Finite Group Databasebeta

← #676463

Subgroups — #676463

Order 512.

2890 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2582C211yesmaximal, characteristic, complemented
2C2×#2355C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Q8C211yesmaximal, characteristic
4C2×C4×C22⋊Q8C211yesmaximal, characteristic
5#15873C214yesmaximal, complemented
6#15441C214yesmaximal
7#15237C212yesmaximal, complemented
8#15220C212yesmaximal
9#15192C212yesmaximal, complemented
10#15182C212yesmaximal
11#14686C211yesmaximal, characteristic
12#14151C212yesmaximal, complemented
13#14046C212yesmaximal, complemented
14#13997C212yesmaximal
15#13993C212yesmaximal
16#13926C211yesmaximal, characteristic, complemented
17#13910C211yesmaximal, characteristic, complemented
18C22×C22⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C4×Q8C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22C23×C42C2211yescharacteristic
23#2582—28no—
24C2×#398C2214yes—
25#2355—28no—
26C4×C22⋊Q8—28no—
27C4×C22⋊Q8—28no—
28C2×#391C2212yes—
29C2×#391C2212yes—
30C2×#391C2211yescharacteristic
31C2×#391C2211yescharacteristic
32C2×#391C2212yes—
33C2×#391C2212yes—
34C2×#389C2211yescharacteristic
35C2×#389C2212yes—
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#389C2211yescharacteristic
39C2×#389C2214yes—
40C2×#389C2212yes—
41C2×#387C2212yes—
42C2×#387C2212yes—
43C2×#387C2214yes—
44C2×#385C2212yes—
45C2×#385C2212yes—
46C2×#384C2211yescharacteristic
47C2×#384C2212yes—
48C2×#384C2211yescharacteristic
49C2×#382C2212yes—
50C2×#380C2212yes—
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2212yes—
54C2×#380C2212yes—
55C2×C4×C4⋊C4C2212yes—
56C2×C4×C4⋊C4C2212yes—
57C2×C4×C4⋊C4C2212yes—
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C4⋊C4C2212yes—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2212yes—
62C2×C4×C22⋊C4C2212yes—
63#1445C2214yes—
64#1444C2214yes—
65#1443C2214yes—
66#1443C2214yes—
67#1443C2214yes—
68#1442C2214yes—
69#1441C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1437C2214yes—
78#1436C2214yes—
79C4⋊#95C2212yes—
80C4⋊#95C2214yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85C4⋊#95C2212yes—
86C4⋊#95C2212yes—
87C23×Q8C2311yescharacteristic
88C23×Q8C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C2×C22⋊Q8—24no—
93C2×C22⋊Q8—24no—
94C2×C22⋊Q8—24no—
95C2×C22⋊Q8—24no—
96C2×C22⋊Q8—24no—
97C2×C22⋊Q8Q818yescomplemented
98C2×C4×Q8—24no—
99C2×C4×Q8—24no—
100C2×C4×Q8—24no—
101C2×C4×Q8—24no—
102C2×C4×Q8—24no—
103C2×C4×Q8D418yes—
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2314yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C42—24no—
131C22×C42—24no—
132C22×C42—24no—
133C22×C42C2311yescharacteristic
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136C22×C42C2312yes—
137C22×C42C2312yes—
138C22×C42C2312yes—
139C22×C42C2312yes—
140C22×C42C2314yes—
141C22×C42C2311yescharacteristic
142#398—216no—
143#391—28no—
144#391—24no—
145#391—24no—
146#391—28no—
147#391—28no—
148#391—44no—
149#389—28no—
150#389—24no—
151#389—24no—
152#389—28no—
153#389—28no—
154#389—48no—
155#389—44no—
156#387—28no—
157#387—216no—
158#387—28no—
159#385—28no—
160#385—28no—
161#384—28no—
162#384—24no—
163#384—24no—
164#382—28no—
165#380—28no—
166#380—24no—
167#380—24no—
168#380—44no—
169#380—44no—
170C4×C4⋊C4—28no—
171C4×C4⋊C4—28no—
172C4×C4⋊C4—28no—
173C4×C4⋊C4—28no—
174C4×C4⋊C4—24no—
175C4×C4⋊C4D418yes—
176C4×C22⋊C4—28no—
177C4×C22⋊C4—28no—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2312yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C25C2411yescharacteristic
204C22×Q8—22no—
205C22×Q8—22no—
206C22×Q8—22no—
207C22×Q8—22no—
208C22×Q8—22no—
209C22×Q8—22no—
210C22×Q8—22no—
211C22×Q8—22no—
212C22×Q8—22no—
213C22×Q8—22no—
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8C2×D414yes—
217C22×Q8C2×Q814yes—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—41no—
236C23×C4—41no—
237C23×C4C2×Q814yes—
238C23×C4#4114yes—
239C23×C4C2414yes—
240C23×C4C2412yes—
241C23×C4C2414yes—
242C23×C4C2412yes—
243C23×C4C2412yes—
244C23×C4C2412yes—
245C23×C4C2412yes—
246C23×C4C2412yes—
247C23×C4C2411yescharacteristic
248C23×C4C2412yes—
249C23×C4C2411yescharacteristic
250C23×C4C2411yescharacteristic
251C23×C4C2411yescharacteristic
252C23×C4C2412yes—
253C23×C4C2411yescharacteristic
254C23×C4C2411yescharacteristic
255C22⋊Q8—232no—
256C22⋊Q8—232no—
257C4×Q8—232no—
258C4×Q8—416no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—28no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4C2×D414yes—
315C2×C4⋊C4C2×D418yes—
316C2×C4⋊C4C2×D414yes—
317C2×C4⋊C4C2×D414yes—
318C2×C4⋊C4C2×Q818yes—
319C2×C4⋊C4C2×Q814yes—
320C2×C4⋊C4#4114yes—
321C2×C4⋊C4#4114yes—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4C2×Q818yes—
337C2×C42—24no—
338C2×C42—24no—
339C2×C42—24no—
340C2×C42—24no—
341C2×C42—24no—
342C2×C42—24no—
343C2×C42—24no—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—24no—
351C2×C42—24no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—24no—
356C2×C42—28no—
357C2×C42—416no—
358C2×C42—44no—
359C2×C42—44no—
360C2×C42C2×D418yes—
361C2×C42C2×D418yes—
362C2×C42C2×D414yes—
363C2×C42C2×D414yes—
364C2×C42#4114yes—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—28no—
372#95—24no—
373#95—24no—
374#95—24no—
375#95—28no—
376#95—28no—
377#95—28no—
378#95—28no—
379#95—28no—
380#95—28no—
381#95—28no—
382#95—28no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95—44no—
387#95—44no—
388#95—44no—
389#95C2×D418yes—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24C22×Q812yes—
403C24C2×#4112yes—
404C242−1+412yes—
405C24C2511yescharacteristic
406C2×Q8—28no—
407C2×Q8—28no—
408C2×Q8—28no—
409C2×Q8—28no—
410C2×Q8—28no—
411C2×Q8—28no—
412C2×Q8—44no—
413C2×Q8—44no—
414C2×Q8—44no—
415C2×Q8—44no—
416C2×Q8—44no—
417C2×Q8—44no—
418C2×Q8—44no—
419C2×Q8—44no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—28no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4C22×D414yes—
526C22×C4C22×D414yes—
527C22×C4C22×D414yes—
528C22×C4C22×D412yes—
529C22×C4C22×D412yes—
530C22×C4C22×D414yes—
531C22×C4C22×D412yes—
532C22×C4C22×D412yes—
533C22×C4C22×D412yes—
534C22×C4C22×D412yes—
535C22×C4C22×Q814yes—
536C22×C4C22×Q812yes—
537C22×C4C22×Q814yes—
538C22×C4C22×Q812yes—
539C22×C4C2×#4112yes—
540C22×C4C2×#4114yes—
541C22×C4C2×#4112yes—
542C22×C4C2×#4114yes—
543C22×C4C2×#4112yes—
544C22×C4C2×#4112yes—
545C22×C4C2×#4112yes—
546C22×C4C2×#4112yes—
547C22×C4C2×#4112yes—
548C22×C4H(5,𝔽2)12yes—
549C22×C4H(5,𝔽2)12yes—
550C22×C42−1+412yes—
551C22×C42−1+412yes—
552C22×C42−1+412yes—
553C4⋊C4—216no—
554C4⋊C4—28no—
555C4⋊C4—216no—
556C4⋊C4—216no—
557C4⋊C4—28no—
558C4⋊C4—28no—
559C4⋊C4—416no—
560C4⋊C4—48no—
561C4⋊C4—48no—
562C4⋊C4—48no—
563C4⋊C4—44no—
564C4⋊C4—48no—
565C4⋊C4—44no—
566C4⋊C4—48no—
567C4⋊C4—48no—
568C4⋊C4—48no—
569C4⋊C4—84no—
570C4⋊C4—84no—
571C4⋊C4—88no—
572C4⋊C4—88no—
573C4⋊C4C22⋊Q8116yescomplemented
574C22⋊C4—216no—
575C22⋊C4—216no—
576C22⋊C4—48no—
577C22⋊C4—48no—
578C22⋊C4—88no—
579C42—216no—
580C42—216no—
581C42—44no—
582C42—44no—
583C42—44no—
584C42—48no—
585C42—48no—
586C42—88no—
587C42#121116yes—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23#55714yes—
623C23C23×D411yescharacteristic
624C23C23×D411yescharacteristic
625C23C23×Q811yescharacteristic
626C23C22×#4111yescharacteristic
627C23C22×#4111yescharacteristic
628C23C22×#4111yescharacteristic
629C23C22×#4111yescharacteristic
630C23C2×H(5,𝔽2)11yescharacteristic
631C23C2×H(5,𝔽2)11yescharacteristic
632C23C2×2−1+411yescharacteristic
633C23C2×2−1+411yescharacteristic
634C23C2×2−1+411yescharacteristic
635C23C2×2−1+411yescharacteristic
636C23#58511yescharacteristic
637C23#58511yescharacteristic
638Q8—416no—
639Q8—416no—
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—22no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—416no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—416no—
710C2×C4—416no—
711C2×C4—42no—
712C2×C4—44no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4C2×#12114yes—
740C2×C4C2×#12114yes—
741C2×C4C2×#12114yes—
742C2×C4C2×C22⋊Q818yes—
743C2×C4C2×C22⋊Q814yes—
744C2×C4#52514yes—
745C2×C4#53614yes—
746C2×C4#53714yes—
747C2×C4#54714yes—
748C2×C4#54814yes—
749C2×C4D4×Q814yes—
750C2×C4#55014yes—
751C2×C4#55214yes—
752C2×C4#55414yes—
753C2×C4#55614yes—
754C2×C4#55614yes—
755C22—24no—
756C22—24no—
757C22—24no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22C22×#12111yescharacteristic
771C22C22×C22⋊Q811yescharacteristic
772C22C2×#52511yescharacteristic
773C22C2×#53611yescharacteristic
774C22C2×#53711yescharacteristic
775C22C2×#54711yescharacteristic
776C22C2×#54811yescharacteristic
777C22C2×D4×Q811yescharacteristic
778C22C2×#55011yescharacteristic
779C22C2×#55211yescharacteristic
780C22C2×#55411yescharacteristic
781C22C2×#55611yescharacteristic
782C22C2×#55611yescharacteristic
783C22C2×#55711yescharacteristic
784C22Q8×#4111yescharacteristic
785C22#348011yescharacteristic
786C22#348111yescharacteristic
787C22#348811yescharacteristic
788C22#348811yescharacteristic
789C22#348911yescharacteristic
790C22#348911yescharacteristic
791C22#349211yescharacteristic
792C22#349311yescharacteristic
793C22#350211yescharacteristic
794C22#350311yescharacteristic
795C22#350711yescharacteristic
796C22#350811yescharacteristic
797C22#351411yescharacteristic
798C22#351511yescharacteristic
799C22#352311yescharacteristic
800C22#352311yescharacteristic
801C22#355011yescharacteristic
802C22#355211yescharacteristic
803C22#355411yescharacteristic
804C22#355511yescharacteristic
805C4—28no—
806C4—24no—
807C4—44no—
808C4—42no—
809C4—44no—
810C4—44no—
811C4—42no—
812C4—44no—
813C4—44no—
814C4—42no—
815C4—84no—
816C4—84no—
817C4—82no—
818C4—82no—
819C4#241518yes—
820C4#253818yes—
821C2—44no—
822C2C2×#241511yescharacteristic
823C2C2×#253811yescharacteristic
824C2#3551811yescharacteristic
825C2#3627511yescharacteristic
826C2#3649311yescharacteristic
827C2#3654511yescharacteristic
828C2#3657711yescharacteristic
829C2#3892311yescharacteristic
830C2#3913911yescharacteristic
831C2#3959711yescharacteristic
832C2#3972611yescharacteristic
833C2#5924211yescharacteristic
834C2#5924511yescharacteristic
835C2#5924811yescharacteristic
836C2#5932111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2582C2semidirect
2. C2×#2355C2semidirect
5. #15873C2semidirect
7. #15237C2semidirect
9. #15192C2semidirect
12. #14151C2semidirect
13. #14046C2semidirect
16. #13926C2semidirect
17. #13910C2semidirect
97. C2×C22⋊Q8Q8semidirect
573. C4⋊C4C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25822
C2×#23552
C2×C4×C22⋊Q82
#158732
#154412
#152372
#152202
#151922
#151822
#146862
#141512
#140462
#139972
#139932
#139262
#139102