Finite Group Databasebeta

← #395919

Subgroups — #395919

Order 512.

1644 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#428C211yesmaximal, characteristic
2C2×#2068C211yesmaximal, characteristic, complemented
3C2×#2066C211yesmaximal, characteristic, complemented
4C2×#1894C211yesmaximal, characteristic
5C2×#1872C211yesmaximal, characteristic
6C2×#1851C211yesmaximal, characteristic
7#14138C211yesmaximal, characteristic
8#13907C211yesmaximal, characteristic
9#11232C211yesmaximal, characteristic, complemented
10#11231C211yesmaximal, characteristic, complemented
11#11220C211yesmaximal, characteristic, complemented
12#11219C211yesmaximal, characteristic, complemented
13#11124C211yesmaximal, characteristic, complemented
14#11122C211yesmaximal, characteristic, complemented
15#10731C211yesmaximal, characteristic
16C23×M16C2211yescharacteristic
17C22×C22⋊Q8C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C2×#428—24no—
21C2×#428—24no—
22C2×#428—24no—
23C22×#107C2211yescharacteristic
24C22×#107C2211yescharacteristic
25C22×#106C2211yescharacteristic
26C22×#106C2211yescharacteristic
27C22×C4⋊C8C2211yescharacteristic
28C22×C4⋊C8C2211yescharacteristic
29C22×#103C2211yescharacteristic
30C22×#103C2211yescharacteristic
31C22×#103C2211yescharacteristic
32C22×#103C2211yescharacteristic
33C22×C22⋊C8C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#389C2211yescharacteristic
38C2×#380—21no—
39C2×#380C2211yescharacteristic
40C2×C4×C22⋊C4C2211yescharacteristic
41#2068—24no—
42#2066—24no—
43#1894—24no—
44#1872—24no—
45#1851—24no—
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56#1441—21no—
57#1441—21no—
58#1440—21no—
59#1440—21no—
60#1436—21no—
61#1436—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C4⋊#95C2211yescharacteristic
65C4⋊#95C2211yescharacteristic
66C22⋊#95—21no—
67C23×Q8C2311yescharacteristic
68C24×C4—21no—
69C24×C4C2311yescharacteristic
70C22×M16—22no—
71C22×M16—22no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—22no—
75C22×M16—22no—
76C22×M16D414yes—
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C23×C8C2311yescharacteristic
81C2×C22⋊Q8—22no—
82C2×C22⋊Q8—22no—
83C2×C22⋊Q8—22no—
84C2×C22⋊Q8—22no—
85C2×C22⋊Q8—22no—
86C2×C22⋊Q8Q814yes—
87C2×#117—22no—
88C2×#117—22no—
89C2×#117—22no—
90C2×#117—22no—
91C2×#117—41no—
92C2×#117—41no—
93C22×C4⋊C4—22no—
94C22×C4⋊C4—22no—
95C22×C4⋊C4—21no—
96C22×C4⋊C4—21no—
97C22×C4⋊C4—22no—
98C22×C4⋊C4—21no—
99C22×C4⋊C4—21no—
100C22×C4⋊C4—41no—
101C22×C4⋊C4—41no—
102C22×C4⋊C4D414yes—
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2311yescharacteristic
110C22×C22⋊C4—21no—
111C22×C22⋊C4—21no—
112C22×C22⋊C4—21no—
113C22×C22⋊C4D411yescharacteristic
114C22×C22⋊C4D411yescharacteristic
115C22×C42—21no—
116C22×C42C2311yescharacteristic
117C22×C42C2311yescharacteristic
118#428—232no—
119C2×#107—22no—
120C2×#107—22no—
121C2×#107—22no—
122C2×#107—22no—
123C2×#107—22no—
124C2×#107D414yes—
125C2×#106—22no—
126C2×#106—22no—
127C2×#106—22no—
128C2×#106—22no—
129C2×#106—22no—
130C2×#106D414yes—
131C2×C4⋊C8—22no—
132C2×C4⋊C8—22no—
133C2×C4⋊C8—22no—
134C2×C4⋊C8—22no—
135C2×C4⋊C8—22no—
136C2×C4⋊C8—22no—
137C2×#103—22no—
138C2×#103—22no—
139C2×#103—22no—
140C2×#103—22no—
141C2×#103—22no—
142C2×#103—22no—
143C2×#103—22no—
144C2×#103—22no—
145C2×#103—22no—
146C2×#103—22no—
147C2×#103—41no—
148C2×#103—41no—
149C2×C22⋊C8—22no—
150C2×C22⋊C8—22no—
151C2×C22⋊C8—22no—
152#391—22no—
153#391—22no—
154#391—41no—
155#391—41no—
156#389—22no—
157#389—22no—
158#389—41no—
159#389—41no—
160#380—22no—
161#380—22no—
162#380—44no—
163C4×C22⋊C4—22no—
164C4×C22⋊C4—22no—
165C2×#95—21no—
166C2×#95—21no—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95—21no—
170C2×#95—21no—
171C2×#95—21no—
172C2×#95—21no—
173C2×#95—21no—
174C2×#95—21no—
175C2×#95—21no—
176C2×#95—21no—
177C2×#95—21no—
178C2×#95—21no—
179C2×#95—21no—
180C2×#95D411yescharacteristic
181C2×#95D411yescharacteristic
182#340—22no—
183#340—22no—
184#340—22no—
185#340—22no—
186#340—22no—
187#340—22no—
188#340—41no—
189#340—41no—
190#336—22no—
191#336—22no—
192C25C2×D411yescharacteristic
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×Q8—21no—
202C22×Q8—21no—
203C22×Q8—21no—
204C22×Q8—21no—
205C22×Q8—21no—
206C22×Q8C2×Q812yes—
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—24no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—42no—
225C23×C4—42no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4—81no—
229C23×C4—81no—
230C23×C4C2×D411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C23×C4C2×D411yescharacteristic
235C23×C4C2×D412yes—
236C23×C4C2×D412yes—
237C23×C4C2×Q812yes—
238C23×C4#4112yes—
239C23×C4#4112yes—
240C23×C4#4112yes—
241C23×C4C2411yescharacteristic
242C2×M16—28no—
243C2×M16—28no—
244C2×M16—28no—
245C2×M16—28no—
246C2×M16—28no—
247C2×M16—28no—
248C2×M16—28no—
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×C8C2×D412yes—
273C22×C8C2×D412yes—
274C22×C8C2×D412yes—
275C22×C8#4112yes—
276C22×C8#4112yes—
277C22⋊Q8—28no—
278C22⋊Q8—28no—
279C22⋊Q8—44no—
280C22⋊Q8—44no—
281#117—28no—
282#117—44no—
283#117—44no—
284#117—44no—
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—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
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—44no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—81no—
335C2×C4⋊C4—81no—
336C2×C4⋊C4C2×D412yes—
337C2×C4⋊C4C2×D412yes—
338C2×C4⋊C4C2×D412yes—
339C2×C4⋊C4C2×D412yes—
340C2×C4⋊C4C2×D412yes—
341C2×C4⋊C4C2×D412yes—
342C2×C4⋊C4C2×Q812yes—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—41no—
349C2×C22⋊C4—41no—
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×C42—21no—
359C2×C42—21no—
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—21no—
369C2×C42—21no—
370C2×C42—42no—
371C2×C42—42no—
372C2×C42—42no—
373#107—28no—
374#107—28no—
375#106—28no—
376#106—28no—
377C4⋊C8—44no—
378C4⋊C8—44no—
379#103—44no—
380#103—44no—
381#103—44no—
382#103—44no—
383C22⋊C8—44no—
384#95—22no—
385#95—22no—
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—42no—
396#95—42no—
397#95—42no—
398#95—42no—
399#95—81no—
400#95—81no—
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#12112yes—
414C24#12112yes—
415C24C22⋊Q812yes—
416C24C22×D411yescharacteristic
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—41no—
424C2×Q8—41no—
425C2×Q8—41no—
426C2×Q8—41no—
427C2×Q8—41no—
428C2×Q8—41no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×Q8—41no—
432C2×Q8—41no—
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—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
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—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—48no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—48no—
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—84no—
558C22×C4—84no—
559C22×C4—84no—
560C22×C4—84no—
561C22×C4—84no—
562C22×C4#12114yes—
563C22×C4#12112yes—
564C22×C4#12112yes—
565C22×C4C22⋊Q814yes—
566C22×C4C22⋊Q814yes—
567C22×C4C22⋊Q812yes—
568C22×C4#12614yes—
569C22×C4AGL(1,ℤ/8)12yes—
570C22×C4#13712yes—
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×Q811yescharacteristic
576C22×C4C2×#4111yescharacteristic
577C22×C4C2×#4111yescharacteristic
578C22×C4C2×#4111yescharacteristic
579C22×C4C2×#4111yescharacteristic
580C22×C4C2×#4111yescharacteristic
581C22×C4H(5,𝔽2)11yescharacteristic
582C22×C4H(5,𝔽2)11yescharacteristic
583C22×C42−1+411yescharacteristic
584C22×C42−1+411yescharacteristic
585M16—232no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—41no—
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#12114yes—
613C2×C8#12114yes—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—48no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—41no—
629C4⋊C4—41no—
630C4⋊C4—41no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4—41no—
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—84no—
644C4⋊C4—84no—
645C4⋊C4#12014yes—
646C22⋊C4—44no—
647C22⋊C4—44no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—84no—
651C42—48no—
652C42—41no—
653C42—41no—
654C42—41no—
655C42—41no—
656C42—41no—
657C42—41no—
658C42—41no—
659C42—41no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23#39614yes—
695C23C2×#12111yescharacteristic
696C23C2×#12111yescharacteristic
697C23C2×C22⋊Q811yescharacteristic
698C23D4211yescharacteristic
699C23D4211yescharacteristic
700C23#54711yescharacteristic
701C23#54711yescharacteristic
702C23C2×AGL(1,ℤ/8)11yescharacteristic
703C23C2×#13711yescharacteristic
704C23#57511yescharacteristic
705C23#57511yescharacteristic
706C23#57711yescharacteristic
707C23#57711yescharacteristic
708C23#57811yescharacteristic
709C23#57811yescharacteristic
710Q8—42no—
711Q8—42no—
712Q8—42no—
713Q8—42no—
714Q8—81no—
715Q8—81no—
716Q8—81no—
717Q8—81no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—816no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4—81no—
792C2×C4—81no—
793C2×C4—81no—
794C2×C4—81no—
795C2×C4—81no—
796C2×C4—81no—
797C2×C4—81no—
798C2×C4—81no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4—81no—
807C2×C4—81no—
808C2×C4—81no—
809C2×C4—81no—
810C2×C4—81no—
811C2×C4—81no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—81no—
816C2×C4—81no—
817C2×C4#39614yes—
818C2×C4C2×#12011yescharacteristic
819C2×C4C2×#12111yescharacteristic
820C2×C4C2×#12111yescharacteristic
821C2×C4C2×#12111yescharacteristic
822C2×C4C2×C22⋊Q811yescharacteristic
823C2×C4C2×C22⋊Q811yescharacteristic
824C2×C4#52511yescharacteristic
825C2×C4#52511yescharacteristic
826C2×C4#52511yescharacteristic
827C2×C4C2×#12611yescharacteristic
828C2×C4#53411yescharacteristic
829C2×C4#53611yescharacteristic
830C2×C4#53711yescharacteristic
831C2×C4#53711yescharacteristic
832C2×C4#53911yescharacteristic
833C2×C4#53911yescharacteristic
834C2×C4#54611yescharacteristic
835C2×C4#54611yescharacteristic
836C2×C4#54811yescharacteristic
837C2×C4#54811yescharacteristic
838C2×C4D4×Q811yescharacteristic
839C2×C4D4×Q811yescharacteristic
840C2×C4#55211yescharacteristic
841C2×C4#55211yescharacteristic
842C2×C4#55311yescharacteristic
843C2×C4#55311yescharacteristic
844C2×C4#55411yescharacteristic
845C2×C4#55411yescharacteristic
846C8—24no—
847C8—24no—
848C8—81no—
849C8—81no—
850C22—24no—
851C22—24no—
852C22—24no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22C2×#39611yescharacteristic
866C22#241011yescharacteristic
867C22#241311yescharacteristic
868C22#241611yescharacteristic
869C22#241611yescharacteristic
870C22#244911yescharacteristic
871C22#244911yescharacteristic
872C22#303611yescharacteristic
873C22#303711yescharacteristic
874C22#304211yescharacteristic
875C22#304411yescharacteristic
876C22#305511yescharacteristic
877C22#305611yescharacteristic
878C22#306311yescharacteristic
879C22#306311yescharacteristic
880C22#307911yescharacteristic
881C22#308011yescharacteristic
882C22#308211yescharacteristic
883C22#308211yescharacteristic
884C22#326511yescharacteristic
885C22#326711yescharacteristic
886C22#326911yescharacteristic
887C22#327011yescharacteristic
888C22#327211yescharacteristic
889C22#327511yescharacteristic
890C22#327611yescharacteristic
891C22#327711yescharacteristic
892C22#334311yescharacteristic
893C22#334411yescharacteristic
894C22#334911yescharacteristic
895C22#335011yescharacteristic
896C22#335111yescharacteristic
897C22#335211yescharacteristic
898C22#335311yescharacteristic
899C22#335611yescharacteristic
900C4—24no—
901C4—44no—
902C4—42no—
903C4—42no—
904C4—82no—
905C4—82no—
906C4—82no—
907C4—82no—
908C4—82no—
909C4—81no—
910C4—81no—
911C4—161no—
912C4—161no—
913C4#240911yescharacteristic
914C4#241711yescharacteristic
915C4#241711yescharacteristic
916C4#248111yescharacteristic
917C4#248111yescharacteristic
918C4#257911yescharacteristic
919C4#261811yescharacteristic
920C4#284711yescharacteristic
921C2—44no—
922C2#1472911yescharacteristic
923C2#2361511yescharacteristic
924C2#2361711yescharacteristic
925C2#2436711yescharacteristic
926C2#2436911yescharacteristic
927C2#2458811yescharacteristic
928C2#2459011yescharacteristic
929C2#2478911yescharacteristic
930C2#2479111yescharacteristic
931C2#2479311yescharacteristic
932C2#2479411yescharacteristic
933C2#2635311yescharacteristic
934C2#2635511yescharacteristic
935C2#2636511yescharacteristic
936C2#2636711yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C23×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×#2068C2semidirect
3. C2×#2066C2semidirect
9. #11232C2semidirect
10. #11231C2semidirect
11. #11220C2semidirect
12. #11219C2semidirect
13. #11124C2semidirect
14. #11122C2semidirect

Maximal subgroups

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

subgroupindex
C22×#4282
C2×#20682
C2×#20662
C2×#18942
C2×#18722
C2×#18512
#141382
#139072
#112322
#112312
#112202
#112192
#111242
#111222
#107312