Finite Group Databasebeta

← #6683993

Subgroups — #6683993

Order 512.

1883 conjugacy classes of subgroups.

The subgroup lattice has 833 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3228C211yesmaximal, characteristic, complemented
2C2×#3160C211yesmaximal, characteristic, complemented
3#36150C211yesmaximal, characteristic
4#36134C211yesmaximal, characteristic, complemented
5#33042C211yesmaximal, characteristic, complemented
6#30951C214yesmaximal, complemented
7#30788C214yesmaximal, complemented
8#30277C211yesmaximal, characteristic, complemented
9#29877C211yesmaximal, characteristic, complemented
10#28689C211yesmaximal, characteristic, complemented
11#28655C211yesmaximal, characteristic, complemented
12#26345C214yesmaximal, complemented
13#26141C214yesmaximal, complemented
14#25905C211yesmaximal, characteristic, complemented
15#25812C211yesmaximal, characteristic, complemented
16#25812C211yesmaximal, characteristic, complemented
17#25673C211yesmaximal, characteristic, complemented
18#22246C211yesmaximal, characteristic, complemented
19#21101C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C2×#533C2211yescharacteristic
23C2×#532C2211yescharacteristic
24#3228—28no—
25#3160—28no—
26C2×#500C2211yescharacteristic
27C2×#500C2211yescharacteristic
28C2×#500C2211yescharacteristic
29C2×#499C2214yes—
30C2×#498C2211yescharacteristic
31C2×#498C2211yescharacteristic
32C2×#498C2211yescharacteristic
33C2×#486C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#482C2214yes—
37C2×#478C2214yes—
38C2×#431C2211yescharacteristic
39C2×#427C2214yes—
40C22×C4×C8C2211yescharacteristic
41#2868C2211yescharacteristic
42#2858C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2856C2211yescharacteristic
47#2552C2212yes—
48#2542—21no—
49#2540—21no—
50#2538—21no—
51#2490C2212yes—
52#2454C2212yes—
53#2448—21no—
54#2441C2212yes—
55#2441C2212yes—
56#2429—21no—
57#2429—21no—
58#2427—21no—
59#2426—21no—
60#2426—21no—
61#2423—21no—
62#2423—21no—
63#2414C2212yes—
64#2407—21no—
65#2367—21no—
66#2365—21no—
67#2363C2212yes—
68#2354C2212yes—
69Q8×C4⋊C4—21no—
70#2341—21no—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2094C2214yes—
75#2094C2214yes—
76#2088C2214yes—
77#2083C2214yes—
78#2077C2214yes—
79#2067C2214yes—
80#2059C2214yes—
81#2059C2214yes—
82#2033C2214yes—
83#2025C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1990C2211yescharacteristic
89#1957C2211yescharacteristic
90#1947C2214yes—
91#1934C2214yes—
92#1925C2214yes—
93#1923C2212yes—
94#1920C2214yes—
95#1919C2214yes—
96#1916C2212yes—
97#1893C2214yes—
98#1875C2214yes—
99#1869C2212yes—
100#1862C2214yes—
101#1854C2214yes—
102#1854C2214yes—
103#1850C2212yes—
104#1834C2211yescharacteristic
105C4×C4⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108#1744C2211yescharacteristic
109C22×#41—21no—
110C23×C8C2312yes—
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⋊Q8—21no—
120C2×C4⋊Q8—21no—
121C2×C4⋊Q8C2311yescharacteristic
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2311yescharacteristic
126C2×#127C2311yescharacteristic
127C2×#125C2312yes—
128C2×#125C2312yes—
129C2×#125C2312yes—
130C2×#124—21no—
131C2×#124—21no—
132C2×#124—21no—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8—21no—
135C2×C22⋊Q8—21no—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8—21no—
139C2×C22⋊Q8—21no—
140C2×C22⋊Q8—21no—
141C2×C22⋊Q8—21no—
142C2×#121—21no—
143C2×#121—21no—
144C2×#121—21no—
145C2×#121C2312yes—
146C2×#121C2312yes—
147C2×C4×Q8—21no—
148C2×C4×Q8—21no—
149C2×C4×Q8—21no—
150C2×C4×Q8—21no—
151C2×C4×Q8—21no—
152C2×C4×Q8—21no—
153C2×C4×Q8—21no—
154C2×C4×Q8—21no—
155C2×C4×D4—21no—
156C2×C4×D4D411yescharacteristic
157C2×C4×D4D411yescharacteristic
158C2×C4×D4C2312yes—
159C2×C4×D4C2311yescharacteristic
160C2×#117C2312yes—
161C2×#117C2312yes—
162C2×#117C2312yes—
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165#500—24no—
166#500—24no—
167#500—24no—
168#499—216no—
169#498—24no—
170#498—42no—
171#498D418yescomplemented
172#486—24no—
173#486—24no—
174#486—42no—
175#482—216no—
176#478—216no—
177#431—24no—
178#427—216no—
179C2×#107C2314yes—
180C2×#107C2314yes—
181C2×#107C2314yes—
182C2×#106C2314yes—
183C2×#106C2314yes—
184C2×#106C2314yes—
185C2×C4⋊C8C2312yes—
186C2×C4⋊C8C2312yes—
187C2×#102C2314yes—
188C2×#102C2314yes—
189C2×#102C2314yes—
190C2×#102C2314yes—
191C2×C22⋊C8C2312yes—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×C4×C8—24no—
195C2×C4×C8C2312yes—
196C2×C4×C8C2311yescharacteristic
197C2×C4×C8C2311yescharacteristic
198C2×C4×C8C2311yescharacteristic
199C2×C4×C8C2311yescharacteristic
200#399—22no—
201#399—22no—
202#399—22no—
203#398—22no—
204#398—22no—
205#397—22no—
206#396—22no—
207#396—22no—
208#396—22no—
209#394—22no—
210#394—22no—
211#392—22no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391—21no—
216#391—21no—
217#390—22no—
218#390—22no—
219#390—22no—
220#390—22no—
221#390—21no—
222#390—21no—
223#390—21no—
224#390—21no—
225#390C2312yes—
226#390C2312yes—
227#390C2312yes—
228#389—22no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389—21no—
233#389—21no—
234#389—22no—
235#389—22no—
236#389C2312yes—
237#389C2312yes—
238#389C2312yes—
239#389C2312yes—
240#389C2312yes—
241#388—22no—
242#388—22no—
243#388—22no—
244#388—22no—
245#388—22no—
246#387—22no—
247#387—22no—
248#386—22no—
249#385—22no—
250#384—22no—
251#384—21no—
252#384—21no—
253#384C2311yescharacteristic
254#384C2311yescharacteristic
255#384C2312yes—
256#384C2312yes—
257#380—21no—
258#380—21no—
259#380—21no—
260#380—22no—
261#380C2312yes—
262#380C2312yes—
263#380C2312yes—
264C4×C4⋊C4—22no—
265C4×C4⋊C4—21no—
266C4×C4⋊C4—21no—
267C4×C4⋊C4D411yescharacteristic
268C4×C4⋊C4D411yescharacteristic
269C4×C4⋊C4C2312yes—
270C4×C4⋊C4C2312yes—
271C4×C4⋊C4C2311yescharacteristic
272C4×C22⋊C4—22no—
273C4×C22⋊C4D411yescharacteristic
274C4×C22⋊C4D411yescharacteristic
275C4×C22⋊C4D411yescharacteristic
276C4×C22⋊C4D411yescharacteristic
277C4×C22⋊C4C2311yescharacteristic
278C4×C22⋊C4C2311yescharacteristic
279C43C2311yescharacteristic
280#340C2314yes—
281#340C2314yes—
282#340C2314yes—
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#336C2312yes—
287#336C2312yes—
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×Q8—21no—
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
312C22×C8—24no—
313C22×C8—24no—
314C22×C8—24no—
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⋊Q8—44no—
328C4⋊Q8—82no—
329C4⋊Q8C2×D414yes—
330C4⋊Q8C2×D414yes—
331#127—22no—
332#127—22no—
333#125—24no—
334#125—24no—
335#125—24no—
336#125—42no—
337#125—42no—
338#125—42no—
339#124—44no—
340#124—44no—
341#124—82no—
342C22⋊Q8—44no—
343C22⋊Q8—44no—
344C22⋊Q8—44no—
345C22⋊Q8—44no—
346C22⋊Q8—44no—
347C22⋊Q8—44no—
348C22⋊Q8—82no—
349C22⋊Q8—82no—
350C22⋊Q8—82no—
351#121—28no—
352#121—24no—
353#121—42no—
354#121—44no—
355#121—82no—
356#121—82no—
357C4×Q8—44no—
358C4×Q8—44no—
359C4×Q8—44no—
360C4×Q8—44no—
361C4×Q8—44no—
362C4×Q8—44no—
363C4×Q8—44no—
364C4×Q8—82no—
365C4×D4—24no—
366C4×D4—24no—
367C4×D4—24no—
368C4×D4—42no—
369C4×D4—44no—
370C4×D4—42no—
371#117—24no—
372#117—24no—
373#117—24no—
374#117—42no—
375#117—42no—
376#117—42no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4C2×D411yescharacteristic
402C2×C4⋊C4C2×D411yescharacteristic
403C2×C4⋊C4C2×D411yescharacteristic
404C2×C4⋊C4C2412yes—
405C2×C4⋊C4C2412yes—
406C2×C4⋊C4C2412yes—
407C2×C4⋊C4C2412yes—
408C2×C4⋊C4C2412yes—
409C2×C4⋊C4C2412yes—
410C2×C4⋊C4C2412yes—
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⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4C2×D411yescharacteristic
427C2×C22⋊C4C2×D411yescharacteristic
428C2×C22⋊C4C2×D411yescharacteristic
429C2×C22⋊C4C2×D411yescharacteristic
430C2×C22⋊C4C2×D411yescharacteristic
431C2×C22⋊C4C2×D411yescharacteristic
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2411yescharacteristic
450C2×C42C2411yescharacteristic
451C2×C42C2411yescharacteristic
452C2×C42C2411yescharacteristic
453C2×C42C2411yescharacteristic
454#107—28no—
455#107—28no—
456#107—28no—
457#106—28no—
458#106—44no—
459#106C2×D4116yes—
460C4⋊C8—24no—
461C4⋊C8—24no—
462#102—28no—
463#102—28no—
464#102—28no—
465#102—44no—
466C22⋊C8—24no—
467C22⋊C8—24no—
468C22⋊C8—24no—
469C4×C8—24no—
470C4×C8—22no—
471C4×C8—22no—
472C4×C8—22no—
473C4×C8C2×D414yes—
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—
494C2×Q8—24no—
495C2×Q8—24no—
496C2×Q8—42no—
497C2×Q8—42no—
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×D4—22no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—24no—
514C2×D4—24no—
515C2×D4—41no—
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×D4—82no—
526C2×D4—82no—
527C2×D4—82no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
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—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—82no—
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
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×C42−1+414yes—
570C22×C4C2511yescharacteristic
571C2×C8—216no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8C22×D414yes—
583C2×C82−1+414yes—
584C4⋊C4—22no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—22no—
588C4⋊C4—22no—
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—44no—
600C4⋊C4—44no—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—44no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—82no—
616C4⋊C4—82no—
617C4⋊C4—82no—
618C4⋊C4—82no—
619C4⋊C4—82no—
620C4⋊C4—82no—
621C4⋊C4C22×D414yes—
622C4⋊C4C22×D414yes—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—41no—
628C22⋊C4—41no—
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—
642C22⋊C4—82no—
643C22⋊C4—82no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42—21no—
655C42—22no—
656C42—22no—
657C42—44no—
658C42—44no—
659C42—44no—
660C42—44no—
661C42—82no—
662C42#13514yes—
663C42C22×D412yes—
664C42H(5,𝔽2)12yes—
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—21no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23#53612yes—
686C23C23×D411yescharacteristic
687Q8—48no—
688Q8—48no—
689Q8—84no—
690Q8—84no—
691Q8—84no—
692D4—44no—
693D4—44no—
694D4—44no—
695D4—88no—
696D4—84no—
697D4—84no—
698D4—164no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—24no—
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—42no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
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×C4#53612yes—
757C2×C4D4212yes—
758C2×C4D4212yes—
759C2×C4C2×#13512yes—
760C2×C4C2×#13512yes—
761C2×C4C2×#13512yes—
762C2×C4#57512yes—
763C2×C4#57612yes—
764C2×C4#57712yes—
765C2×C4C23×D411yescharacteristic
766C2×C4C2×H(5,𝔽2)11yescharacteristic
767C2×C4C2×2−1+412yes—
768C2×C4C2×2−1+412yes—
769C8—24no—
770C8—24no—
771C8—42no—
772C8—42no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22C2×#53611yescharacteristic
795C22C2×D4211yescharacteristic
796C22#349911yescharacteristic
797C22C22×#13511yescharacteristic
798C22C2×#57511yescharacteristic
799C22C2×#57611yescharacteristic
800C22C2×#57711yescharacteristic
801C4—22no—
802C4—22no—
803C4—22no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—44no—
809C4—41no—
810C4—41no—
811C4—44no—
812C4—41no—
813C4—82no—
814C4—82no—
815C4—82no—
816C4—82no—
817C4—82no—
818C4#326814yes—
819C4#328414yes—
820C4#348612yes—
821C4#355212yes—
822C2—42no—
823C2—81no—
824C2—162no—
825C2#3767511yescharacteristic
826C2#6084611yescharacteristic
827C2#6087711yescharacteristic
828C2C2×#326811yescharacteristic
829C2C2×#328411yescharacteristic
830C2#6247411yescharacteristic
831C2#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×#3228C2semidirect
2. C2×#3160C2semidirect
4. #36134C2semidirect
5. #33042C2semidirect
6. #30951C2semidirect
7. #30788C2semidirect
8. #30277C2semidirect
9. #29877C2semidirect
10. #28689C2semidirect
11. #28655C2semidirect
12. #26345C2semidirect
13. #26141C2semidirect
14. #25905C2semidirect
15. #25812C2semidirect
16. #25812C2semidirect
17. #25673C2semidirect
18. #22246C2semidirect
19. #21101C2semidirect
171. #498D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32282
C2×#31602
#361502
#361342
#330422
#309512
#307882
#302772
#298772
#286892
#286552
#263452
#261412
#259052
#258122
#256732
#222462
#211012