Finite Group Databasebeta

← C2×#19144607 #25964606

Subgroups — C2×#19144607 #25964606

Order 11008.

2202 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10621898C211yesmaximal, characteristic, complemented
2#19144607C2116yesmaximal, direct product factor
3C2×#14583237C211yesmaximal, characteristic, complemented
4C2×#14583220C211yesmaximal, characteristic, complemented
5C2×#14583203C211yesmaximal, characteristic, complemented
6C2×#14583196C211yesmaximal, characteristic, complemented
7C2×#14583118C211yesmaximal, characteristic, complemented
8C2×#14583111C211yesmaximal, characteristic, complemented
9C2×#14583059C211yesmaximal, characteristic, complemented
10C2×#14583042C211yesmaximal, characteristic
11C2×C4×#10621885C211yesmaximal, characteristic, complemented
12C2×C4×#10621884C211yesmaximal, characteristic, complemented
13C2×C4×#10621883C211yesmaximal, characteristic, complemented
14C2×C4×#10621882C211yesmaximal, characteristic, complemented
15C2×#14582952C211yesmaximal, characteristic, complemented
16C2×C43×#529C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621883C2211yescharacteristic
20C22×#10621884C2211yescharacteristic
21C22×#10621882C2211yescharacteristic
22C4×#10621898—24no—
23C4×#10621898C2218yescomplemented
24C2×C4×Dic86C2211yescharacteristic
25C2×C4×Dic86C2211yescharacteristic
26C2×C4×D172C2211yescharacteristic
27C2×C4×D172C2211yescharacteristic
28C2×C4×C22⋊D43—21no—
29C2×C4×C22⋊D43—21no—
30C2×#13063284C2211yescharacteristic
31C2×#13063282—21no—
32C2×C42×D43—21no—
33#14583237C2218yescomplemented
34#14583220C2218yescomplemented
35#14583203C2218yescomplemented
36#14583196C2218yescomplemented
37#14583118C2218yescomplemented
38#14583111C2218yescomplemented
39#14583059C2218yescomplemented
40#14583042C2218yes—
41C4×#10621885C2218yescomplemented
42C4×#10621884C2218yescomplemented
43C4×#10621883C2218yescomplemented
44C4×#10621882C2218yescomplemented
45#14582952C2218yescomplemented
46C2×#13063258C2211yescharacteristic
47C2×#13063258C2211yescharacteristic
48C2×#13063256C2211yescharacteristic
49C2×#13063256C2211yescharacteristic
50C2×C4⋊(C43⋊C8)C2211yescharacteristic
51C2×C4⋊(C43⋊C8)C2211yescharacteristic
52C2×#13063249C2211yescharacteristic
53C2×#13063249C2211yescharacteristic
54C2×#13063248C2211yescharacteristic
55C2×#13063248C2211yescharacteristic
56C2×#13063246C2211yescharacteristic
57C2×#13063246C2211yescharacteristic
58C2×#13063245C2211yescharacteristic
59C2×#13063245C2211yescharacteristic
60C2×C22⋊(C43⋊C8)C2211yescharacteristic
61C2×C22⋊(C43⋊C8)C2211yescharacteristic
62C2×C4×C43⋊C8C2211yescharacteristic
63C2×C4×C43⋊C8C2211yescharacteristic
64C43×#529—24no—
65C43×#529C2218yescomplemented
66C2×#126×C43—21no—
67C2×#125×C43C2211yescharacteristic
68C2×#124×C43C2211yescharacteristic
69C2×#123×C43—21no—
70C2×C22⋊Q8×C43C2211yescharacteristic
71C2×#121×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic
73C2×C4×D4×C43—21no—
74C2×C4×D4×C43C2211yescharacteristic
75C2×#117×C43—21no—
76C22×C42×C43C2211yescharacteristic
77C2×#10621898—22no—
78C2×#10621898—24no—
79C2×#10621898—24no—
80C2×#10621898C2314yes—
81C22×Dic86C2311yescharacteristic
82C22×D172C2311yescharacteristic
83C22×C22⋊D43—21no—
84C22×C4×D43—21no—
85C22×C4×D43—21no—
86C22×C4×D43—21no—
87C2×#10621885—24no—
88C2×#10621885C2314yes—
89C2×#10621883—24no—
90C2×#10621883C2314yes—
91C2×#10621884—24no—
92C2×#10621884C2314yes—
93C2×#10621882—24no—
94C2×#10621882C2314yes—
95C22×C43⋊C8C2311yescharacteristic
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2311yescharacteristic
98C22×C43⋊C8C2311yescharacteristic
99C4×Dic86—22no—
100C4×Dic86—22no—
101C4×Dic86C2314yes—
102C4×Dic86C2314yes—
103C4×D172—22no—
104C4×D172—22no—
105C4×D172C2314yes—
106C4×D172C2314yes—
107C4×C22⋊D43—28no—
108C4×C22⋊D43—28no—
109#13063284—22no—
110#13063284C2314yes—
111#13063282—28no—
112C2×C4⋊Dic43C2311yescharacteristic
113C2×C4⋊Dic43C2311yescharacteristic
114C2×Dic43⋊C4—21no—
115C2×Dic43⋊C4—21no—
116C2×C22⋊Dic43—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C2×C4×Dic43—21no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43—21no—
122C42×D43—28no—
123#13063258C2314yes—
124#13063258C2314yes—
125#13063256C2314yes—
126#13063256C2314yes—
127C4⋊(C43⋊C8)C2314yes—
128C4⋊(C43⋊C8)C2314yes—
129#13063249C2314yes—
130#13063249C2314yes—
131#13063248C2314yes—
132#13063248C2314yes—
133#13063246C2314yes—
134#13063246C2314yes—
135#13063245C2314yes—
136#13063245C2314yes—
137C22⋊(C43⋊C8)C2314yes—
138C22⋊(C43⋊C8)C2314yes—
139C4×C43⋊C8C2314yes—
140C4×C43⋊C8C2314yes—
141C22×Q8×C43C2311yescharacteristic
142C22×D4×C43—21no—
143C22×D4×C43C2311yescharacteristic
144C23×C4×C43—21no—
145C23×C4×C43D411yescharacteristic
146C23×C4×C43D411yescharacteristic
147C23×C4×C43C2311yescharacteristic
148#126×C43—28no—
149#125×C43—22no—
150#125×C43C2314yes—
151#124×C43—22no—
152#124×C43C2314yes—
153#123×C43—28no—
154C22⋊Q8×C43—22no—
155C22⋊Q8×C43C2314yes—
156#121×C43—22no—
157#121×C43C2314yes—
158C4×Q8×C43—22no—
159C4×Q8×C43C2314yes—
160C4×D4×C43—28no—
161C4×D4×C43—22no—
162C4×D4×C43C2314yes—
163#117×C43—28no—
164C2×C4⋊C4×C43—21no—
165C2×C4⋊C4×C43—21no—
166C2×C4⋊C4×C43—21no—
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43C2311yescharacteristic
169C2×C4⋊C4×C43C2311yescharacteristic
170C2×C22⋊C4×C43—21no—
171C2×C22⋊C4×C43—21no—
172C2×C22⋊C4×C43—21no—
173C2×C22⋊C4×C43—21no—
174C2×C22⋊C4×C43—21no—
175C2×C42×C43—21no—
176C2×C42×C43D411yescharacteristic
177C2×C42×C43D411yescharacteristic
178C2×C42×C43D414yes—
179C2×C42×C43C2311yescharacteristic
180C2×C42×C43C2311yescharacteristic
181C2×C42×C43C2314yes—
182C24×C43—21no—
183C24×C43C2×D411yescharacteristic
184C23×D43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—22no—
187C2×Q8×C43—22no—
188C2×Q8×C43C2412yes—
189C2×D4×C43—21no—
190C2×D4×C43—24no—
191C2×D4×C43—22no—
192C2×D4×C43—22no—
193C2×D4×C43—44no—
194C2×D4×C43C2412yes—
195C22×C4×C43—24no—
196C22×C4×C43—22no—
197C22×C4×C43—22no—
198C22×C4×C43—24no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—42no—
203C22×C4×C43—44no—
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D412yes—
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2×D414yes—
210C22×C4×C43C2×D414yes—
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2412yes—
213C22×C4×C43C2411yescharacteristic
214C2×C22⋊D43—28no—
215C2×C22⋊D43—24no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219#10621898—216no—
220#10621898—28no—
221#10621898—28no—
222C2×D172—21no—
223C2×D172—22no—
224C2×D172#4114yes—
225C2×D172C2412yes—
226C2×C4×D43—28no—
227C2×C4×D43—24no—
228C2×C4×D43—24no—
229C2×C4×D43—24no—
230C2×C4×D43—44no—
231C2×C4×D43—44no—
232C2×Dic86—21no—
233C2×Dic86—22no—
234C2×Dic86#4114yes—
235C2×Dic86C2412yes—
236C4⋊C4×C43—24no—
237C4⋊C4×C43—24no—
238C4⋊C4×C43—24no—
239C4⋊C4×C43—24no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43C2412yes—
243C4⋊C4×C43C2412yes—
244C22⋊C4×C43—24no—
245C22⋊C4×C43—24no—
246C22⋊C4×C43—24no—
247C22⋊C4×C43—24no—
248C22⋊C4×C43—24no—
249C42×C43—24no—
250C42×C43C2×D414yes—
251C42×C43C2×D412yes—
252C42×C43C2×D412yes—
253C42×C43C2×D414yes—
254C42×C43C2412yes—
255C42×C43C2412yes—
256C22⋊Dic43—24no—
257#10621885—28no—
258#10621884—28no—
259#10621883—28no—
260#10621882—28no—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—24no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43C2412yes—
266C4⋊Dic43C2412yes—
267Dic43⋊C4—24no—
268Dic43⋊C4—24no—
269C4×Dic43—24no—
270C4×Dic43—24no—
271C4×Dic43—24no—
272C2×C43⋊C8—22no—
273C2×C43⋊C8—22no—
274C2×C43⋊C8—22no—
275C2×C43⋊C8—22no—
276C2×C43⋊C8C2412yes—
277C2×C43⋊C8C2412yes—
278C2×C43⋊C8C2412yes—
279C2×C43⋊C8C2412yes—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—22no—
283C23×C43—22no—
284C23×C43—42no—
285C23×C43—42no—
286C23×C43—42no—
287C23×C43C22×D412yes—
288C23×C43C22×D411yescharacteristic
289C22×D43—24no—
290C22×D43—22no—
291C22×D43—42no—
292C22×D43—42no—
293Q8×C43—22no—
294Q8×C43—22no—
295Q8×C43—42no—
296D4×C43—22no—
297D4×C43—22no—
298D4×C43—48no—
299D4×C43—42no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—24no—
305C2×C4×C43—28no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—44no—
312C2×C4×C43—42no—
313C2×C4×C43—42no—
314C2×C4×C43—42no—
315C2×C4×C43—48no—
316C2×C4×C43#13514yes—
317C2×C4×C43C22×D412yes—
318C2×C4×C43C22×D412yes—
319C2×C4×C43C22×D412yes—
320C2×C4×C43C22×D412yes—
321C2×C4×C43C22×D411yescharacteristic
322C2×C4×C43C22×D412yes—
323C2×C4×C43C2×#4112yes—
324C2×C4×C43C2×#4112yes—
325C2×C4×C43C2511yescharacteristic
326C22⋊D43—216no—
327C2×Dic43—24no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—42no—
332C2×Dic43—42no—
333D172—24no—
334D172—22no—
335D172C2×#4114yes—
336C4×D43—216no—
337C4×D43—48no—
338C4×D43—48no—
339Dic86—24no—
340Dic86—22no—
341Dic86C2×#4114yes—
342C43⋊C8—22no—
343C43⋊C8—22no—
344C43⋊C8—22no—
345C43⋊C8—22no—
346C2×#3102—431nomaximal, Sylow
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—44no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—84no—
355C22×C43#52512yes—
356C22×C43C2×#13512yes—
357C22×C43#57512yes—
358C22×C43C23×D411yescharacteristic
359C2×D43—24no—
360C2×D43—48no—
361C2×D43—42no—
362C2×D43—42no—
363C4×C43—22no—
364C4×C43—22no—
365C4×C43—22no—
366C4×C43—22no—
367C4×C43—42no—
368C4×C43—42no—
369C4×C43—42no—
370C4×C43#52512yes—
371C4×C43C2×#13514yes—
372C4×C43C22×#4111yescharacteristic
373C4×C43C22×#4111yescharacteristic
374Dic43—24no—
375Dic43—42no—
376Dic43—42no—
377C2×#529D4311yescharacteristic, complemented
378C2×C4×#41—431no—
379#3102—4316no—
380C2×#485—431no—
381C2×#482—431no—
382C2×#479—431no—
383C2×#478—431no—
384C2×#464—431no—
385C2×#463—431no—
386C2×#452—431no—
387C2×#449—431no—
388C2×C4×Q16—431no—
389C2×C4×SD16—431no—
390C2×C4×SD16—431no—
391C2×C4×D8—431no—
392C2×#431—431no—
393C2×C43—42no—
394C2×C43—82no—
395C2×C43#310214yescomplemented
396C2×C43C2×#52511yescharacteristic
397C2×C43C22×#13511yescharacteristic
398C2×C43C2×#57511yescharacteristic
399D43—44no—
400C22×#41—431no—
401C22×Q16—431no—
402C22×SD16—431no—
403C22×SD16—431no—
404C22×D8—431no—
405#529—24no—
406#529C2×D4318yescomplemented
407C2×#126—21no—
408C2×#125C2×D4311yescharacteristic
409C2×#124C2×D4311yescharacteristic
410C2×#123—21no—
411C2×C22⋊Q8C2×D4311yescharacteristic
412C2×#121C2×D4311yescharacteristic
413C4×#41—438no—
414C4×#41—864no—
415C2×C4×Q8—431no—
416C2×C4×Q8—431no—
417C2×C4×Q8C2×D4311yescharacteristic
418C2×C4×D4—21no—
419C2×C4×D4—431no—
420C2×C4×D4—431no—
421C2×C4×D4—861no—
422C2×C4×D4—861no—
423C2×C4×D4C2×D4311yescharacteristic
424C2×#117—21no—
425C2×#117—431no—
426C2×#117—861no—
427C22×C42—861no—
428C22×C42C2×D4311yescharacteristic
429#485—438no—
430#482—438no—
431#479—438no—
432#478—438no—
433#464—438no—
434#463—438no—
435#452—438no—
436#449—438no—
437C4×Q16—438no—
438C4×SD16—438no—
439C4×SD16—438no—
440C4×D8—438no—
441#431—438no—
442C2×#107—431no—
443C2×#107—431no—
444C2×#106—431no—
445C2×#106—431no—
446C2×C4⋊C8—431no—
447C2×C4⋊C8—431no—
448C2×#103—431no—
449C2×#103—431no—
450C2×#103—431no—
451C2×#103—431no—
452C2×#102—431no—
453C2×#102—431no—
454C2×#102—431no—
455C2×#102—431no—
456C2×C22⋊C8—431no—
457C2×C22⋊C8—431no—
458C2×C4×C8—431no—
459C2×C4×C8—431no—
460C43C2×#310211yescharacteristic, complemented, Sylow
461C2×#41—434no—
462C2×#41—864no—
463C2×#41—864no—
464C2×#41—862no—
465C22×Q8—431no—
466C22×Q8C22×D4311yescharacteristic
467C22×D4—21no—
468C22×D4—431no—
469C22×D4—861no—
470C22×D4C22×D4311yescharacteristic
471C23×C4—21no—
472C23×C4—861no—
473C23×C4—861no—
474C23×C4—861no—
475C23×C4C22⋊D4311yescharacteristic
476C23×C4C22⋊D4311yescharacteristic
477C23×C4C22×D4311yescharacteristic
478C2×Q16—434no—
479C2×Q16—864no—
480C2×SD16—434no—
481C2×SD16—434no—
482C2×SD16—864no—
483C2×SD16—864no—
484C2×D8—434no—
485C2×D8—864no—
486C22×C8—431no—
487C22×C8—431no—
488C22×C8—431no—
489C22×C8—431no—
490#126—28no—
491#125—22no—
492#125C22×D4314yes—
493#124—22no—
494#124C22×D4314yes—
495#123—28no—
496C22⋊Q8—22no—
497C22⋊Q8C22×D4314yes—
498#121—22no—
499#121C22×D4314yes—
500C4×Q8—22no—
501C4×Q8—434no—
502C4×Q8—434no—
503C4×Q8—862no—
504C4×Q8—862no—
505C4×Q8C22×D4314yes—
506C4×D4—28no—
507C4×D4—22no—
508C4×D4—434no—
509C4×D4—434no—
510C4×D4—868no—
511C4×D4—868no—
512C4×D4—862no—
513C4×D4—862no—
514C4×D4C22×D4314yes—
515#117—28no—
516#117—434no—
517#117—862no—
518#117—868no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—431no—
524C2×C4⋊C4—431no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4—861no—
527C2×C4⋊C4C22×D4311yescharacteristic
528C2×C4⋊C4C22×D4311yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C42—21no—
538C2×C42—861no—
539C2×C42—861no—
540C2×C42—861no—
541C2×C42—868no—
542C2×C42C22⋊D4311yescharacteristic
543C2×C42C22⋊D4314yes—
544C2×C42C22⋊D4311yescharacteristic
545C2×C42C22×D4311yescharacteristic
546C2×C42C22×D4314yes—
547C2×C42C22×D4311yescharacteristic
548#107—434no—
549#107—434no—
550#106—434no—
551#106—434no—
552C4⋊C8—434no—
553C4⋊C8—434no—
554#103—434no—
555#103—434no—
556#103—434no—
557#103—434no—
558#102—434no—
559#102—434no—
560#102—434no—
561#102—434no—
562C22⋊C8—434no—
563C22⋊C8—434no—
564C4×C8—434no—
565C4×C8—434no—
566C24—21no—
567C24—861no—
568C24C2×C22⋊D4311yescharacteristic
569#41—868no—
570#41—868no—
571#41—8616no—
572C2×Q8—21no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—434no—
576C2×Q8—432no—
577C2×Q8—861no—
578C2×Q8—862no—
579C2×Q8C23×D4312yes—
580C2×D4—24no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—44no—
585C2×D4—434no—
586C2×D4—432no—
587C2×D4—868no—
588C2×D4—864no—
589C2×D4—861no—
590C2×D4—862no—
591C2×D4C23×D4312yes—
592C22×C4—24no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—42no—
600C22×C4—44no—
601C22×C4—868no—
602C22×C4—861no—
603C22×C4—864no—
604C22×C4—861no—
605C22×C4—861no—
606C22×C4—864no—
607C22×C4—864no—
608C22×C4—1724no—
609C22×C4—1724no—
610C22×C4C2×C22⋊D4311yescharacteristic
611C22×C4C2×C22⋊D4311yescharacteristic
612C22×C4C2×C22⋊D4311yescharacteristic
613C22×C4C2×C22⋊D4311yescharacteristic
614C22×C4C2×C22⋊D4314yes—
615C22×C4C2×C22⋊D4312yes—
616C22×C4C2×C22⋊D4314yes—
617C22×C4C2×C22⋊D4311yescharacteristic
618C22×C4C23×D4312yes—
619C22×C4C23×D4311yescharacteristic
620Q16—868no—
621SD16—868no—
622SD16—868no—
623D8—868no—
624C2×C8—432no—
625C2×C8—432no—
626C2×C8—432no—
627C2×C8—432no—
628C2×C8—862no—
629C2×C8—862no—
630C2×C8—862no—
631C2×C8—862no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—432no—
639C4⋊C4—432no—
640C4⋊C4—861no—
641C4⋊C4—861no—
642C4⋊C4—864no—
643C4⋊C4—864no—
644C4⋊C4C23×D4312yes—
645C4⋊C4C23×D4312yes—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—864no—
652C22⋊C4—864no—
653C22⋊C4—864no—
654C42—24no—
655C42—864no—
656C42—864no—
657C42—864no—
658C42C2×C22⋊D4314yes—
659C42C2×C22⋊D4314yes—
660C42C2×C22⋊D4312yes—
661C42C2×C22⋊D4312yes—
662C42C23×D4312yes—
663C42C23×D4312yes—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—864no—
672C23—862no—
673C23—1722no—
674C23—1722no—
675C23C22×C22⋊D4312yes—
676C23C22×C22⋊D4311yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—42no—
680Q8—434no—
681Q8—864no—
682Q8—862no—
683D4—22no—
684D4—22no—
685D4—48no—
686D4—42no—
687D4—434no—
688D4—8616no—
689D4—864no—
690D4—862no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—44no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—48no—
707C2×C4—8616no—
708C2×C4—864no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—1728no—
713C2×C4—1722no—
714C2×C4—1722no—
715C2×C4—1728no—
716C2×C4#1306334514yes—
717C2×C4C22×C22⋊D4312yes—
718C2×C4C22×C22⋊D4312yes—
719C2×C4C22×C22⋊D4312yes—
720C2×C4C22×C22⋊D4312yes—
721C2×C4C22×C22⋊D4311yescharacteristic
722C2×C4C22×C22⋊D4312yes—
723C2×C4#41×D4312yes—
724C2×C4#41×D4312yes—
725C2×C4C24×D4311yescharacteristic
726C8—862no—
727C8—862no—
728C8—862no—
729C8—862no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—84no—
738C22—864no—
739C22—1722no—
740C22—1722no—
741C22—1728no—
742C22#1458340612yes—
743C22C2×#1306334512yes—
744C22#1458369712yes—
745C22C23×C22⋊D4311yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—864no—
754C4—1722no—
755C4—1722no—
756C4#1458340612yes—
757C4C2×#1306334514yes—
758C4C2×#41×D4311yescharacteristic
759C4C2×#41×D4311yescharacteristic
760C2—42no—
761C2—82no—
762C2—1724no—
763C2#1914460714yesdirect product factor
764C2C2×#1458340611yescharacteristic
765C2C22×#1306334511yescharacteristic
766C2C2×#1458369711yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#529C2
socleC23×C43C22×D4
prime radicalC2×#14583042C2
hypercenterC2×#529D43
hypocenterC43C2×#3102
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×C4×#10621898C2semidirect
2. #19144607C2direct (N × H)
3. C2×#14583237C2semidirect
4. C2×#14583220C2semidirect
5. C2×#14583203C2semidirect
6. C2×#14583196C2semidirect
7. C2×#14583118C2semidirect
8. C2×#14583111C2semidirect
9. C2×#14583059C2semidirect
11. C2×C4×#10621885C2semidirect
12. C2×C4×#10621884C2semidirect
13. C2×C4×#10621883C2semidirect
14. C2×C4×#10621882C2semidirect
15. C2×#14582952C2semidirect
16. C2×C43×#529C2semidirect
23. C4×#10621898C22semidirect
33. #14583237C22semidirect
34. #14583220C22semidirect
35. #14583203C22semidirect
36. #14583196C22semidirect
37. #14583118C22semidirect
38. #14583111C22semidirect
39. #14583059C22semidirect
41. C4×#10621885C22semidirect
42. C4×#10621884C22semidirect
43. C4×#10621883C22semidirect
44. C4×#10621882C22semidirect
45. #14582952C22semidirect
65. C43×#529C22semidirect
377. C2×#529D43semidirect
395. C2×C43#3102semidirect
406. #529C2×D43semidirect
460. C43C2×#3102semidirect
763. C2#19144607direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#106218982
#191446072
C2×#145832372
C2×#145832202
C2×#145832032
C2×#145831962
C2×#145831182
C2×#145831112
C2×#145830592
C2×#145830422
C2×C4×#106218852
C2×C4×#106218842
C2×C4×#106218832
C2×C4×#106218822
C2×#145829522
C2×C43×#5292
C2×#310243