Finite Group Databasebeta

← #678100

Subgroups — #678100

Order 512.

2766 conjugacy classes of subgroups.

The subgroup lattice has 809 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2354C211yesmaximal, characteristic
2C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
3#16008C214yesmaximal, complemented
4#15362C214yesmaximal, complemented
5#15223C212yesmaximal, complemented
6#15222C212yesmaximal
7#15157C212yesmaximal
8#15125C212yesmaximal, complemented
9#14712C211yesmaximal, characteristic, complemented
10#14129C212yesmaximal, complemented
11#14041C212yesmaximal, complemented
12#13925C212yesmaximal, complemented
13#13911C211yesmaximal, characteristic, complemented
14#13911C211yesmaximal, characteristic, complemented
15#13906C211yesmaximal, characteristic
16#13879C212yesmaximal, complemented
17C4×#390C211yesmaximal, characteristic
18C22×C4⋊Q8C2211yescharacteristic
19C22×C4×Q8C2212yes—
20C22×C4×D4C2211yescharacteristic
21C22×#117C2212yes—
22C2×#393C2214yes—
23#2354—28no—
24C4×C4⋊Q8—28no—
25C2×#391C2212yes—
26C2×#390C2211yescharacteristic
27C2×#390C2212yes—
28C2×#390C2211yescharacteristic
29C2×#390C2212yes—
30C2×#389C2211yescharacteristic
31C2×#389C2212yes—
32C2×#389C2211yescharacteristic
33C2×#389C2212yes—
34C2×#389C2212yes—
35C2×#389C2212yes—
36C2×#388C2214yes—
37C2×#384C2211yescharacteristic
38C2×#384C2211yescharacteristic
39C2×#384C2211yescharacteristic
40C2×#382C2212yes—
41C2×#382C2212yes—
42C2×#380C2212yes—
43C2×#380C2212yes—
44C2×#380C2212yes—
45C2×C4×C4⋊C4C2212yes—
46C2×C4×C4⋊C4C2211yescharacteristic
47C2×C4×C4⋊C4C2211yescharacteristic
48C2×C4×C4⋊C4C2212yes—
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C22⋊C4C2212yes—
51C2×C4×C22⋊C4C2212yes—
52C2×C43C2211yescharacteristic
53#1446C2214yes—
54#1445C2214yes—
55#1445C2214yes—
56#1442C2214yes—
57#1442C2214yes—
58#1442C2214yes—
59#1439C2214yes—
60#1439C2214yes—
61#1439C2214yes—
62#1439C2214yes—
63#1439C2214yes—
64#1439C2214yes—
65#1439C2214yes—
66#1439C2214yes—
67#1437C2212yes—
68#1437C2212yes—
69#1436C2214yes—
70#1436C2214yes—
71#1436C2214yes—
72#1436C2214yes—
73C4⋊#95C2212yes—
74C4⋊#95C2212yes—
75C4⋊#95C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2212yes—
84C4⋊#95C2211yescharacteristic
85C23×Q8C2312yes—
86C23×D4C2311yescharacteristic
87C24×C4C2312yes—
88C2×C4⋊Q8—24no—
89C2×C4⋊Q8—24no—
90C2×C4⋊Q8—24no—
91C2×C4×Q8—28no—
92C2×C4×Q8—28no—
93C2×C4×Q8—44no—
94C2×C4×D4—24no—
95C2×C4×D4—24no—
96C2×C4×D4Q818yescomplemented
97C2×#117—28no—
98C2×#117—44no—
99C2×#117—44no—
100C22×C4⋊C4C2312yes—
101C22×C4⋊C4C2312yes—
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2314yes—
119C22×C22⋊C4C2312yes—
120C22×C22⋊C4C2312yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2314yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2314yes—
128C22×C42C2312yes—
129C22×C42C2312yes—
130C22×C42C2311yescharacteristic
131C22×C42C2311yescharacteristic
132C22×C42C2311yescharacteristic
133C22×C42C2312yes—
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136C22×C42C2311yescharacteristic
137C22×C42C2314yes—
138C22×C42C2311yescharacteristic
139#393—48no—
140#391—28no—
141#390—28no—
142#390—24no—
143#390—24no—
144#390—44no—
145#389—24no—
146#389—24no—
147#389—28no—
148#389—28no—
149#389—44no—
150#389—44no—
151#388—216no—
152#384—24no—
153#384—24no—
154#384—24no—
155#382—44no—
156#382—44no—
157#380—28no—
158#380—28no—
159#380—44no—
160C4×C4⋊C4—28no—
161C4×C4⋊C4—24no—
162C4×C4⋊C4—28no—
163C4×C4⋊C4—24no—
164C4×C4⋊C4D418yes—
165C4×C22⋊C4—28no—
166C4×C22⋊C4—44no—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2312yes—
170C2×#95C2312yes—
171C2×#95C2314yes—
172C2×#95C2312yes—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2312yes—
190C43—24no—
191C25C2412yes—
192C22×Q8—24no—
193C22×Q8—24no—
194C22×Q8—24no—
195C22×Q8—24no—
196C22×Q8—24no—
197C22×Q8—42no—
198C22×Q8—42no—
199C22×D4—22no—
200C22×D4—22no—
201C22×D4—22no—
202C22×D4—22no—
203C22×D4—22no—
204C22×D4—22no—
205C22×D4C2×Q814yes—
206C23×C4—24no—
207C23×C4—24no—
208C23×C4—24no—
209C23×C4—24no—
210C23×C4—24no—
211C23×C4—24no—
212C23×C4C2×Q818yes—
213C23×C4C2414yes—
214C23×C4C2412yes—
215C23×C4C2414yes—
216C23×C4C2412yes—
217C23×C4C2412yes—
218C23×C4C2412yes—
219C23×C4C2412yes—
220C23×C4C2412yes—
221C23×C4C2411yescharacteristic
222C23×C4C2411yescharacteristic
223C23×C4C2412yes—
224C23×C4C2411yescharacteristic
225C23×C4C2411yescharacteristic
226C23×C4C2411yescharacteristic
227C23×C4C2411yescharacteristic
228C23×C4C2411yescharacteristic
229C4⋊Q8—232no—
230C4×Q8—432no—
231C4×D4—232no—
232#117—432no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—24no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—24no—
238C2×C4⋊C4—24no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4—24no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—24no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—28no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—44no—
286C2×C4⋊C4C2×D414yes—
287C2×C4⋊C4C2×D414yes—
288C2×C4⋊C4C2×Q814yes—
289C2×C4⋊C4#4114yes—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—28no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—28no—
302C2×C22⋊C4—28no—
303C2×C22⋊C4—42no—
304C2×C22⋊C4—42no—
305C2×C22⋊C4—44no—
306C2×C22⋊C4—44no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4—42no—
309C2×C22⋊C4—44no—
310C2×C22⋊C4—44no—
311C2×C22⋊C4—44no—
312C2×C22⋊C4—44no—
313C2×C22⋊C4—44no—
314C2×C22⋊C4—44no—
315C2×C22⋊C4—44no—
316C2×C22⋊C4C2×Q818yes—
317C2×C42—22no—
318C2×C42—22no—
319C2×C42—22no—
320C2×C42—24no—
321C2×C42—22no—
322C2×C42—22no—
323C2×C42—24no—
324C2×C42—22no—
325C2×C42—28no—
326C2×C42—24no—
327C2×C42—22no—
328C2×C42—22no—
329C2×C42—22no—
330C2×C42—24no—
331C2×C42—24no—
332C2×C42—24no—
333C2×C42—24no—
334C2×C42—22no—
335C2×C42—24no—
336C2×C42—22no—
337C2×C42—22no—
338C2×C42—22no—
339C2×C42—44no—
340C2×C42—44no—
341C2×C42—41no—
342C2×C42—41no—
343C2×C42C2×D418yes—
344C2×C42C2×D414yes—
345C2×C42C2×Q814yes—
346C2×C42#4114yes—
347C2×C42#4114yes—
348C2×C42#4114yes—
349C2×C42#4114yes—
350#95—28no—
351#95—24no—
352#95—24no—
353#95—24no—
354#95—24no—
355#95—24no—
356#95—24no—
357#95—28no—
358#95—28no—
359#95—28no—
360#95—44no—
361#95—44no—
362#95—42no—
363#95—42no—
364#95—44no—
365#95—44no—
366#95—44no—
367#95—44no—
368#95—44no—
369#95—44no—
370#95—44no—
371#95—44no—
372#95C2×D418yes—
373C24—22no—
374C24—22no—
375C24—22no—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24C22×Q814yes—
388C24C2511yescharacteristic
389C2×Q8—216no—
390C2×Q8—48no—
391C2×Q8—48no—
392C2×Q8—48no—
393C2×Q8—48no—
394C2×Q8—48no—
395C2×Q8—48no—
396C2×D4—28no—
397C2×D4—28no—
398C2×D4—28no—
399C2×D4—44no—
400C2×D4—44no—
401C2×D4—44no—
402C2×D4—44no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—216no—
452C22×C4—216no—
453C22×C4—216no—
454C22×C4—22no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—48no—
490C22×C4—48no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4C22×D414yes—
494C22×C4C22×D414yes—
495C22×C4C22×D412yes—
496C22×C4C22×D412yes—
497C22×C4C22×D412yes—
498C22×C4C22×Q814yes—
499C22×C4C22×Q812yes—
500C22×C4C22×Q812yes—
501C22×C4C22×Q812yes—
502C22×C4C2×#4114yes—
503C22×C4C2×#4112yes—
504C22×C4C2×#4112yes—
505C22×C4C2×#4112yes—
506C22×C4C2×#4112yes—
507C22×C4C2×#4112yes—
508C22×C4C2×#4112yes—
509C22×C4C2×#4112yes—
510C22×C4C2×#4112yes—
511C22×C4C2×#4112yes—
512C22×C4C2×#4112yes—
513C22×C4C2×#4112yes—
514C22×C4C2×#4112yes—
515C22×C4C2×#4112yes—
516C22×C4H(5,𝔽2)12yes—
517C22×C4H(5,𝔽2)12yes—
518C22×C4H(5,𝔽2)12yes—
519C22×C4H(5,𝔽2)12yes—
520C22×C42−1+412yes—
521C22×C42−1+412yes—
522C4⋊C4—216no—
523C4⋊C4—28no—
524C4⋊C4—28no—
525C4⋊C4—28no—
526C4⋊C4—28no—
527C4⋊C4—48no—
528C4⋊C4—48no—
529C4⋊C4—48no—
530C4⋊C4—48no—
531C4⋊C4—48no—
532C4⋊C4—44no—
533C4⋊C4—48no—
534C4⋊C4—48no—
535C4⋊C4—44no—
536C4⋊C4—48no—
537C4⋊C4—44no—
538C4⋊C4—48no—
539C4⋊C4—84no—
540C4⋊C4—88no—
541C22⋊C4—216no—
542C22⋊C4—48no—
543C22⋊C4—48no—
544C22⋊C4—416no—
545C22⋊C4—48no—
546C22⋊C4—48no—
547C22⋊C4—88no—
548C22⋊C4—88no—
549C22⋊C4—88no—
550C42—28no—
551C42—216no—
552C42—28no—
553C42—28no—
554C42—44no—
555C42—44no—
556C42—416no—
557C42—44no—
558C42—48no—
559C42—48no—
560C42C22⋊Q8116yes—
561C23—24no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23C23×D411yescharacteristic
597C23C23×Q811yescharacteristic
598C23C22×#4111yescharacteristic
599C23C22×#4111yescharacteristic
600C23C22×#4111yescharacteristic
601C23C22×#4111yescharacteristic
602C23C22×#4111yescharacteristic
603C23C2×H(5,𝔽2)11yescharacteristic
604C23C2×H(5,𝔽2)11yescharacteristic
605C23C2×H(5,𝔽2)11yescharacteristic
606C23C2×H(5,𝔽2)11yescharacteristic
607C23C2×2−1+411yescharacteristic
608C23C2×2−1+411yescharacteristic
609C23#58511yescharacteristic
610C23#58511yescharacteristic
611Q8—432no—
612D4—416no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—22no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—41no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—432no—
674C2×C4—44no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—44no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—44no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—42no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—44no—
709C2×C4C2×C22⋊Q814yes—
710C2×C4C2×C22⋊Q814yes—
711C2×C4C2×C22⋊Q814yes—
712C2×C4#52514yes—
713C2×C4#53314yes—
714C2×C4#53514yes—
715C2×C4#54414yes—
716C2×C4#54614yes—
717C2×C4#54814yes—
718C2×C4#55414yes—
719C2×C4#55414yes—
720C2×C4#55514yes—
721C2×C4#55514yes—
722C2×C4#55614yes—
723C2×C4#55614yes—
724C2×C4#55914yes—
725C2×C4#55914yes—
726C22—44no—
727C22—44no—
728C22—44no—
729C22—44no—
730C22—44no—
731C22—44no—
732C22—44no—
733C22—82no—
734C22—82no—
735C22—82no—
736C22—82no—
737C22—82no—
738C22—82no—
739C22—82no—
740C22—82no—
741C22C22×C22⋊Q811yescharacteristic
742C22C2×#52511yescharacteristic
743C22C2×#53311yescharacteristic
744C22C2×#53511yescharacteristic
745C22C2×#54411yescharacteristic
746C22C2×#54611yescharacteristic
747C22C2×#54811yescharacteristic
748C22C2×#55411yescharacteristic
749C22C2×#55411yescharacteristic
750C22C2×#55511yescharacteristic
751C22C2×#55511yescharacteristic
752C22C2×#55611yescharacteristic
753C22C2×#55611yescharacteristic
754C22#347511yescharacteristic
755C22C2×#55911yescharacteristic
756C22C2×#55911yescharacteristic
757C22#348011yescharacteristic
758C22#348811yescharacteristic
759C22#348911yescharacteristic
760C22#350311yescharacteristic
761C22#350411yescharacteristic
762C22#350611yescharacteristic
763C22#350611yescharacteristic
764C22#350611yescharacteristic
765C22#350611yescharacteristic
766C22#350711yescharacteristic
767C22#350711yescharacteristic
768C22#350811yescharacteristic
769C22#351111yescharacteristic
770C22#351911yescharacteristic
771C22#352311yescharacteristic
772C22#354611yescharacteristic
773C22#354811yescharacteristic
774C22#354811yescharacteristic
775C22#355411yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—42no—
780C4—44no—
781C4—42no—
782C4—44no—
783C4—44no—
784C4—44no—
785C4—84no—
786C4—82no—
787C4—82no—
788C4—82no—
789C4—84no—
790C4#243918yes—
791C4#258018yes—
792C2—84no—
793C2C2×#243911yescharacteristic
794C2C2×#258011yescharacteristic
795C2#3551911yescharacteristic
796C2#3616011yescharacteristic
797C2#3619411yescharacteristic
798C2#3641611yescharacteristic
799C2#3657911yescharacteristic
800C2#3896511yescharacteristic
801C2#3947111yescharacteristic
802C2#3949811yescharacteristic
803C2#3972511yescharacteristic
804C2#5963911yescharacteristic
805C2#5964011yescharacteristic
806C2#5986311yescharacteristic
807C2#5986311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×C4×C4⋊Q8C2semidirect
3. #16008C2semidirect
4. #15362C2semidirect
5. #15223C2semidirect
8. #15125C2semidirect
9. #14712C2semidirect
10. #14129C2semidirect
11. #14041C2semidirect
12. #13925C2semidirect
13. #13911C2semidirect
14. #13911C2semidirect
16. #13879C2semidirect
96. C2×C4×D4Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#23542
C2×C4×C4⋊Q82
#160082
#153622
#152232
#152222
#151572
#151252
#147122
#141292
#140412
#139252
#139112
#139062
#138792
C4×#3902