Finite Group Databasebeta

← #6624373

Subgroups — #6624373

Order 512.

1598 conjugacy classes of subgroups.

The subgroup lattice has 889 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39607C211yesmaximal, characteristic, complemented
2#34186C211yesmaximal, characteristic
3#33157C212yesmaximal, complemented
4#32956C211yesmaximal, characteristic
5#29115C212yesmaximal
6#28130C212yesmaximal
7#27962C211yesmaximal, characteristic, complemented
8#27649C211yesmaximal, characteristic, complemented
9#27449C212yesmaximal, complemented
10#27436C212yesmaximal, complemented
11#27386C212yesmaximal, complemented
12#27367C212yesmaximal, complemented
13#26025C211yesmaximal, characteristic, complemented
14#26021C211yesmaximal, characteristic, complemented
15#24680C211yesmaximal, characteristic, complemented
16#24680C211yesmaximal, characteristic, complemented
17#23067C211yesmaximal, characteristic, complemented
18#23061C211yesmaximal, characteristic, complemented
19#22767C211yesmaximal, characteristic, complemented
20#22759C211yesmaximal, characteristic, complemented
21#22626C211yesmaximal, characteristic, complemented
22#21591C212yesmaximal, complemented
23C4×#450C211yesmaximal, characteristic
24C22×C4×D4C2211yescharacteristic
25C2×#485C2212yes—
26C2×#476C2211yescharacteristic
27C2×#476C2211yescharacteristic
28C2×#450C2211yescharacteristic
29C2×C4×SD16C2211yescharacteristic
30C2×C4×SD16C2211yescharacteristic
31#2857C2211yescharacteristic
32#2755—22no—
33#2704—22no—
34#2629C2212yes—
35#2567C2211yescharacteristic, complemented
36#2552—21no—
37#2552C2211yescharacteristic, complemented
38#2507—21no—
39#2506C2212yescomplemented
40#2497—21no—
41#2497—21no—
42#2453C2212yescomplemented
43#2369C2211yescharacteristic, complemented
44#2357—22no—
45#2357C2212yes—
46#2357C2212yes—
47#2354—21no—
48#2354—21no—
49#2354C2211yescharacteristic
50#2354C2211yescharacteristic
51#2354C2211yescharacteristic
52#2354C2211yescharacteristic
53Q8×C4⋊C4C2211yescharacteristic, complemented
54#2323C2212yes—
55#2312—22no—
56#2309C2212yes—
57C4×C22⋊Q8C2211yescharacteristic
58#2285C2211yescharacteristic
59#2285C2211yescharacteristic
60#2280—21no—
61#2280—21no—
62#2274C2212yes—
63#2101C2212yescomplemented
64#2101C2212yescomplemented
65#2085C2212yescomplemented
66#2074C2212yescomplemented
67#2071C2212yes—
68#2071C2212yes—
69#2067C2212yes—
70#2065C2212yes—
71#2055C2212yes—
72#2055C2212yes—
73#2025C2212yes—
74#2025C2212yes—
75#1990C2211yescharacteristic, complemented
76#1990C2211yescharacteristic, complemented
77#1989C2212yescomplemented
78#1989C2212yescomplemented
79#1948C2211yescharacteristic, complemented
80#1948C2212yescomplemented
81#1948C2212yescomplemented
82#1947C2211yescharacteristic, complemented
83#1939C2211yescharacteristic, complemented
84#1939C2211yescharacteristic, complemented
85#1936C2212yes—
86#1936C2212yes—
87#1934C2212yes—
88#1934C2212yes—
89#1927C2212yescomplemented
90#1927C2212yescomplemented
91#1926C2212yes—
92#1925C2212yes—
93#1921C2212yescomplemented
94#1920C2212yescomplemented
95#1920C2212yescomplemented
96#1919C2212yescomplemented
97#1919C2212yescomplemented
98#1919C2212yescomplemented
99#1917C2212yescomplemented
100#1916C2212yescomplemented
101#1880C2212yes—
102#1880C2212yes—
103#1877C2211yescharacteristic
104#1877C2211yescharacteristic
105#1872C2211yescharacteristic
106#1864C2212yes—
107#1864C2212yes—
108#1864C2211yescharacteristic
109#1864C2211yescharacteristic
110#1853C2212yes—
111#1853C2211yescharacteristic
112#1834C2211yescharacteristic, complemented
113#1834C2211yescharacteristic, complemented
114#1825C2212yes—
115#1825C2212yes—
116#1825C2212yes—
117#1803C2211yescharacteristic, complemented
118#1803C2211yescharacteristic, complemented
119#1802C2211yescharacteristic
120#1802C2211yescharacteristic
121#1798C2212yes—
122#1797C2211yescharacteristic
123#1786C2211yescharacteristic
124#1786C2212yes—
125#1776C2212yescomplemented
126C4×#106C2212yescomplemented
127#1770C2211yescharacteristic, complemented
128C8×C4⋊C4C2211yescharacteristic, complemented
129#1763C2212yescomplemented
130C4×#103C2212yescomplemented
131C4×#102C2211yescharacteristic
132C4×#102C2211yescharacteristic
133#1750C2212yes—
134C4×C22⋊C8C2211yescharacteristic
135C23×D4C2311yescharacteristic
136C24×C4—21no—
137C22×SD16C2311yescharacteristic
138C22×SD16C2311yescharacteristic
139C2×C4⋊Q8C2311yescharacteristic
140C2×#125—22no—
141C2×#125C2312yes—
142C2×C22⋊Q8—21no—
143C2×C22⋊Q8C2311yescharacteristic
144C2×C4×Q8C2311yescharacteristic
145C2×C4×Q8C2312yes—
146C2×C4×D4—24no—
147C2×C4×D4—24no—
148C2×C4×D4—21no—
149C2×C4×D4—21no—
150C2×C4×D4C2311yescharacteristic
151C2×C4×D4C2311yescharacteristic
152C2×C4×D4C2311yescharacteristic
153C2×C4×D4C2311yescharacteristic
154C2×#117—21no—
155C2×#117—21no—
156C2×#117—21no—
157C2×#117—21no—
158C2×#117C2312yes—
159C2×#117C2312yes—
160C22×C4⋊C4C2311yescharacteristic
161C22×C22⋊C4—21no—
162C22×C42C2311yescharacteristic
163#485—28no—
164#476—24no—
165#476—24no—
166#450—24no—
167C4×SD16—24no—
168C4×SD16—24no—
169C2×#107C2312yes—
170C2×#106C2312yes—
171C2×#106C2311yescharacteristic
172C2×#106C2311yescharacteristic
173C2×#106C2312yes—
174C2×#106C2312yes—
175C2×C4⋊C8C2311yescharacteristic
176C2×C4⋊C8C2311yescharacteristic
177C2×C4⋊C8C2312yes—
178C2×C4⋊C8C2312yes—
179C2×#103C2312yes—
180C2×#103C2312yes—
181C2×#103C2311yescharacteristic
182C2×#103C2311yescharacteristic
183C2×#102C2312yes—
184C2×#102C2312yes—
185C2×#102C2311yescharacteristic
186C2×#102C2311yescharacteristic
187C2×#102C2311yescharacteristic
188C2×#102C2311yescharacteristic
189C2×#102C2312yes—
190C2×#102C2312yes—
191C2×#102C2311yescharacteristic
192C2×#102C2311yescharacteristic
193C2×C22⋊C8C2312yes—
194C2×C22⋊C8C2311yescharacteristic
195C2×C22⋊C8C2311yescharacteristic
196C2×#97C2312yes—
197C2×C4×C8C2311yescharacteristic
198C2×C4×C8C2311yescharacteristic
199C2×C4×C8C2312yes—
200#400—22no—
201#400—22no—
202#398—22no—
203#398—22no—
204#398—22no—
205#398—22no—
206#398—22no—
207#396—22no—
208#396—22no—
209#395—22no—
210#391—21no—
211#391—22no—
212#391C2312yes—
213#391C2311yescharacteristic
214#390—22no—
215#390—22no—
216#390C2312yes—
217#390C2312yes—
218#390C2312yes—
219#390C2312yes—
220#389—21no—
221#389—21no—
222#389—22no—
223#389—21no—
224#389—22no—
225#389—21no—
226#389—21no—
227#389—22no—
228#389C2312yes—
229#389C2311yescharacteristic
230#389C2312yes—
231#389C2312yes—
232#389C2312yes—
233#388—22no—
234#388—22no—
235#388—22no—
236#388—22no—
237#388—22no—
238#388—22no—
239#388—22no—
240#388—22no—
241#388—22no—
242#388—22no—
243#387—22no—
244#387—21no—
245#387—22no—
246#387—22no—
247#385—21no—
248#384—21no—
249#384—21no—
250#384D411yescharacteristic
251#384D411yescharacteristic
252#384C2312yes—
253#384C2311yescharacteristic
254#384C2311yescharacteristic
255#384C2311yescharacteristic
256#382D412yes—
257#382C2312yes—
258#381—22no—
259#381—22no—
260#380—21no—
261#380—21no—
262#380—21no—
263#380—21no—
264#380—21no—
265#380—21no—
266#380—21no—
267#380D412yes—
268#380D411yescharacteristic
269#380D411yescharacteristic
270#380C2312yes—
271#380C2311yescharacteristic
272#379—22no—
273#379—22no—
274C4×C4⋊C4—21no—
275C4×C4⋊C4—22no—
276C4×C4⋊C4—22no—
277C4×C4⋊C4—21no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4—21no—
280C4×C4⋊C4—21no—
281C4×C4⋊C4C2312yes—
282C4×C4⋊C4C2312yes—
283C4×C4⋊C4C2312yes—
284C4×C4⋊C4C2312yes—
285C4×C4⋊C4C2312yes—
286C4×C4⋊C4C2311yescharacteristic
287C4×C4⋊C4C2311yescharacteristic
288C4×C4⋊C4C2311yescharacteristic
289C4×C4⋊C4C2312yes—
290C4×C22⋊C4—21no—
291C4×C22⋊C4—22no—
292C4×C22⋊C4—22no—
293C4×C22⋊C4—22no—
294C4×C22⋊C4—22no—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2312yes—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2312yes—
307#340C2312yes—
308#340C2312yes—
309#340C2311yescharacteristic
310#340C2311yescharacteristic
311#340C2311yescharacteristic
312#340C2311yescharacteristic
313#336C2312yes—
314#336C2312yes—
315#336C2312yes—
316#336C2312yes—
317#336C2312yes—
318#336C2311yescharacteristic
319#336C2311yescharacteristic
320C25—21no—
321C22×Q8—21no—
322C22×Q8C2411yescharacteristic
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—21no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—41no—
329C22×D4—41no—
330C22×D4C2411yescharacteristic
331C22×D4C2411yescharacteristic
332C23×C4—28no—
333C23×C4—21no—
334C23×C4—21no—
335C23×C4—21no—
336C23×C4—21no—
337C23×C4—21no—
338C23×C4—82no—
339C23×C4—82no—
340C23×C4C2×D411yescharacteristic
341C23×C4C2×D411yescharacteristic
342C23×C4C2411yescharacteristic
343C2×SD16—22no—
344C2×SD16—22no—
345C2×SD16—22no—
346C2×SD16—22no—
347C2×SD16—41no—
348C2×SD16—41no—
349C22×C8C2411yescharacteristic
350C22×C8C2411yescharacteristic
351C22×C8C2411yescharacteristic
352C22×C8C2411yescharacteristic
353C22×C8C2412yes—
354C22×C8C2412yes—
355C4⋊Q8—22no—
356C4⋊Q8—22no—
357#125—42no—
358#125—42no—
359#125—84no—
360C22⋊Q8—22no—
361C22⋊Q8—82no—
362C22⋊Q8#4114yes—
363C4×Q8—22no—
364C4×Q8—22no—
365C4×Q8—42no—
366C4×Q8—42no—
367C4×D4—28no—
368C4×D4—28no—
369C4×D4—22no—
370C4×D4—22no—
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4#4114yes—
376C4×D4#4114yes—
377#117—24no—
378#117—24no—
379#117—42no—
380#117—42no—
381#117—82no—
382#117—82no—
383#117—82no—
384#117—82no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4C2×D411yescharacteristic
408C2×C4⋊C4C2×D411yescharacteristic
409C2×C4⋊C4C2×D411yescharacteristic
410C2×C4⋊C4C2×D411yescharacteristic
411C2×C4⋊C4C2×D412yes—
412C2×C4⋊C4C2×D412yes—
413C2×C4⋊C4C2×D412yes—
414C2×C4⋊C4C2×D412yes—
415C2×C4⋊C4C2412yes—
416C2×C4⋊C4C2412yes—
417C2×C4⋊C4C2412yes—
418C2×C4⋊C4C2411yescharacteristic
419C2×C4⋊C4C2411yescharacteristic
420C2×C4⋊C4C2412yes—
421C2×C4⋊C4C2411yescharacteristic
422C2×C4⋊C4C2411yescharacteristic
423C2×C4⋊C4C2411yescharacteristic
424C2×C22⋊C4—28no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4C2×D412yes—
442C2×C22⋊C4C2×D412yes—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—22no—
454C2×C42C2×D411yescharacteristic
455C2×C42C2×D411yescharacteristic
456C2×C42C2412yes—
457C2×C42C2412yes—
458C2×C42C2411yescharacteristic
459C2×C42C2411yescharacteristic
460#107—24no—
461#106—22no—
462#106—22no—
463#106—24no—
464#106—24no—
465#106—24no—
466C4⋊C8—22no—
467C4⋊C8—22no—
468C4⋊C8—42no—
469C4⋊C8—42no—
470#103—24no—
471#103—24no—
472#103—22no—
473#103—22no—
474#102—22no—
475#102—22no—
476#102—24no—
477#102—24no—
478#102—22no—
479#102—22no—
480#102—42no—
481#102—42no—
482#102—41no—
483#102—41no—
484C22⋊C8—22no—
485C22⋊C8—24no—
486C22⋊C8—22no—
487#97—42no—
488C4×C8—22no—
489C4×C8—22no—
490C4×C8—42no—
491#95—22no—
492#95—22no—
493#95—22no—
494#95—22no—
495#95—22no—
496#95—21no—
497#95—21no—
498#95—22no—
499#95—21no—
500#95—21no—
501#95—22no—
502#95—22no—
503#95—21no—
504#95—22no—
505#95—22no—
506#95—22no—
507#95—22no—
508#95—22no—
509#95—22no—
510#95C2×D412yes—
511#95C2×D412yes—
512#95C2×D412yes—
513#95C2×D412yes—
514C24—24no—
515C24—21no—
516C24—21no—
517C24—42no—
518C24—42no—
519C24—81no—
520C24—81no—
521C24—81no—
522C24—81no—
523C24C22×D411yescharacteristic
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—42no—
530C2×Q8—81no—
531C2×Q8—81no—
532C2×Q8C2×#4112yes—
533C2×D4—24no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—44no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4C2×#4112yes—
551C2×D4C2×#4112yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4—81no—
585C22×C4—816no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D411yescharacteristic
597C22×C4C2×#4112yes—
598C22×C42−1+412yes—
599C22×C4C2511yescharacteristic
600SD16—44no—
601SD16—44no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—22no—
616C2×C8—21no—
617C2×C8—22no—
618C2×C8—21no—
619C2×C8—21no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—42no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4—42no—
645C4⋊C4—44no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—81no—
653C4⋊C4—81no—
654C4⋊C4—82no—
655C4⋊C4—82no—
656C4⋊C4—82no—
657C4⋊C4—81no—
658C4⋊C4—82no—
659C4⋊C4—82no—
660C4⋊C4—82no—
661C4⋊C4—82no—
662C4⋊C4—82no—
663C4⋊C4C2×#4112yes—
664C4⋊C4C2×#4112yes—
665C4⋊C4C2×#4112yes—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—44no—
674C22⋊C4—82no—
675C22⋊C4—82no—
676C22⋊C4—82no—
677C22⋊C4—82no—
678C22⋊C4—82no—
679C22⋊C4—82no—
680C22⋊C4—82no—
681C22⋊C4—82no—
682C22⋊C4—81no—
683C22⋊C4—82no—
684C42—22no—
685C42—22no—
686C42—21no—
687C42—21no—
688C42—22no—
689C42—22no—
690C42—22no—
691C42—22no—
692C42—42no—
693C42—44no—
694C42—42no—
695C42—82no—
696C42—82no—
697C42—82no—
698C42—82no—
699C42—82no—
700C42—82no—
701C42C2×#4112yes—
702C42C2×#4112yes—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—22no—
710C23—22no—
711C23—48no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23—84no—
729C23—84no—
730C23#54812yes—
731C23C23×D411yescharacteristic
732Q8—22no—
733Q8—22no—
734Q8—41no—
735Q8—41no—
736Q8—162no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—48no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
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—21no—
775C2×C4—21no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—44no—
785C2×C4—48no—
786C2×C4—48no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—82no—
806C2×C4—84no—
807C2×C4—84no—
808C2×C4—84no—
809C2×C4#52512yes—
810C2×C4#52512yes—
811C2×C4#54812yes—
812C2×C4#57712yes—
813C2×C4#57712yes—
814C2×C4C22×#4111yescharacteristic
815C2×C4C22×#4111yescharacteristic
816C2×C4C22×#4111yescharacteristic
817C2×C4C2×2−1+411yescharacteristic
818C2×C4#58511yescharacteristic
819C2×C4#58511yescharacteristic
820C8—42no—
821C8—42no—
822C8—41no—
823C8—41no—
824C8—41no—
825C8—41no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—816no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22C2×#52511yescharacteristic
849C22C2×#54811yescharacteristic
850C22#348511yescharacteristic
851C22C2×#57711yescharacteristic
852C22C2×#57711yescharacteristic
853C22#358411yescharacteristic
854C22#358511yescharacteristic
855C4—22no—
856C4—22no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4—41no—
867C4—81no—
868C4—82no—
869C4—82no—
870C4—82no—
871C4—81no—
872C4—82no—
873C4#312314yes—
874C4#347511yescharacteristic
875C4#347511yescharacteristic
876C4#349511yescharacteristic
877C4#349511yescharacteristic
878C2—42no—
879C2—82no—
880C2—82no—
881C2#3651611yescharacteristic
882C2C2×#312311yescharacteristic
883C2#6058711yescharacteristic
884C2#6132711yescharacteristic
885C2#6134711yescharacteristic
886C2#6178511yescharacteristic
887C2#6180811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2285 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39607C2semidirect
3. #33157C2semidirect
7. #27962C2semidirect
8. #27649C2semidirect
9. #27449C2semidirect
10. #27436C2semidirect
11. #27386C2semidirect
12. #27367C2semidirect
13. #26025C2semidirect
14. #26021C2semidirect
15. #24680C2semidirect
16. #24680C2semidirect
17. #23067C2semidirect
18. #23061C2semidirect
19. #22767C2semidirect
20. #22759C2semidirect
21. #22626C2semidirect
22. #21591C2semidirect
35. #2567C22semidirect
37. #2552C22semidirect
39. #2506C22semidirect
42. #2453C22semidirect
43. #2369C22semidirect
53. Q8×C4⋊C4C22semidirect
63. #2101C22semidirect
64. #2101C22semidirect
65. #2085C22semidirect
66. #2074C22semidirect
75. #1990C22semidirect
76. #1990C22semidirect
77. #1989C22semidirect
78. #1989C22semidirect
79. #1948C22semidirect
80. #1948C22semidirect
81. #1948C22semidirect
82. #1947C22semidirect
83. #1939C22semidirect
84. #1939C22semidirect
89. #1927C22semidirect
90. #1927C22semidirect
93. #1921C22semidirect
94. #1920C22semidirect
95. #1920C22semidirect
96. #1919C22semidirect
97. #1919C22semidirect
98. #1919C22semidirect
99. #1917C22semidirect
100. #1916C22semidirect
112. #1834C22semidirect
113. #1834C22semidirect
117. #1803C22semidirect
118. #1803C22semidirect
125. #1776C22semidirect
126. C4×#106C22semidirect
127. #1770C22semidirect
128. C8×C4⋊C4C22semidirect
129. #1763C22semidirect
130. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#396072
#341862
#331572
#329562
#291152
#281302
#279622
#276492
#274492
#274362
#273862
#273672
#260252
#260212
#246802
#230672
#230612
#227672
#227592
#226262
#215912
C4×#4502