Finite Group Databasebeta

← #6825343

Subgroups — #6825343

Order 512.

1711 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40140C212yesmaximal, complemented
2#33267C211yesmaximal, characteristic, complemented
3#32605C212yesmaximal, complemented
4#31838C212yesmaximal, complemented
5#31293C212yesmaximal, complemented
6#31017C212yesmaximal, complemented
7#30128C212yesmaximal, complemented
8#28740C211yesmaximal, characteristic, complemented
9#28263C211yesmaximal, characteristic, complemented
10#27930C211yesmaximal, characteristic, complemented
11#27840C211yesmaximal, characteristic, complemented
12#26617C212yesmaximal, complemented
13#25777C211yesmaximal, characteristic, complemented
14#25414C211yesmaximal, characteristic, complemented
15#25413C211yesmaximal, characteristic, complemented
16#25034C211yesmaximal, characteristic, complemented
17#24899C212yesmaximal, complemented
18#24780C211yesmaximal, characteristic, complemented
19#24266C211yesmaximal, characteristic, complemented
20#23025C211yesmaximal, characteristic, complemented
21#22448C211yesmaximal, characteristic, complemented
22C4×#493C211yesmaximal, characteristic, complemented
23C8×#124C211yesmaximal, characteristic, complemented
24C22×#135C2211yescharacteristic
25C2×#495C2211yescharacteristic
26C2×#493C2211yescharacteristic
27C2×#484C2212yes—
28C2×#467C2211yescharacteristic
29C2×#466C2211yescharacteristic
30C2×#466C2211yescharacteristic
31C2×#466C2211yescharacteristic
32C2×#449C2212yes—
33C2×C8×Q8C2211yescharacteristic
34C2×C4×D8C2212yes—
35C2×C4×D8C2211yescharacteristic
36C2×C4×D8C2211yescharacteristic
37C2×C4×D8C2211yescharacteristic
38C2×C8×D4C2211yescharacteristic
39C22×#107C2211yescharacteristic
40#2863C2212yes—
41#2761—22no—
42#2756—22no—
43#2749—22no—
44#2676—22no—
45#2630—22no—
46#2592C2212yes—
47#2538C2212yes—
48#2502C2212yes—
49#2497C2212yes—
50#2456—22no—
51#2450—22no—
52#2431C2212yes—
53#2428C2212yes—
54#2427C2212yes—
55#2422C2212yes—
56#2416C2212yes—
57#2407C2212yes—
58#2361C2212yes—
59#2339C2212yes—
60#2325—22no—
61C4×#127C2212yes—
62C4×#124C2211yescharacteristic
63#2100C2212yes—
64#2095C2212yes—
65#2095C2212yes—
66#2076C2212yes—
67#2071C2212yes—
68#2067C2212yes—
69#2067C2212yes—
70#2067C2212yes—
71#2055C2212yes—
72#2055C2212yes—
73#2055C2212yes—
74#2042C2212yes—
75#2041C2212yes—
76#2033C2212yes—
77#2033C2212yes—
78#2014C2212yes—
79#2012C2212yes—
80#2000C2212yes—
81#2000C2212yes—
82#1999C2212yes—
83#1984C2211yescharacteristic
84#1983C2212yes—
85#1970C2212yes—
86#1970C2211yescharacteristic
87#1970C2211yescharacteristic
88#1970C2211yescharacteristic
89#1970C2211yescharacteristic
90#1969C2211yescharacteristic
91#1969C2211yescharacteristic
92#1969C2211yescharacteristic
93#1969C2211yescharacteristic
94#1957C2212yes—
95#1954C2211yescharacteristic
96#1942C2211yescharacteristic
97#1942C2211yescharacteristic
98#1942C2211yescharacteristic
99#1942C2211yescharacteristic
100#1933C2212yes—
101#1933C2212yes—
102#1933C2212yes—
103#1925C2212yes—
104#1923C2211yescharacteristic
105#1923C2211yescharacteristic
106#1923C2211yescharacteristic
107#1923C2211yescharacteristic
108#1921C2212yes—
109#1879C2212yes—
110#1877C2212yes—
111#1877C2212yes—
112#1877C2212yes—
113#1874C2212yes—
114#1874C2212yes—
115#1862C2212yes—
116#1862C2212yes—
117#1845C2211yescharacteristic
118#1845C2211yescharacteristic
119#1831C2211yescharacteristic
120#1808C2211yescharacteristic
121#1808C2211yescharacteristic
122#1802C2212yes—
123#1788C2212yes—
124#1788C2212yes—
125C4×#107C2211yescharacteristic
126C8×C22⋊C4C2211yescharacteristic
127C8×C22⋊C4C2211yescharacteristic
128C8×C22⋊C4C2211yescharacteristic
129C8×C22⋊C4C2211yescharacteristic
130C42×C8C2211yescharacteristic
131C22×#41C2312yes—
132C2×#135—24no—
133C2×#135—42no—
134C2×#135—42no—
135C22×Q16C2311yescharacteristic
136C22×SD16C2312yes—
137C22×SD16C2312yes—
138C22×D8C2311yescharacteristic
139C22×D8C2312yes—
140C22×D8C2311yescharacteristic
141C23×C8C2311yescharacteristic
142C23×C8C2311yescharacteristic
143C2×#127C2312yes—
144C2×#124D411yescharacteristic
145C2×#124C2312yes—
146C2×#123—22no—
147C2×C22⋊Q8—22no—
148C2×C22⋊Q8C2312yes—
149C2×#121—22no—
150C2×#121—22no—
151C2×#121C2312yes—
152C2×#121C2312yes—
153C2×#121C2312yes—
154C2×C4×Q8C2311yescharacteristic
155C2×C4×D4—22no—
156C2×C4×D4—22no—
157C2×C4×D4—22no—
158C2×C4×D4C2312yes—
159C2×C4×D4C2312yes—
160C2×C4×D4C2312yes—
161C2×C4×D4C2311yescharacteristic
162C22×C4⋊C4C2312yes—
163#495—42no—
164#493—24no—
165#484—44no—
166#467—42no—
167#466—24no—
168#466—42no—
169#466—42no—
170#449—44no—
171C8×Q8—42no—
172C4×D8—42no—
173C4×D8—42no—
174C4×D8—44no—
175C4×D8—42no—
176C8×D4—42no—
177C2×#107—42no—
178C2×#107C2311yescharacteristic
179C2×#107C2311yescharacteristic
180C2×#107C2311yescharacteristic
181C2×#107C2311yescharacteristic
182C2×#107C2312yes—
183C2×#107C2311yescharacteristic
184C2×#107C2312yes—
185C2×#107C2312yes—
186C2×C4⋊C8C2311yescharacteristic
187C2×C4⋊C8C2311yescharacteristic
188C2×C4⋊C8C2311yescharacteristic
189C2×C4⋊C8C2311yescharacteristic
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#102C2312yes—
196C2×#102C2312yes—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×#102C2312yes—
201C2×#102C2312yes—
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2312yes—
205C2×C22⋊C8C2311yescharacteristic
206C2×C22⋊C8C2311yescharacteristic
207C2×C22⋊C8C2311yescharacteristic
208C2×C22⋊C8C2311yescharacteristic
209C2×C22⋊C8C2311yescharacteristic
210C2×C22⋊C8C2311yescharacteristic
211C2×C4×C8C2311yescharacteristic
212C2×C4×C8C2311yescharacteristic
213C2×C4×C8C2311yescharacteristic
214C2×C4×C8C2311yescharacteristic
215C2×C4×C8C2311yescharacteristic
216C2×C4×C8C2311yescharacteristic
217C2×C4×C8C2311yescharacteristic
218C2×C4×C8C2311yescharacteristic
219#400—22no—
220#398—22no—
221#398—22no—
222#397—22no—
223#397—22no—
224#397—22no—
225#396—22no—
226#396—22no—
227#396—22no—
228#396—22no—
229#394—22no—
230#394—22no—
231#394—22no—
232#394—22no—
233#394—22no—
234#393—22no—
235#392—22no—
236#392—22no—
237#392—22no—
238#392—22no—
239#391D411yescharacteristic
240#391C2312yes—
241#391C2312yes—
242#391C2312yes—
243#391C2312yes—
244#390—22no—
245#390—22no—
246#390D411yescharacteristic
247#390C2312yes—
248#390C2312yes—
249#390C2312yes—
250#390C2312yes—
251#389C2312yes—
252#389C2312yes—
253#389C2312yes—
254#389C2312yes—
255#388—22no—
256#388—22no—
257#388—22no—
258#388—22no—
259#388D411yescharacteristic
260#388D411yescharacteristic
261#388D411yescharacteristic
262#388D411yescharacteristic
263#387—22no—
264#387—22no—
265#387—22no—
266#387—22no—
267#386—22no—
268#386—22no—
269#386—22no—
270#386—22no—
271#386—22no—
272#386—22no—
273#386—22no—
274#386—22no—
275#386—22no—
276#385—22no—
277#385—22no—
278#385—22no—
279#385—22no—
280#385—22no—
281#384C2312yes—
282#384C2312yes—
283#383—22no—
284#382D411yescharacteristic
285#381—22no—
286#380—22no—
287#380—22no—
288#380C2312yes—
289#380C2312yes—
290C4×C4⋊C4C2312yes—
291C4×C22⋊C4C2311yescharacteristic
292C4×C22⋊C4C2311yescharacteristic
293C4×C22⋊C4C2311yescharacteristic
294C4×C22⋊C4C2311yescharacteristic
295C2×#95—22no—
296C43C2311yescharacteristic
297#340C2312yes—
298#340C2312yes—
299#340C2312yes—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#336C2311yescharacteristic
305#336C2311yescharacteristic
306#336C2311yescharacteristic
307#336C2311yescharacteristic
308#336C2311yescharacteristic
309#336C2311yescharacteristic
310#336C2311yescharacteristic
311#336C2311yescharacteristic
312C2×#41—24no—
313C2×#41—42no—
314C2×#41—42no—
315C2×#41—42no—
316C2×#41—42no—
317C2×#41—42no—
318C22×Q8C2×D411yescharacteristic
319C22×Q8C2412yes—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4C2×D411yescharacteristic
327C22×D4C2412yes—
328C22×D4C2412yes—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4C2411yescharacteristic
335C23×C4C2411yescharacteristic
336#135—416no—
337C2×Q16—22no—
338C2×Q16—22no—
339C2×Q16—22no—
340C2×SD16—24no—
341C2×SD16—42no—
342C2×SD16—42no—
343C2×SD16—42no—
344C2×SD16—42no—
345C2×SD16—42no—
346C2×D8—24no—
347C2×D8—22no—
348C2×D8—22no—
349C2×D8—22no—
350C2×D8—24no—
351C2×D8—22no—
352C2×D8—22no—
353C2×D8—42no—
354C2×D8#4114yes—
355C22×C8—22no—
356C22×C8—22no—
357C22×C8—22no—
358C22×C8—22no—
359C22×C8—22no—
360C22×C8—22no—
361C22×C8C2411yescharacteristic
362C22×C8C2411yescharacteristic
363C22×C8C2411yescharacteristic
364C22×C8C2411yescharacteristic
365C22×C8C2411yescharacteristic
366C22×C8C2411yescharacteristic
367C22×C8C2411yescharacteristic
368C22×C8C2411yescharacteristic
369#127—24no—
370#127—42no—
371#124—24no—
372#124—42no—
373#124—42no—
374#123—84no—
375C22⋊Q8—42no—
376C22⋊Q8—42no—
377C22⋊Q8—84no—
378#121—24no—
379#121—42no—
380#121—48no—
381#121—42no—
382#121—42no—
383#121—42no—
384#121—42no—
385#121—84no—
386C4×Q8—41no—
387C4×Q8—41no—
388C4×D4—41no—
389C4×D4—41no—
390C4×D4—42no—
391C4×D4—42no—
392C4×D4—42no—
393C4×D4—42no—
394C4×D4—42no—
395C4×D4—42no—
396C4×D4—84no—
397C4×D4—84no—
398C4×D4—84no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—42no—
410C2×C4⋊C4—42no—
411C2×C4⋊C4C2×D411yescharacteristic
412C2×C4⋊C4C2×D411yescharacteristic
413C2×C4⋊C4C2×D411yescharacteristic
414C2×C4⋊C4C2×D411yescharacteristic
415C2×C4⋊C4C2412yes—
416C2×C4⋊C4C2412yes—
417C2×C4⋊C4C2412yes—
418C2×C4⋊C4C2412yes—
419C2×C4⋊C4C2412yes—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4C2×D411yescharacteristic
440C2×C22⋊C4C2×D411yescharacteristic
441C2×C22⋊C4C2×D411yescharacteristic
442C2×C22⋊C4C2×D411yescharacteristic
443C2×C22⋊C4C2×D411yescharacteristic
444C2×C22⋊C4C2×D411yescharacteristic
445C2×C22⋊C4C2×D411yescharacteristic
446C2×C22⋊C4C2×D411yescharacteristic
447C2×C22⋊C4C2×D411yescharacteristic
448C2×C22⋊C4C2×D411yescharacteristic
449C2×C42—22no—
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D411yescharacteristic
453C2×C42C2×D411yescharacteristic
454C2×C42C2411yescharacteristic
455C2×C42C2411yescharacteristic
456C2×C42C2411yescharacteristic
457C2×C42C2411yescharacteristic
458C2×C42C2411yescharacteristic
459#107—22no—
460#107—22no—
461#107—22no—
462#107—22no—
463#107—22no—
464#107—24no—
465#107—42no—
466#107—42no—
467C4⋊C8—41no—
468C4⋊C8—41no—
469C4⋊C8—41no—
470C4⋊C8—41no—
471#103—24no—
472#103—42no—
473#103—42no—
474#103—42no—
475#103—42no—
476#102—24no—
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—
486C22⋊C8—22no—
487C22⋊C8—22no—
488C22⋊C8—41no—
489C22⋊C8—41no—
490C22⋊C8—41no—
491C22⋊C8—41no—
492C4×C8—22no—
493C4×C8—22no—
494C4×C8—22no—
495C4×C8—22no—
496C4×C8—22no—
497C4×C8—22no—
498C4×C8—41no—
499C4×C8—41no—
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#95—22no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95C2×D411yescharacteristic
516#95C2×D411yescharacteristic
517#95C2×D411yescharacteristic
518#95C2×D411yescharacteristic
519#95C2×D411yescharacteristic
520#95C2×D411yescharacteristic
521#95C2×D411yescharacteristic
522#95C2×D411yescharacteristic
523C24—22no—
524C24—22no—
525C24C22×D411yescharacteristic
526C24C22×D411yescharacteristic
527#41—48no—
528#41—84no—
529#41—84no—
530#41—84no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—41no—
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—22no—
552C2×D4—22no—
553C2×D4—41no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—44no—
560C2×D4—44no—
561C2×D4—44no—
562C2×D4—82no—
563C2×D4—82no—
564C2×D4—82no—
565C2×D4—82no—
566C2×D4—82no—
567C2×D4—82no—
568C2×D4—82no—
569C2×D4—82no—
570C2×D4—82no—
571C2×D4—82no—
572C2×D4C2×#4114yes—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—82no—
596C22×C4—82no—
597C22×C4—82no—
598C22×C4—82no—
599C22×C4—82no—
600C22×C4—82no—
601C22×C4—82no—
602C22×C4—82no—
603C22×C4—82no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C2511yescharacteristic
619Q16—44no—
620SD16—48no—
621SD16—84no—
622D8—28no—
623D8—48no—
624D8—44no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—44no—
646C2×C8—44no—
647C2×C8C2×#4112yes—
648C2×C8H(5,𝔽2)12yes—
649C2×C8H(5,𝔽2)12yes—
650C2×C8H(5,𝔽2)12yes—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—41no—
662C4⋊C4—41no—
663C4⋊C4—41no—
664C4⋊C4—41no—
665C4⋊C4—44no—
666C4⋊C4—44no—
667C4⋊C4—44no—
668C4⋊C4—82no—
669C4⋊C4—82no—
670C4⋊C4—82no—
671C4⋊C4—82no—
672C4⋊C4—82no—
673C4⋊C4—82no—
674C4⋊C4—82no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—41no—
683C22⋊C4—41no—
684C22⋊C4—44no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—44no—
688C22⋊C4—82no—
689C22⋊C4—82no—
690C22⋊C4—82no—
691C22⋊C4—82no—
692C22⋊C4—82no—
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#13514yescomplemented
704C42—22no—
705C42—22no—
706C42—22no—
707C42—22no—
708C42—21no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—21no—
714C42—21no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—82no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—24no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23C2×#13512yes—
747C23C23×D411yescharacteristic
748Q8—44no—
749Q8—42no—
750Q8—42no—
751Q8—42no—
752Q8—42no—
753D4—24no—
754D4—24no—
755D4—44no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—42no—
762D4—88no—
763D4—88no—
764D4—88no—
765D4—88no—
766D4—164no—
767D4—164no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—88no—
826C2×C4—164no—
827C2×C4—164no—
828C2×C4—164no—
829C2×C4—164no—
830C2×C4C2×#13512yes—
831C2×C4C2×#13512yes—
832C2×C4#57612yes—
833C2×C4#57612yes—
834C2×C4#57812yes—
835C2×C4C22×#4111yescharacteristic
836C2×C4C2×H(5,𝔽2)11yescharacteristic
837C2×C4C2×H(5,𝔽2)11yescharacteristic
838C2×C4C2×H(5,𝔽2)11yescharacteristic
839C2×C4#58511yescharacteristic
840C2×C4#58511yescharacteristic
841C8—22no—
842C8—41no—
843C8—41no—
844C8—41no—
845C8—41no—
846C8—41no—
847C8—41no—
848C8#53814yes—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—44no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—44no—
864C22—44no—
865C22—41no—
866C22—82no—
867C22—82no—
868C22—82no—
869C22—82no—
870C22—82no—
871C22—82no—
872C22—82no—
873C22—82no—
874C22—82no—
875C22—82no—
876C22—82no—
877C22D4×#4111yescharacteristic
878C22#349611yescharacteristic
879C22#349811yescharacteristic
880C22C22×#13511yescharacteristic
881C22C2×#57611yescharacteristic
882C22C2×#57611yescharacteristic
883C22C2×#57811yescharacteristic
884C4—22no—
885C4—22no—
886C4—22no—
887C4—22no—
888C4—22no—
889C4—41no—
890C4—41no—
891C4—41no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—82no—
897C4—82no—
898C4—82no—
899C4—82no—
900C4—82no—
901C4—82no—
902C4C2×#53811yescharacteristic
903C4#351311yescharacteristic
904C4#354611yescharacteristic
905C4#356211yescharacteristic
906C2—42no—
907C2—81no—
908C2—84no—
909C2—162no—
910C2#3939611yescharacteristic
911C2#6143111yescharacteristic
912C2#6148211yescharacteristic
913C2#6225111yescharacteristic
914C2#6233211yescharacteristic
915C2#6241811yescharacteristic
916C2#6243111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40140C2semidirect
2. #33267C2semidirect
3. #32605C2semidirect
4. #31838C2semidirect
5. #31293C2semidirect
6. #31017C2semidirect
7. #30128C2semidirect
8. #28740C2semidirect
9. #28263C2semidirect
10. #27930C2semidirect
11. #27840C2semidirect
12. #26617C2semidirect
13. #25777C2semidirect
14. #25414C2semidirect
15. #25413C2semidirect
16. #25034C2semidirect
17. #24899C2semidirect
18. #24780C2semidirect
19. #24266C2semidirect
20. #23025C2semidirect
21. #22448C2semidirect
22. C4×#493C2semidirect
23. C8×#124C2semidirect
703. C22⋊C4#135semidirect

Maximal subgroups

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

subgroupindex
#401402
#332672
#326052
#318382
#312932
#310172
#301282
#287402
#282632
#279302
#278402
#266172
#257772
#254142
#254132
#250342
#248992
#247802
#242662
#230252
#224482
C4×#4932
C8×#1242