Finite Group Databasebeta

← #6816652

Subgroups — #6816652

Order 512.

1795 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3231C211yesmaximal, characteristic, complemented
2C2×#3230C211yesmaximal, characteristic, complemented
3#36134C211yesmaximal, characteristic
4#36129C211yesmaximal, characteristic
5#33314C211yesmaximal, characteristic, complemented
6#31105C214yesmaximal, complemented
7#31099C214yesmaximal, complemented
8#29877C211yesmaximal, characteristic, complemented
9#29876C211yesmaximal, characteristic, complemented
10#28719C211yesmaximal, characteristic, complemented
11#28689C211yesmaximal, characteristic, complemented
12#26055C214yesmaximal, complemented
13#25813C211yesmaximal, characteristic, complemented
14#25812C211yesmaximal, characteristic, complemented
15#25674C211yesmaximal, characteristic, complemented
16#25672C211yesmaximal, characteristic, complemented
17#25028C214yesmaximal
18#21647C211yesmaximal, characteristic, complemented
19#21265C211yesmaximal, characteristic
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C2×#533C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24#3231—28no—
25#3230—28no—
26C2×#500C2211yescharacteristic
27C2×#500C2211yescharacteristic
28C2×#500C2211yescharacteristic
29C2×#500C2211yescharacteristic
30C2×#498C2211yescharacteristic
31C2×#498C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#487C2211yescharacteristic
35C2×#484C2214yes—
36C2×#485C2214yes—
37C2×#479C2214yes—
38C2×#477C2214yes—
39C2×#431C2211yescharacteristic
40C2×#431C2211yescharacteristic
41#2868C2211yescharacteristic
42#2862C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2552—21no—
48#2550C2212yes—
49#2542—21no—
50#2538C2212yes—
51#2492—21no—
52#2451—21no—
53#2446—21no—
54#2442C2212yes—
55#2441—21no—
56#2441—21no—
57#2439C2212yes—
58#2429—21no—
59#2429—21no—
60#2429—21no—
61#2423C2212yes—
62#2423C2212yes—
63#2417—21no—
64#2409—21no—
65#2365—21no—
66#2360—21no—
67#2354—21no—
68#2352C2212yes—
69Q8×C4⋊C4C2212yes—
70Q8×C22⋊C4—21no—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2088C2214yes—
75#2086C2214yes—
76#2083C2214yes—
77#2077C2214yes—
78#2075C2214yes—
79#2074C2214yes—
80#2059C2214yes—
81#2057C2214yes—
82#2036C2214yes—
83#2035C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1990C2211yescharacteristic
89#1956C2211yescharacteristic
90#1955C2212yes—
91#1947C2214yes—
92#1940C2212yes—
93#1935C2214yes—
94#1924C2212yes—
95#1924C2212yes—
96#1865C2214yes—
97#1863C2214yes—
98#1854C2214yes—
99#1852C2214yes—
100#1847C2214yes—
101#1847C2214yes—
102#1834C2211yescharacteristic
103#1805C2214yes—
104C4×C4⋊C8C2211yescharacteristic
105#1763C2214yes—
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108C4×#97C2211yescharacteristic
109C23×Q8—21no—
110#533—24no—
111#533—24no—
112#533—24no—
113#533—42no—
114#533—42no—
115#533—42no—
116C2×C4⋊Q8—24no—
117C2×C4⋊Q8—21no—
118C2×C4⋊Q8—21no—
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⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2312yes—
128C2×C4⋊Q8C2311yescharacteristic
129C2×#125—21no—
130C2×#125—21no—
131C2×#125C2312yes—
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×C22⋊Q8—21no—
140C2×C22⋊Q8C2312yes—
141C2×C22⋊Q8C2312yes—
142C2×C4×Q8—21no—
143C2×C4×Q8—21no—
144C2×C4×Q8—21no—
145C2×C4×Q8—21no—
146C2×C4×Q8—21no—
147C2×C4×Q8C2312yes—
148C2×C4×Q8C2312yes—
149C2×C4×Q8C2312yes—
150C2×C4×D4D411yescharacteristic
151C2×C4×D4D411yescharacteristic
152C2×C4×D4C2311yescharacteristic
153C2×#117—21no—
154C2×#117—21no—
155C2×#117C2312yes—
156C22×C4⋊C4—21no—
157C22×C4⋊C4C2312yes—
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160#500—24no—
161#500—24no—
162#500—24no—
163#500—42no—
164#498—24no—
165#498—42no—
166#487—24no—
167#487—24no—
168#487D418yescomplemented
169#485—216no—
170#484—216no—
171#479—216no—
172#477—216no—
173#431—24no—
174#431—24no—
175C2×#107C2314yes—
176C2×#107C2314yes—
177C2×#107C2314yes—
178C2×#107C2314yes—
179C2×#106C2314yes—
180C2×#106C2314yes—
181C2×C4⋊C8C2312yes—
182C2×C4⋊C8C2312yes—
183C2×C4⋊C8C2312yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×C22⋊C8C2312yes—
189C2×C22⋊C8C2312yes—
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2312yes—
192C2×#97C2312yes—
193C2×#97C2312yes—
194C2×C4×C8C2311yescharacteristic
195C2×C4×C8C2311yescharacteristic
196C2×C4×C8C2311yescharacteristic
197C2×C4×C8C2311yescharacteristic
198#400—22no—
199#399—22no—
200#399—22no—
201#398—22no—
202#398—22no—
203#398—22no—
204#398—22no—
205#396—22no—
206#396—22no—
207#396—22no—
208#395—22no—
209#393—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#391C2312yes—
222#390—22no—
223#389—22no—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—22no—
232#389—22no—
233#389—22no—
234#389C2312yes—
235#389C2312yes—
236#389C2312yes—
237#389C2312yes—
238#389C2312yes—
239#388—22no—
240#388—22no—
241#388—22no—
242#387—22no—
243#387—22no—
244#387—22no—
245#387—22no—
246#386—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#380—21no—
258#380—21no—
259#380—21no—
260#380—21no—
261#380—22no—
262#380C2312yes—
263#380C2312yes—
264#380C2312yes—
265#380C2312yes—
266C4×C4⋊C4—22no—
267C4×C4⋊C4—21no—
268C4×C4⋊C4—21no—
269C4×C4⋊C4—21no—
270C4×C4⋊C4D411yescharacteristic
271C4×C4⋊C4D411yescharacteristic
272C4×C4⋊C4C2312yes—
273C4×C4⋊C4C2311yescharacteristic
274C4×C22⋊C4—22no—
275C4×C22⋊C4D411yescharacteristic
276C4×C22⋊C4D411yescharacteristic
277C4×C22⋊C4D411yescharacteristic
278C4×C22⋊C4D411yescharacteristic
279C4×C22⋊C4C2311yescharacteristic
280C4×C22⋊C4C2311yescharacteristic
281C43C2311yescharacteristic
282#340C2314yes—
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#340C2314yes—
287#340C2314yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291C22×Q8—21no—
292C22×Q8—21no—
293C22×Q8—21no—
294C22×Q8—21no—
295C22×Q8—21no—
296C22×Q8—22no—
297C22×Q8—44no—
298C22×Q8—44no—
299C22×Q8—82no—
300C22×Q8C2412yes—
301C22×D4C2×D411yescharacteristic
302C23×C4—22no—
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C22×C8C2412yes—
310C22×C8C2412yes—
311C22×C8C2412yes—
312C22×C8C2412yes—
313C4⋊Q8—24no—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319C4⋊Q8—22no—
320C4⋊Q8—22no—
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324C4⋊Q8—42no—
325C4⋊Q8—44no—
326C4⋊Q8—44no—
327C4⋊Q8—44no—
328C4⋊Q8—82no—
329C4⋊Q8C2×D414yes—
330C4⋊Q8C2×D414yes—
331#125—24no—
332#125—42no—
333#125—44no—
334#125—44no—
335C22⋊Q8—24no—
336C22⋊Q8—24no—
337C22⋊Q8—42no—
338C22⋊Q8—42no—
339C22⋊Q8—44no—
340C22⋊Q8—44no—
341C22⋊Q8—44no—
342C22⋊Q8—44no—
343C22⋊Q8—44no—
344C22⋊Q8—82no—
345C22⋊Q8—82no—
346C22⋊Q8—82no—
347C4×Q8—24no—
348C4×Q8—24no—
349C4×Q8—28no—
350C4×Q8—42no—
351C4×Q8—42no—
352C4×Q8—44no—
353C4×Q8—44no—
354C4×Q8—44no—
355C4×Q8—44no—
356C4×Q8—82no—
357C4×D4—24no—
358C4×D4—24no—
359C4×D4—42no—
360#117—24no—
361#117—42no—
362#117—44no—
363#117—44no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
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⋊C4C2×D411yescharacteristic
414C2×C22⋊C4C2×D411yescharacteristic
415C2×C22⋊C4C2×D411yescharacteristic
416C2×C22⋊C4C2×D411yescharacteristic
417C2×C22⋊C4C2×D411yescharacteristic
418C2×C22⋊C4C2×D411yescharacteristic
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
436C2×C42C2411yescharacteristic
437C2×C42C2411yescharacteristic
438C2×C42C2411yescharacteristic
439C2×C42C2411yescharacteristic
440C2×C42C2411yescharacteristic
441#107—28no—
442#107—28no—
443#107—28no—
444#107—44no—
445#106—28no—
446#106—44no—
447C4⋊C8—24no—
448C4⋊C8—24no—
449C4⋊C8—24no—
450#103—28no—
451#103—28no—
452#103—28no—
453#103C2×D4116yes—
454C22⋊C8—24no—
455C22⋊C8—24no—
456C22⋊C8—24no—
457C22⋊C8—24no—
458#97—24no—
459#97—24no—
460C4×C8—22no—
461C4×C8—22no—
462C4×C8—22no—
463C4×C8C2×D414yes—
464#95—22no—
465#95—22no—
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#95C2×D411yescharacteristic
481#95C2×D411yescharacteristic
482#95C2×D411yescharacteristic
483#95C2×D411yescharacteristic
484#95C2×D411yescharacteristic
485#95C2×D411yescharacteristic
486C24C22×D411yescharacteristic
487C24C22×D411yescharacteristic
488C2×Q8—24no—
489C2×Q8—22no—
490C2×Q8—24no—
491C2×Q8—24no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—42no—
495C2×Q8—42no—
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—82no—
509C2×Q8—816no—
510C2×Q8C22×D414yes—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—41no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
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—44no—
542C22×C4—44no—
543C22×C4—82no—
544C22×C4#13714yes—
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C2511yescharacteristic
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8C22×D414yes—
569C2×C82−1+414yes—
570C4⋊C4—22no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—41no—
587C4⋊C4—44no—
588C4⋊C4—44no—
589C4⋊C4—44no—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—44no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—82no—
608C4⋊C4—82no—
609C4⋊C4—82no—
610C4⋊C4—82no—
611C4⋊C4—82no—
612C4⋊C4—82no—
613C4⋊C4C22×D414yes—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—41no—
619C22⋊C4—41no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—82no—
625C22⋊C4—82no—
626C22⋊C4—82no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—22no—
640C42—44no—
641C42—44no—
642C42—44no—
643C42—44no—
644C42—82no—
645C42C22×D412yes—
646C42H(5,𝔽2)12yes—
647C422−1+414yes—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23C2×#13712yes—
662C23C23×D411yescharacteristic
663Q8—28no—
664Q8—48no—
665Q8—44no—
666Q8—88no—
667Q8—84no—
668Q8—84no—
669Q8—84no—
670Q8—84no—
671D4—44no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—28no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—88no—
732C2×C4#53612yes—
733C2×C4#53612yes—
734C2×C4D4212yes—
735C2×C4D4212yes—
736C2×C4C2×#13712yes—
737C2×C4C2×#13712yes—
738C2×C4#57512yes—
739C2×C4#57612yes—
740C2×C4#57812yes—
741C2×C4C23×D411yescharacteristic
742C2×C4C2×H(5,𝔽2)11yescharacteristic
743C2×C4C2×2−1+412yes—
744C2×C4C2×2−1+412yes—
745C8—24no—
746C8—24no—
747C8—42no—
748C8—42no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22C2×#53611yescharacteristic
764C22C2×D4211yescharacteristic
765C22#349911yescharacteristic
766C22C22×#13711yescharacteristic
767C22C2×#57511yescharacteristic
768C22C2×#57611yescharacteristic
769C22C2×#57811yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—41no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—44no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—44no—
782C4—82no—
783C4—82no—
784C4—82no—
785C4—82no—
786C4—82no—
787C4—82no—
788C4#326814yes—
789C4#327014yes—
790C4#349912yes—
791C4#355212yes—
792C2—42no—
793C2—81no—
794C2#3936011yescharacteristic
795C2#6086511yescharacteristic
796C2#6088011yescharacteristic
797C2C2×#326811yescharacteristic
798C2C2×#327011yescharacteristic
799C2#6248011yescharacteristic
800C2#6248211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
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×#3230C2semidirect
5. #33314C2semidirect
6. #31105C2semidirect
7. #31099C2semidirect
8. #29877C2semidirect
9. #29876C2semidirect
10. #28719C2semidirect
11. #28689C2semidirect
12. #26055C2semidirect
13. #25813C2semidirect
14. #25812C2semidirect
15. #25674C2semidirect
16. #25672C2semidirect
18. #21647C2semidirect
168. #487D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32312
C2×#32302
#361342
#361292
#333142
#311052
#310992
#298772
#298762
#287192
#286892
#260552
#258132
#258122
#256742
#256722
#250282
#216472
#212652