Finite Group Databasebeta

← C4×#14583039 #25102190

Subgroups — C4×#14583039 #25102190

Order 11008.

1532 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D43C211yesmaximal, characteristic, complemented
2C2×#14583039C211yesmaximal, characteristic
3C2×C4×#10621873C211yesmaximal, characteristic, complemented
4C2×C4×#10621884C211yesmaximal, characteristic, complemented
5C4×#13063300C211yesmaximal, characteristic
6#19134951C211yesmaximal, characteristic, complemented
7#19134948C211yesmaximal, characteristic, complemented
8#19134911C211yesmaximal, characteristic
9#19134865C211yesmaximal, characteristic, complemented
10#19134864C211yesmaximal, characteristic, complemented
11#19134789C211yesmaximal, characteristic, complemented
12#19134528C211yesmaximal, characteristic, complemented
13C4×#13063248C211yesmaximal, characteristic, complemented
14C4×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
15C4×#103×C43C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C2×#13063300C2211yescharacteristic
20C2×Q8×Dic43C2211yescharacteristic
21C2×C4×Dic86—21no—
22C2×C4×Dic86C2211yescharacteristic
23C2×#13063290—21no—
24C2×#13063290C2211yescharacteristic
25C4×Q8×D43—24no—
26C4×Q8×D43—24no—
27C2×C4×D172—21no—
28C2×C4×D172C2211yescharacteristic
29C2×C4⋊C4×D43—21no—
30C2×C4⋊C4×D43C2211yescharacteristic
31C2×C42×D43—21no—
32C2×C42×D43C2211yescharacteristic
33#14583039C418yesdirect product factor
34C4×#10621873—24no—
35C4×#10621884—24no—
36C2×#13063257C2211yescharacteristic
37C2×#13063256C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×#13063247C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×C4×C43⋊C8C2211yescharacteristic
47#14582800C2211yescharacteristic
48#14582798C2211yescharacteristic
49#14582791—21no—
50#14582777—21no—
51#14582756C2211yescharacteristic
52C4×(C2×D43)⋊C4—21no—
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582653C2211yescharacteristic
56#14582653C2211yescharacteristic
57C2×C4×Q8×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×C4×C8×C43C2211yescharacteristic
61C4×C4⋊C4×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#340C2211yescharacteristic
64C22×Dic86—21no—
65C22×Dic86C2311yescharacteristic
66C2×Q8×D43—22no—
67C2×Q8×D43—22no—
68C2×Q8×D43—22no—
69C2×Q8×D43—22no—
70C2×Q8×D43—22no—
71C2×Q8×D43C2×C414yescomplemented
72C22×D172—21no—
73C22×D172C2311yescharacteristic
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C22×C4×D43—21no—
77C22×C4×D43D411yescharacteristic
78C22×C4×D43D411yescharacteristic
79C22×C4×D43C2311yescharacteristic
80C2×#10621873—22no—
81C2×#10621873—22no—
82C2×#10621873C2×C414yescomplemented
83C2×#10621884—22no—
84C2×#10621884—22no—
85C2×#10621884C2×C414yescomplemented
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88#13063300—22no—
89#13063300C2×C414yes—
90Q8×Dic43—22no—
91Q8×Dic43—22no—
92C4×Dic86—28no—
93C4×Dic86—22no—
94C4×Dic86D414yescomplemented
95#13063290—28no—
96#13063290—22no—
97#13063290—22no—
98C4×D172—22no—
99C4×D172—22no—
100C4×D172—44no—
101C2×C4⋊Dic43—21no—
102C2×C4⋊Dic43—21no—
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C4⋊C4×D43—28no—
109C4⋊C4×D43—22no—
110C4⋊C4×D43—22no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×C4×Dic43—21no—
117C2×C4×Dic43—21no—
118C2×C4×Dic43—21no—
119C2×C4×Dic43D411yescharacteristic
120C2×C4×Dic43D411yescharacteristic
121C2×C4×Dic43C2311yescharacteristic
122C42×D43—28no—
123C42×D43—22no—
124C42×D43—22no—
125#13063257—22no—
126#13063256—22no—
127#13063250—22no—
128#13063249—22no—
129#13063248—22no—
130#13063248C2×C414yescomplemented
131#13063247—22no—
132#13063245—22no—
133(C2×D43)⋊C8—22no—
134(C2×D43)⋊C8C2×C414yescomplemented
135C4×C43⋊C8—22no—
136C43⋊#95—21no—
137C43⋊#95—21no—
138C22×Q8×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141C4×Q8×C43—22no—
142C4×Q8×C43D414yescomplemented
143C2×C4⋊C4×C43—21no—
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C42×C43—21no—
148C2×C42×C43—21no—
149C2×C42×C43C2311yescharacteristic
150#103×C43—22no—
151#103×C43C2×C414yescomplemented
152C4×C8×C43—22no—
153#95×C43—21no—
154C23×D43—21no—
155C23×D43C2×D411yescharacteristic
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43C22×C412yes—
160C2×Q8×C43C2×D412yes—
161C2×Q8×C43#4112yes—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2411yescharacteristic
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175Q8×D43—28no—
176Q8×D43—28no—
177Q8×D43—28no—
178Q8×D43—28no—
179C2×D172—21no—
180C2×D172—24no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172—42no—
186C2×D172—42no—
187C2×D172C22×C412yes—
188C2×C4×D43—24no—
189C2×C4×D43—24no—
190C2×C4×D43—22no—
191C2×C4×D43—22no—
192C2×C4×D43—21no—
193C2×C4×D43—21no—
194C2×C4×D43—21no—
195C2×C4×D43—21no—
196C2×C4×D43—24no—
197C2×C4×D43—22no—
198C2×C4×D43—24no—
199C2×C4×D43—22no—
200C2×C4×D43—41no—
201C2×C4×D43—42no—
202C2×C4×D43—42no—
203C2×C4×D43—42no—
204C2×C4×D43—42no—
205C2×C4×D43—42no—
206C2×C4×D43SD1614yescomplemented
207C2×C4×D43C22×C412yes—
208C2×C4×D43#4112yes—
209C2×Dic86—24no—
210C2×Dic86—24no—
211C2×Dic86—21no—
212C2×Dic86—21no—
213C2×Dic86—21no—
214C2×Dic86—24no—
215C2×Dic86C22×C412yes—
216C2×Dic86C2×D412yes—
217C2×Dic86#4112yes—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43C22×C412yes—
224C4⋊C4×C43—24no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43C22×C412yes—
230C4⋊C4×C43C2×D412yes—
231C42×C43—24no—
232C42×C43—42no—
233C42×C43C2×D412yes—
234C42×C43C2×D412yes—
235#10621884—28no—
236(C2×D43)⋊C4—24no—
237(C2×D43)⋊C4—42no—
238(C2×D43)⋊C4—42no—
239(C2×D43)⋊C4—42no—
240(C2×D43)⋊C4—42no—
241C4⋊Dic43—24no—
242C4⋊Dic43—21no—
243C4⋊Dic43—21no—
244C4⋊Dic43—21no—
245C4⋊Dic43—42no—
246C4⋊Dic43C2×D412yes—
247Dic43⋊C4—24no—
248Dic43⋊C4—24no—
249Dic43⋊C4—24no—
250C4×Dic43—24no—
251C4×Dic43—24no—
252C4×Dic43—24no—
253C4×Dic43—22no—
254C4×Dic43—22no—
255C4×Dic43—21no—
256C4×Dic43—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8C22×C412yes—
263#10621873—28no—
264C23×C43C22×D411yescharacteristic
265C22×D43—21no—
266C22×D43—21no—
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—22no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43—41no—
274C22×D43—41no—
275C22×D43—41no—
276C22×D43C4×D412yes—
277C22×D43C2×SD1612yes—
278C22×D43#13512yes—
279Q8×C43—22no—
280Q8×C43—22no—
281Q8×C43—22no—
282Q8×C43C4×D414yescomplemented
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43#12012yes—
298C2×C4×C43#12012yes—
299C2×C4×C43C2×SD1612yes—
300C2×C4×C43#13712yes—
301C2×C4×C43C23×C411yescharacteristic
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C2×C4×C43C2×#4111yescharacteristic
306C2×C4×C43C2×#4111yescharacteristic
307C2×Dic43—22no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—22no—
311C2×Dic43—21no—
312C2×Dic43—22no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—22no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43C4×D412yes—
324C2×Dic43C2×SD1612yes—
325D172—22no—
326D172—22no—
327D172—48no—
328D172—41no—
329D172—41no—
330C4×D43—216no—
331C4×D43—22no—
332C4×D43—22no—
333C4×D43—22no—
334C4×D43—22no—
335C4×D43—28no—
336C4×D43—44no—
337C4×D43—48no—
338C4×D43—84no—
339Dic86—216no—
340Dic86—22no—
341Dic86—22no—
342Dic86—22no—
343Dic86C4×D414yescomplemented
344C8×C43—22no—
345C8×C43—41no—
346C43⋊C8—22no—
347C43⋊C8—41no—
348C4×#448—431nomaximal, Sylow
349C22×C43C2×C4×D411yescharacteristic
350C22×C43C2×#12011yescharacteristic
351C22×C43#52511yescharacteristic
352C22×C43C22×SD1611yescharacteristic
353C22×C43C2×#13511yescharacteristic
354C22×C43C2×#13711yescharacteristic
355C22×C43#57511yescharacteristic
356C2×D43—22no—
357C2×D43—22no—
358C2×D43—22no—
359C2×D43—22no—
360C2×D43—22no—
361C2×D43—22no—
362C2×D43—42no—
363C2×D43—42no—
364C2×D43—42no—
365C2×D43—81no—
366C2×D43—81no—
367C2×D43—81no—
368C2×D43—81no—
369C2×D43C4×SD1614yescomplemented
370C4×C43—22no—
371C4×C43—24no—
372C4×C43—42no—
373C4×C43—42no—
374C4×C43—81no—
375C4×C43#44814yescomplemented
376C4×C43C2×C4×D411yescharacteristic
377C4×C43C2×C4×D411yescharacteristic
378C4×C43#52511yescharacteristic
379C4×C43#52511yescharacteristic
380Dic43—22no—
381Dic43—22no—
382Dic43—24no—
383Dic43—41no—
384Dic43—42no—
385Dic43—81no—
386C22×C4×Q8—431no—
387C2×#448—431no—
388C2×C4×SD16—431no—
389C2×C4×SD16—431no—
390C4×#121—431no—
391#1880—431no—
392#1880—431no—
393#1874—431no—
394#1865—431no—
395#1865—431no—
396#1853—431no—
397#1787—431no—
398C4×#103—431no—
399C4×#103D4311yescharacteristic, complemented
400C4×C22⋊C8—431no—
401C2×C43C4×#12011yescharacteristic
402C2×C43C2×C4×SD1611yescharacteristic
403C2×C43C4×#13711yescharacteristic
404C2×C43C2×#44811yescharacteristic
405C2×C43#300211yescharacteristic
406C2×C43#310311yescharacteristic
407C2×C43#310811yescharacteristic
408D43—24no—
409D43—82no—
410C23×Q8—431no—
411C22×SD16—431no—
412C22×SD16—431no—
413C2×#121—431no—
414C2×C4×Q8—431no—
415C2×C4×Q8—431no—
416C2×C4×Q8—431no—
417C2×C4×Q8—861no—
418C2×C4×Q8—861no—
419C2×C4×Q8—864no—
420C2×C4×Q8—864no—
421C2×C4×Q8C2×D4311yescharacteristic
422C2×C4×D4—431no—
423C2×C4×D4—861no—
424C22×C4⋊C4—431no—
425C22×C4⋊C4—861no—
426C22×C42—431no—
427C22×C42—861no—
428#448—438no—
429C4×SD16—864no—
430C4×SD16—864no—
431C2×#106—431no—
432C2×#106—431no—
433C2×#103—431no—
434C2×#103—431no—
435C2×#103—431no—
436C2×#103—431no—
437C2×#103C2×D4311yescharacteristic
438C2×#103C2×D4311yescharacteristic
439C2×#102—431no—
440C2×#102—431no—
441C2×C22⋊C8—431no—
442C2×C22⋊C8—431no—
443C2×C4×C8—431no—
444C2×C4×C8C2×D4311yescharacteristic
445#390—431no—
446#389—431no—
447#388—861no—
448#386—861no—
449#380—431no—
450C4×C4⋊C4C2×D4311yescharacteristic
451C4×C22⋊C4—861no—
452#340—431no—
453#340—431no—
454#340C2×D4311yescharacteristic
455#340C2×D4311yescharacteristic
456#336—431no—
457#336—431no—
458C43C4×#44811yescharacteristic, complemented, Sylow
459C22×Q8—434no—
460C22×Q8—431no—
461C22×Q8—861no—
462C22×Q8—862no—
463C22×Q8—862no—
464C22×Q8—862no—
465C22×Q8—862no—
466C22×Q8—862no—
467C22×Q8C22×D4311yescharacteristic
468C22×D4—431no—
469C22×D4—861no—
470C23×C4—431no—
471C23×C4—431no—
472C23×C4—431no—
473C23×C4—861no—
474C23×C4—861no—
475C23×C4—861no—
476C2×SD16—434no—
477C2×SD16—434no—
478C2×SD16—862no—
479C2×SD16—862no—
480C2×SD16—862no—
481C2×SD16—862no—
482C22×C8—431no—
483C22×C8—431no—
484C22×C8C22×D4311yescharacteristic
485C22×C8C22×D4311yescharacteristic
486#121—434no—
487#121—862no—
488C4×Q8—22no—
489C4×Q8—434no—
490C4×Q8—868no—
491C4×Q8—862no—
492C4×Q8—868no—
493C4×Q8—862no—
494C4×Q8—862no—
495C4×Q8—862no—
496C4×Q8—862no—
497C4×Q8D17214yescomplemented
498C4×D4—862no—
499C4×D4—862no—
500C4×D4—1724no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—862no—
505C2×C4⋊C4—868no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—862no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4C22×D4311yescharacteristic
513C2×C4⋊C4C22×D4311yescharacteristic
514C2×C4⋊C4C22×D4311yescharacteristic
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4—861no—
520C2×C42—21no—
521C2×C42—21no—
522C2×C42—431no—
523C2×C42—431no—
524C2×C42—431no—
525C2×C42—868no—
526C2×C42—861no—
527C2×C42—861no—
528C2×C42—861no—
529C2×C42—862no—
530C2×C42—862no—
531C2×C42C22×D4311yescharacteristic
532#106—862no—
533#106—862no—
534#103—22no—
535#103—434no—
536#103—862no—
537#103—862no—
538#103—862no—
539#103C4×D4314yescomplemented
540#102—862no—
541#102—862no—
542C22⋊C8—434no—
543C22⋊C8—862no—
544C4×C8—22no—
545C4×C8—862no—
546#95—21no—
547#95—861no—
548#95—861no—
549C24—431no—
550C24—861no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—432no—
555C2×Q8—432no—
556C2×Q8—432no—
557C2×Q8—864no—
558C2×Q8—864no—
559C2×Q8—864no—
560C2×Q8—868no—
561C2×Q8—868no—
562C2×Q8—868no—
563C2×Q8—868no—
564C2×Q8—861no—
565C2×Q8—861no—
566C2×Q8—861no—
567C2×Q8C2×C4×D4312yes—
568C2×Q8C2×D17212yes—
569C2×Q8#1062189812yes—
570C2×D4—432no—
571C2×D4—864no—
572C2×D4—861no—
573C2×D4—861no—
574C2×D4—861no—
575C2×D4—861no—
576C2×D4—861no—
577C2×D4—1722no—
578C2×D4—1722no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—431no—
584C22×C4—431no—
585C22×C4—434no—
586C22×C4—432no—
587C22×C4—432no—
588C22×C4—431no—
589C22×C4—864no—
590C22×C4—864no—
591C22×C4—864no—
592C22×C4—862no—
593C22×C4—864no—
594C22×C4—861no—
595C22×C4—862no—
596C22×C4—862no—
597C22×C4—861no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—862no—
603C22×C4—861no—
604C22×C4—1721no—
605C22×C4—1722no—
606C22×C4—1722no—
607C22×C4—1722no—
608C22×C4—1722no—
609C22×C4—1722no—
610C22×C4D4×D4311yescharacteristic
611C22×C4D4×D4311yescharacteristic
612C22×C4C23×D4311yescharacteristic
613SD16—868no—
614SD16—868no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—432no—
621C2×C8—861no—
622C2×C8—861no—
623C2×C8—861no—
624C2×C8—861no—
625C2×C8—861no—
626C2×C8C2×C4×D4312yes—
627C4⋊C4—24no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—432no—
633C4⋊C4—864no—
634C4⋊C4—864no—
635C4⋊C4—864no—
636C4⋊C4—864no—
637C4⋊C4—861no—
638C4⋊C4—861no—
639C4⋊C4—861no—
640C4⋊C4—1722no—
641C4⋊C4C2×C4×D4312yes—
642C4⋊C4C2×D17212yes—
643C22⋊C4—864no—
644C22⋊C4—1722no—
645C22⋊C4—1722no—
646C22⋊C4—1722no—
647C22⋊C4—1722no—
648C42—24no—
649C42—42no—
650C42—864no—
651C42—864no—
652C42—862no—
653C42—862no—
654C42—864no—
655C42—861no—
656C42—861no—
657C42C2×D17212yes—
658C42D4×D4312yes—
659C23—432no—
660C23—432no—
661C23—432no—
662C23—861no—
663C23—861no—
664C23—861no—
665C23—861no—
666C23—862no—
667C23—1721no—
668C23—1721no—
669C23—1721no—
670C23—1721no—
671C23—1721no—
672C23—1721no—
673C23C2×D4×D4311yescharacteristic
674Q8—22no—
675Q8—22no—
676Q8—22no—
677Q8—434no—
678Q8—8616no—
679Q8—862no—
680Q8—862no—
681Q8—862no—
682Q8C4×D17214yescomplemented
683D4—862no—
684D4—862no—
685D4—1728no—
686D4—1721no—
687D4—1721no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—432no—
703C2×C4—432no—
704C2×C4—8616no—
705C2×C4—862no—
706C2×C4—861no—
707C2×C4—861no—
708C2×C4—862no—
709C2×C4—861no—
710C2×C4—862no—
711C2×C4—861no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—862no—
716C2×C4—868no—
717C2×C4—862no—
718C2×C4—861no—
719C2×C4—861no—
720C2×C4—861no—
721C2×C4—3444no—
722C2×C4—1724no—
723C2×C4—1728no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1721no—
729C2×C4#1306329512yes—
730C2×C4#1306329512yes—
731C2×C4SD16×D4312yes—
732C2×C4#1306335712yes—
733C2×C4C22×C4×D4311yescharacteristic
734C2×C4C2×D4×D4311yescharacteristic
735C2×C4C22×D17211yescharacteristic
736C2×C4#41×D4311yescharacteristic
737C2×C4#41×D4311yescharacteristic
738C2×C4C2×#1062189811yescharacteristic
739C8—22no—
740C8—41no—
741C8—862no—
742C8—1721no—
743C22—434no—
744C22—862no—
745C22—862no—
746C22—862no—
747C22—862no—
748C22—862no—
749C22—862no—
750C22—3441no—
751C22—3441no—
752C22—3441no—
753C22—3441no—
754C22—1722no—
755C22—1722no—
756C22—1722no—
757C22C4×D4×D4311yescharacteristic
758C22C2×#1306329511yescharacteristic
759C22#1458340811yescharacteristic
760C22C2×SD16×D4311yescharacteristic
761C22#135×D4311yescharacteristic
762C22C2×#1306335711yescharacteristic
763C22#1458369611yescharacteristic
764C4—24no—
765C4—22no—
766C4—42no—
767C4—42no—
768C4—81no—
769C4—862no—
770C4—864no—
771C4—862no—
772C4—3441no—
773C4—1721no—
774C4—1722no—
775C4#1458303914yesdirect product factor
776C4C4×D4×D4311yescharacteristic
777C4C2×C4×D17211yescharacteristic
778C4#1458340811yescharacteristic
779C4#1458341111yescharacteristic
780C2—864no—
781C2—3442no—
782C2C4×#1306329511yescharacteristic
783C2C4×SD16×D4311yescharacteristic
784C2C4×#1306335711yescharacteristic
785C2C2×#1458303911yescharacteristic
786C2#1914381511yescharacteristic
787C2#1914462411yescharacteristic
788C2#1914467911yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#103×C43C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
cosocleC22×C4×C43C24
hypercenterC4×#103D43
hypocenterC43C4×#448
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q8×D43C2semidirect
3. C2×C4×#10621873C2semidirect
4. C2×C4×#10621884C2semidirect
6. #19134951C2semidirect
7. #19134948C2semidirect
9. #19134865C2semidirect
10. #19134864C2semidirect
11. #19134789C2semidirect
12. #19134528C2semidirect
13. C4×#13063248C2semidirect
14. C4×(C2×D43)⋊C8C2semidirect
15. C4×#103×C43C2semidirect
33. #14583039C4direct (N × H)
71. C2×Q8×D43C2×C4semidirect
82. C2×#10621873C2×C4semidirect
85. C2×#10621884C2×C4semidirect
94. C4×Dic86D4semidirect
130. #13063248C2×C4semidirect
134. (C2×D43)⋊C8C2×C4semidirect
142. C4×Q8×C43D4semidirect
151. #103×C43C2×C4semidirect
206. C2×C4×D43SD16semidirect
282. Q8×C43C4×D4semidirect
343. Dic86C4×D4semidirect
369. C2×D43C4×SD16semidirect
375. C4×C43#448semidirect
399. C4×#103D43semidirect
458. C43C4×#448semidirect
497. C4×Q8D172semidirect
539. #103C4×D43semidirect
682. Q8C4×D172semidirect
775. C4#14583039direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D432
C2×#145830392
C2×C4×#106218732
C2×C4×#106218842
C4×#130633002
#191349512
#191349482
#191349112
#191348652
#191348642
#191347892
#191345282
C4×#130632482
C4×(C2×D43)⋊C82
C4×#103×C432
C4×#44843