Finite Group Databasebeta

← #6404450

Subgroups — #6404450

Order 512.

1705 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×#3374C211yesmaximal, characteristic
2#34337C211yesmaximal, characteristic
3#34328C211yesmaximal, characteristic
4#23227C212yesmaximal
5#23214C211yesmaximal, characteristic
6#23110C212yesmaximal
7#23096C211yesmaximal, characteristic
8#22976C212yesmaximal
9#22964C211yesmaximal, characteristic
10#22779C212yesmaximal
11#22771C211yesmaximal, characteristic
12#22742C211yesmaximal, characteristic
13#22547C211yesmaximal, characteristic
14#22524C211yesmaximal, characteristic
15#22154C211yesmaximal, characteristic
16#22154C212yesmaximal
17#22121C212yesmaximal
18#22118C211yesmaximal, characteristic
19C4×#491C212yesmaximal
20#21647C211yesmaximal, characteristic
21#21287C212yesmaximal
22#21278C211yesmaximal, characteristic
23#20520C211yesmaximal, characteristic
24C2×#557C2211yescharacteristic
25C2×#557C2211yescharacteristic
26#3374C4116yescomplemented
27C2×#491C2212yes—
28C2×#487C2211yescharacteristic
29C2×#479C2212yes—
30C2×#475C2211yescharacteristic
31C2×#462C2211yescharacteristic
32C2×#462C2212yes—
33C2×#446C2211yescharacteristic
34C2×#446C2211yescharacteristic
35C2×#441C2212yes—
36C2×C4×Q16C2211yescharacteristic
37#2371—22no—
38#2370—22no—
39#2370—21no—
40#2370C2212yes—
41#2365—21no—
42#2365C2211yescharacteristic
43#2365C2211yescharacteristic
44#2365C2212yes—
45#2356—21no—
46#2356C2212yes—
47#2355C2211yescharacteristic
48#2355C2211yescharacteristic
49Q8×C4⋊C4—21no—
50Q8×C4⋊C4C2211yescharacteristic
51Q8×C4⋊C4C2211yescharacteristic
52Q8×C4⋊C4C2212yes—
53#2336—22no—
54#2330—21no—
55#2330—22no—
56#2327—21no—
57C4×C4⋊Q8C2211yescharacteristic
58C4×C4⋊Q8C2211yescharacteristic
59C4×C4⋊Q8C2212yes—
60C4×#125C2212yes—
61#2295C2211yescharacteristic
62#2295C2212yes—
63#2295C2211yescharacteristic
64#2295C2212yes—
65#2276—21no—
66#2276—21no—
67C42×Q8C2211yescharacteristic
68#1992C2212yes—
69#1990C2211yescharacteristic
70#1989C2212yes—
71#1988C2211yescharacteristic
72#1981C2211yescharacteristic
73#1981C2212yes—
74#1971C2211yescharacteristic
75#1971C2211yescharacteristic
76#1971C2212yes—
77#1969C2212yes—
78#1960C2212yes—
79#1956C2211yescharacteristic
80#1949C2212yes—
81#1948C2211yescharacteristic
82#1948C2212yes—
83#1947C2211yescharacteristic
84#1944C2212yes—
85#1943C2211yescharacteristic
86#1943C2211yescharacteristic
87#1941C2212yes—
88#1935C2211yescharacteristic
89#1935C2211yescharacteristic
90#1935C2211yescharacteristic
91#1935C2211yescharacteristic
92#1935C2212yes—
93#1935C2212yes—
94#1935C2212yes—
95#1935C2212yes—
96#1933C2212yes—
97#1933C2212yes—
98#1928C2212yes—
99#1928C2212yes—
100#1927C2212yes—
101#1921C2212yes—
102#1920C2212yes—
103#1919C2212yes—
104#1878C2212yes—
105#1878C2212yes—
106#1878C2212yes—
107#1865C2212yes—
108#1865C2212yes—
109#1865C2212yes—
110#1836C2212yes—
111#1834C2211yescharacteristic
112#1805C2212yes—
113#1803C2211yescharacteristic
114#1803C2211yescharacteristic
115#1803C2212yes—
116#1776C2212yes—
117C4×#106C2211yescharacteristic
118#1771C2212yes—
119#1771C2212yes—
120C8×C4⋊C4C2211yescharacteristic
121C8×C4⋊C4C2211yescharacteristic
122#1767C2211yescharacteristic
123#1767C2212yes—
124#1763C2212yes—
125#1763C2212yes—
126#1763C2212yes—
127#1763C2212yes—
128C4×#103C2211yescharacteristic
129C4×#103C2211yescharacteristic
130C4×#103C2212yes—
131C4×#103C2212yes—
132C4×#103C2212yes—
133C4×#103C2212yes—
134C4×#97C2211yescharacteristic
135C4×#97C2212yes—
136C22×Q16C2311yescharacteristic
137C22×Q16C2312yes—
138#557—24no—
139#557—24no—
140#557C2×C418yes—
141#557C2×C418yes—
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8C2311yescharacteristic
144C2×C4⋊Q8C2312yes—
145C2×C4⋊Q8C2311yescharacteristic
146C2×#125—21no—
147C2×#125—22no—
148C2×#125—22no—
149C2×#125C2312yes—
150C2×C4×Q8—21no—
151C2×C4×Q8—21no—
152C2×C4×Q8—21no—
153C2×C4×Q8—21no—
154C2×C4×Q8—21no—
155C2×C4×Q8D411yescharacteristic
156C2×C4×Q8D411yescharacteristic
157C2×C4×Q8C2311yescharacteristic
158C2×C4×Q8C2312yes—
159C2×C4×Q8C2311yescharacteristic
160C2×C4×Q8C2312yes—
161C2×C4×Q8C2312yes—
162C2×C4×Q8C2312yes—
163C2×C4×Q8C2312yes—
164C2×C4×Q8C2311yescharacteristic
165#491C2×C4116yes—
166#487C2×C418yes—
167#479C2×C4116yes—
168#475C2×C418yes—
169#462C2×C4116yes—
170#462C2×C418yes—
171#446—24no—
172#446C2×C418yes—
173#441C2×C4116yes—
174C4×Q16C2×C418yes—
175C2×#107C2312yes—
176C2×#107C2311yescharacteristic
177C2×#106C2312yes—
178C2×#106C2311yescharacteristic
179C2×#106C2311yescharacteristic
180C2×#106C2312yes—
181C2×C4⋊C8C2311yescharacteristic
182C2×C4⋊C8C2312yes—
183C2×C4⋊C8C2311yescharacteristic
184C2×C4⋊C8C2312yes—
185C2×#103C2312yes—
186C2×#103C2311yescharacteristic
187C2×#103C2311yescharacteristic
188C2×#103C2312yes—
189C2×#103C2311yescharacteristic
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2311yescharacteristic
195C2×#103C2312yes—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#103C2311yescharacteristic
200C2×#103C2311yescharacteristic
201C2×#97C2311yescharacteristic
202C2×#97C2312yes—
203C2×#97C2311yescharacteristic
204C2×#97C2312yes—
205C2×#97C2311yescharacteristic
206C2×#97C2311yescharacteristic
207C2×#97C2312yes—
208C2×C4×C8C2311yescharacteristic
209C2×C4×C8C2312yes—
210C2×C4×C8C2312yes—
211C2×C4×C8C2311yescharacteristic
212#391—21no—
213#391—21no—
214#391—21no—
215#391C2312yes—
216#391C2311yescharacteristic
217#391C2312yes—
218#391C2311yescharacteristic
219#391C2312yes—
220#391C2311yescharacteristic
221#391C2311yescharacteristic
222#389—21no—
223#389—22no—
224#389—21no—
225#389—22no—
226#389—22no—
227#389—22no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—22no—
232#389—22no—
233#389—22no—
234#389—22no—
235#389C2311yescharacteristic
236#389C2312yes—
237#389C2311yescharacteristic
238#389C2312yes—
239#389C2312yes—
240#389C2311yescharacteristic
241#389C2311yescharacteristic
242#387—22no—
243#387—22no—
244#387—22no—
245#387—22no—
246#387—22no—
247#387—22no—
248#387—22no—
249#387—22no—
250#387—21no—
251#387—21no—
252#387—22no—
253#387—22no—
254#387—21no—
255#387—21no—
256#387—22no—
257#387—22no—
258#387—22no—
259#387—22no—
260#387—22no—
261#387—22no—
262#384—21no—
263#384—22no—
264#384C2311yescharacteristic
265#384C2311yescharacteristic
266#384C2312yes—
267#383—22no—
268#382—21no—
269#382C2312yes—
270C4×C4⋊C4—22no—
271C4×C4⋊C4—21no—
272C4×C4⋊C4—21no—
273C4×C4⋊C4—21no—
274C4×C4⋊C4—22no—
275C4×C4⋊C4—21no—
276C4×C4⋊C4—22no—
277C4×C4⋊C4—22no—
278C4×C4⋊C4—22no—
279C4×C4⋊C4—21no—
280C4×C4⋊C4—22no—
281C4×C4⋊C4—21no—
282C4×C4⋊C4—21no—
283C4×C4⋊C4—22no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4—22no—
286C4×C4⋊C4—21no—
287C4×C4⋊C4—22no—
288C4×C4⋊C4D411yescharacteristic
289C4×C4⋊C4D412yes—
290C4×C4⋊C4D412yes—
291C4×C4⋊C4D411yescharacteristic
292C4×C4⋊C4C2312yes—
293C4×C4⋊C4C2312yes—
294C4×C4⋊C4C2312yes—
295C4×C4⋊C4C2311yescharacteristic
296C4×C4⋊C4C2312yes—
297C4×C4⋊C4C2311yescharacteristic
298C4×C4⋊C4C2312yes—
299C4×C4⋊C4C2311yescharacteristic
300C4×C4⋊C4C2312yes—
301#376—21no—
302#376—22no—
303#376—21no—
304#376—22no—
305#376—22no—
306C43C2312yes—
307C43C2311yescharacteristic
308#340C2312yes—
309#340C2312yes—
310#340C2312yes—
311#340C2312yes—
312#340C2311yescharacteristic
313#340C2312yes—
314#340C2312yes—
315#340C2311yescharacteristic
316#340C2312yes—
317#340C2312yes—
318#340C2312yes—
319#340C2311yescharacteristic
320#340C2311yescharacteristic
321#340C2311yescharacteristic
322#340C2312yes—
323#340C2311yescharacteristic
324#336C2312yes—
325#336C2312yes—
326#336C2312yes—
327C22×Q8—21no—
328C22×Q8C2×D411yescharacteristic
329C22×Q8C2411yescharacteristic
330C22×Q8C2412yes—
331C22×Q8C2411yescharacteristic
332C2×Q16—42no—
333C2×Q16—41no—
334C2×Q16—41no—
335C2×Q16—42no—
336C2×Q16C22×C414yes—
337C2×Q16C22×C418yes—
338C22×C8C2411yescharacteristic
339C22×C8C2412yes—
340C22×C8C2412yes—
341C22×C8C2411yescharacteristic
342C22×C8C2411yescharacteristic
343C22×C8C2411yescharacteristic
344C4⋊Q8—28no—
345C4⋊Q8—22no—
346C4⋊Q8—22no—
347C4⋊Q8—24no—
348C4⋊Q8C22×C414yes—
349C4⋊Q8C22×C418yes—
350C4⋊Q8C22×C414yes—
351#125—216no—
352#125—28no—
353#125—216no—
354#125—24no—
355#125C22×C418yes—
356C4×Q8—28no—
357C4×Q8—28no—
358C4×Q8—24no—
359C4×Q8—22no—
360C4×Q8—24no—
361C4×Q8—24no—
362C4×Q8—22no—
363C4×Q8—42no—
364C4×Q8—44no—
365C4×Q8—42no—
366C4×Q8—42no—
367C4×Q8—42no—
368C4×Q8—42no—
369C4×Q8—42no—
370C4×Q8—42no—
371C4×Q8—44no—
372C4×Q8—44no—
373C4×Q8C22×C414yes—
374C4×Q8C22×C414yes—
375C4×Q8C22×C418yes—
376C4×Q8C22×C418yes—
377C4×Q8C22×C414yes—
378C4×Q8#4114yes—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4C2×D412yes—
407C2×C4⋊C4C2×D411yescharacteristic
408C2×C4⋊C4C2×D412yes—
409C2×C4⋊C4C2×D411yescharacteristic
410C2×C4⋊C4C2×D412yes—
411C2×C4⋊C4C2×D411yescharacteristic
412C2×C4⋊C4C2411yescharacteristic
413C2×C4⋊C4C2412yes—
414C2×C4⋊C4C2411yescharacteristic
415C2×C4⋊C4C2412yes—
416C2×C4⋊C4C2411yescharacteristic
417C2×C4⋊C4C2411yescharacteristic
418C2×C4⋊C4C2411yescharacteristic
419C2×C4⋊C4C2411yescharacteristic
420C2×C4⋊C4C2412yes—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D412yes—
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D412yes—
439C2×C42C2×D412yes—
440C2×C42C2×D412yes—
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2412yes—
444C2×C42C2411yescharacteristic
445C2×C42C2411yescharacteristic
446C2×C42C2412yes—
447C2×C42C2411yescharacteristic
448#107—42no—
449#107C22×C414yes—
450#106—41no—
451#106—42no—
452#106—41no—
453#106C22×C418yes—
454C4⋊C8—22no—
455C4⋊C8—24no—
456C4⋊C8C22×C414yes—
457C4⋊C8C22×C418yes—
458#103—24no—
459#103—22no—
460#103—22no—
461#103—42no—
462#103—41no—
463#103—42no—
464#103—42no—
465#103—42no—
466#103—42no—
467#103—41no—
468#103C22×C414yes—
469#103C22×C414yes—
470#103C22×C418yes—
471#103C22×C418yes—
472#103C22×C418yes—
473#103C22×C418yes—
474#97—22no—
475#97—24no—
476#97—41no—
477#97—42no—
478#97—41no—
479#97—41no—
480#97C22×C418yes—
481C4×C8—22no—
482C4×C8—42no—
483C4×C8—42no—
484C4×C8C22×C414yes—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—22no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—22no—
493#95—21no—
494#95—22no—
495#95—22no—
496#95—21no—
497#95—22no—
498#95—22no—
499#95—21no—
500#95—22no—
501#95—22no—
502#95—21no—
503#95—22no—
504#95—22no—
505#95—21no—
506#95—22no—
507#95—21no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95—21no—
512#95—22no—
513#95—21no—
514#95—22no—
515#95C2×D412yes—
516#95C2×D412yes—
517#95C2×D412yes—
518C2×Q8—24no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—22no—
529C2×Q8—21no—
530C2×Q8—22no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—22no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—42no—
537C2×Q8—42no—
538C2×Q8C4×D414yes—
539C2×Q8C23×C412yes—
540C2×Q8C23×C414yes—
541C2×Q8C23×C412yes—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D412yes—
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D412yes—
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D412yes—
562C22×C4C22×D412yes—
563C22×C4C22×D411yescharacteristic
564C22×C4C2511yescharacteristic
565Q16—44no—
566Q16—48no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—22no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—22no—
575C2×C8—21no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—21no—
579C2×C8—22no—
580C2×C8—21no—
581C2×C8C23×C412yes—
582C2×C8C23×C412yes—
583C2×C8C23×C414yes—
584C2×C82−1+412yes—
585C4⋊C4—28no—
586C4⋊C4—28no—
587C4⋊C4—24no—
588C4⋊C4—28no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—28no—
592C4⋊C4—28no—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—28no—
596C4⋊C4—24no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—22no—
612C4⋊C4—21no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—81no—
622C4⋊C4—82no—
623C4⋊C4—81no—
624C4⋊C4—81no—
625C4⋊C4—82no—
626C4⋊C4—81no—
627C4⋊C4—82no—
628C4⋊C4—82no—
629C4⋊C4—82no—
630C4⋊C4C4×D414yes—
631C4⋊C4C4×D418yes—
632C4⋊C4#13714yes—
633C4⋊C4C23×C414yes—
634C4⋊C4C23×C412yes—
635C4⋊C4C23×C412yes—
636C42—28no—
637C42—24no—
638C42—28no—
639C42—24no—
640C42—24no—
641C42—22no—
642C42—22no—
643C42—21no—
644C42—22no—
645C42—22no—
646C42—21no—
647C42—21no—
648C42—21no—
649C42—42no—
650C42—42no—
651C42—41no—
652C42—41no—
653C42—42no—
654C42—44no—
655C42—44no—
656C42—44no—
657C42—42no—
658C42—42no—
659C42—82no—
660C42—82no—
661C42—82no—
662C42—82no—
663C42—82no—
664C42C23×C412yes—
665C42C23×C414yes—
666C42C2×#4112yes—
667C42C2×#4114yes—
668C23C23×D411yescharacteristic
669Q8—28no—
670Q8—22no—
671Q8—22no—
672Q8—24no—
673Q8—22no—
674Q8—22no—
675Q8—24no—
676Q8—48no—
677Q8—41no—
678Q8—41no—
679Q8—42no—
680Q8—41no—
681Q8—41no—
682Q8—42no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4C2×C4×D414yes—
743C2×C4C2×C4×D414yes—
744C2×C4C2×C4×D412yes—
745C2×C4C2×C4×D412yes—
746C2×C4C2×#13714yes—
747C2×C4C2×#13712yes—
748C2×C4#57512yes—
749C2×C4C24×C411yescharacteristic
750C2×C4C22×#4111yescharacteristic
751C2×C4C2×2−1+411yescharacteristic
752C2×C4#58511yescharacteristic
753C2×C4#58511yescharacteristic
754C2×C4#58511yescharacteristic
755C8—24no—
756C8—22no—
757C8—22no—
758C8—22no—
759C8—41no—
760C8—42no—
761C22C22×C4×D411yescharacteristic
762C22#349711yescharacteristic
763C22#350011yescharacteristic
764C22C22×#13711yescharacteristic
765C22C2×#57511yescharacteristic
766C22#358611yescharacteristic
767C22#358611yescharacteristic
768C4—24no—
769C4—22no—
770C4—24no—
771C4—24no—
772C4—42no—
773C4—44no—
774C4—42no—
775C4—42no—
776C4—42no—
777C4—41no—
778C4—41no—
779C4—42no—
780C4—41no—
781C4—41no—
782C4—44no—
783C4—81no—
784C4—82no—
785C4—81no—
786C4—82no—
787C4—81no—
788C4—81no—
789C4C4×#13714yes—
790C4#342811yescharacteristic
791C4C4×2−1+411yescharacteristic
792C4#351611yescharacteristic
793C4#352411yescharacteristic
794C2#3431211yescharacteristic
795C2C2×C4×#13711yescharacteristic
796C2#6017511yescharacteristic
797C2#6239611yescharacteristic
798C2#6239811yescharacteristic
799C2#6257711yescharacteristic
800C2#6258711yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
26. #3374C4semidirect

Maximal subgroups

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

subgroupindex
C2×#33742
#343372
#343282
#232272
#232142
#231102
#230962
#229762
#229642
#227792
#227712
#227422
#225472
#225242
#221542
#221212
#221182
C4×#4912
#216472
#212872
#212782
#205202