Finite Group Databasebeta

← #6795102

Subgroups — #6795102

Order 512.

1566 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36200C211yesmaximal, characteristic
2C2×#2568C211yesmaximal, characteristic, complemented
3#32960C211yesmaximal, characteristic, complemented
4#32453C212yesmaximal, complemented
5#32441C212yesmaximal, complemented
6#32369C212yesmaximal, complemented
7#32355C212yesmaximal, complemented
8#29912C211yesmaximal, characteristic
9#29912C211yesmaximal, characteristic
10#28547C212yesmaximal, complemented
11#27742C212yesmaximal, complemented
12#27589C211yesmaximal, characteristic, complemented
13#27583C211yesmaximal, characteristic, complemented
14#25816C211yesmaximal, characteristic, complemented
15#25468C212yesmaximal, complemented
16#24697C212yesmaximal, complemented
17#24509C211yesmaximal, characteristic
18#24503C211yesmaximal, characteristic
19#24299C211yesmaximal, characteristic
20#22601C211yesmaximal, characteristic, complemented
21#21986C211yesmaximal, characteristic, complemented
22#21983C211yesmaximal, characteristic, complemented
23#21454C211yesmaximal, characteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C2×#501C2212yes—
27C2×#479C2212yes—
28C2×#476C2212yes—
29C2×#448C2211yescharacteristic
30C2×#440C2212yes—
31C2×#432C2211yescharacteristic
32C2×#431C2211yescharacteristic
33#2854C2211yescharacteristic
34#2854C2211yescharacteristic
35#2851C2211yescharacteristic
36#2570C2211yescharacteristic
37#2568—21no—
38#2568—21no—
39#2568—21no—
40#2568—21no—
41#2568C2212yes—
42#2568C2212yes—
43#2568C2212yes—
44#2568C2212yes—
45#2566C2211yescharacteristic
46#2529—21no—
47#2525—21no—
48#2515—21no—
49#2513C2211yescharacteristic
50#2512C2211yescharacteristic
51#2509C2211yescharacteristic
52#2507C2211yescharacteristic
53#2481—21no—
54#2419—21no—
55#2413—21no—
56C2×#400—21no—
57C2×#400—21no—
58#2373—21no—
59#2370C2211yescharacteristic
60#2359—21no—
61#2357C2211yescharacteristic
62C4×#121C2211yescharacteristic
63C2×#391—21no—
64C2×#391—21no—
65C2×#391C2211yescharacteristic
66C2×#391C2211yescharacteristic
67#2285C2211yescharacteristic
68#2283C2211yescharacteristic
69C2×#382C2211yescharacteristic
70C2×#382C2211yescharacteristic
71C2×C4×C4⋊C4C2211yescharacteristic
72#2101C2212yes—
73#2101C2212yes—
74#2097C2212yes—
75#2096C2212yes—
76#2092C2212yes—
77#2092C2212yes—
78#2085C2212yes—
79#2085C2212yes—
80#2074C2212yes—
81#2073C2212yes—
82#2073C2212yes—
83#2072C2212yes—
84#2068C2212yes—
85#2066C2212yes—
86#2058C2212yes—
87#2058C2212yes—
88#2057C2212yes—
89#2055C2212yes—
90#2055C2212yes—
91#2023C2212yes—
92#1993C2212yes—
93#1987C2212yes—
94#1973C2212yes—
95#1968C2212yes—
96#1949C2212yes—
97#1949C2212yes—
98#1949C2212yes—
99#1949C2212yes—
100#1940C2212yes—
101#1935C2212yes—
102#1933C2212yes—
103#1928C2212yes—
104#1927C2212yes—
105#1927C2212yes—
106#1927C2212yes—
107#1917C2212yes—
108#1916C2212yes—
109#1880C2212yes—
110#1874C2211yescharacteristic
111#1874C2211yescharacteristic
112#1874C2211yescharacteristic
113#1865C2212yes—
114#1863C2212yes—
115#1863C2212yes—
116#1853C2211yescharacteristic
117#1853C2211yescharacteristic
118#1853C2211yescharacteristic
119#1853C2211yescharacteristic
120#1853C2211yescharacteristic
121#1852C2211yescharacteristic
122#1852C2211yescharacteristic
123#1852C2211yescharacteristic
124#1852C2211yescharacteristic
125#1847C2212yes—
126#1846C2212yes—
127#1836C2212yes—
128#1835C2212yes—
129#1817C2211yescharacteristic
130#1817C2211yescharacteristic
131#1805C2212yes—
132#1797C2211yescharacteristic
133#1787C2211yescharacteristic
134#1787C2211yescharacteristic
135#1787C2211yescharacteristic
136#1771C2212yes—
137#1763C2212yes—
138#1749C2211yescharacteristic
139C23×Q8—21no—
140C23×Q8C2311yescharacteristic
141C22×SD16C2312yes—
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8—21no—
144C2×C4⋊Q8—44no—
145C2×C4⋊Q8C2312yes—
146C2×C4⋊Q8C2312yes—
147C2×#126—21no—
148C2×#125C2311yescharacteristic
149C2×#123—21no—
150C2×#123—21no—
151C2×#121C2311yescharacteristic
152C2×C4×Q8—21no—
153C2×C4×Q8—21no—
154C2×C4×Q8—44no—
155C2×C4×Q8C2312yes—
156C2×C4×Q8C2312yes—
157C2×C4×D4—21no—
158C2×C4×D4C2311yescharacteristic
159C2×#117—21no—
160C22×C4⋊C4—21no—
161C22×C4⋊C4—21no—
162C22×C4⋊C4D411yescharacteristic
163C22×C4⋊C4D411yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C42—21no—
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171#501—44no—
172#479—44no—
173#476—44no—
174#448—24no—
175#440—44no—
176#432—24no—
177#431—24no—
178C2×#107C2312yes—
179C2×#107C2312yes—
180C2×#107C2312yes—
181C2×#107C2312yes—
182C2×#106C2312yes—
183C2×#106C2312yes—
184C2×#106C2312yes—
185C2×#106C2312yes—
186C2×#106C2312yes—
187C2×C4⋊C8C2312yes—
188C2×C4⋊C8C2312yes—
189C2×C4⋊C8C2312yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#103C2312yes—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×C22⋊C8C2311yescharacteristic
201C2×C22⋊C8C2311yescharacteristic
202C2×C22⋊C8C2311yescharacteristic
203C2×C22⋊C8C2311yescharacteristic
204C2×#97C2312yes—
205C2×#97C2312yes—
206C2×C4×C8C2312yes—
207#400—21no—
208#400—21no—
209#400—22no—
210#400—22no—
211#400—22no—
212#400—22no—
213#400—22no—
214#400—22no—
215#400—22no—
216#400—22no—
217#400—21no—
218#398—21no—
219#398—21no—
220#398—21no—
221#397—21no—
222#397—21no—
223#397—21no—
224#396—21no—
225#396—21no—
226#396—21no—
227#391—22no—
228#391—22no—
229#391—22no—
230#391—22no—
231#391—22no—
232#391—22no—
233#391—22no—
234#391—22no—
235#391—21no—
236#391—21no—
237#391—21no—
238#391—21no—
239#391C2312yes—
240#391C2312yes—
241#391C2312yes—
242#391C2312yes—
243#390C2311yescharacteristic
244#390C2311yescharacteristic
245#390C2311yescharacteristic
246#390C2311yescharacteristic
247#390C2311yescharacteristic
248#389—21no—
249#389—21no—
250#389—21no—
251#389C2311yescharacteristic
252#389C2311yescharacteristic
253#389C2311yescharacteristic
254#389C2311yescharacteristic
255#389C2311yescharacteristic
256#389C2311yescharacteristic
257#389C2311yescharacteristic
258#388—21no—
259#388—21no—
260#388—21no—
261#388—21no—
262#388—21no—
263#388—21no—
264#388—21no—
265#388—21no—
266#388—21no—
267#388—21no—
268#387—21no—
269#387—21no—
270#387—21no—
271#387—21no—
272#387—21no—
273#387—21no—
274#387—21no—
275#387—21no—
276#386—21no—
277#386—21no—
278#386—21no—
279#385—21no—
280#385—21no—
281#385—21no—
282#385—21no—
283#384C2311yescharacteristic
284#384C2311yescharacteristic
285#383—21no—
286#382—21no—
287#382—21no—
288#382—21no—
289#382—21no—
290#382—21no—
291#382C2311yescharacteristic
292#382C2312yes—
293#382C2312yes—
294#382C2312yes—
295#382C2312yes—
296#382C2311yescharacteristic
297#382C2311yescharacteristic
298#381—21no—
299#381—21no—
300#380—21no—
301#380C2311yescharacteristic
302#380C2311yescharacteristic
303#380C2311yescharacteristic
304C4×C4⋊C4—21no—
305C4×C4⋊C4—21no—
306C4×C4⋊C4D411yescharacteristic
307C4×C4⋊C4D411yescharacteristic
308C4×C4⋊C4D411yescharacteristic
309C4×C4⋊C4D411yescharacteristic
310C4×C4⋊C4C2311yescharacteristic
311C4×C4⋊C4C2311yescharacteristic
312C4×C4⋊C4C2311yescharacteristic
313C4×C4⋊C4C2311yescharacteristic
314C4×C4⋊C4C2311yescharacteristic
315C4×C4⋊C4C2311yescharacteristic
316C4×C4⋊C4C2311yescharacteristic
317C4×C4⋊C4C2311yescharacteristic
318C4×C4⋊C4C2311yescharacteristic
319C4×C22⋊C4—21no—
320C4×C22⋊C4—21no—
321C4×C22⋊C4—21no—
322#376—21no—
323C2×#95—21no—
324C2×#95—21no—
325C2×#95—21no—
326C2×#95—21no—
327C2×#95—21no—
328C2×#95—21no—
329C2×#95—21no—
330C2×#95—21no—
331C2×#95D411yescharacteristic
332C2×#95D411yescharacteristic
333#340C2312yes—
334#340C2312yes—
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#340C2312yes—
341#340C2312yes—
342#340C2312yes—
343#340C2312yes—
344#340C2312yes—
345#336C2312yes—
346#336C2312yes—
347#336C2312yes—
348#336C2312yes—
349#336C2312yes—
350#336C2312yes—
351C22×Q8—24no—
352C22×Q8—21no—
353C22×Q8—22no—
354C22×Q8—22no—
355C22×Q8—22no—
356C22×Q8—22no—
357C22×Q8—42no—
358C22×Q8—44no—
359C22×Q8—44no—
360C22×Q8—44no—
361C22×Q8C2412yes—
362C22×D4—21no—
363C22×D4C2411yescharacteristic
364C23×C4—21no—
365C23×C4—21no—
366C23×C4—21no—
367C23×C4—21no—
368C23×C4—21no—
369C23×C4C2×D411yescharacteristic
370C23×C4C2×D411yescharacteristic
371C23×C4C2×D411yescharacteristic
372C23×C4C2×D411yescharacteristic
373C23×C4C2×D411yescharacteristic
374C23×C4C2×D411yescharacteristic
375C23×C4C2411yescharacteristic
376C2×SD16—24no—
377C2×SD16—24no—
378C2×SD16—42no—
379C22×C8C2412yes—
380C22×C8C2412yes—
381C22×C8C2412yes—
382C22×C8C2412yes—
383C4⋊Q8—24no—
384C4⋊Q8—24no—
385C4⋊Q8—42no—
386C4⋊Q8—42no—
387C4⋊Q8—44no—
388C4⋊Q8—44no—
389#126—44no—
390#125—24no—
391#123—44no—
392#123—82no—
393#121—22no—
394#121—22no—
395C4×Q8—24no—
396C4×Q8—24no—
397C4×Q8—42no—
398C4×Q8—42no—
399C4×Q8—44no—
400C4×Q8—44no—
401C4×D4—24no—
402C4×D4—82no—
403#117—82no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4—42no—
429C2×C4⋊C4—44no—
430C2×C4⋊C4—44no—
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⋊C4C2412yes—
440C2×C4⋊C4C2412yes—
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2411yescharacteristic
448C2×C4⋊C4C2411yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C42—22no—
465C2×C42—22no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—24no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—44no—
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D411yescharacteristic
480C2×C42C2×D411yescharacteristic
481C2×C42C2×D411yescharacteristic
482C2×C42C2×D411yescharacteristic
483C2×C42C2411yescharacteristic
484C2×C42C2411yescharacteristic
485C2×C42C2411yescharacteristic
486C2×C42C2411yescharacteristic
487C2×C42C2411yescharacteristic
488C2×C42C2411yescharacteristic
489#107—42no—
490#107—42no—
491#107—42no—
492#107—42no—
493#106—42no—
494#106—42no—
495#106—42no—
496#106—42no—
497#106—42no—
498C4⋊C8—24no—
499C4⋊C8—24no—
500C4⋊C8—24no—
501#103—24no—
502#103—24no—
503#103—24no—
504#103—24no—
505#103—42no—
506#103—42no—
507#103—42no—
508#102—42no—
509#102—42no—
510#102—42no—
511C22⋊C8—22no—
512C22⋊C8—22no—
513C22⋊C8—22no—
514C22⋊C8#4114yes—
515#97—24no—
516#97—24no—
517C4×C8—24no—
518#95—22no—
519#95—22no—
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—21no—
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#95C2×D411yescharacteristic
556#95C2×D411yescharacteristic
557#95C2×D411yescharacteristic
558#95C2×D411yescharacteristic
559#95C2×D411yescharacteristic
560#95C2×D411yescharacteristic
561#95C2×D411yescharacteristic
562#95C2×D411yescharacteristic
563C24—21no—
564C24C22×D411yescharacteristic
565C2×Q8—24no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—48no—
572C2×Q8—48no—
573C2×Q8—42no—
574C2×Q8—44no—
575C2×Q8—44no—
576C2×Q8—44no—
577C2×Q8—44no—
578C2×Q8—44no—
579C2×Q8—42no—
580C2×Q8—44no—
581C2×Q8—816no—
582C2×Q82−1+414yes—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—22no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—42no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—24no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—21no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—81no—
635C22×C4—81no—
636C22×C4C22×D411yescharacteristic
637C22×C4C22×D411yescharacteristic
638C22×C4C22×D411yescharacteristic
639C22×C4C22×D411yescharacteristic
640C22×C4C22×D411yescharacteristic
641C22×C4C22×D411yescharacteristic
642C22×C4C22×D411yescharacteristic
643C22×C4C22×D411yescharacteristic
644C22×C4C22×D411yescharacteristic
645C22×C4C22×D411yescharacteristic
646C22×C4C22×D411yescharacteristic
647C22×C4C22×D411yescharacteristic
648C22×C4C22×D411yescharacteristic
649C22×C4C2×#4112yes—
650C22×C42−1+412yes—
651C22×C4C2511yescharacteristic
652SD16—48no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8C2×#4114yes—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—21no—
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—21no—
681C4⋊C4—41no—
682C4⋊C4—41no—
683C4⋊C4—41no—
684C4⋊C4—41no—
685C4⋊C4—41no—
686C4⋊C4—41no—
687C4⋊C4—42no—
688C4⋊C4—44no—
689C4⋊C4—42no—
690C4⋊C4—42no—
691C4⋊C4—44no—
692C4⋊C4—42no—
693C4⋊C4—42no—
694C4⋊C4—42no—
695C4⋊C4—44no—
696C4⋊C4—44no—
697C4⋊C4—42no—
698C4⋊C4—42no—
699C4⋊C4—42no—
700C4⋊C4—81no—
701C4⋊C4—81no—
702C4⋊C4—81no—
703C4⋊C4—81no—
704C4⋊C4—81no—
705C4⋊C4—81no—
706C4⋊C4—81no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—81no—
718C22⋊C4—81no—
719C22⋊C4—81no—
720C22⋊C4—81no—
721C22⋊C4—81no—
722C42—22no—
723C42—22no—
724C42—22no—
725C42—22no—
726C42—22no—
727C42—22no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42—21no—
732C42—22no—
733C42—21no—
734C42—21no—
735C42—21no—
736C42—21no—
737C42—44no—
738C42—42no—
739C42—44no—
740C42—81no—
741C42—81no—
742C42—81no—
743C42—81no—
744C42H(5,𝔽2)14yes—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23#54712yes—
757C23#57512yes—
758C23#57712yes—
759C23C23×D411yescharacteristic
760Q8—24no—
761Q8—24no—
762Q8—48no—
763Q8—42no—
764Q8—42no—
765Q8—88no—
766Q8—88no—
767D4—42no—
768D4—42no—
769D4—84no—
770C2×C4—28no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—21no—
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—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—24no—
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—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—44no—
810C2×C4—48no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
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—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—42no—
845C2×C4—82no—
846C2×C4—82no—
847C2×C4—84no—
848C2×C4—84no—
849C2×C4—84no—
850C2×C4—162no—
851C2×C4#53512yes—
852C2×C4#53512yes—
853C2×C4#54712yes—
854C2×C4#57512yes—
855C2×C4C22×#4111yescharacteristic
856C2×C4C2×H(5,𝔽2)12yes—
857C2×C4C2×2−1+412yes—
858C2×C4C2×2−1+411yescharacteristic
859C8—24no—
860C8—42no—
861C8—42no—
862C8—42no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22#335014yes—
877C22C2×#53511yescharacteristic
878C22C2×#54711yescharacteristic
879C22#348611yescharacteristic
880C22C2×#57511yescharacteristic
881C22C2×#57511yescharacteristic
882C22C2×#57711yescharacteristic
883C22#358611yescharacteristic
884C4—22no—
885C4—22no—
886C4—22no—
887C4—22no—
888C4—44no—
889C4—41no—
890C4—41no—
891C4—41no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—41no—
897C4—41no—
898C4—81no—
899C4—81no—
900C4—82no—
901C4—82no—
902C4—81no—
903C4—81no—
904C4—81no—
905C4—81no—
906C4—82no—
907C4—81no—
908C4#352012yes—
909C4#353812yes—
910C2—24no—
911C2—161no—
912C2#3891711yescharacteristic
913C2#6079911yescharacteristic
914C2#6081311yescharacteristic
915C2C2×#335011yescharacteristic
916C2#6125711yescharacteristic
917C2#6183211yescharacteristic
918C2#6183611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
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
2. C2×#2568C2semidirect
3. #32960C2semidirect
4. #32453C2semidirect
5. #32441C2semidirect
6. #32369C2semidirect
7. #32355C2semidirect
10. #28547C2semidirect
11. #27742C2semidirect
12. #27589C2semidirect
13. #27583C2semidirect
14. #25816C2semidirect
15. #25468C2semidirect
16. #24697C2semidirect
20. #22601C2semidirect
21. #21986C2semidirect
22. #21983C2semidirect

Maximal subgroups

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

subgroupindex
#362002
C2×#25682
#329602
#324532
#324412
#323692
#323552
#299122
#285472
#277422
#275892
#275832
#258162
#254682
#246972
#245092
#245032
#242992
#226012
#219862
#219832
#214542