Finite Group Databasebeta

← #7544309

Subgroups — #7544309

Order 512.

1751 conjugacy classes of subgroups.

The subgroup lattice has 903 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59127C211yesmaximal, characteristic, complemented
2#36587C211yesmaximal, characteristic, complemented
3#32242C212yesmaximal, complemented
4#31831C212yesmaximal, complemented
5#28648C211yesmaximal, characteristic, complemented
6#27736C211yesmaximal, characteristic, complemented
7#27711C212yesmaximal, complemented
8#27450C212yesmaximal, complemented
9#26509C211yesmaximal, characteristic, complemented
10#26410C212yesmaximal, complemented
11#26281C211yesmaximal, characteristic, complemented
12#26036C212yesmaximal, complemented
13#25933C211yesmaximal, characteristic, complemented
14#25903C211yesmaximal, characteristic, complemented
15#25318C211yesmaximal, characteristic, complemented
16#25214C212yesmaximal, complemented
17#24750C211yesmaximal, characteristic
18#23220C211yesmaximal, characteristic, complemented
19#23132C212yesmaximal, complemented
20#22956C211yesmaximal, characteristic, complemented
21#22523C211yesmaximal, characteristic, complemented
22C4×#481C211yesmaximal, characteristic, complemented
23C2×#1988C211yesmaximal, characteristic, complemented
24C2×D4×Q8—21no—
25C2×D4×Q8C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C2×#486C2211yescharacteristic
28C2×#486C2211yescharacteristic
29C2×#481C2211yescharacteristic
30C2×#466C2212yes—
31C2×#459C2211yescharacteristic
32C2×#446C2211yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34#2856C2211yescharacteristic
35#2850—21no—
36#2677—22no—
37#2597—22no—
38#2571C2211yescharacteristic
39#2551C2212yes—
40#2548C2211yescharacteristic
41#2546C2211yescharacteristic
42#2542C2211yescharacteristic
43#2513—21no—
44#2513C2212yes—
45#2504C2212yes—
46#2452C2212yes—
47#2449—22no—
48#2447—21no—
49#2444—22no—
50#2440C2212yes—
51#2434—21no—
52#2429—21no—
53#2409—21no—
54#2366C2211yescharacteristic
55#2365C2211yescharacteristic
56#2361C2212yes—
57#2361C2212yes—
58#2357C2212yes—
59#2355C2211yescharacteristic
60C4×C22⋊Q8C2211yescharacteristic
61C4×#121—21no—
62C4×#121C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64#2101C2212yes—
65#2101C2212yes—
66#2100C2212yes—
67#2088C2212yes—
68#2085C2212yes—
69#2073C2212yes—
70#2071C2212yes—
71#2067C2212yes—
72#2065C2212yes—
73#2065C2212yes—
74#2054C2212yes—
75#2054C2212yes—
76#2023C2212yes—
77#2023C2212yes—
78#2023C2212yes—
79#2023C2212yes—
80#1993C2212yes—
81#1990C2211yescharacteristic
82#1990C2211yescharacteristic
83#1988C2212yes—
84#1988C2211yescharacteristic
85#1988C2212yes—
86#1988C2211yescharacteristic
87#1988C2211yescharacteristic
88#1988C2211yescharacteristic
89#1987C2212yes—
90#1984C2211yescharacteristic
91#1982C2211yescharacteristic
92#1949C2212yes—
93#1947C2211yescharacteristic
94#1940C2212yes—
95#1939C2211yescharacteristic
96#1936C2212yes—
97#1936C2212yes—
98#1936C2212yes—
99#1936C2212yes—
100#1926C2211yescharacteristic
101#1926C2211yescharacteristic
102#1926C2212yes—
103#1921C2212yes—
104#1921C2212yes—
105#1920C2212yes—
106#1919C2211yescharacteristic
107#1919C2211yescharacteristic
108#1917C2212yes—
109#1893C2212yes—
110#1879C2212yes—
111#1879C2212yes—
112#1879C2212yes—
113#1874C2212yes—
114#1874C2212yes—
115#1874C2211yescharacteristic
116#1864C2212yes—
117#1853C2211yescharacteristic
118#1850C2212yes—
119#1836C2212yes—
120#1824C2211yescharacteristic
121#1804C2212yes—
122#1802C2212yes—
123#1802C2211yescharacteristic
124C4×#106C2211yescharacteristic
125C4×#106C2211yescharacteristic
126#1770C2211yescharacteristic
127#1762C2212yes—
128#1762C2212yes—
129C4×#102C2211yescharacteristic
130C4×#102C2211yescharacteristic
131#1752C2212yes—
132C4×C22⋊C8C2211yescharacteristic
133C2×#340C2212yes—
134C2×#340C2212yes—
135C23×Q8—21no—
136C23×Q8—21no—
137C22×D8C2312yes—
138C23×C8C2312yes—
139D4×Q8—24no—
140D4×Q8—42no—
141D4×Q8—48no—
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8—22no—
144C2×C4⋊Q8—24no—
145C2×C4⋊Q8—21no—
146C2×C4⋊Q8—21no—
147C2×C4⋊Q8—42no—
148C2×C4⋊Q8C2311yescharacteristic
149C2×C4⋊Q8C2312yes—
150C2×C4⋊Q8C2312yes—
151C2×C4⋊Q8C2311yescharacteristic
152C2×#127C2311yescharacteristic
153C2×#124—21no—
154C2×C22⋊Q8—21no—
155C2×C22⋊Q8—22no—
156C2×C22⋊Q8—22no—
157C2×C22⋊Q8—21no—
158C2×C22⋊Q8—21no—
159C2×C22⋊Q8—22no—
160C2×C22⋊Q8D411yescharacteristic
161C2×#121—21no—
162C2×#121—21no—
163C2×#121C2312yes—
164C2×#121C2311yescharacteristic
165C2×C4×Q8—21no—
166C2×C4×Q8C2311yescharacteristic
167C2×C4×D4—21no—
168C2×C4×D4—21no—
169C2×C4×D4—22no—
170C2×C4×D4—22no—
171C2×C4×D4C2311yescharacteristic
172C2×C4×D4C2312yes—
173C2×C4×D4C2312yes—
174C22×C4⋊C4—21no—
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2312yes—
178C22×C42—21no—
179C22×C42C2311yescharacteristic
180#486—24no—
181#486—42no—
182#481—24no—
183#466—28no—
184#459—42no—
185#446—42no—
186C2×#107C2312yes—
187C2×#106C2311yescharacteristic
188C2×#106C2311yescharacteristic
189C2×#106C2311yescharacteristic
190C2×#106C2311yescharacteristic
191C2×C4⋊C8—42no—
192C2×C4⋊C8C2311yescharacteristic
193C2×C4⋊C8C2311yescharacteristic
194C2×C4⋊C8C2312yes—
195C2×C4⋊C8C2312yes—
196C2×C4⋊C8C2312yes—
197C2×#102C2311yescharacteristic
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×#102C2311yescharacteristic
201C2×#102C2312yes—
202C2×#102C2312yes—
203C2×#102C2311yescharacteristic
204C2×#102C2312yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2311yescharacteristic
209C2×C22⋊C8C2311yescharacteristic
210C2×C22⋊C8C2311yescharacteristic
211C2×#97C2312yes—
212C2×#97C2312yes—
213C2×C4×C8C2311yescharacteristic
214C2×C4×C8C2311yescharacteristic
215#400—22no—
216#399—22no—
217#398—22no—
218#398—22no—
219#397—22no—
220#397—22no—
221#397—22no—
222#397—22no—
223#396—22no—
224#395—22no—
225#395—22no—
226#395—22no—
227#394—22no—
228#393—22no—
229#391—21no—
230#391—21no—
231#391—21no—
232#391D411yescharacteristic
233#390—21no—
234#390—21no—
235#390—21no—
236#390—21no—
237#390C2311yescharacteristic
238#390C2312yes—
239#390C2312yes—
240#390C2312yes—
241#390C2312yes—
242#390C2312yes—
243#389—21no—
244#389—22no—
245#389D411yescharacteristic
246#389C2312yes—
247#389C2312yes—
248#389C2312yes—
249#389C2311yescharacteristic
250#389C2312yes—
251#388—22no—
252#388—22no—
253#388—22no—
254#388—21no—
255#388—22no—
256#388—22no—
257#388—22no—
258#387—22no—
259#387—22no—
260#387D412yes—
261#386—21no—
262#386—22no—
263#386—22no—
264#386—22no—
265#386—22no—
266#386—22no—
267#385—22no—
268#385—22no—
269#385—22no—
270#385—22no—
271#385D412yes—
272#384C2311yescharacteristic
273#384C2312yes—
274#382—21no—
275#382C2312yes—
276#382C2312yes—
277#381—22no—
278#380D411yescharacteristic
279#380C2311yescharacteristic
280C4×C4⋊C4—21no—
281C4×C4⋊C4—21no—
282C4×C4⋊C4—21no—
283C4×C4⋊C4C2311yescharacteristic
284C4×C4⋊C4C2312yes—
285C4×C4⋊C4C2311yescharacteristic
286C4×C4⋊C4C2311yescharacteristic
287C4×C4⋊C4C2312yes—
288C4×C4⋊C4C2311yescharacteristic
289C4×C4⋊C4C2311yescharacteristic
290C4×C4⋊C4C2311yescharacteristic
291C4×C4⋊C4C2312yes—
292C4×C22⋊C4—21no—
293C4×C22⋊C4—22no—
294C4×C22⋊C4C2312yes—
295C2×#95—21no—
296#340C2312yes—
297#340C2312yes—
298#340C2311yescharacteristic
299#340C2312yes—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2312yes—
305#340C2311yescharacteristic
306#340C2312yes—
307#340C2311yescharacteristic
308#340C2311yescharacteristic
309#340C2311yescharacteristic
310#340C2312yes—
311#340C2312yes—
312#340C2311yescharacteristic
313#340C2312yes—
314#340C2312yes—
315#340C2312yes—
316#340C2311yescharacteristic
317#340C2311yescharacteristic
318#336C2312yes—
319#336C2312yes—
320#336C2312yes—
321#336C2312yes—
322#336C2311yescharacteristic
323#336C2311yescharacteristic
324C22×Q8—21no—
325C22×Q8—21no—
326C22×Q8—22no—
327C22×Q8—22no—
328C22×Q8—44no—
329C22×Q8—44no—
330C22×Q8—44no—
331C22×Q8—44no—
332C22×Q8—82no—
333C22×Q8—82no—
334C22×Q8C2×D411yescharacteristic
335C22×D4—21no—
336C22×D4—22no—
337C22×D4—21no—
338C22×D4—21no—
339C22×D4C2412yes—
340C22×D4C2411yescharacteristic
341C23×C4—22no—
342C23×C4—21no—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4C2×D411yescharacteristic
348C23×C4C2×D411yescharacteristic
349C23×C4C2411yescharacteristic
350C2×D8—24no—
351C2×D8—42no—
352C2×D8—42no—
353C22×C8—24no—
354C22×C8—42no—
355C22×C8—42no—
356C22×C8C2412yes—
357C22×C8C2412yes—
358C22×C8C2411yescharacteristic
359C22×C8C2411yescharacteristic
360C22×C8C2411yescharacteristic
361C22×C8C2411yescharacteristic
362C4⋊Q8—24no—
363C4⋊Q8—24no—
364C4⋊Q8—22no—
365C4⋊Q8—22no—
366C4⋊Q8—22no—
367C4⋊Q8—42no—
368C4⋊Q8—42no—
369C4⋊Q8—44no—
370C4⋊Q8—44no—
371C4⋊Q8—48no—
372C4⋊Q8—44no—
373C4⋊Q8#4114yes—
374#127—22no—
375#127—22no—
376#124—82no—
377C22⋊Q8—24no—
378C22⋊Q8—48no—
379C22⋊Q8—48no—
380C22⋊Q8—44no—
381C22⋊Q8—44no—
382C22⋊Q8—48no—
383C22⋊Q8—82no—
384#121—22no—
385#121—24no—
386#121—24no—
387#121—44no—
388#121—82no—
389#121#4114yes—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8—44no—
393C4×D4—24no—
394C4×D4—24no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—42no—
398C4×D4—42no—
399C4×D4—48no—
400C4×D4—44no—
401C4×D4—82no—
402C4×D4—84no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—41no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—44no—
426C2×C4⋊C4C2×D411yescharacteristic
427C2×C4⋊C4C2×D411yescharacteristic
428C2×C4⋊C4C2×D411yescharacteristic
429C2×C4⋊C4C2×D412yes—
430C2×C4⋊C4C2×D412yes—
431C2×C4⋊C4C2×D412yes—
432C2×C4⋊C4C2412yes—
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2412yes—
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4C2×D412yes—
461C2×C22⋊C4C2×D412yes—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—21no—
465C2×C42—22no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—22no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—82no—
472C2×C42C2×D411yescharacteristic
473C2×C42C2×D411yescharacteristic
474C2×C42C2412yes—
475C2×C42C2412yes—
476C2×C42C2411yescharacteristic
477C2×C42C2411yescharacteristic
478#107—24no—
479#106—22no—
480#106—22no—
481#106—22no—
482#106—41no—
483C4⋊C8—22no—
484C4⋊C8—22no—
485C4⋊C8—42no—
486C4⋊C8—42no—
487C4⋊C8—42no—
488#102—24no—
489#102—22no—
490#102—22no—
491#102—24no—
492#102—24no—
493#102—24no—
494#102—22no—
495#102—42no—
496#102—41no—
497#102—42no—
498#102—42no—
499#102—42no—
500C22⋊C8—22no—
501C22⋊C8—22no—
502#97—42no—
503#97—42no—
504C4×C8—22no—
505C4×C8—22no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—22no—
512#95—21no—
513#95—22no—
514#95—22no—
515#95—22no—
516#95—21no—
517#95—22no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95C2×D412yes—
524#95C2×D412yes—
525#95C2×D412yes—
526#95C2×D412yes—
527#95C2×D412yes—
528C24—21no—
529C24—22no—
530C24C22×D411yescharacteristic
531C2×Q8—22no—
532C2×Q8—24no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—44no—
536C2×Q8—44no—
537C2×Q8—44no—
538C2×Q8—42no—
539C2×Q8—42no—
540C2×Q8—44no—
541C2×Q8—42no—
542C2×Q8—42no—
543C2×Q8—42no—
544C2×Q8—82no—
545C2×Q8—82no—
546C2×Q8—816no—
547C2×Q8—816no—
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—22no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—22no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4—44no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4C2×#4112yes—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—41no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—42no—
595C22×C4—44no—
596C22×C4—42no—
597C22×C4—44no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—82no—
603C22×C4—82no—
604C22×C4—82no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—82no—
609C22×C4AGL(1,ℤ/8)14yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C2×#4112yes—
620C22×C42−1+412yes—
621C22×C4C2511yescharacteristic
622D8—84no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—22no—
639C2×C8—21no—
640C2×C8—22no—
641C2×C8—84no—
642C4⋊C4—24no—
643C4⋊C4—22no—
644C4⋊C4—24no—
645C4⋊C4—22no—
646C4⋊C4—24no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—22no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—44no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—44no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—82no—
679C4⋊C4—81no—
680C4⋊C4—82no—
681C4⋊C4C2×#4112yes—
682C4⋊C4C2×#4114yes—
683C4⋊C42−1+412yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—42no—
690C22⋊C4—44no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—44no—
694C22⋊C4—42no—
695C22⋊C4—44no—
696C22⋊C4—82no—
697C22⋊C4—82no—
698C22⋊C4—82no—
699C22⋊C4—82no—
700C22⋊C4—82no—
701C22⋊C4—82no—
702C22⋊C4—82no—
703C22⋊C4—82no—
704C42—22no—
705C42—22no—
706C42—21no—
707C42—22no—
708C42—22no—
709C42—21no—
710C42—22no—
711C42—22no—
712C42—44no—
713C42—42no—
714C42—42no—
715C42—42no—
716C42—81no—
717C42—81no—
718C42—82no—
719C42C2×#4112yes—
720C42H(5,𝔽2)12yes—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—22no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23#54812yes—
740C23C2×AGL(1,ℤ/8)12yes—
741C23#57712yes—
742C23C23×D411yescharacteristic
743Q8—44no—
744Q8—48no—
745Q8—88no—
746Q8—88no—
747Q8—84no—
748D4—22no—
749D4—22no—
750D4—48no—
751D4—42no—
752D4—42no—
753D4—41no—
754D4—42no—
755D4—41no—
756D4—42no—
757D4—88no—
758D4—84no—
759D4—162no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—28no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—21no—
789C2×C4—44no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—88no—
818C2×C4—84no—
819C2×C4—88no—
820C2×C4—84no—
821C2×C4—84no—
822C2×C4—164no—
823C2×C4#54612yes—
824C2×C4#54612yes—
825C2×C4#54812yes—
826C2×C4C2×AGL(1,ℤ/8)12yes—
827C2×C4C2×AGL(1,ℤ/8)12yes—
828C2×C4#57612yes—
829C2×C4C22×#4111yescharacteristic
830C2×C4C22×#4111yescharacteristic
831C2×C4C2×H(5,𝔽2)11yescharacteristic
832C2×C4C2×2−1+411yescharacteristic
833C2×C4C2×2−1+411yescharacteristic
834C2×C4#58511yescharacteristic
835C8—41no—
836C8—41no—
837C8—42no—
838C8—42no—
839C8—41no—
840C8—41no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22#337314yes—
862C22C2×#54611yescharacteristic
863C22C2×#54811yescharacteristic
864C22#348911yescharacteristic
865C22C22×AGL(1,ℤ/8)11yescharacteristic
866C22C2×#57611yescharacteristic
867C22C2×#57711yescharacteristic
868C22#358611yescharacteristic
869C4—22no—
870C4—22no—
871C4—22no—
872C4—42no—
873C4—41no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—44no—
878C4—42no—
879C4—42no—
880C4—82no—
881C4—81no—
882C4—81no—
883C4—81no—
884C4—81no—
885C4—82no—
886C4—81no—
887C4#331814yes—
888C4#348211yescharacteristic
889C4#351411yescharacteristic
890C4#351611yescharacteristic
891C4#355211yescharacteristic
892C2—24no—
893C2—82no—
894C2—162no—
895C2#5907511yescharacteristic
896C2C2×#331811yescharacteristic
897C2#6118511yescharacteristic
898C2C2×#337311yescharacteristic
899C2#6134511yescharacteristic
900C2#6211111yescharacteristic
901C2#6219911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24750C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59127C2semidirect
2. #36587C2semidirect
3. #32242C2semidirect
4. #31831C2semidirect
5. #28648C2semidirect
6. #27736C2semidirect
7. #27711C2semidirect
8. #27450C2semidirect
9. #26509C2semidirect
10. #26410C2semidirect
11. #26281C2semidirect
12. #26036C2semidirect
13. #25933C2semidirect
14. #25903C2semidirect
15. #25318C2semidirect
16. #25214C2semidirect
18. #23220C2semidirect
19. #23132C2semidirect
20. #22956C2semidirect
21. #22523C2semidirect
22. C4×#481C2semidirect
23. C2×#1988C2semidirect

Maximal subgroups

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

subgroupindex
#591272
#365872
#322422
#318312
#286482
#277362
#277112
#274502
#265092
#264102
#262812
#260362
#259332
#259032
#253182
#252142
#247502
#232202
#231322
#229562
#225232
C4×#4812
C2×#19882