Finite Group Databasebeta

← #6630379

Subgroups — #6630379

Order 512.

2096 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36645C211yesmaximal, characteristic, complemented
2C42×#41C211yesmaximal, characteristic
3#33198C211yesmaximal, characteristic, complemented
4#33197C211yesmaximal, characteristic, complemented
5#33196C211yesmaximal, characteristic, complemented
6#33195C211yesmaximal, characteristic, complemented
7#33154C212yesmaximal, complemented
8#33153C212yesmaximal, complemented
9#33073C212yesmaximal, complemented
10#33072C212yesmaximal, complemented
11#32958C212yesmaximal
12#32955C212yesmaximal
13C4×#477C212yesmaximal, complemented
14C4×#475C212yesmaximal, complemented
15C4×#476C212yesmaximal, complemented
16C4×#474C212yesmaximal, complemented
17#21362C212yesmaximal, complemented
18#20808C211yesmaximal, characteristic, complemented
19#20737C212yesmaximal
20C2×#533—21no—
21C2×C4×#41C2211yescharacteristic
22C2×C4×#41C2211yescharacteristic
23C2×C4×#41C2211yescharacteristic
24C2×#477C2212yes—
25C2×#475C2212yes—
26C2×#476C2212yes—
27C2×#474C2212yes—
28C2×#431C2212yes—
29#2868C2211yescharacteristic
30#2868C2211yescharacteristic
31#2862—21no—
32#2859—21no—
33#2859C2212yes—
34#2857—21no—
35#2857—21no—
36#2857C2212yes—
37#2857C2212yes—
38C4×C4⋊Q8—21no—
39C4×C4⋊Q8—21no—
40C4×C4⋊Q8C2212yes—
41C4×C4⋊Q8C2212yes—
42#2285—21no—
43#2285C2212yes—
44C42×Q8C2211yescharacteristic
45C42×Q8C2211yescharacteristic
46C42×Q8C2211yescharacteristic
47C42×Q8C2211yescharacteristic
48C42×D4—21no—
49C42×D4—21no—
50C42×D4—21no—
51C42×D4—21no—
52C42×D4C2211yescharacteristic
53C42×D4C2211yescharacteristic
54C42×D4C2211yescharacteristic
55C42×D4C2211yescharacteristic
56C4×#117—21no—
57C4×#117—21no—
58C4×#117—21no—
59C4×#117C2211yescharacteristic
60C4×#117C2211yescharacteristic
61C4×#117C2211yescharacteristic
62C2×C43—21no—
63C2×C43C2211yescharacteristic
64#1988C2212yes—
65#1988C2212yes—
66#1987C2212yes—
67#1987C2212yes—
68#1948C2212yes—
69#1948C2212yes—
70#1948C2212yes—
71#1948C2212yes—
72#1947C2212yes—
73#1947C2212yes—
74#1947C2212yes—
75#1947C2212yes—
76#1921C2214yes—
77#1920C2214yes—
78#1919C2214yes—
79#1918C2214yes—
80#1865C2214yes—
81#1864C2214yes—
82#1863C2214yes—
83#1862C2214yes—
84#1854C2214yes—
85#1854C2214yes—
86#1842C2211yescharacteristic
87#1842C2211yescharacteristic
88#1831C2212yes—
89#1825C2214yes—
90#1803C2212yes—
91#1803C2212yes—
92#1803C2212yes—
93#1803C2212yes—
94#1802C2212yes—
95#1802C2212yes—
96#1802C2212yes—
97#1802C2212yes—
98#1797C2212yes—
99#1797C2212yes—
100#1788C2214yes—
101C4×#107C2214yes—
102C4×#106C2214yes—
103C4×C4⋊C8C2212yes—
104C4×C4⋊C8C2212yes—
105C4×#103C2214yes—
106C4×#102C2214yes—
107C22×#41C2311yescharacteristic
108#533—48no—
109C2×C4⋊Q8—21no—
110C2×C4⋊Q8—21no—
111C2×C4⋊Q8—21no—
112C2×C4⋊Q8—21no—
113C2×C4⋊Q8C2312yes—
114C2×C4⋊Q8C2312yes—
115C2×#125—22no—
116C2×C22⋊Q8—22no—
117C2×C22⋊Q8—22no—
118C4×#41—24no—
119C4×#41—24no—
120C4×#41—24no—
121C4×#41—24no—
122C4×#41—24no—
123C4×#41Q818yescomplemented
124C2×C4×Q8—22no—
125C2×C4×Q8—22no—
126C2×C4×Q8C2311yescharacteristic
127C2×C4×Q8C2311yescharacteristic
128C2×C4×Q8C2311yescharacteristic
129C2×C4×Q8C2311yescharacteristic
130C2×C4×Q8C2311yescharacteristic
131C2×C4×Q8C2311yescharacteristic
132C2×C4×D4—21no—
133C2×C4×D4—21no—
134C2×C4×D4—21no—
135C2×C4×D4—21no—
136C2×C4×D4—21no—
137C2×C4×D4—21no—
138C2×C4×D4C2311yescharacteristic
139C2×C4×D4C2311yescharacteristic
140C2×C4×D4C2311yescharacteristic
141C2×C4×D4C2311yescharacteristic
142C2×C4×D4C2311yescharacteristic
143C2×C4×D4C2311yescharacteristic
144C2×#117—22no—
145C2×#117—21no—
146C2×#117—21no—
147C2×#117—21no—
148C2×#117C2311yescharacteristic
149C2×#117C2311yescharacteristic
150C2×#117C2311yescharacteristic
151C22×C42—21no—
152C22×C42—21no—
153C22×C42—21no—
154C22×C42—21no—
155C22×C42—21no—
156C22×C42—21no—
157C22×C42—21no—
158C22×C42D411yescharacteristic
159C22×C42D411yescharacteristic
160C22×C42D411yescharacteristic
161C22×C42D411yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165#477—28no—
166#476—28no—
167#475—28no—
168#474—28no—
169#431—28no—
170C2×#107C2314yes—
171C2×#107C2314yes—
172C2×#106C2314yes—
173C2×#106C2314yes—
174C2×C4⋊C8C2312yes—
175C2×C4⋊C8C2312yes—
176C2×C4⋊C8C2312yes—
177C2×C4⋊C8C2312yes—
178C2×C4⋊C8C2312yes—
179C2×C4⋊C8C2312yes—
180C2×#103C2314yes—
181C2×#103C2314yes—
182C2×#102C2314yes—
183C2×#102C2314yes—
184C2×C22⋊C8C2314yes—
185C2×C4×C8C2314yes—
186#391—22no—
187#391—22no—
188#391—22no—
189#391—22no—
190#389—22no—
191#389—22no—
192#389—22no—
193#389—22no—
194#389—22no—
195#389—22no—
196#389C2314yes—
197#389C2314yes—
198#384—21no—
199#384—21no—
200#384—21no—
201#384—21no—
202#384C2312yes—
203#384C2312yes—
204#384C2312yes—
205#384C2312yes—
206#382—22no—
207#382—22no—
208#380—22no—
209#380—22no—
210#380—22no—
211#380C2314yes—
212C4×C4⋊C4—22no—
213C4×C4⋊C4—22no—
214C4×C4⋊C4—22no—
215C4×C4⋊C4—21no—
216C4×C4⋊C4—21no—
217C4×C4⋊C4—21no—
218C4×C4⋊C4—21no—
219C4×C4⋊C4—21no—
220C4×C4⋊C4—21no—
221C4×C4⋊C4—21no—
222C4×C4⋊C4—21no—
223C4×C4⋊C4—21no—
224C4×C4⋊C4—21no—
225C4×C4⋊C4—21no—
226C4×C4⋊C4—21no—
227C4×C4⋊C4C2314yes—
228C4×C4⋊C4C2311yescharacteristic
229C4×C4⋊C4C2311yescharacteristic
230C4×C4⋊C4C2311yescharacteristic
231C4×C4⋊C4C2311yescharacteristic
232C4×C4⋊C4C2311yescharacteristic
233C4×C4⋊C4C2311yescharacteristic
234C4×C4⋊C4C2311yescharacteristic
235C4×C4⋊C4C2311yescharacteristic
236C4×C4⋊C4C2311yescharacteristic
237C4×C4⋊C4C2311yescharacteristic
238C4×C4⋊C4C2311yescharacteristic
239C4×C4⋊C4C2311yescharacteristic
240C4×C22⋊C4—21no—
241C4×C22⋊C4—21no—
242C4×C22⋊C4—21no—
243C4×C22⋊C4—21no—
244C4×C22⋊C4—21no—
245C4×C22⋊C4—21no—
246C4×C22⋊C4—21no—
247C4×C22⋊C4—21no—
248C4×C22⋊C4—21no—
249C4×C22⋊C4—21no—
250C4×C22⋊C4—21no—
251C4×C22⋊C4—21no—
252C4×C22⋊C4—21no—
253C4×C22⋊C4—21no—
254C4×C22⋊C4—21no—
255C4×C22⋊C4—21no—
256C4×C22⋊C4—21no—
257C4×C22⋊C4—21no—
258#376—21no—
259#376—21no—
260#376—21no—
261C43—21no—
262C43—21no—
263C43—21no—
264C43—21no—
265C43—21no—
266C43—21no—
267C43—21no—
268C43D411yescharacteristic
269C43D411yescharacteristic
270C43D411yescharacteristic
271C43D411yescharacteristic
272C43C2311yescharacteristic
273C43C2311yescharacteristic
274C43C2311yescharacteristic
275C43C2311yescharacteristic
276#340C2314yes—
277#340C2314yes—
278#340C2314yes—
279#340C2314yes—
280#340C2314yes—
281#340C2314yes—
282#340C2314yes—
283#340C2314yes—
284#336C2314yes—
285#336C2314yes—
286C2×#41—22no—
287C2×#41—22no—
288C2×#41—22no—
289C2×#41—22no—
290C2×#41—22no—
291C2×#41C2×Q814yes—
292C22×Q8—22no—
293C22×Q8—22no—
294C22×Q8C2411yescharacteristic
295C22×D4—21no—
296C22×D4C2411yescharacteristic
297C23×C4—21no—
298C23×C4—21no—
299C23×C4—21no—
300C23×C4—21no—
301C23×C4—21no—
302C23×C4—21no—
303C23×C4—21no—
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2411yescharacteristic
311C22×C8C2414yes—
312C22×C8C2414yes—
313C4⋊Q8—24no—
314C4⋊Q8—24no—
315C4⋊Q8—24no—
316C4⋊Q8—24no—
317C4⋊Q8—44no—
318C4⋊Q8—44no—
319C4⋊Q8—44no—
320C4⋊Q8—44no—
321#125—48no—
322C22⋊Q8—48no—
323C22⋊Q8—48no—
324C4×Q8—22no—
325C4×Q8—22no—
326C4×Q8—22no—
327C4×Q8—22no—
328C4×Q8—22no—
329C4×Q8—22no—
330C4×Q8—22no—
331C4×Q8—22no—
332C4×Q8—48no—
333C4×Q8—48no—
334C4×Q8C2×Q814yes—
335C4×Q8C2×Q814yes—
336C4×Q8#4114yes—
337C4×Q8#4114yes—
338C4×D4—28no—
339C4×D4—28no—
340C4×D4—28no—
341C4×D4—28no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—28no—
345C4×D4—28no—
346C4×D4—22no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4C2×Q814yes—
353C4×D4C2×Q814yes—
354C4×D4#4114yes—
355C4×D4#4114yes—
356#117—28no—
357#117—28no—
358#117—22no—
359#117—22no—
360#117—22no—
361#117—22no—
362#117—22no—
363#117—28no—
364#117—48no—
365#117C2×Q814yes—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4C2414yes—
385C2×C4⋊C4C2414yes—
386C2×C4⋊C4C2411yescharacteristic
387C2×C4⋊C4C2411yescharacteristic
388C2×C4⋊C4C2411yescharacteristic
389C2×C4⋊C4C2411yescharacteristic
390C2×C4⋊C4C2411yescharacteristic
391C2×C4⋊C4C2411yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—24no—
402C2×C42—28no—
403C2×C42—28no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—28no—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—24no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—21no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—21no—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—24no—
432C2×C42—21no—
433C2×C42—21no—
434C2×C42—42no—
435C2×C42—44no—
436C2×C42—44no—
437C2×C42—44no—
438C2×C42—44no—
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D411yescharacteristic
453C2×C42C2×D411yescharacteristic
454C2×C42C2×D411yescharacteristic
455C2×C42C2×D411yescharacteristic
456C2×C42C2×D411yescharacteristic
457C2×C42C2×D411yescharacteristic
458C2×C42C2×D411yescharacteristic
459C2×C42C2×D411yescharacteristic
460C2×C42C2×D411yescharacteristic
461C2×C42C2×Q814yes—
462C2×C42#4114yes—
463C2×C42C2411yescharacteristic
464C2×C42C2411yescharacteristic
465C2×C42C2411yescharacteristic
466C2×C42C2411yescharacteristic
467C2×C42C2411yescharacteristic
468C2×C42C2411yescharacteristic
469#107—28no—
470#107—28no—
471#106—28no—
472#106—28no—
473C4⋊C8—24no—
474C4⋊C8—24no—
475C4⋊C8—24no—
476C4⋊C8—24no—
477C4⋊C8—24no—
478C4⋊C8—24no—
479#103—28no—
480#103—28no—
481#102—28no—
482#102—28no—
483C22⋊C8—28no—
484C4×C8—28no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—24no—
498#95—24no—
499#95—24no—
500#95—24no—
501C24—21no—
502C24C22×D411yescharacteristic
503#41—28no—
504#41—28no—
505#41—28no—
506#41—28no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—44no—
511C2×Q8—44no—
512C2×Q8—44no—
513C2×Q8—44no—
514C2×Q8—44no—
515C2×Q8—44no—
516C2×Q8C22×Q812yes—
517C2×Q8C2×#4112yes—
518C2×Q8C2×#4112yes—
519C2×D4—24no—
520C2×D4—24no—
521C2×D4—24no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4C22×Q812yes—
526C2×D4C2×#4112yes—
527C2×D4C2×#4112yes—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—21no—
531C22×C4—24no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4C22⋊Q814yes—
579C22×C4C22⋊Q814yes—
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×Q812yes—
594C22×C4C2×#4112yes—
595C22×C4C2511yescharacteristic
596C2×C8—24no—
597C2×C8—24no—
598C2×C8—24no—
599C2×C8—24no—
600C2×C8—24no—
601C2×C8—24no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—48no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—48no—
628C4⋊C4—44no—
629C4⋊C4—44no—
630C4⋊C4C22×Q812yes—
631C4⋊C4C22×Q812yes—
632C4⋊C4C2×#4112yes—
633C4⋊C4C2×#4112yes—
634C4⋊C4C2×#4112yes—
635C4⋊C4C2×#4112yes—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—48no—
646C42—24no—
647C42—24no—
648C42—24no—
649C42—24no—
650C42—24no—
651C42—24no—
652C42—24no—
653C42—22no—
654C42—22no—
655C42—24no—
656C42—24no—
657C42—22no—
658C42—22no—
659C42—22no—
660C42—22no—
661C42—22no—
662C42—22no—
663C42—22no—
664C42—22no—
665C42—22no—
666C42—22no—
667C42—22no—
668C42—22no—
669C42—22no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—41no—
675C42—41no—
676C42—42no—
677C42—42no—
678C42—42no—
679C42—42no—
680C42—42no—
681C42—42no—
682C42—42no—
683C42—42no—
684C42—48no—
685C42—42no—
686C42—42no—
687C42—42no—
688C42—42no—
689C42C22⋊Q814yes—
690C42C22⋊Q814yes—
691C42#13514yes—
692C42AGL(1,ℤ/8)14yes—
693C42#13714yes—
694C42C22×Q812yes—
695C42C22×Q812yes—
696C42C2×#4112yes—
697C42C2×#4112yes—
698C42C2×#4112yes—
699C42C2×#4112yes—
700C42C2×#4112yes—
701C42C2×#4112yes—
702C23—22no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—22no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23C2×C22⋊Q812yes—
716C23C23×D411yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—88no—
721Q8—88no—
722Q8#53314yescomplemented
723D4—216no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4#53314yescomplemented
728C2×C4—216no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—28no—
747C2×C4—28no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—48no—
767C2×C4—48no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—48no—
781C2×C4—48no—
782C2×C4—44no—
783C2×C4—48no—
784C2×C4—44no—
785C2×C4—48no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4C2×C22⋊Q812yes—
793C2×C4C2×C22⋊Q812yes—
794C2×C4C2×C22⋊Q812yes—
795C2×C4C2×C22⋊Q812yes—
796C2×C4C2×C22⋊Q812yes—
797C2×C4#52512yes—
798C2×C4#52512yes—
799C2×C4#52512yes—
800C2×C4#52512yes—
801C2×C4C2×#13512yes—
802C2×C4C2×#13512yes—
803C2×C4C2×#13512yes—
804C2×C4C2×AGL(1,ℤ/8)12yes—
805C2×C4C2×AGL(1,ℤ/8)12yes—
806C2×C4C2×AGL(1,ℤ/8)12yes—
807C2×C4C2×#13712yes—
808C2×C4C2×#13712yes—
809C2×C4C2×#13712yes—
810C2×C4#57512yes—
811C2×C4C23×Q811yescharacteristic
812C2×C4C22×#4111yescharacteristic
813C2×C4C22×#4111yescharacteristic
814C2×C4C22×#4111yescharacteristic
815C2×C4C22×#4111yescharacteristic
816C2×C4C22×#4111yescharacteristic
817C8—44no—
818C8—44no—
819C22—22no—
820C22—24no—
821C22—22no—
822C22—22no—
823C22—42no—
824C22—42no—
825C22—41no—
826C22—42no—
827C22—41no—
828C22—42no—
829C22—41no—
830C22—42no—
831C22—41no—
832C22—42no—
833C22C22×C22⋊Q811yescharacteristic
834C22C2×#52511yescharacteristic
835C22C2×#52511yescharacteristic
836C22C22×#13511yescharacteristic
837C22C22×AGL(1,ℤ/8)11yescharacteristic
838C22C22×#13711yescharacteristic
839C22C2×#57511yescharacteristic
840C4—22no—
841C4—24no—
842C4—22no—
843C4—22no—
844C4—22no—
845C4—22no—
846C4—22no—
847C4—22no—
848C4—42no—
849C4—42no—
850C4—41no—
851C4—42no—
852C4—41no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—84no—
857C4—84no—
858C4#307614yes—
859C4#307914yes—
860C4#310614yes—
861C4#310714yes—
862C4C2×#53311yescharacteristic
863C4C2×#53311yescharacteristic
864C4#344411yescharacteristic
865C4#344411yescharacteristic
866C2—42no—
867C2—44no—
868C2#3662511yescharacteristic
869C2C2×#307611yescharacteristic
870C2C2×#307911yescharacteristic
871C2C2×#310611yescharacteristic
872C2C2×#310711yescharacteristic
873C2#6056111yescharacteristic
874C2#6056211yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36645C2semidirect
3. #33198C2semidirect
4. #33197C2semidirect
5. #33196C2semidirect
6. #33195C2semidirect
7. #33154C2semidirect
8. #33153C2semidirect
9. #33073C2semidirect
10. #33072C2semidirect
13. C4×#477C2semidirect
14. C4×#475C2semidirect
15. C4×#476C2semidirect
16. C4×#474C2semidirect
17. #21362C2semidirect
18. #20808C2semidirect
123. C4×#41Q8semidirect
722. Q8#533semidirect
727. D4#533semidirect

Maximal subgroups

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

subgroupindex
#366452
C42×#412
#331982
#331972
#331962
#331952
#331542
#331532
#330732
#330722
#329582
#329552
C4×#4772
C4×#4752
C4×#4762
C4×#4742
#213622
#208082
#207372