Finite Group Databasebeta

← #711885

Subgroups — #711885

Order 512.

3780 conjugacy classes of subgroups.

The subgroup lattice has 843 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#552C211yesmaximal, characteristic
2C2×#2623C211yesmaximal, characteristic
3C22×#400C211yesmaximal, characteristic, complemented
4C2×#2317C211yesmaximal, characteristic, complemented
5#16674C212yesmaximal, complemented
6#16634C212yesmaximal, complemented
7#15928C212yesmaximal, complemented
8#15881C212yesmaximal, complemented
9#15850C212yesmaximal, complemented
10#15670C212yesmaximal, complemented
11#14914C212yesmaximal, complemented
12#14912C212yesmaximal
13#14893C212yesmaximal, complemented
14#14884C212yesmaximal, complemented
15#14135C211yesmaximal, characteristic
16#14128C212yesmaximal, complemented
17#14016C212yesmaximal
18#13958C211yesmaximal, characteristic, complemented
19#13870C211yesmaximal, characteristic, complemented
20C2×#552—28no—
21C2×#552—28no—
22C2×#552—28no—
23C22×#126C2211yescharacteristic
24C22×#126C2211yescharacteristic
25C22×#125C2211yescharacteristic
26C22×#125C2211yescharacteristic
27C22×#125C2211yescharacteristic
28C22×#123C2211yescharacteristic
29C22×#123C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C22×#117C2211yescharacteristic
35C22×#117C2211yescharacteristic
36C22×#117C2211yescharacteristic
37C22×#117C2211yescharacteristic
38C23×C4⋊C4C2211yescharacteristic
39C23×C4⋊C4C2211yescharacteristic
40#2623—28no—
41C2×#400—28no—
42C2×#400C2212yes—
43C2×#400C2212yes—
44C2×#400C2212yes—
45C2×#400C2212yes—
46C2×#400C2212yes—
47C2×#399C2212yes—
48C2×#398C2212yes—
49C2×#397C2212yes—
50#2317—28no—
51C2×#389C2212yes—
52C2×#389C2212yes—
53C2×#386C2212yes—
54C2×#386C2212yes—
55C2×#385C2212yes—
56C2×#385C2212yes—
57C2×#385C2212yes—
58C2×#384C2212yes—
59C2×#382C2212yes—
60C2×#381C2211yescharacteristic
61C2×#381C2212yes—
62C22×#95C2212yes—
63C22×#95C2211yescharacteristic
64C22×#95C2212yes—
65#1446C2214yes—
66#1445C2212yes—
67#1445C2212yes—
68#1444C2214yes—
69#1444C2214yes—
70#1442C2214yes—
71#1442C2214yes—
72#1442C2214yes—
73#1441C2214yes—
74#1441C2212yes—
75#1441C2212yes—
76#1441C2212yes—
77#1441C2214yes—
78#1441C2214yes—
79#1440C2214yes—
80#1439C2212yes—
81#1439C2214yes—
82#1439C2214yes—
83#1437C2212yes—
84#1436C2214yes—
85#1436C2212yes—
86#1436C2212yes—
87#1436C2214yes—
88#1436C2214yes—
89#1436C2212yes—
90#1434C2212yes—
91#1434C2212yes—
92C22⋊#95C2214yes—
93C22⋊#95C2212yes—
94C22⋊#95C2212yes—
95C22⋊#95C2212yes—
96C22⋊#95C2212yes—
97C23×Q8C2311yescharacteristic
98C23×D4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2312yes—
104C24×C4C2312yes—
105#552—2128no—
106C2×#126—24no—
107C2×#126—24no—
108C2×#126—24no—
109C2×#126—24no—
110C2×#126—24no—
111C2×#126—24no—
112C2×#125—24no—
113C2×#125—24no—
114C2×#125—24no—
115C2×#125—24no—
116C2×#125—24no—
117C2×#125—24no—
118C2×#125—24no—
119C2×#125—24no—
120C2×#125—24no—
121C2×#123—24no—
122C2×#123—24no—
123C2×#123—24no—
124C2×#123—24no—
125C2×#123—24no—
126C2×#123D418yes—
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×C4×Q8—24no—
134C2×C4×Q8—24no—
135C2×C4×Q8—24no—
136C2×C4×D4—24no—
137C2×C4×D4—24no—
138C2×C4×D4—24no—
139C2×#117—24no—
140C2×#117—24no—
141C2×#117—24no—
142C2×#117—24no—
143C2×#117—24no—
144C2×#117—24no—
145C2×#117—24no—
146C2×#117—24no—
147C2×#117—28no—
148C2×#117—24no—
149C2×#117D418yes—
150C22×C4⋊C4—24no—
151C22×C4⋊C4—24no—
152C22×C4⋊C4—24no—
153C22×C4⋊C4—24no—
154C22×C4⋊C4—24no—
155C22×C4⋊C4D418yes—
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2311yescharacteristic
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⋊C4C2314yes—
176C22×C4⋊C4C2314yes—
177C22×C4⋊C4C2314yes—
178C22×C22⋊C4C2311yescharacteristic
179C22×C22⋊C4C2311yescharacteristic
180C22×C22⋊C4C2311yescharacteristic
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2314yes—
189C22×C22⋊C4C2314yes—
190C22×C42C2311yescharacteristic
191C22×C42C2311yescharacteristic
192C22×C42C2312yes—
193C22×C42C2311yescharacteristic
194C22×C42C2311yescharacteristic
195C22×C42C2311yescharacteristic
196#400—28no—
197#400—28no—
198#400—28no—
199#400—28no—
200#400—28no—
201#399—28no—
202#398—28no—
203#397—28no—
204#389—28no—
205#389—28no—
206#386—28no—
207#386—28no—
208#385—28no—
209#385—28no—
210#385—28no—
211#384—28no—
212#382—28no—
213#381—24no—
214#381—28no—
215C2×#95—28no—
216C2×#95—28no—
217C2×#95—24no—
218C2×#95C2312yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2312yes—
222C2×#95C2314yes—
223C2×#95C2312yes—
224C2×#95C2314yes—
225C2×#95C2312yes—
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—24no—
247C22×Q8—42no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—24no—
251C22×D4—24no—
252C22×D4C2×D414yes—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—44no—
275C23×C4—44no—
276C23×C4—44no—
277C23×C4—44no—
278C23×C4C2×D414yes—
279C23×C4C2×D414yes—
280C23×C4C2×D414yes—
281C23×C4C2×D414yes—
282C23×C4C2×D414yes—
283C23×C4C2414yes—
284C23×C4C2414yes—
285C23×C4C2414yes—
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2414yes—
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300#126—232no—
301#126—232no—
302#125—232no—
303#125—232no—
304#125—232no—
305#123—232no—
306#123—232no—
307C22⋊Q8—232no—
308C22⋊Q8—232no—
309C4×Q8—232no—
310C4×D4—232no—
311#117—232no—
312#117—232no—
313#117—232no—
314#117—232no—
315C2×C4⋊C4—232no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
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—24no—
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—28no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—28no—
365C2×C4⋊C4—28no—
366C2×C4⋊C4—28no—
367C2×C4⋊C4—416no—
368C2×C4⋊C4—44no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4C2×D414yes—
375C2×C4⋊C4C2×D414yes—
376C2×C4⋊C4C2×D414yes—
377C2×C4⋊C4C2×D414yes—
378C2×C4⋊C4C2×D414yes—
379C2×C4⋊C4C2×D414yes—
380C2×C4⋊C4C2×D414yes—
381C2×C4⋊C4C2×D414yes—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—24no—
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—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—28no—
407C2×C22⋊C4—28no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4C2×D414yes—
413C2×C22⋊C4C2×D414yes—
414C2×C22⋊C4C2×D414yes—
415C2×C22⋊C4C2×D414yes—
416C2×C22⋊C4C2×D414yes—
417C2×C22⋊C4#4118yes—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—24no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—28no—
433C2×C42C2×D414yes—
434C2×C42C2×D414yes—
435#95—24no—
436#95—24no—
437#95—28no—
438#95—28no—
439#95—28no—
440#95—28no—
441#95—24no—
442#95—24no—
443#95—28no—
444#95—28no—
445#95—28no—
446#95—28no—
447#95—28no—
448#95—28no—
449#95—28no—
450#95—28no—
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—
467C24—22no—
468C24C22×D412yes—
469C24C22×D412yes—
470C24C22×D412yes—
471C24C22×D412yes—
472C24C2×#4114yes—
473C242−1+414yes—
474C24C2511yescharacteristic
475C2×Q8—28no—
476C2×Q8—48no—
477C2×Q8—48no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×D4—28no—
481C2×D4—216no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—48no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—216no—
488C22×C4—216no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—28no—
499C22×C4—216no—
500C22×C4—24no—
501C22×C4—21no—
502C22×C4—21no—
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—24no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—28no—
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—44no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—48no—
574C22×C4—44no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—88no—
582C22×C4—88no—
583C22×C4—88no—
584C22×C4—88no—
585C22×C4#120116yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C2×#4118yes—
604C22×C42−1+414yes—
605C4⋊C4—216no—
606C4⋊C4—28no—
607C4⋊C4—28no—
608C4⋊C4—28no—
609C4⋊C4—28no—
610C4⋊C4—28no—
611C4⋊C4—28no—
612C4⋊C4—28no—
613C4⋊C4—28no—
614C4⋊C4—28no—
615C4⋊C4—28no—
616C4⋊C4—28no—
617C4⋊C4—28no—
618C4⋊C4—28no—
619C4⋊C4—28no—
620C4⋊C4—28no—
621C4⋊C4—28no—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C4⋊C4—88no—
625C4⋊C4—88no—
626C4⋊C4—88no—
627C22⋊C4—28no—
628C22⋊C4—28no—
629C22⋊C4—28no—
630C22⋊C4—28no—
631C22⋊C4—28no—
632C22⋊C4—28no—
633C22⋊C4—216no—
634C22⋊C4—28no—
635C22⋊C4—28no—
636C22⋊C4—48no—
637C22⋊C4—88no—
638C22⋊C4—88no—
639C42—216no—
640C42—28no—
641C42—28no—
642C42—28no—
643C42—28no—
644C42—28no—
645C23—22no—
646C23—22no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—28no—
653C23—28no—
654C23—28no—
655C23—28no—
656C23—22no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23C2×#12014yes—
673C23#52514yes—
674C23#53614yes—
675C23#54718yes—
676C23#54718yes—
677C23C23×D411yescharacteristic
678C23C23×D411yescharacteristic
679C23C23×D411yescharacteristic
680C23C22×#4112yes—
681C23C2×2−1+412yes—
682C23C2×2−1+412yes—
683C23#58512yes—
684C23#58514yes—
685Q8—416no—
686D4—416no—
687C2×C4—232no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—28no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—28no—
723C2×C4—28no—
724C2×C4—416no—
725C2×C4—416no—
726C2×C4—416no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
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—816no—
779C2×C4—816no—
780C2×C4C2×#12014yes—
781C2×C4C2×#12014yes—
782C2×C4#53614yes—
783C22—28no—
784C22—24no—
785C22—28no—
786C22—28no—
787C22—216no—
788C22—28no—
789C22—24no—
790C22—42no—
791C22—42no—
792C22—48no—
793C22—42no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22#240618yes—
799C22C22×#12011yescharacteristic
800C22C2×#52511yescharacteristic
801C22C2×#53611yescharacteristic
802C22C2×#53611yescharacteristic
803C22#344911yescharacteristic
804C22C2×#54712yes—
805C22C2×#54712yes—
806C22#348712yes—
807C22#348912yes—
808C22#348912yes—
809C22#350012yes—
810C22#350012yes—
811C22#351514yes—
812C22#352114yes—
813C22#356314yes—
814C22#356414yes—
815C4—24no—
816C4—24no—
817C4—24no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—48no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—84no—
830C4—84no—
831C4—84no—
832C2—28no—
833C2—82no—
834C2C2×#240611yescharacteristic
835C2#3530511yescharacteristic
836C2#3567611yescharacteristic
837C2#3607012yes—
838C2#3804712yes—
839C2#3891912yes—
840C2#4215012yes—
841C2#4447514yes—
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. C22×#400C2semidirect
4. C2×#2317C2semidirect
5. #16674C2semidirect
6. #16634C2semidirect
7. #15928C2semidirect
8. #15881C2semidirect
9. #15850C2semidirect
10. #15670C2semidirect
11. #14914C2semidirect
13. #14893C2semidirect
14. #14884C2semidirect
16. #14128C2semidirect
18. #13958C2semidirect
19. #13870C2semidirect

Maximal subgroups

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

subgroupindex
C22×#5522
C2×#26232
C22×#4002
C2×#23172
#166742
#166342
#159282
#158812
#158502
#156702
#149142
#149122
#148932
#148842
#141352
#141282
#140162
#139582
#138702