Finite Group Databasebeta

← #373673

Subgroups — #373673

Order 512.

2352 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#419C211yesmaximal, characteristic
2C2×Q8×C22⋊C4C211yesmaximal, characteristic
3C2×#1865C211yesmaximal, characteristic, complemented
4C2×#1863C211yesmaximal, characteristic, complemented
5C2×#1854C211yesmaximal, characteristic
6C2×#1787C211yesmaximal, characteristic
7#14129C211yesmaximal, characteristic
8#11124C211yesmaximal, characteristic, complemented
9#11122C211yesmaximal, characteristic, complemented
10#11067C211yesmaximal, characteristic, complemented
11#11067C211yesmaximal, characteristic, complemented
12#10789C211yesmaximal, characteristic, complemented
13#10789C211yesmaximal, characteristic, complemented
14#10722C211yesmaximal, characteristic
15#10715C211yesmaximal, characteristic
16C24×Q8C2211yescharacteristic
17C23×M16C2211yescharacteristic
18C22×C4×Q8C2211yescharacteristic
19C22×C4×Q8C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C22×#107C2211yescharacteristic
22C22×#106C2211yescharacteristic
23C2×#419—24no—
24C2×#419—24no—
25C2×#419—24no—
26C22×#103C2211yescharacteristic
27C22×#103C2211yescharacteristic
28C22×#103C2211yescharacteristic
29C22×#103C2211yescharacteristic
30C22×#103C2211yescharacteristic
31C22×#103C2211yescharacteristic
32C22×#103C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×C22⋊C8C2211yescharacteristic
35Q8×C22⋊C4—24no—
36Q8×C22⋊C4—24no—
37C2×#391—21no—
38C2×#391—21no—
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#389C2211yescharacteristic
43C2×#380—21no—
44C2×#380C2211yescharacteristic
45C2×#380C2211yescharacteristic
46C2×C4×C22⋊C4—21no—
47C2×C4×C22⋊C4C2211yescharacteristic
48#1865—24no—
49#1863—24no—
50#1854—24no—
51#1787C418yescomplemented
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60C2×#336C2211yescharacteristic
61C2×#336C2211yescharacteristic
62#1439—21no—
63#1439—21no—
64#1436—21no—
65#1436—21no—
66C4⋊#95C2211yescharacteristic
67C4⋊#95C2211yescharacteristic
68C23×Q8—22no—
69C23×Q8—21no—
70C23×Q8—22no—
71C23×Q8—22no—
72C23×Q8—22no—
73C23×Q8—22no—
74C23×Q8—22no—
75C23×Q8—22no—
76C23×Q8—41no—
77C23×Q8—41no—
78C23×Q8—41no—
79C23×Q8—41no—
80C23×Q8C2×C414yes—
81C23×Q8D414yes—
82C23×Q8Q814yes—
83C23×Q8C2311yescharacteristic
84C23×Q8C2311yescharacteristic
85C24×C4—21no—
86C24×C4C2311yescharacteristic
87C22×M16—22no—
88C22×M16—22no—
89C22×M16—22no—
90C22×M16—22no—
91C22×M16—22no—
92C22×M16—41no—
93C22×M16—41no—
94C23×C8C2311yescharacteristic
95C23×C8C2311yescharacteristic
96C23×C8C2311yescharacteristic
97C23×C8C2311yescharacteristic
98C2×C4×Q8—22no—
99C2×C4×Q8—22no—
100C2×C4×Q8—22no—
101C2×C4×Q8—22no—
102C2×C4×Q8—22no—
103C2×C4×Q8—22no—
104C2×C4×Q8—22no—
105C2×C4×Q8—22no—
106C2×C4×Q8—41no—
107C2×C4×Q8—41no—
108C2×C4×Q8—41no—
109C2×C4×Q8—41no—
110C2×#117—22no—
111C2×#117—22no—
112C2×#117—22no—
113C2×#117—22no—
114C2×#117—41no—
115C2×#117—41no—
116C22×C4⋊C4—21no—
117C22×C4⋊C4—21no—
118C22×C4⋊C4—21no—
119C22×C4⋊C4—21no—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C22⋊C4—21no—
127C22×C22⋊C4—21no—
128C22×C22⋊C4—21no—
129C22×C22⋊C4D411yescharacteristic
130C22×C22⋊C4D411yescharacteristic
131C22×C42—21no—
132C22×C42—21no—
133C22×C42—21no—
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136C2×#107—22no—
137C2×#107—22no—
138C2×#107—41no—
139C2×#106—22no—
140C2×#106—22no—
141C2×#106—41no—
142#419—232no—
143C2×#103—22no—
144C2×#103—22no—
145C2×#103—22no—
146C2×#103—22no—
147C2×#103—22no—
148C2×#103—22no—
149C2×#103—22no—
150C2×#103—22no—
151C2×#103—22no—
152C2×#103—22no—
153C2×#103—22no—
154C2×#103—22no—
155C2×#103—22no—
156C2×#103—22no—
157C2×#103—41no—
158C2×#103—41no—
159C2×#103—41no—
160C2×#103—41no—
161C2×#103C2×C414yes—
162C2×#103C2×C414yes—
163C2×#103C2×C414yes—
164C2×#103C2×C414yes—
165C2×#103D414yes—
166C2×#103D414yes—
167C2×C22⋊C8—22no—
168C2×C22⋊C8—22no—
169C2×C22⋊C8C2×C414yes—
170#391—28no—
171#391—28no—
172#391—22no—
173#391—22no—
174#391—22no—
175#391—22no—
176#389—22no—
177#389—22no—
178#389—41no—
179#389—41no—
180#380—28no—
181#380—22no—
182#380—22no—
183#380C2×C414yes—
184#380D414yes—
185C4×C22⋊C4—28no—
186C4×C22⋊C4—22no—
187C4×C22⋊C4—22no—
188C2×#95—21no—
189C2×#95—21no—
190C2×#95—21no—
191C2×#95—21no—
192C2×#95—21no—
193C2×#95—21no—
194C2×#95—21no—
195C2×#95—21no—
196C2×#95—21no—
197C2×#95—21no—
198C2×#95—21no—
199C2×#95—21no—
200C2×#95D411yescharacteristic
201C2×#95D411yescharacteristic
202#340—22no—
203#340—22no—
204#340—22no—
205#340—22no—
206#340—41no—
207#340—41no—
208#336—22no—
209#336—22no—
210#336—41no—
211#336—41no—
212C25C2×D411yescharacteristic
213C22×Q8—24no—
214C22×Q8—28no—
215C22×Q8—24no—
216C22×Q8—24no—
217C22×Q8—28no—
218C22×Q8—28no—
219C22×Q8—21no—
220C22×Q8—21no—
221C22×Q8—21no—
222C22×Q8—21no—
223C22×Q8—21no—
224C22×Q8—21no—
225C22×Q8—21no—
226C22×Q8—21no—
227C22×Q8—21no—
228C22×Q8—21no—
229C22×Q8—28no—
230C22×Q8—28no—
231C22×Q8—28no—
232C22×Q8—28no—
233C22×Q8—28no—
234C22×Q8—28no—
235C22×Q8—21no—
236C22×Q8—21no—
237C22×Q8—21no—
238C22×Q8—21no—
239C22×Q8—21no—
240C22×Q8—21no—
241C22×Q8—21no—
242C22×Q8—21no—
243C22×Q8—42no—
244C22×Q8—42no—
245C22×Q8—42no—
246C22×Q8—42no—
247C22×Q8—44no—
248C22×Q8—44no—
249C22×Q8—44no—
250C22×Q8—44no—
251C22×Q8—44no—
252C22×Q8—44no—
253C22×Q8—44no—
254C22×Q8—44no—
255C22×Q8—44no—
256C22×Q8—44no—
257C22×Q8—44no—
258C22×Q8—44no—
259C22×Q8—44no—
260C22×Q8—44no—
261C22×Q8—44no—
262C22×Q8—44no—
263C22×Q8—44no—
264C22×Q8—44no—
265C22×Q8C4⋊C4116yescomplemented
266C22×Q8C22×C412yes—
267C22×Q8C22×C412yes—
268C22×Q8C2×D412yes—
269C22×Q8C2×D412yes—
270C22×Q8C2×D412yes—
271C22×Q8C2×D412yes—
272C22×Q8C2×Q812yes—
273C22×Q8C2×Q812yes—
274C22×Q8#4112yes—
275C22×Q8#4112yes—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—21no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—42no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4C22×C412yes—
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D412yes—
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D412yes—
307C23×C4C2×Q812yes—
308C23×C4#4112yes—
309C23×C4#4112yes—
310C23×C4C2411yescharacteristic
311C2×M16—28no—
312C2×M16—44no—
313C2×M16—44no—
314C2×M16—44no—
315C2×M16—44no—
316C2×M16—44no—
317C2×M16—44no—
318C22×C8—21no—
319C22×C8—21no—
320C22×C8—21no—
321C22×C8—21no—
322C22×C8—21no—
323C22×C8—21no—
324C22×C8—21no—
325C22×C8—21no—
326C22×C8—21no—
327C22×C8—21no—
328C22×C8—21no—
329C22×C8—21no—
330C22×C8—21no—
331C22×C8—21no—
332C22×C8—21no—
333C22×C8—21no—
334C22×C8—21no—
335C22×C8—21no—
336C22×C8—21no—
337C22×C8—21no—
338C22×C8—21no—
339C22×C8—21no—
340C22×C8—21no—
341C22×C8—21no—
342C22×C8C22×C412yes—
343C22×C8C22×C412yes—
344C22×C8C2×D412yes—
345C22×C8C2×D412yes—
346C4×Q8—44no—
347C4×Q8—44no—
348C4×Q8—44no—
349C4×Q8—44no—
350C4×Q8—44no—
351C4×Q8—44no—
352C4×Q8—44no—
353C4×Q8—44no—
354#117—28no—
355#117—44no—
356#117—44no—
357#117—44no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
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—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4—42no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4—42no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4—81no—
399C2×C4⋊C4—81no—
400C2×C4⋊C4C22×C412yes—
401C2×C4⋊C4C22×C412yes—
402C2×C4⋊C4C2×D412yes—
403C2×C4⋊C4C2×D412yes—
404C2×C4⋊C4C2×D412yes—
405C2×C4⋊C4C2×D412yes—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—41no—
413C2×C22⋊C4—41no—
414C2×C22⋊C4—42no—
415C2×C22⋊C4—42no—
416C2×C22⋊C4—42no—
417C2×C22⋊C4—42no—
418C2×C22⋊C4—42no—
419C2×C22⋊C4—81no—
420C2×C22⋊C4—81no—
421C2×C42—24no—
422C2×C42—24no—
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—21no—
432C2×C42—21no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—42no—
436C2×C42—42no—
437C2×C42—42no—
438C2×C42—42no—
439C2×C42—42no—
440C2×C42—42no—
441C2×C42—42no—
442#107—44no—
443#106—44no—
444#103—28no—
445#103—28no—
446#103—28no—
447#103—28no—
448#103—28no—
449#103—28no—
450#103—44no—
451#103—44no—
452C22⋊C8—28no—
453#95—24no—
454#95—24no—
455#95—24no—
456#95—24no—
457#95—24no—
458#95—24no—
459#95—22no—
460#95—22no—
461#95—42no—
462#95—42no—
463#95—42no—
464#95—42no—
465#95—81no—
466#95—81no—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—21no—
475C24—21no—
476C24—21no—
477C24—21no—
478C24—21no—
479C24C4×D412yes—
480C24#12012yes—
481C24C22⋊Q812yes—
482C24C22×D411yescharacteristic
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×Q8—22no—
492C2×Q8—22no—
493C2×Q8—22no—
494C2×Q8—22no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8—22no—
504C2×Q8—22no—
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8—216no—
508C2×Q8—232no—
509C2×Q8—22no—
510C2×Q8—22no—
511C2×Q8—22no—
512C2×Q8—22no—
513C2×Q8—22no—
514C2×Q8—22no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—48no—
522C2×Q8—48no—
523C2×Q8—48no—
524C2×Q8—48no—
525C2×Q8—48no—
526C2×Q8—48no—
527C2×Q8—416no—
528C2×Q8—416no—
529C2×Q8—416no—
530C2×Q8—416no—
531C2×Q8—416no—
532C2×Q8—416no—
533C2×Q8—416no—
534C2×Q8—41no—
535C2×Q8—41no—
536C2×Q8—41no—
537C2×Q8—41no—
538C2×Q8—41no—
539C2×Q8—41no—
540C2×Q8—41no—
541C2×Q8—41no—
542C2×Q8—41no—
543C2×Q8—41no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8C2×C4⋊C414yes—
547C2×Q8C2×C4⋊C414yes—
548C2×Q8C4×D414yes—
549C2×Q8C4×D414yes—
550C2×Q8#12014yes—
551C2×Q8C22⋊Q814yes—
552C2×Q8C22⋊Q814yes—
553C2×Q8#12314yes—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—216no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—21no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—48no—
626C22×C4—48no—
627C22×C4—48no—
628C22×C4—48no—
629C22×C4—48no—
630C22×C4—48no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—41no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4—41no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—41no—
664C22×C4—41no—
665C22×C4—41no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—41no—
670C22×C4—41no—
671C22×C4C2×C4⋊C414yes—
672C22×C4C4×D414yes—
673C22×C4C4×D412yes—
674C22×C4#12012yes—
675C22×C4C22⋊Q814yes—
676C22×C4C22⋊Q812yes—
677C22×C4#12314yes—
678C22×C4#13712yes—
679C22×C4#13712yes—
680C22×C4C23×C411yescharacteristic
681C22×C4C22×D411yescharacteristic
682C22×C4C22×D411yescharacteristic
683C22×C4C22×D411yescharacteristic
684C22×C4C22×D411yescharacteristic
685C22×C4C22×Q811yescharacteristic
686C22×C4C2×#4111yescharacteristic
687C22×C4C2×#4111yescharacteristic
688C22×C4C2×#4111yescharacteristic
689C22×C4C2×#4111yescharacteristic
690C22×C4H(5,𝔽2)11yescharacteristic
691C22×C4H(5,𝔽2)11yescharacteristic
692C22×C4H(5,𝔽2)11yescharacteristic
693C22×C4H(5,𝔽2)11yescharacteristic
694M16—416no—
695C2×C8—22no—
696C2×C8—22no—
697C2×C8—22no—
698C2×C8—22no—
699C2×C8—22no—
700C2×C8—22no—
701C2×C8—22no—
702C2×C8—22no—
703C2×C8—22no—
704C2×C8—22no—
705C2×C8—22no—
706C2×C8—22no—
707C2×C8—41no—
708C2×C8—41no—
709C2×C8—41no—
710C2×C8—41no—
711C2×C8—41no—
712C2×C8—41no—
713C2×C8—41no—
714C2×C8—41no—
715C2×C8—41no—
716C2×C8—41no—
717C2×C8—41no—
718C2×C8—41no—
719C2×C8—41no—
720C2×C8—41no—
721C2×C8—41no—
722C2×C8—41no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—22no—
726C4⋊C4—22no—
727C4⋊C4—22no—
728C4⋊C4—22no—
729C4⋊C4—22no—
730C4⋊C4—22no—
731C4⋊C4—22no—
732C4⋊C4—22no—
733C4⋊C4—22no—
734C4⋊C4—22no—
735C4⋊C4—48no—
736C4⋊C4—48no—
737C4⋊C4—41no—
738C4⋊C4—41no—
739C4⋊C4—41no—
740C4⋊C4—41no—
741C4⋊C4—41no—
742C4⋊C4—41no—
743C4⋊C4—41no—
744C4⋊C4—41no—
745C4⋊C4—41no—
746C4⋊C4—41no—
747C4⋊C4—41no—
748C4⋊C4—41no—
749C4⋊C4—84no—
750C4⋊C4—84no—
751C22⋊C4—28no—
752C22⋊C4—44no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C22⋊C4—84no—
756C42—48no—
757C42—48no—
758C42—48no—
759C42—41no—
760C42—41no—
761C42—41no—
762C42—41no—
763C42—41no—
764C42—41no—
765C42—41no—
766C42—41no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23#38514yes—
802C23C2×C4×D411yescharacteristic
803C23C2×#12011yescharacteristic
804C23C2×C22⋊Q811yescharacteristic
805C23D4211yescharacteristic
806C23D4211yescharacteristic
807C23#54611yescharacteristic
808C23#54611yescharacteristic
809C23C2×#13711yescharacteristic
810C23C2×#13711yescharacteristic
811C23#57511yescharacteristic
812C23#57511yescharacteristic
813C23#57711yescharacteristic
814C23#57711yescharacteristic
815C23#57811yescharacteristic
816C23#57811yescharacteristic
817Q8—24no—
818Q8—24no—
819Q8—24no—
820Q8—24no—
821Q8—24no—
822Q8—24no—
823Q8—24no—
824Q8—24no—
825Q8—24no—
826Q8—432no—
827Q8—42no—
828Q8—42no—
829Q8—42no—
830Q8—42no—
831Q8—42no—
832Q8—42no—
833Q8#38518yes—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—22no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—24no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—432no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—41no—
868C2×C4—42no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—41no—
883C2×C4—42no—
884C2×C4—41no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—41no—
899C2×C4—42no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—81no—
910C2×C4—81no—
911C2×C4—81no—
912C2×C4—81no—
913C2×C4—81no—
914C2×C4—81no—
915C2×C4—81no—
916C2×C4—81no—
917C2×C4—81no—
918C2×C4—81no—
919C2×C4—81no—
920C2×C4—81no—
921C2×C4—81no—
922C2×C4—81no—
923C2×C4—81no—
924C2×C4—81no—
925C2×C4—81no—
926C2×C4—81no—
927C2×C4—81no—
928C2×C4—81no—
929C2×C4—81no—
930C2×C4—81no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4#38514yes—
934C2×C4C22×C4⋊C411yescharacteristic
935C2×C4C2×C4×D411yescharacteristic
936C2×C4C2×C4×D411yescharacteristic
937C2×C4C2×C4×D411yescharacteristic
938C2×C4#51811yescharacteristic
939C2×C4#51811yescharacteristic
940C2×C4C2×#12011yescharacteristic
941C2×C4C2×C22⋊Q811yescharacteristic
942C2×C4C2×C22⋊Q811yescharacteristic
943C2×C4C2×C22⋊Q811yescharacteristic
944C2×C4C2×#12311yescharacteristic
945C2×C4C2×#12311yescharacteristic
946C2×C4#53411yescharacteristic
947C2×C4#53411yescharacteristic
948C2×C4#54311yescharacteristic
949C2×C4#54311yescharacteristic
950C2×C4D4211yescharacteristic
951C2×C4D4211yescharacteristic
952C2×C4#54611yescharacteristic
953C2×C4#54611yescharacteristic
954C2×C4#54611yescharacteristic
955C2×C4#54611yescharacteristic
956C2×C4#54611yescharacteristic
957C2×C4#54611yescharacteristic
958C2×C4#55111yescharacteristic
959C2×C4#55111yescharacteristic
960C2×C4#55111yescharacteristic
961C2×C4#55111yescharacteristic
962C8—42no—
963C8—42no—
964C8—42no—
965C8—42no—
966C22—24no—
967C22—24no—
968C22—24no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22C2×#38511yescharacteristic
982C22#235811yescharacteristic
983C22#235811yescharacteristic
984C22#240311yescharacteristic
985C22#240511yescharacteristic
986C22#243711yescharacteristic
987C22#243711yescharacteristic
988C22C4×#13711yescharacteristic
989C22C4×#13711yescharacteristic
990C22#294911yescharacteristic
991C22#295011yescharacteristic
992C22#300411yescharacteristic
993C22#300511yescharacteristic
994C22#301311yescharacteristic
995C22#301311yescharacteristic
996C22#307811yescharacteristic
997C22#307811yescharacteristic
998C22#308211yescharacteristic
999C22#308211yescharacteristic
1000C22#326611yescharacteristic
1001C22#326911yescharacteristic
1002C22#327011yescharacteristic
1003C22#327111yescharacteristic
1004C22#327511yescharacteristic
1005C22#327611yescharacteristic
1006C22#327711yescharacteristic
1007C22#327811yescharacteristic
1008C22#331211yescharacteristic
1009C22#331311yescharacteristic
1010C22#332011yescharacteristic
1011C22#332111yescharacteristic
1012C22#332611yescharacteristic
1013C22#332711yescharacteristic
1014C22#332811yescharacteristic
1015C22#332911yescharacteristic
1016C4—24no—
1017C4—28no—
1018C4—44no—
1019C4—42no—
1020C4—42no—
1021C4—82no—
1022C4—81no—
1023C4—82no—
1024C4—82no—
1025C4—82no—
1026C4—82no—
1027C4—81no—
1028C4—82no—
1029C4C2×#38511yescharacteristic
1030C4#231511yescharacteristic
1031C4#235811yescharacteristic
1032C4#235811yescharacteristic
1033C4#240511yescharacteristic
1034C4#243711yescharacteristic
1035C4#243711yescharacteristic
1036C4#248311yescharacteristic
1037C2—44no—
1038C2#1412711yescharacteristic
1039C2#2087411yescharacteristic
1040C2#2088011yescharacteristic
1041C2#2286511yescharacteristic
1042C2#2286911yescharacteristic
1043C2#2288111yescharacteristic
1044C2#2288511yescharacteristic
1045C2#2386811yescharacteristic
1046C2#2387111yescharacteristic
1047C2#2404711yescharacteristic
1048C2#2405311yescharacteristic
1049C2#2597111yescharacteristic
1050C2#2597311yescharacteristic
1051C2#2597911yescharacteristic
1052C2#2598111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
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
3. C2×#1865C2semidirect
4. C2×#1863C2semidirect
8. #11124C2semidirect
9. #11122C2semidirect
10. #11067C2semidirect
11. #11067C2semidirect
12. #10789C2semidirect
13. #10789C2semidirect
51. #1787C4semidirect
265. C22×Q8C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4192
C2×Q8×C22⋊C42
C2×#18652
C2×#18632
C2×#18542
C2×#17872
#141292
#111242
#111222
#110672
#107892
#107222
#107152