Finite Group Databasebeta

← #6816621

Subgroups — #6816621

Order 512.

1945 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3228C211yesmaximal, characteristic, complemented
2C2×#3227C211yesmaximal, characteristic, complemented
3#36149C211yesmaximal, characteristic
4#36129C211yesmaximal, characteristic, complemented
5#33313C211yesmaximal, characteristic, complemented
6#31090C214yesmaximal, complemented
7#31088C214yesmaximal, complemented
8#29877C211yesmaximal, characteristic, complemented
9#29877C211yesmaximal, characteristic, complemented
10#28718C211yesmaximal, characteristic, complemented
11#28688C211yesmaximal, characteristic, complemented
12#26051C214yesmaximal, complemented
13#25813C211yesmaximal, characteristic, complemented
14#25812C211yesmaximal, characteristic, complemented
15#25673C211yesmaximal, characteristic, complemented
16#25673C211yesmaximal, characteristic, complemented
17#25018C214yesmaximal, complemented
18C4×#486C211yesmaximal, characteristic, complemented
19#21264C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#532C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24#3228—28no—
25#3227—28no—
26C2×#500C2211yescharacteristic
27C2×#500C2211yescharacteristic
28C2×#500C2211yescharacteristic
29C2×#498C2211yescharacteristic
30C2×#498C2211yescharacteristic
31C2×#498C2211yescharacteristic
32C2×#486C2211yescharacteristic
33C2×#486C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#481C2214yes—
36C2×#482C2214yes—
37C2×#478C2214yes—
38C2×#476C2214yes—
39C2×#431C2211yescharacteristic
40C2×#431C2211yescharacteristic
41#2862C2211yescharacteristic
42#2862C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2550C2212yes—
48#2535C2212yes—
49#2492—21no—
50#2451—21no—
51#2447—21no—
52#2447—21no—
53#2446—21no—
54#2442C2212yes—
55#2439C2212yes—
56#2429—21no—
57#2427—21no—
58#2427—21no—
59#2420C2212yes—
60#2420C2212yes—
61#2417—21no—
62#2409—21no—
63#2407—21no—
64#2407—21no—
65#2360—21no—
66#2352C2212yes—
67#2349C2212yes—
68Q8×C22⋊C4—21no—
69#2339—21no—
70#2339—21no—
71C4×C4⋊Q8C2211yescharacteristic
72C4×#127C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2088C2214yes—
75#2088C2214yes—
76#2085C2214yes—
77#2077C2214yes—
78#2077C2214yes—
79#2073C2214yes—
80#2059C2214yes—
81#2057C2214yes—
82#2033C2214yes—
83#2033C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1990C2211yescharacteristic
89#1957C2211yescharacteristic
90#1954C2212yes—
91#1949C2214yes—
92#1939C2212yes—
93#1934C2214yes—
94#1923C2212yes—
95#1923C2212yes—
96#1862C2214yes—
97#1862C2214yes—
98#1854C2214yes—
99#1852C2214yes—
100#1846C2214yes—
101#1846C2214yes—
102#1834C2211yescharacteristic
103#1804C2214yes—
104C4×C4⋊C8C2211yescharacteristic
105C4×#102C2214yes—
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108C42×C8C2211yescharacteristic
109C22×#41—21no—
110C22×#41—21no—
111C23×Q8—21no—
112#533—24no—
113#533—42no—
114#532—24no—
115#532—24no—
116#532—42no—
117#532—42no—
118C2×C4⋊Q8—24no—
119C2×C4⋊Q8—21no—
120C2×C4⋊Q8—21no—
121C2×C4⋊Q8—42no—
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2311yescharacteristic
126C2×C4⋊Q8C2312yes—
127C2×C4⋊Q8C2311yescharacteristic
128C2×#127C2311yescharacteristic
129C2×#125C2312yes—
130C2×#124—21no—
131C2×#124—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×#121—21no—
139C2×#121—21no—
140C2×#121C2312yes—
141C2×#121C2312yes—
142C2×C4×Q8—21no—
143C2×C4×Q8—21no—
144C2×C4×Q8—21no—
145C2×C4×D4—21no—
146C2×C4×D4—21no—
147C2×C4×D4—21no—
148C2×C4×D4—21no—
149C2×C4×D4D411yescharacteristic
150C2×C4×D4D411yescharacteristic
151C2×C4×D4C2312yes—
152C2×C4×D4C2312yes—
153C2×C4×D4C2312yes—
154C2×C4×D4C2311yescharacteristic
155C2×#117C2312yes—
156C22×C4⋊C4—21no—
157C22×C4⋊C4C2312yes—
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160#500—24no—
161#500—42no—
162#500—42no—
163#498—24no—
164#498—24no—
165#498—24no—
166#486—24no—
167#486—24no—
168#486D418yescomplemented
169#482—216no—
170#481—216no—
171#478—216no—
172#476—216no—
173#431—24no—
174#431—24no—
175C2×#107C2314yes—
176C2×#107C2314yes—
177C2×#107C2314yes—
178C2×#106C2314yes—
179C2×#106C2314yes—
180C2×#106C2314yes—
181C2×C4⋊C8C2312yes—
182C2×C4⋊C8C2312yes—
183C2×C4⋊C8C2312yes—
184C2×#102C2314yes—
185C2×#102C2314yes—
186C2×#102C2314yes—
187C2×#102C2314yes—
188C2×C22⋊C8C2312yes—
189C2×C22⋊C8C2312yes—
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2312yes—
192C2×C4×C8C2312yes—
193C2×C4×C8C2312yes—
194C2×C4×C8C2311yescharacteristic
195C2×C4×C8C2311yescharacteristic
196C2×C4×C8C2311yescharacteristic
197C2×C4×C8C2311yescharacteristic
198#400—22no—
199#398—22no—
200#398—22no—
201#397—22no—
202#397—22no—
203#397—22no—
204#396—22no—
205#395—22no—
206#394—22no—
207#394—22no—
208#393—22no—
209#392—22no—
210#391—21no—
211#391—21no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391—21no—
216#391—21no—
217#391—21no—
218#391—21no—
219#391—21no—
220#391—21no—
221#391—21no—
222#391—21no—
223#391—22no—
224#391—22no—
225#390—21no—
226#390—21no—
227#390C2312yes—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389—21no—
233#389—22no—
234#389C2312yes—
235#389C2312yes—
236#389C2312yes—
237#389C2312yes—
238#389C2312yes—
239#388—22no—
240#387—22no—
241#387—22no—
242#386—22no—
243#386—22no—
244#386—22no—
245#386—22no—
246#386—22no—
247#385—22no—
248#385—22no—
249#385—22no—
250#384C2311yescharacteristic
251#384C2311yescharacteristic
252#382C2312yes—
253#382C2312yes—
254#382C2312yes—
255#382C2312yes—
256#381—22no—
257#381—22no—
258#380—21no—
259#380—21no—
260#380—21no—
261#380—21no—
262#380—22no—
263#380—22no—
264#380C2312yes—
265#380C2312yes—
266#380C2312yes—
267#380C2312yes—
268C4×C4⋊C4—21no—
269C4×C4⋊C4D411yescharacteristic
270C4×C4⋊C4D411yescharacteristic
271C4×C4⋊C4C2312yes—
272C4×C4⋊C4C2311yescharacteristic
273C4×C22⋊C4—22no—
274C4×C22⋊C4D411yescharacteristic
275C4×C22⋊C4D411yescharacteristic
276C4×C22⋊C4D411yescharacteristic
277C4×C22⋊C4D411yescharacteristic
278C4×C22⋊C4C2311yescharacteristic
279C4×C22⋊C4C2311yescharacteristic
280C2×#95—22no—
281C43C2311yescharacteristic
282#340C2314yes—
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#340C2314yes—
287#340C2314yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291C2×#41—44no—
292C2×#41—44no—
293C2×#41—44no—
294C2×#41—44no—
295C2×#41—82no—
296C2×#41—82no—
297C22×Q8—21no—
298C22×Q8—21no—
299C22×Q8—21no—
300C22×Q8—21no—
301C22×Q8—21no—
302C22×Q8—22no—
303C22×Q8—44no—
304C22×Q8—44no—
305C22×Q8—82no—
306C22×D4—22no—
307C22×D4—22no—
308C22×D4—21no—
309C22×D4—21no—
310C22×D4C2×D411yescharacteristic
311C22×D4C2412yes—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2411yescharacteristic
321C23×C4C2411yescharacteristic
322C22×C8C2412yes—
323C22×C8C2412yes—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C4⋊Q8—24no—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8—42no—
337C4⋊Q8—44no—
338C4⋊Q8—44no—
339C4⋊Q8C2×D414yes—
340#127—22no—
341#127C2×D414yes—
342#125—24no—
343#125—42no—
344#124—44no—
345#124—44no—
346C22⋊Q8—44no—
347C22⋊Q8—44no—
348C22⋊Q8—44no—
349C22⋊Q8—82no—
350C22⋊Q8—82no—
351C22⋊Q8—82no—
352#121—24no—
353#121—24no—
354#121—42no—
355#121—42no—
356#121—44no—
357#121—44no—
358C4×Q8—44no—
359C4×Q8—44no—
360C4×Q8—82no—
361C4×D4—24no—
362C4×D4—24no—
363C4×D4—24no—
364C4×D4—24no—
365C4×D4—28no—
366C4×D4—42no—
367C4×D4—42no—
368C4×D4—42no—
369C4×D4—44no—
370C4×D4—44no—
371C4×D4—82no—
372C4×D4—82no—
373#117—24no—
374#117—42no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4—44no—
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×C4⋊C4C2412yes—
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⋊C4C2×D411yescharacteristic
419C2×C22⋊C4C2×D411yescharacteristic
420C2×C22⋊C4C2×D411yescharacteristic
421C2×C22⋊C4C2×D411yescharacteristic
422C2×C22⋊C4C2×D411yescharacteristic
423C2×C22⋊C4C2×D411yescharacteristic
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2411yescharacteristic
439C2×C42C2411yescharacteristic
440C2×C42C2411yescharacteristic
441C2×C42C2411yescharacteristic
442C2×C42C2411yescharacteristic
443#107—28no—
444#107—44no—
445#107—44no—
446#106—28no—
447#106—28no—
448#106—28no—
449C4⋊C8—24no—
450C4⋊C8—24no—
451C4⋊C8—24no—
452#102—28no—
453#102—28no—
454#102—28no—
455#102C2×D4116yes—
456C22⋊C8—24no—
457C22⋊C8—24no—
458C22⋊C8—24no—
459C22⋊C8—24no—
460C4×C8—24no—
461C4×C8—22no—
462C4×C8—22no—
463C4×C8—22no—
464C4×C8—24no—
465C4×C8C2×D414yes—
466#95—22no—
467#95—22no—
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#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95C2×D411yescharacteristic
485#95C2×D411yescharacteristic
486#95C2×D411yescharacteristic
487#95C2×D411yescharacteristic
488#95C2×D411yescharacteristic
489#95C2×D411yescharacteristic
490C24—22no—
491C24C22×D411yescharacteristic
492C24C22×D411yescharacteristic
493#41—816no—
494#41—816no—
495C2×Q8—24no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—42no—
499C2×Q8—42no—
500C2×Q8—42no—
501C2×Q8—42no—
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×Q8—82no—
513C2×Q8—816no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—22no—
519C2×D4—24no—
520C2×D4—24no—
521C2×D4—41no—
522C2×D4—44no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—82no—
531C2×D4—82no—
532C2×D4C22×D414yes—
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—22no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—82no—
567C22×C4—82no—
568C22×C4—82no—
569C22×C4—82no—
570C22×C4—82no—
571C22×C4#13514yes—
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C22×D411yescharacteristic
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C2511yescharacteristic
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—
595C2×C8C22×D414yes—
596C2×C82−1+414yes—
597C4⋊C4—22no—
598C4⋊C4—24no—
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—22no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—41no—
612C4⋊C4—44no—
613C4⋊C4—44no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—44no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—82no—
626C4⋊C4—82no—
627C4⋊C4—82no—
628C4⋊C4—82no—
629C4⋊C4C22×D414yes—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—41no—
635C22⋊C4—41no—
636C22⋊C4—44no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—82no—
644C22⋊C4—82no—
645C22⋊C4—82no—
646C22⋊C4—82no—
647C22⋊C4—82no—
648C42—22no—
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—44no—
662C42—82no—
663C42C22×D412yes—
664C42H(5,𝔽2)12yes—
665C422−1+414yes—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—24no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23C2×#13512yes—
687C23C23×D411yescharacteristic
688Q8—48no—
689Q8—88no—
690Q8—84no—
691Q8—84no—
692Q8—84no—
693Q8—84no—
694D4—28no—
695D4—44no—
696D4—48no—
697D4—48no—
698D4—44no—
699D4—88no—
700D4—88no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—28no—
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—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—21no—
729C2×C4—21no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
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—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—88no—
758C2×C4—88no—
759C2×C4—88no—
760C2×C4—164no—
761C2×C4#53612yes—
762C2×C4#53612yes—
763C2×C4D4212yes—
764C2×C4D4212yes—
765C2×C4C2×#13512yes—
766C2×C4C2×#13512yes—
767C2×C4#57512yes—
768C2×C4#57612yes—
769C2×C4#57712yes—
770C2×C4C23×D411yescharacteristic
771C2×C4C2×H(5,𝔽2)11yescharacteristic
772C2×C4C2×2−1+412yes—
773C2×C4C2×2−1+412yes—
774C8—24no—
775C8—24no—
776C8—42no—
777C8—42no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—44no—
789C22—41no—
790C22—44no—
791C22—41no—
792C22—41no—
793C22—44no—
794C22—41no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22C2×#53611yescharacteristic
800C22C2×D4211yescharacteristic
801C22#349911yescharacteristic
802C22C22×#13511yescharacteristic
803C22C2×#57511yescharacteristic
804C22C2×#57611yescharacteristic
805C22C2×#57711yescharacteristic
806C4—22no—
807C4—22no—
808C4—22no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—44no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—82no—
818C4—82no—
819C4—82no—
820C4—82no—
821C4—82no—
822C4—82no—
823C4#327314yes—
824C4#328214yes—
825C4#349912yes—
826C4#355212yes—
827C2—42no—
828C2—81no—
829C2—84no—
830C2#3936011yescharacteristic
831C2#6084611yescharacteristic
832C2#6087711yescharacteristic
833C2C2×#327311yescharacteristic
834C2C2×#328211yescharacteristic
835C2#6247411yescharacteristic
836C2#6248311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36149C2
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×#3228C2semidirect
2. C2×#3227C2semidirect
4. #36129C2semidirect
5. #33313C2semidirect
6. #31090C2semidirect
7. #31088C2semidirect
8. #29877C2semidirect
9. #29877C2semidirect
10. #28718C2semidirect
11. #28688C2semidirect
12. #26051C2semidirect
13. #25813C2semidirect
14. #25812C2semidirect
15. #25673C2semidirect
16. #25673C2semidirect
17. #25018C2semidirect
18. C4×#486C2semidirect
19. #21264C2semidirect
168. #486D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32282
C2×#32272
#361492
#361292
#333132
#310902
#310882
#298772
#287182
#286882
#260512
#258132
#258122
#256732
#250182
C4×#4862
#212642