Finite Group Databasebeta

← #7527936

Subgroups — #7527936

Order 512.

1653 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59305C211yesmaximal, characteristic, complemented
2#36275C211yesmaximal, characteristic, complemented
3#31892C212yesmaximal, complemented
4#31532C212yesmaximal, complemented
5#28788C212yesmaximal, complemented
6#28264C211yesmaximal, characteristic, complemented
7#27948C211yesmaximal, characteristic, complemented
8#27824C211yesmaximal, characteristic, complemented
9#27296C212yesmaximal, complemented
10#26436C212yesmaximal, complemented
11#26045C211yesmaximal, characteristic, complemented
12#25972C212yesmaximal, complemented
13#25061C211yesmaximal, characteristic, complemented
14#24843C211yesmaximal, characteristic, complemented
15#24823C212yesmaximal, complemented
16#24815C211yesmaximal, characteristic, complemented
17#24327C211yesmaximal, characteristic, complemented
18#22953C211yesmaximal, characteristic, complemented
19#22866C212yesmaximal
20#22670C211yesmaximal, characteristic, complemented
21#22519C211yesmaximal, characteristic, complemented
22C4×#449C211yesmaximal, characteristic
23#20648C211yesmaximal, characteristic, complemented
24C2×#554C2211yescharacteristic
25C2×C4×#41C2211yescharacteristic
26C2×#478C2212yes—
27C2×#476C2211yescharacteristic
28C2×#449C2211yescharacteristic
29C2×C8×Q8C2211yescharacteristic
30C2×#442C2212yes—
31C2×C4×SD16C2211yescharacteristic
32C2×C4×D8C2211yescharacteristic
33C2×#423C2211yescharacteristic
34C2×#417C2212yes—
35#2857C2211yescharacteristic
36#2855—21no—
37#2790—22no—
38#2582C2211yescharacteristic
39#2579—22no—
40#2567C2211yescharacteristic
41#2566C2212yes—
42#2552C2211yescharacteristic
43#2538C2211yescharacteristic
44#2507C2212yes—
45#2502—21no—
46#2497—21no—
47#2487—21no—
48#2453C2212yes—
49#2449—22no—
50#2442C2212yes—
51#2441C2212yes—
52#2438—22no—
53#2417—21no—
54#2417—21no—
55#2361C2212yes—
56#2355C2211yescharacteristic
57D4×C4⋊C4—21no—
58D4×C4⋊C4C2211yescharacteristic
59D4×C4⋊C4C2211yescharacteristic
60D4×C4⋊C4C2212yes—
61#2339C2212yes—
62C4×C22⋊Q8C2211yescharacteristic
63C4×#121C2211yescharacteristic
64C2×#389—21no—
65C2×#384C2211yescharacteristic
66#2099C2212yes—
67#2097C2212yes—
68#2088C2212yes—
69#2088C2212yes—
70#2085C2212yes—
71#2084C2212yes—
72#2084C2212yes—
73#2084C2212yes—
74#2067C2212yes—
75#2066C2212yes—
76#2066C2212yes—
77#2065C2212yes—
78#2059C2212yes—
79#2059C2212yes—
80#2026C2212yes—
81#2025C2212yes—
82#1992C2212yes—
83#1991C2212yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1989C2212yes—
87#1987C2211yescharacteristic
88#1984C2211yescharacteristic
89#1968C2212yes—
90#1947C2211yescharacteristic
91#1943C2212yes—
92#1941C2212yes—
93#1940C2212yes—
94#1939C2211yescharacteristic
95#1935C2212yes—
96#1927C2212yes—
97#1919C2212yes—
98#1916C2212yes—
99#1895C2212yes—
100#1880C2211yescharacteristic
101#1879C2212yes—
102#1879C2211yescharacteristic
103#1877C2212yes—
104#1875C2211yescharacteristic
105#1864C2212yes—
106#1864C2212yes—
107#1864C2212yes—
108#1864C2212yes—
109#1864C2211yescharacteristic
110#1863C2211yescharacteristic
111#1854C2211yescharacteristic
112#1853C2212yes—
113#1853C2212yes—
114#1851C2212yes—
115#1844C2211yescharacteristic
116#1844C2211yescharacteristic
117#1809C2212yes—
118#1804C2212yes—
119#1803C2212yes—
120#1803C2211yescharacteristic
121#1803C2211yescharacteristic
122#1802C2211yescharacteristic
123#1802C2211yescharacteristic
124#1802C2212yes—
125#1802C2211yescharacteristic
126#1802C2212yes—
127#1788C2211yescharacteristic
128#1770C2211yescharacteristic
129C4×#103C2211yescharacteristic
130C4×#102C2212yes—
131C4×#102C2211yescharacteristic
132#1753C2212yes—
133C4×C22⋊C8C2211yescharacteristic
134#1736C2212yes—
135C22×#41C2311yescharacteristic
136C22×SD16C2311yescharacteristic
137C22×D8C2311yescharacteristic
138C22×M16C2312yes—
139#554—24no—
140#554—42no—
141C2×C4⋊Q8C2311yescharacteristic
142C2×#125C2312yes—
143C2×#125C2312yes—
144C2×C22⋊Q8—21no—
145C2×C22⋊Q8—21no—
146C2×C22⋊Q8—21no—
147C2×C22⋊Q8—22no—
148C2×C22⋊Q8D411yescharacteristic
149C2×#121C2311yescharacteristic
150C4×#41—24no—
151C4×#41—42no—
152C2×C4×Q8C2311yescharacteristic
153C2×C4×Q8C2311yescharacteristic
154C2×C4×Q8C2311yescharacteristic
155C2×C4×D4—21no—
156C2×C4×D4—21no—
157C2×C4×D4—21no—
158C2×C4×D4—22no—
159C2×C4×D4C2311yescharacteristic
160C2×C4×D4C2312yes—
161C2×C4×D4C2311yescharacteristic
162C2×C4×D4C2312yes—
163C2×C4×D4C2311yescharacteristic
164C2×C4×D4C2312yes—
165C2×#117—21no—
166C2×#117C2311yescharacteristic
167C22×C4⋊C4—21no—
168C22×C4⋊C4—21no—
169C22×C4⋊C4—21no—
170C22×C4⋊C4—21no—
171C22×C4⋊C4—21no—
172C22×C4⋊C4—22no—
173C22×C4⋊C4C2312yes—
174C22×C42—21no—
175C22×C42C2311yescharacteristic
176#478—44no—
177#476—42no—
178#449Q818yescomplemented
179C8×Q8—42no—
180#442—44no—
181C4×SD16—42no—
182C4×D8—24no—
183C2×#107C2311yescharacteristic
184C2×#107C2312yes—
185C2×#106C2312yes—
186C2×#106C2312yes—
187C2×#106C2312yes—
188C2×#106C2311yescharacteristic
189C2×#106C2312yes—
190C2×#106C2312yes—
191#423—42no—
192C2×C4⋊C8C2311yescharacteristic
193C2×C4⋊C8C2311yescharacteristic
194C2×C4⋊C8C2312yes—
195C2×C4⋊C8C2312yes—
196C2×C4⋊C8C2312yes—
197#417—44no—
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2311yescharacteristic
201C2×#103C2311yescharacteristic
202C2×#103C2311yescharacteristic
203C2×#102C2311yescharacteristic
204C2×#102C2312yes—
205C2×#102C2312yes—
206C2×#102C2311yescharacteristic
207C2×#102C2311yescharacteristic
208C2×#102C2311yescharacteristic
209C2×#102C2312yes—
210C2×#102C2312yes—
211C2×#102C2311yescharacteristic
212C2×C22⋊C8C2311yescharacteristic
213C2×C22⋊C8C2311yescharacteristic
214C2×#97C2312yes—
215C2×C4×C8C2311yescharacteristic
216C2×C4×C8C2311yescharacteristic
217C2×C4×C8C2312yes—
218#400—22no—
219#400—22no—
220#399—22no—
221#398—22no—
222#398—22no—
223#398—22no—
224#398—22no—
225#398—22no—
226#398—22no—
227#396—22no—
228#396—22no—
229#396—22no—
230#396—22no—
231#395—22no—
232#391—21no—
233#391—21no—
234#391—21no—
235#391D411yescharacteristic
236#391C2312yes—
237#391C2312yes—
238#390C2311yescharacteristic
239#390C2312yes—
240#389—21no—
241#389—21no—
242#389—21no—
243#389—21no—
244#389—22no—
245#389—21no—
246#389—22no—
247#389—22no—
248#389D411yescharacteristic
249#389C2312yes—
250#389C2312yes—
251#389C2312yes—
252#389C2312yes—
253#389C2312yes—
254#389C2311yescharacteristic
255#389C2312yes—
256#388—21no—
257#388—22no—
258#387—22no—
259#387—22no—
260#387—22no—
261#387—22no—
262#387D412yes—
263#386—21no—
264#386—22no—
265#386—22no—
266#386—22no—
267#385—22no—
268#385—22no—
269#385—22no—
270#385—22no—
271#385—22no—
272#385—22no—
273#385—22no—
274#385—22no—
275#385D412yes—
276#384—21no—
277#384—21no—
278#384—21no—
279#384C2312yes—
280#384C2312yes—
281#384C2311yescharacteristic
282#384C2311yescharacteristic
283#384C2311yescharacteristic
284#382C2312yes—
285#381—22no—
286#380—21no—
287#380—21no—
288#380—21no—
289#380—22no—
290#380—21no—
291#380—22no—
292#380D411yescharacteristic
293#380C2311yescharacteristic
294#380C2312yes—
295C4×C4⋊C4—21no—
296C4×C4⋊C4C2312yes—
297C4×C4⋊C4C2311yescharacteristic
298C4×C4⋊C4C2312yes—
299C4×C4⋊C4C2311yescharacteristic
300C4×C22⋊C4—21no—
301C4×C22⋊C4C2312yes—
302C2×#95—22no—
303#340C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2312yes—
307#340C2312yes—
308#340C2312yes—
309#340C2311yescharacteristic
310#340C2312yes—
311#340C2312yes—
312#340C2312yes—
313#340C2312yes—
314#340C2311yescharacteristic
315#340C2311yescharacteristic
316#340C2312yes—
317#340C2312yes—
318#340C2311yescharacteristic
319#336C2312yes—
320#336C2312yes—
321#336C2311yescharacteristic
322#336C2311yescharacteristic
323#336C2312yes—
324#336C2312yes—
325C2×#41—22no—
326C2×#41—22no—
327C2×#41—22no—
328C2×#41—41no—
329C2×#41—41no—
330C2×#41C2×Q814yes—
331C22×Q8—21no—
332C22×Q8C2×D411yescharacteristic
333C22×Q8C2411yescharacteristic
334C22×D4—21no—
335C22×D4—21no—
336C22×D4C2411yescharacteristic
337C22×D4C2411yescharacteristic
338C23×C4—21no—
339C23×C4—21no—
340C23×C4—22no—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4C2×D411yescharacteristic
347C23×C4C2×D411yescharacteristic
348C23×C4C2411yescharacteristic
349C2×SD16—41no—
350C2×SD16—41no—
351C2×SD16C2×Q814yes—
352C2×D8—22no—
353C2×D8—22no—
354C2×D8C2×Q814yes—
355C2×M16—24no—
356C2×M16—42no—
357C2×M16—42no—
358C22×C8C2412yes—
359C22×C8C2412yes—
360C22×C8C2411yescharacteristic
361C22×C8C2411yescharacteristic
362C22×C8C2411yescharacteristic
363C22×C8C2411yescharacteristic
364C4⋊Q8—22no—
365C4⋊Q8—22no—
366#125—24no—
367#125—42no—
368#125—42no—
369#125—42no—
370C22⋊Q8—48no—
371C22⋊Q8—42no—
372C22⋊Q8—44no—
373C22⋊Q8—82no—
374C22⋊Q8—82no—
375#121—22no—
376#121C2×Q814yes—
377C4×Q8—22no—
378C4×Q8—22no—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8—41no—
383C4×D4—22no—
384C4×D4—24no—
385C4×D4—24no—
386C4×D4—22no—
387C4×D4—22no—
388C4×D4—22no—
389C4×D4—42no—
390C4×D4—41no—
391C4×D4—42no—
392C4×D4—42no—
393C4×D4—42no—
394C4×D4—44no—
395C4×D4—44no—
396C4×D4—44no—
397C4×D4—84no—
398C4×D4#4114yes—
399#117—22no—
400#117—44no—
401#117—41no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4—42no—
429C2×C4⋊C4—44no—
430C2×C4⋊C4—44no—
431C2×C4⋊C4—82no—
432C2×C4⋊C4—84no—
433C2×C4⋊C4—82no—
434C2×C4⋊C4—82no—
435C2×C4⋊C4C2×D411yescharacteristic
436C2×C4⋊C4C2×D411yescharacteristic
437C2×C4⋊C4C2×D411yescharacteristic
438C2×C4⋊C4C2×D412yes—
439C2×C4⋊C4C2×D412yes—
440C2×C4⋊C4C2×D412yes—
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2412yes—
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2412yes—
445C2×C4⋊C4C2412yes—
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—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
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—44no—
474C2×C42C2×D411yescharacteristic
475C2×C42C2×D411yescharacteristic
476C2×C42C2412yes—
477C2×C42C2412yes—
478C2×C42C2411yescharacteristic
479C2×C42C2411yescharacteristic
480#107—22no—
481#107—42no—
482#106—42no—
483#106—42no—
484#106—41no—
485#106—42no—
486#106—42no—
487#106—42no—
488C4⋊C8—22no—
489C4⋊C8—22no—
490C4⋊C8—42no—
491C4⋊C8—42no—
492C4⋊C8—42no—
493#103—41no—
494#103—42no—
495#103—42no—
496#103—41no—
497#103C2×Q814yes—
498#102—22no—
499#102—24no—
500#102—24no—
501#102—22no—
502#102—22no—
503#102—41no—
504#102—42no—
505#102—42no—
506#102C2×Q814yes—
507C22⋊C8—22no—
508C22⋊C8C2×Q814yes—
509#97—42no—
510C4×C8—22no—
511C4×C8—22no—
512C4×C8—42no—
513#95—22no—
514#95—22no—
515#95—22no—
516#95—21no—
517#95—21no—
518#95—22no—
519#95—22no—
520#95—21no—
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#95C2×D412yes—
531#95C2×D412yes—
532#95C2×D412yes—
533#95C2×D412yes—
534#95C2×D412yes—
535C24—21no—
536C24—21no—
537C24C22×D411yescharacteristic
538#41—28no—
539#41—44no—
540#41—44no—
541#41—44no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—42no—
551C2×Q8—81no—
552C2×Q8—81no—
553C2×Q8C22×Q812yes—
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4C22×Q812yes—
569C2×D4C22×Q812yes—
570C2×D4C2×#4112yes—
571C2×D4H(5,𝔽2)12yes—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—41no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—44no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—82no—
608C22×C4—81no—
609C22×C4—82no—
610C22×C4—82no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4—82no—
614C22×C4—82no—
615C22×C4—82no—
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4C22×D412yes—
619C22×C4C22×D412yes—
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×Q812yes—
626C22×C42−1+412yes—
627C22×C4C2511yescharacteristic
628SD16—44no—
629D8—28no—
630M16—84no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—21no—
641C2×C8—22no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—21no—
647C2×C8C22×Q812yes—
648C2×C8C22×Q812yes—
649C4⋊C4—22no—
650C4⋊C4—24no—
651C4⋊C4—22no—
652C4⋊C4—24no—
653C4⋊C4—22no—
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—21no—
664C4⋊C4—22no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—42no—
671C4⋊C4—44no—
672C4⋊C4—42no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—44no—
682C4⋊C4—82no—
683C4⋊C4—82no—
684C4⋊C4—82no—
685C4⋊C4—81no—
686C4⋊C4—81no—
687C4⋊C4—82no—
688C4⋊C4—82no—
689C4⋊C4—82no—
690C4⋊C4—82no—
691C4⋊C4—82no—
692C4⋊C4—81no—
693C4⋊C4—82no—
694C4⋊C4—82no—
695C4⋊C4—82no—
696C4⋊C4C22×Q812yes—
697C4⋊C4C2×#4112yes—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—44no—
705C22⋊C4—44no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—82no—
711C22⋊C4—82no—
712C22⋊C4—82no—
713C22⋊C4—82no—
714C42—22no—
715C42—22no—
716C42—21no—
717C42—22no—
718C42—22no—
719C42—22no—
720C42—21no—
721C42—22no—
722C42—42no—
723C42—42no—
724C42—42no—
725C42—42no—
726C42—82no—
727C42C2×#4112yes—
728C42H(5,𝔽2)12yes—
729C23—21no—
730C23—22no—
731C23—21no—
732C23—22no—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—22no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23D4×Q812yes—
750C23C23×D411yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—41no—
754Q8—41no—
755Q8—44no—
756Q8—162no—
757D4—22no—
758D4—22no—
759D4—22no—
760D4—22no—
761D4—22no—
762D4—48no—
763D4—48no—
764D4—41no—
765D4—41no—
766D4#55414yes—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—21no—
795C2×C4—44no—
796C2×C4—48no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—44no—
804C2×C4—48no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—84no—
827C2×C4—88no—
828C2×C4—84no—
829C2×C4—164no—
830C2×C4—164no—
831C2×C4—164no—
832C2×C4#54612yes—
833C2×C4#54612yes—
834C2×C4D4×Q812yes—
835C2×C4#57512yes—
836C2×C4#57712yes—
837C2×C4#57712yes—
838C2×C4C23×Q811yescharacteristic
839C2×C4C22×#4111yescharacteristic
840C2×C4C2×H(5,𝔽2)11yescharacteristic
841C2×C4C2×H(5,𝔽2)11yescharacteristic
842C2×C4C2×2−1+411yescharacteristic
843C2×C4#58511yescharacteristic
844C8—22no—
845C8—22no—
846C8—41no—
847C8—41no—
848C8—42no—
849C8—42no—
850C22—22no—
851C22—24no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—42no—
856C22—42no—
857C22—41no—
858C22—41no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—41no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22C2×#54611yescharacteristic
872C22C2×D4×Q811yescharacteristic
873C22#348811yescharacteristic
874C22C2×#57511yescharacteristic
875C22C2×#57711yescharacteristic
876C22C2×#57711yescharacteristic
877C22#358511yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—42no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—42no—
886C4—41no—
887C4—42no—
888C4—42no—
889C4—81no—
890C4—82no—
891C4—81no—
892C4—82no—
893C4—82no—
894C4—82no—
895C4—81no—
896C4#330714yes—
897C4C2×#55411yescharacteristic
898C4#349511yescharacteristic
899C4#350111yescharacteristic
900C4#353611yescharacteristic
901C2—42no—
902C2—44no—
903C2—82no—
904C2#5901611yescharacteristic
905C2C2×#330711yescharacteristic
906C2#6119211yescharacteristic
907C2#6136711yescharacteristic
908C2#6137411yescharacteristic
909C2#6199611yescharacteristic
910C2#6203311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#449C22
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. #59305C2semidirect
2. #36275C2semidirect
3. #31892C2semidirect
4. #31532C2semidirect
5. #28788C2semidirect
6. #28264C2semidirect
7. #27948C2semidirect
8. #27824C2semidirect
9. #27296C2semidirect
10. #26436C2semidirect
11. #26045C2semidirect
12. #25972C2semidirect
13. #25061C2semidirect
14. #24843C2semidirect
15. #24823C2semidirect
16. #24815C2semidirect
17. #24327C2semidirect
18. #22953C2semidirect
20. #22670C2semidirect
21. #22519C2semidirect
23. #20648C2semidirect
178. #449Q8semidirect

Maximal subgroups

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

subgroupindex
#593052
#362752
#318922
#315322
#287882
#282642
#279482
#278242
#272962
#264362
#260452
#259722
#250612
#248432
#248232
#248152
#243272
#229532
#228662
#226702
#225192
C4×#4492
#206482