Finite Group Databasebeta

← #388411

Subgroups — #388411

Order 512.

1614 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2000C211yesmaximal, characteristic
2C2×#1933C211yesmaximal, characteristic, complemented
3C2×#1874C211yesmaximal, characteristic
4#14139C211yesmaximal, characteristic, complemented
5#13998C211yesmaximal, characteristic
6#11293C211yesmaximal, characteristic, complemented
7#11189C211yesmaximal, characteristic, complemented
8#11023C211yesmaximal, characteristic, complemented
9#11023C211yesmaximal, characteristic, complemented
10#10970C211yesmaximal, characteristic, complemented
11#10932C211yesmaximal, characteristic, complemented
12#10925C211yesmaximal, characteristic, complemented
13#10921C211yesmaximal, characteristic, complemented
14#10806C211yesmaximal, characteristic, complemented
15#10730C211yesmaximal, characteristic, complemented
16C23×SD16C2211yescharacteristic
17C22×C22⋊Q8C2211yescharacteristic
18C22×#121C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×#102C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×C4×C8C2211yescharacteristic
29C2×#391C2211yescharacteristic
30C2×#391C2211yescharacteristic
31C2×#390—21no—
32C2×#390C2211yescharacteristic
33C2×#390C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#380C2211yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C22⋊C4C2211yescharacteristic
38#2000C418yescomplemented
39#1933—24no—
40#1874—24no—
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53#1441—21no—
54#1441—21no—
55#1439—21no—
56#1438—21no—
57#1437—21no—
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C22⋊#95—21no—
61C22⋊#95—21no—
62C23×Q8C2311yescharacteristic
63C23×D4—21no—
64C23×D4C2311yescharacteristic
65C24×C4—21no—
66C24×C4C2311yescharacteristic
67C22×SD16—41no—
68C22×SD16—41no—
69C22×SD16—41no—
70C22×SD16—41no—
71C22×SD16—41no—
72C22×SD16—41no—
73C22×SD16C2×C414yescomplemented
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C2×C22⋊Q8—22no—
79C2×C22⋊Q8—41no—
80C2×C22⋊Q8—41no—
81C2×C22⋊Q8—41no—
82C2×C22⋊Q8—41no—
83C2×C22⋊Q8C2×C414yes—
84C2×#121—22no—
85C2×#121—22no—
86C2×#121—22no—
87C2×#121—41no—
88C2×#121—41no—
89C2×#121C2×C414yes—
90C22×C4⋊C4—21no—
91C22×C4⋊C4—22no—
92C22×C4⋊C4—22no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4—21no—
95C22×C4⋊C4—41no—
96C22×C4⋊C4—41no—
97C22×C4⋊C4—41no—
98C22×C4⋊C4—41no—
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C22⋊C4—21no—
106C22×C22⋊C4—21no—
107C22×C22⋊C4—21no—
108C22×C22⋊C4—21no—
109C22×C22⋊C4—21no—
110C22×C22⋊C4—21no—
111C22×C22⋊C4—21no—
112C22×C22⋊C4D411yescharacteristic
113C22×C22⋊C4D411yescharacteristic
114C22×C42—21no—
115C22×C42C2311yescharacteristic
116C22×C42C2311yescharacteristic
117C2×#103—22no—
118C2×#103—22no—
119C2×#103—22no—
120C2×#103—22no—
121C2×#103—41no—
122C2×#103—41no—
123C2×#103—41no—
124C2×#103—41no—
125C2×#103C2×C414yescomplemented
126C2×#102—22no—
127C2×#102—22no—
128C2×#102—22no—
129C2×#102—41no—
130C2×#102—41no—
131C2×#102—41no—
132C2×#102—41no—
133C2×#102—41no—
134C2×#102C2×C414yescomplemented
135C2×C22⋊C8—22no—
136C2×C22⋊C8—22no—
137C2×C22⋊C8—41no—
138C2×C22⋊C8—41no—
139C2×C22⋊C8—41no—
140C2×C22⋊C8C2×C414yes—
141C2×C4×C8—22no—
142C2×C4×C8—41no—
143C2×C4×C8—41no—
144#391—22no—
145#391—22no—
146#391—41no—
147#391—41no—
148#390—22no—
149#390—41no—
150#390—41no—
151#390—41no—
152#390—44no—
153#389—22no—
154#389—41no—
155#380—22no—
156#380—41no—
157C4×C4⋊C4—22no—
158C4×C4⋊C4—41no—
159C4×C22⋊C4—41no—
160C4×C22⋊C4—41no—
161C2×#95—21no—
162C2×#95—21no—
163C2×#95—21no—
164C2×#95—21no—
165C2×#95—21no—
166C2×#95—21no—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95—21no—
170C2×#95—21no—
171C2×#95—21no—
172C2×#95D411yescharacteristic
173C2×#95D411yescharacteristic
174#340—22no—
175#340—22no—
176#340—41no—
177#340—41no—
178#340—41no—
179#340—41no—
180#340—41no—
181#340C2×C414yescomplemented
182#340D414yes—
183#336—41no—
184#336—41no—
185#336—41no—
186C25—21no—
187C25C2×D411yescharacteristic
188C22×Q8—21no—
189C22×Q8—21no—
190C22×Q8—21no—
191C22×Q8—21no—
192C22×Q8—21no—
193C22×Q8—21no—
194C22×Q8—21no—
195C22×Q8—21no—
196C22×Q8—21no—
197C22×Q8—21no—
198C22×Q8—21no—
199C22×Q8—21no—
200C22×Q8—21no—
201C22×Q8C22×C412yes—
202C22×D4—24no—
203C22×D4—21no—
204C22×D4—21no—
205C22×D4—21no—
206C22×D4—21no—
207C22×D4—21no—
208C22×D4—21no—
209C22×D4—21no—
210C22×D4—21no—
211C22×D4—21no—
212C22×D4—21no—
213C22×D4—21no—
214C22×D4—21no—
215C22×D4—21no—
216C22×D4—42no—
217C22×D4—42no—
218C22×D4—42no—
219C22×D4—42no—
220C22×D4—81no—
221C22×D4—81no—
222C22×D4C22×C412yes—
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×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—42no—
243C23×C4—42no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—81no—
248C23×C4—81no—
249C23×C4C22×C412yes—
250C23×C4C2×D411yescharacteristic
251C23×C4C2×D411yescharacteristic
252C23×C4C2×D411yescharacteristic
253C23×C4C2×D411yescharacteristic
254C23×C4C2×D411yescharacteristic
255C23×C4#4112yes—
256C23×C4C2411yescharacteristic
257C2×SD16—44no—
258C2×SD16—44no—
259C2×SD16—44no—
260C2×SD16—44no—
261C2×SD16—44no—
262C2×SD16—44no—
263C2×SD16—44no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8C22×C412yes—
290C22×C8C22×C412yes—
291C22×C8C2×D412yes—
292C22⋊Q8—44no—
293C22⋊Q8—44no—
294C22⋊Q8—44no—
295C22⋊Q8—44no—
296#121—28no—
297#121—44no—
298#121—44no—
299#121—44no—
300C2×C4⋊C4—21no—
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—24no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—81no—
342C2×C4⋊C4C22×C412yes—
343C2×C4⋊C4C22×C412yes—
344C2×C4⋊C4C2×D412yes—
345C2×C4⋊C4C2×D412yes—
346C2×C4⋊C4#4112yes—
347C2×C4⋊C4#4112yes—
348C2×C4⋊C4#4112yes—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—41no—
354C2×C22⋊C4—41no—
355C2×C22⋊C4—41no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—81no—
371C2×C22⋊C4—81no—
372C2×C22⋊C4—81no—
373C2×C22⋊C4—81no—
374C2×C22⋊C4—81no—
375C2×C22⋊C4SD1614yescomplemented
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—42no—
389C2×C42—42no—
390C2×C42—81no—
391#103—28no—
392#103—44no—
393#103—44no—
394#102—44no—
395#102—44no—
396#102—44no—
397C22⋊C8—44no—
398C22⋊C8—44no—
399C4×C8—44no—
400#95—41no—
401#95—41no—
402#95—42no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—81no—
410#95—81no—
411#95—81no—
412#95—81no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—22no—
426C24—41no—
427C24—41no—
428C24—41no—
429C24—41no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24—41no—
435C24—41no—
436C24—41no—
437C24—41no—
438C24—41no—
439C24—41no—
440C24C4×D412yes—
441C24C2×SD1612yes—
442C24#13512yes—
443C24C22×D411yescharacteristic
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—41no—
451C2×Q8—41no—
452C2×Q8—41no—
453C2×Q8—41no—
454C2×Q8—41no—
455C2×Q8—41no—
456C2×Q8—41no—
457C2×Q8—41no—
458C2×Q8—41no—
459C2×Q8—41no—
460C2×Q8—41no—
461C2×Q8—41no—
462C2×Q8—41no—
463C2×Q8—41no—
464C2×Q8—41no—
465C2×Q8—41no—
466C2×Q8—41no—
467C2×Q8—41no—
468C2×Q8—41no—
469C2×Q8—41no—
470C2×Q8—41no—
471C2×Q8—41no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4—41no—
493C2×D4—41no—
494C2×D4—41no—
495C2×D4—41no—
496C2×D4—41no—
497C2×D4—41no—
498C2×D4—41no—
499C2×D4—41no—
500C2×D4—41no—
501C2×D4—41no—
502C2×D4—84no—
503C2×D4—84no—
504C2×D4—84no—
505C2×D4—84no—
506C2×D4—84no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
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—48no—
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—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—84no—
617C22×C4—84no—
618C22×C4—84no—
619C22×C4—84no—
620C22×C4—84no—
621C22×C4—84no—
622C22×C4C4×D412yes—
623C22×C4C2×SD1612yes—
624C22×C4C2×SD1612yes—
625C22×C4#13712yes—
626C22×C4C23×C411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C2×#4111yescharacteristic
629C22×C4C2×#4111yescharacteristic
630C22×C4C2×#4111yescharacteristic
631C22×C4C2×#4111yescharacteristic
632C22×C4H(5,𝔽2)11yescharacteristic
633C22×C4H(5,𝔽2)11yescharacteristic
634C22×C4H(5,𝔽2)11yescharacteristic
635C22×C4H(5,𝔽2)11yescharacteristic
636C22×C4H(5,𝔽2)11yescharacteristic
637C22×C4H(5,𝔽2)11yescharacteristic
638C22×C4H(5,𝔽2)11yescharacteristic
639C22×C4H(5,𝔽2)11yescharacteristic
640SD16—416no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—41no—
651C2×C8—41no—
652C2×C8—41no—
653C2×C8—41no—
654C2×C8—41no—
655C2×C8—41no—
656C2×C8—41no—
657C2×C8—41no—
658C2×C8—41no—
659C2×C8—41no—
660C2×C8—41no—
661C2×C8—41no—
662C2×C8—41no—
663C2×C8—41no—
664C2×C8—41no—
665C2×C8—41no—
666C2×C8—41no—
667C2×C8—41no—
668C2×C8—41no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—48no—
681C4⋊C4—48no—
682C4⋊C4—41no—
683C4⋊C4—41no—
684C4⋊C4—41no—
685C4⋊C4—41no—
686C4⋊C4—41no—
687C4⋊C4—41no—
688C4⋊C4—41no—
689C4⋊C4—41no—
690C4⋊C4—41no—
691C4⋊C4—41no—
692C4⋊C4—41no—
693C4⋊C4—41no—
694C4⋊C4—84no—
695C4⋊C4C4×D414yes—
696C22⋊C4—44no—
697C22⋊C4—48no—
698C22⋊C4—44no—
699C22⋊C4—48no—
700C22⋊C4—84no—
701C22⋊C4—84no—
702C22⋊C4—84no—
703C22⋊C4—84no—
704C22⋊C4—84no—
705C42—41no—
706C42—41no—
707C42—41no—
708C42—41no—
709C42—41no—
710C42—41no—
711C42—41no—
712C42—41no—
713C42—84no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
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—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—81no—
756C23—81no—
757C23—81no—
758C23—81no—
759C23—81no—
760C23—81no—
761C23—81no—
762C23—81no—
763C23—81no—
764C23—81no—
765C23—81no—
766C23—81no—
767C23—81no—
768C23—81no—
769C23—81no—
770C23—81no—
771C23—81no—
772C23—81no—
773C23—81no—
774C23—81no—
775C23—81no—
776C23—81no—
777C23—81no—
778C23—81no—
779C23—81no—
780C23—81no—
781C23—81no—
782C23—81no—
783C23C4×SD1614yes—
784C23C2×C4×D411yescharacteristic
785C23#53411yescharacteristic
786C23#53511yescharacteristic
787C23D4211yescharacteristic
788C23#54611yescharacteristic
789C23#54611yescharacteristic
790C23#54611yescharacteristic
791C23C22×SD1611yescharacteristic
792C23C2×#13511yescharacteristic
793C23C2×#13711yescharacteristic
794C23#57511yescharacteristic
795C23#57611yescharacteristic
796C23#57611yescharacteristic
797C23#57711yescharacteristic
798C23#57811yescharacteristic
799Q8—42no—
800Q8—42no—
801Q8—42no—
802Q8—42no—
803Q8—81no—
804Q8—81no—
805Q8—81no—
806Q8—81no—
807D4—42no—
808D4—42no—
809D4—42no—
810D4—42no—
811D4—816no—
812D4—81no—
813D4—81no—
814D4—81no—
815D4—81no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—24no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—42no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—41no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—816no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—81no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—81no—
906C2×C4—81no—
907C2×C4—81no—
908C2×C4—81no—
909C2×C4C2×C4×D411yescharacteristic
910C2×C4C4×#4111yescharacteristic
911C2×C4#51811yescharacteristic
912C2×C4#51811yescharacteristic
913C2×C4#51811yescharacteristic
914C2×C4#51811yescharacteristic
915C2×C4#53511yescharacteristic
916C2×C4#53511yescharacteristic
917C2×C4#53811yescharacteristic
918C2×C4#53811yescharacteristic
919C2×C4#53811yescharacteristic
920C2×C4#53811yescharacteristic
921C2×C4#54011yescharacteristic
922C2×C4#54011yescharacteristic
923C2×C4#54011yescharacteristic
924C2×C4#54011yescharacteristic
925C2×C4#54611yescharacteristic
926C2×C4#54611yescharacteristic
927C2×C4#55011yescharacteristic
928C2×C4#55111yescharacteristic
929C2×C4#55311yescharacteristic
930C2×C4#55311yescharacteristic
931C2×C4#55311yescharacteristic
932C2×C4#55511yescharacteristic
933C2×C4#56011yescharacteristic
934C2×C4#56011yescharacteristic
935C2×C4#56011yescharacteristic
936C2×C4H(3,𝔽4)11yescharacteristic
937C8—42no—
938C8—42no—
939C8—42no—
940C8—81no—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—82no—
957C22—82no—
958C22—82no—
959C22—82no—
960C22—82no—
961C22—82no—
962C22—82no—
963C22—161no—
964C22—161no—
965C22—161no—
966C22—161no—
967C22—161no—
968C22—161no—
969C22—161no—
970C22—161no—
971C22#232111yescharacteristic
972C22#235811yescharacteristic
973C22#236411yescharacteristic
974C22#267011yescharacteristic
975C22#267311yescharacteristic
976C22#269911yescharacteristic
977C22#270311yescharacteristic
978C22C2×C4×SD1611yescharacteristic
979C22C4×#13711yescharacteristic
980C22#294611yescharacteristic
981C22#295111yescharacteristic
982C22#318711yescharacteristic
983C22#319011yescharacteristic
984C22#319811yescharacteristic
985C22#320311yescharacteristic
986C22#320611yescharacteristic
987C22#321111yescharacteristic
988C22#322011yescharacteristic
989C22#322511yescharacteristic
990C22#326811yescharacteristic
991C22#327011yescharacteristic
992C22#328011yescharacteristic
993C22D4×SD1611yescharacteristic
994C22#329511yescharacteristic
995C22#329511yescharacteristic
996C22#329611yescharacteristic
997C22#329711yescharacteristic
998C22#329811yescharacteristic
999C22#330011yescharacteristic
1000C22#331411yescharacteristic
1001C22#331711yescharacteristic
1002C22#332211yescharacteristic
1003C22#332711yescharacteristic
1004C22#332911yescharacteristic
1005C22#333311yescharacteristic
1006C4—44no—
1007C4—42no—
1008C4—42no—
1009C4—42no—
1010C4—42no—
1011C4—82no—
1012C4—82no—
1013C4—82no—
1014C4—82no—
1015C4—82no—
1016C4—81no—
1017C4—161no—
1018C4#232811yescharacteristic
1019C4#233311yescharacteristic
1020C4#236311yescharacteristic
1021C4#237511yescharacteristic
1022C4#270311yescharacteristic
1023C4#271411yescharacteristic
1024C4#275311yescharacteristic
1025C4#275611yescharacteristic
1026C2—44no—
1027C2—162no—
1028C2#1452011yescharacteristic
1029C2#2204111yescharacteristic
1030C2#2205511yescharacteristic
1031C2#2287411yescharacteristic
1032C2#2287911yescharacteristic
1033C2#2312611yescharacteristic
1034C2#2314511yescharacteristic
1035C2#3052211yescharacteristic
1036C2#3052311yescharacteristic
1037C2#3070311yescharacteristic
1038C2#3070911yescharacteristic
1039C2#3172011yescharacteristic
1040C2#3172511yescharacteristic
1041C2#3183811yescharacteristic
1042C2#3184511yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1933C2semidirect
4. #14139C2semidirect
6. #11293C2semidirect
7. #11189C2semidirect
8. #11023C2semidirect
9. #11023C2semidirect
10. #10970C2semidirect
11. #10932C2semidirect
12. #10925C2semidirect
13. #10921C2semidirect
14. #10806C2semidirect
15. #10730C2semidirect
38. #2000C4semidirect
73. C22×SD16C2×C4semidirect
125. C2×#103C2×C4semidirect
134. C2×#102C2×C4semidirect
181. #340C2×C4semidirect
375. C2×C22⋊C4SD16semidirect

Maximal subgroups

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

subgroupindex
C2×#20002
C2×#19332
C2×#18742
#141392
#139982
#112932
#111892
#110232
#109702
#109322
#109252
#109212
#108062
#107302