Finite Group Databasebeta

← #465804

Subgroups — #465804

Order 512.

1356 conjugacy classes of subgroups.

The subgroup lattice has 1019 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2077C211yesmaximal, characteristic, complemented
2C2×#2035C211yesmaximal, characteristic, complemented
3#15177C211yesmaximal, characteristic
4#13905C211yesmaximal, characteristic
5#11268C211yesmaximal, characteristic, complemented
6#11200C211yesmaximal, characteristic, complemented
7#11200C211yesmaximal, characteristic, complemented
8#11199C211yesmaximal, characteristic, complemented
9#11052C211yesmaximal, characteristic, complemented
10#10970C211yesmaximal, characteristic, complemented
11#10970C211yesmaximal, characteristic, complemented
12#10970C211yesmaximal, characteristic, complemented
13#10964C211yesmaximal, characteristic
14#10932C211yesmaximal, characteristic, complemented
15#10908C211yesmaximal, characteristic, complemented
16C22×C22⋊Q8C2211yescharacteristic
17C22×C22⋊Q8C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×#106C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C2×#391C2211yescharacteristic
29C2×#382C2211yescharacteristic
30C2×#380C2211yescharacteristic
31C2×#380C2211yescharacteristic
32C2×#380C2211yescharacteristic
33C2×#380C2211yescharacteristic
34C2×#380C2211yescharacteristic
35C2×#380C2211yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37#2077—24no—
38#2035—24no—
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52#1445—21no—
53#1444—21no—
54#1439—21no—
55#1439—21no—
56#1438—21no—
57#1438—21no—
58#1437—21no—
59#1437—21no—
60C4⋊#95C2211yescharacteristic
61C23×Q8C2311yescharacteristic
62C23×D4D411yescharacteristic
63C24×C4C2311yescharacteristic
64C24×C4C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C2×C22⋊Q8—22no—
70C2×C22⋊Q8—22no—
71C2×C22⋊Q8—22no—
72C2×C22⋊Q8—22no—
73C2×C22⋊Q8—41no—
74C2×C22⋊Q8—41no—
75C2×C22⋊Q8—41no—
76C2×C22⋊Q8—41no—
77C2×C22⋊Q8—41no—
78C2×C22⋊Q8—41no—
79C2×C22⋊Q8—41no—
80C2×C22⋊Q8—41no—
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4—41no—
84C2×C4×D4—41no—
85C2×C4×D4—41no—
86C2×C4×D4—41no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4—21no—
89C22×C4⋊C4D411yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C22⋊C4—21no—
98C22×C22⋊C4—21no—
99C22×C22⋊C4—21no—
100C22×C22⋊C4—21no—
101C22×C22⋊C4—21no—
102C22×C22⋊C4—21no—
103C22×C22⋊C4—21no—
104C22×C22⋊C4—21no—
105C22×C22⋊C4D411yescharacteristic
106C22×C22⋊C4D411yescharacteristic
107C22×C42—21no—
108C22×C42C2311yescharacteristic
109C2×#106—41no—
110C2×#106—41no—
111C2×#106D414yescomplemented
112C2×#103—22no—
113C2×#103—22no—
114C2×#103—22no—
115C2×#103—22no—
116C2×#103—41no—
117C2×#103—41no—
118C2×#103—41no—
119C2×#103—41no—
120C2×#103—41no—
121C2×#103—41no—
122C2×#103—41no—
123C2×#103—41no—
124C2×C22⋊C8—22no—
125C2×C22⋊C8—22no—
126C2×C22⋊C8—41no—
127C2×C22⋊C8—41no—
128C2×C22⋊C8—41no—
129C2×C22⋊C8—41no—
130C2×C22⋊C8—41no—
131C2×C22⋊C8—41no—
132C2×C22⋊C8—41no—
133C2×C22⋊C8—41no—
134C2×C22⋊C8—41no—
135C2×C22⋊C8—41no—
136#391—22no—
137#391—22no—
138#382—41no—
139#382—41no—
140#380—22no—
141#380—22no—
142#380—22no—
143#380—22no—
144#380—22no—
145#380—22no—
146#380—41no—
147#380—41no—
148#380—41no—
149#380—41no—
150#380—41no—
151#380—41no—
152C4×C4⋊C4—41no—
153C4×C4⋊C4—41no—
154C2×#95—21no—
155C2×#95—21no—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95—21no—
159C2×#95—21no—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95—21no—
163C2×#95—21no—
164C2×#95—21no—
165C2×#95—21no—
166C2×#95—21no—
167#340—22no—
168#340—22no—
169#340—22no—
170#340—22no—
171#340—22no—
172#340—41no—
173#340—41no—
174#340—41no—
175#340—41no—
176#340—41no—
177#340—41no—
178#336—22no—
179#336—22no—
180C25C2×D411yescharacteristic
181C25C2×D411yescharacteristic
182C22×Q8—21no—
183C22×Q8—21no—
184C22×Q8—21no—
185C22×Q8—21no—
186C22×Q8—21no—
187C22×Q8—21no—
188C22×Q8—21no—
189C22×Q8—21no—
190C22×Q8—21no—
191C22×Q8—21no—
192C22×Q8—21no—
193C22×Q8—21no—
194C22×Q8—21no—
195C22×Q8#4112yes—
196C22×D4—22no—
197C22×D4—22no—
198C22×D4—22no—
199C22×D4—41no—
200C22×D4—41no—
201C22×D4—41no—
202C22×D4—41no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4C2×D411yescharacteristic
240C23×C4C2×D411yescharacteristic
241C23×C4C2×D411yescharacteristic
242C23×C4C2×D411yescharacteristic
243C23×C4C2411yescharacteristic
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8C2×D412yes—
272C22⋊Q8—44no—
273C22⋊Q8—44no—
274C22⋊Q8—44no—
275C22⋊Q8—44no—
276C22⋊Q8—44no—
277C22⋊Q8—44no—
278C22⋊Q8—44no—
279C22⋊Q8—44no—
280C4×D4—44no—
281C4×D4—44no—
282C4×D4—44no—
283C4×D4—44no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—41no—
324C2×C4⋊C4—41no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4C2×D412yes—
332C2×C4⋊C4C2×D412yes—
333C2×C4⋊C4#4112yes—
334C2×C4⋊C4#4112yes—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—41no—
338C2×C22⋊C4—41no—
339C2×C22⋊C4—41no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—81no—
360C2×C22⋊C4—81no—
361C2×C22⋊C4—81no—
362C2×C22⋊C4—81no—
363C2×C22⋊C4—81no—
364C2×C22⋊C4—81no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—42no—
370C2×C42—81no—
371C2×C42—81no—
372C2×C42#4112yes—
373C2×C42#4112yes—
374#106—44no—
375#103—44no—
376#103—44no—
377#103—44no—
378#103—44no—
379C22⋊C8—44no—
380C22⋊C8—44no—
381C22⋊C8—44no—
382C22⋊C8—44no—
383#95—42no—
384#95—42no—
385#95—42no—
386#95—42no—
387#95—42no—
388#95—42no—
389#95—42no—
390#95—42no—
391#95—42no—
392#95—42no—
393#95—42no—
394#95—42no—
395#95—81no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24#13512yes—
425C24#13712yes—
426C24C22×D411yescharacteristic
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—41no—
434C2×Q8—41no—
435C2×Q8—41no—
436C2×Q8—41no—
437C2×Q8—41no—
438C2×Q8—41no—
439C2×Q8—41no—
440C2×Q8—41no—
441C2×Q8—41no—
442C2×Q8—41no—
443C2×Q8—41no—
444C2×Q8—41no—
445C2×Q8—41no—
446C2×Q8—41no—
447C2×Q8—41no—
448C2×Q8—41no—
449C2×Q8—41no—
450C2×Q8—41no—
451C2×Q8—41no—
452C2×Q8—41no—
453C2×Q8—41no—
454C2×Q8—41no—
455C2×D4—44no—
456C2×D4—44no—
457C2×D4—44no—
458C2×D4—44no—
459C2×D4—44no—
460C2×D4—44no—
461C2×D4—44no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
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—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4#12312yes—
601C22×C4#12312yes—
602C22×C4C22×D411yescharacteristic
603C22×C4C2×#4111yescharacteristic
604C22×C4C2×#4111yescharacteristic
605C22×C4C2×#4111yescharacteristic
606C22×C4C2×#4111yescharacteristic
607C22×C4C2×#4111yescharacteristic
608C22×C4H(5,𝔽2)11yescharacteristic
609C22×C4H(5,𝔽2)11yescharacteristic
610C22×C4H(5,𝔽2)11yescharacteristic
611C22×C4H(5,𝔽2)11yescharacteristic
612C22×C4H(5,𝔽2)11yescharacteristic
613C22×C4H(5,𝔽2)11yescharacteristic
614C22×C4H(5,𝔽2)11yescharacteristic
615C22×C4H(5,𝔽2)11yescharacteristic
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—41no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—41no—
625C2×C8—41no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—41no—
631C2×C8—41no—
632C2×C8—41no—
633C2×C8—41no—
634C2×C8—41no—
635C2×C8—41no—
636C2×C8—41no—
637C2×C8—41no—
638C2×C8—41no—
639C2×C8—41no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8—41no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—44no—
653C4⋊C4—48no—
654C4⋊C4—48no—
655C4⋊C4—41no—
656C4⋊C4—41no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4—41no—
661C4⋊C4—41no—
662C4⋊C4—41no—
663C4⋊C4—41no—
664C4⋊C4—41no—
665C4⋊C4—41no—
666C4⋊C4—41no—
667C4⋊C4—41no—
668C4⋊C4—41no—
669C4⋊C4—41no—
670C4⋊C4—41no—
671C4⋊C4—41no—
672C4⋊C4—41no—
673C4⋊C4—41no—
674C4⋊C4—41no—
675C22⋊C4—44no—
676C22⋊C4—44no—
677C22⋊C4—48no—
678C22⋊C4—48no—
679C22⋊C4—84no—
680C22⋊C4—84no—
681C22⋊C4—84no—
682C22⋊C4—84no—
683C22⋊C4—84no—
684C22⋊C4—84no—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—22no—
689C42—84no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23C2×#12311yescharacteristic
761C23#53411yescharacteristic
762C23#53411yescharacteristic
763C23D4211yescharacteristic
764C23#54611yescharacteristic
765C23#54611yescharacteristic
766C23#54611yescharacteristic
767C23C2×#13511yescharacteristic
768C23C2×#13711yescharacteristic
769C23#57511yescharacteristic
770C23#57511yescharacteristic
771C23#57711yescharacteristic
772C23#57711yescharacteristic
773C23#57711yescharacteristic
774C23#57811yescharacteristic
775Q8—42no—
776Q8—42no—
777Q8—42no—
778Q8—42no—
779Q8—81no—
780Q8—81no—
781Q8—81no—
782Q8—81no—
783D4—416no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—81no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—81no—
841C2×C4—81no—
842C2×C4—81no—
843C2×C4—81no—
844C2×C4—81no—
845C2×C4—81no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4—81no—
850C2×C4—81no—
851C2×C4—81no—
852C2×C4—81no—
853C2×C4—81no—
854C2×C4—81no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4—81no—
863C2×C4—81no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—81no—
870C2×C4—81no—
871C2×C4—81no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—81no—
875C2×C4—81no—
876C2×C4—81no—
877C2×C4—81no—
878C2×C4—81no—
879C2×C4—81no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4#52911yescharacteristic
885C2×C4#53211yescharacteristic
886C2×C4#53411yescharacteristic
887C2×C4#53511yescharacteristic
888C2×C4#53811yescharacteristic
889C2×C4#53811yescharacteristic
890C2×C4#53811yescharacteristic
891C2×C4#53811yescharacteristic
892C2×C4#53811yescharacteristic
893C2×C4#53811yescharacteristic
894C2×C4#53811yescharacteristic
895C2×C4#53811yescharacteristic
896C2×C4#54011yescharacteristic
897C2×C4#54011yescharacteristic
898C2×C4#54011yescharacteristic
899C2×C4#54011yescharacteristic
900C2×C4#54611yescharacteristic
901C2×C4#55011yescharacteristic
902C2×C4#55011yescharacteristic
903C2×C4#55111yescharacteristic
904C2×C4#55311yescharacteristic
905C2×C4#55311yescharacteristic
906C2×C4#55511yescharacteristic
907C2×C4#55911yescharacteristic
908C2×C4#56011yescharacteristic
909C2×C4#56011yescharacteristic
910C2×C4#56011yescharacteristic
911C2×C4H(3,𝔽4)11yescharacteristic
912C8—42no—
913C8—81no—
914C8—81no—
915C8—81no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22—81no—
940C22—81no—
941C22—81no—
942C22—81no—
943C22—81no—
944C22—81no—
945C22—81no—
946C22#242011yescharacteristic
947C22#244511yescharacteristic
948C22#262211yescharacteristic
949C22#266811yescharacteristic
950C22#267311yescharacteristic
951C22#268411yescharacteristic
952C22#268811yescharacteristic
953C22#309111yescharacteristic
954C22#309511yescharacteristic
955C22#309711yescharacteristic
956C22#309911yescharacteristic
957C22#319011yescharacteristic
958C22#319111yescharacteristic
959C22#319611yescharacteristic
960C22#319711yescharacteristic
961C22#320011yescharacteristic
962C22#320111yescharacteristic
963C22#320111yescharacteristic
964C22#320411yescharacteristic
965C22#326611yescharacteristic
966C22#326911yescharacteristic
967C22#327511yescharacteristic
968C22#328211yescharacteristic
969C22#329611yescharacteristic
970C22#330011yescharacteristic
971C22#330111yescharacteristic
972C22#330711yescharacteristic
973C22#331111yescharacteristic
974C22#331211yescharacteristic
975C22#331611yescharacteristic
976C22#331711yescharacteristic
977C22#332011yescharacteristic
978C22#332311yescharacteristic
979C22#332611yescharacteristic
980C22#332711yescharacteristic
981C4—42no—
982C4—42no—
983C4—82no—
984C4—81no—
985C4—81no—
986C4—82no—
987C4—82no—
988C4—82no—
989C4—82no—
990C4—161no—
991C4—161no—
992C4—161no—
993C4#255411yescharacteristic
994C4#264811yescharacteristic
995C4#266111yescharacteristic
996C4#271411yescharacteristic
997C4#273311yescharacteristic
998C4#279711yescharacteristic
999C4#280311yescharacteristic
1000C4#282811yescharacteristic
1001C2—82no—
1002C2—82no—
1003C2#1653011yescharacteristic
1004C2#2497511yescharacteristic
1005C2#2498311yescharacteristic
1006C2#2623911yescharacteristic
1007C2#2624711yescharacteristic
1008C2#2989711yescharacteristic
1009C2#2990011yescharacteristic
1010C2#3040311yescharacteristic
1011C2#3042211yescharacteristic
1012C2#3070211yescharacteristic
1013C2#3072711yescharacteristic
1014C2#3126511yescharacteristic
1015C2#3127711yescharacteristic
1016C2#3139011yescharacteristic
1017C2#3140111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC23×D4D4
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2077C2semidirect
2. C2×#2035C2semidirect
5. #11268C2semidirect
6. #11200C2semidirect
7. #11200C2semidirect
8. #11199C2semidirect
9. #11052C2semidirect
10. #10970C2semidirect
11. #10970C2semidirect
12. #10970C2semidirect
14. #10932C2semidirect
15. #10908C2semidirect
111. C2×#106D4semidirect

Maximal subgroups

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

subgroupindex
C2×#20772
C2×#20352
#151772
#139052
#112682
#112002
#111992
#110522
#109702
#109642
#109322
#109082