Finite Group Databasebeta

← #25018544

Subgroups — #25018544

Order 11008.

1846 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582787C212yesmaximal
2C2×#14582768C211yesmaximal, characteristic, complemented
3C2×#14582759C211yesmaximal, characteristic
4C2×C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic43C211yesmaximal, characteristic
6#19132850C212yesmaximal, complemented
7#19132838C212yesmaximal
8#19132826C212yesmaximal, complemented
9#19132824C211yesmaximal, characteristic, complemented
10#19132824C211yesmaximal, characteristic, complemented
11C2×C43×#380C211yesmaximal, characteristic
12C22×C4⋊Dic43C2211yescharacteristic
13C22×C4⋊Dic43C2211yescharacteristic
14C22×Dic43⋊C4C2212yes—
15C22×Dic43⋊C4C2212yes—
16C22×C22⋊Dic43C2212yes—
17C22×C22⋊Dic43C2211yescharacteristic
18C22×C22⋊Dic43C2211yescharacteristic
19C22×C4×Dic43C2212yes—
20C22×C4×Dic43C2211yescharacteristic
21C22×C4×Dic43C2211yescharacteristic
22#14582787—28no—
23#14582768—24no—
24#14582759—24no—
25C4⋊C4×Dic43—24no—
26C4×C22⋊Dic43C418yescomplemented
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2211yescharacteristic
34C2×C43⋊#95C2211yescharacteristic
35C24×C4×C43C2211yescharacteristic
36C22×C4⋊C4×C43C2211yescharacteristic
37C22×C4⋊C4×C43C2211yescharacteristic
38C22×C22⋊C4×C43C2212yes—
39C43×#380—24no—
40C2×#95×C43C2212yes—
41C23×Dic43C2312yes—
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2312yes—
44C23×Dic43C2311yescharacteristic
45C23×Dic43C2311yescharacteristic
46C23×Dic43C2311yescharacteristic
47C2×C4⋊Dic43—22no—
48C2×C4⋊Dic43—22no—
49C2×C4⋊Dic43—22no—
50C2×C4⋊Dic43—22no—
51C2×C4⋊Dic43—22no—
52C2×C4⋊Dic43D414yes—
53C2×Dic43⋊C4—24no—
54C2×Dic43⋊C4—24no—
55C2×Dic43⋊C4—24no—
56C2×Dic43⋊C4—24no—
57C2×Dic43⋊C4—42no—
58C2×Dic43⋊C4—42no—
59C2×C22⋊Dic43—22no—
60C2×C22⋊Dic43—22no—
61C2×C22⋊Dic43—24no—
62C2×C22⋊Dic43—24no—
63C2×C22⋊Dic43—42no—
64C2×C22⋊Dic43C2×C414yes—
65C2×C22⋊Dic43C2×C414yes—
66C2×C22⋊Dic43D414yes—
67C2×C22⋊Dic43Q814yes—
68C2×C4×Dic43—22no—
69C2×C4×Dic43—22no—
70C2×C4×Dic43—22no—
71C2×C4×Dic43—22no—
72C2×C4×Dic43—24no—
73C2×C4×Dic43—24no—
74C2×C4×Dic43—42no—
75C2×C4×Dic43C2×C414yes—
76C2×C4×Dic43C2×C414yes—
77C43⋊#95—24no—
78C43⋊#95—24no—
79C43⋊#95—24no—
80C43⋊#95—24no—
81C43⋊#95—24no—
82C43⋊#95—42no—
83C43⋊#95C2×C414yes—
84C43⋊#95C2×C414yes—
85C25×C43C2311yescharacteristic
86C23×C4×C43—22no—
87C23×C4×C43—22no—
88C23×C4×C43—22no—
89C23×C4×C43—22no—
90C23×C4×C43—22no—
91C23×C4×C43—22no—
92C23×C4×C43C2×C414yes—
93C23×C4×C43C2312yes—
94C23×C4×C43C2311yescharacteristic
95C23×C4×C43C2312yes—
96C23×C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43—22no—
98C2×C4⋊C4×C43—22no—
99C2×C4⋊C4×C43—22no—
100C2×C4⋊C4×C43—22no—
101C2×C4⋊C4×C43—22no—
102C2×C4⋊C4×C43D414yes—
103C2×C22⋊C4×C43—24no—
104C2×C22⋊C4×C43—24no—
105C2×C22⋊C4×C43—42no—
106#95×C43—24no—
107C24×C43—21no—
108C24×C43—21no—
109C24×C43—21no—
110C24×C43—21no—
111C24×C43—21no—
112C24×C43—21no—
113C24×C43—21no—
114C24×C43—21no—
115C24×C43—21no—
116C24×C43—21no—
117C24×C43—21no—
118C24×C43—21no—
119C24×C43C22×C412yes—
120C24×C43C2×D412yes—
121C24×C43C2×Q812yes—
122C24×C43C2411yescharacteristic
123C22×C4×C43—28no—
124C22×C4×C43—28no—
125C22×C4×C43—28no—
126C22×C4×C43—21no—
127C22×C4×C43—22no—
128C22×C4×C43—21no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—44no—
146C22×C4×C43—44no—
147C22×C4×C43—44no—
148C22×C4×C43—44no—
149C22×C4×C43C22×C412yes—
150C22×C4×C43C22×C412yes—
151C22×C4×C43C2×D412yes—
152C22×C4×C43C2×D414yes—
153C22×C4×C43C2×D412yes—
154C22×C4×C43#4112yes—
155C22×C4×C43#4112yes—
156C22×C4×C43#4112yes—
157C22×C4×C43#4112yes—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—22no—
163C22×Dic43—22no—
164C22×Dic43—22no—
165C22×Dic43—22no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—22no—
173C22×Dic43—22no—
174C22×Dic43—22no—
175C22×Dic43—22no—
176C22×Dic43—22no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—22no—
189C22×Dic43C22×C412yes—
190C22×Dic43C22×C412yes—
191C22×Dic43C22×C412yes—
192C22×Dic43C22×C412yes—
193C22×Dic43C2×D414yes—
194C22×Dic43C2×D412yes—
195C22×Dic43C2×D412yes—
196C22×Dic43C2×Q812yes—
197C22×Dic43C2×Q812yes—
198C22×Dic43#4112yes—
199C22×Dic43#4112yes—
200C4⋊C4×C43—28no—
201C4⋊C4×C43—44no—
202C22⋊C4×C43—48no—
203C22⋊Dic43—28no—
204C22⋊Dic43—48no—
205C22⋊Dic43C4⋊C4116yescomplemented
206C4⋊Dic43—28no—
207C4⋊Dic43—44no—
208Dic43⋊C4—48no—
209Dic43⋊C4—48no—
210C4×Dic43—28no—
211C4×Dic43—28no—
212C4×Dic43—48no—
213C23×C43—22no—
214C23×C43—22no—
215C23×C43—22no—
216C23×C43—22no—
217C23×C43—22no—
218C23×C43—22no—
219C23×C43—22no—
220C23×C43—22no—
221C23×C43—22no—
222C23×C43—22no—
223C23×C43—22no—
224C23×C43—22no—
225C23×C43—22no—
226C23×C43—22no—
227C23×C43—22no—
228C23×C43—22no—
229C23×C43—22no—
230C23×C43—22no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43—41no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43C2×C4⋊C414yes—
248C23×C43C23×C411yescharacteristic
249C23×C43C22×D411yescharacteristic
250C23×C43C22×D411yescharacteristic
251C23×C43C22×D411yescharacteristic
252C23×C43C22×Q811yescharacteristic
253C23×C43C2×#4111yescharacteristic
254C23×C43C2×#4111yescharacteristic
255C23×C43C2×#4111yescharacteristic
256C23×C43C2×#4111yescharacteristic
257C23×C43C2×#4111yescharacteristic
258C23×C43C2×#4111yescharacteristic
259C23×C43H(5,𝔽2)11yescharacteristic
260C23×C43H(5,𝔽2)11yescharacteristic
261C23×C432−1+411yescharacteristic
262C23×C432−1+411yescharacteristic
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—24no—
267C2×C4×C43—24no—
268C2×C4×C43—24no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—42no—
274C2×C4×C43—42no—
275C2×C4×C43—42no—
276C2×C4×C43—42no—
277C2×C4×C43—416no—
278C2×C4×C43—42no—
279C2×C4×C43—42no—
280C2×C4×C43—42no—
281C2×C4×C43—42no—
282C2×C4×C43—42no—
283C2×C4×C43—42no—
284C2×C4×C43—42no—
285C2×C4×C43#11714yes—
286C2×C4×C43C4×D414yes—
287C2×C4×C43C4×D414yes—
288C2×C4×C43#12114yes—
289C2×C4×C43#12314yes—
290C2×C4×C43#12414yes—
291C2×C4×C43#12614yes—
292C2×Dic43—22no—
293C2×Dic43—22no—
294C2×Dic43—22no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—24no—
314C2×Dic43—24no—
315C2×Dic43—24no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—42no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43—42no—
329C2×Dic43—42no—
330C2×Dic43—42no—
331C2×Dic43C2×C4⋊C414yes—
332C2×Dic43C2×C4⋊C414yes—
333C2×Dic43#11714yes—
334#13876—431nomaximal, Sylow
335C22×C43—24no—
336C22×C43—24no—
337C22×C43—24no—
338C22×C43—42no—
339C22×C43—42no—
340C22×C43—42no—
341C22×C43—42no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43C22×C4⋊C411yescharacteristic
351C22×C43C2×#11711yescharacteristic
352C22×C43C2×#11711yescharacteristic
353C22×C43C2×C4×D411yescharacteristic
354C22×C43C2×C4×D411yescharacteristic
355C22×C43#52011yescharacteristic
356C22×C43#52011yescharacteristic
357C22×C43C2×#12111yescharacteristic
358C22×C43C2×#12311yescharacteristic
359C22×C43C2×#12411yescharacteristic
360C22×C43C2×#12611yescharacteristic
361C22×C43#53211yescharacteristic
362C22×C43#53211yescharacteristic
363C22×C43#53311yescharacteristic
364C22×C43#53311yescharacteristic
365C22×C43#54011yescharacteristic
366C22×C43#54111yescharacteristic
367C22×C43#54211yescharacteristic
368C22×C43#54211yescharacteristic
369C22×C43D4211yescharacteristic
370C22×C43D4211yescharacteristic
371C22×C43#54611yescharacteristic
372C22×C43#54711yescharacteristic
373C22×C43#54711yescharacteristic
374C22×C43#54711yescharacteristic
375C22×C43#54811yescharacteristic
376C22×C43D4×Q811yescharacteristic
377C22×C43D4×Q811yescharacteristic
378C22×C43#55011yescharacteristic
379C22×C43#55211yescharacteristic
380C22×C43#55311yescharacteristic
381C22×C43#55411yescharacteristic
382C22×C43#55411yescharacteristic
383C22×C43#55511yescharacteristic
384C22×C43#55611yescharacteristic
385C4×C43—44no—
386C4×C43—42no—
387C4×C43—82no—
388C4×C43#38818yescomplemented
389Dic43—24no—
390Dic43—24no—
391Dic43—24no—
392Dic43—42no—
393Dic43—44no—
394Dic43—82no—
395C2×#388—432no—
396C2×#384—431no—
397C2×#380—431no—
398C2×#380D4311yescharacteristic
399C2×C4×C4⋊C4—431no—
400C2×C4×C22⋊C4—431no—
401#1442—432no—
402#1439—432no—
403#1436—432no—
404C4⋊#95—431no—
405C4⋊#95—431no—
406C2×C43—44no—
407C2×C43#228511yescharacteristic
408C2×C43C2×#38811yescharacteristic
409C2×C43#231411yescharacteristic
410C2×C43D4×C4⋊C411yescharacteristic
411C2×C43D4×C4⋊C411yescharacteristic
412C2×C43#235211yescharacteristic
413C2×C43#235411yescharacteristic
414C2×C43#242211yescharacteristic
415C2×C43#242311yescharacteristic
416C2×C43#242811yescharacteristic
417C2×C43#242911yescharacteristic
418C2×C43#249111yescharacteristic
419C2×C43#249211yescharacteristic
420C2×C43#249611yescharacteristic
421C2×C43#249711yescharacteristic
422C24×C4C2×D4311yescharacteristic
423C22×C4⋊C4—431no—
424C22×C4⋊C4—431no—
425C22×C4⋊C4—432no—
426C22×C4⋊C4—432no—
427C22×C4⋊C4C2×D4311yescharacteristic
428C22×C4⋊C4C2×D4311yescharacteristic
429C22×C22⋊C4—431no—
430C22×C22⋊C4—431no—
431C22×C22⋊C4—432no—
432C22×C22⋊C4C2×D4312yes—
433C22×C42—431no—
434C22×C42—431no—
435C22×C42—432no—
436#388—868no—
437#384—864no—
438#380—24no—
439#380—864no—
440C4×C4⋊C4—864no—
441C4×C22⋊C4—438no—
442C2×#95—431no—
443C2×#95—431no—
444C2×#95—432no—
445C2×#95—432no—
446C2×#95—432no—
447C2×#95—432no—
448C2×#95—432no—
449C2×#95—432no—
450C2×#95C2×D4312yes—
451C43#1387611yescharacteristic, complemented, Sylow
452C25C22×D4311yescharacteristic
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—22no—
457C23×C4—22no—
458C23×C4—22no—
459C23×C4—431no—
460C23×C4—431no—
461C23×C4—431no—
462C23×C4—432no—
463C23×C4—431no—
464C23×C4—432no—
465C23×C4C4×D4314yes—
466C23×C4C22×D4312yes—
467C23×C4C22×D4311yescharacteristic
468C23×C4C22×D4312yes—
469C23×C4C22×D4311yescharacteristic
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—434no—
476C2×C4⋊C4—862no—
477C2×C4⋊C4—862no—
478C2×C4⋊C4—864no—
479C2×C4⋊C4—864no—
480C2×C4⋊C4—864no—
481C2×C4⋊C4—864no—
482C2×C4⋊C4—862no—
483C2×C4⋊C4—862no—
484C2×C4⋊C4—862no—
485C2×C4⋊C4—1722no—
486C2×C4⋊C4—1722no—
487C2×C4⋊C4C22⋊D4314yes—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—434no—
492C2×C22⋊C4—434no—
493C2×C22⋊C4—434no—
494C2×C22⋊C4—434no—
495C2×C22⋊C4—862no—
496C2×C22⋊C4—862no—
497C2×C22⋊C4—864no—
498C2×C22⋊C4—864no—
499C2×C22⋊C4—1722no—
500C2×C42—434no—
501C2×C42—434no—
502C2×C42—862no—
503C2×C42—862no—
504C2×C42—862no—
505C2×C42—862no—
506C2×C42—864no—
507C2×C42—864no—
508C2×C42—1722no—
509#95—24no—
510#95—434no—
511#95—434no—
512#95—864no—
513#95—864no—
514#95—864no—
515#95—864no—
516#95—864no—
517#95—1722no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24C2×C4×D4312yes—
531C24D4×D4312yes—
532C24Q8×D4312yes—
533C24C23×D4311yescharacteristic
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—432no—
561C22×C4—432no—
562C22×C4—432no—
563C22×C4—432no—
564C22×C4—432no—
565C22×C4—432no—
566C22×C4—432no—
567C22×C4—432no—
568C22×C4—432no—
569C22×C4—432no—
570C22×C4—434no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—862no—
584C22×C4—861no—
585C22×C4—862no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—861no—
591C22×C4—862no—
592C22×C4—861no—
593C22×C4—862no—
594C22×C4—861no—
595C22×C4—862no—
596C22×C4—862no—
597C22×C4—862no—
598C22×C4—862no—
599C22×C4—862no—
600C22×C4—862no—
601C22×C4—862no—
602C22×C4C2×C4×D4312yes—
603C22×C4C2×C4×D4312yes—
604C22×C4#1062189812yes—
605C22×C4D4×D4312yes—
606C22×C4#1062190012yes—
607C22×C4#1062190012yes—
608C22×C4#1062190012yes—
609C22×C4C2×C22⋊D4314yes—
610C22×C4C2×C22⋊D4312yes—
611C4⋊C4—28no—
612C4⋊C4—44no—
613C4⋊C4—868no—
614C4⋊C4—1728no—
615C4⋊C4—1728no—
616C4⋊C4—1724no—
617C22⋊C4—48no—
618C22⋊C4—4316no—
619C22⋊C4—868no—
620C22⋊C4—1728no—
621C42—868no—
622C42—868no—
623C42—1728no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23C4⋊C4×D4314yes—
659C23C22×C4×D4311yescharacteristic
660C23C2×D4×D4311yescharacteristic
661C23C2×D4×D4311yescharacteristic
662C23C22×C22⋊D4311yescharacteristic
663C23C2×Q8×D4311yescharacteristic
664C23#41×D4311yescharacteristic
665C23#41×D4311yescharacteristic
666C23C2×#1062190011yescharacteristic
667C23C2×#1062190011yescharacteristic
668C23C2×#1062190011yescharacteristic
669C23C2×#1062189811yescharacteristic
670C23#1306337011yescharacteristic
671C23#1306337111yescharacteristic
672C23#1306337211yescharacteristic
673C23#1306337311yescharacteristic
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—416no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—434no—
697C2×C4—434no—
698C2×C4—434no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—862no—
707C2×C4—862no—
708C2×C4—862no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—862no—
716C2×C4—862no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—864no—
721C2×C4—864no—
722C2×C4—864no—
723C2×C4—1722no—
724C2×C4—1722no—
725C2×C4—1722no—
726C2×C4—1722no—
727C2×C4—1722no—
728C2×C4—1722no—
729C2×C4—1722no—
730C2×C4—1721no—
731C2×C4—1722no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4—1722no—
735C2×C4—1722no—
736C2×C4—1722no—
737C2×C4—1721no—
738C2×C4#1306328114yes—
739C2×C4(C22⋊D43)⋊C414yes—
740C2×C4C4×C22⋊D4314yes—
741C2×C4#1306329614yes—
742C2×C4#1306330614yes—
743C2×C4#1306331114yes—
744C2×C4#1306331814yes—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22C2×C4⋊C4×D4311yescharacteristic
761C22#117×D4311yescharacteristic
762C22C2×#1306328111yescharacteristic
763C22C2×(C22⋊D43)⋊C411yescharacteristic
764C22C2×C4×C22⋊D4311yescharacteristic
765C22#1458337911yescharacteristic
766C22#1458338011yescharacteristic
767C22C2×#1306329611yescharacteristic
768C22C2×#1306330611yescharacteristic
769C22C2×#1306331111yescharacteristic
770C22C2×#1306331811yescharacteristic
771C22#1458344411yescharacteristic
772C22#1458344411yescharacteristic
773C22#1458345111yescharacteristic
774C22#1458345111yescharacteristic
775C22#1458350211yescharacteristic
776C22#1458350911yescharacteristic
777C22#1458351611yescharacteristic
778C22#1458352211yescharacteristic
779C22D4×C22⋊D4311yescharacteristic
780C22#1458353311yescharacteristic
781C22#1458354611yescharacteristic
782C22#1458354811yescharacteristic
783C22#1458354911yescharacteristic
784C22#1458355011yescharacteristic
785C22#1458355911yescharacteristic
786C22#1458356211yescharacteristic
787C22Q8×C22⋊D4311yescharacteristic
788C22#1458356811yescharacteristic
789C22#1458358311yescharacteristic
790C22#1458359611yescharacteristic
791C22#1458360411yescharacteristic
792C22#1458360711yescharacteristic
793C22#1458361211yescharacteristic
794C22#1458361711yescharacteristic
795C4—42no—
796C4—44no—
797C4—82no—
798C4—864no—
799C4—864no—
800C4—864no—
801C4—3442no—
802C4—1722no—
803C4—1724no—
804C4#1458278718yescomplemented
805C2—44no—
806C2#1913699711yescharacteristic
807C2C2×#1458278711yescharacteristic
808C2#1913720211yescharacteristic
809C2#1913749111yescharacteristic
810C2C4⋊C4×C22⋊D4311yescharacteristic
811C2#1913751711yescharacteristic
812C2#1913754511yescharacteristic
813C2#1913810511yescharacteristic
814C2#1913811611yescharacteristic
815C2#1913817911yescharacteristic
816C2#1913819011yescharacteristic
817C2#1913895411yescharacteristic
818C2#1913896511yescharacteristic
819C2#1913901311yescharacteristic
820C2#1913902411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#380C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC2×#380D43
hypocenterC43#13876
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#14582768C2semidirect
4. C2×C4⋊C4×Dic43C2semidirect
6. #19132850C2semidirect
8. #19132826C2semidirect
9. #19132824C2semidirect
10. #19132824C2semidirect
26. C4×C22⋊Dic43C4semidirect
205. C22⋊Dic43C4⋊C4semidirect
388. C4×C43#388semidirect
451. C43#13876semidirect
804. C4#14582787semidirect

Maximal subgroups

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

subgroupindex
C2×#145827872
C2×#145827682
C2×#145827592
C2×C4⋊C4×Dic432
C2×C4×C22⋊Dic432
#191328502
#191328382
#191328262
#191328242
C2×C43×#3802
#1387643