Finite Group Databasebeta

← #6441640

Subgroups — #6441640

Order 512.

2296 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3093C211yesmaximal, characteristic
2C2×#3056C211yesmaximal, characteristic
3C2×#2499C211yesmaximal, characteristic, complemented
4#34136C211yesmaximal, characteristic
5#25220C214yesmaximal, complemented
6#25216C214yesmaximal, complemented
7#25205C214yesmaximal, complemented
8#25201C214yesmaximal, complemented
9#23658C211yesmaximal, characteristic, complemented
10#23631C211yesmaximal, characteristic, complemented
11#23619C211yesmaximal, characteristic, complemented
12#23547C211yesmaximal, characteristic, complemented
13#21172C211yesmaximal, characteristic, complemented
14#21061C211yesmaximal, characteristic, complemented
15#20927C211yesmaximal, characteristic, complemented
16#20911C211yesmaximal, characteristic, complemented
17#20837C211yesmaximal, characteristic, complemented
18#20648C211yesmaximal, characteristic, complemented
19#20347C211yesmaximal, characteristic, complemented
20C22×#137C2211yescharacteristic
21C23×M16C2211yescharacteristic
22C2×#525C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C2×C4×#41C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C22×#117C2211yescharacteristic
27#3093—28no—
28C2×#485C2212yes—
29C2×#485C2212yes—
30C2×#482C2212yes—
31C2×#482C2212yes—
32#3056—28no—
33C2×#470C2212yes—
34C2×#468C2212yes—
35C2×#467C2212yes—
36C2×#465C2212yes—
37C2×#428C2211yescharacteristic
38C2×#428C2211yescharacteristic
39C2×#428C2211yescharacteristic
40C2×#423C2211yescharacteristic
41C2×#423C2211yescharacteristic
42C2×#417C2211yescharacteristic
43C2×#417C2211yescharacteristic
44C2×#417C2211yescharacteristic
45C2×#419C2211yescharacteristic
46C2×#419C2211yescharacteristic
47C2×#419C2211yescharacteristic
48C2×#407C2211yescharacteristic
49#2499—21no—
50#2499—21no—
51#2499—21no—
52#2499—21no—
53#2499C2214yes—
54#2499C2214yes—
55C2×#397—22no—
56#2363C2212yes—
57#2362C2212yes—
58#2361C2212yes—
59#2360C2212yes—
60#2359—22no—
61#2358—22no—
62#2297C2211yescharacteristic
63#2296C2211yescharacteristic
64C2×#391C2211yescharacteristic
65C2×#391C2211yescharacteristic
66#2293—21no—
67#2290—21no—
68#2290—21no—
69C2×#387—22no—
70C2×#384C2211yescharacteristic
71C2×#382C2211yescharacteristic
72C42×D4—21no—
73C4×#117C2211yescharacteristic
74C2×C4×C22⋊C4C2211yescharacteristic
75#2084C2214yescomplemented
76#2083C2214yescomplemented
77#2074C2214yescomplemented
78#2073C2214yescomplemented
79#2068C2214yescomplemented
80#2066C2214yescomplemented
81#2056C2214yescomplemented
82#2055C2214yescomplemented
83#1949C2214yescomplemented
84#1949C2214yescomplemented
85#1928C2214yescomplemented
86#1927C2214yescomplemented
87#1878C2214yescomplemented
88#1877C2214yescomplemented
89#1873C2214yes—
90#1872C2214yes—
91#1851C2214yes—
92#1850C2214yes—
93#1803C2214yescomplemented
94#1802C2214yescomplemented
95#1736C2211yescharacteristic
96#1736C2211yescharacteristic
97#1736C2211yescharacteristic
98#1736C2211yescharacteristic
99#1736C2214yes—
100#1736C2211yescharacteristic
101#1736C2211yescharacteristic
102#1735C2214yes—
103#1728C2211yescharacteristic
104#1728C2211yescharacteristic
105C22×#41C2311yescharacteristic
106C23×Q8C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C2×#137—24no—
109C2×#137—24no—
110C2×#137—42no—
111C22×Q16C2312yes—
112C22×SD16C2312yes—
113C22×M16—24no—
114C22×M16—24no—
115C22×M16—42no—
116C22×M16C2311yescharacteristic
117C22×M16C2311yescharacteristic
118C22×M16C2311yescharacteristic
119C22×M16C2312yes—
120C22×M16C2311yescharacteristic
121C23×C8C2312yes—
122#525—24no—
123#525D418yes—
124C2×#123—21no—
125C2×C22⋊Q8—21no—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8—24no—
128C2×C22⋊Q8—24no—
129C2×C22⋊Q8C2312yes—
130C2×C22⋊Q8C2312yes—
131C2×C22⋊Q8C2311yescharacteristic
132C2×C22⋊Q8C2311yescharacteristic
133C2×#121C2311yescharacteristic
134C2×#121C2311yescharacteristic
135C2×#120—21no—
136C4×#41—24no—
137C4×#41—42no—
138C2×C4×Q8C2312yes—
139C2×C4×D4—21no—
140C2×C4×D4—21no—
141C2×C4×D4—22no—
142C2×C4×D4—22no—
143C2×C4×D4C2312yes—
144C2×#117—21no—
145C2×#117—21no—
146C2×#117—21no—
147C2×#117—21no—
148C2×#117—21no—
149C2×#117—24no—
150C2×#117—24no—
151C2×#117—24no—
152C2×#117—42no—
153C2×#117C2312yes—
154C2×#117C2312yes—
155C2×#117C2311yescharacteristic
156C2×#117C2312yes—
157C2×#117C2311yescharacteristic
158C2×#117C2311yescharacteristic
159C22×C4⋊C4—22no—
160C22×C4⋊C4—21no—
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2312yes—
165C22×C22⋊C4—21no—
166C22×C22⋊C4—21no—
167C22×C22⋊C4—21no—
168C22×C22⋊C4D412yes—
169C22×C42—21no—
170C22×C42—21no—
171C22×C42—21no—
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174#485—28no—
175#485—28no—
176#482—28no—
177#482—28no—
178#470—28no—
179#468—28no—
180#467—28no—
181#465—28no—
182#428—24no—
183#428—24no—
184#428—24no—
185C2×#107C2312yes—
186C2×#107C2312yes—
187C2×#107C2312yes—
188C2×#106C2312yes—
189C2×#106C2312yes—
190C2×#106C2312yes—
191#423—24no—
192#423—42no—
193C2×C4⋊C8C2314yes—
194C2×C4⋊C8C2314yes—
195#419—24no—
196#419—24no—
197#419—42no—
198#417—24no—
199#417—24no—
200#417—24no—
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#103C2312yes—
206C2×#103C2314yes—
207C2×#103C2314yes—
208C2×#102C2312yes—
209C2×#102C2312yes—
210C2×#102C2312yes—
211#407—24no—
212C2×C22⋊C8C2312yes—
213C2×C22⋊C8C2312yes—
214#397—24no—
215#397—24no—
216#397—24no—
217#397—24no—
218#391—21no—
219#391—21no—
220#391—21no—
221#391—21no—
222#391C2314yes—
223#391C2312yes—
224#391C2314yes—
225#390—22no—
226#390C2312yes—
227#389—22no—
228#389C2312yes—
229#389C2312yes—
230#388—22no—
231#388—22no—
232#388—22no—
233#388—22no—
234#387—22no—
235#387—22no—
236#387—24no—
237#387—24no—
238#387—24no—
239#387—24no—
240#386—22no—
241#386—22no—
242#386—22no—
243#385—22no—
244#385—22no—
245#385—22no—
246#384—21no—
247#384—21no—
248#384C2314yes—
249#382—21no—
250#382—21no—
251#382C2314yes—
252C4×C4⋊C4—21no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4—22no—
255C4×C4⋊C4C2312yes—
256C4×C4⋊C4C2312yes—
257C4×C22⋊C4—22no—
258C4×C22⋊C4—22no—
259C4×C22⋊C4—21no—
260C4×C22⋊C4—21no—
261C4×C22⋊C4—22no—
262C4×C22⋊C4D411yescharacteristic
263C4×C22⋊C4D411yescharacteristic
264C4×C22⋊C4D411yescharacteristic
265C4×C22⋊C4D411yescharacteristic
266C4×C22⋊C4C2312yes—
267C4×C22⋊C4C2312yes—
268#376—21no—
269C2×#95—22no—
270C2×#95—22no—
271C2×#95—22no—
272C2×#95D412yes—
273C43—21no—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278#340C2314yes—
279#340C2314yes—
280#336C2314yes—
281#336C2314yes—
282C25C2×D411yescharacteristic
283C2×#41—22no—
284C2×#41—22no—
285C2×#41—22no—
286C2×#41—22no—
287C2×#41—22no—
288C2×#41C2×D414yes—
289C22×Q8—21no—
290C22×Q8—22no—
291C22×Q8—22no—
292C22×Q8—22no—
293C22×Q8—22no—
294C22×Q8—22no—
295C22×Q8—22no—
296C22×Q8C2412yes—
297C22×Q8C2411yescharacteristic
298C22×D4—21no—
299C22×D4—21no—
300C22×D4—21no—
301C22×D4C2411yescharacteristic
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—21no—
307C23×C4—21no—
308C23×C4—21no—
309C23×C4—21no—
310C23×C4—21no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4C2×D412yes—
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D414yes—
318C23×C4C2×D412yes—
319C23×C4#4114yes—
320C23×C4C2411yescharacteristic
321C23×C4C2411yescharacteristic
322C23×C4C2411yescharacteristic
323#137—416no—
324C2×Q16—24no—
325C2×Q16—24no—
326C2×Q16—42no—
327C2×SD16—24no—
328C2×SD16—24no—
329C2×SD16—42no—
330C2×M16—22no—
331C2×M16—22no—
332C2×M16—22no—
333C2×M16—24no—
334C2×M16—22no—
335C2×M16—22no—
336C2×M16—22no—
337C2×M16—22no—
338C2×M16—22no—
339C2×M16—22no—
340C2×M16—22no—
341C2×M16—22no—
342C2×M16—24no—
343C2×M16—42no—
344C2×M16—416no—
345C2×M16#4114yes—
346C22×C8—24no—
347C22×C8—24no—
348C22×C8—42no—
349C22×C8C2412yes—
350C22×C8C2412yes—
351C22×C8C2412yes—
352C22×C8C2412yes—
353#123—28no—
354C22⋊Q8—22no—
355C22⋊Q8—22no—
356C22⋊Q8—24no—
357C22⋊Q8—24no—
358C22⋊Q8—24no—
359C22⋊Q8—24no—
360C22⋊Q8—44no—
361C22⋊Q8—44no—
362C22⋊Q8C2×D414yes—
363C22⋊Q8C2×D414yes—
364#121—22no—
365#121—22no—
366#121C2×D414yes—
367#121C2×D414yes—
368#120—28no—
369C4×Q8—24no—
370C4×Q8—42no—
371C4×D4—28no—
372C4×D4—28no—
373C4×D4—24no—
374C4×D4—42no—
375C4×D4—48no—
376C4×D4—48no—
377#117—22no—
378#117—22no—
379#117—24no—
380#117—24no—
381#117—24no—
382#117—24no—
383#117—22no—
384#117—22no—
385#117—24no—
386#117—44no—
387#117—44no—
388#117—44no—
389#117—42no—
390#117—44no—
391#117—44no—
392#117C2×D414yes—
393#117#4114yes—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—42no—
415C2×C4⋊C4—48no—
416C2×C4⋊C4—44no—
417C2×C4⋊C4C2412yes—
418C2×C4⋊C4C2412yes—
419C2×C4⋊C4C2412yes—
420C2×C4⋊C4C2412yes—
421C2×C4⋊C4C2411yescharacteristic
422C2×C4⋊C4C2411yescharacteristic
423C2×C4⋊C4C2412yes—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
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—44no—
440C2×C22⋊C4—44no—
441C2×C22⋊C4—44no—
442C2×C22⋊C4—44no—
443C2×C22⋊C4C2×D412yes—
444C2×C22⋊C4C2×D412yes—
445C2×C22⋊C4C2×D412yes—
446C2×C22⋊C4C2×D412yes—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42—22no—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—21no—
454C2×C42—22no—
455C2×C42—22no—
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—22no—
460C2×C42—44no—
461C2×C42—44no—
462C2×C42—44no—
463C2×C42C2×D411yescharacteristic
464C2×C42C2×D411yescharacteristic
465C2×C42C2×D411yescharacteristic
466C2×C42C2×D411yescharacteristic
467C2×C42C2412yes—
468C2×C42C2412yes—
469#107—24no—
470#107—24no—
471#107—24no—
472#106—24no—
473#106—24no—
474#106—24no—
475C4⋊C8—28no—
476C4⋊C8—44no—
477#103—24no—
478#103—24no—
479#103—24no—
480#103—24no—
481#103—24no—
482#103—28no—
483#103—44no—
484#102—24no—
485#102—24no—
486#102—24no—
487C22⋊C8—24no—
488C22⋊C8—24no—
489#95—24no—
490#95—24no—
491#95—24no—
492#95—24no—
493#95—24no—
494#95—24no—
495#95—22no—
496#95—22no—
497#95—22no—
498#95—22no—
499#95—22no—
500#95—22no—
501#95C2×D412yes—
502#95C2×D412yes—
503#95C2×D412yes—
504#95C2×D412yes—
505C24—22no—
506C24—22no—
507C24—21no—
508C24—42no—
509C24—42no—
510C24#12114yes—
511C24C22×D411yescharacteristic
512C24C22×D411yescharacteristic
513C24C22×D411yescharacteristic
514#41—28no—
515#41—28no—
516#41—44no—
517#41—44no—
518C2×Q8—21no—
519C2×Q8—22no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—21no—
526C2×Q8—22no—
527C2×Q8—21no—
528C2×Q8—22no—
529C2×Q8—42no—
530C2×Q8—42no—
531C2×Q8—42no—
532C2×Q8—44no—
533C2×Q8—44no—
534C2×Q8—44no—
535C2×Q8—44no—
536C2×Q8C22×D412yes—
537C2×D4—24no—
538C2×D4—24no—
539C2×D4—24no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—44no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—82no—
549C2×D4C22×D412yes—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—28no—
553C22×C4—28no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—28no—
557C22×C4—28no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—24no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—44no—
599C22×C4—82no—
600C22×C4—82no—
601C22×C4#12114yes—
602C22×C4#12114yes—
603C22×C4#12114yes—
604C22×C4C22×D412yes—
605C22×C4C22×D412yes—
606C22×C4C22×D412yes—
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D412yes—
614C22×C4C2×#4112yes—
615C22×C4C2×#4112yes—
616C22×C4C2×#4112yes—
617C22×C4C2×#4112yes—
618C22×C4C2×#4112yes—
619C22×C4H(5,𝔽2)12yes—
620C22×C42−1+412yes—
621C22×C4C2511yescharacteristic
622Q16—48no—
623SD16—48no—
624M16—28no—
625M16—48no—
626M16—44no—
627M16—44no—
628M16—44no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—48no—
641C2×C8C2×#4114yes—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—44no—
656C4⋊C4—44no—
657C4⋊C4—48no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—44no—
662C4⋊C4—44no—
663C4⋊C4—48no—
664C4⋊C4—44no—
665C4⋊C4—82no—
666C4⋊C4C22×D412yes—
667C4⋊C4C22×D412yes—
668C4⋊C4C2×#4114yes—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—24no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C22⋊C4—44no—
683C22⋊C4—44no—
684C22⋊C4—44no—
685C22⋊C4—44no—
686C22⋊C4—42no—
687C22⋊C4—82no—
688C42—24no—
689C42—22no—
690C42—22no—
691C42—24no—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—22no—
696C42—22no—
697C42—22no—
698C42—44no—
699C42—44no—
700C42—44no—
701C42—44no—
702C42—44no—
703C42—42no—
704C42—82no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—22no—
714C23—22no—
715C23—28no—
716C23—22no—
717C23—44no—
718C23—44no—
719C23—42no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—84no—
724C23—84no—
725C23C2×#12112yes—
726C23C2×#12112yes—
727C23C2×#12112yes—
728C23#54612yes—
729C23#54712yes—
730C23C23×D411yescharacteristic
731Q8—22no—
732Q8—22no—
733Q8—41no—
734Q8—41no—
735Q8—42no—
736Q8—42no—
737Q8—42no—
738Q8—42no—
739Q8—84no—
740D4—22no—
741D4—22no—
742D4—48no—
743D4—48no—
744D4—41no—
745D4—41no—
746D4—84no—
747C2×C4—22no—
748C2×C4—28no—
749C2×C4—22no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—28no—
757C2×C4—28no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
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—24no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—48no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—48no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—88no—
798C2×C4—84no—
799C2×C4—88no—
800C2×C4—84no—
801C2×C4—84no—
802C2×C4—84no—
803C2×C4—84no—
804C2×C4C2×#12112yes—
805C2×C4C2×#12112yes—
806C2×C4C2×#12112yes—
807C2×C4#52914yes—
808C2×C4#53914yes—
809C2×C4#54612yes—
810C2×C4#54614yes—
811C2×C4#54712yes—
812C2×C4#54714yes—
813C2×C4#57514yes—
814C2×C4C23×D411yescharacteristic
815C2×C4C22×#4111yescharacteristic
816C2×C4C22×#4111yescharacteristic
817C2×C4C22×#4111yescharacteristic
818C2×C4C2×H(5,𝔽2)11yescharacteristic
819C2×C4C2×2−1+411yescharacteristic
820C8—24no—
821C8—42no—
822C8—42no—
823C8—42no—
824C22—22no—
825C22—24no—
826C22—24no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—88no—
842C22—82no—
843C22—82no—
844C22#242514yes—
845C22C22×#12111yescharacteristic
846C22C2×#54611yescharacteristic
847C22C2×#54711yescharacteristic
848C22C2×#57512yes—
849C22#358612yes—
850C4—22no—
851C4—22no—
852C4—24no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—44no—
859C4—42no—
860C4—82no—
861C4—82no—
862C4—82no—
863C4—82no—
864C4—82no—
865C4#242514yes—
866C4C2×#52911yescharacteristic
867C4C2×#53911yescharacteristic
868C4C2×#54611yescharacteristic
869C4C2×#54711yescharacteristic
870C2—24no—
871C2—42no—
872C2—42no—
873C2—82no—
874C2C2×#242511yescharacteristic
875C2#6041511yescharacteristic
876C2#6042711yescharacteristic
877C2#6116312yes—
878C2#6125712yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#525C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#2499C2semidirect
5. #25220C2semidirect
6. #25216C2semidirect
7. #25205C2semidirect
8. #25201C2semidirect
9. #23658C2semidirect
10. #23631C2semidirect
11. #23619C2semidirect
12. #23547C2semidirect
13. #21172C2semidirect
14. #21061C2semidirect
15. #20927C2semidirect
16. #20911C2semidirect
17. #20837C2semidirect
18. #20648C2semidirect
19. #20347C2semidirect
75. #2084C22semidirect
76. #2083C22semidirect
77. #2074C22semidirect
78. #2073C22semidirect
79. #2068C22semidirect
80. #2066C22semidirect
81. #2056C22semidirect
82. #2055C22semidirect
83. #1949C22semidirect
84. #1949C22semidirect
85. #1928C22semidirect
86. #1927C22semidirect
87. #1878C22semidirect
88. #1877C22semidirect
93. #1803C22semidirect
94. #1802C22semidirect

Maximal subgroups

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

subgroupindex
C2×#30932
C2×#30562
C2×#24992
#341362
#252202
#252162
#252052
#252012
#236582
#236312
#236192
#235472
#211722
#210612
#209272
#209112
#208372
#206482
#203472