Finite Group Databasebeta

← #6589384

Subgroups — #6589384

Order 512.

1695 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36551C211yesmaximal, characteristic, complemented
2#36404C211yesmaximal, characteristic
3#33210C211yesmaximal, characteristic, complemented
4#33146C211yesmaximal, characteristic, complemented
5#32958C211yesmaximal, characteristic, complemented
6#28854C212yesmaximal, complemented
7#28103C212yesmaximal, complemented
8#27737C211yesmaximal, characteristic, complemented
9#27178C212yesmaximal, complemented
10#27053C212yesmaximal, complemented
11#26086C211yesmaximal, characteristic, complemented
12#25699C211yesmaximal, characteristic, complemented
13#25454C211yesmaximal, characteristic, complemented
14#25340C211yesmaximal, characteristic, complemented
15#25016C211yesmaximal, characteristic, complemented
16#24956C212yesmaximal, complemented
17#24883C212yesmaximal, complemented
18#23067C211yesmaximal, characteristic, complemented
19#22932C212yesmaximal, complemented
20#22709C212yesmaximal, complemented
21#22485C211yesmaximal, characteristic, complemented
22#21486C211yesmaximal, characteristic, complemented
23C4×#417C211yesmaximal, characteristic, complemented
24C2×#547C2211yescharacteristic
25C2×C4×#41C2211yescharacteristic
26C2×#498C2211yescharacteristic
27C2×#484C2212yes—
28C2×#477C2211yescharacteristic
29C2×#476C2211yescharacteristic
30C2×#435C2212yes—
31C2×C8×D4C2211yescharacteristic
32C2×#417C2211yescharacteristic
33C2×#417C2211yescharacteristic
34C2×C4×M16C2211yescharacteristic
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2855—21no—
38#2851—21no—
39#2589—22no—
40#2568C2211yescharacteristic
41#2563C2211yescharacteristic
42#2552C2211yescharacteristic
43#2538C2211yescharacteristic
44#2509—21no—
45#2497C2212yes—
46#2487C2212yes—
47#2470—22no—
48#2457—22no—
49#2454—21no—
50#2450—22no—
51#2420C2212yes—
52#2415—21no—
53#2407—21no—
54#2407C2212yes—
55#2369C2211yescharacteristic
56#2360C2212yes—
57#2354C2211yescharacteristic
58#2352C2212yes—
59D4×C4⋊C4C2212yes—
60D4×C4⋊C4C2211yescharacteristic
61#2345C2212yes—
62C4×#121—21no—
63C4×#121C2211yescharacteristic
64#2297—21no—
65C2×C4×C4⋊C4C2211yescharacteristic
66#2101C2212yes—
67#2093C2212yes—
68#2085C2212yes—
69#2076C2212yes—
70#2076C2212yes—
71#2072C2212yes—
72#2067C2212yes—
73#2066C2212yes—
74#2036C2212yes—
75#2036C2212yes—
76#2034C2212yes—
77#2034C2212yes—
78#1990C2211yescharacteristic
79#1990C2211yescharacteristic
80#1988C2211yescharacteristic
81#1988C2211yescharacteristic
82#1954C2211yescharacteristic
83#1949C2212yes—
84#1947C2211yescharacteristic
85#1947C2211yescharacteristic
86#1947C2212yes—
87#1943C2212yes—
88#1943C2212yes—
89#1939C2211yescharacteristic
90#1936C2212yes—
91#1935C2212yes—
92#1927C2212yes—
93#1925C2212yes—
94#1924C2212yes—
95#1919C2212yes—
96#1918C2212yes—
97#1918C2212yes—
98#1918C2212yes—
99#1893C2212yes—
100#1892C2212yes—
101#1874C2212yes—
102#1870C2212yes—
103#1865C2212yes—
104#1862C2212yes—
105#1854C2212yes—
106#1853C2212yes—
107#1853C2212yes—
108#1852C2212yes—
109#1852C2212yes—
110#1845C2211yescharacteristic
111#1836C2212yes—
112#1823C2212yes—
113#1823C2212yes—
114#1809C2212yes—
115#1809C2212yes—
116#1808C2212yes—
117#1803C2211yescharacteristic
118#1802C2211yescharacteristic
119#1797C2211yescharacteristic
120#1788C2212yes—
121#1776C2212yes—
122#1770C2211yescharacteristic
123#1763C2211yescharacteristic
124#1763C2211yescharacteristic
125#1762C2211yescharacteristic
126#1762C2211yescharacteristic
127C4×#103C2211yescharacteristic
128C4×#103C2211yescharacteristic
129C4×#102C2211yescharacteristic
130C4×#102C2211yescharacteristic
131#1752C2212yes—
132#1736C2211yescharacteristic
133#1736C2211yescharacteristic
134C2×#340C2212yes—
135C22×#41—21no—
136C22×#41C2311yescharacteristic
137C22×M16C2311yescharacteristic
138C22×M16C2311yescharacteristic
139C23×C8C2312yes—
140#547—24no—
141#547—42no—
142C2×C4⋊Q8C2311yescharacteristic
143C2×C4⋊Q8C2311yescharacteristic
144C2×#125—21no—
145C2×#123—22no—
146C2×C22⋊Q8—21no—
147C2×C22⋊Q8—21no—
148C2×C22⋊Q8—21no—
149C2×C22⋊Q8C2312yes—
150C2×#121D411yescharacteristic
151C2×#121C2312yes—
152C4×#41—24no—
153C4×#41—42no—
154C2×C4×Q8C2311yescharacteristic
155C2×C4×Q8C2311yescharacteristic
156C2×C4×D4—21no—
157C2×C4×D4—21no—
158C2×C4×D4—22no—
159C2×C4×D4—21no—
160C2×C4×D4C2311yescharacteristic
161C2×C4×D4C2311yescharacteristic
162C2×C4×D4C2311yescharacteristic
163C2×C4×D4C2312yes—
164C2×#117—21no—
165C2×#117—21no—
166C2×#117C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2311yescharacteristic
171C22×C42—21no—
172C22×C42—21no—
173C22×C42C2311yescharacteristic
174#498—42no—
175#484—28no—
176#477—42no—
177#476—24no—
178#435—28no—
179C8×D4—42no—
180C2×#107C2312yes—
181C2×#107C2312yes—
182C2×#107C2312yes—
183C2×#107C2312yes—
184C2×#107C2312yes—
185C2×#106C2312yes—
186C2×#106C2312yes—
187C2×#106C2312yes—
188C2×C4⋊C8C2311yescharacteristic
189C2×C4⋊C8C2311yescharacteristic
190C2×C4⋊C8C2312yes—
191#417—24no—
192#417—24no—
193C2×#103C2312yes—
194C2×#103C2311yescharacteristic
195C2×#103C2311yescharacteristic
196C2×#103C2311yescharacteristic
197C2×#103C2312yes—
198C2×#103C2311yescharacteristic
199C2×#102C2311yescharacteristic
200C2×#102C2311yescharacteristic
201C2×#102C2312yes—
202C2×#102C2311yescharacteristic
203C2×#102C2311yescharacteristic
204C2×#102C2312yes—
205C2×C22⋊C8C2312yes—
206C2×C22⋊C8C2312yes—
207C2×C22⋊C8C2312yes—
208C2×C22⋊C8C2312yes—
209C4×M16—42no—
210C2×#97C2312yes—
211C2×#97C2311yescharacteristic
212C2×#97C2311yescharacteristic
213C2×C4×C8C2311yescharacteristic
214C2×C4×C8C2311yescharacteristic
215#400—22no—
216#400—22no—
217#400—22no—
218#399—22no—
219#398—22no—
220#397—22no—
221#396—22no—
222#396—22no—
223#394—22no—
224#394—22no—
225#393—22no—
226#392—22no—
227#391—21no—
228#391—21no—
229#391—21no—
230#391—21no—
231#391—22no—
232#391C2312yes—
233#390—21no—
234#390—21no—
235#390D411yescharacteristic
236#390C2312yes—
237#389—22no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389—21no—
242#389—21no—
243#389—21no—
244#389—22no—
245#389D411yescharacteristic
246#389C2312yes—
247#389C2312yes—
248#389C2312yes—
249#389C2312yes—
250#388—22no—
251#388—22no—
252#388—22no—
253#388D412yes—
254#387—22no—
255#387—22no—
256#387—22no—
257#387—22no—
258#387—22no—
259#386—22no—
260#386—22no—
261#386—22no—
262#386—22no—
263#386D412yes—
264#385—22no—
265#385—22no—
266#385—22no—
267#385—22no—
268#385—22no—
269#385—22no—
270#384C2311yescharacteristic
271#384C2312yes—
272#384C2311yescharacteristic
273#382—21no—
274#382C2312yes—
275#381—22no—
276#380—21no—
277#380—21no—
278#380—21no—
279#380—22no—
280#380D411yescharacteristic
281#380C2312yes—
282#380C2312yes—
283#380C2312yes—
284#380C2312yes—
285#380C2312yes—
286#380C2312yes—
287C4×C4⋊C4—21no—
288C4×C4⋊C4—21no—
289C4×C4⋊C4—21no—
290C4×C4⋊C4C2311yescharacteristic
291C4×C4⋊C4C2311yescharacteristic
292C4×C4⋊C4C2312yes—
293C4×C4⋊C4C2311yescharacteristic
294C4×C4⋊C4C2312yes—
295C4×C4⋊C4C2311yescharacteristic
296C4×C4⋊C4C2311yescharacteristic
297C4×C22⋊C4—22no—
298C4×C22⋊C4—22no—
299C4×C22⋊C4—22no—
300C4×C22⋊C4C2312yes—
301C2×#95—21no—
302#340C2312yes—
303#340C2312yes—
304#340C2311yescharacteristic
305#340C2312yes—
306#340C2312yes—
307#340C2312yes—
308#340C2312yes—
309#340C2312yes—
310#340C2312yes—
311#340C2312yes—
312#340C2311yescharacteristic
313#340C2311yescharacteristic
314#340C2312yes—
315#340C2311yescharacteristic
316#340C2312yes—
317#340C2311yescharacteristic
318#340C2312yes—
319#340C2311yescharacteristic
320#340C2311yescharacteristic
321#340C2311yescharacteristic
322#336C2312yes—
323#336C2312yes—
324#336C2312yes—
325C2×#41—22no—
326C2×#41—22no—
327C2×#41—22no—
328C2×#41—22no—
329C2×#41—41no—
330C2×#41—41no—
331C2×#41—44no—
332C2×#41—44no—
333C2×#41—82no—
334C22×Q8—21no—
335C22×Q8—21no—
336C22×Q8C2411yescharacteristic
337C22×D4—21no—
338C22×D4—22no—
339C22×D4C2×D412yes—
340C22×D4C2×D411yescharacteristic
341C22×D4C2411yescharacteristic
342C23×C4—21no—
343C23×C4—21no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—21no—
347C23×C4—21no—
348C23×C4—21no—
349C23×C4C2×D411yescharacteristic
350C23×C4C2×D411yescharacteristic
351C23×C4C2412yes—
352C23×C4C2411yescharacteristic
353C2×M16—22no—
354C2×M16—22no—
355C2×M16—41no—
356C2×M16—41no—
357C2×M16—41no—
358C2×M16#4114yescomplemented
359C22×C8—24no—
360C22×C8—42no—
361C22×C8—42no—
362C22×C8C2412yes—
363C22×C8C2411yescharacteristic
364C22×C8C2412yes—
365C22×C8C2411yescharacteristic
366C22×C8C2411yescharacteristic
367C22×C8C2411yescharacteristic
368C4⋊Q8—22no—
369C4⋊Q8—22no—
370C4⋊Q8—22no—
371C4⋊Q8—22no—
372#125—82no—
373#123—48no—
374C22⋊Q8—24no—
375C22⋊Q8—42no—
376C22⋊Q8—44no—
377C22⋊Q8—82no—
378C22⋊Q8—82no—
379#121—24no—
380#121—24no—
381#121—42no—
382C4×Q8—22no—
383C4×Q8—22no—
384C4×Q8—22no—
385C4×Q8—41no—
386C4×D4—24no—
387C4×D4—24no—
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—41no—
393C4×D4—44no—
394C4×D4—44no—
395C4×D4—82no—
396C4×D4—84no—
397C4×D4#4114yes—
398#117—22no—
399#117—44no—
400#117—41no—
401#117—82no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—22no—
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—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4—41no—
428C2×C4⋊C4—42no—
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D412yes—
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2412yes—
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2412yes—
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2412yes—
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—22no—
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⋊C4C2×D412yes—
457C2×C22⋊C4C2×D412yes—
458C2×C22⋊C4C2×D412yes—
459C2×C22⋊C4C2×D412yes—
460C2×C22⋊C4C2×D412yes—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—44no—
473C2×C42—82no—
474C2×C42C2×D411yescharacteristic
475C2×C42C2×D411yescharacteristic
476C2×C42C2411yescharacteristic
477C2×C42C2412yes—
478C2×C42C2411yescharacteristic
479#107—24no—
480#107—24no—
481#107—42no—
482#107—42no—
483#107—42no—
484#106—24no—
485#106—42no—
486#106—42no—
487C4⋊C8—24no—
488C4⋊C8—22no—
489C4⋊C8—22no—
490#103—22no—
491#103—24no—
492#103—22no—
493#103—22no—
494#103—42no—
495#103#4114yescomplemented
496#102—24no—
497#102—22no—
498#102—22no—
499#102—22no—
500#102—22no—
501#102—42no—
502C22⋊C8—24no—
503C22⋊C8—24no—
504C22⋊C8—24no—
505C22⋊C8—42no—
506#97—24no—
507#97—41no—
508#97—41no—
509C4×C8—22no—
510C4×C8—22no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—22no—
516#95—22no—
517#95—22no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95C2×D412yes—
532#95C2×D412yes—
533#95C2×D412yes—
534C24—21no—
535C24C22×D411yescharacteristic
536C24C22×D412yes—
537#41—28no—
538#41—44no—
539#41—44no—
540#41—44no—
541#41—816no—
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×Q8—81no—
552C2×Q8—81no—
553C2×Q8C2×#4112yes—
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—82no—
570C2×D4#13714yes—
571C2×D4C2×#4112yes—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—24no—
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—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—42no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—44no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—44no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—44no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4—81no—
616C22×C4—81no—
617C22×C4—82no—
618C22×C4—82no—
619C22×C4—82no—
620C22×C4C22×D412yes—
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D412yes—
623C22×C4C22×D412yes—
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C2×#4112yes—
629C22×C42−1+412yes—
630C22×C4C2511yescharacteristic
631M16—44no—
632M16—44no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—21no—
643C2×C8—22no—
644C2×C8—21no—
645C2×C8—22no—
646C2×C8—21no—
647C2×C8—22no—
648C2×C8—84no—
649C2×C8C2×#4112yes—
650C2×C8C2×#4112yes—
651C2×C8C2×#4112yes—
652C4⋊C4—22no—
653C4⋊C4—24no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—21no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—22no—
672C4⋊C4—21no—
673C4⋊C4—22no—
674C4⋊C4—42no—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C4⋊C4—42no—
678C4⋊C4—44no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4—42no—
685C4⋊C4—81no—
686C4⋊C4—82no—
687C4⋊C4—82no—
688C4⋊C4—81no—
689C4⋊C4—82no—
690C4⋊C4—82no—
691C4⋊C4—82no—
692C4⋊C4—82no—
693C4⋊C4C2×#4112yes—
694C4⋊C4C2×#4112yes—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—44no—
704C22⋊C4—44no—
705C22⋊C4—44no—
706C22⋊C4—82no—
707C22⋊C4—82no—
708C22⋊C4—82no—
709C22⋊C4—82no—
710C22⋊C4—82no—
711C22⋊C4—82no—
712C22⋊C4—82no—
713C42—22no—
714C42—22no—
715C42—22no—
716C42—21no—
717C42—21no—
718C42—22no—
719C42—42no—
720C42—42no—
721C42—42no—
722C42—42no—
723C42—42no—
724C42—81no—
725C42—81no—
726C42—82no—
727C42—82no—
728C42C2×#4112yes—
729C42H(5,𝔽2)12yes—
730C23—21no—
731C23—22no—
732C23—22no—
733C23—21no—
734C23—22no—
735C23—21no—
736C23—22no—
737C23—22no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—22no—
742C23—22no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23#54712yes—
750C23C2×#13714yes—
751C23C23×D411yescharacteristic
752Q8—22no—
753Q8—22no—
754Q8—41no—
755Q8—41no—
756Q8—84no—
757Q8—162no—
758D4—22no—
759D4—22no—
760D4—28no—
761D4—48no—
762D4—48no—
763D4—41no—
764D4—41no—
765D4—88no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
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—21no—
789C2×C4—22no—
790C2×C4—21no—
791C2×C4—22no—
792C2×C4—48no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—48no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—82no—
830C2×C4—88no—
831C2×C4—84no—
832C2×C4—84no—
833C2×C4—84no—
834C2×C4—164no—
835C2×C4#54612yes—
836C2×C4#54612yes—
837C2×C4#54712yes—
838C2×C4C2×#13712yes—
839C2×C4#57612yes—
840C2×C4C22×#4111yescharacteristic
841C2×C4C22×#4111yescharacteristic
842C2×C4C22×#4111yescharacteristic
843C2×C4C2×H(5,𝔽2)11yescharacteristic
844C2×C4C2×2−1+411yescharacteristic
845C2×C4#58511yescharacteristic
846C8—22no—
847C8—22no—
848C8—22no—
849C8—42no—
850C8—42no—
851C8—41no—
852C22—24no—
853C22—22no—
854C22—22no—
855C22—24no—
856C22—22no—
857C22—24no—
858C22—41no—
859C22—42no—
860C22—42no—
861C22—41no—
862C22—42no—
863C22—41no—
864C22—41no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22C2×#54611yescharacteristic
874C22C2×#54711yescharacteristic
875C22D4×#4111yescharacteristic
876C22C22×#13711yescharacteristic
877C22C2×#57611yescharacteristic
878C22#358511yescharacteristic
879C22#358611yescharacteristic
880C4—22no—
881C4—22no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—42no—
886C4—42no—
887C4—41no—
888C4—42no—
889C4—41no—
890C4—81no—
891C4—81no—
892C4—82no—
893C4—81no—
894C4—82no—
895C4—82no—
896C4—81no—
897C4—82no—
898C4#331414yes—
899C4#344411yescharacteristic
900C4#349511yescharacteristic
901C4#350511yescharacteristic
902C4#352011yescharacteristic
903C2—44no—
904C2—42no—
905C2—82no—
906C2#3614311yescharacteristic
907C2C2×#331411yescharacteristic
908C2#6118211yescharacteristic
909C2#6125411yescharacteristic
910C2#6127811yescharacteristic
911C2#6145711yescharacteristic
912C2#6155511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36404C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36551C2semidirect
3. #33210C2semidirect
4. #33146C2semidirect
5. #32958C2semidirect
6. #28854C2semidirect
7. #28103C2semidirect
8. #27737C2semidirect
9. #27178C2semidirect
10. #27053C2semidirect
11. #26086C2semidirect
12. #25699C2semidirect
13. #25454C2semidirect
14. #25340C2semidirect
15. #25016C2semidirect
16. #24956C2semidirect
17. #24883C2semidirect
18. #23067C2semidirect
19. #22932C2semidirect
20. #22709C2semidirect
21. #22485C2semidirect
22. #21486C2semidirect
23. C4×#417C2semidirect
358. C2×M16#41semidirect
495. #103#41semidirect

Maximal subgroups

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

subgroupindex
#365512
#364042
#332102
#331462
#329582
#288542
#281032
#277372
#271782
#270532
#260862
#256992
#254542
#253402
#250162
#249562
#248832
#230672
#229322
#227092
#224852
#214862
C4×#4172