Finite Group Databasebeta

← #6449569

Subgroups — #6449569

Order 512.

1903 conjugacy classes of subgroups.

The subgroup lattice has 895 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34929C211yesmaximal, characteristic, complemented
2C4×#547C211yesmaximal, characteristic
3#27413C212yesmaximal, complemented
4#27349C212yesmaximal, complemented
5#26739C212yesmaximal, complemented
6#26641C212yesmaximal, complemented
7#26440C211yesmaximal, characteristic, complemented
8#26236C211yesmaximal, characteristic, complemented
9#26020C211yesmaximal, characteristic, complemented
10#25571C211yesmaximal, characteristic
11#25276C211yesmaximal, characteristic, complemented
12#24971C211yesmaximal, characteristic, complemented
13#24630C211yesmaximal, characteristic, complemented
14#24120C211yesmaximal, characteristic
15#23711C212yesmaximal, complemented
16#23574C212yesmaximal, complemented
17#21647C211yesmaximal, characteristic, complemented
18#21615C211yesmaximal, characteristic, complemented
19#21581C212yesmaximal, complemented
20#21504C211yesmaximal, characteristic, complemented
21#21394C212yesmaximal, complemented
22#21270C211yesmaximal, characteristic, complemented
23C4×#440C211yesmaximal, characteristic, complemented
24C2×#547C2211yescharacteristic
25C2×#533C2212yes—
26C2×C4×#41—21no—
27C2×#487C2211yescharacteristic
28C2×#484C2212yes—
29C2×#475C2211yescharacteristic
30C2×#461C2211yescharacteristic
31C2×#440C2211yescharacteristic
32C2×#440C2211yescharacteristic
33C2×#440C2212yes—
34C2×C4×SD16C2211yescharacteristic
35C2×#432C2212yes—
36#2556—22no—
37#2551C2211yescharacteristic
38#2546C2211yescharacteristic
39#2542C2211yescharacteristic
40#2538C2211yescharacteristic
41#2506—21no—
42#2492C2212yes—
43#2452—21no—
44#2429C2212yes—
45#2396—22no—
46#2365C2211yescharacteristic
47#2362—21no—
48#2361C2212yes—
49#2359—22no—
50#2354C2211yescharacteristic
51D4×C4⋊C4C2211yescharacteristic
52#2344C2212yes—
53#2339—21no—
54C4×C4⋊Q8—21no—
55C4×C4⋊Q8C2211yescharacteristic
56C4×C4⋊Q8C2211yescharacteristic
57C4×C22⋊Q8—21no—
58C4×C22⋊Q8C2212yes—
59C4×#123—22no—
60C4×#121C2212yes—
61#2293—21no—
62C42×Q8C2211yescharacteristic
63C42×D4C2211yescharacteristic
64C42×D4C2211yescharacteristic
65C2×C4×C4⋊C4C2212yes—
66#2086C2212yes—
67#2076C2212yes—
68#2067C2212yes—
69#2066C2212yes—
70#2057C2212yes—
71#2055C2212yes—
72#2043C2212yes—
73#2036C2212yes—
74#2036C2212yes—
75#2036C2212yes—
76#2034C2212yes—
77#2023C2212yes—
78#2013C2212yes—
79#2000C2212yes—
80#2000C2212yes—
81#2000C2212yes—
82#1990C2211yescharacteristic
83#1988C2211yescharacteristic
84#1988C2212yes—
85#1988C2212yes—
86#1981C2211yescharacteristic
87#1981C2212yes—
88#1981C2212yes—
89#1956C2211yescharacteristic
90#1954C2211yescharacteristic
91#1954C2211yescharacteristic
92#1947C2211yescharacteristic
93#1947C2211yescharacteristic
94#1939C2211yescharacteristic
95#1939C2211yescharacteristic
96#1935C2212yes—
97#1935C2212yes—
98#1928C2212yes—
99#1927C2212yes—
100#1927C2212yes—
101#1924C2212yes—
102#1924C2212yes—
103#1920C2212yes—
104#1918C2212yes—
105#1918C2212yes—
106#1877C2212yes—
107#1872C2212yes—
108#1872C2212yes—
109#1872C2212yes—
110#1872C2212yes—
111#1872C2212yes—
112#1863C2212yes—
113#1853C2212yes—
114#1834C2211yescharacteristic
115#1824C2212yes—
116#1803C2211yescharacteristic
117#1802C2211yescharacteristic
118#1776C2211yescharacteristic
119#1776C2211yescharacteristic
120#1776C2212yes—
121C4×#107C2211yescharacteristic
122#1767C2211yescharacteristic
123#1763C2212yes—
124#1763C2211yescharacteristic
125#1763C2211yescharacteristic
126#1763C2212yes—
127#1763C2212yes—
128#1763C2212yes—
129#1762C2211yescharacteristic
130#1762C2211yescharacteristic
131C4×#103C2211yescharacteristic
132C4×#102C2211yescharacteristic
133#1749C2212yes—
134C4×#97C2211yescharacteristic
135C22×#41—21no—
136C22×SD16C2311yescharacteristic
137C22×SD16C2312yes—
138#547—24no—
139#547—24no—
140#533—28no—
141#533—44no—
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8C2311yescharacteristic
144C2×C4⋊Q8C2312yes—
145C2×C4⋊Q8C2312yes—
146C2×C4⋊Q8C2311yescharacteristic
147C2×#125—22no—
148C2×#123—22no—
149C2×C22⋊Q8—22no—
150C2×C22⋊Q8—21no—
151C2×C22⋊Q8C2312yes—
152C2×C22⋊Q8C2312yes—
153C2×C22⋊Q8C2312yes—
154C2×#121C2312yes—
155C4×#41—48no—
156C2×C4×Q8—21no—
157C2×C4×Q8—22no—
158C2×C4×Q8—21no—
159C2×C4×Q8C2311yescharacteristic
160C2×C4×Q8C2312yes—
161C2×C4×Q8C2311yescharacteristic
162C2×C4×Q8C2311yescharacteristic
163C2×C4×D4—21no—
164C2×C4×D4—22no—
165C2×C4×D4—22no—
166C2×C4×D4D411yescharacteristic
167C2×C4×D4D411yescharacteristic
168C2×C4×D4C2311yescharacteristic
169C2×C4×D4C2311yescharacteristic
170C2×C4×D4C2311yescharacteristic
171C2×C4×D4C2311yescharacteristic
172C2×#117—22no—
173C2×#117—21no—
174C2×#117—22no—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C42—22no—
178C22×C42—21no—
179C22×C42C2312yes—
180#487—24no—
181#484—28no—
182#475—24no—
183#461—24no—
184#440—24no—
185#440—24no—
186#440—44no—
187C4×SD16—24no—
188#432—44no—
189C2×#107C2311yescharacteristic
190C2×#107C2312yes—
191C2×#107C2312yes—
192C2×#107C2311yescharacteristic
193C2×#106C2312yes—
194C2×#106C2311yescharacteristic
195C2×C4⋊C8C2311yescharacteristic
196C2×C4⋊C8C2311yescharacteristic
197C2×C4⋊C8C2312yes—
198C2×C4⋊C8C2312yes—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#103C2311yescharacteristic
205C2×#103C2311yescharacteristic
206C2×#103C2312yes—
207C2×#103C2311yescharacteristic
208C2×#103C2312yes—
209C2×#103C2312yes—
210C2×#103C2312yes—
211C2×#102C2311yescharacteristic
212C2×#102C2311yescharacteristic
213C2×#102C2311yescharacteristic
214C2×#102C2312yes—
215C2×C22⋊C8C2312yes—
216C2×C22⋊C8C2312yes—
217C2×C22⋊C8C2312yes—
218C2×C22⋊C8C2312yes—
219C2×#97C2311yescharacteristic
220C2×#97C2312yes—
221C2×#97C2311yescharacteristic
222C2×#97C2311yescharacteristic
223C2×#97C2311yescharacteristic
224C2×C4×C8C2311yescharacteristic
225C2×C4×C8C2311yescharacteristic
226#400—22no—
227#399—22no—
228#398—22no—
229#398—22no—
230#396—22no—
231#396—22no—
232#395—22no—
233#393—22no—
234#391—21no—
235#391—21no—
236#391—22no—
237#391C2312yes—
238#391C2312yes—
239#390—21no—
240#390—21no—
241#390C2312yes—
242#389—21no—
243#389—21no—
244#389—21no—
245#389—21no—
246#389—21no—
247#389—21no—
248#389—21no—
249#389—21no—
250#389—22no—
251#389C2312yes—
252#389C2312yes—
253#389C2312yes—
254#388—22no—
255#388—22no—
256#388—22no—
257#388—22no—
258#388—22no—
259#387—22no—
260#387—22no—
261#387—22no—
262#387—22no—
263#386—22no—
264#386—22no—
265#385—22no—
266#385—22no—
267#385—22no—
268#384—21no—
269#384C2311yescharacteristic
270#384C2311yescharacteristic
271#381—22no—
272#380—21no—
273#380C2312yes—
274#380C2312yes—
275C4×C4⋊C4—21no—
276C4×C4⋊C4—22no—
277C4×C4⋊C4—21no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4—22no—
280C4×C4⋊C4—21no—
281C4×C4⋊C4—21no—
282C4×C4⋊C4—22no—
283C4×C4⋊C4—21no—
284C4×C4⋊C4D411yescharacteristic
285C4×C4⋊C4D411yescharacteristic
286C4×C4⋊C4C2312yes—
287C4×C4⋊C4C2311yescharacteristic
288C4×C4⋊C4C2312yes—
289C4×C4⋊C4C2311yescharacteristic
290C4×C4⋊C4C2312yes—
291C4×C4⋊C4C2311yescharacteristic
292C4×C4⋊C4C2311yescharacteristic
293C4×C4⋊C4C2311yescharacteristic
294C4×C4⋊C4C2311yescharacteristic
295C4×C4⋊C4C2311yescharacteristic
296C4×C22⋊C4—22no—
297C4×C22⋊C4—21no—
298C4×C22⋊C4—21no—
299C4×C22⋊C4—21no—
300C4×C22⋊C4—22no—
301C4×C22⋊C4D412yes—
302C4×C22⋊C4D412yes—
303C4×C22⋊C4C2312yes—
304C2×#95—22no—
305C43—21no—
306C43C2311yescharacteristic
307#340C2312yes—
308#340C2312yes—
309#340C2312yes—
310#340C2312yes—
311#340C2311yescharacteristic
312#340C2312yes—
313#340C2311yescharacteristic
314#340C2312yes—
315#340C2312yes—
316#340C2311yescharacteristic
317#340C2312yes—
318#340C2312yes—
319#340C2311yescharacteristic
320#340C2311yescharacteristic
321#340C2311yescharacteristic
322#340C2312yes—
323#336C2312yes—
324#336C2312yes—
325#336C2312yes—
326C2×#41—28no—
327C2×#41—44no—
328C2×#41—44no—
329C22×Q8—21no—
330C22×Q8—22no—
331C22×Q8C2412yes—
332C22×Q8C2411yescharacteristic
333C22×D4—22no—
334C22×D4C2×D411yescharacteristic
335C22×D4C2411yescharacteristic
336C23×C4—22no—
337C23×C4—21no—
338C23×C4—22no—
339C23×C4—21no—
340C23×C4—21no—
341C23×C4C2×D412yes—
342C23×C4C2×D412yes—
343C23×C4C2412yes—
344C2×SD16—22no—
345C2×SD16—22no—
346C2×SD16—24no—
347C2×SD16—22no—
348C2×SD16—42no—
349C2×SD16—42no—
350C22×C8C2412yes—
351C22×C8C2411yescharacteristic
352C22×C8C2412yes—
353C22×C8C2411yescharacteristic
354C22×C8C2411yescharacteristic
355C22×C8C2411yescharacteristic
356C4⋊Q8—24no—
357C4⋊Q8—24no—
358C4⋊Q8—22no—
359C4⋊Q8—22no—
360C4⋊Q8—22no—
361C4⋊Q8—42no—
362C4⋊Q8—42no—
363C4⋊Q8—44no—
364C4⋊Q8#4114yes—
365#125—48no—
366#123—216no—
367C22⋊Q8—28no—
368C22⋊Q8—24no—
369C22⋊Q8—24no—
370C22⋊Q8—24no—
371C22⋊Q8—42no—
372C22⋊Q8—42no—
373C22⋊Q8—42no—
374C22⋊Q8—48no—
375#121—24no—
376#121—24no—
377C4×Q8—22no—
378C4×Q8—22no—
379C4×Q8—24no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8—24no—
383C4×Q8—48no—
384C4×Q8—41no—
385C4×Q8—44no—
386C4×Q8—44no—
387C4×Q8#4114yescomplemented
388C4×D4—24no—
389C4×D4—24no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—41no—
397C4×D4—48no—
398C4×D4—48no—
399C4×D4—44no—
400C4×D4#4114yes—
401#117—48no—
402#117—48no—
403#117—44no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2412yes—
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2412yes—
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4C2×D412yes—
454C2×C22⋊C4C2×D412yes—
455C2×C22⋊C4C2×D412yes—
456C2×C42—21no—
457C2×C42—24no—
458C2×C42—24no—
459C2×C42—21no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—21no—
464C2×C42—22no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—44no—
472C2×C42—48no—
473C2×C42C2×D411yescharacteristic
474C2×C42C2×D411yescharacteristic
475C2×C42C2×D412yes—
476C2×C42C2×D412yes—
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42C2411yescharacteristic
480C2×C42C2412yes—
481C2×C42C2411yescharacteristic
482C2×C42C2411yescharacteristic
483#107—22no—
484#107—24no—
485#107—42no—
486#107#4114yescomplemented
487#106—22no—
488#106—24no—
489C4⋊C8—22no—
490C4⋊C8—22no—
491C4⋊C8—42no—
492C4⋊C8—42no—
493#103—22no—
494#103—24no—
495#103—22no—
496#103—22no—
497#103—24no—
498#103—24no—
499#103—24no—
500#103—24no—
501#103—24no—
502#103—42no—
503#103—42no—
504#103—42no—
505#102—22no—
506#102—22no—
507#102—22no—
508#102—42no—
509C22⋊C8—24no—
510C22⋊C8—42no—
511C22⋊C8—42no—
512C22⋊C8—42no—
513#97—22no—
514#97—22no—
515#97—22no—
516#97—24no—
517#97—41no—
518C4×C8—22no—
519C4×C8—22no—
520#95—21no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—21no—
525#95—21no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95C2×D412yes—
539#95C2×D412yes—
540#95C2×D412yes—
541C24—21no—
542C24C22×D412yes—
543#41—432no—
544C2×Q8—24no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—44no—
557C2×Q8—42no—
558C2×Q8—44no—
559C2×Q8—42no—
560C2×Q8—82no—
561C2×Q8C2×#4112yes—
562C2×D4—28no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4#13714yes—
573C2×D4C2×#4112yes—
574C22×C4—28no—
575C22×C4—24no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—44no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—44no—
609C22×C4—42no—
610C22×C4—81no—
611C22×C4—82no—
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D412yes—
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D412yes—
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D412yes—
620C22×C4C22×D411yescharacteristic
621C22×C4C2511yescharacteristic
622SD16—28no—
623SD16—48no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—22no—
641C2×C8C2×#4112yes—
642C4⋊C4—28no—
643C4⋊C4—24no—
644C4⋊C4—22no—
645C4⋊C4—24no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—22no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—22no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—22no—
660C4⋊C4—44no—
661C4⋊C4—44no—
662C4⋊C4—44no—
663C4⋊C4—42no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—44no—
667C4⋊C4—44no—
668C4⋊C4—44no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—44no—
673C4⋊C4—44no—
674C4⋊C4—42no—
675C4⋊C4—44no—
676C4⋊C4—42no—
677C4⋊C4—81no—
678C4⋊C4—81no—
679C4⋊C4AGL(1,ℤ/8)14yes—
680C4⋊C4C2×#4112yes—
681C4⋊C4C2×#4112yes—
682C4⋊C4C2×#4112yes—
683C4⋊C4C2×#4114yes—
684C4⋊C4C2×#4112yes—
685C22⋊C4—28no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—42no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—44no—
694C22⋊C4—44no—
695C22⋊C4—42no—
696C22⋊C4—44no—
697C22⋊C4—82no—
698C22⋊C4—82no—
699C42—24no—
700C42—24no—
701C42—24no—
702C42—22no—
703C42—22no—
704C42—21no—
705C42—22no—
706C42—22no—
707C42—21no—
708C42—41no—
709C42—41no—
710C42—42no—
711C42—42no—
712C42—42no—
713C42—42no—
714C42—44no—
715C42—42no—
716C42—44no—
717C42—44no—
718C42—44no—
719C42—42no—
720C42—42no—
721C42—81no—
722C42C2×#4112yes—
723C42C2×#4112yes—
724C42C2×#4112yes—
725C42H(5,𝔽2)12yes—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23C2×#13714yes—
740C23C23×D411yescharacteristic
741Q8—22no—
742Q8—22no—
743Q8—48no—
744Q8—41no—
745Q8—41no—
746Q8—42no—
747Q8—42no—
748Q8—42no—
749Q8—42no—
750Q8—88no—
751D4—28no—
752D4—22no—
753D4—22no—
754D4—416no—
755D4—41no—
756D4—41no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—48no—
784C2×C4—48no—
785C2×C4—416no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—48no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—84no—
819C2×C4—84no—
820C2×C4—88no—
821C2×C4#52512yes—
822C2×C4#52512yes—
823C2×C4#54612yes—
824C2×C4#54612yes—
825C2×C4C2×AGL(1,ℤ/8)14yes—
826C2×C4C2×AGL(1,ℤ/8)12yes—
827C2×C4C2×#13712yes—
828C2×C4C22×#4111yescharacteristic
829C2×C4C22×#4111yescharacteristic
830C2×C4C22×#4111yescharacteristic
831C2×C4C22×#4111yescharacteristic
832C2×C4C2×H(5,𝔽2)11yescharacteristic
833C2×C4#58511yescharacteristic
834C8—22no—
835C8—41no—
836C8—42no—
837C8—41no—
838C8—41no—
839C8—42no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22C2×#52511yescharacteristic
855C22C2×#54611yescharacteristic
856C22D4×#4111yescharacteristic
857C22C22×AGL(1,ℤ/8)11yescharacteristic
858C22C22×#13711yescharacteristic
859C22#358611yescharacteristic
860C22#358611yescharacteristic
861C4—22no—
862C4—22no—
863C4—22no—
864C4—24no—
865C4—41no—
866C4—41no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—44no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—42no—
875C4—82no—
876C4—82no—
877C4—81no—
878C4—81no—
879C4—82no—
880C4#311014yes—
881C4#344411yescharacteristic
882C4#346011yescharacteristic
883C4#348011yescharacteristic
884C4#348311yescharacteristic
885C2—44no—
886C2—82no—
887C2#3471511yescharacteristic
888C2C2×#311011yescharacteristic
889C2#6057711yescharacteristic
890C2#6115711yescharacteristic
891C2#6116111yescharacteristic
892C2#6145711yescharacteristic
893C2#6146611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#547C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #34929C2semidirect
3. #27413C2semidirect
4. #27349C2semidirect
5. #26739C2semidirect
6. #26641C2semidirect
7. #26440C2semidirect
8. #26236C2semidirect
9. #26020C2semidirect
11. #25276C2semidirect
12. #24971C2semidirect
13. #24630C2semidirect
15. #23711C2semidirect
16. #23574C2semidirect
17. #21647C2semidirect
18. #21615C2semidirect
19. #21581C2semidirect
20. #21504C2semidirect
21. #21394C2semidirect
22. #21270C2semidirect
23. C4×#440C2semidirect
387. C4×Q8#41semidirect
486. #107#41semidirect

Maximal subgroups

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

subgroupindex
#349292
C4×#5472
#274132
#273492
#267392
#266412
#264402
#262362
#260202
#255712
#252762
#249712
#246302
#241202
#237112
#235742
#216472
#216152
#215812
#215042
#213942
#212702
C4×#4402