Finite Group Databasebeta

← #6461851

Subgroups — #6461851

Order 512.

1813 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34255C211yesmaximal, characteristic
2#34254C211yesmaximal, characteristic, complemented
3#29548C212yesmaximal, complemented
4#29547C212yesmaximal, complemented
5#29544C212yesmaximal, complemented
6#29543C212yesmaximal, complemented
7#29538C212yesmaximal, complemented
8#29537C212yesmaximal, complemented
9#29535C212yesmaximal, complemented
10#29534C212yesmaximal, complemented
11#23666C211yesmaximal, characteristic, complemented
12#23619C211yesmaximal, characteristic, complemented
13#23618C211yesmaximal, characteristic
14C2×#2055C211yesmaximal, characteristic
15#21066C211yesmaximal, characteristic, complemented
16#21065C211yesmaximal, characteristic
17#21035C211yesmaximal, characteristic, complemented
18#21035C211yesmaximal, characteristic, complemented
19#20936C211yesmaximal, characteristic
20#20933C211yesmaximal, characteristic
21#20877C211yesmaximal, characteristic, complemented
22#20876C211yesmaximal, characteristic
23#20755C211yesmaximal, characteristic, complemented
24C23×SD16C2211yescharacteristic
25C2×#519C2211yescharacteristic
26C2×#518C2211yescharacteristic
27C2×#428C2211yescharacteristic
28C2×#428C2211yescharacteristic
29C2×#427C2211yescharacteristic
30C2×#423C2211yescharacteristic
31C22×C4⋊C8C2211yescharacteristic
32C2×#419C2211yescharacteristic
33C2×#419C2211yescharacteristic
34C2×#418C2211yescharacteristic
35C2×#418C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#102C2211yescharacteristic
38#2357—21no—
39#2357—21no—
40#2356—21no—
41#2356—21no—
42#2355—21no—
43#2355—21no—
44#2354—21no—
45#2354—21no—
46#2343—22no—
47#2343—22no—
48#2342—22no—
49#2342—22no—
50#2320C2212yescomplemented
51#2320C2212yescomplemented
52#2319C2212yes—
53#2319C2212yes—
54#2317C2211yescharacteristic
55#2317C2211yescharacteristic
56#2310C2211yescharacteristic
57#2309C2211yescharacteristic
58#2296C2211yescharacteristic
59#2296C2211yescharacteristic
60#2295C2212yescomplemented
61#2295C2212yescomplemented
62C2×#391C2211yescharacteristic
63#2293C2212yes—
64#2293C2212yes—
65C2×#390C2211yescharacteristic
66#2274C2211yescharacteristic
67#2274C2211yescharacteristic
68C4×#117C2211yescharacteristic
69#2088C2211yescharacteristic, complemented
70#2088C2211yescharacteristic, complemented
71#2088C2211yescharacteristic, complemented
72#2088C2211yescharacteristic, complemented
73#2087C2211yescharacteristic, complemented
74#2087C2211yescharacteristic, complemented
75#2086C2211yescharacteristic, complemented
76#2086C2211yescharacteristic, complemented
77#2068C2212yescomplemented
78#2068C2212yescomplemented
79#2067C2212yes—
80#2067C2212yes—
81#2066C2212yescomplemented
82#2066C2212yescomplemented
83#2065C2212yes—
84#2065C2212yes—
85#2055C2212yes—
86#2055C2212yes—
87#2055C2212yes—
88#2055C2212yes—
89#1928C2212yescomplemented
90#1928C2212yescomplemented
91#1927C2212yescomplemented
92#1927C2212yescomplemented
93#1926C2212yes—
94#1926C2212yes—
95#1925C2212yes—
96#1925C2212yes—
97#1921C2212yescomplemented
98#1921C2212yescomplemented
99#1920C2212yescomplemented
100#1920C2212yescomplemented
101#1919C2212yescomplemented
102#1919C2212yescomplemented
103#1918C2212yescomplemented
104#1918C2212yescomplemented
105#1880C2212yes—
106#1880C2212yes—
107#1880C2212yes—
108#1880C2212yes—
109#1877C2212yes—
110#1877C2212yes—
111#1877C2212yes—
112#1877C2212yes—
113#1865C2212yescomplemented
114#1865C2212yescomplemented
115#1864C2212yes—
116#1864C2212yes—
117#1863C2212yescomplemented
118#1863C2212yescomplemented
119#1862C2212yes—
120#1862C2212yes—
121#1832C2212yescomplemented
122#1832C2212yescomplemented
123#1831C2212yescomplemented
124#1831C2212yescomplemented
125#1736C2211yescharacteristic
126#1736C2211yescharacteristic
127#1735C2211yescharacteristic
128#1735C2211yescharacteristic
129#1735C2211yescharacteristic
130C2×#340C2211yescharacteristic
131#1729C2211yescharacteristic
132#1729C2211yescharacteristic
133#1729C2211yescharacteristic
134#1729C2211yescharacteristic
135C23×Q8C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C22×SD16—24no—
138C22×SD16—24no—
139C22×SD16—42no—
140C22×SD16C2312yes—
141C22×SD16C2312yes—
142C22×M16C2311yescharacteristic
143C22×M16C2311yescharacteristic
144C23×C8C2311yescharacteristic
145C23×C8C2311yescharacteristic
146#519—24no—
147#519—24no—
148#518—24no—
149#518—24no—
150C2×C4×Q8—21no—
151C2×C4×Q8—21no—
152C2×C4×Q8C2312yes—
153C2×C4×Q8C2312yes—
154C2×C4×D4—21no—
155C2×C4×D4—21no—
156C2×C4×D4C2312yes—
157C2×C4×D4C2312yes—
158C2×#117—22no—
159C2×#117—22no—
160C2×#117—22no—
161C2×#117C2311yescharacteristic
162C2×#117C2311yescharacteristic
163C2×#117C2311yescharacteristic
164C2×#117C2311yescharacteristic
165C2×#117C2311yescharacteristic
166C2×#117C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C22⋊C4—22no—
170C22×C22⋊C4—21no—
171C22×C22⋊C4—21no—
172C22×C42C2311yescharacteristic
173#428—24no—
174#428—24no—
175#427—42no—
176C2×#107C2312yes—
177C2×#107C2312yes—
178C2×#107C2311yescharacteristic
179C2×#107C2311yescharacteristic
180C2×#106C2312yes—
181C2×#106C2312yes—
182C2×#106C2311yescharacteristic
183C2×#106C2311yescharacteristic
184#423—42no—
185C2×C4⋊C8—42no—
186C2×C4⋊C8C2311yescharacteristic
187C2×C4⋊C8C2311yescharacteristic
188C2×C4⋊C8C2311yescharacteristic
189C2×C4⋊C8C2311yescharacteristic
190C2×C4⋊C8C2312yes—
191C2×C4⋊C8C2312yes—
192#419—24no—
193#419—42no—
194#418—24no—
195#418—42no—
196C2×#103—24no—
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#102—24no—
204C2×#102C2312yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2312yes—
209C2×#102C2312yes—
210#391—21no—
211#391—21no—
212#391—21no—
213#391—21no—
214#391C2312yes—
215#391C2312yes—
216#391C2312yes—
217#391C2312yes—
218#390—21no—
219#390—21no—
220#390—21no—
221#390—21no—
222#390C2312yes—
223#390C2312yes—
224#390C2312yes—
225#390C2312yes—
226#389C2312yes—
227#389C2312yes—
228#389C2312yes—
229#389C2312yes—
230#389C2311yescharacteristic
231#389C2311yescharacteristic
232#389C2311yescharacteristic
233#389C2311yescharacteristic
234#389C2311yescharacteristic
235#389C2311yescharacteristic
236#389C2311yescharacteristic
237#389C2311yescharacteristic
238#388—22no—
239#388—22no—
240#388—22no—
241#388—22no—
242#388—22no—
243#388—22no—
244#388—22no—
245#388—22no—
246#387—22no—
247#387—22no—
248#387—22no—
249#387—22no—
250#387—22no—
251#387—22no—
252#387—22no—
253#387—22no—
254#385—21no—
255#385—21no—
256#385—21no—
257#385—21no—
258#385—22no—
259#385—22no—
260#384—21no—
261#384—21no—
262#383—22no—
263#383—22no—
264#382—21no—
265#382—21no—
266#382—22no—
267#382—22no—
268#381—22no—
269#381—22no—
270#381—22no—
271#380—22no—
272#380—22no—
273#379—22no—
274C4×C4⋊C4—21no—
275C4×C4⋊C4—21no—
276C4×C4⋊C4—21no—
277C4×C4⋊C4—21no—
278C4×C4⋊C4—22no—
279C4×C4⋊C4—22no—
280C4×C4⋊C4—21no—
281C4×C4⋊C4—21no—
282C4×C4⋊C4—21no—
283C4×C4⋊C4—21no—
284C4×C4⋊C4D411yescharacteristic
285C4×C4⋊C4D411yescharacteristic
286C4×C4⋊C4D411yescharacteristic
287C4×C4⋊C4D411yescharacteristic
288C4×C4⋊C4C2312yes—
289C4×C4⋊C4C2312yes—
290C4×C4⋊C4C2312yes—
291C4×C4⋊C4C2312yes—
292C4×C22⋊C4—22no—
293C4×C22⋊C4—22no—
294C4×C22⋊C4—22no—
295C4×C22⋊C4—22no—
296C4×C22⋊C4D412yes—
297C4×C22⋊C4D412yes—
298#376—22no—
299#376—22no—
300#376C2312yes—
301C2×#95—21no—
302C2×#95—21no—
303C43C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2312yes—
307#340C2312yes—
308#340C2312yes—
309#340C2312yes—
310#340C2311yescharacteristic
311#340C2311yescharacteristic
312#340C2311yescharacteristic
313#340C2311yescharacteristic
314#340C2311yescharacteristic
315#340C2311yescharacteristic
316#340C2311yescharacteristic
317#340C2311yescharacteristic
318#340C2311yescharacteristic
319#340C2311yescharacteristic
320#340C2311yescharacteristic
321#340C2311yescharacteristic
322#336C2312yes—
323#336C2312yes—
324#336C2312yes—
325#336C2312yes—
326#336C2312yes—
327#336C2312yes—
328#336C2312yes—
329#336C2312yes—
330C25—21no—
331C22×Q8—21no—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8#4114yes—
338C22×Q8C2412yes—
339C22×D4—21no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4#4114yes—
346C22×D4C2412yes—
347C23×C4—21no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—21no—
351C23×C4—21no—
352C23×C4C2×D411yescharacteristic
353C23×C4C2×D411yescharacteristic
354C23×C4C2411yescharacteristic
355C2×SD16—24no—
356C2×SD16—24no—
357C2×SD16—24no—
358C2×SD16—24no—
359C2×SD16—42no—
360C2×SD16—42no—
361C2×SD16—416no—
362C2×M16—22no—
363C2×M16—22no—
364C2×M16—22no—
365C2×M16—22no—
366C2×M16—22no—
367C2×M16—22no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8—22no—
371C22×C8—22no—
372C22×C8—22no—
373C22×C8—22no—
374C22×C8C2411yescharacteristic
375C22×C8C2411yescharacteristic
376C22×C8C2411yescharacteristic
377C22×C8C2411yescharacteristic
378C22×C8C2412yes—
379C22×C8C2412yes—
380C4×Q8—28no—
381C4×Q8—28no—
382C4×Q8—24no—
383C4×Q8—24no—
384C4×Q8—24no—
385C4×Q8—24no—
386C4×D4—28no—
387C4×D4—28no—
388C4×D4—24no—
389C4×D4—24no—
390C4×D4—24no—
391C4×D4—24no—
392#117—216no—
393#117—22no—
394#117—22no—
395#117—22no—
396#117—22no—
397#117—22no—
398#117—22no—
399#117—22no—
400#117—22no—
401#117—22no—
402#117—22no—
403#117—84no—
404#117—84no—
405#117#4114yes—
406#117#4114yes—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
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—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4C2×D411yescharacteristic
428C2×C4⋊C4C2×D411yescharacteristic
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2412yes—
432C2×C4⋊C4C2412yes—
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2411yescharacteristic
440C2×C4⋊C4C2411yescharacteristic
441C2×C22⋊C4—216no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
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—82no—
457C2×C22⋊C4—82no—
458C2×C22⋊C4C2×D412yes—
459C2×C22⋊C4C2×D412yes—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—22no—
465C2×C42—22no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42C2×D412yes—
473C2×C42C2×D411yescharacteristic
474C2×C42C2×D411yescharacteristic
475C2×C42C2×D412yes—
476C2×C42C2×D412yes—
477C2×C42C2×D412yes—
478C2×C42C2412yes—
479C2×C42C2412yes—
480C2×C42C2411yescharacteristic
481C2×C42C2411yescharacteristic
482#107—24no—
483#107—24no—
484#107—41no—
485#107—41no—
486#106—24no—
487#106—24no—
488#106—41no—
489#106—41no—
490C4⋊C8—41no—
491C4⋊C8—41no—
492C4⋊C8—41no—
493C4⋊C8—41no—
494C4⋊C8—42no—
495C4⋊C8—42no—
496#103—24no—
497#103—24no—
498#103—24no—
499#103—24no—
500#103—42no—
501#103—42no—
502#102—24no—
503#102—24no—
504#102—24no—
505#102—24no—
506#102—42no—
507#102—42no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95—22no—
512#95—21no—
513#95—21no—
514#95—22no—
515#95—22no—
516#95—22no—
517#95—22no—
518#95—21no—
519#95—21no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—21no—
527#95—21no—
528#95—22no—
529#95—22no—
530#95—21no—
531#95—21no—
532#95C2×D412yes—
533#95C2×D412yes—
534#95C2×D412yes—
535#95C2×D412yes—
536C24—22no—
537C24—24no—
538C24—42no—
539C24—42no—
540C24—81no—
541C24—81no—
542C24—81no—
543C24—81no—
544C24C22×D411yescharacteristic
545C2×Q8—24no—
546C2×Q8—22no—
547C2×Q8—28no—
548C2×Q8—28no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—42no—
554C2×Q8—42no—
555C2×Q8—44no—
556C2×Q8—44no—
557C2×Q8C2×#4114yes—
558C2×D4—24no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4C2×#4114yes—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—82no—
596C22×C4—82no—
597C22×C4—82no—
598C22×C4—82no—
599C22×C4—81no—
600C22×C4—81no—
601C22×C4—81no—
602C22×C4—81no—
603C22×C4C22×D412yes—
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D412yes—
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C2×#4112yes—
613C22×C4C2×#4112yes—
614C22×C4C2×#4112yes—
615C22×C4C2×#4112yes—
616C22×C4H(5,𝔽2)12yes—
617C22×C42−1+412yes—
618C22×C4C2511yescharacteristic
619SD16—48no—
620SD16—48no—
621M16—44no—
622M16—44no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—22no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—44no—
642C2×C8—44no—
643C4⋊C4—28no—
644C4⋊C4—28no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—82no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—82no—
675C4⋊C4—81no—
676C4⋊C4—81no—
677C4⋊C4—82no—
678C4⋊C4—82no—
679C4⋊C4C2×#4112yes—
680C4⋊C4C2×#4112yes—
681C4⋊C4C2×#4112yes—
682C4⋊C4C2×#4112yes—
683C22⋊C4—28no—
684C22⋊C4—28no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—44no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—44no—
693C22⋊C4—82no—
694C22⋊C4—82no—
695C22⋊C4—82no—
696C22⋊C4—82no—
697C22⋊C4—82no—
698C22⋊C4—82no—
699C42—28no—
700C42—28no—
701C42—24no—
702C42—24no—
703C42—22no—
704C42—22no—
705C42—24no—
706C42—22no—
707C42—22no—
708C42—22no—
709C42—22no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—21no—
714C42—42no—
715C42—42no—
716C42—42no—
717C42—42no—
718C42—42no—
719C42—82no—
720C42—82no—
721C42—82no—
722C42—82no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—24no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—48no—
735C23—84no—
736C23—84no—
737C23—162no—
738C23—162no—
739C23—162no—
740C23—162no—
741C23#52512yes—
742C23#52512yes—
743C23#53712yes—
744C23C23×D411yescharacteristic
745Q8—24no—
746Q8—24no—
747Q8—48no—
748Q8—42no—
749Q8—42no—
750D4—24no—
751D4—24no—
752D4—48no—
753D4—42no—
754D4—42no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—21no—
783C2×C4—44no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—48no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—82no—
814C2×C4—88no—
815C2×C4—88no—
816C2×C4—162no—
817C2×C4—162no—
818C2×C4#52512yes—
819C2×C4#52512yes—
820C2×C4#53712yes—
821C2×C4#55114yes—
822C2×C4#55214yes—
823C2×C4#55214yes—
824C2×C4#55514yes—
825C2×C4#57712yes—
826C2×C4C22×#4111yescharacteristic
827C2×C4C22×#4111yescharacteristic
828C2×C4C22×#4111yescharacteristic
829C2×C4C22×#4111yescharacteristic
830C2×C4C2×H(5,𝔽2)11yescharacteristic
831C2×C4C2×2−1+411yescharacteristic
832C8—41no—
833C8—41no—
834C8—41no—
835C8—41no—
836C8—42no—
837C8—42no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—44no—
845C22—44no—
846C22—44no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—168no—
852C22#260914yes—
853C22C2×#52511yescharacteristic
854C22C2×#52511yescharacteristic
855C22C2×#53711yescharacteristic
856C22C2×#57711yescharacteristic
857C22#358411yescharacteristic
858C22#358511yescharacteristic
859C22#358611yescharacteristic
860C4—22no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—44no—
865C4—42no—
866C4—42no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—81no—
874C4—81no—
875C4—81no—
876C4—81no—
877C4—82no—
878C4—82no—
879C4#260914yes—
880C4C2×#55111yescharacteristic
881C4C2×#55211yescharacteristic
882C4C2×#55211yescharacteristic
883C4C2×#55511yescharacteristic
884C2—24no—
885C2—84no—
886C2C2×#260911yescharacteristic
887C2#6059111yescharacteristic
888C2#6059211yescharacteristic
889C2#6059311yescharacteristic
890C2#6059511yescharacteristic
891C2#6093511yescharacteristic
892C2#6093811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34254C2semidirect
3. #29548C2semidirect
4. #29547C2semidirect
5. #29544C2semidirect
6. #29543C2semidirect
7. #29538C2semidirect
8. #29537C2semidirect
9. #29535C2semidirect
10. #29534C2semidirect
11. #23666C2semidirect
12. #23619C2semidirect
15. #21066C2semidirect
17. #21035C2semidirect
18. #21035C2semidirect
21. #20877C2semidirect
23. #20755C2semidirect
50. #2320C22semidirect
51. #2320C22semidirect
60. #2295C22semidirect
61. #2295C22semidirect
69. #2088C22semidirect
70. #2088C22semidirect
71. #2088C22semidirect
72. #2088C22semidirect
73. #2087C22semidirect
74. #2087C22semidirect
75. #2086C22semidirect
76. #2086C22semidirect
77. #2068C22semidirect
78. #2068C22semidirect
81. #2066C22semidirect
82. #2066C22semidirect
89. #1928C22semidirect
90. #1928C22semidirect
91. #1927C22semidirect
92. #1927C22semidirect
97. #1921C22semidirect
98. #1921C22semidirect
99. #1920C22semidirect
100. #1920C22semidirect
101. #1919C22semidirect
102. #1919C22semidirect
103. #1918C22semidirect
104. #1918C22semidirect
113. #1865C22semidirect
114. #1865C22semidirect
117. #1863C22semidirect
118. #1863C22semidirect
121. #1832C22semidirect
122. #1832C22semidirect
123. #1831C22semidirect
124. #1831C22semidirect

Maximal subgroups

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

subgroupindex
#342552
#342542
#295482
#295472
#295442
#295432
#295382
#295372
#295352
#295342
#236662
#236192
#236182
C2×#20552
#210662
#210652
#210352
#209362
#209332
#208772
#208762
#207552