Finite Group Databasebeta

← #7532139

Subgroups — #7532139

Order 512.

1769 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#59127C211yesmaximal, characteristic
2#36301C211yesmaximal, characteristic
3#31501C212yesmaximal, complemented
4#31312C212yesmaximal, complemented
5#28598C211yesmaximal, characteristic, complemented
6#28102C212yesmaximal, complemented
7#27757C211yesmaximal, characteristic, complemented
8#27413C212yesmaximal, complemented
9#26527C211yesmaximal, characteristic, complemented
10#26234C211yesmaximal, characteristic, complemented
11#25888C211yesmaximal, characteristic, complemented
12#25856C211yesmaximal, characteristic, complemented
13#25278C211yesmaximal, characteristic, complemented
14#24884C212yesmaximal, complemented
15#24846C211yesmaximal, characteristic, complemented
16#24480C212yesmaximal, complemented
17#24053C212yesmaximal, complemented
18#23221C211yesmaximal, characteristic, complemented
19#22986C211yesmaximal, characteristic
20#22425C212yesmaximal, complemented
21D4×#103C211yesmaximal, characteristic, complemented
22C4×#485C211yesmaximal, characteristic, complemented
23#21259C211yesmaximal, characteristic, complemented
24C2×D4×Q8C2211yescharacteristic
25C2×D4×Q8C2212yes—
26C22×C4⋊Q8C2211yescharacteristic
27C2×#487C2211yescharacteristic
28C2×#487C2211yescharacteristic
29C2×#485C2211yescharacteristic
30C2×#483C2212yes—
31C2×#477C2211yescharacteristic
32C2×#435C2212yes—
33C2×C8×D4C2211yescharacteristic
34C2×#423C2211yescharacteristic
35C2×#419C2212yes—
36C2×#419C2212yes—
37C22×#103C2212yes—
38#2864—21no—
39#2857C2211yescharacteristic
40#2677—22no—
41#2571C2211yescharacteristic
42#2563C2211yescharacteristic
43#2551—21no—
44#2546C2211yescharacteristic
45#2542C2211yescharacteristic
46#2527—22no—
47#2494—21no—
48#2494C2212yes—
49#2485C2212yes—
50#2477—22no—
51#2452—21no—
52#2449—22no—
53#2440—21no—
54#2434C2212yes—
55#2429C2212yes—
56#2420—21no—
57#2409C2212yes—
58#2369C2211yescharacteristic
59#2365C2211yescharacteristic
60#2361—21no—
61#2352C2212yes—
62D4×C4⋊C4C2211yescharacteristic
63#2344C2212yes—
64C4×C22⋊Q8C2211yescharacteristic
65C4×#121C2211yescharacteristic
66#2293—21no—
67C4×#117C2211yescharacteristic
68#2097C2212yes—
69#2086C2212yes—
70#2074C2212yes—
71#2068C2212yes—
72#2066C2212yes—
73#2066C2212yes—
74#2043C2212yes—
75#2043C2212yes—
76#2043C2212yes—
77#2043C2212yes—
78#2036C2212yes—
79#2036C2212yes—
80#2036C2212yes—
81#2036C2212yes—
82#2035C2212yes—
83#2035C2212yes—
84#1987C2211yescharacteristic
85#1981C2212yes—
86#1981C2212yes—
87#1981C2211yescharacteristic
88#1981C2211yescharacteristic
89#1981C2211yescharacteristic
90#1981C2211yescharacteristic
91#1981C2212yes—
92#1960C2212yes—
93#1956C2211yescharacteristic
94#1956C2211yescharacteristic
95#1954C2211yescharacteristic
96#1948C2211yescharacteristic
97#1939C2211yescharacteristic
98#1935C2212yes—
99#1935C2212yes—
100#1928C2212yes—
101#1928C2211yescharacteristic
102#1927C2212yes—
103#1927C2211yescharacteristic
104#1924C2212yes—
105#1919C2211yescharacteristic
106#1918C2211yescharacteristic
107#1894C2212yes—
108#1892C2212yes—
109#1892C2212yes—
110#1892C2212yes—
111#1873C2211yescharacteristic
112#1872C2212yes—
113#1872C2212yes—
114#1870C2212yes—
115#1865C2212yes—
116#1863C2212yes—
117#1854C2211yescharacteristic
118#1850C2212yes—
119#1825C2211yescharacteristic
120#1809C2212yes—
121#1805C2212yes—
122#1803C2211yescharacteristic
123#1787C2212yes—
124#1787C2212yes—
125#1787C2212yes—
126#1787C2212yes—
127#1787C2212yes—
128C4×#107C2211yescharacteristic
129C4×#106C2211yescharacteristic
130#1770C2211yescharacteristic
131#1763C2212yes—
132C4×#103C2211yescharacteristic
133C4×#103C2211yescharacteristic
134C4×C22⋊C8C2211yescharacteristic
135C23×Q8C2312yes—
136C23×Q8C2312yes—
137C22×M16C2312yes—
138C23×C8C2312yes—
139D4×Q8—24no—
140D4×Q8—28no—
141D4×Q8—42no—
142D4×Q8—44no—
143C2×C4⋊Q8—22no—
144C2×C4⋊Q8—21no—
145C2×C4⋊Q8—24no—
146C2×C4⋊Q8—21no—
147C2×C4⋊Q8—21no—
148C2×C4⋊Q8—42no—
149C2×C4⋊Q8C2311yescharacteristic
150C2×C4⋊Q8C2312yes—
151C2×C4⋊Q8C2312yes—
152C2×C4⋊Q8C2311yescharacteristic
153C2×C4⋊Q8C2311yescharacteristic
154C2×C22⋊Q8—21no—
155C2×C22⋊Q8—22no—
156C2×C22⋊Q8—22no—
157C2×C22⋊Q8—22no—
158C2×C22⋊Q8C2312yes—
159C2×C22⋊Q8C2312yes—
160C2×C22⋊Q8C2311yescharacteristic
161C2×C22⋊Q8C2312yes—
162C2×#121D411yescharacteristic
163C2×C4×Q8C2311yescharacteristic
164C2×C4×Q8C2312yes—
165C2×C4×D4—21no—
166C2×C4×D4—22no—
167C2×C4×D4—21no—
168C2×C4×D4C2311yescharacteristic
169C2×C4×D4C2312yes—
170C2×#117—22no—
171C2×#117C2311yescharacteristic
172C2×#117C2311yescharacteristic
173C22×C4⋊C4—21no—
174C22×C4⋊C4—21no—
175C22×C4⋊C4C2312yes—
176C22×C42C2311yescharacteristic
177#487—24no—
178#487—42no—
179#485—24no—
180#483—44no—
181#477—42no—
182#435—44no—
183C8×D4—42no—
184C2×#107C2311yescharacteristic
185C2×#107C2312yes—
186C2×#107C2311yescharacteristic
187C2×#106C2311yescharacteristic
188C2×#106C2311yescharacteristic
189C2×#106C2312yes—
190#423—42no—
191C2×C4⋊C8C2311yescharacteristic
192C2×C4⋊C8C2311yescharacteristic
193C2×C4⋊C8C2312yes—
194C2×C4⋊C8C2312yes—
195#419—44no—
196#419—44no—
197C2×#103—44no—
198C2×#103C2312yes—
199C2×#103C2311yescharacteristic
200C2×#103C2311yescharacteristic
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2311yescharacteristic
204C2×#103C2312yes—
205C2×#103C2312yes—
206C2×#103C2312yes—
207C2×#103C2312yes—
208C2×#103C2312yes—
209C2×#103C2312yes—
210C2×#103C2312yes—
211C2×#103C2312yes—
212C2×#103C2312yes—
213C2×#103C2312yes—
214C2×#103C2312yes—
215C2×#103C2312yes—
216C2×#103C2312yes—
217C2×#103C2312yes—
218C2×#103C2312yes—
219C2×#103C2311yescharacteristic
220C2×C22⋊C8C2311yescharacteristic
221C2×C22⋊C8C2311yescharacteristic
222C2×C22⋊C8C2312yes—
223C2×C22⋊C8C2312yes—
224C2×C22⋊C8C2312yes—
225C2×#97C2312yes—
226C2×C4×C8C2311yescharacteristic
227C2×C4×C8C2311yescharacteristic
228#401—22no—
229#400—22no—
230#399—22no—
231#398—22no—
232#398—22no—
233#397—22no—
234#397—22no—
235#396—22no—
236#395—22no—
237#395—22no—
238#395—22no—
239#394—22no—
240#393—22no—
241#393—22no—
242#391—21no—
243#391—22no—
244#391C2311yescharacteristic
245#391C2312yes—
246#391C2312yes—
247#390—21no—
248#390—21no—
249#390D411yescharacteristic
250#389—21no—
251#389—21no—
252#389—21no—
253#389—21no—
254#389—21no—
255#389—21no—
256#389—21no—
257#389—22no—
258#389D411yescharacteristic
259#389C2312yes—
260#389C2312yes—
261#389C2312yes—
262#389C2311yescharacteristic
263#388—22no—
264#388—22no—
265#388—22no—
266#388—22no—
267#388D412yes—
268#387—22no—
269#387—22no—
270#387—21no—
271#387—22no—
272#387—22no—
273#387—22no—
274#387—22no—
275#386—22no—
276#386—22no—
277#386D412yes—
278#385—21no—
279#385—22no—
280#385—22no—
281#385—22no—
282#385—22no—
283#384—21no—
284#384C2311yescharacteristic
285#382—21no—
286#382—21no—
287#382C2312yes—
288#381—22no—
289#380—21no—
290#380D411yescharacteristic
291#380C2312yes—
292#380C2312yes—
293#380C2311yescharacteristic
294#380C2312yes—
295#380C2312yes—
296C4×C4⋊C4—21no—
297C4×C4⋊C4—21no—
298C4×C4⋊C4—21no—
299C4×C4⋊C4C2311yescharacteristic
300C4×C4⋊C4C2311yescharacteristic
301C4×C4⋊C4C2312yes—
302C4×C4⋊C4C2311yescharacteristic
303C4×C4⋊C4C2311yescharacteristic
304C4×C4⋊C4C2311yescharacteristic
305C4×C4⋊C4C2311yescharacteristic
306C4×C22⋊C4—21no—
307C4×C22⋊C4—21no—
308C4×C22⋊C4—21no—
309C4×C22⋊C4—22no—
310C4×C22⋊C4C2312yes—
311#376—21no—
312C43—21no—
313#340C2312yes—
314#340C2311yescharacteristic
315#340C2312yes—
316#340C2312yes—
317#340C2311yescharacteristic
318#340C2311yescharacteristic
319#340C2311yescharacteristic
320#340C2311yescharacteristic
321#340C2311yescharacteristic
322#340C2312yes—
323#340C2311yescharacteristic
324#340C2311yescharacteristic
325#336C2312yes—
326#336C2312yes—
327#336C2311yescharacteristic
328#336C2311yescharacteristic
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8—21no—
332C22×Q8—24no—
333C22×Q8—24no—
334C22×Q8—24no—
335C22×Q8—24no—
336C22×Q8—24no—
337C22×Q8—42no—
338C22×Q8—42no—
339C22×Q8—42no—
340C22×Q8—42no—
341C22×Q8—42no—
342C22×Q8—42no—
343C22×Q8—42no—
344C22×Q8C2412yes—
345C22×Q8C2411yescharacteristic
346C22×Q8C2412yes—
347C22×D4C2×D412yes—
348C22×D4C2×D411yescharacteristic
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4C2×D411yescharacteristic
353C23×C4C2×D411yescharacteristic
354C23×C4C2412yes—
355C23×C4C2411yescharacteristic
356C2×M16—24no—
357C2×M16—42no—
358C2×M16—42no—
359C22×C8—42no—
360C22×C8—42no—
361C22×C8—42no—
362C22×C8C2411yescharacteristic
363C22×C8C2412yes—
364C22×C8C2412yes—
365C22×C8C2411yescharacteristic
366C22×C8C2411yescharacteristic
367C22×C8C2411yescharacteristic
368C4⋊Q8—24no—
369C4⋊Q8—24no—
370C4⋊Q8—22no—
371C4⋊Q8—22no—
372C4⋊Q8—22no—
373C4⋊Q8—22no—
374C4⋊Q8—22no—
375C4⋊Q8—44no—
376C4⋊Q8—44no—
377C4⋊Q8—42no—
378C4⋊Q8—42no—
379C4⋊Q8—48no—
380C4⋊Q8—44no—
381C4⋊Q8#4114yes—
382C22⋊Q8—22no—
383C22⋊Q8—24no—
384C22⋊Q8—24no—
385C22⋊Q8—48no—
386C22⋊Q8—48no—
387C22⋊Q8—48no—
388C22⋊Q8—42no—
389C22⋊Q8—42no—
390C22⋊Q8—42no—
391C22⋊Q8—42no—
392C22⋊Q8—82no—
393C22⋊Q8#4114yes—
394#121—24no—
395C4×Q8—24no—
396C4×Q8—22no—
397C4×Q8—22no—
398C4×Q8—42no—
399C4×D4—24no—
400C4×D4—24no—
401C4×D4—22no—
402C4×D4—22no—
403C4×D4—48no—
404C4×D4—44no—
405C4×D4—44no—
406#117—22no—
407#117—22no—
408#117—22no—
409#117—41no—
410#117—84no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4—44no—
436C2×C4⋊C4—44no—
437C2×C4⋊C4C2×D411yescharacteristic
438C2×C4⋊C4C2×D412yes—
439C2×C4⋊C4C2×D411yescharacteristic
440C2×C4⋊C4C2×D411yescharacteristic
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2412yes—
448C2×C4⋊C4C2411yescharacteristic
449C2×C4⋊C4C2411yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4C2×D412yes—
462C2×C22⋊C4C2×D412yes—
463C2×C22⋊C4C2×D412yes—
464C2×C22⋊C4C2×D412yes—
465C2×C22⋊C4C2×D412yes—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—22no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—22no—
477C2×C42—21no—
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D411yescharacteristic
480C2×C42C2412yes—
481C2×C42C2411yescharacteristic
482C2×C42C2411yescharacteristic
483#107—22no—
484#107—41no—
485#107—42no—
486#106—22no—
487#106—22no—
488#106—42no—
489C4⋊C8—22no—
490C4⋊C8—22no—
491C4⋊C8—42no—
492C4⋊C8—42no—
493#103—22no—
494#103—22no—
495#103—24no—
496#103—24no—
497#103—22no—
498#103—24no—
499#103—24no—
500#103—42no—
501#103—42no—
502#103—42no—
503#103—42no—
504#103—41no—
505#103—42no—
506#103—42no—
507#103—42no—
508#103—42no—
509#103—42no—
510#103—42no—
511#103—42no—
512#103—42no—
513#103—42no—
514#103—42no—
515C22⋊C8—22no—
516C22⋊C8—22no—
517C22⋊C8—42no—
518C22⋊C8—42no—
519C22⋊C8—42no—
520#97—42no—
521C4×C8—22no—
522C4×C8—22no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—22no—
528#95—22no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—21no—
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#95C2×D412yes—
547#95C2×D412yes—
548#95C2×D412yes—
549C24C22×D411yescharacteristic
550C24C22×D412yes—
551C2×Q8—21no—
552C2×Q8—22no—
553C2×Q8—21no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—21no—
558C2×Q8—22no—
559C2×Q8—21no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—21no—
566C2×Q8—22no—
567C2×Q8—44no—
568C2×Q8—44no—
569C2×Q8—44no—
570C2×Q8—48no—
571C2×Q8—48no—
572C2×Q8—44no—
573C2×Q8—42no—
574C2×Q8—48no—
575C2×Q8—82no—
576C2×Q8—82no—
577C2×Q8—81no—
578C2×Q8—81no—
579C2×Q8—84no—
580C2×Q8—84no—
581C2×Q8—84no—
582C2×Q8—84no—
583C2×Q8—84no—
584C2×Q8C2×#4114yes—
585C2×Q8C2×#4112yes—
586C2×D4—24no—
587C2×D4—24no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—42no—
591C2×D4#13714yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—41no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—82no—
627C22×C4—82no—
628C22×C4—82no—
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D412yes—
631C22×C4C22×D412yes—
632C22×C4C22×D412yes—
633C22×C4C22×D411yescharacteristic
634C22×C4C22×D411yescharacteristic
635C22×C4C22×D411yescharacteristic
636C22×C4C22×D411yescharacteristic
637C22×C4C2×#4112yes—
638C22×C4H(5,𝔽2)12yes—
639C22×C4C2511yescharacteristic
640M16—84no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—22no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—21no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—84no—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—24no—
663C4⋊C4—24no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—22no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—44no—
684C4⋊C4—44no—
685C4⋊C4—44no—
686C4⋊C4—44no—
687C4⋊C4—44no—
688C4⋊C4—44no—
689C4⋊C4—44no—
690C4⋊C4—44no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4—42no—
694C4⋊C4—42no—
695C4⋊C4—42no—
696C4⋊C4—42no—
697C4⋊C4—44no—
698C4⋊C4—82no—
699C4⋊C4—82no—
700C4⋊C4—82no—
701C4⋊C4—81no—
702C4⋊C4C2×#4112yes—
703C4⋊C4H(5,𝔽2)12yes—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—24no—
707C22⋊C4—24no—
708C22⋊C4—24no—
709C22⋊C4—24no—
710C22⋊C4—42no—
711C22⋊C4—44no—
712C22⋊C4—44no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—44no—
716C22⋊C4—82no—
717C22⋊C4—82no—
718C22⋊C4—82no—
719C22⋊C4—82no—
720C42—22no—
721C42—22no—
722C42—21no—
723C42—22no—
724C42—22no—
725C42—21no—
726C42—42no—
727C42—44no—
728C42—42no—
729C42—42no—
730C42—42no—
731C42—42no—
732C42—42no—
733C42—42no—
734C42—81no—
735C42—82no—
736C42C2×#4112yes—
737C42H(5,𝔽2)12yes—
738C23—21no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—21no—
743C23—21no—
744C23—22no—
745C23—21no—
746C23—22no—
747C23—21no—
748C23—21no—
749C23—22no—
750C23#54612yes—
751C23C2×#13714yes—
752C23C23×D411yescharacteristic
753Q8—24no—
754Q8—22no—
755Q8—24no—
756Q8—22no—
757Q8—41no—
758Q8—42no—
759Q8—41no—
760Q8—42no—
761Q8—42no—
762Q8—42no—
763Q8—42no—
764Q8—42no—
765Q8—88no—
766Q8—88no—
767Q8—162no—
768D4—28no—
769D4—48no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—44no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—44no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—41no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—88no—
835C2×C4—88no—
836C2×C4—88no—
837C2×C4#54612yes—
838C2×C4#54612yes—
839C2×C4#54612yes—
840C2×C4C2×#13712yes—
841C2×C4#57712yes—
842C2×C4#57812yes—
843C2×C4C22×#4111yescharacteristic
844C2×C4C22×#4111yescharacteristic
845C2×C4C2×H(5,𝔽2)11yescharacteristic
846C2×C4C2×H(5,𝔽2)11yescharacteristic
847C2×C4C2×H(5,𝔽2)11yescharacteristic
848C2×C4#58511yescharacteristic
849C8—41no—
850C8—41no—
851C8—41no—
852C8—41no—
853C8—42no—
854C8—42no—
855C22—24no—
856C22—22no—
857C22—22no—
858C22—24no—
859C22—22no—
860C22—24no—
861C22—41no—
862C22—42no—
863C22—41no—
864C22—42no—
865C22—41no—
866C22—42no—
867C22—42no—
868C22—41no—
869C22C2×#54611yescharacteristic
870C22C2×#54611yescharacteristic
871C22#348811yescharacteristic
872C22C22×#13711yescharacteristic
873C22C2×#57711yescharacteristic
874C22C2×#57811yescharacteristic
875C22#358611yescharacteristic
876C4—22no—
877C4—22no—
878C4—22no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—42no—
884C4—44no—
885C4—41no—
886C4—42no—
887C4—81no—
888C4—82no—
889C4—82no—
890C4—81no—
891C4—81no—
892C4—81no—
893C4—82no—
894C4—81no—
895C4#331214yes—
896C4#348111yescharacteristic
897C4#351311yescharacteristic
898C4#351411yescharacteristic
899C4#354311yescharacteristic
900C2—44no—
901C2—42no—
902C2#5903011yescharacteristic
903C2C2×#331211yescharacteristic
904C2#6115711yescharacteristic
905C2#6118511yescharacteristic
906C2#6121711yescharacteristic
907C2#6198011yescharacteristic
908C2#6203611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #31501C2semidirect
4. #31312C2semidirect
5. #28598C2semidirect
6. #28102C2semidirect
7. #27757C2semidirect
8. #27413C2semidirect
9. #26527C2semidirect
10. #26234C2semidirect
11. #25888C2semidirect
12. #25856C2semidirect
13. #25278C2semidirect
14. #24884C2semidirect
15. #24846C2semidirect
16. #24480C2semidirect
17. #24053C2semidirect
18. #23221C2semidirect
20. #22425C2semidirect
21. D4×#103C2semidirect
22. C4×#485C2semidirect
23. #21259C2semidirect

Maximal subgroups

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

subgroupindex
#591272
#363012
#315012
#313122
#285982
#281022
#277572
#274132
#265272
#262342
#258882
#258562
#252782
#248842
#248462
#244802
#240532
#232212
#229862
#224252
D4×#1032
C4×#4852
#212592