Finite Group Databasebeta

← #7527904

Subgroups — #7527904

Order 512.

1604 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59214C211yesmaximal, characteristic, complemented
2#36445C211yesmaximal, characteristic, complemented
3#31883C212yesmaximal, complemented
4#31535C212yesmaximal, complemented
5#28778C212yesmaximal, complemented
6#28273C211yesmaximal, characteristic, complemented
7#27949C211yesmaximal, characteristic, complemented
8#27822C211yesmaximal, characteristic, complemented
9#27316C212yesmaximal, complemented
10#26421C212yesmaximal, complemented
11#26043C211yesmaximal, characteristic, complemented
12#25961C212yesmaximal, complemented
13#25056C211yesmaximal, characteristic, complemented
14#24835C211yesmaximal, characteristic, complemented
15#24824C212yesmaximal, complemented
16#24811C211yesmaximal, characteristic, complemented
17#24328C211yesmaximal, characteristic, complemented
18#22956C211yesmaximal, characteristic, complemented
19#22857C212yesmaximal
20#22671C211yesmaximal, characteristic, complemented
21#22524C211yesmaximal, characteristic, complemented
22C4×#449C211yesmaximal, characteristic
23#20645C211yesmaximal, characteristic, complemented
24C2×#557C2211yescharacteristic
25C2×C4×#41C2211yescharacteristic
26C2×#479C2212yes—
27C2×#474C2211yescharacteristic
28C2×#449C2211yescharacteristic
29C2×#446C2211yescharacteristic
30C2×#440C2212yes—
31C2×C4×SD16C2211yescharacteristic
32C2×C4×D8C2211yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34C2×#416C2212yes—
35#2857—21no—
36#2857C2211yescharacteristic
37#2780—22no—
38#2587—22no—
39#2566C2212yes—
40#2552C2211yescharacteristic
41#2542—21no—
42#2542C2211yescharacteristic
43#2538—21no—
44#2538—21no—
45#2538C2211yescharacteristic
46#2538C2211yescharacteristic
47#2509C2212yes—
48#2497—21no—
49#2487—21no—
50#2454—22no—
51#2454C2212yes—
52#2441—22no—
53#2441C2212yes—
54#2441C2212yes—
55#2363C2212yes—
56#2360—21no—
57Q8×C4⋊C4C2211yescharacteristic
58Q8×C4⋊C4C2211yescharacteristic
59Q8×C4⋊C4C2212yes—
60D4×C4⋊C4C2211yescharacteristic
61#2341C2212yes—
62C4×C22⋊Q8—21no—
63C4×C22⋊Q8C2211yescharacteristic
64C4×#121C2211yescharacteristic
65#2285C2211yescharacteristic
66#2100C2212yes—
67#2093C2212yes—
68#2088C2212yes—
69#2086C2212yes—
70#2085C2212yes—
71#2085C2212yes—
72#2083C2212yes—
73#2083C2212yes—
74#2067C2212yes—
75#2067C2212yes—
76#2065C2212yes—
77#2065C2212yes—
78#2059C2212yes—
79#2059C2212yes—
80#2025C2212yes—
81#2025C2212yes—
82#1992C2212yes—
83#1992C2212yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1989C2212yes—
87#1988C2211yescharacteristic
88#1984C2211yescharacteristic
89#1972C2212yes—
90#1947C2211yescharacteristic
91#1944C2212yes—
92#1944C2212yes—
93#1940C2212yes—
94#1939C2211yescharacteristic
95#1936C2212yes—
96#1925C2212yes—
97#1918C2212yes—
98#1917C2212yes—
99#1893C2212yes—
100#1880C2212yes—
101#1880C2211yescharacteristic
102#1879C2211yescharacteristic
103#1879C2212yes—
104#1875C2211yescharacteristic
105#1865C2212yes—
106#1864C2211yescharacteristic
107#1863C2212yes—
108#1863C2212yes—
109#1863C2211yescharacteristic
110#1862C2212yes—
111#1854C2212yes—
112#1854C2212yes—
113#1854C2211yescharacteristic
114#1850C2212yes—
115#1845C2211yescharacteristic
116#1844C2211yescharacteristic
117#1808C2212yes—
118#1805C2212yes—
119#1804C2212yes—
120#1803C2211yescharacteristic
121#1803C2212yes—
122#1803C2211yescharacteristic
123#1802C2211yescharacteristic
124#1802C2212yes—
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—
139#557—24no—
140#557—42no—
141C2×C4⋊Q8—21no—
142C2×C4⋊Q8C2311yescharacteristic
143C2×#125—22no—
144C2×#125C2312yes—
145C2×#125C2312yes—
146C2×C22⋊Q8—21no—
147C2×C22⋊Q8—21no—
148C2×C22⋊Q8—21no—
149C2×C22⋊Q8—21no—
150C2×C22⋊Q8—21no—
151C2×C22⋊Q8D411yescharacteristic
152C2×#121C2311yescharacteristic
153C4×#41—24no—
154C4×#41—42no—
155C2×C4×Q8—21no—
156C2×C4×Q8—21no—
157C2×C4×Q8C2312yes—
158C2×C4×Q8C2312yes—
159C2×C4×Q8C2311yescharacteristic
160C2×C4×Q8C2311yescharacteristic
161C2×C4×Q8C2311yescharacteristic
162C2×C4×D4—21no—
163C2×C4×D4—21no—
164C2×C4×D4—21no—
165C2×C4×D4C2311yescharacteristic
166C2×C4×D4C2311yescharacteristic
167C2×C4×D4C2311yescharacteristic
168C2×C4×D4C2312yes—
169C2×#117—21no—
170C2×#117C2311yescharacteristic
171C2×#117C2312yes—
172C22×C4⋊C4—21no—
173C22×C42—21no—
174C22×C42C2311yescharacteristic
175#479—44no—
176#474—42no—
177#449Q818yescomplemented
178#446—42no—
179#440—44no—
180C4×SD16—24no—
181C4×D8—42no—
182C2×#107C2312yes—
183C2×#107C2312yes—
184C2×#107C2311yescharacteristic
185C2×#107C2312yes—
186C2×#107C2312yes—
187C2×#106C2311yescharacteristic
188C2×#106C2312yes—
189C2×#106C2312yes—
190C2×C4⋊C8—42no—
191C2×C4⋊C8C2311yescharacteristic
192C2×C4⋊C8C2311yescharacteristic
193C2×C4⋊C8C2312yes—
194C2×C4⋊C8C2312yes—
195C2×C4⋊C8C2312yes—
196#416—44no—
197C2×#103C2311yescharacteristic
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2311yescharacteristic
201C2×#103C2311yescharacteristic
202C2×#102C2311yescharacteristic
203C2×#102C2311yescharacteristic
204C2×#102C2312yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2311yescharacteristic
209C2×#102C2311yescharacteristic
210C2×#102C2311yescharacteristic
211C2×C22⋊C8C2311yescharacteristic
212C2×C22⋊C8C2311yescharacteristic
213C2×#97C2312yes—
214C2×#97C2312yes—
215C2×C4×C8C2311yescharacteristic
216C2×C4×C8C2311yescharacteristic
217#400—22no—
218#400—22no—
219#399—22no—
220#399—22no—
221#399—22no—
222#399—22no—
223#398—22no—
224#396—22no—
225#396—22no—
226#396—22no—
227#396—22no—
228#396—22no—
229#396—22no—
230#396—22no—
231#391—21no—
232#391D411yescharacteristic
233#390—22no—
234#390—22no—
235#390—22no—
236#390C2311yescharacteristic
237#390C2312yes—
238#390C2312yes—
239#390C2312yes—
240#389—22no—
241#389—22no—
242#389—21no—
243#389—21no—
244#389—21no—
245#389—22no—
246#389—22no—
247#389—22no—
248#389—22no—
249#389—22no—
250#389D411yescharacteristic
251#389C2312yes—
252#389C2312yes—
253#389C2312yes—
254#389C2312yes—
255#389C2312yes—
256#389C2311yescharacteristic
257#389C2312yes—
258#388—21no—
259#388—22no—
260#387—22no—
261#387—22no—
262#387—22no—
263#387D412yes—
264#386—21no—
265#386—22no—
266#385—22no—
267#385—22no—
268#385—22no—
269#385—22no—
270#385D412yes—
271#384—21no—
272#384—22no—
273#384—21no—
274#384C2312yes—
275#384C2311yescharacteristic
276#384C2311yescharacteristic
277#384C2312yes—
278#384C2311yescharacteristic
279#382C2312yes—
280#380—21no—
281#380—21no—
282#380—21no—
283#380—21no—
284#380—21no—
285#380—21no—
286#380—22no—
287#380—22no—
288#380D411yescharacteristic
289#380C2311yescharacteristic
290#380C2312yes—
291C4×C4⋊C4—22no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4—21no—
295C4×C4⋊C4C2312yes—
296C4×C4⋊C4C2311yescharacteristic
297C4×C4⋊C4C2312yes—
298C4×C4⋊C4C2311yescharacteristic
299C4×C22⋊C4—21no—
300C4×C22⋊C4—22no—
301C4×C22⋊C4—22no—
302C4×C22⋊C4C2312yes—
303#340C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2312yes—
307#340C2312yes—
308#340C2312yes—
309#340C2312yes—
310#340C2311yescharacteristic
311#340C2312yes—
312#340C2311yescharacteristic
313#340C2312yes—
314#340C2312yes—
315#340C2312yes—
316#340C2312yes—
317#340C2311yescharacteristic
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—21no—
341C23×C4—21no—
342C23×C4—22no—
343C23×C4C2×D411yescharacteristic
344C23×C4C2×D411yescharacteristic
345C23×C4C2411yescharacteristic
346C2×SD16—22no—
347C2×SD16—22no—
348C2×SD16C2×Q814yes—
349C2×D8—41no—
350C2×D8—41no—
351C2×D8C2×Q814yes—
352C22×C8—24no—
353C22×C8—42no—
354C22×C8—42no—
355C22×C8C2412yes—
356C22×C8C2412yes—
357C22×C8C2411yescharacteristic
358C22×C8C2411yescharacteristic
359C22×C8C2411yescharacteristic
360C22×C8C2411yescharacteristic
361C4⋊Q8—22no—
362C4⋊Q8—22no—
363C4⋊Q8—44no—
364#125—24no—
365#125—42no—
366#125—42no—
367#125—42no—
368#125—48no—
369C22⋊Q8—42no—
370C22⋊Q8—44no—
371C22⋊Q8—44no—
372C22⋊Q8—82no—
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—24no—
382C4×Q8—24no—
383C4×Q8—42no—
384C4×Q8—41no—
385C4×Q8—42no—
386C4×Q8—44no—
387C4×Q8—82no—
388C4×Q8#4114yes—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—41no—
395C4×D4—44no—
396C4×D4—42no—
397C4×D4—42no—
398C4×D4—44no—
399C4×D4—82no—
400#117—22no—
401#117—44no—
402#117—41no—
403#117—42no—
404#117—42no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
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—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—82no—
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2×D411yescharacteristic
434C2×C4⋊C4C2×D412yes—
435C2×C4⋊C4C2×D411yescharacteristic
436C2×C4⋊C4C2×D412yes—
437C2×C4⋊C4C2×D412yes—
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2412yes—
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2412yes—
443C2×C4⋊C4C2412yes—
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2411yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4C2×D412yes—
465C2×C22⋊C4C2×D412yes—
466C2×C42—21no—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—22no—
473C2×C42—22no—
474C2×C42—22no—
475C2×C42—22no—
476C2×C42—44no—
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42C2412yes—
480C2×C42C2411yescharacteristic
481C2×C42C2412yes—
482C2×C42C2411yescharacteristic
483#107—42no—
484#107—41no—
485#107—42no—
486#107—42no—
487#107—42no—
488#106—22no—
489#106—42no—
490#106—42no—
491C4⋊C8—22no—
492C4⋊C8—22no—
493C4⋊C8—42no—
494C4⋊C8—42no—
495C4⋊C8—42no—
496#103—22no—
497#103—24no—
498#103—24no—
499#103—22no—
500#103C2×Q814yes—
501#102—22no—
502#102—41no—
503#102—42no—
504#102—42no—
505#102—41no—
506#102—41no—
507#102—42no—
508#102—42no—
509#102C2×Q814yes—
510C22⋊C8—22no—
511C22⋊C8C2×Q814yes—
512#97—42no—
513#97—42no—
514C4×C8—22no—
515C4×C8—22no—
516#95—22no—
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—21no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95C2×D412yes—
530#95C2×D412yes—
531#95C2×D412yes—
532#95C2×D412yes—
533#95C2×D412yes—
534C24—21no—
535C24—21no—
536C24C22×D411yescharacteristic
537#41—28no—
538#41—44no—
539#41—44no—
540#41—44no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—42no—
548C2×Q8—42no—
549C2×Q8—42no—
550C2×Q8C22×Q812yes—
551C2×Q8C2×#4112yes—
552C2×Q8H(5,𝔽2)12yes—
553C2×D4—24no—
554C2×D4—24no—
555C2×D4—21no—
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—21no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4C22×Q812yes—
570C2×D4C22×Q812yes—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—81no—
603C22×C4—82no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D412yes—
608C22×C4C22×D412yes—
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×Q812yes—
616C22×C42−1+412yes—
617C22×C4C2511yescharacteristic
618SD16—28no—
619D8—44no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—21no—
636C2×C8—84no—
637C2×C8C22×Q812yes—
638C2×C8C22×Q812yes—
639C4⋊C4—24no—
640C4⋊C4—22no—
641C4⋊C4—24no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—44no—
667C4⋊C4—44no—
668C4⋊C4—44no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—81no—
674C4⋊C4—81no—
675C4⋊C4—81no—
676C4⋊C4—82no—
677C4⋊C4—82no—
678C4⋊C4—82no—
679C4⋊C4—82no—
680C4⋊C4—81no—
681C4⋊C4—82no—
682C4⋊C4—82no—
683C4⋊C4—82no—
684C4⋊C4—82no—
685C4⋊C4—82no—
686C4⋊C4—82no—
687C4⋊C4C22×Q812yes—
688C4⋊C4C2×#4112yes—
689C22⋊C4—24no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—44no—
695C22⋊C4—44no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—82no—
699C22⋊C4—81no—
700C22⋊C4—82no—
701C22⋊C4—82no—
702C22⋊C4—81no—
703C22⋊C4—82no—
704C22⋊C4—82no—
705C22⋊C4—82no—
706C22⋊C4—81no—
707C22⋊C4—82no—
708C42—22no—
709C42—22no—
710C42—24no—
711C42—21no—
712C42—22no—
713C42—22no—
714C42—22no—
715C42—21no—
716C42—22no—
717C42—42no—
718C42—42no—
719C42—44no—
720C42—44no—
721C42—42no—
722C42—82no—
723C42—82no—
724C42C2×#4112yes—
725C42H(5,𝔽2)12yes—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—22no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23D4×Q812yes—
747C23C23×D411yescharacteristic
748Q8—22no—
749Q8—22no—
750Q8—22no—
751Q8—44no—
752Q8—84no—
753Q8#55414yes—
754D4—22no—
755D4—22no—
756D4—22no—
757D4—22no—
758D4—48no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—84no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—21no—
795C2×C4—48no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—82no—
823C2×C4—84no—
824C2×C4—84no—
825C2×C4—84no—
826C2×C4—164no—
827C2×C4#54612yes—
828C2×C4#54612yes—
829C2×C4D4×Q812yes—
830C2×C4#57512yes—
831C2×C4#57612yes—
832C2×C4C23×Q811yescharacteristic
833C2×C4C22×#4111yescharacteristic
834C2×C4C2×H(5,𝔽2)11yescharacteristic
835C2×C4C2×H(5,𝔽2)11yescharacteristic
836C2×C4C2×2−1+411yescharacteristic
837C2×C4#58511yescharacteristic
838C8—22no—
839C8—22no—
840C8—41no—
841C8—41no—
842C8—42no—
843C8—42no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22C2×#54611yescharacteristic
866C22C2×D4×Q811yescharacteristic
867C22#348811yescharacteristic
868C22C2×#57511yescharacteristic
869C22C2×#57611yescharacteristic
870C22#358411yescharacteristic
871C22#358611yescharacteristic
872C4—22no—
873C4—22no—
874C4—24no—
875C4—42no—
876C4—41no—
877C4—42no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—41no—
882C4—42no—
883C4—82no—
884C4—82no—
885C4—81no—
886C4—82no—
887C4—81no—
888C4—81no—
889C4—82no—
890C4#330914yes—
891C4C2×#55411yescharacteristic
892C4#349511yescharacteristic
893C4#350111yescharacteristic
894C4#353611yescharacteristic
895C2—42no—
896C2—82no—
897C2—82no—
898C2#5901611yescharacteristic
899C2C2×#330911yescharacteristic
900C2#6119811yescharacteristic
901C2#6136511yescharacteristic
902C2#6138111yescharacteristic
903C2#6197611yescharacteristic
904C2#6207411yescharacteristic
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. #59214C2semidirect
2. #36445C2semidirect
3. #31883C2semidirect
4. #31535C2semidirect
5. #28778C2semidirect
6. #28273C2semidirect
7. #27949C2semidirect
8. #27822C2semidirect
9. #27316C2semidirect
10. #26421C2semidirect
11. #26043C2semidirect
12. #25961C2semidirect
13. #25056C2semidirect
14. #24835C2semidirect
15. #24824C2semidirect
16. #24811C2semidirect
17. #24328C2semidirect
18. #22956C2semidirect
20. #22671C2semidirect
21. #22524C2semidirect
23. #20645C2semidirect
177. #449Q8semidirect

Maximal subgroups

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

subgroupindex
#592142
#364452
#318832
#315352
#287782
#282732
#279492
#278222
#273162
#264212
#260432
#259612
#250562
#248352
#248242
#248112
#243282
#229562
#228572
#226712
#225242
C4×#4492
#206452