Finite Group Databasebeta

← #6399947

Subgroups — #6399947

Order 512.

1729 conjugacy classes of subgroups.

The subgroup lattice has 795 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3387C211yesmaximal, characteristic
2#34335C211yesmaximal, characteristic
3C4×#557C211yesmaximal, characteristic
4#23169C212yesmaximal
5#23156C211yesmaximal, characteristic
6#23078C212yesmaximal
7#23062C211yesmaximal, characteristic
8#22981C212yesmaximal
9#22965C211yesmaximal, characteristic
10#22777C212yesmaximal
11#22771C211yesmaximal, characteristic
12#22742C211yesmaximal, characteristic
13#22525C211yesmaximal, characteristic
14#22524C211yesmaximal, characteristic
15#22250C212yesmaximal
16#22246C211yesmaximal, characteristic
17#22118C211yesmaximal, characteristic
18#22115C212yesmaximal
19#21616C211yesmaximal, characteristic
20C4×#475C212yesmaximal
21#21123C212yesmaximal
22#21116C211yesmaximal, characteristic
23#20573C211yesmaximal, characteristic
24C2×Q82C2211yescharacteristic
25C2×#557C2211yescharacteristic
26#3387C4116yescomplemented
27C2×#501C2212yes—
28C2×#498C2211yescharacteristic
29C2×#479C2212yes—
30C2×#477C2211yescharacteristic
31C2×#475C2211yescharacteristic
32C2×#475C2212yes—
33C2×#446C2211yescharacteristic
34C2×#446C2211yescharacteristic
35C2×#441C2212yes—
36C2×C4×Q16C2211yescharacteristic
37#2370—22no—
38#2370C2212yes—
39#2369C2211yescharacteristic
40#2369C2212yes—
41#2365—22no—
42#2365—21no—
43#2365—21no—
44#2365C2211yescharacteristic
45#2355—21no—
46#2355C2211yescharacteristic
47#2355C2212yes—
48#2355C2211yescharacteristic
49#2351—21no—
50#2351C2212yes—
51Q8×C4⋊C4C2211yescharacteristic
52Q8×C4⋊C4C2211yescharacteristic
53#2331—21no—
54#2331—22no—
55C4×C4⋊Q8—21no—
56C4×C4⋊Q8C2212yes—
57C4×C4⋊Q8C2211yescharacteristic
58C4×C4⋊Q8C2211yescharacteristic
59C4×#125—22no—
60C4×#125C2212yes—
61#2295C2212yes—
62#2295C2211yescharacteristic
63#2276—21no—
64C42×Q8—21no—
65C42×Q8C2212yes—
66C42×Q8C2211yescharacteristic
67C42×Q8C2211yescharacteristic
68#1993C2212yes—
69#1992C2212yes—
70#1990C2211yescharacteristic
71#1990C2211yescharacteristic
72#1989C2212yes—
73#1988C2211yescharacteristic
74#1988C2212yes—
75#1987C2211yescharacteristic
76#1949C2212yes—
77#1948C2211yescharacteristic
78#1948C2212yes—
79#1947C2211yescharacteristic
80#1944C2212yes—
81#1942C2212yes—
82#1941C2212yes—
83#1935C2212yes—
84#1933C2212yes—
85#1933C2212yes—
86#1928C2212yes—
87#1927C2212yes—
88#1927C2211yescharacteristic
89#1927C2211yescharacteristic
90#1921C2212yes—
91#1921C2212yes—
92#1920C2212yes—
93#1920C2212yes—
94#1920C2212yes—
95#1919C2212yes—
96#1919C2212yes—
97#1919C2212yes—
98#1919C2212yes—
99#1919C2212yes—
100#1918C2212yes—
101#1918C2211yescharacteristic
102#1918C2211yescharacteristic
103#1878C2211yescharacteristic
104#1878C2211yescharacteristic
105#1878C2212yes—
106#1865C2211yescharacteristic
107#1865C2212yes—
108#1865C2211yescharacteristic
109#1863C2212yes—
110#1836C2212yes—
111#1834C2211yescharacteristic
112#1805C2212yes—
113#1803C2211yescharacteristic
114#1803C2212yes—
115#1803C2211yescharacteristic
116#1776C2212yes—
117#1776C2212yes—
118C4×#106C2212yes—
119C4×#106C2212yes—
120C4×#106C2211yescharacteristic
121#1771C2212yes—
122#1771C2212yes—
123C8×C4⋊C4C2211yescharacteristic
124C8×C4⋊C4C2211yescharacteristic
125#1767C2211yescharacteristic
126C4×C4⋊C8C2212yes—
127#1763C2212yes—
128#1763C2212yes—
129#1763C2212yes—
130C4×#103C2211yescharacteristic
131C4×#103C2212yes—
132C4×#103C2212yes—
133C4×#103C2211yescharacteristic
134#1745C2212yes—
135#1744C2211yescharacteristic
136C22×Q16C2311yescharacteristic
137Q82—24no—
138Q82C2×C418yes—
139#557—24no—
140#557C2×C418yes—
141C2×C4⋊Q8—21no—
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8—22no—
144C2×C4⋊Q8C2311yescharacteristic
145C2×C4⋊Q8C2312yes—
146C2×C4⋊Q8C2311yescharacteristic
147C2×#125—22no—
148C2×#125C2312yes—
149C2×C4×Q8—21no—
150C2×C4×Q8—21no—
151C2×C4×Q8—21no—
152C2×C4×Q8—21no—
153C2×C4×Q8—21no—
154C2×C4×Q8—22no—
155C2×C4×Q8—21no—
156C2×C4×Q8D411yescharacteristic
157C2×C4×Q8D411yescharacteristic
158C2×C4×Q8C2311yescharacteristic
159C2×C4×Q8C2312yes—
160C2×C4×Q8C2311yescharacteristic
161C2×C4×Q8C2312yes—
162C2×C4×Q8C2311yescharacteristic
163C2×C4×Q8C2311yescharacteristic
164C2×C4×Q8C2312yes—
165C2×C4×Q8C2311yescharacteristic
166#501C2×C4116yes—
167#498C2×C418yes—
168#479C2×C4116yes—
169#477C2×C418yes—
170#475C2×C4116yes—
171#475C2×C418yes—
172#446—24no—
173#446C2×C418yes—
174#441C2×C4116yes—
175C4×Q16C2×C418yes—
176C2×#107C2312yes—
177C2×#107C2312yes—
178C2×#107C2311yescharacteristic
179C2×#106C2311yescharacteristic
180C2×#106C2312yes—
181C2×#106C2311yescharacteristic
182C2×#106C2312yes—
183C2×#106C2312yes—
184C2×#106C2312yes—
185C2×C4⋊C8C2311yescharacteristic
186C2×C4⋊C8C2312yes—
187C2×C4⋊C8C2311yescharacteristic
188C2×C4⋊C8C2312yes—
189C2×#103C2311yescharacteristic
190C2×#103C2312yes—
191C2×#103C2311yescharacteristic
192C2×#103C2311yescharacteristic
193C2×#103C2312yes—
194C2×#103C2311yescharacteristic
195C2×#103C2311yescharacteristic
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2311yescharacteristic
199C2×#97C2312yes—
200C2×#97C2312yes—
201C2×#97C2312yes—
202C2×C4×C8C2311yescharacteristic
203C2×C4×C8C2312yes—
204C2×C4×C8C2312yes—
205C2×C4×C8C2311yescharacteristic
206#391—21no—
207#391—21no—
208#391—22no—
209#391—21no—
210#391—21no—
211#391—22no—
212#391—22no—
213#391—22no—
214#391C2312yes—
215#391C2311yescharacteristic
216#391C2311yescharacteristic
217#389—22no—
218#389—22no—
219#389—22no—
220#389—21no—
221#389—22no—
222#389—21no—
223#389—22no—
224#389—21no—
225#389—22no—
226#389—21no—
227#389—22no—
228#389C2312yes—
229#389C2312yes—
230#389C2311yescharacteristic
231#389C2312yes—
232#389C2312yes—
233#389C2312yes—
234#389C2311yescharacteristic
235#387—22no—
236#387—22no—
237#387—22no—
238#387—22no—
239#387—22no—
240#387—21no—
241#387—22no—
242#387—21no—
243#387—22no—
244#387—22no—
245#387—22no—
246#387—22no—
247#387—22no—
248#384—21no—
249#384C2311yescharacteristic
250#384C2311yescharacteristic
251#384C2312yes—
252#382—21no—
253#382—22no—
254#382—22no—
255#382C2312yes—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4—22no—
259C4×C4⋊C4—21no—
260C4×C4⋊C4—22no—
261C4×C4⋊C4—21no—
262C4×C4⋊C4—21no—
263C4×C4⋊C4—21no—
264C4×C4⋊C4—22no—
265C4×C4⋊C4—22no—
266C4×C4⋊C4—22no—
267C4×C4⋊C4—22no—
268C4×C4⋊C4—21no—
269C4×C4⋊C4—21no—
270C4×C4⋊C4—22no—
271C4×C4⋊C4—21no—
272C4×C4⋊C4—22no—
273C4×C4⋊C4—22no—
274C4×C4⋊C4—21no—
275C4×C4⋊C4—22no—
276C4×C4⋊C4—22no—
277C4×C4⋊C4D412yes—
278C4×C4⋊C4D411yescharacteristic
279C4×C4⋊C4D412yes—
280C4×C4⋊C4D411yescharacteristic
281C4×C4⋊C4C2311yescharacteristic
282C4×C4⋊C4C2312yes—
283C4×C4⋊C4C2312yes—
284C4×C4⋊C4C2312yes—
285C4×C4⋊C4C2312yes—
286C4×C4⋊C4C2311yescharacteristic
287C4×C4⋊C4C2312yes—
288C4×C4⋊C4C2311yescharacteristic
289C4×C4⋊C4C2312yes—
290C4×C4⋊C4C2312yes—
291C4×C4⋊C4C2311yescharacteristic
292C4×C4⋊C4C2311yescharacteristic
293C4×C4⋊C4C2312yes—
294#376—22no—
295#376—21no—
296C43—22no—
297C43—21no—
298C43C2312yes—
299C43C2311yescharacteristic
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2312yes—
307#340C2312yes—
308#340C2311yescharacteristic
309#340C2312yes—
310#340C2312yes—
311#340C2312yes—
312#340C2311yescharacteristic
313#340C2311yescharacteristic
314#340C2312yes—
315#340C2311yescharacteristic
316#340C2311yescharacteristic
317#340C2311yescharacteristic
318#340C2312yes—
319#340C2312yes—
320#336C2312yes—
321#336C2312yes—
322#336C2311yescharacteristic
323#336C2311yescharacteristic
324#336C2311yescharacteristic
325#336C2311yescharacteristic
326#336C2312yes—
327C22×Q8—21no—
328C22×Q8—22no—
329C22×Q8—21no—
330C22×Q8C2×D411yescharacteristic
331C22×Q8C2411yescharacteristic
332C22×Q8C2411yescharacteristic
333C2×Q16—22no—
334C2×Q16—22no—
335C2×Q16C22×C414yes—
336C22×C8C2411yescharacteristic
337C22×C8C2411yescharacteristic
338C22×C8C2412yes—
339C22×C8C2411yescharacteristic
340C22×C8C2411yescharacteristic
341C22×C8C2412yes—
342C4⋊Q8—28no—
343C4⋊Q8—28no—
344C4⋊Q8—216no—
345C4⋊Q8—22no—
346C4⋊Q8—22no—
347C4⋊Q8—24no—
348C4⋊Q8C22×C414yes—
349C4⋊Q8C22×C418yes—
350C4⋊Q8C22×C414yes—
351#125—216no—
352#125—24no—
353#125C22×C418yes—
354C4×Q8—28no—
355C4×Q8—22no—
356C4×Q8—28no—
357C4×Q8—24no—
358C4×Q8—22no—
359C4×Q8—24no—
360C4×Q8—22no—
361C4×Q8—22no—
362C4×Q8—24no—
363C4×Q8—24no—
364C4×Q8—22no—
365C4×Q8—42no—
366C4×Q8—42no—
367C4×Q8—41no—
368C4×Q8—44no—
369C4×Q8—44no—
370C4×Q8—44no—
371C4×Q8—84no—
372C4×Q8—82no—
373C4×Q8C22×C414yes—
374C4×Q8C22×C418yes—
375C4×Q8C22×C414yes—
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—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—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4C2×D412yes—
405C2×C4⋊C4C2×D411yescharacteristic
406C2×C4⋊C4C2×D412yes—
407C2×C4⋊C4C2×D411yescharacteristic
408C2×C4⋊C4C2×D412yes—
409C2×C4⋊C4C2×D411yescharacteristic
410C2×C4⋊C4C2411yescharacteristic
411C2×C4⋊C4C2412yes—
412C2×C4⋊C4C2412yes—
413C2×C4⋊C4C2411yescharacteristic
414C2×C4⋊C4C2411yescharacteristic
415C2×C4⋊C4C2411yescharacteristic
416C2×C4⋊C4C2412yes—
417C2×C4⋊C4C2411yescharacteristic
418C2×C4⋊C4C2412yes—
419C2×C4⋊C4C2411yescharacteristic
420C2×C42—22no—
421C2×C42—21no—
422C2×C42—22no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—21no—
428C2×C42—22no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—22no—
432C2×C42—21no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—21no—
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D412yes—
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D412yes—
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D412yes—
444C2×C42C2×D412yes—
445C2×C42C2×D411yescharacteristic
446C2×C42C2411yescharacteristic
447C2×C42C2412yes—
448C2×C42C2411yescharacteristic
449C2×C42C2412yes—
450C2×C42C2411yescharacteristic
451#107—42no—
452#107C22×C414yes—
453#107C22×C418yes—
454#106—22no—
455#106—24no—
456#106—41no—
457#106C22×C418yes—
458#106C22×C418yes—
459#106C22×C418yes—
460C4⋊C8—22no—
461C4⋊C8—24no—
462C4⋊C8C22×C414yes—
463C4⋊C8C22×C418yes—
464#103—22no—
465#103—24no—
466#103—22no—
467#103—22no—
468#103—41no—
469#103—42no—
470#103C22×C414yes—
471#103C22×C414yes—
472#103C22×C418yes—
473#103C22×C418yes—
474#97—24no—
475#97—42no—
476#97C22×C418yes—
477C4×C8—22no—
478C4×C8—42no—
479C4×C8—42no—
480C4×C8C22×C414yes—
481#95—21no—
482#95—21no—
483#95—22no—
484#95—21no—
485#95—22no—
486#95—22no—
487#95—21no—
488#95—22no—
489#95—21no—
490#95—22no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—22no—
495#95—22no—
496#95—22no—
497#95—22no—
498#95—21no—
499#95—22no—
500#95—22no—
501#95—22no—
502#95—22no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—21no—
507#95C2×D412yes—
508#95C2×D412yes—
509#95C2×D412yes—
510C2×Q8—24no—
511C2×Q8—28no—
512C2×Q8—24no—
513C2×Q8—22no—
514C2×Q8—22no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—42no—
524C2×Q8—42no—
525C2×Q8—82no—
526C2×Q8—81no—
527C2×Q8—82no—
528C2×Q8—81no—
529C2×Q8C4×D414yes—
530C2×Q8C23×C412yes—
531C2×Q8C23×C412yes—
532C2×Q82−1+412yes—
533C2×Q82−1+412yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D412yes—
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D412yes—
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D412yes—
553C22×C4C22×D412yes—
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C2511yescharacteristic
557Q16—28no—
558C2×C8—21no—
559C2×C8—22no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—22no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—22no—
567C2×C8—21no—
568C2×C8—22no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—22no—
573C2×C8C23×C412yes—
574C2×C8C23×C412yes—
575C2×C8C23×C414yes—
576C4⋊C4—24no—
577C4⋊C4—28no—
578C4⋊C4—28no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—28no—
582C4⋊C4—28no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—28no—
586C4⋊C4—24no—
587C4⋊C4—22no—
588C4⋊C4—21no—
589C4⋊C4—22no—
590C4⋊C4—21no—
591C4⋊C4—22no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—21no—
601C4⋊C4—22no—
602C4⋊C4—21no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—44no—
613C4⋊C4—81no—
614C4⋊C4—81no—
615C4⋊C4—82no—
616C4⋊C4—82no—
617C4⋊C4—82no—
618C4⋊C4—81no—
619C4⋊C4C4×D414yes—
620C4⋊C4C4×D418yes—
621C4⋊C4#13714yes—
622C4⋊C4C23×C414yes—
623C4⋊C4C23×C412yes—
624C4⋊C4C23×C414yes—
625C4⋊C4C23×C412yes—
626C4⋊C42−1+412yes—
627C42—24no—
628C42—28no—
629C42—24no—
630C42—28no—
631C42—24no—
632C42—24no—
633C42—22no—
634C42—22no—
635C42—24no—
636C42—22no—
637C42—21no—
638C42—21no—
639C42—22no—
640C42—21no—
641C42—22no—
642C42—21no—
643C42—42no—
644C42—41no—
645C42—42no—
646C42—44no—
647C42—42no—
648C42—44no—
649C42—44no—
650C42—44no—
651C42—42no—
652C42—42no—
653C42—42no—
654C42—82no—
655C42—81no—
656C42—82no—
657C42—82no—
658C42—82no—
659C42C23×C412yes—
660C42C23×C414yes—
661C42C2×#4112yes—
662C42C2×#4114yes—
663C23C23×D411yescharacteristic
664Q8—22no—
665Q8—28no—
666Q8—22no—
667Q8—22no—
668Q8—22no—
669Q8—22no—
670Q8—48no—
671Q8—41no—
672Q8—41no—
673Q8—88no—
674Q8—84no—
675Q8#51914yes—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4C2×C4×D414yes—
735C2×C4C2×C4×D414yes—
736C2×C4C2×C4×D412yes—
737C2×C4C2×C4×D412yes—
738C2×C4C2×#13714yes—
739C2×C4C2×#13712yes—
740C2×C4#57512yes—
741C2×C4#57712yes—
742C2×C4C24×C411yescharacteristic
743C2×C4C22×#4111yescharacteristic
744C2×C4C2×2−1+411yescharacteristic
745C2×C4C2×2−1+411yescharacteristic
746C2×C4C2×2−1+411yescharacteristic
747C2×C4#58511yescharacteristic
748C8—22no—
749C8—22no—
750C8—24no—
751C8—41no—
752C8—42no—
753C8—41no—
754C22C22×C4×D411yescharacteristic
755C22#348611yescharacteristic
756C22#348911yescharacteristic
757C22C22×#13711yescharacteristic
758C22C2×#57511yescharacteristic
759C22C2×#57711yescharacteristic
760C22#358411yescharacteristic
761C4—24no—
762C4—22no—
763C4—22no—
764C4—24no—
765C4—24no—
766C4—24no—
767C4—42no—
768C4—44no—
769C4—42no—
770C4—41no—
771C4—42no—
772C4—41no—
773C4—41no—
774C4—42no—
775C4—42no—
776C4—44no—
777C4—82no—
778C4—81no—
779C4—81no—
780C4—82no—
781C4—81no—
782C4C4×#13714yes—
783C4C2×#51911yescharacteristic
784C4C4×2−1+411yescharacteristic
785C4#351611yescharacteristic
786C4#352311yescharacteristic
787C2#3429111yescharacteristic
788C2C2×C4×#13711yescharacteristic
789C2C4×#57711yescharacteristic
790C2#6183611yescharacteristic
791C2#6184611yescharacteristic
792C2#6213111yescharacteristic
793C2#6214211yescharacteristic
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. #3387C4semidirect

Maximal subgroups

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

subgroupindex
C2×#33872
#343352
C4×#5572
#231692
#231562
#230782
#230622
#229812
#229652
#227772
#227712
#227422
#225252
#225242
#222502
#222462
#221182
#221152
#216162
C4×#4752
#211232
#211162
#205732