Finite Group Databasebeta

← #367656

Subgroups — #367656

Order 512.

1406 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1927C211yesmaximal, characteristic, complemented
2C2×#1872C211yesmaximal, characteristic
3C2×#1824C211yesmaximal, characteristic
4#13997C211yesmaximal, characteristic
5C22⋊C4×C4⋊C4C211yesmaximal, characteristic
6#11292C211yesmaximal, characteristic, complemented
7#11190C211yesmaximal, characteristic, complemented
8#11095C211yesmaximal, characteristic
9#10970C211yesmaximal, characteristic
10#10932C211yesmaximal, characteristic, complemented
11#10928C211yesmaximal, characteristic, complemented
12#10922C211yesmaximal, characteristic
13#10908C211yesmaximal, characteristic, complemented
14#10884C211yesmaximal, characteristic, complemented
15#10703C211yesmaximal, characteristic, complemented
16C22×C22⋊Q8C2211yescharacteristic
17C23×C4⋊C4C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×#103C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×#97C2211yescharacteristic
26C2×#391C2211yescharacteristic
27C2×#391C2211yescharacteristic
28C2×#389C2211yescharacteristic
29C2×#380C2211yescharacteristic
30C2×#380C2211yescharacteristic
31C2×C4×C4⋊C4C2211yescharacteristic
32C2×C4×C4⋊C4C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C22⋊C4—21no—
35C2×C4×C22⋊C4C2211yescharacteristic
36#1927—24no—
37#1872C418yescomplemented
38#1824—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
52C2×#336C2211yescharacteristic
53#1445—21no—
54#1439—21no—
55#1437—21no—
56#1436—21no—
57#1436—21no—
58C4⋊#95—21no—
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C22⋊#95—21no—
62C23×Q8C2311yescharacteristic
63C24×C4—21no—
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—41no—
73C2×C22⋊Q8—41no—
74C2×C22⋊Q8C2×C414yes—
75C22×C4⋊C4—22no—
76C22×C4⋊C4—22no—
77C22×C4⋊C4—21no—
78C22×C4⋊C4—21no—
79C22×C4⋊C4—22no—
80C22×C4⋊C4—21no—
81C22×C4⋊C4—41no—
82C22×C4⋊C4—41no—
83C22×C4⋊C4C2×C414yes—
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C22⋊C4—21no—
92C22×C22⋊C4—21no—
93C22×C22⋊C4—21no—
94C22×C22⋊C4D411yescharacteristic
95C22×C22⋊C4D411yescharacteristic
96C22×C42—21no—
97C22×C42—21no—
98C22×C42—21no—
99C22×C42C2311yescharacteristic
100C22×C42C2311yescharacteristic
101C2×#106—22no—
102C2×#106—22no—
103C2×#106—41no—
104C2×#103—22no—
105C2×#103—22no—
106C2×#103—22no—
107C2×#103—22no—
108C2×#103—22no—
109C2×#103—41no—
110C2×#103—41no—
111C2×#103—41no—
112C2×#103—41no—
113C2×#103—41no—
114C2×#103C2×C414yes—
115C2×#103C2×C414yes—
116C2×C22⋊C8—22no—
117C2×C22⋊C8—22no—
118C2×C22⋊C8—41no—
119C2×C22⋊C8—41no—
120C2×C22⋊C8—41no—
121C2×C22⋊C8C2×C414yes—
122C2×#97—22no—
123C2×#97—41no—
124C2×#97—41no—
125#391—22no—
126#391—22no—
127#391—22no—
128#391—41no—
129#389—22no—
130#389—41no—
131#380—22no—
132#380—22no—
133#380—22no—
134#380—41no—
135C4×C4⋊C4—22no—
136C4×C4⋊C4—22no—
137C4×C4⋊C4—22no—
138C4×C4⋊C4—41no—
139C4×C4⋊C4—41no—
140C4×C4⋊C4—41no—
141C4×C22⋊C4—22no—
142C4×C22⋊C4—22no—
143C4×C22⋊C4—44no—
144C2×#95—21no—
145C2×#95—21no—
146C2×#95—21no—
147C2×#95—21no—
148C2×#95—21no—
149C2×#95—21no—
150C2×#95—21no—
151C2×#95—21no—
152C2×#95—21no—
153C2×#95—21no—
154C2×#95—21no—
155C2×#95—21no—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95D411yescharacteristic
159C2×#95D411yescharacteristic
160#340—22no—
161#340—22no—
162#340—22no—
163#340—22no—
164#340—22no—
165#340—22no—
166#340—41no—
167#340—41no—
168#340C2×C414yes—
169#340C2×C414yes—
170#340D414yes—
171#336—22no—
172#336—22no—
173#336—41no—
174C25C2×D411yescharacteristic
175C22×Q8—21no—
176C22×Q8—21no—
177C22×Q8—21no—
178C22×Q8—21no—
179C22×Q8—21no—
180C22×Q8—21no—
181C22×Q8—21no—
182C22×Q8—21no—
183C22×Q8—21no—
184C22×Q8—21no—
185C22×Q8—21no—
186C22×Q8—21no—
187C22×Q8—21no—
188C22×Q8C22×C412yes—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—24no—
209C23×C4—21no—
210C23×C4—42no—
211C23×C4—42no—
212C23×C4—42no—
213C23×C4—42no—
214C23×C4—81no—
215C23×C4—81no—
216C23×C4C22×C412yes—
217C23×C4C2×D411yescharacteristic
218C23×C4C2×D411yescharacteristic
219C23×C4C2×D411yescharacteristic
220C23×C4C2×D411yescharacteristic
221C23×C4C2×D411yescharacteristic
222C23×C4#4112yes—
223C23×C4C2411yescharacteristic
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
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×C8C22×C412yes—
250C22×C8C22×C412yes—
251C22×C8C2×D412yes—
252C22⋊Q8—28no—
253C22⋊Q8—44no—
254C22⋊Q8—44no—
255C22⋊Q8—44no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
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—28no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
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—44no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—81no—
301C2×C4⋊C4C22×C412yes—
302C2×C4⋊C4C22×C412yes—
303C2×C4⋊C4C22×C412yes—
304C2×C4⋊C4C2×D412yes—
305C2×C4⋊C4C2×D412yes—
306C2×C4⋊C4#4112yes—
307C2×C4⋊C4#4112yes—
308C2×C4⋊C4#4112yes—
309C2×C4⋊C4#4112yes—
310C2×C4⋊C4#4112yes—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—41no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—81no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—42no—
337C2×C42—42no—
338C2×C42—42no—
339C2×C42—42no—
340C2×C42—42no—
341C2×C42—42no—
342C2×C42—81no—
343C2×C42—81no—
344C2×C42—81no—
345C2×C42#4112yes—
346C2×C42#4112yes—
347#106—44no—
348#103—28no—
349#103—44no—
350#103—44no—
351#103—44no—
352C22⋊C8—44no—
353C22⋊C8—44no—
354#97—44no—
355#95—24no—
356#95—22no—
357#95—22no—
358#95—42no—
359#95—42no—
360#95—42no—
361#95—42no—
362#95—42no—
363#95—42no—
364#95—42no—
365#95—42no—
366#95—42no—
367#95—42no—
368#95—42no—
369#95—81no—
370#95—81no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—21no—
377C24—21no—
378C24—21no—
379C24—21no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24C4×D412yes—
384C24#13712yes—
385C24#13712yes—
386C24C22×D411yescharacteristic
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—41no—
394C2×Q8—41no—
395C2×Q8—41no—
396C2×Q8—41no—
397C2×Q8—41no—
398C2×Q8—41no—
399C2×Q8—41no—
400C2×Q8—41no—
401C2×Q8—41no—
402C2×Q8—41no—
403C2×Q8—41no—
404C2×Q8—41no—
405C2×Q8—41no—
406C2×Q8—41no—
407C2×Q8—41no—
408C2×Q8—41no—
409C2×Q8—41no—
410C2×Q8—41no—
411C2×Q8—41no—
412C2×Q8—41no—
413C2×Q8—41no—
414C2×Q8—41no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
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—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—48no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—48no—
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—84no—
533C22×C4—84no—
534C22×C4—84no—
535C22×C4—84no—
536C22×C4—84no—
537C22×C4C4×D412yes—
538C22×C4#12312yes—
539C22×C4#12312yes—
540C22×C4AGL(1,ℤ/8)12yes—
541C22×C4C23×C411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C2×#4111yescharacteristic
544C22×C4C2×#4111yescharacteristic
545C22×C4C2×#4111yescharacteristic
546C22×C4C2×#4111yescharacteristic
547C22×C4C2×#4111yescharacteristic
548C22×C4C2×#4111yescharacteristic
549C22×C4C2×#4111yescharacteristic
550C22×C4C2×#4111yescharacteristic
551C22×C4H(5,𝔽2)11yescharacteristic
552C22×C4H(5,𝔽2)11yescharacteristic
553C22×C4H(5,𝔽2)11yescharacteristic
554C22×C4H(5,𝔽2)11yescharacteristic
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—48no—
598C4⋊C4—48no—
599C4⋊C4—41no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—41no—
605C4⋊C4—41no—
606C4⋊C4—41no—
607C4⋊C4—41no—
608C4⋊C4—41no—
609C4⋊C4—41no—
610C4⋊C4—41no—
611C4⋊C4—84no—
612C4⋊C4#11714yes—
613C4⋊C4C4×D414yes—
614C22⋊C4—28no—
615C22⋊C4—44no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—84no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—41no—
624C42—41no—
625C42—41no—
626C42—41no—
627C42—84no—
628C42—84no—
629C42—84no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23#44114yes—
665C23C2×C4×D411yescharacteristic
666C23C2×#12311yescharacteristic
667C23#52511yescharacteristic
668C23D4211yescharacteristic
669C23#54611yescharacteristic
670C23#54611yescharacteristic
671C23#54611yescharacteristic
672C23C2×AGL(1,ℤ/8)11yescharacteristic
673C23C2×#13711yescharacteristic
674C23C2×#13711yescharacteristic
675C23#57511yescharacteristic
676C23#57711yescharacteristic
677C23#57711yescharacteristic
678C23#57711yescharacteristic
679C23#57811yescharacteristic
680Q8—42no—
681Q8—42no—
682Q8—42no—
683Q8—42no—
684Q8—81no—
685Q8—81no—
686Q8—81no—
687Q8—81no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—42no—
760C2×C4—816no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4—81no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4C2×#11711yescharacteristic
789C2×C4C2×C4×D411yescharacteristic
790C2×C4C4×#4111yescharacteristic
791C2×C4C4×#4111yescharacteristic
792C2×C4#51811yescharacteristic
793C2×C4#51811yescharacteristic
794C2×C4#52911yescharacteristic
795C2×C4#52911yescharacteristic
796C2×C4#52911yescharacteristic
797C2×C4#52911yescharacteristic
798C2×C4#53211yescharacteristic
799C2×C4#53211yescharacteristic
800C2×C4#53811yescharacteristic
801C2×C4#53811yescharacteristic
802C2×C4#54011yescharacteristic
803C2×C4#54011yescharacteristic
804C2×C4#54611yescharacteristic
805C2×C4#54611yescharacteristic
806C2×C4#55011yescharacteristic
807C2×C4#55111yescharacteristic
808C2×C4#55111yescharacteristic
809C2×C4#55111yescharacteristic
810C2×C4#55311yescharacteristic
811C2×C4#55311yescharacteristic
812C2×C4#55311yescharacteristic
813C2×C4#55511yescharacteristic
814C2×C4#55911yescharacteristic
815C2×C4#55911yescharacteristic
816C8—42no—
817C8—42no—
818C8—42no—
819C8—81no—
820C22—24no—
821C22—24no—
822C22—24no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22C4×#12311yescharacteristic
836C22#234211yescharacteristic
837C22#235811yescharacteristic
838C22#244411yescharacteristic
839C22#244511yescharacteristic
840C22#245911yescharacteristic
841C22#246411yescharacteristic
842C22C2×#44111yescharacteristic
843C22C4×AGL(1,ℤ/8)11yescharacteristic
844C22#294711yescharacteristic
845C22#294911yescharacteristic
846C22#309211yescharacteristic
847C22#309511yescharacteristic
848C22#309711yescharacteristic
849C22#309911yescharacteristic
850C22#311011yescharacteristic
851C22#311711yescharacteristic
852C22#312011yescharacteristic
853C22#312511yescharacteristic
854C22#326511yescharacteristic
855C22#326611yescharacteristic
856C22#326711yescharacteristic
857C22#327011yescharacteristic
858C22#330611yescharacteristic
859C22#331211yescharacteristic
860C22#331511yescharacteristic
861C22#331611yescharacteristic
862C22#331611yescharacteristic
863C22#331611yescharacteristic
864C22#332011yescharacteristic
865C22#332011yescharacteristic
866C22#332311yescharacteristic
867C22#332311yescharacteristic
868C22#332411yescharacteristic
869C22#333011yescharacteristic
870C4—44no—
871C4—44no—
872C4—42no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—82no—
877C4—82no—
878C4—82no—
879C4—82no—
880C4—81no—
881C4—82no—
882C4—161no—
883C4#229311yescharacteristic
884C4#233311yescharacteristic
885C4#235711yescharacteristic
886C4#236311yescharacteristic
887C4#251611yescharacteristic
888C4#252611yescharacteristic
889C4#255411yescharacteristic
890C4#255711yescharacteristic
891C2—44no—
892C2#1400711yescharacteristic
893C2#2158111yescharacteristic
894C2#2158711yescharacteristic
895C2#2256711yescharacteristic
896C2#2258211yescharacteristic
897C2#2285911yescharacteristic
898C2#2288411yescharacteristic
899C2#2621711yescharacteristic
900C2#2622011yescharacteristic
901C2#2624211yescharacteristic
902C2#2624911yescharacteristic
903C2#2673911yescharacteristic
904C2#2674011yescharacteristic
905C2#2694511yescharacteristic
906C2#2694611yescharacteristic
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
1. C2×#1927C2semidirect
6. #11292C2semidirect
7. #11190C2semidirect
10. #10932C2semidirect
11. #10928C2semidirect
13. #10908C2semidirect
14. #10884C2semidirect
15. #10703C2semidirect
37. #1872C4semidirect

Maximal subgroups

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

subgroupindex
C2×#19272
C2×#18722
C2×#18242
#139972
C22⋊C4×C4⋊C42
#112922
#111902
#110952
#109702
#109322
#109282
#109222
#109082
#108842
#107032