Finite Group Databasebeta

← #6568336

Subgroups — #6568336

Order 512.

1625 conjugacy classes of subgroups.

The subgroup lattice has 879 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39513C211yesmaximal, characteristic, complemented
2#34493C211yesmaximal, characteristic
3#30178C212yesmaximal, complemented
4#29864C211yesmaximal, characteristic, complemented
5#29256C211yesmaximal, characteristic, complemented
6#29115C212yesmaximal, complemented
7#28716C211yesmaximal, characteristic, complemented
8#27591C212yesmaximal, complemented
9#27541C212yesmaximal, complemented
10#27520C212yesmaximal, complemented
11#27124C212yesmaximal, complemented
12#27109C212yesmaximal, complemented
13#26303C211yesmaximal, characteristic, complemented
14#26301C211yesmaximal, characteristic, complemented
15#25885C211yesmaximal, characteristic
16#25885C211yesmaximal, characteristic
17#23778C211yesmaximal, characteristic, complemented
18#23767C212yesmaximal, complemented
19#23220C211yesmaximal, characteristic, complemented
20#23216C211yesmaximal, characteristic, complemented
21#23066C211yesmaximal, characteristic, complemented
22#23060C211yesmaximal, characteristic, complemented
23#22836C211yesmaximal, characteristic, complemented
24C2×D42C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#486C2211yescharacteristic
27C2×#474C2211yescharacteristic
28C2×#474C2211yescharacteristic
29#2868C2211yescharacteristic, complemented
30#2793—22no—
31#2793—22no—
32#2629C2212yescomplemented
33#2547C2211yescharacteristic
34#2547C2211yescharacteristic
35#2545—21no—
36#2545—21no—
37#2497C2212yescomplemented
38#2497C2212yescomplemented
39#2446—21no—
40#2446—21no—
41#2375—22no—
42#2366C2211yescharacteristic
43#2365C2211yescharacteristic, complemented
44#2365C2211yescharacteristic, complemented
45#2363—21no—
46#2363C2212yes—
47#2354C2211yescharacteristic
48#2354C2211yescharacteristic
49D4×C22⋊C4—21no—
50D4×C22⋊C4C2212yes—
51#2324—21no—
52#2324C2212yes—
53#2321—22no—
54#2314C2212yescomplemented
55#2309—21no—
56#2309C2212yes—
57C4×#127C2211yescharacteristic
58C4×#125C2211yescharacteristic, complemented
59#2293C2211yescharacteristic
60#2293C2211yescharacteristic
61#2101C2211yescharacteristic, complemented
62#2092C2211yescharacteristic
63#2092C2212yescomplemented
64#2088C2211yescharacteristic, complemented
65#2087C2211yescharacteristic, complemented
66#2083C2212yescomplemented
67#2083C2212yescomplemented
68#2077C2212yescomplemented
69#2077C2212yescomplemented
70#2076C2212yescomplemented
71#2076C2212yescomplemented
72#2071C2212yes—
73#2071C2212yes—
74#2071C2212yescomplemented
75#2071C2212yescomplemented
76#2067C2211yescharacteristic
77#2065C2211yescharacteristic
78#2059C2211yescharacteristic, complemented
79#2033C2212yes—
80#2033C2212yes—
81#2033C2212yes—
82#2033C2212yes—
83#2025C2211yescharacteristic
84#2025C2212yescomplemented
85#1990C2211yescharacteristic, complemented
86#1990C2211yescharacteristic, complemented
87#1988C2211yescharacteristic, complemented
88#1988C2211yescharacteristic, complemented
89#1982C2211yescharacteristic
90#1982C2211yescharacteristic
91#1954C2211yescharacteristic
92#1954C2211yescharacteristic
93#1948C2211yescharacteristic, complemented
94#1947C2211yescharacteristic, complemented
95#1936C2212yes—
96#1936C2212yescomplemented
97#1934C2212yes—
98#1934C2212yescomplemented
99#1926C2212yes—
100#1926C2212yescomplemented
101#1925C2212yes—
102#1925C2212yescomplemented
103#1924C2212yescomplemented
104#1923C2212yescomplemented
105#1921C2212yescomplemented
106#1918C2212yescomplemented
107#1864C2212yescomplemented
108#1864C2212yescomplemented
109#1862C2212yescomplemented
110#1862C2212yescomplemented
111#1854C2212yescomplemented
112#1854C2212yescomplemented
113#1831C2211yescharacteristic, complemented
114#1825C2212yescomplemented
115#1825C2212yescomplemented
116#1818C2212yescomplemented
117#1802C2212yescomplemented
118#1802C2212yescomplemented
119#1786C2212yes—
120#1786C2212yes—
121#1786C2212yes—
122#1786C2212yes—
123#1776C2212yescomplemented
124C4×#107C2212yescomplemented
125C4×#107C2211yescharacteristic, complemented
126C4×#106C2211yescharacteristic, complemented
127#1770C2211yescharacteristic, complemented
128C8×C4⋊C4C2211yescharacteristic, complemented
129C4×C4⋊C8C2211yescharacteristic, complemented
130#1762C2212yescomplemented
131C4×#102C2211yescharacteristic
132C4×#102C2211yescharacteristic
133C4×#102C2212yescomplemented
134#1750C2212yescomplemented
135C23×D4—21no—
136C23×D4C2312yes—
137D42—24no—
138D42—24no—
139C2×C4⋊Q8—21no—
140C2×C4⋊Q8—21no—
141C2×C4⋊Q8C2311yescharacteristic
142C2×C4⋊Q8C2311yescharacteristic
143C2×#127C2311yescharacteristic
144C2×#125C2311yescharacteristic
145C2×#124—21no—
146C2×#124—21no—
147C2×#121—21no—
148C2×#121C2312yes—
149C2×#120—22no—
150C2×C4×Q8—21no—
151C2×C4×Q8—21no—
152C2×C4×D4—21no—
153C2×C4×D4—21no—
154C2×C4×D4—21no—
155C2×C4×D4C2311yescharacteristic
156C2×C4×D4C2312yes—
157C2×C4×D4C2312yes—
158C2×C4×D4C2311yescharacteristic
159C2×#117—21no—
160C2×#117—21no—
161C2×#117C2312yes—
162C2×#117C2312yes—
163C22×C22⋊C4—22no—
164#486—24no—
165#486—24no—
166#474—24no—
167#474—24no—
168C2×#107C2312yes—
169C2×#107C2312yes—
170C2×#107C2311yescharacteristic
171C2×#107C2312yes—
172C2×#107C2311yescharacteristic
173C2×#106C2311yescharacteristic
174C2×#106C2312yes—
175C2×#106C2311yescharacteristic
176C2×C4⋊C8C2311yescharacteristic
177C2×C4⋊C8C2311yescharacteristic
178C2×C4⋊C8C2311yescharacteristic
179C2×C4⋊C8C2311yescharacteristic
180C2×#102C2312yes—
181C2×#102C2312yes—
182C2×#102C2312yes—
183C2×#102C2312yes—
184C2×#102C2312yes—
185C2×#102C2312yes—
186C2×#102C2311yescharacteristic
187C2×#102C2311yescharacteristic
188C2×#102C2311yescharacteristic
189C2×#102C2311yescharacteristic
190C2×#102C2312yes—
191C2×#102C2312yes—
192C2×#102C2312yes—
193C2×#102C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196C2×C22⋊C8C2312yes—
197C2×C22⋊C8C2312yes—
198C2×#97C2312yes—
199C2×C4×C8C2311yescharacteristic
200C2×C4×C8C2311yescharacteristic
201C2×C4×C8C2312yes—
202#400—22no—
203#400—22no—
204#398—22no—
205#398—22no—
206#397—22no—
207#397—22no—
208#396—22no—
209#396—22no—
210#396—22no—
211#396—22no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391—21no—
216#390—21no—
217#390—21no—
218#390—22no—
219#390—22no—
220#390—22no—
221#390—22no—
222#390—21no—
223#390—21no—
224#390D411yescharacteristic
225#390D411yescharacteristic
226#390C2312yes—
227#390C2311yescharacteristic
228#390C2312yes—
229#390C2312yes—
230#390C2311yescharacteristic
231#389D411yescharacteristic
232#389D411yescharacteristic
233#389C2311yescharacteristic
234#389C2311yescharacteristic
235#389C2311yescharacteristic
236#389C2311yescharacteristic
237#389C2312yes—
238#389C2312yes—
239#388—22no—
240#388—22no—
241#388—22no—
242#388—22no—
243#388—22no—
244#388—22no—
245#388—21no—
246#388—21no—
247#388—22no—
248#388—22no—
249#388D412yes—
250#388D412yes—
251#387—22no—
252#387—22no—
253#387—21no—
254#387—21no—
255#387—22no—
256#387—22no—
257#387—22no—
258#387—22no—
259#386—22no—
260#386—22no—
261#386—22no—
262#386—22no—
263#386—22no—
264#385—22no—
265#384—21no—
266#384—21no—
267#384C2311yescharacteristic
268#384C2312yes—
269#384C2312yes—
270#382C2311yescharacteristic
271#380—21no—
272#380C2312yes—
273#380C2312yes—
274#380C2312yes—
275#380C2312yes—
276#380C2312yes—
277#379—22no—
278#379—22no—
279#379—22no—
280C4×C4⋊C4—21no—
281C4×C4⋊C4—21no—
282C4×C4⋊C4—21no—
283C4×C4⋊C4C2311yescharacteristic
284C4×C4⋊C4C2311yescharacteristic
285C4×C4⋊C4C2312yes—
286C4×C4⋊C4C2312yes—
287C4×C4⋊C4C2312yes—
288C4×C4⋊C4C2311yescharacteristic
289C4×C4⋊C4C2311yescharacteristic
290C4×C22⋊C4—21no—
291C4×C22⋊C4—22no—
292C4×C22⋊C4C2312yes—
293C43C2311yescharacteristic
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2311yescharacteristic
299#340C2311yescharacteristic
300#340C2311yescharacteristic
301#340C2311yescharacteristic
302#340C2312yes—
303#340C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2312yes—
307#340C2312yes—
308#340C2311yescharacteristic
309#340C2311yescharacteristic
310#340C2311yescharacteristic
311#340C2311yescharacteristic
312#336C2311yescharacteristic
313#336C2312yes—
314#336C2312yes—
315#336C2311yescharacteristic
316#336C2312yes—
317#336C2312yes—
318C25—22no—
319C22×Q8—21no—
320C22×Q8—21no—
321C22×D4—28no—
322C22×D4—22no—
323C22×D4—24no—
324C22×D4—24no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—22no—
328C22×D4—42no—
329C22×D4—42no—
330C22×D4—42no—
331C22×D4—42no—
332C22×D4—82no—
333C22×D4—82no—
334C22×D4C2×D411yescharacteristic
335C22×D4C2412yes—
336C22×D4C2411yescharacteristic
337C23×C4—21no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4C2412yes—
341C22×C8C2411yescharacteristic
342C22×C8C2411yescharacteristic
343C22×C8C2412yes—
344C22×C8C2412yes—
345C22×C8C2411yescharacteristic
346C22×C8C2411yescharacteristic
347C4⋊Q8—22no—
348C4⋊Q8—22no—
349C4⋊Q8—22no—
350C4⋊Q8—22no—
351C4⋊Q8—82no—
352C4⋊Q8—82no—
353#127—22no—
354#127#4114yes—
355#125—41no—
356#125—41no—
357#124—82no—
358#124—82no—
359#121—28no—
360#121—24no—
361#121—24no—
362#120—216no—
363C4×Q8—82no—
364C4×Q8—82no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—42no—
369C4×D4—42no—
370C4×D4—42no—
371C4×D4—42no—
372C4×D4—82no—
373C4×D4—82no—
374C4×D4—82no—
375C4×D4#4114yes—
376#117—42no—
377#117—42no—
378#117—42no—
379#117—42no—
380#117—82no—
381#117—82no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4C2×D411yescharacteristic
399C2×C4⋊C4C2×D411yescharacteristic
400C2×C4⋊C4C2×D411yescharacteristic
401C2×C4⋊C4C2×D412yes—
402C2×C4⋊C4C2×D412yes—
403C2×C4⋊C4C2411yescharacteristic
404C2×C4⋊C4C2412yes—
405C2×C4⋊C4C2411yescharacteristic
406C2×C4⋊C4C2411yescharacteristic
407C2×C4⋊C4C2411yescharacteristic
408C2×C4⋊C4C2412yes—
409C2×C4⋊C4C2412yes—
410C2×C4⋊C4C2411yescharacteristic
411C2×C4⋊C4C2411yescharacteristic
412C2×C4⋊C4C2411yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—84no—
434C2×C22⋊C4C2×D412yes—
435C2×C22⋊C4C2×D412yes—
436C2×C22⋊C4C2×D412yes—
437C2×C22⋊C4C2×D412yes—
438C2×C22⋊C4C2×D412yes—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2411yescharacteristic
451C2×C42C2412yes—
452C2×C42C2411yescharacteristic
453C2×C42C2411yescharacteristic
454#107—24no—
455#107—24no—
456#107—41no—
457#107—42no—
458#107—41no—
459#106—41no—
460#106—42no—
461#106—41no—
462C4⋊C8—22no—
463C4⋊C8—22no—
464C4⋊C8—41no—
465C4⋊C8—41no—
466#102—24no—
467#102—24no—
468#102—24no—
469#102—24no—
470#102—24no—
471#102—24no—
472#102—42no—
473#102—42no—
474#102—42no—
475#102—42no—
476#102—41no—
477#102—41no—
478#102—41no—
479#102—41no—
480C22⋊C8—42no—
481C22⋊C8—42no—
482C22⋊C8—42no—
483C22⋊C8—42no—
484#97—42no—
485C4×C8—22no—
486C4×C8—22no—
487C4×C8—42no—
488#95—21no—
489#95—21no—
490#95—22no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—22no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—22no—
500#95—22no—
501#95—22no—
502#95—22no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—22no—
507#95C2×D412yes—
508#95C2×D412yes—
509#95C2×D412yes—
510C24—28no—
511C24—21no—
512C24—22no—
513C24—82no—
514C24—82no—
515C24—82no—
516C24—82no—
517C24—82no—
518C24—82no—
519C24C22×D412yes—
520C2×Q8—42no—
521C2×Q8—42no—
522C2×Q8—42no—
523C2×Q8—42no—
524C2×Q8—42no—
525C2×Q8—42no—
526C2×D4—28no—
527C2×D4—28no—
528C2×D4—22no—
529C2×D4—24no—
530C2×D4—24no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—21no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—81no—
546C2×D4—81no—
547C2×D4—82no—
548C2×D4—82no—
549C2×D4—84no—
550C2×D4—84no—
551C2×D4—84no—
552C2×D4—84no—
553C2×D4—816no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4C2×#4112yes—
557C2×D4C2×#4114yes—
558C22×C4—21no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—44no—
578C22×C4—82no—
579C22×C4—82no—
580C22×C4—82no—
581C22×C4—82no—
582C22×C4—82no—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D411yescharacteristic
592C22×C4C2511yescharacteristic
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—21no—
600C2×C8—22no—
601C2×C8—21no—
602C2×C8—22no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—21no—
610C2×C8—21no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—21no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—22no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—22no—
632C4⋊C4—21no—
633C4⋊C4—42no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—42no—
641C4⋊C4—42no—
642C4⋊C4—81no—
643C4⋊C4—81no—
644C4⋊C4—81no—
645C4⋊C4—82no—
646C4⋊C4—82no—
647C4⋊C4—82no—
648C4⋊C4—82no—
649C4⋊C4—82no—
650C4⋊C4—82no—
651C4⋊C4C2×#4112yes—
652C22⋊C4—28no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—81no—
661C22⋊C4—82no—
662C22⋊C4—82no—
663C22⋊C4—81no—
664C22⋊C4—81no—
665C22⋊C4—82no—
666C22⋊C4—82no—
667C22⋊C4—82no—
668C22⋊C4—82no—
669C22⋊C4—82no—
670C22⋊C4—82no—
671C22⋊C4—82no—
672C22⋊C4—82no—
673C22⋊C4—82no—
674C22⋊C4—82no—
675C22⋊C4—82no—
676C22⋊C4—82no—
677C42—22no—
678C42—22no—
679C42—22no—
680C42—22no—
681C42—22no—
682C42—21no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—41no—
687C42—42no—
688C42—42no—
689C42—42no—
690C42—82no—
691C42—82no—
692C42—82no—
693C42—82no—
694C42C2×#4112yes—
695C42C2×#4112yes—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—24no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—41no—
707C23—42no—
708C23—41no—
709C23—42no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—42no—
715C23—41no—
716C23—42no—
717C23—88no—
718C23—88no—
719C23—88no—
720C23—164no—
721C23—164no—
722C23—164no—
723C23—164no—
724C23C23×D411yescharacteristic
725Q8—84no—
726Q8—84no—
727D4—22no—
728D4—22no—
729D4—24no—
730D4—24no—
731D4—44no—
732D4—48no—
733D4—42no—
734D4—42no—
735D4—41no—
736D4—41no—
737D4—84no—
738D4—88no—
739D4—88no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—48no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—164no—
798C2×C4—164no—
799C2×C4#52512yes—
800C2×C4#52512yes—
801C2×C4#57612yes—
802C2×C4#57612yes—
803C2×C4#57712yes—
804C2×C4C22×#4111yescharacteristic
805C2×C4C22×#4111yescharacteristic
806C2×C4#58511yescharacteristic
807C2×C4#58511yescharacteristic
808C2×C4#58511yescharacteristic
809C2×C4#58511yescharacteristic
810C8—42no—
811C8—42no—
812C8—41no—
813C8—41no—
814C8—41no—
815C8—41no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—44no—
822C22—42no—
823C22—44no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—82no—
830C22—81no—
831C22—82no—
832C22—81no—
833C22—82no—
834C22—81no—
835C22—82no—
836C22—81no—
837C22—1616no—
838C22C2×#52511yescharacteristic
839C22#348511yescharacteristic
840C22#350011yescharacteristic
841C22C2×#57611yescharacteristic
842C22C2×#57611yescharacteristic
843C22C2×#57711yescharacteristic
844C22#358611yescharacteristic
845C4—22no—
846C4—22no—
847C4—41no—
848C4—42no—
849C4—41no—
850C4—42no—
851C4—42no—
852C4—41no—
853C4—42no—
854C4—81no—
855C4—82no—
856C4—81no—
857C4—81no—
858C4—81no—
859C4—82no—
860C4—82no—
861C4—81no—
862C4—81no—
863C4#312214yes—
864C4#351011yescharacteristic
865C4#351011yescharacteristic
866C4#352111yescharacteristic
867C4#352111yescharacteristic
868C2—82no—
869C2—84no—
870C2—82no—
871C2#3603311yescharacteristic
872C2C2×#312211yescharacteristic
873C2#6059111yescharacteristic
874C2#6178811yescharacteristic
875C2#6181111yescharacteristic
876C2#6255011yescharacteristic
877C2#6261811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×D42C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39513C2semidirect
3. #30178C2semidirect
4. #29864C2semidirect
5. #29256C2semidirect
6. #29115C2semidirect
7. #28716C2semidirect
8. #27591C2semidirect
9. #27541C2semidirect
10. #27520C2semidirect
11. #27124C2semidirect
12. #27109C2semidirect
13. #26303C2semidirect
14. #26301C2semidirect
17. #23778C2semidirect
18. #23767C2semidirect
19. #23220C2semidirect
20. #23216C2semidirect
21. #23066C2semidirect
22. #23060C2semidirect
23. #22836C2semidirect
29. #2868C22semidirect
32. #2629C22semidirect
37. #2497C22semidirect
38. #2497C22semidirect
43. #2365C22semidirect
44. #2365C22semidirect
54. #2314C22semidirect
58. C4×#125C22semidirect
61. #2101C22semidirect
63. #2092C22semidirect
64. #2088C22semidirect
65. #2087C22semidirect
66. #2083C22semidirect
67. #2083C22semidirect
68. #2077C22semidirect
69. #2077C22semidirect
70. #2076C22semidirect
71. #2076C22semidirect
74. #2071C22semidirect
75. #2071C22semidirect
78. #2059C22semidirect
84. #2025C22semidirect
85. #1990C22semidirect
86. #1990C22semidirect
87. #1988C22semidirect
88. #1988C22semidirect
93. #1948C22semidirect
94. #1947C22semidirect
96. #1936C22semidirect
98. #1934C22semidirect
100. #1926C22semidirect
102. #1925C22semidirect
103. #1924C22semidirect
104. #1923C22semidirect
105. #1921C22semidirect
106. #1918C22semidirect
107. #1864C22semidirect
108. #1864C22semidirect
109. #1862C22semidirect
110. #1862C22semidirect
111. #1854C22semidirect
112. #1854C22semidirect
113. #1831C22semidirect
114. #1825C22semidirect
115. #1825C22semidirect
116. #1818C22semidirect
117. #1802C22semidirect
118. #1802C22semidirect
123. #1776C22semidirect
124. C4×#107C22semidirect
125. C4×#107C22semidirect
126. C4×#106C22semidirect
127. #1770C22semidirect
128. C8×C4⋊C4C22semidirect
129. C4×C4⋊C8C22semidirect
130. #1762C22semidirect
133. C4×#102C22semidirect
134. #1750C22semidirect

Maximal subgroups

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

subgroupindex
#395132
#344932
#301782
#298642
#292562
#291152
#287162
#275912
#275412
#275202
#271242
#271092
#263032
#263012
#258852
#237782
#237672
#232202
#232162
#230662
#230602
#228362