Finite Group Databasebeta

← #4382005

Subgroups — #4382005

Order 512.

3596 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#539C211yesmaximal, characteristic
2C2×#2503C211yesmaximal, characteristic, complemented
3C2×#2487C211yesmaximal, characteristic, complemented
4C2×#2623C211yesmaximal, characteristic, complemented
5#16674C212yesmaximal, complemented
6#16634C212yesmaximal, complemented
7#16024C212yesmaximal, complemented
8#15984C212yesmaximal
9#15982C212yesmaximal, complemented
10#15982C212yesmaximal, complemented
11#15881C212yesmaximal, complemented
12#15669C212yesmaximal, complemented
13#15466C212yesmaximal, complemented
14#15465C212yesmaximal, complemented
15#14825C212yesmaximal, complemented
16#14822C212yesmaximal, complemented
17#14660C211yesmaximal, characteristic, complemented
18#14287C211yesmaximal, characteristic, complemented
19#13940C211yesmaximal, characteristic, complemented
20C2×#539—28no—
21C2×#539—28no—
22C2×#539—28no—
23C22×#126C2211yescharacteristic
24C22×#126C2211yescharacteristic
25C22×#125C2211yescharacteristic
26C22×#125C2211yescharacteristic
27C22×#123C2211yescharacteristic
28C22×#123C2211yescharacteristic
29C22×#123C2211yescharacteristic
30C22×#123C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C22×C22⋊Q8C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C22×#121C2211yescharacteristic
35C22×C4×D4C2211yescharacteristic
36C22×C4×D4C2211yescharacteristic
37C23×C4⋊C4C2211yescharacteristic
38C23×C4⋊C4C2211yescharacteristic
39#2623—28no—
40#2503—28no—
41#2487—28no—
42C2×#400C2212yes—
43C2×#400C2212yes—
44C2×#400C2212yes—
45C2×#400C2212yes—
46C2×#399C2212yes—
47C2×#399C2212yes—
48C2×#398C2212yes—
49C2×#397C2212yes—
50C2×#391C2212yes—
51C2×#389C2212yes—
52C2×#386C2212yes—
53C2×#386C2212yes—
54C2×#385C2212yes—
55C2×#385C2212yes—
56C2×#382C2212yes—
57C2×#381C2211yescharacteristic
58C2×#381C2212yes—
59C2×#381C2212yes—
60C2×#380C2211yescharacteristic
61C2×#380C2212yes—
62C2×C4×C22⋊C4C2211yescharacteristic
63#1446C2212yes—
64#1445C2212yes—
65#1444C2214yes—
66#1442C2214yes—
67#1442C2214yes—
68#1442C2214yes—
69#1442C2214yes—
70#1441C2214yes—
71#1441C2212yes—
72#1441C2214yes—
73#1441C2212yes—
74#1441C2214yes—
75#1441C2212yes—
76#1440C2214yes—
77#1440C2212yes—
78#1440C2212yes—
79#1440C2212yes—
80#1440C2212yes—
81#1439C2214yes—
82#1439C2212yes—
83#1439C2214yes—
84#1438C2214yes—
85#1438C2212yes—
86#1438C2212yes—
87#1437C2212yes—
88#1437C2212yes—
89#1436C2212yes—
90#1436C2212yes—
91#1436C2214yes—
92#1434C2212yes—
93C22⋊#95C2214yes—
94C22⋊#95C2214yes—
95C22⋊#95C2214yes—
96C22⋊#95C2212yes—
97C23×Q8C2311yescharacteristic
98C23×D4C2311yescharacteristic
99C23×D4C2311yescharacteristic
100C23×D4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2312yes—
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107#539—2128no—
108C2×#126—24no—
109C2×#126—24no—
110C2×#126—24no—
111C2×#126—24no—
112C2×#126—24no—
113C2×#126—24no—
114C2×#125—24no—
115C2×#125—24no—
116C2×#125—24no—
117C2×#125—24no—
118C2×#125—24no—
119C2×#125—24no—
120C2×#123—24no—
121C2×#123—24no—
122C2×#123—24no—
123C2×#123—24no—
124C2×#123—24no—
125C2×#123—24no—
126C2×#123—24no—
127C2×#123—24no—
128C2×#123—24no—
129C2×#123—24no—
130C2×#123—24no—
131C2×#123D418yes—
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⋊Q8—24no—
140C2×C22⋊Q8D418yes—
141C2×#121—24no—
142C2×#121—24no—
143C2×#121—24no—
144C2×C4×D4—24no—
145C2×C4×D4—24no—
146C2×C4×D4—24no—
147C2×C4×D4—24no—
148C2×C4×D4—24no—
149C2×C4×D4D418yes—
150C22×C4⋊C4—24no—
151C22×C4⋊C4—24no—
152C22×C4⋊C4—24no—
153C22×C4⋊C4—24no—
154C22×C4⋊C4—24no—
155C22×C4⋊C4—24no—
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
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⋊C4C2314yes—
173C22×C4⋊C4C2314yes—
174C22×C4⋊C4C2312yes—
175C22×C22⋊C4C2311yescharacteristic
176C22×C22⋊C4C2311yescharacteristic
177C22×C22⋊C4C2311yescharacteristic
178C22×C22⋊C4C2311yescharacteristic
179C22×C22⋊C4C2311yescharacteristic
180C22×C22⋊C4C2311yescharacteristic
181C22×C22⋊C4C2311yescharacteristic
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2314yes—
186C22×C22⋊C4C2314yes—
187C22×C22⋊C4C2314yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2314yes—
192C22×C42C2311yescharacteristic
193C22×C42C2311yescharacteristic
194C22×C42C2312yes—
195#400—28no—
196#400—28no—
197#400—28no—
198#400—28no—
199#399—28no—
200#399—28no—
201#398—28no—
202#397—28no—
203#391—28no—
204#389—28no—
205#386—28no—
206#386—28no—
207#385—28no—
208#385—28no—
209#382—28no—
210#381—24no—
211#381—28no—
212#381—28no—
213#380—28no—
214#380—24no—
215C4×C22⋊C4—24no—
216C2×#95C2312yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
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—
238C25C2411yescharacteristic
239C25C2411yescharacteristic
240C25C2411yescharacteristic
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—44no—
244C22×Q8C2×D414yes—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—24no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—24no—
253C22×D4—22no—
254C22×D4—42no—
255C22×D4—42no—
256C22×D4—44no—
257C22×D4C2×D414yes—
258C22×D4C2×D414yes—
259C23×C4—22no—
260C23×C4—22no—
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—22no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—44no—
275C23×C4—42no—
276C23×C4—44no—
277C23×C4—44no—
278C23×C4—44no—
279C23×C4—44no—
280C23×C4—44no—
281C23×C4C2×D414yes—
282C23×C4C2×D414yes—
283C23×C4C2×D414yes—
284C23×C4C2×D414yes—
285C23×C4C2414yes—
286C23×C4C2414yes—
287C23×C4C2414yes—
288C23×C4C2414yes—
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301#126—232no—
302#126—232no—
303#125—232no—
304#125—232no—
305#123—232no—
306#123—232no—
307#123—232no—
308#123—232no—
309C22⋊Q8—232no—
310C22⋊Q8—232no—
311C22⋊Q8—232no—
312#121—232no—
313C4×D4—232no—
314C4×D4—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—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—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—28no—
360C2×C4⋊C4—28no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—416no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4C2×D414yes—
368C2×C4⋊C4C2×D414yes—
369C2×C4⋊C4C2×D414yes—
370C2×C4⋊C4C2×D414yes—
371C2×C4⋊C4C2×D414yes—
372C2×C4⋊C4C2×D414yes—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
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—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—28no—
401C2×C22⋊C4—28no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4C2×D414yes—
415C2×C22⋊C4C2×D414yes—
416C2×C22⋊C4C2×D414yes—
417C2×C22⋊C4C2×D414yes—
418C2×C22⋊C4C2×D414yes—
419C2×C22⋊C4C2×D414yes—
420C2×C22⋊C4C2×D414yes—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—24no—
427C2×C42—44no—
428C2×C42C2×D414yes—
429#95—24no—
430#95—28no—
431#95—24no—
432#95—28no—
433#95—28no—
434#95—28no—
435#95—28no—
436#95—24no—
437#95—24no—
438#95—28no—
439#95—28no—
440#95—28no—
441#95—44no—
442#95—44no—
443#95—44no—
444#95—44no—
445#95—44no—
446#95—44no—
447#95—44no—
448#95—44no—
449#95—44no—
450#95—44no—
451C24—21no—
452C24—21no—
453C24—22no—
454C24—24no—
455C24—22no—
456C24—24no—
457C24—24no—
458C24—24no—
459C24—22no—
460C24—21no—
461C24—21no—
462C24—22no—
463C24—24no—
464C24—22no—
465C24—24no—
466C24C22×D412yes—
467C24C22×D412yes—
468C24C22×D412yes—
469C24C22×D412yes—
470C24C22×D412yes—
471C242−1+414yes—
472C24C2511yescharacteristic
473C2×Q8—28no—
474C2×Q8—48no—
475C2×Q8—84no—
476C2×Q8—84no—
477C2×D4—28no—
478C2×D4—28no—
479C2×D4—28no—
480C2×D4—28no—
481C2×D4—44no—
482C2×D4—48no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—48no—
486C2×D4—48no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—84no—
490C2×D4—84no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—28no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
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—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—28no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
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—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—84no—
571C22×C4—84no—
572C22×C4—84no—
573C22×C4—84no—
574C22×C4—84no—
575C22×C4—84no—
576C22×C4—84no—
577C22×C4—84no—
578C22×C4—88no—
579C22×C4—88no—
580C22×C4#120116yes—
581C22×C4C22×D412yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
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—
597C4⋊C4—28no—
598C4⋊C4—28no—
599C4⋊C4—28no—
600C4⋊C4—28no—
601C4⋊C4—28no—
602C4⋊C4—28no—
603C4⋊C4—28no—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—28no—
607C4⋊C4—28no—
608C4⋊C4—28no—
609C4⋊C4—28no—
610C4⋊C4—28no—
611C4⋊C4—48no—
612C4⋊C4—48no—
613C4⋊C4—48no—
614C4⋊C4—88no—
615C4⋊C4—88no—
616C22⋊C4—28no—
617C22⋊C4—28no—
618C22⋊C4—28no—
619C22⋊C4—28no—
620C22⋊C4—28no—
621C22⋊C4—28no—
622C22⋊C4—28no—
623C22⋊C4—28no—
624C22⋊C4—28no—
625C22⋊C4—28no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—88no—
630C22⋊C4—88no—
631C22⋊C4—88no—
632C22⋊C4—88no—
633C42—28no—
634C42—28no—
635C42—48no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—28no—
653C23—28no—
654C23—22no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—41no—
669C23—41no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23C2×#12014yes—
680C23#53614yes—
681C23C23×D411yescharacteristic
682C23C23×D411yescharacteristic
683C23C23×D411yescharacteristic
684C23C2×2−1+412yes—
685C23#58512yes—
686C23#58514yes—
687C23#58514yes—
688Q8—88no—
689D4—416no—
690D4—416no—
691D4—88no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
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—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—416no—
720C2×C4—416no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
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—88no—
773C2×C4—88no—
774C2×C4—88no—
775C2×C4—816no—
776C2×C4C2×#12014yes—
777C2×C4C2×#12014yes—
778C22—24no—
779C22—24no—
780C22—28no—
781C22—24no—
782C22—24no—
783C22—42no—
784C22—42no—
785C22—48no—
786C22—48no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—48no—
791C22—48no—
792C22—42no—
793C22—42no—
794C22—48no—
795C22—42no—
796C22—84no—
797C22—82no—
798C22—82no—
799C22C22×#12011yescharacteristic
800C22C2×#53611yescharacteristic
801C22#344911yescharacteristic
802C22#348512yes—
803C22#348512yes—
804C22#348512yes—
805C22#348712yes—
806C22#348912yes—
807C22#348912yes—
808C22#350012yes—
809C22#350012yes—
810C22#355314yes—
811C22#356414yes—
812C22#356614yes—
813C22#356714yes—
814C4—24no—
815C4—24no—
816C4—42no—
817C4—42no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—42no—
826C4—84no—
827C4—84no—
828C4—84no—
829C4—84no—
830C2—44no—
831C2—44no—
832C2—82no—
833C2#3530511yescharacteristic
834C2#3544611yescharacteristic
835C2#3567611yescharacteristic
836C2#4137412yes—
837C2#4138212yes—
838C2#4682214yes—
839C2#4878714yes—
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
2. C2×#2503C2semidirect
3. C2×#2487C2semidirect
4. C2×#2623C2semidirect
5. #16674C2semidirect
6. #16634C2semidirect
7. #16024C2semidirect
9. #15982C2semidirect
10. #15982C2semidirect
11. #15881C2semidirect
12. #15669C2semidirect
13. #15466C2semidirect
14. #15465C2semidirect
15. #14825C2semidirect
16. #14822C2semidirect
17. #14660C2semidirect
18. #14287C2semidirect
19. #13940C2semidirect

Maximal subgroups

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

subgroupindex
C22×#5392
C2×#25032
C2×#24872
C2×#26232
#166742
#166342
#160242
#159842
#159822
#158812
#156692
#154662
#154652
#148252
#148222
#146602
#142872
#139402