Finite Group Databasebeta

← #722654

Subgroups — #722654

Order 512.

4026 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#554C211yesmaximal, characteristic
2C2×#2502C211yesmaximal, characteristic, complemented
3C2×#2487C211yesmaximal, characteristic
4C22×#398C211yesmaximal, characteristic, complemented
5#16607C212yesmaximal, complemented
6#16365C212yesmaximal, complemented
7#15850C212yesmaximal, complemented
8#15783C212yesmaximal, complemented
9#15466C212yesmaximal, complemented
10#15430C212yesmaximal, complemented
11#14914C212yesmaximal, complemented
12#14880C212yesmaximal, complemented
13#14821C212yesmaximal, complemented
14#14720C212yesmaximal, complemented
15#14281C211yesmaximal, characteristic, complemented
16#14016C212yesmaximal
17#14015C212yesmaximal
18#13923C211yesmaximal, characteristic, complemented
19#13784C211yesmaximal, characteristic
20C2×#554—28no—
21C2×#554—28no—
22C2×#554—28no—
23C22×C4⋊Q8C2211yescharacteristic
24C22×#125C2211yescharacteristic
25C22×#125C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C22×C4×D4C2211yescharacteristic
36C23×C4⋊C4C2211yescharacteristic
37C23×C4⋊C4C2211yescharacteristic
38C23×C4⋊C4C2211yescharacteristic
39C23×C4⋊C4C2212yes—
40#2502—28no—
41#2487—28no—
42C2×#400C2212yes—
43C2×#399C2212yes—
44C2×#398—28no—
45C2×#398C2212yes—
46C2×#398C2212yes—
47C2×#398C2212yes—
48C2×#398C2212yes—
49C2×#398C2212yes—
50C2×#398C2212yes—
51C2×#395C2214yes—
52C2×#391C2212yes—
53C2×#389C2212yes—
54C2×#386C2212yes—
55C2×#386C2212yes—
56C2×#385C2212yes—
57C2×#385C2212yes—
58C2×#385C2212yes—
59C2×#385C2214yes—
60C2×#384C2212yes—
61C2×#380C2211yescharacteristic
62C2×#380C2212yes—
63C2×C4×C22⋊C4C2211yescharacteristic
64C22×#95C2212yes—
65C22×#95C2211yescharacteristic
66#1446C2214yes—
67#1446C2212yes—
68#1445C2212yes—
69#1444C2214yes—
70#1444C2214yes—
71#1444C2214yes—
72#1444C2214yes—
73#1442C2214yes—
74#1441C2214yes—
75#1441C2212yes—
76#1441C2212yes—
77#1441C2214yes—
78#1441C2212yes—
79#1441C2214yes—
80#1441C2212yes—
81#1439C2214yes—
82#1439C2214yes—
83#1437C2212yes—
84#1436C2214yes—
85#1436C2214yes—
86#1436C2212yes—
87#1436C2212yes—
88#1436C2212yes—
89#1434C2212yes—
90C22⋊#95C2212yes—
91C22⋊#95C2212yes—
92C22⋊#95C2212yes—
93C22⋊#95C2212yes—
94C22⋊#95C2214yes—
95C22⋊#95C2212yes—
96C22⋊#95C2212yes—
97C23×Q8C2311yescharacteristic
98C23×Q8C2311yescharacteristic
99C23×Q8C2311yescharacteristic
100C23×D4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2312yes—
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2312yes—
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×C22⋊Q8—24no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—24no—
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⋊Q8D418yes—
137C2×C4×Q8—24no—
138C2×C4×Q8—24no—
139C2×C4×Q8—24no—
140C2×C4×D4—24no—
141C2×C4×D4—24no—
142C2×C4×D4—24no—
143C2×C4×D4—24no—
144C2×C4×D4—24no—
145C2×C4×D4—24no—
146C2×C4×D4—24no—
147C2×C4×D4—24no—
148C2×C4×D4D418yes—
149C22×C4⋊C4—24no—
150C22×C4⋊C4—24no—
151C22×C4⋊C4—24no—
152C22×C4⋊C4—24no—
153C22×C4⋊C4—24no—
154C22×C4⋊C4—28no—
155C22×C4⋊C4—24no—
156C22×C4⋊C4—24no—
157C22×C4⋊C4—24no—
158C22×C4⋊C4—48no—
159C22×C4⋊C4D418yes—
160C22×C4⋊C4C2314yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2311yescharacteristic
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⋊C4C2314yes—
180C22×C4⋊C4C2314yes—
181C22×C4⋊C4C2314yes—
182C22×C4⋊C4C2314yes—
183C22×C4⋊C4C2312yes—
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2314yes—
193C22×C22⋊C4C2314yes—
194C22×C42C2311yescharacteristic
195C22×C42C2311yescharacteristic
196C22×C42C2311yescharacteristic
197C22×C42C2312yes—
198#400—28no—
199#399—28no—
200#398—28no—
201#398—28no—
202#398—28no—
203#398—28no—
204#398—28no—
205#398—28no—
206#395—48no—
207#391—28no—
208#389—28no—
209#386—28no—
210#386Q8116yescomplemented
211#385—28no—
212#385—28no—
213#385—28no—
214#385—48no—
215#384—28no—
216#380—28no—
217#380—24no—
218C4×C22⋊C4—24no—
219C2×#95—24no—
220C2×#95—28no—
221C2×#95C2314yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2314yes—
225C2×#95C2312yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C2×#95C2312yes—
230C2×#95C2314yes—
231C2×#95C2314yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2314yes—
237C2×#95C2314yes—
238C2×#95C2314yes—
239C2×#95C2314yes—
240C2×#95C2314yes—
241C2×#95C2314yes—
242C25C2411yescharacteristic
243C25C2411yescharacteristic
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—24no—
253C22×Q8—42no—
254C22×Q8—44no—
255C22×Q8—44no—
256C22×Q8C2×D414yes—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—24no—
260C22×D4C2×D414yes—
261C22×D4C2×Q818yes—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—24no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—44no—
282C23×C4—44no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—44no—
286C23×C4—44no—
287C23×C4—44no—
288C23×C4—44no—
289C23×C4—44no—
290C23×C4—44no—
291C23×C4C2×D414yes—
292C23×C4C2×D414yes—
293C23×C4C2×D414yes—
294C23×C4C2×D414yes—
295C23×C4C2×D414yes—
296C23×C4C2×D414yes—
297C23×C4C2×Q818yes—
298C23×C4C2414yes—
299C23×C4C2414yes—
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2414yes—
310C23×C4C2414yes—
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C23×C4C2411yescharacteristic
314C23×C4C2411yescharacteristic
315C4⋊Q8—232no—
316#125—232no—
317#125—232no—
318C22⋊Q8—232no—
319C22⋊Q8—232no—
320C22⋊Q8—232no—
321C22⋊Q8—232no—
322C22⋊Q8—232no—
323C22⋊Q8—232no—
324C4×Q8—232no—
325C4×D4—232no—
326C4×D4—232no—
327C4×D4—232no—
328C2×C4⋊C4—232no—
329C2×C4⋊C4—232no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
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—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—28no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—28no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—28no—
380C2×C4⋊C4—28no—
381C2×C4⋊C4—28no—
382C2×C4⋊C4—28no—
383C2×C4⋊C4—28no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4—44no—
387C2×C4⋊C4—432no—
388C2×C4⋊C4—416no—
389C2×C4⋊C4—44no—
390C2×C4⋊C4—44no—
391C2×C4⋊C4—44no—
392C2×C4⋊C4—44no—
393C2×C4⋊C4—44no—
394C2×C4⋊C4—44no—
395C2×C4⋊C4C2×D414yes—
396C2×C4⋊C4C2×D414yes—
397C2×C4⋊C4C2×D414yes—
398C2×C4⋊C4C2×D414yes—
399C2×C4⋊C4C2×D414yes—
400C2×C4⋊C4C2×D414yes—
401C2×C4⋊C4C2×D414yes—
402C2×C4⋊C4C2×D414yes—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—24no—
420C2×C22⋊C4—24no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—28no—
423C2×C22⋊C4—44no—
424C2×C22⋊C4—44no—
425C2×C22⋊C4—44no—
426C2×C22⋊C4—44no—
427C2×C22⋊C4C2×D414yes—
428C2×C22⋊C4C2×D414yes—
429C2×C22⋊C4C2×D414yes—
430C2×C22⋊C4C2×D414yes—
431C2×C22⋊C4C2×Q818yes—
432C2×C22⋊C4C2×Q8116yes—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—24no—
442C2×C42—44no—
443C2×C42C2×D414yes—
444#95—24no—
445#95—24no—
446#95—28no—
447#95—28no—
448#95—24no—
449#95—28no—
450#95—24no—
451#95—28no—
452#95—28no—
453#95—28no—
454#95—28no—
455#95—44no—
456#95—44no—
457#95—44no—
458#95—44no—
459#95—44no—
460#95—44no—
461#95—44no—
462#95—44no—
463#95—44no—
464#95C2×Q8116yes—
465C24—22no—
466C24—22no—
467C24—24no—
468C24—21no—
469C24—21no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—24no—
474C24C22×D412yes—
475C24C22×D412yes—
476C24C22×D412yes—
477C24C22×D412yes—
478C24C22×Q814yes—
479C24C22×Q814yes—
480C242−1+414yes—
481C24C2511yescharacteristic
482C2×Q8—28no—
483C2×Q8—28no—
484C2×Q8—28no—
485C2×Q8—48no—
486C2×Q8—48no—
487C2×Q8—48no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—84no—
491C2×Q8—84no—
492C2×Q8—84no—
493C2×Q8—84no—
494C2×Q8—84no—
495C2×D4—28no—
496C2×D4—28no—
497C2×D4—216no—
498C2×D4—216no—
499C2×D4C4⋊Q8116yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—28no—
509C22×C4—28no—
510C22×C4—216no—
511C22×C4—24no—
512C22×C4—24no—
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—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—22no—
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—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—28no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—28no—
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—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—44no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—416no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—44no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—416no—
587C22×C4—44no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—84no—
592C22×C4—84no—
593C22×C4—84no—
594C22×C4—84no—
595C22×C4—84no—
596C22×C4—84no—
597C22×C4—84no—
598C22×C4—88no—
599C22×C4—88no—
600C22×C4#120116yes—
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×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4C22×Q818yes—
619C22×C4C22×Q818yes—
620C22×C4C22×Q814yes—
621C22×C4H(5,𝔽2)14yes—
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—28no—
634C4⋊C4—28no—
635C4⋊C4—28no—
636C4⋊C4—28no—
637C4⋊C4—28no—
638C4⋊C4—48no—
639C4⋊C4—416no—
640C4⋊C4—48no—
641C4⋊C4—48no—
642C4⋊C4—416no—
643C4⋊C4—88no—
644C4⋊C4—88no—
645C4⋊C4—88no—
646C22⋊C4—28no—
647C22⋊C4—28no—
648C22⋊C4—28no—
649C22⋊C4—28no—
650C22⋊C4—28no—
651C22⋊C4—216no—
652C22⋊C4—28no—
653C22⋊C4—416no—
654C22⋊C4—48no—
655C22⋊C4—88no—
656C42—28no—
657C42—28no—
658C42—28no—
659C42—48no—
660C23—22no—
661C23—22no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—28no—
668C23—28no—
669C23—28no—
670C23—28no—
671C23—22no—
672C23—22no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—28no—
678C23—28no—
679C23—41no—
680C23—41no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—44no—
685C23—44no—
686C23C2×#12014yes—
687C23C2×C4⋊Q814yes—
688C23C2×C4⋊Q814yes—
689C23#53614yes—
690C23D4×Q818yes—
691C23D4×Q818yes—
692C23C23×D411yescharacteristic
693C23C23×D411yescharacteristic
694C23C23×D411yescharacteristic
695C23C23×Q812yes—
696C23C2×H(5,𝔽2)12yes—
697C23C2×2−1+412yes—
698C23#58512yes—
699C23#58514yes—
700Q8—416no—
701Q8—88no—
702Q8—88no—
703D4—232no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—28no—
730C2×C4—28no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—28no—
740C2×C4—28no—
741C2×C4—28no—
742C2×C4—28no—
743C2×C4—416no—
744C2×C4—416no—
745C2×C4—416no—
746C2×C4—432no—
747C2×C4—44no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
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—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—88no—
791C2×C4—88no—
792C2×C4—88no—
793C2×C4—816no—
794C2×C4C2×#12014yes—
795C2×C4C2×#12014yes—
796C2×C4C2×C4⋊Q814yes—
797C2×C4#53514yes—
798C22—216no—
799C22—28no—
800C22—24no—
801C22—28no—
802C22—28no—
803C22—24no—
804C22—28no—
805C22—28no—
806C22—24no—
807C22—48no—
808C22—42no—
809C22—44no—
810C22—44no—
811C22—42no—
812C22—44no—
813C22#243418yes—
814C22C22×#12011yescharacteristic
815C22C22×C4⋊Q811yescharacteristic
816C22C2×#53511yescharacteristic
817C22C2×#53611yescharacteristic
818C22#344911yescharacteristic
819C22C2×D4×Q812yes—
820C22C2×D4×Q812yes—
821C22#348512yes—
822C22#348512yes—
823C22#348512yes—
824C22#348812yes—
825C22#348812yes—
826C22#350114yes—
827C22#350414yes—
828C22#354114yes—
829C22#355314yes—
830C4—24no—
831C4—24no—
832C4—24no—
833C4—24no—
834C4—48no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—42no—
839C4—42no—
840C4—48no—
841C4—42no—
842C4—42no—
843C4—42no—
844C4—42no—
845C4—84no—
846C4—84no—
847C2—28no—
848C2—44no—
849C2C2×#243411yescharacteristic
850C2#3525011yescharacteristic
851C2#3544611yescharacteristic
852C2#3595012yes—
853C2#3958912yes—
854C2#3959412yes—
855C2#4140612yes—
856C2#4352914yes—
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×#2502C2semidirect
4. C22×#398C2semidirect
5. #16607C2semidirect
6. #16365C2semidirect
7. #15850C2semidirect
8. #15783C2semidirect
9. #15466C2semidirect
10. #15430C2semidirect
11. #14914C2semidirect
12. #14880C2semidirect
13. #14821C2semidirect
14. #14720C2semidirect
15. #14281C2semidirect
18. #13923C2semidirect
210. #386Q8semidirect

Maximal subgroups

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

subgroupindex
C22×#5542
C2×#25022
C2×#24872
C22×#3982
#166072
#163652
#158502
#157832
#154662
#154302
#149142
#148802
#148212
#147202
#142812
#140162
#140152
#139232
#137842