Finite Group Databasebeta

← #6432486

Subgroups — #6432486

Order 512.

2240 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#525C211yesmaximal, characteristic
2C2×#2285C211yesmaximal, characteristic, complemented
3#23763C212yesmaximal, complemented
4#23762C212yesmaximal, complemented
5#23761C212yesmaximal, complemented
6#23760C212yesmaximal, complemented
7#23757C212yesmaximal, complemented
8#23756C212yesmaximal, complemented
9#23755C212yesmaximal, complemented
10#23754C212yesmaximal, complemented
11#23745C211yesmaximal, characteristic, complemented
12#23734C211yesmaximal, characteristic, complemented
13#23658C211yesmaximal, characteristic, complemented
14#23642C212yesmaximal, complemented
15#23630C211yesmaximal, characteristic, complemented
16#23482C212yesmaximal
17C4×#428C212yesmaximal, complemented
18C4×#417C212yesmaximal, complemented
19C4×#407C211yesmaximal, characteristic, complemented
20C2×#525C2211yescharacteristic
21C2×C4×#41C2211yescharacteristic
22C22×#117—21no—
23C23×C42C2211yescharacteristic
24C2×#428C2212yes—
25C2×#428C2212yes—
26C2×#417C2212yes—
27C2×#417C2212yes—
28C2×#407C2212yes—
29C2×C4×M16C2212yes—
30C4×C22⋊Q8C2211yescharacteristic
31C4×C22⋊Q8C2211yescharacteristic
32C4×C22⋊Q8C2211yescharacteristic
33C4×C22⋊Q8C2211yescharacteristic
34C4×#123—21no—
35C4×#123—21no—
36C4×#121C2211yescharacteristic
37C4×#121C2211yescharacteristic
38C4×#121C2211yescharacteristic
39C4×#121C2211yescharacteristic
40C4×#120—21no—
41C4×#120—21no—
42#2297C2211yescharacteristic
43#2296C2211yescharacteristic
44#2290—21no—
45#2290—21no—
46#2285—21no—
47#2285—21no—
48#2285—21no—
49#2285—21no—
50#2285C2212yes—
51#2285C2212yes—
52#2285C2212yes—
53#2285C2212yes—
54C2×#384C2211yescharacteristic
55C2×#384C2211yescharacteristic
56C2×#382—21no—
57#2280C2211yescharacteristic
58C2×#380—21no—
59C2×#380C2212yes—
60C42×D4—21no—
61C42×D4—21no—
62C4×#117C2211yescharacteristic
63C2×C4×C4⋊C4—21no—
64C2×C4×C4⋊C4C2212yes—
65#2100C2212yescomplemented
66#2100C2212yescomplemented
67#2099C2212yescomplemented
68#2099C2212yescomplemented
69#2096C2212yescomplemented
70#2095C2212yescomplemented
71#2094C2212yescomplemented
72#2093C2212yescomplemented
73#2084C2212yescomplemented
74#2084C2212yescomplemented
75#2083C2212yescomplemented
76#2083C2212yescomplemented
77#2077C2214yes—
78#2077C2214yes—
79#2076C2214yes—
80#2075C2214yes—
81#2072C2212yescomplemented
82#2072C2212yescomplemented
83#2071C2212yescomplemented
84#2071C2212yescomplemented
85#2036C2214yes—
86#2035C2214yes—
87#2034C2214yes—
88#2033C2214yes—
89#1776C2214yescomplemented
90#1776C2214yescomplemented
91C4×#107C2214yescomplemented
92C4×#106C2214yescomplemented
93#1763C2214yescomplemented
94#1762C2214yescomplemented
95C4×#103C2214yescomplemented
96C4×#102C2214yescomplemented
97#1749C2212yes—
98#1749C2212yes—
99C4×C22⋊C8C2212yes—
100C4×C22⋊C8C2212yes—
101#1736C2212yes—
102#1736C2212yes—
103#1736C2212yes—
104#1736C2212yes—
105#1728C2211yescharacteristic
106#1728C2211yescharacteristic
107C22×#41C2311yescharacteristic
108C24×C4D411yescharacteristic
109C24×C4D411yescharacteristic
110C24×C4C2311yescharacteristic
111C22×M16C2312yes—
112C22×M16C2312yes—
113#525—24no—
114#525—24no—
115C2×#123—21no—
116C2×C22⋊Q8C2311yescharacteristic
117C2×C22⋊Q8C2311yescharacteristic
118C2×#121C2311yescharacteristic
119C2×#121C2311yescharacteristic
120C2×#120—21no—
121C4×#41—28no—
122C2×C4×Q8C2311yescharacteristic
123C2×C4×Q8C2311yescharacteristic
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×D4—21no—
132C2×C4×D4C2311yescharacteristic
133C2×C4×D4C2311yescharacteristic
134C2×#117—22no—
135C2×#117—22no—
136C2×#117—22no—
137C2×#117—22no—
138C2×#117—21no—
139C2×#117—48no—
140C2×#117C2311yescharacteristic
141C2×#117C2311yescharacteristic
142C2×#117C2311yescharacteristic
143C22×C4⋊C4—21no—
144C22×C4⋊C4—21no—
145C22×C4⋊C4—21no—
146C22×C4⋊C4—21no—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C22⋊C4—22no—
150C22×C42—28no—
151C22×C42—22no—
152C22×C42—21no—
153C22×C42D411yescharacteristic
154C22×C42D411yescharacteristic
155C22×C42D411yescharacteristic
156C22×C42D411yescharacteristic
157C22×C42D411yescharacteristic
158C22×C42D411yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165#428—28no—
166#428—28no—
167C2×#107C2314yes—
168C2×#107C2314yes—
169C2×#106C2314yes—
170C2×#106C2314yes—
171#417—28no—
172#417—28no—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177#407—28no—
178C2×C22⋊C8C2314yes—
179C2×C22⋊C8C2314yes—
180C4×M16—28no—
181C2×#97C2314yes—
182C2×C4×C8C2314yes—
183#391C2311yescharacteristic
184#391C2311yescharacteristic
185#390C2311yescharacteristic
186#390C2311yescharacteristic
187#389C2311yescharacteristic
188#389C2311yescharacteristic
189#389C2311yescharacteristic
190#389C2311yescharacteristic
191#388—21no—
192#388—21no—
193#388—21no—
194#388—21no—
195#387—21no—
196#387—21no—
197#387—21no—
198#387—21no—
199#386—21no—
200#386—21no—
201#386—21no—
202#386—21no—
203#386—21no—
204#386—21no—
205#385—21no—
206#385—21no—
207#385—21no—
208#385—21no—
209#385—21no—
210#385—21no—
211#384—21no—
212#384—21no—
213#384—21no—
214#384—21no—
215#384C2312yes—
216#384C2312yes—
217#384C2312yes—
218#384C2312yes—
219#382—22no—
220#382—22no—
221#382—22no—
222#382—22no—
223#381—21no—
224#380—22no—
225#380—22no—
226#380—22no—
227#380—22no—
228#380—22no—
229#380—22no—
230#380C2311yescharacteristic
231#380C2314yes—
232#380C2311yescharacteristic
233#380C2314yes—
234#380C2311yescharacteristic
235#380C2311yescharacteristic
236#379—21no—
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—21no—
244C4×C4⋊C4—21no—
245C4×C4⋊C4—21no—
246C4×C4⋊C4—21no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4C2314yes—
250C4×C4⋊C4C2314yes—
251C4×C4⋊C4C2311yescharacteristic
252C4×C4⋊C4C2311yescharacteristic
253C4×C4⋊C4C2311yescharacteristic
254C4×C4⋊C4C2311yescharacteristic
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—
268C4×C22⋊C4—21no—
269#376—21no—
270C2×#95—22no—
271C2×#95—22no—
272C43—21no—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278#340C2314yes—
279#340C2314yes—
280#340C2314yes—
281#336C2312yes—
282#336C2312yes—
283#336C2312yes—
284#336C2312yes—
285C25C2×D411yescharacteristic
286C2×#41—22no—
287C2×#41—24no—
288C2×#41—24no—
289C2×#41#4114yes—
290C22×Q8C2411yescharacteristic
291C22×D4—21no—
292C22×D4—21no—
293C22×D4—21no—
294C22×D4C2411yescharacteristic
295C23×C4—24no—
296C23×C4—24no—
297C23×C4—24no—
298C23×C4—24no—
299C23×C4—21no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—24no—
303C23×C4—24no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—21no—
307C23×C4—21no—
308C23×C4—42no—
309C23×C4—42no—
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×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2×D411yescharacteristic
325C23×C4C2411yescharacteristic
326C23×C4C2411yescharacteristic
327C23×C4C2411yescharacteristic
328C2×M16—24no—
329C2×M16—24no—
330C2×M16—24no—
331C2×M16—24no—
332C2×M16—24no—
333C2×M16#4118yes—
334C22×C8C2414yes—
335C22×C8C2414yes—
336#123—28no—
337C22⋊Q8—22no—
338C22⋊Q8—22no—
339C22⋊Q8—22no—
340C22⋊Q8—22no—
341#121—22no—
342#121—22no—
343#121—22no—
344#121—22no—
345#120—28no—
346C4×Q8—24no—
347C4×Q8—24no—
348C4×D4—28no—
349C4×D4—28no—
350C4×D4—24no—
351C4×D4—24no—
352C4×D4—44no—
353C4×D4—44no—
354C4×D4—44no—
355C4×D4—44no—
356C4×D4—44no—
357C4×D4—44no—
358#117—22no—
359#117—24no—
360#117—24no—
361#117—48no—
362#117—48no—
363#117—48no—
364#117—48no—
365#117—44no—
366#117#4114yes—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—44no—
390C2×C4⋊C4—44no—
391C2×C4⋊C4—44no—
392C2×C4⋊C4—44no—
393C2×C4⋊C4C2414yes—
394C2×C4⋊C4C2414yes—
395C2×C4⋊C4C2411yescharacteristic
396C2×C4⋊C4C2411yescharacteristic
397C2×C4⋊C4C2411yescharacteristic
398C2×C4⋊C4C2411yescharacteristic
399C2×C4⋊C4C2411yescharacteristic
400C2×C4⋊C4C2411yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4—24no—
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—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—48no—
421C2×C42—24no—
422C2×C42—24no—
423C2×C42—21no—
424C2×C42—24no—
425C2×C42—24no—
426C2×C42—24no—
427C2×C42—24no—
428C2×C42—24no—
429C2×C42—24no—
430C2×C42—24no—
431C2×C42—24no—
432C2×C42—24no—
433C2×C42—24no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—24no—
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42—48no—
444C2×C42—44no—
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D411yescharacteristic
453C2×C42C2×D411yescharacteristic
454C2×C42C2×D411yescharacteristic
455C2×C42C2×D411yescharacteristic
456C2×C42C2×D411yescharacteristic
457C2×C42#4118yes—
458C2×C42C2411yescharacteristic
459C2×C42C2411yescharacteristic
460C2×C42C2411yescharacteristic
461C2×C42C2411yescharacteristic
462#107—28no—
463#107—28no—
464#106—28no—
465#106—28no—
466#103—28no—
467#103—28no—
468#102—28no—
469#102—28no—
470C22⋊C8—28no—
471C22⋊C8—28no—
472#97—28no—
473C4×C8—28no—
474#95—24no—
475#95—24no—
476#95—24no—
477#95—24no—
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—
491#95—21no—
492#95—21no—
493#95—21no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—21no—
500C24—41no—
501C24—41no—
502C24C22×D411yescharacteristic
503C24C22×D411yescharacteristic
504C24C22×D411yescharacteristic
505#41—216no—
506#41—48no—
507C2×Q8—21no—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8C2×#4112yes—
511C2×D4—24no—
512C2×D4—24no—
513C2×D4—24no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—21no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4C2×#4112yes—
524C22×C4—232no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
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—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
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—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—416no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—42no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4#12314yes—
602C22×C4#12314yes—
603C22×C4AGL(1,ℤ/8)14yes—
604C22×C4#13714yes—
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C2×#4114yes—
617C22×C4C2×#4112yes—
618C22×C4C2×#4112yes—
619C22×C4C2×#4114yes—
620C22×C4C2511yescharacteristic
621M16—216no—
622M16—48no—
623C2×C8—24no—
624C2×C8—24no—
625C2×C8—24no—
626C2×C8—24no—
627C2×C8—24no—
628C2×C8C2×#4118yes—
629C4⋊C4—24no—
630C4⋊C4—24no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—22no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—44no—
642C4⋊C4—44no—
643C4⋊C4—44no—
644C4⋊C4—44no—
645C4⋊C4—42no—
646C4⋊C4—42no—
647C4⋊C4—44no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—44no—
654C4⋊C4—44no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4C2×#4112yes—
658C4⋊C4C2×#4112yes—
659C22⋊C4—24no—
660C22⋊C4—24no—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—24no—
664C22⋊C4—48no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—48no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C42—22no—
679C42—22no—
680C42—22no—
681C42—22no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—24no—
689C42—22no—
690C42—22no—
691C42—48no—
692C42—42no—
693C42—42no—
694C42—42no—
695C42—42no—
696C42—42no—
697C42—42no—
698C42—48no—
699C42—42no—
700C42—42no—
701C42#12314yes—
702C42#12314yes—
703C42C2×#4114yes—
704C42C2×#4114yes—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—28no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—22no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23C2×#12312yes—
736C23#52512yes—
737C23#53212yes—
738C23C2×AGL(1,ℤ/8)12yes—
739C23C2×#13712yes—
740C23C23×D411yescharacteristic
741Q8—24no—
742Q8—42no—
743D4—24no—
744D4—48no—
745D4—48no—
746D4—48no—
747D4—42no—
748C2×C4—28no—
749C2×C4—28no—
750C2×C4—28no—
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—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—48no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—44no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—84no—
816C2×C4—88no—
817C2×C4—88no—
818C2×C4—84no—
819C2×C4C2×#12312yes—
820C2×C4C2×#12312yes—
821C2×C4C2×#12312yes—
822C2×C4C2×#12312yes—
823C2×C4C2×#12312yes—
824C2×C4#52512yes—
825C2×C4#52918yes—
826C2×C4#52918yes—
827C2×C4#53212yes—
828C2×C4C2×AGL(1,ℤ/8)12yes—
829C2×C4C2×AGL(1,ℤ/8)12yes—
830C2×C4C2×#13712yes—
831C2×C4C2×#13712yes—
832C2×C4#57512yes—
833C2×C4#57512yes—
834C2×C4C22×#4112yes—
835C2×C4C22×#4111yescharacteristic
836C2×C4C22×#4111yescharacteristic
837C2×C4C22×#4112yes—
838C8—28no—
839C8—44no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—416no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22#239514yes—
869C22C22×#12311yescharacteristic
870C22C2×#52511yescharacteristic
871C22C2×#53211yescharacteristic
872C22C22×AGL(1,ℤ/8)11yescharacteristic
873C22C22×#13711yescharacteristic
874C22C2×#57511yescharacteristic
875C22C2×#57511yescharacteristic
876C4—22no—
877C4—22no—
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—22no—
883C4—42no—
884C4—42no—
885C4—41no—
886C4—41no—
887C4—42no—
888C4—81no—
889C4—84no—
890C4—81no—
891C4—81no—
892C4—81no—
893C4—84no—
894C4#239514yes—
895C4#309214yes—
896C4C2×#52912yes—
897C4C2×#52912yes—
898C2—24no—
899C2—42no—
900C2—42no—
901C2—82no—
902C2C2×#239511yescharacteristic
903C2C2×#309211yescharacteristic
904C2#6051111yescharacteristic
905C2#6056111yescharacteristic
906C2#6056211yescharacteristic
907C2#6070011yescharacteristic
908C2#6070111yescharacteristic
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. #23763C2semidirect
4. #23762C2semidirect
5. #23761C2semidirect
6. #23760C2semidirect
7. #23757C2semidirect
8. #23756C2semidirect
9. #23755C2semidirect
10. #23754C2semidirect
11. #23745C2semidirect
12. #23734C2semidirect
13. #23658C2semidirect
14. #23642C2semidirect
15. #23630C2semidirect
17. C4×#428C2semidirect
18. C4×#417C2semidirect
19. C4×#407C2semidirect
65. #2100C22semidirect
66. #2100C22semidirect
67. #2099C22semidirect
68. #2099C22semidirect
69. #2096C22semidirect
70. #2095C22semidirect
71. #2094C22semidirect
72. #2093C22semidirect
73. #2084C22semidirect
74. #2084C22semidirect
75. #2083C22semidirect
76. #2083C22semidirect
81. #2072C22semidirect
82. #2072C22semidirect
83. #2071C22semidirect
84. #2071C22semidirect
89. #1776C22semidirect
90. #1776C22semidirect
91. C4×#107C22semidirect
92. C4×#106C22semidirect
93. #1763C22semidirect
94. #1762C22semidirect
95. C4×#103C22semidirect
96. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
C4×#5252
C2×#22852
#237632
#237622
#237612
#237602
#237572
#237562
#237552
#237542
#237452
#237342
#236582
#236422
#236302
#234822
C4×#4282
C4×#4172
C4×#4072