Finite Group Databasebeta

← #6508480

Subgroups — #6508480

Order 512.

1610 conjugacy classes of subgroups.

The subgroup lattice has 913 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35087C211yesmaximal, characteristic
2C2×#2451C211yesmaximal, characteristic
3#29106C211yesmaximal, characteristic
4#29089C212yesmaximal, complemented
5#29081C212yesmaximal, complemented
6#28970C212yesmaximal, complemented
7#28947C212yesmaximal, complemented
8#28313C211yesmaximal, characteristic
9#26838C212yesmaximal, complemented
10#26822C212yesmaximal, complemented
11#26497C212yesmaximal, complemented
12#26489C212yesmaximal, complemented
13#25902C211yesmaximal, characteristic
14#25816C211yesmaximal, characteristic
15#24609C211yesmaximal, characteristic
16#24601C211yesmaximal, characteristic
17#24508C211yesmaximal, characteristic
18#24502C211yesmaximal, characteristic
19#22084C211yesmaximal, characteristic
20#22078C211yesmaximal, characteristic
21#21455C211yesmaximal, characteristic
22C4×#451C211yesmaximal, characteristic
23#20535C211yesmaximal, characteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C2×#501C2212yes—
27C2×#487C2212yes—
28C2×#483C2211yescharacteristic
29C2×#483C2211yescharacteristic
30C2×#451C2211yescharacteristic
31C2×#451C2211yescharacteristic
32C2×#441C2212yes—
33C2×C4×Q16C2212yes—
34C2×#432C2211yescharacteristic
35C2×#431C2211yescharacteristic
36#2857C2211yescharacteristic
37#2855C2211yescharacteristic
38#2855C2211yescharacteristic
39#2851C2211yescharacteristic
40#2655—21no—
41#2655—21no—
42#2514C2211yescharacteristic
43#2514C2211yescharacteristic
44#2506C2211yescharacteristic
45#2506C2211yescharacteristic
46#2493—21no—
47#2493—21no—
48#2473—21no—
49#2473—21no—
50#2453C2211yescharacteristic
51#2453C2211yescharacteristic
52#2451—21no—
53#2451—21no—
54#2451—21no—
55#2451—21no—
56#2451C2212yes—
57#2451C2212yes—
58#2451C2212yes—
59#2451C2212yes—
60#2446C2211yescharacteristic
61#2446C2211yescharacteristic
62C2×#398—21no—
63C2×#395—21no—
64#2336—21no—
65#2336—21no—
66C4×C22⋊Q8C2211yescharacteristic
67C4×C22⋊Q8C2211yescharacteristic
68C2×#391—21no—
69C2×#391C2211yescharacteristic
70C2×#391C2211yescharacteristic
71C2×#389C2211yescharacteristic
72C2×#389C2211yescharacteristic
73C2×#387—21no—
74C2×C4×C4⋊C4C2211yescharacteristic
75#2096C2212yes—
76#2088C2212yes—
77#2088C2212yes—
78#2074C2212yes—
79#2068C2212yes—
80#2068C2212yes—
81#2066C2212yes—
82#2066C2212yes—
83#2058C2212yes—
84#2057C2212yes—
85#2056C2212yes—
86#2056C2212yes—
87#2026C2212yes—
88#2024C2212yes—
89#2024C2212yes—
90#2016C2212yes—
91#1993C2212yes—
92#1990C2212yes—
93#1971C2212yes—
94#1971C2212yes—
95#1971C2212yes—
96#1969C2212yes—
97#1944C2212yes—
98#1943C2212yes—
99#1941C2212yes—
100#1941C2212yes—
101#1935C2212yes—
102#1935C2212yes—
103#1935C2212yes—
104#1933C2212yes—
105#1933C2212yes—
106#1933C2212yes—
107#1933C2212yes—
108#1933C2212yes—
109#1920C2212yes—
110#1919C2212yes—
111#1878C2212yes—
112#1878C2212yes—
113#1872C2211yescharacteristic
114#1872C2211yescharacteristic
115#1872C2211yescharacteristic
116#1872C2211yescharacteristic
117#1865C2212yes—
118#1865C2212yes—
119#1863C2212yes—
120#1863C2212yes—
121#1853C2211yescharacteristic
122#1853C2211yescharacteristic
123#1852C2211yescharacteristic
124#1852C2211yescharacteristic
125#1823C2211yescharacteristic
126#1823C2211yescharacteristic
127#1787C2211yescharacteristic
128#1787C2211yescharacteristic
129#1771C2212yes—
130#1771C2212yes—
131#1770C2212yes—
132C8×C4⋊C4C2212yes—
133#1763C2212yes—
134C4×#103C2212yes—
135#1749C2211yescharacteristic
136#1749C2211yescharacteristic
137C4×C22⋊C8C2211yescharacteristic
138C4×C22⋊C8C2211yescharacteristic
139C23×Q8—21no—
140C23×Q8C2311yescharacteristic
141C22×Q16C2312yes—
142C22×Q16C2312yes—
143C2×C4⋊Q8—21no—
144C2×C4⋊Q8—21no—
145C2×C4⋊Q8—44no—
146C2×C4⋊Q8C2311yescharacteristic
147C2×C4⋊Q8C2312yes—
148C2×C4⋊Q8C2312yes—
149C2×#125—21no—
150C2×#125—21no—
151C2×#125C2311yescharacteristic
152C2×C22⋊Q8C2311yescharacteristic
153C2×C22⋊Q8C2311yescharacteristic
154C2×C4×Q8—21no—
155C2×C4×Q8—21no—
156C2×C4×Q8—44no—
157C2×C4×Q8C2312yes—
158C2×C4×Q8C2312yes—
159C2×C4×Q8C2311yescharacteristic
160C2×C4×Q8C2311yescharacteristic
161C22×C4⋊C4—21no—
162C22×C4⋊C4—21no—
163C22×C4⋊C4—21no—
164C22×C4⋊C4—21no—
165C22×C4⋊C4D411yescharacteristic
166C22×C4⋊C4D411yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C42—21no—
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174#501—44no—
175#487—44no—
176#483—24no—
177#483—24no—
178#451—24no—
179#451—24no—
180#441—44no—
181C4×Q16—44no—
182#432—24no—
183#431—24no—
184C2×#107C2312yes—
185C2×#107C2312yes—
186C2×#106C2312yes—
187C2×#106C2312yes—
188C2×#106C2312yes—
189C2×#106C2312yes—
190C2×C4⋊C8C2312yes—
191C2×C4⋊C8C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×C22⋊C8C2311yescharacteristic
205C2×C22⋊C8C2311yescharacteristic
206C2×C22⋊C8C2311yescharacteristic
207C2×C22⋊C8C2311yescharacteristic
208C2×#97C2312yes—
209C2×#97C2312yes—
210C2×#97C2312yes—
211C2×C4×C8C2312yes—
212C2×C4×C8C2312yes—
213C2×C4×C8C2312yes—
214#401—21no—
215#401—21no—
216#400—21no—
217#400—21no—
218#400—21no—
219#400—21no—
220#400—21no—
221#400—21no—
222#400—21no—
223#400—21no—
224#398—21no—
225#398—21no—
226#398—21no—
227#398—21no—
228#398—21no—
229#398—21no—
230#398—22no—
231#398—22no—
232#398—22no—
233#398—22no—
234#395—22no—
235#395—22no—
236#395—22no—
237#395—22no—
238#391—21no—
239#391—21no—
240#391—21no—
241#391—21no—
242#391—22no—
243#391—22no—
244#391—22no—
245#391—22no—
246#391C2311yescharacteristic
247#391C2311yescharacteristic
248#391C2312yes—
249#391C2312yes—
250#391C2311yescharacteristic
251#391C2311yescharacteristic
252#391C2312yes—
253#391C2311yescharacteristic
254#391C2311yescharacteristic
255#391C2312yes—
256#391C2311yescharacteristic
257#391C2311yescharacteristic
258#389—21no—
259#389—21no—
260#389—21no—
261#389—21no—
262#389—21no—
263#389—21no—
264#389—21no—
265#389—21no—
266#389C2311yescharacteristic
267#389C2311yescharacteristic
268#389C2311yescharacteristic
269#389C2312yes—
270#389C2311yescharacteristic
271#389C2312yes—
272#389C2311yescharacteristic
273#389C2311yescharacteristic
274#389C2311yescharacteristic
275#389C2312yes—
276#389C2311yescharacteristic
277#389C2312yes—
278#387—21no—
279#387—21no—
280#387—21no—
281#387—21no—
282#387—22no—
283#387—22no—
284#387—22no—
285#387—22no—
286#387—21no—
287#387—21no—
288#387—21no—
289#387—21no—
290#387—21no—
291#387—21no—
292#387—21no—
293#387—21no—
294#387—21no—
295#387—21no—
296#387—21no—
297#387—21no—
298#387—21no—
299#387—21no—
300#385—21no—
301#385—21no—
302#385—21no—
303#385—21no—
304#385—21no—
305#385—21no—
306#384C2311yescharacteristic
307#383—21no—
308#383—21no—
309#382C2311yescharacteristic
310#381—21no—
311#381—21no—
312#380—21no—
313#380—21no—
314#380C2311yescharacteristic
315#380C2311yescharacteristic
316C4×C4⋊C4—21no—
317C4×C4⋊C4—21no—
318C4×C4⋊C4D411yescharacteristic
319C4×C4⋊C4D411yescharacteristic
320C4×C4⋊C4D411yescharacteristic
321C4×C4⋊C4D411yescharacteristic
322C4×C4⋊C4C2311yescharacteristic
323C4×C4⋊C4C2311yescharacteristic
324C4×C4⋊C4C2311yescharacteristic
325C4×C4⋊C4C2311yescharacteristic
326C4×C4⋊C4C2311yescharacteristic
327C4×C4⋊C4C2311yescharacteristic
328C4×C22⋊C4—21no—
329C4×C22⋊C4—21no—
330C2×#95—21no—
331C2×#95—21no—
332C2×#95—21no—
333C2×#95—21no—
334C2×#95—21no—
335C2×#95—21no—
336C2×#95D411yescharacteristic
337C2×#95D411yescharacteristic
338#340C2312yes—
339#340C2312yes—
340#340C2312yes—
341#340C2312yes—
342#340C2312yes—
343#340C2312yes—
344#340C2312yes—
345#340C2312yes—
346#340C2312yes—
347#340C2312yes—
348#340C2312yes—
349#340C2312yes—
350#336C2312yes—
351#336C2312yes—
352#336C2312yes—
353#336C2312yes—
354C22×Q8—24no—
355C22×Q8—21no—
356C22×Q8—22no—
357C22×Q8—22no—
358C22×Q8—22no—
359C22×Q8—22no—
360C22×Q8—42no—
361C22×Q8—44no—
362C22×Q8—44no—
363C22×Q8—82no—
364C22×Q8C2411yescharacteristic
365C22×Q8C2411yescharacteristic
366C22×Q8C2412yes—
367C23×C4—21no—
368C23×C4—21no—
369C23×C4—21no—
370C23×C4—21no—
371C23×C4C2×D411yescharacteristic
372C23×C4C2×D411yescharacteristic
373C23×C4C2×D411yescharacteristic
374C23×C4C2×D411yescharacteristic
375C23×C4C2×D411yescharacteristic
376C23×C4C2×D411yescharacteristic
377C23×C4C2411yescharacteristic
378C2×Q16—24no—
379C2×Q16—24no—
380C2×Q16—24no—
381C2×Q16—24no—
382C2×Q16—42no—
383C2×Q16—42no—
384C22×C8C2412yes—
385C22×C8C2412yes—
386C22×C8C2412yes—
387C22×C8C2412yes—
388C4⋊Q8—24no—
389C4⋊Q8—24no—
390C4⋊Q8—42no—
391C4⋊Q8—42no—
392C4⋊Q8—42no—
393C4⋊Q8—44no—
394C4⋊Q8—44no—
395#125—42no—
396#125—44no—
397#125—44no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402C4×Q8—24no—
403C4×Q8—24no—
404C4×Q8—42no—
405C4×Q8—42no—
406C4×Q8—42no—
407C4×Q8—42no—
408C4×Q8—44no—
409C4×Q8—44no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—24no—
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—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4—44no—
446C2×C4⋊C4—44no—
447C2×C4⋊C4—82no—
448C2×C4⋊C4—82no—
449C2×C4⋊C4C2×D411yescharacteristic
450C2×C4⋊C4C2×D411yescharacteristic
451C2×C4⋊C4C2×D411yescharacteristic
452C2×C4⋊C4C2×D411yescharacteristic
453C2×C4⋊C4C2×D411yescharacteristic
454C2×C4⋊C4C2×D411yescharacteristic
455C2×C4⋊C4C2×D411yescharacteristic
456C2×C4⋊C4C2×D411yescharacteristic
457C2×C4⋊C4C2412yes—
458C2×C4⋊C4C2412yes—
459C2×C4⋊C4C2411yescharacteristic
460C2×C4⋊C4C2411yescharacteristic
461C2×C4⋊C4C2411yescharacteristic
462C2×C4⋊C4C2411yescharacteristic
463C2×C4⋊C4C2411yescharacteristic
464C2×C4⋊C4C2411yescharacteristic
465C2×C4⋊C4C2412yes—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42—22no—
473C2×C42—22no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—21no—
478C2×C42—42no—
479C2×C42—42no—
480C2×C42—44no—
481C2×C42C2×D411yescharacteristic
482C2×C42C2×D411yescharacteristic
483C2×C42C2×D411yescharacteristic
484C2×C42C2×D411yescharacteristic
485C2×C42C2×D411yescharacteristic
486C2×C42C2×D411yescharacteristic
487C2×C42C2411yescharacteristic
488C2×C42C2411yescharacteristic
489C2×C42C2411yescharacteristic
490C2×C42C2411yescharacteristic
491C2×C42C2411yescharacteristic
492C2×C42C2411yescharacteristic
493#107—24no—
494#107—42no—
495#106—24no—
496#106—24no—
497#106—24no—
498#106—42no—
499C4⋊C8—24no—
500C4⋊C8—24no—
501#103—24no—
502#103—24no—
503#103—24no—
504#103—24no—
505#103—24no—
506#103—24no—
507#103—24no—
508#103—24no—
509#103—42no—
510#103—42no—
511#103—42no—
512#103—42no—
513C22⋊C8—22no—
514C22⋊C8—22no—
515C22⋊C8#4114yes—
516C22⋊C8#4114yes—
517#97—24no—
518#97—42no—
519#97—42no—
520C4×C8—24no—
521C4×C8—42no—
522C4×C8—42no—
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—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—21no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95—21no—
557#95—21no—
558#95—21no—
559#95—21no—
560#95—21no—
561#95—21no—
562#95—21no—
563#95—21no—
564#95—21no—
565#95C2×D411yescharacteristic
566#95C2×D411yescharacteristic
567#95C2×D411yescharacteristic
568#95C2×D411yescharacteristic
569#95C2×D411yescharacteristic
570#95C2×D411yescharacteristic
571#95C2×D411yescharacteristic
572#95C2×D411yescharacteristic
573C24C22×D411yescharacteristic
574C2×Q8—24no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—22no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—44no—
589C2×Q8—44no—
590C2×Q8—48no—
591C2×Q8—48no—
592C2×Q8—42no—
593C2×Q8—44no—
594C2×Q8—42no—
595C2×Q8—44no—
596C2×Q8—82no—
597C2×Q8—82no—
598C2×Q8—816no—
599C2×Q82−1+414yes—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4C22×D411yescharacteristic
645C22×C4C22×D411yescharacteristic
646C22×C4C22×D411yescharacteristic
647C22×C4C22×D411yescharacteristic
648C22×C4C22×D411yescharacteristic
649C22×C4C22×D411yescharacteristic
650C22×C4C22×D411yescharacteristic
651C22×C4C22×D411yescharacteristic
652C22×C4C22×D411yescharacteristic
653C22×C4C22×D411yescharacteristic
654C22×C4C22×D411yescharacteristic
655C22×C4C22×D411yescharacteristic
656C22×C4C22×D411yescharacteristic
657C22×C4C2×#4112yes—
658C22×C4C2×#4112yes—
659C22×C4C2511yescharacteristic
660Q16—48no—
661Q16—48no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—22no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—22no—
672C2×C8C2×#4114yes—
673C2×C8C2×#4114yes—
674C4⋊C4—24no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—41no—
694C4⋊C4—41no—
695C4⋊C4—44no—
696C4⋊C4—44no—
697C4⋊C4—44no—
698C4⋊C4—44no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C4⋊C4—42no—
702C4⋊C4—42no—
703C4⋊C4—42no—
704C4⋊C4—42no—
705C4⋊C4—42no—
706C4⋊C4—42no—
707C4⋊C4—42no—
708C4⋊C4—42no—
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—81no—
718C4⋊C4—81no—
719C4⋊C4—81no—
720C4⋊C4—81no—
721C4⋊C4—81no—
722C4⋊C4—81no—
723C4⋊C4#13714yes—
724C4⋊C4H(5,𝔽2)14yes—
725C22⋊C4—42no—
726C22⋊C4—42no—
727C22⋊C4—42no—
728C22⋊C4—42no—
729C42—22no—
730C42—22no—
731C42—21no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—22no—
736C42—22no—
737C42—22no—
738C42—22no—
739C42—41no—
740C42—41no—
741C42—41no—
742C42—41no—
743C42—44no—
744C42—44no—
745C42—42no—
746C42—42no—
747C42—81no—
748C42—81no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23#53212yes—
754C23#57712yes—
755C23#57812yes—
756C23C23×D411yescharacteristic
757Q8—24no—
758Q8—24no—
759Q8—48no—
760Q8—42no—
761Q8—42no—
762Q8—42no—
763Q8—42no—
764Q8—42no—
765Q8—42no—
766Q8—88no—
767Q8—88no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—48no—
811C2×C4—48no—
812C2×C4—44no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—42no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—42no—
847C2×C4—82no—
848C2×C4—84no—
849C2×C4—84no—
850C2×C4#53212yes—
851C2×C4C2×#13712yes—
852C2×C4C2×#13712yes—
853C2×C4C2×#13712yes—
854C2×C4#57512yes—
855C2×C4C22×#4111yescharacteristic
856C2×C4C22×#4111yescharacteristic
857C2×C4C2×H(5,𝔽2)12yes—
858C2×C4C2×2−1+412yes—
859C8—24no—
860C8—24no—
861C8—42no—
862C8—42no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22#317814yes—
870C22C2×#53211yescharacteristic
871C22#348411yescharacteristic
872C22#348611yescharacteristic
873C22C22×#13711yescharacteristic
874C22C2×#57511yescharacteristic
875C22C2×#57711yescharacteristic
876C22C2×#57811yescharacteristic
877C4—22no—
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—41no—
883C4—41no—
884C4—41no—
885C4—44no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—44no—
890C4—41no—
891C4—41no—
892C4—82no—
893C4—81no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4—81no—
898C4—81no—
899C4—81no—
900C4—82no—
901C4—81no—
902C4#352012yes—
903C4#352012yes—
904C2—24no—
905C2#3539711yescharacteristic
906C2C2×#317811yescharacteristic
907C2#6070111yescharacteristic
908C2#6160111yescharacteristic
909C2#6160211yescharacteristic
910C2#6183811yescharacteristic
911C2#6184211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #29089C2semidirect
5. #29081C2semidirect
6. #28970C2semidirect
7. #28947C2semidirect
9. #26838C2semidirect
10. #26822C2semidirect
11. #26497C2semidirect
12. #26489C2semidirect

Maximal subgroups

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

subgroupindex
#350872
C2×#24512
#291062
#290892
#290812
#289702
#289472
#283132
#268382
#268222
#264972
#264892
#259022
#258162
#246092
#246012
#245082
#245022
#220842
#220782
#214552
C4×#4512
#205352