Finite Group Databasebeta

← #6396455

Subgroups — #6396455

Order 512.

2144 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3207C211yesmaximal, characteristic
2#34226C211yesmaximal, characteristic, complemented
3#34226C211yesmaximal, characteristic, complemented
4#23104C214yesmaximal, complemented
5#23005C214yesmaximal, complemented
6#22860C214yesmaximal, complemented
7#22857C214yesmaximal, complemented
8#22269C211yesmaximal, characteristic, complemented
9#22268C211yesmaximal, characteristic, complemented
10#22220C211yesmaximal, characteristic, complemented
11#22218C211yesmaximal, characteristic, complemented
12#21984C211yesmaximal, characteristic, complemented
13#21692C211yesmaximal, characteristic, complemented
14#21690C211yesmaximal, characteristic, complemented
15#21647C211yesmaximal, characteristic, complemented
16#21646C211yesmaximal, characteristic, complemented
17#21401C211yesmaximal, characteristic, complemented
18#21195C211yesmaximal, characteristic, complemented
19#20473C211yesmaximal, characteristic, complemented
20C2×#532C2211yescharacteristic
21C2×#532C2211yescharacteristic
22#3207C4116yescomplemented
23C2×#493C2211yescharacteristic
24C2×#492C2211yescharacteristic
25C2×#487C2211yescharacteristic
26C2×#486C2211yescharacteristic
27C2×#463C2214yes—
28C2×#449C2214yes—
29C2×#442C2214yes—
30C2×#440C2214yes—
31C2×#431C2211yescharacteristic
32C2×#416C2214yes—
33C22×C4×C8C2211yescharacteristic
34#2367—21no—
35#2367—21no—
36#2367C2212yes—
37#2367C2212yes—
38#2363—21no—
39#2363—21no—
40#2363C2212yes—
41#2363C2212yes—
42#2357—21no—
43#2357C2212yes—
44#2349—21no—
45#2349C2212yes—
46#2341—21no—
47#2341C2212yes—
48#2339—21no—
49#2339C2212yes—
50#2324—21no—
51#2324—21no—
52#2324—21no—
53#2324—21no—
54#2319—21no—
55#2319—21no—
56C4×C4⋊Q8C2211yescharacteristic
57C4×C4⋊Q8C2211yescharacteristic
58C4×C4⋊Q8C2211yescharacteristic
59C4×C4⋊Q8C2211yescharacteristic
60C4×#127C2211yescharacteristic
61C4×#127C2211yescharacteristic
62C4×#127C2211yescharacteristic
63C4×#127C2211yescharacteristic
64#2285C2211yescharacteristic
65#2285C2211yescharacteristic
66#2275—21no—
67#2275—21no—
68C4×#117C2211yescharacteristic
69#1990C2211yescharacteristic
70#1990C2211yescharacteristic
71#1973C2214yes—
72#1972C2214yes—
73#1958C2214yes—
74#1957C2211yescharacteristic
75#1957C2211yescharacteristic
76#1957C2211yescharacteristic
77#1957C2211yescharacteristic
78#1956C2211yescharacteristic
79#1956C2211yescharacteristic
80#1949C2214yes—
81#1936C2214yes—
82#1935C2214yes—
83#1927C2214yes—
84#1925C2214yes—
85#1893C2214yes—
86#1880C2214yes—
87#1879C2214yes—
88#1879C2214yes—
89#1877C2214yes—
90#1865C2214yes—
91#1862C2214yes—
92#1854C2214yes—
93#1845C2211yescharacteristic
94#1844C2211yescharacteristic
95#1834C2211yescharacteristic
96#1834C2211yescharacteristic
97#1770C2212yes—
98#1770C2212yes—
99#1763C2214yes—
100#1762C2214yes—
101C4×#102C2214yes—
102#1752C2212yes—
103#1752C2212yes—
104#1744C2211yescharacteristic
105#1744C2211yescharacteristic
106C4×#97C2211yescharacteristic
107C4×#97C2211yescharacteristic
108C22×#41—21no—
109C22×#41C2312yes—
110C22×SD16C2314yes—
111C22×D8C2314yes—
112C23×C8C2312yes—
113#532—24no—
114#532—24no—
115#532C2×C418yescomplemented
116#532C2×C418yescomplemented
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2311yescharacteristic
119C2×#127C2311yescharacteristic
120C2×#127C2311yescharacteristic
121C2×#124—21no—
122C2×#124C2312yes—
123C2×#121—21no—
124C2×#121—21no—
125C2×#121—21no—
126C2×#121C2312yes—
127C2×C4×Q8—21no—
128C2×C4×Q8—21no—
129C2×C4×Q8C2312yes—
130C2×C4×Q8C2312yes—
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×C4×D4—21no—
134C2×C4×D4—21no—
135C2×C4×D4—21no—
136C2×C4×D4—21no—
137C2×C4×D4—21no—
138C2×C4×D4—21no—
139C2×C4×D4—21no—
140C2×C4×D4—21no—
141C2×C4×D4—21no—
142C2×C4×D4C2312yes—
143C2×C4×D4C2312yes—
144C2×C4×D4C2312yes—
145C2×C4×D4C2312yes—
146C2×C4×D4C2312yes—
147C2×#117—21no—
148C2×#117D411yescharacteristic
149C2×#117D411yescharacteristic
150C2×#117C2312yes—
151C22×C42C2311yescharacteristic
152#493C2×C418yes—
153#492C2×C418yescomplemented
154#487C2×C418yescomplemented
155#486C2×C418yescomplemented
156#463C2×C4132yescomplemented
157#449C2×C4132yescomplemented
158#442—48no—
159#440—48no—
160#431C2×C418yescomplemented
161C2×#107C2314yes—
162C2×#106C2314yes—
163C2×C4⋊C8C2312yes—
164#416—48no—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×C22⋊C8C2312yes—
174C2×#97C2312yes—
175C2×#97C2312yes—
176C2×#97C2312yes—
177C2×#97C2312yes—
178C2×C4×C8—24no—
179C2×C4×C8C2311yescharacteristic
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2312yes—
182C2×C4×C8C2311yescharacteristic
183C2×C4×C8C2311yescharacteristic
184#391—21no—
185#391—21no—
186#391C2312yes—
187#391C2312yes—
188#390—22no—
189#390—22no—
190#390—22no—
191#390—22no—
192#390—21no—
193#390—21no—
194#390—21no—
195#390—21no—
196#390—21no—
197#390—21no—
198#390—21no—
199#390—21no—
200#390C2312yes—
201#390C2312yes—
202#390C2312yes—
203#390C2312yes—
204#389—21no—
205#389—21no—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389C2312yes—
211#389C2312yes—
212#388—22no—
213#388—22no—
214#388—22no—
215#388—22no—
216#388—22no—
217#388—22no—
218#388—22no—
219#388—22no—
220#386—22no—
221#386—22no—
222#386—22no—
223#386—22no—
224#385—22no—
225#385—22no—
226#385—22no—
227#385—22no—
228#384C2311yescharacteristic
229#384C2311yescharacteristic
230#384C2311yescharacteristic
231#384C2311yescharacteristic
232#382—21no—
233#382C2312yes—
234#381—22no—
235#381—22no—
236#380—21no—
237#380—21no—
238#380—21no—
239#380—22no—
240#380—22no—
241#380C2312yes—
242C4×C4⋊C4—21no—
243C4×C4⋊C4—21no—
244C4×C4⋊C4—21no—
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⋊C4D411yescharacteristic
252C4×C4⋊C4D411yescharacteristic
253C4×C4⋊C4C2312yes—
254C4×C4⋊C4C2312yes—
255C4×C4⋊C4C2312yes—
256C4×C4⋊C4C2311yescharacteristic
257C4×C4⋊C4C2311yescharacteristic
258C4×C22⋊C4—22no—
259C4×C22⋊C4—22no—
260C4×C22⋊C4—22no—
261C4×C22⋊C4—22no—
262C4×C22⋊C4—22no—
263C4×C22⋊C4—22no—
264C4×C22⋊C4D411yescharacteristic
265C4×C22⋊C4D411yescharacteristic
266C4×C22⋊C4C2311yescharacteristic
267C4×C22⋊C4C2311yescharacteristic
268#376D411yescharacteristic
269#376D411yescharacteristic
270C2×#95—22no—
271C2×#95—22no—
272C43C2311yescharacteristic
273C43C2311yescharacteristic
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278#336C2312yes—
279#336C2312yes—
280#336C2312yes—
281#336C2312yes—
282C2×#41—28no—
283C2×#41—24no—
284C2×#41—44no—
285C2×#41—44no—
286C2×#41—82no—
287C2×#41—82no—
288C2×#41C22×C418yes—
289C22×Q8—21no—
290C22×Q8C2412yes—
291C22×D4—22no—
292C22×D4—22no—
293C22×D4—21no—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4—21no—
297C22×D4C2412yes—
298C22×D4C2412yes—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2411yescharacteristic
308C2×SD16—44no—
309C2×SD16—44no—
310C2×SD16C22×C4116yes—
311C2×D8—44no—
312C2×D8—44no—
313C2×D8C22×C4116yes—
314C22×C8—24no—
315C22×C8—24no—
316C22×C8—42no—
317C22×C8C2412yes—
318C22×C8C2412yes—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323C4⋊Q8C22×C414yes—
324C4⋊Q8C22×C414yes—
325#127—22no—
326#127—22no—
327#127C22×C414yes—
328#127C22×C414yes—
329#124—28no—
330#124—24no—
331#124C22×C418yes—
332#121—28no—
333#121—28no—
334#121—28no—
335#121—24no—
336#121C22×C418yes—
337C4×Q8—44no—
338C4×Q8—44no—
339C4×Q8—82no—
340C4×Q8—82no—
341C4×D4—28no—
342C4×D4—28no—
343C4×D4—28no—
344C4×D4—24no—
345C4×D4—44no—
346C4×D4—44no—
347C4×D4—44no—
348C4×D4—44no—
349C4×D4—44no—
350C4×D4—44no—
351C4×D4—44no—
352C4×D4—44no—
353C4×D4—82no—
354C4×D4—82no—
355C4×D4—82no—
356C4×D4—82no—
357C4×D4C22×C418yes—
358#117—42no—
359#117—42no—
360#117—44no—
361#117—82no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4C2×D411yescharacteristic
378C2×C4⋊C4C2×D411yescharacteristic
379C2×C4⋊C4C2×D411yescharacteristic
380C2×C4⋊C4C2×D411yescharacteristic
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
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×C42C22×C414yes—
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
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×C42#4114yes—
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432#107—44no—
433#106—44no—
434C4⋊C8C22×C418yes—
435#103—28no—
436#103—44no—
437#103C22×C4116yes—
438#102—28no—
439#102—28no—
440#102—44no—
441#102—44no—
442#102C22×C4116yes—
443C22⋊C8C22×C418yes—
444#97—24no—
445#97—24no—
446#97—42no—
447#97—42no—
448C4×C8—24no—
449C4×C8—22no—
450C4×C8—22no—
451C4×C8C22×C414yes—
452C4×C8C22×C414yes—
453#95—22no—
454#95—22no—
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#95C2×D411yescharacteristic
466#95C2×D411yescharacteristic
467#95C2×D411yescharacteristic
468#95C2×D411yescharacteristic
469#95C2×D411yescharacteristic
470#95C2×D411yescharacteristic
471#95C2×D411yescharacteristic
472#95C2×D411yescharacteristic
473C24—22no—
474C24—22no—
475C24C22×D411yescharacteristic
476#41—416no—
477#41—88no—
478#41—816no—
479C2×Q8—24no—
480C2×Q8—22no—
481C2×Q8—24no—
482C2×Q8—24no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8C23×C414yes—
486C2×D4—28no—
487C2×D4—28no—
488C2×D4—24no—
489C2×D4—24no—
490C2×D4—24no—
491C2×D4—24no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—24no—
497C2×D4—24no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—82no—
507C2×D4—82no—
508C2×D4—82no—
509C2×D4—82no—
510C2×D4C23×C414yes—
511C2×D4C23×C414yes—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—28no—
521C22×C4—28no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—44no—
527C22×C4—44no—
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×C4—82no—
539C22×C4—82no—
540C22×C4—82no—
541C22×C4—82no—
542C22×C4C4×D414yes—
543C22×C4C4×D414yes—
544C22×C4C23×C412yes—
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×C4C22×D411yescharacteristic
558C22×C4C2×#4112yes—
559C22×C4C2511yescharacteristic
560SD16—416no—
561D8—416no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—48no—
572C2×C8C23×C414yes—
573C2×C8C23×C414yes—
574C2×C8H(5,𝔽2)14yes—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—22no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—41no—
584C4⋊C4—41no—
585C4⋊C4—41no—
586C4⋊C4—41no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—82no—
596C4⋊C4—82no—
597C4⋊C4—82no—
598C4⋊C4—82no—
599C4⋊C4C23×C414yes—
600C22⋊C4—28no—
601C22⋊C4—28no—
602C22⋊C4—28no—
603C22⋊C4—28no—
604C22⋊C4—41no—
605C22⋊C4—41no—
606C22⋊C4—41no—
607C22⋊C4—41no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—82no—
613C22⋊C4—82no—
614C22⋊C4—82no—
615C22⋊C4—82no—
616C22⋊C4—82no—
617C22⋊C4—82no—
618C22⋊C4—82no—
619C22⋊C4—82no—
620C22⋊C4—82no—
621C22⋊C4—82no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—82no—
635C42—82no—
636C42—82no—
637C42—82no—
638C42—82no—
639C42—82no—
640C42C4×D414yes—
641C42C4×D414yes—
642C42C23×C412yes—
643C42C23×C412yes—
644C42C2×#4112yes—
645C42C2×#4112yes—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—24no—
653C23—24no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23C2×C4×D412yes—
667C23C23×D411yescharacteristic
668Q8—28no—
669Q8—48no—
670Q8—44no—
671D4—28no—
672D4—28no—
673D4—48no—
674D4—48no—
675D4—48no—
676D4—48no—
677D4—44no—
678D4—44no—
679D4—88no—
680D4—88no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—24no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
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—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
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—42no—
732C2×C4—42no—
733C2×C4—88no—
734C2×C4—88no—
735C2×C4—164no—
736C2×C4—164no—
737C2×C4—164no—
738C2×C4—164no—
739C2×C4C2×C4×D412yes—
740C2×C4C2×C4×D412yes—
741C2×C4C2×C4×D412yes—
742C2×C4C2×C4×D412yes—
743C2×C4C2×C4×D412yes—
744C2×C4#57512yes—
745C2×C4#57512yes—
746C2×C4#57612yes—
747C2×C4#57712yes—
748C2×C4C24×C411yescharacteristic
749C2×C4C22×#4111yescharacteristic
750C2×C4C2×H(5,𝔽2)12yes—
751C2×C4#58512yes—
752C8—24no—
753C8—24no—
754C8—24no—
755C8—42no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22C22×C4×D411yescharacteristic
778C22#349811yescharacteristic
779C22#350011yescharacteristic
780C22C2×#57511yescharacteristic
781C22C2×#57511yescharacteristic
782C22C2×#57611yescharacteristic
783C22C2×#57711yescharacteristic
784C4—22no—
785C4—22no—
786C4—22no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—44no—
796C4—44no—
797C4—82no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4#294314yes—
802C4#294614yes—
803C4C4×H(5,𝔽2)12yes—
804C4#349412yes—
805C2—42no—
806C2—84no—
807C2—84no—
808C2#3427511yescharacteristic
809C2C2×#294311yescharacteristic
810C2C2×#294611yescharacteristic
811C2#6242611yescharacteristic
812C2#6242711yescharacteristic
813C2#6254311yescharacteristic
814C2#6254611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3207C2
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
2. #34226C2semidirect
3. #34226C2semidirect
4. #23104C2semidirect
5. #23005C2semidirect
6. #22860C2semidirect
7. #22857C2semidirect
8. #22269C2semidirect
9. #22268C2semidirect
10. #22220C2semidirect
11. #22218C2semidirect
12. #21984C2semidirect
13. #21692C2semidirect
14. #21690C2semidirect
15. #21647C2semidirect
16. #21646C2semidirect
17. #21401C2semidirect
18. #21195C2semidirect
19. #20473C2semidirect
22. #3207C4semidirect
115. #532C2×C4semidirect
116. #532C2×C4semidirect
153. #492C2×C4semidirect
154. #487C2×C4semidirect
155. #486C2×C4semidirect
156. #463C2×C4semidirect
157. #449C2×C4semidirect
160. #431C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#32072
#342262
#231042
#230052
#228602
#228572
#222692
#222682
#222202
#222182
#219842
#216922
#216902
#216472
#216462
#214012
#211952
#204732