Finite Group Databasebeta

← #676493

Subgroups — #676493

Order 512.

3030 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2538C211yesmaximal, characteristic
2C2×#2538C211yesmaximal, characteristic
3C2×#2355C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
5#15531C214yesmaximal, complemented
6#15361C214yesmaximal, complemented
7#15222C212yesmaximal
8#15221C212yesmaximal, complemented
9#15179C212yesmaximal, complemented
10#15178C212yesmaximal, complemented
11#14712C211yesmaximal, characteristic, complemented
12#14045C212yesmaximal, complemented
13#14022C212yesmaximal
14#13997C212yesmaximal, complemented
15#13926C211yesmaximal, characteristic, complemented
16#13876C212yesmaximal, complemented
17C4×#390C211yesmaximal, characteristic
18C22×C4⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2212yes—
20C22×C22⋊Q8C2212yes—
21C22×C4×Q8C2211yescharacteristic
22C22×C4×Q8C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24#2538—28no—
25#2538—28no—
26C2×#396C2214yes—
27C2×#396C2214yes—
28#2355—28no—
29C4×C4⋊Q8—28no—
30C2×#391C2212yes—
31C2×#391C2211yescharacteristic
32C2×#391C2211yescharacteristic
33C2×#391C2212yes—
34C2×#390C2212yes—
35C2×#390C2212yes—
36C2×#390C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#389C2212yes—
39C2×#389C2212yes—
40C2×#389C2212yes—
41C2×#389C2212yes—
42C2×#389C2212yes—
43C2×#389C2212yes—
44C2×#389C2212yes—
45C2×#388C2214yes—
46C2×#387C2214yes—
47C2×#384C2211yescharacteristic
48C2×#384C2211yescharacteristic
49C2×#384C2211yescharacteristic
50C2×#382C2212yes—
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×C4×C4⋊C4C2212yes—
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C4⋊C4C2212yes—
56C2×C4×C4⋊C4C2212yes—
57C2×C4×C4⋊C4C2212yes—
58C2×C4×C22⋊C4C2212yes—
59C2×C4×C22⋊C4C2212yes—
60C2×C43C2211yescharacteristic
61#1445C2214yes—
62#1444C2214yes—
63#1444C2214yes—
64#1442C2214yes—
65#1442C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1440C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1437C2212yes—
75#1437C2212yes—
76#1437C2214yes—
77#1436C2214yes—
78C4⋊#95C2214yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2212yes—
85C4⋊#95C2212yes—
86C4⋊#95C2211yescharacteristic
87C23×Q8C2311yescharacteristic
88C23×Q8C2311yescharacteristic
89C23×D4C2311yescharacteristic
90C24×C4C2312yes—
91C2×C4⋊Q8—24no—
92C2×C4⋊Q8—24no—
93C2×C4⋊Q8—24no—
94C2×C22⋊Q8—28no—
95C2×C22⋊Q8—28no—
96C2×C22⋊Q8—28no—
97C2×C22⋊Q8—44no—
98C2×C22⋊Q8—44no—
99C2×C22⋊Q8—44no—
100C2×C4×Q8—24no—
101C2×C4×Q8—24no—
102C2×C4×Q8—24no—
103C2×C4×Q8—24no—
104C2×C4×Q8—24no—
105C2×C4×Q8D418yes—
106C2×C4×D4—24no—
107C2×C4×D4—24no—
108C2×C4×D4—24no—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2314yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C42C2312yes—
139C22×C42C2312yes—
140C22×C42C2311yescharacteristic
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2312yes—
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2314yes—
148C22×C42C2311yescharacteristic
149#396—216no—
150#396—216no—
151#391—24no—
152#391—24no—
153#391—28no—
154#391—44no—
155#390—28no—
156#390—28no—
157#390—24no—
158#390Q818yescomplemented
159#389—28no—
160#389—28no—
161#389—28no—
162#389—28no—
163#389—28no—
164#389—44no—
165#389—44no—
166#388—48no—
167#387—216no—
168#384—24no—
169#384—24no—
170#384D418yes—
171#382—28no—
172#380—28no—
173#380—28no—
174C4×C4⋊C4—28no—
175C4×C4⋊C4—28no—
176C4×C4⋊C4—28no—
177C4×C4⋊C4—28no—
178C4×C4⋊C4—24no—
179C4×C22⋊C4—28no—
180C4×C22⋊C4—44no—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2312yes—
185C2×#95C2314yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C43—24no—
203C25C2412yes—
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×Q8#4114yes—
218C22×D4—22no—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4C2×Q814yes—
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4C2414yes—
233C23×C4C2412yes—
234C23×C4C2412yes—
235C23×C4C2412yes—
236C23×C4C2412yes—
237C23×C4C2414yes—
238C23×C4C2412yes—
239C23×C4C2412yes—
240C23×C4C2411yescharacteristic
241C23×C4C2412yes—
242C23×C4C2411yescharacteristic
243C23×C4C2411yescharacteristic
244C23×C4C2411yescharacteristic
245C23×C4C2411yescharacteristic
246C23×C4C2411yescharacteristic
247C23×C4C2411yescharacteristic
248C4⋊Q8—232no—
249C22⋊Q8—432no—
250C22⋊Q8—432no—
251C4×Q8—232no—
252C4×Q8—416no—
253C4×D4—416no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
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—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—28no—
278C2×C4⋊C4—28no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—44no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4C2×D414yes—
309C2×C4⋊C4C2×D418yes—
310C2×C4⋊C4C2×D418yes—
311C2×C4⋊C4C2×D418yes—
312C2×C4⋊C4C2×D418yes—
313C2×C4⋊C4C2×Q814yes—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4C2×Q818yes—
340C2×C22⋊C4C2×Q818yes—
341C2×C42—24no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—24no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—24no—
350C2×C42—24no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—24no—
355C2×C42—24no—
356C2×C42—24no—
357C2×C42—22no—
358C2×C42—24no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—28no—
363C2×C42—41no—
364C2×C42—41no—
365C2×C42—44no—
366C2×C42—44no—
367C2×C42C2×D418yes—
368C2×C42C2×D414yes—
369C2×C42C2×D414yes—
370C2×C42C2×Q814yes—
371C2×C42#4114yes—
372C2×C42#4114yes—
373C2×C42#4114yes—
374#95—28no—
375#95—24no—
376#95—28no—
377#95—24no—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—28no—
382#95—28no—
383#95—28no—
384#95—24no—
385#95—24no—
386#95—28no—
387#95—28no—
388#95—44no—
389#95—42no—
390#95—42no—
391#95—44no—
392#95—44no—
393#95—44no—
394#95—44no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24C22×Q814yes—
410C24C2511yescharacteristic
411C2×Q8—28no—
412C2×Q8—28no—
413C2×Q8—28no—
414C2×Q8—28no—
415C2×Q8—28no—
416C2×Q8—28no—
417C2×Q8—44no—
418C2×Q8—44no—
419C2×Q8—44no—
420C2×Q8—44no—
421C2×Q8—44no—
422C2×Q8—44no—
423C2×Q8—44no—
424C2×Q8—44no—
425C2×D4—28no—
426C2×D4—28no—
427C2×D4—28no—
428C2×D4—44no—
429C2×D4—44no—
430C2×D4—44no—
431C2×D4—44no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—24no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—24no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—24no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—48no—
515C22×C4—48no—
516C22×C4—48no—
517C22×C4—48no—
518C22×C4—48no—
519C22×C4—48no—
520C22×C4—48no—
521C22×C4C22×D418yes—
522C22×C4C22×D414yes—
523C22×C4C22×D414yes—
524C22×C4C22×D412yes—
525C22×C4C22×D412yes—
526C22×C4C22×D412yes—
527C22×C4C22×D412yes—
528C22×C4C22×D412yes—
529C22×C4C22×D412yes—
530C22×C4C22×Q812yes—
531C22×C4C22×Q814yes—
532C22×C4C22×Q812yes—
533C22×C4C22×Q812yes—
534C22×C4C2×#4112yes—
535C22×C4C2×#4114yes—
536C22×C4C2×#4112yes—
537C22×C4C2×#4112yes—
538C22×C4C2×#4112yes—
539C22×C4C2×#4112yes—
540C22×C4C2×#4112yes—
541C22×C4C2×#4112yes—
542C22×C4C2×#4112yes—
543C22×C4C2×#4112yes—
544C22×C4C2×#4112yes—
545C22×C4H(5,𝔽2)12yes—
546C22×C4H(5,𝔽2)12yes—
547C22×C4H(5,𝔽2)12yes—
548C22×C42−1+412yes—
549C22×C42−1+412yes—
550C22×C42−1+412yes—
551C4⋊C4—216no—
552C4⋊C4—216no—
553C4⋊C4—28no—
554C4⋊C4—216no—
555C4⋊C4—216no—
556C4⋊C4—216no—
557C4⋊C4—28no—
558C4⋊C4—48no—
559C4⋊C4—48no—
560C4⋊C4—48no—
561C4⋊C4—416no—
562C4⋊C4—416no—
563C4⋊C4—44no—
564C4⋊C4—48no—
565C4⋊C4—44no—
566C4⋊C4—48no—
567C4⋊C4—44no—
568C4⋊C4—48no—
569C4⋊C4—84no—
570C4⋊C4—88no—
571C22⋊C4—216no—
572C22⋊C4—48no—
573C22⋊C4—416no—
574C22⋊C4—48no—
575C22⋊C4—416no—
576C22⋊C4—48no—
577C22⋊C4—48no—
578C22⋊C4—88no—
579C22⋊C4—88no—
580C42—216no—
581C42—28no—
582C42—28no—
583C42—28no—
584C42—44no—
585C42—44no—
586C42—48no—
587C42—44no—
588C42—48no—
589C42—88no—
590C42#121116yes—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23C23×D411yescharacteristic
627C23C23×D411yescharacteristic
628C23C23×Q811yescharacteristic
629C23C22×#4111yescharacteristic
630C23C22×#4111yescharacteristic
631C23C22×#4111yescharacteristic
632C23C22×#4111yescharacteristic
633C23C2×H(5,𝔽2)11yescharacteristic
634C23C2×H(5,𝔽2)11yescharacteristic
635C23C2×H(5,𝔽2)11yescharacteristic
636C23C2×2−1+411yescharacteristic
637C23C2×2−1+411yescharacteristic
638C23C2×2−1+411yescharacteristic
639C23#58511yescharacteristic
640C23#58511yescharacteristic
641Q8—416no—
642Q8—416no—
643D4—416no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—28no—
669C2×C4—28no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—28no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—44no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—44no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—816no—
740C2×C4C2×#12114yes—
741C2×C4C2×#12114yes—
742C2×C4C2×#12114yes—
743C2×C4#52514yes—
744C2×C4#53314yes—
745C2×C4#53514yes—
746C2×C4#54114yes—
747C2×C4#54614yes—
748C2×C4#54714yes—
749C2×C4#54814yes—
750C2×C4D4×Q814yes—
751C2×C4D4×Q814yes—
752C2×C4#55014yes—
753C2×C4#55314yes—
754C2×C4#55414yes—
755C2×C4#55514yes—
756C2×C4#55614yes—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22C22×#12111yescharacteristic
773C22C2×#52511yescharacteristic
774C22C2×#53311yescharacteristic
775C22C2×#53511yescharacteristic
776C22C2×#54111yescharacteristic
777C22C2×#54611yescharacteristic
778C22C2×#54711yescharacteristic
779C22C2×#54811yescharacteristic
780C22C2×D4×Q811yescharacteristic
781C22C2×D4×Q811yescharacteristic
782C22C2×#55011yescharacteristic
783C22C2×#55311yescharacteristic
784C22C2×#55411yescharacteristic
785C22C2×#55511yescharacteristic
786C22C2×#55611yescharacteristic
787C22Q8×#4111yescharacteristic
788C22#348011yescharacteristic
789C22#348811yescharacteristic
790C22#348911yescharacteristic
791C22#349611yescharacteristic
792C22#349711yescharacteristic
793C22#350111yescharacteristic
794C22#350311yescharacteristic
795C22#350611yescharacteristic
796C22#350711yescharacteristic
797C22#350711yescharacteristic
798C22#350811yescharacteristic
799C22#351111yescharacteristic
800C22#351211yescharacteristic
801C22#352211yescharacteristic
802C22#352311yescharacteristic
803C22#354811yescharacteristic
804C22#355011yescharacteristic
805C22#355411yescharacteristic
806C22#355411yescharacteristic
807C4—24no—
808C4—24no—
809C4—24no—
810C4—48no—
811C4—42no—
812C4—44no—
813C4—44no—
814C4—42no—
815C4—44no—
816C4—44no—
817C4—84no—
818C4—82no—
819C4—82no—
820C4—82no—
821C4#241418yes—
822C4#242918yes—
823C2—84no—
824C2C2×#242911yescharacteristic
825C2C2×#241411yescharacteristic
826C2#3556411yescharacteristic
827C2#3619411yescharacteristic
828C2#3647711yescharacteristic
829C2#3654411yescharacteristic
830C2#3657911yescharacteristic
831C2#3919211yescharacteristic
832C2#3950611yescharacteristic
833C2#3959611yescharacteristic
834C2#3972511yescharacteristic
835C2#5941111yescharacteristic
836C2#5941311yescharacteristic
837C2#5982111yescharacteristic
838C2#5982311yescharacteristic
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
3. C2×#2355C2semidirect
4. C2×C4×C4⋊Q8C2semidirect
5. #15531C2semidirect
6. #15361C2semidirect
8. #15221C2semidirect
9. #15179C2semidirect
10. #15178C2semidirect
11. #14712C2semidirect
12. #14045C2semidirect
14. #13997C2semidirect
15. #13926C2semidirect
16. #13876C2semidirect
158. #390Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25382
C2×#23552
C2×C4×C4⋊Q82
#155312
#153612
#152222
#152212
#151792
#151782
#147122
#140452
#140222
#139972
#139262
#138762
C4×#3902