Finite Group Databasebeta

← #6606402

Subgroups — #6606402

Order 512.

1829 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3338C211yesmaximal, characteristic, complemented
2C2×#2966C211yesmaximal, characteristic
3#38040C212yesmaximal
4#33215C211yesmaximal, characteristic, complemented
5#33139C211yesmaximal, characteristic, complemented
6#33130C211yesmaximal, characteristic, complemented
7#28675C211yesmaximal, characteristic, complemented
8#28268C211yesmaximal, characteristic, complemented
9#27662C211yesmaximal, characteristic, complemented
10#27661C211yesmaximal, characteristic, complemented
11#25483C212yesmaximal, complemented
12#25256C212yesmaximal, complemented
13#25248C212yesmaximal, complemented
14#24781C211yesmaximal, characteristic, complemented
15#24779C211yesmaximal, characteristic, complemented
16#24714C212yesmaximal, complemented
17#24614C212yesmaximal, complemented
18#24606C212yesmaximal, complemented
19#22656C211yesmaximal, characteristic, complemented
20#22497C212yesmaximal, complemented
21#21525C211yesmaximal, characteristic, complemented
22#21156C211yesmaximal, characteristic, complemented
23C2×#1942C211yesmaximal, characteristic, complemented
24C2×#554C2212yes—
25C2×#529C2211yescharacteristic
26#3338—28no—
27C2×#500C2211yescharacteristic
28C2×#484C2212yes—
29C2×#484C2212yes—
30C2×#477C2212yes—
31C2×#467C2211yescharacteristic
32C2×#467C2211yescharacteristic
33C2×#467C2211yescharacteristic
34#2966—28no—
35C2×#446C2211yescharacteristic
36C2×C8×Q8C2211yescharacteristic
37C2×C4×Q16C2211yescharacteristic
38C2×#436C2211yescharacteristic
39C2×#435C2211yescharacteristic
40C2×#435C2211yescharacteristic
41C2×C8×D4C2211yescharacteristic
42C2×C8×D4C2211yescharacteristic
43C2×C8×D4C2211yescharacteristic
44C2×#433C2211yescharacteristic
45C2×#433C2211yescharacteristic
46C2×#432C2211yescharacteristic
47C2×#427C2211yescharacteristic
48C22×#107C2211yescharacteristic
49C22×#107C2211yescharacteristic
50C22×#107C2211yescharacteristic
51C2×#405C2211yescharacteristic
52C2×#405C2211yescharacteristic
53C22×C4×C8C2211yescharacteristic
54#2855C2212yes—
55#2721—22no—
56#2719—22no—
57#2689—22no—
58#2674—22no—
59#2628C2212yes—
60#2625C2212yes—
61#2581C2212yes—
62#2546C2212yes—
63#2488—22no—
64#2487C2212yes—
65#2486C2212yes—
66#2443—22no—
67#2440—22no—
68#2419—22no—
69#2417C2212yes—
70#2415C2212yes—
71#2352C2212yes—
72#2323C2212yes—
73#2317C2212yes—
74C2×#389C2212yes—
75#2087C2212yes—
76#2086C2212yes—
77#2086C2212yes—
78#2086C2212yes—
79#2076C2212yes—
80#2075C2212yes—
81#2068C2212yes—
82#2066C2212yes—
83#2066C2212yes—
84#2066C2212yes—
85#2036C2212yes—
86#2035C2212yes—
87#1993C2212yes—
88#1988C2212yes—
89#1969C2211yescharacteristic
90#1969C2211yescharacteristic
91#1969C2211yescharacteristic
92#1949C2212yes—
93#1944C2212yes—
94#1944C2212yes—
95#1944C2212yes—
96#1942C2211yescharacteristic
97#1942C2211yescharacteristic
98#1942C2211yescharacteristic
99#1942C2211yescharacteristic
100#1942C2211yescharacteristic
101#1942C2211yescharacteristic
102#1942C2211yescharacteristic
103#1942C2212yes—
104#1942C2211yescharacteristic
105#1942C2211yescharacteristic
106#1942C2212yes—
107#1935C2212yes—
108#1935C2212yes—
109#1935C2212yes—
110#1933C2212yes—
111#1933C2212yes—
112#1894C2212yes—
113#1894C2212yes—
114#1892C2212yes—
115#1873C2212yes—
116#1872C2212yes—
117#1854C2212yes—
118#1853C2212yes—
119#1846C2211yescharacteristic
120#1824C2212yes—
121#1823C2212yes—
122#1809C2212yes—
123#1808C2211yescharacteristic
124#1808C2211yescharacteristic
125#1808C2211yescharacteristic
126#1808C2211yescharacteristic
127#1808C2211yescharacteristic
128#1805C2212yes—
129C4×#107C2211yescharacteristic
130#1763C2212yes—
131#1736C2212yes—
132C2×#340C2212yes—
133C22×Q16C2311yescharacteristic
134C22×M16C2311yescharacteristic
135C22×M16C2311yescharacteristic
136C23×C8C2311yescharacteristic
137C23×C8C2311yescharacteristic
138C23×C8C2311yescharacteristic
139C23×C8C2311yescharacteristic
140#554—28no—
141#554—28no—
142C2×C4⋊Q8—22no—
143C2×C4⋊Q8C2312yes—
144#529—24no—
145#529—24no—
146C2×#126D411yescharacteristic
147C2×#126D411yescharacteristic
148C2×#125—22no—
149C2×#125D411yescharacteristic
150C2×#124D411yescharacteristic
151C2×#123—22no—
152C2×#123D411yescharacteristic
153C2×#123D411yescharacteristic
154C2×C22⋊Q8—22no—
155C2×C22⋊Q8—22no—
156C2×C22⋊Q8D411yescharacteristic
157C2×C22⋊Q8C2312yes—
158C2×C22⋊Q8C2312yes—
159C2×C22⋊Q8C2312yes—
160C2×#121D411yescharacteristic
161C2×C4×Q8C2312yes—
162C2×C4×Q8C2311yescharacteristic
163C2×C4×D4—22no—
164C2×C4×D4C2311yescharacteristic
165C2×C4×D4C2311yescharacteristic
166C2×C4×D4C2311yescharacteristic
167C2×#117C2312yes—
168C2×#117C2311yescharacteristic
169C2×#117C2311yescharacteristic
170C22×C4⋊C4—22no—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C42C2311yescharacteristic
175#500—24no—
176#484—28no—
177#484—28no—
178#477—28no—
179#467—24no—
180#467—24no—
181#467—24no—
182#446—24no—
183C8×Q8—24no—
184C4×Q16—24no—
185#436—24no—
186#435—24no—
187#435—24no—
188C8×D4—24no—
189C8×D4—24no—
190C8×D4D418yes—
191#433—24no—
192#433—24no—
193#432—24no—
194#427—24no—
195C2×#107—24no—
196C2×#107—24no—
197C2×#107—24no—
198C2×#107C2312yes—
199C2×#107C2312yes—
200C2×#107C2311yescharacteristic
201C2×#107C2311yescharacteristic
202C2×#107C2311yescharacteristic
203C2×#107C2311yescharacteristic
204C2×#107C2311yescharacteristic
205C2×#107C2311yescharacteristic
206C2×#107C2312yes—
207C2×#107C2312yes—
208C2×#107C2311yescharacteristic
209C2×#106C2312yes—
210C2×#106C2312yes—
211C2×C4⋊C8C2311yescharacteristic
212C2×C4⋊C8C2311yescharacteristic
213C2×C4⋊C8C2311yescharacteristic
214C2×C4⋊C8C2311yescharacteristic
215C2×C4⋊C8C2311yescharacteristic
216C2×C4⋊C8C2311yescharacteristic
217C2×#103C2312yes—
218C2×#103C2312yes—
219C2×#103C2312yes—
220C2×#103C2312yes—
221C2×#103C2312yes—
222C2×#103C2312yes—
223C2×#103C2312yes—
224C2×C22⋊C8C2311yescharacteristic
225C2×C22⋊C8C2311yescharacteristic
226C2×C22⋊C8C2311yescharacteristic
227C2×C22⋊C8C2311yescharacteristic
228C2×C22⋊C8C2311yescharacteristic
229C2×C22⋊C8C2311yescharacteristic
230#405—24no—
231#405—24no—
232C2×#97C2311yescharacteristic
233C2×#97C2311yescharacteristic
234C2×#97C2311yescharacteristic
235C2×#97C2311yescharacteristic
236C2×C4×C8—24no—
237C2×C4×C8C2311yescharacteristic
238C2×C4×C8C2311yescharacteristic
239C2×C4×C8C2311yescharacteristic
240C2×C4×C8C2311yescharacteristic
241C2×C4×C8C2311yescharacteristic
242C2×C4×C8C2311yescharacteristic
243#400—22no—
244#400—22no—
245#400—22no—
246#400—22no—
247#399—22no—
248#399—22no—
249#398—22no—
250#398—22no—
251#398—22no—
252#398—22no—
253#398—22no—
254#397—22no—
255#397—22no—
256#397—22no—
257#397—22no—
258#396—22no—
259#395—22no—
260#395—22no—
261#394—22no—
262#393—22no—
263#391—22no—
264#391C2312yes—
265#391C2312yes—
266#391C2312yes—
267#389—22no—
268#389—22no—
269#389—22no—
270#389—22no—
271#389C2312yes—
272#389C2312yes—
273#389C2312yes—
274#389C2312yes—
275#389C2312yes—
276#389C2312yes—
277#389C2312yes—
278#389C2312yes—
279#389C2312yes—
280#388—22no—
281#388—22no—
282#388—22no—
283#388—22no—
284#387—22no—
285#387—22no—
286#387—22no—
287#387—22no—
288#387—22no—
289#387—22no—
290#386—22no—
291#386—22no—
292#386—22no—
293#385—22no—
294#385—22no—
295#385—22no—
296#385—22no—
297#384—22no—
298#382—22no—
299#382C2312yes—
300#381—22no—
301#381—22no—
302#380—22no—
303#380C2312yes—
304#380C2312yes—
305#380C2312yes—
306#380C2312yes—
307#380C2312yes—
308C4×C4⋊C4C2312yes—
309C4×C22⋊C4—22no—
310C2×#95—22no—
311#340C2312yes—
312#340C2312yes—
313#340C2312yes—
314#340C2312yes—
315#340C2312yes—
316#340C2312yes—
317#340C2312yes—
318#340C2312yes—
319#340C2312yes—
320#340C2312yes—
321#340C2312yes—
322#340C2312yes—
323#340C2312yes—
324#340C2312yes—
325#340C2312yes—
326C22×Q8—22no—
327C22×Q8C2×D411yescharacteristic
328C22×Q8C2412yes—
329C22×D4C2×D411yescharacteristic
330C22×D4C2×D411yescharacteristic
331C22×D4C2×D411yescharacteristic
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4C2×D411yescharacteristic
336C23×C4C2×D411yescharacteristic
337C23×C4C2411yescharacteristic
338C23×C4C2411yescharacteristic
339C23×C4C2411yescharacteristic
340C2×Q16—22no—
341C2×Q16—22no—
342C2×Q16—22no—
343C2×M16—22no—
344C2×M16—22no—
345C2×M16—22no—
346C2×M16—22no—
347C2×M16—41no—
348C2×M16—41no—
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—22no—
352C22×C8—22no—
353C22×C8—22no—
354C22×C8—22no—
355C22×C8—22no—
356C22×C8—22no—
357C22×C8—22no—
358C22×C8—41no—
359C22×C8C2×D414yes—
360C22×C8C2×D414yes—
361C22×C8C2411yescharacteristic
362C22×C8C2411yescharacteristic
363C22×C8C2411yescharacteristic
364C22×C8C2411yescharacteristic
365C22×C8C2411yescharacteristic
366C22×C8C2411yescharacteristic
367C22×C8C2411yescharacteristic
368C22×C8C2411yescharacteristic
369C4⋊Q8—24no—
370C4⋊Q8—24no—
371C4⋊Q8—84no—
372#126—24no—
373#126—24no—
374#125—24no—
375#125—48no—
376#124—24no—
377#123—24no—
378#123—24no—
379#123—84no—
380C22⋊Q8—24no—
381C22⋊Q8—24no—
382C22⋊Q8—24no—
383C22⋊Q8—24no—
384C22⋊Q8—24no—
385C22⋊Q8—24no—
386C22⋊Q8—42no—
387C22⋊Q8—48no—
388C22⋊Q8—48no—
389#121—24no—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8—24no—
393C4×Q8—24no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—48no—
399C4×D4C2×D414yes—
400C4×D4#4114yes—
401#117—22no—
402#117—22no—
403#117—22no—
404#117—22no—
405#117—24no—
406#117—42no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
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—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4—84no—
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2×D411yescharacteristic
434C2×C4⋊C4C2×D411yescharacteristic
435C2×C4⋊C4C2×D411yescharacteristic
436C2×C4⋊C4C2×D411yescharacteristic
437C2×C4⋊C4C2×D411yescharacteristic
438C2×C4⋊C4C2×D411yescharacteristic
439C2×C4⋊C4C2×D411yescharacteristic
440C2×C4⋊C4C2×D411yescharacteristic
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2412yes—
443C2×C4⋊C4C2412yes—
444C2×C4⋊C4C2412yes—
445C2×C4⋊C4C2412yes—
446C2×C4⋊C4C2412yes—
447C2×C4⋊C4C2412yes—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
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⋊C4C2×D411yescharacteristic
458C2×C22⋊C4C2×D411yescharacteristic
459C2×C22⋊C4C2×D411yescharacteristic
460C2×C22⋊C4C2×D411yescharacteristic
461C2×C22⋊C4C2×D411yescharacteristic
462C2×C22⋊C4C2×D411yescharacteristic
463C2×C22⋊C4C2×D411yescharacteristic
464C2×C22⋊C4C2×D411yescharacteristic
465C2×C22⋊C4C2×D411yescharacteristic
466C2×C22⋊C4C2×D411yescharacteristic
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42C2×D411yescharacteristic
473C2×C42C2×D411yescharacteristic
474C2×C42C2411yescharacteristic
475C2×C42C2411yescharacteristic
476C2×C42C2411yescharacteristic
477C2×C42C2411yescharacteristic
478#107—22no—
479#107—22no—
480#107—22no—
481#107—24no—
482#107—24no—
483#107—24no—
484#107—22no—
485#107—22no—
486#107—22no—
487#107—24no—
488#107#4114yes—
489#106—24no—
490#106—42no—
491C4⋊C8—22no—
492C4⋊C8—22no—
493C4⋊C8—22no—
494C4⋊C8—22no—
495C4⋊C8—22no—
496C4⋊C8C2×D414yes—
497#103—24no—
498#103—24no—
499#103—24no—
500#103—24no—
501#103—24no—
502#103—42no—
503#103—42no—
504C22⋊C8—22no—
505C22⋊C8—22no—
506C22⋊C8—22no—
507C22⋊C8—22no—
508C22⋊C8C2×D414yes—
509C22⋊C8C2×D414yes—
510#97—22no—
511#97—22no—
512#97—22no—
513#97—22no—
514C4×C8—22no—
515C4×C8—22no—
516C4×C8—22no—
517C4×C8—22no—
518C4×C8—22no—
519C4×C8C2×D414yes—
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#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95—22no—
543C24C22×D411yescharacteristic
544C24C22×D411yescharacteristic
545C24C22×D411yescharacteristic
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—41no—
555C2×Q8—44no—
556C2×Q8—82no—
557C2×Q8—82no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—41no—
566C2×D4#12114yes—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—41no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—82no—
600C22×C4—82no—
601C22×C4—82no—
602C22×C4—82no—
603C22×C4—82no—
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C22×D411yescharacteristic
617C22×C4C2×#4112yes—
618C22×C4C2×#4112yes—
619C22×C4C2511yescharacteristic
620Q16—44no—
621M16—44no—
622M16—44no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—28no—
632C2×C8—28no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—44no—
643C2×C8—44no—
644C2×C8C22×D412yes—
645C2×C8C22×D412yes—
646C2×C8C22×D412yes—
647C2×C8C22×D412yes—
648C2×C8C2×#4112yes—
649C2×C82−1+412yes—
650C2×C82−1+412yes—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C4⋊C4—44no—
682C4⋊C4—44no—
683C4⋊C4—44no—
684C4⋊C4—82no—
685C4⋊C4—82no—
686C4⋊C4—82no—
687C4⋊C4—82no—
688C4⋊C4—82no—
689C4⋊C4—82no—
690C4⋊C4#12114yes—
691C4⋊C4C2×#4114yes—
692C22⋊C4—22no—
693C22⋊C4—22no—
694C22⋊C4—22no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—22no—
698C22⋊C4—22no—
699C22⋊C4—22no—
700C22⋊C4—44no—
701C22⋊C4—44no—
702C22⋊C4—44no—
703C22⋊C4—44no—
704C22⋊C4—44no—
705C22⋊C4—82no—
706C22⋊C4—82no—
707C22⋊C4—82no—
708C22⋊C4—82no—
709C22⋊C4#12114yes—
710C22⋊C4#12114yes—
711C42—22no—
712C42—22no—
713C42—21no—
714C42—21no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—44no—
720C42—44no—
721C42—82no—
722C42C22×D412yes—
723C42C2×#4112yes—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23C2×#12112yes—
742C23C2×#12112yes—
743C23#57812yes—
744C23#57812yes—
745C23C23×D411yescharacteristic
746Q8—44no—
747Q8—42no—
748Q8—42no—
749Q8—42no—
750Q8—42no—
751Q8—164no—
752D4—28no—
753D4—44no—
754D4—44no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—24no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—88no—
822C2×C4—164no—
823C2×C4—164no—
824C2×C4C2×#12112yes—
825C2×C4C2×#12112yes—
826C2×C4C2×#12112yes—
827C2×C4C2×#12112yes—
828C2×C4#57612yes—
829C2×C4C23×D411yescharacteristic
830C2×C4C22×#4111yescharacteristic
831C2×C4C22×#4111yescharacteristic
832C2×C4C2×2−1+411yescharacteristic
833C2×C4C2×2−1+411yescharacteristic
834C2×C4#58511yescharacteristic
835C8—22no—
836C8—22no—
837C8—22no—
838C8—22no—
839C8—41no—
840C8—41no—
841C8—41no—
842C8#54714yes—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22#305914yes—
864C22C22×#12111yescharacteristic
865C22D4×#4111yescharacteristic
866C22#349911yescharacteristic
867C22C2×#57611yescharacteristic
868C22C2×#57811yescharacteristic
869C22C2×#57811yescharacteristic
870C22#358411yescharacteristic
871C4—22no—
872C4—22no—
873C4—22no—
874C4—22no—
875C4—22no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—44no—
882C4—41no—
883C4—82no—
884C4—82no—
885C4—82no—
886C4—82no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4C2×#54711yescharacteristic
891C4#348211yescharacteristic
892C4#348911yescharacteristic
893C4#351511yescharacteristic
894C2—24no—
895C2—42no—
896C2—81no—
897C2#3625911yescharacteristic
898C2C2×#305911yescharacteristic
899C2#6045811yescharacteristic
900C2#6147311yescharacteristic
901C2#6148211yescharacteristic
902C2#6248811yescharacteristic
903C2#6249311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#529 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3338C2semidirect
4. #33215C2semidirect
5. #33139C2semidirect
6. #33130C2semidirect
7. #28675C2semidirect
8. #28268C2semidirect
9. #27662C2semidirect
10. #27661C2semidirect
11. #25483C2semidirect
12. #25256C2semidirect
13. #25248C2semidirect
14. #24781C2semidirect
15. #24779C2semidirect
16. #24714C2semidirect
17. #24614C2semidirect
18. #24606C2semidirect
19. #22656C2semidirect
20. #22497C2semidirect
21. #21525C2semidirect
22. #21156C2semidirect
23. C2×#1942C2semidirect

Maximal subgroups

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

subgroupindex
C2×#33382
C2×#29662
#380402
#332152
#331392
#331302
#286752
#282682
#276622
#276612
#254832
#252562
#252482
#247812
#247792
#247142
#246142
#246062
#226562
#224972
#215252
#211562
C2×#19422