Finite Group Databasebeta

← #6400977

Subgroups — #6400977

Order 512.

1903 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3394C211yesmaximal, characteristic
2#34498C211yesmaximal, characteristic, complemented
3#34324C211yesmaximal, characteristic, complemented
4#23190C211yesmaximal, characteristic, complemented
5#23186C212yesmaximal, complemented
6#23111C212yesmaximal, complemented
7#23093C211yesmaximal, characteristic
8#23011C212yesmaximal, complemented
9#22998C211yesmaximal, characteristic, complemented
10#22770C212yesmaximal, complemented
11#22759C211yesmaximal, characteristic, complemented
12#22740C211yesmaximal, characteristic, complemented
13#22546C211yesmaximal, characteristic, complemented
14#22544C211yesmaximal, characteristic, complemented
15#22274C212yesmaximal, complemented
16#22268C211yesmaximal, characteristic, complemented
17#22157C212yesmaximal, complemented
18#22148C211yesmaximal, characteristic, complemented
19#21512C212yesmaximal, complemented
20C4×#459C211yesmaximal, characteristic
21#21136C212yesmaximal, complemented
22#21114C211yesmaximal, characteristic, complemented
23#20571C211yesmaximal, 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×C4×Q16C2212yes—
37C2×C4×SD16C2211yescharacteristic
38C2×C4×SD16C2212yes—
39C2×C4×D8C2212yes—
40#2376—22no—
41#2373—22no—
42#2367—21no—
43#2367C2212yes—
44#2367C2212yes—
45#2366C2211yescharacteristic
46#2365C2211yescharacteristic
47#2362—21no—
48#2355C2212yes—
49#2354C2211yescharacteristic
50Q8×C4⋊C4C2211yescharacteristic
51Q8×C4⋊C4C2211yescharacteristic
52Q8×C4⋊C4C2211yescharacteristic
53D4×C4⋊C4—21no—
54D4×C4⋊C4C2212yes—
55#2346—21no—
56#2334—22no—
57#2326—21no—
58#2326C2212yes—
59#2326C2212yes—
60#2322—22no—
61#2319—21no—
62#2319C2212yes—
63C4×C4⋊Q8C2211yescharacteristic
64C4×#127C2211yescharacteristic
65C4×C22⋊Q8—21no—
66#2296—21no—
67#2295C2211yescharacteristic
68#2295C2211yescharacteristic
69#2276C2212yes—
70C42×D4C2211yescharacteristic
71#1983C2212yes—
72#1983C2212yes—
73#1982C2211yescharacteristic
74#1981C2211yescharacteristic
75#1973C2212yes—
76#1970C2212yes—
77#1969C2212yes—
78#1959C2212yes—
79#1959C2212yes—
80#1957C2211yescharacteristic
81#1956C2211yescharacteristic
82#1947C2212yes—
83#1947C2211yescharacteristic
84#1947C2212yes—
85#1947C2211yescharacteristic
86#1936C2212yes—
87#1933C2212yes—
88#1933C2212yes—
89#1928C2211yescharacteristic
90#1928C2211yescharacteristic
91#1925C2212yes—
92#1925C2212yes—
93#1919C2211yescharacteristic
94#1919C2211yescharacteristic
95#1919C2212yes—
96#1880C2212yes—
97#1880C2212yes—
98#1880C2212yes—
99#1880C2212yes—
100#1879C2212yes—
101#1879C2212yes—
102#1878C2212yes—
103#1878C2212yes—
104#1877C2211yescharacteristic
105#1877C2212yes—
106#1877C2212yes—
107#1877C2211yescharacteristic
108#1877C2212yes—
109#1863C2212yes—
110#1863C2212yes—
111#1862C2211yescharacteristic
112#1862C2211yescharacteristic
113#1834C2212yes—
114#1834C2211yescharacteristic
115#1803C2212yes—
116#1803C2211yescharacteristic
117#1802C2211yescharacteristic
118#1802C2212yes—
119C4×#107C2211yescharacteristic
120C4×#107C2212yes—
121#1771C2212yes—
122#1770C2211yescharacteristic
123C8×C4⋊C4C2211yescharacteristic
124C8×C4⋊C4C2212yes—
125#1768C2212yes—
126C4×C4⋊C8C2211yescharacteristic
127#1763C2212yes—
128#1763C2212yes—
129#1762C2212yes—
130C4×#103C2211yescharacteristic
131C4×#102C2212yes—
132C4×#102C2211yescharacteristic
133C4×#102C2212yes—
134#1746C2212yes—
135#1744C2211yescharacteristic
136C22×Q16C2312yes—
137C22×SD16C2312yes—
138C22×SD16C2312yes—
139C22×SD16C2311yescharacteristic
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×D4C2311yescharacteristic
166C2×C4×D4C2312yes—
167C2×C4×D4C2311yescharacteristic
168C2×C4×D4C2312yes—
169C2×C4×D4C2311yescharacteristic
170C2×C4×D4C2312yes—
171C2×#117—21no—
172C2×#117—21no—
173C22×C4⋊C4—22no—
174C22×C42—21no—
175#495C2×C4116yescomplemented
176#492C2×C418yescomplemented
177#464C2×C4116yescomplemented
178#463C2×C4116yescomplemented
179#462C2×C418yescomplemented
180#459C2×C418yes—
181#446—24no—
182C8×Q8C2×C418yescomplemented
183#440—44no—
184C4×Q16—44no—
185C4×SD16C2×C418yescomplemented
186C4×SD16C2×C4116yescomplemented
187C4×D8—44no—
188C2×#107C2311yescharacteristic
189C2×#107C2312yes—
190C2×#107C2311yescharacteristic
191C2×#107C2312yes—
192C2×#106C2311yescharacteristic
193C2×C4⋊C8C2311yescharacteristic
194C2×C4⋊C8C2312yes—
195C2×C4⋊C8C2311yescharacteristic
196C2×C4⋊C8C2312yes—
197C2×#103C2311yescharacteristic
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2311yescharacteristic
204C2×#103C2312yes—
205C2×#103C2311yescharacteristic
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2312yes—
209C2×#102C2312yes—
210C2×#102C2311yescharacteristic
211C2×#102C2311yescharacteristic
212C2×#102C2312yes—
213C2×#102C2311yescharacteristic
214C2×#102C2312yes—
215C2×#97C2312yes—
216C2×#97C2312yes—
217C2×C4×C8C2311yescharacteristic
218C2×C4×C8C2312yes—
219C2×C4×C8C2312yes—
220C2×C4×C8C2311yescharacteristic
221C2×C4×C8C2312yes—
222#391D411yescharacteristic
223#391D411yescharacteristic
224#391C2312yes—
225#391C2311yescharacteristic
226#391C2312yes—
227#391C2311yescharacteristic
228#390—21no—
229#390—21no—
230#390—21no—
231#390C2312yes—
232#390C2312yes—
233#390C2312yes—
234#389—21no—
235#389—22no—
236#389—22no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389—22no—
242#389D411yescharacteristic
243#389D411yescharacteristic
244#389C2311yescharacteristic
245#389C2312yes—
246#389C2311yescharacteristic
247#388—22no—
248#388—22no—
249#388—22no—
250#388—22no—
251#388—22no—
252#388—22no—
253#388—22no—
254#388—22no—
255#388—22no—
256#388—22no—
257#388—22no—
258#387—21no—
259#387—21no—
260#387—22no—
261#387—22no—
262#387—22no—
263#387D412yes—
264#387D412yes—
265#386—22no—
266#385—22no—
267#385—22no—
268#385—22no—
269#385—22no—
270#385—22no—
271#385—22no—
272#385—22no—
273#385—22no—
274#384—21no—
275#384C2311yescharacteristic
276#384C2311yescharacteristic
277#384C2312yes—
278#384C2312yes—
279#382—22no—
280#381—22no—
281#380—22no—
282#380—21no—
283#380—22no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4—21no—
286C4×C4⋊C4—22no—
287C4×C4⋊C4—21no—
288C4×C4⋊C4—21no—
289C4×C4⋊C4—21no—
290C4×C4⋊C4—22no—
291C4×C4⋊C4—22no—
292C4×C4⋊C4—22no—
293C4×C4⋊C4C2312yes—
294C4×C4⋊C4C2311yescharacteristic
295C4×C4⋊C4C2311yescharacteristic
296C4×C4⋊C4C2312yes—
297C4×C4⋊C4C2312yes—
298C4×C4⋊C4C2311yescharacteristic
299C4×C4⋊C4C2311yescharacteristic
300C4×C4⋊C4C2312yes—
301C4×C4⋊C4C2311yescharacteristic
302C4×C22⋊C4—21no—
303C4×C22⋊C4—21no—
304C4×C22⋊C4—21no—
305C4×C22⋊C4—22no—
306C4×C22⋊C4—22no—
307#376—21no—
308#376—22no—
309#376C2312yes—
310C43C2311yescharacteristic
311#340C2311yescharacteristic
312#340C2312yes—
313#340C2312yes—
314#340C2311yescharacteristic
315#340C2311yescharacteristic
316#340C2312yes—
317#340C2312yes—
318#340C2312yes—
319#340C2312yes—
320#340C2311yescharacteristic
321#340C2311yescharacteristic
322#340C2311yescharacteristic
323#336C2311yescharacteristic
324#336C2311yescharacteristic
325#336C2312yes—
326#336C2312yes—
327#336C2311yescharacteristic
328#336C2311yescharacteristic
329#336C2312yes—
330C22×Q8C2×D411yescharacteristic
331C22×Q8C2411yescharacteristic
332C22×Q8C2412yes—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4C2411yescharacteristic
336C22×D4C2412yes—
337C23×C4—21no—
338C23×C4—22no—
339C23×C4—21no—
340C23×C4—22no—
341C23×C4—21no—
342C23×C4—22no—
343C2×Q16—42no—
344C2×Q16—42no—
345C2×Q16C22×C418yes—
346C2×SD16—42no—
347C2×SD16—42no—
348C2×SD16—41no—
349C2×SD16—41no—
350C2×SD16—42no—
351C2×SD16—42no—
352C2×SD16C22×C418yes—
353C2×SD16C22×C414yes—
354C2×SD16C22×C418yes—
355C2×D8—42no—
356C2×D8—42no—
357C2×D8C22×C418yes—
358C22×C8C2411yescharacteristic
359C22×C8C2411yescharacteristic
360C22×C8C2412yes—
361C22×C8C2412yes—
362C22×C8C2411yescharacteristic
363C22×C8C2411yescharacteristic
364C4⋊Q8—22no—
365C4⋊Q8C22×C414yes—
366#127—22no—
367#127C22×C414yes—
368#126—216no—
369#124—28no—
370#124—24no—
371#124—24no—
372#124C22×C418yes—
373#124C22×C418yes—
374#123—216no—
375C22⋊Q8—28no—
376C4×Q8—24no—
377C4×Q8—22no—
378C4×Q8—24no—
379C4×Q8—42no—
380C4×Q8—42no—
381C4×Q8—42no—
382C4×Q8—42no—
383C4×Q8—42no—
384C4×Q8—82no—
385C4×Q8—82no—
386C4×Q8C22×C418yes—
387C4×Q8C22×C414yes—
388C4×Q8C22×C414yes—
389C4×Q8#4114yes—
390C4×D4—28no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—24no—
394C4×D4—41no—
395C4×D4—41no—
396C4×D4—41no—
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—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—84no—
427C2×C4⋊C4C2×D412yes—
428C2×C4⋊C4C2×D411yescharacteristic
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2×D412yes—
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2×D412yes—
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2412yes—
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2412yes—
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2411yescharacteristic
440C2×C4⋊C4C2411yescharacteristic
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C42—22no—
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—22no—
465C2×C42—22no—
466C2×C42—22no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—82no—
470C2×C42C2×D411yescharacteristic
471C2×C42C2×D411yescharacteristic
472C2×C42C2×D411yescharacteristic
473C2×C42C2×D411yescharacteristic
474C2×C42C2411yescharacteristic
475C2×C42C2411yescharacteristic
476C2×C42C2412yes—
477C2×C42C2412yes—
478C2×C42C2411yescharacteristic
479#107—24no—
480#107—22no—
481#107—42no—
482#107—41no—
483#106C22×C414yes—
484C4⋊C8—22no—
485C4⋊C8—24no—
486C4⋊C8C22×C414yes—
487C4⋊C8C22×C418yes—
488#103—22no—
489#103—42no—
490#103—42no—
491#103—41no—
492#103—42no—
493#103—42no—
494#103—42no—
495#103C22×C418yes—
496#103C22×C414yes—
497#102—24no—
498#102—42no—
499#102—41no—
500#102—42no—
501#102—42no—
502#102—41no—
503#102—42no—
504#102C22×C418yes—
505#102C22×C414yes—
506#97—24no—
507#97—42no—
508C4×C8—22no—
509C4×C8—42no—
510C4×C8—42no—
511C4×C8C22×C414yes—
512C4×C8C22×C418yes—
513#95—21no—
514#95—22no—
515#95—22no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—21no—
528#95—22no—
529#95—22no—
530#95—21no—
531#95C2×D412yes—
532#95C2×D412yes—
533#95C2×D412yes—
534#95C2×D412yes—
535#95C2×D412yes—
536#95C2×D412yes—
537#95C2×D412yes—
538C24—21no—
539C24—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—21no—
543C2×Q8—22no—
544C2×Q8—21no—
545C2×Q8—22no—
546C2×Q8—21no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8C4×D414yes—
553C2×Q8C23×C412yes—
554C2×Q8C23×C414yes—
555C2×D4—24no—
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—22no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—21no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4C23×C412yes—
572C2×D4C23×C414yes—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—28no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—44no—
591C22×C4—81no—
592C22×C4—81no—
593C22×C4—82no—
594C22×C4—82no—
595C22×C4—81no—
596C22×C4—82no—
597C22×C4—82no—
598C22×C4—82no—
599C22×C4—82no—
600C22×C4—82no—
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D412yes—
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D412yes—
606C22×C4C22×D412yes—
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D412yes—
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C2511yescharacteristic
612Q16—48no—
613SD16—48no—
614SD16—44no—
615SD16—48no—
616D8—48no—
617C2×C8—22no—
618C2×C8—21no—
619C2×C8—22no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—22no—
626C2×C8—21no—
627C2×C8—22no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—22no—
631C2×C8—21no—
632C2×C8C23×C412yes—
633C2×C8C23×C414yes—
634C2×C8C23×C412yes—
635C4⋊C4—24no—
636C4⋊C4—28no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—24no—
641C4⋊C4—22no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—22no—
654C4⋊C4—21no—
655C4⋊C4—42no—
656C4⋊C4—44no—
657C4⋊C4—44no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—81no—
662C4⋊C4—82no—
663C4⋊C4—81no—
664C4⋊C4—82no—
665C4⋊C4—82no—
666C4⋊C4—81no—
667C4⋊C4—82no—
668C4⋊C4—82no—
669C4⋊C4—82no—
670C4⋊C4C4×D414yes—
671C4⋊C4C4×D418yes—
672C4⋊C4C23×C412yes—
673C4⋊C4C23×C412yes—
674C4⋊C4H(5,𝔽2)12yes—
675C22⋊C4—28no—
676C22⋊C4—28no—
677C22⋊C4—28no—
678C22⋊C4—24no—
679C22⋊C4—28no—
680C22⋊C4—28no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—82no—
684C22⋊C4—82no—
685C22⋊C4—82no—
686C22⋊C4—82no—
687C22⋊C4—82no—
688C22⋊C4—82no—
689C22⋊C4—82no—
690C22⋊C4—82no—
691C42—28no—
692C42—24no—
693C42—22no—
694C42—22no—
695C42—22no—
696C42—21no—
697C42—22no—
698C42—21no—
699C42—21no—
700C42—21no—
701C42—22no—
702C42—41no—
703C42—44no—
704C42—44no—
705C42—42no—
706C42—42no—
707C42—81no—
708C42—81no—
709C42—82no—
710C42—82no—
711C42—82no—
712C42—82no—
713C42C23×C414yes—
714C42C23×C412yes—
715C42C2×#4112yes—
716C42C2×#4114yes—
717C23—22no—
718C23—24no—
719C23—41no—
720C23—42no—
721C23—41no—
722C23—42no—
723C23—41no—
724C23—42no—
725C23—41no—
726C23—42no—
727C23—42no—
728C23—41no—
729C23—41no—
730C23—42no—
731C23C23×D411yescharacteristic
732Q8—28no—
733Q8—22no—
734Q8—24no—
735Q8—24no—
736Q8—22no—
737Q8—41no—
738Q8—42no—
739Q8—41no—
740Q8—42no—
741D4—24no—
742D4—22no—
743D4—22no—
744D4—24no—
745D4—48no—
746D4—41no—
747D4—42no—
748D4—41no—
749D4—42no—
750D4—84no—
751C2×C4—21no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—48no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
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—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—88no—
806C2×C4—84no—
807C2×C4—84no—
808C2×C4—164no—
809C2×C4—164no—
810C2×C4C2×C4×D414yes—
811C2×C4C2×C4×D414yes—
812C2×C4C2×C4×D412yes—
813C2×C4C2×C4×D412yes—
814C2×C4#57612yes—
815C2×C4#57712yes—
816C2×C4#57812yes—
817C2×C4C24×C411yescharacteristic
818C2×C4C22×#4111yescharacteristic
819C2×C4C2×H(5,𝔽2)11yescharacteristic
820C2×C4#58511yescharacteristic
821C2×C4#58511yescharacteristic
822C2×C4#58511yescharacteristic
823C8—22no—
824C8—24no—
825C8—22no—
826C8—41no—
827C8—42no—
828C8—41no—
829C22—42no—
830C22—44no—
831C22—44no—
832C22—42no—
833C22—42no—
834C22—44no—
835C22—81no—
836C22—82no—
837C22—81no—
838C22—82no—
839C22—81no—
840C22—82no—
841C22—81no—
842C22—82no—
843C22C22×C4×D411yescharacteristic
844C22#348711yescharacteristic
845C22#348811yescharacteristic
846C22C2×#57611yescharacteristic
847C22C2×#57711yescharacteristic
848C22C2×#57811yescharacteristic
849C22#358411yescharacteristic
850C4—24no—
851C4—24no—
852C4—22no—
853C4—22no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—41no—
859C4—42no—
860C4—41no—
861C4—41no—
862C4—42no—
863C4—44no—
864C4—82no—
865C4—81no—
866C4—81no—
867C4—82no—
868C4—81no—
869C4#295114yes—
870C4#342811yescharacteristic
871C4C4×H(5,𝔽2)11yescharacteristic
872C4#351711yescharacteristic
873C4#352411yescharacteristic
874C2—82no—
875C2—84no—
876C2#3429511yescharacteristic
877C2C2×#295111yescharacteristic
878C2C4×#57711yescharacteristic
879C2#6192611yescharacteristic
880C2#6193411yescharacteristic
881C2#6205311yescharacteristic
882C2#6207211yescharacteristic
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. #34324C2semidirect
4. #23190C2semidirect
5. #23186C2semidirect
6. #23111C2semidirect
8. #23011C2semidirect
9. #22998C2semidirect
10. #22770C2semidirect
11. #22759C2semidirect
12. #22740C2semidirect
13. #22546C2semidirect
14. #22544C2semidirect
15. #22274C2semidirect
16. #22268C2semidirect
17. #22157C2semidirect
18. #22148C2semidirect
19. #21512C2semidirect
21. #21136C2semidirect
22. #21114C2semidirect
23. #20571C2semidirect
26. #3394C4semidirect
142. #559C2×C4semidirect
144. #556C2×C4semidirect
175. #495C2×C4semidirect
176. #492C2×C4semidirect
177. #464C2×C4semidirect
178. #463C2×C4semidirect
179. #462C2×C4semidirect
182. C8×Q8C2×C4semidirect
185. C4×SD16C2×C4semidirect
186. 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
#343242
#231902
#231862
#231112
#230932
#230112
#229982
#227702
#227592
#227402
#225462
#225442
#222742
#222682
#221572
#221482
#215122
C4×#4592
#211362
#211142
#205712