Finite Group Databasebeta

← #734803

Subgroups — #734803

Order 512.

3858 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#554C211yesmaximal, characteristic
2C2×#2503C211yesmaximal, characteristic, complemented
3C2×#2486C211yesmaximal, characteristic
4C22×#400C211yesmaximal, characteristic, complemented
5#16634C212yesmaximal, complemented
6#16366C212yesmaximal, complemented
7#15881C212yesmaximal, complemented
8#15783C212yesmaximal, complemented
9#15670C212yesmaximal, complemented
10#15465C212yesmaximal, complemented
11#14934C212yesmaximal, complemented
12#14934C212yesmaximal, complemented
13#14884C212yesmaximal, complemented
14#14822C212yesmaximal, complemented
15#14281C211yesmaximal, characteristic, complemented
16#13968C212yesmaximal
17#13968C212yesmaximal
18#13923C211yesmaximal, characteristic, complemented
19#13784C211yesmaximal, characteristic
20C2×#554—28no—
21C2×#554—28no—
22C2×#554—28no—
23C22×C4⋊Q8C2211yescharacteristic
24C22×#125C2211yescharacteristic
25C22×#125C2211yescharacteristic
26C22×#123C2212yes—
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C22×C22⋊Q8C2211yescharacteristic
33C22×C4×Q8C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C22×C4×D4C2211yescharacteristic
36C22×C4×D4C2211yescharacteristic
37C23×C4⋊C4C2211yescharacteristic
38C23×C4⋊C4C2211yescharacteristic
39C23×C4⋊C4C2211yescharacteristic
40#2503—28no—
41#2486—28no—
42C2×#400—28no—
43C2×#400C2212yes—
44C2×#400C2212yes—
45C2×#400C2212yes—
46C2×#400C2212yes—
47C2×#400C2212yes—
48C2×#400C2212yes—
49C2×#398C2212yes—
50C2×#397C2212yes—
51C2×#391C2212yes—
52C2×#389C2212yes—
53C2×#386C2212yes—
54C2×#382C2212yes—
55C2×#381C2212yes—
56C2×#381C2212yes—
57C2×#381C2212yes—
58C2×#380C2211yescharacteristic
59C2×#380C2212yes—
60C2×C4×C22⋊C4C2211yescharacteristic
61C22×#95C2212yes—
62C22×#95C2212yes—
63C22×#95C2211yescharacteristic
64#1446C2214yes—
65#1446C2214yes—
66#1446C2212yes—
67#1445C2212yes—
68#1442C2214yes—
69#1442C2214yes—
70#1442C2214yes—
71#1442C2214yes—
72#1442C2214yes—
73#1442C2214yes—
74#1441C2214yes—
75#1441C2212yes—
76#1441C2212yes—
77#1441C2212yes—
78#1441C2214yes—
79#1441C2212yes—
80#1440C2214yes—
81#1440C2214yes—
82#1437C2212yes—
83#1436C2214yes—
84#1436C2212yes—
85#1436C2212yes—
86#1436C2214yes—
87#1436C2212yes—
88#1434C2212yes—
89C22⋊#95C2214yes—
90C22⋊#95C2212yes—
91C22⋊#95C2212yes—
92C22⋊#95C2212yes—
93C22⋊#95C2212yes—
94C22⋊#95C2212yes—
95C22⋊#95C2214yes—
96C22⋊#95C2212yes—
97C23×Q8C2311yescharacteristic
98C23×Q8C2311yescharacteristic
99C23×Q8C2311yescharacteristic
100C23×D4C2311yescharacteristic
101C24×C4C2312yes—
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2312yes—
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109#554—2128no—
110C2×C4⋊Q8—24no—
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—24no—
113C2×#125—24no—
114C2×#125—24no—
115C2×#125—24no—
116C2×#125—24no—
117C2×#125—24no—
118C2×#125—24no—
119C2×#123—28no—
120C2×#123—28no—
121C2×#123—28no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8—24no—
125C2×C22⋊Q8—24no—
126C2×C22⋊Q8—24no—
127C2×C22⋊Q8—24no—
128C2×C22⋊Q8—24no—
129C2×C22⋊Q8—24no—
130C2×C22⋊Q8—24no—
131C2×C22⋊Q8—24no—
132C2×C22⋊Q8—24no—
133C2×C22⋊Q8—24no—
134C2×C22⋊Q8—24no—
135C2×C22⋊Q8—24no—
136C2×C22⋊Q8—24no—
137C2×C22⋊Q8—24no—
138C2×C22⋊Q8—24no—
139C2×C22⋊Q8D418yes—
140C2×C4×Q8—24no—
141C2×C4×Q8—24no—
142C2×C4×Q8—24no—
143C2×C4×D4—24no—
144C2×C4×D4—24no—
145C2×C4×D4—24no—
146C2×C4×D4—24no—
147C2×C4×D4—24no—
148C2×C4×D4—24no—
149C2×C4×D4—24no—
150C2×C4×D4—24no—
151C2×C4×D4D418yes—
152C22×C4⋊C4—24no—
153C22×C4⋊C4—24no—
154C22×C4⋊C4—24no—
155C22×C4⋊C4—24no—
156C22×C4⋊C4—24no—
157C22×C4⋊C4—24no—
158C22×C4⋊C4—24no—
159C22×C4⋊C4—24no—
160C22×C4⋊C4D418yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2314yes—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2312yes—
181C22×C22⋊C4C2314yes—
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2314yes—
191C22×C42C2311yescharacteristic
192C22×C42C2311yescharacteristic
193C22×C42C2311yescharacteristic
194C22×C42C2312yes—
195#400—28no—
196#400—28no—
197#400—28no—
198#400—28no—
199#400—28no—
200#400—28no—
201#398—28no—
202#397—28no—
203#391—28no—
204#389—28no—
205#386—28no—
206#382—28no—
207#381—28no—
208#381—28no—
209#381—28no—
210#380—28no—
211#380—24no—
212C4×C22⋊C4—24no—
213C2×#95—28no—
214C2×#95—28no—
215C2×#95—24no—
216C2×#95C2312yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2312yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C2×#95C2314yes—
230C2×#95C2314yes—
231C2×#95C2314yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2314yes—
237C2×#95C2314yes—
238C2×#95C2314yes—
239C2×#95C2314yes—
240C2×#95C2314yes—
241C25C2411yescharacteristic
242C25C2411yescharacteristic
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—24no—
252C22×Q8—42no—
253C22×Q8—44no—
254C22×Q8—44no—
255C22×Q8C2×D414yes—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—24no—
259C22×D4C2×D414yes—
260C22×D4#4118yes—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—24no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—24no—
285C23×C4—44no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—44no—
289C23×C4—44no—
290C23×C4—44no—
291C23×C4—44no—
292C23×C4—44no—
293C23×C4C2×D414yes—
294C23×C4C2×D414yes—
295C23×C4C2×D414yes—
296C23×C4C2×D414yes—
297C23×C4C2×D414yes—
298C23×C4C2×D414yes—
299C23×C4C2414yes—
300C23×C4C2414yes—
301C23×C4C2414yes—
302C23×C4C2414yes—
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C23×C4C2411yescharacteristic
314C23×C4C2411yescharacteristic
315C23×C4C2411yescharacteristic
316C4⋊Q8—232no—
317#125—232no—
318#125—232no—
319#123—432no—
320C22⋊Q8—232no—
321C22⋊Q8—232no—
322C22⋊Q8—232no—
323C22⋊Q8—232no—
324C22⋊Q8—232no—
325C22⋊Q8—232no—
326C4×Q8—232no—
327C4×D4—232no—
328C4×D4—232no—
329C4×D4—232no—
330C2×C4⋊C4—232no—
331C2×C4⋊C4—232no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—28no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—28no—
381C2×C4⋊C4—28no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—416no—
384C2×C4⋊C4C2×D414yes—
385C2×C4⋊C4C2×D414yes—
386C2×C4⋊C4C2×D414yes—
387C2×C4⋊C4C2×D414yes—
388C2×C4⋊C4C2×D414yes—
389C2×C4⋊C4C2×D414yes—
390C2×C4⋊C4C2×D414yes—
391C2×C4⋊C4C2×D414yes—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4—28no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—28no—
412C2×C22⋊C4—28no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—28no—
416C2×C22⋊C4—44no—
417C2×C22⋊C4—44no—
418C2×C22⋊C4C2×D414yes—
419C2×C22⋊C4C2×D414yes—
420C2×C22⋊C4C2×D414yes—
421C2×C22⋊C4C2×D414yes—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—24no—
431C2×C42—44no—
432C2×C42C2×D414yes—
433#95—24no—
434#95—24no—
435#95—28no—
436#95—28no—
437#95—28no—
438#95—28no—
439#95—24no—
440#95—28no—
441#95—24no—
442#95—28no—
443#95—28no—
444#95—28no—
445#95—28no—
446#95—28no—
447#95—28no—
448#95—28no—
449#95—44no—
450#95—44no—
451#95—44no—
452#95—44no—
453#95—44no—
454#95—44no—
455#95—44no—
456#95—44no—
457#95—44no—
458C24—22no—
459C24—22no—
460C24—24no—
461C24—21no—
462C24—21no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—24no—
467C24C22×D412yes—
468C24C22×D412yes—
469C24C22×D412yes—
470C24C22×D412yes—
471C24C2×#4114yes—
472C24C2×#4114yes—
473C242−1+414yes—
474C24C2511yescharacteristic
475C2×Q8—28no—
476C2×Q8—28no—
477C2×Q8—28no—
478C2×Q8—48no—
479C2×Q8—48no—
480C2×Q8—48no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—84no—
484C2×Q8—84no—
485C2×Q8—84no—
486C2×Q8—84no—
487C2×Q8—84no—
488C2×D4—28no—
489C2×D4—28no—
490C2×D4—216no—
491C2×D4—216no—
492C2×D4#124116yes—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—28no—
537C22×C4—28no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—44no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—84no—
589C22×C4—84no—
590C22×C4—84no—
591C22×C4—84no—
592C22×C4—84no—
593C22×C4—84no—
594C22×C4—84no—
595C22×C4—88no—
596C22×C4—88no—
597C22×C4#120116yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C22×D412yes—
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×D412yes—
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C2×#4114yes—
616C22×C42−1+414yes—
617C4⋊C4—28no—
618C4⋊C4—28no—
619C4⋊C4—28no—
620C4⋊C4—28no—
621C4⋊C4—28no—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—28no—
626C4⋊C4—28no—
627C4⋊C4—28no—
628C4⋊C4—28no—
629C4⋊C4—28no—
630C4⋊C4—28no—
631C4⋊C4—28no—
632C4⋊C4—28no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—48no—
636C4⋊C4—416no—
637C22⋊C4—28no—
638C22⋊C4—28no—
639C22⋊C4—28no—
640C22⋊C4—28no—
641C22⋊C4—28no—
642C22⋊C4—28no—
643C22⋊C4—48no—
644C22⋊C4—416no—
645C22⋊C4—48no—
646C22⋊C4—88no—
647C42—28no—
648C42—28no—
649C42—28no—
650C42—48no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—28no—
659C23—28no—
660C23—28no—
661C23—28no—
662C23—22no—
663C23—22no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—28no—
669C23—28no—
670C23—41no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—44no—
676C23—44no—
677C23C2×#12014yes—
678C23C2×#12414yes—
679C23C2×#12414yes—
680C23#53614yes—
681C23#54818yes—
682C23#54818yes—
683C23C23×D411yescharacteristic
684C23C23×D411yescharacteristic
685C23C23×D411yescharacteristic
686C23C22×#4112yes—
687C23C2×2−1+412yes—
688C23C2×2−1+412yes—
689C23#58512yes—
690C23#58514yes—
691Q8—416no—
692Q8—88no—
693Q8—88no—
694D4—232no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—416no—
729C2×C4—416no—
730C2×C4—416no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—88no—
781C2×C4—88no—
782C2×C4—88no—
783C2×C4—816no—
784C2×C4—816no—
785C2×C4C2×#12014yes—
786C2×C4C2×#12014yes—
787C2×C4C2×#12414yes—
788C2×C4#53614yes—
789C22—216no—
790C22—24no—
791C22—28no—
792C22—28no—
793C22—28no—
794C22—28no—
795C22—24no—
796C22—24no—
797C22—28no—
798C22—48no—
799C22—42no—
800C22—44no—
801C22—44no—
802C22—44no—
803C22—42no—
804C22#243618yes—
805C22C22×#12011yescharacteristic
806C22C22×#12411yescharacteristic
807C22C2×#53611yescharacteristic
808C22C2×#53611yescharacteristic
809C22#344911yescharacteristic
810C22C2×#54812yes—
811C22C2×#54812yes—
812C22#348512yes—
813C22#348512yes—
814C22#348512yes—
815C22#348912yes—
816C22#348912yes—
817C22#351514yes—
818C22#352114yes—
819C22#356314yes—
820C22#356414yes—
821C4—24no—
822C4—24no—
823C4—24no—
824C4—24no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—42no—
830C4—42no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—84no—
835C4—84no—
836C4—84no—
837C4—84no—
838C2—28no—
839C2—44no—
840C2C2×#243611yescharacteristic
841C2#3530511yescharacteristic
842C2#3544611yescharacteristic
843C2#3604212yes—
844C2#3911712yes—
845C2#3912212yes—
846C2#4141112yes—
847C2#4353214yes—
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
2. C2×#2503C2semidirect
4. C22×#400C2semidirect
5. #16634C2semidirect
6. #16366C2semidirect
7. #15881C2semidirect
8. #15783C2semidirect
9. #15670C2semidirect
10. #15465C2semidirect
11. #14934C2semidirect
12. #14934C2semidirect
13. #14884C2semidirect
14. #14822C2semidirect
15. #14281C2semidirect
18. #13923C2semidirect

Maximal subgroups

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

subgroupindex
C22×#5542
C2×#25032
C2×#24862
C22×#4002
#166342
#163662
#158812
#157832
#156702
#154652
#149342
#148842
#148222
#142812
#139682
#139232
#137842