Finite Group Databasebeta

← #6669413

Subgroups — #6669413

Order 512.

1874 conjugacy classes of subgroups.

The subgroup lattice has 899 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3299C211yesmaximal, characteristic
2C22×#477C211yesmaximal, characteristic, complemented
3#39592C211yesmaximal, characteristic
4Q8×#123C211yesmaximal, characteristic
5#33010C211yesmaximal, characteristic, complemented
6#31151C212yesmaximal, complemented
7#31081C212yesmaximal, complemented
8#30816C212yesmaximal, complemented
9#30672C212yesmaximal, complemented
10#29771C211yesmaximal, characteristic, complemented
11#29642C211yesmaximal, characteristic, complemented
12#27930C211yesmaximal, characteristic, complemented
13#27662C211yesmaximal, characteristic
14#27228C212yesmaximal, complemented
15#26381C212yesmaximal, complemented
16#26046C212yesmaximal, complemented
17#25963C212yesmaximal, complemented
18#24582C211yesmaximal, characteristic, complemented
19#24532C211yesmaximal, characteristic, complemented
20#24098C211yesmaximal, characteristic
21#24042C211yesmaximal, characteristic
22#22575C211yesmaximal, characteristic, complemented
23#22063C211yesmaximal, characteristic
24C2×#554C2211yescharacteristic
25C2×D4×Q8C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28#3299—28no—
29C2×#487C2211yescharacteristic
30C2×#484C2211yescharacteristic
31C2×#484C2211yescharacteristic
32C2×#484C2211yescharacteristic
33C2×#484C2211yescharacteristic
34C2×#477—28no—
35C2×#477C2212yes—
36C2×#477C2212yes—
37C2×#477C2212yes—
38C2×#477C2212yes—
39C2×#477C2211yescharacteristic
40C2×#467C2211yescharacteristic
41C2×#467C2211yescharacteristic
42C2×#462C2211yescharacteristic
43C2×#451C2211yescharacteristic
44C2×#451C2211yescharacteristic
45C2×C4×Q16C2211yescharacteristic
46C2×C8×D4C2211yescharacteristic
47C22×#107C2211yescharacteristic
48C22×#107C2211yescharacteristic
49C22×C4⋊C8C2211yescharacteristic
50C22×#103C2211yescharacteristic
51C22×#103C2211yescharacteristic
52C22×#103C2211yescharacteristic
53#2855—21no—
54#2855C2211yescharacteristic
55#2855C2211yescharacteristic
56#2713—22no—
57#2677—22no—
58#2627—21no—
59#2551C2212yes—
60#2502—21no—
61#2502C2211yescharacteristic
62#2502C2211yescharacteristic
63#2492C2212yes—
64#2487—21no—
65#2487C2211yescharacteristic
66#2487C2211yescharacteristic
67#2451C2212yes—
68#2446—22no—
69#2446C2212yes—
70#2440C2212yes—
71#2434—21no—
72#2423—22no—
73#2423C2212yes—
74#2409—21no—
75Q8×C4⋊C4C2212yes—
76#2345C2211yescharacteristic
77Q8×C22⋊C4C2211yescharacteristic
78Q8×C22⋊C4C2212yes—
79#2322—21no—
80C4×#123—21no—
81C4×#123C2211yescharacteristic
82#2095C2212yes—
83#2095C2212yes—
84#2087C2212yes—
85#2087C2212yes—
86#2083C2212yes—
87#2076C2212yes—
88#2072C2212yes—
89#2068C2212yes—
90#2068C2212yes—
91#2068C2212yes—
92#2057C2212yes—
93#2057C2212yes—
94#2057C2212yes—
95#2056C2212yes—
96#2056C2212yes—
97#2043C2212yes—
98#2036C2212yes—
99#2036C2212yes—
100#2024C2212yes—
101#2024C2212yes—
102#1969C2212yes—
103#1947C2212yes—
104#1942C2212yes—
105#1939C2212yes—
106#1933C2212yes—
107#1928C2212yes—
108#1928C2212yes—
109#1923C2212yes—
110#1916C2212yes—
111#1892C2211yescharacteristic
112#1892C2211yescharacteristic
113#1878C2212yes—
114#1878C2212yes—
115#1878C2212yes—
116#1869C2211yescharacteristic
117#1863C2212yes—
118#1863C2212yes—
119#1863C2212yes—
120#1863C2212yes—
121#1863C2212yes—
122#1852C2212yes—
123#1850C2211yescharacteristic
124#1850C2212yes—
125#1845C2212yes—
126#1824C2211yescharacteristic
127#1824C2211yescharacteristic
128#1824C2211yescharacteristic
129#1817C2211yescharacteristic
130#1808C2211yescharacteristic
131#1808C2212yes—
132#1803C2212yes—
133#1787C2211yescharacteristic
134#1787C2212yes—
135C4×#103C2212yes—
136C8×C22⋊C4C2211yescharacteristic
137C23×Q8—21no—
138C23×Q8C2311yescharacteristic
139C23×Q8C2311yescharacteristic
140C22×Q16C2311yescharacteristic
141C22×Q16C2311yescharacteristic
142C22×Q16C2311yescharacteristic
143C23×C8C2311yescharacteristic
144C23×C8C2311yescharacteristic
145C23×C8C2311yescharacteristic
146#554—24no—
147#554—42no—
148D4×Q8—24no—
149D4×Q8—42no—
150C2×C4⋊Q8—21no—
151C2×C4⋊Q8—22no—
152C2×C4⋊Q8—24no—
153C2×C4⋊Q8—22no—
154C2×C4⋊Q8—42no—
155C2×C4⋊Q8C2311yescharacteristic
156C2×C4⋊Q8C2312yes—
157C2×C4⋊Q8C2312yes—
158C2×C4⋊Q8C2311yescharacteristic
159C2×#125—21no—
160C2×#123D411yescharacteristic
161C2×C22⋊Q8—21no—
162C2×C22⋊Q8—21no—
163C2×C22⋊Q8—21no—
164C2×C22⋊Q8—21no—
165C2×C22⋊Q8—22no—
166C2×C22⋊Q8C2311yescharacteristic
167C2×C22⋊Q8C2311yescharacteristic
168C2×C22⋊Q8C2311yescharacteristic
169C2×C22⋊Q8C2311yescharacteristic
170C2×C4×Q8—22no—
171C2×C4×Q8—24no—
172C2×C4×Q8—42no—
173C2×C4×Q8C2312yes—
174C2×C4×Q8C2312yes—
175C2×C4×Q8C2311yescharacteristic
176C2×C4×Q8C2312yes—
177C2×C4×Q8C2311yescharacteristic
178C2×C4×D4—21no—
179C2×C4×D4—21no—
180C2×C4×D4C2311yescharacteristic
181C22×C4⋊C4—21no—
182C22×C4⋊C4—21no—
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C42—21no—
188C22×C42C2311yescharacteristic
189#487—24no—
190#484—24no—
191#484—24no—
192#484—42no—
193#484—42no—
194#477—28no—
195#477—28no—
196#477—28no—
197#477—28no—
198#477—24no—
199#467—24no—
200#467—24no—
201#462—24no—
202#451—24no—
203#451—24no—
204C4×Q16—24no—
205C8×D4—24no—
206C2×#107—24no—
207C2×#107—24no—
208C2×#107C2312yes—
209C2×#107C2312yes—
210C2×#107C2312yes—
211C2×#107C2312yes—
212C2×#107C2311yescharacteristic
213C2×#107C2311yescharacteristic
214C2×#107C2311yescharacteristic
215C2×#107C2312yes—
216C2×#107C2312yes—
217C2×#107C2312yes—
218C2×C4⋊C8—24no—
219C2×C4⋊C8C2312yes—
220C2×C4⋊C8C2312yes—
221C2×C4⋊C8C2311yescharacteristic
222C2×C4⋊C8C2312yes—
223C2×#103—24no—
224C2×#103—24no—
225C2×#103D418yes—
226C2×#103C2312yes—
227C2×#103C2312yes—
228C2×#103C2311yescharacteristic
229C2×#103C2311yescharacteristic
230C2×#103C2311yescharacteristic
231C2×#103C2311yescharacteristic
232C2×#103C2311yescharacteristic
233C2×#103C2311yescharacteristic
234C2×#103C2312yes—
235C2×#103C2312yes—
236C2×#103C2312yes—
237C2×#103C2312yes—
238C2×#103C2312yes—
239C2×#103C2312yes—
240C2×#103C2311yescharacteristic
241C2×#103C2311yescharacteristic
242C2×#103C2311yescharacteristic
243C2×#103C2311yescharacteristic
244C2×C22⋊C8C2311yescharacteristic
245C2×C22⋊C8C2311yescharacteristic
246C2×C22⋊C8C2311yescharacteristic
247C2×C22⋊C8C2312yes—
248C2×C4×C8C2311yescharacteristic
249C2×C4×C8C2312yes—
250#400—21no—
251#400—21no—
252#400—22no—
253#400—22no—
254#399—21no—
255#399—21no—
256#399—22no—
257#398—22no—
258#398—22no—
259#398—22no—
260#398—22no—
261#398—22no—
262#398—22no—
263#395—22no—
264#395—22no—
265#395—22no—
266#395—22no—
267#393—22no—
268#391—22no—
269#391—22no—
270#391—22no—
271#391—22no—
272#391—22no—
273#391C2312yes—
274#391C2312yes—
275#391C2312yes—
276#391C2312yes—
277#391C2312yes—
278#389—22no—
279#389—22no—
280#389—22no—
281#389C2312yes—
282#389C2312yes—
283#389C2312yes—
284#389C2312yes—
285#389C2312yes—
286#388—22no—
287#388—22no—
288#388D412yes—
289#387—22no—
290#387—22no—
291#387—22no—
292#387—22no—
293#387—22no—
294#387—22no—
295#387—22no—
296#387D412yes—
297#386—21no—
298#386—21no—
299#386D411yescharacteristic
300#385—21no—
301#385—21no—
302#385—22no—
303#385—21no—
304#385—21no—
305#385—21no—
306#385—21no—
307#385—21no—
308#385—21no—
309#385D411yescharacteristic
310#384—22no—
311#384C2312yes—
312#384C2312yes—
313#381—21no—
314#381—21no—
315#381D411yescharacteristic
316#380—21no—
317#380—22no—
318#380—21no—
319#380C2312yes—
320#380C2312yes—
321#380C2311yescharacteristic
322#380C2311yescharacteristic
323C4×C4⋊C4—22no—
324C4×C4⋊C4C2312yes—
325C4×C4⋊C4C2312yes—
326C4×C22⋊C4—21no—
327C4×C22⋊C4—22no—
328C4×C22⋊C4—21no—
329C4×C22⋊C4C2311yescharacteristic
330C4×C22⋊C4C2312yes—
331#340C2312yes—
332#340C2312yes—
333#340C2312yes—
334#340C2312yes—
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#336C2312yes—
341#336C2312yes—
342#336C2312yes—
343#336C2312yes—
344#336C2312yes—
345C22×Q8—21no—
346C22×Q8—21no—
347C22×Q8—22no—
348C22×Q8—22no—
349C22×Q8—21no—
350C22×Q8—22no—
351C22×Q8—24no—
352C22×Q8—22no—
353C22×Q8—24no—
354C22×Q8—44no—
355C22×Q8—42no—
356C22×Q8—41no—
357C22×Q8—42no—
358C22×Q8—84no—
359C22×Q8C2×D414yes—
360C22×Q8C2411yescharacteristic
361C22×Q8C2411yescharacteristic
362C22×Q8C2411yescharacteristic
363C22×Q8C2411yescharacteristic
364C22×D4C2×D411yescharacteristic
365C23×C4—21no—
366C23×C4—21no—
367C23×C4—21no—
368C23×C4—21no—
369C23×C4—21no—
370C23×C4—21no—
371C23×C4C2×D411yescharacteristic
372C23×C4C2×D411yescharacteristic
373C23×C4C2411yescharacteristic
374C23×C4C2411yescharacteristic
375C2×Q16—22no—
376C2×Q16—24no—
377C2×Q16—22no—
378C2×Q16—22no—
379C2×Q16—42no—
380C2×Q16—42no—
381C22×C8—22no—
382C22×C8—22no—
383C22×C8—42no—
384C22×C8—42no—
385C22×C8—42no—
386C22×C8C2×D414yes—
387C22×C8C2411yescharacteristic
388C22×C8C2412yes—
389C22×C8C2411yescharacteristic
390C22×C8C2412yes—
391C22×C8C2411yescharacteristic
392C22×C8C2411yescharacteristic
393C4⋊Q8—24no—
394C4⋊Q8—24no—
395C4⋊Q8—22no—
396C4⋊Q8—22no—
397C4⋊Q8—42no—
398C4⋊Q8—42no—
399C4⋊Q8—41no—
400C4⋊Q8—48no—
401C4⋊Q8—41no—
402C4⋊Q8—44no—
403C4⋊Q8—84no—
404#125—44no—
405#123Q1618yescomplemented
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409C22⋊Q8—22no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8—44no—
413C22⋊Q8—44no—
414C22⋊Q8—44no—
415C22⋊Q8—44no—
416C22⋊Q8—41no—
417C22⋊Q8—41no—
418C22⋊Q8—84no—
419C4×Q8—24no—
420C4×Q8—24no—
421C4×Q8—22no—
422C4×Q8—24no—
423C4×Q8—22no—
424C4×Q8—42no—
425C4×Q8—42no—
426C4×Q8—42no—
427C4×Q8—41no—
428C4×Q8—41no—
429C4×Q8—48no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—44no—
433C4×D4—44no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—41no—
468C2×C4⋊C4—44no—
469C2×C4⋊C4—44no—
470C2×C4⋊C4C2×D411yescharacteristic
471C2×C4⋊C4C2×D414yes—
472C2×C4⋊C4C2×D412yes—
473C2×C4⋊C4C2×D412yes—
474C2×C4⋊C4C2412yes—
475C2×C4⋊C4C2411yescharacteristic
476C2×C4⋊C4C2412yes—
477C2×C4⋊C4C2411yescharacteristic
478C2×C4⋊C4C2412yes—
479C2×C4⋊C4C2412yes—
480C2×C4⋊C4C2411yescharacteristic
481C2×C4⋊C4C2411yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4C2×D411yescharacteristic
491C2×C22⋊C4C2×D411yescharacteristic
492C2×C22⋊C4C2×D411yescharacteristic
493C2×C22⋊C4C2×D412yes—
494C2×C22⋊C4C2×D411yescharacteristic
495C2×C22⋊C4C2×D412yes—
496C2×C42—22no—
497C2×C42—22no—
498C2×C42—21no—
499C2×C42—21no—
500C2×C42—22no—
501C2×C42—22no—
502C2×C42—22no—
503C2×C42—22no—
504C2×C42—44no—
505C2×C42C2×D412yes—
506C2×C42C2411yescharacteristic
507C2×C42C2412yes—
508C2×C42C2412yes—
509#107—24no—
510#107—24no—
511#107—22no—
512#107—24no—
513#107—24no—
514#107—22no—
515#107—22no—
516#107—42no—
517#107—42no—
518#107—42no—
519C4⋊C8—24no—
520C4⋊C8—24no—
521C4⋊C8—22no—
522C4⋊C8—42no—
523#103—22no—
524#103—24no—
525#103—24no—
526#103—22no—
527#103—24no—
528#103—22no—
529#103—22no—
530#103—22no—
531#103—22no—
532#103—42no—
533#103—42no—
534#103—42no—
535#103—42no—
536#103—42no—
537#103C2×D414yes—
538#103C2×D414yes—
539#103C2×D414yes—
540#103C2×D414yes—
541C22⋊C8—22no—
542C22⋊C8—22no—
543C22⋊C8—22no—
544C22⋊C8—42no—
545C4×C8—22no—
546C4×C8—42no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—22no—
552#95—22no—
553#95—22no—
554#95—22no—
555#95—22no—
556#95—22no—
557#95—22no—
558#95—22no—
559#95—21no—
560#95—21no—
561#95—22no—
562#95—22no—
563#95—22no—
564#95—22no—
565#95—22no—
566#95—22no—
567#95C2×D412yes—
568#95C2×D412yes—
569#95C2×D412yes—
570#95C2×D412yes—
571#95C2×D412yes—
572C24C22×D411yescharacteristic
573C24C22×D411yescharacteristic
574C2×Q8—24no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—22no—
578C2×Q8—28no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—22no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—44no—
590C2×Q8—42no—
591C2×Q8—44no—
592C2×Q8—44no—
593C2×Q8—44no—
594C2×Q8—42no—
595C2×Q8—44no—
596C2×Q8—48no—
597C2×Q8—44no—
598C2×Q8—44no—
599C2×Q8—44no—
600C2×Q8—82no—
601C2×Q8—82no—
602C2×Q8—82no—
603C2×Q8—82no—
604C2×Q8—84no—
605C2×Q8—816no—
606C2×Q8C22×D412yes—
607C2×Q8C22×D412yes—
608C2×Q82−1+414yes—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4C2×Q1614yes—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—24no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—24no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—44no—
637C22×C4—42no—
638C22×C4—44no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—82no—
643C22×C4—82no—
644C22×C4—82no—
645C22×C4—82no—
646C22×C4C2×Q1614yes—
647C22×C4C22×D412yes—
648C22×C4C22×D411yescharacteristic
649C22×C4C22×D412yes—
650C22×C4C22×D411yescharacteristic
651C22×C4C22×D411yescharacteristic
652C22×C4C22×D412yes—
653C22×C4C22×D412yes—
654C22×C4C22×D412yes—
655C22×C4C22×D411yescharacteristic
656C22×C4H(5,𝔽2)12yes—
657C22×C4C2511yescharacteristic
658Q16—44no—
659Q16—82no—
660Q16—82no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—22no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—44no—
674C2×C8—44no—
675C2×C8—82no—
676C2×C8C22×D412yes—
677C2×C8C22×D412yes—
678C4⋊C4—24no—
679C4⋊C4—22no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—22no—
684C4⋊C4—21no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—42no—
695C4⋊C4—42no—
696C4⋊C4—44no—
697C4⋊C4—44no—
698C4⋊C4—44no—
699C4⋊C4—44no—
700C4⋊C4—42no—
701C4⋊C4—42no—
702C4⋊C4—44no—
703C4⋊C4—42no—
704C4⋊C4—42no—
705C4⋊C4—42no—
706C4⋊C4—42no—
707C4⋊C4—42no—
708C4⋊C4—44no—
709C4⋊C4—42no—
710C4⋊C4—42no—
711C4⋊C4—42no—
712C4⋊C4—42no—
713C4⋊C4—82no—
714C4⋊C4—82no—
715C4⋊C4—82no—
716C4⋊C4—82no—
717C4⋊C4—82no—
718C4⋊C4—82no—
719C4⋊C4—82no—
720C4⋊C4—82no—
721C4⋊C4C2×Q1618yes—
722C4⋊C4C22×D412yes—
723C4⋊C4C22×D412yes—
724C22⋊C4—22no—
725C22⋊C4—22no—
726C22⋊C4—22no—
727C22⋊C4—42no—
728C22⋊C4—42no—
729C22⋊C4—42no—
730C22⋊C4—42no—
731C22⋊C4—42no—
732C22⋊C4—42no—
733C22⋊C4—42no—
734C22⋊C4—82no—
735C22⋊C4—82no—
736C22⋊C4C2×Q1614yes—
737C22⋊C4C2×Q1618yes—
738C42—24no—
739C42—21no—
740C42—22no—
741C42—22no—
742C42—21no—
743C42—22no—
744C42—22no—
745C42—44no—
746C42—44no—
747C42—42no—
748C42—42no—
749C42—44no—
750C42—82no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—21no—
755C23—22no—
756C23—21no—
757C23D4212yes—
758C23C22×Q1612yes—
759C23C22×Q1612yes—
760C23#57812yes—
761C23C23×D411yescharacteristic
762Q8—22no—
763Q8—24no—
764Q8—22no—
765Q8—22no—
766Q8—48no—
767Q8—42no—
768Q8—41no—
769Q8—41no—
770Q8—41no—
771Q8—41no—
772Q8—42no—
773Q8—42no—
774Q8—84no—
775Q8—88no—
776Q8—88no—
777Q8—162no—
778Q8#53614yes—
779D4—28no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—24no—
786C2×C4—22no—
787C2×C4—28no—
788C2×C4—22no—
789C2×C4—21no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—24no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—48no—
807C2×C4—44no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
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—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—84no—
835C2×C4—84no—
836C2×C4—84no—
837C2×C4—84no—
838C2×C4—162no—
839C2×C4D4212yes—
840C2×C4C22×Q1614yes—
841C2×C4C22×Q1614yes—
842C2×C4C22×Q1612yes—
843C2×C4C23×D411yescharacteristic
844C2×C4C2×H(5,𝔽2)11yescharacteristic
845C2×C4C2×2−1+412yes—
846C2×C4#58512yes—
847C8—22no—
848C8—22no—
849C8—41no—
850C8—42no—
851C8—41no—
852C8—42no—
853C22—22no—
854C22—22no—
855C22—24no—
856C22—24no—
857C22—22no—
858C22—24no—
859C22—41no—
860C22—41no—
861C22—42no—
862C22D4×Q1614yes—
863C22C2×D4211yescharacteristic
864C22#348912yes—
865C22C23×Q1611yescharacteristic
866C22C2×#57811yescharacteristic
867C22#358512yes—
868C4—22no—
869C4—24no—
870C4—24no—
871C4—22no—
872C4—24no—
873C4—41no—
874C4—42no—
875C4—42no—
876C4—41no—
877C4—42no—
878C4—42no—
879C4—42no—
880C4—81no—
881C4—81no—
882C4—81no—
883C4—82no—
884C4—82no—
885C4—81no—
886C4—82no—
887C4—82no—
888C4C2×#53611yescharacteristic
889C4#348511yescharacteristic
890C4#353512yes—
891C2—24no—
892C2—42no—
893C2#3764711yescharacteristic
894C2C2×D4×Q1611yescharacteristic
895C2#6105911yescharacteristic
896C2#6210012yes—
897C2#6215812yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#477C2semidirect
5. #33010C2semidirect
6. #31151C2semidirect
7. #31081C2semidirect
8. #30816C2semidirect
9. #30672C2semidirect
10. #29771C2semidirect
11. #29642C2semidirect
12. #27930C2semidirect
14. #27228C2semidirect
15. #26381C2semidirect
16. #26046C2semidirect
17. #25963C2semidirect
18. #24582C2semidirect
19. #24532C2semidirect
22. #22575C2semidirect
405. #123Q16semidirect

Maximal subgroups

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

subgroupindex
C2×#32992
C22×#4772
#395922
Q8×#1232
#330102
#311512
#310812
#308162
#306722
#297712
#296422
#279302
#276622
#272282
#263812
#260462
#259632
#245822
#245322
#240982
#240422
#225752
#220632