Finite Group Databasebeta

← #6457198

Subgroups — #6457198

Order 512.

2362 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3091C212yesmaximal
2C4×#525C211yesmaximal, characteristic
3C2×#2285C211yesmaximal, characteristic, complemented
4#27653C212yesmaximal, complemented
5#27652C212yesmaximal, complemented
6#27651C212yesmaximal, complemented
7#27650C212yesmaximal, complemented
8#27649C212yesmaximal, complemented
9#27648C211yesmaximal, characteristic, complemented
10#27647C211yesmaximal, characteristic, complemented
11#27646C212yesmaximal, complemented
12#27645C211yesmaximal, characteristic, complemented
13#27644C211yesmaximal, characteristic, complemented
14#23656C212yesmaximal, complemented
15#23627C212yesmaximal, complemented
16#21169C212yesmaximal, complemented
17#20699C212yesmaximal, complemented
18#20645C212yesmaximal, complemented
19C2×#1797C211yesmaximal, characteristic, complemented
20C2×#525C2211yescharacteristic
21C2×C4×#41C2211yescharacteristic
22C22×#117C2212yes—
23C23×C42C2211yescharacteristic
24#3091—216no—
25C2×#484C2212yes—
26C2×#481C2212yes—
27C2×#485C2214yes—
28C2×#482C2214yes—
29C2×#483C2212yes—
30C2×#480C2212yes—
31C2×#427C2214yes—
32C22×C4⋊C8C2212yes—
33C2×#416C2214yes—
34C22×C22⋊C8C2212yes—
35C4×C22⋊Q8C2211yescharacteristic
36C4×C22⋊Q8C2211yescharacteristic
37C4×C22⋊Q8C2211yescharacteristic
38C4×C22⋊Q8C2211yescharacteristic
39C4×#123—21no—
40C4×#123—21no—
41C4×#121C2211yescharacteristic
42C4×#121C2211yescharacteristic
43C4×#121C2211yescharacteristic
44C4×#121C2211yescharacteristic
45C4×#120—21no—
46C4×#120—21no—
47#2297C2211yescharacteristic
48#2296C2211yescharacteristic
49#2290—21no—
50#2290—21no—
51#2285—21no—
52#2285—21no—
53#2285—21no—
54#2285—21no—
55#2285C2212yes—
56#2285C2212yes—
57#2285C2212yes—
58#2285C2212yes—
59C2×#384C2211yescharacteristic
60C2×#384C2211yescharacteristic
61C2×#382C2212yes—
62#2280C2211yescharacteristic
63C2×#380—21no—
64C2×#380—21no—
65C42×D4—21no—
66C42×D4—21no—
67C4×#117C2211yescharacteristic
68C2×C4×C4⋊C4—21no—
69C2×C4×C4⋊C4—21no—
70#2085C2214yescomplemented
71#2085C2214yescomplemented
72#2084C2212yescomplemented
73#2084C2212yescomplemented
74#2083C2212yescomplemented
75#2083C2212yescomplemented
76#2074C2214yescomplemented
77#2073C2214yescomplemented
78#2072C2212yescomplemented
79#2072C2212yescomplemented
80#2071C2212yescomplemented
81#2071C2212yescomplemented
82#1949C2214yescomplemented
83#1949C2214yescomplemented
84#1948C2212yescomplemented
85#1948C2212yescomplemented
86#1947C2212yescomplemented
87#1947C2212yescomplemented
88#1825C2214yes—
89#1825C2214yes—
90#1824C2212yes—
91#1824C2212yes—
92#1823C2212yes—
93#1823C2212yes—
94#1805C2214yescomplemented
95#1804C2214yescomplemented
96#1803C2212yescomplemented
97#1803C2212yescomplemented
98#1802C2212yescomplemented
99#1802C2212yescomplemented
100#1797C2211yescharacteristic
101#1797C2212yes—
102#1797C2212yes—
103#1797C2212yes—
104#1797C2211yescharacteristic
105#1735C2214yes—
106#1735C2214yes—
107C2×#336C2212yes—
108C22×#41C2311yescharacteristic
109C24×C4D411yescharacteristic
110C24×C4D411yescharacteristic
111C24×C4C2311yescharacteristic
112C23×C8C2314yes—
113#525—24no—
114#525D418yes—
115C2×#123—21no—
116C2×C22⋊Q8C2311yescharacteristic
117C2×C22⋊Q8C2311yescharacteristic
118C2×#121C2311yescharacteristic
119C2×#121C2311yescharacteristic
120C2×#120—21no—
121C4×#41—28no—
122C2×C4×Q8C2311yescharacteristic
123C2×C4×Q8C2311yescharacteristic
124C2×C4×D4—21no—
125C2×C4×D4—21no—
126C2×C4×D4—21no—
127C2×C4×D4—21no—
128C2×C4×D4—21no—
129C2×C4×D4—21no—
130C2×C4×D4—21no—
131C2×C4×D4—21no—
132C2×C4×D4C2311yescharacteristic
133C2×C4×D4C2311yescharacteristic
134C2×#117—22no—
135C2×#117—22no—
136C2×#117—21no—
137C2×#117—28no—
138C2×#117—28no—
139C2×#117C2314yes—
140C2×#117C2314yes—
141C2×#117C2311yescharacteristic
142C2×#117C2311yescharacteristic
143C2×#117C2311yescharacteristic
144C22×C4⋊C4—21no—
145C22×C4⋊C4—21no—
146C22×C4⋊C4—21no—
147C22×C4⋊C4—21no—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C22⋊C4—22no—
151C22×C42—28no—
152C22×C42—22no—
153C22×C42—21no—
154C22×C42D411yescharacteristic
155C22×C42D411yescharacteristic
156C22×C42D411yescharacteristic
157C22×C42D411yescharacteristic
158C22×C42D411yescharacteristic
159C22×C42D411yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166#485—216no—
167#484—28no—
168#483—28no—
169#482—216no—
170#481—28no—
171#480—28no—
172#427—216no—
173C2×#107C2314yes—
174C2×#107C2314yes—
175C2×#106C2314yes—
176C2×#106C2314yes—
177C2×C4⋊C8—28no—
178C2×C4⋊C8C2312yes—
179C2×C4⋊C8C2312yes—
180C2×C4⋊C8C2314yes—
181#416—216no—
182C2×#103C2314yes—
183C2×#103C2314yes—
184C2×#102C2314yes—
185C2×#102C2314yes—
186C2×C22⋊C8—28no—
187C2×C22⋊C8C2312yes—
188C2×C22⋊C8C2312yes—
189C2×C22⋊C8C2314yes—
190#391C2311yescharacteristic
191#391C2311yescharacteristic
192#390C2311yescharacteristic
193#390C2311yescharacteristic
194#389C2311yescharacteristic
195#389C2311yescharacteristic
196#389C2311yescharacteristic
197#389C2311yescharacteristic
198#388—21no—
199#388—21no—
200#388—21no—
201#388—21no—
202#387—21no—
203#387—21no—
204#387—21no—
205#387—21no—
206#386—21no—
207#386—21no—
208#386—21no—
209#386—21no—
210#386—21no—
211#386—21no—
212#385—21no—
213#385—21no—
214#385—21no—
215#385—21no—
216#385—21no—
217#385—21no—
218#384—21no—
219#384—21no—
220#384—21no—
221#384—21no—
222#384C2312yes—
223#384C2312yes—
224#384C2312yes—
225#384C2312yes—
226#382—22no—
227#382—22no—
228#382C2314yes—
229#382C2314yes—
230#381—21no—
231#380—22no—
232#380—22no—
233#380—22no—
234#380—22no—
235#380—22no—
236#380—22no—
237#380—22no—
238#380—22no—
239#380C2311yescharacteristic
240#380C2311yescharacteristic
241#380C2311yescharacteristic
242#380C2311yescharacteristic
243#379—21no—
244C4×C4⋊C4—22no—
245C4×C4⋊C4—22no—
246C4×C4⋊C4—22no—
247C4×C4⋊C4—22no—
248C4×C4⋊C4—22no—
249C4×C4⋊C4—22no—
250C4×C4⋊C4—22no—
251C4×C4⋊C4—22no—
252C4×C4⋊C4—21no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4C2311yescharacteristic
259C4×C4⋊C4C2311yescharacteristic
260C4×C4⋊C4C2311yescharacteristic
261C4×C4⋊C4C2311yescharacteristic
262C4×C22⋊C4—21no—
263C4×C22⋊C4—21no—
264C4×C22⋊C4—21no—
265C4×C22⋊C4—21no—
266C4×C22⋊C4—21no—
267C4×C22⋊C4—21no—
268C4×C22⋊C4—21no—
269C4×C22⋊C4—21no—
270C4×C22⋊C4—21no—
271C4×C22⋊C4—21no—
272C4×C22⋊C4—21no—
273C4×C22⋊C4—21no—
274C4×C22⋊C4—21no—
275C4×C22⋊C4—21no—
276#376—21no—
277C2×#95—22no—
278C2×#95—22no—
279C43—21no—
280#340C2314yes—
281#340C2314yes—
282#340C2314yes—
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#340C2314yes—
287#340C2314yes—
288#336C2312yes—
289#336C2312yes—
290#336C2314yes—
291C25C2×D411yescharacteristic
292C2×#41—22no—
293C2×#41—24no—
294C2×#41—24no—
295C2×#41C2×D414yes—
296C22×Q8C2411yescharacteristic
297C22×D4—21no—
298C22×D4—21no—
299C22×D4—21no—
300C22×D4C2411yescharacteristic
301C23×C4—24no—
302C23×C4—24no—
303C23×C4—24no—
304C23×C4—24no—
305C23×C4—24no—
306C23×C4—21no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—21no—
310C23×C4—21no—
311C23×C4—42no—
312C23×C4—42no—
313C23×C4—42no—
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2×D411yescharacteristic
325C23×C4C2×D414yes—
326C23×C4C2×D411yescharacteristic
327C23×C4C2×D411yescharacteristic
328C23×C4C2×D411yescharacteristic
329C23×C4C2×D411yescharacteristic
330C23×C4#4114yes—
331C23×C4C2411yescharacteristic
332C23×C4C2411yescharacteristic
333C23×C4C2411yescharacteristic
334C22×C8—28no—
335C22×C8—28no—
336C22×C8—28no—
337C22×C8C2414yes—
338C22×C8C2414yes—
339#123—28no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342C22⋊Q8C2×D414yes—
343C22⋊Q8C2×D414yes—
344#121—22no—
345#121—22no—
346#121C2×D414yes—
347#121C2×D414yes—
348#120—28no—
349C4×Q8—24no—
350C4×Q8—24no—
351C4×D4—28no—
352C4×D4—28no—
353C4×D4—24no—
354C4×D4—24no—
355C4×D4—44no—
356C4×D4—44no—
357C4×D4—44no—
358C4×D4—44no—
359C4×D4—44no—
360C4×D4—44no—
361#117—22no—
362#117—28no—
363#117—28no—
364#117—28no—
365#117—28no—
366#117—24no—
367#117—24no—
368#117—48no—
369#117—48no—
370#117—44no—
371#117C2×D414yes—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
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⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—44no—
395C2×C4⋊C4—44no—
396C2×C4⋊C4—44no—
397C2×C4⋊C4—44no—
398C2×C4⋊C4C2414yes—
399C2×C4⋊C4C2414yes—
400C2×C4⋊C4C2411yescharacteristic
401C2×C4⋊C4C2411yescharacteristic
402C2×C4⋊C4C2411yescharacteristic
403C2×C4⋊C4C2411yescharacteristic
404C2×C4⋊C4C2411yescharacteristic
405C2×C4⋊C4C2411yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—48no—
426C2×C42—24no—
427C2×C42—24no—
428C2×C42—21no—
429C2×C42—24no—
430C2×C42—24no—
431C2×C42—24no—
432C2×C42—24no—
433C2×C42—24no—
434C2×C42—24no—
435C2×C42—24no—
436C2×C42—24no—
437C2×C42—24no—
438C2×C42—24no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—21no—
446C2×C42—24no—
447C2×C42—21no—
448C2×C42—48no—
449C2×C42—44no—
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×D411yescharacteristic
462C2×C42#4118yes—
463C2×C42C2411yescharacteristic
464C2×C42C2411yescharacteristic
465C2×C42C2411yescharacteristic
466C2×C42C2411yescharacteristic
467#107—28no—
468#107—28no—
469#106—28no—
470#106—28no—
471C4⋊C8—24no—
472C4⋊C8—24no—
473C4⋊C8—28no—
474#103—28no—
475#103—28no—
476#102—28no—
477#102—28no—
478C22⋊C8—24no—
479C22⋊C8—24no—
480C22⋊C8—28no—
481#95—24no—
482#95—24no—
483#95—24no—
484#95—24no—
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—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—21no—
506C24—41no—
507C24—41no—
508C24#12114yes—
509C24C22×D411yescharacteristic
510C24C22×D411yescharacteristic
511C24C22×D411yescharacteristic
512#41—216no—
513#41—48no—
514C2×Q8—21no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8C22×D412yes—
518C2×D4—24no—
519C2×D4—24no—
520C2×D4—24no—
521C2×D4—22no—
522C2×D4—21no—
523C2×D4—22no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4C22×D412yes—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—216no—
541C22×C4—216no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—416no—
587C22×C4—416no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4#12114yes—
603C22×C4#12114yes—
604C22×C4#12114yes—
605C22×C4#12314yes—
606C22×C4#12314yes—
607C22×C4#13514yes—
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D412yes—
613C22×C4C22×D412yes—
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D412yes—
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C2×#4112yes—
623C22×C4C2×#4112yes—
624C22×C4C2×#4112yes—
625C22×C4C2×#4114yes—
626C22×C42−1+414yes—
627C22×C4C2511yescharacteristic
628C2×C8—24no—
629C2×C8—24no—
630C2×C8—24no—
631C2×C8—24no—
632C2×C8—24no—
633C2×C8—24no—
634C2×C8—416no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—44no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—44no—
654C4⋊C4—44no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—44no—
658C4⋊C4—44no—
659C4⋊C4—42no—
660C4⋊C4—44no—
661C4⋊C4—44no—
662C4⋊C4—42no—
663C4⋊C4C22×D412yes—
664C4⋊C4C22×D412yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—48no—
675C22⋊C4—48no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C42—24no—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—22no—
689C42—22no—
690C42—22no—
691C42—22no—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—22no—
696C42—22no—
697C42—42no—
698C42—42no—
699C42—48no—
700C42—48no—
701C42—42no—
702C42—42no—
703C42—42no—
704C42—42no—
705C42—42no—
706C42—42no—
707C42#12314yes—
708C42#12314yes—
709C42C2×#4114yes—
710C42C2×#4114yes—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—28no—
722C23—28no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—22no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23C2×#12112yes—
740C23C2×#12112yes—
741C23C2×#12112yes—
742C23C2×#12312yes—
743C23#53612yes—
744C23C2×#13512yes—
745C23#57512yes—
746C23C23×D411yescharacteristic
747Q8—24no—
748Q8—42no—
749D4—24no—
750D4—48no—
751D4—48no—
752D4—48no—
753D4—42no—
754C2×C4—28no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—28no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—28no—
771C2×C4—28no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—28no—
777C2×C4—28no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—44no—
802C2×C4—48no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—44no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—84no—
822C2×C4—88no—
823C2×C4—88no—
824C2×C4—84no—
825C2×C4C2×#12112yes—
826C2×C4C2×#12112yes—
827C2×C4C2×#12112yes—
828C2×C4C2×#12312yes—
829C2×C4C2×#12312yes—
830C2×C4C2×#12312yes—
831C2×C4C2×#12312yes—
832C2×C4C2×#12312yes—
833C2×C4#53612yes—
834C2×C4#54718yes—
835C2×C4#55218yes—
836C2×C4C2×#13512yes—
837C2×C4C2×#13512yes—
838C2×C4#57512yes—
839C2×C4#57512yes—
840C2×C4C23×D411yescharacteristic
841C2×C4C22×#4112yes—
842C2×C4C22×#4111yescharacteristic
843C2×C4C2×2−1+412yes—
844C8—44no—
845C8—44no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—416no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22#248614yes—
874C22#303514yes—
875C22C22×#12111yescharacteristic
876C22C22×#12311yescharacteristic
877C22C2×#53611yescharacteristic
878C22C22×#13511yescharacteristic
879C22C2×#57511yescharacteristic
880C22C2×#57511yescharacteristic
881C22C2×#57511yescharacteristic
882C4—22no—
883C4—22no—
884C4—22no—
885C4—22no—
886C4—22no—
887C4—22no—
888C4—22no—
889C4—41no—
890C4—41no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4—81no—
898C4—84no—
899C4—84no—
900C4#248614yes—
901C4#309114yescomplemented
902C4C2×#54712yes—
903C4C2×#55212yes—
904C2—24no—
905C2—24no—
906C2—42no—
907C2—82no—
908C2C2×#248611yescharacteristic
909C2C2×#303511yescharacteristic
910C2#6041511yescharacteristic
911C2C2×#309111yescharacteristic
912C2#6051111yescharacteristic
913C2#6084611yescharacteristic
914C2#6085411yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radicalC2×#525C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#2285C2semidirect
4. #27653C2semidirect
5. #27652C2semidirect
6. #27651C2semidirect
7. #27650C2semidirect
8. #27649C2semidirect
9. #27648C2semidirect
10. #27647C2semidirect
11. #27646C2semidirect
12. #27645C2semidirect
13. #27644C2semidirect
14. #23656C2semidirect
15. #23627C2semidirect
16. #21169C2semidirect
17. #20699C2semidirect
18. #20645C2semidirect
19. C2×#1797C2semidirect
70. #2085C22semidirect
71. #2085C22semidirect
72. #2084C22semidirect
73. #2084C22semidirect
74. #2083C22semidirect
75. #2083C22semidirect
76. #2074C22semidirect
77. #2073C22semidirect
78. #2072C22semidirect
79. #2072C22semidirect
80. #2071C22semidirect
81. #2071C22semidirect
82. #1949C22semidirect
83. #1949C22semidirect
84. #1948C22semidirect
85. #1948C22semidirect
86. #1947C22semidirect
87. #1947C22semidirect
94. #1805C22semidirect
95. #1804C22semidirect
96. #1803C22semidirect
97. #1803C22semidirect
98. #1802C22semidirect
99. #1802C22semidirect
901. C4#3091semidirect

Maximal subgroups

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

subgroupindex
C2×#30912
C4×#5252
C2×#22852
#276532
#276522
#276512
#276502
#276492
#276482
#276472
#276462
#276452
#276442
#236562
#236272
#211692
#206992
#206452
C2×#17972