Finite Group Databasebeta

← #6763540

Subgroups — #6763540

Order 512.

1879 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#37865C211yesmaximal, characteristic, complemented
2#37694C211yesmaximal, characteristic
3#33053C211yesmaximal, characteristic, complemented
4#31855C212yesmaximal, complemented
5#31854C212yesmaximal, complemented
6#31662C212yesmaximal, complemented
7#31661C212yesmaximal, complemented
8#30209C211yesmaximal, characteristic, complemented
9#29811C211yesmaximal, characteristic, complemented
10#29152C211yesmaximal, characteristic, complemented
11#28623C211yesmaximal, characteristic, complemented
12#27986C211yesmaximal, characteristic, complemented
13#27964C211yesmaximal, characteristic, complemented
14#25717C211yesmaximal, characteristic, complemented
15#25606C211yesmaximal, characteristic, complemented
16#24530C212yesmaximal, complemented
17#24527C212yesmaximal, complemented
18#23969C212yesmaximal, complemented
19#23966C212yesmaximal, complemented
20#22275C211yesmaximal, characteristic, complemented
21#21872C211yesmaximal, characteristic, complemented
22C2×#1961C211yesmaximal, characteristic, complemented
23#21105C211yesmaximal, characteristic, complemented
24C2×#554C2211yescharacteristic
25C2×#552C2211yescharacteristic
26C2×#540C2211yescharacteristic
27C22×#127C2211yescharacteristic
28C2×#492C2211yescharacteristic
29C2×#492C2211yescharacteristic
30C2×#491C2211yescharacteristic, complemented
31C2×#450C2212yes—
32C2×#450C2212yes—
33C2×#433C2211yescharacteristic, complemented
34C22×#102C2212yes—
35C22×#102C2212yes—
36C22×#97C2211yescharacteristic
37#2857C2211yescharacteristic
38#2851C2211yescharacteristic
39#2719—22no—
40#2709—22no—
41#2698—22no—
42#2673—22no—
43#2660C2211yescharacteristic, complemented
44#2641C2211yescharacteristic
45#2621C2211yescharacteristic, complemented
46#2619C2211yescharacteristic
47#2568C2211yescharacteristic, complemented
48#2565C2211yescharacteristic, complemented
49#2503C2211yescharacteristic
50#2503C2211yescharacteristic, complemented
51#2502C2211yescharacteristic
52#2499C2211yescharacteristic, complemented
53#2445C2212yes—
54#2438—22no—
55#2428C2212yes—
56#2419—22no—
57#2410—22no—
58#2408C2212yes—
59#2405—22no—
60D4×C22⋊C4C2212yes—
61#2328C2211yescharacteristic
62#2327C2211yescharacteristic, complemented
63#2317C2211yescharacteristic, complemented
64#2290C2211yescharacteristic
65C2×#382C2211yescharacteristic
66#2101C2212yescomplemented
67#2101C2212yescomplemented
68#2073C2212yescomplemented
69#2073C2212yescomplemented
70#2071C2212yescomplemented
71#2071C2212yescomplemented
72#2055C2212yescomplemented
73#2055C2212yescomplemented
74#2055C2212yescomplemented
75#2055C2212yescomplemented
76#2025C2212yescomplemented
77#2025C2212yescomplemented
78#2023C2212yescomplemented
79#2023C2212yescomplemented
80#2014C2212yes—
81#2014C2212yes—
82#2000C2212yescomplemented
83#2000C2212yescomplemented
84#2000C2212yescomplemented
85#2000C2212yescomplemented
86#1992C2211yescharacteristic, complemented
87#1991C2211yescharacteristic, complemented
88#1991C2211yescharacteristic, complemented
89#1961C2211yescharacteristic
90#1961C2211yescharacteristic
91#1961C2211yescharacteristic
92#1961C2211yescharacteristic
93#1961C2212yes—
94#1961C2212yes—
95#1960C2211yescharacteristic, complemented
96#1957C2211yescharacteristic
97#1957C2211yescharacteristic
98#1935C2212yescomplemented
99#1935C2212yescomplemented
100#1924C2212yescomplemented
101#1917C2212yescomplemented
102#1892C2212yes—
103#1892C2212yes—
104#1880C2212yescomplemented
105#1880C2212yescomplemented
106#1880C2212yescomplemented
107#1880C2212yescomplemented
108#1877C2212yescomplemented
109#1877C2212yescomplemented
110#1877C2212yescomplemented
111#1877C2212yescomplemented
112#1875C2212yescomplemented
113#1875C2212yescomplemented
114#1874C2212yescomplemented
115#1874C2212yescomplemented
116#1869C2212yes—
117#1850C2212yes—
118#1836C2211yescharacteristic, complemented
119#1835C2211yescharacteristic, complemented
120#1835C2211yescharacteristic, complemented
121#1824C2212yes—
122#1823C2212yes—
123#1804C2212yescomplemented
124#1804C2212yescomplemented
125#1802C2212yescomplemented
126#1802C2212yescomplemented
127#1768C2211yescharacteristic, complemented
128#1750C2211yescharacteristic, complemented
129C4×C22⋊C8C2211yescharacteristic
130#1746C2211yescharacteristic, complemented
131C23×D4—22no—
132C23×D4C2312yes—
133C22×SD16C2312yes—
134C22×SD16C2312yes—
135C22×SD16C2312yes—
136C22×SD16C2312yes—
137C23×C8C2312yes—
138#554—44no—
139#552—44no—
140#540—24no—
141#540—42no—
142C2×C4⋊Q8C2311yescharacteristic
143C2×C4⋊Q8C2311yescharacteristic
144C2×#127—24no—
145C2×#127—22no—
146C2×#127—42no—
147C2×#127C2311yescharacteristic
148C2×#127C2312yes—
149C2×#127C2311yescharacteristic
150C2×#126—21no—
151C2×#125—21no—
152C2×#125—21no—
153C2×#125C2311yescharacteristic
154C2×#125C2311yescharacteristic
155C2×#123—21no—
156C2×#123—22no—
157C2×#123—22no—
158C2×C22⋊Q8—21no—
159C2×C22⋊Q8—21no—
160C2×C22⋊Q8C2311yescharacteristic
161C2×C22⋊Q8C2311yescharacteristic
162C2×C22⋊Q8C2311yescharacteristic
163C2×C22⋊Q8C2311yescharacteristic
164C2×#121—22no—
165C2×#121—22no—
166C2×#121C2312yes—
167C2×#121C2312yes—
168C2×#120—22no—
169C2×C4×Q8C2311yescharacteristic
170C2×C4×Q8C2311yescharacteristic
171C2×C4×D4—21no—
172C2×C4×D4C2312yes—
173C2×C4×D4C2312yes—
174C2×C4×D4C2311yescharacteristic
175C2×#117—21no—
176C2×#117C2311yescharacteristic
177C2×#117C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C22⋊C4—22no—
182C22×C42C2311yescharacteristic
183#492—24no—
184#492—42no—
185#491—42no—
186#450—44no—
187#450—44no—
188#433—42no—
189C2×C4⋊C8C2312yes—
190C2×C4⋊C8C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#102—44no—
196C2×#102—44no—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×#102C2312yes—
201C2×#102C2312yes—
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2312yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2312yes—
209C2×C22⋊C8C2312yes—
210C2×C22⋊C8C2312yes—
211C2×C22⋊C8C2312yes—
212C2×#97—42no—
213C2×#97C2311yescharacteristic
214C2×#97C2311yescharacteristic
215C2×#97C2312yes—
216C2×C4×C8C2311yescharacteristic
217C2×C4×C8C2311yescharacteristic
218#400—22no—
219#400—22no—
220#400—22no—
221#398—22no—
222#398—22no—
223#398—22no—
224#398—22no—
225#397—22no—
226#397—22no—
227#395—22no—
228#394—22no—
229#394—22no—
230#394—22no—
231#394—22no—
232#394—22no—
233#394—22no—
234#394—22no—
235#392—22no—
236#392—22no—
237#392—22no—
238#391—22no—
239#391C2311yescharacteristic
240#391C2311yescharacteristic
241#391C2311yescharacteristic
242#391C2311yescharacteristic
243#391C2311yescharacteristic
244#391C2311yescharacteristic
245#390C2312yes—
246#390C2312yes—
247#390C2312yes—
248#390C2312yes—
249#389—22no—
250#389—22no—
251#389C2312yes—
252#388D412yes—
253#387—22no—
254#387—22no—
255#387—22no—
256#387—22no—
257#387—22no—
258#387D412yes—
259#386—22no—
260#386—22no—
261#386—22no—
262#386—22no—
263#386—22no—
264#386—22no—
265#386D412yes—
266#385—22no—
267#385—22no—
268#385—22no—
269#385D412yes—
270#384C2311yescharacteristic
271#384C2311yescharacteristic
272#384C2311yescharacteristic
273#382—22no—
274#382C2311yescharacteristic
275#382C2311yescharacteristic
276#382C2311yescharacteristic
277#382C2311yescharacteristic
278#382C2311yescharacteristic
279#382C2311yescharacteristic
280#382C2311yescharacteristic
281#381—22no—
282#381—22no—
283#380—22no—
284#380C2312yes—
285#379—22no—
286#379—22no—
287C4×C4⋊C4C2311yescharacteristic
288C4×C22⋊C4C2311yescharacteristic
289C4×C22⋊C4C2311yescharacteristic
290#376C2311yescharacteristic
291C2×#95—22no—
292#340C2312yes—
293#340C2312yes—
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2312yes—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#336C2312yes—
305#336C2312yes—
306#336C2312yes—
307#336C2312yes—
308#336C2312yes—
309C25—22no—
310C22×Q8—21no—
311C22×Q8C2411yescharacteristic
312C22×Q8C2411yescharacteristic
313C22×D4—24no—
314C22×D4—22no—
315C22×D4—22no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—24no—
322C22×D4—24no—
323C22×D4—42no—
324C22×D4—42no—
325C22×D4—42no—
326C22×D4—48no—
327C22×D4—84no—
328C22×D4—84no—
329C22×D4C2×D411yescharacteristic
330C22×D4C2412yes—
331C22×D4C2412yes—
332C23×C4—21no—
333C23×C4—21no—
334C23×C4—21no—
335C23×C4—22no—
336C23×C4—22no—
337C23×C4C2×D412yes—
338C23×C4C2411yescharacteristic
339C23×C4C2411yescharacteristic
340C2×SD16—24no—
341C2×SD16—24no—
342C2×SD16—42no—
343C2×SD16—42no—
344C2×SD16—42no—
345C2×SD16—42no—
346C2×SD16—42no—
347C2×SD16—42no—
348C2×SD16—42no—
349C2×SD16—42no—
350C2×SD16—42no—
351C2×SD16—42no—
352C22×C8—24no—
353C22×C8—42no—
354C22×C8—42no—
355C22×C8C2412yes—
356C22×C8C2412yes—
357C22×C8C2412yes—
358C22×C8C2412yes—
359C4⋊Q8—22no—
360C4⋊Q8—22no—
361C4⋊Q8—42no—
362#127—24no—
363#127—22no—
364#127—22no—
365#127—22no—
366#127—42no—
367#127—48no—
368#127#4114yes—
369#126—44no—
370#125—22no—
371#125—22no—
372#125—42no—
373#125—44no—
374#125—44no—
375#123—48no—
376#123—44no—
377#123—84no—
378C22⋊Q8—24no—
379C22⋊Q8—24no—
380C22⋊Q8—44no—
381C22⋊Q8—44no—
382C22⋊Q8—42no—
383C22⋊Q8—42no—
384#121—24no—
385#121—48no—
386#121—42no—
387#121—42no—
388#121—42no—
389#121—84no—
390#120—84no—
391C4×Q8—42no—
392C4×Q8—42no—
393C4×D4—24no—
394C4×D4—24no—
395C4×D4—42no—
396C4×D4—42no—
397C4×D4—42no—
398C4×D4—44no—
399#117—22no—
400#117—22no—
401#117—44no—
402#117—42no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—42no—
424C2×C4⋊C4C2×D412yes—
425C2×C4⋊C4C2×D411yescharacteristic
426C2×C4⋊C4C2×D412yes—
427C2×C4⋊C4C2411yescharacteristic
428C2×C4⋊C4C2411yescharacteristic
429C2×C4⋊C4C2411yescharacteristic
430C2×C4⋊C4C2411yescharacteristic
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2412yes—
434C2×C4⋊C4C2412yes—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
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—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—84no—
454C2×C22⋊C4C2×D412yes—
455C2×C22⋊C4C2×D411yescharacteristic
456C2×C22⋊C4C2×D412yes—
457C2×C22⋊C4C2×D411yescharacteristic
458C2×C22⋊C4C2×D412yes—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42C2×D412yes—
465C2×C42C2411yescharacteristic
466C2×C42C2411yescharacteristic
467C2×C42C2411yescharacteristic
468C2×C42C2411yescharacteristic
469C2×C42C2411yescharacteristic
470C4⋊C8—42no—
471C4⋊C8—42no—
472#103—42no—
473#103—42no—
474#103—42no—
475#103—42no—
476#102—42no—
477#102—42no—
478#102—42no—
479#102—42no—
480#102—42no—
481#102—42no—
482#102—42no—
483#102—42no—
484#102—42no—
485#102—42no—
486#102—42no—
487#102—42no—
488C22⋊C8—24no—
489C22⋊C8—42no—
490C22⋊C8—42no—
491#97—22no—
492#97—22no—
493#97—42no—
494C4×C8—22no—
495C4×C8—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#95—22no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95C2×D412yes—
512#95C2×D412yes—
513#95C2×D412yes—
514#95C2×D412yes—
515#95C2×D412yes—
516C24—22no—
517C24—22no—
518C24—44no—
519C24—44no—
520C24—44no—
521C24—44no—
522C24—82no—
523C24—82no—
524C24—82no—
525C24C22×D411yescharacteristic
526C24C22×D411yescharacteristic
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—42no—
536C2×Q8—82no—
537C2×D4—22no—
538C2×D4—24no—
539C2×D4—28no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—48no—
552C2×D4—48no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—44no—
560C2×D4—44no—
561C2×D4—84no—
562C2×D4—84no—
563C2×D4—82no—
564C2×D4—82no—
565C2×D4—82no—
566C2×D4—82no—
567C2×D4—82no—
568C2×D4—82no—
569C2×D4—82no—
570C2×D4—832no—
571C2×D4—82no—
572C2×D4—82no—
573C2×D4—82no—
574C2×D4—82no—
575C2×D4—82no—
576C2×D4C2×#4114yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—42no—
597C22×C4—44no—
598C22×C4—42no—
599C22×C4—44no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—82no—
603C22×C4—82no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4—82no—
607C22×C4—82no—
608C22×C4—82no—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D412yes—
617C22×C4H(5,𝔽2)14yes—
618C22×C4C2511yescharacteristic
619SD16—84no—
620SD16—84no—
621SD16—84no—
622SD16—84no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
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—48no—
636C4⋊C4—22no—
637C4⋊C4—24no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—44no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—82no—
665C4⋊C4—82no—
666C4⋊C4—82no—
667C22⋊C4—22no—
668C22⋊C4—24no—
669C22⋊C4—22no—
670C22⋊C4—24no—
671C22⋊C4—42no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—44no—
680C22⋊C4—82no—
681C22⋊C4—82no—
682C22⋊C4—82no—
683C22⋊C4—82no—
684C22⋊C4—82no—
685C22⋊C4—82no—
686C22⋊C4—82no—
687C22⋊C4—82no—
688C22⋊C4—82no—
689C22⋊C4—82no—
690C42—24no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C42—22no—
696C42—22no—
697C42—42no—
698C42—42no—
699C42—42no—
700C42C2×#4112yes—
701C42H(5,𝔽2)12yes—
702C23—22no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—21no—
707C23—21no—
708C23—24no—
709C23—21no—
710C23—22no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—88no—
725C23—88no—
726C23—88no—
727C23—88no—
728C23—164no—
729C23—164no—
730C23—164no—
731C23#53512yes—
732C23#57714yes—
733C23C23×D411yescharacteristic
734Q8—42no—
735Q8—42no—
736Q8—42no—
737Q8—42no—
738Q8—162no—
739D4—24no—
740D4—24no—
741D4—44no—
742D4—42no—
743D4—42no—
744D4—42no—
745D4—42no—
746D4—42no—
747D4—42no—
748D4—88no—
749D4—88no—
750D4—88no—
751D4—88no—
752D4—88no—
753D4—164no—
754D4—164no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—48no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—84no—
805C2×C4—164no—
806C2×C4—164no—
807C2×C4—162no—
808C2×C4—162no—
809C2×C4#53512yes—
810C2×C4#54614yes—
811C2×C4C22×#4111yescharacteristic
812C2×C4C2×H(5,𝔽2)12yes—
813C2×C4C2×H(5,𝔽2)11yescharacteristic
814C2×C4#58512yes—
815C8—42no—
816C8—42no—
817C8—42no—
818C8—42no—
819C22—24no—
820C22—24no—
821C22—22no—
822C22—22no—
823C22—44no—
824C22—44no—
825C22—42no—
826C22—41no—
827C22—42no—
828C22—41no—
829C22—41no—
830C22—44no—
831C22—82no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22—82no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—1616no—
843C22#322114yes—
844C22C2×#53511yescharacteristic
845C22C2×#54611yescharacteristic
846C22#350011yescharacteristic
847C22C2×#57712yes—
848C22#358512yes—
849C4—24no—
850C4—22no—
851C4—42no—
852C4—42no—
853C4—41no—
854C4—42no—
855C4—41no—
856C4—41no—
857C4—82no—
858C4—81no—
859C4—81no—
860C4—82no—
861C4—81no—
862C4—81no—
863C4—81no—
864C4—81no—
865C4—81no—
866C4—81no—
867C4#351312yes—
868C4#354212yes—
869C2—24no—
870C2—81no—
871C2—84no—
872C2—162no—
873C2#3808211yescharacteristic
874C2C2×#322111yescharacteristic
875C2#6082511yescharacteristic
876C2#6118412yes—
877C2#6259612yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#37694C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37865C2semidirect
3. #33053C2semidirect
4. #31855C2semidirect
5. #31854C2semidirect
6. #31662C2semidirect
7. #31661C2semidirect
8. #30209C2semidirect
9. #29811C2semidirect
10. #29152C2semidirect
11. #28623C2semidirect
12. #27986C2semidirect
13. #27964C2semidirect
14. #25717C2semidirect
15. #25606C2semidirect
16. #24530C2semidirect
17. #24527C2semidirect
18. #23969C2semidirect
19. #23966C2semidirect
20. #22275C2semidirect
21. #21872C2semidirect
22. C2×#1961C2semidirect
23. #21105C2semidirect
30. C2×#491C22semidirect
33. C2×#433C22semidirect
43. #2660C22semidirect
45. #2621C22semidirect
47. #2568C22semidirect
48. #2565C22semidirect
50. #2503C22semidirect
52. #2499C22semidirect
62. #2327C22semidirect
63. #2317C22semidirect
66. #2101C22semidirect
67. #2101C22semidirect
68. #2073C22semidirect
69. #2073C22semidirect
70. #2071C22semidirect
71. #2071C22semidirect
72. #2055C22semidirect
73. #2055C22semidirect
74. #2055C22semidirect
75. #2055C22semidirect
76. #2025C22semidirect
77. #2025C22semidirect
78. #2023C22semidirect
79. #2023C22semidirect
82. #2000C22semidirect
83. #2000C22semidirect
84. #2000C22semidirect
85. #2000C22semidirect
86. #1992C22semidirect
87. #1991C22semidirect
88. #1991C22semidirect
95. #1960C22semidirect
98. #1935C22semidirect
99. #1935C22semidirect
100. #1924C22semidirect
101. #1917C22semidirect
104. #1880C22semidirect
105. #1880C22semidirect
106. #1880C22semidirect
107. #1880C22semidirect
108. #1877C22semidirect
109. #1877C22semidirect
110. #1877C22semidirect
111. #1877C22semidirect
112. #1875C22semidirect
113. #1875C22semidirect
114. #1874C22semidirect
115. #1874C22semidirect
118. #1836C22semidirect
119. #1835C22semidirect
120. #1835C22semidirect
123. #1804C22semidirect
124. #1804C22semidirect
125. #1802C22semidirect
126. #1802C22semidirect
127. #1768C22semidirect
128. #1750C22semidirect
130. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#378652
#376942
#330532
#318552
#318542
#316622
#316612
#302092
#298112
#291522
#286232
#279862
#279642
#257172
#256062
#245302
#245272
#239692
#239662
#222752
#218722
C2×#19612
#211052