Finite Group Databasebeta

← #6456761

Subgroups — #6456761

Order 512.

1880 conjugacy classes of subgroups.

The subgroup lattice has 913 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34937C211yesmaximal, characteristic
2#34127C211yesmaximal, characteristic, complemented
3#26323C211yesmaximal, characteristic, complemented
4#26321C211yesmaximal, characteristic, complemented
5#26298C211yesmaximal, characteristic, complemented
6#26296C211yesmaximal, characteristic, complemented
7#26283C211yesmaximal, characteristic, complemented
8#26281C211yesmaximal, characteristic, complemented
9#26232C211yesmaximal, characteristic, complemented
10#26230C211yesmaximal, characteristic, complemented
11#26219C212yesmaximal, complemented
12#26215C212yesmaximal, complemented
13#26147C212yesmaximal, complemented
14#26143C212yesmaximal, complemented
15#23764C212yesmaximal, complemented
16#23764C212yesmaximal, complemented
17#21580C212yesmaximal, complemented
18#21578C212yesmaximal, complemented
19#21410C211yesmaximal, characteristic, complemented
20#21393C211yesmaximal, characteristic, complemented
21#21380C211yesmaximal, characteristic, complemented
22#21365C211yesmaximal, characteristic, complemented
23C4×#428C211yesmaximal, characteristic, complemented
24C2×#532—21no—
25C2×#532C2211yescharacteristic
26C2×C4×#41C2211yescharacteristic
27C2×#481C2212yes—
28C2×#480C2212yes—
29C2×#432C2211yescharacteristic
30C2×#428C2211yescharacteristic
31C2×#428C2211yescharacteristic
32C2×C4×M16C2211yescharacteristic
33#2548C2211yescharacteristic
34#2547C2211yescharacteristic
35#2546C2211yescharacteristic
36#2545—21no—
37#2544—21no—
38#2543—22no—
39#2541C2211yescharacteristic
40#2416C2212yes—
41#2416C2212yes—
42#2392—22no—
43#2355C2211yescharacteristic
44#2355C2211yescharacteristic
45#2352C2212yes—
46#2352C2212yes—
47D4×C4⋊C4C2211yescharacteristic
48D4×C4⋊C4C2211yescharacteristic
49#2347—21no—
50#2343—22no—
51#2339—21no—
52C4×#121C2212yes—
53C4×#121C2212yes—
54#2297—21no—
55#2295—21no—
56#2290—22no—
57#2285C2211yescharacteristic
58#2283C2212yes—
59C42×D4—21no—
60C4×#117C2211yescharacteristic
61C2×C4×C4⋊C4C2212yes—
62C2×C4×C4⋊C4C2211yescharacteristic
63#2101C2212yes—
64#2101C2212yes—
65#2092C2212yes—
66#2092C2212yes—
67#2085C2212yes—
68#2085C2212yes—
69#2077C2212yes—
70#2077C2212yes—
71#2075C2212yes—
72#2075C2212yes—
73#2073C2212yes—
74#2073C2212yes—
75#2034C2212yes—
76#2034C2212yes—
77#2033C2212yes—
78#2033C2212yes—
79#1990C2211yescharacteristic
80#1990C2211yescharacteristic
81#1988C2211yescharacteristic
82#1988C2211yescharacteristic
83#1984C2211yescharacteristic
84#1984C2211yescharacteristic
85#1982C2211yescharacteristic
86#1982C2211yescharacteristic
87#1957C2211yescharacteristic
88#1957C2211yescharacteristic
89#1954C2211yescharacteristic
90#1954C2211yescharacteristic
91#1948C2211yescharacteristic
92#1948C2211yescharacteristic
93#1947C2211yescharacteristic
94#1947C2211yescharacteristic
95#1926C2212yes—
96#1926C2212yes—
97#1925C2212yes—
98#1925C2212yes—
99#1921C2212yes—
100#1921C2212yes—
101#1920C2212yes—
102#1920C2212yes—
103#1895C2212yes—
104#1895C2212yes—
105#1875C2212yes—
106#1875C2212yes—
107#1874C2212yes—
108#1874C2212yes—
109#1870C2212yes—
110#1870C2212yes—
111#1853C2212yes—
112#1853C2212yes—
113#1852C2212yes—
114#1852C2212yes—
115#1824C2212yes—
116#1823C2212yes—
117#1776C2211yescharacteristic
118#1776C2212yes—
119#1776C2211yescharacteristic
120#1776C2212yes—
121#1776C2211yescharacteristic
122#1776C2211yescharacteristic
123C4×#107C2211yescharacteristic
124C4×#107C2211yescharacteristic
125C4×#106C2211yescharacteristic
126C4×#106C2211yescharacteristic
127#1762C2212yes—
128#1762C2212yes—
129#1762C2212yes—
130#1762C2212yes—
131#1749C2212yes—
132#1749C2212yes—
133#1736C2211yescharacteristic
134#1736C2211yescharacteristic
135C22×#41—21no—
136C22×#41D411yescharacteristic
137C22×M16C2311yescharacteristic
138C22×M16C2311yescharacteristic
139#532—24no—
140#532—24no—
141#532—48no—
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8C2311yescharacteristic
144C2×#127—21no—
145C2×#127C2311yescharacteristic
146C2×#124—21no—
147C2×#124—21no—
148C2×#124—21no—
149C2×#121—22no—
150C2×#121—22no—
151C2×#121—21no—
152C2×#121C2312yes—
153C2×#121C2312yes—
154C2×#121C2312yes—
155C4×#41—24no—
156C4×#41—24no—
157C2×C4×Q8D411yescharacteristic
158C2×C4×Q8C2311yescharacteristic
159C2×C4×D4—21no—
160C2×C4×D4—21no—
161C2×C4×D4—22no—
162C2×C4×D4—22no—
163C2×C4×D4—21no—
164C2×C4×D4D411yescharacteristic
165C2×C4×D4D412yes—
166C2×C4×D4C2312yes—
167C2×C4×D4C2311yescharacteristic
168C2×C4×D4C2312yes—
169C2×#117—21no—
170C2×#117D412yes—
171C2×#117D411yescharacteristic
172C2×#117C2311yescharacteristic
173C2×#117C2311yescharacteristic
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C42—21no—
179C22×C42—22no—
180C22×C42C2312yes—
181C22×C42C2311yescharacteristic
182#481—28no—
183#480—28no—
184#432—24no—
185#428—24no—
186#428—24no—
187C2×#107C2312yes—
188C2×#107C2311yescharacteristic
189C2×#107C2311yescharacteristic
190C2×#107C2311yescharacteristic
191C2×#107C2312yes—
192C2×#107C2311yescharacteristic
193C2×#106C2312yes—
194C2×#106C2311yescharacteristic
195C2×#106C2311yescharacteristic
196C2×#106C2311yescharacteristic
197C2×#106C2312yes—
198C2×#106C2311yescharacteristic
199C2×C4⋊C8C2311yescharacteristic
200C2×C4⋊C8C2311yescharacteristic
201C2×#102C2312yes—
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2312yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2312yes—
209C2×C22⋊C8C2312yes—
210C2×C22⋊C8C2312yes—
211C2×C22⋊C8C2312yes—
212C2×C22⋊C8C2312yes—
213C2×C22⋊C8C2312yes—
214C4×M16—24no—
215C2×#97C2311yescharacteristic
216C2×#97C2311yescharacteristic
217C2×#97C2312yes—
218C2×C4×C8C2311yescharacteristic
219C2×C4×C8C2311yescharacteristic
220#398—22no—
221#397—22no—
222#396—22no—
223#396—22no—
224#394—22no—
225#394—22no—
226#394—22no—
227#392—22no—
228#391—21no—
229#391—21no—
230#391—21no—
231#391—21no—
232#390—21no—
233#390—21no—
234#390C2312yes—
235#390C2312yes—
236#389—21no—
237#389—21no—
238#389C2312yes—
239#389C2312yes—
240#388—22no—
241#388—22no—
242#388—22no—
243#388—22no—
244#387—22no—
245#387—22no—
246#387—22no—
247#387—22no—
248#386—22no—
249#386—22no—
250#386—22no—
251#386—22no—
252#386—22no—
253#386—22no—
254#385—22no—
255#385—22no—
256#384C2311yescharacteristic
257#384C2311yescharacteristic
258#383—22no—
259#382—21no—
260#382C2312yes—
261#382C2312yes—
262#381—22no—
263#380—21no—
264#380C2312yes—
265#380C2312yes—
266#380C2312yes—
267#380C2312yes—
268#380C2312yes—
269C4×C4⋊C4—21no—
270C4×C4⋊C4—21no—
271C4×C4⋊C4—22no—
272C4×C4⋊C4—21no—
273C4×C4⋊C4—21no—
274C4×C4⋊C4—22no—
275C4×C4⋊C4—21no—
276C4×C4⋊C4C2311yescharacteristic
277C4×C4⋊C4C2311yescharacteristic
278C4×C4⋊C4C2312yes—
279C4×C4⋊C4C2312yes—
280C4×C4⋊C4C2311yescharacteristic
281C4×C4⋊C4C2311yescharacteristic
282C4×C4⋊C4C2311yescharacteristic
283C4×C4⋊C4C2312yes—
284C4×C4⋊C4C2311yescharacteristic
285C4×C4⋊C4C2311yescharacteristic
286C4×C4⋊C4C2311yescharacteristic
287C4×C22⋊C4—21no—
288C4×C22⋊C4—21no—
289C4×C22⋊C4—22no—
290C4×C22⋊C4—22no—
291C4×C22⋊C4—22no—
292C4×C22⋊C4—22no—
293C4×C22⋊C4—22no—
294#376—21no—
295#376—22no—
296C2×#95—22no—
297C2×#95—21no—
298C43—21no—
299#340C2311yescharacteristic
300#340C2311yescharacteristic
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2312yes—
307#340C2312yes—
308#340C2312yes—
309#340C2311yescharacteristic
310#340C2312yes—
311#340C2311yescharacteristic
312#340C2312yes—
313#340C2311yescharacteristic
314#340C2311yescharacteristic
315#340C2312yes—
316#340C2312yes—
317#340C2311yescharacteristic
318#340C2311yescharacteristic
319#336C2312yes—
320#336C2312yes—
321#336C2312yes—
322#336C2312yes—
323C2×#41—24no—
324C2×#41—24no—
325C2×#41—42no—
326C2×#41—44no—
327C2×#41—44no—
328C2×#41—44no—
329C22×Q8—21no—
330C22×Q8C2×D411yescharacteristic
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4C2×D412yes—
337C22×D4C2×D411yescharacteristic
338C22×D4C2412yes—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4—22no—
344C23×C4C2×D412yes—
345C23×C4C2×D411yescharacteristic
346C23×C4C2×D412yes—
347C23×C4C2×D411yescharacteristic
348C23×C4C2412yes—
349C23×C4C2411yescharacteristic
350C2×M16—22no—
351C2×M16—22no—
352C2×M16—22no—
353C2×M16—22no—
354C2×M16—41no—
355C2×M16—41no—
356C22×C8C2411yescharacteristic
357C22×C8C2411yescharacteristic
358C22×C8C2412yes—
359C22×C8C2412yes—
360C22×C8C2411yescharacteristic
361C22×C8C2411yescharacteristic
362C4⋊Q8—22no—
363C4⋊Q8—22no—
364C4⋊Q8—44no—
365#127—22no—
366#127—22no—
367#127—44no—
368#124—44no—
369#124—44no—
370#124—44no—
371#121—24no—
372#121—24no—
373#121—24no—
374#121—24no—
375#121—42no—
376#121—42no—
377#121—48no—
378#121—48no—
379#121—44no—
380C4×Q8—24no—
381C4×Q8—22no—
382C4×Q8—22no—
383C4×D4—28no—
384C4×D4—24no—
385C4×D4—24no—
386C4×D4—24no—
387C4×D4—22no—
388C4×D4—22no—
389C4×D4—24no—
390C4×D4—24no—
391C4×D4—48no—
392C4×D4—48no—
393C4×D4—44no—
394C4×D4—44no—
395C4×D4—44no—
396#117—24no—
397#117—28no—
398#117—22no—
399#117—22no—
400#117—41no—
401#117—41no—
402#117—82no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—42no—
419C2×C4⋊C4—42no—
420C2×C4⋊C4—41no—
421C2×C4⋊C4—41no—
422C2×C4⋊C4C2×D411yescharacteristic
423C2×C4⋊C4C2×D412yes—
424C2×C4⋊C4C2×D412yes—
425C2×C4⋊C4C2×D411yescharacteristic
426C2×C4⋊C4C2412yes—
427C2×C4⋊C4C2412yes—
428C2×C4⋊C4C2411yescharacteristic
429C2×C4⋊C4C2411yescharacteristic
430C2×C4⋊C4C2411yescharacteristic
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2412yes—
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
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×C22⋊C4C2×D412yes—
455C2×C42—24no—
456C2×C42—24no—
457C2×C42—22no—
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—44no—
471C2×C42—84no—
472C2×C42C2×D412yes—
473C2×C42C2×D412yes—
474C2×C42C2×D411yescharacteristic
475C2×C42C2×D411yescharacteristic
476C2×C42#4114yes—
477C2×C42#4114yes—
478C2×C42C2412yes—
479C2×C42C2411yescharacteristic
480C2×C42C2411yescharacteristic
481#107—22no—
482#107—22no—
483#107—22no—
484#107—24no—
485#107—42no—
486#107#4114yescomplemented
487#106—22no—
488#106—22no—
489#106—22no—
490#106—24no—
491#106—42no—
492#106#4114yescomplemented
493C4⋊C8—22no—
494C4⋊C8—22no—
495#102—24no—
496#102—24no—
497#102—24no—
498#102—24no—
499#102—42no—
500#102—42no—
501#102—42no—
502#102—42no—
503C22⋊C8—24no—
504C22⋊C8—24no—
505C22⋊C8—24no—
506C22⋊C8—42no—
507C22⋊C8—42no—
508#97—22no—
509#97—22no—
510#97—24no—
511C4×C8—22no—
512C4×C8—22no—
513#95—21no—
514#95—22no—
515#95—21no—
516#95—21no—
517#95—22no—
518#95—22no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—22no—
525#95—22no—
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—
535C24—22no—
536C24C22×D411yescharacteristic
537C24C22×D412yes—
538#41—416no—
539#41—816no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—42no—
544C2×Q8—42no—
545C2×Q8—42no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—42no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—44no—
560C2×D4—44no—
561C2×D4—44no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—82no—
571C2×D4—82no—
572C2×D4AGL(1,ℤ/8)14yes—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—42no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—82no—
616C22×C4—82no—
617C22×C4—81no—
618C22×C4—81no—
619C22×C4#12314yes—
620C22×C4#12314yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×D412yes—
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C2×#4112yes—
630C22×C4C2×#4112yes—
631C22×C4C2511yescharacteristic
632M16—28no—
633M16—44no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8C2×#4112yes—
651C2×C8C2×#4112yes—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—44no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—44no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—81no—
684C4⋊C4—81no—
685C4⋊C4C2×#4112yes—
686C4⋊C4C2×#4112yes—
687C4⋊C4C2×#4112yes—
688C4⋊C4C2×#4112yes—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—44no—
693C22⋊C4—44no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—44no—
699C22⋊C4—44no—
700C22⋊C4—44no—
701C22⋊C4—44no—
702C22⋊C4—44no—
703C22⋊C4—44no—
704C22⋊C4—82no—
705C22⋊C4—82no—
706C22⋊C4—82no—
707C42—24no—
708C42—24no—
709C42—22no—
710C42—22no—
711C42—42no—
712C42—42no—
713C42—42no—
714C42—42no—
715C42—42no—
716C42—42no—
717C42—44no—
718C42—42no—
719C42—42no—
720C42—42no—
721C42—42no—
722C42—82no—
723C42—82no—
724C42#12314yes—
725C42#12314yes—
726C42C2×#4112yes—
727C42C2×#4112yes—
728C42C2×#4112yes—
729C42C2×#4112yes—
730C23—21no—
731C23—22no—
732C23—21no—
733C23—22no—
734C23—22no—
735C23—21no—
736C23—21no—
737C23—22no—
738C23—22no—
739C23—21no—
740C23—22no—
741C23—21no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23C2×#12312yes—
750C23C2×AGL(1,ℤ/8)14yes—
751C23C23×D411yescharacteristic
752Q8—44no—
753Q8—84no—
754D4—28no—
755D4—48no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—42no—
760D4—84no—
761D4—88no—
762D4—88no—
763D4—88no—
764D4—84no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—28no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—44no—
792C2×C4—48no—
793C2×C4—48no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—88no—
828C2×C4—88no—
829C2×C4—84no—
830C2×C4—84no—
831C2×C4—88no—
832C2×C4C2×#12312yes—
833C2×C4C2×#12312yes—
834C2×C4C2×#12312yes—
835C2×C4C2×#12312yes—
836C2×C4C2×#12312yes—
837C2×C4C2×AGL(1,ℤ/8)12yes—
838C2×C4#57512yes—
839C2×C4C22×#4111yescharacteristic
840C2×C4C22×#4111yescharacteristic
841C2×C4C22×#4111yescharacteristic
842C2×C4C22×#4111yescharacteristic
843C2×C4#58511yescharacteristic
844C2×C4#58511yescharacteristic
845C8—22no—
846C8—22no—
847C8—41no—
848C8—41no—
849C8—42no—
850C8—42no—
851C22—24no—
852C22—24no—
853C22—22no—
854C22—24no—
855C22—22no—
856C22—22no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—42no—
861C22—42no—
862C22—41no—
863C22—42no—
864C22—42no—
865C22—82no—
866C22—82no—
867C22—82no—
868C22—82no—
869C22—82no—
870C22—82no—
871C22—82no—
872C22C22×#12311yescharacteristic
873C22D4×#4111yescharacteristic
874C22D4×#4111yescharacteristic
875C22C22×AGL(1,ℤ/8)11yescharacteristic
876C22C2×#57511yescharacteristic
877C22#358511yescharacteristic
878C22#358611yescharacteristic
879C4—22no—
880C4—22no—
881C4—22no—
882C4—22no—
883C4—42no—
884C4—42no—
885C4—42no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—82no—
891C4—81no—
892C4—81no—
893C4—81no—
894C4—81no—
895C4—82no—
896C4—82no—
897C4#309414yes—
898C4#344411yescharacteristic
899C4#345511yescharacteristic
900C4#348011yescharacteristic
901C4#348011yescharacteristic
902C2—44no—
903C2—42no—
904C2—162no—
905C2#3474411yescharacteristic
906C2C2×#309411yescharacteristic
907C2#6051711yescharacteristic
908C2#6145111yescharacteristic
909C2#6145211yescharacteristic
910C2#6146711yescharacteristic
911C2#6146811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#34937C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34127C2semidirect
3. #26323C2semidirect
4. #26321C2semidirect
5. #26298C2semidirect
6. #26296C2semidirect
7. #26283C2semidirect
8. #26281C2semidirect
9. #26232C2semidirect
10. #26230C2semidirect
11. #26219C2semidirect
12. #26215C2semidirect
13. #26147C2semidirect
14. #26143C2semidirect
15. #23764C2semidirect
16. #23764C2semidirect
17. #21580C2semidirect
18. #21578C2semidirect
19. #21410C2semidirect
20. #21393C2semidirect
21. #21380C2semidirect
22. #21365C2semidirect
23. C4×#428C2semidirect
486. #107#41semidirect
492. #106#41semidirect

Maximal subgroups

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

subgroupindex
#349372
#341272
#263232
#263212
#262982
#262962
#262832
#262812
#262322
#262302
#262192
#262152
#261472
#261432
#237642
#215802
#215782
#214102
#213932
#213802
#213652
C4×#4282