Finite Group Databasebeta

← #6763398

Subgroups — #6763398

Order 512.

2050 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36179C211yesmaximal, characteristic
2#36129C211yesmaximal, characteristic, complemented
3#33042C211yesmaximal, characteristic, complemented
4#31836C214yesmaximal, complemented
5#31636C214yesmaximal, complemented
6#30205C211yesmaximal, characteristic, complemented
7#29807C211yesmaximal, characteristic, complemented
8#29141C211yesmaximal, characteristic, complemented
9#28613C211yesmaximal, characteristic, complemented
10#27972C211yesmaximal, characteristic, complemented
11#27960C211yesmaximal, characteristic, complemented
12#25718C211yesmaximal, characteristic, complemented
13#25598C211yesmaximal, characteristic, complemented
14#24528C214yesmaximal, complemented
15#23961C214yesmaximal, complemented
16#22268C211yesmaximal, characteristic, complemented
17#21860C211yesmaximal, characteristic, complemented
18C2×#1956C211yesmaximal, characteristic, complemented
19#21101C211yesmaximal, characteristic, complemented
20C2×#547—21no—
21C2×#547—21no—
22C2×#547C2212yes—
23C2×#533C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25C2×#492C2211yescharacteristic
26C2×#492C2211yescharacteristic
27C2×#486C2211yescharacteristic
28C2×#448C2214yes—
29C2×#431C2211yescharacteristic
30C22×#103C2214yes—
31C22×C4×C8C2211yescharacteristic
32#2868C2211yescharacteristic
33#2862C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2856C2211yescharacteristic
37#2856C2211yescharacteristic
38#2550—21no—
39#2542—21no—
40#2542—21no—
41#2542C2212yes—
42#2501—21no—
43#2501—21no—
44#2501—21no—
45#2501—21no—
46#2501C2212yes—
47#2501C2212yes—
48#2492—21no—
49#2451—21no—
50#2446C2212yes—
51#2442—21no—
52#2439—21no—
53#2429C2212yes—
54#2417—21no—
55#2409C2212yes—
56#2360—21no—
57#2352—21no—
58Q8×C22⋊C4C2212yes—
59C4×C4⋊Q8C2211yescharacteristic
60C4×#127C2211yescharacteristic
61C2×#384C2211yescharacteristic
62C2×#384C2211yescharacteristic
63C42×D4C2211yescharacteristic
64#2099C2214yes—
65#2072C2214yes—
66#2072C2214yes—
67#2055C2214yes—
68#2055C2214yes—
69#2024C2214yes—
70#2024C2214yes—
71#2013C2214yes—
72#2000C2214yes—
73#2000C2214yes—
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1957C2211yescharacteristic
78#1956C2211yescharacteristic
79#1956C2211yescharacteristic
80#1956C2214yes—
81#1956C2211yescharacteristic
82#1956C2211yescharacteristic
83#1956C2211yescharacteristic
84#1956C2211yescharacteristic
85#1934C2214yes—
86#1923C2212yes—
87#1916C2212yes—
88#1893C2214yes—
89#1880C2214yes—
90#1880C2214yes—
91#1877C2214yes—
92#1877C2214yes—
93#1872C2214yes—
94#1872C2214yes—
95#1869C2212yes—
96#1850C2212yes—
97#1834C2211yescharacteristic
98#1834C2211yescharacteristic
99#1834C2211yescharacteristic
100#1823C2214yes—
101#1803C2214yes—
102#1803C2214yes—
103C4×C4⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106#1744C2211yescharacteristic
107C22×#41—22no—
108C23×Q8C2312yes—
109C22×SD16C2314yes—
110C22×SD16C2314yes—
111C23×C8C2312yes—
112#547—48no—
113#547—48no—
114#547—48no—
115#533—24no—
116#533—42no—
117C2×C4⋊Q8—24no—
118C2×C4⋊Q8—21no—
119C2×C4⋊Q8—21no—
120C2×C4⋊Q8—21no—
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8—42no—
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2312yes—
125C2×C4⋊Q8C2311yescharacteristic
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2312yes—
128C2×#127C2311yescharacteristic
129C2×#125—21no—
130C2×#123—22no—
131C2×#123—22no—
132C2×#123—22no—
133C2×#123—22no—
134C2×#123—22no—
135C2×#123—22no—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8—22no—
139C2×C22⋊Q8—22no—
140C2×C22⋊Q8—22no—
141C2×C22⋊Q8C2312yes—
142C2×C22⋊Q8C2312yes—
143C2×#121—21no—
144C2×#121—21no—
145C2×#121—21no—
146C2×#121—21no—
147C2×#121C2312yes—
148C2×#121C2312yes—
149C2×C4×Q8—21no—
150C2×C4×Q8C2312yes—
151C2×C4×Q8C2312yes—
152C2×C4×D4—21no—
153C2×C4×D4—21no—
154C2×C4×D4D411yescharacteristic
155C2×C4×D4D411yescharacteristic
156C2×C4×D4C2312yes—
157C2×C4×D4C2311yescharacteristic
158C2×#117—21no—
159C22×C4⋊C4—21no—
160C22×C4⋊C4—21no—
161C22×C4⋊C4—21no—
162C22×C4⋊C4—21no—
163C22×C4⋊C4—21no—
164C22×C4⋊C4—21no—
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2312yes—
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169#492—24no—
170#492—42no—
171#486—42no—
172#448—48no—
173#431—42no—
174C2×C4⋊C8C2312yes—
175C2×C4⋊C8C2312yes—
176C2×#103—48no—
177C2×#103C2314yes—
178C2×#103C2314yes—
179C2×#103C2314yes—
180C2×#103C2314yes—
181C2×#103C2314yes—
182C2×#103C2314yes—
183C2×#102C2314yes—
184C2×#102C2314yes—
185C2×C22⋊C8C2312yes—
186C2×C22⋊C8C2312yes—
187C2×C22⋊C8C2312yes—
188C2×C4×C8—42no—
189C2×C4×C8C2311yescharacteristic
190C2×C4×C8C2311yescharacteristic
191C2×C4×C8C2311yescharacteristic
192C2×C4×C8C2311yescharacteristic
193C2×C4×C8C2312yes—
194#400—22no—
195#399—22no—
196#399—22no—
197#399—22no—
198#399—22no—
199#399—22no—
200#399—22no—
201#398—22no—
202#398—22no—
203#396—22no—
204#395—22no—
205#393—22no—
206#391—21no—
207#391—21no—
208#391—21no—
209#391—22no—
210#391—22no—
211#391C2312yes—
212#391C2312yes—
213#391C2312yes—
214#391C2312yes—
215#390—21no—
216#390—21no—
217#390—21no—
218#390—21no—
219#390—21no—
220#390—21no—
221#390C2312yes—
222#390C2312yes—
223#390C2312yes—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—21no—
228#389—21no—
229#389—22no—
230#389C2312yes—
231#388—22no—
232#387—22no—
233#387—22no—
234#386—22no—
235#385—22no—
236#384—21no—
237#384—21no—
238#384—21no—
239#384—21no—
240#384—21no—
241#384—21no—
242#384C2311yescharacteristic
243#384C2311yescharacteristic
244#384C2312yes—
245#384C2312yes—
246#384C2311yescharacteristic
247#384C2311yescharacteristic
248#384C2312yes—
249#382—21no—
250#382—21no—
251#380—21no—
252#380—21no—
253#380—21no—
254#380—22no—
255#380C2312yes—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4D411yescharacteristic
259C4×C4⋊C4D411yescharacteristic
260C4×C4⋊C4C2311yescharacteristic
261C4×C22⋊C4—22no—
262C4×C22⋊C4D411yescharacteristic
263C4×C22⋊C4D411yescharacteristic
264C4×C22⋊C4D411yescharacteristic
265C4×C22⋊C4D411yescharacteristic
266C4×C22⋊C4C2311yescharacteristic
267C4×C22⋊C4C2311yescharacteristic
268C43C2311yescharacteristic
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#336C2312yes—
276#336C2312yes—
277#336C2312yes—
278#336C2312yes—
279#336C2312yes—
280C2×#41—48no—
281C2×#41—48no—
282C2×#41—48no—
283C22×Q8—21no—
284C22×Q8—22no—
285C22×Q8—22no—
286C22×Q8—24no—
287C22×Q8—28no—
288C22×Q8—42no—
289C22×Q8—44no—
290C22×Q8C2412yes—
291C22×Q8C2412yes—
292C22×D4—22no—
293C22×D4—22no—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4C2×D411yescharacteristic
297C22×D4C2412yes—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C2×SD16—28no—
309C2×SD16—44no—
310C2×SD16—44no—
311C2×SD16—44no—
312C2×SD16—44no—
313C2×SD16—44no—
314C22×C8—24no—
315C22×C8—42no—
316C22×C8—42no—
317C22×C8C2412yes—
318C22×C8C2412yes—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C4⋊Q8—24no—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326C4⋊Q8—22no—
327C4⋊Q8—44no—
328C4⋊Q8—44no—
329C4⋊Q8—44no—
330C4⋊Q8—42no—
331C4⋊Q8—44no—
332C4⋊Q8—44no—
333C4⋊Q8#4114yescomplemented
334#127—22no—
335#127—22no—
336#125—44no—
337#123—48no—
338#123—48no—
339#123—48no—
340#123—48no—
341#123—48no—
342#123—48no—
343C22⋊Q8—24no—
344C22⋊Q8—42no—
345C22⋊Q8—44no—
346C22⋊Q8—48no—
347C22⋊Q8—48no—
348C22⋊Q8—44no—
349C22⋊Q8—48no—
350C22⋊Q8—44no—
351#121—28no—
352#121—44no—
353#121—44no—
354#121—44no—
355#121—44no—
356#121—44no—
357C4×Q8—24no—
358C4×Q8—42no—
359C4×Q8—44no—
360C4×Q8—44no—
361C4×D4—24no—
362C4×D4—24no—
363C4×D4—44no—
364C4×D4—44no—
365C4×D4—44no—
366C4×D4SD1618yescomplemented
367#117—44no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—28no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—44no—
399C2×C4⋊C4—44no—
400C2×C4⋊C4—44no—
401C2×C4⋊C4—44no—
402C2×C4⋊C4—44no—
403C2×C4⋊C4—44no—
404C2×C4⋊C4—44no—
405C2×C4⋊C4C2×D411yescharacteristic
406C2×C4⋊C4C2×D411yescharacteristic
407C2×C4⋊C4C2×D411yescharacteristic
408C2×C4⋊C4C2412yes—
409C2×C4⋊C4C2412yes—
410C2×C4⋊C4C2412yes—
411C2×C4⋊C4C2412yes—
412C2×C4⋊C4C2412yes—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4C2×D411yescharacteristic
426C2×C22⋊C4C2×D411yescharacteristic
427C2×C22⋊C4C2×D411yescharacteristic
428C2×C22⋊C4C2×D411yescharacteristic
429C2×C22⋊C4C2×D411yescharacteristic
430C2×C22⋊C4C2×D411yescharacteristic
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2411yescharacteristic
446C2×C42C2411yescharacteristic
447C2×C42C2411yescharacteristic
448C2×C42C2411yescharacteristic
449C2×C42C2411yescharacteristic
450C4⋊C8—42no—
451C4⋊C8—42no—
452#103—44no—
453#103—44no—
454#103—44no—
455#103—44no—
456#103—44no—
457#103—44no—
458#102—44no—
459#102—44no—
460C22⋊C8—24no—
461C22⋊C8—42no—
462C22⋊C8—42no—
463C4×C8—22no—
464C4×C8—22no—
465C4×C8—22no—
466C4×C8—22no—
467C4×C8—42no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95C2×D411yescharacteristic
479#95C2×D411yescharacteristic
480#95C2×D411yescharacteristic
481#95C2×D411yescharacteristic
482#95C2×D411yescharacteristic
483#95C2×D411yescharacteristic
484C24—22no—
485C24C22×D411yescharacteristic
486C24C22×D411yescharacteristic
487#41—832no—
488C2×Q8—22no—
489C2×Q8—22no—
490C2×Q8—24no—
491C2×Q8—24no—
492C2×Q8—22no—
493C2×Q8—24no—
494C2×Q8—24no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—416no—
499C2×Q8—44no—
500C2×Q8—42no—
501C2×Q8—44no—
502C2×Q8—42no—
503C2×Q8—42no—
504C2×Q8—82no—
505C2×Q8—88no—
506C2×Q8C2×#4114yes—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—24no—
512C2×D4—24no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—44no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4C2×SD1614yes—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—82no—
561C22×C4C2×SD1614yes—
562C22×C4C2×SD1614yes—
563C22×C4AGL(1,ℤ/8)14yes—
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4H(5,𝔽2)14yes—
577C22×C4C2511yescharacteristic
578SD16—88no—
579SD16—88no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
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—48no—
593C4⋊C4—22no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—44no—
625C4⋊C4—42no—
626C4⋊C4—44no—
627C4⋊C4—42no—
628C4⋊C4—82no—
629C4⋊C4—82no—
630C4⋊C4C2×SD1614yes—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—82no—
647C22⋊C4C2×SD1614yes—
648C22⋊C4C2×SD1614yes—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—22no—
653C42—22no—
654C42—22no—
655C42—22no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—22no—
661C42—22no—
662C42—44no—
663C42—82no—
664C42C2×SD1614yes—
665C42C2×#4112yes—
666C42H(5,𝔽2)12yes—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23#53512yes—
685C23C22×SD1612yes—
686C23C22×SD1612yes—
687C23C2×AGL(1,ℤ/8)12yes—
688C23C23×D411yescharacteristic
689Q8—28no—
690Q8—44no—
691Q8—44no—
692Q8—44no—
693Q8—88no—
694Q8—88no—
695Q8—84no—
696D4—28no—
697D4—44no—
698D4—44no—
699D4—88no—
700D4—88no—
701D4—84no—
702D4—84no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—24no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—44no—
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—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—88no—
757C2×C4—88no—
758C2×C4—88no—
759C2×C4—88no—
760C2×C4#53512yes—
761C2×C4#54612yes—
762C2×C4#54612yes—
763C2×C4C22×SD1612yes—
764C2×C4C22×SD1612yes—
765C2×C4C22×SD1612yes—
766C2×C4C22×SD1612yes—
767C2×C4C22×SD1612yes—
768C2×C4C2×AGL(1,ℤ/8)12yes—
769C2×C4C2×AGL(1,ℤ/8)12yes—
770C2×C4#57812yes—
771C2×C4#57812yes—
772C2×C4C22×#4111yescharacteristic
773C2×C4C2×H(5,𝔽2)12yes—
774C2×C4C2×H(5,𝔽2)11yescharacteristic
775C2×C4#58512yes—
776C8—42no—
777C8—42no—
778C8—42no—
779C8—42no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22#320814yes—
801C22C2×#53511yescharacteristic
802C22C2×#54611yescharacteristic
803C22#350011yescharacteristic
804C22C23×SD1611yescharacteristic
805C22C22×AGL(1,ℤ/8)11yescharacteristic
806C22C2×#57811yescharacteristic
807C22C2×#57811yescharacteristic
808C4—22no—
809C4—22no—
810C4—22no—
811C4—22no—
812C4—22no—
813C4—22no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—44no—
818C4—41no—
819C4—82no—
820C4—82no—
821C4—82no—
822C4—82no—
823C4—82no—
824C4—82no—
825C4#329814yes—
826C4#330814yes—
827C4#351312yes—
828C4#354212yes—
829C2—24no—
830C2—42no—
831C2—162no—
832C2#3808211yescharacteristic
833C2C2×#320811yescharacteristic
834C2#6082111yescharacteristic
835C2C2×#329811yescharacteristic
836C2C2×#330811yescharacteristic
837C2#6252611yescharacteristic
838C2#6253811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36179C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36129C2semidirect
3. #33042C2semidirect
4. #31836C2semidirect
5. #31636C2semidirect
6. #30205C2semidirect
7. #29807C2semidirect
8. #29141C2semidirect
9. #28613C2semidirect
10. #27972C2semidirect
11. #27960C2semidirect
12. #25718C2semidirect
13. #25598C2semidirect
14. #24528C2semidirect
15. #23961C2semidirect
16. #22268C2semidirect
17. #21860C2semidirect
18. C2×#1956C2semidirect
19. #21101C2semidirect
333. C4⋊Q8#41semidirect
366. C4×D4SD16semidirect

Maximal subgroups

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

subgroupindex
#361792
#361292
#330422
#318362
#316362
#302052
#298072
#291412
#286132
#279722
#279602
#257182
#255982
#245282
#239612
#222682
#218602
C2×#19562
#211012