Finite Group Databasebeta

← #6799225

Subgroups — #6799225

Order 512.

1473 conjugacy classes of subgroups.

The subgroup lattice has 915 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36561C211yesmaximal, characteristic
2C2×#2514C211yesmaximal, characteristic, complemented
3#33149C211yesmaximal, characteristic, complemented
4#32483C212yesmaximal, complemented
5#32448C212yesmaximal, complemented
6#32248C212yesmaximal, complemented
7#31811C212yesmaximal, complemented
8#29966C211yesmaximal, characteristic, complemented
9#29953C211yesmaximal, characteristic, complemented
10#29111C211yesmaximal, characteristic, complemented
11#29105C211yesmaximal, characteristic, complemented
12#29083C212yesmaximal, complemented
13#28118C211yesmaximal, characteristic
14#28115C211yesmaximal, characteristic
15#28057C212yesmaximal, complemented
16#27969C211yesmaximal, characteristic, complemented
17#27651C211yesmaximal, characteristic
18#27566C212yesmaximal, complemented
19#27142C212yesmaximal, complemented
20#22629C211yesmaximal, characteristic, complemented
21#22075C211yesmaximal, characteristic
22#22047C211yesmaximal, characteristic
23#21580C211yesmaximal, characteristic
24C2×#554—21no—
25C2×#481C2211yescharacteristic
26C2×#480C2211yescharacteristic
27C2×#448C2211yescharacteristic
28#2857C2211yescharacteristic
29#2857C2211yescharacteristic
30#2857C2211yescharacteristic
31#2564—21no—
32#2564—21no—
33#2556—21no—
34#2556—21no—
35#2551C2211yescharacteristic
36#2542C2211yescharacteristic
37#2514—21no—
38#2514—21no—
39#2514—21no—
40#2514—21no—
41#2514C2212yes—
42#2514C2212yes—
43#2514C2212yes—
44#2514C2212yes—
45#2506C2211yescharacteristic
46#2506C2211yescharacteristic
47#2492—21no—
48#2452C2211yescharacteristic
49#2452C2211yescharacteristic
50#2417—21no—
51C2×#401—21no—
52C2×#400—21no—
53#2365C2211yescharacteristic
54#2360—21no—
55D4×C4⋊C4C2211yescharacteristic
56C4×#121C2211yescharacteristic
57C4×#121C2211yescharacteristic
58C4×#121C2211yescharacteristic
59C2×#391C2211yescharacteristic
60C2×#391C2211yescharacteristic
61C2×#391C2211yescharacteristic
62C2×#389C2211yescharacteristic
63C2×#387—21no—
64C2×#383—21no—
65C2×#382C2211yescharacteristic
66C2×C4×C4⋊C4C2211yescharacteristic
67C2×C4×C4⋊C4C2211yescharacteristic
68#2101C2212yes—
69#2101C2212yes—
70#2099C2212yes—
71#2095C2212yes—
72#2086C2212yes—
73#2086C2212yes—
74#2085C2212yes—
75#2073C2212yes—
76#2072C2212yes—
77#2072C2212yes—
78#2068C2212yes—
79#2068C2212yes—
80#2068C2212yes—
81#2066C2212yes—
82#2057C2212yes—
83#2055C2212yes—
84#2055C2212yes—
85#2024C2212yes—
86#2024C2212yes—
87#2024C2212yes—
88#1993C2212yes—
89#1987C2212yes—
90#1973C2212yes—
91#1949C2212yes—
92#1947C2212yes—
93#1942C2212yes—
94#1939C2212yes—
95#1935C2212yes—
96#1935C2212yes—
97#1935C2212yes—
98#1934C2212yes—
99#1933C2212yes—
100#1933C2212yes—
101#1928C2212yes—
102#1928C2212yes—
103#1927C2212yes—
104#1925C2212yes—
105#1921C2212yes—
106#1921C2212yes—
107#1920C2212yes—
108#1918C2212yes—
109#1917C2212yes—
110#1917C2212yes—
111#1877C2212yes—
112#1877C2212yes—
113#1877C2212yes—
114#1874C2211yescharacteristic
115#1862C2212yes—
116#1852C2211yescharacteristic
117#1852C2211yescharacteristic
118#1852C2211yescharacteristic
119#1836C2212yes—
120#1824C2211yescharacteristic
121#1824C2211yescharacteristic
122#1824C2211yescharacteristic
123#1823C2211yescharacteristic
124#1823C2211yescharacteristic
125#1823C2211yescharacteristic
126#1804C2212yes—
127#1797C2211yescharacteristic
128#1797C2211yescharacteristic
129#1797C2211yescharacteristic
130#1787C2211yescharacteristic
131#1787C2211yescharacteristic
132#1787C2211yescharacteristic
133#1776C2212yes—
134#1770C2212yes—
135#1762C2212yes—
136#1749C2211yescharacteristic
137#1749C2211yescharacteristic
138C4×C22⋊C8C2211yescharacteristic
139C23×Q8C2311yescharacteristic
140C22×SD16C2312yes—
141#554—48no—
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8C2311yescharacteristic
144C2×C4⋊Q8C2311yescharacteristic
145C2×C4⋊Q8C2311yescharacteristic
146C2×#125—21no—
147C2×#125—21no—
148C2×C22⋊Q8—21no—
149C2×C22⋊Q8—21no—
150C2×C22⋊Q8—21no—
151C2×C22⋊Q8—21no—
152C2×C22⋊Q8—21no—
153C2×C22⋊Q8—21no—
154C2×C22⋊Q8—21no—
155C2×#121C2311yescharacteristic
156C2×C4×Q8—21no—
157C2×C4×D4—21no—
158C2×C4×D4—21no—
159C2×C4×D4—21no—
160C2×C4×D4C2311yescharacteristic
161C2×C4×D4C2311yescharacteristic
162C2×C4×D4C2311yescharacteristic
163C22×C4⋊C4—21no—
164C22×C4⋊C4—21no—
165C22×C4⋊C4D411yescharacteristic
166C22×C4⋊C4D411yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C42—21no—
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174#481—24no—
175#480—24no—
176#448—24no—
177C2×#107C2312yes—
178C2×#107C2312yes—
179C2×#107C2312yes—
180C2×#107C2312yes—
181C2×#106C2312yes—
182C2×C4⋊C8C2312yes—
183C2×C4⋊C8C2312yes—
184C2×C4⋊C8C2312yes—
185C2×#103C2312yes—
186C2×#103C2312yes—
187C2×#103C2312yes—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#102C2312yes—
193C2×#102C2312yes—
194C2×#102C2312yes—
195C2×C22⋊C8C2311yescharacteristic
196C2×C22⋊C8C2311yescharacteristic
197C2×C22⋊C8C2311yescharacteristic
198C2×C22⋊C8C2311yescharacteristic
199C2×#97C2312yes—
200C2×#97C2312yes—
201C2×C4×C8C2312yes—
202#401—22no—
203#401—22no—
204#401—22no—
205#401—22no—
206#400—22no—
207#400—22no—
208#400—22no—
209#400—22no—
210#400—21no—
211#400—21no—
212#399—21no—
213#399—21no—
214#398—21no—
215#398—21no—
216#396—21no—
217#396—21no—
218#395—21no—
219#395—21no—
220#393—21no—
221#393—21no—
222#391—21no—
223#391—21no—
224#391—21no—
225#391—21no—
226#391—21no—
227#391—21no—
228#391—21no—
229#391—21no—
230#391—21no—
231#391—21no—
232#391C2312yes—
233#391C2312yes—
234#391C2312yes—
235#391C2312yes—
236#391C2312yes—
237#391C2312yes—
238#390C2311yescharacteristic
239#390C2311yescharacteristic
240#390C2311yescharacteristic
241#389—21no—
242#389—21no—
243#389—21no—
244#389—21no—
245#389—21no—
246#389—21no—
247#389C2312yes—
248#389C2311yescharacteristic
249#389C2311yescharacteristic
250#389C2311yescharacteristic
251#389C2311yescharacteristic
252#389C2311yescharacteristic
253#389C2311yescharacteristic
254#389C2311yescharacteristic
255#389C2312yes—
256#389C2311yescharacteristic
257#389C2311yescharacteristic
258#388—21no—
259#388—21no—
260#388—21no—
261#387—22no—
262#387—22no—
263#387—22no—
264#387—22no—
265#387—21no—
266#387—21no—
267#387—21no—
268#387—21no—
269#386—21no—
270#386—21no—
271#386—21no—
272#385—21no—
273#385—21no—
274#385—21no—
275#385—21no—
276#384C2311yescharacteristic
277#384C2311yescharacteristic
278#384C2311yescharacteristic
279#383—22no—
280#383—22no—
281#383—22no—
282#383—22no—
283#382—21no—
284#382—21no—
285#382C2312yes—
286#382C2312yes—
287#380—21no—
288#380—21no—
289#380—21no—
290#380—21no—
291#380C2311yescharacteristic
292#380C2311yescharacteristic
293#380C2311yescharacteristic
294C4×C4⋊C4—21no—
295C4×C4⋊C4—21no—
296C4×C4⋊C4D411yescharacteristic
297C4×C4⋊C4D411yescharacteristic
298C4×C4⋊C4D411yescharacteristic
299C4×C4⋊C4D411yescharacteristic
300C4×C4⋊C4C2311yescharacteristic
301C4×C4⋊C4C2311yescharacteristic
302C4×C4⋊C4C2311yescharacteristic
303C4×C4⋊C4C2312yes—
304C4×C4⋊C4C2312yes—
305C4×C4⋊C4C2311yescharacteristic
306C4×C4⋊C4C2311yescharacteristic
307C4×C4⋊C4C2311yescharacteristic
308C4×C4⋊C4C2311yescharacteristic
309C4×C22⋊C4—21no—
310C4×C22⋊C4—21no—
311C4×C22⋊C4—21no—
312C2×#95—21no—
313C2×#95—21no—
314C2×#95—21no—
315C2×#95—21no—
316C2×#95—21no—
317C2×#95—21no—
318C2×#95—21no—
319C2×#95—21no—
320C2×#95—21no—
321C2×#95—21no—
322C2×#95D411yescharacteristic
323C2×#95D411yescharacteristic
324#340C2312yes—
325#340C2312yes—
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#336C2312yes—
341#336C2312yes—
342#336C2312yes—
343#336C2312yes—
344#336C2312yes—
345#336C2312yes—
346C22×Q8—21no—
347C22×Q8—21no—
348C22×Q8—21no—
349C22×Q8—21no—
350C22×Q8—22no—
351C22×Q8—22no—
352C22×Q8—42no—
353C22×Q8—42no—
354C22×Q8C2412yes—
355C22×D4—21no—
356C22×D4C2411yescharacteristic
357C23×C4—21no—
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—21no—
361C23×C4—21no—
362C23×C4—21no—
363C23×C4—21no—
364C23×C4C2×D411yescharacteristic
365C23×C4C2×D411yescharacteristic
366C23×C4C2×D411yescharacteristic
367C23×C4C2×D411yescharacteristic
368C23×C4C2×D411yescharacteristic
369C23×C4C2×D411yescharacteristic
370C23×C4C2411yescharacteristic
371C2×SD16—24no—
372C2×SD16—42no—
373C2×SD16—42no—
374C22×C8C2412yes—
375C22×C8C2412yes—
376C22×C8C2412yes—
377C22×C8C2412yes—
378C4⋊Q8—42no—
379C4⋊Q8—42no—
380C4⋊Q8—42no—
381C4⋊Q8—44no—
382#125—44no—
383#125—44no—
384C22⋊Q8—44no—
385C22⋊Q8—44no—
386C22⋊Q8—44no—
387C22⋊Q8—44no—
388C22⋊Q8—44no—
389C22⋊Q8—44no—
390C22⋊Q8—44no—
391#121—22no—
392#121#4114yes—
393C4×Q8—44no—
394C4×D4—42no—
395C4×D4—42no—
396C4×D4—42no—
397C4×D4—44no—
398C4×D4—44no—
399C4×D4—44no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
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—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⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—42no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4—44no—
431C2×C4⋊C4—44no—
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2×D411yescharacteristic
434C2×C4⋊C4C2×D411yescharacteristic
435C2×C4⋊C4C2×D411yescharacteristic
436C2×C4⋊C4C2×D411yescharacteristic
437C2×C4⋊C4C2×D411yescharacteristic
438C2×C4⋊C4C2×D411yescharacteristic
439C2×C4⋊C4C2×D411yescharacteristic
440C2×C4⋊C4C2412yes—
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2412yes—
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2411yescharacteristic
448C2×C4⋊C4C2411yescharacteristic
449C2×C4⋊C4C2411yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—42no—
469C2×C42—42no—
470C2×C42—42no—
471C2×C42—44no—
472C2×C42C2×D411yescharacteristic
473C2×C42C2×D411yescharacteristic
474C2×C42C2×D411yescharacteristic
475C2×C42C2×D411yescharacteristic
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42C2411yescharacteristic
479C2×C42C2411yescharacteristic
480C2×C42C2411yescharacteristic
481C2×C42C2411yescharacteristic
482C2×C42C2411yescharacteristic
483C2×C42C2411yescharacteristic
484#107—24no—
485#107—42no—
486#107—42no—
487#107—42no—
488#106—24no—
489C4⋊C8—42no—
490C4⋊C8—42no—
491C4⋊C8—42no—
492#103—24no—
493#103—42no—
494#103—42no—
495#103—42no—
496#103—42no—
497#103—42no—
498#103—42no—
499#102—24no—
500#102—24no—
501#102—42no—
502C22⋊C8—22no—
503C22⋊C8—22no—
504C22⋊C8—22no—
505C22⋊C8—22no—
506#97—42no—
507#97—42no—
508C4×C8—42no—
509#95—22no—
510#95—22no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—22no—
516#95—22no—
517#95—22no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
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—21no—
543#95—21no—
544#95C2×D411yescharacteristic
545#95C2×D411yescharacteristic
546#95C2×D411yescharacteristic
547#95C2×D411yescharacteristic
548#95C2×D411yescharacteristic
549#95C2×D411yescharacteristic
550#95C2×D411yescharacteristic
551#95C2×D411yescharacteristic
552C24—21no—
553C24C22×D411yescharacteristic
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—42no—
561C2×Q8—42no—
562C2×Q8—42no—
563C2×Q8—42no—
564C2×Q8—42no—
565C2×Q8—42no—
566C2×Q8—42no—
567C2×Q8—42no—
568C2×Q8—81no—
569C2×Q8—81no—
570C2×Q8—81no—
571C2×Q8—81no—
572C2×Q8—84no—
573C2×Q8—84no—
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4C2×#4112yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
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—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—81no—
629C22×C4—81no—
630C22×C4—81no—
631C22×C4—81no—
632C22×C4AGL(1,ℤ/8)14yes—
633C22×C4C22×D411yescharacteristic
634C22×C4C22×D411yescharacteristic
635C22×C4C22×D411yescharacteristic
636C22×C4C22×D411yescharacteristic
637C22×C4C22×D411yescharacteristic
638C22×C4C22×D411yescharacteristic
639C22×C4C22×D411yescharacteristic
640C22×C4C22×D411yescharacteristic
641C22×C4C22×D411yescharacteristic
642C22×C4C22×D411yescharacteristic
643C22×C4C22×D411yescharacteristic
644C22×C4C22×D411yescharacteristic
645C22×C4C22×D411yescharacteristic
646C22×C4C2×#4112yes—
647C22×C42−1+412yes—
648C22×C4C2511yescharacteristic
649SD16—84no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—21no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—41no—
682C4⋊C4—41no—
683C4⋊C4—42no—
684C4⋊C4—42no—
685C4⋊C4—42no—
686C4⋊C4—42no—
687C4⋊C4—42no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—42no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4—42no—
694C4⋊C4—42no—
695C4⋊C4—42no—
696C4⋊C4—44no—
697C4⋊C4—44no—
698C4⋊C4—42no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C4⋊C4—42no—
702C4⋊C4—42no—
703C4⋊C4—81no—
704C4⋊C4—81no—
705C4⋊C4—81no—
706C4⋊C4C2×#4112yes—
707C22⋊C4—24no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—81no—
718C22⋊C4—81no—
719C22⋊C4—81no—
720C42—22no—
721C42—22no—
722C42—22no—
723C42—22no—
724C42—22no—
725C42—22no—
726C42—41no—
727C42—41no—
728C42—41no—
729C42—41no—
730C42—41no—
731C42—41no—
732C42—44no—
733C42—42no—
734C42—42no—
735C42—42no—
736C42—44no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—22no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23#54812yes—
749C23C2×AGL(1,ℤ/8)12yes—
750C23#57812yes—
751C23C23×D411yescharacteristic
752Q8—42no—
753Q8—42no—
754Q8—42no—
755Q8—42no—
756Q8—84no—
757Q8—84no—
758Q8—162no—
759Q8—162no—
760D4—24no—
761D4—48no—
762D4—42no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—24no—
772C2×C4—24no—
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—22no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
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—44no—
802C2×C4—44no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—42no—
835C2×C4—84no—
836C2×C4—82no—
837C2×C4—82no—
838C2×C4—82no—
839C2×C4—82no—
840C2×C4—84no—
841C2×C4—84no—
842C2×C4—84no—
843C2×C4—84no—
844C2×C4—162no—
845C2×C4—162no—
846C2×C4#54812yes—
847C2×C4C2×AGL(1,ℤ/8)12yes—
848C2×C4C2×AGL(1,ℤ/8)12yes—
849C2×C4#57512yes—
850C2×C4C22×#4111yescharacteristic
851C2×C4C2×2−1+411yescharacteristic
852C2×C4#58512yes—
853C2×C4#58512yes—
854C8—42no—
855C8—42no—
856C8—42no—
857C8—42no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—22no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22#336714yes—
872C22#344911yescharacteristic
873C22C2×#54811yescharacteristic
874C22#348511yescharacteristic
875C22C22×AGL(1,ℤ/8)11yescharacteristic
876C22C2×#57511yescharacteristic
877C22C2×#57811yescharacteristic
878C22#358611yescharacteristic
879C4—22no—
880C4—22no—
881C4—22no—
882C4—22no—
883C4—41no—
884C4—41no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—41no—
891C4—41no—
892C4—42no—
893C4—81no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4—82no—
898C4—81no—
899C4—81no—
900C4—82no—
901C4—82no—
902C4—82no—
903C4#352112yes—
904C4#356412yes—
905C2—24no—
906C2—82no—
907C2#3911711yescharacteristic
908C2#6095811yescharacteristic
909C2#6098311yescharacteristic
910C2C2×#336711yescharacteristic
911C2#6132311yescharacteristic
912C2#6172211yescharacteristic
913C2#6173811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2514C2semidirect
3. #33149C2semidirect
4. #32483C2semidirect
5. #32448C2semidirect
6. #32248C2semidirect
7. #31811C2semidirect
8. #29966C2semidirect
9. #29953C2semidirect
10. #29111C2semidirect
11. #29105C2semidirect
12. #29083C2semidirect
15. #28057C2semidirect
16. #27969C2semidirect
18. #27566C2semidirect
19. #27142C2semidirect
20. #22629C2semidirect

Maximal subgroups

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

subgroupindex
#365612
C2×#25142
#331492
#324832
#324482
#322482
#318112
#299662
#299532
#291112
#291052
#290832
#281182
#281152
#280572
#279692
#276512
#275662
#271422
#226292
#220752
#220472
#215802