Finite Group Databasebeta

← #7505392

Subgroups — #7505392

Order 512.

2273 conjugacy classes of subgroups.

The subgroup lattice has 821 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2542C211yesmaximal, characteristic, complemented
2#34744C211yesmaximal, characteristic, complemented
3#31656C214yesmaximal, complemented
4#31654C214yesmaximal, complemented
5#31636C214yesmaximal, complemented
6#31634C214yesmaximal, complemented
7#23745C211yesmaximal, characteristic, complemented
8#23630C211yesmaximal, characteristic, complemented
9#23546C211yesmaximal, characteristic, complemented
10#23452C211yesmaximal, characteristic, complemented
11#23452C211yesmaximal, characteristic, complemented
12#23428C211yesmaximal, characteristic
13#21200C211yesmaximal, characteristic, complemented
14#21095C211yesmaximal, characteristic, complemented
15#21023C211yesmaximal, characteristic, complemented
16#20928C211yesmaximal, characteristic, complemented
17#20925C211yesmaximal, characteristic, complemented
18#20925C211yesmaximal, characteristic, complemented
19#20648C211yesmaximal, characteristic, complemented
20C22×AGL(1,ℤ/8)C2211yescharacteristic
21C22×AGL(1,ℤ/8)C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C22⋊Q8—22no—
25C2×C4×#41C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C2×#423C2211yescharacteristic
28C2×#417C2211yescharacteristic
29C2×#417C2211yescharacteristic
30C2×#417C2211yescharacteristic
31C2×#417C2211yescharacteristic
32C2×#417C2211yescharacteristic
33C2×#417C2211yescharacteristic
34C2×#418C2211yescharacteristic
35C2×#418C2211yescharacteristic
36C2×C4×M16C2211yescharacteristic
37#2542—22no—
38#2542—22no—
39#2542C2214yes—
40#2542C2214yes—
41#2448C2212yescomplemented
42#2447C2212yescomplemented
43#2446C2212yescomplemented
44#2445C2212yescomplemented
45#2444—22no—
46#2443—22no—
47#2395—22no—
48C2×#399—22no—
49C4×#123—22no—
50#2297C2211yescharacteristic
51#2297C2211yescharacteristic
52#2297C2211yescharacteristic
53#2296C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#384C2211yescharacteristic
57C2×#384C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic
59#2100C2214yescomplemented
60#2099C2214yescomplemented
61#2072C2214yescomplemented
62#2071C2214yescomplemented
63#2055C2214yes—
64#2054C2214yes—
65#2024C2214yescomplemented
66#2024C2214yescomplemented
67#2023C2214yescomplemented
68#2023C2214yescomplemented
69#2013C2212yes—
70#2012C2212yes—
71#2012C2212yes—
72#2011C2212yes—
73#1959C2212yescomplemented
74#1959C2212yescomplemented
75#1957C2212yescomplemented
76#1956C2212yescomplemented
77#1936C2214yes—
78#1934C2214yes—
79#1917C2214yescomplemented
80#1916C2214yescomplemented
81#1880C2214yes—
82#1879C2214yes—
83#1879C2214yes—
84#1879C2214yes—
85#1877C2214yes—
86#1877C2214yes—
87#1803C2214yescomplemented
88#1802C2214yescomplemented
89#1736C2211yescharacteristic
90#1736C2211yescharacteristic
91#1736C2211yescharacteristic
92#1736C2211yescharacteristic
93#1736C2211yescharacteristic
94#1736C2211yescharacteristic
95#1728C2211yescharacteristic
96#1728C2211yescharacteristic
97#1728C2211yescharacteristic
98#1728C2211yescharacteristic
99C22×#41C2311yescharacteristic
100C22×#41C2311yescharacteristic
101C23×Q8—21no—
102C23×D4C2311yescharacteristic
103C24×C4—21no—
104C2×AGL(1,ℤ/8)—24no—
105C2×AGL(1,ℤ/8)—24no—
106C2×AGL(1,ℤ/8)—24no—
107C2×AGL(1,ℤ/8)—42no—
108C2×AGL(1,ℤ/8)—42no—
109C2×AGL(1,ℤ/8)—42no—
110C22×SD16C2312yes—
111C22×SD16C2312yes—
112C22×D8C2312yes—
113C22×D8C2312yes—
114C22×M16C2311yescharacteristic
115C22×M16C2311yescharacteristic
116C22×M16C2311yescharacteristic
117C22×M16C2311yescharacteristic
118#532—24no—
119#532—42no—
120C2×C4⋊Q8—22no—
121C2×C4⋊Q8—42no—
122C2×C4⋊Q8—42no—
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2314yes—
125C2×#127C2311yescharacteristic
126C2×#124C2311yescharacteristic
127C2×#124C2311yescharacteristic
128C2×#123—22no—
129C2×C22⋊Q8—24no—
130C2×C22⋊Q8—24no—
131C2×C22⋊Q8—24no—
132C2×C22⋊Q8—24no—
133C2×C22⋊Q8—416no—
134C2×#121—22no—
135C4×#41—24no—
136C4×#41—42no—
137C2×C4×Q8C2312yes—
138C2×C4×D4—22no—
139C2×C4×D4—22no—
140C2×C4×D4—22no—
141C2×C4×D4—42no—
142C2×C4×D4—42no—
143C2×C4×D4C2312yes—
144C2×C4×D4C2314yes—
145C2×#117—21no—
146C2×#117C2311yescharacteristic
147C2×#117C2311yescharacteristic
148C22×C4⋊C4—21no—
149C22×C4⋊C4—22no—
150C22×C4⋊C4—22no—
151C22×C4⋊C4D412yes—
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2311yescharacteristic
155C22×C22⋊C4—21no—
156C22×C22⋊C4—22no—
157C22×C22⋊C4—22no—
158C22×C42—21no—
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162#423—42no—
163C2×C4⋊C8C2314yes—
164#418—24no—
165#418—42no—
166#417—42no—
167#417—42no—
168#417—42no—
169#417—42no—
170#417—42no—
171#417—42no—
172C2×#103C2312yes—
173C2×#103C2312yes—
174C2×#103C2312yes—
175C2×#103C2312yes—
176C2×#103C2312yes—
177C2×#103C2312yes—
178C2×#102C2314yes—
179C2×#102C2312yes—
180C2×#102C2312yes—
181C2×#102C2312yes—
182C2×#102C2312yes—
183C2×#102C2312yes—
184C2×#102C2314yes—
185C2×#102C2312yes—
186C4×M16—42no—
187C2×#97C2312yes—
188C2×C4×C8C2312yes—
189#400—22no—
190#399—22no—
191#399—24no—
192#399—24no—
193#399—24no—
194#399—24no—
195#398—22no—
196#397—22no—
197#397—22no—
198#397—22no—
199#394—22no—
200#394—22no—
201#391C2312yes—
202#391C2312yes—
203#391C2312yes—
204#390—21no—
205#390—22no—
206#390—21no—
207#390C2312yes—
208#390C2314yes—
209#390C2312yes—
210#390C2312yes—
211#390C2312yes—
212#390C2312yes—
213#389C2312yes—
214#389C2312yes—
215#388—22no—
216#388—22no—
217#387—22no—
218#387—22no—
219#386—21no—
220#386—21no—
221#386—22no—
222#386—21no—
223#386—21no—
224#386—22no—
225#385—22no—
226#385—22no—
227#384—21no—
228#384—22no—
229#384—21no—
230#384C2314yes—
231#384C2312yes—
232#384C2312yes—
233#381—22no—
234C4×C4⋊C4—22no—
235C4×C4⋊C4D412yes—
236C4×C4⋊C4D412yes—
237C4×C4⋊C4C2312yes—
238C4×C4⋊C4C2312yes—
239C4×C22⋊C4—21no—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—21no—
243C2×#95D412yes—
244#340C2314yes—
245#340C2314yes—
246#340C2314yes—
247#340C2314yes—
248#340C2314yes—
249#340C2314yes—
250#336C2314yes—
251#336C2312yes—
252#336C2312yes—
253#336C2314yes—
254#336C2314yes—
255C25—21no—
256C2×#41—22no—
257C2×#41—22no—
258C2×#41—22no—
259C2×#41—22no—
260C2×#41—22no—
261C2×#41—22no—
262C2×#41—22no—
263C2×#41—22no—
264C2×#41—22no—
265C2×#41—22no—
266C2×#41—22no—
267C2×#41#4114yes—
268C22×Q8—24no—
269C22×Q8—48no—
270C22×Q8—44no—
271C22×Q8C2411yescharacteristic
272C22×Q8C2411yescharacteristic
273C22×D4—21no—
274C22×D4—21no—
275C22×D4—21no—
276C22×D4—22no—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4#4114yes—
283C22×D4C2411yescharacteristic
284C22×D4C2411yescharacteristic
285C22×D4C2412yes—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—24no—
292C23×C4—22no—
293C23×C4—44no—
294C23×C4—48no—
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D412yes—
297C23×C4C2×D412yes—
298C23×C4C2×D411yescharacteristic
299C23×C4C2411yescharacteristic
300AGL(1,ℤ/8)—416no—
301AGL(1,ℤ/8)—416no—
302C2×SD16—24no—
303C2×SD16—24no—
304C2×SD16—24no—
305C2×SD16—42no—
306C2×SD16—42no—
307C2×SD16—42no—
308C2×D8—24no—
309C2×D8—24no—
310C2×D8—24no—
311C2×D8—42no—
312C2×D8—42no—
313C2×D8—42no—
314C2×M16—22no—
315C2×M16—22no—
316C2×M16—22no—
317C2×M16—22no—
318C2×M16—22no—
319C2×M16—22no—
320C2×M16—22no—
321C2×M16—22no—
322C2×M16—22no—
323C2×M16—22no—
324C2×M16—22no—
325C2×M16—22no—
326C22×C8C2412yes—
327C22×C8C2412yes—
328C22×C8C2412yes—
329C22×C8C2412yes—
330C4⋊Q8—22no—
331C4⋊Q8—44no—
332C4⋊Q8—44no—
333C4⋊Q8—41no—
334C4⋊Q8—48no—
335#127—22no—
336#127—41no—
337#124—22no—
338#124—22no—
339#124—41no—
340#124—41no—
341#123—48no—
342C22⋊Q8—416no—
343C22⋊Q8—416no—
344C22⋊Q8—416no—
345C22⋊Q8—416no—
346#121—48no—
347C4×Q8—24no—
348C4×Q8—42no—
349C4×D4—24no—
350C4×D4—44no—
351C4×D4—44no—
352C4×D4—42no—
353C4×D4—48no—
354C4×D4—48no—
355C4×D4—48no—
356#117—22no—
357#117—22no—
358#117—22no—
359#117—22no—
360#117—44no—
361C2×C4⋊C4—28no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—48no—
381C2×C4⋊C4—48no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4C2×D412yes—
384C2×C4⋊C4C2×D412yes—
385C2×C4⋊C4C2×D412yes—
386C2×C4⋊C4C2×D412yes—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C4⋊C4C2412yes—
391C2×C4⋊C4C2412yes—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—48no—
410C2×C22⋊C4—48no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—22no—
420C2×C42—44no—
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D412yes—
423C2×C42C2×D412yes—
424C2×C42C2×D411yescharacteristic
425C2×C42C2412yes—
426C2×C42C2412yes—
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429C4⋊C8—44no—
430#103—42no—
431#103—42no—
432#103—42no—
433#103—42no—
434#103—42no—
435#103—42no—
436#102—28no—
437#102—42no—
438#102—42no—
439#102—42no—
440#102—42no—
441#102—42no—
442#102—42no—
443#102—44no—
444#97—42no—
445C4×C8—42no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95C2×D412yes—
455#95C2×D412yes—
456#95C2×D412yes—
457#95C2×D412yes—
458C24—24no—
459C24—22no—
460C24—21no—
461C24—21no—
462C24—44no—
463C24—44no—
464C24—42no—
465C24—42no—
466C24C22×D411yescharacteristic
467#41—28no—
468#41—28no—
469#41—44no—
470#41—44no—
471#41—44no—
472#41—44no—
473#41—44no—
474#41—44no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—48no—
487C2×Q8—48no—
488C2×Q8—48no—
489C2×Q8—816no—
490C2×Q8C2×#4112yes—
491C2×D4—24no—
492C2×D4—28no—
493C2×D4—24no—
494C2×D4—28no—
495C2×D4—21no—
496C2×D4—22no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—22no—
510C2×D4—21no—
511C2×D4—44no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—44no—
519C2×D4—42no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—82no—
523C2×D4C2×#4114yes—
524C2×D4C2×#4112yes—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—21no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—44no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—48no—
558C22×C4—44no—
559C22×C4—82no—
560C22×C4—816no—
561C22×C4C22×D412yes—
562C22×C4C22×D412yes—
563C22×C4C22×D412yes—
564C22×C4C22×D412yes—
565C22×C4C22×D412yes—
566C22×C4C22×D412yes—
567C22×C4C22×D411yescharacteristic
568C22×C4C2×#4112yes—
569C22×C4C2×#4112yes—
570C22×C4H(5,𝔽2)12yes—
571C22×C4H(5,𝔽2)12yes—
572C22×C4H(5,𝔽2)12yes—
573C22×C42−1+412yes—
574C22×C4C2511yescharacteristic
575SD16—48no—
576SD16—48no—
577D8—48no—
578D8—48no—
579M16—44no—
580M16—44no—
581M16—44no—
582M16—44no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—48no—
611C4⋊C4—48no—
612C4⋊C4—48no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—48no—
617C4⋊C4—48no—
618C4⋊C4—44no—
619C4⋊C4—82no—
620C4⋊C4AGL(1,ℤ/8)18yescomplemented
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—82no—
635C22⋊C4—82no—
636C22⋊C4—82no—
637C42—24no—
638C42—22no—
639C42—22no—
640C42—24no—
641C42—22no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—44no—
650C42—42no—
651C42—42no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—416no—
657C23—42no—
658C23—44no—
659C23—42no—
660C23—41no—
661C23—42no—
662C23—48no—
663C23—41no—
664C23—44no—
665C23—42no—
666C23—42no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—42no—
671C23—84no—
672C23—84no—
673C23—88no—
674C23#53512yes—
675C23#54612yes—
676C23#54812yes—
677C23C23×D411yescharacteristic
678Q8—22no—
679Q8—22no—
680Q8—41no—
681Q8—41no—
682Q8—41no—
683Q8—41no—
684Q8—41no—
685Q8—41no—
686Q8—816no—
687D4—24no—
688D4—22no—
689D4—22no—
690D4—24no—
691D4—48no—
692D4—41no—
693D4—41no—
694D4—42no—
695D4—41no—
696D4—48no—
697D4—41no—
698D4—42no—
699D4—41no—
700D4—41no—
701D4—88no—
702D4—84no—
703C2×C4—28no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—48no—
721C2×C4—48no—
722C2×C4—44no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—48no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—88no—
742C2×C4—816no—
743C2×C4—84no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4#53512yes—
748C2×C4#53814yes—
749C2×C4#53914yes—
750C2×C4#54612yes—
751C2×C4#54812yes—
752C2×C4#55114yes—
753C2×C4#56214yes—
754C2×C4C2×AGL(1,ℤ/8)14yes—
755C2×C4C2×AGL(1,ℤ/8)14yes—
756C2×C4C2×AGL(1,ℤ/8)14yes—
757C2×C4C22×#4111yescharacteristic
758C2×C4C22×#4111yescharacteristic
759C2×C4C2×H(5,𝔽2)11yescharacteristic
760C2×C4C2×H(5,𝔽2)11yescharacteristic
761C2×C4C2×H(5,𝔽2)11yescharacteristic
762C2×C4C2×2−1+411yescharacteristic
763C8—42no—
764C8—42no—
765C8—42no—
766C8—42no—
767C22—22no—
768C22—24no—
769C22—22no—
770C22—24no—
771C22—48no—
772C22—42no—
773C22—44no—
774C22—44no—
775C22—816no—
776C22—82no—
777C22—81no—
778C22—82no—
779C22—81no—
780C22—82no—
781C22—84no—
782C22—81no—
783C22—82no—
784C22—81no—
785C22—81no—
786C22—82no—
787C22#269614yes—
788C22C2×#53511yescharacteristic
789C22C2×#54611yescharacteristic
790C22C2×#54811yescharacteristic
791C22C22×AGL(1,ℤ/8)12yes—
792C22#358612yes—
793C4—24no—
794C4—24no—
795C4—24no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—42no—
800C4—82no—
801C4—82no—
802C4—82no—
803C4—82no—
804C4—81no—
805C4—82no—
806C4#269614yes—
807C4C2×#53811yescharacteristic
808C4C2×#53911yescharacteristic
809C4C2×#55111yescharacteristic
810C4C2×#56211yescharacteristic
811C2—24no—
812C2—82no—
813C2—84no—
814C2—161no—
815C2C2×#269611yescharacteristic
816C2#6079811yescharacteristic
817C2#6080711yescharacteristic
818C2#6116112yes—
819C2#6131712yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23428C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2542C2semidirect
2. #34744C2semidirect
3. #31656C2semidirect
4. #31654C2semidirect
5. #31636C2semidirect
6. #31634C2semidirect
7. #23745C2semidirect
8. #23630C2semidirect
9. #23546C2semidirect
10. #23452C2semidirect
11. #23452C2semidirect
13. #21200C2semidirect
14. #21095C2semidirect
15. #21023C2semidirect
16. #20928C2semidirect
17. #20925C2semidirect
18. #20925C2semidirect
19. #20648C2semidirect
41. #2448C22semidirect
42. #2447C22semidirect
43. #2446C22semidirect
44. #2445C22semidirect
59. #2100C22semidirect
60. #2099C22semidirect
61. #2072C22semidirect
62. #2071C22semidirect
65. #2024C22semidirect
66. #2024C22semidirect
67. #2023C22semidirect
68. #2023C22semidirect
73. #1959C22semidirect
74. #1959C22semidirect
75. #1957C22semidirect
76. #1956C22semidirect
79. #1917C22semidirect
80. #1916C22semidirect
87. #1803C22semidirect
88. #1802C22semidirect
620. C4⋊C4AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C2×#25422
#347442
#316562
#316542
#316362
#316342
#237452
#236302
#235462
#234522
#234282
#212002
#210952
#210232
#209282
#209252
#206482