Finite Group Databasebeta

← #6389861

Subgroups — #6389861

Order 512.

2294 conjugacy classes of subgroups.

The subgroup lattice has 799 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3152C211yesmaximal, characteristic
2#34226C211yesmaximal, characteristic
3#34216C211yesmaximal, characteristic, complemented
4#23194C214yesmaximal, complemented
5#23192C214yesmaximal, complemented
6#22445C214yesmaximal, complemented
7#22444C214yesmaximal, complemented
8#22270C211yesmaximal, characteristic, complemented
9#22270C211yesmaximal, characteristic, complemented
10#22268C211yesmaximal, characteristic, complemented
11#22268C211yesmaximal, characteristic, complemented
12#21805C211yesmaximal, characteristic
13#21804C211yesmaximal, characteristic, complemented
14#21692C211yesmaximal, characteristic, complemented
15#21691C211yesmaximal, characteristic, complemented
16C4×#494C211yesmaximal, characteristic, complemented
17C4×#492C211yesmaximal, characteristic, complemented
18#20824C211yesmaximal, characteristic, complemented
19#20472C211yesmaximal, characteristic, complemented
20C22×#137C2214yes—
21C2×#532C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23#3152C4116yescomplemented
24C2×#497C2214yes—
25C2×#494C2211yescharacteristic
26C2×#494C2211yescharacteristic
27C2×#492C2211yescharacteristic
28C2×#492C2211yescharacteristic
29C2×#441C2214yes—
30C2×#440C2214yes—
31C2×C4×Q16C2214yes—
32C2×C4×SD16C2214yes—
33C2×#431C2211yescharacteristic
34C2×C4×M16C2211yescharacteristic
35#2369—21no—
36#2369—21no—
37#2367C2212yes—
38#2367C2212yes—
39#2365C2212yes—
40#2365C2212yes—
41#2363—21no—
42#2363—21no—
43#2357—21no—
44#2349—21no—
45#2345—21no—
46#2345—21no—
47#2341C2212yes—
48Q8×C22⋊C4C2212yes—
49Q8×C22⋊C4C2212yes—
50#2339C2212yes—
51#2331—21no—
52#2331—21no—
53#2324—21no—
54#2324—21no—
55#2319—21no—
56#2316—21no—
57C4×C4⋊Q8C2211yescharacteristic
58C4×C4⋊Q8C2211yescharacteristic
59C4×C4⋊Q8C2211yescharacteristic
60C4×C4⋊Q8C2211yescharacteristic
61C4×C4⋊Q8C2211yescharacteristic
62C4×C4⋊Q8C2211yescharacteristic
63C4×#127C2211yescharacteristic
64C4×#127C2211yescharacteristic
65#2285C2211yescharacteristic
66#2285C2211yescharacteristic
67#2275—21no—
68#2274—21no—
69C4×#117C2211yescharacteristic
70#1983C2214yes—
71#1981C2214yes—
72#1973C2214yes—
73#1971C2214yes—
74#1969C2214yes—
75#1968C2214yes—
76#1957C2211yescharacteristic
77#1957C2211yescharacteristic
78#1956C2211yescharacteristic
79#1956C2211yescharacteristic
80#1956C2211yescharacteristic
81#1956C2211yescharacteristic
82#1956C2211yescharacteristic
83#1956C2211yescharacteristic
84#1880C2214yes—
85#1880C2214yes—
86#1878C2214yes—
87#1878C2214yes—
88#1878C2214yes—
89#1878C2214yes—
90#1877C2214yes—
91#1877C2214yes—
92#1845C2211yescharacteristic
93#1844C2211yescharacteristic
94#1834C2211yescharacteristic
95#1834C2211yescharacteristic
96#1809C2214yes—
97#1788C2214yes—
98#1787C2214yes—
99#1776C2214yes—
100#1771C2212yes—
101#1771C2212yes—
102#1753C2212yes—
103#1753C2212yes—
104#1744C2211yescharacteristic
105#1744C2211yescharacteristic
106C4×#97C2211yescharacteristic
107C42×C8C2211yescharacteristic
108C22×#41C2312yes—
109C23×Q8C2312yes—
110C2×#137—48no—
111C2×#137—48no—
112C2×#137C2×C4132yescomplemented
113C22×Q16C2314yes—
114C22×Q16C2314yes—
115C22×SD16C2314yes—
116C22×SD16C2314yes—
117C22×M16C2312yes—
118#532—24no—
119#532C2×C418yes—
120C2×C4⋊Q8—21no—
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8—24no—
123C2×C4⋊Q8C2×C418yescomplemented
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2311yescharacteristic
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2312yes—
128C2×#127C2311yescharacteristic
129C2×#124C2312yes—
130C2×#121—21no—
131C2×#121—21no—
132C2×C4×Q8C2312yes—
133C2×C4×Q8C2312yes—
134C2×C4×Q8C2312yes—
135C2×C4×Q8C2312yes—
136C2×C4×Q8C2312yes—
137C2×C4×Q8C2312yes—
138C2×C4×D4—21no—
139C2×C4×D4—21no—
140C2×C4×D4—21no—
141C2×C4×D4—21no—
142C2×C4×D4—21no—
143C2×C4×D4—21no—
144C2×C4×D4C2312yes—
145C2×C4×D4C2312yes—
146C2×#117—21no—
147C2×#117—21no—
148C2×#117D411yescharacteristic
149C2×#117D411yescharacteristic
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C42C2311yescharacteristic
153#497C2×C4132yescomplemented
154#494C2×C418yescomplemented
155#494C2×C418yescomplemented
156#492C2×C418yes—
157#492C2×C418yes—
158#441—48no—
159#440—48no—
160C4×Q16—48no—
161C4×SD16—48no—
162#431—24no—
163C2×#107C2314yes—
164C2×#106C2314yes—
165C2×C4⋊C8C2312yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×C22⋊C8C2312yes—
175C4×M16C2×C418yescomplemented
176C2×#97C2312yes—
177C2×#97C2312yes—
178C2×#97C2312yes—
179C2×C4×C8C2311yescharacteristic
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2312yes—
182C2×C4×C8C2312yes—
183C2×C4×C8C2311yescharacteristic
184C2×C4×C8C2311yescharacteristic
185#391—22no—
186#391—22no—
187#391—22no—
188#391—22no—
189#391C2312yes—
190#391C2312yes—
191#391C2312yes—
192#391C2312yes—
193#391C2312yes—
194#391C2312yes—
195#390—22no—
196#390—22no—
197#390—21no—
198#390—21no—
199#390—21no—
200#390—21no—
201#390C2312yes—
202#390C2312yes—
203#389—22no—
204#389—22no—
205#389—21no—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389—21no—
215#389—21no—
216#389—21no—
217#388—22no—
218#388—22no—
219#388—22no—
220#388—22no—
221#387—22no—
222#387—22no—
223#387—22no—
224#387—22no—
225#386—22no—
226#386—22no—
227#385—22no—
228#385—22no—
229#384C2311yescharacteristic
230#384C2311yescharacteristic
231#384C2311yescharacteristic
232#384C2311yescharacteristic
233#382—21no—
234#382—21no—
235#381—22no—
236#380—21no—
237#380—21no—
238#380—22no—
239#380—22no—
240#380—22no—
241#380C2312yes—
242#380C2312yes—
243C4×C4⋊C4—22no—
244C4×C4⋊C4—22no—
245C4×C4⋊C4—21no—
246C4×C4⋊C4—21no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4—21no—
250C4×C4⋊C4—21no—
251C4×C4⋊C4—21no—
252C4×C4⋊C4—21no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4D411yescharacteristic
260C4×C4⋊C4D411yescharacteristic
261C4×C4⋊C4C2312yes—
262C4×C4⋊C4C2312yes—
263C4×C4⋊C4C2311yescharacteristic
264C4×C4⋊C4C2311yescharacteristic
265C4×C22⋊C4—22no—
266C4×C22⋊C4—22no—
267C4×C22⋊C4—22no—
268C4×C22⋊C4—22no—
269C4×C22⋊C4—22no—
270C4×C22⋊C4D411yescharacteristic
271C4×C22⋊C4D411yescharacteristic
272C4×C22⋊C4C2311yescharacteristic
273C4×C22⋊C4C2311yescharacteristic
274#376D411yescharacteristic
275#376D411yescharacteristic
276C2×#95—22no—
277C43C2311yescharacteristic
278C43C2311yescharacteristic
279#340C2314yes—
280#340C2314yes—
281#336C2312yes—
282#336C2312yes—
283#336C2312yes—
284#336C2312yes—
285C2×#41—24no—
286C2×#41—44no—
287C2×#41—44no—
288C2×#41C22×C418yes—
289C22×Q8—22no—
290C22×Q8—24no—
291C22×Q8—44no—
292C22×Q8—44no—
293C22×Q8C22×C418yes—
294C22×Q8C2412yes—
295C22×Q8C2412yes—
296C22×Q8C2412yes—
297C22×D4—22no—
298C22×D4—21no—
299C22×D4—21no—
300C22×D4C2412yes—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2411yescharacteristic
308#137—464no—
309C2×Q16—28no—
310C2×Q16—28no—
311C2×Q16—44no—
312C2×Q16—44no—
313C2×Q16C22×C4116yes—
314C2×Q16C22×C4116yes—
315C2×SD16—28no—
316C2×SD16—28no—
317C2×SD16—44no—
318C2×SD16—44no—
319C2×SD16C22×C4116yes—
320C2×SD16C22×C4116yes—
321C2×M16—24no—
322C2×M16—24no—
323C2×M16C22×C418yes—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C22×C8C2412yes—
327C22×C8C2412yes—
328C4⋊Q8—28no—
329C4⋊Q8—28no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—24no—
333C4⋊Q8—22no—
334C4⋊Q8C22×C414yes—
335C4⋊Q8C22×C414yes—
336C4⋊Q8C22×C418yes—
337C4⋊Q8C22×C414yes—
338#127—22no—
339#127C22×C414yes—
340#124—24no—
341#124C22×C418yes—
342#121—28no—
343#121—28no—
344C4×Q8—44no—
345C4×Q8—44no—
346C4×Q8—44no—
347C4×Q8—44no—
348C4×Q8—44no—
349C4×Q8—44no—
350C4×D4—28no—
351C4×D4—28no—
352C4×D4—44no—
353C4×D4—44no—
354C4×D4—44no—
355C4×D4—44no—
356C4×D4—82no—
357C4×D4—82no—
358#117—24no—
359#117—42no—
360#117—44no—
361#117—82no—
362C2×C4⋊C4—28no—
363C2×C4⋊C4—28no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4C2×D411yescharacteristic
387C2×C4⋊C4C2×D411yescharacteristic
388C2×C4⋊C4C2×D411yescharacteristic
389C2×C4⋊C4C2×D411yescharacteristic
390C2×C4⋊C4C2412yes—
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4C2×D411yescharacteristic
405C2×C22⋊C4C2×D411yescharacteristic
406C2×C22⋊C4C2×D411yescharacteristic
407C2×C22⋊C4C2×D411yescharacteristic
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42C22×C414yes—
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42#4114yes—
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434#107—28no—
435#106—28no—
436C4⋊C8—24no—
437#103—44no—
438#103—44no—
439#103—44no—
440#103—44no—
441#103—44no—
442#103—44no—
443#102—44no—
444#102—44no—
445C22⋊C8—24no—
446#97—24no—
447#97—24no—
448#97C22×C418yes—
449C4×C8—24no—
450C4×C8—24no—
451C4×C8—22no—
452C4×C8—22no—
453C4×C8C22×C414yes—
454C4×C8C22×C414yes—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95C2×D411yescharacteristic
472#95C2×D411yescharacteristic
473#95C2×D411yescharacteristic
474#95C2×D411yescharacteristic
475#95C2×D411yescharacteristic
476#95C2×D411yescharacteristic
477#95C2×D411yescharacteristic
478#95C2×D411yescharacteristic
479C24—22no—
480C24C22×D411yescharacteristic
481#41—416no—
482#41—88no—
483C2×Q8—28no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—24no—
488C2×Q8—24no—
489C2×Q8—24no—
490C2×Q8—24no—
491C2×Q8—24no—
492C2×Q8—24no—
493C2×Q8—416no—
494C2×Q8—82no—
495C2×Q8—82no—
496C2×Q8—88no—
497C2×Q8C23×C414yes—
498C2×Q8C23×C414yes—
499C2×Q8C23×C414yes—
500C2×D4—28no—
501C2×D4—24no—
502C2×D4—24no—
503C2×D4—22no—
504C2×D4—24no—
505C2×D4—24no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—82no—
511C2×D4—82no—
512C2×D4C23×C414yes—
513C22×C4—22no—
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—28no—
523C22×C4—28no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—82no—
531C22×C4—82no—
532C22×C4—82no—
533C22×C4—82no—
534C22×C4—82no—
535C22×C4—82no—
536C22×C4—82no—
537C22×C4—82no—
538C22×C4C4×D414yes—
539C22×C4C4×D414yes—
540C22×C4C23×C412yes—
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
555C22×C4C2511yescharacteristic
556Q16—232no—
557Q16—416no—
558SD16—232no—
559SD16—416no—
560M16—216no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8C23×C414yes—
570C2×C8C23×C414yes—
571C2×C8H(5,𝔽2)14yes—
572C2×C8H(5,𝔽2)14yes—
573C4⋊C4—28no—
574C4⋊C4—28no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—41no—
588C4⋊C4—41no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—82no—
598C4⋊C4—82no—
599C4⋊C4—82no—
600C4⋊C4—82no—
601C4⋊C4—82no—
602C4⋊C4—82no—
603C22⋊C4—28no—
604C22⋊C4—28no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—41no—
608C22⋊C4—41no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—82no—
613C22⋊C4—82no—
614C22⋊C4—82no—
615C22⋊C4—82no—
616C22⋊C4—82no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—44no—
629C42—82no—
630C42—82no—
631C42—82no—
632C42—82no—
633C42—82no—
634C42—82no—
635C42—82no—
636C42C4×D414yes—
637C42C4×D414yes—
638C42#13714yescomplemented
639C42C23×C412yes—
640C42C23×C412yes—
641C42C2×#4112yes—
642C42C2×#4112yes—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—24no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23C2×C4×D412yes—
657C23C23×D411yescharacteristic
658Q8—28no—
659Q8—28no—
660Q8—28no—
661Q8—44no—
662Q8—44no—
663Q8—44no—
664Q8—88no—
665D4—28no—
666D4—48no—
667D4—48no—
668D4—44no—
669D4—88no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—24no—
681C2×C4—28no—
682C2×C4—28no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—21no—
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—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
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—88no—
724C2×C4—88no—
725C2×C4—164no—
726C2×C4—164no—
727C2×C4C2×C4×D412yes—
728C2×C4C2×C4×D412yes—
729C2×C4C2×C4×D412yes—
730C2×C4C2×C4×D412yes—
731C2×C4C2×C4×D412yes—
732C2×C4C2×#13712yes—
733C2×C4C2×#13712yes—
734C2×C4C2×#13712yes—
735C2×C4#57512yes—
736C2×C4#57712yes—
737C2×C4#57812yes—
738C2×C4C24×C411yescharacteristic
739C2×C4C22×#4111yescharacteristic
740C2×C4C2×H(5,𝔽2)12yes—
741C2×C4C2×H(5,𝔽2)12yes—
742C8—24no—
743C8—42no—
744C8—42no—
745C8#51818yes—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—82no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22C22×C4×D411yescharacteristic
761C22#349811yescharacteristic
762C22#349811yescharacteristic
763C22C22×#13711yescharacteristic
764C22C2×#57511yescharacteristic
765C22C2×#57711yescharacteristic
766C22C2×#57811yescharacteristic
767C4—22no—
768C4—22no—
769C4—22no—
770C4—22no—
771C4—22no—
772C4—44no—
773C4—44no—
774C4—44no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—82no—
782C4—82no—
783C4—82no—
784C4—82no—
785C4C4×#13714yes—
786C4#294714yes—
787C4C2×#51812yes—
788C4#350812yes—
789C2—42no—
790C2—84no—
791C2#3421011yescharacteristic
792C2C2×C4×#13711yescharacteristic
793C2C2×#294711yescharacteristic
794C2#6242211yescharacteristic
795C2#6242411yescharacteristic
796C2#6242511yescharacteristic
797C2#6242711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#532C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #34216C2semidirect
4. #23194C2semidirect
5. #23192C2semidirect
6. #22445C2semidirect
7. #22444C2semidirect
8. #22270C2semidirect
9. #22270C2semidirect
10. #22268C2semidirect
11. #22268C2semidirect
13. #21804C2semidirect
14. #21692C2semidirect
15. #21691C2semidirect
16. C4×#494C2semidirect
17. C4×#492C2semidirect
18. #20824C2semidirect
19. #20472C2semidirect
23. #3152C4semidirect
112. C2×#137C2×C4semidirect
123. C2×C4⋊Q8C2×C4semidirect
153. #497C2×C4semidirect
154. #494C2×C4semidirect
155. #494C2×C4semidirect
175. C4×M16C2×C4semidirect
638. C42#137semidirect

Maximal subgroups

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

subgroupindex
C2×#31522
#342262
#342162
#231942
#231922
#224452
#224442
#222702
#222682
#218052
#218042
#216922
#216912
C4×#4942
C4×#4922
#208242
#204722