Finite Group Databasebeta

← #6508795

Subgroups — #6508795

Order 512.

2013 conjugacy classes of subgroups.

The subgroup lattice has 921 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3194C211yesmaximal, characteristic
2C2×#3094C211yesmaximal, characteristic, complemented
3#35157C211yesmaximal, characteristic, complemented
4#34379C211yesmaximal, characteristic, complemented
5#28129C212yesmaximal, complemented
6#28127C212yesmaximal, complemented
7#27655C212yesmaximal, complemented
8#27654C212yesmaximal, complemented
9#25230C212yesmaximal, complemented
10#25228C212yesmaximal, complemented
11#25218C212yesmaximal, complemented
12#25216C212yesmaximal, complemented
13#24591C212yesmaximal, complemented
14#24590C212yesmaximal, complemented
15#24539C212yesmaximal, complemented
16#24538C212yesmaximal, complemented
17#21935C211yesmaximal, characteristic, complemented
18#21769C211yesmaximal, characteristic, complemented
19#20702C211yesmaximal, characteristic, complemented
20C2×#525C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×#117C2211yescharacteristic
23#3194—28no—
24#3094—28no—
25C2×#481C2212yes—
26C2×#482C2212yes—
27C2×#482C2212yes—
28C2×#482C2212yes—
29C2×#483C2211yescharacteristic
30C2×#480C2212yes—
31C2×#480C2211yescharacteristic
32C2×#469C2212yes—
33C2×#468C2212yes—
34C2×#449C2212yes—
35C2×#450C2211yescharacteristic
36C2×#447C2211yescharacteristic
37C2×#428C2212yes—
38C2×#418C2212yes—
39C2×#407C2211yescharacteristic
40C2×#407C2211yescharacteristic
41#2853—22no—
42#2622—22no—
43#2500C2212yes—
44#2500C2212yescomplemented
45#2499C2212yes—
46#2499C2212yescomplemented
47#2485—21no—
48#2485—21no—
49#2485—21no—
50#2485—21no—
51#2377—22no—
52#2361C2212yes—
53#2361C2212yes—
54#2345C2212yes—
55D4×C22⋊C4—22no—
56D4×C22⋊C4C2212yes—
57#2325—21no—
58#2325—21no—
59#2324C2212yes—
60#2324C2212yes—
61#2317C2211yescharacteristic, complemented
62#2317C2211yescharacteristic, complemented
63#2315—21no—
64#2312—21no—
65#2311C2211yescharacteristic, complemented
66#2311C2211yescharacteristic, complemented
67#2280C2211yescharacteristic
68C2×#380C2211yescharacteristic
69#2085C2212yescomplemented
70#2085C2212yescomplemented
71#2084C2212yescomplemented
72#2083C2212yescomplemented
73#2073C2212yescomplemented
74#2073C2212yescomplemented
75#2071C2212yescomplemented
76#2071C2212yescomplemented
77#2068C2212yescomplemented
78#2067C2212yescomplemented
79#2066C2212yescomplemented
80#2065C2212yescomplemented
81#2055C2212yescomplemented
82#2055C2212yescomplemented
83#2054C2212yescomplemented
84#2054C2212yescomplemented
85#1949C2212yescomplemented
86#1949C2212yescomplemented
87#1948C2212yescomplemented
88#1947C2212yescomplemented
89#1928C2212yescomplemented
90#1927C2212yescomplemented
91#1926C2212yescomplemented
92#1925C2212yescomplemented
93#1895C2212yes—
94#1894C2212yes—
95#1879C2212yescomplemented
96#1879C2212yescomplemented
97#1877C2212yescomplemented
98#1877C2212yescomplemented
99#1874C2211yescharacteristic, complemented
100#1874C2211yescharacteristic, complemented
101#1872C2211yescharacteristic, complemented
102#1872C2211yescharacteristic, complemented
103#1851C2212yes—
104#1851C2212yes—
105#1851C2212yescomplemented
106#1851C2212yescomplemented
107#1825C2212yes—
108#1825C2212yes—
109#1825C2212yescomplemented
110#1824C2212yescomplemented
111#1823C2212yescomplemented
112#1804C2212yescomplemented
113#1804C2212yescomplemented
114#1802C2212yescomplemented
115#1802C2212yescomplemented
116#1798C2212yescomplemented
117#1798C2212yescomplemented
118#1788C2212yescomplemented
119#1736C2212yescomplemented
120#1736C2212yescomplemented
121C22×#41C2311yescharacteristic
122C23×D4—21no—
123C23×D4C2311yescharacteristic
124C24×C4C2311yescharacteristic
125C22×SD16C2312yes—
126C22×D8C2312yes—
127C22×M16C2312yes—
128C22×M16C2312yes—
129#525—24no—
130#525—24no—
131C2×#123—21no—
132C2×C22⋊Q8C2311yescharacteristic
133C2×C22⋊Q8C2311yescharacteristic
134C2×#121—21no—
135C2×#121—21no—
136C2×#121—24no—
137C2×#121D418yes—
138C2×#121C2311yescharacteristic
139C2×#121C2311yescharacteristic
140C2×#121C2312yes—
141C2×#121C2312yes—
142C2×#120—21no—
143C2×C4×D4—21no—
144C2×C4×D4—21no—
145C2×C4×D4—22no—
146C2×C4×D4—22no—
147C2×C4×D4C2312yes—
148C2×C4×D4C2312yes—
149C2×#117—21no—
150C2×#117—21no—
151C2×#117—24no—
152C2×#117—24no—
153C2×#117C2311yescharacteristic
154C2×#117C2312yes—
155C2×#117C2312yes—
156C2×#117C2311yescharacteristic
157C2×#117C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C22⋊C4—21no—
164C22×C22⋊C4—21no—
165C22×C22⋊C4—21no—
166C22×C22⋊C4—22no—
167C22×C42—21no—
168#483—24no—
169#482—28no—
170#482—28no—
171#482—28no—
172#481—28no—
173#480—28no—
174#480—24no—
175#469—28no—
176#468—28no—
177#450—24no—
178#449—28no—
179#447—24no—
180#428—28no—
181C2×#107C2312yes—
182C2×#107C2312yes—
183C2×#107C2312yes—
184C2×#106C2312yes—
185C2×#106C2312yes—
186C2×#106C2312yes—
187C2×C4⋊C8C2312yes—
188C2×C4⋊C8C2312yes—
189C2×C4⋊C8C2312yes—
190C2×C4⋊C8C2312yes—
191#418—28no—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#102C2312yes—
196C2×#102C2312yes—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×#102C2312yes—
201C2×#102C2312yes—
202C2×#102C2312yes—
203C2×#102C2312yes—
204#407—24no—
205#407—24no—
206C2×C22⋊C8C2312yes—
207C2×C22⋊C8C2312yes—
208C2×C22⋊C8C2311yescharacteristic
209C2×C22⋊C8C2311yescharacteristic
210C2×C22⋊C8C2311yescharacteristic
211C2×C22⋊C8C2311yescharacteristic
212#397—22no—
213#397—22no—
214#397—22no—
215#397—22no—
216#394—22no—
217#394—22no—
218#394—22no—
219#394—22no—
220#391C2312yes—
221#391C2312yes—
222#390—22no—
223#390—22no—
224#390C2312yes—
225#390C2312yes—
226#390C2312yes—
227#390C2312yes—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389C2312yes—
233#389C2312yes—
234#388—22no—
235#388—22no—
236#388—22no—
237#388—22no—
238#388—22no—
239#388—22no—
240#388—22no—
241#388—22no—
242#387—22no—
243#387—22no—
244#387—22no—
245#387—22no—
246#387—22no—
247#387—22no—
248#386—22no—
249#386—22no—
250#386—22no—
251#386—22no—
252#386—22no—
253#386—22no—
254#386—22no—
255#386—22no—
256#385—22no—
257#385—22no—
258#385—22no—
259#385—22no—
260#385—22no—
261#385—22no—
262#384C2312yes—
263#384C2312yes—
264#382C2312yes—
265#382C2312yes—
266#381D412yes—
267#380—21no—
268#380—21no—
269#380—21no—
270#380—21no—
271#380—21no—
272#380—21no—
273#380—22no—
274#380D411yescharacteristic
275#380D411yescharacteristic
276#380D411yescharacteristic
277#380D411yescharacteristic
278#380C2312yes—
279#380C2312yes—
280#379—22no—
281#379D412yes—
282C4×C4⋊C4C2312yes—
283C4×C4⋊C4C2312yes—
284C4×C22⋊C4—22no—
285C4×C22⋊C4C2312yes—
286C4×C22⋊C4C2312yes—
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#336C2312yes—
301#336C2312yes—
302#336C2312yes—
303#336C2312yes—
304C25—21no—
305C25C2×D411yescharacteristic
306C2×#41—22no—
307C2×#41—22no—
308C2×#41—42no—
309C2×#41—42no—
310C22×Q8C2411yescharacteristic
311C22×D4—22no—
312C22×D4—28no—
313C22×D4—22no—
314C22×D4—21no—
315C22×D4—21no—
316C22×D4—21no—
317C22×D4—21no—
318C22×D4—22no—
319C22×D4—42no—
320C22×D4—42no—
321C22×D4—82no—
322C22×D4—82no—
323C22×D4C2×D414yes—
324C22×D4C2411yescharacteristic
325C22×D4C2412yes—
326C23×C4—21no—
327C23×C4—21no—
328C23×C4—21no—
329C23×C4—21no—
330C23×C4—21no—
331C23×C4—21no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—42no—
335C23×C4—42no—
336C23×C4C2×D411yescharacteristic
337C23×C4C2×D411yescharacteristic
338C23×C4C2×D411yescharacteristic
339C23×C4C2×D414yes—
340C23×C4#4114yes—
341C23×C4C2411yescharacteristic
342C23×C4C2411yescharacteristic
343C23×C4C2411yescharacteristic
344C2×SD16—24no—
345C2×SD16—42no—
346C2×SD16—42no—
347C2×D8—24no—
348C2×D8—42no—
349C2×D8—42no—
350C2×M16—24no—
351C2×M16—24no—
352C2×M16—42no—
353C2×M16—42no—
354C2×M16—42no—
355C2×M16—42no—
356C22×C8C2412yes—
357C22×C8C2412yes—
358C22×C8C2412yes—
359C22×C8C2412yes—
360#123—44no—
361C22⋊Q8—22no—
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364C22⋊Q8—22no—
365#121—28no—
366#121—28no—
367#121—24no—
368#121—24no—
369#121—22no—
370#121—22no—
371#121—22no—
372#121—22no—
373#121C2×D418yes—
374#121C2×D418yes—
375#120—44no—
376C4×D4—42no—
377C4×D4—42no—
378C4×D4—42no—
379C4×D4—42no—
380C4×D4—44no—
381C4×D4—44no—
382C4×D4—84no—
383C4×D4—84no—
384#117—24no—
385#117—24no—
386#117—22no—
387#117—24no—
388#117—24no—
389#117—22no—
390#117—42no—
391#117—42no—
392#117—44no—
393#117—44no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
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—42no—
413C2×C4⋊C4—42no—
414C2×C4⋊C4C2×D414yes—
415C2×C4⋊C4C2×D411yescharacteristic
416C2×C4⋊C4C2×D411yescharacteristic
417C2×C4⋊C4C2×D411yescharacteristic
418C2×C4⋊C4C2×D411yescharacteristic
419C2×C4⋊C4C2412yes—
420C2×C4⋊C4C2412yes—
421C2×C4⋊C4C2412yes—
422C2×C4⋊C4C2412yes—
423C2×C4⋊C4C2411yescharacteristic
424C2×C4⋊C4C2411yescharacteristic
425C2×C4⋊C4C2412yes—
426C2×C22⋊C4—28no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
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—44no—
449C2×C22⋊C4—84no—
450C2×C22⋊C4—82no—
451C2×C22⋊C4C2×D412yes—
452C2×C22⋊C4C2×D412yes—
453C2×C22⋊C4C2×D412yes—
454C2×C22⋊C4C2×D412yes—
455C2×C22⋊C4C2×D412yes—
456C2×C22⋊C4C2×D412yes—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—21no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—44no—
463C2×C42C2412yes—
464C2×C42C2412yes—
465#107—24no—
466#107—24no—
467#107—24no—
468#106—24no—
469#106—24no—
470#106—24no—
471C4⋊C8—42no—
472C4⋊C8—42no—
473C4⋊C8—42no—
474C4⋊C8—42no—
475#103—24no—
476#103—42no—
477#103—42no—
478#102—24no—
479#102—24no—
480#102—24no—
481#102—24no—
482#102—24no—
483#102—24no—
484#102—24no—
485#102—42no—
486#102—42no—
487C22⋊C8—22no—
488C22⋊C8—24no—
489C22⋊C8—22no—
490C22⋊C8—24no—
491C22⋊C8—22no—
492C22⋊C8—22no—
493#95—22no—
494#95—22no—
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#95—22no—
505#95—22no—
506#95—22no—
507#95C2×D412yes—
508#95C2×D412yes—
509#95C2×D412yes—
510#95C2×D412yes—
511C24—22no—
512C24—24no—
513C24—21no—
514C24—41no—
515C24—41no—
516C24—41no—
517C24—41no—
518C24—41no—
519C24—41no—
520C24—42no—
521C24—42no—
522C24—81no—
523C24—81no—
524C24—81no—
525C24—81no—
526C24#12114yes—
527C24C22×D411yescharacteristic
528C24C22×D411yescharacteristic
529C24C22×D411yescharacteristic
530#41—84no—
531#41—84no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×D4—28no—
537C2×D4—28no—
538C2×D4—24no—
539C2×D4—21no—
540C2×D4—22no—
541C2×D4—21no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—48no—
549C2×D4—44no—
550C2×D4—44no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—84no—
557C2×D4—81no—
558C2×D4—81no—
559C2×D4—81no—
560C2×D4—81no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—82no—
564C2×D4—82no—
565C2×D4—816no—
566C2×D4C22×D414yes—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—82no—
598C22×C4—82no—
599C22×C4—82no—
600C22×C4—82no—
601C22×C4—82no—
602C22×C4—82no—
603C22×C4—81no—
604C22×C4—81no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4#12114yes—
614C22×C4#12114yes—
615C22×C4#12114yes—
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4C22×D412yes—
619C22×C4C22×D412yes—
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C22×D412yes—
626C22×C4C2×#4112yes—
627C22×C4C2×#4112yes—
628C22×C4C2×#4112yes—
629C22×C4C2511yescharacteristic
630SD16—84no—
631D8—84no—
632M16—48no—
633M16—84no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C4⋊C4—24no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—21no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—41no—
661C4⋊C4—41no—
662C4⋊C4—41no—
663C4⋊C4—41no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—82no—
669C4⋊C4—82no—
670C4⋊C4—82no—
671C4⋊C4—82no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—82no—
675C4⋊C4—82no—
676C4⋊C4C22×D414yes—
677C22⋊C4—28no—
678C22⋊C4—28no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—44no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—82no—
694C22⋊C4—82no—
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—
704C42—22no—
705C42—22no—
706C42—22no—
707C42—22no—
708C42—44no—
709C42—44no—
710C42—42no—
711C42—82no—
712C42—82no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—24no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—48no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—84no—
750C23—84no—
751C23—82no—
752C23—82no—
753C23—82no—
754C23—82no—
755C23—162no—
756C23—162no—
757C23—162no—
758C23—162no—
759C23C2×#12112yes—
760C23C2×#12112yes—
761C23C2×#12112yes—
762C23C23×D411yescharacteristic
763Q8—42no—
764Q8—42no—
765D4—24no—
766D4—24no—
767D4—416no—
768D4—42no—
769D4—42no—
770D4—42no—
771D4—42no—
772D4—84no—
773D4—88no—
774D4—84no—
775D4—84no—
776D4—84no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—84no—
829C2×C4—84no—
830C2×C4—84no—
831C2×C4—84no—
832C2×C4—164no—
833C2×C4—164no—
834C2×C4—162no—
835C2×C4—162no—
836C2×C4C2×#12112yes—
837C2×C4C2×#12112yes—
838C2×C4C2×#12112yes—
839C2×C4C23×D411yescharacteristic
840C2×C4C22×#4111yescharacteristic
841C2×C4#58512yes—
842C2×C4#58512yes—
843C8—42no—
844C8—42no—
845C8—42no—
846C8—42no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—44no—
869C22—44no—
870C22—44no—
871C22—88no—
872C22—82no—
873C22—82no—
874C22—82no—
875C22—82no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—168no—
884C22C22×#12111yescharacteristic
885C22#348511yescharacteristic
886C22#348511yescharacteristic
887C22#358511yescharacteristic
888C22#358511yescharacteristic
889C22#358511yescharacteristic
890C22#358611yescharacteristic
891C4—22no—
892C4—22no—
893C4—22no—
894C4—44no—
895C4—42no—
896C4—42no—
897C4—42no—
898C4—42no—
899C4—82no—
900C4—81no—
901C4—82no—
902C4—81no—
903C4—82no—
904C4—82no—
905C4—81no—
906C4#348512yes—
907C4#349112yes—
908C2—42no—
909C2—42no—
910C2—42no—
911C2—84no—
912C2—161no—
913C2#3544711yescharacteristic
914C2#6042311yescharacteristic
915C2#6042511yescharacteristic
916C2#6177611yescharacteristic
917C2#6177711yescharacteristic
918C2#6177811yescharacteristic
919C2#6177811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3194C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2280 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3094C2semidirect
3. #35157C2semidirect
4. #34379C2semidirect
5. #28129C2semidirect
6. #28127C2semidirect
7. #27655C2semidirect
8. #27654C2semidirect
9. #25230C2semidirect
10. #25228C2semidirect
11. #25218C2semidirect
12. #25216C2semidirect
13. #24591C2semidirect
14. #24590C2semidirect
15. #24539C2semidirect
16. #24538C2semidirect
17. #21935C2semidirect
18. #21769C2semidirect
19. #20702C2semidirect
44. #2500C22semidirect
46. #2499C22semidirect
61. #2317C22semidirect
62. #2317C22semidirect
65. #2311C22semidirect
66. #2311C22semidirect
69. #2085C22semidirect
70. #2085C22semidirect
71. #2084C22semidirect
72. #2083C22semidirect
73. #2073C22semidirect
74. #2073C22semidirect
75. #2071C22semidirect
76. #2071C22semidirect
77. #2068C22semidirect
78. #2067C22semidirect
79. #2066C22semidirect
80. #2065C22semidirect
81. #2055C22semidirect
82. #2055C22semidirect
83. #2054C22semidirect
84. #2054C22semidirect
85. #1949C22semidirect
86. #1949C22semidirect
87. #1948C22semidirect
88. #1947C22semidirect
89. #1928C22semidirect
90. #1927C22semidirect
91. #1926C22semidirect
92. #1925C22semidirect
95. #1879C22semidirect
96. #1879C22semidirect
97. #1877C22semidirect
98. #1877C22semidirect
99. #1874C22semidirect
100. #1874C22semidirect
101. #1872C22semidirect
102. #1872C22semidirect
105. #1851C22semidirect
106. #1851C22semidirect
109. #1825C22semidirect
110. #1824C22semidirect
111. #1823C22semidirect
112. #1804C22semidirect
113. #1804C22semidirect
114. #1802C22semidirect
115. #1802C22semidirect
116. #1798C22semidirect
117. #1798C22semidirect
118. #1788C22semidirect
119. #1736C22semidirect
120. #1736C22semidirect

Maximal subgroups

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

subgroupindex
C2×#31942
C2×#30942
#351572
#343792
#281292
#281272
#276552
#276542
#252302
#252282
#252182
#252162
#245912
#245902
#245392
#245382
#219352
#217692
#207022