Finite Group Databasebeta

← #6606432

Subgroups — #6606432

Order 512.

1956 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3334C211yesmaximal, characteristic, complemented
2C2×#2968C211yesmaximal, characteristic, complemented
3#38041C212yesmaximal, complemented
4#33215C211yesmaximal, characteristic, complemented
5#33135C211yesmaximal, characteristic, complemented
6#33132C211yesmaximal, characteristic, complemented
7#28682C211yesmaximal, characteristic, complemented
8#28269C211yesmaximal, characteristic, complemented
9#27667C211yesmaximal, characteristic, complemented
10#27666C211yesmaximal, characteristic, complemented
11#25481C212yesmaximal, complemented
12#25240C212yesmaximal, complemented
13#25232C212yesmaximal, complemented
14#24784C211yesmaximal, characteristic, complemented
15#24782C211yesmaximal, characteristic, complemented
16#24712C212yesmaximal, complemented
17#24612C212yesmaximal, complemented
18#24600C212yesmaximal, complemented
19#22654C211yesmaximal, characteristic, complemented
20#22495C212yesmaximal, complemented
21#21536C211yesmaximal, characteristic, complemented
22#21156C211yesmaximal, characteristic, complemented
23C2×#1944C211yesmaximal, characteristic, complemented
24C2×#547C2212yes—
25C2×#529C2211yescharacteristic
26#3334—28no—
27C2×#500C2211yescharacteristic
28C2×#480C2212yes—
29C2×#480C2212yes—
30C2×#474C2212yes—
31C2×#469C2211yescharacteristic
32C2×#466C2211yescharacteristic
33C2×#466C2211yescharacteristic
34#2968—28no—
35C2×#446C2211yescharacteristic
36C2×#446C2211yescharacteristic
37C2×C4×D8C2211yescharacteristic
38C2×#435C2211yescharacteristic
39C2×#435C2211yescharacteristic
40C2×#435C2211yescharacteristic
41C2×#435C2211yescharacteristic
42C2×C8×D4C2211yescharacteristic
43C2×C8×D4C2211yescharacteristic
44C2×#433C2211yescharacteristic
45C2×#433C2211yescharacteristic
46C2×#431C2211yescharacteristic
47C2×#427C2211yescharacteristic
48C22×#107C2211yescharacteristic
49C22×#107C2211yescharacteristic
50C22×#106C2211yescharacteristic
51C2×#405C2211yescharacteristic
52C2×#405C2211yescharacteristic
53C22×#97C2211yescharacteristic
54#2854C2212yes—
55#2723—22no—
56#2720—22no—
57#2718—22no—
58#2710—22no—
59#2628C2212yes—
60#2624C2212yes—
61#2580C2212yes—
62#2567C2212yes—
63#2501—22no—
64#2488—22no—
65#2487C2212yes—
66#2486C2212yes—
67#2430—22no—
68#2416C2212yes—
69#2414C2212yes—
70#2406—22no—
71#2352C2212yes—
72#2324C2212yes—
73#2317C2212yes—
74C2×#389C2212yes—
75#2087C2212yes—
76#2086C2212yes—
77#2086C2212yes—
78#2086C2212yes—
79#2076C2212yes—
80#2075C2212yes—
81#2067C2212yes—
82#2067C2212yes—
83#2067C2212yes—
84#2065C2212yes—
85#2034C2212yes—
86#2033C2212yes—
87#1993C2212yes—
88#1987C2212yes—
89#1972C2211yescharacteristic
90#1972C2211yescharacteristic
91#1972C2211yescharacteristic
92#1949C2212yes—
93#1944C2211yescharacteristic
94#1944C2211yescharacteristic
95#1944C2211yescharacteristic
96#1944C2211yescharacteristic
97#1944C2211yescharacteristic
98#1944C2211yescharacteristic
99#1944C2211yescharacteristic
100#1944C2212yes—
101#1944C2211yescharacteristic
102#1944C2211yescharacteristic
103#1944C2212yes—
104#1942C2212yes—
105#1942C2212yes—
106#1942C2212yes—
107#1936C2212yes—
108#1936C2212yes—
109#1934C2212yes—
110#1934C2212yes—
111#1934C2212yes—
112#1895C2212yes—
113#1893C2212yes—
114#1893C2212yes—
115#1875C2212yes—
116#1874C2212yes—
117#1854C2212yes—
118#1852C2212yes—
119#1846C2211yescharacteristic
120#1824C2212yes—
121#1823C2212yes—
122#1809C2211yescharacteristic
123#1809C2211yescharacteristic
124#1809C2211yescharacteristic
125#1808C2212yes—
126#1807C2211yescharacteristic
127#1807C2211yescharacteristic
128#1804C2212yes—
129C4×#106C2211yescharacteristic
130#1762C2212yes—
131#1736C2212yes—
132C2×#340C2212yes—
133C22×#41—22no—
134C22×D8C2311yescharacteristic
135C22×M16C2311yescharacteristic
136C22×M16C2311yescharacteristic
137C23×C8C2311yescharacteristic
138C23×C8C2311yescharacteristic
139C23×C8C2311yescharacteristic
140C23×C8C2311yescharacteristic
141#547—28no—
142#547—28no—
143C2×C4⋊Q8C2312yes—
144#529—24no—
145#529—24no—
146C2×#126D411yescharacteristic
147C2×#126D411yescharacteristic
148C2×#125D411yescharacteristic
149C2×#124D411yescharacteristic
150C2×#123—22no—
151C2×#123—22no—
152C2×#123—22no—
153C2×#123—22no—
154C2×#123D411yescharacteristic
155C2×#123D411yescharacteristic
156C2×C22⋊Q8—22no—
157C2×C22⋊Q8D411yescharacteristic
158C2×#121—22no—
159C2×#121D411yescharacteristic
160C2×#121C2312yes—
161C2×#121C2312yes—
162C2×#121C2312yes—
163C2×C4×Q8C2311yescharacteristic
164C2×C4×D4C2312yes—
165C2×C4×D4C2311yescharacteristic
166C2×C4×D4C2311yescharacteristic
167C2×C4×D4C2311yescharacteristic
168C2×#117C2312yes—
169C2×#117C2311yescharacteristic
170C2×#117C2311yescharacteristic
171C22×C4⋊C4—22no—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C42C2311yescharacteristic
176#500—24no—
177#480—28no—
178#480—28no—
179#474—28no—
180#469—24no—
181#466—24no—
182#466—24no—
183#446—24no—
184#446—24no—
185C4×D8—24no—
186#435—24no—
187#435—24no—
188#435—24no—
189#435—24no—
190C8×D4—24no—
191C8×D4D418yescomplemented
192#433—24no—
193#433—24no—
194#431—24no—
195#427—24no—
196C2×#107—24no—
197C2×#107—24no—
198C2×#107C2312yes—
199C2×#107C2312yes—
200C2×#107C2312yes—
201C2×#107C2311yescharacteristic
202C2×#107C2311yescharacteristic
203C2×#107C2311yescharacteristic
204C2×#107C2312yes—
205C2×#107C2312yes—
206C2×#106—24no—
207C2×#106C2311yescharacteristic
208C2×#106C2311yescharacteristic
209C2×#106C2311yescharacteristic
210C2×#106C2312yes—
211C2×#106C2311yescharacteristic
212C2×C4⋊C8C2311yescharacteristic
213C2×C4⋊C8C2311yescharacteristic
214C2×C4⋊C8C2311yescharacteristic
215C2×C4⋊C8C2311yescharacteristic
216C2×C4⋊C8C2311yescharacteristic
217C2×C4⋊C8C2311yescharacteristic
218C2×#102C2312yes—
219C2×#102C2312yes—
220C2×#102C2312yes—
221C2×#102C2312yes—
222C2×#102C2312yes—
223C2×#102C2312yes—
224C2×#102C2312yes—
225C2×C22⋊C8C2311yescharacteristic
226C2×C22⋊C8C2311yescharacteristic
227C2×C22⋊C8C2311yescharacteristic
228C2×C22⋊C8C2311yescharacteristic
229C2×C22⋊C8C2311yescharacteristic
230C2×C22⋊C8C2311yescharacteristic
231#405—24no—
232#405—24no—
233C2×#97—24no—
234C2×#97C2311yescharacteristic
235C2×#97C2311yescharacteristic
236C2×#97C2311yescharacteristic
237C2×#97C2311yescharacteristic
238C2×#97C2311yescharacteristic
239C2×#97C2311yescharacteristic
240C2×C4×C8C2311yescharacteristic
241C2×C4×C8C2311yescharacteristic
242C2×C4×C8C2311yescharacteristic
243C2×C4×C8C2311yescharacteristic
244#400—22no—
245#400—22no—
246#399—22no—
247#399—22no—
248#399—22no—
249#399—22no—
250#398—22no—
251#397—22no—
252#397—22no—
253#396—22no—
254#395—22no—
255#395—22no—
256#395—22no—
257#394—22no—
258#394—22no—
259#394—22no—
260#394—22no—
261#393—22no—
262#393—22no—
263#392—22no—
264#391—22no—
265#390—22no—
266#390—22no—
267#390C2312yes—
268#390C2312yes—
269#390C2312yes—
270#389—22no—
271#389—22no—
272#389C2312yes—
273#389C2312yes—
274#389C2312yes—
275#389C2312yes—
276#389C2312yes—
277#389C2312yes—
278#389C2312yes—
279#389C2312yes—
280#389C2312yes—
281#388—22no—
282#388—22no—
283#388—22no—
284#388—22no—
285#388—22no—
286#387—22no—
287#386—22no—
288#386—22no—
289#386—22no—
290#386—22no—
291#386—22no—
292#385—22no—
293#385—22no—
294#385—22no—
295#385—22no—
296#385—22no—
297#385—22no—
298#384—22no—
299#384—22no—
300#382—22no—
301#382C2312yes—
302#381—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—
326C2×#41—48no—
327C2×#41—84no—
328C2×#41—84no—
329C22×Q8—22no—
330C22×Q8C2×D411yescharacteristic
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4C2×D411yescharacteristic
335C22×D4C2×D411yescharacteristic
336C22×D4C2×D411yescharacteristic
337C22×D4C2412yes—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4C2×D411yescharacteristic
343C23×C4C2×D411yescharacteristic
344C23×C4C2411yescharacteristic
345C23×C4C2411yescharacteristic
346C23×C4C2411yescharacteristic
347C2×D8—22no—
348C2×D8—22no—
349C2×D8—22no—
350C2×M16—22no—
351C2×M16—22no—
352C2×M16—22no—
353C2×M16—22no—
354C2×M16—22no—
355C2×M16—41no—
356C22×C8—22no—
357C22×C8—22no—
358C22×C8—22no—
359C22×C8—22no—
360C22×C8—22no—
361C22×C8—22no—
362C22×C8—22no—
363C22×C8—22no—
364C22×C8—41no—
365C22×C8—41no—
366C22×C8C2×D414yes—
367C22×C8C2×D414yes—
368C22×C8C2411yescharacteristic
369C22×C8C2411yescharacteristic
370C22×C8C2411yescharacteristic
371C22×C8C2411yescharacteristic
372C22×C8C2411yescharacteristic
373C22×C8C2411yescharacteristic
374C22×C8C2411yescharacteristic
375C22×C8C2411yescharacteristic
376C4⋊Q8—24no—
377C4⋊Q8—24no—
378#126—24no—
379#126—24no—
380#125—24no—
381#124—24no—
382#123—24no—
383#123—24no—
384#123—48no—
385#123—48no—
386#123—84no—
387#123—84no—
388C22⋊Q8—24no—
389C22⋊Q8—48no—
390#121—24no—
391#121—24no—
392#121—24no—
393#121—24no—
394#121—24no—
395#121—24no—
396#121—42no—
397#121—84no—
398C4×Q8—22no—
399C4×Q8—22no—
400C4×D4—22no—
401C4×D4—22no—
402C4×D4—22no—
403C4×D4—22no—
404C4×D4—24no—
405C4×D4—24no—
406C4×D4C2×D414yes—
407C4×D4#4114yes—
408#117—22no—
409#117—22no—
410#117—22no—
411#117—22no—
412#117—24no—
413#117—42no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
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—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—42no—
433C2×C4⋊C4—84no—
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⋊C4C2×D411yescharacteristic
442C2×C4⋊C4C2×D411yescharacteristic
443C2×C4⋊C4C2×D411yescharacteristic
444C2×C4⋊C4C2412yes—
445C2×C4⋊C4C2412yes—
446C2×C4⋊C4C2412yes—
447C2×C4⋊C4C2412yes—
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2412yes—
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⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4C2×D411yescharacteristic
468C2×C22⋊C4C2×D411yescharacteristic
469C2×C22⋊C4C2×D411yescharacteristic
470C2×C22⋊C4C2×D411yescharacteristic
471C2×C22⋊C4C2×D411yescharacteristic
472C2×C22⋊C4C2×D411yescharacteristic
473C2×C22⋊C4C2×D411yescharacteristic
474C2×C22⋊C4C2×D411yescharacteristic
475C2×C22⋊C4C2×D411yescharacteristic
476C2×C22⋊C4C2×D411yescharacteristic
477C2×C42—22no—
478C2×C42—22no—
479C2×C42—22no—
480C2×C42—22no—
481C2×C42C2×D411yescharacteristic
482C2×C42C2×D411yescharacteristic
483C2×C42C2411yescharacteristic
484C2×C42C2411yescharacteristic
485C2×C42C2411yescharacteristic
486C2×C42C2411yescharacteristic
487#107—22no—
488#107—22no—
489#107—22no—
490#107—24no—
491#107—24no—
492#107—24no—
493#107—24no—
494#107—42no—
495#106—22no—
496#106—22no—
497#106—22no—
498#106—24no—
499#106#4114yescomplemented
500C4⋊C8—22no—
501C4⋊C8—22no—
502C4⋊C8—22no—
503C4⋊C8—22no—
504C4⋊C8—22no—
505C4⋊C8C2×D414yes—
506#102—24no—
507#102—24no—
508#102—24no—
509#102—24no—
510#102—24no—
511#102—42no—
512#102—42no—
513C22⋊C8—22no—
514C22⋊C8—22no—
515C22⋊C8—22no—
516C22⋊C8—22no—
517C22⋊C8C2×D414yes—
518C22⋊C8C2×D414yes—
519#97—22no—
520#97—22no—
521#97—22no—
522#97—22no—
523#97—22no—
524#97—22no—
525C4×C8—22no—
526C4×C8—22no—
527C4×C8—22no—
528C4×C8C2×D414yes—
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—
543#95—22no—
544#95—22no—
545#95—22no—
546C24—22no—
547C24C22×D411yescharacteristic
548C24C22×D411yescharacteristic
549C24C22×D411yescharacteristic
550#41—832no—
551C2×Q8—22no—
552C2×Q8—42no—
553C2×Q8—44no—
554C2×Q8—82no—
555C2×Q8—82no—
556C2×D4—24no—
557C2×D4—22no—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—42no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4—82no—
573C2×D4—82no—
574C2×D4—82no—
575C2×D4—82no—
576C2×D4#12114yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—42no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—82no—
610C22×C4—82no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4—82no—
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D412yes—
626C22×C4C22×D412yes—
627C22×C4C2×#4112yes—
628C22×C4C2×#4112yes—
629C22×C4C2511yescharacteristic
630D8—44no—
631M16—44no—
632M16—44no—
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—28no—
642C2×C8—28no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—44no—
653C2×C8—44no—
654C2×C8C22×D412yes—
655C2×C8C22×D412yes—
656C2×C8C22×D412yes—
657C2×C8C22×D412yes—
658C2×C8C2×#4112yes—
659C2×C82−1+412yes—
660C2×C82−1+412yes—
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—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—44no—
684C4⋊C4—44no—
685C4⋊C4—44no—
686C4⋊C4—44no—
687C4⋊C4—82no—
688C4⋊C4—82no—
689C4⋊C4—82no—
690C4⋊C4—82no—
691C4⋊C4—82no—
692C4⋊C4—82no—
693C4⋊C4—82no—
694C4⋊C4—82no—
695C4⋊C4—82no—
696C4⋊C4#12114yes—
697C4⋊C4C2×#4114yes—
698C22⋊C4—22no—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—44no—
707C22⋊C4—44no—
708C22⋊C4—44no—
709C22⋊C4—44no—
710C22⋊C4—44no—
711C22⋊C4—44no—
712C22⋊C4—44no—
713C22⋊C4—82no—
714C22⋊C4—82no—
715C22⋊C4—82no—
716C22⋊C4—82no—
717C22⋊C4—82no—
718C22⋊C4—82no—
719C22⋊C4—82no—
720C22⋊C4—82no—
721C22⋊C4—82no—
722C22⋊C4#12114yes—
723C22⋊C4#12114yes—
724C42—22no—
725C42—22no—
726C42—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42—21no—
732C42—44no—
733C42—82no—
734C42C22×D412yes—
735C42C2×#4112yes—
736C23—22no—
737C23—21no—
738C23—21no—
739C23—22no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—22no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—22no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23C2×#12112yes—
756C23C2×#12112yes—
757C23#57614yes—
758C23C23×D411yescharacteristic
759Q8—82no—
760Q8—88no—
761D4—28no—
762D4—44no—
763D4—42no—
764D4—42no—
765D4—42no—
766D4—42no—
767D4—82no—
768D4—88no—
769D4—88no—
770D4—164no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—24no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
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—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—88no—
827C2×C4—82no—
828C2×C4—88no—
829C2×C4—88no—
830C2×C4—88no—
831C2×C4C2×#12112yes—
832C2×C4C2×#12112yes—
833C2×C4C2×#12112yes—
834C2×C4C2×#12112yes—
835C2×C4C23×D411yescharacteristic
836C2×C4C22×#4111yescharacteristic
837C2×C4C22×#4111yescharacteristic
838C2×C4C2×2−1+411yescharacteristic
839C2×C4C2×2−1+411yescharacteristic
840C2×C4#58511yescharacteristic
841C8—22no—
842C8—22no—
843C8—22no—
844C8—22no—
845C8—41no—
846C8—41no—
847C8—41no—
848C8#54714yes—
849C22—22no—
850C22—24no—
851C22—24no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—42no—
857C22—42no—
858C22—41no—
859C22—41no—
860C22—42no—
861C22—42no—
862C22—41no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22—82no—
868C22—82no—
869C22—82no—
870C22#305814yes—
871C22C22×#12111yescharacteristic
872C22D4×#4111yescharacteristic
873C22#349911yescharacteristic
874C22C2×#57612yes—
875C22#358612yes—
876C4—22no—
877C4—22no—
878C4—22no—
879C4—22no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—41no—
884C4—41no—
885C4—41no—
886C4—44no—
887C4—41no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4—82no—
893C4—82no—
894C4C2×#54711yescharacteristic
895C4#348211yescharacteristic
896C4#348911yescharacteristic
897C4#351511yescharacteristic
898C2—24no—
899C2—42no—
900C2—81no—
901C2—162no—
902C2#3625911yescharacteristic
903C2C2×#305811yescharacteristic
904C2#6046211yescharacteristic
905C2#6152312yes—
906C2#6251512yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
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×#3334C2semidirect
2. C2×#2968C2semidirect
3. #38041C2semidirect
4. #33215C2semidirect
5. #33135C2semidirect
6. #33132C2semidirect
7. #28682C2semidirect
8. #28269C2semidirect
9. #27667C2semidirect
10. #27666C2semidirect
11. #25481C2semidirect
12. #25240C2semidirect
13. #25232C2semidirect
14. #24784C2semidirect
15. #24782C2semidirect
16. #24712C2semidirect
17. #24612C2semidirect
18. #24600C2semidirect
19. #22654C2semidirect
20. #22495C2semidirect
21. #21536C2semidirect
22. #21156C2semidirect
23. C2×#1944C2semidirect
191. C8×D4D4semidirect
499. #106#41semidirect

Maximal subgroups

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

subgroupindex
C2×#33342
C2×#29682
#380412
#332152
#331352
#331322
#286822
#282692
#276672
#276662
#254812
#252402
#252322
#247842
#247822
#247122
#246122
#246002
#226542
#224952
#215362
#211562
C2×#19442