Finite Group Databasebeta

← #7684824

Subgroups — #7684824

Order 512.

5926 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59484C216yesmaximal, complemented
2#59424C216yesmaximal, complemented
3#59375C213yesmaximal, complemented
4#45377C213yesmaximal, complemented
5#45188C216yesmaximal, complemented
6#45115C213yesmaximal, complemented
7#39563C216yesmaximal, complemented
8#39070C216yesmaximal, complemented
9#36578C211yesmaximal, characteristic, complemented
10#36458C212yesmaximal, complemented
11#36456C212yesmaximal, complemented
12#36262C216yesmaximal, complemented
13#36082C211yesmaximal, characteristic
14#35996C212yesmaximal, complemented
15#35948C211yesmaximal, characteristic, complemented
16#34906C213yesmaximal, complemented
17#34263C212yesmaximal, complemented
18#34258C212yesmaximal, complemented
19C4×#548C212yesmaximal, complemented
20C22×H(5,𝔽2)C2211yescharacteristic
21C2×Q82C2211yescharacteristic, complemented
22C2×#551C2216yescomplemented
23C2×#548C2212yes—
24C2×#548C2211yescharacteristic
25C2×#520C2212yes—
26C2×C4×#41C2212yes—
27C22×C4×Q8C2211yescharacteristic, complemented
28#2860C2216yescomplemented
29#2857C2216yescomplemented
30#2854C2213yescomplemented
31#2799C2216yescomplemented
32#2786C22112yescomplemented
33#2751C22112yescomplemented
34#2750C22112yescomplemented
35#2740C22112yescomplemented
36#2736C22112yescomplemented
37#2735C2216yescomplemented
38#2693C2216yescomplemented
39#2684C2216yescomplemented
40#2640C2213yescomplemented
41#2625C2216yescomplemented
42#2616C2213yes—
43#2607C2211yescharacteristic, complemented
44#2602C2216yescomplemented
45#2601C22112yescomplemented
46#2600C2213yescomplemented
47#2595C2216yescomplemented
48#2592C2213yescomplemented
49#2588C2216yescomplemented
50#2578C2216yescomplemented
51#2572C2216yescomplemented
52#2563C2216yescomplemented
53#2561C22112yescomplemented
54#2560C2216yescomplemented
55#2560C22112yescomplemented
56#2557C22112yescomplemented
57#2547C2213yescomplemented
58#2538C2216yescomplemented
59#2534C22112yescomplemented
60#2523C2213yescomplemented
61#2513C2216yescomplemented
62#2512C2216yescomplemented
63#2512C2216yescomplemented
64#2504C2213yescomplemented
65#2502C2216yescomplemented
66#2497C2216yescomplemented
67#2496C2216yescomplemented
68#2495C2216yescomplemented
69#2492C2216yescomplemented
70#2491C2216yescomplemented
71#2487C2213yescomplemented
72#2486C2216yescomplemented
73#2480C22112yescomplemented
74#2480C22112yescomplemented
75#2477C22112yescomplemented
76#2467C2216yescomplemented
77#2463C2213yescomplemented
78#2452C2216yescomplemented
79#2452C2216yescomplemented
80#2448C2216yescomplemented
81#2447C2216yescomplemented
82#2447C2216yescomplemented
83#2439C2216yescomplemented
84#2439C2216yescomplemented
85#2437C2216yescomplemented
86#2435C2216yes—
87#2435C2213yes—
88#2422C2216yescomplemented
89#2422C2216yescomplemented
90#2421C2216yescomplemented
91#2408C2213yes—
92#2408C2216yes—
93#2398C2213yescomplemented
94#2395C2216yescomplemented
95#2388C2213yes—
96#2367C2216yescomplemented
97#2362C2216yescomplemented
98#2361C2216yescomplemented
99#2357C2216yescomplemented
100#2354C2216yescomplemented
101#2352C2216yescomplemented
102#2351C2212yescomplemented
103#2351C2212yescomplemented
104Q8×C4⋊C4C2212yescomplemented
105Q8×C4⋊C4C2212yescomplemented
106#2345C2216yescomplemented
107#2344C2216yescomplemented
108#2342C22112yescomplemented
109#2341C2212yes—
110#2341C2212yes—
111#2341C2211yescharacteristic
112#2341C2212yes—
113#2341C2212yes—
114#2341C2212yes—
115Q8×C22⋊C4C2212yescomplemented
116Q8×C22⋊C4C2211yescharacteristic, complemented
117D4×C22⋊C4C2216yes—
118D4×C22⋊C4C2216yes—
119D4×C22⋊C4C2216yes—
120D4×C22⋊C4C2216yes—
121#2319C2216yescomplemented
122#2314C2216yescomplemented
123#2311C2216yes—
124#2309C2216yes—
125C4×#126C2216yescomplemented
126C4×#124C2216yescomplemented
127C4×C22⋊Q8C2216yescomplemented
128C4×C22⋊Q8C2216yescomplemented
129C4×#123C2213yescomplemented
130C4×#121C2216yescomplemented
131#2298C2216yescomplemented
132#2297C2216yes—
133#2293C2216yescomplemented
134C2×#390C2216yes—
135#2276C2211yescharacteristic, complemented
136C42×Q8C2212yescomplemented
137C42×D4C2216yescomplemented
138C2×H(5,𝔽2)—216no—
139C2×H(5,𝔽2)—44no—
140C22×#41C2311yescharacteristic
141C22×#41C2313yes—
142C22×#41C2312yes—
143C23×Q8C2311yescharacteristic
144C23×D4C2316yes—
145C23×D4C2313yes—
146Q82—44no—
147#551—424no—
148#548—216no—
149#548—44no—
150C2×C4⋊Q8C2316yes—
151C2×C4⋊Q8C2313yes—
152C2×#126C2316yes—
153C2×#126C23112yes—
154C2×#124C2316yes—
155C2×#124C2313yes—
156C2×#124C2316yes—
157C2×#123C2313yes—
158C2×#123C23112yes—
159C2×C22⋊Q8C2316yes—
160C2×C22⋊Q8C23112yes—
161C2×C22⋊Q8C2316yes—
162C2×C22⋊Q8C2313yes—
163C2×#121C2316yes—
164C2×#121C2313yes—
165C2×#120C2316yes—
166#520—216no—
167C4×#41—48no—
168C2×C4×Q8—44no—
169C2×C4×Q8C2312yes—
170C2×C4×Q8C2312yes—
171C2×C4×Q8C2312yes—
172C2×C4×Q8C2312yes—
173C2×C4×Q8C2312yes—
174C2×C4×Q8C2311yescharacteristic
175C2×C4×Q8C2313yes—
176C2×C4×Q8C2316yes—
177C2×C4×D4C2316yes—
178C2×C4×D4C2316yes—
179C2×C4×D4C2316yes—
180C2×C4×D4C2316yes—
181C2×C4×D4C2316yes—
182C2×C4×D4C2316yes—
183C2×C4×D4C2316yes—
184C2×C4×D4C2313yes—
185C2×#117C2316yes—
186C2×#117C2316yes—
187C2×#117C23112yes—
188C22×C4⋊C4C2316yes—
189C22×C4⋊C4C2313yes—
190C22×C22⋊C4C23112yes—
191C22×C22⋊C4C23112yes—
192C22×C42C2313yes—
193C22×C42C2316yes—
194#400C2316yes—
195#400C2316yes—
196#400C2316yes—
197#400C23112yes—
198#399C2312yes—
199#399C2316yes—
200#398C2316yes—
201#398C23112yes—
202#397C23112yes—
203#397C2316yes—
204#397C23112yes—
205#397C2316yes—
206#397C2316yes—
207#397C2313yes—
208#397C2313yes—
209#397C2316yes—
210#397C23112yes—
211#397C23112yes—
212#397C23112yes—
213#396C23112yes—
214#396C23112yes—
215#396C23112yes—
216#395C2313yes—
217#394C2316yes—
218#394C23112yes—
219#394C2313yes—
220#394C2316yes—
221#394C2316yes—
222#394C2316yes—
223#394C2316yes—
224#393C2313yes—
225#393C23112yes—
226#393C23112yes—
227#393C23112yes—
228#393C2311yescharacteristic
229#393C2311yescharacteristic
230#392C2313yes—
231#392C2316yes—
232#391C2312yes—
233#391C23112yes—
234#391C2316yes—
235#391C2316yes—
236#391C2312yes—
237#391C2316yes—
238#391C2316yes—
239#391C2316yes—
240#390C23112yes—
241#390C2316yes—
242#390C2316yes—
243#390C2316yes—
244#390C2316yes—
245#390C2316yes—
246#390C2316yes—
247#390C2316yes—
248#390C2316yes—
249#390C2316yes—
250#390C2316yes—
251#390C2316yes—
252#390C2316yes—
253#390C2316yes—
254#389C2316yes—
255#389C2316yes—
256#389C2316yes—
257#389C2316yes—
258#389C2316yes—
259#389C2316yes—
260#389C2316yes—
261#389C2316yes—
262#389C2316yes—
263#388C2316yes—
264#388C2316yes—
265#388C2316yes—
266#388C23112yes—
267#388C23112yes—
268#388C2316yes—
269#388C2316yes—
270#388C23112yes—
271#388C2316yes—
272#388C23112yes—
273#388C23112yes—
274#388C23112yes—
275#388C2316yes—
276#388C2316yes—
277#388C23112yes—
278#388C23112yes—
279#388C23112yes—
280#387C2312yes—
281#387C2316yes—
282#387C2316yes—
283#387C2316yes—
284#387C2316yes—
285#387C2316yes—
286#387C23112yes—
287#387C2316yes—
288#387C2316yes—
289#387C2312yes—
290#387C2316yes—
291#387C23112yes—
292#386C2316yes—
293#386C2316yes—
294#386C23112yes—
295#386C23112yes—
296#386C2316yes—
297#386C2316yes—
298#386C2316yes—
299#386C23112yes—
300#386C2313yes—
301#385C2316yes—
302#385C2316yes—
303#385C23112yes—
304#385C23112yes—
305#385C23112yes—
306#385C2313yes—
307#384C2316yes—
308#384C2316yes—
309#383C2316yes—
310#382C2316yes—
311#382C2316yes—
312#381C23112yes—
313#381C23112yes—
314#381C2311yescharacteristic
315#380C2316yes—
316#380C23112yes—
317#380C2316yes—
318#380C2316yes—
319#380C2316yes—
320#380C2316yes—
321#380C2316yes—
322#380C23112yes—
323#380C2313yes—
324#380C2316yes—
325#380C2313yes—
326#379C23112yes—
327#379C23112yes—
328#379C23112yes—
329#379C2316yes—
330C4×C4⋊C4C2316yes—
331C4×C4⋊C4C2316yes—
332C4×C4⋊C4C2316yes—
333C4×C4⋊C4C2316yes—
334C4×C4⋊C4C2316yes—
335C4×C4⋊C4C2316yes—
336C4×C4⋊C4C2316yes—
337C4×C4⋊C4C2313yes—
338C4×C4⋊C4C2316yes—
339C4×C4⋊C4C2316yes—
340C4×C4⋊C4C2316yes—
341C4×C22⋊C4C2313yes—
342C4×C22⋊C4C2316yes—
343C4×C22⋊C4C2316yes—
344C4×C22⋊C4C2316yes—
345C4×C22⋊C4C23112yes—
346C4×C22⋊C4C2316yes—
347C4×C22⋊C4C23112yes—
348C4×C22⋊C4C2316yes—
349C4×C22⋊C4C2316yes—
350C4×C22⋊C4C2316yes—
351C4×C22⋊C4C2313yes—
352C4×C22⋊C4C2316yes—
353C4×C22⋊C4C2312yes—
354C4×C22⋊C4C2316yes—
355#376C2313yes—
356C43C2316yes—
357C25C2416yes—
358H(5,𝔽2)—464no—
359C2×#41—28no—
360C2×#41—28no—
361C2×#41—28no—
362C2×#41—24no—
363C2×#41—224no—
364C2×#41—46no—
365C2×#41#41116yes—
366C22×Q8—28no—
367C22×Q8—24no—
368C22×Q8C2413yes—
369C22×Q8C2411yescharacteristic
370C22×Q8C2411yescharacteristic
371C22×Q8C2416yes—
372C22×Q8C2411yescharacteristic
373C22×D4—224no—
374C22×D4—224no—
375C22×D4—224no—
376C22×D4—412no—
377C22×D4—46no—
378C22×D4C2413yes—
379C22×D4C2416yes—
380C22×D4C2413yes—
381C22×D4C2416yes—
382C22×D4C2416yes—
383C22×D4C2413yes—
384C23×C4C2413yes—
385C23×C4C2413yes—
386C23×C4C2416yes—
387C23×C4C24112yes—
388C23×C4C2416yes—
389C23×C4C2416yes—
390C23×C4C2413yes—
391C23×C4C2411yescharacteristic
392C4⋊Q8—412no—
393C4⋊Q8—46no—
394#126—424no—
395#126—412no—
396#124—224no—
397#124—46no—
398#124—412no—
399#123—212no—
400#123—424no—
401C22⋊Q8—224no—
402C22⋊Q8—412no—
403C22⋊Q8—424no—
404C22⋊Q8—46no—
405#121—224no—
406#121—46no—
407#120—412no—
408C4×Q8—28no—
409C4×Q8—28no—
410C4×Q8—28no—
411C4×Q8—28no—
412C4×Q8—28no—
413C4×Q8—24no—
414C4×Q8—46no—
415C4×Q8—412no—
416C4×D4—224no—
417C4×D4—224no—
418C4×D4—224no—
419C4×D4—224no—
420C4×D4—412no—
421C4×D4—412no—
422C4×D4—46no—
423C4×D4—412no—
424#117—224no—
425#117—424no—
426#117—412no—
427C2×C4⋊C4—224no—
428C2×C4⋊C4—46no—
429C2×C4⋊C4C2416yes—
430C2×C4⋊C4C2416yes—
431C2×C4⋊C4C2416yes—
432C2×C4⋊C4C2416yes—
433C2×C4⋊C4C2412yes—
434C2×C4⋊C4C2416yes—
435C2×C4⋊C4C2416yes—
436C2×C4⋊C4C2416yes—
437C2×C4⋊C4C2416yes—
438C2×C4⋊C4C2416yes—
439C2×C4⋊C4C2413yes—
440C2×C4⋊C4C2416yes—
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2416yes—
443C2×C4⋊C4C24112yes—
444C2×C4⋊C4C2413yes—
445C2×C4⋊C4C2416yes—
446C2×C4⋊C4C2413yes—
447C2×C4⋊C4C24112yes—
448C2×C4⋊C4C2416yes—
449C2×C4⋊C4C2416yes—
450C2×C4⋊C4C2416yes—
451C2×C4⋊C4C2412yes—
452C2×C22⋊C4—424no—
453C2×C22⋊C4—424no—
454C2×C22⋊C4C2416yes—
455C2×C22⋊C4C2416yes—
456C2×C22⋊C4C2416yes—
457C2×C22⋊C4C2416yes—
458C2×C22⋊C4C2416yes—
459C2×C22⋊C4C2416yes—
460C2×C22⋊C4C2412yes—
461C2×C22⋊C4C2412yes—
462C2×C22⋊C4C2416yes—
463C2×C22⋊C4C2416yes—
464C2×C22⋊C4C24112yes—
465C2×C22⋊C4C2413yes—
466C2×C22⋊C4C24112yes—
467C2×C22⋊C4C24112yes—
468C2×C22⋊C4C24112yes—
469C2×C22⋊C4C24112yes—
470C2×C22⋊C4C24112yes—
471C2×C22⋊C4C24112yes—
472C2×C22⋊C4C2411yescharacteristic
473C2×C22⋊C4C2413yes—
474C2×C22⋊C4C2416yes—
475C2×C22⋊C4C2416yes—
476C2×C22⋊C4C2416yes—
477C2×C22⋊C4C2416yes—
478C2×C22⋊C4C2416yes—
479C2×C22⋊C4C2416yes—
480C2×C22⋊C4C2416yes—
481C2×C22⋊C4C2411yescharacteristic
482C2×C22⋊C4C2416yes—
483C2×C22⋊C4C2416yes—
484C2×C42—46no—
485C2×C42—412no—
486C2×C42C2416yes—
487C2×C42C2416yes—
488C2×C42C2416yes—
489C2×C42C2413yes—
490C2×C42C2416yes—
491C2×C42C2416yes—
492C2×C42C2416yes—
493C2×C42C2416yes—
494C2×C42C2416yes—
495C2×C42C2416yes—
496C2×C42C2416yes—
497C2×C42C2416yes—
498C2×C42C2412yes—
499C2×C42C2412yes—
500#95C2411yescharacteristic
501#95C2413yes—
502#95C2416yes—
503#95C2412yes—
504#95C2412yes—
505#95C2412yes—
506#95C2411yescharacteristic
507#95C2412yes—
508#95C2412yes—
509#95C2412yes—
510#95C2416yes—
511#95C2416yes—
512#95C2416yes—
513#95C2416yes—
514#95C2416yes—
515#95C2416yes—
516#95C2416yes—
517#95C2416yes—
518#95C2416yes—
519#95C2413yes—
520#95C24112yes—
521#95C24112yes—
522#95C24112yes—
523#95C2416yes—
524#95C24112yes—
525#95C2412yes—
526#95C2416yes—
527#95C2416yes—
528#95C2416yes—
529#95C2416yes—
530#95C2416yes—
531C24—224no—
532C24—46no—
533C24—46no—
534C24—412no—
535C24—46no—
536C24C2513yes—
537C24C2516yes—
538C24C2511yescharacteristic
539#41—264no—
540#41—448no—
541#41—416no—
542C2×Q8—212no—
543C2×Q8—24no—
544C2×Q8—26no—
545C2×Q8—24no—
546C2×Q8—41no—
547C2×Q8—41no—
548C2×Q8—46no—
549C2×Q8—46no—
550C2×Q8—46no—
551C2×Q8—416no—
552C2×Q8C2×#4118yes—
553C2×Q8H(5,𝔽2)14yes—
554C2×D4—212no—
555C2×D4—212no—
556C2×D4—212no—
557C2×D4—212no—
558C2×D4—26no—
559C2×D4—212no—
560C2×D4—212no—
561C2×D4—212no—
562C2×D4—212no—
563C2×D4—26no—
564C2×D4—496no—
565C2×D4—46no—
566C2×D4—46no—
567C2×D4—43no—
568C2×D4—43no—
569C2×D4—43no—
570C2×D4—448no—
571C2×D4C2×#41124yes—
572C22×C4—212no—
573C22×C4—212no—
574C22×C4—224no—
575C22×C4—212no—
576C22×C4—212no—
577C22×C4—26no—
578C22×C4—26no—
579C22×C4—212no—
580C22×C4—212no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—43no—
584C22×C4—46no—
585C22×C4—46no—
586C22×C4—412no—
587C22×C4—412no—
588C22×C4—46no—
589C22×C4—46no—
590C22×C4—46no—
591C22×C4C2×#41124yes—
592C22×C4H(5,𝔽2)14yescomplemented
593C22×C4C2511yescharacteristic
594C22×C4C2512yes—
595C22×C4C2512yes—
596C22×C4C2512yes—
597C22×C4C2513yes—
598C22×C4C2516yes—
599C22×C4C2516yes—
600C22×C4C2513yes—
601C22×C4C2516yes—
602C22×C4C2516yes—
603C22×C4C2511yescharacteristic
604C22×C4C2516yes—
605C22×C4C2512yes—
606C22×C4C2512yes—
607C22×C4C2512yes—
608C22×C4C2513yes—
609C4⋊C4—212no—
610C4⋊C4—212no—
611C4⋊C4—212no—
612C4⋊C4—24no—
613C4⋊C4—212no—
614C4⋊C4—212no—
615C4⋊C4—212no—
616C4⋊C4—212no—
617C4⋊C4—212no—
618C4⋊C4—212no—
619C4⋊C4—26no—
620C4⋊C4—212no—
621C4⋊C4—24no—
622C4⋊C4—46no—
623C4⋊C4—42no—
624C4⋊C4—412no—
625C4⋊C4—43no—
626C4⋊C4—46no—
627C4⋊C4—43no—
628C4⋊C4—46no—
629C4⋊C4—46no—
630C4⋊C4—412no—
631C4⋊C4—46no—
632C22⋊C4—212no—
633C22⋊C4—212no—
634C22⋊C4—212no—
635C22⋊C4—224no—
636C22⋊C4—212no—
637C22⋊C4—26no—
638C22⋊C4—24no—
639C22⋊C4—212no—
640C22⋊C4—212no—
641C22⋊C4—212no—
642C22⋊C4—212no—
643C22⋊C4—24no—
644C22⋊C4—412no—
645C22⋊C4—412no—
646C22⋊C4—412no—
647C22⋊C4—412no—
648C22⋊C4—46no—
649C22⋊C4—46no—
650C22⋊C4—41no—
651C22⋊C4—46no—
652C22⋊C4—412no—
653C22⋊C4—412no—
654C22⋊C4—46no—
655C22⋊C4—41no—
656C22⋊C4—43no—
657C22⋊C4—46no—
658C22⋊C4—46no—
659C22⋊C4—46no—
660C22⋊C4—46no—
661C22⋊C4—46no—
662C42—212no—
663C42—212no—
664C42—212no—
665C42—212no—
666C42—212no—
667C42—212no—
668C42—26no—
669C42—42no—
670C42—46no—
671C42—46no—
672C42—42no—
673C42—46no—
674C42—46no—
675C42—46no—
676C23—22no—
677C23—26no—
678C23—26no—
679C23—26no—
680C23—21no—
681C23—26no—
682C23—22no—
683C23—26no—
684C23—26no—
685C23—21no—
686C23—26no—
687C23—23no—
688C23—23no—
689C23—26no—
690C23—23no—
691C23—424no—
692C23—824no—
693C23—824no—
694C23—166no—
695C23—166no—
696C23C22×#41112yes—
697C23C2×H(5,𝔽2)12yes—
698C23C2611yescharacteristic
699Q8—44no—
700Q8—44no—
701Q8—412no—
702Q8—166no—
703Q8#551116yescomplemented
704D4—248no—
705D4—424no—
706D4—424no—
707D4—412no—
708D4—412no—
709D4—86no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—248no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—26no—
721C2×C4—26no—
722C2×C4—26no—
723C2×C4—26no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—26no—
727C2×C4—26no—
728C2×C4—26no—
729C2×C4—26no—
730C2×C4—23no—
731C2×C4—23no—
732C2×C4—23no—
733C2×C4—26no—
734C2×C4—26no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—26no—
739C2×C4—26no—
740C2×C4—26no—
741C2×C4—26no—
742C2×C4—26no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—26no—
749C2×C4—23no—
750C2×C4—44no—
751C2×C4—412no—
752C2×C4—412no—
753C2×C4—812no—
754C2×C4—812no—
755C2×C4—824no—
756C2×C4—86no—
757C2×C4C22×#4114yes—
758C2×C4C22×#41112yes—
759C2×C4C2×H(5,𝔽2)14yes—
760C2×C4C2×H(5,𝔽2)16yes—
761C2×C4#58514yes—
762C22—212no—
763C22—212no—
764C22—24no—
765C22—22no—
766C22—212no—
767C22—42no—
768C22—46no—
769C22—41no—
770C22—46no—
771C22—46no—
772C22—46no—
773C22—41no—
774C22—46no—
775C22—43no—
776C22—46no—
777C22—43no—
778C22—43no—
779C22—1624no—
780C22C23×#4112yes—
781C22C22×H(5,𝔽2)11yescharacteristic
782C22C22×H(5,𝔽2)11yescharacteristic
783C22C2×#58512yes—
784C222−1+611yescharacteristic
785C4—24no—
786C4—24no—
787C4—24no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—46no—
792C4—41no—
793C4—46no—
794C4—46no—
795C4—46no—
796C4—46no—
797C4—43no—
798C4—41no—
799C4—43no—
800C4C2×#551112yes—
801C2—42no—
802C2—412no—
803C2—83no—
804C2C22×#55111yescharacteristic
805C2#6280012yes—
806C2#6289511yescharacteristic
807C2#6299512yes—
808C2#6302011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36082C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59484C2semidirect
2. #59424C2semidirect
3. #59375C2semidirect
4. #45377C2semidirect
5. #45188C2semidirect
6. #45115C2semidirect
7. #39563C2semidirect
8. #39070C2semidirect
9. #36578C2semidirect
10. #36458C2semidirect
11. #36456C2semidirect
12. #36262C2semidirect
14. #35996C2semidirect
15. #35948C2semidirect
16. #34906C2semidirect
17. #34263C2semidirect
18. #34258C2semidirect
19. C4×#548C2semidirect
21. C2×Q82C22semidirect
22. C2×#551C22semidirect
27. C22×C4×Q8C22semidirect
28. #2860C22semidirect
29. #2857C22semidirect
30. #2854C22semidirect
31. #2799C22semidirect
32. #2786C22semidirect
33. #2751C22semidirect
34. #2750C22semidirect
35. #2740C22semidirect
36. #2736C22semidirect
37. #2735C22semidirect
38. #2693C22semidirect
39. #2684C22semidirect
40. #2640C22semidirect
41. #2625C22semidirect
43. #2607C22semidirect
44. #2602C22semidirect
45. #2601C22semidirect
46. #2600C22semidirect
47. #2595C22semidirect
48. #2592C22semidirect
49. #2588C22semidirect
50. #2578C22semidirect
51. #2572C22semidirect
52. #2563C22semidirect
53. #2561C22semidirect
54. #2560C22semidirect
55. #2560C22semidirect
56. #2557C22semidirect
57. #2547C22semidirect
58. #2538C22semidirect
59. #2534C22semidirect
60. #2523C22semidirect
61. #2513C22semidirect
62. #2512C22semidirect
63. #2512C22semidirect
64. #2504C22semidirect
65. #2502C22semidirect
66. #2497C22semidirect
67. #2496C22semidirect
68. #2495C22semidirect
69. #2492C22semidirect
70. #2491C22semidirect
71. #2487C22semidirect
72. #2486C22semidirect
73. #2480C22semidirect
74. #2480C22semidirect
75. #2477C22semidirect
76. #2467C22semidirect
77. #2463C22semidirect
78. #2452C22semidirect
79. #2452C22semidirect
80. #2448C22semidirect
81. #2447C22semidirect
82. #2447C22semidirect
83. #2439C22semidirect
84. #2439C22semidirect
85. #2437C22semidirect
88. #2422C22semidirect
89. #2422C22semidirect
90. #2421C22semidirect
93. #2398C22semidirect
94. #2395C22semidirect
96. #2367C22semidirect
97. #2362C22semidirect
98. #2361C22semidirect
99. #2357C22semidirect
100. #2354C22semidirect
101. #2352C22semidirect
102. #2351C22semidirect
103. #2351C22semidirect
104. Q8×C4⋊C4C22semidirect
105. Q8×C4⋊C4C22semidirect
106. #2345C22semidirect
107. #2344C22semidirect
108. #2342C22semidirect
115. Q8×C22⋊C4C22semidirect
116. Q8×C22⋊C4C22semidirect
121. #2319C22semidirect
122. #2314C22semidirect
125. C4×#126C22semidirect
126. C4×#124C22semidirect
127. C4×C22⋊Q8C22semidirect
128. C4×C22⋊Q8C22semidirect
129. C4×#123C22semidirect
130. C4×#121C22semidirect
131. #2298C22semidirect
133. #2293C22semidirect
135. #2276C22semidirect
136. C42×Q8C22semidirect
137. C42×D4C22semidirect
592. C22×C4H(5,𝔽2)semidirect
703. Q8#551semidirect

Maximal subgroups

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

subgroupindex
#594842
#594242
#593752
#453772
#451882
#451152
#395632
#390702
#365782
#364582
#364562
#362622
#360822
#359962
#359482
#349062
#342632
#342582
C4×#5482