Finite Group Databasebeta

← #25019685

Subgroups — #25019685

Order 11008.

1746 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582756C211yesmaximal, characteristic
2C2×#14582756C211yesmaximal, characteristic
3C2×C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
4C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic
5#19132856C212yesmaximal, complemented
6#19132837C212yesmaximal
7#19132831C212yesmaximal
8#19132827C212yesmaximal, complemented
9#19132825C211yesmaximal, characteristic, complemented
10#19132824C211yesmaximal, characteristic, complemented
11C2×C43×#389C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C22×C4⋊Dic43C2211yescharacteristic
14C22×C4⋊Dic43C2211yescharacteristic
15C22×(C2×D43)⋊C4C2211yescharacteristic
16C22×(C2×D43)⋊C4C2212yes—
17C22×(C2×D43)⋊C4C2211yescharacteristic
18C22×(C2×D43)⋊C4C2212yes—
19C22×C4×Dic43C2211yescharacteristic
20C22×C4×Dic43C2212yes—
21#14582756—24no—
22#14582756C418yescomplemented
23C4⋊C4×Dic43—24no—
24C4×(C2×D43)⋊C4—24no—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2211yescharacteristic
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2211yescharacteristic
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C22×C4⋊C4×C43C2212yes—
35C22×C4⋊C4×C43C2211yescharacteristic
36C22×C4⋊C4×C43C2211yescharacteristic
37C22×C42×C43C2211yescharacteristic
38C43×#389—24no—
39C2×#95×C43C2212yes—
40C24×D43C2311yescharacteristic
41C23×Dic43C2312yes—
42C23×Dic43C2312yes—
43C23×Dic43C2311yescharacteristic
44C23×Dic43C2311yescharacteristic
45C23×Dic43C2311yescharacteristic
46C22×C4×D43—22no—
47C22×C4×D43—22no—
48C22×C4×D43—22no—
49C22×C4×D43—22no—
50C22×C4×D43—22no—
51C22×C4×D43—22no—
52C22×C4×D43C2×C414yes—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43—22no—
55C2×C4⋊Dic43—22no—
56C2×C4⋊Dic43—22no—
57C2×C4⋊Dic43—22no—
58C2×C4⋊Dic43C2×C414yes—
59C2×(C2×D43)⋊C4—22no—
60C2×(C2×D43)⋊C4—22no—
61C2×(C2×D43)⋊C4—22no—
62C2×(C2×D43)⋊C4—22no—
63C2×(C2×D43)⋊C4—22no—
64C2×(C2×D43)⋊C4—24no—
65C2×(C2×D43)⋊C4—24no—
66C2×(C2×D43)⋊C4—42no—
67C2×(C2×D43)⋊C4—42no—
68C2×(C2×D43)⋊C4—42no—
69C2×(C2×D43)⋊C4C2×C418yes—
70C2×(C2×D43)⋊C4Q814yes—
71C2×C4×Dic43—22no—
72C2×C4×Dic43—22no—
73C2×C4×Dic43—24no—
74C2×C4×Dic43—42no—
75C2×C4×Dic43—42no—
76C2×C4×Dic43D414yes—
77C43⋊#95—24no—
78C43⋊#95—22no—
79C43⋊#95—22no—
80C43⋊#95—24no—
81C43⋊#95—24no—
82C43⋊#95—42no—
83C43⋊#95—42no—
84C43⋊#95—42no—
85C43⋊#95C2×C418yes—
86C23×C4×C43C2312yes—
87C23×C4×C43C2312yes—
88C23×C4×C43C2311yescharacteristic
89C23×C4×C43C2311yescharacteristic
90C23×C4×C43C2311yescharacteristic
91C2×C4⋊C4×C43—22no—
92C2×C4⋊C4×C43—22no—
93C2×C4⋊C4×C43—22no—
94C2×C4⋊C4×C43—22no—
95C2×C4⋊C4×C43—24no—
96C2×C4⋊C4×C43—24no—
97C2×C4⋊C4×C43—42no—
98C2×C4⋊C4×C43C2×C414yes—
99C2×C4⋊C4×C43D414yes—
100C2×C42×C43—22no—
101C2×C42×C43—22no—
102C2×C42×C43—22no—
103#95×C43—24no—
104C24×C43C2411yescharacteristic
105C23×D43—21no—
106C23×D43—21no—
107C23×D43—21no—
108C23×D43—21no—
109C23×D43—21no—
110C23×D43—21no—
111C23×D43—21no—
112C23×D43—21no—
113C23×D43—21no—
114C23×D43—21no—
115C23×D43—21no—
116C23×D43—21no—
117C23×D43C22×C412yes—
118C23×D43C2×Q812yes—
119C23×D43#4112yes—
120C22×C4×C43—21no—
121C22×C4×C43—22no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—22no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—21no—
134C22×C4×C43—22no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—21no—
144C22×C4×C43C22×C414yes—
145C22×C4×C43C22×C412yes—
146C22×C4×C43C2×D412yes—
147C22×C4×C43C2×D414yes—
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×Q812yes—
150C22×C4×C43#4112yes—
151C22×C4×C43#4112yes—
152C22×C4×C43#4112yes—
153C22×C4×C43#4112yes—
154C22×C4×C43#4112yes—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—22no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—22no—
171C22×Dic43—22no—
172C22×Dic43—22no—
173C22×Dic43—22no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—22no—
178C22×Dic43—22no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—21no—
184C22×Dic43C22×C412yes—
185C22×Dic43C22×C414yes—
186C22×Dic43C2×D412yes—
187C22×Dic43C2×D412yes—
188C22×Dic43C2×Q812yes—
189C22×Dic43#4112yes—
190C2×C4×D43—28no—
191C2×C4×D43—28no—
192C2×C4×D43—28no—
193C2×C4×D43—44no—
194C2×C4×D43—44no—
195C2×C4×D43—44no—
196C2×C4×D43—44no—
197C4⋊C4×C43—28no—
198C4⋊C4×C43—28no—
199C4⋊C4×C43—48no—
200C42×C43—44no—
201(C2×D43)⋊C4—28no—
202(C2×D43)⋊C4—28no—
203(C2×D43)⋊C4—48no—
204(C2×D43)⋊C4—48no—
205C4⋊Dic43—28no—
206C4⋊Dic43—44no—
207C4×Dic43—28no—
208C4×Dic43—48no—
209C23×C43C23×C411yescharacteristic
210C23×C43C22×D411yescharacteristic
211C23×C43C22×D411yescharacteristic
212C23×C43C22×Q811yescharacteristic
213C23×C43C2×#4111yescharacteristic
214C23×C43C2×#4111yescharacteristic
215C23×C43C2×#4111yescharacteristic
216C23×C43C2×#4111yescharacteristic
217C23×C43C2×#4111yescharacteristic
218C23×C43C2×#4111yescharacteristic
219C23×C43C2×#4111yescharacteristic
220C23×C43H(5,𝔽2)11yescharacteristic
221C23×C43H(5,𝔽2)11yescharacteristic
222C23×C43H(5,𝔽2)11yescharacteristic
223C23×C432−1+411yescharacteristic
224C22×D43—22no—
225C22×D43—22no—
226C22×D43—22no—
227C22×D43—22no—
228C22×D43—22no—
229C22×D43—22no—
230C22×D43—22no—
231C22×D43—22no—
232C22×D43—22no—
233C22×D43—22no—
234C22×D43—22no—
235C22×D43—22no—
236C22×D43—22no—
237C22×D43—22no—
238C22×D43—22no—
239C22×D43—22no—
240C22×D43—22no—
241C22×D43—22no—
242C22×D43—41no—
243C22×D43—41no—
244C22×D43—41no—
245C22×D43—41no—
246C22×D43—41no—
247C22×D43—41no—
248C22×D43—41no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43—41no—
252C22×D43—41no—
253C22×D43—41no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43C4×Q814yes—
259C2×C4×C43—24no—
260C2×C4×C43—24no—
261C2×C4×C43—24no—
262C2×C4×C43—24no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—24no—
266C2×C4×C43—22no—
267C2×C4×C43—24no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—42no—
274C2×C4×C43—42no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—42no—
278C2×C4×C43—41no—
279C2×C4×C43—42no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—42no—
283C2×C4×C43—42no—
284C2×C4×C43—42no—
285C2×C4×C43—42no—
286C2×C4×C43—41no—
287C2×C4×C43#11714yes—
288C2×C4×C43C4×D414yes—
289C2×C4×C43C4×D414yes—
290C2×C4×C43#12114yes—
291C2×C4×C43#12314yes—
292C2×C4×C43#12414yes—
293C2×C4×C43#12614yes—
294C2×Dic43—22no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—24no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—24no—
305C2×Dic43—24no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—42no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—42no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43C22⋊Q814yes—
329C4×D43—416no—
330#13993—431nomaximal, Sylow
331C22×C43C2×#11711yescharacteristic
332C22×C43C2×C4×D411yescharacteristic
333C22×C43C2×C4×D411yescharacteristic
334C22×C43C2×C4×Q811yescharacteristic
335C22×C43C4×#4111yescharacteristic
336C22×C43#51811yescharacteristic
337C22×C43#52011yescharacteristic
338C22×C43C2×#12111yescharacteristic
339C22×C43C2×C22⋊Q811yescharacteristic
340C22×C43C2×#12311yescharacteristic
341C22×C43#52511yescharacteristic
342C22×C43C2×#12411yescharacteristic
343C22×C43C2×#12611yescharacteristic
344C22×C43#52911yescharacteristic
345C22×C43#53311yescharacteristic
346C22×C43#53511yescharacteristic
347C22×C43#53711yescharacteristic
348C22×C43#54011yescharacteristic
349C22×C43#54211yescharacteristic
350C22×C43#54611yescharacteristic
351C22×C43#54611yescharacteristic
352C22×C43D4×Q811yescharacteristic
353C22×C43#55011yescharacteristic
354C22×C43#55211yescharacteristic
355C22×C43#55311yescharacteristic
356C22×C43#55311yescharacteristic
357C22×C43#55311yescharacteristic
358C22×C43#55311yescharacteristic
359C22×C43#55311yescharacteristic
360C22×C43#55411yescharacteristic
361C22×C43#55411yescharacteristic
362C22×C43#55411yescharacteristic
363C22×C43#55511yescharacteristic
364C22×C43#55611yescharacteristic
365C22×C43#55611yescharacteristic
366C2×D43—24no—
367C2×D43—24no—
368C2×D43—24no—
369C2×D43—42no—
370C2×D43—42no—
371C2×D43—42no—
372C2×D43—42no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—42no—
377C2×D43—42no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—42no—
381C4×C43—44no—
382C4×C43—44no—
383C4×C43—42no—
384C4×C43—42no—
385C4×C43#38818yes—
386Dic43—24no—
387Dic43—44no—
388Dic43—42no—
389Dic43—42no—
390Dic43—82no—
391C2×#389D4311yescharacteristic, complemented
392C2×#380—431no—
393C2×#380—431no—
394C2×C4×C4⋊C4—431no—
395C2×C4×C22⋊C4—431no—
396#1443—432no—
397#1439—432no—
398#1437—432no—
399#1436—432no—
400C4⋊#95—431no—
401C4⋊#95—431no—
402C2×C43C2×#38811yescharacteristic
403C2×C43C4×C22⋊Q811yescharacteristic
404C2×C43#232411yescharacteristic
405C2×C43#234511yescharacteristic
406C2×C43#234711yescharacteristic
407C2×C43#236011yescharacteristic
408C2×C43#236311yescharacteristic
409C2×C43#248511yescharacteristic
410C2×C43#248711yescharacteristic
411C2×C43#249011yescharacteristic
412C2×C43#249211yescharacteristic
413C2×C43#249411yescharacteristic
414C2×C43#249711yescharacteristic
415C2×C43#253511yescharacteristic
416C2×C43#253811yescharacteristic
417D43—44no—
418C24×C4—431no—
419C22×C4⋊C4—431no—
420C22×C4⋊C4—431no—
421C22×C4⋊C4C2×D4312yes—
422C22×C4⋊C4C2×D4311yescharacteristic
423C22×C4⋊C4C2×D4311yescharacteristic
424C22×C22⋊C4—431no—
425C22×C22⋊C4—432no—
426C22×C22⋊C4—431no—
427C22×C22⋊C4—432no—
428C22×C42—431no—
429C22×C42—432no—
430C22×C42C2×D4311yescharacteristic
431#389—24no—
432#380—438no—
433#380—864no—
434C4×C4⋊C4—864no—
435C4×C22⋊C4—864no—
436C2×#95—432no—
437C2×#95—432no—
438C2×#95—431no—
439C2×#95—432no—
440C2×#95—432no—
441C2×#95—431no—
442C2×#95—432no—
443C2×#95—432no—
444C2×#95—432no—
445C2×#95C2×D4312yes—
446C43#1399311yescharacteristic, complemented, Sylow
447C25—431no—
448C23×C4—431no—
449C23×C4—432no—
450C23×C4—431no—
451C23×C4—431no—
452C23×C4—434no—
453C23×C4—432no—
454C23×C4—862no—
455C23×C4—862no—
456C23×C4—862no—
457C23×C4—862no—
458C23×C4—862no—
459C23×C4—862no—
460C23×C4C22×D4312yes—
461C23×C4C22×D4311yescharacteristic
462C23×C4C22×D4311yescharacteristic
463C23×C4C22×D4312yes—
464C23×C4C22×D4311yescharacteristic
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—434no—
473C2×C4⋊C4—862no—
474C2×C4⋊C4—862no—
475C2×C4⋊C4—862no—
476C2×C4⋊C4—862no—
477C2×C4⋊C4—862no—
478C2×C4⋊C4C4×D4314yes—
479C2×C4⋊C4C22⋊D4314yes—
480C2×C22⋊C4—434no—
481C2×C22⋊C4—438no—
482C2×C22⋊C4—862no—
483C2×C22⋊C4—862no—
484C2×C22⋊C4—862no—
485C2×C22⋊C4—862no—
486C2×C22⋊C4—862no—
487C2×C22⋊C4—864no—
488C2×C22⋊C4—864no—
489C2×C22⋊C4—1722no—
490C2×C22⋊C4—1722no—
491C2×C22⋊C4—1722no—
492C2×C42—22no—
493C2×C42—22no—
494C2×C42—22no—
495C2×C42—434no—
496C2×C42—862no—
497C2×C42—862no—
498C2×C42—864no—
499C2×C42—1722no—
500C2×C42—1722no—
501#95—24no—
502#95—438no—
503#95—864no—
504#95—862no—
505#95—862no—
506#95—864no—
507#95—864no—
508#95—1722no—
509#95—1722no—
510#95—1722no—
511C24—432no—
512C24—432no—
513C24—432no—
514C24—861no—
515C24—861no—
516C24—861no—
517C24—861no—
518C24—861no—
519C24—861no—
520C24—861no—
521C24—861no—
522C24—861no—
523C24—861no—
524C24—861no—
525C24—861no—
526C24C23×D4311yescharacteristic
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
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—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—432no—
552C22×C4—432no—
553C22×C4—432no—
554C22×C4—432no—
555C22×C4—434no—
556C22×C4—432no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—862no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—862no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—862no—
574C22×C4—861no—
575C22×C4—862no—
576C22×C4—862no—
577C22×C4—862no—
578C22×C4—861no—
579C22×C4—868no—
580C22×C4—868no—
581C22×C4—868no—
582C22×C4—862no—
583C22×C4—862no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4—1724no—
590C22×C4—1724no—
591C22×C4—1724no—
592C22×C4—1724no—
593C22×C4C2×C4×D4314yes—
594C22×C4C2×C4×D4312yes—
595C22×C4#1062189812yes—
596C22×C4D4×D4312yes—
597C22×C4#1062190012yes—
598C22×C4#1062190012yes—
599C22×C4Q8×D4312yes—
600C22×C4#1062190212yes—
601C22×C4#1062190212yes—
602C22×C4C2×C22⋊D4314yes—
603C22×C4C2×C22⋊D4312yes—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—48no—
607C4⋊C4—868no—
608C4⋊C4—1724no—
609C22⋊C4—868no—
610C22⋊C4—868no—
611C22⋊C4—1728no—
612C22⋊C4—1728no—
613C42—44no—
614C42—868no—
615C42—1728no—
616C23—434no—
617C23—862no—
618C23—862no—
619C23—862no—
620C23—862no—
621C23—862no—
622C23—862no—
623C23—862no—
624C23—862no—
625C23—862no—
626C23—862no—
627C23—862no—
628C23—862no—
629C23—862no—
630C23—862no—
631C23—862no—
632C23—862no—
633C23—862no—
634C23—862no—
635C23—1721no—
636C23—1721no—
637C23—1721no—
638C23—1721no—
639C23—1721no—
640C23—1721no—
641C23—1721no—
642C23—1721no—
643C23—1721no—
644C23—1721no—
645C23—1721no—
646C23—1721no—
647C23—1721no—
648C23—1721no—
649C23—1721no—
650C23—1721no—
651C23C22×C4×D4311yescharacteristic
652C23C2×D4×D4311yescharacteristic
653C23C22×C22⋊D4311yescharacteristic
654C23C2×Q8×D4311yescharacteristic
655C23#41×D4311yescharacteristic
656C23#41×D4311yescharacteristic
657C23C2×#1062190011yescharacteristic
658C23C2×#1062190011yescharacteristic
659C23C2×#1062189811yescharacteristic
660C23C2×#1062190211yescharacteristic
661C23C2×#1062190211yescharacteristic
662C23#1306337011yescharacteristic
663C23#1306337111yescharacteristic
664C23#1306337111yescharacteristic
665C23#1306337311yescharacteristic
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—42no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—434no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—864no—
704C2×C4—862no—
705C2×C4—864no—
706C2×C4—864no—
707C2×C4—862no—
708C2×C4—862no—
709C2×C4—862no—
710C2×C4—1722no—
711C2×C4—1722no—
712C2×C4—1722no—
713C2×C4—1722no—
714C2×C4—1722no—
715C2×C4—1722no—
716C2×C4—1722no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1722no—
726C2×C4—1722no—
727C2×C4—1722no—
728C2×C4—1722no—
729C2×C4—17216no—
730C2×C4#1306328314yes—
731C2×C4C4×C22⋊D4314yes—
732C2×C4#1306328714yes—
733C2×C4#1306329714yes—
734C2×C4#1306331014yes—
735C2×C4#1306331414yes—
736C2×C4#1306332014yes—
737C22—864no—
738C22—864no—
739C22—864no—
740C22—1722no—
741C22—1722no—
742C22—1722no—
743C22—1722no—
744C22—1722no—
745C22—1722no—
746C22—1722no—
747C22—1722no—
748C22—1722no—
749C22—1722no—
750C22—1722no—
751C22—1722no—
752C22C2×#1306328311yescharacteristic
753C22C2×C4×C22⋊D4311yescharacteristic
754C22C2×#1306328711yescharacteristic
755C22C4×Q8×D4311yescharacteristic
756C22C4×#1062190011yescharacteristic
757C22#1458337111yescharacteristic
758C22#1458338111yescharacteristic
759C22C2×#1306329711yescharacteristic
760C22C22⋊Q8×D4311yescharacteristic
761C22C2×#1306331011yescharacteristic
762C22#1458340911yescharacteristic
763C22C2×#1306331411yescharacteristic
764C22C2×#1306332011yescharacteristic
765C22#1458343411yescharacteristic
766C22#1458345411yescharacteristic
767C22#1458346511yescharacteristic
768C22#1458347911yescharacteristic
769C22#1458350511yescharacteristic
770C22#1458352311yescharacteristic
771C22#1458353711yescharacteristic
772C22#1458354311yescharacteristic
773C22Q8×C22⋊D4311yescharacteristic
774C22#1458356811yescharacteristic
775C22#1458359011yescharacteristic
776C22#1458359611yescharacteristic
777C22#1458359911yescharacteristic
778C22#1458360111yescharacteristic
779C22#1458360211yescharacteristic
780C22#1458360211yescharacteristic
781C22#1458360711yescharacteristic
782C22#1458360911yescharacteristic
783C22#1458361011yescharacteristic
784C22#1458361411yescharacteristic
785C22#1458362011yescharacteristic
786C22#1458362311yescharacteristic
787C4—44no—
788C4—42no—
789C4—44no—
790C4—42no—
791C4—864no—
792C4—3442no—
793C4—1722no—
794C4—1724no—
795C4—1722no—
796C4#1458278918yes—
797C2—1724no—
798C2C2×#1458278911yescharacteristic
799C2#1913712511yescharacteristic
800C2#1913728611yescharacteristic
801C2#1913747111yescharacteristic
802C2#1913748711yescharacteristic
803C2#1913759611yescharacteristic
804C2#1913762911yescharacteristic
805C2#1913889011yescharacteristic
806C2#1913891011yescharacteristic
807C2#1913895011yescharacteristic
808C2#1913897211yescharacteristic
809C2#1913899311yescharacteristic
810C2#1913902611yescharacteristic
811C2#1913949411yescharacteristic
812C2#1913951411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#389C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenterC2×#389D43
hypocenterC43#13993
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#389

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic43C2semidirect
5. #19132856C2semidirect
8. #19132827C2semidirect
9. #19132825C2semidirect
10. #19132824C2semidirect
11. C2×C43×#389C2semidirect
22. #14582756C4semidirect
391. C2×#389D43semidirect
446. C43#13993semidirect

Maximal subgroups

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

subgroupindex
C2×#145827562
C2×C4⋊C4×Dic432
C2×C4×(C2×D43)⋊C42
#191328562
#191328372
#191328312
#191328272
#191328252
#191328242
C2×C43×#3892
#1399343