Finite Group Databasebeta

← #424655

Subgroups — #424655

Order 512.

1462 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2451C211yesmaximal, characteristic
2C2×#2024C211yesmaximal, characteristic
3C2×#1878C211yesmaximal, characteristic
4C2×#1878C211yesmaximal, characteristic
5C2×#1863C211yesmaximal, characteristic
6#13926C211yesmaximal, characteristic
7#11384C211yesmaximal, characteristic
8#11346C211yesmaximal, characteristic
9#11219C211yesmaximal, characteristic
10#11207C211yesmaximal, characteristic
11#11124C211yesmaximal, characteristic
12#11067C211yesmaximal, characteristic
13#11050C211yesmaximal, characteristic
14#11024C211yesmaximal, characteristic
15#10789C211yesmaximal, characteristic
16C23×Q16C2211yescharacteristic
17C22×C4⋊Q8C2211yescharacteristic
18C22×C4×Q8C2211yescharacteristic
19C22×C4×Q8C2211yescharacteristic
20C22×#107C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C22×#103C2211yescharacteristic
26C22×#103C2211yescharacteristic
27#2451—24no—
28#2451—24no—
29C2×#398—21no—
30C2×#395—21no—
31C2×#391—21no—
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#389C2211yescharacteristic
38C2×#387—21no—
39C2×#384C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41#2024—24no—
42#1878—24no—
43#1878—24no—
44#1863—24no—
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59#1441—21no—
60#1441—21no—
61C4⋊#95—21no—
62C4⋊#95—21no—
63C4⋊#95C2211yescharacteristic
64C4⋊#95C2211yescharacteristic
65C23×Q8—21no—
66C23×Q8C2311yescharacteristic
67C23×Q8C2311yescharacteristic
68C22×Q16—22no—
69C22×Q16—22no—
70C22×Q16—22no—
71C22×Q16—22no—
72C22×Q16—41no—
73C22×Q16—41no—
74C22×Q16Q814yescomplemented
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C2×C4⋊Q8—22no—
80C2×C4⋊Q8—22no—
81C2×C4⋊Q8—22no—
82C2×C4⋊Q8—22no—
83C2×C4⋊Q8—41no—
84C2×C4⋊Q8—41no—
85C2×C4×Q8—22no—
86C2×C4×Q8—22no—
87C2×C4×Q8—22no—
88C2×C4×Q8—22no—
89C2×C4×Q8—22no—
90C2×C4×Q8—22no—
91C2×C4×Q8—22no—
92C2×C4×Q8—22no—
93C2×C4×Q8—41no—
94C2×C4×Q8—41no—
95C2×C4×Q8—41no—
96C2×C4×Q8—41no—
97C22×C4⋊C4—21no—
98C22×C4⋊C4—21no—
99C22×C4⋊C4—21no—
100C22×C4⋊C4—21no—
101C22×C4⋊C4—21no—
102C22×C4⋊C4—21no—
103C22×C4⋊C4—21no—
104C22×C4⋊C4D411yescharacteristic
105C22×C4⋊C4D411yescharacteristic
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C42—21no—
113C22×C42—21no—
114C22×C42C2311yescharacteristic
115C22×C42C2311yescharacteristic
116C22×C42C2311yescharacteristic
117C2×#107—22no—
118C2×#107—22no—
119C2×#107—41no—
120C2×#103—22no—
121C2×#103—22no—
122C2×#103—22no—
123C2×#103—22no—
124C2×#103—22no—
125C2×#103—22no—
126C2×#103—22no—
127C2×#103—22no—
128C2×#103—22no—
129C2×#103—22no—
130C2×#103—22no—
131C2×#103—41no—
132C2×#103—41no—
133C2×#103—41no—
134C2×#103—41no—
135C2×#103—41no—
136C2×#103—41no—
137C2×#103D414yes—
138#398—28no—
139#395—28no—
140#391—28no—
141#391—22no—
142#391—22no—
143#391—22no—
144#391—22no—
145#391—22no—
146#391—41no—
147#391—41no—
148#391D414yes—
149#389—22no—
150#389—22no—
151#389—22no—
152#389D414yes—
153#387—28no—
154#384—41no—
155#384—41no—
156C4×C4⋊C4—22no—
157C4×C4⋊C4—22no—
158C2×#95—21no—
159C2×#95—21no—
160C2×#95—21no—
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—22no—
177#340—22no—
178#340—22no—
179#340—41no—
180#340—41no—
181#340—41no—
182#336—22no—
183#336—22no—
184#336—22no—
185#336—22no—
186#336—41no—
187#336—41no—
188C22×Q8—24no—
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×Q8—21no—
202C22×Q8—21no—
203C22×Q8—21no—
204C22×Q8—21no—
205C22×Q8—21no—
206C22×Q8—21no—
207C22×Q8—21no—
208C22×Q8—21no—
209C22×Q8—21no—
210C22×Q8—21no—
211C22×Q8—42no—
212C22×Q8—42no—
213C22×Q8—42no—
214C22×Q8—42no—
215C22×Q8—81no—
216C22×Q8—81no—
217C22×Q8C2×D412yes—
218C22×Q8C2×D412yes—
219C22×Q8C2×Q812yes—
220C22×Q8C2×Q812yes—
221C22×Q8#4112yes—
222C22×Q8#4112yes—
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×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C23×C4C2×D411yescharacteristic
235C23×C4C2×D411yescharacteristic
236C23×C4C2×D411yescharacteristic
237C23×C4C2411yescharacteristic
238C2×Q16—28no—
239C2×Q16—28no—
240C2×Q16—44no—
241C2×Q16—44no—
242C2×Q16—44no—
243C2×Q16—44no—
244C2×Q16—44no—
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—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8C2×D412yes—
272C22×C8C2×Q812yes—
273C4⋊Q8—44no—
274C4⋊Q8—44no—
275C4⋊Q8—44no—
276C4⋊Q8—44no—
277C4×Q8—44no—
278C4×Q8—44no—
279C4×Q8—44no—
280C4×Q8—44no—
281C4×Q8—44no—
282C4×Q8—44no—
283C4×Q8—44no—
284C4×Q8—44no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
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—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
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—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—41no—
325C2×C4⋊C4—42no—
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—42no—
335C2×C4⋊C4—81no—
336C2×C4⋊C4—81no—
337C2×C4⋊C4—81no—
338C2×C4⋊C4—81no—
339C2×C4⋊C4—81no—
340C2×C4⋊C4—81no—
341C2×C4⋊C4Q1614yescomplemented
342C2×C4⋊C4C2×D412yes—
343C2×C4⋊C4C2×D412yes—
344C2×C4⋊C4C2×D412yes—
345C2×C4⋊C4C2×D412yes—
346C2×C4⋊C4#4112yes—
347C2×C4⋊C4#4112yes—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—21no—
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—42no—
367C2×C42—42no—
368C2×C42—42no—
369C2×C42—42no—
370C2×C42C2×D412yes—
371C2×C42C2×D412yes—
372#107—44no—
373#103—28no—
374#103—44no—
375#103—44no—
376#103—44no—
377#103—44no—
378#103—44no—
379#95—24no—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—22no—
386#95—22no—
387#95—42no—
388#95—42no—
389#95—42no—
390#95—42no—
391#95—81no—
392#95—81no—
393#95—81no—
394#95—81no—
395C24C22×D411yescharacteristic
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—48no—
427C2×Q8—48no—
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—
445C2×Q8—41no—
446C2×Q8—41no—
447C2×Q8—41no—
448C2×Q8—41no—
449C2×Q8—41no—
450C2×Q8—41no—
451C2×Q8—41no—
452C2×Q8—84no—
453C2×Q8—84no—
454C2×Q8—84no—
455C2×Q8—84no—
456C2×Q8—84no—
457C2×Q8C22⋊Q814yes—
458C2×Q8C22⋊Q814yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
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—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#12012yes—
551C22×C4#12012yes—
552C22×C4C2×Q1612yes—
553C22×C4C2×Q1612yes—
554C22×C4C2×Q1612yes—
555C22×C4#13712yes—
556C22×C4#13712yes—
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×Q811yescharacteristic
561C22×C4C2×#4111yescharacteristic
562C22×C4C2×#4111yescharacteristic
563C22×C4C2×#4111yescharacteristic
564C22×C4C2×#4111yescharacteristic
565C22×C4H(5,𝔽2)11yescharacteristic
566C22×C4H(5,𝔽2)11yescharacteristic
567C22×C4H(5,𝔽2)11yescharacteristic
568C22×C4H(5,𝔽2)11yescharacteristic
569C22×C42−1+411yescharacteristic
570C22×C42−1+411yescharacteristic
571Q16—416no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C2×C8—41no—
598C2×C8—41no—
599C2×C8—41no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—28no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—44no—
611C4⋊C4—48no—
612C4⋊C4—48no—
613C4⋊C4—48no—
614C4⋊C4—41no—
615C4⋊C4—41no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4—41no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—41no—
623C4⋊C4—41no—
624C4⋊C4—41no—
625C4⋊C4—41no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—84no—
629C4⋊C4—84no—
630C4⋊C4—84no—
631C4⋊C4—84no—
632C4⋊C4#12114yes—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—48no—
638C42—48no—
639C42—41no—
640C42—41no—
641C42—41no—
642C42—41no—
643C42—41no—
644C42—41no—
645C42—41no—
646C42—41no—
647C23C2×#12011yescharacteristic
648C23#52511yescharacteristic
649C23#53511yescharacteristic
650C23D4211yescharacteristic
651C23#54611yescharacteristic
652C23#54811yescharacteristic
653C23D4×Q811yescharacteristic
654C23C22×Q1611yescharacteristic
655C23C2×#13711yescharacteristic
656C23C2×#13711yescharacteristic
657C23#57511yescharacteristic
658C23#57611yescharacteristic
659C23#57711yescharacteristic
660C23#57711yescharacteristic
661C23#57811yescharacteristic
662Q8—24no—
663Q8—24no—
664Q8—24no—
665Q8—24no—
666Q8—42no—
667Q8—42no—
668Q8—42no—
669Q8—42no—
670Q8—42no—
671Q8—42no—
672Q8—42no—
673Q8—42no—
674Q8—42no—
675Q8—42no—
676Q8—42no—
677Q8—42no—
678Q8—816no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—81no—
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#45114yes—
777C2×C4C2×#12111yescharacteristic
778C2×C4C2×C22⋊Q811yescharacteristic
779C2×C4C2×C22⋊Q811yescharacteristic
780C2×C4#52911yescharacteristic
781C2×C4#53511yescharacteristic
782C2×C4#53611yescharacteristic
783C2×C4#53711yescharacteristic
784C2×C4#53811yescharacteristic
785C2×C4#53911yescharacteristic
786C2×C4#54211yescharacteristic
787C2×C4#54211yescharacteristic
788C2×C4#54311yescharacteristic
789C2×C4D4211yescharacteristic
790C2×C4#54611yescharacteristic
791C2×C4#54611yescharacteristic
792C2×C4#54611yescharacteristic
793C2×C4#54611yescharacteristic
794C2×C4#54611yescharacteristic
795C2×C4#54611yescharacteristic
796C2×C4#54711yescharacteristic
797C2×C4#54811yescharacteristic
798C2×C4D4×Q811yescharacteristic
799C2×C4#55111yescharacteristic
800C2×C4#55211yescharacteristic
801C2×C4#55411yescharacteristic
802C2×C4#55411yescharacteristic
803C2×C4#56211yescharacteristic
804C2×C4#56211yescharacteristic
805C8—42no—
806C8—42no—
807C8—81no—
808C8—81no—
809C22#240411yescharacteristic
810C22#240811yescharacteristic
811C22#240911yescharacteristic
812C22#244911yescharacteristic
813C22#247711yescharacteristic
814C22#267611yescharacteristic
815C22#269211yescharacteristic
816C22C2×#45111yescharacteristic
817C22#300711yescharacteristic
818C22#301211yescharacteristic
819C22#301311yescharacteristic
820C22#310411yescharacteristic
821C22#311311yescharacteristic
822C22#312411yescharacteristic
823C22#312511yescharacteristic
824C22#320911yescharacteristic
825C22#321511yescharacteristic
826C22#322411yescharacteristic
827C22#322511yescharacteristic
828C22#326611yescharacteristic
829C22#326811yescharacteristic
830C22#327811yescharacteristic
831C22D4×Q1611yescharacteristic
832C22#329911yescharacteristic
833C22#331111yescharacteristic
834C22#331411yescharacteristic
835C22#332811yescharacteristic
836C22#336311yescharacteristic
837C22#337111yescharacteristic
838C22#337411yescharacteristic
839C22#337511yescharacteristic
840C22Q8×Q1611yescharacteristic
841C22#338711yescharacteristic
842C22#338711yescharacteristic
843C22#339011yescharacteristic
844C4—24no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—42no—
849C4—44no—
850C4—44no—
851C4—44no—
852C4—82no—
853C4—82no—
854C4—81no—
855C4—82no—
856C4—161no—
857C4—161no—
858C4#241711yescharacteristic
859C4#242711yescharacteristic
860C4#243711yescharacteristic
861C4#245011yescharacteristic
862C4#267211yescharacteristic
863C4#268711yescharacteristic
864C4#269211yescharacteristic
865C4#269611yescharacteristic
866C2#1532311yescharacteristic
867C2#2393411yescharacteristic
868C2#2394711yescharacteristic
869C2#2424311yescharacteristic
870C2#2425911yescharacteristic
871C2#2433311yescharacteristic
872C2#2434811yescharacteristic
873C2#2638111yescharacteristic
874C2#2638911yescharacteristic
875C2#2742811yescharacteristic
876C2#2744111yescharacteristic
877C2#3088011yescharacteristic
878C2#3090511yescharacteristic
879C2#3152411yescharacteristic
880C2#3154511yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
74. C22×Q16Q8semidirect
341. C2×C4⋊C4Q16semidirect

Maximal subgroups

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

subgroupindex
C2×#24512
C2×#20242
C2×#18782
C2×#18632
#139262
#113842
#113462
#112192
#112072
#111242
#110672
#110502
#110242
#107892