Finite Group Databasebeta

← #6815273

Subgroups — #6815273

Order 512.

1866 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3231C211yesmaximal, characteristic, complemented
2C2×#3228C211yesmaximal, characteristic, complemented
3#36151C211yesmaximal, characteristic, complemented
4#36150C211yesmaximal, characteristic
5#33239C211yesmaximal, characteristic, complemented
6#31243C214yesmaximal, complemented
7#31191C214yesmaximal, complemented
8#29845C211yesmaximal, characteristic, complemented
9#29843C211yesmaximal, characteristic, complemented
10#28656C211yesmaximal, characteristic, complemented
11#28655C211yesmaximal, characteristic, complemented
12#26796C214yesmaximal, complemented
13#26794C214yesmaximal, complemented
14#25812C211yesmaximal, characteristic, complemented
15#25812C211yesmaximal, characteristic, complemented
16#25598C211yesmaximal, characteristic, complemented
17#25597C211yesmaximal, characteristic, complemented
18C4×#498C211yesmaximal, characteristic, complemented
19#21264C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C2×#533C2211yescharacteristic
23C2×#532C2211yescharacteristic
24#3231—28no—
25#3228—28no—
26C2×#500C2211yescharacteristic
27C2×#500C2211yescharacteristic
28C2×#498C2211yescharacteristic
29C2×#498C2211yescharacteristic
30C2×#492C2211yescharacteristic
31C2×#487C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#486C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#485C2214yes—
36C2×#482C2214yes—
37C2×#479C2214yes—
38C2×#478C2214yes—
39C2×#431C2211yescharacteristic
40C2×#431C2211yescharacteristic
41#2862C2211yescharacteristic
42#2858C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2856C2211yescharacteristic
47#2540—21no—
48#2536—21no—
49#2490C2212yes—
50#2489—21no—
51#2489C2212yes—
52#2454C2212yes—
53#2453—21no—
54#2453C2212yes—
55#2448—21no—
56#2427—21no—
57#2426—21no—
58#2426—21no—
59#2421—21no—
60#2421—21no—
61#2415—21no—
62#2415C2212yes—
63#2414C2212yes—
64#2407—21no—
65#2367—21no—
66#2363C2212yes—
67#2362—21no—
68#2362C2212yes—
69#2351—21no—
70#2341—21no—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2068C2214yes—
75#2067C2214yes—
76#2066C2214yes—
77#2065C2214yes—
78#2059C2214yes—
79#2059C2214yes—
80#2035C2214yes—
81#2034C2214yes—
82#2000C2214yes—
83#2000C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1968C2214yes—
89#1968C2214yes—
90#1957C2211yescharacteristic
91#1956C2211yescharacteristic
92#1954C2212yes—
93#1941C2214yes—
94#1939C2212yes—
95#1928C2214yes—
96#1925C2214yes—
97#1923C2212yes—
98#1923C2212yes—
99#1880C2214yes—
100#1877C2214yes—
101#1854C2214yes—
102#1854C2214yes—
103#1844C2211yescharacteristic
104C4×#106C2214yes—
105C4×C4⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108C42×C8C2211yescharacteristic
109C22×#41—21no—
110C22×SD16C2314yes—
111#533—24no—
112#533—24no—
113#533—24no—
114#533—42no—
115#533—42no—
116#533—42no—
117#532—24no—
118#532—42no—
119C2×C4⋊Q8C2311yescharacteristic
120C2×C4⋊Q8C2311yescharacteristic
121C2×C4⋊Q8C2311yescharacteristic
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2311yescharacteristic
124C2×#127C2311yescharacteristic
125C2×#125—21no—
126C2×#125C2312yes—
127C2×#125C2312yes—
128C2×#124—21no—
129C2×#124—21no—
130C2×#124—21no—
131C2×C22⋊Q8—21no—
132C2×C22⋊Q8—21no—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8—21no—
135C2×C22⋊Q8—21no—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8C2312yes—
139C2×C22⋊Q8C2312yes—
140C2×#121—21no—
141C2×#121—21no—
142C2×#121—21no—
143C2×#121C2312yes—
144C2×#121C2312yes—
145C2×C4×Q8—21no—
146C2×C4×Q8—21no—
147C2×C4×Q8—21no—
148C2×C4×Q8—21no—
149C2×C4×Q8—21no—
150C2×C4×Q8—21no—
151C2×C4×Q8—21no—
152C2×C4×Q8C2312yes—
153C2×C4×D4—21no—
154C2×C4×D4D411yescharacteristic
155C2×C4×D4D411yescharacteristic
156C2×C4×D4C2312yes—
157C2×C4×D4C2311yescharacteristic
158C2×#117—21no—
159C2×#117C2312yes—
160C2×#117C2312yes—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163#500—24no—
164#500—24no—
165#498—42no—
166#498D418yescomplemented
167#492—42no—
168#487—24no—
169#487—24no—
170#486—24no—
171#486—24no—
172#485—216no—
173#482—216no—
174#479—216no—
175#478—216no—
176#431—24no—
177#431—24no—
178C2×#107C2314yes—
179C2×#107C2314yes—
180C2×#106C2314yes—
181C2×#106C2314yes—
182C2×#106C2314yes—
183C2×C4⋊C8C2312yes—
184C2×C4⋊C8C2312yes—
185C2×C4⋊C8C2312yes—
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×#103C2314yes—
189C2×#102C2314yes—
190C2×#102C2314yes—
191C2×#102C2314yes—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196C2×C4×C8C2311yescharacteristic
197C2×C4×C8C2311yescharacteristic
198C2×C4×C8C2311yescharacteristic
199C2×C4×C8C2312yes—
200C2×C4×C8C2312yes—
201C2×C4×C8C2311yescharacteristic
202#400—22no—
203#400—22no—
204#399—22no—
205#398—22no—
206#397—22no—
207#397—22no—
208#397—22no—
209#396—22no—
210#394—22no—
211#394—22no—
212#394—22no—
213#392—22no—
214#391—21no—
215#391—21no—
216#391—21no—
217#391—21no—
218#391—21no—
219#391—21no—
220#391C2312yes—
221#391C2312yes—
222#391C2312yes—
223#390—22no—
224#390—22no—
225#390—22no—
226#390—21no—
227#390—21no—
228#390—21no—
229#390—21no—
230#390C2312yes—
231#390C2312yes—
232#390C2312yes—
233#389—22no—
234#389—22no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389C2312yes—
242#389C2312yes—
243#389C2312yes—
244#389C2312yes—
245#388—22no—
246#388—22no—
247#388—22no—
248#388—22no—
249#388—22no—
250#388—22no—
251#388—22no—
252#387—22no—
253#387—22no—
254#386—22no—
255#385—22no—
256#384C2311yescharacteristic
257#384C2311yescharacteristic
258#382—21no—
259#382—21no—
260#382—22no—
261#380—21no—
262#380—21no—
263#380—21no—
264#380—21no—
265#380—22no—
266#380C2312yes—
267#380C2312yes—
268C4×C4⋊C4—21no—
269C4×C4⋊C4—21no—
270C4×C4⋊C4—22no—
271C4×C4⋊C4D411yescharacteristic
272C4×C4⋊C4D411yescharacteristic
273C4×C4⋊C4C2312yes—
274C4×C4⋊C4C2312yes—
275C4×C4⋊C4C2311yescharacteristic
276C4×C22⋊C4—22no—
277C4×C22⋊C4D411yescharacteristic
278C4×C22⋊C4D411yescharacteristic
279C4×C22⋊C4D411yescharacteristic
280C4×C22⋊C4D411yescharacteristic
281C4×C22⋊C4C2311yescharacteristic
282C4×C22⋊C4C2311yescharacteristic
283C43C2311yescharacteristic
284#340C2314yes—
285#340C2314yes—
286#340C2314yes—
287#340C2314yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291C2×#41—44no—
292C2×#41—44no—
293C2×#41—82no—
294C22×Q8—21no—
295C22×Q8—21no—
296C22×Q8—21no—
297C22×Q8—21no—
298C22×Q8C2412yes—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—21no—
302C22×D4—21no—
303C22×D4C2×D411yescharacteristic
304C22×D4C2412yes—
305C23×C4—22no—
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C2×SD16—28no—
313C2×SD16—44no—
314C2×SD16—44no—
315C22×C8C2412yes—
316C22×C8C2412yes—
317C22×C8C2412yes—
318C22×C8C2412yes—
319C4⋊Q8—22no—
320C4⋊Q8—22no—
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326C4⋊Q8—22no—
327C4⋊Q8C2×D414yes—
328C4⋊Q8C2×D414yes—
329#127—22no—
330#127—22no—
331#125—24no—
332#125—24no—
333#125—42no—
334#125—42no—
335#125—44no—
336#124—44no—
337#124—44no—
338#124—82no—
339C22⋊Q8—24no—
340C22⋊Q8—44no—
341C22⋊Q8—42no—
342C22⋊Q8—44no—
343C22⋊Q8—44no—
344C22⋊Q8—44no—
345C22⋊Q8—44no—
346C22⋊Q8—44no—
347C22⋊Q8—44no—
348C22⋊Q8—82no—
349#121—24no—
350#121—44no—
351#121—42no—
352#121—44no—
353#121—82no—
354#121—82no—
355C4×Q8—24no—
356C4×Q8—42no—
357C4×Q8—44no—
358C4×Q8—44no—
359C4×Q8—44no—
360C4×Q8—44no—
361C4×Q8—44no—
362C4×Q8—44no—
363C4×Q8—82no—
364C4×D4—24no—
365C4×D4—24no—
366C4×D4—42no—
367C4×D4—44no—
368C4×D4—42no—
369C4×D4—42no—
370#117—24no—
371#117—24no—
372#117—42no—
373#117—42no—
374#117—44no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
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—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4C2×D411yescharacteristic
397C2×C4⋊C4C2×D411yescharacteristic
398C2×C4⋊C4C2×D411yescharacteristic
399C2×C4⋊C4C2412yes—
400C2×C4⋊C4C2412yes—
401C2×C4⋊C4C2412yes—
402C2×C4⋊C4C2412yes—
403C2×C4⋊C4C2412yes—
404C2×C4⋊C4C2412yes—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
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⋊C4C2×D411yescharacteristic
421C2×C22⋊C4C2×D411yescharacteristic
422C2×C22⋊C4C2×D411yescharacteristic
423C2×C22⋊C4C2×D411yescharacteristic
424C2×C22⋊C4C2×D411yescharacteristic
425C2×C22⋊C4C2×D411yescharacteristic
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2411yescharacteristic
444C2×C42C2411yescharacteristic
445C2×C42C2411yescharacteristic
446C2×C42C2411yescharacteristic
447C2×C42C2411yescharacteristic
448#107—28no—
449#107—28no—
450#106—44no—
451#106—44no—
452#106C2×D4116yes—
453C4⋊C8—24no—
454C4⋊C8—24no—
455C4⋊C8—42no—
456#103—28no—
457#103—28no—
458#103—44no—
459#102—28no—
460#102—28no—
461#102—44no—
462C22⋊C8—24no—
463C22⋊C8—24no—
464C22⋊C8—24no—
465C22⋊C8—24no—
466C4×C8—24no—
467C4×C8—22no—
468C4×C8—22no—
469C4×C8—22no—
470C4×C8—42no—
471C4×C8C2×D414yes—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95C2×D411yescharacteristic
487#95C2×D411yescharacteristic
488#95C2×D411yescharacteristic
489#95C2×D411yescharacteristic
490#95C2×D411yescharacteristic
491#95C2×D411yescharacteristic
492C24—22no—
493C24C22×D411yescharacteristic
494C24C22×D411yescharacteristic
495#41—816no—
496C2×Q8—24no—
497C2×Q8—24no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—24no—
501C2×Q8—24no—
502C2×Q8—42no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8—42no—
506C2×Q8—42no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—82no—
529C2×D4—82no—
530C2×D4—82no—
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—21no—
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—22no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—82no—
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
574SD16—88no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8C22×D414yes—
586C2×C82−1+414yes—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—41no—
599C4⋊C4—41no—
600C4⋊C4—44no—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C4⋊C4—44no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—44no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—82no—
618C4⋊C4—82no—
619C4⋊C4C22×D414yes—
620C4⋊C4C22×D414yes—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—41no—
624C22⋊C4—41no—
625C22⋊C4—41no—
626C22⋊C4—41no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—82no—
638C22⋊C4—82no—
639C22⋊C4—82no—
640C22⋊C4—82no—
641C22⋊C4—82no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—22no—
654C42—22no—
655C42—44no—
656C42—44no—
657C42—44no—
658C42—44no—
659C42—82no—
660C42#13514yes—
661C42C22×D412yes—
662C42H(5,𝔽2)12yes—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
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—
684C23C23×D411yescharacteristic
685Q8—48no—
686Q8—48no—
687Q8—44no—
688Q8—44no—
689Q8—84no—
690Q8—84no—
691D4—44no—
692D4—44no—
693D4—44no—
694D4—88no—
695D4—84no—
696D4—84no—
697D4—164no—
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—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—21no—
714C2×C4—21no—
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—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
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—88no—
756C2×C4D4212yes—
757C2×C4D4212yes—
758C2×C4C2×#13512yes—
759C2×C4C2×#13512yes—
760C2×C4C2×#13512yes—
761C2×C4#57512yes—
762C2×C4#57712yes—
763C2×C4#57712yes—
764C2×C4C23×D411yescharacteristic
765C2×C4C2×H(5,𝔽2)11yescharacteristic
766C2×C4C2×2−1+412yes—
767C2×C4#58512yes—
768C8—24no—
769C8—24no—
770C8—42no—
771C8—42no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22#344911yescharacteristic
794C22C2×D4211yescharacteristic
795C22#349911yescharacteristic
796C22C22×#13511yescharacteristic
797C22C2×#57511yescharacteristic
798C22C2×#57711yescharacteristic
799C22C2×#57711yescharacteristic
800C4—22no—
801C4—22no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—44no—
807C4—41no—
808C4—41no—
809C4—44no—
810C4—41no—
811C4—41no—
812C4—82no—
813C4—82no—
814C4—82no—
815C4—82no—
816C4—82no—
817C4#327514yes—
818C4#328414yes—
819C4#349712yes—
820C4#356112yes—
821C2—81no—
822C2—81no—
823C2—162no—
824C2#3935611yescharacteristic
825C2#6094411yescharacteristic
826C2#6101211yescharacteristic
827C2C2×#327511yescharacteristic
828C2C2×#328411yescharacteristic
829C2#6247011yescharacteristic
830C2#6248311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36150C2
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
1. C2×#3231C2semidirect
2. C2×#3228C2semidirect
3. #36151C2semidirect
5. #33239C2semidirect
6. #31243C2semidirect
7. #31191C2semidirect
8. #29845C2semidirect
9. #29843C2semidirect
10. #28656C2semidirect
11. #28655C2semidirect
12. #26796C2semidirect
13. #26794C2semidirect
14. #25812C2semidirect
15. #25812C2semidirect
16. #25598C2semidirect
17. #25597C2semidirect
18. C4×#498C2semidirect
19. #21264C2semidirect
166. #498D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32312
C2×#32282
#361512
#361502
#332392
#312432
#311912
#298452
#298432
#286562
#286552
#267962
#267942
#258122
#255982
#255972
C4×#4982
#212642