Finite Group Databasebeta

← C4×#14583034 #25102168

Subgroups — C4×#14583034 #25102168

Order 11008.

1964 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D43C211yesmaximal, characteristic, complemented
2C2×#14583034C211yesmaximal, characteristic
3C2×C4×D344C211yesmaximal, characteristic, complemented
4C2×C4×#10621882C211yesmaximal, characteristic, complemented
5C4×#13063300C211yesmaximal, characteristic, complemented
6#19134944C211yesmaximal, characteristic, complemented
7#19134941C211yesmaximal, characteristic, complemented
8#19134911C211yesmaximal, characteristic, complemented
9#19134844C211yesmaximal, characteristic, complemented
10#19134843C211yesmaximal, characteristic, complemented
11#19134784C211yesmaximal, characteristic, complemented
12#19134524C211yesmaximal, characteristic, complemented
13C4×#13063245C211yesmaximal, characteristic, complemented
14C4×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
15C4×#102×C43C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C23×C4×D43—21no—
18C22×D344C2211yescharacteristic
19C22×#10621882C2211yescharacteristic
20C2×#13063300C2211yescharacteristic
21C2×C4×D172—21no—
22C2×C4×D172C2211yescharacteristic
23C2×C4×D172C2211yescharacteristic, complemented
24C2×D4×Dic43C2211yescharacteristic
25C2×#13063287C2211yescharacteristic
26C2×C4×C22⋊D43—21no—
27C2×(C22⋊D43)⋊C4—21no—
28C4×D4×D43—24no—
29C4×D4×D43—24no—
30C2×C4⋊C4×D43C2211yescharacteristic
31C2×C22⋊C4×D43—21no—
32C2×C42×D43C2211yescharacteristic
33#14583034C418yesdirect product factor
34C4×D344—24no—
35C4×#10621882—24no—
36C2×#13063259C2211yescharacteristic, complemented
37C2×#13063258C2211yescharacteristic, complemented
38C2×#13063247C2211yescharacteristic
39C2×#13063247C2211yescharacteristic, complemented
40C2×#13063246C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×#13063245C2211yescharacteristic, complemented
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×C4×C43⋊C8C2211yescharacteristic, complemented
47#14582800C2211yescharacteristic, complemented
48#14582798C2211yescharacteristic, complemented
49#14582791—21no—
50#14582777—21no—
51#14582756C2211yescharacteristic
52C4×(C2×D43)⋊C4—21no—
53#14582661C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582653C2211yescharacteristic, complemented
56#14582653C2211yescharacteristic, complemented
57C2×C4×D4×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C4×C8×C43C2211yescharacteristic, complemented
61C4×C4⋊C4×C43C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C43×#340C2211yescharacteristic, complemented
64C24×D43—21no—
65C22×D172—21no—
66C22×D172C2311yescharacteristic
67C22×D172C2311yescharacteristic
68C22×C22⋊D43—21no—
69C2×D4×D43—22no—
70C2×D4×D43—22no—
71C2×D4×D43—22no—
72C2×D4×D43—22no—
73C2×D4×D43—22no—
74C2×D4×D43C2×C414yescomplemented
75C23×Dic43—21no—
76C22×C4×D43—28no—
77C22×C4×D43—21no—
78C22×C4×D43—21no—
79C22×C4×D43—21no—
80C22×C4×D43—21no—
81C22×C4×D43—44no—
82C22×C4×D43—44no—
83C22×C4×D43D411yescharacteristic
84C22×C4×D43D411yescharacteristic
85C22×C4×D43C2311yescharacteristic
86C2×D344—22no—
87C2×D344—22no—
88C2×D344C2×C414yescomplemented
89C2×#10621882—22no—
90C2×#10621882—22no—
91C2×#10621882C2×C414yescomplemented
92C22×C43⋊C8C2311yescharacteristic
93C22×C43⋊C8C2311yescharacteristic
94#13063300—22no—
95#13063300C2×C414yescomplemented
96C4×D172—22no—
97C4×D172—22no—
98C4×D172—22no—
99C4×D172—44no—
100C4×D172D414yescomplemented
101D4×Dic43—22no—
102D4×Dic43—22no—
103#13063287—22no—
104#13063287—22no—
105C4×C22⋊D43—28no—
106(C22⋊D43)⋊C4—28no—
107C2×C4⋊Dic43—21no—
108C2×C4⋊Dic43C2311yescharacteristic
109C2×C4⋊Dic43C2311yescharacteristic
110C2×Dic43⋊C4—21no—
111C4⋊C4×D43—22no—
112C4⋊C4×D43—22no—
113C2×C22⋊Dic43—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C2×(C2×D43)⋊C4—21no—
120C2×(C2×D43)⋊C4—21no—
121C22⋊C4×D43—28no—
122C2×C4×Dic43D411yescharacteristic
123C2×C4×Dic43D411yescharacteristic
124C2×C4×Dic43C2311yescharacteristic
125C42×D43—22no—
126C42×D43—22no—
127#13063259—22no—
128#13063258—22no—
129#13063247—22no—
130#13063247—22no—
131#13063246—22no—
132#13063245—22no—
133#13063245—22no—
134#13063245C2×C414yescomplemented
135(C2×D43)⋊C8—22no—
136(C2×D43)⋊C8C2×C414yescomplemented
137C4×C43⋊C8—22no—
138C43⋊#95—21no—
139C43⋊#95—21no—
140C22×D4×C43C2311yescharacteristic
141C23×C4×C43—21no—
142C22×C8×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144C4×D4×C43—22no—
145C4×D4×C43D414yescomplemented
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C4⋊C4×C43C2311yescharacteristic
149C2×C22⋊C4×C43—21no—
150C2×C42×C43—21no—
151C2×C42×C43C2311yescharacteristic
152#102×C43—22no—
153#102×C43C2×C414yescomplemented
154C4×C8×C43—22no—
155#95×C43—21no—
156C24×C43—21no—
157C23×D43—24no—
158C23×D43—24no—
159C23×D43—21no—
160C23×D43—24no—
161C23×D43—21no—
162C23×D43—42no—
163C23×D43—42no—
164C23×D43—42no—
165C23×D43—42no—
166C23×D43C2×D411yescharacteristic
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43C22×C412yes—
171C2×D4×C43C2×D412yes—
172C2×D4×C43#4112yes—
173C22×C4×C43—24no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—42no—
178C22×C4×C43—42no—
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2411yescharacteristic
182C2×C22⋊D43—24no—
183C2×C22⋊D43—24no—
184C2×C22⋊D43—24no—
185C22×Dic43—24no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—42no—
189C22×Dic43—42no—
190C22×Dic43C2×D411yescharacteristic
191C22×Dic43C2×D411yescharacteristic
192C22×Dic43C2×D411yescharacteristic
193D4×D43—28no—
194D4×D43—28no—
195D4×D43—28no—
196D4×D43—28no—
197C2×D172—21no—
198C2×D172—21no—
199C2×D172—21no—
200C2×D172—21no—
201C2×D172—24no—
202C2×D172—21no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172—42no—
207C2×D172—42no—
208C2×D172C22×C412yes—
209C2×D172C22×C412yescomplemented
210C2×D172C2×D412yes—
211C2×D172#4112yes—
212C2×C4×D43—22no—
213C2×C4×D43—22no—
214C2×C4×D43—21no—
215C2×C4×D43—21no—
216C2×C4×D43—21no—
217C2×C4×D43—21no—
218C2×C4×D43—24no—
219C2×C4×D43—24no—
220C2×C4×D43—22no—
221C2×C4×D43—24no—
222C2×C4×D43—22no—
223C2×C4×D43—41no—
224C2×C4×D43—42no—
225C2×C4×D43—432no—
226C2×C4×D43—42no—
227C2×C4×D43—42no—
228C2×C4×D43—42no—
229C2×C4×D43—42no—
230C2×C4×D43—42no—
231C2×C4×D43—42no—
232C2×C4×D43—42no—
233C2×C4×D43—42no—
234C2×C4×D43D814yescomplemented
235C2×C4×D43C22×C412yes—
236C2×C4×D43#4112yes—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43C22×C412yescomplemented
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43C22×C412yescomplemented
248C4⋊C4×C43C2×D412yes—
249C22⋊C4×C43—24no—
250C42×C43—42no—
251C42×C43C2×D412yes—
252C42×C43C2×D412yes—
253C22⋊Dic43—24no—
254#10621882—28no—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—42no—
259(C2×D43)⋊C4—42no—
260(C2×D43)⋊C4—42no—
261(C2×D43)⋊C4—42no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—42no—
266C4⋊Dic43C2×D412yes—
267Dic43⋊C4—24no—
268C4×Dic43—22no—
269C4×Dic43—22no—
270C4×Dic43—21no—
271C4×Dic43—21no—
272C2×C43⋊C8—21no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8C22×C412yescomplemented
278D344—28no—
279C23×C43—22no—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43C22×D411yescharacteristic
287C22×D43—21no—
288C22×D43—21no—
289C22×D43—21no—
290C22×D43—21no—
291C22×D43—216no—
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—48no—
297C22×D43—48no—
298C22×D43—48no—
299C22×D43—48no—
300C22×D43—48no—
301C22×D43—41no—
302C22×D43—41no—
303C22×D43—41no—
304C22×D43—41no—
305C22×D43—48no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—41no—
311C22×D43—41no—
312C22×D43C4×D412yes—
313C22×D43C2×D812yes—
314C22×D43#13512yes—
315D4×C43—22no—
316D4×C43—22no—
317D4×C43—22no—
318D4×C43C4×D414yescomplemented
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—48no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43#12012yes—
332C2×C4×C43#12012yes—
333C2×C4×C43C2×D812yes—
334C2×C4×C43AGL(1,ℤ/8)12yes—
335C2×C4×C43C23×C411yescharacteristic
336C2×C4×C43C22×D411yescharacteristic
337C2×C4×C43C22×D411yescharacteristic
338C2×C4×C43C2×#4111yescharacteristic
339C2×C4×C43C2×#4111yescharacteristic
340C2×C4×C43C2×#4111yescharacteristic
341C22⋊D43—216no—
342C2×Dic43—21no—
343C2×Dic43—21no—
344C2×Dic43—21no—
345C2×Dic43—21no—
346C2×Dic43—21no—
347C2×Dic43—22no—
348C2×Dic43—21no—
349C2×Dic43—21no—
350C2×Dic43—48no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43C4×D412yes—
357C2×Dic43C2×D812yes—
358D172—22no—
359D172—22no—
360D172—22no—
361D172—22no—
362D172—22no—
363D172—48no—
364D172—41no—
365D172—41no—
366D172C4×D414yescomplemented
367C4×D43—22no—
368C4×D43—22no—
369C4×D43—22no—
370C4×D43—22no—
371C4×D43—28no—
372C4×D43—48no—
373C4×D43—44no—
374C4×D43—48no—
375C4×D43—48no—
376C4×D43—84no—
377C8×C43—22no—
378C8×C43—41no—
379C43⋊C8—22no—
380C43⋊C8—41no—
381C4×#447—431nomaximal, Sylow
382C22×C43—24no—
383C22×C43—42no—
384C22×C43—42no—
385C22×C43—42no—
386C22×C43—42no—
387C22×C43—42no—
388C22×C43—42no—
389C22×C43C2×C4×D411yescharacteristic
390C22×C43C2×#12011yescharacteristic
391C22×C43#52511yescharacteristic
392C22×C43C22×D811yescharacteristic
393C22×C43C2×#13511yescharacteristic
394C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
395C22×C43#57511yescharacteristic
396C2×D43—22no—
397C2×D43—22no—
398C2×D43—22no—
399C2×D43—22no—
400C2×D43—22no—
401C2×D43—22no—
402C2×D43—24no—
403C2×D43—432no—
404C2×D43—42no—
405C2×D43—42no—
406C2×D43—42no—
407C2×D43—42no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—42no—
412C2×D43—42no—
413C2×D43—81no—
414C2×D43—81no—
415C2×D43—81no—
416C2×D43—81no—
417C2×D43C4×D814yescomplemented
418C4×C43—22no—
419C4×C43—42no—
420C4×C43—42no—
421C4×C43—81no—
422C4×C43#44714yescomplemented
423C4×C43C2×C4×D411yescharacteristic
424C4×C43C2×C4×D411yescharacteristic
425C4×C43#52511yescharacteristic
426C4×C43#52511yescharacteristic
427Dic43—22no—
428Dic43—22no—
429Dic43—42no—
430Dic43—41no—
431Dic43—81no—
432C22×C4×D4—431no—
433C2×#447—431no—
434C2×C4×D8—431no—
435C2×C4×D8—431no—
436C4×#121—431no—
437#1879—431no—
438#1879—431no—
439#1874—431no—
440#1862—431no—
441#1862—431no—
442#1852—431no—
443#1786—431no—
444C4×#102—431no—
445C4×#102D4311yescharacteristic, complemented
446C4×C22⋊C8—431no—
447C2×C43—44no—
448C2×C43C4×#12011yescharacteristic
449C2×C43C2×C4×D811yescharacteristic
450C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
451C2×C43C2×#44711yescharacteristic
452C2×C43#300211yescharacteristic
453C2×C43#310011yescharacteristic
454C2×C43#310511yescharacteristic
455D43—24no—
456D43—44no—
457D43—82no—
458C23×D4—431no—
459C24×C4—861no—
460C22×D8—431no—
461C22×D8—431no—
462C2×#121—431no—
463C2×C4×D4—431no—
464C2×C4×D4—431no—
465C2×C4×D4—431no—
466C2×C4×D4—431no—
467C2×C4×D4—861no—
468C2×C4×D4—861no—
469C2×C4×D4—861no—
470C2×C4×D4—864no—
471C2×C4×D4—864no—
472C2×C4×D4C2×D4311yescharacteristic
473C22×C4⋊C4—431no—
474C22×C22⋊C4—861no—
475C22×C42—431no—
476#447—438no—
477C4×D8—864no—
478C4×D8—864no—
479C2×#107—431no—
480C2×#107—431no—
481C2×#102—431no—
482C2×#102—431no—
483C2×#102—431no—
484C2×#102—431no—
485C2×#102—431no—
486C2×#102—431no—
487C2×#102C2×D4311yescharacteristic
488C2×#102C2×D4311yescharacteristic
489C2×C22⋊C8—431no—
490C2×C22⋊C8—431no—
491C2×C4×C8—431no—
492C2×C4×C8C2×D4311yescharacteristic, complemented
493#390—431no—
494#389—431no—
495#388—861no—
496#386—861no—
497#380—431no—
498C4×C4⋊C4C2×D4311yescharacteristic, complemented
499C4×C22⋊C4—861no—
500#340—431no—
501#340—431no—
502#340C2×D4311yescharacteristic, complemented
503#340C2×D4311yescharacteristic, complemented
504#336—431no—
505#336—431no—
506C43C4×#44711yescharacteristic, complemented, Sylow
507C25—861no—
508C22×D4—434no—
509C22×D4—431no—
510C22×D4—431no—
511C22×D4—861no—
512C22×D4—862no—
513C22×D4—861no—
514C22×D4—862no—
515C22×D4—862no—
516C22×D4—862no—
517C22×D4—862no—
518C22×D4C22×D4311yescharacteristic
519C23×C4—21no—
520C23×C4—431no—
521C23×C4—431no—
522C23×C4—431no—
523C23×C4—861no—
524C23×C4—861no—
525C23×C4—868no—
526C23×C4—861no—
527C23×C4—861no—
528C23×C4—861no—
529C23×C4—1724no—
530C23×C4—1724no—
531C2×D8—434no—
532C2×D8—434no—
533C2×D8—862no—
534C2×D8—862no—
535C2×D8—862no—
536C2×D8—862no—
537C22×C8—431no—
538C22×C8—431no—
539C22×C8C22×D4311yescharacteristic
540C22×C8C22×D4311yescharacteristic
541#121—434no—
542#121—862no—
543C4×D4—22no—
544C4×D4—434no—
545C4×D4—868no—
546C4×D4—862no—
547C4×D4—862no—
548C4×D4—868no—
549C4×D4—862no—
550C4×D4—862no—
551C4×D4—862no—
552C4×D4—862no—
553C4×D4—862no—
554C4×D4—1724no—
555C4×D4D17214yescomplemented
556C2×C4⋊C4—431no—
557C2×C4⋊C4—431no—
558C2×C4⋊C4—862no—
559C2×C4⋊C4—861no—
560C2×C4⋊C4—862no—
561C2×C4⋊C4—861no—
562C2×C4⋊C4C22×D4311yescharacteristic
563C2×C4⋊C4C22×D4311yescharacteristic
564C2×C4⋊C4C22×D4311yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—868no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C42—21no—
576C2×C42—431no—
577C2×C42—431no—
578C2×C42—431no—
579C2×C42—862no—
580C2×C42—862no—
581C2×C42C22×D4311yescharacteristic
582#107—862no—
583#107—862no—
584#102—22no—
585#102—434no—
586#102—862no—
587#102—862no—
588#102—862no—
589#102—862no—
590#102—862no—
591#102C4×D4314yescomplemented
592C22⋊C8—434no—
593C22⋊C8—862no—
594C4×C8—22no—
595C4×C8—862no—
596#95—21no—
597#95—861no—
598#95—861no—
599C24—21no—
600C24—431no—
601C24—864no—
602C24—864no—
603C24—864no—
604C24—861no—
605C24—861no—
606C24—1722no—
607C24—1722no—
608C24—1722no—
609C24—1722no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—432no—
614C2×D4—432no—
615C2×D4—432no—
616C2×D4—432no—
617C2×D4—864no—
618C2×D4—864no—
619C2×D4—868no—
620C2×D4—868no—
621C2×D4—868no—
622C2×D4—864no—
623C2×D4—864no—
624C2×D4—868no—
625C2×D4—861no—
626C2×D4—861no—
627C2×D4—861no—
628C2×D4—861no—
629C2×D4—861no—
630C2×D4—861no—
631C2×D4—861no—
632C2×D4—861no—
633C2×D4—1722no—
634C2×D4—1722no—
635C2×D4C2×C4×D4312yes—
636C2×D4C2×D17212yes—
637C2×D4#1062189812yes—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—21no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—431no—
645C22×C4—431no—
646C22×C4—434no—
647C22×C4—432no—
648C22×C4—432no—
649C22×C4—431no—
650C22×C4—862no—
651C22×C4—864no—
652C22×C4—864no—
653C22×C4—862no—
654C22×C4—862no—
655C22×C4—861no—
656C22×C4—861no—
657C22×C4—861no—
658C22×C4—861no—
659C22×C4—864no—
660C22×C4—861no—
661C22×C4—862no—
662C22×C4—864no—
663C22×C4—861no—
664C22×C4—1721no—
665C22×C4—1722no—
666C22×C4—1722no—
667C22×C4—17232no—
668C22×C4—1722no—
669C22×C4—1722no—
670C22×C4—1722no—
671C22×C4—1722no—
672C22×C4—1722no—
673C22×C4—1722no—
674C22×C4—1722no—
675C22×C4—1722no—
676C22×C4—1722no—
677C22×C4D4×D4311yescharacteristic
678C22×C4D4×D4311yescharacteristic
679C22×C4C23×D4311yescharacteristic
680D8—868no—
681D8—868no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—432no—
688C2×C8—861no—
689C2×C8—861no—
690C2×C8—861no—
691C2×C8—861no—
692C2×C8—861no—
693C2×C8C2×C4×D4312yescomplemented
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—432no—
699C4⋊C4—864no—
700C4⋊C4—861no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C4⋊C4—1722no—
704C4⋊C4C2×C4×D4312yescomplemented
705C4⋊C4C2×D17212yes—
706C22⋊C4—24no—
707C22⋊C4—864no—
708C22⋊C4—864no—
709C22⋊C4—864no—
710C22⋊C4—864no—
711C22⋊C4—1722no—
712C22⋊C4—1722no—
713C22⋊C4—1722no—
714C22⋊C4—1722no—
715C42—42no—
716C42—862no—
717C42—862no—
718C42—861no—
719C42—861no—
720C42C2×D17212yes—
721C42D4×D4312yes—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—432no—
730C23—432no—
731C23—432no—
732C23—8616no—
733C23—861no—
734C23—861no—
735C23—861no—
736C23—861no—
737C23—862no—
738C23—862no—
739C23—862no—
740C23—862no—
741C23—1728no—
742C23—1728no—
743C23—1728no—
744C23—1728no—
745C23—1728no—
746C23—1728no—
747C23—1721no—
748C23—1721no—
749C23—1721no—
750C23—1721no—
751C23—1721no—
752C23—1721no—
753C23—1721no—
754C23—1721no—
755C23—1721no—
756C23—1721no—
757C23C2×D4×D4311yescharacteristic
758D4—22no—
759D4—22no—
760D4—22no—
761D4—434no—
762D4—8616no—
763D4—862no—
764D4—862no—
765D4—862no—
766D4—862no—
767D4—862no—
768D4—1728no—
769D4—1721no—
770D4—1721no—
771D4C4×D17214yescomplemented
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—48no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—432no—
785C2×C4—432no—
786C2×C4—861no—
787C2×C4—861no—
788C2×C4—861no—
789C2×C4—861no—
790C2×C4—862no—
791C2×C4—862no—
792C2×C4—862no—
793C2×C4—862no—
794C2×C4—868no—
795C2×C4—861no—
796C2×C4—862no—
797C2×C4—861no—
798C2×C4—861no—
799C2×C4—3444no—
800C2×C4—1724no—
801C2×C4—1728no—
802C2×C4—1728no—
803C2×C4—1728no—
804C2×C4—1721no—
805C2×C4—1721no—
806C2×C4—1721no—
807C2×C4—1721no—
808C2×C4—1721no—
809C2×C4—1728no—
810C2×C4#1306329512yes—
811C2×C4#1306329512yes—
812C2×C4D8×D4312yes—
813C2×C4#1306335212yes—
814C2×C4C22×C4×D4311yescharacteristic
815C2×C4C2×D4×D4311yescharacteristic
816C2×C4C22×D17211yescharacteristic
817C2×C4#41×D4311yescharacteristic
818C2×C4#41×D4311yescharacteristic
819C2×C4C2×#1062189811yescharacteristic
820C8—22no—
821C8—41no—
822C8—862no—
823C8—1721no—
824C22—24no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—434no—
832C22—862no—
833C22—862no—
834C22—862no—
835C22—862no—
836C22—862no—
837C22—862no—
838C22—864no—
839C22—3441no—
840C22—3441no—
841C22—3441no—
842C22—3441no—
843C22—17232no—
844C22—1722no—
845C22—1722no—
846C22—1722no—
847C22—1722no—
848C22—1722no—
849C22—1722no—
850C22—1722no—
851C22—1722no—
852C22—1722no—
853C22C4×D4×D4311yescharacteristic
854C22C2×#1306329511yescharacteristic
855C22#1458340811yescharacteristic
856C22C2×D8×D4311yescharacteristic
857C22#135×D4311yescharacteristic
858C22C2×#1306335211yescharacteristic
859C22#1458369611yescharacteristic
860C4—22no—
861C4—42no—
862C4—42no—
863C4—81no—
864C4—862no—
865C4—862no—
866C4—3441no—
867C4—1722no—
868C4—1721no—
869C4#1458303414yesdirect product factor
870C4C4×D4×D4311yescharacteristic
871C4C2×C4×D17211yescharacteristic
872C4#1458340811yescharacteristic
873C4#1458341111yescharacteristic
874C2—44no—
875C2—864no—
876C2—3442no—
877C2—1724no—
878C2C4×#1306329511yescharacteristic
879C2C4×D8×D4311yescharacteristic
880C2C4×#1306335211yescharacteristic
881C2C2×#1458303411yescharacteristic
882C2#1914381511yescharacteristic
883C2#1914459311yescharacteristic
884C2#1914464611yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#102×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583034C2
cosocleC22×C4×C43C24
hypercenterC4×#102D43
hypocenterC43C4×#447
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. C2×C4×D4×D43C2semidirect
3. C2×C4×D344C2semidirect
4. C2×C4×#10621882C2semidirect
5. C4×#13063300C2semidirect
6. #19134944C2semidirect
7. #19134941C2semidirect
8. #19134911C2semidirect
9. #19134844C2semidirect
10. #19134843C2semidirect
11. #19134784C2semidirect
12. #19134524C2semidirect
13. C4×#13063245C2semidirect
14. C4×(C2×D43)⋊C8C2semidirect
15. C4×#102×C43C2semidirect
23. C2×C4×D172C22semidirect
33. #14583034C4direct (N × H)
36. C2×#13063259C22semidirect
37. C2×#13063258C22semidirect
39. C2×#13063247C22semidirect
43. C2×#13063245C22semidirect
46. C2×C4×C43⋊C8C22semidirect
47. #14582800C22semidirect
48. #14582798C22semidirect
53. #14582661C22semidirect
54. #14582661C22semidirect
55. #14582653C22semidirect
56. #14582653C22semidirect
60. C2×C4×C8×C43C22semidirect
61. C4×C4⋊C4×C43C22semidirect
62. C43×#340C22semidirect
63. C43×#340C22semidirect
74. C2×D4×D43C2×C4semidirect
88. C2×D344C2×C4semidirect
91. C2×#10621882C2×C4semidirect
95. #13063300C2×C4semidirect
100. C4×D172D4semidirect
134. #13063245C2×C4semidirect
136. (C2×D43)⋊C8C2×C4semidirect
145. C4×D4×C43D4semidirect
153. #102×C43C2×C4semidirect
209. C2×D172C22×C4semidirect
234. C2×C4×D43D8semidirect
242. C2×C8×C43C22×C4semidirect
247. C4⋊C4×C43C22×C4semidirect
277. C2×C43⋊C8C22×C4semidirect
318. D4×C43C4×D4semidirect
366. D172C4×D4semidirect
417. C2×D43C4×D8semidirect
422. C4×C43#447semidirect
445. C4×#102D43semidirect
492. C2×C4×C8C2×D43semidirect
498. C4×C4⋊C4C2×D43semidirect
502. #340C2×D43semidirect
503. #340C2×D43semidirect
506. C43C4×#447semidirect
555. C4×D4D172semidirect
591. #102C4×D43semidirect
693. C2×C8C2×C4×D43semidirect
704. C4⋊C4C2×C4×D43semidirect
771. D4C4×D172semidirect
869. C4#14583034direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D4×D432
C2×#145830342
C2×C4×D3442
C2×C4×#106218822
C4×#130633002
#191349442
#191349412
#191349112
#191348442
#191348432
#191347842
#191345242
C4×#130632452
C4×(C2×D43)⋊C82
C4×#102×C432
C4×#44743