Finite Group Databasebeta

← #6491694

Subgroups — #6491694

Order 512.

2274 conjugacy classes of subgroups.

The subgroup lattice has 921 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3210C211yesmaximal, characteristic, complemented
2C2×#2920C211yesmaximal, characteristic, complemented
3#36625C211yesmaximal, characteristic, complemented
4#36624C211yesmaximal, characteristic
5#33176C211yesmaximal, characteristic, complemented
6#33174C211yesmaximal, characteristic, complemented
7#33049C211yesmaximal, characteristic, complemented
8#33048C211yesmaximal, characteristic, complemented
9#29844C211yesmaximal, characteristic, complemented
10#29843C211yesmaximal, characteristic, complemented
11#29808C211yesmaximal, characteristic, complemented
12#29807C211yesmaximal, characteristic, complemented
13#24757C214yesmaximal, complemented
14#24657C214yesmaximal, complemented
15#24511C214yesmaximal, complemented
16#24389C214yesmaximal, complemented
17#21984C211yesmaximal, characteristic, complemented
18#21864C211yesmaximal, characteristic, complemented
19#21805C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#532C2211yescharacteristic
22C2×#525C2212yes—
23C23×C42C2211yescharacteristic
24#3210—28no—
25C2×#494C2211yescharacteristic, complemented
26C2×#492C2211yescharacteristic, complemented
27C2×#487C2211yescharacteristic, complemented
28C2×#486C2211yescharacteristic, complemented
29C2×#470C2214yes—
30C2×#468C2214yes—
31C2×#464C2214yescomplemented
32C2×#452C2214yes—
33#2920—28no—
34C2×#432C2212yes—
35C2×#432C2212yes—
36C2×#431C2211yescharacteristic
37C2×#431C2211yescharacteristic
38C2×#431C2211yescharacteristic
39C2×#431C2211yescharacteristic
40C2×#423C2212yes—
41C2×#407C2212yes—
42C2×C4×M16C2211yescharacteristic
43C2×C4×M16C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2857C2211yescharacteristic
50#2856C2211yescharacteristic
51#2856C2211yescharacteristic
52#2855—21no—
53#2855C2212yes—
54#2854—21no—
55#2854—21no—
56#2851—21no—
57#2851—21no—
58#2850C2212yes—
59#2850C2212yes—
60#2848—21no—
61#2848C2212yes—
62#2847—21no—
63#2847—21no—
64C4×C22⋊Q8—21no—
65C4×C22⋊Q8—21no—
66C4×C22⋊Q8C2212yes—
67C4×C22⋊Q8C2212yes—
68C4×#121—21no—
69C4×#121—21no—
70C4×#121—21no—
71C4×#121—21no—
72#2297C2212yes—
73#2296—21no—
74#2285C2211yescharacteristic
75#2285C2211yescharacteristic
76#2280—21no—
77#2068C2214yescomplemented
78#2065C2214yescomplemented
79#2056C2214yescomplemented
80#2055C2214yescomplemented
81#2036C2214yes—
82#2034C2214yes—
83#2001C2214yes—
84#2000C2214yes—
85#1990C2211yescharacteristic, complemented
86#1990C2211yescharacteristic, complemented
87#1983C2214yescomplemented
88#1973C2214yescomplemented
89#1971C2214yescomplemented
90#1957C2211yescharacteristic, complemented
91#1957C2211yescharacteristic, complemented
92#1956C2211yescharacteristic, complemented
93#1956C2211yescharacteristic, complemented
94#1956C2211yescharacteristic, complemented
95#1956C2211yescharacteristic, complemented
96#1949C2214yescomplemented
97#1936C2214yescomplemented
98#1935C2214yescomplemented
99#1895C2214yes—
100#1894C2214yes—
101#1873C2214yes—
102#1854C2214yes—
103#1845C2211yescharacteristic, complemented
104#1844C2211yescharacteristic, complemented
105#1834C2211yescharacteristic, complemented
106#1834C2211yescharacteristic, complemented
107#1805C2214yescomplemented
108#1788C2214yes—
109C22×#41C2312yes—
110C24×C4D411yescharacteristic
111C24×C4D411yescharacteristic
112C24×C4C2311yescharacteristic
113C22×Q16C2314yes—
114C22×SD16C2314yes—
115C22×M16C2312yes—
116C22×M16C2312yes—
117#533—24no—
118#533—24no—
119#532—24no—
120#532—24no—
121C2×C4⋊Q8C2311yescharacteristic
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2311yescharacteristic
124C2×#127C2311yescharacteristic
125C2×#125—21no—
126C2×#124C2312yes—
127#525—48no—
128C2×#123—22no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8—21no—
131C2×C22⋊Q8—21no—
132C2×C22⋊Q8C2312yes—
133C2×C22⋊Q8C2312yes—
134C2×C22⋊Q8C2312yes—
135C2×C22⋊Q8C2312yes—
136C2×C22⋊Q8C2312yes—
137C2×#121—21no—
138C2×#121—21no—
139C2×#121—21no—
140C2×#121—21no—
141C2×#121—21no—
142C2×#121—21no—
143C2×#121C2312yes—
144C2×#121C2312yes—
145C2×#120—22no—
146C2×C4×Q8—21no—
147C2×C4×Q8C2312yes—
148C2×C4×D4—22no—
149C2×C4×D4—22no—
150C2×C4×D4—21no—
151C2×C4×D4—21no—
152C2×#117—21no—
153C2×#117—21no—
154C2×#117C2312yes—
155C22×C42—24no—
156C22×C42—24no—
157C22×C42D411yescharacteristic
158C22×C42D411yescharacteristic
159C22×C42D411yescharacteristic
160C22×C42D411yescharacteristic
161C22×C42D411yescharacteristic
162C22×C42D411yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169#494—24no—
170#492—24no—
171#487—24no—
172#486—24no—
173#470—48no—
174#468—48no—
175#464—216no—
176#452—216no—
177#432—28no—
178#432—28no—
179#431—24no—
180#431—24no—
181#431—24no—
182#431D418yescomplemented
183C2×#107C2314yes—
184C2×#106C2314yes—
185#423—28no—
186C2×C4⋊C8C2312yes—
187C2×C4⋊C8C2312yes—
188C2×C4⋊C8C2312yes—
189C2×C4⋊C8C2312yes—
190C2×#103C2314yes—
191C2×#103C2314yes—
192C2×#103C2314yes—
193C2×#103C2314yes—
194C2×#103C2314yes—
195C2×#102C2314yes—
196C2×#102C2314yes—
197C2×#102C2314yes—
198#407—28no—
199C2×C22⋊C8C2312yes—
200C2×C22⋊C8C2312yes—
201C2×C22⋊C8C2312yes—
202C2×C22⋊C8C2312yes—
203C4×M16—24no—
204C4×M16—24no—
205C2×#97C2312yes—
206C2×#97C2312yes—
207C2×C4×C8C2311yescharacteristic
208C2×C4×C8C2311yescharacteristic
209C2×C4×C8C2311yescharacteristic
210C2×C4×C8C2311yescharacteristic
211#391—21no—
212#391—21no—
213#391C2312yes—
214#391C2312yes—
215#391C2312yes—
216#391C2312yes—
217#390—21no—
218#390—21no—
219#390—21no—
220#390—21no—
221#390C2312yes—
222#390C2312yes—
223#389—21no—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389—21no—
233#389C2312yes—
234#389C2312yes—
235#388—22no—
236#388—22no—
237#388—22no—
238#388—22no—
239#387—22no—
240#387—22no—
241#387—22no—
242#387—22no—
243#386—22no—
244#386—22no—
245#386—22no—
246#386—22no—
247#386—22no—
248#386—22no—
249#385—22no—
250#385—22no—
251#385—22no—
252#385—22no—
253#385—22no—
254#385—22no—
255#384C2311yescharacteristic
256#384C2311yescharacteristic
257#384C2311yescharacteristic
258#384C2311yescharacteristic
259#382—21no—
260#382C2312yes—
261#381—22no—
262#380—21no—
263#380—21no—
264#380—21no—
265#380—21no—
266#380—21no—
267#380—21no—
268#380—21no—
269#380—21no—
270#380—21no—
271#380—21no—
272#380—21no—
273#380—21no—
274#380—21no—
275#380C2312yes—
276#380C2312yes—
277#380C2312yes—
278#379—22no—
279C4×C4⋊C4—21no—
280C4×C4⋊C4—21no—
281C4×C4⋊C4—21no—
282C4×C4⋊C4—22no—
283C4×C4⋊C4—22no—
284C4×C4⋊C4C2312yes—
285C4×C22⋊C4—22no—
286C4×C22⋊C4—22no—
287C4×C22⋊C4—22no—
288C4×C22⋊C4—22no—
289#340C2314yes—
290#340C2314yes—
291#340C2314yes—
292#340C2314yes—
293C25C2×D411yescharacteristic
294C2×#41—24no—
295C2×#41—24no—
296C2×#41—44no—
297C2×#41—44no—
298C22×Q8—21no—
299C22×Q8C2412yes—
300C22×Q8C2412yes—
301C22×D4—22no—
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4C2412yes—
307C23×C4—24no—
308C23×C4—24no—
309C23×C4—24no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—24no—
313C23×C4—22no—
314C23×C4—42no—
315C23×C4—42no—
316C23×C4—42no—
317C23×C4—42no—
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2×D411yescharacteristic
325C23×C4C2×D411yescharacteristic
326C23×C4C2×D411yescharacteristic
327C23×C4C2×D411yescharacteristic
328C23×C4C2×D411yescharacteristic
329C23×C4C2×D411yescharacteristic
330C23×C4C2×D411yescharacteristic
331C23×C4C2×D411yescharacteristic
332C23×C4C2×D411yescharacteristic
333C23×C4C2411yescharacteristic
334C23×C4C2411yescharacteristic
335C23×C4C2411yescharacteristic
336C2×Q16—28no—
337C2×Q16—44no—
338C2×Q16—44no—
339C2×SD16—28no—
340C2×SD16—44no—
341C2×SD16—44no—
342C2×M16—24no—
343C2×M16—24no—
344C2×M16—24no—
345C2×M16—24no—
346C2×M16—42no—
347C2×M16—42no—
348C22×C8C2412yes—
349C22×C8C2412yes—
350C22×C8C2412yes—
351C22×C8C2412yes—
352C4⋊Q8—22no—
353C4⋊Q8—22no—
354C4⋊Q8—22no—
355C4⋊Q8—22no—
356C4⋊Q8—22no—
357C4⋊Q8—22no—
358#127—22no—
359#127—22no—
360#125—44no—
361#124—24no—
362#124—24no—
363#123—48no—
364C22⋊Q8—24no—
365C22⋊Q8—24no—
366C22⋊Q8—28no—
367C22⋊Q8—28no—
368C22⋊Q8—44no—
369C22⋊Q8—44no—
370C22⋊Q8—44no—
371C22⋊Q8—44no—
372C22⋊Q8—44no—
373#121—28no—
374#121—44no—
375#121—44no—
376#121—44no—
377#121—44no—
378#121—44no—
379#121—44no—
380#121—44no—
381#120—48no—
382C4×Q8—24no—
383C4×Q8—24no—
384C4×Q8—44no—
385C4×D4—48no—
386C4×D4—48no—
387C4×D4—44no—
388C4×D4—44no—
389#117—44no—
390#117—44no—
391#117—44no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4C2412yes—
414C2×C4⋊C4C2412yes—
415C2×C4⋊C4C2412yes—
416C2×C4⋊C4C2412yes—
417C2×C4⋊C4C2412yes—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C42—24no—
436C2×C42—24no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—24no—
440C2×C42—24no—
441C2×C42—24no—
442C2×C42—24no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—22no—
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×C42C2×D411yescharacteristic
457C2×C42C2×D411yescharacteristic
458C2×C42C2×D411yescharacteristic
459C2×C42C2×D411yescharacteristic
460C2×C42C2×D411yescharacteristic
461C2×C42C2×D411yescharacteristic
462C2×C42C2×D411yescharacteristic
463C2×C42C2×D411yescharacteristic
464C2×C42C2×D411yescharacteristic
465C2×C42C2×D411yescharacteristic
466C2×C42C2×D414yes—
467C2×C42#4114yes—
468C2×C42C2411yescharacteristic
469C2×C42C2411yescharacteristic
470C2×C42C2411yescharacteristic
471C2×C42C2411yescharacteristic
472#107—44no—
473#106—44no—
474C4⋊C8—24no—
475C4⋊C8—24no—
476C4⋊C8—24no—
477C4⋊C8C2×D418yes—
478#103—28no—
479#103—44no—
480#103—44no—
481#103—44no—
482#103—44no—
483#102—28no—
484#102—44no—
485#102—44no—
486C22⋊C8—24no—
487C22⋊C8—24no—
488C22⋊C8—24no—
489C22⋊C8C2×D418yes—
490#97—24no—
491#97—24no—
492C4×C8—22no—
493C4×C8—22no—
494C4×C8C2×D414yes—
495C4×C8C2×D414yes—
496#95—22no—
497#95—22no—
498#95—22no—
499#95—22no—
500#95—22no—
501#95—22no—
502#95—22no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—22no—
507#95—22no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—41no—
517C24—41no—
518C24—41no—
519C24—41no—
520C24C22×D411yescharacteristic
521C24C22×D411yescharacteristic
522C24C22×D411yescharacteristic
523#41—88no—
524#41—88no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—24no—
530C2×Q8—24no—
531C2×Q8—24no—
532C2×Q8—24no—
533C2×Q8—42no—
534C2×Q8—42no—
535C2×Q8—42no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—24no—
539C2×D4—24no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—42no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
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—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—416no—
616C22×C4—416no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4#12114yes—
621C22×C4#12114yes—
622C22×C4#13714yes—
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D412yes—
631C22×C4C22×D411yescharacteristic
632C22×C4C22×D411yescharacteristic
633C22×C4C22×D411yescharacteristic
634C22×C4C22×D411yescharacteristic
635C22×C4C2×#4112yes—
636C22×C4H(5,𝔽2)14yes—
637C22×C4C2511yescharacteristic
638Q16—88no—
639SD16—88no—
640M16—48no—
641M16—48no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8C22×D414yes—
653C2×C8C22×D414yes—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—44no—
661C4⋊C4—44no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—42no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C22⋊C4—44no—
682C22⋊C4—44no—
683C22⋊C4—44no—
684C22⋊C4—44no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—44no—
694C22⋊C4—44no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—22no—
702C42—22no—
703C42—22no—
704C42—22no—
705C42—22no—
706C42—22no—
707C42—22no—
708C42—21no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—44no—
713C42—44no—
714C42—44no—
715C42#12114yes—
716C42#12114yes—
717C42C22×D412yes—
718C42C22×D412yes—
719C42C2×#4112yes—
720C42C2×#4112yes—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23C2×#12112yes—
754C23#53512yes—
755C23C2×#13712yes—
756C23C23×D411yescharacteristic
757Q8—44no—
758Q8—44no—
759Q8—44no—
760Q8—44no—
761Q8—84no—
762D4—44no—
763D4—44no—
764D4—88no—
765D4—88no—
766D4—88no—
767D4—84no—
768D4—84no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—28no—
784C2×C4—28no—
785C2×C4—28no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—88no—
834C2×C4C2×#12112yes—
835C2×C4C2×#12112yes—
836C2×C4C2×#12112yes—
837C2×C4C2×#12112yes—
838C2×C4C2×#12112yes—
839C2×C4#53512yes—
840C2×C4C2×#13712yes—
841C2×C4C2×#13712yes—
842C2×C4#57512yes—
843C2×C4#57512yes—
844C2×C4#57512yes—
845C2×C4C23×D411yescharacteristic
846C2×C4C22×#4111yescharacteristic
847C2×C4C2×H(5,𝔽2)12yes—
848C2×C4#58512yes—
849C8—24no—
850C8—24no—
851C8—42no—
852C8—42no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—416no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—82no—
876C22—82no—
877C22—82no—
878C22—82no—
879C22—82no—
880C22—82no—
881C22—82no—
882C22C22×#12111yescharacteristic
883C22C2×#53511yescharacteristic
884C22#344911yescharacteristic
885C22C22×#13711yescharacteristic
886C22C2×#57511yescharacteristic
887C22C2×#57511yescharacteristic
888C22C2×#57511yescharacteristic
889C4—22no—
890C4—22no—
891C4—22no—
892C4—22no—
893C4—22no—
894C4—41no—
895C4—41no—
896C4—41no—
897C4—41no—
898C4—82no—
899C4—82no—
900C4—82no—
901C4—82no—
902C4—82no—
903C4—82no—
904C4—82no—
905C4#305414yes—
906C4#305614yes—
907C4#348812yes—
908C4#349412yes—
909C2—42no—
910C2—42no—
911C2—42no—
912C2—162no—
913C2#3525211yescharacteristic
914C2C2×#305411yescharacteristic
915C2C2×#305611yescharacteristic
916C2#6080111yescharacteristic
917C2#6080411yescharacteristic
918C2#6096611yescharacteristic
919C2#6097211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36624C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3210C2semidirect
2. C2×#2920C2semidirect
3. #36625C2semidirect
5. #33176C2semidirect
6. #33174C2semidirect
7. #33049C2semidirect
8. #33048C2semidirect
9. #29844C2semidirect
10. #29843C2semidirect
11. #29808C2semidirect
12. #29807C2semidirect
13. #24757C2semidirect
14. #24657C2semidirect
15. #24511C2semidirect
16. #24389C2semidirect
17. #21984C2semidirect
18. #21864C2semidirect
19. #21805C2semidirect
25. C2×#494C22semidirect
26. C2×#492C22semidirect
27. C2×#487C22semidirect
28. C2×#486C22semidirect
31. C2×#464C22semidirect
77. #2068C22semidirect
78. #2065C22semidirect
79. #2056C22semidirect
80. #2055C22semidirect
85. #1990C22semidirect
86. #1990C22semidirect
87. #1983C22semidirect
88. #1973C22semidirect
89. #1971C22semidirect
90. #1957C22semidirect
91. #1957C22semidirect
92. #1956C22semidirect
93. #1956C22semidirect
94. #1956C22semidirect
95. #1956C22semidirect
96. #1949C22semidirect
97. #1936C22semidirect
98. #1935C22semidirect
103. #1845C22semidirect
104. #1844C22semidirect
105. #1834C22semidirect
106. #1834C22semidirect
107. #1805C22semidirect
182. #431D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32102
C2×#29202
#366252
#366242
#331762
#331742
#330492
#330482
#298442
#298432
#298082
#298072
#247572
#246572
#245112
#243892
#219842
#218642
#218052