Finite Group Databasebeta

← C2×C4×#14524075 #31719906

Subgroups — C2×C4×#14524075 #31719906

Order 17152.

2810 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524075C211yesmaximal, characteristic
2C2×C4×#11761629C211yesmaximal, characteristic
3C2×C4×Q8×D67C211yesmaximal, characteristic, complemented
4C4×#14524075C2116yesmaximal, direct product factor
5C2×#16863503C211yesmaximal, characteristic, complemented
6C2×#16863500C211yesmaximal, characteristic, complemented
7C2×#16863499C211yesmaximal, characteristic, complemented
8C2×#16863495C211yesmaximal, characteristic, complemented
9C2×C4×#11761618C211yesmaximal, characteristic, complemented
10C2×C4×#11761617C211yesmaximal, characteristic, complemented
11C2×C4×#11761615C211yesmaximal, characteristic, complemented
12C2×#16863437C211yesmaximal, characteristic, complemented
13C2×#16863396C211yesmaximal, characteristic
14C2×#16863403C211yesmaximal, characteristic, complemented
15C2×C4×#11761611C211yesmaximal, characteristic, complemented
16C2×C4×Q16×C67C211yesmaximal, characteristic, complemented
17C22×#11761629C2211yescharacteristic
18C22×Q8×D67C2211yescharacteristic
19C2×#14524075C4116yesdirect product factor
20C2×#14524075C2218yes—
21C22×#11761618C2211yescharacteristic
22C22×#11761617C2211yescharacteristic
23C22×#11761615C2211yescharacteristic
24C22×#11761611C2211yescharacteristic
25C22×#11761611C2211yescharacteristic
26C4×#11761629—24no—
27C4×#11761629C2218yes—
28C2×Q8×Dic67C2211yescharacteristic
29C2×Q8×Dic67C2211yescharacteristic
30C2×C4×Dic134—21no—
31C2×C4×Dic134C2211yescharacteristic
32C2×#14524008—21no—
33C2×#14524008C2211yescharacteristic
34C4×Q8×D67—24no—
35C4×Q8×D67C2218yescomplemented
36C2×C4×D268—21no—
37C2×C4×D268C2211yescharacteristic
38C2×#14524005—21no—
39C2×#14524005C2211yescharacteristic
40C2×#14524001—21no—
41C2×#14524001C2211yescharacteristic
42C2×C4⋊C4×D67—21no—
43C2×C4⋊C4×D67C2211yescharacteristic
44C2×C42×D67—21no—
45C2×C42×D67—21no—
46C2×C42×D67C2211yescharacteristic
47#16863503C2218yescomplemented
48#16863500C2218yescomplemented
49#16863499C2218yescomplemented
50#16863495C2218yescomplemented
51C4×#11761618C2218yescomplemented
52C4×#11761617C2218yescomplemented
53C4×#11761615C2218yescomplemented
54#16863437C2218yescomplemented
55C2×#14523976C2211yescharacteristic
56C2×#14523975C2211yescharacteristic
57C2×#14523974C2211yescharacteristic
58#16863403C2218yescomplemented
59#16863396C2218yes—
60C2×#14523968C2211yescharacteristic
61C2×#14523967C2211yescharacteristic
62C2×#14523967C2211yescharacteristic
63C2×#14523966C2211yescharacteristic
64C2×#14523965C2211yescharacteristic
65C2×#14523963C2211yescharacteristic
66C4×#11761611C2218yescomplemented
67C2×#14523953C2211yescharacteristic
68C2×#14523953C2211yescharacteristic
69C2×C4×C67⋊C8C2211yescharacteristic
70C22×Q16×C67C2211yescharacteristic
71C2×C4×Q8×C67C2211yescharacteristic
72C2×C4×Q8×C67C2211yescharacteristic
73C4×Q16×C67C2218yescomplemented
74C2×#107×C67C2211yescharacteristic
75C2×#103×C67C2211yescharacteristic
76C2×#103×C67C2211yescharacteristic
77C2×C4×C8×C67C2211yescharacteristic
78C2×#11761629—22no—
79C2×#11761629—24no—
80C2×#11761629C2×C418yes—
81C2×#11761629C2314yes—
82C22×Dic134—21no—
83C22×Dic134C2311yescharacteristic
84C2×Q8×D67—22no—
85C2×Q8×D67—24no—
86C2×Q8×D67C2×C418yescomplemented
87C2×Q8×D67C2314yes—
88C22×D268—21no—
89C22×D268C2311yescharacteristic
90C22×C4×D67—21no—
91C22×C4×D67—21no—
92C22×C4×D67—21no—
93C22×C4×D67—21no—
94C22×C4×D67—21no—
95C22×C4×D67D411yescharacteristic
96C22×C4×D67D411yescharacteristic
97C22×C4×D67C2311yescharacteristic
98#14524075C2×C4164yesdirect product factor
99C2×#11761618C2×C418yescomplemented
100C2×#11761618C2314yes—
101C2×#11761617C2×C418yescomplemented
102C2×#11761617C2314yes—
103C2×#11761615C2×C418yescomplemented
104C2×#11761615C2314yes—
105C2×#11761611—24no—
106C2×#11761611C2×C418yescomplemented
107C2×#11761611C2314yes—
108C2×#11761611C2314yes—
109C22×C67⋊C8C2311yescharacteristic
110C22×C67⋊C8C2311yescharacteristic
111Q8×Dic67—22no—
112Q8×Dic67—22no—
113Q8×Dic67C2314yes—
114Q8×Dic67C2314yes—
115C4×Dic134—28no—
116C4×Dic134—22no—
117C4×Dic134C2314yes—
118#14524008—22no—
119#14524008—28no—
120#14524008C2314yes—
121C4×D268—28no—
122C4×D268—22no—
123C4×D268C2314yes—
124#14524005—28no—
125#14524005—22no—
126#14524005C2314yes—
127#14524001—22no—
128#14524001—28no—
129#14524001C2314yes—
130C2×C4⋊Dic67—21no—
131C2×C4⋊Dic67—21no—
132C2×C4⋊Dic67C2311yescharacteristic
133C2×C4⋊Dic67C2311yescharacteristic
134C2×Dic67⋊C4—21no—
135C2×Dic67⋊C4—21no—
136C2×Dic67⋊C4—21no—
137C4⋊C4×D67—28no—
138C4⋊C4×D67—22no—
139C4⋊C4×D67C2314yes—
140C2×(C2×D67)⋊C4—21no—
141C2×(C2×D67)⋊C4—21no—
142C2×(C2×D67)⋊C4—21no—
143C2×C4×Dic67—21no—
144C2×C4×Dic67—21no—
145C2×C4×Dic67—21no—
146C2×C4×Dic67—21no—
147C2×C4×Dic67—21no—
148C2×C4×Dic67D411yescharacteristic
149C2×C4×Dic67D411yescharacteristic
150C2×C4×Dic67C2311yescharacteristic
151C42×D67—28no—
152C42×D67—28no—
153C42×D67D414yes—
154C42×D67C2314yes—
155#14523976C2314yes—
156#14523975C2314yes—
157#14523974C2314yes—
158#14523968C2314yes—
159#14523967C2314yes—
160#14523967C2314yes—
161#14523966C2314yes—
162#14523965C2314yes—
163#14523963C2314yes—
164#14523953C2314yes—
165#14523953C2314yes—
166C4×C67⋊C8C2314yes—
167C22×Q8×C67C2311yescharacteristic
168C22×Q8×C67C2311yescharacteristic
169C2×Q16×C67C2×C418yescomplemented
170C2×Q16×C67C2314yes—
171C22×C8×C67C2311yescharacteristic
172C22×C8×C67C2311yescharacteristic
173C4×Q8×C67—22no—
174C4×Q8×C67—22no—
175C4×Q8×C67C2314yes—
176C4×Q8×C67C2314yes—
177C2×C4⋊C4×C67—21no—
178C2×C4⋊C4×C67—21no—
179C2×C4⋊C4×C67C2311yescharacteristic
180C2×C4⋊C4×C67C2311yescharacteristic
181C2×C42×C67—21no—
182C2×C42×C67—21no—
183C2×C42×C67C2311yescharacteristic
184#107×C67C2314yes—
185#103×C67C2314yes—
186#103×C67C2314yes—
187C4×C8×C67C2314yes—
188C23×D67—21no—
189C23×D67C2×D411yescharacteristic
190#11761629—216no—
191#11761629—28no—
192#11761629C22×C4116yes—
193C2×Dic134—21no—
194C2×Dic134—22no—
195C2×Dic134—28no—
196C2×Dic134—24no—
197C2×Dic134C22×C414yes—
198C2×Dic134C2412yes—
199Q8×D67—216no—
200Q8×D67—28no—
201Q8×D67C22×C4116yescomplemented
202C2×D268—28no—
203C2×D268—24no—
204C2×D268—21no—
205C2×D268—22no—
206C2×D268C22×C414yes—
207C2×D268C2412yes—
208C22×Dic67—21no—
209C22×Dic67—21no—
210C22×Dic67—21no—
211C22×Dic67C2×D411yescharacteristic
212C22×Dic67C2×D411yescharacteristic
213C22×Dic67C2×D411yescharacteristic
214C2×C4×D67—28no—
215C2×C4×D67—24no—
216C2×C4×D67—24no—
217C2×C4×D67—28no—
218C2×C4×D67—24no—
219C2×C4×D67—24no—
220C2×C4×D67—24no—
221C2×C4×D67—24no—
222C2×C4×D67—42no—
223C2×C4×D67—44no—
224C2×C4×D67—44no—
225C2×C4×D67—44no—
226C2×C4×D67C22×C414yes—
227C2×C4×D67C2×D414yes—
228C2×C4×D67C2×D414yes—
229C2×C4×D67C2×D412yes—
230C2×C4×D67#4114yes—
231C2×C4×D67C2412yes—
232#11761618C22×C4116yescomplemented
233#11761617C22×C4116yescomplemented
234#11761615C22×C4116yescomplemented
235#11761611—28no—
236#11761611C22×C4116yescomplemented
237C2×C67⋊C8—22no—
238C2×C67⋊C8C22×C414yes—
239C2×C67⋊C8C2412yes—
240C2×C67⋊C8C2412yes—
241C4⋊Dic67—21no—
242C4⋊Dic67—21no—
243C4⋊Dic67—24no—
244C4⋊Dic67—24no—
245C4⋊Dic67C2412yes—
246C4⋊Dic67C2412yes—
247Dic67⋊C4—24no—
248Dic67⋊C4—24no—
249Dic67⋊C4—24no—
250(C2×D67)⋊C4—24no—
251(C2×D67)⋊C4—24no—
252(C2×D67)⋊C4—24no—
253C4×Dic67—24no—
254C4×Dic67—24no—
255C4×Dic67—24no—
256C4×Dic67—24no—
257C4×Dic67—24no—
258C4×Dic67C2×D414yes—
259C4×Dic67C2×D412yes—
260C4×Dic67C2×D414yes—
261C4×Dic67C2412yes—
262C2×Q8×C67—21no—
263C2×Q8×C67—21no—
264C2×Q8×C67—22no—
265C2×Q8×C67—22no—
266C2×Q8×C67C22×C414yes—
267C2×Q8×C67C22×C414yes—
268C2×Q8×C67C2412yes—
269C2×Q8×C67C2412yes—
270C22×C4×C67—21no—
271C22×C4×C67—21no—
272C22×C4×C67—21no—
273C22×C4×C67—21no—
274C22×C4×C67C2×D411yescharacteristic
275C22×C4×C67C2×D411yescharacteristic
276C22×C4×C67C2411yescharacteristic
277Q16×C67C22×C4116yescomplemented
278C2×C8×C67—22no—
279C2×C8×C67C22×C414yes—
280C2×C8×C67C2412yes—
281C2×C8×C67C2412yes—
282C4⋊C4×C67—24no—
283C4⋊C4×C67—24no—
284C4⋊C4×C67—21no—
285C4⋊C4×C67—21no—
286C4⋊C4×C67C2412yes—
287C4⋊C4×C67C2412yes—
288C42×C67—24no—
289C42×C67—24no—
290C42×C67C2×D412yes—
291C42×C67C2412yes—
292C23×C67C22×D411yescharacteristic
293C22×D67—22no—
294C22×D67—22no—
295C22×D67—24no—
296C22×D67—22no—
297C22×D67—42no—
298C22×D67—42no—
299C22×D67C4×D414yes—
300C22×D67C22×D412yes—
301Q8×C67—24no—
302Q8×C67—24no—
303Q8×C67—22no—
304Q8×C67—22no—
305Q8×C67C23×C414yes—
306Q8×C67C23×C414yes—
307C2×C4×C67—24no—
308C2×C4×C67—24no—
309C2×C4×C67—22no—
310C2×C4×C67—22no—
311C2×C4×C67—22no—
312C2×C4×C67—22no—
313C2×C4×C67—22no—
314C2×C4×C67—42no—
315C2×C4×C67—42no—
316C2×C4×C67#13714yescomplemented
317C2×C4×C67C23×C412yes—
318C2×C4×C67C22×D412yes—
319C2×C4×C67C22×D411yescharacteristic
320C2×C4×C67C22×D412yes—
321C2×C4×C67C2×#4112yes—
322C2×C4×C67C2511yescharacteristic
323C2×Dic67—24no—
324C2×Dic67—22no—
325C2×Dic67—22no—
326C2×Dic67—22no—
327C2×Dic67—22no—
328C2×Dic67—22no—
329C2×Dic67—42no—
330C2×Dic67—42no—
331C2×Dic67C4×D414yes—
332C2×Dic67C22×D412yes—
333C2×Dic67C22×D412yes—
334C2×Dic67C22×D412yes—
335D268—216no—
336D268—24no—
337D268—22no—
338D268C23×C414yes—
339C4×D67—216no—
340C4×D67—28no—
341C4×D67—216no—
342C4×D67—44no—
343C4×D67—48no—
344C4×D67—48no—
345C4×D67—48no—
346C4×D67C4×D418yes—
347C4×D67C23×C414yes—
348C4×D67C2×#4114yes—
349Dic134—24no—
350Dic134—22no—
351Dic134—216no—
352Dic134C23×C414yes—
353C8×C67—22no—
354C8×C67C23×C414yes—
355C67⋊C8—22no—
356C67⋊C8C23×C414yes—
357C22×C67C2×C4×D412yes—
358C22×C67C2×#13712yes—
359C22×C67#57512yes—
360C22×C67C23×D411yescharacteristic
361C2×D67—28no—
362C2×D67—22no—
363C2×D67—22no—
364C2×D67—24no—
365C2×D67—48no—
366C2×D67—42no—
367C2×D67—42no—
368C2×D67C2×C4×D414yes—
369C4×C67—24no—
370C4×C67—24no—
371C4×C67—22no—
372C4×C67—42no—
373C4×C67—42no—
374C4×C67C2×C4×D412yes—
375C4×C67C2×#13714yescomplemented
376C4×C67C24×C411yescharacteristic
377C4×C67C22×#4111yescharacteristic
378Dic67—24no—
379Dic67—22no—
380Dic67—22no—
381Dic67—42no—
382Dic67—42no—
383Dic67C2×C4×D414yes—
384C2×C4×#137—671nomaximal, Sylow
385C2×C67C4×#13714yescomplemented
386C2×C67C22×C4×D411yescharacteristic
387C2×C67C22×#13711yescharacteristic
388C2×C67C2×#57511yescharacteristic
389D67—24no—
390D67—44no—
391C22×#137—671no—
392C2×C4×#41—671no—
393C22×C4×Q8—671no—
394C4×#137—6716no—
395C2×#441—671no—
396C2×#441—671no—
397C2×#440—671no—
398C2×#440—671no—
399C2×C4×Q16—671no—
400C2×C4×Q16D6711yescharacteristic, complemented
401C2×C4×SD16—671no—
402C2×C4×SD16—671no—
403C2×#428—671no—
404C2×#417—671no—
405C2×#419—671no—
406C2×C4×M16—671no—
407C67C2×C4×#13711yescharacteristic, complemented, Sylow
408C22×#41—671no—
409C23×Q8—671no—
410C2×#137—6716no—
411C2×#137—678no—
412C22×Q16—671no—
413C22×Q16C2×D6711yescharacteristic
414C22×SD16—671no—
415C22×SD16—671no—
416C22×M16—671no—
417C22×M16—671no—
418C4×#41—678no—
419C4×#41—1344no—
420C2×C4×Q8—671no—
421C2×C4×Q8—671no—
422C2×C4×Q8—678no—
423C2×C4×Q8—671no—
424C2×C4×Q8—671no—
425C2×C4×Q8—1341no—
426C2×C4×Q8—1341no—
427C2×C4×Q8—1344no—
428C2×C4×Q8C2×D6711yescharacteristic
429C2×C4×Q8C2×D6711yescharacteristic
430C2×C4×D4—671no—
431C2×C4×D4—671no—
432C2×C4×D4—1341no—
433C2×C4×D4—1341no—
434C2×#117—671no—
435C2×#117—1341no—
436C22×C4⋊C4—671no—
437C22×C4⋊C4—1341no—
438C22×C42—671no—
439C22×C42—1341no—
440C22×C42—1341no—
441#441—678no—
442#441—678no—
443#440—678no—
444#440—678no—
445C4×Q16—678no—
446C4×Q16C2×D6718yescomplemented
447C4×SD16—678no—
448C4×SD16—678no—
449#428—678no—
450C2×#107—671no—
451C2×#107C2×D6711yescharacteristic
452C2×#106—671no—
453C2×#106—671no—
454#419—678no—
455#417—678no—
456C2×#103—671no—
457C2×#103—671no—
458C2×#103—671no—
459C2×#103—671no—
460C2×#103C2×D6711yescharacteristic
461C2×#103C2×D6711yescharacteristic
462C2×#102—671no—
463C2×#102—671no—
464C4×M16—678no—
465C2×#97—671no—
466C2×#97—671no—
467C2×C4×C8—671no—
468C2×C4×C8C2×D6711yescharacteristic
469C2×#41—678no—
470C2×#41—674no—
471C2×#41—1342no—
472C2×#41—1344no—
473C22×Q8—678no—
474C22×Q8—674no—
475C22×Q8—671no—
476C22×Q8—1341no—
477C22×Q8—1342no—
478C22×Q8—1344no—
479C22×Q8C22×D6711yescharacteristic
480C22×Q8C22×D6711yescharacteristic
481C22×D4—671no—
482C22×D4—1341no—
483C23×C4—671no—
484C23×C4—671no—
485C23×C4—671no—
486C23×C4—1341no—
487C23×C4—1341no—
488C23×C4—1341no—
489C23×C4—1341no—
490C23×C4—1341no—
491#137—6764no—
492C2×Q16—678no—
493C2×Q16—674no—
494C2×Q16C4×D6718yescomplemented
495C2×Q16C22×D6714yes—
496C2×SD16—678no—
497C2×SD16—674no—
498C2×SD16—678no—
499C2×SD16—674no—
500C2×M16—678no—
501C2×M16—674no—
502C2×M16—674no—
503C2×M16—1344no—
504C22×C8—671no—
505C22×C8—671no—
506C22×C8C22×D6711yescharacteristic
507C22×C8C22×D6711yescharacteristic
508C4×Q8—22no—
509C4×Q8—22no—
510C4×Q8—674no—
511C4×Q8—674no—
512C4×Q8—674no—
513C4×Q8—674no—
514C4×Q8—1348no—
515C4×Q8—1348no—
516C4×Q8—1342no—
517C4×Q8—1342no—
518C4×Q8—1342no—
519C4×Q8—1342no—
520C4×Q8C22×D6714yes—
521C4×Q8C22×D6714yes—
522C4×D4—674no—
523C4×D4—674no—
524C4×D4—1348no—
525C4×D4—1342no—
526C4×D4—1348no—
527C4×D4—1342no—
528#117—674no—
529#117—1348no—
530#117—1342no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—671no—
534C2×C4⋊C4—671no—
535C2×C4⋊C4—674no—
536C2×C4⋊C4—1342no—
537C2×C4⋊C4—1348no—
538C2×C4⋊C4—1341no—
539C2×C4⋊C4—1341no—
540C2×C4⋊C4—1341no—
541C2×C4⋊C4—1341no—
542C2×C4⋊C4—1341no—
543C2×C4⋊C4C22×D6711yescharacteristic
544C2×C4⋊C4C22×D6711yescharacteristic
545C2×C22⋊C4—1341no—
546C2×C22⋊C4—1341no—
547C2×C22⋊C4—1341no—
548C2×C42—21no—
549C2×C42—21no—
550C2×C42—671no—
551C2×C42—671no—
552C2×C42—671no—
553C2×C42—674no—
554C2×C42—674no—
555C2×C42—1348no—
556C2×C42—1348no—
557C2×C42—1341no—
558C2×C42—1341no—
559C2×C42—1341no—
560C2×C42—1341no—
561C2×C42—1341no—
562C2×C42C22×D6711yescharacteristic
563#107—674no—
564#107C22×D6714yes—
565#106—674no—
566#106—674no—
567#103—674no—
568#103—674no—
569#103—674no—
570#103—674no—
571#103C22×D6714yes—
572#103C22×D6714yes—
573#102—674no—
574#102—674no—
575#97—674no—
576#97—674no—
577C4×C8—674no—
578C4×C8C22×D6714yes—
579C24—671no—
580C24—1341no—
581#41—6716no—
582#41—13416no—
583#41—1348no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—6716no—
589C2×Q8—674no—
590C2×Q8—672no—
591C2×Q8—1344no—
592C2×Q8—1348no—
593C2×Q8—13416no—
594C2×Q8—1348no—
595C2×Q8—1341no—
596C2×Q8—1342no—
597C2×Q8C2×C4×D6714yes—
598C2×Q8C2×C4×D6714yes—
599C2×Q8C23×D6712yes—
600C2×Q8C23×D6712yes—
601C2×D4—674no—
602C2×D4—672no—
603C2×D4—1344no—
604C2×D4—1348no—
605C2×D4—1341no—
606C2×D4—1342no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—2682no—
612C22×C4—2684no—
613C22×C4—2684no—
614C22×C4—2684no—
615C22×C4—674no—
616C22×C4—671no—
617C22×C4—674no—
618C22×C4—672no—
619C22×C4—674no—
620C22×C4—672no—
621C22×C4—671no—
622C22×C4—671no—
623C22×C4—674no—
624C22×C4—1344no—
625C22×C4—1344no—
626C22×C4—1344no—
627C22×C4—1348no—
628C22×C4—1344no—
629C22×C4—1348no—
630C22×C4—1341no—
631C22×C4—1341no—
632C22×C4—1344no—
633C22×C4—1341no—
634C22×C4—1344no—
635C22×C4D4×D6711yescharacteristic
636C22×C4D4×D6711yescharacteristic
637C22×C4C23×D6711yescharacteristic
638Q16—6716no—
639Q16C2×C4×D67116yescomplemented
640SD16—6716no—
641SD16—6716no—
642M16—6716no—
643M16—1348no—
644C2×C8—22no—
645C2×C8—674no—
646C2×C8—672no—
647C2×C8—672no—
648C2×C8—1342no—
649C2×C8C2×C4×D6714yes—
650C2×C8C23×D6712yes—
651C2×C8C23×D6712yes—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—672no—
657C4⋊C4—672no—
658C4⋊C4—1344no—
659C4⋊C4—1344no—
660C4⋊C4—1344no—
661C4⋊C4—1344no—
662C4⋊C4—1341no—
663C4⋊C4—1341no—
664C4⋊C4—1344no—
665C4⋊C4C23×D6712yes—
666C4⋊C4C23×D6712yes—
667C22⋊C4—1344no—
668C22⋊C4—1344no—
669C22⋊C4—1344no—
670C42—24no—
671C42—24no—
672C42—674no—
673C42—674no—
674C42—672no—
675C42—672no—
676C42—1344no—
677C42—1344no—
678C42—1344no—
679C42—1344no—
680C42—1344no—
681C42D4×D6712yes—
682C42C23×D6712yes—
683C23—2682no—
684C23—2682no—
685C23—674no—
686C23—672no—
687C23—1344no—
688C23—1342no—
689C23—1342no—
690C23—1342no—
691C23C2×D4×D6711yescharacteristic
692Q8—24no—
693Q8—24no—
694Q8—22no—
695Q8—22no—
696Q8—674no—
697Q8—13416no—
698Q8—1344no—
699Q8—1342no—
700Q8C22×C4×D6714yes—
701Q8C22×C4×D6714yes—
702D4—674no—
703D4—13416no—
704D4—1344no—
705D4—1342no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—2684no—
716C2×C4—2688no—
717C2×C4—2688no—
718C2×C4—2682no—
719C2×C4—2682no—
720C2×C4—2688no—
721C2×C4—674no—
722C2×C4—672no—
723C2×C4—678no—
724C2×C4—674no—
725C2×C4—674no—
726C2×C4—672no—
727C2×C4—672no—
728C2×C4—13416no—
729C2×C4—13416no—
730C2×C4—1342no—
731C2×C4—1342no—
732C2×C4—1344no—
733C2×C4—1342no—
734C2×C4—1342no—
735C2×C4—1342no—
736C2×C4—1348no—
737C2×C4#1452407514yesdirect product factor
738C2×C4C22×C4×D6712yes—
739C2×C4C2×D4×D6712yes—
740C2×C4C2×D4×D6711yescharacteristic
741C2×C4C2×D4×D6712yes—
742C2×C4#41×D6712yes—
743C2×C4C24×D6711yescharacteristic
744C8—22no—
745C8—674no—
746C8—1342no—
747C8C22×C4×D6714yes—
748C22—2688no—
749C22—2682no—
750C22—2682no—
751C22—674no—
752C22—1344no—
753C22—1348no—
754C22—1342no—
755C22—1342no—
756C22C4×D4×D6712yes—
757C22C2×#1452407512yes—
758C22#1686419312yes—
759C22C22×D4×D6711yescharacteristic
760C4—24no—
761C4—24no—
762C4—22no—
763C4—42no—
764C4—42no—
765C4—2682no—
766C4—2682no—
767C4—674no—
768C4—1344no—
769C4—1342no—
770C4—1342no—
771C4C4×D4×D6712yes—
772C4C2×#1452407514yesdirect product factor
773C4C23×C4×D6711yescharacteristic
774C4C2×#41×D6711yescharacteristic
775C2—2684no—
776C2—1344no—
777C2C4×#1452407514yesdirect product factor
778C2C2×C4×D4×D6711yescharacteristic
779C2C22×#1452407511yescharacteristic
780C2C2×#1686419311yescharacteristic
subgroupG/H
centerC22×C4D4×D67
commutatorC4×C67C24×C4
FrattiniC2×C4C24×D67
FittingC2×C4×Q16×C67C2
socleC23×C67C22×D4
prime radicalC22×#11761629C22
cosocleC2×C4×C67C25
hypercenterC2×C4×Q16D67
hypocenterC67C2×C4×#137
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. C2×C4×Q8×D67C2semidirect
4. C4×#14524075C2direct (N × H)
5. C2×#16863503C2semidirect
6. C2×#16863500C2semidirect
7. C2×#16863499C2semidirect
8. C2×#16863495C2semidirect
9. C2×C4×#11761618C2semidirect
10. C2×C4×#11761617C2semidirect
11. C2×C4×#11761615C2semidirect
12. C2×#16863437C2semidirect
14. C2×#16863403C2semidirect
15. C2×C4×#11761611C2semidirect
16. C2×C4×Q16×C67C2semidirect
19. C2×#14524075C4direct (N × H)
35. C4×Q8×D67C22semidirect
47. #16863503C22semidirect
48. #16863500C22semidirect
49. #16863499C22semidirect
50. #16863495C22semidirect
51. C4×#11761618C22semidirect
52. C4×#11761617C22semidirect
53. C4×#11761615C22semidirect
54. #16863437C22semidirect
58. #16863403C22semidirect
66. C4×#11761611C22semidirect
73. C4×Q16×C67C22semidirect
86. C2×Q8×D67C2×C4semidirect
98. #14524075C2×C4direct (N × H)
99. C2×#11761618C2×C4semidirect
101. C2×#11761617C2×C4semidirect
103. C2×#11761615C2×C4semidirect
106. C2×#11761611C2×C4semidirect
169. C2×Q16×C67C2×C4semidirect
201. Q8×D67C22×C4semidirect
232. #11761618C22×C4semidirect
233. #11761617C22×C4semidirect
234. #11761615C22×C4semidirect
236. #11761611C22×C4semidirect
277. Q16×C67C22×C4semidirect
316. C2×C4×C67#137semidirect
375. C4×C67C2×#137semidirect
385. C2×C67C4×#137semidirect
400. C2×C4×Q16D67semidirect
407. C67C2×C4×#137semidirect
446. C4×Q16C2×D67semidirect
494. C2×Q16C4×D67semidirect
639. Q16C2×C4×D67semidirect
737. C2×C4#14524075direct (N × H)
772. C4C2×#14524075direct (N × H)
777. C2C4×#14524075direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240752
C2×C4×#117616292
C2×C4×Q8×D672
C4×#145240752
C2×#168635032
C2×#168635002
C2×#168634992
C2×#168634952
C2×C4×#117616182
C2×C4×#117616172
C2×C4×#117616152
C2×#168634372
C2×#168633962
C2×#168634032
C2×C4×#117616112
C2×C4×Q16×C672
C2×C4×#13767