Finite Group Databasebeta

← #6568324

Subgroups — #6568324

Order 512.

1621 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#39514C211yesmaximal, characteristic, complemented
2#34493C211yesmaximal, characteristic
3#30180C212yesmaximal, complemented
4#29868C211yesmaximal, characteristic, complemented
5#29256C211yesmaximal, characteristic, complemented
6#29115C212yesmaximal, complemented
7#28716C211yesmaximal, characteristic, complemented
8#27591C212yesmaximal, complemented
9#27539C212yesmaximal, complemented
10#27518C212yesmaximal, complemented
11#27122C212yesmaximal, complemented
12#27107C212yesmaximal, complemented
13#26299C211yesmaximal, characteristic, complemented
14#26297C211yesmaximal, characteristic, complemented
15#25881C211yesmaximal, characteristic
16#25881C211yesmaximal, characteristic
17#23778C211yesmaximal, characteristic, complemented
18#23771C212yesmaximal, complemented
19#23223C211yesmaximal, characteristic, complemented
20#23215C211yesmaximal, characteristic, complemented
21#23067C211yesmaximal, characteristic, complemented
22#23061C211yesmaximal, characteristic, complemented
23#22836C211yesmaximal, characteristic, complemented
24C2×D42C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#486C2211yescharacteristic
27C2×#476C2211yescharacteristic
28C2×#476C2211yescharacteristic
29#2868C2211yescharacteristic, complemented
30#2716—22no—
31#2716—22no—
32#2629C2212yescomplemented
33#2570—21no—
34#2570—21no—
35#2563C2211yescharacteristic
36#2563C2211yescharacteristic
37#2512—21no—
38#2512—21no—
39#2496C2212yescomplemented
40#2496C2212yescomplemented
41#2375—22no—
42#2369C2211yescharacteristic, complemented
43#2369C2211yescharacteristic, complemented
44#2366C2211yescharacteristic
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#2084C2212yescomplemented
67#2084C2212yescomplemented
68#2077C2212yescomplemented
69#2077C2212yescomplemented
70#2075C2212yescomplemented
71#2075C2212yescomplemented
72#2071C2212yes—
73#2071C2212yes—
74#2071C2212yescomplemented
75#2071C2212yescomplemented
76#2067C2211yescharacteristic
77#2065C2211yescharacteristic
78#2059C2211yescharacteristic, complemented
79#2034C2212yes—
80#2034C2212yes—
81#2034C2212yes—
82#2034C2212yes—
83#2025C2211yescharacteristic
84#2025C2212yescomplemented
85#1990C2211yescharacteristic, complemented
86#1990C2211yescharacteristic, complemented
87#1987C2211yescharacteristic, complemented
88#1987C2211yescharacteristic, 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#1920C2212yescomplemented
106#1919C2212yescomplemented
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×#107C2211yescharacteristic, complemented
125C4×#106C2212yescomplemented
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×#126—22no—
145C2×#126—22no—
146C2×#125C2311yescharacteristic
147C2×#121—21no—
148C2×#121C2312yes—
149C2×#120—22no—
150C2×C4×D4—21no—
151C2×C4×D4—21no—
152C2×C4×D4—21no—
153C2×C4×D4C2311yescharacteristic
154C2×C4×D4C2312yes—
155C2×C4×D4C2312yes—
156C2×C4×D4C2311yescharacteristic
157C2×#117—21no—
158C2×#117—21no—
159C2×#117C2312yes—
160C2×#117C2312yes—
161C22×C22⋊C4—22no—
162#486—24no—
163#486—24no—
164#476—24no—
165#476—24no—
166C2×#107C2311yescharacteristic
167C2×#107C2312yes—
168C2×#107C2311yescharacteristic
169C2×#106C2312yes—
170C2×#106C2312yes—
171C2×#106C2311yescharacteristic
172C2×#106C2312yes—
173C2×#106C2311yescharacteristic
174C2×C4⋊C8C2311yescharacteristic
175C2×C4⋊C8C2311yescharacteristic
176C2×C4⋊C8C2311yescharacteristic
177C2×C4⋊C8C2311yescharacteristic
178C2×#102C2312yes—
179C2×#102C2312yes—
180C2×#102C2312yes—
181C2×#102C2312yes—
182C2×#102C2312yes—
183C2×#102C2312yes—
184C2×#102C2311yescharacteristic
185C2×#102C2311yescharacteristic
186C2×#102C2311yescharacteristic
187C2×#102C2311yescharacteristic
188C2×#102C2312yes—
189C2×#102C2312yes—
190C2×#102C2312yes—
191C2×#102C2312yes—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196C2×#97C2312yes—
197C2×C4×C8C2311yescharacteristic
198C2×C4×C8C2311yescharacteristic
199C2×C4×C8C2312yes—
200#400—22no—
201#400—22no—
202#398—22no—
203#398—22no—
204#397—22no—
205#397—22no—
206#396—22no—
207#396—22no—
208#393—22no—
209#393—22no—
210#391—22no—
211#391—22no—
212#390—21no—
213#390—21no—
214#390—21no—
215#390—21no—
216#390—22no—
217#390—22no—
218#390—22no—
219#390—22no—
220#390—21no—
221#390—21no—
222#390D411yescharacteristic
223#390D411yescharacteristic
224#390C2312yes—
225#390C2311yescharacteristic
226#390C2312yes—
227#390C2312yes—
228#390C2311yescharacteristic
229#389—21no—
230#389—21no—
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—21no—
244#388—21no—
245#388—22no—
246#388—22no—
247#388D412yes—
248#388D412yes—
249#387—22no—
250#387—22no—
251#387—21no—
252#387—21no—
253#387—22no—
254#387—22no—
255#386—22no—
256#386—22no—
257#386—22no—
258#386—22no—
259#386—22no—
260#385—22no—
261#384—21no—
262#384—21no—
263#384C2311yescharacteristic
264#384C2312yes—
265#384C2312yes—
266#382—21no—
267#382—21no—
268#382C2311yescharacteristic
269#380—21no—
270#380C2312yes—
271#380C2312yes—
272#380C2312yes—
273#380C2312yes—
274#380C2312yes—
275#379—22no—
276#379—22no—
277#379—22no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4—21no—
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×C8C2412yes—
343C22×C8C2411yescharacteristic
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#126—84no—
356#126—84no—
357#125—41no—
358#125—41no—
359#121—28no—
360#121—24no—
361#121—24no—
362#120—216no—
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—22no—
386C2×C4⋊C4—22no—
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⋊C4C2×D411yescharacteristic
397C2×C4⋊C4C2×D411yescharacteristic
398C2×C4⋊C4C2×D411yescharacteristic
399C2×C4⋊C4C2×D412yes—
400C2×C4⋊C4C2×D412yes—
401C2×C4⋊C4C2411yescharacteristic
402C2×C4⋊C4C2412yes—
403C2×C4⋊C4C2411yescharacteristic
404C2×C4⋊C4C2411yescharacteristic
405C2×C4⋊C4C2411yescharacteristic
406C2×C4⋊C4C2412yes—
407C2×C4⋊C4C2412yes—
408C2×C4⋊C4C2411yescharacteristic
409C2×C4⋊C4C2411yescharacteristic
410C2×C4⋊C4C2411yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—84no—
432C2×C22⋊C4C2×D412yes—
433C2×C22⋊C4C2×D412yes—
434C2×C22⋊C4C2×D412yes—
435C2×C22⋊C4C2×D412yes—
436C2×C22⋊C4C2×D412yes—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—21no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2411yescharacteristic
449C2×C42C2412yes—
450C2×C42C2411yescharacteristic
451C2×C42C2411yescharacteristic
452#107—41no—
453#107—42no—
454#107—41no—
455#106—24no—
456#106—24no—
457#106—41no—
458#106—42no—
459#106—41no—
460C4⋊C8—22no—
461C4⋊C8—22no—
462C4⋊C8—41no—
463C4⋊C8—41no—
464#102—24no—
465#102—24no—
466#102—24no—
467#102—24no—
468#102—24no—
469#102—24no—
470#102—42no—
471#102—42no—
472#102—42no—
473#102—42no—
474#102—41no—
475#102—41no—
476#102—41no—
477#102—41no—
478C22⋊C8—42no—
479C22⋊C8—42no—
480C22⋊C8—42no—
481C22⋊C8—42no—
482#97—42no—
483C4×C8—22no—
484C4×C8—22no—
485C4×C8—42no—
486#95—21no—
487#95—21no—
488#95—22no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—22no—
494#95—22no—
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#95C2×D412yes—
506#95C2×D412yes—
507#95C2×D412yes—
508C24—28no—
509C24—21no—
510C24—22no—
511C24—82no—
512C24—82no—
513C24—82no—
514C24—82no—
515C24—82no—
516C24—82no—
517C24C22×D412yes—
518C2×Q8—42no—
519C2×Q8—42no—
520C2×Q8—81no—
521C2×Q8—81no—
522C2×Q8—81no—
523C2×Q8—81no—
524C2×D4—28no—
525C2×D4—28no—
526C2×D4—22no—
527C2×D4—24no—
528C2×D4—24no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—21no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—81no—
544C2×D4—81no—
545C2×D4—82no—
546C2×D4—82no—
547C2×D4—84no—
548C2×D4—84no—
549C2×D4—84no—
550C2×D4—84no—
551C2×D4—816no—
552C2×D4—82no—
553C2×D4—82no—
554C2×D4C2×#4112yes—
555C2×D4C2×#4114yes—
556C22×C4—21no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—44no—
576C22×C4—82no—
577C22×C4—82no—
578C22×C4—82no—
579C22×C4—82no—
580C22×C4—82no—
581C22×C4C22×D412yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C2511yescharacteristic
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—21no—
598C2×C8—22no—
599C2×C8—21no—
600C2×C8—22no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—21no—
608C2×C8—21no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—21no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—22no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—22no—
630C4⋊C4—21no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—42no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—44no—
637C4⋊C4—42no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—44no—
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⋊C4C2×#4112yes—
650C22⋊C4—28no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—81no—
659C22⋊C4—82no—
660C22⋊C4—82no—
661C22⋊C4—81no—
662C22⋊C4—81no—
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—
674C22⋊C4—82no—
675C42—22no—
676C42—22no—
677C42—22no—
678C42—22no—
679C42—22no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—41no—
685C42—42no—
686C42—42no—
687C42—42no—
688C42—82no—
689C42—82no—
690C42—82no—
691C42—82no—
692C42C2×#4112yes—
693C42C2×#4112yes—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—24no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—42no—
704C23—41no—
705C23—42no—
706C23—41no—
707C23—42no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—42no—
715C23—88no—
716C23—88no—
717C23—88no—
718C23—164no—
719C23—164no—
720C23—164no—
721C23—164no—
722C23C23×D411yescharacteristic
723Q8—162no—
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—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
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—41no—
762C2×C4—41no—
763C2×C4—48no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—42no—
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—42no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—164no—
796C2×C4—164no—
797C2×C4#52512yes—
798C2×C4#52512yes—
799C2×C4#57612yes—
800C2×C4#57712yes—
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
841C22C2×#57711yescharacteristic
842C22#358511yescharacteristic
843C4—22no—
844C4—22no—
845C4—41no—
846C4—42no—
847C4—41no—
848C4—42no—
849C4—42no—
850C4—41no—
851C4—42no—
852C4—81no—
853C4—82no—
854C4—81no—
855C4—81no—
856C4—81no—
857C4—81no—
858C4—81no—
859C4—82no—
860C4—82no—
861C4#312314yes—
862C4#351011yescharacteristic
863C4#351011yescharacteristic
864C4#352111yescharacteristic
865C4#352111yescharacteristic
866C2—82no—
867C2—84no—
868C2—82no—
869C2#3603311yescharacteristic
870C2C2×#312311yescharacteristic
871C2#6059011yescharacteristic
872C2#6178811yescharacteristic
873C2#6181511yescharacteristic
874C2#6255211yescharacteristic
875C2#6261711yescharacteristic
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. #39514C2semidirect
3. #30180C2semidirect
4. #29868C2semidirect
5. #29256C2semidirect
6. #29115C2semidirect
7. #28716C2semidirect
8. #27591C2semidirect
9. #27539C2semidirect
10. #27518C2semidirect
11. #27122C2semidirect
12. #27107C2semidirect
13. #26299C2semidirect
14. #26297C2semidirect
17. #23778C2semidirect
18. #23771C2semidirect
19. #23223C2semidirect
20. #23215C2semidirect
21. #23067C2semidirect
22. #23061C2semidirect
23. #22836C2semidirect
29. #2868C22semidirect
32. #2629C22semidirect
39. #2496C22semidirect
40. #2496C22semidirect
42. #2369C22semidirect
43. #2369C22semidirect
54. #2314C22semidirect
58. C4×#125C22semidirect
61. #2101C22semidirect
63. #2092C22semidirect
64. #2088C22semidirect
65. #2087C22semidirect
66. #2084C22semidirect
67. #2084C22semidirect
68. #2077C22semidirect
69. #2077C22semidirect
70. #2075C22semidirect
71. #2075C22semidirect
74. #2071C22semidirect
75. #2071C22semidirect
78. #2059C22semidirect
84. #2025C22semidirect
85. #1990C22semidirect
86. #1990C22semidirect
87. #1987C22semidirect
88. #1987C22semidirect
93. #1948C22semidirect
94. #1947C22semidirect
96. #1936C22semidirect
98. #1934C22semidirect
100. #1926C22semidirect
102. #1925C22semidirect
103. #1924C22semidirect
104. #1923C22semidirect
105. #1920C22semidirect
106. #1919C22semidirect
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×#106C22semidirect
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
#395142
#344932
#301802
#298682
#292562
#291152
#287162
#275912
#275392
#275182
#271222
#271072
#262992
#262972
#258812
#237782
#237712
#232232
#232152
#230672
#230612
#228362