Finite Group Databasebeta

← #6464659

Subgroups — #6464659

Order 512.

1651 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36638C211yesmaximal, characteristic
2C4×#533C211yesmaximal, characteristic, complemented
3#29514C211yesmaximal, characteristic, complemented
4#29512C211yesmaximal, characteristic, complemented
5#29495C211yesmaximal, characteristic, complemented
6#29494C211yesmaximal, characteristic, complemented
7#29467C212yesmaximal
8#29463C212yesmaximal, complemented
9#29350C211yesmaximal, characteristic, complemented
10#29315C211yesmaximal, characteristic, complemented
11#29126C211yesmaximal, characteristic, complemented
12#28377C211yesmaximal, characteristic, complemented
13#24705C212yesmaximal, complemented
14#24655C212yesmaximal
15#23756C211yesmaximal, characteristic, complemented
16#23754C211yesmaximal, characteristic
17#23571C211yesmaximal, characteristic, complemented
18#23568C211yesmaximal, characteristic
19C4×#479C212yesmaximal, complemented
20C4×#464C212yesmaximal, complemented
21#21276C212yesmaximal, complemented
22#21274C212yesmaximal, complemented
23C4×#431C211yesmaximal, characteristic, complemented
24C2×#533C2211yescharacteristic
25C2×#479C2212yes—
26C2×#464C2212yes—
27C2×C4×Q16C2212yes—
28C2×C4×SD16C2212yes—
29C2×#431C2212yes—
30#2866—21no—
31#2865—21no—
32#2864C2211yescharacteristic
33#2863C2211yescharacteristic
34#2861C2211yescharacteristic
35#2860C2211yescharacteristic
36#2855C2211yescharacteristic
37#2854C2211yescharacteristic
38#2853—21no—
39#2852—21no—
40#2851C2211yescharacteristic
41#2850C2211yescharacteristic
42C4×C4⋊Q8C2211yescharacteristic
43C4×C4⋊Q8C2211yescharacteristic
44C4×C4⋊Q8C2211yescharacteristic
45C4×C4⋊Q8C2211yescharacteristic
46C4×#125—21no—
47C4×#125—21no—
48C4×#125C2211yescharacteristic
49C4×#126—21no—
50C4×#124C2211yescharacteristic
51C4×C22⋊Q8—21no—
52C4×C22⋊Q8—21no—
53C4×C22⋊Q8C2211yescharacteristic
54C4×C22⋊Q8C2212yes—
55C4×C22⋊Q8C2212yes—
56C4×#123—21no—
57C4×#121C2211yescharacteristic
58#2298—21no—
59#2296—21no—
60#2295—21no—
61#2295C2212yes—
62#2295C2211yescharacteristic
63#2293C2211yescharacteristic
64#2290—21no—
65#2285C2211yescharacteristic
66C42×Q8—21no—
67C42×Q8C2212yes—
68C4×#117—21no—
69C2×C43C2211yescharacteristic
70#2099C2211yescharacteristic
71#2099C2211yescharacteristic
72#2096C2211yescharacteristic
73#2093C2211yescharacteristic
74#2084C2211yescharacteristic
75#2083C2211yescharacteristic
76#2077C2212yes—
77#2075C2212yes—
78#2072C2211yescharacteristic
79#2071C2211yescharacteristic
80#2058C2211yescharacteristic
81#2057C2211yescharacteristic
82#2043C2211yescharacteristic
83#2043C2211yescharacteristic
84#2036C2212yes—
85#2035C2212yes—
86#2035C2212yes—
87#2033C2212yes—
88#2024C2211yescharacteristic
89#2023C2211yescharacteristic
90#2016C2211yescharacteristic
91#2013C2211yescharacteristic
92#2001C2212yes—
93#2000C2212yes—
94#1989C2212yes—
95#1983C2212yes—
96#1969C2212yes—
97#1969C2212yes—
98#1968C2212yes—
99#1968C2212yes—
100#1949C2212yes—
101#1949C2212yes—
102#1942C2212yes—
103#1942C2212yes—
104#1941C2212yes—
105#1941C2212yes—
106#1934C2212yes—
107#1934C2212yes—
108#1933C2212yes—
109#1933C2212yes—
110#1933C2212yes—
111#1933C2212yes—
112#1933C2212yes—
113#1933C2212yes—
114#1927C2212yes—
115#1925C2212yes—
116#1920C2212yes—
117#1918C2212yes—
118#1880C2212yes—
119#1878C2212yes—
120#1865C2212yes—
121#1863C2212yes—
122#1805C2212yes—
123#1805C2212yes—
124C4×#107C2212yes—
125C4×#106C2212yes—
126C4×C4⋊C8C2212yes—
127C4×C4⋊C8C2211yescharacteristic
128C4×C4⋊C8C2211yescharacteristic
129C4×#103C2212yes—
130C4×#103C2212yes—
131C4×#103C2212yes—
132C4×#102C2212yes—
133C4×C22⋊C8C2211yescharacteristic
134C4×C22⋊C8C2211yescharacteristic
135C4×C22⋊C8C2212yes—
136#1744C2211yescharacteristic
137#1744C2211yescharacteristic
138C42×C8C2212yes—
139C22×Q16C2312yes—
140C22×SD16C2312yes—
141#533—28no—
142C2×C4⋊Q8C2311yescharacteristic
143C2×C4⋊Q8C2311yescharacteristic
144C2×#126—21no—
145C2×#125—21no—
146C2×#125C2311yescharacteristic
147C2×#124C2311yescharacteristic
148C2×#123—21no—
149C2×C22⋊Q8—21no—
150C2×C22⋊Q8C2312yes—
151C2×C22⋊Q8C2311yescharacteristic
152C2×#121C2311yescharacteristic
153C2×C4×Q8—21no—
154C2×C4×Q8—21no—
155C2×C4×Q8—21no—
156C2×C4×Q8C2312yes—
157C2×C4×Q8C2311yescharacteristic
158C2×C4×Q8C2312yes—
159C2×C4×Q8C2312yes—
160C2×C4×D4—21no—
161C2×C4×D4C2311yescharacteristic
162C2×#117—21no—
163C2×#117—21no—
164C2×#117—21no—
165C22×C42D411yescharacteristic
166C22×C42D411yescharacteristic
167C22×C42D411yescharacteristic
168C22×C42D411yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172#479—28no—
173#464—28no—
174C4×Q16—28no—
175C4×SD16—28no—
176#431—28no—
177C2×#107C2312yes—
178C2×#107C2312yes—
179C2×#107C2312yes—
180C2×#106C2312yes—
181C2×#106C2312yes—
182C2×#106C2312yes—
183C2×C4⋊C8C2312yes—
184C2×C4⋊C8C2312yes—
185C2×#103C2312yes—
186C2×#103C2312yes—
187C2×#103C2312yes—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#102C2312yes—
195C2×#102C2312yes—
196C2×#102C2312yes—
197C2×C22⋊C8C2312yes—
198C2×C22⋊C8C2312yes—
199C2×C4×C8C2312yes—
200C2×C4×C8C2312yes—
201C2×C4×C8C2312yes—
202C2×C4×C8C2312yes—
203C2×C4×C8C2312yes—
204C2×C4×C8C2312yes—
205#391—21no—
206#391—21no—
207#391C2312yes—
208#391C2312yes—
209#391C2311yescharacteristic
210#391C2311yescharacteristic
211#391C2311yescharacteristic
212#391C2311yescharacteristic
213#390C2311yescharacteristic
214#390C2311yescharacteristic
215#390C2311yescharacteristic
216#390C2311yescharacteristic
217#389—21no—
218#389—21no—
219#389—21no—
220#389—21no—
221#389—21no—
222#389—21no—
223#389C2311yescharacteristic
224#389C2311yescharacteristic
225#389C2312yes—
226#389C2312yes—
227#389C2311yescharacteristic
228#389C2311yescharacteristic
229#389C2311yescharacteristic
230#389C2311yescharacteristic
231#389C2311yescharacteristic
232#389C2311yescharacteristic
233#388—21no—
234#388—21no—
235#388—21no—
236#388—21no—
237#388—21no—
238#388—21no—
239#388—21no—
240#388—21no—
241#388—21no—
242#388—21no—
243#388—21no—
244#388—21no—
245#388—21no—
246#388—21no—
247#388—21no—
248#388—21no—
249#387—21no—
250#387—21no—
251#387—21no—
252#387—22no—
253#387—22no—
254#387—22no—
255#387—22no—
256#387—21no—
257#387—21no—
258#387—21no—
259#387—21no—
260#387—21no—
261#387—21no—
262#387—21no—
263#387—21no—
264#387—21no—
265#387—21no—
266#387—21no—
267#387—21no—
268#387—21no—
269#386—21no—
270#386—21no—
271#386—21no—
272#386—21no—
273#385—21no—
274#385—21no—
275#385—21no—
276#385—21no—
277#385—22no—
278#385—22no—
279#384C2311yescharacteristic
280#384C2311yescharacteristic
281#383—21no—
282#382—21no—
283#382C2311yescharacteristic
284#382C2311yescharacteristic
285#381—21no—
286#380—21no—
287#380C2311yescharacteristic
288#380C2312yes—
289#380C2311yescharacteristic
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⋊C4—21no—
297C4×C4⋊C4—22no—
298C4×C4⋊C4—22no—
299C4×C4⋊C4—22no—
300C4×C4⋊C4—22no—
301C4×C4⋊C4—21no—
302C4×C4⋊C4—21no—
303C4×C4⋊C4—21no—
304C4×C4⋊C4—21no—
305C4×C4⋊C4—22no—
306C4×C4⋊C4—22no—
307C4×C4⋊C4C2311yescharacteristic
308C4×C4⋊C4C2311yescharacteristic
309C4×C4⋊C4C2312yes—
310C4×C4⋊C4C2312yes—
311C4×C4⋊C4C2312yes—
312C4×C22⋊C4—22no—
313C4×C22⋊C4—22no—
314C4×C22⋊C4—21no—
315C4×C22⋊C4—21no—
316C4×C22⋊C4—21no—
317C4×C22⋊C4—21no—
318C4×C22⋊C4—21no—
319#376—22no—
320#376—21no—
321C43—22no—
322C43D411yescharacteristic
323C43D411yescharacteristic
324C43D411yescharacteristic
325C43D411yescharacteristic
326C43C2311yescharacteristic
327C43C2311yescharacteristic
328C43C2311yescharacteristic
329C43C2311yescharacteristic
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#336C2311yescharacteristic
343#336C2311yescharacteristic
344#336C2311yescharacteristic
345#336C2311yescharacteristic
346#336C2312yes—
347#336C2312yes—
348C22×Q8—21no—
349C22×Q8C2411yescharacteristic
350C22×Q8C2412yes—
351C22×D4—21no—
352C22×D4C2411yescharacteristic
353C23×C4—21no—
354C23×C4C2×D411yescharacteristic
355C23×C4C2×D411yescharacteristic
356C23×C4C2×D411yescharacteristic
357C23×C4C2×D411yescharacteristic
358C23×C4C2×D411yescharacteristic
359C23×C4C2×D411yescharacteristic
360C23×C4C2411yescharacteristic
361C2×Q16—24no—
362C2×Q16—24no—
363C2×Q16—42no—
364C2×SD16—24no—
365C2×SD16—24no—
366C2×SD16—42no—
367C22×C8C2412yes—
368C22×C8C2412yes—
369C22×C8C2412yes—
370C22×C8C2412yes—
371C4⋊Q8—24no—
372C4⋊Q8—24no—
373#126—44no—
374#125—28no—
375#125—24no—
376#124—24no—
377#123—44no—
378C22⋊Q8—28no—
379C22⋊Q8—24no—
380C22⋊Q8—24no—
381C22⋊Q8—41no—
382C22⋊Q8—41no—
383#121—41no—
384#121—41no—
385C4×Q8—28no—
386C4×Q8—24no—
387C4×Q8—24no—
388C4×Q8—24no—
389C4×Q8—24no—
390C4×Q8—42no—
391C4×Q8—42no—
392C4×Q8—44no—
393C4×Q8—44no—
394C4×Q8#4118yes—
395C4×D4—24no—
396C4×D4—44no—
397#117—28no—
398#117—44no—
399#117—44no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
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—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4C2411yescharacteristic
426C2×C4⋊C4C2412yes—
427C2×C4⋊C4C2412yes—
428C2×C4⋊C4C2411yescharacteristic
429C2×C4⋊C4C2411yescharacteristic
430C2×C4⋊C4C2411yescharacteristic
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2412yes—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C42—24no—
452C2×C42—22no—
453C2×C42—24no—
454C2×C42—24no—
455C2×C42—24no—
456C2×C42—24no—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—42no—
466C2×C42—41no—
467C2×C42—41no—
468C2×C42C2×D411yescharacteristic
469C2×C42C2×D411yescharacteristic
470C2×C42C2×D411yescharacteristic
471C2×C42C2×D411yescharacteristic
472C2×C42C2×D411yescharacteristic
473C2×C42C2×D411yescharacteristic
474C2×C42C2×D411yescharacteristic
475C2×C42C2×D411yescharacteristic
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×C42C2×D411yescharacteristic
487C2×C42C2×D411yescharacteristic
488C2×C42C2×D411yescharacteristic
489C2×C42C2×D411yescharacteristic
490C2×C42C2411yescharacteristic
491C2×C42C2411yescharacteristic
492C2×C42C2411yescharacteristic
493C2×C42C2411yescharacteristic
494C2×C42C2411yescharacteristic
495C2×C42C2411yescharacteristic
496#107—24no—
497#107—24no—
498#107—42no—
499#106—24no—
500#106—24no—
501#106—42no—
502C4⋊C8—24no—
503C4⋊C8#4118yes—
504#103—24no—
505#103—24no—
506#103—24no—
507#103—24no—
508#103—24no—
509#103—24no—
510#103—42no—
511#103—42no—
512#103—42no—
513#102—24no—
514#102—24no—
515#102—42no—
516C22⋊C8—24no—
517C22⋊C8—24no—
518C4×C8—24no—
519C4×C8—24no—
520C4×C8—24no—
521C4×C8—24no—
522C4×C8—42no—
523C4×C8—42no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95—21no—
557#95—21no—
558C24—21no—
559C24C22×D411yescharacteristic
560C2×Q8—24no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—42no—
571C2×Q8—42no—
572C2×Q8C2×#4114yes—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4#13514yes—
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×C4C22×D411yescharacteristic
629C22×C4C2511yescharacteristic
630Q16—48no—
631SD16—48no—
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—
641C2×C8—22no—
642C2×C8C2×#4114yes—
643C2×C8C2×#4114yes—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—28no—
647C4⋊C4—24no—
648C4⋊C4—28no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—42no—
663C4⋊C4—44no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—44no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—44no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—44no—
681C4⋊C4—42no—
682C4⋊C4C2×#4114yes—
683C22⋊C4—28no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—44no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C42—22no—
701C42—22no—
702C42—28no—
703C42—22no—
704C42—22no—
705C42—22no—
706C42—22no—
707C42—22no—
708C42—22no—
709C42—22no—
710C42—22no—
711C42—22no—
712C42—22no—
713C42—22no—
714C42—22no—
715C42—22no—
716C42—22no—
717C42—22no—
718C42—22no—
719C42—21no—
720C42—21no—
721C42—21no—
722C42—21no—
723C42—41no—
724C42—41no—
725C42—41no—
726C42—41no—
727C42—44no—
728C42—44no—
729C42—42no—
730C42—44no—
731C42—44no—
732C42—42no—
733C42—44no—
734C42—42no—
735C42#13514yes—
736C42#13714yes—
737C42C2×#4114yes—
738C42C2×#4114yes—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23C2×#13512yes—
753C23C23×D411yescharacteristic
754Q8—24no—
755Q8—24no—
756Q8—48no—
757Q8—42no—
758Q8—42no—
759Q8—42no—
760Q8—42no—
761D4—42no—
762D4—42no—
763D4—84no—
764C2×C4—28no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—28no—
786C2×C4—21no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—84no—
832C2×C4#52512yes—
833C2×C4#52512yes—
834C2×C4#53212yes—
835C2×C4#53212yes—
836C2×C4C2×#13512yes—
837C2×C4C2×#13512yes—
838C2×C4C2×#13512yes—
839C2×C4C2×#13512yes—
840C2×C4C2×#13512yes—
841C2×C4C2×#13712yes—
842C2×C4C2×#13712yes—
843C2×C4C2×#13712yes—
844C2×C4#57512yes—
845C2×C4C22×#4112yes—
846C2×C4C22×#4112yes—
847C2×C4#58511yescharacteristic
848C2×C4#58511yescharacteristic
849C8—24no—
850C8—24no—
851C8—42no—
852C8—42no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22C2×#52511yescharacteristic
868C22C2×#53211yescharacteristic
869C22#344911yescharacteristic
870C22C22×#13511yescharacteristic
871C22C22×#13511yescharacteristic
872C22C22×#13711yescharacteristic
873C22C2×#57511yescharacteristic
874C4—22no—
875C4—22no—
876C4—22no—
877C4—22no—
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—22no—
883C4—22no—
884C4—41no—
885C4—41no—
886C4—44no—
887C4—44no—
888C4—82no—
889C4—81no—
890C4—82no—
891C4—81no—
892C4—81no—
893C4—81no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4#310814yes—
898C4#347512yes—
899C4#348012yes—
900C2—42no—
901C2—161no—
902C2#3491111yescharacteristic
903C2C2×#310811yescharacteristic
904C2#6053611yescharacteristic
905C2#6067311yescharacteristic
906C2#6070111yescharacteristic
907C2#6094211yescharacteristic
908C2#6094711yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C4×#533C2semidirect
3. #29514C2semidirect
4. #29512C2semidirect
5. #29495C2semidirect
6. #29494C2semidirect
8. #29463C2semidirect
9. #29350C2semidirect
10. #29315C2semidirect
11. #29126C2semidirect
12. #28377C2semidirect
13. #24705C2semidirect
15. #23756C2semidirect
17. #23571C2semidirect
19. C4×#479C2semidirect
20. C4×#464C2semidirect
21. #21276C2semidirect
22. #21274C2semidirect
23. C4×#431C2semidirect

Maximal subgroups

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

subgroupindex
#366382
C4×#5332
#295142
#295122
#294952
#294942
#294672
#294632
#293502
#293152
#291262
#283772
#247052
#246552
#237562
#237542
#235712
#235682
C4×#4792
C4×#4642
#212762
#212742
C4×#4312