Finite Group Databasebeta

← C2×#22570457 #31724131

Subgroups — C2×#22570457 #31724131

Order 17152.

2210 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864006C211yesmaximal, characteristic, complemented
2C2×#16863870C211yesmaximal, characteristic
3#22570457C2116yesmaximal, direct product factor
4C2×#16863737C211yesmaximal, characteristic, complemented
5C2×#16863699C211yesmaximal, characteristic, complemented
6C2×#16863695C211yesmaximal, characteristic, complemented
7C2×#16863600C211yesmaximal, characteristic, complemented
8C2×#16863600C211yesmaximal, characteristic, complemented
9C2×#16863549C211yesmaximal, characteristic
10C2×#16863546C211yesmaximal, characteristic
11C2×#16863499C211yesmaximal, characteristic, complemented
12C2×#16863495C211yesmaximal, characteristic, complemented
13C2×#16863483C211yesmaximal, characteristic, complemented
14C2×#16863481C211yesmaximal, characteristic, complemented
15C2×#16863454C211yesmaximal, characteristic, complemented
16C2×#485×C67C211yesmaximal, characteristic, complemented
17C23×D268C2211yescharacteristic
18C22×#11761617C2211yescharacteristic
19C22×#11761617C2211yescharacteristic
20C22×#11761615C2211yescharacteristic
21C22×#11761615C2211yescharacteristic
22#16864006—24no—
23#16864006C2218yescomplemented
24C2×#14524041C2211yescharacteristic, complemented
25C2×#14524036—21no—
26C2×#14524036—21no—
27C2×#14524034—21no—
28C2×#14524034C2211yescharacteristic, complemented
29C2×#14524033—21no—
30C2×#14524022C2211yescharacteristic
31#16863870—24no—
32#16863870C2218yes—
33C2×Q8×Dic67C2211yescharacteristic, complemented
34C2×#14524008C2211yescharacteristic, complemented
35C2×C4×D268—21no—
36C2×C4×D268—21no—
37C2×#14524005C2211yescharacteristic
38C2×#14524005C2211yescharacteristic
39C2×#14524005C2211yescharacteristic
40C2×#14524005C2211yescharacteristic
41C2×#14524002C2211yescharacteristic
42C2×C22⋊C4×D67—21no—
43C2×C22⋊C4×D67—21no—
44#16863737C2218yescomplemented
45#16863699C2218yescomplemented
46#16863695C2218yescomplemented
47#16863600C2218yescomplemented
48#16863600C2218yescomplemented
49#16863549C2218yes—
50#16863546C2218yes—
51#16863499C2218yescomplemented
52#16863495C2218yescomplemented
53#16863483C2218yescomplemented
54#16863481C2218yescomplemented
55#16863454C2218yescomplemented
56C2×#14523976C2211yescharacteristic, complemented
57C2×#14523974C2211yescharacteristic, complemented
58C2×Dic67⋊C8C2211yescharacteristic, complemented
59C2×Dic67⋊C8C2211yescharacteristic, complemented
60C2×#14523966C2211yescharacteristic, complemented
61C2×#14523966C2211yescharacteristic, complemented
62C2×#14523965C2211yescharacteristic
63C2×#14523965C2211yescharacteristic
64C2×#14523963C2211yescharacteristic
65C2×#14523963C2211yescharacteristic
66C2×C22⋊(C67⋊C8)C2211yescharacteristic
67C2×#14523953C2211yescharacteristic, complemented
68C2×C8×Dic67C2211yescharacteristic, complemented
69C2×C22⋊Q8×C67C2211yescharacteristic
70C2×#117×C67C2211yescharacteristic
71#485×C67C2218yescomplemented
72C2×#107×C67C2211yescharacteristic, complemented
73C2×#106×C67C2211yescharacteristic, complemented
74C2×#103×C67C2211yescharacteristic, complemented
75C2×#103×C67C2211yescharacteristic, complemented
76C2×C22⋊C8×C67C2211yescharacteristic
77C24×D67—21no—
78C22×Dic134C2311yescharacteristic
79C22×D268—24no—
80C22×D268—24no—
81C22×D268—21no—
82C22×D268—22no—
83C22×D268C2314yes—
84C22×D268C2311yescharacteristic
85C22×D268C2311yescharacteristic
86C22×C4×D67—21no—
87C22×C4×D67—21no—
88C22×C4×D67—21no—
89C22×C4×D67—21no—
90C2×#11761617—24no—
91C2×#11761617—24no—
92C2×#11761617C2314yes—
93C2×#11761617C2314yes—
94C2×#11761615—24no—
95C2×#11761615—24no—
96C2×#11761615C2314yes—
97C2×#11761615C2314yes—
98C22×C67⋊C8C2311yescharacteristic
99C22×C67⋊C8C2311yescharacteristic
100#14524041—22no—
101#14524041C2314yescomplemented
102#14524036—28no—
103#14524036—28no—
104#14524034—28no—
105#14524034—22no—
106#14524034C2314yescomplemented
107#14524033—28no—
108#14524022—22no—
109#14524022C2314yes—
110Q8×Dic67—22no—
111Q8×Dic67C2314yescomplemented
112#14524008—22no—
113#14524008C2314yescomplemented
114C4×D268—28no—
115C4×D268—28no—
116#14524005—22no—
117#14524005—22no—
118#14524005—22no—
119#14524005—22no—
120#14524005C2314yes—
121#14524005C2314yes—
122#14524005C2314yes—
123#14524005C2314yes—
124#14524002D414yes—
125#14524002C2314yes—
126C2×C4⋊Dic67—21no—
127C2×C4⋊Dic67—21no—
128C2×C4⋊Dic67D411yescharacteristic
129C2×C4⋊Dic67D411yescharacteristic
130C2×C4⋊Dic67C2311yescharacteristic
131C2×Dic67⋊C4—21no—
132C2×Dic67⋊C4—21no—
133C2×Dic67⋊C4—21no—
134C2×Dic67⋊C4—21no—
135C2×Dic67⋊C4—21no—
136C2×C22⋊Dic67—21no—
137C2×C22⋊Dic67D411yescharacteristic
138C2×C22⋊Dic67D411yescharacteristic
139C2×(C2×D67)⋊C4—21no—
140C2×(C2×D67)⋊C4—21no—
141C2×(C2×D67)⋊C4—21no—
142C2×(C2×D67)⋊C4—21no—
143C22⋊C4×D67—28no—
144C22⋊C4×D67—28no—
145C2×C4×Dic67—21no—
146C2×C4×Dic67—21no—
147C2×C4×Dic67C2311yescharacteristic
148C2×C4×Dic67C2311yescharacteristic
149#14523976C2314yescomplemented
150#14523974C2314yescomplemented
151Dic67⋊C8C2314yescomplemented
152Dic67⋊C8C2314yescomplemented
153#14523966C2314yescomplemented
154#14523966C2314yescomplemented
155#14523965C2314yes—
156#14523965C2314yes—
157#14523963C2314yes—
158#14523963C2314yes—
159C22⋊(C67⋊C8)C2314yes—
160#14523953C2314yescomplemented
161C8×Dic67C2314yescomplemented
162C22×Q8×C67C2311yescharacteristic
163C23×C4×C67C2311yescharacteristic
164C22×C8×C67C2311yescharacteristic
165C22×C8×C67C2311yescharacteristic
166C22⋊Q8×C67—22no—
167C22⋊Q8×C67C2314yes—
168#117×C67—22no—
169#117×C67C2314yes—
170C2×C4⋊C4×C67—21no—
171C2×C4⋊C4×C67C2311yescharacteristic
172C2×C4⋊C4×C67C2311yescharacteristic
173C2×C4⋊C4×C67C2311yescharacteristic
174C2×C22⋊C4×C67—21no—
175C2×C22⋊C4×C67—21no—
176C2×C42×C67—21no—
177#107×C67C2314yescomplemented
178#106×C67C2314yescomplemented
179#103×C67C2314yescomplemented
180#103×C67C2314yescomplemented
181C22⋊C8×C67C2314yes—
182C23×D67—21no—
183C23×D67—21no—
184C23×D67—28no—
185C23×D67—24no—
186C23×D67—82no—
187C23×D67—82no—
188C2×Dic134—22no—
189C2×Dic134—22no—
190C2×Dic134—21no—
191C2×Dic134C2412yes—
192C2×D268—28no—
193C2×D268—216no—
194C2×D268—21no—
195C2×D268—21no—
196C2×D268—24no—
197C2×D268—22no—
198C2×D268—22no—
199C2×D268—28no—
200C2×D268—28no—
201C2×D268#4114yes—
202C2×D268#4114yes—
203C2×D268C2412yes—
204C2×D268C2412yes—
205C22×Dic67—21no—
206C22×Dic67—21no—
207C22×Dic67C2×D411yescharacteristic
208C22×Dic67C2×D411yescharacteristic
209C22×Dic67C2×D411yescharacteristic
210C22×Dic67C2×D411yescharacteristic
211C2×C4×D67—24no—
212C2×C4×D67—24no—
213C2×C4×D67—24no—
214C2×C4×D67—24no—
215C2×C4×D67—82no—
216C2×C4×D67—82no—
217C2×C4×D67—82no—
218C2×C4×D67—82no—
219#11761617—28no—
220#11761617—28no—
221#11761615—28no—
222#11761615—28no—
223C2×C67⋊C8—22no—
224C2×C67⋊C8—22no—
225C2×C67⋊C8C2412yes—
226C2×C67⋊C8C2412yes—
227C4⋊Dic67—21no—
228C4⋊Dic67—24no—
229C4⋊Dic67—24no—
230C4⋊Dic67C2×D414yes—
231C4⋊Dic67C2×D414yes—
232C4⋊Dic67C2412yes—
233Dic67⋊C4—24no—
234Dic67⋊C4—24no—
235Dic67⋊C4—24no—
236Dic67⋊C4—24no—
237Dic67⋊C4—24no—
238C22⋊Dic67—24no—
239C22⋊Dic67C2×D414yes—
240C22⋊Dic67C2×D414yes—
241(C2×D67)⋊C4—24no—
242(C2×D67)⋊C4—24no—
243(C2×D67)⋊C4—24no—
244(C2×D67)⋊C4—24no—
245C4×Dic67—24no—
246C4×Dic67—24no—
247C4×Dic67C2×D412yes—
248C4×Dic67C2×D412yes—
249C4×Dic67C2412yes—
250C4×Dic67C2412yes—
251C24×C67C2×D411yescharacteristic
252C2×Q8×C67—21no—
253C2×Q8×C67—22no—
254C2×Q8×C67—22no—
255C2×Q8×C67C2412yes—
256C22×C4×C67—22no—
257C22×C4×C67—22no—
258C22×C4×C67—21no—
259C22×C4×C67—21no—
260C22×C4×C67—21no—
261C22×C4×C67—21no—
262C22×C4×C67C2×D411yescharacteristic
263C22×C4×C67C2×D412yes—
264C22×C4×C67C2412yes—
265C22×C4×C67C2411yescharacteristic
266C2×C8×C67—22no—
267C2×C8×C67—22no—
268C2×C8×C67C2412yes—
269C2×C8×C67C2412yes—
270C4⋊C4×C67—24no—
271C4⋊C4×C67—21no—
272C4⋊C4×C67—21no—
273C4⋊C4×C67—21no—
274C4⋊C4×C67C2412yes—
275C4⋊C4×C67C2412yes—
276C4⋊C4×C67C2412yes—
277C22⋊C4×C67—24no—
278C22⋊C4×C67—24no—
279C42×C67—24no—
280C23×C67—22no—
281C23×C67—22no—
282C23×C67—22no—
283C23×C67C22×D412yes—
284C23×C67C22×D411yescharacteristic
285C22×D67—24no—
286C22×D67—24no—
287C22×D67—22no—
288C22×D67—22no—
289C22×D67—216no—
290C22×D67—42no—
291C22×D67—42no—
292C22×D67—42no—
293C22×D67—42no—
294C22×D67—84no—
295C22×D67—84no—
296C22×D67—816no—
297Q8×C67—22no—
298Q8×C67—22no—
299Q8×C67—42no—
300C2×C4×C67—22no—
301C2×C4×C67—24no—
302C2×C4×C67—22no—
303C2×C4×C67—22no—
304C2×C4×C67—22no—
305C2×C4×C67—22no—
306C2×C4×C67—22no—
307C2×C4×C67—22no—
308C2×C4×C67—42no—
309C2×C4×C67—42no—
310C2×C4×C67—42no—
311C2×C4×C67—42no—
312C2×C4×C67C22×D412yes—
313C2×C4×C67C22×D411yescharacteristic
314C2×C4×C67C2×#4112yes—
315C2×C4×C67C2×#4112yes—
316C2×C4×C67C2511yescharacteristic
317C2×Dic67—22no—
318C2×Dic67—22no—
319C2×Dic67—22no—
320C2×Dic67—22no—
321C2×Dic67—22no—
322C2×Dic67—22no—
323C2×Dic67—42no—
324C2×Dic67—42no—
325C2×Dic67C22×D412yes—
326C2×Dic67C22×D412yes—
327C2×Dic67C22×D412yes—
328C2×Dic67C22×D412yes—
329D268—216no—
330D268—24no—
331D268—24no—
332D268—22no—
333D268—22no—
334D268C2×#4114yes—
335D268C2×#4114yes—
336C4×D67—84no—
337C4×D67—84no—
338C4×D67—84no—
339C4×D67—84no—
340Dic134—22no—
341Dic134—22no—
342Dic134—42no—
343C8×C67—22no—
344C8×C67—22no—
345C67⋊C8—22no—
346C67⋊C8—22no—
347C22×C67—22no—
348C22×C67—22no—
349C22×C67—22no—
350C22×C67—44no—
351C22×C67#52512yes—
352C22×C67#57712yes—
353C22×C67#57712yes—
354C22×C67C23×D411yescharacteristic
355C2×D67—24no—
356C2×D67—24no—
357C2×D67—48no—
358C2×D67—48no—
359C2×D67—42no—
360C2×D67—42no—
361C2×D67—42no—
362C2×D67—42no—
363C2×D67—816no—
364C4×C67—22no—
365C4×C67—42no—
366C4×C67—42no—
367C4×C67—42no—
368C4×C67—42no—
369C4×C67#52512yes—
370C4×C67C22×#4111yescharacteristic
371C4×C67C22×#4111yescharacteristic
372Dic67—22no—
373Dic67—22no—
374Dic67—22no—
375Dic67—22no—
376Dic67—42no—
377Dic67—42no—
378C2×#3123—671nomaximal, Sylow
379C2×C67—42no—
380C2×C67#312314yescomplemented
381C2×C67C2×#52511yescharacteristic
382C2×C67C2×#57711yescharacteristic
383C2×C67C2×#57711yescharacteristic
384D67—44no—
385D67—44no—
386C2×#541—671no—
387C2×#518—671no—
388#3123—6716no—
389C2×#485—671no—
390C2×#485D6711yescharacteristic, complemented
391C2×#478—671no—
392C2×#478—671no—
393C2×#461—671no—
394C2×#461—671no—
395C2×#450—671no—
396C2×#450—671no—
397C2×#440—671no—
398C2×#440—671no—
399C2×C4×SD16—671no—
400C2×C4×SD16—671no—
401C2×#433—671no—
402C67C2×#312311yescharacteristic, complemented, Sylow
403C23×D4—671no—
404C22×SD16—671no—
405C22×SD16—671no—
406C22×SD16—671no—
407C22×SD16—671no—
408#541—678no—
409#541—1344no—
410C2×C4⋊Q8—671no—
411C2×#126—1341no—
412C2×#126—1341no—
413C2×#125—671no—
414C2×#125—1341no—
415C2×#125—1341no—
416C2×C22⋊Q8—671no—
417C2×C22⋊Q8C2×D6711yescharacteristic
418#518—678no—
419#518—1344no—
420C2×C4×Q8—671no—
421C2×C4×Q8—671no—
422C2×C4×D4—671no—
423C2×C4×D4—671no—
424C2×C4×D4—671no—
425C2×C4×D4—671no—
426C2×C4×D4—1341no—
427C2×C4×D4—1341no—
428C2×#117—671no—
429C2×#117C2×D6711yescharacteristic
430C22×C22⋊C4—1341no—
431C22×C22⋊C4—1341no—
432#485—678no—
433#485C2×D6718yescomplemented
434#478—678no—
435#478—678no—
436#461—678no—
437#461—678no—
438#450—678no—
439#450—678no—
440#440—678no—
441#440—678no—
442C4×SD16—678no—
443C4×SD16—678no—
444#433—678no—
445C2×#107—671no—
446C2×#107C2×D6711yescharacteristic, complemented
447C2×#106—671no—
448C2×#106C2×D6711yescharacteristic, complemented
449C2×C4⋊C8—671no—
450C2×C4⋊C8—671no—
451C2×#103—671no—
452C2×#103—671no—
453C2×#103C2×D6711yescharacteristic, complemented
454C2×#103C2×D6711yescharacteristic, complemented
455C2×#102—671no—
456C2×#102—671no—
457C2×#102—671no—
458C2×#102—671no—
459C2×C22⋊C8—671no—
460C2×C22⋊C8C2×D6711yescharacteristic
461C2×#97—671no—
462C2×C4×C8—671no—
463C25—1341no—
464C22×Q8—671no—
465C22×Q8C22×D6711yescharacteristic
466C22×D4—671no—
467C22×D4—671no—
468C22×D4—674no—
469C22×D4—1344no—
470C22×D4—1344no—
471C22×D4—1341no—
472C22×D4—1342no—
473C23×C4—1341no—
474C23×C4—1341no—
475C23×C4—1341no—
476C23×C4—1341no—
477C23×C4C22×D6711yescharacteristic
478C2×SD16—674no—
479C2×SD16—674no—
480C2×SD16—674no—
481C2×SD16—674no—
482C2×SD16—1344no—
483C2×SD16—1344no—
484C2×SD16—1344no—
485C2×SD16—1344no—
486C22×C8—671no—
487C22×C8—671no—
488C22×C8C22×D6711yescharacteristic
489C22×C8C22×D6711yescharacteristic
490C4⋊Q8—674no—
491C4⋊Q8—1342no—
492#126—1348no—
493#126—1348no—
494#125—674no—
495#125—1342no—
496#125—1348no—
497#125—1348no—
498C22⋊Q8—22no—
499C22⋊Q8—674no—
500C22⋊Q8—1342no—
501C22⋊Q8C22×D6714yes—
502C4×Q8—674no—
503C4×Q8—674no—
504C4×Q8—1342no—
505C4×Q8—1342no—
506C4×D4—674no—
507C4×D4—674no—
508C4×D4—674no—
509C4×D4—674no—
510C4×D4—1348no—
511C4×D4—1348no—
512C4×D4—1342no—
513C4×D4—1342no—
514C4×D4—1342no—
515C4×D4—1342no—
516#117—22no—
517#117—674no—
518#117—674no—
519#117C22×D6714yes—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—671no—
522C2×C4⋊C4—671no—
523C2×C4⋊C4—671no—
524C2×C4⋊C4—1341no—
525C2×C4⋊C4—1341no—
526C2×C4⋊C4—1341no—
527C2×C4⋊C4—1341no—
528C2×C4⋊C4—1341no—
529C2×C4⋊C4—1341no—
530C2×C4⋊C4—1341no—
531C2×C4⋊C4C22×D6711yescharacteristic
532C2×C4⋊C4C22×D6711yescharacteristic
533C2×C4⋊C4C22×D6711yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—671no—
537C2×C22⋊C4—671no—
538C2×C22⋊C4—1348no—
539C2×C22⋊C4—1348no—
540C2×C22⋊C4—1341no—
541C2×C22⋊C4—1341no—
542C2×C22⋊C4—1341no—
543C2×C22⋊C4—1341no—
544C2×C22⋊C4—1341no—
545C2×C42—21no—
546C2×C42—671no—
547C2×C42—671no—
548C2×C42—1341no—
549C2×C42—1341no—
550#107—674no—
551#107C22×D6714yescomplemented
552#106—674no—
553#106C22×D6714yescomplemented
554C4⋊C8—674no—
555C4⋊C8—674no—
556#103—674no—
557#103—674no—
558#103C22×D6714yescomplemented
559#103C22×D6714yescomplemented
560#102—674no—
561#102—674no—
562#102—674no—
563#102—674no—
564C22⋊C8—674no—
565C22⋊C8C22×D6714yes—
566#97—674no—
567C4×C8—674no—
568C24—5362no—
569C24—5362no—
570C24—1348no—
571C24—1341no—
572C24—1341no—
573C24—1344no—
574C24D4×D6711yescharacteristic
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—672no—
579C2×Q8—1342no—
580C2×Q8—1342no—
581C2×Q8—1341no—
582C2×Q8C23×D6712yes—
583C2×D4—674no—
584C2×D4—674no—
585C2×D4—672no—
586C2×D4—672no—
587C2×D4—1348no—
588C2×D4—1348no—
589C2×D4—1348no—
590C2×D4—13416no—
591C2×D4—1344no—
592C2×D4—1341no—
593C2×D4—1341no—
594C2×D4—1342no—
595C2×D4—1342no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—5362no—
603C22×C4—5362no—
604C22×C4—5362no—
605C22×C4—5362no—
606C22×C4—671no—
607C22×C4—671no—
608C22×C4—671no—
609C22×C4—671no—
610C22×C4—1344no—
611C22×C4—1344no—
612C22×C4—1344no—
613C22×C4—1344no—
614C22×C4—1341no—
615C22×C4—1341no—
616C22×C4D4×D6712yes—
617C22×C4D4×D6711yescharacteristic
618C22×C4C23×D6712yes—
619C22×C4C23×D6711yescharacteristic
620SD16—1348no—
621SD16—1348no—
622SD16—1348no—
623SD16—1348no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—672no—
627C2×C8—672no—
628C2×C8—1342no—
629C2×C8—1342no—
630C2×C8C23×D6712yes—
631C2×C8C23×D6712yes—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—674no—
637C4⋊C4—674no—
638C4⋊C4—672no—
639C4⋊C4—1344no—
640C4⋊C4—1344no—
641C4⋊C4—1344no—
642C4⋊C4—1344no—
643C4⋊C4—1344no—
644C4⋊C4—1344no—
645C4⋊C4—1341no—
646C4⋊C4—1344no—
647C4⋊C4C23×D6712yes—
648C4⋊C4C23×D6712yes—
649C4⋊C4C23×D6712yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—674no—
653C22⋊C4—674no—
654C22⋊C4—1344no—
655C22⋊C4—1344no—
656C22⋊C4—1344no—
657C22⋊C4—1344no—
658C22⋊C4—1344no—
659C42—24no—
660C42—672no—
661C42—672no—
662C42—672no—
663C42—672no—
664C42—1344no—
665C42—1344no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—2682no—
670C23—2682no—
671C23—2682no—
672C23—2682no—
673C23—5364no—
674C23—5364no—
675C23—53616no—
676C23—13416no—
677C23—1344no—
678C23—1344no—
679C23—1342no—
680C23—1342no—
681C23C2×D4×D6712yes—
682C23C2×D4×D6711yescharacteristic
683Q8—22no—
684Q8—22no—
685Q8—42no—
686Q8—2682no—
687Q8—1342no—
688Q8—1342no—
689D4—674no—
690D4—674no—
691D4—13416no—
692D4—1344no—
693D4—1344no—
694D4—1342no—
695D4—1342no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—2682no—
709C2×C4—2682no—
710C2×C4—5364no—
711C2×C4—5364no—
712C2×C4—5364no—
713C2×C4—5364no—
714C2×C4—672no—
715C2×C4—672no—
716C2×C4—672no—
717C2×C4—672no—
718C2×C4—1342no—
719C2×C4—1342no—
720C2×C4—1342no—
721C2×C4—1342no—
722C2×C4—1342no—
723C2×C4—1342no—
724C2×C4C2×D4×D6712yes—
725C2×C4C2×D4×D6711yescharacteristic
726C2×C4#41×D6712yes—
727C2×C4#41×D6712yes—
728C2×C4C24×D6711yescharacteristic
729C8—22no—
730C8—22no—
731C8—1342no—
732C8—1342no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—2682no—
738C22—2682no—
739C22—2682no—
740C22—2682no—
741C22—2688no—
742C22—2688no—
743C22—53616no—
744C22—1344no—
745C22—1344no—
746C22#1686390412yes—
747C22#1686420312yes—
748C22#1686420512yes—
749C22C22×D4×D6711yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—2682no—
756C4—2682no—
757C4—1342no—
758C4—1342no—
759C4—1342no—
760C4—1342no—
761C4#1686390412yes—
762C4C2×#41×D6711yescharacteristic
763C4C2×#41×D6711yescharacteristic
764C2—42no—
765C2—2684no—
766C2—2684no—
767C2#2257045714yesdirect product factor
768C2C2×#1686390411yescharacteristic
769C2C2×#1686420311yescharacteristic
770C2C2×#1686420511yescharacteristic
subgroupG/H
centerC23C2×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#485×C67C2
socleC23×C67C22×D4
prime radicalC23×D268C22
hypercenterC2×#485D67
hypocenterC67C2×#3123
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#16864006C2semidirect
3. #22570457C2direct (N × H)
4. C2×#16863737C2semidirect
5. C2×#16863699C2semidirect
6. C2×#16863695C2semidirect
7. C2×#16863600C2semidirect
8. C2×#16863600C2semidirect
11. C2×#16863499C2semidirect
12. C2×#16863495C2semidirect
13. C2×#16863483C2semidirect
14. C2×#16863481C2semidirect
15. C2×#16863454C2semidirect
16. C2×#485×C67C2semidirect
23. #16864006C22semidirect
24. C2×#14524041C22semidirect
28. C2×#14524034C22semidirect
33. C2×Q8×Dic67C22semidirect
34. C2×#14524008C22semidirect
44. #16863737C22semidirect
45. #16863699C22semidirect
46. #16863695C22semidirect
47. #16863600C22semidirect
48. #16863600C22semidirect
51. #16863499C22semidirect
52. #16863495C22semidirect
53. #16863483C22semidirect
54. #16863481C22semidirect
55. #16863454C22semidirect
56. C2×#14523976C22semidirect
57. C2×#14523974C22semidirect
58. C2×Dic67⋊C8C22semidirect
59. C2×Dic67⋊C8C22semidirect
60. C2×#14523966C22semidirect
61. C2×#14523966C22semidirect
67. C2×#14523953C22semidirect
68. C2×C8×Dic67C22semidirect
71. #485×C67C22semidirect
72. C2×#107×C67C22semidirect
73. C2×#106×C67C22semidirect
74. C2×#103×C67C22semidirect
75. C2×#103×C67C22semidirect
101. #14524041C23semidirect
106. #14524034C23semidirect
111. Q8×Dic67C23semidirect
113. #14524008C23semidirect
149. #14523976C23semidirect
150. #14523974C23semidirect
151. Dic67⋊C8C23semidirect
152. Dic67⋊C8C23semidirect
153. #14523966C23semidirect
154. #14523966C23semidirect
160. #14523953C23semidirect
161. C8×Dic67C23semidirect
177. #107×C67C23semidirect
178. #106×C67C23semidirect
179. #103×C67C23semidirect
180. #103×C67C23semidirect
380. C2×C67#3123semidirect
390. C2×#485D67semidirect
402. C67C2×#3123semidirect
433. #485C2×D67semidirect
446. C2×#107C2×D67semidirect
448. C2×#106C2×D67semidirect
453. C2×#103C2×D67semidirect
454. C2×#103C2×D67semidirect
551. #107C22×D67semidirect
553. #106C22×D67semidirect
558. #103C22×D67semidirect
559. #103C22×D67semidirect
767. C2#22570457direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640062
C2×#168638702
#225704572
C2×#168637372
C2×#168636992
C2×#168636952
C2×#168636002
C2×#168635492
C2×#168635462
C2×#168634992
C2×#168634952
C2×#168634832
C2×#168634812
C2×#168634542
C2×#485×C672
C2×#312367