Finite Group Databasebeta

← #6400882

Subgroups — #6400882

Order 512.

1894 conjugacy classes of subgroups.

The subgroup lattice has 873 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3393C211yesmaximal, characteristic
2#34322C211yesmaximal, characteristic, complemented
3C4×#556C211yesmaximal, characteristic, complemented
4#23184C211yesmaximal, characteristic, complemented
5#23183C212yesmaximal
6#23097C212yesmaximal, complemented
7#23094C211yesmaximal, characteristic, complemented
8#23000C212yesmaximal, complemented
9#22996C211yesmaximal, characteristic, complemented
10#22769C212yesmaximal, complemented
11#22766C211yesmaximal, characteristic
12#22741C211yesmaximal, characteristic, complemented
13#22541C211yesmaximal, characteristic, complemented
14#22541C211yesmaximal, characteristic, complemented
15#22271C212yesmaximal
16#22270C211yesmaximal, characteristic, complemented
17#22150C212yesmaximal, complemented
18#22146C211yesmaximal, characteristic, complemented
19C4×#464C212yesmaximal, complemented
20C4×#461C211yesmaximal, characteristic, complemented
21#21116C212yesmaximal, complemented
22#21113C211yesmaximal, characteristic
23#20569C211yesmaximal, characteristic, complemented
24C2×#556C2211yescharacteristic
25C2×#556C2211yescharacteristic
26#3393C4116yescomplemented
27C2×#495C2212yes—
28C2×#494C2211yescharacteristic
29C2×#464C2212yes—
30C2×#464C2212yes—
31C2×#461C2211yescharacteristic
32C2×#461C2211yescharacteristic
33C2×C8×Q8C2211yescharacteristic
34C2×C8×Q8C2211yescharacteristic
35C2×C4×Q16C2212yes—
36C2×C4×Q16C2212yes—
37C2×C4×SD16C2212yes—
38C2×C4×SD16C2212yes—
39C2×C4×D8C2211yescharacteristic
40#2373—22no—
41#2373—22no—
42#2367C2212yes—
43#2367C2212yes—
44#2365C2211yescharacteristic
45#2365C2211yescharacteristic
46#2362—21no—
47#2360—21no—
48#2356C2212yes—
49#2355C2211yescharacteristic
50#2355C2211yescharacteristic
51#2354C2211yescharacteristic
52#2351C2212yes—
53D4×C4⋊C4C2211yescharacteristic
54#2347—21no—
55#2346—21no—
56#2334—22no—
57#2323—21no—
58C4×C4⋊Q8C2211yescharacteristic
59C4×C4⋊Q8C2211yescharacteristic
60C4×#126—22no—
61C4×#124C2212yes—
62C4×#124C2212yes—
63C4×C22⋊Q8—21no—
64#2295C2212yes—
65#2293C2211yescharacteristic
66#2274—21no—
67C42×Q8C2212yes—
68C42×Q8C2211yescharacteristic
69C42×D4C2211yescharacteristic
70C4×#117—21no—
71#1983C2212yes—
72#1983C2212yes—
73#1981C2211yescharacteristic
74#1981C2211yescharacteristic
75#1969C2212yes—
76#1968C2212yes—
77#1968C2212yes—
78#1958C2212yes—
79#1958C2212yes—
80#1956C2211yescharacteristic
81#1956C2211yescharacteristic
82#1949C2212yes—
83#1949C2212yes—
84#1948C2211yescharacteristic
85#1948C2211yescharacteristic
86#1934C2212yes—
87#1933C2212yes—
88#1933C2212yes—
89#1927C2212yes—
90#1927C2212yes—
91#1925C2211yescharacteristic
92#1925C2211yescharacteristic
93#1918C2211yescharacteristic
94#1918C2211yescharacteristic
95#1918C2212yes—
96#1880C2212yes—
97#1880C2212yes—
98#1879C2211yescharacteristic
99#1879C2211yescharacteristic
100#1879C2212yes—
101#1878C2212yes—
102#1878C2212yes—
103#1878C2212yes—
104#1878C2212yes—
105#1878C2212yes—
106#1878C2212yes—
107#1877C2212yes—
108#1877C2212yes—
109#1865C2212yes—
110#1865C2212yes—
111#1862C2211yescharacteristic
112#1862C2211yescharacteristic
113#1835C2212yes—
114#1834C2211yescharacteristic
115#1805C2212yes—
116#1805C2212yes—
117#1802C2211yescharacteristic
118#1802C2211yescharacteristic
119C4×#107C2211yescharacteristic
120C4×#106C2212yes—
121C8×C4⋊C4C2211yescharacteristic
122C8×C4⋊C4C2212yes—
123C8×C4⋊C4C2212yes—
124C8×C4⋊C4C2211yescharacteristic
125C4×C4⋊C8C2211yescharacteristic
126C4×C4⋊C8C2212yes—
127C4×#103C2212yes—
128C4×#103C2212yes—
129C4×#103C2212yes—
130C4×#103C2212yes—
131C4×#102C2211yescharacteristic
132C4×#102C2211yescharacteristic
133C4×#102C2212yes—
134#1744C2211yescharacteristic
135#1744C2212yes—
136C22×Q16C2312yes—
137C22×Q16C2312yes—
138C22×SD16C2312yes—
139C22×SD16C2312yes—
140C22×D8C2311yescharacteristic
141#556—24no—
142#556—24no—
143#556C2×C418yescomplemented
144#556C2×C418yescomplemented
145C2×C4⋊Q8C2311yescharacteristic
146C2×C4⋊Q8C2311yescharacteristic
147C2×#126—22no—
148C2×#126—22no—
149C2×#124C2312yes—
150C2×#124C2312yes—
151C2×C22⋊Q8—21no—
152C2×C22⋊Q8—21no—
153C2×C4×Q8D411yescharacteristic
154C2×C4×Q8D411yescharacteristic
155C2×C4×Q8C2312yes—
156C2×C4×Q8C2312yes—
157C2×C4×Q8C2312yes—
158C2×C4×Q8C2312yes—
159C2×C4×Q8C2312yes—
160C2×C4×Q8C2312yes—
161C2×C4×Q8C2311yescharacteristic
162C2×C4×D4C2311yescharacteristic
163C2×C4×D4C2311yescharacteristic
164C2×C4×D4C2311yescharacteristic
165C2×C4×D4C2312yes—
166C2×C4×D4C2311yescharacteristic
167C2×#117—21no—
168C2×#117—21no—
169C2×#117—21no—
170C2×#117—21no—
171C22×C4⋊C4—21no—
172C22×C42—21no—
173#495C2×C4116yes—
174#494C2×C418yescomplemented
175#464C2×C4116yescomplemented
176#464C2×C4116yescomplemented
177#461C2×C418yescomplemented
178#461C2×C418yescomplemented
179C8×Q8—24no—
180C8×Q8C2×C418yescomplemented
181C4×Q16—44no—
182C4×Q16C2×C4116yescomplemented
183C4×SD16—44no—
184C4×SD16—44no—
185C4×D8C2×C418yes—
186C2×#107C2311yescharacteristic
187C2×#107C2311yescharacteristic
188C2×#107C2311yescharacteristic
189C2×#106C2312yes—
190C2×#106C2312yes—
191C2×C4⋊C8C2311yescharacteristic
192C2×C4⋊C8C2312yes—
193C2×C4⋊C8C2311yescharacteristic
194C2×C4⋊C8C2312yes—
195C2×#103C2312yes—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#102C2311yescharacteristic
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2311yescharacteristic
209C2×#102C2311yescharacteristic
210C2×#102C2311yescharacteristic
211C2×#102C2311yescharacteristic
212C2×#102C2311yescharacteristic
213C2×C4×C8C2311yescharacteristic
214C2×C4×C8C2312yes—
215C2×C4×C8C2312yes—
216C2×C4×C8C2312yes—
217C2×C4×C8C2312yes—
218C2×C4×C8C2311yescharacteristic
219C2×C4×C8C2312yes—
220#391—21no—
221#391—21no—
222#391C2312yes—
223#391C2312yes—
224#391C2312yes—
225#391C2312yes—
226#390C2312yes—
227#390C2311yescharacteristic
228#390C2311yescharacteristic
229#389—21no—
230#389—22no—
231#389—22no—
232#389—21no—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389C2312yes—
238#389C2311yescharacteristic
239#389C2311yescharacteristic
240#388—22no—
241#388—22no—
242#388—22no—
243#388—21no—
244#388—22no—
245#388—22no—
246#388—22no—
247#388—21no—
248#388—22no—
249#388—22no—
250#388—22no—
251#387—22no—
252#387—22no—
253#387—22no—
254#387—22no—
255#387—22no—
256#387—22no—
257#387—22no—
258#387—22no—
259#385—22no—
260#385—22no—
261#385—22no—
262#384C2311yescharacteristic
263#384C2311yescharacteristic
264#383—22no—
265#382—22no—
266#382C2312yes—
267#382C2312yes—
268#380—21no—
269#380—21no—
270C4×C4⋊C4—21no—
271C4×C4⋊C4—21no—
272C4×C4⋊C4—21no—
273C4×C4⋊C4—21no—
274C4×C4⋊C4—21no—
275C4×C4⋊C4—22no—
276C4×C4⋊C4—21no—
277C4×C4⋊C4—21no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4—22no—
280C4×C4⋊C4—22no—
281C4×C4⋊C4—22no—
282C4×C4⋊C4—22no—
283C4×C4⋊C4D412yes—
284C4×C4⋊C4D411yescharacteristic
285C4×C4⋊C4D412yes—
286C4×C4⋊C4D411yescharacteristic
287C4×C4⋊C4C2312yes—
288C4×C4⋊C4C2311yescharacteristic
289C4×C4⋊C4C2311yescharacteristic
290C4×C4⋊C4C2312yes—
291C4×C4⋊C4C2312yes—
292C4×C4⋊C4C2311yescharacteristic
293C4×C4⋊C4C2311yescharacteristic
294C4×C4⋊C4C2311yescharacteristic
295C4×C4⋊C4C2312yes—
296C4×C22⋊C4—21no—
297C4×C22⋊C4—22no—
298C4×C22⋊C4—22no—
299C4×C22⋊C4—22no—
300C4×C22⋊C4—21no—
301C4×C22⋊C4—21no—
302C4×C22⋊C4—22no—
303C4×C22⋊C4—21no—
304C4×C22⋊C4—22no—
305C4×C22⋊C4—22no—
306#376—22no—
307#376—22no—
308C43—22no—
309C43C2311yescharacteristic
310C43C2312yes—
311#340C2312yes—
312#340C2312yes—
313#340C2311yescharacteristic
314#340C2311yescharacteristic
315#340C2312yes—
316#340C2312yes—
317#340C2311yescharacteristic
318#340C2312yes—
319#340C2312yes—
320#340C2311yescharacteristic
321#340C2311yescharacteristic
322#340C2311yescharacteristic
323#336C2311yescharacteristic
324#336C2311yescharacteristic
325#336C2312yes—
326#336C2312yes—
327#336C2311yescharacteristic
328#336C2312yes—
329#336C2311yescharacteristic
330C22×Q8C2×D411yescharacteristic
331C22×Q8C2412yes—
332C22×Q8C2412yes—
333C22×D4C2411yescharacteristic
334C22×D4C2411yescharacteristic
335C23×C4—21no—
336C23×C4—21no—
337C23×C4—21no—
338C23×C4—21no—
339C23×C4—22no—
340C2×Q16—42no—
341C2×Q16—42no—
342C2×Q16—42no—
343C2×Q16—42no—
344C2×Q16C22×C418yes—
345C2×Q16C22×C418yes—
346C2×SD16—42no—
347C2×SD16—42no—
348C2×SD16—42no—
349C2×SD16—42no—
350C2×SD16C22×C418yes—
351C2×SD16C22×C418yes—
352C2×D8—41no—
353C2×D8—41no—
354C2×D8C22×C414yes—
355C22×C8C2411yescharacteristic
356C22×C8C2411yescharacteristic
357C22×C8C2412yes—
358C22×C8C2411yescharacteristic
359C22×C8C2412yes—
360C22×C8C2411yescharacteristic
361C4⋊Q8—22no—
362C4⋊Q8—22no—
363C4⋊Q8C22×C414yes—
364C4⋊Q8C22×C414yes—
365#126—216no—
366#126—216no—
367#124—24no—
368#124—24no—
369#124C22×C418yes—
370#124C22×C418yes—
371C22⋊Q8—28no—
372C22⋊Q8—28no—
373C4×Q8—24no—
374C4×Q8—24no—
375C4×Q8—24no—
376C4×Q8—24no—
377C4×Q8—24no—
378C4×Q8—42no—
379C4×Q8—42no—
380C4×Q8—42no—
381C4×Q8—42no—
382C4×Q8—42no—
383C4×Q8—42no—
384C4×Q8—42no—
385C4×Q8C22×C418yes—
386C4×Q8C22×C418yes—
387C4×Q8C22×C414yes—
388C4×Q8#4114yes—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—41no—
393C4×D4—41no—
394C4×D4—41no—
395C4×D4—42no—
396C4×D4—42no—
397C4×D4C22×C414yes—
398C4×D4C22×C414yes—
399#117—28no—
400#117—28no—
401#117—44no—
402#117—44no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—44no—
421C2×C4⋊C4C2×D411yescharacteristic
422C2×C4⋊C4C2×D412yes—
423C2×C4⋊C4C2×D412yes—
424C2×C4⋊C4C2×D411yescharacteristic
425C2×C4⋊C4C2×D412yes—
426C2×C4⋊C4C2×D411yescharacteristic
427C2×C4⋊C4C2412yes—
428C2×C4⋊C4C2411yescharacteristic
429C2×C4⋊C4C2411yescharacteristic
430C2×C4⋊C4C2412yes—
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2411yescharacteristic
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—21no—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—21no—
454C2×C42—22no—
455C2×C42—22no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—44no—
464C2×C42C2×D411yescharacteristic
465C2×C42C2×D412yes—
466C2×C42C2×D412yes—
467C2×C42C2×D412yes—
468C2×C42C2×D412yes—
469C2×C42C2×D411yescharacteristic
470C2×C42C2×D411yescharacteristic
471C2×C42C2×D411yescharacteristic
472C2×C42C2411yescharacteristic
473C2×C42C2411yescharacteristic
474C2×C42C2412yes—
475C2×C42C2411yescharacteristic
476C2×C42C2412yes—
477#107—22no—
478#107—41no—
479#107C22×C414yes—
480#106—24no—
481#106—42no—
482C4⋊C8—22no—
483C4⋊C8—24no—
484C4⋊C8C22×C414yes—
485C4⋊C8C22×C418yes—
486#103—24no—
487#103—42no—
488#103—42no—
489#103—42no—
490#103—42no—
491#103—42no—
492#103—42no—
493#103—42no—
494#103C22×C418yes—
495#103C22×C418yes—
496#102—22no—
497#102—41no—
498#102—42no—
499#102—41no—
500#102—41no—
501#102—42no—
502#102C22×C414yes—
503#102C22×C414yes—
504C4×C8—22no—
505C4×C8—24no—
506C4×C8—42no—
507C4×C8—42no—
508C4×C8—42no—
509C4×C8C22×C414yes—
510C4×C8C22×C418yes—
511#95—21no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—22no—
516#95—22no—
517#95—22no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—21no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—21no—
533#95C2×D412yes—
534#95C2×D412yes—
535#95C2×D412yes—
536C24—21no—
537C24—21no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8C4×D414yes—
551C2×Q8C23×C414yes—
552C2×Q8C23×C414yes—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4C23×C412yes—
564C2×D4C23×C412yes—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—44no—
587C22×C4—81no—
588C22×C4—82no—
589C22×C4—82no—
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D412yes—
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D412yes—
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C2511yescharacteristic
601Q16—48no—
602Q16—48no—
603SD16—48no—
604SD16—48no—
605D8—44no—
606C2×C8—22no—
607C2×C8—21no—
608C2×C8—22no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—22no—
615C2×C8—21no—
616C2×C8—22no—
617C2×C8—21no—
618C2×C8—22no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8C23×C412yes—
622C2×C8C23×C412yes—
623C2×C8C23×C414yes—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—28no—
627C4⋊C4—28no—
628C4⋊C4—24no—
629C4⋊C4—24no—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—22no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—22no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—21no—
646C4⋊C4—44no—
647C4⋊C4—44no—
648C4⋊C4—44no—
649C4⋊C4—42no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—81no—
654C4⋊C4—81no—
655C4⋊C4—82no—
656C4⋊C4—82no—
657C4⋊C4C4×D414yes—
658C4⋊C4C4×D418yes—
659C4⋊C4#13514yes—
660C4⋊C4C23×C412yes—
661C4⋊C4C23×C412yes—
662C4⋊C4H(5,𝔽2)12yes—
663C22⋊C4—28no—
664C22⋊C4—28no—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—28no—
668C22⋊C4—28no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—44no—
674C22⋊C4—42no—
675C22⋊C4—81no—
676C22⋊C4—82no—
677C22⋊C4—82no—
678C42—28no—
679C42—28no—
680C42—24no—
681C42—24no—
682C42—22no—
683C42—21no—
684C42—22no—
685C42—21no—
686C42—21no—
687C42—22no—
688C42—21no—
689C42—42no—
690C42—41no—
691C42—42no—
692C42—41no—
693C42—44no—
694C42—44no—
695C42—42no—
696C42—42no—
697C42—42no—
698C42—44no—
699C42—42no—
700C42—82no—
701C42—82no—
702C42—82no—
703C42—82no—
704C42#13514yes—
705C42C23×C412yes—
706C42C23×C414yes—
707C42C2×#4112yes—
708C42C2×#4114yes—
709C23—22no—
710C23—22no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23C23×D411yescharacteristic
724Q8—28no—
725Q8—24no—
726Q8—24no—
727Q8—24no—
728Q8—24no—
729Q8—42no—
730Q8—42no—
731Q8—42no—
732Q8—42no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—41no—
741C2×C4—21no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—48no—
778C2×C4—48no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—84no—
795C2×C4—84no—
796C2×C4—164no—
797C2×C4C2×C4×D414yes—
798C2×C4C2×C4×D412yes—
799C2×C4C2×C4×D414yes—
800C2×C4C2×C4×D412yes—
801C2×C4C2×#13512yes—
802C2×C4C2×#13514yes—
803C2×C4C2×#13512yes—
804C2×C4C2×#13512yes—
805C2×C4C2×#13512yes—
806C2×C4C24×C411yescharacteristic
807C2×C4C22×#4111yescharacteristic
808C2×C4C2×H(5,𝔽2)11yescharacteristic
809C2×C4#58511yescharacteristic
810C2×C4#58511yescharacteristic
811C2×C4#58511yescharacteristic
812C8—22no—
813C8—24no—
814C8—22no—
815C8—41no—
816C8—42no—
817C8—41no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22C22×C4×D411yescharacteristic
833C22#348711yescharacteristic
834C22#348811yescharacteristic
835C22C22×#13511yescharacteristic
836C22C22×#13511yescharacteristic
837C22#358611yescharacteristic
838C22#358611yescharacteristic
839C4—24no—
840C4—24no—
841C4—22no—
842C4—22no—
843C4—24no—
844C4—22no—
845C4—41no—
846C4—41no—
847C4—44no—
848C4—44no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4—82no—
854C4—81no—
855C4—81no—
856C4—82no—
857C4—81no—
858C4C4×#13514yes—
859C4#342811yescharacteristic
860C4C4×H(5,𝔽2)11yescharacteristic
861C4#351711yescharacteristic
862C4#352411yescharacteristic
863C2—82no—
864C2—82no—
865C2#3429511yescharacteristic
866C2C2×C4×#13511yescharacteristic
867C2#6017511yescharacteristic
868C2#6188211yescharacteristic
869C2#6188711yescharacteristic
870C2#6195011yescharacteristic
871C2#6195611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC22×D8C23
LCSG ▷ C2×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
2. #34322C2semidirect
3. C4×#556C2semidirect
4. #23184C2semidirect
6. #23097C2semidirect
7. #23094C2semidirect
8. #23000C2semidirect
9. #22996C2semidirect
10. #22769C2semidirect
12. #22741C2semidirect
13. #22541C2semidirect
14. #22541C2semidirect
16. #22270C2semidirect
17. #22150C2semidirect
18. #22146C2semidirect
19. C4×#464C2semidirect
20. C4×#461C2semidirect
21. #21116C2semidirect
23. #20569C2semidirect
26. #3393C4semidirect
143. #556C2×C4semidirect
144. #556C2×C4semidirect
174. #494C2×C4semidirect
175. #464C2×C4semidirect
176. #464C2×C4semidirect
177. #461C2×C4semidirect
178. #461C2×C4semidirect
180. C8×Q8C2×C4semidirect
182. C4×Q16C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#33932
#343222
C4×#5562
#231842
#231832
#230972
#230942
#230002
#229962
#227692
#227662
#227412
#225412
#222712
#222702
#221502
#221462
C4×#4642
C4×#4612
#211162
#211132
#205692