Finite Group Databasebeta

← #360862

Subgroups — #360862

Order 512.

1436 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C4⋊C4C211yesmaximal, characteristic
2C2×#1916C211yesmaximal, characteristic
3C2×#1805C211yesmaximal, characteristic
4C2×C4×#103C211yesmaximal, characteristic
5#13885C211yesmaximal, characteristic
6#11373C211yesmaximal, characteristic
7#11357C211yesmaximal, characteristic
8#11227C211yesmaximal, characteristic
9#11208C211yesmaximal, characteristic
10#10885C211yesmaximal, characteristic
11#10880C211yesmaximal, characteristic
12#10789C211yesmaximal, characteristic
13#10789C211yesmaximal, characteristic
14#10789C211yesmaximal, characteristic
15#10789C211yesmaximal, characteristic
16C22×C4×Q8C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×C4×Q8C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×C4×C8C2211yescharacteristic
25Q8×C4⋊C4—24no—
26Q8×C4⋊C4C418yescomplemented
27C2×#389—21no—
28C2×#389—21no—
29C2×#389C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#384—21no—
32C2×#384C2211yescharacteristic
33C2×#382C2211yescharacteristic
34C2×C4×C4⋊C4—21no—
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37#1916—24no—
38#1805—24no—
39C4×#103—24no—
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56#1445—21no—
57#1443—21no—
58#1436—21no—
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63#1434—21no—
64C23×Q8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C2×C4×Q8—22no—
70C2×C4×Q8—22no—
71C2×C4×Q8—22no—
72C2×C4×Q8—22no—
73C2×C4×Q8—22no—
74C2×C4×Q8—22no—
75C2×C4×Q8—22no—
76C2×C4×Q8—22no—
77C2×C4×Q8—22no—
78C2×C4×Q8—22no—
79C2×C4×Q8—22no—
80C2×C4×Q8—41no—
81C2×C4×Q8—41no—
82C2×C4×Q8—41no—
83C2×C4×Q8—41no—
84C2×C4×Q8C2×C414yes—
85C2×C4×Q8C2×C414yes—
86C2×C4×Q8C2×C414yes—
87C22×C4⋊C4—21no—
88C22×C4⋊C4—21no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4—21no—
91C22×C4⋊C4—21no—
92C22×C4⋊C4—21no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4D411yescharacteristic
95C22×C4⋊C4D411yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C42—21no—
104C22×C42—21no—
105C22×C42—21no—
106C22×C42—21no—
107C22×C42C2311yescharacteristic
108C22×C42C2311yescharacteristic
109C22×C42C2311yescharacteristic
110C2×C4⋊C8—22no—
111C2×C4⋊C8—22no—
112C2×C4⋊C8—41no—
113C2×#103—22no—
114C2×#103—22no—
115C2×#103—22no—
116C2×#103—22no—
117C2×#103—22no—
118C2×#103—22no—
119C2×#103—22no—
120C2×#103—22no—
121C2×#103—22no—
122C2×#103—22no—
123C2×#103D414yes—
124C2×#103Q814yes—
125C2×C4×C8—22no—
126C2×C4×C8—22no—
127C2×C4×C8—41no—
128#389—22no—
129#389—22no—
130#389—28no—
131#389—28no—
132#389C2×C414yes—
133#389C2×C414yes—
134#384—28no—
135#384—22no—
136#384C2×C414yes—
137#382—22no—
138#382—41no—
139C4×C4⋊C4—28no—
140C4×C4⋊C4—22no—
141C4×C4⋊C4—41no—
142C4×C4⋊C4C2×C414yes—
143C4×C4⋊C4D414yes—
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×#95D411yescharacteristic
158C2×#95D411yescharacteristic
159#340—22no—
160#340—22no—
161#340—22no—
162#340—22no—
163#340—22no—
164#340—22no—
165#340—22no—
166#340—22no—
167#340—41no—
168#340—41no—
169#340—41no—
170#340—41no—
171#336—22no—
172#336—22no—
173#336—22no—
174#336—22no—
175C22×Q8—21no—
176C22×Q8—21no—
177C22×Q8—21no—
178C22×Q8—21no—
179C22×Q8—21no—
180C22×Q8—21no—
181C22×Q8—21no—
182C22×Q8C22×C412yes—
183C22×Q8C2×D412yes—
184C22×Q8C2×Q812yes—
185C22×Q8#4112yes—
186C22×Q8#4112yes—
187C22×Q8#4112yes—
188C22×Q8#4112yes—
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×C4C2×D411yescharacteristic
198C23×C4C2×D411yescharacteristic
199C23×C4C2×D411yescharacteristic
200C23×C4C2×D411yescharacteristic
201C23×C4C2×D411yescharacteristic
202C23×C4C2×D411yescharacteristic
203C23×C4C2411yescharacteristic
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8C2×D412yes—
231C22×C8C2×Q812yes—
232C4×Q8—28no—
233C4×Q8—28no—
234C4×Q8—28no—
235C4×Q8—28no—
236C4×Q8—28no—
237C4×Q8—28no—
238C4×Q8—44no—
239C4×Q8—44no—
240C4×Q8—44no—
241C4×Q8—44no—
242C4×Q8—44no—
243C4×Q8—44no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
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—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
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—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—81no—
299C2×C4⋊C4—81no—
300C2×C4⋊C4—81no—
301C2×C4⋊C4—81no—
302C2×C4⋊C4—81no—
303C2×C4⋊C4—81no—
304C2×C4⋊C4C22⋊C414yes—
305C2×C4⋊C4C22⋊C414yes—
306C2×C4⋊C4C22×C412yes—
307C2×C4⋊C4C22×C412yes—
308C2×C4⋊C4C22×C412yes—
309C2×C4⋊C4C2×D412yes—
310C2×C4⋊C4C2×Q812yes—
311C2×C4⋊C4#4112yes—
312C2×C4⋊C4#4112yes—
313C2×C42—24no—
314C2×C42—24no—
315C2×C42—24no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—24no—
329C2×C42—24no—
330C2×C42—42no—
331C2×C42—42no—
332C2×C42—42no—
333C2×C42—42no—
334C2×C42—42no—
335C2×C42—42no—
336C2×C42—81no—
337C2×C42C22×C412yes—
338C2×C42C22×C412yes—
339C2×C42C22×C412yes—
340C2×C42C2×D412yes—
341C2×C42C2×D412yes—
342C2×C42C2×D412yes—
343C4⋊C8—44no—
344#103—28no—
345#103—28no—
346#103—44no—
347#103—44no—
348C4×C8—44no—
349#95—24no—
350#95—24no—
351#95—42no—
352#95—42no—
353#95—42no—
354#95—42no—
355#95—42no—
356#95—42no—
357#95—81no—
358#95—81no—
359#95—81no—
360#95—81no—
361#95—81no—
362#95C22⋊C414yes—
363#95C22⋊C414yes—
364C24C22×D411yescharacteristic
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8#11714yes—
387C2×Q8C4×D414yes—
388C2×Q8C4×Q814yes—
389C2×Q8C22⋊Q814yes—
390C2×Q8#12314yes—
391C2×Q8#12514yes—
392C2×Q8#12614yes—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
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×C4C2×C22⋊C412yes—
482C22×C4C2×C22⋊C412yes—
483C22×C4C2×C22⋊C412yes—
484C22×C4C2×C22⋊C412yes—
485C22×C4C2×C22⋊C412yes—
486C22×C4C2×C22⋊C412yes—
487C22×C4#13512yes—
488C22×C4#13512yes—
489C22×C4#13712yes—
490C22×C4#13712yes—
491C22×C4C23×C411yescharacteristic
492C22×C4C22×D411yescharacteristic
493C22×C4C22×D411yescharacteristic
494C22×C4C22×Q811yescharacteristic
495C22×C4C2×#4111yescharacteristic
496C22×C4C2×#4111yescharacteristic
497C22×C4C2×#4111yescharacteristic
498C22×C4C2×#4111yescharacteristic
499C22×C4C2×#4111yescharacteristic
500C22×C4C2×#4111yescharacteristic
501C22×C4H(5,𝔽2)11yescharacteristic
502C22×C4H(5,𝔽2)11yescharacteristic
503C22×C42−1+411yescharacteristic
504C22×C42−1+411yescharacteristic
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C2×C8—41no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C4⋊C4—216no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—28no—
538C4⋊C4—28no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—48no—
548C4⋊C4—48no—
549C4⋊C4—41no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—41no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—48no—
558C4⋊C4—41no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C4⋊C4—41no—
562C4⋊C4—41no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—84no—
567C4⋊C4—84no—
568C4⋊C4—84no—
569C4⋊C4#11714yes—
570C42—216no—
571C42—22no—
572C42—22no—
573C42—22no—
574C42—22no—
575C42—22no—
576C42—22no—
577C42—22no—
578C42—22no—
579C42—22no—
580C42—22no—
581C42—22no—
582C42—22no—
583C42—48no—
584C42—48no—
585C42—84no—
586C23C22×C22⋊C411yescharacteristic
587C23#52511yescharacteristic
588C23#52511yescharacteristic
589C23D4211yescharacteristic
590C23#54611yescharacteristic
591C23#54811yescharacteristic
592C23D4×Q811yescharacteristic
593C23C2×#13511yescharacteristic
594C23C2×#13511yescharacteristic
595C23C2×#13711yescharacteristic
596C23C2×#13711yescharacteristic
597C23#57611yescharacteristic
598C23#57711yescharacteristic
599C23#57711yescharacteristic
600C23#57811yescharacteristic
601Q8—24no—
602Q8—24no—
603Q8—24no—
604Q8—24no—
605Q8—24no—
606Q8—24no—
607Q8—24no—
608Q8#38718yes—
609C2×C4—22no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—24no—
641C2×C4—41no—
642C2×C4—42no—
643C2×C4—41no—
644C2×C4—42no—
645C2×C4—41no—
646C2×C4—42no—
647C2×C4—41no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—81no—
676C2×C4—81no—
677C2×C4—81no—
678C2×C4—81no—
679C2×C4—81no—
680C2×C4—81no—
681C2×C4—81no—
682C2×C4—81no—
683C2×C4—81no—
684C2×C4—81no—
685C2×C4—81no—
686C2×C4—81no—
687C2×C4—81no—
688C2×C4—81no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4—81no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—81no—
705C2×C4#41614yes—
706C2×C4#41914yes—
707C2×C4C2×#11711yescharacteristic
708C2×C4C2×#11711yescharacteristic
709C2×C4C2×C4×D411yescharacteristic
710C2×C4C2×C4×Q811yescharacteristic
711C2×C4#51811yescharacteristic
712C2×C4#51911yescharacteristic
713C2×C4C2×C22⋊Q811yescharacteristic
714C2×C4C2×#12311yescharacteristic
715C2×C4#52511yescharacteristic
716C2×C4#52511yescharacteristic
717C2×C4C2×#12511yescharacteristic
718C2×C4C2×#12611yescharacteristic
719C2×C4#53911yescharacteristic
720C2×C4#53911yescharacteristic
721C2×C4#53911yescharacteristic
722C2×C4#53911yescharacteristic
723C2×C4D4211yescharacteristic
724C2×C4#54611yescharacteristic
725C2×C4#54711yescharacteristic
726C2×C4#54711yescharacteristic
727C2×C4#54811yescharacteristic
728C2×C4D4×Q811yescharacteristic
729C2×C4#55211yescharacteristic
730C2×C4#55211yescharacteristic
731C2×C4#55311yescharacteristic
732C2×C4#55311yescharacteristic
733C2×C4#55411yescharacteristic
734C2×C4#55411yescharacteristic
735C8—42no—
736C8—42no—
737C8—81no—
738C8—81no—
739C22#228011yescharacteristic
740C22D4×C22⋊C411yescharacteristic
741C22Q8×C22⋊C411yescharacteristic
742C22#244311yescharacteristic
743C22#244911yescharacteristic
744C22#247311yescharacteristic
745C22#248111yescharacteristic
746C22C2×#41611yescharacteristic
747C22C2×#41911yescharacteristic
748C22#289711yescharacteristic
749C22#289811yescharacteristic
750C22#310811yescharacteristic
751C22#310811yescharacteristic
752C22#310811yescharacteristic
753C22#310811yescharacteristic
754C22#311911yescharacteristic
755C22#312011yescharacteristic
756C22#312411yescharacteristic
757C22#312511yescharacteristic
758C22#326611yescharacteristic
759C22#327011yescharacteristic
760C22#328411yescharacteristic
761C22#328711yescharacteristic
762C22#330411yescharacteristic
763C22#330511yescharacteristic
764C22#331211yescharacteristic
765C22#332011yescharacteristic
766C22#336411yescharacteristic
767C22#336511yescharacteristic
768C22#336911yescharacteristic
769C22#337511yescharacteristic
770C22#338111yescharacteristic
771C22#338311yescharacteristic
772C22#338511yescharacteristic
773C22#338711yescharacteristic
774C4—28no—
775C4—24no—
776C4—24no—
777C4—42no—
778C4—44no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—82no—
783C4—82no—
784C4—82no—
785C4—82no—
786C4—161no—
787C4—161no—
788C4C2×#38711yescharacteristic
789C4#231311yescharacteristic
790C4#234411yescharacteristic
791C4#234511yescharacteristic
792C4#244311yescharacteristic
793C4#244911yescharacteristic
794C4#247311yescharacteristic
795C4#248111yescharacteristic
796C2#1388211yescharacteristic
797C2#2073511yescharacteristic
798C2#2074611yescharacteristic
799C2#2241811yescharacteristic
800C2#2242511yescharacteristic
801C2#2252111yescharacteristic
802C2#2252511yescharacteristic
803C2#2616111yescharacteristic
804C2#2616911yescharacteristic
805C2#2637111yescharacteristic
806C2#2637911yescharacteristic
807C2#2729511yescharacteristic
808C2#2729711yescharacteristic
809C2#2755111yescharacteristic
810C2#2755311yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C22×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
26. Q8×C4⋊C4C4semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C4⋊C42
C2×#19162
C2×#18052
C2×C4×#1032
#138852
#113732
#113572
#112272
#112082
#108852
#108802
#107892