Finite Group Databasebeta

← C2×#22569063 #31719962

Subgroups — C2×#22569063 #31719962

Order 17152.

2870 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×SD16×D67C211yesmaximal, characteristic
2C2×#16863872C211yesmaximal, characteristic, complemented
3C2×#16863868C211yesmaximal, characteristic
4#22569063C2116yesmaximal, direct product factor
5C2×#16863499C211yesmaximal, characteristic, complemented
6C2×#16863496C211yesmaximal, characteristic, complemented
7C2×#16863494C211yesmaximal, characteristic, complemented
8C2×#16863493C211yesmaximal, characteristic, complemented
9C2×C4×#11761617C211yesmaximal, characteristic, complemented
10C2×SD16×Dic67C211yesmaximal, characteristic, complemented
11C2×#16863483C211yesmaximal, characteristic, complemented
12C2×#16863431C211yesmaximal, characteristic, complemented
13C2×#16863403C211yesmaximal, characteristic, complemented
14C2×#16863399C211yesmaximal, characteristic
15C2×#16863350C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C67C211yesmaximal, characteristic, complemented
17C22×Q8×D67C2211yescharacteristic
18C22×D4×D67C2211yescharacteristic
19C22×#11761617C2211yescharacteristic
20C22×#11761616C2211yescharacteristic
21C22×#11761615C2211yescharacteristic
22C2×SD16×D67C4116yescomplemented
23C2×SD16×D67C2218yes—
24C22×#11761611C2211yescharacteristic
25C22×C8×D67C2211yescharacteristic
26#16863872—24no—
27#16863872C2218yescomplemented
28#16863868—24no—
29#16863868C2218yes—
30C2×Q8×Dic67C2211yescharacteristic, complemented
31C2×C4×Dic134—21no—
32C2×C4×Dic134C2211yescharacteristic, complemented
33C2×#14524008—21no—
34C2×#14524008C2211yescharacteristic, complemented
35C2×C4×D268C2211yescharacteristic
36C2×D4×Dic67C2211yescharacteristic
37C2×#14524005C2211yescharacteristic
38C2×C4×C22⋊D67—21no—
39C2×(C22⋊D67)⋊C4—21no—
40C2×#14524001—21no—
41C2×#14524001C2211yescharacteristic
42C2×#14524001C2211yescharacteristic
43C2×#14524000—21no—
44C2×#14524000C2211yescharacteristic
45C22×(C2×D67)⋊C4—21no—
46C2×C22⋊C4×D67—21no—
47#16863499C2218yescomplemented
48#16863496C2218yescomplemented
49#16863494C2218yescomplemented
50#16863493C2218yescomplemented
51C4×#11761617C2218yescomplemented
52SD16×Dic67C2218yescomplemented
53#16863483C2218yescomplemented
54#16863431C2218yescomplemented
55C2×#14523976C2211yescharacteristic, complemented
56C2×#14523976C2211yescharacteristic, complemented
57C2×#14523975C2211yescharacteristic, complemented
58#16863403C2218yescomplemented
59#16863399C2218yes—
60C2×#14523968C2211yescharacteristic, complemented
61C2×#14523967C2211yescharacteristic, complemented
62C2×#14523966C2211yescharacteristic, complemented
63C2×#14523965C2211yescharacteristic
64C2×#14523964C2211yescharacteristic
65C2×#14523963C2211yescharacteristic
66#16863350C2218yescomplemented
67C2×#14523954C2211yescharacteristic, complemented
68C2×#14523953C2211yescharacteristic, complemented
69C2×C8×Dic67C2211yescharacteristic, complemented
70C22×SD16×C67C2211yescharacteristic
71C2×C4×Q8×C67C2211yescharacteristic, complemented
72C2×C4×D4×C67C2211yescharacteristic
73C4×SD16×C67C2218yescomplemented
74C2×#106×C67C2211yescharacteristic, complemented
75C2×#103×C67C2211yescharacteristic, complemented
76C2×#102×C67C2211yescharacteristic
77C2×C4×C8×C67C2211yescharacteristic, complemented
78C24×D67—21no—
79C22×Dic134—21no—
80C22×Dic134C2311yescharacteristic
81C2×Q8×D67—22no—
82C2×Q8×D67—24no—
83C2×Q8×D67C2×C418yescomplemented
84C2×Q8×D67C2314yes—
85C22×D268C2311yescharacteristic
86C22×C22⋊D67—21no—
87C2×D4×D67—22no—
88C2×D4×D67—24no—
89C2×D4×D67C2×C418yes—
90C2×D4×D67C2314yes—
91C23×Dic67—21no—
92C22×C4×D67—21no—
93C22×C4×D67—21no—
94C22×C4×D67—21no—
95C22×C4×D67C2311yescharacteristic
96C2×#11761617C2×C418yescomplemented
97C2×#11761617C2314yes—
98C2×#11761616C2×C418yescomplemented
99C2×#11761616C2314yes—
100C2×#11761615C2×C418yescomplemented
101C2×#11761615C2314yes—
102SD16×D67C2×C4164yescomplemented
103C2×#11761611—24no—
104C2×#11761611C2314yes—
105C22×C67⋊C8C2311yescharacteristic
106C22×C67⋊C8C2311yescharacteristic
107C2×C8×D67C2×C418yescomplemented
108C2×C8×D67C2314yes—
109Q8×Dic67—22no—
110Q8×Dic67C2314yescomplemented
111C4×Dic134—28no—
112C4×Dic134—22no—
113C4×Dic134C2314yescomplemented
114#14524008—28no—
115#14524008—22no—
116#14524008C2314yescomplemented
117C4×D268—22no—
118C4×D268C2314yes—
119D4×Dic67—22no—
120D4×Dic67C2314yes—
121#14524005—22no—
122#14524005C2314yes—
123C4×C22⋊D67—28no—
124(C22⋊D67)⋊C4—28no—
125#14524001—22no—
126#14524001—22no—
127#14524001—28no—
128#14524001C2314yes—
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⋊C4—21no—
138C2×Dic67⋊C4D411yescharacteristic
139C2×Dic67⋊C4D411yescharacteristic
140C2×C22⋊Dic67—21no—
141C2×(C2×D67)⋊C4—21no—
142C2×(C2×D67)⋊C4—21no—
143C2×(C2×D67)⋊C4—21no—
144C2×(C2×D67)⋊C4—28no—
145C2×(C2×D67)⋊C4—21no—
146C2×(C2×D67)⋊C4D411yescharacteristic
147C2×(C2×D67)⋊C4D411yescharacteristic
148C22⋊C4×D67—28no—
149C2×C4×Dic67—21no—
150C2×C4×Dic67—21no—
151C2×C4×Dic67—21no—
152C2×C4×Dic67—21no—
153C2×C4×Dic67—21no—
154C2×C4×Dic67C2311yescharacteristic
155#14523976C2314yescomplemented
156#14523976C2314yescomplemented
157#14523975C2314yescomplemented
158#14523968C2314yescomplemented
159#14523967C2314yescomplemented
160#14523966C2314yescomplemented
161#14523965C2314yes—
162#14523964C2314yes—
163#14523963C2314yes—
164#14523954C2314yescomplemented
165#14523953C2314yescomplemented
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#106×C67C2314yescomplemented
185#103×C67C2314yescomplemented
186#102×C67C2314yes—
187C4×C8×C67C2314yescomplemented
188C23×D67—21no—
189C23×D67—28no—
190C23×D67—24no—
191C23×D67—82no—
192C23×D67—82no—
193C23×D67C2×D411yescharacteristic
194C2×Dic134—21no—
195C2×Dic134—22no—
196C2×Dic134—28no—
197C2×Dic134—24no—
198C2×Dic134C22×C414yes—
199C2×Dic134C2412yes—
200Q8×D67—216no—
201Q8×D67—28no—
202Q8×D67C22×C4116yescomplemented
203C2×D268—21no—
204C2×D268—22no—
205C2×D268C22×C414yes—
206C2×D268C2412yes—
207C2×C22⋊D67—28no—
208C2×C22⋊D67—24no—
209D4×D67—216no—
210D4×D67—28no—
211D4×D67C22×C4116yes—
212C22×Dic67—21no—
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—82no—
225C2×C4×D67—82no—
226C2×C4×D67C22×C414yes—
227C2×C4×D67C2×D412yes—
228C2×C4×D67#4114yes—
229C2×C4×D67C2412yes—
230#11761617C22×C4116yescomplemented
231#11761616C22×C4116yescomplemented
232#11761615C22×C4116yescomplemented
233#11761611—28no—
234C2×C67⋊C8—22no—
235C2×C67⋊C8C22×C414yes—
236C2×C67⋊C8C2412yes—
237C2×C67⋊C8C2412yes—
238C8×D67C22×C4116yescomplemented
239C4⋊Dic67—21no—
240C4⋊Dic67—21no—
241C4⋊Dic67—24no—
242C4⋊Dic67C2412yes—
243C4⋊Dic67C2412yes—
244Dic67⋊C4—24no—
245Dic67⋊C4—24no—
246Dic67⋊C4C2×D414yes—
247Dic67⋊C4C2×D414yes—
248C22⋊Dic67—24no—
249(C2×D67)⋊C4—24no—
250(C2×D67)⋊C4—24no—
251(C2×D67)⋊C4—24no—
252(C2×D67)⋊C4—24no—
253(C2×D67)⋊C4C2×D414yes—
254(C2×D67)⋊C4C2×D414yes—
255C4×Dic67—24no—
256C4×Dic67—24no—
257C4×Dic67—24no—
258C4×Dic67—24no—
259C4×Dic67—24no—
260C4×Dic67C2×D412yes—
261C4×Dic67C2412yes—
262C24×C67—21no—
263C2×Q8×C67—21no—
264C2×Q8×C67—22no—
265C2×Q8×C67C22×C414yes—
266C2×Q8×C67C2412yes—
267C2×D4×C67—21no—
268C2×D4×C67—22no—
269C2×D4×C67C22×C414yes—
270C2×D4×C67C2412yes—
271C22×C4×C67—21no—
272C22×C4×C67—21no—
273C22×C4×C67—21no—
274C22×C4×C67—24no—
275C22×C4×C67—82no—
276C22×C4×C67C2×D411yescharacteristic
277C22×C4×C67C2×D411yescharacteristic
278C22×C4×C67C2411yescharacteristic
279SD16×C67C22×C4116yescomplemented
280C2×C8×C67—22no—
281C2×C8×C67C22×C414yes—
282C2×C8×C67C2412yes—
283C2×C8×C67C2412yes—
284C4⋊C4×C67—24no—
285C4⋊C4×C67—21no—
286C4⋊C4×C67—21no—
287C4⋊C4×C67C2412yes—
288C4⋊C4×C67C2412yes—
289C22⋊C4×C67—24no—
290C42×C67—24no—
291C42×C67C2×D412yes—
292C42×C67C2412yes—
293C23×C67—24no—
294C23×C67—22no—
295C23×C67—42no—
296C23×C67—42no—
297C23×C67C22×D411yescharacteristic
298C22×D67—22no—
299C22×D67—22no—
300C22×D67—24no—
301C22×D67—22no—
302C22×D67—216no—
303C22×D67—42no—
304C22×D67—42no—
305C22×D67—816no—
306C22×D67—84no—
307C22×D67—84no—
308C22×D67C4×D414yes—
309C22×D67C22×D412yes—
310Q8×C67—24no—
311Q8×C67—22no—
312Q8×C67C23×C414yes—
313D4×C67—24no—
314D4×C67—22no—
315D4×C67C23×C414yes—
316C2×C4×C67—24no—
317C2×C4×C67—22no—
318C2×C4×C67—22no—
319C2×C4×C67—22no—
320C2×C4×C67—22no—
321C2×C4×C67—22no—
322C2×C4×C67—42no—
323C2×C4×C67—42no—
324C2×C4×C67—84no—
325C2×C4×C67C23×C412yes—
326C2×C4×C67C22×D412yes—
327C2×C4×C67C22×D412yes—
328C2×C4×C67C22×D411yescharacteristic
329C2×C4×C67C2×#4112yes—
330C2×C4×C67C2511yescharacteristic
331C22⋊D67—216no—
332C2×Dic67—24no—
333C2×Dic67—22no—
334C2×Dic67—22no—
335C2×Dic67—22no—
336C2×Dic67—22no—
337C2×Dic67—22no—
338C2×Dic67—42no—
339C2×Dic67—42no—
340C2×Dic67—84no—
341C2×Dic67C4×D414yes—
342C2×Dic67C22×D412yes—
343C2×Dic67C22×D412yes—
344C2×Dic67C22×D412yes—
345D268—24no—
346D268—22no—
347D268C23×C414yes—
348C4×D67—216no—
349C4×D67—84no—
350C4×D67—84no—
351C4×D67C4×D418yes—
352C4×D67C23×C414yes—
353C4×D67C2×#4114yes—
354Dic134—24no—
355Dic134—22no—
356Dic134—216no—
357Dic134C23×C414yes—
358C8×C67—22no—
359C8×C67C23×C414yes—
360C67⋊C8—22no—
361C67⋊C8C23×C414yes—
362C22×C67—24no—
363C22×C67—48no—
364C22×C67—42no—
365C22×C67—42no—
366C22×C67C2×C4×D412yes—
367C22×C67#57712yes—
368C22×C67#57712yes—
369C22×C67C23×D411yescharacteristic
370C2×D67—28no—
371C2×D67—22no—
372C2×D67—22no—
373C2×D67—24no—
374C2×D67—48no—
375C2×D67—42no—
376C2×D67—42no—
377C2×D67—816no—
378C2×D67C2×C4×D414yes—
379C4×C67—24no—
380C4×C67—22no—
381C4×C67—22no—
382C4×C67—42no—
383C4×C67—42no—
384C4×C67C2×C4×D412yes—
385C4×C67C24×C411yescharacteristic
386C4×C67C22×#4111yescharacteristic
387Dic67—24no—
388Dic67—22no—
389Dic67—22no—
390Dic67—42no—
391Dic67—42no—
392Dic67C2×C4×D414yes—
393C2×#2949—671nomaximal, Sylow
394C2×C67—44no—
395C2×C67#294914yescomplemented
396C2×C67C22×C4×D411yescharacteristic
397C2×C67C2×#57711yescharacteristic
398C2×C67C2×#57711yescharacteristic
399D67—24no—
400D67—44no—
401C23×SD16—671no—
402C2×#519—671no—
403C2×#518—671no—
404#2949—6716no—
405C2×#440—671no—
406C2×#440—671no—
407C2×#440—671no—
408C2×#440—671no—
409C2×C4×SD16—671no—
410C2×C4×SD16—671no—
411C2×C4×SD16—671no—
412C2×C4×SD16D6711yescharacteristic, complemented
413C2×#427—671no—
414C2×#419—671no—
415C2×#418—671no—
416C2×#405—671no—
417C67C2×#294911yescharacteristic, complemented, Sylow
418C23×Q8—671no—
419C23×D4—671no—
420C22×SD16—671no—
421C22×SD16—671no—
422C22×SD16—6716no—
423C22×SD16—678no—
424C22×SD16—671no—
425C22×SD16C2×D6711yescharacteristic
426C22×M16—671no—
427C23×C8—671no—
428#519—678no—
429#519—1344no—
430#518—678no—
431#518—1344no—
432C2×C4×Q8—671no—
433C2×C4×Q8—671no—
434C2×C4×Q8—671no—
435C2×C4×Q8—1341no—
436C2×C4×Q8—1341no—
437C2×C4×Q8C2×D6711yescharacteristic, complemented
438C2×C4×D4—671no—
439C2×C4×D4—671no—
440C2×C4×D4—671no—
441C2×C4×D4—1341no—
442C2×C4×D4—1341no—
443C2×C4×D4C2×D6711yescharacteristic
444C2×#117—671no—
445C2×#117—671no—
446C2×#117—671no—
447C2×#117—1341no—
448C2×#117—1341no—
449C22×C22⋊C4—1341no—
450C22×C22⋊C4—1341no—
451#440—678no—
452#440—678no—
453#440—678no—
454#440—678no—
455C4×SD16—678no—
456C4×SD16—678no—
457C4×SD16—678no—
458C4×SD16C2×D6718yescomplemented
459#427—678no—
460C2×#107—671no—
461C2×#107—671no—
462C2×#106—671no—
463C2×#106C2×D6711yescharacteristic, complemented
464#419—678no—
465#418—678no—
466C2×#103—671no—
467C2×#103—671no—
468C2×#103—671no—
469C2×#103C2×D6711yescharacteristic, complemented
470C2×#102—671no—
471C2×#102—671no—
472C2×#102—671no—
473C2×#102C2×D6711yescharacteristic
474#405—678no—
475C2×#97—671no—
476C2×#97—671no—
477C2×C4×C8—671no—
478C2×C4×C8C2×D6711yescharacteristic, complemented
479C25—1341no—
480C22×Q8—678no—
481C22×Q8—674no—
482C22×Q8—671no—
483C22×Q8—1341no—
484C22×Q8—1342no—
485C22×Q8—1344no—
486C22×Q8C22×D6711yescharacteristic
487C22×D4—678no—
488C22×D4—674no—
489C22×D4—671no—
490C22×D4—1342no—
491C22×D4—1344no—
492C22×D4—1341no—
493C22×D4C22×D6711yescharacteristic
494C23×C4—21no—
495C23×C4—671no—
496C23×C4—1341no—
497C23×C4—1341no—
498C23×C4—1341no—
499C23×C4—1341no—
500C2×SD16—678no—
501C2×SD16—674no—
502C2×SD16—678no—
503C2×SD16—674no—
504C2×SD16—6764no—
505C2×SD16—678no—
506C2×SD16—674no—
507C2×SD16C4×D6718yescomplemented
508C2×SD16C22×D6714yes—
509C2×M16—674no—
510C2×M16—1344no—
511C22×C8—671no—
512C22×C8—678no—
513C22×C8—674no—
514C22×C8—671no—
515C22×C8C22×D6711yescharacteristic
516C22×C8C22×D6711yescharacteristic
517C4×Q8—22no—
518C4×Q8—674no—
519C4×Q8—674no—
520C4×Q8—674no—
521C4×Q8—1348no—
522C4×Q8—1342no—
523C4×Q8—1342no—
524C4×Q8—1348no—
525C4×Q8—1342no—
526C4×Q8C22×D6714yescomplemented
527C4×D4—22no—
528C4×D4—674no—
529C4×D4—674no—
530C4×D4—674no—
531C4×D4—1342no—
532C4×D4—1342no—
533C4×D4—1348no—
534C4×D4—1348no—
535C4×D4—1342no—
536C4×D4C22×D6714yes—
537#117—674no—
538#117—674no—
539#117—674no—
540#117—674no—
541#117—1348no—
542#117—1348no—
543#117—1342no—
544#117—1342no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—671no—
547C2×C4⋊C4—671no—
548C2×C4⋊C4—671no—
549C2×C4⋊C4—671no—
550C2×C4⋊C4—1341no—
551C2×C4⋊C4—1341no—
552C2×C4⋊C4—1341no—
553C2×C4⋊C4C22×D6711yescharacteristic
554C2×C4⋊C4C22×D6711yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—671no—
557C2×C22⋊C4—671no—
558C2×C22⋊C4—1348no—
559C2×C22⋊C4—1348no—
560C2×C22⋊C4—1341no—
561C2×C22⋊C4—1341no—
562C2×C22⋊C4—1341no—
563C2×C22⋊C4—1341no—
564C2×C22⋊C4—1341no—
565C2×C42—21no—
566C2×C42—671no—
567C2×C42—1341no—
568C2×C42—1341no—
569C2×C42—1341no—
570C2×C42—1341no—
571C2×C42—1341no—
572C2×C42C22×D6711yescharacteristic
573#107—674no—
574#107—674no—
575#106—674no—
576#106C22×D6714yescomplemented
577#103—674no—
578#103—674no—
579#103—674no—
580#103C22×D6714yescomplemented
581#102—674no—
582#102—674no—
583#102—674no—
584#102C22×D6714yes—
585#97—674no—
586#97—674no—
587C4×C8—674no—
588C4×C8C22×D6714yescomplemented
589C24—21no—
590C24—5362no—
591C24—5362no—
592C24—671no—
593C24—1344no—
594C24—1348no—
595C24—1341no—
596C2×Q8—21no—
597C2×Q8—22no—
598C2×Q8—6716no—
599C2×Q8—674no—
600C2×Q8—672no—
601C2×Q8—1344no—
602C2×Q8—1348no—
603C2×Q8—13416no—
604C2×Q8—1348no—
605C2×Q8—1341no—
606C2×Q8—1342no—
607C2×Q8C2×C4×D6714yes—
608C2×Q8C23×D6712yes—
609C2×D4—21no—
610C2×D4—22no—
611C2×D4—6716no—
612C2×D4—674no—
613C2×D4—672no—
614C2×D4—13416no—
615C2×D4—1348no—
616C2×D4—1344no—
617C2×D4—1348no—
618C2×D4—1341no—
619C2×D4—1342no—
620C2×D4C2×C4×D6714yes—
621C2×D4C23×D6712yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—24no—
626C22×C4—82no—
627C22×C4—5362no—
628C22×C4—5362no—
629C22×C4—5362no—
630C22×C4—671no—
631C22×C4—674no—
632C22×C4—672no—
633C22×C4—674no—
634C22×C4—672no—
635C22×C4—671no—
636C22×C4—671no—
637C22×C4—1344no—
638C22×C4—1344no—
639C22×C4—1348no—
640C22×C4—1341no—
641C22×C4—1341no—
642C22×C4—1344no—
643C22×C4—1344no—
644C22×C4—1341no—
645C22×C4D4×D6711yescharacteristic
646C22×C4D4×D6711yescharacteristic
647C22×C4C23×D6711yescharacteristic
648SD16—6716no—
649SD16—6716no—
650SD16—6716no—
651SD16C2×C4×D67116yescomplemented
652M16—1348no—
653C2×C8—22no—
654C2×C8—674no—
655C2×C8—672no—
656C2×C8—6716no—
657C2×C8—672no—
658C2×C8—1342no—
659C2×C8C2×C4×D6714yes—
660C2×C8C23×D6712yes—
661C2×C8C23×D6712yes—
662C4⋊C4—24no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—674no—
666C4⋊C4—674no—
667C4⋊C4—672no—
668C4⋊C4—672no—
669C4⋊C4—1344no—
670C4⋊C4—1344no—
671C4⋊C4—1341no—
672C4⋊C4—1341no—
673C4⋊C4—1344no—
674C4⋊C4C23×D6712yes—
675C4⋊C4C23×D6712yes—
676C22⋊C4—24no—
677C22⋊C4—674no—
678C22⋊C4—674no—
679C22⋊C4—1344no—
680C22⋊C4—1344no—
681C22⋊C4—1344no—
682C22⋊C4—1344no—
683C22⋊C4—1344no—
684C42—24no—
685C42—672no—
686C42—672no—
687C42—1344no—
688C42—1344no—
689C42—1344no—
690C42—1344no—
691C42—1344no—
692C42D4×D6712yes—
693C42C23×D6712yes—
694C23—24no—
695C23—22no—
696C23—42no—
697C23—42no—
698C23—2682no—
699C23—2682no—
700C23—53616no—
701C23—5364no—
702C23—5364no—
703C23—674no—
704C23—672no—
705C23—13416no—
706C23—1344no—
707C23—1342no—
708C23—1342no—
709C23—1342no—
710C23C2×D4×D6711yescharacteristic
711Q8—24no—
712Q8—22no—
713Q8—674no—
714Q8—13416no—
715Q8—1344no—
716Q8—1342no—
717Q8C22×C4×D6714yes—
718D4—24no—
719D4—22no—
720D4—674no—
721D4—13416no—
722D4—1344no—
723D4—1342no—
724D4C22×C4×D6714yes—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—84no—
734C2×C4—2682no—
735C2×C4—2682no—
736C2×C4—5364no—
737C2×C4—5364no—
738C2×C4—5364no—
739C2×C4—674no—
740C2×C4—672no—
741C2×C4—678no—
742C2×C4—674no—
743C2×C4—674no—
744C2×C4—672no—
745C2×C4—672no—
746C2×C4—13416no—
747C2×C4—1342no—
748C2×C4—1342no—
749C2×C4—1344no—
750C2×C4—1342no—
751C2×C4—1342no—
752C2×C4—1342no—
753C2×C4C22×C4×D6712yes—
754C2×C4C2×D4×D6712yes—
755C2×C4C2×D4×D6712yes—
756C2×C4C2×D4×D6711yescharacteristic
757C2×C4#41×D6712yes—
758C2×C4C24×D6711yescharacteristic
759C8—22no—
760C8—674no—
761C8—1342no—
762C8C22×C4×D6714yes—
763C22—24no—
764C22—48no—
765C22—42no—
766C22—42no—
767C22—2688no—
768C22—2682no—
769C22—2682no—
770C22—53616no—
771C22—674no—
772C22—1344no—
773C22—1348no—
774C22—1342no—
775C22—1342no—
776C22C4×D4×D6712yes—
777C22#1686420212yes—
778C22#1686420312yes—
779C22C22×D4×D6711yescharacteristic
780C4—24no—
781C4—22no—
782C4—22no—
783C4—42no—
784C4—42no—
785C4—2682no—
786C4—2682no—
787C4—674no—
788C4—1344no—
789C4—1342no—
790C4—1342no—
791C4C4×D4×D6712yes—
792C4C23×C4×D6711yescharacteristic
793C4C2×#41×D6711yescharacteristic
794C2—44no—
795C2—2684no—
796C2—1344no—
797C2#2256906314yesdirect product factor
798C2C2×C4×D4×D6711yescharacteristic
799C2C2×#1686420211yescharacteristic
800C2C2×#1686420311yescharacteristic
subgroupG/H
centerC23C2×D4×D67
commutatorC4×C67C24×C4
FrattiniC2×C4C24×D67
FittingC2×C4×SD16×C67C2
socleC23×C67C22×D4
prime radicalC22×D4×D67C22
cosocleC2×C4×C67C25
hypercenterC2×C4×SD16D67
hypocenterC67C2×#2949
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#16863872C2semidirect
4. #22569063C2direct (N × H)
5. C2×#16863499C2semidirect
6. C2×#16863496C2semidirect
7. C2×#16863494C2semidirect
8. C2×#16863493C2semidirect
9. C2×C4×#11761617C2semidirect
10. C2×SD16×Dic67C2semidirect
11. C2×#16863483C2semidirect
12. C2×#16863431C2semidirect
13. C2×#16863403C2semidirect
15. C2×#16863350C2semidirect
16. C2×C4×SD16×C67C2semidirect
22. C2×SD16×D67C4semidirect
27. #16863872C22semidirect
30. C2×Q8×Dic67C22semidirect
32. C2×C4×Dic134C22semidirect
34. C2×#14524008C22semidirect
47. #16863499C22semidirect
48. #16863496C22semidirect
49. #16863494C22semidirect
50. #16863493C22semidirect
51. C4×#11761617C22semidirect
52. SD16×Dic67C22semidirect
53. #16863483C22semidirect
54. #16863431C22semidirect
55. C2×#14523976C22semidirect
56. C2×#14523976C22semidirect
57. C2×#14523975C22semidirect
58. #16863403C22semidirect
60. C2×#14523968C22semidirect
61. C2×#14523967C22semidirect
62. C2×#14523966C22semidirect
66. #16863350C22semidirect
67. C2×#14523954C22semidirect
68. C2×#14523953C22semidirect
69. C2×C8×Dic67C22semidirect
71. C2×C4×Q8×C67C22semidirect
73. C4×SD16×C67C22semidirect
74. C2×#106×C67C22semidirect
75. C2×#103×C67C22semidirect
77. C2×C4×C8×C67C22semidirect
83. C2×Q8×D67C2×C4semidirect
96. C2×#11761617C2×C4semidirect
98. C2×#11761616C2×C4semidirect
100. C2×#11761615C2×C4semidirect
102. SD16×D67C2×C4semidirect
107. C2×C8×D67C2×C4semidirect
110. Q8×Dic67C23semidirect
113. C4×Dic134C23semidirect
116. #14524008C23semidirect
155. #14523976C23semidirect
156. #14523976C23semidirect
157. #14523975C23semidirect
158. #14523968C23semidirect
159. #14523967C23semidirect
160. #14523966C23semidirect
164. #14523954C23semidirect
165. #14523953C23semidirect
166. C8×Dic67C23semidirect
170. C2×SD16×C67C2×C4semidirect
175. C4×Q8×C67C23semidirect
184. #106×C67C23semidirect
185. #103×C67C23semidirect
187. C4×C8×C67C23semidirect
202. Q8×D67C22×C4semidirect
230. #11761617C22×C4semidirect
231. #11761616C22×C4semidirect
232. #11761615C22×C4semidirect
238. C8×D67C22×C4semidirect
279. SD16×C67C22×C4semidirect
395. C2×C67#2949semidirect
412. C2×C4×SD16D67semidirect
417. C67C2×#2949semidirect
437. C2×C4×Q8C2×D67semidirect
458. C4×SD16C2×D67semidirect
463. C2×#106C2×D67semidirect
469. C2×#103C2×D67semidirect
478. C2×C4×C8C2×D67semidirect
507. C2×SD16C4×D67semidirect
526. C4×Q8C22×D67semidirect
576. #106C22×D67semidirect
580. #103C22×D67semidirect
588. C4×C8C22×D67semidirect
651. SD16C2×C4×D67semidirect
797. C2#22569063direct (N × H)

Maximal subgroups

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

subgroupindex
C22×SD16×D672
C2×#168638722
C2×#168638682
#225690632
C2×#168634992
C2×#168634962
C2×#168634942
C2×#168634932
C2×C4×#117616172
C2×SD16×Dic672
C2×#168634832
C2×#168634312
C2×#168634032
C2×#168633992
C2×#168633502
C2×C4×SD16×C672
C2×#294967