Finite Group Databasebeta

← #4381680

Subgroups — #4381680

Order 512.

3878 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#539C211yesmaximal, characteristic
2C2×#2821C211yesmaximal, characteristic, complemented
3C2×#2542C211yesmaximal, characteristic, complemented
4C2×#2660C211yesmaximal, characteristic, complemented
5#16254C212yesmaximal, complemented
6#16251C212yesmaximal, complemented
7#15927C212yesmaximal, complemented
8#15850C212yesmaximal, complemented
9#15669C212yesmaximal, complemented
10#15464C212yesmaximal, complemented
11#15430C212yesmaximal, complemented
12#15430C212yesmaximal, complemented
13#15384C212yesmaximal, complemented
14#15340C212yesmaximal
15#14723C212yesmaximal, complemented
16#14720C212yesmaximal, complemented
17#14289C211yesmaximal, characteristic, complemented
18#14166C211yesmaximal, characteristic, complemented
19#13959C211yesmaximal, characteristic, complemented
20C2×#539—28no—
21C2×#539—28no—
22C2×#539—28no—
23C22×C4⋊Q8C2211yescharacteristic
24C22×#126C2211yescharacteristic
25C22×#126C2211yescharacteristic
26C22×#125C2211yescharacteristic
27C22×#125C2211yescharacteristic
28C22×#123C2211yescharacteristic
29C22×#123C2211yescharacteristic
30C22×#123C2211yescharacteristic
31C22×#123C2211yescharacteristic
32C22×C22⋊Q8C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C22×C22⋊Q8C2211yescharacteristic
35C22×C22⋊Q8C2212yes—
36C22×C22⋊Q8C2212yes—
37C22×#121C2211yescharacteristic
38C22×C4×D4C2211yescharacteristic
39C22×C4×D4C2211yescharacteristic
40C23×C4⋊C4C2211yescharacteristic
41#2821—28no—
42#2660—28no—
43#2542—28no—
44C2×#400C2212yes—
45C2×#399C2212yes—
46C2×#399C2212yes—
47C2×#399C2212yes—
48C2×#398C2212yes—
49C2×#398C2212yes—
50C2×#398C2212yes—
51C2×#397C2212yes—
52C2×#395C2212yes—
53C2×#395C2212yes—
54C2×#395C2212yes—
55C2×#395C2214yes—
56C2×#394C2214yes—
57C2×#393C2212yes—
58C2×#390C2212yes—
59C2×#385C2214yes—
60C2×#385C2214yes—
61C2×#384C2212yes—
62C2×#384C2212yes—
63C2×#383C2211yescharacteristic
64C2×#382C2212yes—
65C2×C4×C4⋊C4C2211yescharacteristic
66C2×#376C2211yescharacteristic
67#1445C2212yes—
68#1445C2212yes—
69#1445C2212yes—
70#1444C2214yes—
71#1444C2214yes—
72#1444C2214yes—
73#1441C2214yes—
74#1441C2212yes—
75#1441C2212yes—
76#1441C2212yes—
77#1440C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2212yes—
83#1438C2214yes—
84#1438C2212yes—
85#1437C2212yes—
86#1437C2212yes—
87#1437C2212yes—
88#1437C2212yes—
89#1436C2212yes—
90#1436C2214yes—
91#1436C2212yes—
92#1436C2212yes—
93#1436C2212yes—
94C22⋊#95C2214yes—
95C22⋊#95C2212yes—
96C22⋊#95C2212yes—
97C23×Q8C2312yes—
98C23×Q8C2311yescharacteristic
99C23×D4C2311yescharacteristic
100C23×D4C2311yescharacteristic
101C23×D4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107#539—2128no—
108C2×C4⋊Q8—24no—
109C2×C4⋊Q8—24no—
110C2×C4⋊Q8—24no—
111C2×#126—24no—
112C2×#126—24no—
113C2×#126—24no—
114C2×#126—24no—
115C2×#126—24no—
116C2×#126D418yes—
117C2×#125—24no—
118C2×#125—24no—
119C2×#125—24no—
120C2×#125—24no—
121C2×#125—24no—
122C2×#125D418yes—
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×#123—24no—
132C2×#123—24no—
133C2×#123—24no—
134C2×#123—24no—
135C2×C22⋊Q8—24no—
136C2×C22⋊Q8—28no—
137C2×C22⋊Q8—28no—
138C2×C22⋊Q8—24no—
139C2×C22⋊Q8—24no—
140C2×C22⋊Q8—24no—
141C2×C22⋊Q8—24no—
142C2×C22⋊Q8—24no—
143C2×C22⋊Q8—24no—
144C2×C22⋊Q8—24no—
145C2×C22⋊Q8—24no—
146C2×C22⋊Q8—48no—
147C2×C22⋊Q8—48no—
148C2×#121—24no—
149C2×#121—24no—
150C2×#121—24no—
151C2×C4×D4—24no—
152C2×C4×D4—24no—
153C2×C4×D4—24no—
154C2×C4×D4—24no—
155C2×C4×D4—24no—
156C2×C4×D4D418yes—
157C22×C4⋊C4—24no—
158C22×C4⋊C4—24no—
159C22×C4⋊C4—24no—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2314yes—
168C22×C4⋊C4C2314yes—
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×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2314yes—
188C22×C22⋊C4C2314yes—
189C22×C22⋊C4C2314yes—
190C22×C22⋊C4C2314yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2314yes—
197C22×C22⋊C4C2314yes—
198C22×C42C2311yescharacteristic
199C22×C42C2312yes—
200C22×C42C2312yes—
201C22×C42C2311yescharacteristic
202#400—28no—
203#399—28no—
204#399—28no—
205#399—28no—
206#398—28no—
207#398—28no—
208#398—28no—
209#397—28no—
210#395—28no—
211#395—28no—
212#395—28no—
213#395—48no—
214#394—48no—
215#393—28no—
216#390—28no—
217#385—48no—
218#385—48no—
219#384—28no—
220#384—28no—
221#383—24no—
222#382—28no—
223C4×C4⋊C4—24no—
224#376—24no—
225C2×#95C2312yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2312yes—
229C2×#95C2314yes—
230C2×#95C2314yes—
231C2×#95C2314yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2314yes—
239C2×#95C2314yes—
240C2×#95C2314yes—
241C2×#95C2314yes—
242C2×#95C2314yes—
243C2×#95C2314yes—
244C25C2411yescharacteristic
245C25C2411yescharacteristic
246C25C2411yescharacteristic
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—24no—
251C22×Q8—24no—
252C22×Q8—24no—
253C22×Q8—44no—
254C22×Q8—44no—
255C22×Q8—44no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—24no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—24no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4—42no—
267C22×D4—42no—
268C22×D4—44no—
269C22×D4C2×D414yes—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—24no—
284C23×C4—42no—
285C23×C4—44no—
286C23×C4—44no—
287C23×C4—44no—
288C23×C4—44no—
289C23×C4C2×D414yes—
290C23×C4C2×D414yes—
291C23×C4C2414yes—
292C23×C4C2414yes—
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2414yes—
303C23×C4C2414yes—
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307C4⋊Q8—416no—
308#126—232no—
309#126—232no—
310#125—232no—
311#125—232no—
312#123—232no—
313#123—232no—
314#123—232no—
315#123—232no—
316C22⋊Q8—232no—
317C22⋊Q8—232no—
318C22⋊Q8—232no—
319C22⋊Q8—432no—
320C22⋊Q8—432no—
321#121—232no—
322C4×D4—232no—
323C4×D4—232no—
324C2×C4⋊C4—232no—
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—24no—
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—28no—
359C2×C4⋊C4—28no—
360C2×C4⋊C4—28no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—28no—
368C2×C4⋊C4—28no—
369C2×C4⋊C4—28no—
370C2×C4⋊C4—28no—
371C2×C4⋊C4—28no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—44no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4C2×D414yes—
381C2×C4⋊C4C2×D414yes—
382C2×C4⋊C4C2×D414yes—
383C2×C4⋊C4C2×D414yes—
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×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—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—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—28no—
416C2×C22⋊C4—28no—
417C2×C22⋊C4—28no—
418C2×C22⋊C4—28no—
419C2×C22⋊C4—28no—
420C2×C22⋊C4—28no—
421C2×C22⋊C4—28no—
422C2×C22⋊C4—28no—
423C2×C22⋊C4—28no—
424C2×C22⋊C4—28no—
425C2×C22⋊C4—44no—
426C2×C22⋊C4—44no—
427C2×C22⋊C4—44no—
428C2×C22⋊C4—44no—
429C2×C22⋊C4—44no—
430C2×C22⋊C4—44no—
431C2×C22⋊C4—44no—
432C2×C22⋊C4—44no—
433C2×C22⋊C4C2×D414yes—
434C2×C22⋊C4C2×D414yes—
435C2×C22⋊C4C2×D414yes—
436C2×C22⋊C4C2×D414yes—
437C2×C22⋊C4C2×D414yes—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—24no—
442C2×C42—28no—
443C2×C42—24no—
444C2×C42—44no—
445C2×C42C2×D414yes—
446C2×C42C2×D414yes—
447C2×C42C2×D414yes—
448#95—24no—
449#95—24no—
450#95—24no—
451#95—28no—
452#95—28no—
453#95—24no—
454#95—24no—
455#95—24no—
456#95—28no—
457#95—28no—
458#95—28no—
459#95—28no—
460#95—28no—
461#95—28no—
462#95—44no—
463#95—44no—
464#95—44no—
465#95—44no—
466#95—44no—
467C24—21no—
468C24—21no—
469C24—24no—
470C24—24no—
471C24—22no—
472C24—21no—
473C24—21no—
474C24—21no—
475C24—21no—
476C24—24no—
477C24—24no—
478C24—24no—
479C24—24no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24C22×D412yes—
485C24C22×D412yes—
486C24C22×D412yes—
487C242−1+414yes—
488C24C2511yescharacteristic
489C2×Q8—28no—
490C2×Q8—48no—
491C2×Q8—48no—
492C2×Q8—48no—
493C2×Q8—88no—
494C2×Q8—88no—
495C2×Q8—84no—
496C2×Q8—84no—
497C2×Q8—84no—
498C2×D4—28no—
499C2×D4—28no—
500C2×D4—28no—
501C2×D4—28no—
502C2×D4—44no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—48no—
507C2×D4—44no—
508C2×D4—44no—
509C2×D4—84no—
510C2×D4—84no—
511C2×D4—84no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—28no—
517C22×C4—24no—
518C22×C4—24no—
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—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
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—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—28no—
562C22×C4—28no—
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—24no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—84no—
584C22×C4—84no—
585C22×C4—84no—
586C22×C4—84no—
587C22×C4—84no—
588C22×C4—84no—
589C22×C4—84no—
590C22×C4—84no—
591C22×C4—84no—
592C22×C4—84no—
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×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C22×D412yes—
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4H(5,𝔽2)18yes—
612C22×C42−1+418yes—
613C4⋊C4—28no—
614C4⋊C4—28no—
615C4⋊C4—28no—
616C4⋊C4—28no—
617C4⋊C4—216no—
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—416no—
629C4⋊C4—416no—
630C4⋊C4—48no—
631C4⋊C4—48no—
632C4⋊C4—88no—
633C4⋊C4—88no—
634C4⋊C4—88no—
635C22⋊C4—28no—
636C22⋊C4—28no—
637C22⋊C4—28no—
638C22⋊C4—28no—
639C22⋊C4—28no—
640C22⋊C4—28no—
641C22⋊C4—28no—
642C22⋊C4—28no—
643C22⋊C4—28no—
644C22⋊C4—28no—
645C22⋊C4—416no—
646C22⋊C4—416no—
647C22⋊C4—416no—
648C22⋊C4—416no—
649C22⋊C4—88no—
650C22⋊C4—88no—
651C42—216no—
652C42—28no—
653C42—48no—
654C42#120116yes—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—28no—
662C23—28no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—44no—
677C23—44no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—44no—
699C23#53614yes—
700C23C23×D411yescharacteristic
701C23C23×D411yescharacteristic
702C23C23×D411yescharacteristic
703C23C2×H(5,𝔽2)14yes—
704C23C2×2−1+412yes—
705C23C2×2−1+414yes—
706C23#58512yes—
707Q8—816no—
708Q8—88no—
709D4—416no—
710D4—416no—
711D4—88no—
712C2×C4—22no—
713C2×C4—22no—
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—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—28no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—28no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—28no—
743C2×C4—28no—
744C2×C4—28no—
745C2×C4—28no—
746C2×C4—416no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—44no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—44no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—44no—
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—88no—
794C2×C4C2×#12014yes—
795C2×C4C2×#12014yes—
796C2×C4C2×#12014yes—
797C22—28no—
798C22—24no—
799C22—44no—
800C22—48no—
801C22—42no—
802C22—42no—
803C22—48no—
804C22—44no—
805C22—44no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—48no—
811C22—42no—
812C22—42no—
813C22—82no—
814C22—82no—
815C22—84no—
816C22—84no—
817C22—84no—
818C22C22×#12011yescharacteristic
819C22C2×#53611yescharacteristic
820C22#344911yescharacteristic
821C22#348412yes—
822C22#348612yes—
823C22#348912yes—
824C22#348912yes—
825C22#349812yes—
826C22#349812yes—
827C22#349912yes—
828C22#349912yes—
829C22#353514yes—
830C22#353814yes—
831C22#355214yes—
832C22#355914yes—
833C4—24no—
834C4—24no—
835C4—24no—
836C4—48no—
837C4—48no—
838C4—42no—
839C4—42no—
840C4—42no—
841C4—42no—
842C4—42no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—42no—
847C4—84no—
848C4—84no—
849C2—44no—
850C2—82no—
851C2—82no—
852C2#3530511yescharacteristic
853C2#3552711yescharacteristic
854C2#3566611yescharacteristic
855C2#4049512yes—
856C2#4050412yes—
857C2#4769214yes—
858C2#5065114yes—
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×#2821C2semidirect
3. C2×#2542C2semidirect
4. C2×#2660C2semidirect
5. #16254C2semidirect
6. #16251C2semidirect
7. #15927C2semidirect
8. #15850C2semidirect
9. #15669C2semidirect
10. #15464C2semidirect
11. #15430C2semidirect
12. #15430C2semidirect
13. #15384C2semidirect
15. #14723C2semidirect
16. #14720C2semidirect
17. #14289C2semidirect
18. #14166C2semidirect
19. #13959C2semidirect

Maximal subgroups

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

subgroupindex
C22×#5392
C2×#28212
C2×#25422
C2×#26602
#162542
#162512
#159272
#158502
#156692
#154642
#154302
#153842
#153402
#147232
#147202
#142892
#141662
#139592