Finite Group Databasebeta

← #6684013

Subgroups — #6684013

Order 512.

1903 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3228C211yesmaximal, characteristic, complemented
2C2×#3165C211yesmaximal, characteristic, complemented
3#36150C211yesmaximal, characteristic
4#36129C211yesmaximal, characteristic, complemented
5#33048C211yesmaximal, characteristic, complemented
6#30971C214yesmaximal, complemented
7#30802C214yesmaximal, complemented
8#30278C211yesmaximal, characteristic, complemented
9#29877C211yesmaximal, characteristic, complemented
10#28688C211yesmaximal, characteristic, complemented
11#28654C211yesmaximal, characteristic, complemented
12#26363C214yesmaximal, complemented
13#26156C214yesmaximal, complemented
14#25903C211yesmaximal, characteristic, complemented
15#25812C211yesmaximal, characteristic, complemented
16#25812C211yesmaximal, characteristic, complemented
17#25673C211yesmaximal, characteristic, complemented
18#22247C211yesmaximal, characteristic, complemented
19#21102C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24#3228—28no—
25#3165—28no—
26C2×#501C2214yes—
27C2×#500C2211yescharacteristic
28C2×#500C2211yescharacteristic
29C2×#500C2211yescharacteristic
30C2×#498C2211yescharacteristic
31C2×#498C2211yescharacteristic
32C2×#498C2211yescharacteristic
33C2×#486C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#482C2214yes—
37C2×#478C2214yes—
38C2×#431C2211yescharacteristic
39C2×#428C2214yes—
40C2×C4×M16C2211yescharacteristic
41#2862C2211yescharacteristic
42#2858C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2856C2211yescharacteristic
47#2550C2212yes—
48#2540—21no—
49#2492—21no—
50#2490C2212yes—
51#2454C2212yes—
52#2451—21no—
53#2448—21no—
54#2446—21no—
55#2442C2212yes—
56#2439C2212yes—
57#2429—21no—
58#2427—21no—
59#2426—21no—
60#2426—21no—
61#2417—21no—
62#2414C2212yes—
63#2409—21no—
64#2407—21no—
65#2367—21no—
66#2363C2212yes—
67#2360—21no—
68#2352C2212yes—
69#2341—21no—
70Q8×C22⋊C4—21no—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2092C2214yes—
75#2092C2214yes—
76#2088C2214yes—
77#2085C2214yes—
78#2077C2214yes—
79#2065C2214yes—
80#2059C2214yes—
81#2059C2214yes—
82#2033C2214yes—
83#2023C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1990C2211yescharacteristic
89#1957C2211yescharacteristic
90#1949C2214yes—
91#1936C2214yes—
92#1926C2214yes—
93#1924C2212yes—
94#1918C2214yes—
95#1918C2214yes—
96#1917C2212yes—
97#1895C2214yes—
98#1874C2214yes—
99#1870C2212yes—
100#1862C2214yes—
101#1854C2214yes—
102#1854C2214yes—
103#1851C2212yes—
104#1834C2211yescharacteristic
105C4×C4⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108#1744C2211yescharacteristic
109C22×#41—21no—
110C23×Q8—21no—
111C22×M16C2312yes—
112#533—24no—
113#533—24no—
114#533—42no—
115#533—42no—
116#532—24no—
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⋊Q8C2312yes—
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2311yescharacteristic
128C2×#127C2311yescharacteristic
129C2×#125C2312yes—
130C2×#125C2312yes—
131C2×#124—21no—
132C2×#124—21no—
133C2×#124—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×#121—21no—
142C2×#121—21no—
143C2×#121—21no—
144C2×#121C2312yes—
145C2×#121C2312yes—
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×D4—21no—
153C2×C4×D4D411yescharacteristic
154C2×C4×D4D411yescharacteristic
155C2×C4×D4C2312yes—
156C2×C4×D4C2311yescharacteristic
157C2×#117C2312yes—
158C2×#117C2312yes—
159C22×C4⋊C4—21no—
160C22×C4⋊C4C2312yes—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163#501—216no—
164#500—24no—
165#500—42no—
166#500D418yescomplemented
167#498—24no—
168#498—24no—
169#498—24no—
170#486—24no—
171#486—24no—
172#486—42no—
173#482—216no—
174#478—216no—
175#431—24no—
176#428—216no—
177C2×#107C2314yes—
178C2×#107C2314yes—
179C2×#107C2314yes—
180C2×#106C2314yes—
181C2×#106C2314yes—
182C2×#106C2314yes—
183C2×C4⋊C8C2312yes—
184C2×C4⋊C8C2312yes—
185C2×#102C2314yes—
186C2×#102C2314yes—
187C2×#102C2314yes—
188C2×#102C2314yes—
189C2×C22⋊C8C2312yes—
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2312yes—
192C4×M16—24no—
193C2×#97C2312yes—
194C2×C4×C8C2311yescharacteristic
195C2×C4×C8C2311yescharacteristic
196C2×C4×C8C2311yescharacteristic
197C2×C4×C8C2311yescharacteristic
198#400—22no—
199#399—22no—
200#398—22no—
201#398—22no—
202#397—22no—
203#396—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—22no—
220#391—22no—
221#390—22no—
222#390—22no—
223#390—22no—
224#390—21no—
225#390—21no—
226#390—21no—
227#390—21no—
228#390C2312yes—
229#390C2312yes—
230#390C2312yes—
231#389—21no—
232#389—21no—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—22no—
237#389C2312yes—
238#389C2312yes—
239#389C2312yes—
240#389C2312yes—
241#389C2312yes—
242#388—22no—
243#388—22no—
244#388—22no—
245#388—22no—
246#387—22no—
247#387—22no—
248#386—22no—
249#386—22no—
250#385—22no—
251#385—22no—
252#384C2311yescharacteristic
253#384C2311yescharacteristic
254#382C2312yes—
255#382C2312yes—
256#380—21no—
257#380—21no—
258#380—21no—
259#380—22no—
260#380—22no—
261#380C2312yes—
262#380C2312yes—
263#380C2312yes—
264C4×C4⋊C4—21no—
265C4×C4⋊C4—21no—
266C4×C4⋊C4D411yescharacteristic
267C4×C4⋊C4D411yescharacteristic
268C4×C4⋊C4C2312yes—
269C4×C4⋊C4C2312yes—
270C4×C4⋊C4C2311yescharacteristic
271C4×C22⋊C4—22no—
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×Q8—22no—
300C22×Q8—44no—
301C22×Q8—44no—
302C22×Q8—82no—
303C22×D4—22no—
304C22×D4—22no—
305C22×D4—21no—
306C22×D4—21no—
307C22×D4C2×D411yescharacteristic
308C22×D4C2412yes—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2411yescharacteristic
316C23×C4C2411yescharacteristic
317C2×M16—24no—
318C2×M16—24no—
319C2×M16—24no—
320C22×C8C2412yes—
321C22×C8C2412yes—
322C22×C8C2412yes—
323C22×C8C2412yes—
324C4⋊Q8—24no—
325C4⋊Q8—22no—
326C4⋊Q8—22no—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—42no—
334C4⋊Q8—44no—
335C4⋊Q8—44no—
336C4⋊Q8C2×D414yes—
337C4⋊Q8C2×D414yes—
338#127—22no—
339#127—22no—
340#125—24no—
341#125—24no—
342#125—42no—
343#125—42no—
344#124—44no—
345#124—44no—
346#124—82no—
347C22⋊Q8—44no—
348C22⋊Q8—44no—
349C22⋊Q8—44no—
350C22⋊Q8—44no—
351C22⋊Q8—44no—
352C22⋊Q8—82no—
353C22⋊Q8—82no—
354#121—28no—
355#121—24no—
356#121—42no—
357#121—44no—
358#121—82no—
359#121—82no—
360C4×Q8—44no—
361C4×Q8—44no—
362C4×Q8—44no—
363C4×Q8—44no—
364C4×Q8—82no—
365C4×Q8—82no—
366C4×D4—24no—
367C4×D4—24no—
368C4×D4—42no—
369C4×D4—44no—
370C4×D4—42no—
371C4×D4—42no—
372#117—24no—
373#117—24no—
374#117—42no—
375#117—42no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
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—21no—
389C2×C4⋊C4—21no—
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⋊C4—22no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4—44no—
399C2×C4⋊C4C2×D411yescharacteristic
400C2×C4⋊C4C2×D411yescharacteristic
401C2×C4⋊C4C2×D411yescharacteristic
402C2×C4⋊C4C2412yes—
403C2×C4⋊C4C2412yes—
404C2×C4⋊C4C2412yes—
405C2×C4⋊C4C2412yes—
406C2×C4⋊C4C2412yes—
407C2×C4⋊C4C2412yes—
408C2×C4⋊C4C2412yes—
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⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4C2×D411yescharacteristic
424C2×C22⋊C4C2×D411yescharacteristic
425C2×C22⋊C4C2×D411yescharacteristic
426C2×C22⋊C4C2×D411yescharacteristic
427C2×C22⋊C4C2×D411yescharacteristic
428C2×C22⋊C4C2×D411yescharacteristic
429C2×C42—22no—
430C2×C42—22no—
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
450#107—28no—
451#107—44no—
452#107C2×D4116yes—
453#106—28no—
454#106—28no—
455#106—28no—
456C4⋊C8—24no—
457C4⋊C8—24no—
458#102—28no—
459#102—28no—
460#102—28no—
461#102—44no—
462C22⋊C8—24no—
463C22⋊C8—24no—
464C22⋊C8—24no—
465#97—24no—
466C4×C8—22no—
467C4×C8—22no—
468C4×C8—22no—
469C4×C8C2×D414yes—
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—
494C2×Q8—24no—
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—82no—
512C2×Q8—816no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—44no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—82no—
530C2×D4—82no—
531C2×D4—82no—
532C22×C4—21no—
533C22×C4—21no—
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—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
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—44no—
561C22×C4—44no—
562C22×C4—82no—
563C22×C4—82no—
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×C42−1+414yes—
577C22×C4C2511yescharacteristic
578M16—216no—
579C2×C8—22no—
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×C8C22×D414yes—
590C2×C82−1+414yes—
591C4⋊C4—22no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—41no—
605C4⋊C4—41no—
606C4⋊C4—44no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—82no—
621C4⋊C4—82no—
622C4⋊C4—82no—
623C4⋊C4—82no—
624C4⋊C4C22×D414yes—
625C4⋊C4C22×D414yes—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—41no—
629C22⋊C4—41no—
630C22⋊C4—41no—
631C22⋊C4—41no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—82no—
641C22⋊C4—82no—
642C22⋊C4—82no—
643C22⋊C4—82no—
644C22⋊C4—82no—
645C22⋊C4—82no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—22no—
653C42—22no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—22no—
659C42—22no—
660C42—44no—
661C42—44no—
662C42—82no—
663C42—82no—
664C42C22×D412yes—
665C42H(5,𝔽2)12yes—
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—21no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23#53612yes—
687C23C23×D411yescharacteristic
688Q8—48no—
689Q8—48no—
690Q8—88no—
691Q8—84no—
692Q8—84no—
693Q8—84no—
694D4—44no—
695D4—44no—
696D4—44no—
697D4—88no—
698D4—84no—
699D4—84no—
700D4—164no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—24no—
704C2×C4—24no—
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—24no—
714C2×C4—24no—
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—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
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—42no—
758C2×C4—42no—
759C2×C4—88no—
760C2×C4—88no—
761C2×C4#53612yes—
762C2×C4D4212yes—
763C2×C4D4212yes—
764C2×C4#57512yes—
765C2×C4#57512yes—
766C2×C4#57612yes—
767C2×C4#57712yes—
768C2×C4C23×D411yescharacteristic
769C2×C4C2×H(5,𝔽2)11yescharacteristic
770C2×C4C2×2−1+412yes—
771C2×C4C2×2−1+412yes—
772C8—24no—
773C8—24no—
774C8—42no—
775C8—42no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22C2×#53611yescharacteristic
798C22C2×D4211yescharacteristic
799C22#349911yescharacteristic
800C22C2×#57511yescharacteristic
801C22C2×#57511yescharacteristic
802C22C2×#57611yescharacteristic
803C22C2×#57711yescharacteristic
804C4—22no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—44no—
813C4—44no—
814C4—41no—
815C4—41no—
816C4—82no—
817C4—82no—
818C4—82no—
819C4—82no—
820C4—82no—
821C4#327114yes—
822C4#327314yes—
823C4#348612yes—
824C4#355212yes—
825C2—42no—
826C2—81no—
827C2—162no—
828C2#3767511yescharacteristic
829C2#6086211yescharacteristic
830C2#6087711yescharacteristic
831C2C2×#327111yescharacteristic
832C2C2×#327311yescharacteristic
833C2#6248111yescharacteristic
834C2#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×#3165C2semidirect
4. #36129C2semidirect
5. #33048C2semidirect
6. #30971C2semidirect
7. #30802C2semidirect
8. #30278C2semidirect
9. #29877C2semidirect
10. #28688C2semidirect
11. #28654C2semidirect
12. #26363C2semidirect
13. #26156C2semidirect
14. #25903C2semidirect
15. #25812C2semidirect
16. #25812C2semidirect
17. #25673C2semidirect
18. #22247C2semidirect
19. #21102C2semidirect
166. #500D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32282
C2×#31652
#361502
#361292
#330482
#309712
#308022
#302782
#298772
#286882
#286542
#263632
#261562
#259032
#258122
#256732
#222472
#211022