Finite Group Databasebeta

← #678383

Subgroups — #678383

Order 512.

3948 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#552C211yesmaximal, characteristic
2C2×#2565C211yesmaximal, characteristic, complemented
3C2×#2536C211yesmaximal, characteristic
4C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
5#15848C214yesmaximal, complemented
6#15271C214yesmaximal
7#15236C211yesmaximal, characteristic, complemented
8#15182C211yesmaximal, characteristic, complemented
9#15178C211yesmaximal, characteristic, complemented
10#15178C211yesmaximal, characteristic, complemented
11#15072C214yesmaximal, complemented
12#14709C211yesmaximal, characteristic, complemented
13#14139C211yesmaximal, characteristic, complemented
14#14138C211yesmaximal, characteristic, complemented
15#14063C214yesmaximal, complemented
16#13942C211yesmaximal, characteristic, complemented
17#13880C211yesmaximal, characteristic, complemented
18#13879C211yesmaximal, characteristic, complemented
19C4×#390C211yesmaximal, characteristic
20C2×#552—28no—
21C2×#552—28no—
22C2×#552—28no—
23C22×C4⋊Q8C2211yescharacteristic
24C22×#126C2212yes—
25C22×#125C2212yes—
26C22×#125C2211yescharacteristic
27C22×#123C2212yes—
28C22×C22⋊Q8C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C22×C4×Q8C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C22×#117C2211yescharacteristic
36C22×#117C2212yes—
37C23×C4⋊C4C2211yescharacteristic
38#2565—28no—
39#2536—28no—
40C2×#398C2212yes—
41C2×#398C2214yes—
42C2×#394C2212yes—
43C4×C4⋊Q8—28no—
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#390C2212yes—
51C2×#389C2214yes—
52C2×#388C2212yes—
53C2×#388C2212yes—
54C2×#387C2214yes—
55C2×#385C2214yes—
56C2×#384C2211yescharacteristic
57C2×#384C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#382C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2214yes—
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68C2×C43C2211yescharacteristic
69#1444C2214yes—
70#1444C2214yes—
71#1444C2214yes—
72#1442C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1440C2214yes—
77#1440C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1437C2212yes—
83#1437C2212yes—
84#1436C2214yes—
85#1436C2214yes—
86#1436C2214yes—
87#1436C2214yes—
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2211yescharacteristic
94C4⋊#95C2212yes—
95#1434C2214yes—
96C22⋊#95C2214yes—
97C23×Q8C2311yescharacteristic
98C23×Q8C2311yescharacteristic
99C23×D4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103#552—2128no—
104C2×C4⋊Q8—24no—
105C2×C4⋊Q8—24no—
106C2×C4⋊Q8—24no—
107C2×#126—28no—
108C2×#126—28no—
109C2×#126—28no—
110C2×#125—28no—
111C2×#125—28no—
112C2×#125—28no—
113C2×#125—24no—
114C2×#125—24no—
115C2×#125D418yes—
116C2×#123—28no—
117C2×#123—28no—
118C2×#123—28no—
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—42no—
130C2×C22⋊Q8—42no—
131C2×C4×Q8—24no—
132C2×C4×Q8—24no—
133C2×C4×Q8—24no—
134C2×C4×Q8—24no—
135C2×C4×Q8—24no—
136C2×C4×Q8D418yes—
137C2×C4×D4—24no—
138C2×C4×D4—24no—
139C2×C4×D4D418yes—
140C2×#117—24no—
141C2×#117—24no—
142C2×#117—24no—
143C2×#117—28no—
144C2×#117—28no—
145C2×#117—28no—
146C22×C4⋊C4—24no—
147C22×C4⋊C4—24no—
148C22×C4⋊C4—24no—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2314yes—
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2314yes—
161C22×C4⋊C4C2314yes—
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2311yescharacteristic
179C22×C22⋊C4C2311yescharacteristic
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C42C2312yes—
183C22×C42C2312yes—
184C22×C42C2311yescharacteristic
185C22×C42C2311yescharacteristic
186C22×C42C2311yescharacteristic
187C22×C42C2312yes—
188C22×C42C2312yes—
189C22×C42C2312yes—
190C22×C42C2311yescharacteristic
191C22×C42C2311yescharacteristic
192#398—216no—
193#398—28no—
194#394—28no—
195#391—24no—
196#391—24no—
197#391—24no—
198#391—24no—
199#391—42no—
200#391—42no—
201#390—28no—
202#389—216no—
203#388—28no—
204#388—28no—
205#387—216no—
206#385—216no—
207#384—24no—
208#384—24no—
209#382—24no—
210#382—24no—
211#380—24no—
212#380—24no—
213C4×C4⋊C4—216no—
214C4×C4⋊C4—24no—
215C4×C22⋊C4—24no—
216C4×C22⋊C4—24no—
217C4×C22⋊C4—42no—
218C4×C22⋊C4—42no—
219C2×#95C2312yes—
220C2×#95C2314yes—
221C2×#95C2312yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2312yes—
225C2×#95C2314yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2314yes—
229C2×#95C2314yes—
230C2×#95C2314yes—
231C2×#95C2312yes—
232C2×#95C2314yes—
233C2×#95C2312yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2314yes—
237C2×#95C2314yes—
238C2×#95C2314yes—
239C2×#95C2312yes—
240C2×#95C2312yes—
241C43—24no—
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—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8C2×D414yes—
257C22×Q8#4114yes—
258C22×D4—24no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—42no—
262C22×D4C2×D414yes—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
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—28no—
279C23×C4—44no—
280C23×C4C2×D414yes—
281C23×C4C2×D414yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2412yes—
298C23×C4C2411yescharacteristic
299C4⋊Q8—232no—
300#126—264no—
301#125—264no—
302#125—232no—
303#123—264no—
304C22⋊Q8—232no—
305C22⋊Q8—232no—
306C22⋊Q8—416no—
307C22⋊Q8—416no—
308C4×Q8—232no—
309C4×Q8—416no—
310C4×D4—232no—
311#117—232no—
312#117—264no—
313C2×C4⋊C4—232no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—28no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—28no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—28no—
358C2×C4⋊C4—28no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4C2×D414yes—
368C2×C4⋊C4C2×D414yes—
369C2×C4⋊C4C2×D414yes—
370C2×C4⋊C4C2×D418yes—
371C2×C4⋊C4C2×D414yes—
372C2×C4⋊C4C2×D418yes—
373C2×C4⋊C4C2×D418yes—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4C2×D414yes—
409C2×C22⋊C4C2×D414yes—
410C2×C22⋊C4#4118yes—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—22no—
417C2×C42—24no—
418C2×C42—22no—
419C2×C42—24no—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—24no—
423C2×C42—24no—
424C2×C42—24no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—24no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—42no—
436C2×C42C2×D418yes—
437C2×C42C2×D414yes—
438C2×C42C2×D414yes—
439C2×C42C2×D414yes—
440C2×C42#4114yes—
441#95—24no—
442#95—28no—
443#95—28no—
444#95—24no—
445#95—24no—
446#95—28no—
447#95—24no—
448#95—24no—
449#95—28no—
450#95—28no—
451#95—24no—
452#95—24no—
453#95—28no—
454#95—28no—
455#95—28no—
456#95—28no—
457#95—44no—
458#95—44no—
459#95—42no—
460#95—42no—
461#95—44no—
462#95—44no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—22no—
469C24—22no—
470C24—21no—
471C24—22no—
472C24—21no—
473C24—21no—
474C24—21no—
475C24—21no—
476C24—22no—
477C24—21no—
478C24—22no—
479C24—22no—
480C24—21no—
481C24—22no—
482C24C22×D412yes—
483C24C22×D412yes—
484C24C2×#4114yes—
485C24C2511yescharacteristic
486C2×Q8—28no—
487C2×Q8—28no—
488C2×Q8—28no—
489C2×Q8—28no—
490C2×Q8—28no—
491C2×Q8—28no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×D4—28no—
501C2×D4—28no—
502C2×D4—44no—
503C2×D4—48no—
504C2×D4—48no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—216no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—28no—
566C22×C4—28no—
567C22×C4—28no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—24no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—416no—
591C22×C4—416no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4C22×D414yes—
603C22×C4C22×D412yes—
604C22×C4C22×D414yes—
605C22×C4C22×D414yes—
606C22×C4C22×D414yes—
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×C4C2×#4114yes—
618C22×C4C2×#4114yes—
619C22×C4C2×#4114yes—
620C22×C4C2×#4114yes—
621C22×C4C2×#4112yes—
622C22×C4C2×#4112yes—
623C22×C4H(5,𝔽2)12yes—
624C22×C42−1+414yes—
625C22×C42−1+414yes—
626C22×C42−1+412yes—
627C4⋊C4—216no—
628C4⋊C4—216no—
629C4⋊C4—216no—
630C4⋊C4—232no—
631C4⋊C4—28no—
632C4⋊C4—28no—
633C4⋊C4—28no—
634C4⋊C4—216no—
635C4⋊C4—28no—
636C4⋊C4—216no—
637C4⋊C4—216no—
638C4⋊C4—416no—
639C4⋊C4—48no—
640C4⋊C4—416no—
641C4⋊C4—48no—
642C4⋊C4—48no—
643C4⋊C4—48no—
644C4⋊C4—44no—
645C4⋊C4—44no—
646C4⋊C4—44no—
647C22⋊C4—216no—
648C22⋊C4—216no—
649C22⋊C4—216no—
650C22⋊C4—28no—
651C22⋊C4—28no—
652C22⋊C4—216no—
653C22⋊C4—48no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—48no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C42—216no—
661C42—216no—
662C42—216no—
663C42—28no—
664C42—48no—
665C42—48no—
666C42—44no—
667C42—44no—
668C42—44no—
669C42#120116yes—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—22no—
679C23—22no—
680C23—24no—
681C23—24no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23#53214yes—
716C23C23×D411yescharacteristic
717C23C23×D411yescharacteristic
718C23C23×D411yescharacteristic
719C23C22×#4111yescharacteristic
720C23C22×#4111yescharacteristic
721C23C22×#4112yes—
722C23C2×H(5,𝔽2)11yescharacteristic
723C23C2×2−1+411yescharacteristic
724C23C2×2−1+412yes—
725C23C2×2−1+412yes—
726C23#58512yes—
727Q8—416no—
728Q8—416no—
729D4—416no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—28no—
761C2×C4—28no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—28no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—432no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—416no—
803C2×C4—416no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—42no—
816C2×C4—44no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—44no—
822C2×C4—42no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—42no—
826C2×C4C2×#12014yes—
827C2×C4C2×#12014yes—
828C2×C4C2×#12014yes—
829C2×C4#52514yes—
830C2×C4#53714yes—
831C2×C4#54614yes—
832C2×C4#54714yes—
833C2×C4#54814yes—
834C2×C4#55014yes—
835C2×C4#55218yescomplemented
836C22—24no—
837C22—24no—
838C22—24no—
839C22—44no—
840C22—42no—
841C22—44no—
842C22—42no—
843C22—42no—
844C22—44no—
845C22—42no—
846C22—44no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22C22×#12011yescharacteristic
859C22C2×#52511yescharacteristic
860C22C2×#53211yescharacteristic
861C22C2×#53711yescharacteristic
862C22#344911yescharacteristic
863C22C2×#54611yescharacteristic
864C22C2×#54711yescharacteristic
865C22C2×#54811yescharacteristic
866C22C2×#55011yescharacteristic
867C22D4×#4112yes—
868C22D4×#4112yes—
869C22C2×#55212yes—
870C22#348212yes—
871C22#348612yes—
872C22#349912yes—
873C22#349911yescharacteristic
874C22#349911yescharacteristic
875C22#350712yes—
876C22#350912yes—
877C22#351612yes—
878C22#352012yes—
879C22#354712yes—
880C22#356312yes—
881C4—24no—
882C4—28no—
883C4—24no—
884C4—44no—
885C4—44no—
886C4—42no—
887C4—42no—
888C4—44no—
889C4—44no—
890C4—44no—
891C4—44no—
892C4—44no—
893C4—82no—
894C4—82no—
895C4—82no—
896C4—82no—
897C4#240718yes—
898C2—44no—
899C2—82no—
900C2C2×#240711yescharacteristic
901C2#3473811yescharacteristic
902C2#3566611yescharacteristic
903C2#3618111yescharacteristic
904C2#3623212yes—
905C2#3637611yescharacteristic
906C2#3894611yescharacteristic
907C2#3948411yescharacteristic
908C2#3987812yes—
909C2#5944412yes—
910C2#5965612yes—
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×#2565C2semidirect
4. C2×C4×C4⋊Q8C2semidirect
5. #15848C2semidirect
7. #15236C2semidirect
8. #15182C2semidirect
9. #15178C2semidirect
10. #15178C2semidirect
11. #15072C2semidirect
12. #14709C2semidirect
13. #14139C2semidirect
14. #14138C2semidirect
15. #14063C2semidirect
16. #13942C2semidirect
17. #13880C2semidirect
18. #13879C2semidirect
835. C2×C4#552semidirect

Maximal subgroups

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

subgroupindex
C22×#5522
C2×#25652
C2×#25362
C2×C4×C4⋊Q82
#158482
#152712
#152362
#151822
#151782
#150722
#147092
#141392
#141382
#140632
#139422
#138802
#138792
C4×#3902