Finite Group Databasebeta

← #522180

Subgroups — #522180

Order 512.

3002 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic
2C2×#2365C211yesmaximal, characteristic, complemented
3C2×#2285C211yesmaximal, characteristic
4#14386C214yesmaximal, complemented
5#14370C214yesmaximal
6#14264C212yesmaximal
7#14155C211yesmaximal, characteristic, complemented
8#14151C211yesmaximal, characteristic, complemented
9#14045C212yesmaximal, complemented
10#14041C212yesmaximal, complemented
11#14000C212yesmaximal, complemented
12#13997C212yesmaximal
13#13976C212yesmaximal, complemented
14#13969C212yesmaximal
15C4⋊C42C211yesmaximal, characteristic, complemented
16#13777C212yesmaximal
17C4×#380C211yesmaximal, characteristic
18C22×C4⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2212yes—
20C22×C4×Q8C2212yes—
21C22×#117C2212yes—
22C23×C42C2211yescharacteristic
23#2857C4116yescomplemented
24#2365—28no—
25C2×#391C2212yes—
26C2×#391C2212yes—
27C2×#391C2212yes—
28C2×#391C2212yes—
29C2×#389C2212yes—
30C2×#389C2212yes—
31C2×#389C2212yes—
32C2×#389C2212yes—
33C2×#389C2212yes—
34C2×#387C2214yes—
35#2285—28no—
36C2×#384C2211yescharacteristic
37C2×#384C2211yescharacteristic
38C2×#384C2211yescharacteristic
39C2×#382C2212yes—
40C2×#380C2212yes—
41C2×#380C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×#380C2211yescharacteristic
44C2×#380C2212yes—
45C2×#380C2212yes—
46C2×#380C2211yescharacteristic
47C2×C4×C4⋊C4C2211yescharacteristic
48C2×C4×C4⋊C4C2211yescharacteristic
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C4⋊C4C2212yes—
51C2×C4×C4⋊C4C2212yes—
52C2×C4×C4⋊C4C2212yes—
53C2×C4×C4⋊C4C2212yes—
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2212yes—
56#1445C2214yes—
57#1445C2214yes—
58#1444C2214yes—
59#1444C2214yes—
60#1442C2214yes—
61#1442C2214yes—
62#1441C2214yes—
63#1441C2214yes—
64#1439C2214yes—
65#1439C2214yes—
66#1437C2214yes—
67#1437C2214yes—
68#1436C2214yes—
69#1436C2214yes—
70#1436C2214yes—
71#1436C2214yes—
72#1436C2214yes—
73#1436C2214yes—
74C4⋊#95C2214yes—
75C4⋊#95C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83#1434C2212yes—
84C22⋊#95C2212yes—
85C4×#95C2212yes—
86C23×Q8C2312yes—
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C2×C4⋊Q8—24no—
91C2×C4⋊Q8—24no—
92C2×C4⋊Q8C2×C418yes—
93C2×C22⋊Q8—44no—
94C2×C22⋊Q8—44no—
95C2×C22⋊Q8C2×C4116yes—
96C2×C4×Q8—28no—
97C2×C4×Q8—44no—
98C2×C4×Q8—44no—
99C2×#117—28no—
100C2×#117—28no—
101C2×#117—44no—
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2314yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2312yes—
122C22×C22⋊C4C2312yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2312yes—
127C22×C42—24no—
128C22×C42—24no—
129C22×C42C2×C418yes—
130C22×C42C2312yes—
131C22×C42C2312yes—
132C22×C42C2312yes—
133C22×C42C2311yescharacteristic
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136C22×C42C2312yes—
137C22×C42C2314yes—
138C22×C42C2314yes—
139C22×C42C2311yescharacteristic
140#391—28no—
141#391—44no—
142#391—44no—
143#391C2×C4116yes—
144#389—28no—
145#389—44no—
146#389—44no—
147#389C2×C4116yes—
148#389C2×C4116yes—
149#387—216no—
150#384—24no—
151#384—24no—
152#384C2×C418yes—
153#382—28no—
154#380—24no—
155#380—24no—
156#380—24no—
157#380—28no—
158#380C2×C4116yes—
159#380C2×C4116yes—
160#380Q818yescomplemented
161C4×C4⋊C4—24no—
162C4×C4⋊C4—28no—
163C4×C4⋊C4—28no—
164C4×C4⋊C4—24no—
165C4×C4⋊C4—24no—
166C4×C4⋊C4—44no—
167C4×C4⋊C4—44no—
168C4×C4⋊C4D418yes—
169C4×C22⋊C4—44no—
170C2×#95C2312yes—
171C2×#95C2312yes—
172C2×#95C2312yes—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2314yes—
177C2×#95C2312yes—
178C2×#95C2314yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C25C2411yescharacteristic
197C22×Q8—24no—
198C22×Q8—24no—
199C22×Q8—24no—
200C22×Q8—24no—
201C22×Q8—24no—
202C22×Q8—24no—
203C22×Q8C22×C418yes—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—41no—
219C23×C4—41no—
220C23×C4C22×C414yes—
221C23×C4C22×C414yes—
222C23×C4C22×C414yes—
223C23×C4C2×Q814yes—
224C23×C4#4114yes—
225C23×C4C2412yes—
226C23×C4C2412yes—
227C23×C4C2412yes—
228C23×C4C2412yes—
229C23×C4C2414yes—
230C23×C4C2414yes—
231C23×C4C2411yescharacteristic
232C23×C4C2412yes—
233C23×C4C2412yes—
234C23×C4C2412yes—
235C23×C4C2412yes—
236C23×C4C2411yescharacteristic
237C23×C4C2411yescharacteristic
238C23×C4C2411yescharacteristic
239C23×C4C2411yescharacteristic
240C23×C4C2411yescharacteristic
241C4⋊Q8—232no—
242C22⋊Q8—432no—
243C4×Q8—432no—
244#117—432no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—24no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—28no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—44no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4—44no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4C22×C418yes—
296C2×C4⋊C4C22×C418yes—
297C2×C4⋊C4C22×C418yes—
298C2×C4⋊C4C22×C418yes—
299C2×C4⋊C4C22×C4116yes—
300C2×C4⋊C4C22×C418yes—
301C2×C4⋊C4C2×D414yes—
302C2×C4⋊C4C2×D414yes—
303C2×C4⋊C4C2×Q814yes—
304C2×C4⋊C4C2×Q814yes—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4—42no—
312C2×C22⋊C4—42no—
313C2×C22⋊C4—42no—
314C2×C22⋊C4—44no—
315C2×C22⋊C4—44no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4C22×C4116yes—
319C2×C22⋊C4C2×Q818yes—
320C2×C42—22no—
321C2×C42—22no—
322C2×C42—22no—
323C2×C42—24no—
324C2×C42—22no—
325C2×C42—22no—
326C2×C42—22no—
327C2×C42—24no—
328C2×C42—232no—
329C2×C42—24no—
330C2×C42—28no—
331C2×C42—24no—
332C2×C42—24no—
333C2×C42—24no—
334C2×C42—24no—
335C2×C42—24no—
336C2×C42—24no—
337C2×C42—24no—
338C2×C42—24no—
339C2×C42—44no—
340C2×C42—44no—
341C2×C42—44no—
342C2×C42—44no—
343C2×C42—44no—
344C2×C42C22×C414yes—
345C2×C42C22×C414yes—
346C2×C42C22×C414yes—
347C2×C42C22×C414yes—
348C2×C42C2×D418yes—
349C2×C42C2×D414yes—
350C2×C42#4114yes—
351#95—24no—
352#95—24no—
353#95—24no—
354#95—24no—
355#95—28no—
356#95—28no—
357#95—24no—
358#95—24no—
359#95—24no—
360#95—24no—
361#95—44no—
362#95—44no—
363#95—42no—
364#95—42no—
365#95—44no—
366#95—44no—
367#95—44no—
368#95—44no—
369#95—44no—
370#95—44no—
371#95—44no—
372#95—44no—
373#95C22×C4116yes—
374#95C22×C4116yes—
375#95C2×D418yes—
376#95C2×Q818yes—
377C24—21no—
378C24—21no—
379C24—21no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—21no—
389C24C23×C412yes—
390C24C22×Q812yes—
391C24C2×#4112yes—
392C24C2511yescharacteristic
393C2×Q8—216no—
394C2×Q8—216no—
395C2×Q8—216no—
396C2×Q8—48no—
397C2×Q8—48no—
398C2×Q8—48no—
399C2×Q8—48no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
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—28no—
413C22×C4—28no—
414C22×C4—28no—
415C22×C4—28no—
416C22×C4—28no—
417C22×C4—28no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—24no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—24no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—24no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—28no—
461C22×C4—28no—
462C22×C4—28no—
463C22×C4—28no—
464C22×C4—28no—
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—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—44no—
494C22×C4—44no—
495C22×C4—44no—
496C22×C4—44no—
497C22×C4—44no—
498C22×C4—44no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4C4×Q8116yescomplemented
503C22×C4C23×C418yes—
504C22×C4C23×C418yes—
505C22×C4C23×C412yes—
506C22×C4C23×C412yes—
507C22×C4C23×C412yes—
508C22×C4C23×C412yes—
509C22×C4C23×C412yes—
510C22×C4C23×C412yes—
511C22×C4C22×D414yes—
512C22×C4C22×D414yes—
513C22×C4C22×D412yes—
514C22×C4C22×D412yes—
515C22×C4C22×D412yes—
516C22×C4C22×Q814yes—
517C22×C4C22×Q814yes—
518C22×C4C22×Q812yes—
519C22×C4C22×Q812yes—
520C22×C4C2×#4112yes—
521C22×C4C2×#4112yes—
522C22×C4C2×#4112yes—
523C22×C4C2×#4112yes—
524C22×C4C2×#4112yes—
525C22×C4H(5,𝔽2)12yes—
526C22×C4H(5,𝔽2)12yes—
527C22×C4H(5,𝔽2)12yes—
528C22×C4H(5,𝔽2)12yes—
529C22×C42−1+412yes—
530C22×C42−1+412yes—
531C22×C42−1+412yes—
532C22×C42−1+412yes—
533C4⋊C4—216no—
534C4⋊C4—216no—
535C4⋊C4—216no—
536C4⋊C4—216no—
537C4⋊C4—28no—
538C4⋊C4—28no—
539C4⋊C4—28no—
540C4⋊C4—28no—
541C4⋊C4—48no—
542C4⋊C4—416no—
543C4⋊C4—48no—
544C4⋊C4—48no—
545C4⋊C4—48no—
546C4⋊C4—48no—
547C4⋊C4—416no—
548C4⋊C4—44no—
549C4⋊C4—44no—
550C4⋊C4—44no—
551C4⋊C4—44no—
552C4⋊C4—88no—
553C22⋊C4—416no—
554C22⋊C4—48no—
555C22⋊C4—48no—
556C22⋊C4—48no—
557C22⋊C4—48no—
558C42—28no—
559C42—28no—
560C42—28no—
561C42—216no—
562C42—416no—
563C42—48no—
564C42—48no—
565C42—48no—
566C42—88no—
567C42C4×D4116yes—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23C2×C4×Q814yes—
603C23C24×C411yescharacteristic
604C23C23×D411yescharacteristic
605C23C23×Q811yescharacteristic
606C23C22×#4111yescharacteristic
607C23C22×#4111yescharacteristic
608C23C2×H(5,𝔽2)11yescharacteristic
609C23C2×H(5,𝔽2)11yescharacteristic
610C23C2×H(5,𝔽2)11yescharacteristic
611C23C2×H(5,𝔽2)11yescharacteristic
612C23C2×2−1+411yescharacteristic
613C23C2×2−1+411yescharacteristic
614C23C2×2−1+411yescharacteristic
615C23C2×2−1+411yescharacteristic
616C23#58511yescharacteristic
617C23#58511yescharacteristic
618Q8—432no—
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—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—232no—
638C2×C4—22no—
639C2×C4—28no—
640C2×C4—28no—
641C2×C4—28no—
642C2×C4—22no—
643C2×C4—28no—
644C2×C4—22no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—416no—
660C2×C4—42no—
661C2×C4—44no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—44no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—44no—
668C2×C4—41no—
669C2×C4—44no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—42no—
688C2×C4—416no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4C2×C4×D414yes—
718C2×C4C2×C4×D414yes—
719C2×C4C2×C4×D414yes—
720C2×C4C2×C4×Q814yes—
721C2×C4C2×C4×Q814yes—
722C2×C4#51814yes—
723C2×C4#51914yes—
724C2×C4#52014yes—
725C2×C4#52014yes—
726C2×C4#53514yes—
727C2×C4#53714yes—
728C2×C4#54014yes—
729C2×C4#54214yes—
730C2×C4#54614yes—
731C2×C4D4×Q814yes—
732C2×C4#55214yes—
733C2×C4#55414yes—
734C22—24no—
735C22—24no—
736C22—24no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22C22×C4×D411yescharacteristic
750C22C22×C4×Q811yescharacteristic
751C22C2×#51811yescharacteristic
752C22C2×#51911yescharacteristic
753C22C2×#52011yescharacteristic
754C22C2×#52011yescharacteristic
755C22#342811yescharacteristic
756C22C2×#53511yescharacteristic
757C22C2×#53711yescharacteristic
758C22C2×#54011yescharacteristic
759C22C2×#54211yescharacteristic
760C22C2×#54611yescharacteristic
761C22C2×D4×Q811yescharacteristic
762C22C2×#55211yescharacteristic
763C22C2×#55411yescharacteristic
764C22#348911yescharacteristic
765C22#348911yescharacteristic
766C22#349511yescharacteristic
767C22#349511yescharacteristic
768C22#350111yescharacteristic
769C22#350211yescharacteristic
770C22#350311yescharacteristic
771C22#350311yescharacteristic
772C22#350611yescharacteristic
773C22#350711yescharacteristic
774C22#351111yescharacteristic
775C22#351111yescharacteristic
776C22#354611yescharacteristic
777C22#354611yescharacteristic
778C22#354811yescharacteristic
779C22#355011yescharacteristic
780C22#355011yescharacteristic
781C22#355411yescharacteristic
782C22#355411yescharacteristic
783C22#355611yescharacteristic
784C4—24no—
785C4—24no—
786C4—24no—
787C4—42no—
788C4—48no—
789C4—44no—
790C4—44no—
791C4—48no—
792C4—44no—
793C4—44no—
794C4—82no—
795C4—82no—
796C4—82no—
797C4—82no—
798C4#232418yes—
799C4#236018yes—
800C2—44no—
801C2C2×#232411yescharacteristic
802C2C2×#236011yescharacteristic
803C2#3420311yescharacteristic
804C2#3421311yescharacteristic
805C2#3421611yescharacteristic
806C2#3437411yescharacteristic
807C2#3439311yescharacteristic
808C2#3946811yescharacteristic
809C2#3947111yescharacteristic
810C2#3947811yescharacteristic
811C2#3948111yescharacteristic
812C2#3959611yescharacteristic
813C2#3959911yescharacteristic
814C2#3960611yescharacteristic
815C2#3960911yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2365C2semidirect
4. #14386C2semidirect
7. #14155C2semidirect
8. #14151C2semidirect
9. #14045C2semidirect
10. #14041C2semidirect
11. #14000C2semidirect
13. #13976C2semidirect
15. C4⋊C42C2semidirect
23. #2857C4semidirect
160. #380Q8semidirect
502. C22×C4C4×Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×#23652
C2×#22852
#143862
#143702
#142642
#141552
#141512
#140452
#140412
#140002
#139972
#139762
#139692
C4⋊C422
#137772
C4×#3802