Finite Group Databasebeta

← #7630136

Subgroups — #7630136

Order 512.

5456 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36635C213yesmaximal, complemented
2#36454C213yesmaximal, complemented
3#36453C213yesmaximal, complemented
4#36452C216yesmaximal, complemented
5#36451C216yesmaximal, complemented
6#36450C213yesmaximal, complemented
7#36449C213yesmaximal, complemented
8#36448C212yesmaximal, complemented
9#36447C211yesmaximal, characteristic, complemented
10#36446C211yesmaximal, characteristic, complemented
11#36445C211yesmaximal, characteristic, complemented
12#36444C211yesmaximal, characteristic
13#36432C212yesmaximal, complemented
14#34945C213yesmaximal, complemented
15#34932C213yesmaximal, complemented
16#34913C216yesmaximal, complemented
17#34793C216yesmaximal, complemented
18C4×#557C211yesmaximal, characteristic, complemented
19C4×D4×Q8C211yesmaximal, characteristic, complemented
20C4×#548C212yesmaximal, complemented
21Q8×#117C212yesmaximal, complemented
22C4×#529C213yesmaximal, complemented
23C42×#41C211yesmaximal, characteristic, complemented
24C2×#557C2211yescharacteristic
25C2×D4×Q8C2211yescharacteristic
26C2×#548C2212yes—
27C2×#529C2213yes—
28C2×C4×#41C2211yescharacteristic
29C2×C4×#41C2211yescharacteristic
30C2×C4×#41C2211yescharacteristic
31C22×C4×Q8C2212yes—
32#2864C2216yes—
33#2863C2216yes—
34#2863C2216yes—
35#2862C2213yes—
36#2859C2213yes—
37#2857C2213yes—
38#2857C2213yes—
39#2855C2216yes—
40#2855C2216yes—
41#2851C2216yes—
42#2578C22112yes—
43#2577C22112yes—
44#2576C22112yes—
45#2575C22112yes—
46#2573C22112yes—
47#2571C2213yes—
48#2568C2213yes—
49#2553C22112yes—
50#2552C2213yes—
51#2547C2213yes—
52#2547C2213yes—
53#2542C2213yes—
54#2538C2213yes—
55#2537C2213yes—
56#2530C22112yes—
57#2528C22112yes—
58#2517C22112yes—
59#2514C2216yes—
60#2514C2216yes—
61#2511C2216yes—
62#2508C2216yes—
63#2506C2216yes—
64#2499C2216yes—
65#2496C2216yes—
66#2495C2216yes—
67#2494C2216yes—
68#2494C2216yes—
69#2489C2216yes—
70#2489C2216yes—
71#2489C2216yes—
72#2485C2216yes—
73#2460C22112yes—
74#2454C2216yes—
75#2447C2216yes—
76#2447C2216yes—
77#2441C2216yes—
78#2427C2216yes—
79#2427C2216yes—
80#2422C2216yes—
81#2421C2216yes—
82#2420C2216yes—
83#2415C2216yes—
84#2401C22112yes—
85#2395C22112yes—
86#2370C2216yes—
87#2367C2216yes—
88#2365C2213yes—
89#2365C2213yes—
90#2362C2216yes—
91#2361C2216yes—
92#2360C2216yes—
93#2355C2216yes—
94#2355C2216yes—
95#2355C2213yes—
96#2352C2216yes—
97#2351C2212yes—
98#2351C2212yes—
99Q8×C4⋊C4C2212yes—
100Q8×C4⋊C4C2212yes—
101Q8×C4⋊C4C2211yescharacteristic
102Q8×C4⋊C4C2211yescharacteristic
103D4×C4⋊C4C2213yes—
104#2345C2216yes—
105#2345C2216yes—
106#2341C2212yes—
107Q8×C22⋊C4C2212yes—
108Q8×C22⋊C4C2212yes—
109Q8×C22⋊C4C2212yes—
110Q8×C22⋊C4C2212yes—
111C4×C4⋊Q8C2213yes—
112C4×C4⋊Q8C2213yes—
113C4×#125C2216yes—
114C4×#125C2213yes—
115C4×#125C2216yes—
116C4×#125C2213yes—
117C4×#126C2216yes—
118C4×#126C2216yes—
119C4×#124C2213yes—
120C4×#124C2216yes—
121C4×#124C2213yes—
122C4×C22⋊Q8C2216yes—
123C4×C22⋊Q8C2216yes—
124C4×C22⋊Q8C2213yes—
125C4×C22⋊Q8C2216yes—
126C4×C22⋊Q8C2213yes—
127C4×#123C2216yes—
128C4×#123C2216yes—
129C4×#121C2213yes—
130C4×#121C2216yes—
131C4×#121C2213yes—
132#2298C2216yes—
133#2295C2213yes—
134#2295C2216yes—
135#2295C2216yes—
136#2293C2211yescharacteristic
137#2290C2216yes—
138#2285C2216yes—
139#2283C2216yes—
140#2283C2213yes—
141C42×Q8C2211yescharacteristic
142C42×Q8C2212yes—
143C42×Q8C2211yescharacteristic
144C42×Q8C2211yescharacteristic
145C42×Q8C2211yescharacteristic
146C42×Q8C2213yes—
147C42×D4C2213yes—
148C42×D4C2213yes—
149C42×D4C2213yes—
150C42×D4C2216yes—
151C42×D4C2213yes—
152C42×D4C2213yes—
153C4×#117C2216yes—
154C4×#117C2213yes—
155C4×#117C2213yes—
156C4×#117C2213yes—
157C2×C43C2213yes—
158C22×#41C2311yescharacteristic
159C23×Q8C2312yes—
160#557—28no—
161D4×Q8—28no—
162#548—216no—
163C2×C4⋊Q8C2313yes—
164C2×C4⋊Q8C2313yes—
165#529—224no—
166C2×#126C2316yes—
167C2×#125C2313yes—
168C2×#125C2316yes—
169C2×#125C2316yes—
170C2×#124C2316yes—
171C2×#124C2313yes—
172C2×#123C2316yes—
173C2×C22⋊Q8C2316yes—
174C2×C22⋊Q8C2316yes—
175C2×C22⋊Q8C2313yes—
176C2×C22⋊Q8C2316yes—
177C2×#121C2316yes—
178C2×#121C2313yes—
179C4×#41—28no—
180C4×#41—28no—
181C4×#41—28no—
182C2×C4×Q8—216no—
183C2×C4×Q8C2313yes—
184C2×C4×Q8C2316yes—
185C2×C4×Q8C2313yes—
186C2×C4×Q8C2312yes—
187C2×C4×Q8C2311yescharacteristic
188C2×C4×Q8C2311yescharacteristic
189C2×C4×Q8C2311yescharacteristic
190C2×C4×Q8C2311yescharacteristic
191C2×C4×Q8C2312yes—
192C2×C4×Q8C2312yes—
193C2×C4×Q8C2316yes—
194C2×C4×Q8C2313yes—
195C2×C4×Q8C2311yescharacteristic
196C2×C4×Q8C2311yescharacteristic
197C2×C4×D4C2313yes—
198C2×C4×D4C2316yes—
199C2×C4×D4C2313yes—
200C2×C4×D4C2316yes—
201C2×C4×D4C2313yes—
202C2×C4×D4C2313yes—
203C2×C4×D4C2313yes—
204C2×C4×D4C2313yes—
205C2×C4×D4C2313yes—
206C2×C4×D4C2313yes—
207C2×C4×D4C2316yes—
208C2×C4×D4C2311yescharacteristic
209C2×#117C2313yes—
210C2×#117C2316yes—
211C2×#117C2313yes—
212C2×#117C2313yes—
213C2×#117C2312yes—
214C22×C4⋊C4C2316yes—
215C22×C42C2313yes—
216C22×C42C2313yes—
217C22×C42C2316yes—
218C22×C42C2313yes—
219C22×C42C2313yes—
220C22×C42C2313yes—
221C22×C42C2313yes—
222C22×C42C2313yes—
223#401C23112yes—
224#400C23112yes—
225#400C23112yes—
226#400C23112yes—
227#400C23112yes—
228#399C23112yes—
229#398C23112yes—
230#397C23112yes—
231#397C23112yes—
232#397C23112yes—
233#397C23112yes—
234#397C23112yes—
235#397C23112yes—
236#396C23112yes—
237#394C23112yes—
238#394C23112yes—
239#391C2316yes—
240#391C2316yes—
241#391C2316yes—
242#391C2316yes—
243#391C2316yes—
244#391C2316yes—
245#391C2316yes—
246#391C2316yes—
247#391C2316yes—
248#391C2316yes—
249#391C2313yes—
250#391C2313yes—
251#390C2316yes—
252#390C2316yes—
253#390C2311yescharacteristic
254#390C2311yescharacteristic
255#389C2311yescharacteristic
256#389C2311yescharacteristic
257#389C2313yes—
258#389C2313yes—
259#389C2316yes—
260#389C2316yes—
261#389C2316yes—
262#389C2316yes—
263#389C2316yes—
264#389C2316yes—
265#389C2316yes—
266#389C2316yes—
267#389C2316yes—
268#389C2316yes—
269#389C2316yes—
270#389C2316yes—
271#389C2316yes—
272#389C2316yes—
273#389C2316yes—
274#389C2316yes—
275#388C2312yes—
276#388C2312yes—
277#388C2316yes—
278#388C2316yes—
279#388C2316yes—
280#388C2316yes—
281#388C23112yes—
282#388C23112yes—
283#388C23112yes—
284#388C2316yes—
285#388C2316yes—
286#387C2316yes—
287#387C2316yes—
288#387C2316yes—
289#387C2316yes—
290#387C2316yes—
291#387C2316yes—
292#387C23112yes—
293#387C23112yes—
294#387C23112yes—
295#387C23112yes—
296#387C2316yes—
297#387C2316yes—
298#387C23112yes—
299#387C23112yes—
300#387C23112yes—
301#387C23112yes—
302#387C23112yes—
303#387C23112yes—
304#387C23112yes—
305#386C2316yes—
306#386C23112yes—
307#386C2316yes—
308#385C23112yes—
309#385C2316yes—
310#385C23112yes—
311#385C2316yes—
312#385C23112yes—
313#384C2313yes—
314#384C2313yes—
315#384C2316yes—
316#384C2316yes—
317#383C2316yes—
318#383C23112yes—
319#382C2313yes—
320#382C2313yes—
321#382C2316yes—
322#382C2316yes—
323#382C2316yes—
324#382C2316yes—
325#382C2316yes—
326#382C23112yes—
327#381C2316yes—
328#381C23112yes—
329#380C2316yes—
330#380C2316yes—
331#380C2316yes—
332#380C2316yes—
333#380C2316yes—
334#380C2316yes—
335#380C2316yes—
336#380C2316yes—
337#380C23112yes—
338#380C2313yes—
339#380C2313yes—
340C4×C4⋊C4C2316yes—
341C4×C4⋊C4C2316yes—
342C4×C4⋊C4C2316yes—
343C4×C4⋊C4C2316yes—
344C4×C4⋊C4C2316yes—
345C4×C4⋊C4C2316yes—
346C4×C4⋊C4C2316yes—
347C4×C4⋊C4C2316yes—
348C4×C4⋊C4C2313yes—
349C4×C4⋊C4C2316yes—
350C4×C4⋊C4C2316yes—
351C4×C4⋊C4C2316yes—
352C4×C4⋊C4C2313yes—
353C4×C4⋊C4C2316yes—
354C4×C4⋊C4C2316yes—
355C4×C4⋊C4C2313yes—
356C4×C4⋊C4C2313yes—
357C4×C4⋊C4C2313yes—
358C4×C4⋊C4C23112yes—
359C4×C4⋊C4C2313yes—
360C4×C4⋊C4C2313yes—
361C4×C4⋊C4C2313yes—
362C4×C4⋊C4C2313yes—
363C4×C4⋊C4C2316yes—
364C4×C4⋊C4C2316yes—
365C4×C4⋊C4C2313yes—
366C4×C4⋊C4C2313yes—
367C4×C4⋊C4C2313yes—
368C4×C4⋊C4C2313yes—
369C4×C4⋊C4C2313yes—
370C4×C4⋊C4C2313yes—
371C4×C4⋊C4C2313yes—
372C4×C4⋊C4C2313yes—
373C4×C4⋊C4C2311yescharacteristic
374C4×C22⋊C4C2316yes—
375C4×C22⋊C4C2316yes—
376C4×C22⋊C4C2316yes—
377C4×C22⋊C4C2316yes—
378C4×C22⋊C4C2316yes—
379C4×C22⋊C4C2316yes—
380C4×C22⋊C4C2316yes—
381C4×C22⋊C4C2316yes—
382C4×C22⋊C4C2316yes—
383C4×C22⋊C4C2316yes—
384C4×C22⋊C4C2316yes—
385C4×C22⋊C4C2316yes—
386C4×C22⋊C4C2316yes—
387C4×C22⋊C4C2316yes—
388C4×C22⋊C4C2316yes—
389C4×C22⋊C4C23112yes—
390C4×C22⋊C4C2316yes—
391C4×C22⋊C4C2316yes—
392C4×C22⋊C4C2316yes—
393C4×C22⋊C4C2312yes—
394#376C2316yes—
395#376C2316yes—
396#376C2316yes—
397C43C2313yes—
398C43C2313yes—
399C43C2313yes—
400C43C2313yes—
401C43C2313yes—
402C43C2316yes—
403C43C2313yes—
404C43C2311yescharacteristic
405C43C2313yes—
406C2×#41—24no—
407C2×#41—24no—
408C2×#41#4118yes—
409C22×Q8—28no—
410C22×Q8—28no—
411C22×Q8—28no—
412C22×Q8C2413yes—
413C22×Q8C2416yes—
414C22×Q8C2411yescharacteristic
415C22×D4C2416yes—
416C22×D4C2411yescharacteristic
417C22×D4C2413yes—
418C23×C4C2416yes—
419C23×C4C2413yes—
420C23×C4C2413yes—
421C23×C4C2413yes—
422C23×C4C2413yes—
423C23×C4C2413yes—
424C23×C4C2413yes—
425C23×C4C2413yes—
426C23×C4C2412yes—
427C23×C4C2416yes—
428C4⋊Q8—212no—
429C4⋊Q8—212no—
430#126—224no—
431#125—212no—
432#125—224no—
433#125—412no—
434#124—212no—
435#124—224no—
436#123—224no—
437C22⋊Q8—224no—
438C22⋊Q8—212no—
439C22⋊Q8—224no—
440C22⋊Q8—412no—
441#121—212no—
442#121—224no—
443C4×Q8—28no—
444C4×Q8—24no—
445C4×Q8—24no—
446C4×Q8—24no—
447C4×Q8—24no—
448C4×Q8—28no—
449C4×Q8—28no—
450C4×Q8—224no—
451C4×Q8—224no—
452C4×Q8—212no—
453C4×Q8—212no—
454C4×Q8—46no—
455C4×Q8#4118yes—
456C4×Q8#4118yes—
457C4×D4—212no—
458C4×D4—212no—
459C4×D4—224no—
460C4×D4—224no—
461C4×D4—212no—
462C4×D4—212no—
463C4×D4—212no—
464C4×D4—212no—
465C4×D4—212no—
466C4×D4—46no—
467C4×D4—412no—
468C4×D4#4118yescomplemented
469#117—212no—
470#117—224no—
471#117—212no—
472#117—212no—
473#117—28no—
474C2×C4⋊C4—224no—
475C2×C4⋊C4C2416yes—
476C2×C4⋊C4C24112yes—
477C2×C4⋊C4C2413yes—
478C2×C4⋊C4C2413yes—
479C2×C4⋊C4C2413yes—
480C2×C4⋊C4C2413yes—
481C2×C4⋊C4C2416yes—
482C2×C4⋊C4C2416yes—
483C2×C4⋊C4C2412yes—
484C2×C4⋊C4C2412yes—
485C2×C4⋊C4C2413yes—
486C2×C4⋊C4C2416yes—
487C2×C4⋊C4C2416yes—
488C2×C4⋊C4C2416yes—
489C2×C4⋊C4C2413yes—
490C2×C4⋊C4C2411yescharacteristic
491C2×C4⋊C4C2411yescharacteristic
492C2×C4⋊C4C2416yes—
493C2×C4⋊C4C2413yes—
494C2×C4⋊C4C2416yes—
495C2×C4⋊C4C2416yes—
496C2×C4⋊C4C2416yes—
497C2×C4⋊C4C2416yes—
498C2×C4⋊C4C2416yes—
499C2×C4⋊C4C2416yes—
500C2×C4⋊C4C24112yes—
501C2×C4⋊C4C2416yes—
502C2×C4⋊C4C2416yes—
503C2×C4⋊C4C24112yes—
504C2×C4⋊C4C2413yes—
505C2×C4⋊C4C2413yes—
506C2×C4⋊C4C2411yescharacteristic
507C2×C22⋊C4C2416yes—
508C2×C22⋊C4C2416yes—
509C2×C22⋊C4C2416yes—
510C2×C22⋊C4C2416yes—
511C2×C22⋊C4C2416yes—
512C2×C22⋊C4C2412yes—
513C2×C22⋊C4C2412yes—
514C2×C22⋊C4C2412yes—
515C2×C22⋊C4C2412yes—
516C2×C22⋊C4C2416yes—
517C2×C22⋊C4C2416yes—
518C2×C22⋊C4C2416yes—
519C2×C22⋊C4C2416yes—
520C2×C22⋊C4C24112yes—
521C2×C22⋊C4C2416yes—
522C2×C22⋊C4C2416yes—
523C2×C22⋊C4C24112yes—
524C2×C22⋊C4C2412yes—
525C2×C42—212no—
526C2×C42—224no—
527C2×C42—212no—
528C2×C42—212no—
529C2×C42—212no—
530C2×C42—212no—
531C2×C42—46no—
532C2×C42—46no—
533C2×C42C2413yes—
534C2×C42C2413yes—
535C2×C42C2413yes—
536C2×C42C2416yes—
537C2×C42C2413yes—
538C2×C42C2413yes—
539C2×C42C2413yes—
540C2×C42C2413yes—
541C2×C42C2413yes—
542C2×C42C2416yes—
543C2×C42C2416yes—
544C2×C42C2416yes—
545C2×C42C2413yes—
546C2×C42C2413yes—
547C2×C42C2413yes—
548C2×C42C2411yescharacteristic
549C2×C42C2411yescharacteristic
550C2×C42C2411yescharacteristic
551C2×C42C2411yescharacteristic
552C2×C42C2413yes—
553C2×C42C2413yes—
554C2×C42C2413yes—
555C2×C42C2416yes—
556C2×C42C2412yes—
557C2×C42C2416yes—
558C2×C42C2411yescharacteristic
559C2×C42C2413yes—
560C2×C42C2416yes—
561C2×C42C2416yes—
562C2×C42C2413yes—
563C2×C42C2413yes—
564C2×C42C2413yes—
565C2×C42C2413yes—
566C2×C42C2413yes—
567C2×C42C2413yes—
568C2×C42C2411yescharacteristic
569C2×C42C2411yescharacteristic
570#95C2416yes—
571#95C2416yes—
572#95C2416yes—
573#95C2416yes—
574#95C2416yes—
575#95C2416yes—
576#95C2416yes—
577#95C2416yes—
578#95C2416yes—
579#95C2416yes—
580#95C2416yes—
581#95C2416yes—
582#95C2412yes—
583#95C2412yes—
584#95C2416yes—
585#95C2416yes—
586#95C2416yes—
587#95C2416yes—
588#95C2416yes—
589#95C2416yes—
590#95C2416yes—
591#95C24112yes—
592#95C24112yes—
593#95C2412yes—
594#95C24112yes—
595#95C2416yes—
596#95C2416yes—
597#95C24112yes—
598#95C24112yes—
599#95C24112yes—
600#95C24112yes—
601C24C2512yes—
602C24C2513yes—
603#41—232no—
604C2×Q8—212no—
605C2×Q8—26no—
606C2×Q8—26no—
607C2×Q8—212no—
608C2×Q8—212no—
609C2×Q8—26no—
610C2×Q8—432no—
611C2×Q8C2×#4114yes—
612C2×Q8C2×#4114yes—
613C2×Q8C2×#4114yes—
614C2×D4—212no—
615C2×D4—212no—
616C2×D4—22no—
617C2×D4—26no—
618C2×D4—26no—
619C2×D4—22no—
620C2×D4—46no—
621C2×D4C2×#41112yes—
622C2×D4C2×#4114yes—
623C22×C4—24no—
624C22×C4—26no—
625C22×C4—26no—
626C22×C4—24no—
627C22×C4—26no—
628C22×C4—26no—
629C22×C4—212no—
630C22×C4—26no—
631C22×C4—26no—
632C22×C4—26no—
633C22×C4—26no—
634C22×C4—26no—
635C22×C4—26no—
636C22×C4—26no—
637C22×C4—212no—
638C22×C4—212no—
639C22×C4—26no—
640C22×C4—26no—
641C22×C4—26no—
642C22×C4—26no—
643C22×C4—26no—
644C22×C4—212no—
645C22×C4—43no—
646C22×C4—43no—
647C22×C4—43no—
648C22×C4—43no—
649C22×C4—46no—
650C22×C4—46no—
651C22×C4C2×#41112yes—
652C22×C4C2×#4118yes—
653C22×C4C2513yes—
654C22×C4C2513yes—
655C22×C4C2516yes—
656C22×C4C2512yes—
657C22×C4C2512yes—
658C22×C4C2513yes—
659C22×C4C2513yes—
660C22×C4C2516yes—
661C22×C4C2516yes—
662C22×C4C2516yes—
663C22×C4C2511yescharacteristic
664C22×C4C2511yescharacteristic
665C22×C4C2513yes—
666C22×C4C2512yes—
667C22×C4C2513yes—
668C22×C4C2511yescharacteristic
669C22×C4C2511yescharacteristic
670C22×C4C2511yescharacteristic
671C22×C4C2513yes—
672C22×C4C2511yescharacteristic
673C22×C4C2511yescharacteristic
674C4⋊C4—212no—
675C4⋊C4—224no—
676C4⋊C4—26no—
677C4⋊C4—26no—
678C4⋊C4—26no—
679C4⋊C4—26no—
680C4⋊C4—212no—
681C4⋊C4—212no—
682C4⋊C4—212no—
683C4⋊C4—212no—
684C4⋊C4—26no—
685C4⋊C4—22no—
686C4⋊C4—212no—
687C4⋊C4—26no—
688C4⋊C4—212no—
689C4⋊C4—212no—
690C4⋊C4—212no—
691C4⋊C4—212no—
692C4⋊C4—212no—
693C4⋊C4—24no—
694C4⋊C4—24no—
695C4⋊C4—26no—
696C4⋊C4—212no—
697C4⋊C4—22no—
698C4⋊C4—46no—
699C4⋊C4—412no—
700C4⋊C4—46no—
701C4⋊C4—46no—
702C4⋊C4—412no—
703C4⋊C4C2×#41112yes—
704C4⋊C4C2×#41112yes—
705C4⋊C4C2×#4114yes—
706C22⋊C4—212no—
707C22⋊C4—212no—
708C22⋊C4—212no—
709C22⋊C4—212no—
710C22⋊C4—212no—
711C22⋊C4—224no—
712C22⋊C4—212no—
713C22⋊C4—212no—
714C22⋊C4—24no—
715C22⋊C4—212no—
716C22⋊C4—212no—
717C22⋊C4—24no—
718C22⋊C4—24no—
719C22⋊C4—24no—
720C22⋊C4—46no—
721C22⋊C4—46no—
722C22⋊C4—412no—
723C22⋊C4C2×#4118yes—
724C42—22no—
725C42—22no—
726C42—22no—
727C42—26no—
728C42—26no—
729C42—26no—
730C42—26no—
731C42—26no—
732C42—26no—
733C42—26no—
734C42—26no—
735C42—212no—
736C42—212no—
737C42—212no—
738C42—26no—
739C42—26no—
740C42—212no—
741C42—212no—
742C42—212no—
743C42—26no—
744C42—26no—
745C42—26no—
746C42—24no—
747C42—22no—
748C42—22no—
749C42—26no—
750C42—26no—
751C42—43no—
752C42—43no—
753C42—43no—
754C42—43no—
755C42—46no—
756C42—46no—
757C42C2×#41112yes—
758C42C2×#4114yes—
759C42C2×#41112yes—
760C422−1+414yes—
761C23—22no—
762C23—23no—
763C23—23no—
764C23—23no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—23no—
769C23—22no—
770C23—23no—
771C23—22no—
772C23—23no—
773C23C22×#4114yes—
774C23C22×#4116yes—
775C23C2611yescharacteristic
776Q8—424no—
777Q8—412no—
778Q8#529116yescomplemented
779D4—224no—
780D4—28no—
781D4—424no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—23no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—23no—
795C2×C4—21no—
796C2×C4—23no—
797C2×C4—23no—
798C2×C4—224no—
799C2×C4—216no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—23no—
803C2×C4—23no—
804C2×C4—23no—
805C2×C4—23no—
806C2×C4—23no—
807C2×C4—23no—
808C2×C4—23no—
809C2×C4—26no—
810C2×C4—26no—
811C2×C4—26no—
812C2×C4—26no—
813C2×C4—26no—
814C2×C4—26no—
815C2×C4—26no—
816C2×C4—26no—
817C2×C4—23no—
818C2×C4—23no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—23no—
822C2×C4—23no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—23no—
826C2×C4—26no—
827C2×C4—26no—
828C2×C4—26no—
829C2×C4—26no—
830C2×C4—412no—
831C2×C4—412no—
832C2×C4—412no—
833C2×C4—412no—
834C2×C4—424no—
835C2×C4—412no—
836C2×C4—412no—
837C2×C4—812no—
838C2×C4C22×#4112yes—
839C2×C4C22×#4116yes—
840C2×C4C22×#4112yes—
841C2×C4C22×#4116yes—
842C2×C4C22×#4114yes—
843C2×C4C22×#4116yes—
844C2×C4C22×#4116yes—
845C2×C4C22×#4116yes—
846C2×C4C22×#4112yes—
847C2×C4C22×#4112yes—
848C2×C4C22×#4112yes—
849C2×C4C22×#4112yes—
850C2×C4C2×2−1+412yes—
851C2×C4C2×2−1+412yes—
852C2×C4C2×2−1+412yes—
853C2×C4#58512yes—
854C2×C4#58512yes—
855C22—26no—
856C22—26no—
857C22—24no—
858C22—24no—
859C22—26no—
860C22—24no—
861C22—43no—
862C22—42no—
863C22—42no—
864C22—43no—
865C22—42no—
866C22—42no—
867C22—43no—
868C22—43no—
869C22C23×#4111yescharacteristic
870C22C23×#4111yescharacteristic
871C22C23×#4111yescharacteristic
872C22C23×#4111yescharacteristic
873C22C22×2−1+411yescharacteristic
874C22C2×#58511yescharacteristic
875C22C2×#58511yescharacteristic
876C4—22no—
877C4—22no—
878C4—26no—
879C4—22no—
880C4—26no—
881C4—22no—
882C4—24no—
883C4—22no—
884C4—42no—
885C4—42no—
886C4—43no—
887C4—46no—
888C4—46no—
889C4—43no—
890C4—46no—
891C4—43no—
892C4—43no—
893C4—46no—
894C4C2×#529112yes—
895C4#348014yes—
896C4#348214yes—
897C2—46no—
898C2—44no—
899C2C22×#52911yescharacteristic
900C2C2×#348011yescharacteristic
901C2C2×#348211yescharacteristic
902C2#41211yescharacteristic
903C2#6280511yescharacteristic
904C2#6280511yescharacteristic
905C2#6281611yescharacteristic
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
prime radical#36444C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36635C2semidirect
2. #36454C2semidirect
3. #36453C2semidirect
4. #36452C2semidirect
5. #36451C2semidirect
6. #36450C2semidirect
7. #36449C2semidirect
8. #36448C2semidirect
9. #36447C2semidirect
10. #36446C2semidirect
11. #36445C2semidirect
13. #36432C2semidirect
14. #34945C2semidirect
15. #34932C2semidirect
16. #34913C2semidirect
17. #34793C2semidirect
18. C4×#557C2semidirect
19. C4×D4×Q8C2semidirect
20. C4×#548C2semidirect
21. Q8×#117C2semidirect
22. C4×#529C2semidirect
23. C42×#41C2semidirect
468. C4×D4#41semidirect
778. Q8#529semidirect

Maximal subgroups

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

subgroupindex
#366352
#364542
#364532
#364522
#364512
#364502
#364492
#364482
#364472
#364462
#364452
#364442
#364322
#349452
#349322
#349132
#347932
C4×#5572
C4×D4×Q82
C4×#5482
Q8×#1172
C4×#5292
C42×#412