Finite Group Databasebeta

← #6592170

Subgroups — #6592170

Order 512.

1787 conjugacy classes of subgroups.

The subgroup lattice has 911 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39468C211yesmaximal, characteristic
2#34207C211yesmaximal, characteristic
3#33154C211yesmaximal, characteristic, complemented
4#32989C212yesmaximal, complemented
5#27960C211yesmaximal, characteristic, complemented
6#27648C211yesmaximal, characteristic, complemented
7#27606C212yesmaximal, complemented
8#26301C211yesmaximal, characteristic, complemented
9#26296C211yesmaximal, characteristic, complemented
10#26227C212yesmaximal, complemented
11#26200C212yesmaximal, complemented
12#24972C211yesmaximal, characteristic, complemented
13#24971C211yesmaximal, characteristic, complemented
14#24953C212yesmaximal, complemented
15#24942C212yesmaximal, complemented
16#24564C212yesmaximal, complemented
17#22715C211yesmaximal, characteristic, complemented
18#22705C211yesmaximal, characteristic, complemented
19#22504C211yesmaximal, characteristic, complemented
20#22490C211yesmaximal, characteristic, complemented
21#22402C211yesmaximal, characteristic
22C4×#485C211yesmaximal, characteristic, complemented
23#20703C212yesmaximal, complemented
24C2×#556C2211yescharacteristic
25C2×#532C2211yescharacteristic
26C2×#520C2212yes—
27C2×#484C2212yes—
28C2×#485C2211yescharacteristic
29C2×#436C2211yescharacteristic
30C2×C8×D4C2211yescharacteristic
31C2×#408C2212yes—
32#2857C2211yescharacteristic
33#2715—22no—
34#2691—22no—
35#2616C2212yes—
36#2547C2211yescharacteristic
37#2544—21no—
38#2538C2211yescharacteristic
39#2485C2212yes—
40#2451—21no—
41#2427—21no—
42#2426—21no—
43#2417C2212yes—
44#2361—21no—
45#2361—21no—
46#2361—22no—
47#2354C2212yes—
48#2354C2211yescharacteristic
49#2354C2211yescharacteristic
50D4×C4⋊C4C2211yescharacteristic
51D4×C4⋊C4C2212yes—
52D4×C4⋊C4C2211yescharacteristic
53D4×C4⋊C4C2211yescharacteristic
54#2326—22no—
55#2311C2212yes—
56#2311C2212yes—
57C4×C4⋊Q8—21no—
58C4×#127—21no—
59C4×C22⋊Q8C2211yescharacteristic
60C2×#384C2211yescharacteristic
61C4×#117C2211yescharacteristic
62#2099C2212yes—
63#2099C2212yes—
64#2083C2212yes—
65#2077C2212yes—
66#2077C2212yes—
67#2076C2212yes—
68#2076C2212yes—
69#2075C2212yes—
70#2075C2212yes—
71#2072C2212yes—
72#2036C2212yes—
73#2035C2212yes—
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1988C2211yescharacteristic
77#1988C2211yescharacteristic
78#1954C2211yescharacteristic
79#1954C2211yescharacteristic
80#1948C2211yescharacteristic
81#1947C2211yescharacteristic
82#1947C2211yescharacteristic
83#1947C2211yescharacteristic
84#1928C2211yescharacteristic
85#1927C2211yescharacteristic
86#1921C2212yes—
87#1920C2212yes—
88#1919C2211yescharacteristic
89#1918C2211yescharacteristic
90#1894C2212yes—
91#1892C2212yes—
92#1873C2211yescharacteristic
93#1873C2212yes—
94#1873C2212yes—
95#1872C2212yes—
96#1872C2212yes—
97#1870C2212yes—
98#1869C2212yes—
99#1854C2211yescharacteristic
100#1854C2212yes—
101#1854C2212yes—
102#1854C2212yes—
103#1853C2212yes—
104#1852C2212yes—
105#1852C2212yes—
106#1852C2212yes—
107#1834C2211yescharacteristic
108#1834C2211yescharacteristic
109#1825C2211yescharacteristic
110#1825C2212yes—
111#1825C2212yes—
112#1825C2212yes—
113#1825C2212yes—
114#1825C2212yes—
115#1824C2212yes—
116#1824C2212yes—
117#1823C2212yes—
118#1823C2212yes—
119#1823C2212yes—
120#1809C2212yes—
121#1808C2212yes—
122#1803C2211yescharacteristic
123#1803C2211yescharacteristic
124#1797C2211yescharacteristic
125#1780C2212yes—
126C4×#107C2211yescharacteristic
127C4×#106C2211yescharacteristic
128C4×#103C2211yescharacteristic
129C4×#103C2211yescharacteristic
130C4×C22⋊C8C2211yescharacteristic
131#1736C2212yes—
132#1736C2212yes—
133#1735C2212yes—
134C2×#340C2212yes—
135C22×#41C2312yes—
136C22×M16C2312yes—
137C23×C8C2312yes—
138#556—24no—
139#556—24no—
140#532—24no—
141#532—24no—
142C2×C4⋊Q8D411yescharacteristic
143C2×C4⋊Q8C2311yescharacteristic
144C2×#127D411yescharacteristic
145C2×#126—22no—
146C2×#124—21no—
147C2×#124—21no—
148C2×#124D412yes—
149C2×C22⋊Q8—21no—
150C2×C22⋊Q8C2311yescharacteristic
151C2×C22⋊Q8C2312yes—
152C2×C22⋊Q8C2312yes—
153C2×#121D411yescharacteristic
154C2×#121D411yescharacteristic
155C2×#121D412yes—
156#520—28no—
157#520—44no—
158C2×C4×Q8—22no—
159C2×C4×Q8—21no—
160C2×C4×Q8C2311yescharacteristic
161C2×C4×D4—22no—
162C2×C4×D4—22no—
163C2×C4×D4—22no—
164C2×C4×D4—21no—
165C2×C4×D4—22no—
166C2×C4×D4—21no—
167C2×C4×D4—21no—
168C2×C4×D4C2312yes—
169C2×C4×D4C2311yescharacteristic
170C2×C4×D4C2311yescharacteristic
171C2×#117C2312yes—
172C2×#117C2312yes—
173C2×#117C2312yes—
174C2×#117C2311yescharacteristic
175C2×#117C2311yescharacteristic
176C22×C4⋊C4—21no—
177C22×C4⋊C4—21no—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2312yes—
182C22×C42C2311yescharacteristic
183#485—24no—
184#484—44no—
185#436—24no—
186C8×D4—24no—
187C2×#107C2311yescharacteristic
188C2×#107C2312yes—
189C2×#107C2312yes—
190C2×#107C2312yes—
191C2×#107C2311yescharacteristic
192C2×#106C2311yescharacteristic
193C2×#106C2312yes—
194C2×#106C2311yescharacteristic
195C2×C4⋊C8C2311yescharacteristic
196C2×C4⋊C8C2311yescharacteristic
197C2×#103C2311yescharacteristic
198C2×#103C2311yescharacteristic
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2311yescharacteristic
202C2×#103C2311yescharacteristic
203#408—44no—
204C2×C22⋊C8C2312yes—
205C2×C22⋊C8C2311yescharacteristic
206C2×C22⋊C8C2311yescharacteristic
207C2×C22⋊C8C2312yes—
208C2×C22⋊C8C2312yes—
209C2×C22⋊C8C2312yes—
210C2×C22⋊C8C2312yes—
211C2×C22⋊C8C2312yes—
212C2×C22⋊C8C2312yes—
213C2×C4×C8C2311yescharacteristic
214C2×C4×C8C2311yescharacteristic
215#398—22no—
216#397—22no—
217#397—22no—
218#396—22no—
219#396—22no—
220#395—22no—
221#394—22no—
222#394—22no—
223#394—22no—
224#394—22no—
225#391—22no—
226#391—22no—
227#391—21no—
228#391—21no—
229#391C2311yescharacteristic
230#390—22no—
231#390—21no—
232#390—22no—
233#390—21no—
234#390—22no—
235#390—21no—
236#389—22no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389—21no—
242#389C2311yescharacteristic
243#389C2312yes—
244#388—22no—
245#388—22no—
246#388—22no—
247#388—22no—
248#388—22no—
249#387—22no—
250#387—21no—
251#386—22no—
252#386—22no—
253#386—22no—
254#386—22no—
255#386—22no—
256#385—21no—
257#385—22no—
258#385—22no—
259#385—22no—
260#385—22no—
261#385—22no—
262#384—21no—
263#384—21no—
264#384C2311yescharacteristic
265#384C2311yescharacteristic
266#384C2312yes—
267#384C2311yescharacteristic
268#380—21no—
269#380—22no—
270#380C2311yescharacteristic
271#380C2312yes—
272#380C2312yes—
273#380C2312yes—
274#380C2312yes—
275#380C2312yes—
276#380C2312yes—
277#380C2312yes—
278#380C2312yes—
279#380C2312yes—
280C4×C4⋊C4—22no—
281C4×C4⋊C4—21no—
282C4×C4⋊C4—21no—
283C4×C4⋊C4—21no—
284C4×C4⋊C4C2311yescharacteristic
285C4×C4⋊C4C2311yescharacteristic
286C4×C4⋊C4C2311yescharacteristic
287C4×C4⋊C4C2311yescharacteristic
288C4×C4⋊C4C2311yescharacteristic
289C4×C22⋊C4—21no—
290C4×C22⋊C4—21no—
291C4×C22⋊C4—21no—
292#376—21no—
293C43—21no—
294#340C2312yes—
295#340C2312yes—
296#340C2311yescharacteristic
297#340C2312yes—
298#340C2311yescharacteristic
299#340C2312yes—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2312yes—
305#340C2311yescharacteristic
306#340C2312yes—
307#340C2312yes—
308#340C2312yes—
309#340C2311yescharacteristic
310#340C2312yes—
311#340C2312yes—
312#340C2311yescharacteristic
313#340C2312yes—
314#340C2311yescharacteristic
315#340C2312yes—
316#340C2311yescharacteristic
317#340C2311yescharacteristic
318#340C2312yes—
319#340C2312yes—
320#336C2312yes—
321#336C2311yescharacteristic
322#336C2311yescharacteristic
323C2×#41—24no—
324C2×#41—24no—
325C2×#41—24no—
326C2×#41—24no—
327C2×#41—42no—
328C2×#41—42no—
329C22×Q8—21no—
330C22×Q8C2×D412yes—
331C22×Q8C2411yescharacteristic
332C22×D4C2×D411yescharacteristic
333C22×D4C2×D412yes—
334C22×D4C2×D412yes—
335C22×D4C2×D412yes—
336C22×D4C2×D412yes—
337C22×D4C2×D411yescharacteristic
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4C2×D411yescharacteristic
343C23×C4C2×D411yescharacteristic
344C23×C4C2412yes—
345C23×C4C2412yes—
346C23×C4C2411yescharacteristic
347C2×M16—24no—
348C2×M16—42no—
349C2×M16—42no—
350C22×C8—24no—
351C22×C8—42no—
352C22×C8—42no—
353C22×C8C2411yescharacteristic
354C22×C8C2412yes—
355C22×C8C2411yescharacteristic
356C22×C8C2412yes—
357C22×C8C2411yescharacteristic
358C22×C8C2411yescharacteristic
359C4⋊Q8—24no—
360C4⋊Q8—22no—
361C4⋊Q8—22no—
362#127—24no—
363#126—48no—
364#124—28no—
365#124—44no—
366#124—82no—
367C22⋊Q8—24no—
368C22⋊Q8—24no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C22⋊Q8—42no—
372C22⋊Q8—42no—
373C22⋊Q8—82no—
374#121—24no—
375#121—24no—
376#121—28no—
377C4×Q8—22no—
378C4×Q8—22no—
379C4×Q8—48no—
380C4×Q8—44no—
381C4×D4—24no—
382C4×D4—24no—
383C4×D4—22no—
384C4×D4—22no—
385C4×D4—48no—
386C4×D4—48no—
387C4×D4—48no—
388C4×D4—82no—
389C4×D4—82no—
390C4×D4—82no—
391C4×D4—84no—
392C4×D4#4114yes—
393C4×D4#4114yes—
394#117—22no—
395#117—24no—
396#117—24no—
397#117—24no—
398#117—24no—
399#117—41no—
400#117—41no—
401#117—42no—
402#117—42no—
403#117#4114yes—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4—42no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4—42no—
431C2×C4⋊C4—82no—
432C2×C4⋊C4—82no—
433C2×C4⋊C4C2×D412yes—
434C2×C4⋊C4C2×D411yescharacteristic
435C2×C4⋊C4C2×D411yescharacteristic
436C2×C4⋊C4C2412yes—
437C2×C4⋊C4C2412yes—
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2411yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4C2×D412yes—
466C2×C22⋊C4C2×D412yes—
467C2×C22⋊C4C2×D412yes—
468C2×C22⋊C4C2×D412yes—
469C2×C42—21no—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42—22no—
473C2×C42—22no—
474C2×C42—22no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—21no—
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—21no—
482C2×C42C2×D411yescharacteristic
483C2×C42C2×D411yescharacteristic
484C2×C42C2411yescharacteristic
485C2×C42C2411yescharacteristic
486#107—22no—
487#107—41no—
488#107—42no—
489#107—42no—
490#107—42no—
491#106—22no—
492#106—41no—
493#106—42no—
494C4⋊C8—22no—
495C4⋊C8—22no—
496#103—22no—
497#103—22no—
498#103—41no—
499#103—41no—
500#103—42no—
501#103—42no—
502C22⋊C8—24no—
503C22⋊C8—24no—
504C22⋊C8—22no—
505C22⋊C8—22no—
506C22⋊C8—24no—
507C22⋊C8—42no—
508C22⋊C8—42no—
509C22⋊C8—42no—
510C22⋊C8—42no—
511C4×C8—22no—
512C4×C8—22no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532C24C22×D412yes—
533C24C22×D412yes—
534C24C22×D411yescharacteristic
535#41—48no—
536#41—48no—
537#41—48no—
538#41—48no—
539C2×Q8—24no—
540C2×Q8—24no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—42no—
548C2×Q8—42no—
549C2×Q8—42no—
550C2×Q8—42no—
551C2×D4—24no—
552C2×D4—24no—
553C2×D4—24no—
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—22no—
557C2×D4—24no—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—24no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4#12314yes—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—41no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4—82no—
607C22×C4—82no—
608C22×C4—82no—
609C22×C4—82no—
610C22×C4—82no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4C22×D412yes—
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D412yes—
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C2×#4114yes—
621C22×C4C2×#4114yes—
622C22×C4C2×#4112yes—
623C22×C4H(5,𝔽2)12yes—
624C22×C4C2511yescharacteristic
625M16—84no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—84no—
645C4⋊C4—24no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—22no—
667C4⋊C4—44no—
668C4⋊C4—44no—
669C4⋊C4—42no—
670C4⋊C4—44no—
671C4⋊C4—42no—
672C4⋊C4—44no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—44no—
679C4⋊C4—81no—
680C4⋊C4—82no—
681C4⋊C4—81no—
682C4⋊C4—81no—
683C4⋊C4—82no—
684C4⋊C4—82no—
685C4⋊C4—82no—
686C4⋊C4#12314yes—
687C4⋊C4C2×#4112yes—
688C4⋊C4C2×#4112yes—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—44no—
694C22⋊C4—44no—
695C22⋊C4—42no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—42no—
699C22⋊C4—82no—
700C22⋊C4—81no—
701C22⋊C4—82no—
702C22⋊C4—82no—
703C22⋊C4—82no—
704C22⋊C4—82no—
705C22⋊C4—82no—
706C22⋊C4—82no—
707C22⋊C4—82no—
708C22⋊C4—82no—
709C22⋊C4—82no—
710C22⋊C4#12318yes—
711C42—22no—
712C42—22no—
713C42—24no—
714C42—21no—
715C42—21no—
716C42—44no—
717C42—44no—
718C42—42no—
719C42—42no—
720C42—44no—
721C42—42no—
722C42—42no—
723C42—42no—
724C42—42no—
725C42—42no—
726C42C2×#4112yes—
727C42C2×#4112yes—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—22no—
732C23—21no—
733C23—22no—
734C23—21no—
735C23—22no—
736C23—22no—
737C23—21no—
738C23—21no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23C2×#12314yes—
748C23#54612yes—
749C23C23×D411yescharacteristic
750Q8—48no—
751Q8—41no—
752Q8—41no—
753Q8—41no—
754Q8—41no—
755Q8—84no—
756D4—28no—
757D4—48no—
758D4—48no—
759D4—48no—
760D4—48no—
761D4—44no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—44no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—44no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—164no—
827C2×C4—164no—
828C2×C4—164no—
829C2×C4—164no—
830C2×C4C2×#12312yes—
831C2×C4C2×#12314yes—
832C2×C4C2×#12312yes—
833C2×C4#54612yes—
834C2×C4#57612yes—
835C2×C4#57712yes—
836C2×C4#57812yes—
837C2×C4C22×#4111yescharacteristic
838C2×C4C22×#4111yescharacteristic
839C2×C4C22×#4111yescharacteristic
840C2×C4C2×H(5,𝔽2)11yescharacteristic
841C2×C4#58511yescharacteristic
842C2×C4#58511yescharacteristic
843C8—41no—
844C8—41no—
845C8—42no—
846C8—41no—
847C8—42no—
848C8—41no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—24no—
853C22—24no—
854C22—24no—
855C22—42no—
856C22—42no—
857C22—41no—
858C22—42no—
859C22—41no—
860C22—41no—
861C22—42no—
862C22—41no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22C22×#12311yescharacteristic
871C22C2×#54611yescharacteristic
872C22#348511yescharacteristic
873C22C2×#57611yescharacteristic
874C22C2×#57711yescharacteristic
875C22C2×#57811yescharacteristic
876C22#358611yescharacteristic
877C4—24no—
878C4—22no—
879C4—22no—
880C4—22no—
881C4—42no—
882C4—42no—
883C4—42no—
884C4—41no—
885C4—81no—
886C4—82no—
887C4—82no—
888C4—81no—
889C4—81no—
890C4—82no—
891C4—81no—
892C4—81no—
893C4—82no—
894C4—81no—
895C4#309814yes—
896C4#347511yescharacteristic
897C4#347511yescharacteristic
898C4#351311yescharacteristic
899C4#351311yescharacteristic
900C2—42no—
901C2—44no—
902C2—82no—
903C2#3615511yescharacteristic
904C2C2×#309811yescharacteristic
905C2#6052211yescharacteristic
906C2#6121011yescharacteristic
907C2#6121511yescharacteristic
908C2#6178911yescharacteristic
909C2#6181111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#532C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#532 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #33154C2semidirect
4. #32989C2semidirect
5. #27960C2semidirect
6. #27648C2semidirect
7. #27606C2semidirect
8. #26301C2semidirect
9. #26296C2semidirect
10. #26227C2semidirect
11. #26200C2semidirect
12. #24972C2semidirect
13. #24971C2semidirect
14. #24953C2semidirect
15. #24942C2semidirect
16. #24564C2semidirect
17. #22715C2semidirect
18. #22705C2semidirect
19. #22504C2semidirect
20. #22490C2semidirect
22. C4×#485C2semidirect
23. #20703C2semidirect

Maximal subgroups

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

subgroupindex
#394682
#342072
#331542
#329892
#279602
#276482
#276062
#263012
#262962
#262272
#262002
#249722
#249712
#249532
#249422
#245642
#227152
#227052
#225042
#224902
#224022
C4×#4852
#207032