Finite Group Databasebeta

← #6382462

Subgroups — #6382462

Order 512.

2028 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3103C211yesmaximal, characteristic
2#34236C211yesmaximal, characteristic
3#34192C211yesmaximal, characteristic, complemented
4#23106C212yesmaximal, complemented
5#23077C212yesmaximal, complemented
6#23010C212yesmaximal, complemented
7#22981C212yesmaximal, complemented
8#22936C212yesmaximal, complemented
9#22918C212yesmaximal, complemented
10#22875C212yesmaximal, complemented
11#22855C212yesmaximal, complemented
12#21408C211yesmaximal, characteristic
13#21361C211yesmaximal, characteristic, complemented
14#21285C211yesmaximal, characteristic, complemented
15#21280C211yesmaximal, characteristic, complemented
16#21136C211yesmaximal, characteristic, complemented
17#21133C211yesmaximal, characteristic, complemented
18#21131C211yesmaximal, characteristic, complemented
19#21130C211yesmaximal, characteristic, complemented
20#20506C211yesmaximal, characteristic, complemented
21#20504C211yesmaximal, characteristic, complemented
22#20481C211yesmaximal, characteristic, complemented
23C2×#1763C211yesmaximal, characteristic, complemented
24C2×#532C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26#3103C4116yescomplemented
27C2×#481C2211yescharacteristic
28C2×#481C2211yescharacteristic
29C2×#475C2211yescharacteristic
30C2×#475C2211yescharacteristic
31C2×#460C2211yescharacteristic
32C2×#460C2211yescharacteristic
33C2×#448C2211yescharacteristic
34C2×#448C2211yescharacteristic
35C2×#440C2212yes—
36C2×C4×SD16C2212yes—
37C2×C4×SD16C2211yescharacteristic
38C2×C4×SD16C2211yescharacteristic
39C2×C4×SD16C2211yescharacteristic
40C2×C4×SD16C2211yescharacteristic
41C2×#431C2211yescharacteristic
42C22×#103C2212yes—
43C22×#97C2211yescharacteristic
44#2369C2212yes—
45#2366C2212yes—
46#2361C2212yes—
47#2361C2212yes—
48#2357—21no—
49#2356—22no—
50#2356C2212yes—
51#2351C2212yes—
52#2349—21no—
53#2345—22no—
54#2345C2212yes—
55Q8×C22⋊C4C2212yes—
56#2339—21no—
57#2339—21no—
58#2337—22no—
59#2320—21no—
60#2320—21no—
61#2320C2211yescharacteristic
62#2320C2211yescharacteristic
63#2319C2211yescharacteristic
64#2319C2211yescharacteristic
65C4×#121—22no—
66#2283—21no—
67#2283—21no—
68#2283C2211yescharacteristic
69#2283C2211yescharacteristic
70#2276C2211yescharacteristic
71#2276C2211yescharacteristic
72#2275C2211yescharacteristic
73#2275C2211yescharacteristic
74C2×C4×C4⋊C4C2211yescharacteristic
75#1993C2212yes—
76#1973C2212yes—
77#1968C2212yes—
78#1961C2212yes—
79#1949C2212yes—
80#1949C2212yes—
81#1944C2212yes—
82#1941C2212yes—
83#1936C2212yes—
84#1935C2212yes—
85#1934C2212yes—
86#1933C2212yes—
87#1928C2212yes—
88#1927C2212yes—
89#1926C2212yes—
90#1925C2212yes—
91#1920C2212yes—
92#1920C2212yes—
93#1919C2212yes—
94#1919C2212yes—
95#1893C2212yes—
96#1893C2212yes—
97#1880C2212yes—
98#1880C2212yes—
99#1877C2212yes—
100#1877C2212yes—
101#1865C2212yes—
102#1864C2212yes—
103#1863C2212yes—
104#1862C2212yes—
105#1853C2212yes—
106#1852C2212yes—
107#1776C2212yes—
108C4×#107C2211yescharacteristic
109C4×#107C2211yescharacteristic
110C4×#106C2212yes—
111C4×#106C2211yescharacteristic
112C4×#106C2211yescharacteristic
113#1771C2212yes—
114#1771C2212yes—
115#1763C2211yescharacteristic
116#1763C2212yes—
117#1763C2211yescharacteristic
118#1763C2212yes—
119#1763C2211yescharacteristic
120#1763C2211yescharacteristic
121#1763C2212yes—
122#1762C2211yescharacteristic
123#1762C2211yescharacteristic
124#1762C2212yes—
125#1762C2211yescharacteristic
126#1762C2211yescharacteristic
127C4×#103C2212yes—
128C4×#102C2212yes—
129#1752C2212yes—
130C8×C22⋊C4C2212yes—
131#1746C2211yescharacteristic
132#1746C2211yescharacteristic
133C2×#340C2212yes—
134#1726C2211yescharacteristic
135#1726C2211yescharacteristic
136C22×#41—21no—
137C23×Q8C2311yescharacteristic
138C22×SD16C2311yescharacteristic
139C22×SD16C2311yescharacteristic
140C22×SD16C2311yescharacteristic
141C22×SD16C2311yescharacteristic
142C23×C8C2312yes—
143#532—24no—
144#532C2×C418yes—
145C2×C4⋊Q8C2311yescharacteristic
146C2×#127C2311yescharacteristic
147C2×#124—21no—
148C2×#121—21no—
149C2×#121C2311yescharacteristic
150C2×#121C2311yescharacteristic
151C2×C4×Q8—21no—
152C2×C4×Q8—21no—
153C2×C4×Q8—24no—
154C2×C4×Q8C2×C418yescomplemented
155C2×C4×Q8C2312yes—
156C2×C4×Q8C2312yes—
157C2×C4×Q8C2311yescharacteristic
158C2×C4×Q8C2311yescharacteristic
159C2×C4×Q8C2311yescharacteristic
160C2×C4×Q8C2311yescharacteristic
161C2×C4×D4—22no—
162C2×C4×D4—22no—
163C2×C4×D4—22no—
164C2×C4×D4—21no—
165C2×C4×D4C2312yes—
166C2×C4×D4C2312yes—
167C2×C4×D4C2311yescharacteristic
168C2×C4×D4C2311yescharacteristic
169C22×C4⋊C4—21no—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2311yescharacteristic
172C22×C42—21no—
173C22×C42—21no—
174C22×C42C2311yescharacteristic
175#481C2×C418yescomplemented
176#481C2×C418yescomplemented
177#475C2×C418yescomplemented
178#475C2×C418yescomplemented
179#460C2×C418yescomplemented
180#460C2×C418yescomplemented
181#448C2×C418yescomplemented
182#448C2×C418yescomplemented
183#440—28no—
184C4×SD16—28no—
185C4×SD16C2×C418yescomplemented
186C4×SD16C2×C418yescomplemented
187C4×SD16C2×C418yescomplemented
188C4×SD16C2×C418yescomplemented
189#431C2×C418yescomplemented
190C2×#107C2312yes—
191C2×#107C2312yes—
192C2×#106C2312yes—
193C2×#106C2312yes—
194C2×#106C2311yescharacteristic
195C2×#106C2311yescharacteristic
196C2×#106C2311yescharacteristic
197C2×#106C2311yescharacteristic
198C2×C4⋊C8C2311yescharacteristic
199C2×C4⋊C8C2311yescharacteristic
200C2×#103—28no—
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#103C2311yescharacteristic
205C2×#103C2311yescharacteristic
206C2×#103C2311yescharacteristic
207C2×#103C2311yescharacteristic
208C2×#103C2312yes—
209C2×#102C2312yes—
210C2×#102C2312yes—
211C2×#102C2312yes—
212C2×#102C2312yes—
213C2×#102C2311yescharacteristic
214C2×#102C2311yescharacteristic
215C2×#102C2311yescharacteristic
216C2×#102C2311yescharacteristic
217C2×C22⋊C8C2311yescharacteristic
218C2×C22⋊C8C2311yescharacteristic
219C2×#97—24no—
220C2×#97C2312yes—
221C2×#97C2311yescharacteristic
222C2×#97C2311yescharacteristic
223C2×#97C2312yes—
224C2×#97C2312yes—
225C2×C4×C8C2312yes—
226C2×C4×C8C2312yes—
227C2×C4×C8C2311yescharacteristic
228C2×C4×C8C2311yescharacteristic
229#391—22no—
230#391—22no—
231#391—22no—
232#391—22no—
233#391C2312yes—
234#391C2312yes—
235#390—22no—
236#390C2312yes—
237#390C2312yes—
238#389—22no—
239#389—22no—
240#389—22no—
241#389C2312yes—
242#389C2312yes—
243#389C2312yes—
244#389C2312yes—
245#388—22no—
246#388—22no—
247#388—22no—
248#388—22no—
249#387—22no—
250#387—22no—
251#387—22no—
252#387—22no—
253#387—22no—
254#387—22no—
255#386—22no—
256#386—22no—
257#386—22no—
258#386—22no—
259#385—22no—
260#385—22no—
261#383—21no—
262#383—21no—
263#383—21no—
264#383—22no—
265#383D412yes—
266#382—21no—
267#382—21no—
268#382—22no—
269#382D411yescharacteristic
270#382D411yescharacteristic
271#382C2312yes—
272#381—21no—
273#381—21no—
274#381—21no—
275#381D411yescharacteristic
276#381D411yescharacteristic
277#380—22no—
278#380—22no—
279#380—21no—
280#380—21no—
281#380D412yes—
282#380C2312yes—
283C4×C4⋊C4—22no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4—21no—
286C4×C4⋊C4—21no—
287C4×C4⋊C4—21no—
288C4×C4⋊C4—22no—
289C4×C4⋊C4—22no—
290C4×C4⋊C4—22no—
291C4×C4⋊C4C2311yescharacteristic
292C4×C4⋊C4C2311yescharacteristic
293C4×C4⋊C4C2311yescharacteristic
294C4×C4⋊C4C2312yes—
295C4×C4⋊C4C2312yes—
296C4×C4⋊C4C2312yes—
297C4×C4⋊C4C2312yes—
298C4×C4⋊C4C2312yes—
299C4×C4⋊C4C2311yescharacteristic
300C4×C4⋊C4C2312yes—
301C4×C22⋊C4—21no—
302C4×C22⋊C4—22no—
303C4×C22⋊C4—22no—
304C4×C22⋊C4—22no—
305C4×C22⋊C4—22no—
306C4×C22⋊C4—21no—
307C4×C22⋊C4—21no—
308C4×C22⋊C4C2312yes—
309#376—21no—
310#376—21no—
311#376—21no—
312#376—22no—
313#376C2311yescharacteristic
314#376C2311yescharacteristic
315C2×#95—21no—
316C2×#95—21no—
317C2×#95—21no—
318#340C2312yes—
319#340C2312yes—
320#340C2312yes—
321#340C2312yes—
322#340C2312yes—
323#340C2312yes—
324#340C2312yes—
325#340C2312yes—
326#340C2312yes—
327#340C2312yes—
328#340C2312yes—
329#340C2312yes—
330#336C2312yes—
331#336C2312yes—
332#336C2312yes—
333#336C2312yes—
334C2×#41—28no—
335C2×#41—84no—
336C22×Q8—21no—
337C22×Q8—21no—
338C22×Q8—22no—
339C22×Q8—24no—
340C22×Q8—42no—
341C22×Q8C22×C414yes—
342C22×Q8C2411yescharacteristic
343C22×Q8C2411yescharacteristic
344C22×D4—21no—
345C22×D4—21no—
346C22×D4—21no—
347C22×D4—21no—
348C22×D4C2411yescharacteristic
349C22×D4C2411yescharacteristic
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4C2×D411yescharacteristic
358C23×C4C2×D411yescharacteristic
359C23×C4C2411yescharacteristic
360C2×SD16—24no—
361C2×SD16—24no—
362C2×SD16—42no—
363C2×SD16—42no—
364C2×SD16C22×C414yes—
365C2×SD16C22×C414yes—
366C2×SD16C22×C414yes—
367C2×SD16C22×C414yes—
368C22×C8—24no—
369C22×C8—24no—
370C22×C8—42no—
371C22×C8C2412yes—
372C22×C8C2411yescharacteristic
373C22×C8C2411yescharacteristic
374C22×C8C2411yescharacteristic
375C22×C8C2411yescharacteristic
376C22×C8C2412yes—
377C4⋊Q8—22no—
378C4⋊Q8C22×C414yes—
379#127—22no—
380#127C22×C414yes—
381#124—28no—
382#121—28no—
383#121—22no—
384#121—22no—
385#121C22×C414yes—
386#121C22×C414yes—
387C4×Q8—28no—
388C4×Q8—28no—
389C4×Q8—22no—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8—22no—
393C4×Q8—24no—
394C4×Q8—24no—
395C4×Q8—42no—
396C4×Q8—42no—
397C4×Q8C22×C414yes—
398C4×Q8C22×C414yes—
399C4×Q8C22×C414yes—
400C4×Q8C22×C414yes—
401C4×D4—24no—
402C4×D4—24no—
403C4×D4—28no—
404C4×D4—22no—
405C4×D4—22no—
406C4×D4—42no—
407C4×D4—42no—
408C4×D4—84no—
409C4×D4—84no—
410C4×D4—84no—
411C4×D4C22×C414yes—
412C4×D4C22×C414yes—
413C2×C4⋊C4—28no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4C22×C414yes—
431C2×C4⋊C4C2×D412yes—
432C2×C4⋊C4C2×D412yes—
433C2×C4⋊C4C2412yes—
434C2×C4⋊C4C2412yes—
435C2×C4⋊C4C2412yes—
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2411yescharacteristic
440C2×C4⋊C4C2412yes—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4C2×D412yes—
453C2×C22⋊C4C2×D412yes—
454C2×C42—28no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—22no—
465C2×C42—22no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—82no—
471C2×C42C22×C414yes—
472C2×C42C2×D411yescharacteristic
473C2×C42C2×D411yescharacteristic
474C2×C42#4114yes—
475C2×C42C2412yes—
476C2×C42C2412yes—
477C2×C42C2411yescharacteristic
478C2×C42C2411yescharacteristic
479#107—24no—
480#107—42no—
481#106—24no—
482#106—42no—
483#106C22×C414yes—
484#106C22×C414yes—
485#106C22×C414yes—
486#106C22×C414yes—
487C4⋊C8C22×C414yes—
488C4⋊C8C22×C414yes—
489#103—24no—
490#103—24no—
491#103—24no—
492#103C22×C414yes—
493#103C22×C414yes—
494#103C22×C414yes—
495#103C22×C414yes—
496#103#4118yescomplemented
497#102—24no—
498#102—24no—
499#102—42no—
500#102—42no—
501#102C22×C414yes—
502#102C22×C414yes—
503#102C22×C414yes—
504#102C22×C414yes—
505C22⋊C8C22×C414yes—
506C22⋊C8C22×C414yes—
507#97—24no—
508#97—22no—
509#97—22no—
510#97—24no—
511#97—42no—
512C4×C8—24no—
513C4×C8—42no—
514C4×C8C22×C414yes—
515C4×C8C22×C414yes—
516#95—21no—
517#95—22no—
518#95—22no—
519#95—21no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—21no—
525#95—21no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95C2×D411yescharacteristic
537#95C2×D411yescharacteristic
538#95C2×D411yescharacteristic
539#95C2×D412yes—
540#95C2×D412yes—
541#95C2×D412yes—
542#95C2×D411yescharacteristic
543#95C2×D412yes—
544#95C2×D412yes—
545#95C2×D412yes—
546C24—21no—
547C24—21no—
548C24C22×D411yescharacteristic
549#41—816no—
550C2×Q8—24no—
551C2×Q8—24no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—22no—
555C2×Q8—28no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—44no—
559C2×Q8—44no—
560C2×Q8—48no—
561C2×Q8—82no—
562C2×Q8C23×C412yes—
563C2×Q8C23×C412yes—
564C2×Q8C2×#4114yes—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—24no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—44no—
578C2×D4—44no—
579C2×D4—82no—
580C2×D4C23×C412yes—
581C2×D4C23×C412yes—
582C22×C4—24no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—82no—
607C22×C4—82no—
608C22×C4—82no—
609C22×C4—82no—
610C22×C4—82no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C4×D414yes—
616C22×C4C4×D414yes—
617C22×C4C23×C412yes—
618C22×C4C22×D412yes—
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C2×#4112yes—
628C22×C4C2511yescharacteristic
629SD16—28no—
630SD16—28no—
631SD16—44no—
632SD16—44no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—48no—
643C2×C8C23×C412yes—
644C2×C8C23×C412yes—
645C2×C8C23×C412yes—
646C2×C8C23×C412yes—
647C2×C8C2×#4114yes—
648C4⋊C4—24no—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—44no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—82no—
671C4⋊C4—82no—
672C4⋊C4—82no—
673C4⋊C4—82no—
674C4⋊C4C23×C412yes—
675C4⋊C4C23×C412yes—
676C4⋊C4C23×C412yes—
677C4⋊C4C23×C412yes—
678C4⋊C4C2×#4114yes—
679C22⋊C4—24no—
680C22⋊C4—24no—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—44no—
688C22⋊C4—82no—
689C22⋊C4—82no—
690C22⋊C4—82no—
691C22⋊C4—82no—
692C42—24no—
693C42—24no—
694C42—24no—
695C42—24no—
696C42—22no—
697C42—22no—
698C42—22no—
699C42—22no—
700C42—44no—
701C42—44no—
702C42—44no—
703C42—81no—
704C42—81no—
705C42—82no—
706C42—82no—
707C42—81no—
708C42—81no—
709C42—82no—
710C42—82no—
711C42C4×D414yes—
712C42C4×D414yes—
713C42C23×C412yes—
714C42C23×C412yes—
715C42C2×#4112yes—
716C42C2×#4112yes—
717C23—21no—
718C23—21no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23C2×C4×D412yes—
731C23#57714yes—
732C23C23×D411yescharacteristic
733Q8—22no—
734Q8—24no—
735Q8—22no—
736Q8—22no—
737Q8—48no—
738Q8—42no—
739Q8—84no—
740Q8C4×#4114yes—
741D4—22no—
742D4—22no—
743D4—22no—
744D4—22no—
745D4—48no—
746D4—48no—
747D4—48no—
748D4—42no—
749D4—42no—
750D4—84no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—28no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—44no—
783C2×C4—48no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—84no—
803C2×C4—84no—
804C2×C4—84no—
805C2×C4—88no—
806C2×C4—164no—
807C2×C4—164no—
808C2×C4C2×C4×D412yes—
809C2×C4C2×C4×D412yes—
810C2×C4C2×C4×D412yes—
811C2×C4C2×C4×D412yes—
812C2×C4C2×C4×D412yes—
813C2×C4C24×C411yescharacteristic
814C2×C4C22×#4112yes—
815C2×C4C22×#4111yescharacteristic
816C2×C4#58512yes—
817C8—22no—
818C8—22no—
819C8—22no—
820C8—22no—
821C8—24no—
822C8—42no—
823C22—22no—
824C22—24no—
825C22—24no—
826C22—22no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—82no—
834C22—82no—
835C22—82no—
836C22—82no—
837C22#294914yes—
838C22C22×C4×D411yescharacteristic
839C22D4×#4112yes—
840C22C2×#57712yes—
841C22#358511yescharacteristic
842C22#358611yescharacteristic
843C4—22no—
844C4—22no—
845C4—22no—
846C4—22no—
847C4—22no—
848C4—24no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—44no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—82no—
860C4—82no—
861C4—82no—
862C4C2×C4×#4111yescharacteristic
863C4#342811yescharacteristic
864C4#347512yes—
865C2—24no—
866C2—82no—
867C2—82no—
868C2#3413611yescharacteristic
869C2C2×#294911yescharacteristic
870C2#6017011yescharacteristic
871C2#6152112yes—
872C2#6152612yes—
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#532C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #34192C2semidirect
4. #23106C2semidirect
5. #23077C2semidirect
6. #23010C2semidirect
7. #22981C2semidirect
8. #22936C2semidirect
9. #22918C2semidirect
10. #22875C2semidirect
11. #22855C2semidirect
13. #21361C2semidirect
14. #21285C2semidirect
15. #21280C2semidirect
16. #21136C2semidirect
17. #21133C2semidirect
18. #21131C2semidirect
19. #21130C2semidirect
20. #20506C2semidirect
21. #20504C2semidirect
22. #20481C2semidirect
23. C2×#1763C2semidirect
26. #3103C4semidirect
154. C2×C4×Q8C2×C4semidirect
175. #481C2×C4semidirect
176. #481C2×C4semidirect
177. #475C2×C4semidirect
178. #475C2×C4semidirect
179. #460C2×C4semidirect
180. #460C2×C4semidirect
181. #448C2×C4semidirect
182. #448C2×C4semidirect
185. C4×SD16C2×C4semidirect
186. C4×SD16C2×C4semidirect
187. C4×SD16C2×C4semidirect
188. C4×SD16C2×C4semidirect
189. #431C2×C4semidirect
496. #103#41semidirect

Maximal subgroups

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

subgroupindex
C2×#31032
#342362
#341922
#231062
#230772
#230102
#229812
#229362
#229182
#228752
#228552
#214082
#213612
#212852
#212802
#211362
#211332
#211312
#211302
#205062
#205042
#204812
C2×#17632