Finite Group Databasebeta

← #6458232

Subgroups — #6458232

Order 512.

2210 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#525C211yesmaximal, characteristic
2C2×#2285C211yesmaximal, characteristic, complemented
3#27686C212yesmaximal, complemented
4#27685C212yesmaximal, complemented
5#27684C212yesmaximal, complemented
6#27683C212yesmaximal, complemented
7#27682C212yesmaximal, complemented
8#27681C211yesmaximal, characteristic, complemented
9#27680C211yesmaximal, characteristic, complemented
10#27679C212yesmaximal, complemented
11#27678C211yesmaximal, characteristic, complemented
12#27677C211yesmaximal, characteristic, complemented
13#23744C212yesmaximal, complemented
14#23730C212yesmaximal, complemented
15#21169C212yesmaximal, complemented
16#20908C212yesmaximal
17#20843C212yesmaximal, complemented
18#20645C212yesmaximal, complemented
19C2×#1797C211yesmaximal, characteristic, complemented
20C2×#525C2211yescharacteristic
21C2×C4×#41C2211yescharacteristic
22C22×#117C2212yes—
23C23×C42C2211yescharacteristic
24C2×#427C2214yes—
25C22×C4⋊C8C2212yes—
26C2×#416C2214yes—
27C22×C22⋊C8C2212yes—
28C4×C22⋊Q8C2211yescharacteristic
29C4×C22⋊Q8C2211yescharacteristic
30C4×C22⋊Q8C2211yescharacteristic
31C4×C22⋊Q8C2211yescharacteristic
32C4×#123—21no—
33C4×#123—21no—
34C4×#121C2211yescharacteristic
35C4×#121C2211yescharacteristic
36C4×#121C2211yescharacteristic
37C4×#121C2211yescharacteristic
38C4×#120—21no—
39C4×#120—21no—
40#2297C2211yescharacteristic
41#2296C2211yescharacteristic
42#2290—21no—
43#2290—21no—
44#2285—21no—
45#2285—21no—
46#2285—21no—
47#2285—21no—
48#2285C2212yes—
49#2285C2212yes—
50#2285C2212yes—
51#2285C2212yes—
52C2×#384C2211yescharacteristic
53C2×#384C2211yescharacteristic
54C2×#382C2212yes—
55#2280C2211yescharacteristic
56C2×#380—21no—
57C2×#380—21no—
58C42×D4—21no—
59C42×D4—21no—
60C4×#117C2211yescharacteristic
61C2×C4×C4⋊C4—21no—
62C2×C4×C4⋊C4—21no—
63#2101C2214yescomplemented
64#2101C2214yescomplemented
65#2100C2212yescomplemented
66#2100C2212yescomplemented
67#2099C2212yescomplemented
68#2099C2212yescomplemented
69#2097C2214yescomplemented
70#2096C2212yescomplemented
71#2095C2212yescomplemented
72#2094C2212yescomplemented
73#2093C2212yescomplemented
74#2092C2214yescomplemented
75#1949C2214yescomplemented
76#1949C2214yescomplemented
77#1948C2212yescomplemented
78#1948C2212yescomplemented
79#1947C2212yescomplemented
80#1947C2212yescomplemented
81#1875C2214yes—
82#1874C2212yes—
83#1874C2212yes—
84#1873C2214yes—
85#1872C2212yes—
86#1872C2212yes—
87#1854C2214yes—
88#1854C2214yes—
89#1853C2212yes—
90#1853C2212yes—
91#1852C2212yes—
92#1852C2212yes—
93#1805C2214yescomplemented
94#1804C2214yescomplemented
95#1803C2212yescomplemented
96#1803C2212yescomplemented
97#1802C2212yescomplemented
98#1802C2212yescomplemented
99#1797C2211yescharacteristic
100#1797C2211yescharacteristic
101#1797C2212yes—
102#1797C2212yes—
103#1797C2212yes—
104#1735C2214yes—
105#1735C2214yes—
106C2×#336C2212yes—
107C22×#41C2311yescharacteristic
108C24×C4D411yescharacteristic
109C24×C4D411yescharacteristic
110C24×C4C2311yescharacteristic
111C23×C8C2314yes—
112#525—24no—
113#525Q818yes—
114C2×#123—21no—
115C2×C22⋊Q8C2311yescharacteristic
116C2×C22⋊Q8C2311yescharacteristic
117C2×#121C2311yescharacteristic
118C2×#121C2311yescharacteristic
119C2×#120—21no—
120C4×#41—28no—
121C2×C4×Q8C2311yescharacteristic
122C2×C4×Q8C2311yescharacteristic
123C2×C4×D4—21no—
124C2×C4×D4—21no—
125C2×C4×D4—21no—
126C2×C4×D4—21no—
127C2×C4×D4—21no—
128C2×C4×D4—21no—
129C2×C4×D4—21no—
130C2×C4×D4—21no—
131C2×C4×D4C2311yescharacteristic
132C2×C4×D4C2311yescharacteristic
133C2×#117—22no—
134C2×#117—22no—
135C2×#117—21no—
136C2×#117—48no—
137C2×#117C2314yes—
138C2×#117C2311yescharacteristic
139C2×#117C2311yescharacteristic
140C2×#117C2311yescharacteristic
141C2×#117C2314yes—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4—21no—
145C22×C4⋊C4—21no—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C22⋊C4—22no—
149C22×C42—28no—
150C22×C42—22no—
151C22×C42—21no—
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42D411yescharacteristic
155C22×C42D411yescharacteristic
156C22×C42D411yescharacteristic
157C22×C42D411yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164#427—48no—
165C2×#107C2314yes—
166C2×#107C2314yes—
167C2×#106C2314yes—
168C2×#106C2314yes—
169C2×C4⋊C8—28no—
170C2×C4⋊C8C2312yes—
171C2×C4⋊C8C2312yes—
172C2×C4⋊C8C2314yes—
173#416—48no—
174C2×#103C2314yes—
175C2×#103C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×C22⋊C8—28no—
179C2×C22⋊C8C2312yes—
180C2×C22⋊C8C2312yes—
181C2×C22⋊C8C2314yes—
182#391C2311yescharacteristic
183#391C2311yescharacteristic
184#390C2311yescharacteristic
185#390C2311yescharacteristic
186#389C2311yescharacteristic
187#389C2311yescharacteristic
188#389C2311yescharacteristic
189#389C2311yescharacteristic
190#388—21no—
191#388—21no—
192#388—21no—
193#388—21no—
194#387—21no—
195#387—21no—
196#387—21no—
197#387—21no—
198#386—21no—
199#386—21no—
200#386—21no—
201#386—21no—
202#386—21no—
203#386—21no—
204#385—21no—
205#385—21no—
206#385—21no—
207#385—21no—
208#385—21no—
209#385—21no—
210#384—21no—
211#384—21no—
212#384—21no—
213#384—21no—
214#384C2312yes—
215#384C2312yes—
216#384C2312yes—
217#384C2312yes—
218#382—22no—
219#382—22no—
220#382C2314yes—
221#382C2314yes—
222#381—21no—
223#380—22no—
224#380—22no—
225#380—22no—
226#380—22no—
227#380—22no—
228#380—22no—
229#380—22no—
230#380—22no—
231#380C2311yescharacteristic
232#380C2311yescharacteristic
233#380C2311yescharacteristic
234#380C2311yescharacteristic
235#379—21no—
236C4×C4⋊C4—22no—
237C4×C4⋊C4—22no—
238C4×C4⋊C4—22no—
239C4×C4⋊C4—22no—
240C4×C4⋊C4—22no—
241C4×C4⋊C4—22no—
242C4×C4⋊C4—22no—
243C4×C4⋊C4—22no—
244C4×C4⋊C4—21no—
245C4×C4⋊C4—21no—
246C4×C4⋊C4—21no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4—21no—
250C4×C4⋊C4C2311yescharacteristic
251C4×C4⋊C4C2311yescharacteristic
252C4×C4⋊C4C2311yescharacteristic
253C4×C4⋊C4C2311yescharacteristic
254C4×C22⋊C4—21no—
255C4×C22⋊C4—21no—
256C4×C22⋊C4—21no—
257C4×C22⋊C4—21no—
258C4×C22⋊C4—21no—
259C4×C22⋊C4—21no—
260C4×C22⋊C4—21no—
261C4×C22⋊C4—21no—
262C4×C22⋊C4—21no—
263C4×C22⋊C4—21no—
264C4×C22⋊C4—21no—
265C4×C22⋊C4—21no—
266C4×C22⋊C4—21no—
267C4×C22⋊C4—21no—
268#376—21no—
269C2×#95—22no—
270C2×#95—22no—
271C43—21no—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278#340C2314yes—
279#340C2314yes—
280#336C2314yes—
281#336C2312yes—
282#336C2312yes—
283C25C2×D411yescharacteristic
284C2×#41—22no—
285C2×#41—24no—
286C2×#41—24no—
287C2×#41C2×Q814yes—
288C22×Q8C2411yescharacteristic
289C22×D4—21no—
290C22×D4—21no—
291C22×D4—21no—
292C22×D4C2411yescharacteristic
293C23×C4—24no—
294C23×C4—24no—
295C23×C4—24no—
296C23×C4—24no—
297C23×C4—24no—
298C23×C4—21no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—21no—
302C23×C4—21no—
303C23×C4—42no—
304C23×C4—42no—
305C23×C4—42no—
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2×Q814yes—
322C23×C4#4114yes—
323C23×C4C2411yescharacteristic
324C23×C4C2411yescharacteristic
325C23×C4C2411yescharacteristic
326C22×C8—28no—
327C22×C8—28no—
328C22×C8—28no—
329C22×C8C2414yes—
330C22×C8C2414yes—
331#123—28no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8C2×Q814yes—
335C22⋊Q8C2×Q814yes—
336#121—22no—
337#121—22no—
338#121C2×Q814yes—
339#121C2×Q814yes—
340#120—28no—
341C4×Q8—24no—
342C4×Q8—24no—
343C4×D4—28no—
344C4×D4—28no—
345C4×D4—24no—
346C4×D4—24no—
347C4×D4—44no—
348C4×D4—44no—
349C4×D4—44no—
350C4×D4—44no—
351C4×D4—44no—
352C4×D4—44no—
353#117—22no—
354#117—24no—
355#117—28no—
356#117—28no—
357#117—24no—
358#117—44no—
359#117—44no—
360#117—48no—
361#117—48no—
362#117—44no—
363#117C2×Q814yes—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4—44no—
387C2×C4⋊C4—44no—
388C2×C4⋊C4C2414yes—
389C2×C4⋊C4C2414yes—
390C2×C4⋊C4C2411yescharacteristic
391C2×C4⋊C4C2411yescharacteristic
392C2×C4⋊C4C2411yescharacteristic
393C2×C4⋊C4C2411yescharacteristic
394C2×C4⋊C4C2411yescharacteristic
395C2×C4⋊C4C2411yescharacteristic
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—48no—
416C2×C42—24no—
417C2×C42—24no—
418C2×C42—21no—
419C2×C42—24no—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—24no—
423C2×C42—24no—
424C2×C42—24no—
425C2×C42—24no—
426C2×C42—24no—
427C2×C42—24no—
428C2×C42—24no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—21no—
432C2×C42—21no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—24no—
437C2×C42—21no—
438C2×C42—48no—
439C2×C42—44no—
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42#4118yes—
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455C2×C42C2411yescharacteristic
456C2×C42C2411yescharacteristic
457#107—44no—
458#107—44no—
459#106—44no—
460#106—44no—
461C4⋊C8—24no—
462C4⋊C8—24no—
463C4⋊C8—28no—
464#103—44no—
465#103—44no—
466#102—44no—
467#102—44no—
468C22⋊C8—24no—
469C22⋊C8—24no—
470C22⋊C8—28no—
471#95—24no—
472#95—24no—
473#95—24no—
474#95—24no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—21no—
496C24—41no—
497C24—41no—
498C24C22⋊Q814yes—
499C24C22×D411yescharacteristic
500C24C22×D411yescharacteristic
501C24C22×D411yescharacteristic
502#41—216no—
503#41—48no—
504C2×Q8—21no—
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8C22×Q812yes—
508C2×D4—24no—
509C2×D4—24no—
510C2×D4—24no—
511C2×D4—22no—
512C2×D4—21no—
513C2×D4—22no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4C22×Q812yes—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—216no—
531C22×C4—216no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—416no—
577C22×C4—416no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4C22⋊Q814yes—
593C22×C4C22⋊Q814yes—
594C22×C4C22⋊Q814yes—
595C22×C4#12314yes—
596C22×C4#12314yes—
597C22×C4#13514yes—
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×Q812yes—
610C22×C4C22×Q812yes—
611C22×C4C22×Q812yes—
612C22×C4C2×#4112yes—
613C22×C4C2×#4112yes—
614C22×C4C2×#4112yes—
615C22×C4C2×#4114yes—
616C22×C4H(5,𝔽2)14yes—
617C22×C4C2511yescharacteristic
618C2×C8—24no—
619C2×C8—24no—
620C2×C8—24no—
621C2×C8—24no—
622C2×C8—24no—
623C2×C8—24no—
624C2×C8—416no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C4⋊C4—44no—
640C4⋊C4—44no—
641C4⋊C4—44no—
642C4⋊C4—44no—
643C4⋊C4—42no—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C4⋊C4—42no—
647C4⋊C4—44no—
648C4⋊C4—44no—
649C4⋊C4—42no—
650C4⋊C4—44no—
651C4⋊C4—44no—
652C4⋊C4—42no—
653C4⋊C4C22×Q812yes—
654C4⋊C4C22×Q812yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—48no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—48no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C42—24no—
675C42—22no—
676C42—22no—
677C42—22no—
678C42—22no—
679C42—22no—
680C42—22no—
681C42—22no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—22no—
686C42—22no—
687C42—48no—
688C42—42no—
689C42—42no—
690C42—42no—
691C42—42no—
692C42—42no—
693C42—48no—
694C42—42no—
695C42—42no—
696C42—42no—
697C42#12314yes—
698C42#12314yes—
699C42C2×#4114yes—
700C42C2×#4114yes—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—28no—
710C23—21no—
711C23—21no—
712C23—28no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23C2×C22⋊Q812yes—
730C23C2×C22⋊Q812yes—
731C23C2×C22⋊Q812yes—
732C23C2×#12312yes—
733C23#53512yes—
734C23C2×#13512yes—
735C23#57512yes—
736C23C23×D411yescharacteristic
737Q8—24no—
738Q8—42no—
739D4—24no—
740D4—48no—
741D4—48no—
742D4—48no—
743D4—42no—
744C2×C4—28no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—28no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—28no—
761C2×C4—28no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—44no—
792C2×C4—48no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—44no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—84no—
812C2×C4—88no—
813C2×C4—88no—
814C2×C4—84no—
815C2×C4C2×C22⋊Q812yes—
816C2×C4C2×C22⋊Q812yes—
817C2×C4C2×C22⋊Q812yes—
818C2×C4C2×#12312yes—
819C2×C4C2×#12312yes—
820C2×C4C2×#12312yes—
821C2×C4C2×#12312yes—
822C2×C4C2×#12312yes—
823C2×C4#53512yes—
824C2×C4#55318yes—
825C2×C4#55418yes—
826C2×C4C2×#13512yes—
827C2×C4C2×#13512yes—
828C2×C4#57512yes—
829C2×C4#57512yes—
830C2×C4C23×Q811yescharacteristic
831C2×C4C22×#4111yescharacteristic
832C2×C4C22×#4112yes—
833C2×C4C2×H(5,𝔽2)12yes—
834C8—44no—
835C8—44no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—416no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22#248714yes—
864C22#307614yes—
865C22C22×C22⋊Q811yescharacteristic
866C22C22×#12311yescharacteristic
867C22C2×#53511yescharacteristic
868C22C22×#13511yescharacteristic
869C22C2×#57511yescharacteristic
870C22C2×#57511yescharacteristic
871C22C2×#57511yescharacteristic
872C4—22no—
873C4—22no—
874C4—22no—
875C4—22no—
876C4—22no—
877C4—22no—
878C4—22no—
879C4—42no—
880C4—42no—
881C4—41no—
882C4—41no—
883C4—42no—
884C4—81no—
885C4—81no—
886C4—81no—
887C4—84no—
888C4—81no—
889C4—84no—
890C4#248714yes—
891C4#309114yes—
892C4C2×#55312yes—
893C4C2×#55412yes—
894C2—24no—
895C2—24no—
896C2—42no—
897C2—82no—
898C2C2×#248711yescharacteristic
899C2C2×#307611yescharacteristic
900C2#6048411yescharacteristic
901C2C2×#309111yescharacteristic
902C2#6051111yescharacteristic
903C2#6078211yescharacteristic
904C2#6079011yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radicalC2×#525C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2285C2semidirect
3. #27686C2semidirect
4. #27685C2semidirect
5. #27684C2semidirect
6. #27683C2semidirect
7. #27682C2semidirect
8. #27681C2semidirect
9. #27680C2semidirect
10. #27679C2semidirect
11. #27678C2semidirect
12. #27677C2semidirect
13. #23744C2semidirect
14. #23730C2semidirect
15. #21169C2semidirect
17. #20843C2semidirect
18. #20645C2semidirect
19. C2×#1797C2semidirect
63. #2101C22semidirect
64. #2101C22semidirect
65. #2100C22semidirect
66. #2100C22semidirect
67. #2099C22semidirect
68. #2099C22semidirect
69. #2097C22semidirect
70. #2096C22semidirect
71. #2095C22semidirect
72. #2094C22semidirect
73. #2093C22semidirect
74. #2092C22semidirect
75. #1949C22semidirect
76. #1949C22semidirect
77. #1948C22semidirect
78. #1948C22semidirect
79. #1947C22semidirect
80. #1947C22semidirect
93. #1805C22semidirect
94. #1804C22semidirect
95. #1803C22semidirect
96. #1803C22semidirect
97. #1802C22semidirect
98. #1802C22semidirect

Maximal subgroups

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

subgroupindex
C4×#5252
C2×#22852
#276862
#276852
#276842
#276832
#276822
#276812
#276802
#276792
#276782
#276772
#237442
#237302
#211692
#209082
#208432
#206452
C2×#17972