Finite Group Databasebeta

← #6589327

Subgroups — #6589327

Order 512.

1758 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36544C211yesmaximal, characteristic
2#36116C211yesmaximal, characteristic
3#33207C211yesmaximal, characteristic, complemented
4#33148C211yesmaximal, characteristic, complemented
5#32954C211yesmaximal, characteristic, complemented
6#28847C212yesmaximal, complemented
7#28098C212yesmaximal, complemented
8#27729C211yesmaximal, characteristic, complemented
9#27160C212yesmaximal, complemented
10#27034C212yesmaximal, complemented
11#26088C211yesmaximal, characteristic, complemented
12#25702C211yesmaximal, characteristic, complemented
13#25453C211yesmaximal, characteristic, complemented
14#25341C211yesmaximal, characteristic, complemented
15#25014C211yesmaximal, characteristic, complemented
16#24937C212yesmaximal, complemented
17#24863C212yesmaximal, complemented
18#23062C211yesmaximal, characteristic, complemented
19#22920C212yesmaximal, complemented
20#22703C212yesmaximal, complemented
21#22487C211yesmaximal, characteristic, complemented
22C8×#121C211yesmaximal, characteristic
23C2×C4×#103C211yesmaximal, characteristic, complemented
24C2×#554C2211yescharacteristic
25C2×#529—21no—
26C22×C4×Q8C2211yescharacteristic
27C2×#498C2211yescharacteristic
28C2×#483C2212yes—
29C2×#475C2211yescharacteristic
30C2×#475C2211yescharacteristic
31C2×C8×D4C2212yes—
32C2×C8×D4C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×C4×C8C2211yescharacteristic
36#2857C2211yescharacteristic
37#2857C2211yescharacteristic
38#2855—21no—
39#2851—21no—
40#2584—21no—
41#2580—21no—
42#2567C2211yescharacteristic
43#2552C2211yescharacteristic
44#2547C2211yescharacteristic
45#2538C2211yescharacteristic
46#2496C2212yes—
47#2486C2212yes—
48#2478—22no—
49#2465—22no—
50#2453—21no—
51#2449—22no—
52#2447—21no—
53#2423C2212yes—
54#2419—22no—
55#2409C2212yes—
56#2365C2211yescharacteristic
57#2360C2212yes—
58#2355C2211yescharacteristic
59D4×C4⋊C4C2212yes—
60D4×C4⋊C4C2211yescharacteristic
61D4×C4⋊C4C2212yes—
62#2344C2212yes—
63C4×#121—21no—
64C4×#121C2211yescharacteristic
65C2×C4×C4⋊C4C2211yescharacteristic
66#2100C2212yes—
67#2096C2212yes—
68#2084C2212yes—
69#2077C2212yes—
70#2077C2212yes—
71#2072C2212yes—
72#2066C2212yes—
73#2066C2212yes—
74#2035C2212yes—
75#2035C2212yes—
76#2035C2212yes—
77#2035C2212yes—
78#1990C2211yescharacteristic
79#1990C2211yescharacteristic
80#1987C2211yescharacteristic
81#1987C2211yescharacteristic
82#1954C2211yescharacteristic
83#1948C2211yescharacteristic
84#1948C2212yes—
85#1948C2211yescharacteristic
86#1948C2212yes—
87#1941C2212yes—
88#1941C2212yes—
89#1939C2211yescharacteristic
90#1933C2212yes—
91#1933C2212yes—
92#1927C2212yes—
93#1927C2212yes—
94#1923C2212yes—
95#1920C2212yes—
96#1920C2212yes—
97#1919C2212yes—
98#1919C2212yes—
99#1892C2212yes—
100#1892C2212yes—
101#1872C2212yes—
102#1869C2212yes—
103#1865C2212yes—
104#1865C2212yes—
105#1853C2212yes—
106#1853C2212yes—
107#1853C2212yes—
108#1853C2212yes—
109#1853C2212yes—
110#1844C2211yescharacteristic
111#1834C2212yes—
112#1824C2212yes—
113#1823C2212yes—
114#1807C2212yes—
115#1807C2212yes—
116#1807C2212yes—
117#1803C2211yescharacteristic
118#1803C2211yescharacteristic
119#1797C2211yescharacteristic
120#1787C2212yes—
121C4×#106C2212yes—
122C8×C4⋊C4C2211yescharacteristic
123C4×#103C2211yescharacteristic
124C4×#103C2211yescharacteristic
125C4×#103C2211yescharacteristic
126C4×#103C2211yescharacteristic
127C4×#103C2211yescharacteristic
128C4×#103C2211yescharacteristic
129C4×#103C2211yescharacteristic
130C4×#103C2211yescharacteristic
131C8×C22⋊C4C2212yes—
132C2×#340C2211yescharacteristic
133C2×#340C2212yes—
134C2×#340C2211yescharacteristic
135C23×Q8C2311yescharacteristic
136C23×C8C2311yescharacteristic
137C23×C8C2312yes—
138C23×C8C2311yescharacteristic
139#554—24no—
140#554—42no—
141C2×C4⋊Q8C2311yescharacteristic
142C2×C4⋊Q8C2311yescharacteristic
143#529—48no—
144C2×#126—22no—
145C2×#125—21no—
146C2×#125—21no—
147C2×#124—21no—
148C2×#123—22no—
149C2×C22⋊Q8—21no—
150C2×C22⋊Q8—21no—
151C2×C22⋊Q8—22no—
152C2×C22⋊Q8C2312yes—
153C2×C22⋊Q8C2312yes—
154C2×#121D411yescharacteristic
155C2×C4×Q8—21no—
156C2×C4×Q8—21no—
157C2×C4×Q8—21no—
158C2×C4×Q8—24no—
159C2×C4×Q8—42no—
160C2×C4×Q8C2311yescharacteristic
161C2×C4×Q8C2311yescharacteristic
162C2×C4×Q8C2311yescharacteristic
163C2×C4×Q8C2311yescharacteristic
164C2×C4×D4—21no—
165C2×C4×D4—22no—
166C2×C4×D4—21no—
167C2×C4×D4—22no—
168C2×C4×D4C2312yes—
169C2×C4×D4C2311yescharacteristic
170C2×#117—22no—
171C22×C4⋊C4—21no—
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C42—21no—
178C22×C42—21no—
179C22×C42C2311yescharacteristic
180#498—42no—
181#483—28no—
182#475—24no—
183#475—42no—
184C8×D4—28no—
185C8×D4—42no—
186C2×#106C2312yes—
187C2×#106C2312yes—
188C2×#106C2312yes—
189C2×#106C2312yes—
190C2×#106C2312yes—
191C2×#106C2312yes—
192C2×#106C2312yes—
193C2×#106C2312yes—
194C2×C4⋊C8C2311yescharacteristic
195C2×C4⋊C8C2311yescharacteristic
196C2×C4⋊C8C2312yes—
197C2×#103—24no—
198C2×#103—24no—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2311yescharacteristic
202C2×#103C2311yescharacteristic
203C2×#103C2311yescharacteristic
204C2×#103C2311yescharacteristic
205C2×#103C2311yescharacteristic
206C2×#103C2311yescharacteristic
207C2×#103C2311yescharacteristic
208C2×#103C2312yes—
209C2×#103C2312yes—
210C2×#103C2311yescharacteristic
211C2×C22⋊C8C2312yes—
212C2×C22⋊C8C2312yes—
213C2×C22⋊C8C2312yes—
214C2×C22⋊C8C2312yes—
215C2×C4×C8—42no—
216C2×C4×C8C2312yes—
217C2×C4×C8C2311yescharacteristic
218C2×C4×C8C2311yescharacteristic
219C2×C4×C8C2311yescharacteristic
220C2×C4×C8C2311yescharacteristic
221#400—22no—
222#399—22no—
223#398—22no—
224#398—22no—
225#398—22no—
226#397—22no—
227#397—22no—
228#397—22no—
229#396—22no—
230#395—22no—
231#395—22no—
232#393—22no—
233#391—21no—
234#391—21no—
235#391—21no—
236#391—21no—
237#391C2312yes—
238#391C2312yes—
239#390—21no—
240#390D411yescharacteristic
241#389—21no—
242#389—21no—
243#389—21no—
244#389—22no—
245#389—21no—
246#389—21no—
247#389—22no—
248#389—21no—
249#389—21no—
250#389—22no—
251#389D411yescharacteristic
252#389C2312yes—
253#389C2312yes—
254#389C2312yes—
255#389C2312yes—
256#388—22no—
257#388D412yes—
258#387—22no—
259#387—22no—
260#387—22no—
261#387—22no—
262#387—22no—
263#387—22no—
264#387—22no—
265#386—22no—
266#386D412yes—
267#385—22no—
268#385—22no—
269#385—22no—
270#385—22no—
271#385—22no—
272#385—22no—
273#385—22no—
274#384C2312yes—
275#384C2311yescharacteristic
276#384C2312yes—
277#384C2311yescharacteristic
278#382—21no—
279#381—22no—
280#381—22no—
281#380—21no—
282#380—21no—
283#380D411yescharacteristic
284#380C2312yes—
285#380C2312yes—
286#380C2312yes—
287#380C2312yes—
288#380C2312yes—
289#380C2312yes—
290C4×C4⋊C4—21no—
291C4×C4⋊C4—21no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4C2311yescharacteristic
294C4×C4⋊C4C2312yes—
295C4×C4⋊C4C2312yes—
296C4×C4⋊C4C2311yescharacteristic
297C4×C4⋊C4C2311yescharacteristic
298C4×C4⋊C4C2311yescharacteristic
299C4×C4⋊C4C2311yescharacteristic
300C4×C22⋊C4—22no—
301C4×C22⋊C4C2312yes—
302C2×#95—21no—
303#340C2312yes—
304#340C2312yes—
305#340C2311yescharacteristic
306#340C2312yes—
307#340C2312yes—
308#340C2312yes—
309#340C2312yes—
310#340C2312yes—
311#340C2312yes—
312#340C2312yes—
313#340C2311yescharacteristic
314#340C2311yescharacteristic
315#340C2312yes—
316#340C2312yes—
317#340C2311yescharacteristic
318#340C2311yescharacteristic
319#340C2311yescharacteristic
320#340C2311yescharacteristic
321#340C2312yes—
322#340C2311yescharacteristic
323#336C2312yes—
324#336C2312yes—
325#336C2312yes—
326C22×Q8—21no—
327C22×Q8—21no—
328C22×Q8—21no—
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8—22no—
332C22×Q8—22no—
333C22×Q8—41no—
334C22×Q8—41no—
335C22×Q8C2411yescharacteristic
336C22×Q8C2411yescharacteristic
337C22×D4C2×D412yes—
338C22×D4C2×D411yescharacteristic
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—22no—
343C23×C4—21no—
344C23×C4—22no—
345C23×C4C2×D411yescharacteristic
346C23×C4C2×D411yescharacteristic
347C23×C4C2412yes—
348C23×C4C2411yescharacteristic
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—24no—
352C22×C8—41no—
353C22×C8—41no—
354C22×C8—41no—
355C22×C8—42no—
356C22×C8—42no—
357C22×C8#4114yes—
358C22×C8C2411yescharacteristic
359C22×C8C2412yes—
360C22×C8C2412yes—
361C22×C8C2411yescharacteristic
362C22×C8C2411yescharacteristic
363C22×C8C2411yescharacteristic
364C4⋊Q8—22no—
365C4⋊Q8—22no—
366C4⋊Q8—22no—
367C4⋊Q8—22no—
368#126—48no—
369#125—44no—
370#125—44no—
371#124—44no—
372#123—48no—
373C22⋊Q8—24no—
374C22⋊Q8—24no—
375C22⋊Q8—48no—
376C22⋊Q8—42no—
377C22⋊Q8—42no—
378C22⋊Q8—44no—
379C22⋊Q8—82no—
380#121SD1618yes—
381C4×Q8—22no—
382C4×Q8—22no—
383C4×Q8—22no—
384C4×Q8—22no—
385C4×Q8—22no—
386C4×Q8—44no—
387C4×Q8—41no—
388C4×Q8—41no—
389C4×Q8—44no—
390C4×Q8—44no—
391C4×Q8#4114yes—
392C4×D4—24no—
393C4×D4—24no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—44no—
397C4×D4—44no—
398C4×D4—48no—
399C4×D4—84no—
400#117—48no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—42no—
433C2×C4⋊C4—41no—
434C2×C4⋊C4—41no—
435C2×C4⋊C4—42no—
436C2×C4⋊C4—44no—
437C2×C4⋊C4C2×D411yescharacteristic
438C2×C4⋊C4C2×D412yes—
439C2×C4⋊C4C2×D411yescharacteristic
440C2×C4⋊C4C2×D411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2412yes—
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2412yes—
447C2×C4⋊C4C2412yes—
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2411yescharacteristic
450C2×C4⋊C4C2411yescharacteristic
451C2×C22⋊C4—22no—
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⋊C4C2×D412yes—
460C2×C22⋊C4C2×D412yes—
461C2×C22⋊C4C2×D412yes—
462C2×C22⋊C4C2×D412yes—
463C2×C22⋊C4C2×D412yes—
464C2×C42—21no—
465C2×C42—22no—
466C2×C42—22no—
467C2×C42—21no—
468C2×C42—22no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—22no—
476C2×C42—44no—
477C2×C42—44no—
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D411yescharacteristic
480C2×C42C2412yes—
481C2×C42C2411yescharacteristic
482C2×C42C2411yescharacteristic
483#106—24no—
484#106—24no—
485#106—24no—
486#106—42no—
487#106—42no—
488#106—42no—
489#106—42no—
490#106—42no—
491C4⋊C8—24no—
492C4⋊C8—22no—
493C4⋊C8—22no—
494#103—22no—
495#103—24no—
496#103—24no—
497#103—22no—
498#103—22no—
499#103—22no—
500#103—22no—
501#103—22no—
502#103—22no—
503#103—42no—
504#103—42no—
505#103#4114yes—
506C22⋊C8—24no—
507C22⋊C8—24no—
508C22⋊C8—24no—
509C22⋊C8—42no—
510C4×C8—24no—
511C4×C8—22no—
512C4×C8—22no—
513C4×C8—41no—
514C4×C8—41no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
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—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95C2×D412yes—
536#95C2×D412yes—
537#95C2×D412yes—
538C24C22×D412yes—
539C24C22×D411yescharacteristic
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—28no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—42no—
552C2×Q8—42no—
553C2×Q8—44no—
554C2×Q8—44no—
555C2×Q8—44no—
556C2×Q8—42no—
557C2×Q8—42no—
558C2×Q8—42no—
559C2×Q8—42no—
560C2×Q8—42no—
561C2×Q8—81no—
562C2×Q8—81no—
563C2×Q8C2×#4112yes—
564C2×Q8C2×#4112yes—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4C2×SD1618yes—
570C2×D4C2×SD1614yes—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—41no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—44no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—82no—
614C22×C4—82no—
615C22×C4—82no—
616C22×C4C2×SD1614yes—
617C22×C4C22×D412yes—
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D412yes—
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D412yes—
624C22×C4C22×D411yescharacteristic
625C22×C4C2×#4112yes—
626C22×C42−1+412yes—
627C22×C4C2511yescharacteristic
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—21no—
638C2×C8—22no—
639C2×C8—21no—
640C2×C8—22no—
641C2×C8—21no—
642C2×C8—22no—
643C2×C8—44no—
644C2×C8—44no—
645C2×C8—84no—
646C2×C8C2×#4112yes—
647C2×C8C2×#4112yes—
648C2×C8C2×#4112yes—
649C4⋊C4—24no—
650C4⋊C4—22no—
651C4⋊C4—24no—
652C4⋊C4—22no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—22no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—42no—
672C4⋊C4—44no—
673C4⋊C4—42no—
674C4⋊C4—44no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—44no—
684C4⋊C4—44no—
685C4⋊C4—42no—
686C4⋊C4—44no—
687C4⋊C4—44no—
688C4⋊C4—42no—
689C4⋊C4—81no—
690C4⋊C4—82no—
691C4⋊C4—82no—
692C4⋊C4—82no—
693C4⋊C4—81no—
694C4⋊C4—82no—
695C4⋊C4C2×SD1614yes—
696C4⋊C4C2×#4112yes—
697C4⋊C4C2×#4112yes—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—42no—
702C22⋊C4—44no—
703C22⋊C4—44no—
704C22⋊C4—44no—
705C22⋊C4—44no—
706C22⋊C4—44no—
707C22⋊C4—44no—
708C22⋊C4—44no—
709C22⋊C4—82no—
710C22⋊C4C2×SD1618yes—
711C42—22no—
712C42—22no—
713C42—24no—
714C42—22no—
715C42—21no—
716C42—21no—
717C42—22no—
718C42—42no—
719C42—42no—
720C42—42no—
721C42—42no—
722C42—42no—
723C42—42no—
724C42—42no—
725C42—44no—
726C42—82no—
727C42C2×#4112yes—
728C42H(5,𝔽2)12yes—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23#54712yes—
740C23C22×SD1614yes—
741C23C22×SD1612yes—
742C23#57712yes—
743C23C23×D411yescharacteristic
744Q8—22no—
745Q8—22no—
746Q8—22no—
747Q8—22no—
748Q8—48no—
749Q8—41no—
750Q8—41no—
751Q8—41no—
752Q8—41no—
753Q8—84no—
754Q8—162no—
755D4—216no—
756D4—28no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—28no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—44no—
784C2×C4—48no—
785C2×C4—41no—
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—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—84no—
822C2×C4—88no—
823C2×C4—84no—
824C2×C4—84no—
825C2×C4—164no—
826C2×C4#54612yes—
827C2×C4#54612yes—
828C2×C4#54712yes—
829C2×C4C22×SD1612yes—
830C2×C4C22×SD1614yes—
831C2×C4C22×SD1612yes—
832C2×C4#57812yes—
833C2×C4C22×#4111yescharacteristic
834C2×C4C22×#4111yescharacteristic
835C2×C4C22×#4111yescharacteristic
836C2×C4C2×H(5,𝔽2)11yescharacteristic
837C2×C4C2×2−1+411yescharacteristic
838C2×C4#58511yescharacteristic
839C8—22no—
840C8—22no—
841C8—22no—
842C8—42no—
843C8—42no—
844C8—41no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—24no—
852C22—24no—
853C22—24no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22#333514yes—
859C22C2×#54611yescharacteristic
860C22C2×#54711yescharacteristic
861C22D4×#4111yescharacteristic
862C22C23×SD1611yescharacteristic
863C22C2×#57711yescharacteristic
864C22C2×#57811yescharacteristic
865C22#358411yescharacteristic
866C4—24no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—42no—
875C4—41no—
876C4—42no—
877C4—81no—
878C4—81no—
879C4—82no—
880C4—82no—
881C4—81no—
882C4—82no—
883C4—81no—
884C4—82no—
885C4#329814yes—
886C4#344411yescharacteristic
887C4#349511yescharacteristic
888C4#350511yescharacteristic
889C4#352011yescharacteristic
890C2—24no—
891C2—44no—
892C2#3614311yescharacteristic
893C2C2×#329811yescharacteristic
894C2#6117211yescharacteristic
895C2C2×#333511yescharacteristic
896C2#6128611yescharacteristic
897C2SD16×#4111yescharacteristic
898C2#6149911yescharacteristic
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. #33207C2semidirect
4. #33148C2semidirect
5. #32954C2semidirect
6. #28847C2semidirect
7. #28098C2semidirect
8. #27729C2semidirect
9. #27160C2semidirect
10. #27034C2semidirect
11. #26088C2semidirect
12. #25702C2semidirect
13. #25453C2semidirect
14. #25341C2semidirect
15. #25014C2semidirect
16. #24937C2semidirect
17. #24863C2semidirect
18. #23062C2semidirect
19. #22920C2semidirect
20. #22703C2semidirect
21. #22487C2semidirect
23. C2×C4×#103C2semidirect

Maximal subgroups

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

subgroupindex
#365442
#361162
#332072
#331482
#329542
#288472
#280982
#277292
#271602
#270342
#260882
#257022
#254532
#253412
#250142
#249372
#248632
#230622
#229202
#227032
#224872
C8×#1212
C2×C4×#1032