Finite Group Databasebeta

← #6469625

Subgroups — #6469625

Order 512.

2224 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#532C211yesmaximal, characteristic, complemented
2C4×#532C211yesmaximal, characteristic, complemented
3#29536C214yesmaximal, complemented
4#29287C211yesmaximal, characteristic, complemented
5#28280C211yesmaximal, characteristic, complemented
6#28279C211yesmaximal, characteristic, complemented
7#28251C211yesmaximal, characteristic, complemented
8#27627C212yesmaximal, complemented
9#27625C212yesmaximal, complemented
10#24152C212yesmaximal, complemented
11#24150C212yesmaximal, complemented
12#23708C214yesmaximal, complemented
13#21614C212yesmaximal, complemented
14#21613C212yesmaximal, complemented
15#21503C212yesmaximal, complemented
16#21503C212yesmaximal, complemented
17#20810C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic
19C2×#532C2211yescharacteristic
20C2×C4×#41—21no—
21C2×C4×#41—21no—
22C2×#476C2212yes—
23C2×#474C2212yes—
24C2×#459C2212yes—
25C2×#459C2212yes—
26C2×#442C2214yes—
27C2×#432C2212yes—
28C4×C4⋊Q8C2211yescharacteristic
29C4×C4⋊Q8C2211yescharacteristic
30C4×C4⋊Q8C2211yescharacteristic
31C4×C4⋊Q8C2211yescharacteristic
32C4×#127C2211yescharacteristic
33C4×#127C2211yescharacteristic
34C4×#127C2211yescharacteristic
35C4×#127C2211yescharacteristic
36C4×#124—21no—
37C4×#124—21no—
38C4×#124—21no—
39C4×#124—21no—
40C4×#121—21no—
41C4×#121—21no—
42C4×#121—21no—
43C4×#121—21no—
44C4×#121C2212yes—
45C4×#121C2212yes—
46C4×#121C2212yes—
47C4×#121C2212yes—
48#2297—21no—
49#2297—21no—
50#2293—21no—
51#2293—21no—
52#2293C2212yes—
53#2293C2212yes—
54#2285C2211yescharacteristic
55#2285C2211yescharacteristic
56C42×D4—21no—
57C42×D4—21no—
58C42×D4C2212yes—
59C42×D4C2212yes—
60C2×C43C2211yescharacteristic
61#2088C2214yes—
62#2077C2214yes—
63#2067C2214yes—
64#2065C2214yes—
65#2054C2214yes—
66#2034C2214yes—
67#2033C2214yes—
68#1999C2214yes—
69#1988C2212yes—
70#1987C2212yes—
71#1982C2212yes—
72#1982C2212yes—
73#1948C2212yes—
74#1948C2212yes—
75#1948C2212yes—
76#1947C2212yes—
77#1926C2214yes—
78#1926C2214yes—
79#1921C2214yes—
80#1919C2214yes—
81#1879C2214yes—
82#1879C2214yes—
83#1864C2214yes—
84#1862C2214yes—
85#1842C2211yescharacteristic
86#1842C2211yescharacteristic
87#1831C2212yes—
88#1802C2212yes—
89#1802C2212yes—
90#1802C2212yes—
91#1802C2212yes—
92#1797C2212yes—
93#1797C2212yes—
94#1776C2214yes—
95#1767C2212yes—
96#1767C2212yes—
97#1762C2214yes—
98#1762C2214yes—
99C22×#41—21no—
100C22×#41—21no—
101C22×D8C2314yes—
102#532—24no—
103#532—24no—
104#532—24no—
105#532—24no—
106C2×C4⋊Q8C2311yescharacteristic
107C2×C4⋊Q8C2311yescharacteristic
108C2×#127C2311yescharacteristic
109C2×#127C2311yescharacteristic
110C2×#124—21no—
111C2×#124—21no—
112C2×#121—21no—
113C2×#121—21no—
114C2×#121C2312yes—
115C2×#121C2312yes—
116C4×#41—48no—
117C4×#41—48no—
118C2×C4×Q8—21no—
119C2×C4×Q8—21no—
120C2×C4×Q8—21no—
121C2×C4×Q8—21no—
122C2×C4×D4—22no—
123C2×C4×D4—22no—
124C2×C4×D4—22no—
125C2×C4×D4—22no—
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×D4—21no—
133C2×C4×D4—21no—
134C2×C4×D4—21no—
135C2×C4×D4—21no—
136C2×C4×D4C2312yes—
137C2×C4×D4C2312yes—
138C2×C4×D4C2312yes—
139C2×C4×D4C2312yes—
140C2×C4×D4C2312yes—
141C2×C4×D4C2312yes—
142C2×#117—21no—
143C2×#117—21no—
144C2×#117—22no—
145C2×#117—22no—
146C22×C42—22no—
147C22×C42—22no—
148C22×C42D411yescharacteristic
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155#476—28no—
156#474—28no—
157#459—28no—
158#459—28no—
159#442—48no—
160#432—44no—
161C2×#107C2314yes—
162C2×#106C2314yes—
163C2×#106C2314yes—
164C2×C4⋊C8C2312yes—
165C2×C4⋊C8C2312yes—
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2312yes—
168C2×C4⋊C8C2312yes—
169C2×C4⋊C8C2312yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×C22⋊C8C2314yes—
177C2×#97C2314yes—
178#391—21no—
179#391—21no—
180#391—21no—
181#391—21no—
182#390—21no—
183#390—21no—
184#390—21no—
185#390—21no—
186#390—21no—
187#390—21no—
188#390—21no—
189#390—21no—
190#390C2312yes—
191#390C2312yes—
192#390C2312yes—
193#390C2312yes—
194#389—21no—
195#389—21no—
196#389—21no—
197#389—21no—
198#389C2312yes—
199#389C2312yes—
200#389C2312yes—
201#389C2312yes—
202#388—22no—
203#388—22no—
204#388—22no—
205#388—22no—
206#388—22no—
207#388—22no—
208#388—22no—
209#388—22no—
210#386—22no—
211#386—22no—
212#386—22no—
213#386—22no—
214#384C2311yescharacteristic
215#384C2311yescharacteristic
216#384C2311yescharacteristic
217#384C2311yescharacteristic
218#382—21no—
219#382—21no—
220#380—21no—
221#380—21no—
222#380C2312yes—
223#380C2312yes—
224C4×C4⋊C4—21no—
225C4×C4⋊C4—21no—
226C4×C4⋊C4—21no—
227C4×C4⋊C4—21no—
228C4×C4⋊C4—21no—
229C4×C4⋊C4—21no—
230C4×C4⋊C4C2312yes—
231C4×C4⋊C4C2312yes—
232C4×C4⋊C4C2312yes—
233C4×C4⋊C4C2312yes—
234C4×C4⋊C4C2312yes—
235C4×C4⋊C4C2312yes—
236C4×C22⋊C4—22no—
237C4×C22⋊C4—22no—
238C4×C22⋊C4—22no—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C43D411yescharacteristic
249C43D411yescharacteristic
250C43D411yescharacteristic
251C43D411yescharacteristic
252C43C2311yescharacteristic
253C43C2311yescharacteristic
254C43C2311yescharacteristic
255C43C2311yescharacteristic
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#340C2314yes—
260#340C2314yes—
261#340C2314yes—
262#336C2314yes—
263#336C2314yes—
264C2×#41—28no—
265C2×#41—28no—
266C2×#41—44no—
267C2×#41—44no—
268C2×#41—44no—
269C2×#41—44no—
270C22×Q8—21no—
271C22×Q8—21no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—21no—
275C22×D4—21no—
276C22×D4—21no—
277C22×D4—21no—
278C22×D4C2412yes—
279C22×D4C2412yes—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2411yescharacteristic
293C2×D8—28no—
294C2×D8—28no—
295C2×D8—44no—
296C22×C8C2414yes—
297C22×C8C2414yes—
298C4⋊Q8—22no—
299C4⋊Q8—22no—
300C4⋊Q8#4114yescomplemented
301C4⋊Q8#4114yescomplemented
302#127—22no—
303#127—22no—
304#127#4114yescomplemented
305#127#4114yescomplemented
306#124—28no—
307#124—28no—
308#121—28no—
309#121—28no—
310#121—24no—
311#121—24no—
312#121—24no—
313#121—24no—
314C4×Q8—44no—
315C4×Q8—44no—
316C4×Q8—44no—
317C4×Q8—44no—
318C4×D4—28no—
319C4×D4—28no—
320C4×D4—24no—
321C4×D4—24no—
322C4×D4—24no—
323C4×D4—24no—
324C4×D4—24no—
325C4×D4—24no—
326C4×D4—24no—
327C4×D4—24no—
328C4×D4—24no—
329C4×D4—24no—
330C4×D4—24no—
331C4×D4—24no—
332C4×D4—44no—
333C4×D4—44no—
334C4×D4—44no—
335C4×D4—44no—
336C4×D4—44no—
337C4×D4—44no—
338C4×D4—48no—
339C4×D4—48no—
340C4×D4—48no—
341C4×D4—48no—
342C4×D4—44no—
343C4×D4—44no—
344#117—48no—
345#117—48no—
346#117—44no—
347#117—44no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—48no—
403C2×C42—48no—
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432#107—28no—
433#106—28no—
434#106—44no—
435C4⋊C8—24no—
436C4⋊C8—24no—
437C4⋊C8—24no—
438C4⋊C8—24no—
439C4⋊C8—42no—
440C4⋊C8—42no—
441#102—28no—
442#102—28no—
443#102—28no—
444#102—28no—
445#102—44no—
446#102—44no—
447C22⋊C8—44no—
448#97—28no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461C24—22no—
462C24—22no—
463C24C22×D411yescharacteristic
464#41—432no—
465#41—432no—
466C2×Q8—24no—
467C2×Q8—24no—
468C2×Q8—42no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×D4—28no—
473C2×D4—28no—
474C2×D4—24no—
475C2×D4—24no—
476C2×D4—24no—
477C2×D4—24no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4C2×#4114yes—
501C2×D4C2×#4114yes—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—28no—
508C22×C4—28no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4AGL(1,ℤ/8)14yes—
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C2511yescharacteristic
564D8—416no—
565C2×C8—24no—
566C2×C8—24no—
567C2×C8—24no—
568C2×C8—24no—
569C2×C8—24no—
570C2×C8—24no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—44no—
590C4⋊C4—44no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4C2×#4114yes—
596C4⋊C4C2×#4114yes—
597C22⋊C4—28no—
598C22⋊C4—28no—
599C22⋊C4—28no—
600C22⋊C4—28no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42—41no—
639C42—41no—
640C42—41no—
641C42—41no—
642C42—44no—
643C42—44no—
644C42—44no—
645C42—44no—
646C42—44no—
647C42—44no—
648C42AGL(1,ℤ/8)14yes—
649C42C2×#4112yes—
650C42C2×#4112yes—
651C42C2×#4112yes—
652C42C2×#4112yes—
653C42H(5,𝔽2)12yes—
654C422−1+412yes—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—24no—
662C23—24no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23C2×AGL(1,ℤ/8)12yes—
676C23C23×D411yescharacteristic
677Q8—48no—
678Q8—48no—
679D4—24no—
680D4—24no—
681D4—24no—
682D4—24no—
683D4—48no—
684D4—48no—
685D4—416no—
686D4—416no—
687D4—48no—
688D4—48no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—42no—
693C2×C4—28no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—28no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—416no—
727C2×C4—416no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—44no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—88no—
750C2×C4—88no—
751C2×C4—88no—
752C2×C4—88no—
753C2×C4#52512yes—
754C2×C4#52512yes—
755C2×C4#52512yes—
756C2×C4#52512yes—
757C2×C4#53712yes—
758C2×C4#53712yes—
759C2×C4C2×AGL(1,ℤ/8)12yes—
760C2×C4C2×AGL(1,ℤ/8)12yes—
761C2×C4C2×AGL(1,ℤ/8)12yes—
762C2×C4C2×AGL(1,ℤ/8)12yes—
763C2×C4C2×AGL(1,ℤ/8)12yes—
764C2×C4#57512yes—
765C2×C4#57512yes—
766C2×C4C22×#4111yescharacteristic
767C2×C4C22×#4111yescharacteristic
768C2×C4C22×#4111yescharacteristic
769C2×C4C22×#4111yescharacteristic
770C2×C4C2×H(5,𝔽2)11yescharacteristic
771C2×C4C2×2−1+411yescharacteristic
772C8—44no—
773C8—44no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22C2×#52511yescharacteristic
796C22C2×#52511yescharacteristic
797C22C2×#53711yescharacteristic
798C22C22×AGL(1,ℤ/8)11yescharacteristic
799C22C22×AGL(1,ℤ/8)11yescharacteristic
800C22C2×#57511yescharacteristic
801C22C2×#57511yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—22no—
807C4—22no—
808C4—22no—
809C4—41no—
810C4—44no—
811C4—44no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—82no—
816C4—82no—
817C4—82no—
818C4—82no—
819C4#310914yes—
820C4#311514yes—
821C4#348111yescharacteristic
822C4#348211yescharacteristic
823C4#348211yescharacteristic
824C4#348311yescharacteristic
825C2—42no—
826C2—84no—
827C2—84no—
828C2#3497611yescharacteristic
829C2C2×#311511yescharacteristic
830C2C2×#310911yescharacteristic
831C2#6055811yescharacteristic
832C2#6055911yescharacteristic
833C2#6091611yescharacteristic
834C2#6091611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C4×#532C2semidirect
2. C4×#532C2semidirect
3. #29536C2semidirect
4. #29287C2semidirect
5. #28280C2semidirect
6. #28279C2semidirect
7. #28251C2semidirect
8. #27627C2semidirect
9. #27625C2semidirect
10. #24152C2semidirect
11. #24150C2semidirect
12. #23708C2semidirect
13. #21614C2semidirect
14. #21613C2semidirect
15. #21503C2semidirect
16. #21503C2semidirect
17. #20810C2semidirect
300. C4⋊Q8#41semidirect
301. C4⋊Q8#41semidirect
304. #127#41semidirect
305. #127#41semidirect

Maximal subgroups

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

subgroupindex
C4×#5322
#295362
#292872
#282802
#282792
#282512
#276272
#276252
#241522
#241502
#237082
#216142
#216132
#215032
#208102