Finite Group Databasebeta

← #6816658

Subgroups — #6816658

Order 512.

1894 conjugacy classes of subgroups.

The subgroup lattice has 835 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3228C211yesmaximal, characteristic, complemented
2C2×#3228C211yesmaximal, characteristic, complemented
3#36149C211yesmaximal, characteristic
4#36134C211yesmaximal, characteristic, complemented
5#33314C211yesmaximal, characteristic, complemented
6#31106C214yesmaximal, complemented
7#31098C214yesmaximal, complemented
8#29877C211yesmaximal, characteristic, complemented
9#29876C211yesmaximal, characteristic, complemented
10#28716C211yesmaximal, characteristic, complemented
11#28688C211yesmaximal, characteristic, complemented
12#26059C214yesmaximal, complemented
13#25812C211yesmaximal, characteristic, complemented
14#25812C211yesmaximal, characteristic, complemented
15#25673C211yesmaximal, characteristic, complemented
16#25671C211yesmaximal, characteristic, complemented
17#25023C214yesmaximal, complemented
18#21646C211yesmaximal, characteristic, complemented
19#21265C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C2×#532C2211yescharacteristic
24#3228—28no—
25#3228—28no—
26C2×#500C2211yescharacteristic
27C2×#500C2211yescharacteristic
28C2×#500C2211yescharacteristic
29C2×#498C2211yescharacteristic
30C2×#498C2211yescharacteristic
31C2×#498C2211yescharacteristic
32C2×#486C2211yescharacteristic
33C2×#486C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#482C2214yes—
36C2×#482C2214yes—
37C2×#478C2214yes—
38C2×#478C2214yes—
39C2×#431C2211yescharacteristic
40C2×#431C2211yescharacteristic
41#2868C2211yescharacteristic
42#2862C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2552C2212yes—
48#2542—21no—
49#2538—21no—
50#2535C2212yes—
51#2447—21no—
52#2447—21no—
53#2441C2212yes—
54#2441C2212yes—
55#2429—21no—
56#2429—21no—
57#2427—21no—
58#2427—21no—
59#2423—21no—
60#2423—21no—
61#2420C2212yes—
62#2420C2212yes—
63#2407—21no—
64#2407—21no—
65#2365—21no—
66#2354C2212yes—
67Q8×C4⋊C4—21no—
68#2349C2212yes—
69#2339—21no—
70#2339—21no—
71C4×C4⋊Q8C2211yescharacteristic
72C4×#127C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2088C2214yes—
75#2086C2214yes—
76#2085C2214yes—
77#2077C2214yes—
78#2075C2214yes—
79#2071C2214yes—
80#2059C2214yes—
81#2059C2214yes—
82#2034C2214yes—
83#2033C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1990C2211yescharacteristic
89#1957C2211yescharacteristic
90#1955C2212yes—
91#1949C2214yes—
92#1940C2212yes—
93#1936C2214yes—
94#1924C2212yes—
95#1924C2212yes—
96#1864C2214yes—
97#1862C2214yes—
98#1854C2214yes—
99#1854C2214yes—
100#1847C2214yes—
101#1847C2214yes—
102#1834C2211yescharacteristic
103#1802C2214yes—
104C4×C4⋊C8C2211yescharacteristic
105#1762C2214yes—
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108C4×#97C2211yescharacteristic
109C22×#41—21no—
110C22×#41—21no—
111#533—24no—
112#533—24no—
113#533—42no—
114#533—42no—
115#532—24no—
116#532—24no—
117#532—42no—
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×#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⋊Q8—21no—
139C2×#121—21no—
140C2×#121—21no—
141C2×#121C2312yes—
142C2×#121C2312yes—
143C2×C4×Q8—21no—
144C2×C4×Q8—21no—
145C2×C4×Q8—21no—
146C2×C4×Q8—21no—
147C2×C4×Q8—21no—
148C2×C4×D4—21no—
149C2×C4×D4—21no—
150C2×C4×D4—21no—
151C2×C4×D4—21no—
152C2×C4×D4D411yescharacteristic
153C2×C4×D4D411yescharacteristic
154C2×C4×D4C2312yes—
155C2×C4×D4C2312yes—
156C2×C4×D4C2312yes—
157C2×C4×D4C2311yescharacteristic
158C2×#117C2312yes—
159C2×#117C2312yes—
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162#500—24no—
163#500—24no—
164#500—42no—
165#498—24no—
166#498—24no—
167#498—42no—
168#486—24no—
169#486—24no—
170#486D418yescomplemented
171#482—216no—
172#482—216no—
173#478—216no—
174#478—216no—
175#431—24no—
176#431—24no—
177C2×#107C2314yes—
178C2×#107C2314yes—
179C2×#107C2314yes—
180C2×#106C2314yes—
181C2×#106C2314yes—
182C2×#106C2314yes—
183C2×C4⋊C8C2312yes—
184C2×C4⋊C8C2312yes—
185C2×C4⋊C8C2312yes—
186C2×#102C2314yes—
187C2×#102C2314yes—
188C2×#102C2314yes—
189C2×#102C2314yes—
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2312yes—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×#97C2312yes—
195C2×#97C2312yes—
196C2×C4×C8C2311yescharacteristic
197C2×C4×C8C2311yescharacteristic
198C2×C4×C8C2311yescharacteristic
199C2×C4×C8C2311yescharacteristic
200#399—22no—
201#399—22no—
202#398—22no—
203#398—22no—
204#397—22no—
205#397—22no—
206#397—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#391—21no—
218#391—21no—
219#391—21no—
220#391—21no—
221#390—22no—
222#390—21no—
223#390—21no—
224#390C2312yes—
225#389—22no—
226#389—21no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—22no—
232#389—22no—
233#389C2312yes—
234#389C2312yes—
235#389C2312yes—
236#389C2312yes—
237#389C2312yes—
238#388—22no—
239#388—22no—
240#387—22no—
241#387—22no—
242#386—22no—
243#386—22no—
244#386—22no—
245#386—22no—
246#385—22no—
247#385—22no—
248#384—22no—
249#384—21no—
250#384—21no—
251#384C2311yescharacteristic
252#384C2311yescharacteristic
253#384C2312yes—
254#384C2312yes—
255#382C2312yes—
256#382C2312yes—
257#381—22no—
258#381—22no—
259#380—21no—
260#380—21no—
261#380—21no—
262#380—21no—
263#380—22no—
264#380C2312yes—
265#380C2312yes—
266#380C2312yes—
267#380C2312yes—
268C4×C4⋊C4—22no—
269C4×C4⋊C4—21no—
270C4×C4⋊C4D411yescharacteristic
271C4×C4⋊C4D411yescharacteristic
272C4×C4⋊C4C2312yes—
273C4×C4⋊C4C2311yescharacteristic
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×D4—22no—
303C22×D4—22no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4C2×D411yescharacteristic
307C22×D4C2412yes—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2411yescharacteristic
316C23×C4C2411yescharacteristic
317C22×C8C2412yes—
318C22×C8C2412yes—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326C4⋊Q8—22no—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330C4⋊Q8—44no—
331C4⋊Q8—82no—
332C4⋊Q8C2×D414yes—
333#127—22no—
334#127C2×D414yes—
335#125—24no—
336#125—24no—
337#125—42no—
338#125—42no—
339#124—44no—
340#124—44no—
341C22⋊Q8—44no—
342C22⋊Q8—44no—
343C22⋊Q8—44no—
344C22⋊Q8—44no—
345C22⋊Q8—82no—
346C22⋊Q8—82no—
347C22⋊Q8—82no—
348C22⋊Q8—82no—
349#121—24no—
350#121—24no—
351#121—42no—
352#121—42no—
353#121—44no—
354#121—44no—
355C4×Q8—44no—
356C4×Q8—44no—
357C4×Q8—44no—
358C4×Q8—44no—
359C4×Q8—44no—
360C4×D4—24no—
361C4×D4—24no—
362C4×D4—24no—
363C4×D4—28no—
364C4×D4—42no—
365C4×D4—42no—
366C4×D4—42no—
367C4×D4—42no—
368C4×D4—44no—
369C4×D4—44no—
370C4×D4—82no—
371C4×D4—82no—
372#117—24no—
373#117—24no—
374#117—42no—
375#117—42no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4C2×D411yescharacteristic
399C2×C4⋊C4C2×D411yescharacteristic
400C2×C4⋊C4C2×D411yescharacteristic
401C2×C4⋊C4C2412yes—
402C2×C4⋊C4C2412yes—
403C2×C4⋊C4C2412yes—
404C2×C4⋊C4C2412yes—
405C2×C4⋊C4C2412yes—
406C2×C4⋊C4C2412yes—
407C2×C4⋊C4C2412yes—
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⋊C4—22no—
421C2×C22⋊C4C2×D411yescharacteristic
422C2×C22⋊C4C2×D411yescharacteristic
423C2×C22⋊C4C2×D411yescharacteristic
424C2×C22⋊C4C2×D411yescharacteristic
425C2×C22⋊C4C2×D411yescharacteristic
426C2×C22⋊C4C2×D411yescharacteristic
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2411yescharacteristic
443C2×C42C2411yescharacteristic
444C2×C42C2411yescharacteristic
445C2×C42C2411yescharacteristic
446C2×C42C2411yescharacteristic
447#107—28no—
448#107—28no—
449#107—44no—
450#106—28no—
451#106—28no—
452#106—44no—
453C4⋊C8—24no—
454C4⋊C8—24no—
455C4⋊C8—24no—
456#102—28no—
457#102—28no—
458#102—28no—
459#102C2×D4116yes—
460C22⋊C8—24no—
461C22⋊C8—24no—
462C22⋊C8—24no—
463C22⋊C8—24no—
464#97—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—
494#41—816no—
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×Q8—42no—
510C2×D4—22no—
511C2×D4—24no—
512C2×D4—24no—
513C2×D4—22no—
514C2×D4—24no—
515C2×D4—24no—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—82no—
527C2×D4—82no—
528C2×D4C22×D414yes—
529C22×C4—22no—
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—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—82no—
562C22×C4—82no—
563C22×C4—82no—
564C22×C4—82no—
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×C4C22×D411yescharacteristic
577C22×C4C2511yescharacteristic
578C2×C8—22no—
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×C8C22×D414yes—
589C2×C82−1+414yes—
590C4⋊C4—22no—
591C4⋊C4—24no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—41no—
604C4⋊C4—41no—
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—42no—
619C4⋊C4—42no—
620C4⋊C4—82no—
621C4⋊C4—82no—
622C4⋊C4—82no—
623C4⋊C4—82no—
624C4⋊C4—82no—
625C4⋊C4—82no—
626C4⋊C4C22×D414yes—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—41no—
630C22⋊C4—41no—
631C22⋊C4—41no—
632C22⋊C4—41no—
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—44no—
660C42—44no—
661C42—44no—
662C42C22×D412yes—
663C42H(5,𝔽2)12yes—
664C422−1+414yes—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—24no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23C23×D411yescharacteristic
687Q8—48no—
688Q8—84no—
689Q8—84no—
690Q8—84no—
691Q8—84no—
692D4—28no—
693D4—44no—
694D4—48no—
695D4—48no—
696D4—44no—
697D4—88no—
698D4—88no—
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—21no—
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—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—42no—
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—88no—
757C2×C4—88no—
758C2×C4—164no—
759C2×C4#53612yes—
760C2×C4#53612yes—
761C2×C4D4212yes—
762C2×C4D4212yes—
763C2×C4#57512yes—
764C2×C4#57512yes—
765C2×C4#57612yes—
766C2×C4#57712yes—
767C2×C4C23×D411yescharacteristic
768C2×C4C2×H(5,𝔽2)11yescharacteristic
769C2×C4C2×2−1+412yes—
770C2×C4C2×2−1+412yes—
771C8—24no—
772C8—24no—
773C8—42no—
774C8—42no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—44no—
782C22—41no—
783C22—41no—
784C22—44no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—44no—
790C22—41no—
791C22—41no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22C2×#53611yescharacteristic
797C22C2×D4211yescharacteristic
798C22#349911yescharacteristic
799C22C2×#57511yescharacteristic
800C22C2×#57511yescharacteristic
801C22C2×#57611yescharacteristic
802C22C2×#57711yescharacteristic
803C4—22no—
804C4—22no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—44no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—82no—
815C4—82no—
816C4—82no—
817C4—82no—
818C4—82no—
819C4—82no—
820C4#326714yes—
821C4#326814yes—
822C4#349912yes—
823C4#355212yes—
824C2—81no—
825C2—81no—
826C2—84no—
827C2#3936011yescharacteristic
828C2#6086211yescharacteristic
829C2#6087711yescharacteristic
830C2C2×#326711yescharacteristic
831C2C2×#326811yescharacteristic
832C2#6248111yescharacteristic
833C2#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×#3228C2semidirect
4. #36134C2semidirect
5. #33314C2semidirect
6. #31106C2semidirect
7. #31098C2semidirect
8. #29877C2semidirect
9. #29876C2semidirect
10. #28716C2semidirect
11. #28688C2semidirect
12. #26059C2semidirect
13. #25812C2semidirect
14. #25812C2semidirect
15. #25673C2semidirect
16. #25671C2semidirect
17. #25023C2semidirect
18. #21646C2semidirect
19. #21265C2semidirect
170. #486D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32282
#361492
#361342
#333142
#311062
#310982
#298772
#298762
#287162
#286882
#260592
#258122
#256732
#256712
#250232
#216462
#212652