Finite Group Databasebeta

← #6568313

Subgroups — #6568313

Order 512.

1608 conjugacy classes of subgroups.

The subgroup lattice has 877 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39515C211yesmaximal, characteristic, complemented
2#34493C211yesmaximal, characteristic
3#30177C212yesmaximal, complemented
4#29865C211yesmaximal, characteristic, complemented
5#29258C211yesmaximal, characteristic, complemented
6#29116C212yesmaximal, complemented
7#28718C211yesmaximal, characteristic, complemented
8#27594C212yesmaximal, complemented
9#27534C212yesmaximal, complemented
10#27525C212yesmaximal, complemented
11#27125C212yesmaximal, complemented
12#27106C212yesmaximal, complemented
13#26303C211yesmaximal, characteristic, complemented
14#26297C211yesmaximal, characteristic, complemented
15#25885C211yesmaximal, characteristic
16#25881C211yesmaximal, characteristic
17#23774C211yesmaximal, characteristic, complemented
18#23766C212yesmaximal, complemented
19#23223C211yesmaximal, characteristic, complemented
20#23216C211yesmaximal, characteristic, complemented
21#23066C211yesmaximal, characteristic, complemented
22#23061C211yesmaximal, characteristic, complemented
23#22836C211yesmaximal, characteristic, complemented
24C2×D42C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#486C2211yescharacteristic
27C2×#476C2211yescharacteristic
28C2×#474C2211yescharacteristic
29#2862C2211yescharacteristic, complemented
30#2798—22no—
31#2759—22no—
32#2628C2212yescomplemented
33#2592—21no—
34#2581—21no—
35#2563C2211yescharacteristic
36#2547C2211yescharacteristic
37#2514—21no—
38#2495C2212yescomplemented
39#2494C2212yescomplemented
40#2448—21no—
41#2375—22no—
42#2369C2211yescharacteristic, complemented
43#2366C2211yescharacteristic
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×C4⋊Q8C2211yescharacteristic, complemented
58C4×#127C2211yescharacteristic
59#2293C2211yescharacteristic
60#2293C2211yescharacteristic
61#2099C2211yescharacteristic, complemented
62#2094C2212yescomplemented
63#2093C2211yescharacteristic
64#2086C2211yescharacteristic, complemented
65#2086C2211yescharacteristic, complemented
66#2085C2212yescomplemented
67#2085C2212yescomplemented
68#2077C2212yescomplemented
69#2077C2212yescomplemented
70#2076C2212yescomplemented
71#2075C2212yescomplemented
72#2073C2212yes—
73#2073C2212yes—
74#2073C2212yescomplemented
75#2073C2212yescomplemented
76#2067C2211yescharacteristic
77#2067C2211yescharacteristic
78#2057C2211yescharacteristic, complemented
79#2034C2212yes—
80#2034C2212yes—
81#2033C2212yes—
82#2033C2212yes—
83#2023C2211yescharacteristic
84#2023C2212yescomplemented
85#1990C2211yescharacteristic, complemented
86#1990C2211yescharacteristic, complemented
87#1988C2211yescharacteristic, complemented
88#1987C2211yescharacteristic, complemented
89#1982C2211yescharacteristic
90#1982C2211yescharacteristic
91#1954C2211yescharacteristic
92#1954C2211yescharacteristic
93#1948C2211yescharacteristic, complemented
94#1948C2211yescharacteristic, complemented
95#1936C2212yes—
96#1936C2212yescomplemented
97#1934C2212yes—
98#1934C2212yescomplemented
99#1926C2212yes—
100#1926C2212yes—
101#1925C2212yescomplemented
102#1925C2212yescomplemented
103#1924C2212yescomplemented
104#1923C2212yescomplemented
105#1921C2212yescomplemented
106#1920C2212yescomplemented
107#1864C2212yescomplemented
108#1864C2212yescomplemented
109#1862C2212yescomplemented
110#1862C2212yescomplemented
111#1854C2212yescomplemented
112#1854C2212yescomplemented
113#1831C2211yescharacteristic, complemented
114#1825C2212yescomplemented
115#1825C2212yescomplemented
116#1818C2212yescomplemented
117#1804C2212yescomplemented
118#1804C2212yescomplemented
119#1786C2212yes—
120#1786C2212yes—
121#1786C2212yes—
122#1786C2212yes—
123#1776C2212yescomplemented
124C4×#107C2211yescharacteristic, complemented
125C4×#107C2211yescharacteristic, complemented
126C4×#106C2212yescomplemented
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⋊Q8C2311yescharacteristic
140C2×C4⋊Q8C2311yescharacteristic
141C2×C4⋊Q8C2311yescharacteristic
142C2×#127C2311yescharacteristic
143C2×#124—21no—
144C2×#121—21no—
145C2×#121C2312yes—
146C2×#120—22no—
147C2×C4×Q8—21no—
148C2×C4×Q8—21no—
149C2×C4×D4—21no—
150C2×C4×D4—21no—
151C2×C4×D4—21no—
152C2×C4×D4C2311yescharacteristic
153C2×C4×D4C2312yes—
154C2×C4×D4C2312yes—
155C2×C4×D4C2311yescharacteristic
156C2×#117—21no—
157C2×#117—21no—
158C2×#117C2312yes—
159C2×#117C2312yes—
160C22×C22⋊C4—22no—
161#486—24no—
162#486—24no—
163#476—24no—
164#474—24no—
165C2×#107C2312yes—
166C2×#107C2311yescharacteristic
167C2×#107C2311yescharacteristic
168C2×#107C2311yescharacteristic
169C2×#107C2311yescharacteristic
170C2×#106C2312yes—
171C2×#106C2312yes—
172C2×#106C2312yes—
173C2×C4⋊C8C2311yescharacteristic
174C2×C4⋊C8C2311yescharacteristic
175C2×C4⋊C8C2311yescharacteristic
176C2×C4⋊C8C2311yescharacteristic
177C2×#102C2312yes—
178C2×#102C2312yes—
179C2×#102C2312yes—
180C2×#102C2312yes—
181C2×#102C2312yes—
182C2×#102C2312yes—
183C2×#102C2311yescharacteristic
184C2×#102C2311yescharacteristic
185C2×#102C2311yescharacteristic
186C2×#102C2311yescharacteristic
187C2×#102C2312yes—
188C2×#102C2312yes—
189C2×#102C2312yes—
190C2×#102C2312yes—
191C2×C22⋊C8C2312yes—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×C22⋊C8C2312yes—
195C2×#97C2312yes—
196C2×C4×C8C2311yescharacteristic
197C2×C4×C8C2311yescharacteristic
198C2×C4×C8C2312yes—
199#401—22no—
200#400—22no—
201#400—22no—
202#399—22no—
203#397—22no—
204#397—22no—
205#397—22no—
206#395—22no—
207#393—22no—
208#393—22no—
209#391—21no—
210#391—21no—
211#391—21no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391—21no—
216#391—22no—
217#390—21no—
218#390—21no—
219#390—21no—
220#390—22no—
221#390—22no—
222#390—22no—
223#390—22no—
224#390—21no—
225#390—21no—
226#390D411yescharacteristic
227#390D411yescharacteristic
228#390C2312yes—
229#390C2311yescharacteristic
230#390C2312yes—
231#390C2312yes—
232#390C2311yescharacteristic
233#389—21no—
234#389—21no—
235#389D411yescharacteristic
236#389D411yescharacteristic
237#389C2311yescharacteristic
238#389C2311yescharacteristic
239#389C2311yescharacteristic
240#389C2311yescharacteristic
241#389C2312yes—
242#389C2312yes—
243#388—22no—
244#388—22no—
245#388—22no—
246#388—22no—
247#388—22no—
248#388—22no—
249#388—21no—
250#388—21no—
251#388—22no—
252#388—22no—
253#388D412yes—
254#388D412yes—
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#384C2311yescharacteristic
266#384C2311yescharacteristic
267#383—22no—
268#382—21no—
269#382C2312yes—
270#382C2312yes—
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#340C2311yescharacteristic
295#340C2311yescharacteristic
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2312yes—
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×Q8—21no—
322C22×D4—28no—
323C22×D4—22no—
324C22×D4—24no—
325C22×D4—24no—
326C22×D4—21no—
327C22×D4—21no—
328C22×D4—22no—
329C22×D4—42no—
330C22×D4—42no—
331C22×D4—42no—
332C22×D4—42no—
333C22×D4—82no—
334C22×D4—82no—
335C22×D4C2×D411yescharacteristic
336C22×D4C2412yes—
337C22×D4C2411yescharacteristic
338C23×C4—21no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4C2412yes—
342C22×C8C2412yes—
343C22×C8C2411yescharacteristic
344C22×C8C2411yescharacteristic
345C22×C8C2412yes—
346C22×C8C2411yescharacteristic
347C22×C8C2411yescharacteristic
348C4⋊Q8—22no—
349C4⋊Q8—22no—
350C4⋊Q8—22no—
351C4⋊Q8—22no—
352C4⋊Q8—41no—
353C4⋊Q8—41no—
354#127—22no—
355#127#4114yes—
356#124—82no—
357#121—28no—
358#121—24no—
359#121—24no—
360#120—216no—
361C4×Q8—82no—
362C4×Q8—82no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—42no—
367C4×D4—42no—
368C4×D4—42no—
369C4×D4—42no—
370C4×D4—82no—
371C4×D4—82no—
372C4×D4—82no—
373C4×D4#4114yes—
374#117—42no—
375#117—42no—
376#117—42no—
377#117—42no—
378#117—82no—
379#117—82no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
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—22no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4C2×D411yescharacteristic
394C2×C4⋊C4C2×D411yescharacteristic
395C2×C4⋊C4C2×D411yescharacteristic
396C2×C4⋊C4C2×D412yes—
397C2×C4⋊C4C2×D412yes—
398C2×C4⋊C4C2411yescharacteristic
399C2×C4⋊C4C2412yes—
400C2×C4⋊C4C2411yescharacteristic
401C2×C4⋊C4C2412yes—
402C2×C4⋊C4C2412yes—
403C2×C4⋊C4C2411yescharacteristic
404C2×C4⋊C4C2411yescharacteristic
405C2×C4⋊C4C2411yescharacteristic
406C2×C4⋊C4C2411yescharacteristic
407C2×C4⋊C4C2411yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—84no—
429C2×C22⋊C4C2×D412yes—
430C2×C22⋊C4C2×D412yes—
431C2×C22⋊C4C2×D412yes—
432C2×C22⋊C4C2×D412yes—
433C2×C22⋊C4C2×D412yes—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2411yescharacteristic
446C2×C42C2412yes—
447C2×C42C2411yescharacteristic
448C2×C42C2411yescharacteristic
449#107—24no—
450#107—41no—
451#107—41no—
452#107—41no—
453#107—41no—
454#106—24no—
455#106—42no—
456#106—42no—
457C4⋊C8—22no—
458C4⋊C8—22no—
459C4⋊C8—41no—
460C4⋊C8—41no—
461#102—24no—
462#102—24no—
463#102—24no—
464#102—24no—
465#102—24no—
466#102—24no—
467#102—42no—
468#102—42no—
469#102—42no—
470#102—42no—
471#102—41no—
472#102—41no—
473#102—41no—
474#102—41no—
475C22⋊C8—42no—
476C22⋊C8—42no—
477C22⋊C8—42no—
478C22⋊C8—42no—
479#97—42no—
480C4×C8—22no—
481C4×C8—22no—
482C4×C8—42no—
483#95—21no—
484#95—21no—
485#95—22no—
486#95—21no—
487#95—21no—
488#95—22no—
489#95—22no—
490#95—21no—
491#95—22no—
492#95—21no—
493#95—22no—
494#95—21no—
495#95—22no—
496#95—22no—
497#95—22no—
498#95—22no—
499#95—22no—
500#95—22no—
501#95—22no—
502#95—22no—
503#95—22no—
504#95C2×D412yes—
505#95C2×D412yes—
506#95C2×D412yes—
507C24—28no—
508C24—21no—
509C24—22no—
510C24—82no—
511C24—82no—
512C24—82no—
513C24—82no—
514C24—82no—
515C24—82no—
516C24C22×D412yes—
517C2×Q8—42no—
518C2×Q8—42no—
519C2×Q8—42no—
520C2×Q8—42no—
521C2×Q8—42no—
522C2×Q8—81no—
523C2×Q8—81no—
524C2×Q8—81no—
525C2×Q8—81no—
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—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—44no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—82no—
579C22×C4—82no—
580C22×C4—82no—
581C22×C4—82no—
582C22×C4—82no—
583C22×C4C22×D412yes—
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D412yes—
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D412yes—
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—22no—
628C4⋊C4—22no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—42no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4—42no—
639C4⋊C4—81no—
640C4⋊C4—82no—
641C4⋊C4—81no—
642C4⋊C4—81no—
643C4⋊C4—81no—
644C4⋊C4—81no—
645C4⋊C4—81no—
646C4⋊C4—81no—
647C4⋊C4—82no—
648C4⋊C4C2×#4112yes—
649C22⋊C4—28no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—81no—
658C22⋊C4—82no—
659C22⋊C4—82no—
660C22⋊C4—81no—
661C22⋊C4—81no—
662C22⋊C4—82no—
663C22⋊C4—82no—
664C22⋊C4—82no—
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—
674C42—22no—
675C42—22no—
676C42—22no—
677C42—22no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—21no—
682C42—41no—
683C42—41no—
684C42—42no—
685C42—42no—
686C42—42no—
687C42—82no—
688C42—82no—
689C42—82no—
690C42—82no—
691C42C2×#4112yes—
692C42C2×#4112yes—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—24no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—42no—
703C23—41no—
704C23—41no—
705C23—42no—
706C23—42no—
707C23—41no—
708C23—42no—
709C23—41no—
710C23—41no—
711C23—42no—
712C23—41no—
713C23—42no—
714C23—88no—
715C23—88no—
716C23—88no—
717C23—164no—
718C23—164no—
719C23—164no—
720C23—164no—
721C23C23×D411yescharacteristic
722Q8—84no—
723Q8—84no—
724Q8—162no—
725D4—22no—
726D4—22no—
727D4—24no—
728D4—24no—
729D4—44no—
730D4—48no—
731D4—42no—
732D4—42no—
733D4—41no—
734D4—41no—
735D4—84no—
736D4—88no—
737D4—88no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—48no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—164no—
797C2×C4—164no—
798C2×C4#52512yes—
799C2×C4#52512yes—
800C2×C4#57612yes—
801C2×C4#57712yes—
802C2×C4C22×#4111yescharacteristic
803C2×C4C22×#4111yescharacteristic
804C2×C4#58511yescharacteristic
805C2×C4#58511yescharacteristic
806C2×C4#58511yescharacteristic
807C2×C4#58511yescharacteristic
808C8—42no—
809C8—42no—
810C8—41no—
811C8—41no—
812C8—41no—
813C8—41no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—44no—
820C22—42no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—44no—
827C22—82no—
828C22—81no—
829C22—82no—
830C22—81no—
831C22—82no—
832C22—81no—
833C22—82no—
834C22—81no—
835C22—1616no—
836C22C2×#52511yescharacteristic
837C22#348511yescharacteristic
838C22#350011yescharacteristic
839C22C2×#57611yescharacteristic
840C22C2×#57711yescharacteristic
841C22#358411yescharacteristic
842C22#358511yescharacteristic
843C4—22no—
844C4—41no—
845C4—42no—
846C4—41no—
847C4—42no—
848C4—41no—
849C4—42no—
850C4—41no—
851C4—42no—
852C4—81no—
853C4—81no—
854C4—81no—
855C4—81no—
856C4—81no—
857C4—81no—
858C4—82no—
859C4—82no—
860C4—82no—
861C4#311814yes—
862C4#351011yescharacteristic
863C4#351011yescharacteristic
864C4#352111yescharacteristic
865C4#352111yescharacteristic
866C2—82no—
867C2—84no—
868C2—82no—
869C2#3603311yescharacteristic
870C2C2×#311811yescharacteristic
871C2#6059211yescharacteristic
872C2#6178611yescharacteristic
873C2#6180211yescharacteristic
874C2#6256111yescharacteristic
875C2#6260811yescharacteristic
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. #39515C2semidirect
3. #30177C2semidirect
4. #29865C2semidirect
5. #29258C2semidirect
6. #29116C2semidirect
7. #28718C2semidirect
8. #27594C2semidirect
9. #27534C2semidirect
10. #27525C2semidirect
11. #27125C2semidirect
12. #27106C2semidirect
13. #26303C2semidirect
14. #26297C2semidirect
17. #23774C2semidirect
18. #23766C2semidirect
19. #23223C2semidirect
20. #23216C2semidirect
21. #23066C2semidirect
22. #23061C2semidirect
23. #22836C2semidirect
29. #2862C22semidirect
32. #2628C22semidirect
38. #2495C22semidirect
39. #2494C22semidirect
42. #2369C22semidirect
44. #2365C22semidirect
54. #2314C22semidirect
57. C4×C4⋊Q8C22semidirect
61. #2099C22semidirect
62. #2094C22semidirect
64. #2086C22semidirect
65. #2086C22semidirect
66. #2085C22semidirect
67. #2085C22semidirect
68. #2077C22semidirect
69. #2077C22semidirect
70. #2076C22semidirect
71. #2075C22semidirect
74. #2073C22semidirect
75. #2073C22semidirect
78. #2057C22semidirect
84. #2023C22semidirect
85. #1990C22semidirect
86. #1990C22semidirect
87. #1988C22semidirect
88. #1987C22semidirect
93. #1948C22semidirect
94. #1948C22semidirect
96. #1936C22semidirect
98. #1934C22semidirect
101. #1925C22semidirect
102. #1925C22semidirect
103. #1924C22semidirect
104. #1923C22semidirect
105. #1921C22semidirect
106. #1920C22semidirect
107. #1864C22semidirect
108. #1864C22semidirect
109. #1862C22semidirect
110. #1862C22semidirect
111. #1854C22semidirect
112. #1854C22semidirect
113. #1831C22semidirect
114. #1825C22semidirect
115. #1825C22semidirect
116. #1818C22semidirect
117. #1804C22semidirect
118. #1804C22semidirect
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
#395152
#344932
#301772
#298652
#292582
#291162
#287182
#275942
#275342
#275252
#271252
#271062
#263032
#262972
#258852
#258812
#237742
#237662
#232232
#232162
#230662
#230612
#228362