Finite Group Databasebeta

← #617371

Subgroups — #617371

Order 512.

3380 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic, complemented
2C2×#2545C211yesmaximal, characteristic, complemented
3C2×#2620C211yesmaximal, characteristic
4C2×#2620C211yesmaximal, characteristic
5C2×#2323C211yesmaximal, characteristic, complemented
6C2×#2296C211yesmaximal, characteristic, complemented
7#15616C214yesmaximal, complemented
8#15361C214yesmaximal, complemented
9#15303C214yesmaximal, complemented
10#15302C214yesmaximal, complemented
11#15217C211yesmaximal, characteristic, complemented
12#15184C211yesmaximal, characteristic, complemented
13#15180C211yesmaximal, characteristic, complemented
14#15134C211yesmaximal, characteristic, complemented
15#14698C211yesmaximal, characteristic
16#14258C211yesmaximal, characteristic, complemented
17#14153C211yesmaximal, characteristic, complemented
18#13926C211yesmaximal, characteristic, complemented
19#13910C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27C22×#117C2211yescharacteristic
28C22×#117C2211yescharacteristic
29C23×C42C2211yescharacteristic
30#2857—28no—
31#2620—28no—
32#2620—28no—
33#2545—28no—
34C2×#396C2212yes—
35C2×#396C2214yes—
36C2×#396C2214yes—
37C2×#396C2212yes—
38C2×#396C2214yes—
39C2×#394C2212yes—
40C2×#394C2214yes—
41C2×#394C2212yes—
42#2323—28no—
43#2296—28no—
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#389C2212yes—
56C2×#389C2212yes—
57C2×#389C2214yes—
58C2×#389C2212yes—
59C2×#389C2211yescharacteristic
60C2×#389C2214yes—
61C2×#388C2214yes—
62C2×#388C2212yes—
63C2×#388C2212yes—
64C2×#387C2212yes—
65C2×#386C2214yes—
66C2×#385C2212yes—
67C2×#385C2212yes—
68C2×#384C2211yescharacteristic
69C2×#384C2211yescharacteristic
70C2×#384C2211yescharacteristic
71C2×#380C2211yescharacteristic
72C2×#380C2214yes—
73C2×C4×C4⋊C4C2211yescharacteristic
74C2×C4×C4⋊C4C2211yescharacteristic
75C2×C4×C4⋊C4C2211yescharacteristic
76C2×C4×C4⋊C4C2211yescharacteristic
77C2×C4×C4⋊C4C2211yescharacteristic
78#1444C2214yes—
79#1442C2214yes—
80#1441C2214yes—
81#1441C2214yes—
82#1441C2214yes—
83#1441C2214yes—
84#1441C2214yes—
85#1440C2214yes—
86#1440C2214yes—
87#1439C2214yes—
88#1439C2214yes—
89#1439C2214yes—
90#1437C2214yes—
91#1437C2214yes—
92C4⋊#95C2214yes—
93C4⋊#95C2211yescharacteristic
94C4⋊#95C2211yescharacteristic
95C4⋊#95C2211yescharacteristic
96C4⋊#95C2211yescharacteristic
97C23×Q8C2311yescharacteristic
98C23×Q8C2311yescharacteristic
99C23×D4C2311yescharacteristic
100C23×D4C2312yes—
101C24×C4C2312yes—
102C24×C4C2311yescharacteristic
103C2×C4⋊Q8—24no—
104C2×C4⋊Q8—24no—
105C2×C4⋊Q8—42no—
106C2×#124—24no—
107C2×#124—24no—
108C2×#124—24no—
109C2×#124—24no—
110C2×#124—24no—
111C2×#124—42no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8D418yes—
118C2×#121—24no—
119C2×#121—24no—
120C2×#121—24no—
121C2×C4×Q8—24no—
122C2×C4×Q8—24no—
123C2×C4×Q8—24no—
124C2×#117—24no—
125C2×#117—24no—
126C2×#117—24no—
127C2×#117—24no—
128C2×#117—42no—
129C2×#117D418yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2314yes—
139C22×C4⋊C4C2314yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2314yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2311yescharacteristic
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2314yes—
165C22×C22⋊C4C2312yes—
166C22×C42—24no—
167C22×C42—24no—
168C22×C42—42no—
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2312yes—
172C22×C42C2312yes—
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176C22×C42C2312yes—
177C22×C42C2311yescharacteristic
178#396—216no—
179#396—28no—
180#396—28no—
181#396—216no—
182#396—48no—
183#394—216no—
184#394—28no—
185#394—28no—
186#391—24no—
187#391—24no—
188#391—24no—
189#391—24no—
190#391—24no—
191#391—24no—
192#391—42no—
193#390—24no—
194#390—24no—
195#390—24no—
196#390—42no—
197#389—28no—
198#389—216no—
199#389—28no—
200#389—24no—
201#389—28no—
202#389—48no—
203#388—28no—
204#388—28no—
205#388—216no—
206#387—28no—
207#386—48no—
208#385—28no—
209#385—28no—
210#384—24no—
211#384—24no—
212#384—24no—
213#380—24no—
214#380—216no—
215C4×C4⋊C4—24no—
216C4×C4⋊C4—24no—
217C4×C4⋊C4—24no—
218C4×C4⋊C4—24no—
219C4×C4⋊C4D418yescomplemented
220C2×#95C2314yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2314yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2314yes—
236C2×#95C2314yes—
237C2×#95C2314yes—
238C2×#95C2314yes—
239C2×#95C2312yes—
240C25C2412yes—
241C25C2411yescharacteristic
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8C2×D414yes—
256C22×D4—24no—
257C22×D4—24no—
258C22×D4—24no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4—44no—
267C22×D4—44no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4C2×D414yes—
280C23×C4C2×D414yes—
281C23×C4#4114yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2412yes—
298C23×C4C2411yescharacteristic
299C4⋊Q8—416no—
300#124—416no—
301#124—416no—
302C22⋊Q8—232no—
303C22⋊Q8—416no—
304#121—416no—
305C4×Q8—416no—
306#117—232no—
307#117—416no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—28no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—28no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4C2×D414yes—
364C2×C4⋊C4C2×D414yes—
365C2×C4⋊C4C2×D414yes—
366C2×C4⋊C4C2×D418yes—
367C2×C4⋊C4C2×D418yes—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4C2×D414yes—
408C2×C22⋊C4C2×D414yes—
409C2×C22⋊C4C2×D418yes—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—24no—
419C2×C42—24no—
420C2×C42—22no—
421C2×C42—24no—
422C2×C42—24no—
423C2×C42—22no—
424C2×C42—24no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—24no—
428C2×C42—416no—
429C2×C42—42no—
430C2×C42—44no—
431C2×C42C2×D414yes—
432C2×C42C2×D414yes—
433C2×C42C2×D414yes—
434C2×C42C2×D414yes—
435C2×C42C2×D414yes—
436C2×C42#4114yes—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—28no—
443#95—28no—
444#95—24no—
445#95—24no—
446#95—24no—
447#95—28no—
448#95—28no—
449#95—24no—
450#95—24no—
451#95—28no—
452#95—44no—
453#95—44no—
454#95—44no—
455#95—44no—
456#95C2×D418yes—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—22no—
461C24—21no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—24no—
471C24—22no—
472C24—24no—
473C24—24no—
474C24—22no—
475C24—24no—
476C24C22×D412yes—
477C24C22×D412yes—
478C24C2×#4112yes—
479C24C2511yescharacteristic
480C2×Q8—28no—
481C2×Q8—28no—
482C2×Q8—28no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×D4—416no—
495C2×D4—48no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—88no—
504C2×D4—84no—
505C2×D4—84no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—28no—
521C22×C4—28no—
522C22×C4—28no—
523C22×C4—28no—
524C22×C4—216no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4#121116yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D414yes—
599C22×C4C22×D414yes—
600C22×C4C22×D414yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C22×D412yes—
606C22×C4C22×D412yes—
607C22×C4C22×D414yes—
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C2×#4112yes—
612C22×C4C2×#4112yes—
613C22×C4C2×#4112yes—
614C22×C4C2×#4112yes—
615C22×C4C2×#4112yes—
616C22×C4H(5,𝔽2)14yes—
617C22×C4H(5,𝔽2)12yes—
618C22×C42−1+414yes—
619C22×C42−1+414yes—
620C22×C42−1+412yes—
621C4⋊C4—28no—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—216no—
625C4⋊C4—216no—
626C4⋊C4—416no—
627C4⋊C4—48no—
628C4⋊C4—48no—
629C4⋊C4—48no—
630C4⋊C4—416no—
631C4⋊C4—48no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—44no—
635C4⋊C4—48no—
636C4⋊C4—48no—
637C4⋊C4—44no—
638C4⋊C4—84no—
639C4⋊C4—84no—
640C4⋊C4—88no—
641C4⋊C4—84no—
642C22⋊C4—216no—
643C22⋊C4—28no—
644C22⋊C4—28no—
645C22⋊C4—416no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—416no—
652C22⋊C4—88no—
653C22⋊C4—84no—
654C22⋊C4—84no—
655C22⋊C4—88no—
656C22⋊C4—84no—
657C42—28no—
658C42—28no—
659C42—28no—
660C42—48no—
661C42—48no—
662C42—44no—
663C42—44no—
664C42—84no—
665C42#121116yes—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—24no—
673C23—24no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—24no—
679C23—24no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—44no—
691C23—42no—
692C23—44no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23C2×#12114yes—
712C23C23×D411yescharacteristic
713C23C23×D411yescharacteristic
714C23C23×D411yescharacteristic
715C23C22×#4111yescharacteristic
716C23C22×#4111yescharacteristic
717C23C2×H(5,𝔽2)11yescharacteristic
718C23C2×H(5,𝔽2)12yes—
719C23C2×2−1+411yescharacteristic
720C23C2×2−1+412yes—
721C23C2×2−1+412yes—
722C23#58512yes—
723Q8—416no—
724Q8—88no—
725D4—816no—
726D4—88no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—232no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—28no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—432no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—44no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—44no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4C2×#12114yes—
820C2×C4C2×#12114yes—
821C2×C4C2×#12114yes—
822C2×C4C2×#12114yes—
823C2×C4C2×#12114yes—
824C2×C4#53718yes—
825C2×C4#53714yes—
826C2×C4D4214yes—
827C2×C4#54714yes—
828C2×C4#54814yes—
829C2×C4#55314yes—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—42no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—44no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—82no—
842C22—84no—
843C22—84no—
844C22—82no—
845C22—82no—
846C22—84no—
847C22—84no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22C22×#12111yescharacteristic
853C22C22×#12111yescharacteristic
854C22C2×#53711yescharacteristic
855C22C2×#53712yes—
856C22#346112yes—
857C22C2×D4211yescharacteristic
858C22C2×#54711yescharacteristic
859C22C2×#54811yescharacteristic
860C22C2×#55311yescharacteristic
861C22#348612yes—
862C22#348812yes—
863C22#348912yes—
864C22#349811yescharacteristic
865C22#349911yescharacteristic
866C22#349911yescharacteristic
867C22#350011yescharacteristic
868C22#350612yes—
869C22#350912yes—
870C22#351112yes—
871C22#353612yes—
872C22#354112yes—
873C22#355012yes—
874C22#355512yes—
875C4—28no—
876C4—24no—
877C4—24no—
878C4—24no—
879C4—44no—
880C4—44no—
881C4—44no—
882C4—42no—
883C4—44no—
884C4—42no—
885C4—82no—
886C4—82no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4#241618yes—
892C2—44no—
893C2—162no—
894C2C2×#241611yescharacteristic
895C2#3527311yescharacteristic
896C2#3530811yescharacteristic
897C2#3553311yescharacteristic
898C2#3566711yescharacteristic
899C2#3729911yescharacteristic
900C2#3738911yescharacteristic
901C2#3764912yes—
902C2#3779512yes—
903C2#3972712yes—
904C2#3981612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
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×#2857C2semidirect
2. C2×#2545C2semidirect
5. C2×#2323C2semidirect
6. C2×#2296C2semidirect
7. #15616C2semidirect
8. #15361C2semidirect
9. #15303C2semidirect
10. #15302C2semidirect
11. #15217C2semidirect
12. #15184C2semidirect
13. #15180C2semidirect
14. #15134C2semidirect
16. #14258C2semidirect
17. #14153C2semidirect
18. #13926C2semidirect
19. #13910C2semidirect
219. C4×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×#25452
C2×#26202
C2×#23232
C2×#22962
#156162
#153612
#153032
#153022
#152172
#151842
#151802
#151342
#146982
#142582
#141532
#139262
#139102