Finite Group Databasebeta

← #387990

Subgroups — #387990

Order 512.

1684 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2501C211yesmaximal, characteristic
2C2×#1924C211yesmaximal, characteristic, complemented
3#13875C211yesmaximal, characteristic, complemented
4#11371C211yesmaximal, characteristic, complemented
5#11357C211yesmaximal, characteristic, complemented
6#11076C211yesmaximal, characteristic, complemented
7#11051C211yesmaximal, characteristic, complemented
8#10969C211yesmaximal, characteristic
9#10969C211yesmaximal, characteristic
10#10931C211yesmaximal, characteristic, complemented
11#10927C211yesmaximal, characteristic, complemented
12#10849C211yesmaximal, characteristic, complemented
13#10843C211yesmaximal, characteristic, complemented
14#10730C211yesmaximal, characteristic, complemented
15#10730C211yesmaximal, characteristic, complemented
16C22×#123—21no—
17C22×#123—21no—
18C22×#121C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×#97C2211yescharacteristic
28#2501—24no—
29#2501C418yescomplemented
30C2×#399—21no—
31C2×#399—21no—
32C2×#390C2211yescharacteristic
33C2×#390C2211yescharacteristic
34C2×#384C2211yescharacteristic
35C2×#384C2211yescharacteristic
36C2×#382C2211yescharacteristic
37C2×#380C2211yescharacteristic
38C2×#380C2211yescharacteristic
39C2×C4×C4⋊C4C2211yescharacteristic
40C2×C4×C22⋊C4C2211yescharacteristic
41#1924—24no—
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56#1443—21no—
57#1440—21no—
58#1437—21no—
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61#1434—21no—
62C23×D4—21no—
63C23×D4C2311yescharacteristic
64C24×C4—21no—
65C24×C4C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C2×#123—28no—
71C2×#123—28no—
72C2×#123—44no—
73C2×#123—44no—
74C2×#123—44no—
75C2×#123—44no—
76C2×#121—22no—
77C2×#121—41no—
78C2×#121—41no—
79C2×#121—41no—
80C2×#121—41no—
81C2×#121C2×C414yes—
82C22×C4⋊C4—21no—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—21no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—22no—
88C22×C4⋊C4—41no—
89C22×C4⋊C4—41no—
90C22×C4⋊C4—41no—
91C22×C4⋊C4—41no—
92C22×C4⋊C4C2×C414yes—
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C22⋊C4—21no—
101C22×C22⋊C4—21no—
102C22×C22⋊C4—21no—
103C22×C22⋊C4—21no—
104C22×C22⋊C4—21no—
105C22×C22⋊C4—21no—
106C22×C22⋊C4—21no—
107C22×C22⋊C4D411yescharacteristic
108C22×C22⋊C4D411yescharacteristic
109C22×C42—21no—
110C22×C42C2311yescharacteristic
111C22×C42C2311yescharacteristic
112C2×C4⋊C8—22no—
113C2×C4⋊C8—22no—
114C2×C4⋊C8—41no—
115C2×#102—22no—
116C2×#102—22no—
117C2×#102—22no—
118C2×#102—22no—
119C2×#102—41no—
120C2×#102—41no—
121C2×#102—41no—
122C2×#102—41no—
123C2×#102—41no—
124C2×#102—41no—
125C2×#102—41no—
126C2×#102—41no—
127C2×C22⋊C8—22no—
128C2×C22⋊C8—22no—
129C2×C22⋊C8—22no—
130C2×C22⋊C8—22no—
131C2×C22⋊C8—41no—
132C2×C22⋊C8—41no—
133C2×#97—22no—
134C2×#97—22no—
135C2×#97—41no—
136#399—28no—
137#399—28no—
138#390—22no—
139#390—22no—
140#390C2×C414yes—
141#390C2×C414yes—
142#384—22no—
143#384—22no—
144#384C2×C414yes—
145#384C2×C414yes—
146#382—22no—
147#382—41no—
148#380—22no—
149#380—22no—
150#380—41no—
151#380—41no—
152C4×C4⋊C4—22no—
153C4×C4⋊C4—41no—
154C4×C22⋊C4C2×C414yes—
155C4×C22⋊C4D414yes—
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×#95D411yescharacteristic
166C2×#95D411yescharacteristic
167#340—41no—
168#340—41no—
169#340—41no—
170#340—41no—
171#340—41no—
172#340—41no—
173#340—41no—
174#340—41no—
175#340—41no—
176#340—41no—
177#340—41no—
178#340—41no—
179#336—22no—
180#336—22no—
181C25—21no—
182C25C2×D411yescharacteristic
183C22×D4—24no—
184C22×D4—21no—
185C22×D4—21no—
186C22×D4—21no—
187C22×D4—21no—
188C22×D4—21no—
189C22×D4—21no—
190C22×D4—21no—
191C22×D4—21no—
192C22×D4—21no—
193C22×D4—21no—
194C22×D4—21no—
195C22×D4—21no—
196C22×D4—21no—
197C22×D4—42no—
198C22×D4—42no—
199C22×D4—42no—
200C22×D4—42no—
201C22×D4—42no—
202C22×D4—42no—
203C22×D4C22×C412yes—
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—24no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—42no—
225C23×C4—42no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4C22×C412yes—
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C23×C4C2×D411yescharacteristic
235C23×C4C2×D412yes—
236C23×C4C2×D411yescharacteristic
237C23×C4C2411yescharacteristic
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
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#4112yes—
265C22×C8#4112yes—
266#123—432no—
267#123—432no—
268#121—44no—
269#121—44no—
270#121—44no—
271#121—44no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
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—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
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—44no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4C22×C412yes—
329C2×C4⋊C4C22×C412yes—
330C2×C4⋊C4C22×C412yes—
331C2×C4⋊C4#4112yes—
332C2×C4⋊C4#4112yes—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
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—81no—
357C2×C22⋊C4—81no—
358C2×C22⋊C4C22⋊C414yes—
359C2×C22⋊C4C22⋊C414yes—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—42no—
369C2×C42—42no—
370C2×C42—81no—
371C2×C42C22×C412yes—
372C2×C42C22×C412yes—
373C2×C42C2×D412yes—
374C2×C42C2×D412yes—
375C4⋊C8—44no—
376#102—44no—
377#102—44no—
378#102—44no—
379#102—44no—
380C22⋊C8—44no—
381C22⋊C8—44no—
382#97—44no—
383#95—42no—
384#95—42no—
385#95—42no—
386#95—42no—
387#95—42no—
388#95—42no—
389#95—81no—
390#95—81no—
391#95—81no—
392#95C22⋊C414yes—
393#95C22⋊C414yes—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—22no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—41no—
411C24—41no—
412C24—41no—
413C24—41no—
414C24—41no—
415C24—41no—
416C24—41no—
417C24—41no—
418C24—41no—
419C24—41no—
420C24—41no—
421C24C2×C22⋊C412yes—
422C24AGL(1,ℤ/8)12yes—
423C24AGL(1,ℤ/8)12yes—
424C24C22×D411yescharacteristic
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—48no—
432C2×D4—48no—
433C2×D4—48no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—84no—
457C2×D4—84no—
458C2×D4—84no—
459C2×D4—84no—
460C22×C4—21no—
461C22×C4—21no—
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—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
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—48no—
522C22×C4—48no—
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—48no—
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—84no—
569C22×C4—84no—
570C22×C4—84no—
571C22×C4—84no—
572C22×C4C2×C22⋊C412yes—
573C22×C4C2×C22⋊C412yes—
574C22×C4C2×C22⋊C412yes—
575C22×C4C2×C22⋊C412yes—
576C22×C4C2×C22⋊C412yes—
577C22×C4AGL(1,ℤ/8)12yes—
578C22×C4AGL(1,ℤ/8)12yes—
579C22×C4C23×C411yescharacteristic
580C22×C4C22×D411yescharacteristic
581C22×C4C2×#4111yescharacteristic
582C22×C4C2×#4111yescharacteristic
583C22×C4C2×#4111yescharacteristic
584C22×C4C2×#4111yescharacteristic
585C22×C4H(5,𝔽2)11yescharacteristic
586C22×C4H(5,𝔽2)11yescharacteristic
587C22×C4H(5,𝔽2)11yescharacteristic
588C22×C4H(5,𝔽2)11yescharacteristic
589C22×C4H(5,𝔽2)11yescharacteristic
590C22×C4H(5,𝔽2)11yescharacteristic
591C22×C42−1+411yescharacteristic
592C22×C42−1+411yescharacteristic
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—41no—
600C2×C8—41no—
601C2×C8—41no—
602C2×C8—41no—
603C2×C8—41no—
604C2×C8—41no—
605C2×C8—41no—
606C2×C8—41no—
607C2×C8—41no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—41no—
612C2×C8—41no—
613C2×C8—41no—
614C2×C8—41no—
615C2×C8—41no—
616C2×C8—41no—
617C2×C8—41no—
618C2×C8—41no—
619C2×C8—41no—
620C2×C8—41no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—48no—
632C4⋊C4—48no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—41no—
636C4⋊C4—41no—
637C4⋊C4—41no—
638C4⋊C4—41no—
639C4⋊C4—41no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4—41no—
643C4⋊C4—41no—
644C4⋊C4—41no—
645C4⋊C4—48no—
646C4⋊C4—41no—
647C4⋊C4—41no—
648C4⋊C4—41no—
649C4⋊C4—41no—
650C4⋊C4—41no—
651C4⋊C4—41no—
652C4⋊C4—41no—
653C4⋊C4—41no—
654C22⋊C4—28no—
655C22⋊C4—28no—
656C22⋊C4—48no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4—48no—
661C22⋊C4—84no—
662C22⋊C4—84no—
663C42—22no—
664C42—22no—
665C42—22no—
666C42—22no—
667C42—22no—
668C42—22no—
669C42—22no—
670C42—22no—
671C42—84no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—81no—
720C23—81no—
721C23—81no—
722C23—81no—
723C23—81no—
724C23—81no—
725C23—81no—
726C23—81no—
727C23—81no—
728C23—81no—
729C23—81no—
730C23—81no—
731C23—81no—
732C23—81no—
733C23—81no—
734C23—81no—
735C23—81no—
736C23—81no—
737C23—81no—
738C23—81no—
739C23—81no—
740C23—81no—
741C23#41814yes—
742C23C22×C22⋊C411yescharacteristic
743C23#53511yescharacteristic
744C23#53511yescharacteristic
745C23#54611yescharacteristic
746C23#54611yescharacteristic
747C23#54711yescharacteristic
748C23#54711yescharacteristic
749C23C2×AGL(1,ℤ/8)11yescharacteristic
750C23C2×AGL(1,ℤ/8)11yescharacteristic
751C23C2×AGL(1,ℤ/8)11yescharacteristic
752C23C2×AGL(1,ℤ/8)11yescharacteristic
753C23#57711yescharacteristic
754C23#57711yescharacteristic
755C23#57811yescharacteristic
756C23#57811yescharacteristic
757D4—42no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—816no—
762D4—81no—
763D4—81no—
764D4—81no—
765D4—81no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
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—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—816no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
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#41814yes—
859C2×C4C4×#4111yescharacteristic
860C2×C4C4×#4111yescharacteristic
861C2×C4#51811yescharacteristic
862C2×C4#51811yescharacteristic
863C2×C4#52011yescharacteristic
864C2×C4#52011yescharacteristic
865C2×C4#53511yescharacteristic
866C2×C4#53511yescharacteristic
867C2×C4#53811yescharacteristic
868C2×C4#53811yescharacteristic
869C2×C4#53911yescharacteristic
870C2×C4#53911yescharacteristic
871C2×C4#54011yescharacteristic
872C2×C4#54011yescharacteristic
873C2×C4#54211yescharacteristic
874C2×C4#54211yescharacteristic
875C2×C4#54611yescharacteristic
876C2×C4#54611yescharacteristic
877C2×C4#54711yescharacteristic
878C2×C4#54711yescharacteristic
879C2×C4#55111yescharacteristic
880C2×C4#55311yescharacteristic
881C2×C4#55311yescharacteristic
882C2×C4#55911yescharacteristic
883C2×C4#56011yescharacteristic
884C2×C4#56211yescharacteristic
885C2×C4#56211yescharacteristic
886C2×C4#56311yescharacteristic
887C8—42no—
888C8—42no—
889C8—81no—
890C8—81no—
891C22—24no—
892C22—24no—
893C22—24no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—82no—
907C22—82no—
908C22—82no—
909C22—82no—
910C22—82no—
911C22—82no—
912C22—82no—
913C22—161no—
914C22—161no—
915C22—161no—
916C22—161no—
917C22—161no—
918C22—161no—
919C22—161no—
920C22—161no—
921C22#230911yescharacteristic
922C22#233911yescharacteristic
923C22#233911yescharacteristic
924C22#270311yescharacteristic
925C22#270611yescharacteristic
926C22#271011yescharacteristic
927C22#271811yescharacteristic
928C22C2×#41811yescharacteristic
929C22C2×#41811yescharacteristic
930C22#289811yescharacteristic
931C22#289811yescharacteristic
932C22#321711yescharacteristic
933C22#321711yescharacteristic
934C22#321711yescharacteristic
935C22#321711yescharacteristic
936C22#322111yescharacteristic
937C22#322311yescharacteristic
938C22#322511yescharacteristic
939C22#322511yescharacteristic
940C22#330611yescharacteristic
941C22#330611yescharacteristic
942C22#330611yescharacteristic
943C22#330811yescharacteristic
944C22#330811yescharacteristic
945C22#330811yescharacteristic
946C22#333011yescharacteristic
947C22#333211yescharacteristic
948C22#334311yescharacteristic
949C22#334311yescharacteristic
950C22#334311yescharacteristic
951C22#334511yescharacteristic
952C22#334511yescharacteristic
953C22#334511yescharacteristic
954C22#335311yescharacteristic
955C22#335411yescharacteristic
956C4—24no—
957C4—42no—
958C4—42no—
959C4—42no—
960C4—42no—
961C4—82no—
962C4—82no—
963C4—82no—
964C4—82no—
965C4—82no—
966C4—161no—
967C4—161no—
968C4#233511yescharacteristic
969C4#233511yescharacteristic
970C4#237411yescharacteristic
971C4#237611yescharacteristic
972C4#270311yescharacteristic
973C4#270611yescharacteristic
974C4#271011yescharacteristic
975C4#271811yescharacteristic
976C2—44no—
977C2—162no—
978C2#1450611yescharacteristic
979C2#2181011yescharacteristic
980C2#2181411yescharacteristic
981C2#2249511yescharacteristic
982C2#2249511yescharacteristic
983C2#2249511yescharacteristic
984C2#2250011yescharacteristic
985C2#3186211yescharacteristic
986C2#3186411yescharacteristic
987C2#3195811yescharacteristic
988C2#3196011yescharacteristic
989C2#3207211yescharacteristic
990C2#3207611yescharacteristic
991C2#3230411yescharacteristic
992C2#3230811yescharacteristic
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×#1924C2semidirect
3. #13875C2semidirect
4. #11371C2semidirect
5. #11357C2semidirect
6. #11076C2semidirect
7. #11051C2semidirect
10. #10931C2semidirect
11. #10927C2semidirect
12. #10849C2semidirect
13. #10843C2semidirect
14. #10730C2semidirect
15. #10730C2semidirect
29. #2501C4semidirect

Maximal subgroups

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

subgroupindex
C2×#25012
C2×#19242
#138752
#113712
#113572
#110762
#110512
#109692
#109312
#109272
#108492
#108432
#107302