Finite Group Databasebeta

← #6508813

Subgroups — #6508813

Order 512.

2019 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3093C211yesmaximal, characteristic, complemented
2C2×#2973C211yesmaximal, characteristic, complemented
3#35077C211yesmaximal, characteristic
4#34809C211yesmaximal, characteristic, complemented
5#28103C212yesmaximal, complemented
6#28101C212yesmaximal, complemented
7#27669C212yesmaximal, complemented
8#27668C212yesmaximal, complemented
9#25247C212yesmaximal, complemented
10#25245C212yesmaximal, complemented
11#25243C212yesmaximal, complemented
12#25241C212yesmaximal, complemented
13#24611C212yesmaximal, complemented
14#24610C212yesmaximal, complemented
15#24555C212yesmaximal, complemented
16#24554C212yesmaximal, complemented
17#21944C211yesmaximal, characteristic, complemented
18#21766C211yesmaximal, characteristic, complemented
19#20702C211yesmaximal, characteristic, complemented
20C2×#525C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C22×#117C2211yescharacteristic
23#3093—28no—
24C2×#485C2212yes—
25C2×#485C2212yescomplemented
26C2×#482C2212yes—
27C2×#482C2212yescomplemented
28#2973—28no—
29C2×#435C2212yes—
30C2×#435C2212yes—
31C2×#435C2212yes—
32C2×#435C2212yes—
33C2×#432C2212yes—
34C2×#428C2211yescharacteristic, complemented
35C2×#428C2211yescharacteristic, complemented
36C2×#417C2211yescharacteristic, complemented
37C2×#417C2211yescharacteristic, complemented
38C2×#407C2211yescharacteristic
39C2×#407C2211yescharacteristic
40C22×C22⋊C8C2212yes—
41#2855C2211yescharacteristic
42#2854C2211yescharacteristic
43#2848C2211yescharacteristic
44#2847C2211yescharacteristic
45#2630—22no—
46#2579—21no—
47#2534—21no—
48#2487C2212yes—
49#2486C2212yes—
50#2485C2212yes—
51#2485C2212yes—
52#2485C2212yes—
53#2484—21no—
54#2483—21no—
55#2482—21no—
56#2417C2212yes—
57#2416C2212yes—
58#2412—21no—
59#2410—21no—
60#2407C2212yes—
61#2405—21no—
62#2395—22no—
63#2325—22no—
64C4×#123—22no—
65#2296C2212yes—
66#2280C2211yescharacteristic
67#2280C2212yes—
68C2×#380C2211yescharacteristic
69#2088C2212yescomplemented
70#2088C2212yescomplemented
71#2087C2212yescomplemented
72#2086C2212yescomplemented
73#2077C2212yescomplemented
74#2077C2212yescomplemented
75#2076C2212yescomplemented
76#2075C2212yescomplemented
77#2068C2212yescomplemented
78#2067C2212yescomplemented
79#2066C2212yescomplemented
80#2065C2212yescomplemented
81#2036C2212yescomplemented
82#2035C2212yescomplemented
83#2034C2212yescomplemented
84#2033C2212yescomplemented
85#1944C2212yescomplemented
86#1944C2212yescomplemented
87#1943C2212yescomplemented
88#1943C2212yescomplemented
89#1936C2212yescomplemented
90#1936C2212yescomplemented
91#1935C2212yescomplemented
92#1935C2212yescomplemented
93#1895C2211yescharacteristic, complemented
94#1895C2211yescharacteristic, complemented
95#1894C2211yescharacteristic, complemented
96#1894C2211yescharacteristic, complemented
97#1893C2212yescomplemented
98#1893C2212yescomplemented
99#1892C2212yescomplemented
100#1892C2212yescomplemented
101#1875C2212yes—
102#1873C2212yes—
103#1854C2212yes—
104#1854C2212yes—
105#1853C2212yescomplemented
106#1852C2212yescomplemented
107#1825C2212yes—
108#1825C2212yes—
109#1825C2212yescomplemented
110#1824C2212yescomplemented
111#1823C2212yescomplemented
112#1809C2212yescomplemented
113#1809C2212yescomplemented
114#1808C2212yescomplemented
115#1808C2212yescomplemented
116#1807C2212yescomplemented
117#1807C2212yescomplemented
118#1788C2212yescomplemented
119#1736C2212yescomplemented
120#1736C2212yescomplemented
121C22×#41C2311yescharacteristic
122C23×D4D411yescharacteristic
123C24×C4C2311yescharacteristic
124C24×C4C2311yescharacteristic
125C22×M16C2311yescharacteristic
126C22×M16C2311yescharacteristic
127C22×M16C2311yescharacteristic
128C22×M16C2311yescharacteristic
129C23×C8C2312yes—
130C23×C8C2312yes—
131#525—24no—
132#525—24no—
133C2×#123—22no—
134C2×#123—21no—
135C2×#123—21no—
136C2×C22⋊Q8C2311yescharacteristic
137C2×C22⋊Q8C2311yescharacteristic
138C2×C22⋊Q8C2312yes—
139C2×#121—22no—
140C2×#121C2311yescharacteristic
141C2×#121C2311yescharacteristic
142C2×#121C2312yes—
143C2×#120—21no—
144C2×#120—21no—
145C2×C4×D4—24no—
146C2×C4×D4—24no—
147C2×C4×D4—21no—
148C2×C4×D4—21no—
149C2×C4×D4D412yes—
150C2×C4×D4D412yes—
151C2×C4×D4C2312yes—
152C2×C4×D4C2312yes—
153C2×#117—21no—
154C2×#117—21no—
155C2×#117—24no—
156C2×#117—24no—
157C2×#117C2312yes—
158C2×#117C2312yes—
159C2×#117C2311yescharacteristic
160C2×#117C2312yes—
161C22×C4⋊C4D411yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2312yes—
165C22×C22⋊C4—21no—
166C22×C22⋊C4—21no—
167C22×C22⋊C4D411yescharacteristic
168C22×C22⋊C4D411yescharacteristic
169C22×C42—21no—
170C22×C42C2311yescharacteristic
171#485—28no—
172#485—28no—
173#482—28no—
174#482—28no—
175#435—28no—
176#435—28no—
177#435—28no—
178#435—28no—
179#432—28no—
180#428—24no—
181#428—24no—
182C2×#107C2312yes—
183C2×#107C2312yes—
184C2×#107C2312yes—
185C2×#107C2312yes—
186C2×#106C2312yes—
187C2×#106C2312yes—
188C2×#106C2312yes—
189C2×#106C2312yes—
190C2×C4⋊C8C2312yes—
191C2×C4⋊C8C2312yes—
192#417—24no—
193#417—24no—
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×#102C2312yes—
201C2×#102C2312yes—
202#407—24no—
203#407D418yescomplemented
204C2×C22⋊C8—28no—
205C2×C22⋊C8C2312yes—
206C2×C22⋊C8C2312yes—
207C2×C22⋊C8C2312yes—
208C2×C22⋊C8C2312yes—
209C2×C22⋊C8C2312yes—
210C2×C22⋊C8C2312yes—
211C2×#97C2312yes—
212C2×#97C2312yes—
213#400—22no—
214#399—22no—
215#398—22no—
216#398—22no—
217#397—22no—
218#397—22no—
219#397—22no—
220#397—22no—
221#396—22no—
222#396—22no—
223#394—22no—
224#394—22no—
225#394—22no—
226#394—22no—
227#394—22no—
228#392—22no—
229#391C2312yes—
230#390C2312yes—
231#389C2312yes—
232#389C2312yes—
233#389C2312yes—
234#389C2312yes—
235#389C2312yes—
236#389C2312yes—
237#388—22no—
238#388—22no—
239#388—22no—
240#388—22no—
241#387—22no—
242#387—22no—
243#387—22no—
244#387—22no—
245#386—22no—
246#386—22no—
247#386—21no—
248#386—21no—
249#386—22no—
250#386—22no—
251#386—22no—
252#385—21no—
253#385—21no—
254#385—22no—
255#385—22no—
256#385—22no—
257#385—22no—
258#385—22no—
259#381—21no—
260#381—21no—
261#381—22no—
262#381—22no—
263#380—21no—
264#380—21no—
265#380—22no—
266#380C2312yes—
267#380C2312yes—
268#380C2312yes—
269#380C2312yes—
270#380C2312yes—
271#380C2312yes—
272#380C2312yes—
273#380C2312yes—
274#380C2311yescharacteristic
275#380C2311yescharacteristic
276#380C2311yescharacteristic
277#380C2311yescharacteristic
278#379—21no—
279#379—22no—
280#379—21no—
281C4×C4⋊C4—22no—
282C4×C4⋊C4—22no—
283C4×C22⋊C4—21no—
284C4×C22⋊C4—22no—
285C4×C22⋊C4—22no—
286C4×C22⋊C4—21no—
287C2×#95—21no—
288#340C2312yes—
289#340C2312yes—
290#340C2312yes—
291#340C2312yes—
292#340C2312yes—
293#340C2312yes—
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2312yes—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304C25C2×D411yescharacteristic
305C25C2×D411yescharacteristic
306C2×#41—22no—
307C2×#41—22no—
308C2×#41—42no—
309C2×#41—42no—
310C22×Q8C2411yescharacteristic
311C22×D4—24no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—22no—
315C22×D4—21no—
316C22×D4—44no—
317C22×D4C2×D412yes—
318C22×D4C2×D412yes—
319C22×D4C2411yescharacteristic
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—21no—
323C23×C4—22no—
324C23×C4—21no—
325C23×C4—21no—
326C23×C4—42no—
327C23×C4—42no—
328C23×C4—42no—
329C23×C4—42no—
330C23×C4C2×D411yescharacteristic
331C23×C4C2×D411yescharacteristic
332C23×C4C2×D411yescharacteristic
333C23×C4C2×D412yes—
334C23×C4C2×D411yescharacteristic
335C23×C4C2×D411yescharacteristic
336C23×C4C2×D411yescharacteristic
337C23×C4C2×D414yes—
338C23×C4#4114yes—
339C23×C4C2412yes—
340C23×C4C2411yescharacteristic
341C23×C4C2411yescharacteristic
342C23×C4C2411yescharacteristic
343C2×M16—22no—
344C2×M16—22no—
345C2×M16—42no—
346C2×M16—42no—
347C2×M16—42no—
348C2×M16—42no—
349C2×M16C2×D414yes—
350C2×M16C2×D414yes—
351C22×C8—24no—
352C22×C8—24no—
353C22×C8—42no—
354C22×C8—42no—
355C22×C8—42no—
356C22×C8—42no—
357C22×C8C2412yes—
358C22×C8C2412yes—
359C22×C8C2412yes—
360C22×C8C2412yes—
361#123—48no—
362#123—44no—
363#123—82no—
364C22⋊Q8—22no—
365C22⋊Q8—22no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8—42no—
369C22⋊Q8—42no—
370#121—22no—
371#121—22no—
372#121—22no—
373#121—22no—
374#121—48no—
375#121—42no—
376#121—42no—
377#120—44no—
378#120—82no—
379C4×D4—28no—
380C4×D4—28no—
381C4×D4—24no—
382C4×D4—24no—
383C4×D4—24no—
384C4×D4—24no—
385C4×D4—44no—
386C4×D4—44no—
387#117—24no—
388#117—24no—
389#117—22no—
390#117—24no—
391#117—24no—
392#117—22no—
393#117—42no—
394#117—42no—
395#117—44no—
396#117—44no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
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—22no—
414C2×C4⋊C4—42no—
415C2×C4⋊C4—42no—
416C2×C4⋊C4C2×D412yes—
417C2×C4⋊C4C2×D412yes—
418C2×C4⋊C4C2412yes—
419C2×C4⋊C4C2412yes—
420C2×C4⋊C4C2412yes—
421C2×C4⋊C4C2412yes—
422C2×C4⋊C4C2411yescharacteristic
423C2×C4⋊C4C2411yescharacteristic
424C2×C4⋊C4C2412yes—
425C2×C4⋊C4C2412yes—
426C2×C22⋊C4—24no—
427C2×C22⋊C4—24no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—44no—
453C2×C22⋊C4—82no—
454C2×C22⋊C4C2×D412yes—
455C2×C22⋊C4C2×D412yes—
456C2×C22⋊C4C2×D412yes—
457C2×C22⋊C4C2×D412yes—
458C2×C42—22no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—21no—
463C2×C42—22no—
464C2×C42—44no—
465C2×C42C2×D412yes—
466C2×C42C2412yes—
467#107—24no—
468#107—24no—
469#107—42no—
470#107—42no—
471#106—24no—
472#106—24no—
473#106—42no—
474#106—42no—
475C4⋊C8—24no—
476C4⋊C8—24no—
477#103—24no—
478#103—24no—
479#103—42no—
480#103—42no—
481#102—24no—
482#102—24no—
483#102—42no—
484#102—42no—
485C22⋊C8—24no—
486C22⋊C8—24no—
487C22⋊C8—24no—
488C22⋊C8—24no—
489C22⋊C8C2×D418yes—
490C22⋊C8C2×D418yes—
491#97—24no—
492#97—24no—
493#95—21no—
494#95—22no—
495#95—21no—
496#95—22no—
497#95—22no—
498#95—22no—
499#95—22no—
500#95—21no—
501#95—21no—
502#95—22no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—22no—
507#95—22no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95—22no—
512#95—22no—
513C24—22no—
514C24—24no—
515C24—21no—
516C24—41no—
517C24—42no—
518C24—42no—
519C24—41no—
520C24—41no—
521C24—42no—
522C24—41no—
523C24#12114yes—
524C24C22×D411yescharacteristic
525C24C22×D411yescharacteristic
526C24C22×D411yescharacteristic
527C24C22×D412yes—
528#41—44no—
529#41—44no—
530#41—84no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×D4—24no—
536C2×D4—24no—
537C2×D4—24no—
538C2×D4—24no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—416no—
546C2×D4—42no—
547C2×D4—44no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—44no—
553C2×D4—82no—
554C2×D4—82no—
555C2×D4—82no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
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—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—48no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—41no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—41no—
593C22×C4—44no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—82no—
599C22×C4—82no—
600C22×C4—84no—
601C22×C4—82no—
602C22×C4—81no—
603C22×C4—81no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4#12114yes—
607C22×C4#12114yes—
608C22×C4#12114yes—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4C2×#4112yes—
619C22×C4C2×#4112yes—
620C22×C4C2×#4112yes—
621C22×C4C2511yescharacteristic
622M16—44no—
623M16—44no—
624M16—82no—
625M16—82no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—84no—
637C2×C8—84no—
638C2×C8C22×D414yes—
639C2×C8C22×D414yes—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—44no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—82no—
666C4⋊C4—82no—
667C4⋊C4—82no—
668C4⋊C4—82no—
669C4⋊C4—82no—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—44no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—44no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—44no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—82no—
690C22⋊C4—82no—
691C22⋊C4—81no—
692C22⋊C4—82no—
693C22⋊C4—81no—
694C22⋊C4—82no—
695C22⋊C4—82no—
696C22⋊C4—82no—
697C22⋊C4—82no—
698C42—24no—
699C42—22no—
700C42—22no—
701C42—44no—
702C42—44no—
703C42—44no—
704C42—42no—
705C23—28no—
706C23—21no—
707C23—21no—
708C23—22no—
709C23—21no—
710C23—22no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—42no—
731C23—42no—
732C23—82no—
733C23—84no—
734C23—84no—
735C23—82no—
736C23—84no—
737C23—84no—
738C23C2×#12112yes—
739C23C2×#12112yes—
740C23C2×#12112yes—
741C23#57514yes—
742C23C23×D411yescharacteristic
743Q8—41no—
744Q8—41no—
745Q8—42no—
746D4—48no—
747D4—48no—
748D4—41no—
749D4—41no—
750D4—42no—
751D4—84no—
752D4—84no—
753D4—84no—
754D4—164no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—84no—
810C2×C4—84no—
811C2×C4—82no—
812C2×C4—82no—
813C2×C4—84no—
814C2×C4—84no—
815C2×C4—164no—
816C2×C4C2×#12112yes—
817C2×C4C2×#12112yes—
818C2×C4C2×#12112yes—
819C2×C4C23×D411yescharacteristic
820C2×C4C22×#4111yescharacteristic
821C2×C4#58512yes—
822C2×C4#58512yes—
823C8—24no—
824C8—24no—
825C8—42no—
826C8—42no—
827C22—24no—
828C22—24no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—24no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—88no—
850C22—88no—
851C22—82no—
852C22—82no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22C22×#12111yescharacteristic
857C22#348512yes—
858C22C2×#57512yes—
859C22#358511yescharacteristic
860C22#358611yescharacteristic
861C4—22no—
862C4—22no—
863C4—22no—
864C4—42no—
865C4—42no—
866C4—42no—
867C4—82no—
868C4—82no—
869C4—82no—
870C4—82no—
871C4—82no—
872C4—81no—
873C4—82no—
874C4—81no—
875C4—81no—
876C4#348511yescharacteristic
877C4#348511yescharacteristic
878C4#349112yes—
879C2—44no—
880C2—42no—
881C2—42no—
882C2—42no—
883C2—161no—
884C2#3544711yescharacteristic
885C2#6044411yescharacteristic
886C2#6045611yescharacteristic
887C2#6171412yes—
888C2#6171512yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35077C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3093C2semidirect
2. C2×#2973C2semidirect
4. #34809C2semidirect
5. #28103C2semidirect
6. #28101C2semidirect
7. #27669C2semidirect
8. #27668C2semidirect
9. #25247C2semidirect
10. #25245C2semidirect
11. #25243C2semidirect
12. #25241C2semidirect
13. #24611C2semidirect
14. #24610C2semidirect
15. #24555C2semidirect
16. #24554C2semidirect
17. #21944C2semidirect
18. #21766C2semidirect
19. #20702C2semidirect
25. C2×#485C22semidirect
27. C2×#482C22semidirect
34. C2×#428C22semidirect
35. C2×#428C22semidirect
36. C2×#417C22semidirect
37. C2×#417C22semidirect
69. #2088C22semidirect
70. #2088C22semidirect
71. #2087C22semidirect
72. #2086C22semidirect
73. #2077C22semidirect
74. #2077C22semidirect
75. #2076C22semidirect
76. #2075C22semidirect
77. #2068C22semidirect
78. #2067C22semidirect
79. #2066C22semidirect
80. #2065C22semidirect
81. #2036C22semidirect
82. #2035C22semidirect
83. #2034C22semidirect
84. #2033C22semidirect
85. #1944C22semidirect
86. #1944C22semidirect
87. #1943C22semidirect
88. #1943C22semidirect
89. #1936C22semidirect
90. #1936C22semidirect
91. #1935C22semidirect
92. #1935C22semidirect
93. #1895C22semidirect
94. #1895C22semidirect
95. #1894C22semidirect
96. #1894C22semidirect
97. #1893C22semidirect
98. #1893C22semidirect
99. #1892C22semidirect
100. #1892C22semidirect
105. #1853C22semidirect
106. #1852C22semidirect
109. #1825C22semidirect
110. #1824C22semidirect
111. #1823C22semidirect
112. #1809C22semidirect
113. #1809C22semidirect
114. #1808C22semidirect
115. #1808C22semidirect
116. #1807C22semidirect
117. #1807C22semidirect
118. #1788C22semidirect
119. #1736C22semidirect
120. #1736C22semidirect
203. #407D4semidirect

Maximal subgroups

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

subgroupindex
C2×#30932
C2×#29732
#350772
#348092
#281032
#281012
#276692
#276682
#252472
#252452
#252432
#252412
#246112
#246102
#245552
#245542
#219442
#217662
#207022