no—
886C4—41no—
887C4—42no—
888C4—44no—
889C4—81no—
890C4—82no—
891C4—81no—
892C4—82no—
893C4—81no—
894C4#304014yes—
895C4C2×#54811yescharacteristic
896C4#348211yescharacteristic
897C4#349711yescharacteristic
898C4#351611yescharacteristic
899C2—162no—
900C2—161no—
901C2#3643411yescharacteristic
902C2C2×#304011yescharacteristic
903C2#6043111yescharacteristic
904C2#6145011yescharacteristic
905C2#6146211yescharacteristic
906C2#6183311yescharacteristic
907C2#6183611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#550C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3387C2semidirect
4. C4×#557C2semidirect
5. #33031C2semidirect
6. #33025C2semidirect
7. #28661C2semidirect
8. #28654C2semidirect
9. #28208C2semidirect
10. #28203C2semidirect
11. #25466C2semidirect
12. #25452C2semidirect
13. #25291C2semidirect
14. #25279C2semidirect
15. #24828C2semidirect
16. #24814C2semidirect
17. #24747C2semidirect
18. #24733C2semidirect
19. #22736C2semidirect
21. #22525C2semidirect
22. #21508C2semidirect
23. C4×#464C2semidirect
359. C2×Q16#41semidirect

Maximal subgroups

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

subgroupindex
C2×#33872
C2×#33682
#364572
C4×#5572
#330312
#330252
#286612
#286542
#282082
#282032
#254662
#254522
#252912
#252792
#248282
#248142
#247472
#247332
#227362
#225452
#225252
#215082
C4×#4642