Finite Group Databasebeta

← #6460641

Subgroups — #6460641

Order 512.

1707 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35668C211yesmaximal, characteristic, complemented
2#35558C211yesmaximal, characteristic
3#29102C212yesmaximal, complemented
4#29101C212yesmaximal, complemented
5#29094C212yesmaximal, complemented
6#29093C212yesmaximal, complemented
7#29086C212yesmaximal, complemented
8#29085C212yesmaximal, complemented
9#29078C212yesmaximal, complemented
10#29077C212yesmaximal, complemented
11#23666C211yesmaximal, characteristic, complemented
12#23633C211yesmaximal, characteristic, complemented
13C2×#2055C211yesmaximal, characteristic
14#23456C211yesmaximal, characteristic
15#21326C211yesmaximal, characteristic, complemented
16#21231C211yesmaximal, characteristic
17#21095C211yesmaximal, characteristic
18#21094C211yesmaximal, characteristic, complemented
19#21091C211yesmaximal, characteristic
20#21039C211yesmaximal, characteristic, complemented
21#20936C211yesmaximal, characteristic
22#20441C211yesmaximal, characteristic, complemented
23#20417C211yesmaximal, characteristic, complemented
24C23×SD16C2211yescharacteristic
25C2×#544C2211yescharacteristic
26C2×#519C2211yescharacteristic
27C2×#427C2211yescharacteristic
28C22×C4⋊C8C2211yescharacteristic
29C2×#419C2211yescharacteristic
30C2×#419C2211yescharacteristic
31C2×#418C2211yescharacteristic
32C2×#418C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×#102C2211yescharacteristic
35C2×#405C2211yescharacteristic
36C2×#405C2211yescharacteristic
37C2×C4×M16C2211yescharacteristic
38#2568—21no—
39#2567—21no—
40#2565—21no—
41#2565—21no—
42#2513—21no—
43#2513—21no—
44#2513C2212yes—
45#2513C2212yes—
46#2512—21no—
47#2512—21no—
48#2512C2212yes—
49#2512C2212yes—
50#2480—22no—
51#2480—22no—
52#2453C2212yescomplemented
53#2453C2212yescomplemented
54#2451C2212yescomplemented
55#2451C2212yescomplemented
56#2438—22no—
57#2438—22no—
58#2317C2211yescharacteristic
59#2317C2211yescharacteristic
60#2310C2211yescharacteristic
61#2309C2211yescharacteristic
62#2309C2211yescharacteristic
63#2296C2211yescharacteristic
64#2296C2211yescharacteristic
65C2×#391C2211yescharacteristic
66C2×#390C2211yescharacteristic
67#2285C2211yescharacteristic
68#2274C2211yescharacteristic
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#2074C2212yescomplemented
78#2074C2212yescomplemented
79#2072C2212yescomplemented
80#2072C2212yescomplemented
81#2055C2212yes—
82#2055C2212yes—
83#2055C2212yes—
84#2055C2212yes—
85#2025C2212yes—
86#2025C2212yes—
87#2023C2212yes—
88#2023C2212yes—
89#1993C2212yescomplemented
90#1992C2212yescomplemented
91#1991C2212yescomplemented
92#1990C2212yescomplemented
93#1973C2212yes—
94#1973C2212yes—
95#1968C2212yes—
96#1968C2212yes—
97#1936C2212yes—
98#1936C2212yes—
99#1936C2212yes—
100#1936C2212yes—
101#1935C2212yescomplemented
102#1935C2212yescomplemented
103#1934C2212yes—
104#1934C2212yes—
105#1934C2212yes—
106#1934C2212yes—
107#1933C2212yescomplemented
108#1933C2212yescomplemented
109#1921C2212yescomplemented
110#1920C2212yescomplemented
111#1919C2212yescomplemented
112#1918C2212yescomplemented
113#1880C2212yes—
114#1880C2212yes—
115#1880C2212yes—
116#1880C2212yes—
117#1771C2212yescomplemented
118#1771C2212yescomplemented
119#1770C2212yescomplemented
120C8×C4⋊C4C2212yescomplemented
121#1763C2212yescomplemented
122#1763C2212yescomplemented
123C4×#103C2212yescomplemented
124C4×#103C2212yescomplemented
125#1736C2211yescharacteristic
126#1736C2211yescharacteristic
127#1736C2211yescharacteristic
128#1736C2211yescharacteristic
129#1735C2211yescharacteristic
130#1735C2211yescharacteristic
131#1735C2211yescharacteristic
132C2×#340C2211yescharacteristic
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#544—24no—
147#544—42no—
148C2×C4⋊Q8—21no—
149C2×C4⋊Q8C2312yes—
150C2×#126—22no—
151C2×#126—22no—
152C2×#125—21no—
153C2×#125C2312yes—
154C2×C22⋊Q8—22no—
155#519—24no—
156#519—42no—
157C2×C4×Q8—21no—
158C2×C4×Q8—21no—
159C2×C4×Q8C2312yes—
160C2×C4×Q8C2312yes—
161C2×#117—22no—
162C2×#117C2311yescharacteristic
163C2×#117C2311yescharacteristic
164C2×#117C2311yescharacteristic
165C2×#117C2311yescharacteristic
166C2×#117C2311yescharacteristic
167C2×#117C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C22⋊C4—21no—
171C22×C22⋊C4—21no—
172C22×C42C2311yescharacteristic
173#427—24no—
174C2×#107C2311yescharacteristic
175C2×#107C2311yescharacteristic
176C2×#106C2311yescharacteristic
177C2×#106C2311yescharacteristic
178C2×C4⋊C8—24no—
179C2×C4⋊C8C2311yescharacteristic
180C2×C4⋊C8C2311yescharacteristic
181C2×C4⋊C8C2311yescharacteristic
182C2×C4⋊C8C2311yescharacteristic
183#419—24no—
184#419—24no—
185#418—24no—
186#418—24no—
187C2×#103—24no—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#102—42no—
195C2×#102C2312yes—
196C2×#102C2312yes—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×#102C2312yes—
201#405—42no—
202#405—42no—
203C4×M16—24no—
204C2×#97C2312yes—
205C2×#97C2312yes—
206C2×#97C2312yes—
207C2×C4×C8C2312yes—
208C2×C4×C8C2312yes—
209C2×C4×C8C2312yes—
210#400—22no—
211#400—22no—
212#398—22no—
213#398—22no—
214#398—22no—
215#398—22no—
216#397—22no—
217#397—22no—
218#397—22no—
219#397—22no—
220#397—22no—
221#397—22no—
222#396—22no—
223#396—22no—
224#395—22no—
225#395—22no—
226#391—21no—
227#391—21no—
228#391—21no—
229#391—21no—
230#391—22no—
231#391—22no—
232#391C2312yes—
233#391C2312yes—
234#391C2312yes—
235#391C2312yes—
236#390—21no—
237#390—21no—
238#390—21no—
239#390—21no—
240#390—21no—
241#390—21no—
242#390C2312yes—
243#390C2312yes—
244#390C2312yes—
245#390C2312yes—
246#390C2312yes—
247#390C2312yes—
248#389—22no—
249#389—22no—
250#389—21no—
251#389—21no—
252#389C2312yes—
253#389C2312yes—
254#389C2311yescharacteristic
255#389C2311yescharacteristic
256#389C2311yescharacteristic
257#389C2311yescharacteristic
258#389C2311yescharacteristic
259#389C2311yescharacteristic
260#389C2311yescharacteristic
261#389C2311yescharacteristic
262#388—22no—
263#388—22no—
264#388—22no—
265#388—22no—
266#388—22no—
267#388—22no—
268#387—22no—
269#387—22no—
270#387—22no—
271#387—22no—
272#385—21no—
273#385—21no—
274#385—21no—
275#385—21no—
276#385—22no—
277#385—22no—
278#384—21no—
279#384D411yescharacteristic
280#384D411yescharacteristic
281#384C2312yes—
282#382—21no—
283#382D411yescharacteristic
284#382D411yescharacteristic
285#382C2312yes—
286#381—22no—
287#380D412yes—
288#380D412yes—
289#379—22no—
290#379—22no—
291C4×C4⋊C4—21no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4—21no—
295C4×C4⋊C4—21no—
296C4×C4⋊C4—21no—
297C4×C4⋊C4C2312yes—
298C4×C4⋊C4C2312yes—
299C4×C4⋊C4C2312yes—
300C4×C4⋊C4C2312yes—
301C4×C22⋊C4—22no—
302C2×#95—21no—
303C2×#95—21no—
304#340C2312yes—
305#340C2312yes—
306#340C2311yescharacteristic
307#340C2311yescharacteristic
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#340C2312yes—
321#340C2312yes—
322#340C2312yes—
323#340C2312yes—
324#340C2312yes—
325#340C2312yes—
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—22no—
338C22×Q8#4114yes—
339C22×Q8C2412yes—
340C22×D4—21no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4C2412yes—
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—21no—
351C23×C4C2×D411yescharacteristic
352C23×C4C2×D411yescharacteristic
353C23×C4C2411yescharacteristic
354C2×SD16—24no—
355C2×SD16—24no—
356C2×SD16—24no—
357C2×SD16—24no—
358C2×SD16—42no—
359C2×SD16—42no—
360C2×SD16—416no—
361C2×M16—22no—
362C2×M16—22no—
363C2×M16—22no—
364C2×M16—22no—
365C2×M16—22no—
366C2×M16#4114yes—
367C22×C8—22no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8—22no—
371C22×C8—22no—
372C22×C8#4114yes—
373C22×C8C2411yescharacteristic
374C22×C8C2411yescharacteristic
375C22×C8C2412yes—
376C22×C8C2411yescharacteristic
377C22×C8C2411yescharacteristic
378C22×C8C2412yes—
379C4⋊Q8—24no—
380C4⋊Q8—42no—
381C4⋊Q8—44no—
382#126—84no—
383#126—84no—
384#125—24no—
385#125—42no—
386#125—44no—
387C22⋊Q8—48no—
388C4×Q8—24no—
389C4×Q8—24no—
390C4×Q8—42no—
391C4×Q8—42no—
392C4×Q8—44no—
393C4×Q8—44no—
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—22no—
404#117—22no—
405#117—48no—
406#117#4114yes—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2×D411yescharacteristic
434C2×C4⋊C4C2×D412yes—
435C2×C4⋊C4C2×D412yes—
436C2×C4⋊C4C2×D412yes—
437C2×C4⋊C4C2×D412yes—
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2411yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
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—82no—
465C2×C22⋊C4—82no—
466C2×C22⋊C4C2×D412yes—
467C2×C22⋊C4C2×D412yes—
468C2×C42—21no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42—22no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—22no—
477C2×C42—22no—
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D411yescharacteristic
480C2×C42C2412yes—
481C2×C42C2412yes—
482C2×C42C2411yescharacteristic
483C2×C42C2411yescharacteristic
484#107—22no—
485#107—22no—
486#106—22no—
487#106—22no—
488C4⋊C8—22no—
489C4⋊C8—22no—
490C4⋊C8—22no—
491C4⋊C8—22no—
492#103—24no—
493#103—24no—
494#103—24no—
495#103—24no—
496#103—24no—
497#103—24no—
498#102—24no—
499#102—24no—
500#102—24no—
501#102—24no—
502#102—42no—
503#102—42no—
504#97—24no—
505#97—42no—
506#97—42no—
507C4×C8—24no—
508C4×C8—42no—
509C4×C8—42no—
510#95—22no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—22no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
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#95C2×D412yes—
533#95C2×D412yes—
534#95C2×D412yes—
535#95C2×D412yes—
536C24—22no—
537C24—42no—
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—44no—
554C2×Q8—42no—
555C2×Q8—44no—
556C2×Q8—42no—
557C2×Q8—44no—
558C2×Q8—82no—
559C2×Q8—82no—
560C2×Q8C2×#4114yes—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—44no—
568C2×D4—42no—
569C2×D4—44no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—44no—
573C2×D4—44no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—81no—
597C22×C4—81no—
598C22×C4—81no—
599C22×C4—81no—
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C22×D412yes—
606C22×C4C22×D412yes—
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C2×#4112yes—
610C22×C4C2×#4112yes—
611C22×C4C2×#4112yes—
612C22×C4C2×#4112yes—
613C22×C4H(5,𝔽2)12yes—
614C22×C42−1+412yes—
615C22×C4C2511yescharacteristic
616SD16—48no—
617SD16—48no—
618M16—28no—
619M16—44no—
620C2×C8—28no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—22no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—22no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—44no—
637C2×C8C2×#4114yes—
638C2×C8C2×#4112yes—
639C2×C8C2×#4112yes—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—24no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—44no—
667C4⋊C4—44no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—82no—
678C4⋊C4—81no—
679C4⋊C4—81no—
680C4⋊C4—82no—
681C4⋊C4—81no—
682C4⋊C4—81no—
683C4⋊C4—82no—
684C4⋊C4—82no—
685C4⋊C4C2×#4112yes—
686C4⋊C4C2×#4112yes—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—44no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—44no—
695C22⋊C4—82no—
696C22⋊C4—82no—
697C22⋊C4—82no—
698C22⋊C4—82no—
699C22⋊C4—82no—
700C22⋊C4—82no—
701C22⋊C4—82no—
702C22⋊C4—82no—
703C22⋊C4—82no—
704C22⋊C4—82no—
705C42—22no—
706C42—22no—
707C42—24no—
708C42—21no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—22no—
713C42—22no—
714C42—22no—
715C42—22no—
716C42—44no—
717C42—44no—
718C42—42no—
719C42—42no—
720C42—42no—
721C42—82no—
722C42—82no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—84no—
735C23—84no—
736C23—84no—
737C23—162no—
738C23—162no—
739C23—162no—
740C23—162no—
741C23#53212yes—
742C23#54612yes—
743C23#54812yes—
744C23C23×D411yescharacteristic
745Q8—24no—
746Q8—24no—
747Q8—48no—
748Q8—42no—
749Q8—42no—
750Q8—164no—
751D4—42no—
752D4—42no—
753D4—42no—
754D4—42no—
755D4—84no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—44no—
783C2×C4—48no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—82no—
815C2×C4—162no—
816C2×C4—162no—
817C2×C4#52914yes—
818C2×C4#53212yes—
819C2×C4#53914yes—
820C2×C4#54612yes—
821C2×C4#54812yes—
822C2×C4#55114yes—
823C2×C4#55614yes—
824C2×C4#57712yes—
825C2×C4C22×#4111yescharacteristic
826C2×C4C22×#4111yescharacteristic
827C2×C4C22×#4111yescharacteristic
828C2×C4C22×#4111yescharacteristic
829C2×C4C2×H(5,𝔽2)11yescharacteristic
830C2×C4C2×2−1+411yescharacteristic
831C8—24no—
832C8—22no—
833C8—22no—
834C8—42no—
835C8—41no—
836C8—41no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22—168no—
851C22#256014yes—
852C22C2×#53211yescharacteristic
853C22C2×#54611yescharacteristic
854C22C2×#54811yescharacteristic
855C22C2×#57711yescharacteristic
856C22#358411yescharacteristic
857C22#358511yescharacteristic
858C22#358611yescharacteristic
859C4—22no—
860C4—44no—
861C4—42no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4—42no—
867C4—41no—
868C4—41no—
869C4—41no—
870C4—82no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4—81no—
875C4—81no—
876C4—82no—
877C4—81no—
878C4#256014yes—
879C4C2×#52911yescharacteristic
880C4C2×#53911yescharacteristic
881C4C2×#55111yescharacteristic
882C4C2×#55611yescharacteristic
883C2—24no—
884C2—162no—
885C2C2×#256011yescharacteristic
886C2#6070611yescharacteristic
887C2#6070911yescharacteristic
888C2#6120811yescharacteristic
889C2#6120911yescharacteristic
890C2#6134111yescharacteristic
891C2#6134411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2285 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35668C2semidirect
3. #29102C2semidirect
4. #29101C2semidirect
5. #29094C2semidirect
6. #29093C2semidirect
7. #29086C2semidirect
8. #29085C2semidirect
9. #29078C2semidirect
10. #29077C2semidirect
11. #23666C2semidirect
12. #23633C2semidirect
15. #21326C2semidirect
18. #21094C2semidirect
20. #21039C2semidirect
22. #20441C2semidirect
23. #20417C2semidirect
52. #2453C22semidirect
53. #2453C22semidirect
54. #2451C22semidirect
55. #2451C22semidirect
69. #2088C22semidirect
70. #2088C22semidirect
71. #2088C22semidirect
72. #2088C22semidirect
73. #2087C22semidirect
74. #2087C22semidirect
75. #2086C22semidirect
76. #2086C22semidirect
77. #2074C22semidirect
78. #2074C22semidirect
79. #2072C22semidirect
80. #2072C22semidirect
89. #1993C22semidirect
90. #1992C22semidirect
91. #1991C22semidirect
92. #1990C22semidirect
101. #1935C22semidirect
102. #1935C22semidirect
107. #1933C22semidirect
108. #1933C22semidirect
109. #1921C22semidirect
110. #1920C22semidirect
111. #1919C22semidirect
112. #1918C22semidirect
117. #1771C22semidirect
118. #1771C22semidirect
119. #1770C22semidirect
120. C8×C4⋊C4C22semidirect
121. #1763C22semidirect
122. #1763C22semidirect
123. C4×#103C22semidirect
124. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#356682
#355582
#291022
#291012
#290942
#290932
#290862
#290852
#290782
#290772
#236662
#236332
C2×#20552
#234562
#213262
#212312
#210952
#210942
#210912
#210392
#209362
#204412
#204172