Finite Group Databasebeta

← C2×#22569040 #31719927

Subgroups — C2×#22569040 #31719927

Order 17152.

2946 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524070C211yesmaximal, characteristic
2C2×#16863878C211yesmaximal, characteristic, complemented
3C2×#16863868C211yesmaximal, characteristic, complemented
4#22569040C2116yesmaximal, direct product factor
5C2×#16863509C211yesmaximal, characteristic, complemented
6C2×#16863505C211yesmaximal, characteristic, complemented
7C2×#16863499C211yesmaximal, characteristic, complemented
8C2×SD16×Dic67C211yesmaximal, characteristic, complemented
9C2×C4×#11761615C211yesmaximal, characteristic, complemented
10C2×#16863478C211yesmaximal, characteristic, complemented
11C2×C4×#11761613C211yesmaximal, characteristic, complemented
12C2×#16863437C211yesmaximal, characteristic, complemented
13C2×#16863391C211yesmaximal, characteristic, complemented
14C2×#102×D67C211yesmaximal, characteristic, complemented
15C2×#16863353C211yesmaximal, characteristic, complemented
16C2×#440×C67C211yesmaximal, characteristic, complemented
17C22×#11761629C2211yescharacteristic
18C22×D4×D67C2211yescharacteristic
19C2×#14524070C4116yescomplemented
20C2×#14524070C2218yes—
21C22×#11761615C2211yescharacteristic
22C22×D536C2211yescharacteristic
23C22×#11761613C2211yescharacteristic
24C22×#11761611C2211yescharacteristic
25C22×C8×D67C2211yescharacteristic
26#16863878—24no—
27#16863878C2218yescomplemented
28#16863868—24no—
29#16863868C2218yescomplemented
30C2×Q8×Dic67C2211yescharacteristic, complemented
31C2×C4×D268—21no—
32C2×C4×D268C2211yescharacteristic
33C2×C4×D268C2211yescharacteristic, complemented
34C2×D4×Dic67C2211yescharacteristic
35C2×#14524005—21no—
36C2×#14524005C2211yescharacteristic
37C2×#14524005C2211yescharacteristic, complemented
38C2×C4×C22⋊D67—21no—
39C2×(C22⋊D67)⋊C4—21no—
40C2×#14524001C2211yescharacteristic
41C2×#14524000—21no—
42C2×#14524000C2211yescharacteristic
43C2×C4⋊C4×D67—21no—
44C2×C4⋊C4×D67C2211yescharacteristic
45C22×(C2×D67)⋊C4—21no—
46C2×C22⋊C4×D67—21no—
47#16863509C2218yescomplemented
48#16863505C2218yescomplemented
49#16863499C2218yescomplemented
50SD16×Dic67C2218yescomplemented
51C4×#11761615C2218yescomplemented
52#16863478C2218yescomplemented
53C4×#11761613C2218yescomplemented
54#16863437C2218yescomplemented
55C2×#14523976C2211yescharacteristic, complemented
56C2×#14523975C2211yescharacteristic, complemented
57C2×#14523974C2211yescharacteristic, complemented
58#16863391C2218yescomplemented
59C2×#14523967C2211yescharacteristic, complemented
60C2×#14523965C2211yescharacteristic
61C2×#14523965C2211yescharacteristic, complemented
62C2×#14523964C2211yescharacteristic
63C2×#14523963C2211yescharacteristic
64C2×#14523963C2211yescharacteristic, complemented
65#102×D67C2218yescomplemented
66#16863353C2218yescomplemented
67C2×#14523953C2211yescharacteristic, complemented
68C2×C4×C67⋊C8C2211yescharacteristic, complemented
69C2×C8×Dic67C2211yescharacteristic, complemented
70C22×SD16×C67C2211yescharacteristic
71C2×C4×Q8×C67C2211yescharacteristic, complemented
72C2×C4×D4×C67C2211yescharacteristic
73#440×C67C2218yescomplemented
74C2×#107×C67C2211yescharacteristic, complemented
75C2×#103×C67C2211yescharacteristic, complemented
76C2×#102×C67C2211yescharacteristic
77C2×#97×C67C2211yescharacteristic, complemented
78C24×D67—21no—
79C2×#11761629—22no—
80C2×#11761629—24no—
81C2×#11761629C2×C418yescomplemented
82C2×#11761629C2314yes—
83C22×D268—21no—
84C22×D268C2311yescharacteristic
85C22×D268C2311yescharacteristic
86C22×C22⋊D67—21no—
87C2×D4×D67—22no—
88C2×D4×D67—24no—
89C2×D4×D67C2×C418yescomplemented
90C2×D4×D67C2314yes—
91C23×Dic67—21no—
92C22×C4×D67—21no—
93C22×C4×D67—21no—
94C22×C4×D67—21no—
95C22×C4×D67—21no—
96C22×C4×D67—21no—
97C22×C4×D67—21no—
98C22×C4×D67C2311yescharacteristic
99#14524070C2×C4164yescomplemented
100C2×#11761615C2×C418yescomplemented
101C2×#11761615C2314yes—
102C2×D536C2×C418yescomplemented
103C2×D536C2314yes—
104C2×#11761613C2×C418yescomplemented
105C2×#11761613C2314yes—
106C2×#11761611C2×C418yescomplemented
107C2×#11761611C2314yes—
108C22×C67⋊C8C2311yescharacteristic
109C22×C67⋊C8C2311yescharacteristic
110C2×C8×D67—24no—
111C2×C8×D67C2314yes—
112Q8×Dic67—22no—
113Q8×Dic67C2314yescomplemented
114C4×D268—28no—
115C4×D268—22no—
116C4×D268—22no—
117C4×D268C2314yes—
118C4×D268C2314yescomplemented
119D4×Dic67—22no—
120D4×Dic67C2314yes—
121#14524005—28no—
122#14524005—22no—
123#14524005—22no—
124#14524005C2314yes—
125#14524005C2314yescomplemented
126C4×C22⋊D67—28no—
127(C22⋊D67)⋊C4—28no—
128#14524001—22no—
129#14524001C2314yes—
130#14524000—28no—
131#14524000D414yes—
132#14524000C2314yes—
133C2×C4⋊Dic67—21no—
134C2×C4⋊Dic67C2311yescharacteristic
135C2×C4⋊Dic67C2311yescharacteristic
136C2×Dic67⋊C4—21no—
137C2×Dic67⋊C4D411yescharacteristic
138C2×Dic67⋊C4D411yescharacteristic
139C4⋊C4×D67—22no—
140C4⋊C4×D67—28no—
141C4⋊C4×D67C2314yes—
142C2×C22⋊Dic67—21no—
143C2×(C2×D67)⋊C4—21no—
144C2×(C2×D67)⋊C4—21no—
145C2×(C2×D67)⋊C4—21no—
146C2×(C2×D67)⋊C4—28no—
147C2×(C2×D67)⋊C4—21no—
148C2×(C2×D67)⋊C4—21no—
149C2×(C2×D67)⋊C4D411yescharacteristic
150C2×(C2×D67)⋊C4D411yescharacteristic
151C22⋊C4×D67—28no—
152C2×C4×Dic67—21no—
153C2×C4×Dic67—21no—
154C2×C4×Dic67C2311yescharacteristic
155#14523976C2314yescomplemented
156#14523975C2314yescomplemented
157#14523974C2314yescomplemented
158#14523967C2314yescomplemented
159#14523965C2314yes—
160#14523965C2314yescomplemented
161#14523964C2314yes—
162#14523963C2314yes—
163#14523963C2314yescomplemented
164#14523953C2314yescomplemented
165C4×C67⋊C8C2314yescomplemented
166C8×Dic67C2314yescomplemented
167C22×Q8×C67C2311yescharacteristic
168C22×D4×C67C2311yescharacteristic
169C23×C4×C67—21no—
170C2×SD16×C67C2×C418yescomplemented
171C2×SD16×C67C2314yes—
172C22×C8×C67C2311yescharacteristic
173C22×C8×C67C2311yescharacteristic
174C4×Q8×C67—22no—
175C4×Q8×C67C2314yescomplemented
176C4×D4×C67—22no—
177C4×D4×C67C2314yes—
178C2×C4⋊C4×C67—21no—
179C2×C4⋊C4×C67C2311yescharacteristic
180C2×C4⋊C4×C67C2311yescharacteristic
181C2×C22⋊C4×C67—21no—
182C2×C42×C67—21no—
183C2×C42×C67C2311yescharacteristic
184#107×C67C2314yescomplemented
185#103×C67C2314yescomplemented
186#102×C67C2314yes—
187#97×C67C2314yescomplemented
188C23×D67—21no—
189C23×D67—21no—
190C23×D67—28no—
191C23×D67—24no—
192C23×D67—82no—
193C23×D67—82no—
194C23×D67C2×D411yescharacteristic
195#11761629—216no—
196#11761629—28no—
197#11761629C22×C4116yescomplemented
198C2×D268—28no—
199C2×D268—24no—
200C2×D268—21no—
201C2×D268—21no—
202C2×D268—22no—
203C2×D268—22no—
204C2×D268C22×C414yes—
205C2×D268C22×C414yes—
206C2×D268C2412yes—
207C2×D268C2412yes—
208C2×C22⋊D67—28no—
209C2×C22⋊D67—24no—
210D4×D67—216no—
211D4×D67—28no—
212D4×D67C22×C4116yescomplemented
213C22×Dic67—21no—
214C22×Dic67—21no—
215C22×Dic67—24no—
216C22×Dic67—82no—
217C22×Dic67C2×D411yescharacteristic
218C22×Dic67C2×D411yescharacteristic
219C22×Dic67C2×D411yescharacteristic
220C2×C4×D67—28no—
221C2×C4×D67—24no—
222C2×C4×D67—24no—
223C2×C4×D67—24no—
224C2×C4×D67—24no—
225C2×C4×D67—24no—
226C2×C4×D67—24no—
227C2×C4×D67—82no—
228C2×C4×D67—82no—
229C2×C4×D67—82no—
230C2×C4×D67—82no—
231C2×C4×D67—82no—
232C2×C4×D67C22×C414yes—
233C2×C4×D67C2×D412yes—
234C2×C4×D67#4114yes—
235C2×C4×D67C2412yes—
236#11761615C22×C4116yescomplemented
237D536C22×C4116yescomplemented
238#11761613C22×C4116yescomplemented
239#11761611C22×C4116yescomplemented
240C2×C67⋊C8—22no—
241C2×C67⋊C8C22×C414yes—
242C2×C67⋊C8C2412yes—
243C2×C67⋊C8C2412yes—
244C8×D67—28no—
245C4⋊Dic67—21no—
246C4⋊Dic67—21no—
247C4⋊Dic67—24no—
248C4⋊Dic67C2412yes—
249C4⋊Dic67C2412yes—
250Dic67⋊C4—24no—
251Dic67⋊C4C2×D414yes—
252Dic67⋊C4C2×D414yes—
253C22⋊Dic67—24no—
254(C2×D67)⋊C4—24no—
255(C2×D67)⋊C4—24no—
256(C2×D67)⋊C4—24no—
257(C2×D67)⋊C4—24no—
258(C2×D67)⋊C4—24no—
259(C2×D67)⋊C4C2×D414yes—
260(C2×D67)⋊C4C2×D414yes—
261C4×Dic67—24no—
262C4×Dic67—24no—
263C4×Dic67C2×D412yes—
264C4×Dic67C2412yes—
265C24×C67—21no—
266C2×Q8×C67—21no—
267C2×Q8×C67—22no—
268C2×Q8×C67C22×C414yes—
269C2×Q8×C67C2412yes—
270C2×D4×C67—21no—
271C2×D4×C67—22no—
272C2×D4×C67C22×C414yes—
273C2×D4×C67C2412yes—
274C22×C4×C67—21no—
275C22×C4×C67—21no—
276C22×C4×C67—21no—
277C22×C4×C67—24no—
278C22×C4×C67—82no—
279C22×C4×C67C2×D411yescharacteristic
280C22×C4×C67C2×D411yescharacteristic
281C22×C4×C67C2411yescharacteristic
282SD16×C67C22×C4116yescomplemented
283C2×C8×C67—22no—
284C2×C8×C67C22×C414yes—
285C2×C8×C67C2412yes—
286C2×C8×C67C2412yes—
287C4⋊C4×C67—24no—
288C4⋊C4×C67—21no—
289C4⋊C4×C67—21no—
290C4⋊C4×C67C2412yes—
291C4⋊C4×C67C2412yes—
292C22⋊C4×C67—24no—
293C42×C67—24no—
294C42×C67C2×D412yes—
295C42×C67C2412yes—
296C23×C67—24no—
297C23×C67—22no—
298C23×C67—42no—
299C23×C67—42no—
300C23×C67C22×D411yescharacteristic
301C22×D67—22no—
302C22×D67—22no—
303C22×D67—24no—
304C22×D67—24no—
305C22×D67—22no—
306C22×D67—22no—
307C22×D67—216no—
308C22×D67—42no—
309C22×D67—42no—
310C22×D67—42no—
311C22×D67—42no—
312C22×D67—816no—
313C22×D67—84no—
314C22×D67—84no—
315C22×D67C4×D414yes—
316C22×D67C22×D412yes—
317Q8×C67—24no—
318Q8×C67—22no—
319Q8×C67C23×C414yes—
320D4×C67—24no—
321D4×C67—22no—
322D4×C67C23×C414yes—
323C2×C4×C67—24no—
324C2×C4×C67—22no—
325C2×C4×C67—22no—
326C2×C4×C67—22no—
327C2×C4×C67—22no—
328C2×C4×C67—22no—
329C2×C4×C67—42no—
330C2×C4×C67—42no—
331C2×C4×C67—84no—
332C2×C4×C67C23×C412yes—
333C2×C4×C67C22×D412yes—
334C2×C4×C67C22×D412yes—
335C2×C4×C67C22×D411yescharacteristic
336C2×C4×C67C2×#4112yes—
337C2×C4×C67C2511yescharacteristic
338C22⋊D67—216no—
339C2×Dic67—22no—
340C2×Dic67—22no—
341C2×Dic67—22no—
342C2×Dic67—22no—
343C2×Dic67—42no—
344C2×Dic67—42no—
345C2×Dic67—84no—
346C2×Dic67C4×D414yes—
347C2×Dic67C22×D412yes—
348C2×Dic67C22×D412yes—
349C2×Dic67C22×D412yes—
350D268—216no—
351D268—24no—
352D268—24no—
353D268—22no—
354D268—22no—
355D268C23×C414yes—
356D268C23×C414yes—
357C4×D67—216no—
358C4×D67—84no—
359C4×D67—84no—
360C4×D67—84no—
361C4×D67—84no—
362C4×D67—84no—
363C4×D67C4×D418yes—
364C4×D67C23×C414yes—
365C4×D67C2×#4114yes—
366C8×C67—22no—
367C8×C67C23×C414yes—
368C67⋊C8—22no—
369C67⋊C8C23×C414yes—
370C22×C67—24no—
371C22×C67—48no—
372C22×C67—42no—
373C22×C67—42no—
374C22×C67C2×C4×D412yes—
375C22×C67#57612yes—
376C22×C67#57712yes—
377C22×C67C23×D411yescharacteristic
378C2×D67—28no—
379C2×D67—22no—
380C2×D67—22no—
381C2×D67—24no—
382C2×D67—24no—
383C2×D67—48no—
384C2×D67—48no—
385C2×D67—42no—
386C2×D67—42no—
387C2×D67—42no—
388C2×D67—42no—
389C2×D67—816no—
390C2×D67C2×C4×D414yes—
391C4×C67—24no—
392C4×C67—22no—
393C4×C67—22no—
394C4×C67—42no—
395C4×C67—42no—
396C4×C67C2×C4×D412yes—
397C4×C67C24×C411yescharacteristic
398C4×C67C22×#4111yescharacteristic
399Dic67—22no—
400Dic67—22no—
401Dic67—42no—
402Dic67—42no—
403Dic67C2×C4×D414yes—
404C2×#2946—671nomaximal, Sylow
405C2×C67—44no—
406C2×C67#294614yescomplemented
407C2×C67C22×C4×D411yescharacteristic
408C2×C67C2×#57611yescharacteristic
409C2×C67C2×#57711yescharacteristic
410D67—24no—
411D67—44no—
412D67—44no—
413C22×AGL(1,ℤ/8)—671no—
414C2×#520—671no—
415C2×#518—671no—
416#2946—6716no—
417C2×#442—671no—
418C2×#442—671no—
419C2×#440—671no—
420C2×#440D6711yescharacteristic, complemented
421C2×C4×SD16—671no—
422C2×C4×SD16—671no—
423C2×C4×D8—671no—
424C2×C4×D8—671no—
425C2×#428—671no—
426C2×#416—671no—
427C22×#102—671no—
428C2×#405—671no—
429C67C2×#294611yescharacteristic, complemented, Sylow
430C22×#41—671no—
431C23×D4—671no—
432C2×AGL(1,ℤ/8)—6716no—
433C2×AGL(1,ℤ/8)—678no—
434C22×SD16—671no—
435C22×SD16C2×D6711yescharacteristic
436C22×D8—671no—
437C22×D8—671no—
438C22×M16—671no—
439C23×C8—671no—
440#520—678no—
441#520—1344no—
442#518—678no—
443#518—1344no—
444C2×C4×Q8—671no—
445C2×C4×Q8C2×D6711yescharacteristic, complemented
446C2×C4×D4—671no—
447C2×C4×D4—671no—
448C2×C4×D4—671no—
449C2×C4×D4—671no—
450C2×C4×D4—671no—
451C2×C4×D4—1341no—
452C2×C4×D4—1341no—
453C2×C4×D4—1341no—
454C2×C4×D4—1341no—
455C2×C4×D4C2×D6711yescharacteristic
456C2×#117—671no—
457C2×#117—671no—
458C2×#117—1341no—
459C22×C4⋊C4—671no—
460C22×C4⋊C4—1341no—
461C22×C22⋊C4—1341no—
462C22×C22⋊C4—1341no—
463#442—678no—
464#442—678no—
465#440—678no—
466#440C2×D6718yescomplemented
467C4×SD16—678no—
468C4×SD16—678no—
469C4×D8—678no—
470C4×D8—678no—
471#428—678no—
472C2×#107—671no—
473C2×#107C2×D6711yescharacteristic, complemented
474C2×#106—671no—
475C2×#106—671no—
476#416—678no—
477C2×#103—671no—
478C2×#103C2×D6711yescharacteristic, complemented
479C2×#102—671no—
480C2×#102—671no—
481C2×#102—671no—
482C2×#102—671no—
483C2×#102—671no—
484C2×#102—678no—
485C2×#102C2×D6711yescharacteristic
486#405—678no—
487C2×#97—671no—
488C2×#97C2×D6711yescharacteristic, complemented
489C2×C4×C8—671no—
490C2×C4×C8—671no—
491C25—1341no—
492C2×#41—678no—
493C2×#41—674no—
494C2×#41—1342no—
495C2×#41—1344no—
496C22×Q8C22×D6711yescharacteristic
497C22×D4—678no—
498C22×D4—674no—
499C22×D4—671no—
500C22×D4—671no—
501C22×D4—1341no—
502C22×D4—1342no—
503C22×D4—1344no—
504C22×D4—1341no—
505C22×D4C22×D6711yescharacteristic
506C23×C4—21no—
507C23×C4—671no—
508C23×C4—1341no—
509C23×C4—1341no—
510C23×C4—1341no—
511C23×C4—1341no—
512C23×C4—1341no—
513C23×C4—1341no—
514C23×C4—1341no—
515AGL(1,ℤ/8)—6764no—
516C2×SD16—678no—
517C2×SD16—674no—
518C2×SD16C4×D6718yescomplemented
519C2×SD16C22×D6714yes—
520C2×D8—678no—
521C2×D8—674no—
522C2×D8—678no—
523C2×D8—674no—
524C2×M16—678no—
525C2×M16—674no—
526C22×C8—671no—
527C22×C8—671no—
528C22×C8—674no—
529C22×C8—1344no—
530C22×C8C22×D6711yescharacteristic
531C22×C8C22×D6711yescharacteristic
532C4×Q8—22no—
533C4×Q8—674no—
534C4×Q8—1342no—
535C4×Q8C22×D6714yescomplemented
536C4×D4—22no—
537C4×D4—674no—
538C4×D4—674no—
539C4×D4—674no—
540C4×D4—674no—
541C4×D4—674no—
542C4×D4—1348no—
543C4×D4—1342no—
544C4×D4—1342no—
545C4×D4—1342no—
546C4×D4—1348no—
547C4×D4—1348no—
548C4×D4—1348no—
549C4×D4—1342no—
550C4×D4—1342no—
551C4×D4C22×D6714yes—
552#117—674no—
553#117—674no—
554#117—674no—
555#117—1348no—
556#117—1342no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—671no—
559C2×C4⋊C4—671no—
560C2×C4⋊C4—671no—
561C2×C4⋊C4—671no—
562C2×C4⋊C4—674no—
563C2×C4⋊C4—1348no—
564C2×C4⋊C4—1342no—
565C2×C4⋊C4—1341no—
566C2×C4⋊C4—1341no—
567C2×C4⋊C4C22×D6711yescharacteristic
568C2×C4⋊C4C22×D6711yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—671no—
571C2×C22⋊C4—671no—
572C2×C22⋊C4—1348no—
573C2×C22⋊C4—1348no—
574C2×C22⋊C4—1341no—
575C2×C22⋊C4—1341no—
576C2×C22⋊C4—1341no—
577C2×C22⋊C4—1341no—
578C2×C22⋊C4—1341no—
579C2×C22⋊C4—1341no—
580C2×C42—21no—
581C2×C42—671no—
582C2×C42—1341no—
583C2×C42—1341no—
584C2×C42C22×D6711yescharacteristic
585#107—674no—
586#107C22×D6714yescomplemented
587#106—674no—
588#106—674no—
589#103—674no—
590#103C22×D6714yescomplemented
591#102—674no—
592#102—674no—
593#102—674no—
594#102—674no—
595#102—674no—
596#102C22×D6714yes—
597#97—674no—
598#97C22×D6714yescomplemented
599C4×C8—674no—
600C4×C8—674no—
601C24—21no—
602C24—5362no—
603C24—5362no—
604C24—671no—
605C24—1344no—
606C24—1348no—
607C24—1341no—
608C24—1341no—
609#41—6716no—
610#41—13416no—
611#41—1348no—
612C2×Q8—21no—
613C2×Q8—22no—
614C2×Q8C2×C4×D6714yes—
615C2×Q8C23×D6712yes—
616C2×D4—21no—
617C2×D4—22no—
618C2×D4—6716no—
619C2×D4—674no—
620C2×D4—674no—
621C2×D4—672no—
622C2×D4—672no—
623C2×D4—1344no—
624C2×D4—1348no—
625C2×D4—13416no—
626C2×D4—1348no—
627C2×D4—1344no—
628C2×D4—1348no—
629C2×D4—1341no—
630C2×D4—1341no—
631C2×D4—1342no—
632C2×D4—1342no—
633C2×D4C2×C4×D6714yes—
634C2×D4C23×D6712yes—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—24no—
639C22×C4—82no—
640C22×C4—5362no—
641C22×C4—5362no—
642C22×C4—5362no—
643C22×C4—5362no—
644C22×C4—5362no—
645C22×C4—5362no—
646C22×C4—671no—
647C22×C4—674no—
648C22×C4—672no—
649C22×C4—674no—
650C22×C4—672no—
651C22×C4—671no—
652C22×C4—671no—
653C22×C4—1344no—
654C22×C4—1344no—
655C22×C4—1344no—
656C22×C4—1344no—
657C22×C4—1348no—
658C22×C4—1341no—
659C22×C4—1341no—
660C22×C4—1344no—
661C22×C4—1344no—
662C22×C4—1344no—
663C22×C4D4×D6711yescharacteristic
664C22×C4D4×D6711yescharacteristic
665C22×C4C23×D6711yescharacteristic
666SD16—6716no—
667SD16C2×C4×D67116yescomplemented
668D8—6716no—
669D8—6716no—
670M16—6716no—
671C2×C8—22no—
672C2×C8—674no—
673C2×C8—672no—
674C2×C8—672no—
675C2×C8—1348no—
676C2×C8—1342no—
677C2×C8C2×C4×D6714yes—
678C2×C8C23×D6712yes—
679C2×C8C23×D6712yes—
680C4⋊C4—24no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—674no—
684C4⋊C4—674no—
685C4⋊C4—672no—
686C4⋊C4—672no—
687C4⋊C4—1344no—
688C4⋊C4—1344no—
689C4⋊C4—1341no—
690C4⋊C4—1341no—
691C4⋊C4C23×D6712yes—
692C4⋊C4C23×D6712yes—
693C22⋊C4—24no—
694C22⋊C4—674no—
695C22⋊C4—674no—
696C22⋊C4—1344no—
697C22⋊C4—1344no—
698C22⋊C4—1344no—
699C22⋊C4—1344no—
700C22⋊C4—1344no—
701C22⋊C4—1344no—
702C42—24no—
703C42—672no—
704C42—672no—
705C42—1344no—
706C42—1344no—
707C42D4×D6712yes—
708C42C23×D6712yes—
709C23—24no—
710C23—22no—
711C23—42no—
712C23—42no—
713C23—2682no—
714C23—2682no—
715C23—2682no—
716C23—2682no—
717C23—53616no—
718C23—5364no—
719C23—5364no—
720C23—674no—
721C23—672no—
722C23—13416no—
723C23—1344no—
724C23—1344no—
725C23—1342no—
726C23—1342no—
727C23—1342no—
728C23—1342no—
729C23C2×D4×D6711yescharacteristic
730Q8—24no—
731Q8—22no—
732Q8C22×C4×D6714yes—
733D4—24no—
734D4—22no—
735D4—674no—
736D4—674no—
737D4—13416no—
738D4—13416no—
739D4—1344no—
740D4—1344no—
741D4—1342no—
742D4—1342no—
743D4C22×C4×D6714yes—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—84no—
753C2×C4—2682no—
754C2×C4—2682no—
755C2×C4—5364no—
756C2×C4—5364no—
757C2×C4—5364no—
758C2×C4—5364no—
759C2×C4—5364no—
760C2×C4—5364no—
761C2×C4—674no—
762C2×C4—672no—
763C2×C4—678no—
764C2×C4—674no—
765C2×C4—674no—
766C2×C4—672no—
767C2×C4—672no—
768C2×C4—13416no—
769C2×C4—1342no—
770C2×C4—1342no—
771C2×C4—1342no—
772C2×C4—1342no—
773C2×C4C22×C4×D6712yes—
774C2×C4C2×D4×D6712yes—
775C2×C4C2×D4×D6712yes—
776C2×C4C2×D4×D6711yescharacteristic
777C2×C4#41×D6712yes—
778C2×C4C24×D6711yescharacteristic
779C8—22no—
780C8—674no—
781C8—1342no—
782C8C22×C4×D6714yes—
783C22—24no—
784C22—48no—
785C22—42no—
786C22—42no—
787C22—2688no—
788C22—2688no—
789C22—2682no—
790C22—2682no—
791C22—2682no—
792C22—2682no—
793C22—53616no—
794C22—674no—
795C22—1344no—
796C22—1344no—
797C22—1348no—
798C22—1342no—
799C22—1342no—
800C22C4×D4×D6712yes—
801C22#1686420012yes—
802C22#1686420512yes—
803C22C22×D4×D6711yescharacteristic
804C4—24no—
805C4—22no—
806C4—22no—
807C4—42no—
808C4—42no—
809C4—2682no—
810C4—2682no—
811C4—674no—
812C4—1342no—
813C4—1342no—
814C4C4×D4×D6712yes—
815C4C23×C4×D6711yescharacteristic
816C4C2×#41×D6711yescharacteristic
817C2—44no—
818C2—2684no—
819C2—2684no—
820C2—1344no—
821C2#2256904014yesdirect product factor
822C2C2×C4×D4×D6711yescharacteristic
823C2C2×#1686420011yescharacteristic
824C2C2×#1686420511yescharacteristic
subgroupG/H
centerC23C2×D4×D67
commutatorC4×C67C24×C4
FrattiniC2×C4C24×D67
FittingC2×#440×C67C2
socleC23×C67C22×D4
prime radicalC22×#14524070C2
cosocleC2×C4×C67C25
hypercenterC2×#440D67
hypocenterC67C2×#2946
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#16863878C2semidirect
3. C2×#16863868C2semidirect
4. #22569040C2direct (N × H)
5. C2×#16863509C2semidirect
6. C2×#16863505C2semidirect
7. C2×#16863499C2semidirect
8. C2×SD16×Dic67C2semidirect
9. C2×C4×#11761615C2semidirect
10. C2×#16863478C2semidirect
11. C2×C4×#11761613C2semidirect
12. C2×#16863437C2semidirect
13. C2×#16863391C2semidirect
14. C2×#102×D67C2semidirect
15. C2×#16863353C2semidirect
16. C2×#440×C67C2semidirect
19. C2×#14524070C4semidirect
27. #16863878C22semidirect
29. #16863868C22semidirect
30. C2×Q8×Dic67C22semidirect
33. C2×C4×D268C22semidirect
37. C2×#14524005C22semidirect
47. #16863509C22semidirect
48. #16863505C22semidirect
49. #16863499C22semidirect
50. SD16×Dic67C22semidirect
51. C4×#11761615C22semidirect
52. #16863478C22semidirect
53. C4×#11761613C22semidirect
54. #16863437C22semidirect
55. C2×#14523976C22semidirect
56. C2×#14523975C22semidirect
57. C2×#14523974C22semidirect
58. #16863391C22semidirect
59. C2×#14523967C22semidirect
61. C2×#14523965C22semidirect
64. C2×#14523963C22semidirect
65. #102×D67C22semidirect
66. #16863353C22semidirect
67. C2×#14523953C22semidirect
68. C2×C4×C67⋊C8C22semidirect
69. C2×C8×Dic67C22semidirect
71. C2×C4×Q8×C67C22semidirect
73. #440×C67C22semidirect
74. C2×#107×C67C22semidirect
75. C2×#103×C67C22semidirect
77. C2×#97×C67C22semidirect
81. C2×#11761629C2×C4semidirect
89. C2×D4×D67C2×C4semidirect
99. #14524070C2×C4semidirect
100. C2×#11761615C2×C4semidirect
102. C2×D536C2×C4semidirect
104. C2×#11761613C2×C4semidirect
106. C2×#11761611C2×C4semidirect
113. Q8×Dic67C23semidirect
118. C4×D268C23semidirect
125. #14524005C23semidirect
155. #14523976C23semidirect
156. #14523975C23semidirect
157. #14523974C23semidirect
158. #14523967C23semidirect
160. #14523965C23semidirect
163. #14523963C23semidirect
164. #14523953C23semidirect
165. C4×C67⋊C8C23semidirect
166. C8×Dic67C23semidirect
170. C2×SD16×C67C2×C4semidirect
175. C4×Q8×C67C23semidirect
184. #107×C67C23semidirect
185. #103×C67C23semidirect
187. #97×C67C23semidirect
197. #11761629C22×C4semidirect
212. D4×D67C22×C4semidirect
236. #11761615C22×C4semidirect
237. D536C22×C4semidirect
238. #11761613C22×C4semidirect
239. #11761611C22×C4semidirect
282. SD16×C67C22×C4semidirect
406. C2×C67#2946semidirect
420. C2×#440D67semidirect
429. C67C2×#2946semidirect
445. C2×C4×Q8C2×D67semidirect
466. #440C2×D67semidirect
473. C2×#107C2×D67semidirect
478. C2×#103C2×D67semidirect
488. C2×#97C2×D67semidirect
518. C2×SD16C4×D67semidirect
535. C4×Q8C22×D67semidirect
586. #107C22×D67semidirect
590. #103C22×D67semidirect
598. #97C22×D67semidirect
667. SD16C2×C4×D67semidirect
821. C2#22569040direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240702
C2×#168638782
C2×#168638682
#225690402
C2×#168635092
C2×#168635052
C2×#168634992
C2×SD16×Dic672
C2×C4×#117616152
C2×#168634782
C2×C4×#117616132
C2×#168634372
C2×#168633912
C2×#102×D672
C2×#168633532
C2×#440×C672
C2×#294667