Finite Group Databasebeta

← #7527903

Subgroups — #7527903

Order 512.

1610 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59230C211yesmaximal, characteristic, complemented
2#36456C211yesmaximal, characteristic, complemented
3#31895C212yesmaximal, complemented
4#31547C212yesmaximal, complemented
5#28779C212yesmaximal, complemented
6#28273C211yesmaximal, characteristic, complemented
7#27949C211yesmaximal, characteristic, complemented
8#27821C211yesmaximal, characteristic, complemented
9#27319C212yesmaximal, complemented
10#26409C212yesmaximal, complemented
11#26042C211yesmaximal, characteristic, complemented
12#25951C212yesmaximal, complemented
13#25057C211yesmaximal, characteristic, complemented
14#24836C211yesmaximal, characteristic, complemented
15#24828C212yesmaximal, complemented
16#24812C211yesmaximal, characteristic, complemented
17#24329C211yesmaximal, characteristic, complemented
18#22956C211yesmaximal, characteristic, complemented
19#22857C212yesmaximal
20#22671C211yesmaximal, characteristic, complemented
21#22525C211yesmaximal, characteristic, complemented
22C4×#449C211yesmaximal, characteristic
23#20645C211yesmaximal, characteristic, complemented
24C2×Q82C2211yescharacteristic
25C2×C4×#41C2211yescharacteristic
26C2×#475C2212yes—
27C2×#476C2211yescharacteristic
28C2×#449C2211yescharacteristic
29C2×#446C2211yescharacteristic
30C2×#440C2212yes—
31C2×C4×SD16C2211yescharacteristic
32C2×C4×D8C2211yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34C2×#416C2212yes—
35#2857—21no—
36#2857C2211yescharacteristic
37#2784—22no—
38#2574—22no—
39#2563—21no—
40#2563—21no—
41#2563C2212yes—
42#2563C2211yescharacteristic
43#2551C2211yescharacteristic
44#2538—21no—
45#2538C2211yescharacteristic
46#2538C2211yescharacteristic
47#2508C2212yes—
48#2492—21no—
49#2452—22no—
50#2452C2212yes—
51#2439—22no—
52#2439C2212yes—
53#2439C2212yes—
54#2417—21no—
55#2363C2212yes—
56#2355C2211yescharacteristic
57#2351C2212yes—
58Q8×C4⋊C4C2211yescharacteristic
59D4×C4⋊C4C2211yescharacteristic
60#2345—21no—
61#2341C2212yes—
62C4×C22⋊Q8—21no—
63C4×C22⋊Q8C2211yescharacteristic
64C4×#121C2211yescharacteristic
65#2285C2211yescharacteristic
66#2101C2212yes—
67#2092C2212yes—
68#2088C2212yes—
69#2088C2212yes—
70#2085C2212yes—
71#2085C2212yes—
72#2085C2212yes—
73#2085C2212yes—
74#2065C2212yes—
75#2065C2212yes—
76#2065C2212yes—
77#2065C2212yes—
78#2058C2212yes—
79#2058C2212yes—
80#2023C2212yes—
81#2023C2212yes—
82#1993C2212yes—
83#1993C2212yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1988C2212yes—
87#1987C2211yescharacteristic
88#1984C2211yescharacteristic
89#1972C2212yes—
90#1948C2211yescharacteristic
91#1944C2212yes—
92#1944C2212yes—
93#1940C2212yes—
94#1939C2211yescharacteristic
95#1936C2212yes—
96#1925C2212yes—
97#1921C2212yes—
98#1917C2212yes—
99#1893C2212yes—
100#1880C2212yes—
101#1880C2211yescharacteristic
102#1879C2211yescharacteristic
103#1879C2212yes—
104#1875C2211yescharacteristic
105#1865C2212yes—
106#1865C2212yes—
107#1864C2211yescharacteristic
108#1863C2212yes—
109#1863C2211yescharacteristic
110#1862C2212yes—
111#1854C2212yes—
112#1854C2212yes—
113#1854C2211yescharacteristic
114#1850C2212yes—
115#1845C2211yescharacteristic
116#1844C2211yescharacteristic
117#1807C2212yes—
118#1805C2212yes—
119#1805C2212yes—
120#1804C2212yes—
121#1804C2212yes—
122#1803C2211yescharacteristic
123#1803C2211yescharacteristic
124#1802C2211yescharacteristic
125#1802C2211yescharacteristic
126#1802C2211yescharacteristic
127#1788C2211yescharacteristic
128#1770C2211yescharacteristic
129#1763C2212yes—
130C4×#103C2211yescharacteristic
131C4×#102C2211yescharacteristic
132#1752C2212yes—
133C4×C22⋊C8C2211yescharacteristic
134#1735C2212yes—
135C22×#41C2311yescharacteristic
136C22×SD16C2311yescharacteristic
137C22×D8C2311yescharacteristic
138C23×C8C2312yes—
139Q82—24no—
140Q82—42no—
141C2×C4⋊Q8—21no—
142C2×C4⋊Q8—22no—
143C2×C4⋊Q8—21no—
144C2×C4⋊Q8C2311yescharacteristic
145C2×C4⋊Q8C2312yes—
146C2×C4⋊Q8C2312yes—
147C2×C22⋊Q8—21no—
148C2×C22⋊Q8—21no—
149C2×C22⋊Q8—21no—
150C2×C22⋊Q8—22no—
151C2×C22⋊Q8D411yescharacteristic
152C2×#121C2311yescharacteristic
153C4×#41—24no—
154C4×#41—42no—
155C2×C4×Q8—21no—
156C2×C4×Q8C2312yes—
157C2×C4×Q8C2311yescharacteristic
158C2×C4×Q8C2312yes—
159C2×C4×Q8C2311yescharacteristic
160C2×C4×Q8C2311yescharacteristic
161C2×C4×D4—21no—
162C2×C4×D4—21no—
163C2×C4×D4—21no—
164C2×C4×D4C2311yescharacteristic
165C2×C4×D4C2311yescharacteristic
166C2×C4×D4C2311yescharacteristic
167C2×C4×D4C2312yes—
168C2×#117—21no—
169C2×#117C2311yescharacteristic
170C2×#117C2312yes—
171C22×C4⋊C4—21no—
172C22×C42—21no—
173C22×C42C2311yescharacteristic
174#476—42no—
175#475—44no—
176#449Q818yescomplemented
177#446—42no—
178#440—44no—
179C4×SD16—24no—
180C4×D8—42no—
181C2×#107C2312yes—
182C2×#107C2311yescharacteristic
183C2×#107C2312yes—
184C2×#106C2311yescharacteristic
185C2×#106C2312yes—
186C2×#106C2312yes—
187C2×#106C2312yes—
188C2×#106C2312yes—
189C2×C4⋊C8—42no—
190C2×C4⋊C8C2311yescharacteristic
191C2×C4⋊C8C2311yescharacteristic
192C2×C4⋊C8C2312yes—
193C2×C4⋊C8C2312yes—
194C2×C4⋊C8C2312yes—
195#416—44no—
196C2×#103C2311yescharacteristic
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#103C2311yescharacteristic
200C2×#103C2311yescharacteristic
201C2×#102C2311yescharacteristic
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2312yes—
205C2×#102C2311yescharacteristic
206C2×#102C2312yes—
207C2×#102C2311yescharacteristic
208C2×#102C2311yescharacteristic
209C2×#102C2311yescharacteristic
210C2×C22⋊C8C2311yescharacteristic
211C2×C22⋊C8C2311yescharacteristic
212C2×#97C2312yes—
213C2×#97C2312yes—
214C2×C4×C8C2311yescharacteristic
215C2×C4×C8C2311yescharacteristic
216#400—22no—
217#398—22no—
218#396—22no—
219#396—22no—
220#396—22no—
221#396—22no—
222#396—22no—
223#395—22no—
224#393—22no—
225#393—22no—
226#393—22no—
227#393—22no—
228#393—22no—
229#393—22no—
230#391—21no—
231#391—21no—
232#391—22no—
233#391—22no—
234#391D411yescharacteristic
235#390—22no—
236#390—22no—
237#390—22no—
238#390C2311yescharacteristic
239#390C2312yes—
240#390C2312yes—
241#390C2312yes—
242#389—21no—
243#389—22no—
244#389—22no—
245#389—21no—
246#389—22no—
247#389D411yescharacteristic
248#389C2312yes—
249#389C2312yes—
250#389C2312yes—
251#389C2312yes—
252#389C2312yes—
253#389C2311yescharacteristic
254#389C2312yes—
255#388—21no—
256#388—22no—
257#387—22no—
258#387—22no—
259#387—22no—
260#387—22no—
261#387D412yes—
262#386—21no—
263#386—22no—
264#385—22no—
265#385—22no—
266#385D412yes—
267#384—21no—
268#384C2311yescharacteristic
269#384C2311yescharacteristic
270#384C2311yescharacteristic
271#382—22no—
272#382—22no—
273#382C2312yes—
274#382C2312yes—
275#382C2312yes—
276#380—21no—
277#380—21no—
278#380—21no—
279#380—21no—
280#380—21no—
281#380—21no—
282#380—21no—
283#380—22no—
284#380—22no—
285#380—21no—
286#380—22no—
287#380D411yescharacteristic
288#380C2311yescharacteristic
289#380C2312yes—
290C4×C4⋊C4—21no—
291C4×C4⋊C4—21no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4—22no—
295C4×C4⋊C4C2312yes—
296C4×C4⋊C4C2311yescharacteristic
297C4×C4⋊C4C2311yescharacteristic
298C4×C4⋊C4C2312yes—
299C4×C22⋊C4—21no—
300C4×C22⋊C4—22no—
301C4×C22⋊C4—22no—
302C4×C22⋊C4C2312yes—
303#340C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2312yes—
307#340C2311yescharacteristic
308#340C2312yes—
309#340C2312yes—
310#340C2312yes—
311#340C2312yes—
312#340C2312yes—
313#340C2311yescharacteristic
314#340C2312yes—
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—22no—
332C22×Q8—21no—
333C22×Q8—22no—
334C22×Q8C2×D411yescharacteristic
335C22×Q8C2411yescharacteristic
336C22×D4—21no—
337C22×D4—21no—
338C22×D4C2411yescharacteristic
339C22×D4C2411yescharacteristic
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4—21no—
344C23×C4—22no—
345C23×C4C2×D411yescharacteristic
346C23×C4C2×D411yescharacteristic
347C23×C4C2411yescharacteristic
348C2×SD16—22no—
349C2×SD16—22no—
350C2×SD16C2×Q814yes—
351C2×D8—41no—
352C2×D8—41no—
353C2×D8C2×Q814yes—
354C22×C8—24no—
355C22×C8—42no—
356C22×C8—42no—
357C22×C8C2412yes—
358C22×C8C2412yes—
359C22×C8C2411yescharacteristic
360C22×C8C2411yescharacteristic
361C22×C8C2411yescharacteristic
362C22×C8C2411yescharacteristic
363C4⋊Q8—24no—
364C4⋊Q8—22no—
365C4⋊Q8—22no—
366C4⋊Q8—42no—
367C4⋊Q8—42no—
368C4⋊Q8—42no—
369C4⋊Q8—44no—
370C4⋊Q8—48no—
371C4⋊Q8—82no—
372C22⋊Q8—42no—
373C22⋊Q8—44no—
374C22⋊Q8—84no—
375C22⋊Q8—82no—
376C22⋊Q8—82no—
377#121—22no—
378#121C2×Q814yes—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8—22no—
383C4×Q8—24no—
384C4×Q8—24no—
385C4×Q8—42no—
386C4×Q8—41no—
387C4×Q8—42no—
388C4×Q8—44no—
389C4×Q8#4114yes—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—41no—
396C4×D4—44no—
397C4×D4—42no—
398C4×D4—42no—
399C4×D4—44no—
400C4×D4—82no—
401#117—22no—
402#117—44no—
403#117—41no—
404#117—42no—
405#117—42no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
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—44no—
427C2×C4⋊C4C2×D411yescharacteristic
428C2×C4⋊C4C2×D411yescharacteristic
429C2×C4⋊C4C2×D412yes—
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D412yes—
432C2×C4⋊C4C2×D412yes—
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2412yes—
435C2×C4⋊C4C2412yes—
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2412yes—
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2411yescharacteristic
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—21no—
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—21no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4C2×D412yes—
460C2×C22⋊C4C2×D412yes—
461C2×C42—21no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—44no—
472C2×C42C2×D411yescharacteristic
473C2×C42C2×D411yescharacteristic
474C2×C42C2412yes—
475C2×C42C2411yescharacteristic
476C2×C42C2412yes—
477C2×C42C2411yescharacteristic
478#107—42no—
479#107—41no—
480#107—42no—
481#106—22no—
482#106—42no—
483#106—42no—
484#106—42no—
485#106—42no—
486C4⋊C8—22no—
487C4⋊C8—22no—
488C4⋊C8—42no—
489C4⋊C8—42no—
490C4⋊C8—42no—
491#103—22no—
492#103—24no—
493#103—24no—
494#103—22no—
495#103C2×Q814yes—
496#102—22no—
497#102—41no—
498#102—42no—
499#102—42no—
500#102—41no—
501#102—41no—
502#102—42no—
503#102—42no—
504#102C2×Q814yes—
505C22⋊C8—22no—
506C22⋊C8C2×Q814yes—
507#97—42no—
508#97—42no—
509C4×C8—22no—
510C4×C8—22no—
511#95—22no—
512#95—21no—
513#95—21no—
514#95—22no—
515#95—22no—
516#95—22no—
517#95—22no—
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#95C2×D412yes—
529#95C2×D412yes—
530#95C2×D412yes—
531#95C2×D412yes—
532#95C2×D412yes—
533C24—21no—
534C24—21no—
535C24C22×D411yescharacteristic
536#41—28no—
537#41—44no—
538#41—44no—
539#41—44no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—44no—
547C2×Q8—42no—
548C2×Q8—81no—
549C2×Q8—82no—
550C2×Q8—82no—
551C2×Q8—82no—
552C2×Q8—81no—
553C2×Q8—82no—
554C2×Q8—82no—
555C2×Q8C22×Q812yes—
556C2×Q8C2×#4112yes—
557C2×Q8H(5,𝔽2)12yes—
558C2×D4—24no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4C22×Q812yes—
575C2×D4C22×Q812yes—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—44no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—81no—
609C22×C4—82no—
610C22×C4—82no—
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D412yes—
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×Q812yes—
621C22×C42−1+412yes—
622C22×C4C2511yescharacteristic
623SD16—28no—
624D8—44no—
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—22no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—21no—
641C2×C8—84no—
642C2×C8C22×Q812yes—
643C2×C8C22×Q812yes—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—22no—
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—22no—
656C4⋊C4—21no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—42no—
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—81no—
679C4⋊C4—81no—
680C4⋊C4—81no—
681C4⋊C4—81no—
682C4⋊C4—82no—
683C4⋊C4—82no—
684C4⋊C4—82no—
685C4⋊C4—82no—
686C4⋊C4C22×Q812yes—
687C4⋊C4C2×#4112yes—
688C22⋊C4—24no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—44no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—82no—
697C22⋊C4—82no—
698C22⋊C4—81no—
699C22⋊C4—82no—
700C22⋊C4—81no—
701C22⋊C4—82no—
702C22⋊C4—82no—
703C22⋊C4—82no—
704C22⋊C4—82no—
705C22⋊C4—81no—
706C22⋊C4—82no—
707C42—22no—
708C42—22no—
709C42—24no—
710C42—21no—
711C42—22no—
712C42—22no—
713C42—22no—
714C42—21no—
715C42—22no—
716C42—42no—
717C42—42no—
718C42—44no—
719C42—44no—
720C42—42no—
721C42—82no—
722C42—82no—
723C42C2×#4112yes—
724C42H(5,𝔽2)12yes—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—22no—
732C23—22no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23D4×Q812yes—
746C23C23×D411yescharacteristic
747Q8—22no—
748Q8—22no—
749Q8—22no—
750Q8—44no—
751Q8—162no—
752Q8—164no—
753Q8—164no—
754Q8#55414yes—
755D4—22no—
756D4—22no—
757D4—22no—
758D4—22no—
759D4—48no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—41no—
764D4—84no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—48no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—82no—
824C2×C4—84no—
825C2×C4—84no—
826C2×C4—84no—
827C2×C4—164no—
828C2×C4#54612yes—
829C2×C4#54612yes—
830C2×C4D4×Q812yes—
831C2×C4#57512yes—
832C2×C4#57712yes—
833C2×C4C23×Q811yescharacteristic
834C2×C4C22×#4111yescharacteristic
835C2×C4C2×H(5,𝔽2)11yescharacteristic
836C2×C4C2×H(5,𝔽2)11yescharacteristic
837C2×C4C2×2−1+411yescharacteristic
838C2×C4#58511yescharacteristic
839C8—22no—
840C8—22no—
841C8—41no—
842C8—41no—
843C8—42no—
844C8—42no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22C2×#54611yescharacteristic
867C22C2×D4×Q811yescharacteristic
868C22#348811yescharacteristic
869C22C2×#57511yescharacteristic
870C22C2×#57711yescharacteristic
871C22#358411yescharacteristic
872C22#358511yescharacteristic
873C4—22no—
874C4—22no—
875C4—24no—
876C4—41no—
877C4—42no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—41no—
883C4—42no—
884C4—82no—
885C4—82no—
886C4—82no—
887C4—82no—
888C4—81no—
889C4—81no—
890C4—81no—
891C4#332114yes—
892C4C2×#55411yescharacteristic
893C4#349511yescharacteristic
894C4#350111yescharacteristic
895C4#353611yescharacteristic
896C2—42no—
897C2—82no—
898C2—82no—
899C2#5901611yescharacteristic
900C2C2×#332111yescharacteristic
901C2#6119511yescharacteristic
902C2#6136511yescharacteristic
903C2#6138211yescharacteristic
904C2#6197511yescharacteristic
905C2#6207111yescharacteristic
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. #59230C2semidirect
2. #36456C2semidirect
3. #31895C2semidirect
4. #31547C2semidirect
5. #28779C2semidirect
6. #28273C2semidirect
7. #27949C2semidirect
8. #27821C2semidirect
9. #27319C2semidirect
10. #26409C2semidirect
11. #26042C2semidirect
12. #25951C2semidirect
13. #25057C2semidirect
14. #24836C2semidirect
15. #24828C2semidirect
16. #24812C2semidirect
17. #24329C2semidirect
18. #22956C2semidirect
20. #22671C2semidirect
21. #22525C2semidirect
23. #20645C2semidirect
176. #449Q8semidirect

Maximal subgroups

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

subgroupindex
#592302
#364562
#318952
#315472
#287792
#282732
#279492
#278212
#273192
#264092
#260422
#259512
#250572
#248362
#248282
#248122
#243292
#229562
#228572
#226712
#225252
C4×#4492
#206452