Finite Group Databasebeta

← #6404580

Subgroups — #6404580

Order 512.

1931 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3394C211yesmaximal, characteristic
2#34498C211yesmaximal, characteristic, complemented
3#34481C211yesmaximal, characteristic, complemented
4#23191C212yesmaximal, complemented
5#23190C211yesmaximal, characteristic, complemented
6#23011C212yesmaximal, complemented
7#23009C212yesmaximal, complemented
8#22998C211yesmaximal, characteristic, complemented
9#22995C211yesmaximal, characteristic
10Q8×#107C211yesmaximal, characteristic, complemented
11#22671C211yesmaximal, characteristic, complemented
12#22671C212yesmaximal, complemented
13#22546C211yesmaximal, characteristic, complemented
14#22544C211yesmaximal, characteristic, complemented
15#22163C212yesmaximal, complemented
16#22157C212yesmaximal, complemented
17#22148C211yesmaximal, characteristic, complemented
18#22145C211yesmaximal, characteristic
19#21696C212yesmaximal, complemented
20#21692C211yesmaximal, characteristic, complemented
21#21285C212yesmaximal, complemented
22#21279C211yesmaximal, characteristic, complemented
23#20521C211yesmaximal, characteristic, complemented
24C2×#559C2211yescharacteristic
25C2×#556C2211yescharacteristic
26#3394C4116yescomplemented
27C2×#495C2212yes—
28C2×#492C2211yescharacteristic
29C2×#464C2212yes—
30C2×#462C2211yescharacteristic
31C2×#463C2212yes—
32C2×#459C2211yescharacteristic
33C2×#446C2211yescharacteristic
34C2×C8×Q8C2211yescharacteristic
35C2×#440C2212yes—
36C2×#440C2212yes—
37C2×#440C2212yes—
38C2×#440C2212yes—
39C2×C4×Q16C2212yes—
40C2×C4×SD16C2211yescharacteristic
41C2×C4×SD16C2212yes—
42C2×C4×D8C2212yes—
43#2383—22no—
44#2376—22no—
45#2367—21no—
46#2367C2212yes—
47#2367C2212yes—
48#2366C2211yescharacteristic
49#2365C2211yescharacteristic
50#2360—21no—
51Q8×C4⋊C4C2211yescharacteristic
52Q8×C4⋊C4C2211yescharacteristic
53Q8×C4⋊C4C2212yes—
54Q8×C4⋊C4C2211yescharacteristic
55D4×C4⋊C4—21no—
56D4×C4⋊C4C2211yescharacteristic
57D4×C4⋊C4C2212yes—
58#2347—21no—
59#2334—22no—
60#2326—21no—
61#2326C2212yes—
62#2326C2212yes—
63#2323—21no—
64#2322—22no—
65#2320C2212yes—
66#2319—21no—
67#2319C2212yes—
68#2317—21no—
69C4×C4⋊Q8C2211yescharacteristic
70C4×#127C2211yescharacteristic
71#2295C2211yescharacteristic
72#2295C2211yescharacteristic
73#2293C2211yescharacteristic
74#1983C2212yes—
75#1983C2212yes—
76#1982C2211yescharacteristic
77#1981C2211yescharacteristic
78#1973C2211yescharacteristic
79#1973C2211yescharacteristic
80#1973C2212yes—
81#1973C2212yes—
82#1973C2212yes—
83#1970C2212yes—
84#1969C2212yes—
85#1959C2212yes—
86#1959C2212yes—
87#1957C2211yescharacteristic
88#1956C2211yescharacteristic
89#1947C2211yescharacteristic
90#1947C2211yescharacteristic
91#1947C2212yes—
92#1947C2212yes—
93#1944C2211yescharacteristic
94#1944C2211yescharacteristic
95#1944C2212yes—
96#1936C2211yescharacteristic
97#1936C2211yescharacteristic
98#1935C2211yescharacteristic
99#1935C2211yescharacteristic
100#1934C2212yes—
101#1934C2212yes—
102#1933C2212yes—
103#1933C2212yes—
104#1880C2212yes—
105#1879C2212yes—
106#1879C2212yes—
107#1878C2212yes—
108#1878C2212yes—
109#1877C2212yes—
110#1863C2212yes—
111#1863C2212yes—
112#1863C2212yes—
113#1862C2212yes—
114#1862C2212yes—
115#1862C2212yes—
116#1845C2211yescharacteristic
117#1845C2212yes—
118#1803C2212yes—
119#1803C2211yescharacteristic
120#1802C2211yescharacteristic
121#1802C2212yes—
122C4×#107C2211yescharacteristic
123C4×#107C2212yes—
124#1771C2212yes—
125#1770C2211yescharacteristic
126#1770C2212yes—
127C8×C4⋊C4C2211yescharacteristic
128#1768C2212yes—
129C4×C4⋊C8C2211yescharacteristic
130#1763C2212yes—
131#1762C2212yes—
132C4×#103C2211yescharacteristic
133C4×#102C2211yescharacteristic
134#1726C2212yes—
135C4×#97C2211yescharacteristic
136C22×Q16C2312yes—
137C22×SD16C2312yes—
138C22×SD16C2311yescharacteristic
139C22×SD16C2312yes—
140C22×D8C2312yes—
141#559—24no—
142#559C2×C418yescomplemented
143#556—24no—
144#556C2×C418yescomplemented
145C2×C4⋊Q8C2311yescharacteristic
146C2×#127C2311yescharacteristic
147C2×#126—22no—
148C2×#124—21no—
149C2×#124C2312yes—
150C2×#124C2312yes—
151C2×#123—22no—
152C2×C22⋊Q8—21no—
153C2×C4×Q8—21no—
154C2×C4×Q8—21no—
155C2×C4×Q8C2312yes—
156C2×C4×Q8C2311yescharacteristic
157C2×C4×Q8C2312yes—
158C2×C4×Q8C2312yes—
159C2×C4×Q8C2312yes—
160C2×C4×Q8C2311yescharacteristic
161C2×C4×D4—21no—
162C2×C4×D4—21no—
163C2×C4×D4—21no—
164C2×C4×D4—21no—
165C2×C4×D4C2312yes—
166C2×C4×D4C2311yescharacteristic
167C2×C4×D4C2312yes—
168C2×C4×D4C2312yes—
169C2×C4×D4C2312yes—
170C2×#117—21no—
171C2×#117—21no—
172C22×C4⋊C4—21no—
173C22×C4⋊C4—22no—
174#495C2×C4116yescomplemented
175#492C2×C418yescomplemented
176#464C2×C4116yescomplemented
177#463C2×C4116yescomplemented
178#462C2×C418yescomplemented
179#459C2×C418yes—
180#446—24no—
181C8×Q8C2×C418yescomplemented
182#440—44no—
183#440—44no—
184#440—44no—
185#440—44no—
186C4×Q16—44no—
187C4×SD16C2×C418yescomplemented
188C4×SD16C2×C4116yescomplemented
189C4×D8—44no—
190C2×#107C2311yescharacteristic
191C2×#107C2312yes—
192C2×#107C2311yescharacteristic
193C2×#107C2312yes—
194C2×#107C2312yes—
195C2×#107C2312yes—
196C2×#106C2311yescharacteristic
197C2×C4⋊C8C2311yescharacteristic
198C2×C4⋊C8C2312yes—
199C2×C4⋊C8C2311yescharacteristic
200C2×C4⋊C8C2312yes—
201C2×#103C2311yescharacteristic
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#103C2312yes—
206C2×#103C2311yescharacteristic
207C2×#103C2312yes—
208C2×#103C2312yes—
209C2×#103C2311yescharacteristic
210C2×#102C2311yescharacteristic
211C2×#102C2312yes—
212C2×#102C2312yes—
213C2×#102C2312yes—
214C2×#102C2312yes—
215C2×#102C2312yes—
216C2×#102C2311yescharacteristic
217C2×#102C2312yes—
218C2×#102C2311yescharacteristic
219C2×#97C2311yescharacteristic
220C2×#97C2311yescharacteristic
221C2×#97C2312yes—
222C2×#97C2312yes—
223C2×#97C2311yescharacteristic
224C2×#97C2311yescharacteristic
225C2×C4×C8C2312yes—
226C2×C4×C8C2311yescharacteristic
227C2×C4×C8C2312yes—
228C2×C4×C8C2311yescharacteristic
229C2×C4×C8C2312yes—
230#391D411yescharacteristic
231#391D411yescharacteristic
232#391C2312yes—
233#391C2312yes—
234#391C2311yescharacteristic
235#391C2311yescharacteristic
236#390—21no—
237#390—21no—
238#390—21no—
239#390C2312yes—
240#390C2312yes—
241#390C2311yescharacteristic
242#390C2311yescharacteristic
243#389—21no—
244#389—21no—
245#389—21no—
246#389—22no—
247#389—22no—
248#389—21no—
249#389—21no—
250#389—22no—
251#389—22no—
252#389—22no—
253#389D411yescharacteristic
254#389D411yescharacteristic
255#389C2311yescharacteristic
256#389C2312yes—
257#389C2311yescharacteristic
258#389C2312yes—
259#389C2311yescharacteristic
260#389C2311yescharacteristic
261#388—22no—
262#388—22no—
263#388—21no—
264#388—21no—
265#388—22no—
266#388—22no—
267#388—22no—
268#388—22no—
269#388—22no—
270#388—22no—
271#388—22no—
272#388—22no—
273#387—21no—
274#387—21no—
275#387—22no—
276#387—22no—
277#387—22no—
278#387D412yes—
279#387D412yes—
280#386—22no—
281#385—22no—
282#385—22no—
283#385—22no—
284#385—22no—
285#385—22no—
286#385—22no—
287#385—22no—
288#385—22no—
289#385—22no—
290#384—22no—
291#384—21no—
292#384C2311yescharacteristic
293#384C2311yescharacteristic
294#384C2312yes—
295#384C2312yes—
296#383—22no—
297#382—22no—
298#381—22no—
299#380—22no—
300#380—21no—
301#380—22no—
302C4×C4⋊C4—21no—
303C4×C4⋊C4—21no—
304C4×C4⋊C4—22no—
305C4×C4⋊C4—21no—
306C4×C4⋊C4—21no—
307C4×C4⋊C4—21no—
308C4×C4⋊C4C2312yes—
309C4×C4⋊C4C2312yes—
310C4×C4⋊C4C2311yescharacteristic
311C4×C4⋊C4C2311yescharacteristic
312C4×C4⋊C4C2311yescharacteristic
313C4×C4⋊C4C2312yes—
314C4×C22⋊C4—21no—
315C4×C22⋊C4—22no—
316C4×C22⋊C4—22no—
317#376—21no—
318#376C2312yes—
319C43C2311yescharacteristic
320#340C2311yescharacteristic
321#340C2312yes—
322#340C2312yes—
323#340C2311yescharacteristic
324#340C2311yescharacteristic
325#340C2312yes—
326#340C2312yes—
327#340C2311yescharacteristic
328#340C2311yescharacteristic
329#340C2311yescharacteristic
330#336C2312yes—
331#336C2312yes—
332#336C2312yes—
333C22×Q8C2×D411yescharacteristic
334C22×Q8C2411yescharacteristic
335C22×Q8C2412yes—
336C22×D4—21no—
337C22×D4—21no—
338C22×D4C2411yescharacteristic
339C22×D4C2412yes—
340C23×C4—21no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C2×Q16—42no—
346C2×Q16—42no—
347C2×Q16C22×C418yes—
348C2×SD16—24no—
349C2×SD16—22no—
350C2×SD16—24no—
351C2×SD16—22no—
352C2×SD16—42no—
353C2×SD16—42no—
354C2×SD16C22×C418yes—
355C2×SD16C22×C414yes—
356C2×SD16C22×C418yes—
357C2×D8—42no—
358C2×D8—42no—
359C2×D8C22×C418yes—
360C22×C8C2411yescharacteristic
361C22×C8C2412yes—
362C22×C8C2412yes—
363C22×C8C2411yescharacteristic
364C22×C8C2411yescharacteristic
365C22×C8C2411yescharacteristic
366C4⋊Q8—22no—
367C4⋊Q8C22×C414yes—
368#127—22no—
369#127C22×C414yes—
370#126—216no—
371#124—28no—
372#124—24no—
373#124—24no—
374#124C22×C418yes—
375#124C22×C418yes—
376#123—216no—
377C22⋊Q8—28no—
378C4×Q8—24no—
379C4×Q8—22no—
380C4×Q8—42no—
381C4×Q8—42no—
382C4×Q8—42no—
383C4×Q8—42no—
384C4×Q8—42no—
385C4×Q8—42no—
386C4×Q8—82no—
387C4×Q8—82no—
388C4×Q8C22×C418yes—
389C4×Q8C22×C414yes—
390C4×Q8C22×C414yes—
391C4×Q8#4114yes—
392C4×D4—28no—
393C4×D4—22no—
394C4×D4—24no—
395C4×D4—42no—
396C4×D4—42no—
397C4×D4—42no—
398C4×D4—42no—
399C4×D4—42no—
400C4×D4—42no—
401C4×D4—82no—
402C4×D4—82no—
403C4×D4—82no—
404C4×D4C22×C414yes—
405C4×D4C22×C418yes—
406#117—28no—
407#117—82no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—82no—
430C2×C4⋊C4—84no—
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2×D412yes—
434C2×C4⋊C4C2×D412yes—
435C2×C4⋊C4C2×D411yescharacteristic
436C2×C4⋊C4C2×D412yes—
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—21no—
462C2×C42—22no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42C2×D411yescharacteristic
472C2×C42C2×D411yescharacteristic
473C2×C42C2×D411yescharacteristic
474C2×C42C2×D411yescharacteristic
475C2×C42C2411yescharacteristic
476C2×C42C2412yes—
477C2×C42C2411yescharacteristic
478C2×C42C2412yes—
479C2×C42C2411yescharacteristic
480#107—22no—
481#107—24no—
482#107—22no—
483#107—42no—
484#107—42no—
485#107—42no—
486#106C22×C414yes—
487C4⋊C8—22no—
488C4⋊C8—24no—
489C4⋊C8C22×C414yes—
490C4⋊C8C22×C418yes—
491#103—22no—
492#103—24no—
493#103—41no—
494#103—42no—
495#103—42no—
496#103—42no—
497#103—42no—
498#103C22×C418yes—
499#103C22×C414yes—
500#102—22no—
501#102—24no—
502#102—42no—
503#102—41no—
504#102—42no—
505#102—42no—
506#102—42no—
507#102C22×C418yes—
508#102C22×C414yes—
509#97—22no—
510#97—22no—
511#97—24no—
512#97—22no—
513#97—24no—
514#97—41no—
515C4×C8—24no—
516C4×C8—22no—
517C4×C8—42no—
518C4×C8C22×C414yes—
519C4×C8C22×C418yes—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—22no—
527#95—21no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—21no—
534#95—22no—
535#95—22no—
536#95—21no—
537#95—21no—
538#95C2×D412yes—
539#95C2×D412yes—
540#95C2×D412yes—
541#95C2×D412yes—
542#95C2×D412yes—
543#95C2×D412yes—
544#95C2×D412yes—
545C24—21no—
546C24—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—21no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—22no—
555C2×Q8—21no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—21no—
559C2×Q8C4×D414yes—
560C2×Q8C23×C412yes—
561C2×Q8C23×C414yes—
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—21no—
565C2×D4—22no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—81no—
577C2×D4—81no—
578C2×D4C23×C412yes—
579C2×D4C23×C414yes—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—24no—
585C22×C4—28no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—44no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—82no—
596C22×C4—82no—
597C22×C4—82no—
598C22×C4—82no—
599C22×C4—82no—
600C22×C4—82no—
601C22×C4—82no—
602C22×C4—82no—
603C22×C4—82no—
604C22×C4—82no—
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D412yes—
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D412yes—
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D412yes—
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D412yes—
614C22×C4C22×D411yescharacteristic
615C22×C4C2511yescharacteristic
616Q16—48no—
617SD16—216no—
618SD16—28no—
619SD16—48no—
620D8—48no—
621C2×C8—21no—
622C2×C8—22no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—22no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—22no—
629C2×C8—21no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—21no—
633C2×C8C23×C414yes—
634C2×C8C23×C412yes—
635C2×C8C23×C412yes—
636C2×C8H(5,𝔽2)12yes—
637C2×C8H(5,𝔽2)12yes—
638C2×C82−1+412yes—
639C4⋊C4—24no—
640C4⋊C4—28no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—22no—
649C4⋊C4—21no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—81no—
665C4⋊C4—82no—
666C4⋊C4—81no—
667C4⋊C4—82no—
668C4⋊C4—82no—
669C4⋊C4—82no—
670C4⋊C4—81no—
671C4⋊C4—81no—
672C4⋊C4—81no—
673C4⋊C4—82no—
674C4⋊C4—82no—
675C4⋊C4—82no—
676C4⋊C4—82no—
677C4⋊C4—82no—
678C4⋊C4C4×D414yes—
679C4⋊C4C4×D418yes—
680C4⋊C4C23×C412yes—
681C4⋊C4C23×C412yes—
682C22⋊C4—28no—
683C22⋊C4—28no—
684C22⋊C4—28no—
685C22⋊C4—24no—
686C22⋊C4—28no—
687C22⋊C4—28no—
688C22⋊C4—42no—
689C22⋊C4—81no—
690C22⋊C4—82no—
691C22⋊C4—81no—
692C22⋊C4—81no—
693C22⋊C4—82no—
694C22⋊C4—82no—
695C22⋊C4—82no—
696C22⋊C4—82no—
697C22⋊C4—82no—
698C22⋊C4—82no—
699C42—28no—
700C42—24no—
701C42—22no—
702C42—22no—
703C42—22no—
704C42—21no—
705C42—22no—
706C42—21no—
707C42—21no—
708C42—21no—
709C42—41no—
710C42—41no—
711C42—42no—
712C42—42no—
713C42—82no—
714C42—82no—
715C42—82no—
716C42—82no—
717C42—82no—
718C42C23×C414yes—
719C42C23×C412yes—
720C42C2×#4112yes—
721C42C2×#4114yes—
722C23—22no—
723C23—24no—
724C23—42no—
725C23—41no—
726C23—41no—
727C23—42no—
728C23—41no—
729C23—42no—
730C23—41no—
731C23—42no—
732C23—41no—
733C23—42no—
734C23—41no—
735C23—42no—
736C23C23×D411yescharacteristic
737Q8—28no—
738Q8—22no—
739Q8—24no—
740Q8—24no—
741Q8—22no—
742Q8—41no—
743Q8—42no—
744Q8—41no—
745Q8—42no—
746D4—22no—
747D4—24no—
748D4—22no—
749D4—24no—
750D4—48no—
751D4—41no—
752D4—42no—
753D4—41no—
754D4—42no—
755D4—84no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—48no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—88no—
812C2×C4—164no—
813C2×C4—164no—
814C2×C4—164no—
815C2×C4C2×C4×D414yes—
816C2×C4C2×C4×D414yes—
817C2×C4C2×C4×D412yes—
818C2×C4C2×C4×D412yes—
819C2×C4#57612yes—
820C2×C4#57812yes—
821C2×C4C24×C411yescharacteristic
822C2×C4C22×#4111yescharacteristic
823C2×C4C2×H(5,𝔽2)11yescharacteristic
824C2×C4C2×H(5,𝔽2)11yescharacteristic
825C2×C4C2×2−1+411yescharacteristic
826C2×C4#58511yescharacteristic
827C8—24no—
828C8—22no—
829C8—22no—
830C8—41no—
831C8—42no—
832C8#52014yes—
833C22—42no—
834C22—44no—
835C22—42no—
836C22—44no—
837C22—44no—
838C22—42no—
839C22—81no—
840C22—82no—
841C22—81no—
842C22—82no—
843C22—82no—
844C22—81no—
845C22—82no—
846C22—81no—
847C22C22×C4×D411yescharacteristic
848C22#349711yescharacteristic
849C22#349811yescharacteristic
850C22C2×#57611yescharacteristic
851C22C2×#57811yescharacteristic
852C22#358511yescharacteristic
853C22#358611yescharacteristic
854C4—24no—
855C4—24no—
856C4—22no—
857C4—41no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—44no—
862C4—42no—
863C4—41no—
864C4—41no—
865C4—41no—
866C4—42no—
867C4—81no—
868C4—81no—
869C4—81no—
870C4—82no—
871C4—82no—
872C4—81no—
873C4#295114yes—
874C4C2×#52011yescharacteristic
875C4C4×H(5,𝔽2)11yescharacteristic
876C4#351711yescharacteristic
877C4#352211yescharacteristic
878C2—82no—
879C2—84no—
880C2#3431311yescharacteristic
881C2C2×#295111yescharacteristic
882C2#6017411yescharacteristic
883C2#6240311yescharacteristic
884C2#6240411yescharacteristic
885C2#6246311yescharacteristic
886C2#6246411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#459C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2295 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34498C2semidirect
3. #34481C2semidirect
4. #23191C2semidirect
5. #23190C2semidirect
6. #23011C2semidirect
7. #23009C2semidirect
8. #22998C2semidirect
10. Q8×#107C2semidirect
11. #22671C2semidirect
12. #22671C2semidirect
13. #22546C2semidirect
14. #22544C2semidirect
15. #22163C2semidirect
16. #22157C2semidirect
17. #22148C2semidirect
19. #21696C2semidirect
20. #21692C2semidirect
21. #21285C2semidirect
22. #21279C2semidirect
23. #20521C2semidirect
26. #3394C4semidirect
142. #559C2×C4semidirect
144. #556C2×C4semidirect
174. #495C2×C4semidirect
175. #492C2×C4semidirect
176. #464C2×C4semidirect
177. #463C2×C4semidirect
178. #462C2×C4semidirect
181. C8×Q8C2×C4semidirect
187. C4×SD16C2×C4semidirect
188. C4×SD16C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#33942
#344982
#344812
#231912
#231902
#230112
#230092
#229982
#229952
Q8×#1072
#226712
#225462
#225442
#221632
#221572
#221482
#221452
#216962
#216922
#212852
#212792
#205212