Finite Group Databasebeta

← #525324

Subgroups — #525324

Order 512.

3202 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2538C211yesmaximal, characteristic
2C2×D4×C4⋊C4C211yesmaximal, characteristic
3C2×#2295C211yesmaximal, characteristic, complemented
4#14712C211yesmaximal, characteristic, complemented
5#14549C214yesmaximal, complemented
6#14547C214yesmaximal, complemented
7#14266C212yesmaximal, complemented
8#14139C212yesmaximal, complemented
9#14130C212yesmaximal, complemented
10#14045C212yesmaximal, complemented
11#14018C212yesmaximal
12#13997C212yesmaximal, complemented
13#13993C212yesmaximal, complemented
14#13926C211yesmaximal, characteristic, complemented
15C4⋊C42C211yesmaximal, characteristic, complemented
16#13785C212yesmaximal
17C4×#390C211yesmaximal, characteristic
18C22×C22⋊Q8C2212yes—
19C22×C4×Q8C2211yescharacteristic
20C22×C4×D4C2212yes—
21C22×C4×D4C2211yescharacteristic
22C23×C4⋊C4C2212yes—
23#2538C4116yescomplemented
24C2×#396C2214yes—
25D4×C4⋊C4—28no—
26#2295—28no—
27C2×#391C2211yescharacteristic
28C2×#391C2211yescharacteristic
29C2×#391C2212yes—
30C2×#390C2211yescharacteristic
31C2×#390C2212yes—
32C2×#390C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#389C2212yes—
35C2×#389C2211yescharacteristic
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#389C2212yes—
39C2×#389C2212yes—
40C2×#387C2212yes—
41C2×#387C2212yes—
42C2×#385C2214yes—
43C2×#385C2214yes—
44C2×#384C2211yescharacteristic
45C2×#384C2211yescharacteristic
46C2×#380C2212yes—
47C2×#380C2212yes—
48C2×C4×C4⋊C4C2211yescharacteristic
49C2×C4×C4⋊C4C2212yes—
50C2×C4×C4⋊C4C2212yes—
51C2×C4×C4⋊C4C2212yes—
52C2×C4×C4⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2212yes—
54C2×C4×C22⋊C4C2212yes—
55C2×#376C2212yes—
56C2×C43C2211yescharacteristic
57#1445C2214yes—
58#1444C2214yes—
59#1443C2214yes—
60#1442C2214yes—
61#1441C2214yes—
62#1441C2214yes—
63#1441C2214yes—
64#1439C2214yes—
65#1439C2214yes—
66#1437C2214yes—
67#1437C2214yes—
68#1437C2212yes—
69#1437C2212yes—
70#1436C2214yes—
71#1436C2214yes—
72C4⋊#95C2212yes—
73C4⋊#95C2212yes—
74C4⋊#95C2212yes—
75C4⋊#95C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2214yes—
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2212yes—
82C4⋊#95C2211yescharacteristic
83C22⋊#95C2214yes—
84C22⋊#95C2214yes—
85C22⋊#95C2214yes—
86C23×Q8C2311yescharacteristic
87C23×D4C2311yescharacteristic
88C24×C4C2312yes—
89C24×C4C2314yes—
90C2×C22⋊Q8—44no—
91C2×C22⋊Q8—44no—
92C2×C22⋊Q8C2×C4116yescomplemented
93C2×C4×Q8—24no—
94C2×C4×Q8—24no—
95C2×C4×Q8C2×C418yescomplemented
96C2×C4×D4—28no—
97C2×C4×D4—24no—
98C2×C4×D4—28no—
99C2×C4×D4—24no—
100C2×C4×D4—44no—
101C2×C4×D4C2×C418yes—
102C22×C4⋊C4—28no—
103C22×C4⋊C4—44no—
104C22×C4⋊C4—44no—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2314yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2314yes—
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C42C2311yescharacteristic
132C22×C42C2312yes—
133C22×C42C2311yescharacteristic
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136C22×C42C2311yescharacteristic
137C22×C42C2312yes—
138C22×C42C2312yes—
139C22×C42C2311yescharacteristic
140C22×C42C2314yes—
141C22×C42C2311yescharacteristic
142#396C2×C4132yescomplemented
143#391—24no—
144#391—24no—
145#391—44no—
146#390—24no—
147#390C2×C4116yes—
148#390Q818yescomplemented
149#389—24no—
150#389—24no—
151#389—28no—
152#389—44no—
153#389—44no—
154#389—44no—
155#389C2×C4116yescomplemented
156#387—28no—
157#387—28no—
158#385—216no—
159#385—48no—
160#384—24no—
161#384C2×C418yescomplemented
162#380—28no—
163#380C2×C4116yescomplemented
164C4×C4⋊C4—28no—
165C4×C4⋊C4—24no—
166C4×C4⋊C4—44no—
167C4×C4⋊C4—44no—
168C4×C4⋊C4D418yes—
169C4×C22⋊C4—44no—
170C4×C22⋊C4—44no—
171#376—28no—
172C2×#95C2312yes—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2314yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2314yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2314yes—
195C2×#95C2312yes—
196C43—24no—
197C25C2412yes—
198C22×Q8—22no—
199C22×Q8—22no—
200C22×Q8—22no—
201C22×Q8—22no—
202C22×Q8—22no—
203C22×Q8—22no—
204C22×Q8C22×C414yes—
205C22×D4—22no—
206C22×D4—22no—
207C22×D4—22no—
208C22×D4—22no—
209C22×D4C22×C414yes—
210C22×D4C2×Q814yes—
211C22×D4#4114yes—
212C23×C4—24no—
213C23×C4—24no—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—28no—
219C23×C4—28no—
220C23×C4—44no—
221C23×C4—44no—
222C23×C4—44no—
223C23×C4—44no—
224C23×C4—44no—
225C23×C4C22×C418yes—
226C23×C4C2412yes—
227C23×C4C2414yes—
228C23×C4C2414yes—
229C23×C4C2412yes—
230C23×C4C2412yes—
231C23×C4C2412yes—
232C23×C4C2412yes—
233C23×C4C2412yes—
234C23×C4C2412yes—
235C23×C4C2411yescharacteristic
236C23×C4C2411yescharacteristic
237C23×C4C2411yescharacteristic
238C23×C4C2411yescharacteristic
239C23×C4C2411yescharacteristic
240C23×C4C2411yescharacteristic
241C23×C4C2411yescharacteristic
242C22⋊Q8—432no—
243C4×Q8—232no—
244C4×D4—232no—
245C4×D4—432no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—28no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
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—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—28no—
278C2×C4⋊C4—432no—
279C2×C4⋊C4—44no—
280C2×C4⋊C4—44no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—44no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4C22×C414yes—
292C2×C4⋊C4C22×C414yes—
293C2×C4⋊C4C22×C418yes—
294C2×C4⋊C4C22×C418yes—
295C2×C4⋊C4C22×C418yes—
296C2×C4⋊C4C22×C4116yes—
297C2×C4⋊C4C22×C418yes—
298C2×C4⋊C4C2×D414yes—
299C2×C4⋊C4C2×D414yes—
300C2×C4⋊C4C2×Q814yes—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—28no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—28no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—44no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4—42no—
312C2×C22⋊C4—44no—
313C2×C22⋊C4—44no—
314C2×C22⋊C4—44no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—44no—
320C2×C22⋊C4C22×C418yes—
321C2×C22⋊C4C22×C4116yes—
322C2×C22⋊C4C22×C4116yes—
323C2×C22⋊C4C2×Q818yes—
324C2×C22⋊C4C2×Q818yes—
325C2×C42—24no—
326C2×C42—22no—
327C2×C42—24no—
328C2×C42—24no—
329C2×C42—24no—
330C2×C42—22no—
331C2×C42—22no—
332C2×C42—22no—
333C2×C42—22no—
334C2×C42—22no—
335C2×C42—22no—
336C2×C42—24no—
337C2×C42—22no—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—24no—
341C2×C42—24no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—41no—
348C2×C42—41no—
349C2×C42—44no—
350C2×C42—44no—
351C2×C42—44no—
352C2×C42C22×C418yes—
353C2×C42C22×C414yes—
354C2×C42C2×D418yes—
355C2×C42C2×D414yes—
356C2×C42C2×Q814yes—
357C2×C42#4114yes—
358#95—24no—
359#95—24no—
360#95—24no—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—28no—
365#95—24no—
366#95—44no—
367#95—42no—
368#95—42no—
369#95—42no—
370#95—42no—
371#95—44no—
372#95—44no—
373#95—44no—
374#95—44no—
375#95—44no—
376#95—44no—
377#95—44no—
378#95—44no—
379#95—44no—
380#95C22×C4116yes—
381#95C2×D418yes—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24C23×C414yes—
395C24C22×Q814yes—
396C24C2×#4114yes—
397C24C2511yescharacteristic
398C2×Q8—28no—
399C2×Q8—28no—
400C2×Q8—28no—
401C2×Q8—44no—
402C2×Q8—44no—
403C2×Q8—44no—
404C2×Q8—44no—
405C2×D4—28no—
406C2×D4—28no—
407C2×D4—28no—
408C2×D4—28no—
409C2×D4—28no—
410C2×D4—28no—
411C2×D4C4×Q8116yes—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—22no—
445C22×C4—24no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—24no—
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—21no—
476C22×C4—21no—
477C22×C4—24no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—216no—
483C22×C4—216no—
484C22×C4—216no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—416no—
500C22×C4—416no—
501C22×C4—48no—
502C22×C4—48no—
503C22×C4—48no—
504C22×C4—48no—
505C22×C4—88no—
506C22×C4—88no—
507C22×C4—88no—
508C22×C4—88no—
509C22×C4—88no—
510C22×C4C23×C414yes—
511C22×C4C23×C414yes—
512C22×C4C23×C418yes—
513C22×C4C23×C414yes—
514C22×C4C23×C412yes—
515C22×C4C23×C412yes—
516C22×C4C23×C412yes—
517C22×C4C22×D414yes—
518C22×C4C22×D414yes—
519C22×C4C22×D412yes—
520C22×C4C22×D412yes—
521C22×C4C22×D412yes—
522C22×C4C22×Q812yes—
523C22×C4C22×Q812yes—
524C22×C4C22×Q814yes—
525C22×C4C22×Q812yes—
526C22×C4C2×#4112yes—
527C22×C4C2×#4112yes—
528C22×C4C2×#4112yes—
529C22×C4C2×#4112yes—
530C22×C4H(5,𝔽2)12yes—
531C22×C4H(5,𝔽2)12yes—
532C22×C4H(5,𝔽2)12yes—
533C22×C4H(5,𝔽2)12yes—
534C22×C4H(5,𝔽2)12yes—
535C22×C42−1+412yes—
536C22×C42−1+412yes—
537C22×C42−1+412yes—
538C4⋊C4—28no—
539C4⋊C4—28no—
540C4⋊C4—216no—
541C4⋊C4—216no—
542C4⋊C4—216no—
543C4⋊C4—28no—
544C4⋊C4—28no—
545C4⋊C4—28no—
546C4⋊C4—48no—
547C4⋊C4—416no—
548C4⋊C4—48no—
549C4⋊C4—48no—
550C4⋊C4—416no—
551C4⋊C4—48no—
552C4⋊C4—48no—
553C4⋊C4—44no—
554C4⋊C4—84no—
555C4⋊C4—88no—
556C22⋊C4—216no—
557C22⋊C4—416no—
558C22⋊C4—416no—
559C22⋊C4—48no—
560C22⋊C4—48no—
561C22⋊C4—48no—
562C22⋊C4—48no—
563C22⋊C4—416no—
564C42—216no—
565C42—216no—
566C42—28no—
567C42—44no—
568C42—44no—
569C42—44no—
570C42—44no—
571C42—48no—
572C42—44no—
573C42—88no—
574C42C4×D4116yes—
575C23—24no—
576C23—24no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23C2×C4×Q818yes—
610C23C24×C411yescharacteristic
611C23C23×D411yescharacteristic
612C23C23×Q811yescharacteristic
613C23C22×#4111yescharacteristic
614C23C22×#4111yescharacteristic
615C23C2×H(5,𝔽2)11yescharacteristic
616C23C2×H(5,𝔽2)11yescharacteristic
617C23C2×H(5,𝔽2)11yescharacteristic
618C23C2×H(5,𝔽2)11yescharacteristic
619C23C2×H(5,𝔽2)11yescharacteristic
620C23C2×2−1+411yescharacteristic
621C23C2×2−1+411yescharacteristic
622C23C2×2−1+411yescharacteristic
623C23#58511yescharacteristic
624C23#58511yescharacteristic
625Q8—416no—
626D4—232no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—28no—
638C2×C4—24no—
639C2×C4—28no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—28no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—44no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—44no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—44no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—44no—
709C2×C4—41no—
710C2×C4—432no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—832no—
726C2×C4C2×C4×D414yes—
727C2×C4C2×C4×D414yes—
728C2×C4C2×C4×D414yes—
729C2×C4C2×C4×Q814yes—
730C2×C4#51814yes—
731C2×C4#52014yes—
732C2×C4#52014yes—
733C2×C4#53514yes—
734C2×C4#53714yes—
735C2×C4#54014yes—
736C2×C4#54214yes—
737C2×C4#54614yes—
738C2×C4D4×Q814yes—
739C2×C4#55214yes—
740C2×C4#55414yes—
741C22—28no—
742C22—28no—
743C22—28no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—44no—
751C22—44no—
752C22—44no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22C22×C4×D411yescharacteristic
757C22C22×C4×Q811yescharacteristic
758C22C2×#51811yescharacteristic
759C22C2×#52011yescharacteristic
760C22C2×#52011yescharacteristic
761C22C4×H(5,𝔽2)11yescharacteristic
762C22C4×2−1+411yescharacteristic
763C22C2×#53511yescharacteristic
764C22C2×#53711yescharacteristic
765C22C2×#54011yescharacteristic
766C22C2×#54211yescharacteristic
767C22C2×#54611yescharacteristic
768C22C2×D4×Q811yescharacteristic
769C22C2×#55211yescharacteristic
770C22C2×#55411yescharacteristic
771C22#348811yescharacteristic
772C22#348911yescharacteristic
773C22#350111yescharacteristic
774C22#350111yescharacteristic
775C22#350311yescharacteristic
776C22#350311yescharacteristic
777C22#351111yescharacteristic
778C22#351211yescharacteristic
779C22#351411yescharacteristic
780C22#351511yescharacteristic
781C22#351911yescharacteristic
782C22#352011yescharacteristic
783C22#354311yescharacteristic
784C22#354611yescharacteristic
785C22#354611yescharacteristic
786C22#354811yescharacteristic
787C22#355011yescharacteristic
788C22#355211yescharacteristic
789C22#355411yescharacteristic
790C22#355511yescharacteristic
791C4—24no—
792C4—44no—
793C4—44no—
794C4—42no—
795C4—42no—
796C4—48no—
797C4—44no—
798C4—44no—
799C4—44no—
800C4—42no—
801C4—42no—
802C4—44no—
803C4—82no—
804C4—84no—
805C4#232418yes—
806C4#236018yes—
807C2—48no—
808C2C2×#232411yescharacteristic
809C2C2×#236011yescharacteristic
810C2#3426711yescharacteristic
811C2#3433211yescharacteristic
812C2#3433411yescharacteristic
813C2#3448111yescharacteristic
814C2#3449411yescharacteristic
815C2#3890811yescharacteristic
816C2#3891011yescharacteristic
817C2#3897511yescharacteristic
818C2#3897711yescharacteristic
819C2#3959611yescharacteristic
820C2#3959811yescharacteristic
821C2#3963311yescharacteristic
822C2#3963411yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#2295C2semidirect
4. #14712C2semidirect
5. #14549C2semidirect
6. #14547C2semidirect
7. #14266C2semidirect
8. #14139C2semidirect
9. #14130C2semidirect
10. #14045C2semidirect
12. #13997C2semidirect
13. #13993C2semidirect
14. #13926C2semidirect
15. C4⋊C42C2semidirect
23. #2538C4semidirect
92. C2×C22⋊Q8C2×C4semidirect
95. C2×C4×Q8C2×C4semidirect
142. #396C2×C4semidirect
148. #390Q8semidirect
155. #389C2×C4semidirect
161. #384C2×C4semidirect
163. #380C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#25382
C2×D4×C4⋊C42
C2×#22952
#147122
#145492
#145472
#142662
#141392
#141302
#140452
#140182
#139972
#139932
#139262
C4⋊C422
#137852
C4×#3902