Finite Group Databasebeta

← #6497112

Subgroups — #6497112

Order 512.

1465 conjugacy classes of subgroups.

The subgroup lattice has 919 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35291C211yesmaximal, characteristic, complemented
2#34125C211yesmaximal, characteristic
3#33202C211yesmaximal, characteristic, complemented
4#33073C211yesmaximal, characteristic, complemented
5#32958C211yesmaximal, characteristic
6#32955C211yesmaximal, characteristic
7#29995C211yesmaximal, characteristic, complemented
8#29942C211yesmaximal, characteristic, complemented
9#29941C211yesmaximal, characteristic, complemented
10#29865C211yesmaximal, characteristic, complemented
11#27532C212yesmaximal
12#27530C212yesmaximal
13#27468C212yesmaximal, complemented
14#27466C212yesmaximal, complemented
15#27372C212yesmaximal, complemented
16#27370C212yesmaximal, complemented
17#27308C212yesmaximal, complemented
18#27306C212yesmaximal, complemented
19#22111C211yesmaximal, characteristic, complemented
20#22110C211yesmaximal, characteristic, complemented
21#21922C211yesmaximal, characteristic, complemented
22C4×#477C211yesmaximal, characteristic, complemented
23C4×#475C211yesmaximal, characteristic, complemented
24C2×C4×#41C2211yescharacteristic
25C2×#477C2211yescharacteristic
26C2×#475C2211yescharacteristic
27C2×#476C2211yescharacteristic
28C2×#474C2211yescharacteristic
29#2862C2211yescharacteristic
30#2859C2211yescharacteristic
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic
33#2645—21no—
34#2625—21no—
35#2514—21no—
36#2509C2212yes—
37#2508C2212yes—
38#2495C2212yes—
39#2494C2212yes—
40#2489—21no—
41#2453—21no—
42#2421—21no—
43#2357—21no—
44#2357—21no—
45#2357C2211yescharacteristic
46#2357C2211yescharacteristic
47#2351C2211yescharacteristic
48#2351C2211yescharacteristic
49#2347—21no—
50#2347—21no—
51#2347C2211yescharacteristic
52#2347C2211yescharacteristic
53#2341C2211yescharacteristic
54#2341C2211yescharacteristic
55#2323—21no—
56#2320—21no—
57C4×C4⋊Q8C2211yescharacteristic
58C4×C4⋊Q8C2211yescharacteristic
59#2293—21no—
60#2293—21no—
61#2293C2211yescharacteristic
62#2293C2211yescharacteristic
63#2283—21no—
64#2283C2211yescharacteristic
65C42×Q8C2211yescharacteristic
66C42×Q8C2211yescharacteristic
67C4×#117—21no—
68C4×#117C2211yescharacteristic
69#2101C2212yes—
70#2101C2212yes—
71#2088C2212yes—
72#2087C2212yes—
73#2085C2212yes—
74#2085C2212yes—
75#2085C2212yes—
76#2085C2212yes—
77#2077C2212yes—
78#2077C2212yes—
79#2076C2212yes—
80#2075C2212yes—
81#2073C2212yes—
82#2073C2212yes—
83#2067C2212yes—
84#2065C2212yes—
85#1988C2211yescharacteristic
86#1988C2211yescharacteristic
87#1987C2211yescharacteristic
88#1987C2211yescharacteristic
89#1949C2212yes—
90#1949C2212yes—
91#1948C2211yescharacteristic
92#1948C2211yescharacteristic
93#1947C2211yescharacteristic
94#1947C2211yescharacteristic
95#1942C2212yes—
96#1941C2212yes—
97#1934C2212yes—
98#1934C2212yes—
99#1926C2212yes—
100#1925C2212yes—
101#1923C2212yes—
102#1923C2212yes—
103#1921C2212yes—
104#1920C2212yes—
105#1919C2212yes—
106#1919C2212yes—
107#1918C2212yes—
108#1918C2212yes—
109#1916C2212yes—
110#1916C2212yes—
111#1865C2212yes—
112#1865C2212yes—
113#1865C2212yes—
114#1864C2212yes—
115#1863C2212yes—
116#1863C2212yes—
117#1863C2212yes—
118#1862C2212yes—
119#1854C2212yes—
120#1854C2212yes—
121#1842C2211yescharacteristic
122#1831C2211yescharacteristic
123#1805C2212yes—
124#1805C2212yes—
125#1803C2211yescharacteristic
126#1803C2211yescharacteristic
127#1802C2211yescharacteristic
128#1802C2211yescharacteristic
129#1797C2211yescharacteristic
130#1797C2211yescharacteristic
131#1788C2212yes—
132#1788C2212yes—
133C4×#107C2212yes—
134C4×#106C2212yes—
135C4×C4⋊C8C2211yescharacteristic
136C4×C4⋊C8C2211yescharacteristic
137C4×#103C2212yes—
138C4×#103C2212yes—
139C22×#41C2311yescharacteristic
140C2×C4⋊Q8C2311yescharacteristic
141C2×C4⋊Q8C2311yescharacteristic
142C2×#125—21no—
143C2×C22⋊Q8—21no—
144C2×C22⋊Q8—21no—
145C4×#41—24no—
146C4×#41—24no—
147C2×C4×Q8—21no—
148C2×C4×Q8—21no—
149C2×C4×Q8C2311yescharacteristic
150C2×C4×Q8C2311yescharacteristic
151C2×C4×Q8C2311yescharacteristic
152C2×C4×Q8C2311yescharacteristic
153C2×C4×Q8C2311yescharacteristic
154C2×C4×Q8C2311yescharacteristic
155C2×C4×D4—21no—
156C2×C4×D4—21no—
157C2×C4×D4C2311yescharacteristic
158C2×C4×D4C2311yescharacteristic
159C2×#117—21no—
160C2×#117—21no—
161C2×#117—21no—
162C2×#117D411yescharacteristic
163C2×#117D411yescharacteristic
164C2×#117C2311yescharacteristic
165C22×C42—21no—
166C22×C42C2311yescharacteristic
167#477—24no—
168#476—24no—
169#475—24no—
170#474—24no—
171C2×#107C2312yes—
172C2×#107C2312yes—
173C2×#107C2312yes—
174C2×#107C2312yes—
175C2×#106C2312yes—
176C2×#106C2312yes—
177C2×#106C2312yes—
178C2×#106C2312yes—
179C2×C4⋊C8C2311yescharacteristic
180C2×C4⋊C8C2311yescharacteristic
181C2×C4⋊C8C2311yescharacteristic
182C2×C4⋊C8C2311yescharacteristic
183C2×C4⋊C8C2312yes—
184C2×C4⋊C8C2312yes—
185C2×#103C2312yes—
186C2×#103C2312yes—
187C2×#103C2312yes—
188C2×#103C2312yes—
189C2×#102C2312yes—
190C2×#102C2312yes—
191C2×#102C2312yes—
192C2×#102C2312yes—
193C2×C22⋊C8C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C4×C8C2312yes—
196C2×C4×C8C2312yes—
197#401—22no—
198#400—22no—
199#400—22no—
200#400—22no—
201#400—22no—
202#398—22no—
203#397—22no—
204#397—22no—
205#391—21no—
206#391—21no—
207#391—21no—
208#391—21no—
209#391—21no—
210#391—21no—
211#391—21no—
212#391—21no—
213#390—21no—
214#390—21no—
215#390—21no—
216#390—21no—
217#390C2311yescharacteristic
218#390C2311yescharacteristic
219#390C2311yescharacteristic
220#390C2311yescharacteristic
221#389—22no—
222#389—21no—
223#389—21no—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389C2312yes—
233#389C2312yes—
234#389C2312yes—
235#389C2312yes—
236#389C2311yescharacteristic
237#389C2311yescharacteristic
238#389C2312yes—
239#389C2312yes—
240#389C2311yescharacteristic
241#389C2311yescharacteristic
242#388—21no—
243#388—21no—
244#388—21no—
245#388—21no—
246#388—22no—
247#388—22no—
248#388—21no—
249#388—21no—
250#388—21no—
251#388—21no—
252#388—21no—
253#388—21no—
254#388—21no—
255#388—21no—
256#387—22no—
257#387—22no—
258#387—22no—
259#384C2311yescharacteristic
260#384C2311yescharacteristic
261#383—21no—
262#383—22no—
263#383—21no—
264#383—21no—
265#382—21no—
266#382—22no—
267#382—21no—
268#382—21no—
269#382C2312yes—
270#382C2312yes—
271#382C2311yescharacteristic
272#382C2311yescharacteristic
273#381—21no—
274#381—21no—
275#381—21no—
276#380—21no—
277#380—21no—
278#380—21no—
279#380—21no—
280#380C2311yescharacteristic
281#380C2312yes—
282#380C2312yes—
283#380C2311yescharacteristic
284C4×C4⋊C4—21no—
285C4×C4⋊C4—21no—
286C4×C4⋊C4—21no—
287C4×C4⋊C4—21no—
288C4×C4⋊C4—21no—
289C4×C4⋊C4—21no—
290C4×C4⋊C4—21no—
291C4×C4⋊C4—21no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4—21no—
295C4×C4⋊C4—21no—
296C4×C4⋊C4D411yescharacteristic
297C4×C4⋊C4D411yescharacteristic
298C4×C4⋊C4C2312yes—
299C4×C4⋊C4C2312yes—
300C4×C4⋊C4C2311yescharacteristic
301C4×C4⋊C4C2311yescharacteristic
302C4×C4⋊C4C2311yescharacteristic
303C4×C4⋊C4C2311yescharacteristic
304C4×C4⋊C4C2311yescharacteristic
305C4×C4⋊C4C2311yescharacteristic
306C4×C4⋊C4C2311yescharacteristic
307C4×C4⋊C4C2311yescharacteristic
308C4×C22⋊C4—21no—
309C4×C22⋊C4—21no—
310C4×C22⋊C4—21no—
311C4×C22⋊C4—21no—
312C4×C22⋊C4—21no—
313C4×C22⋊C4—21no—
314C4×C22⋊C4—21no—
315C4×C22⋊C4D411yescharacteristic
316C4×C22⋊C4D411yescharacteristic
317C4×C22⋊C4C2311yescharacteristic
318C4×C22⋊C4C2311yescharacteristic
319#376—21no—
320#376D411yescharacteristic
321#376D411yescharacteristic
322C43—21no—
323C43—21no—
324C43C2311yescharacteristic
325C43C2311yescharacteristic
326#340C2312yes—
327#340C2312yes—
328#340C2312yes—
329#340C2312yes—
330#340C2312yes—
331#340C2312yes—
332#340C2312yes—
333#340C2312yes—
334#340C2312yes—
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#340C2312yes—
341#340C2312yes—
342#336C2312yes—
343#336C2312yes—
344#336C2312yes—
345#336C2312yes—
346#336C2312yes—
347#336C2312yes—
348C2×#41—22no—
349C2×#41—22no—
350C2×#41—22no—
351C2×#41—22no—
352C2×#41—41no—
353C2×#41—41no—
354C22×Q8—21no—
355C22×Q8—21no—
356C22×Q8C2411yescharacteristic
357C22×D4—21no—
358C22×D4C2411yescharacteristic
359C23×C4—21no—
360C23×C4—21no—
361C23×C4—21no—
362C23×C4C2×D411yescharacteristic
363C23×C4C2×D411yescharacteristic
364C23×C4C2411yescharacteristic
365C22×C8C2412yes—
366C22×C8C2412yes—
367C22×C8C2412yes—
368C22×C8C2412yes—
369C4⋊Q8—22no—
370C4⋊Q8—22no—
371C4⋊Q8—22no—
372C4⋊Q8—22no—
373#125—82no—
374C22⋊Q8—44no—
375C22⋊Q8—82no—
376C4×Q8—22no—
377C4×Q8—22no—
378C4×Q8—22no—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8—22no—
383C4×Q8—41no—
384C4×Q8—41no—
385C4×Q8—41no—
386C4×Q8—41no—
387C4×Q8—44no—
388C4×Q8—82no—
389C4×Q8#4114yes—
390C4×D4—28no—
391C4×D4—28no—
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4#4114yes—
396#117—28no—
397#117—22no—
398#117—22no—
399#117—24no—
400#117—42no—
401#117—44no—
402#117—44no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4C2×D411yescharacteristic
426C2×C4⋊C4C2×D411yescharacteristic
427C2×C4⋊C4C2×D411yescharacteristic
428C2×C4⋊C4C2×D411yescharacteristic
429C2×C4⋊C4C2411yescharacteristic
430C2×C4⋊C4C2411yescharacteristic
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2412yes—
434C2×C4⋊C4C2412yes—
435C2×C4⋊C4C2412yes—
436C2×C4⋊C4C2412yes—
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2411yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4C2×D411yescharacteristic
455C2×C22⋊C4C2×D411yescharacteristic
456C2×C22⋊C4C2×D411yescharacteristic
457C2×C22⋊C4C2×D411yescharacteristic
458C2×C42—28no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—22no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—22no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D411yescharacteristic
480C2×C42C2×D411yescharacteristic
481C2×C42C2×D411yescharacteristic
482C2×C42C2×D411yescharacteristic
483C2×C42C2×D411yescharacteristic
484C2×C42C2×D411yescharacteristic
485C2×C42C2×D411yescharacteristic
486C2×C42C2411yescharacteristic
487C2×C42C2411yescharacteristic
488C2×C42C2411yescharacteristic
489C2×C42C2411yescharacteristic
490C2×C42C2411yescharacteristic
491C2×C42C2411yescharacteristic
492#107—24no—
493#107—24no—
494#107—42no—
495#107—42no—
496#106—24no—
497#106—24no—
498#106—42no—
499#106—42no—
500C4⋊C8—22no—
501C4⋊C8—22no—
502C4⋊C8—22no—
503C4⋊C8—22no—
504C4⋊C8—42no—
505C4⋊C8—42no—
506#103—24no—
507#103—24no—
508#103—24no—
509#103—24no—
510#102—24no—
511#102—24no—
512#102—42no—
513#102—42no—
514C22⋊C8—42no—
515C22⋊C8—42no—
516C4×C8—42no—
517C4×C8—42no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95C2×D411yescharacteristic
549#95C2×D411yescharacteristic
550#95C2×D411yescharacteristic
551#95C2×D411yescharacteristic
552#95C2×D411yescharacteristic
553#95C2×D411yescharacteristic
554#95C2×D411yescharacteristic
555#95C2×D411yescharacteristic
556C24—21no—
557C24C22×D411yescharacteristic
558#41—44no—
559#41—44no—
560#41—44no—
561#41—44no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—42no—
566C2×Q8—42no—
567C2×Q8—42no—
568C2×Q8—42no—
569C2×Q8—42no—
570C2×Q8—42no—
571C2×Q8C2×#4112yes—
572C2×Q82−1+412yes—
573C2×Q82−1+412yes—
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4C2×#4112yes—
583C22×C4—21no—
584C22×C4—24no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—24no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C2511yescharacteristic
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—41no—
664C4⋊C4—41no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—44no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—44no—
680C4⋊C4—42no—
681C4⋊C4—82no—
682C4⋊C4—82no—
683C4⋊C4—82no—
684C4⋊C4—82no—
685C4⋊C4C2×#4112yes—
686C4⋊C4C2×#4112yes—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—22no—
691C22⋊C4—22no—
692C22⋊C4—41no—
693C22⋊C4—41no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—44no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—81no—
700C22⋊C4—81no—
701C22⋊C4—81no—
702C22⋊C4—81no—
703C22⋊C4—81no—
704C22⋊C4—81no—
705C22⋊C4—82no—
706C42—24no—
707C42—24no—
708C42—22no—
709C42—24no—
710C42—22no—
711C42—22no—
712C42—22no—
713C42—22no—
714C42—21no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—21no—
720C42—21no—
721C42—21no—
722C42—21no—
723C42—21no—
724C42—41no—
725C42—41no—
726C42—41no—
727C42—41no—
728C42—42no—
729C42—42no—
730C42—42no—
731C42—42no—
732C42—42no—
733C42—44no—
734C42—42no—
735C42—81no—
736C42—81no—
737C42—81no—
738C42—81no—
739C42—82no—
740C42#13514yes—
741C42C2×#4112yes—
742C42C2×#4112yes—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—22no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23C23×D411yescharacteristic
758Q8—22no—
759Q8—22no—
760Q8—22no—
761Q8—84no—
762Q8—84no—
763Q8#54114yes—
764D4—22no—
765D4—22no—
766D4—48no—
767D4—41no—
768D4—41no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—48no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—44no—
813C2×C4—48no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—82no—
843C2×C4—84no—
844C2×C4#52512yes—
845C2×C4#52512yes—
846C2×C4C2×#13512yes—
847C2×C4C2×#13512yes—
848C2×C4C2×#13512yes—
849C2×C4#57512yes—
850C2×C4C22×#4111yescharacteristic
851C2×C4C22×#4111yescharacteristic
852C2×C4C2×2−1+411yescharacteristic
853C2×C4C2×2−1+411yescharacteristic
854C2×C4#58511yescharacteristic
855C2×C4#58511yescharacteristic
856C8—42no—
857C8—42no—
858C8—42no—
859C8—42no—
860C22—41no—
861C22—42no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—42no—
866C22—41no—
867C22—41no—
868C22—42no—
869C22—41no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22C2×#52511yescharacteristic
875C22#348911yescharacteristic
876C22#348911yescharacteristic
877C22C22×#13511yescharacteristic
878C22C2×#57511yescharacteristic
879C22#358511yescharacteristic
880C22#358611yescharacteristic
881C4—22no—
882C4—22no—
883C4—22no—
884C4—24no—
885C4—41no—
886C4—42no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—42no—
891C4—41no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—82no—
897C4—81no—
898C4—81no—
899C4—82no—
900C4—82no—
901C4—81no—
902C4—82no—
903C4—81no—
904C4#310214yes—
905C4C2×#54111yescharacteristic
906C4#345511yescharacteristic
907C4#349511yescharacteristic
908C4#349511yescharacteristic
909C2—81no—
910C2—82no—
911C2#3531011yescharacteristic
912C2C2×#310211yescharacteristic
913C2#6056711yescharacteristic
914C2#6210111yescharacteristic
915C2#6210211yescharacteristic
916C2#6211711yescharacteristic
917C2#6211811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#41C23
LCSG ▷ C22×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
1. #35291C2semidirect
3. #33202C2semidirect
4. #33073C2semidirect
7. #29995C2semidirect
8. #29942C2semidirect
9. #29941C2semidirect
10. #29865C2semidirect
13. #27468C2semidirect
14. #27466C2semidirect
15. #27372C2semidirect
16. #27370C2semidirect
17. #27308C2semidirect
18. #27306C2semidirect
19. #22111C2semidirect
20. #22110C2semidirect
21. #21922C2semidirect
22. C4×#477C2semidirect
23. C4×#475C2semidirect

Maximal subgroups

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

subgroupindex
#352912
#341252
#332022
#330732
#329582
#329552
#299952
#299422
#299412
#298652
#275322
#275302
#274682
#274662
#273722
#273702
#273082
#273062
#221112
#221102
#219222
C4×#4772
C4×#4752