Finite Group Databasebeta

← C2×#22573105 #31736305

Subgroups — C2×#22573105 #31736305

Order 17152.

2082 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864102C211yesmaximal, characteristic, complemented
2C2×#16864061C211yesmaximal, characteristic, complemented
3#22573105C2116yesmaximal, direct product factor
4C2×#16863804C211yesmaximal, characteristic, complemented
5C2×#16863793C211yesmaximal, characteristic, complemented
6C2×#16863699C211yesmaximal, characteristic, complemented
7C2×#16863693C211yesmaximal, characteristic, complemented
8C2×#16863685C211yesmaximal, characteristic, complemented
9C2×#16863685C211yesmaximal, characteristic, complemented
10C2×#16863683C211yesmaximal, characteristic, complemented
11C2×#16863675C211yesmaximal, characteristic, complemented
12C2×#16863524C211yesmaximal, characteristic, complemented
13C2×#16863509C211yesmaximal, characteristic
14C2×#16863507C211yesmaximal, characteristic
15C2×#16863478C211yesmaximal, characteristic
16C2×#501×C67C211yesmaximal, characteristic, complemented
17C22×Q8×D67—21no—
18C22×D536C2211yescharacteristic
19#16864102—24no—
20#16864102C2218yescomplemented
21#16864061—24no—
22#16864061C2218yescomplemented
23C2×#14524042C2211yescharacteristic
24C2×#14524042C2211yescharacteristic
25C2×#14524042C2211yescharacteristic
26C2×#14524034C2211yescharacteristic
27C2×#14524023—21no—
28C2×#14524021—21no—
29C2×#14524021—21no—
30C2×#14524021—21no—
31C2×#14524021—21no—
32C2×#14524019—21no—
33C2×C4×Dic134C2211yescharacteristic
34C2×C4×D268C2211yescharacteristic
35C2×C4×D268C2211yescharacteristic
36C2×#14524005C2211yescharacteristic
37C2×#14524005C2211yescharacteristic
38C2×#14524005C2211yescharacteristic
39C2×#14524005C2211yescharacteristic
40C2×C4⋊C4×D67—21no—
41#16863804C2218yescomplemented
42#16863793C2218yescomplemented
43#16863699C2218yescomplemented
44#16863693C2218yescomplemented
45#16863685C2218yescomplemented
46#16863685C2218yescomplemented
47#16863683C2218yescomplemented
48#16863675C2218yescomplemented
49#16863524C2218yescomplemented
50#16863509C2218yes—
51#16863507C2218yes—
52#16863478C2218yes—
53C2×#14523976C2211yescharacteristic
54C2×#14523975C2211yescharacteristic
55C2×#14523974C2211yescharacteristic
56C2×#14523974C2211yescharacteristic
57C2×#14523974C2211yescharacteristic
58C2×C4⋊(C67⋊C8)C2211yescharacteristic
59C2×Dic67⋊C8C2211yescharacteristic
60C2×Dic67⋊C8C2211yescharacteristic
61C2×#14523965C2211yescharacteristic
62C2×#14523965C2211yescharacteristic
63C2×#14523963C2211yescharacteristic
64C2×#14523963C2211yescharacteristic
65C2×#14523963C2211yescharacteristic
66C2×#14523963C2211yescharacteristic
67C2×#14523953C2211yescharacteristic
68C2×C8×Dic67C2211yescharacteristic
69C2×C4⋊Q8×C67C2211yescharacteristic
70C2×#125×C67C2211yescharacteristic
71#501×C67C2218yescomplemented
72C2×#107×C67C2211yescharacteristic
73C2×#107×C67C2211yescharacteristic
74C2×#106×C67C2211yescharacteristic
75C2×#106×C67C2211yescharacteristic
76C2×#97×C67C2211yescharacteristic
77C22×Dic134—21no—
78C22×Dic134—21no—
79C22×Dic134—21no—
80C22×Dic134D411yescharacteristic
81C2×Q8×D67—28no—
82C2×Q8×D67—48no—
83C22×D268C2311yescharacteristic
84C22×D268C2311yescharacteristic
85C22×C4×D67—21no—
86C22×C4×D67—21no—
87C22×C4×D67—21no—
88C22×C4×D67—21no—
89C22×C4×D67—21no—
90C22×C4×D67—21no—
91C2×D536Q818yescomplemented
92C2×D536C2314yes—
93C22×C67⋊C8C2311yescharacteristic
94C22×C67⋊C8C2311yescharacteristic
95#14524042—22no—
96#14524042—22no—
97#14524042—22no—
98#14524042C2314yes—
99#14524042C2314yes—
100#14524042C2314yes—
101#14524034—22no—
102#14524034C2314yes—
103#14524023—28no—
104#14524021—28no—
105#14524021—28no—
106#14524021—28no—
107#14524021—28no—
108#14524019—28no—
109C4×Dic134D414yes—
110C4×Dic134C2314yes—
111C4×D268—22no—
112C4×D268—22no—
113C4×D268C2314yes—
114C4×D268C2314yes—
115#14524005—22no—
116#14524005—22no—
117#14524005—22no—
118#14524005—22no—
119#14524005C2314yes—
120#14524005C2314yes—
121#14524005C2314yes—
122#14524005C2314yes—
123C2×C4⋊Dic67—21no—
124C2×C4⋊Dic67D411yescharacteristic
125C2×C4⋊Dic67C2311yescharacteristic
126C2×C4⋊Dic67C2311yescharacteristic
127C2×Dic67⋊C4—21no—
128C2×Dic67⋊C4—21no—
129C2×Dic67⋊C4—21no—
130C2×Dic67⋊C4—21no—
131C2×Dic67⋊C4D411yescharacteristic
132C2×Dic67⋊C4D411yescharacteristic
133C4⋊C4×D67—28no—
134C2×(C2×D67)⋊C4—21no—
135C2×(C2×D67)⋊C4—21no—
136C2×(C2×D67)⋊C4—21no—
137C2×(C2×D67)⋊C4—21no—
138C2×(C2×D67)⋊C4—21no—
139C2×(C2×D67)⋊C4—21no—
140C2×C4×Dic67C2311yescharacteristic
141C2×C4×Dic67C2311yescharacteristic
142#14523976C2314yes—
143#14523975C2314yes—
144#14523974C2314yes—
145#14523974C2314yes—
146#14523974C2314yes—
147C4⋊(C67⋊C8)C2314yes—
148Dic67⋊C8C2314yes—
149Dic67⋊C8C2314yes—
150#14523965C2314yes—
151#14523965C2314yes—
152#14523963C2314yes—
153#14523963C2314yes—
154#14523963C2314yes—
155#14523963C2314yes—
156#14523953C2314yes—
157C8×Dic67C2314yes—
158C22×Q8×C67—21no—
159C22×C8×C67C2311yescharacteristic
160C22×C8×C67C2311yescharacteristic
161C4⋊Q8×C67—22no—
162C4⋊Q8×C67C2314yes—
163#125×C67—22no—
164#125×C67C2314yes—
165C2×C4⋊C4×C67—21no—
166C2×C4⋊C4×C67—21no—
167C2×C4⋊C4×C67—21no—
168C2×C4⋊C4×C67C2311yescharacteristic
169C2×C4⋊C4×C67C2311yescharacteristic
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C4⋊C4×C67C2311yescharacteristic
172C2×C42×C67C2311yescharacteristic
173#107×C67C2314yes—
174#107×C67C2314yes—
175#106×C67C2314yes—
176#106×C67C2314yes—
177#97×C67C2314yes—
178C23×D67—21no—
179C23×D67—21no—
180C2×Dic134—24no—
181C2×Dic134—24no—
182C2×Dic134—24no—
183C2×Dic134—24no—
184C2×Dic134—44no—
185C2×Dic134—44no—
186C2×Dic134—82no—
187C2×Dic134C2×D414yes—
188Q8×D67—432no—
189C2×D268—21no—
190C2×D268—21no—
191C2×D268—22no—
192C2×D268—22no—
193C2×D268C2×Q814yes—
194C2×D268C2×Q814yescomplemented
195C2×D268C2412yes—
196C2×D268C2412yes—
197C22×Dic67—21no—
198C22×Dic67—21no—
199C22×Dic67C2×D411yescharacteristic
200C22×Dic67C2×D411yescharacteristic
201C22×Dic67C2×D411yescharacteristic
202C22×Dic67C2×D411yescharacteristic
203C2×C4×D67—24no—
204C2×C4×D67—24no—
205C2×C4×D67—24no—
206C2×C4×D67—24no—
207C2×C4×D67—24no—
208C2×C4×D67—24no—
209C2×C4×D67—44no—
210C2×C4×D67—44no—
211C2×C4×D67—44no—
212C2×C4×D67—44no—
213C2×C4×D67—82no—
214C2×C4×D67—82no—
215D536C2×Q8116yescomplemented
216C2×C67⋊C8—22no—
217C2×C67⋊C8—22no—
218C2×C67⋊C8C2412yes—
219C2×C67⋊C8C2412yes—
220C4⋊Dic67—21no—
221C4⋊Dic67—21no—
222C4⋊Dic67—24no—
223C4⋊Dic67C2×D414yes—
224C4⋊Dic67C2412yes—
225C4⋊Dic67C2412yes—
226Dic67⋊C4—24no—
227Dic67⋊C4—24no—
228Dic67⋊C4—24no—
229Dic67⋊C4—24no—
230Dic67⋊C4C2×D414yes—
231Dic67⋊C4C2×D414yes—
232(C2×D67)⋊C4—24no—
233(C2×D67)⋊C4—24no—
234(C2×D67)⋊C4—24no—
235(C2×D67)⋊C4—24no—
236(C2×D67)⋊C4—24no—
237(C2×D67)⋊C4—24no—
238C4×Dic67C2×D412yes—
239C4×Dic67C2×D412yes—
240C4×Dic67C2412yes—
241C4×Dic67C2412yes—
242C2×Q8×C67—24no—
243C2×Q8×C67—44no—
244C22×C4×C67—21no—
245C22×C4×C67—21no—
246C22×C4×C67—21no—
247C22×C4×C67—21no—
248C22×C4×C67C2×D411yescharacteristic
249C22×C4×C67C2×D411yescharacteristic
250C22×C4×C67C2411yescharacteristic
251C2×C8×C67—22no—
252C2×C8×C67C2×Q814yescomplemented
253C2×C8×C67C2412yes—
254C2×C8×C67C2412yes—
255C4⋊C4×C67—24no—
256C4⋊C4×C67—24no—
257C4⋊C4×C67—24no—
258C4⋊C4×C67—21no—
259C4⋊C4×C67—21no—
260C4⋊C4×C67—21no—
261C4⋊C4×C67—21no—
262C4⋊C4×C67C2412yes—
263C4⋊C4×C67C2412yes—
264C4⋊C4×C67C2412yes—
265C4⋊C4×C67C2412yes—
266C42×C67C2×D412yes—
267C42×C67C2412yes—
268C23×C67C22×D411yescharacteristic
269C22×D67—24no—
270C22×D67—24no—
271C22×D67—22no—
272C22×D67—22no—
273C22×D67—42no—
274C22×D67—42no—
275C22×D67—42no—
276C22×D67—42no—
277Q8×C67—48no—
278C2×C4×C67—22no—
279C2×C4×C67—22no—
280C2×C4×C67—22no—
281C2×C4×C67—22no—
282C2×C4×C67—22no—
283C2×C4×C67—22no—
284C2×C4×C67—42no—
285C2×C4×C67—42no—
286C2×C4×C67—42no—
287C2×C4×C67—42no—
288C2×C4×C67C22×D412yes—
289C2×C4×C67C22×D412yes—
290C2×C4×C67C22×D411yescharacteristic
291C2×C4×C67C22×Q812yes—
292C2×C4×C672−1+412yes—
293C2×C4×C67C2511yescharacteristic
294C2×Dic67—22no—
295C2×Dic67—22no—
296C2×Dic67—22no—
297C2×Dic67—22no—
298C2×Dic67—22no—
299C2×Dic67—42no—
300C2×Dic67—42no—
301C2×Dic67AGL(1,ℤ/8)14yes—
302C2×Dic67C22×D412yes—
303C2×Dic67C22×D412yes—
304C2×Dic67C22×D412yes—
305C2×Dic67C22×D412yes—
306D268—24no—
307D268—24no—
308D268—22no—
309D268—22no—
310D268C22×Q814yes—
311D268C22×Q814yescomplemented
312C4×D67—48no—
313C4×D67—48no—
314C4×D67—48no—
315C4×D67—48no—
316C4×D67—84no—
317C4×D67—84no—
318Dic134—28no—
319Dic134—48no—
320Dic134—48no—
321Dic134—84no—
322C8×C67—22no—
323C8×C67C22×Q814yescomplemented
324C67⋊C8—22no—
325C67⋊C8—22no—
326C22×C67D4×Q812yes—
327C22×C67C2×AGL(1,ℤ/8)12yes—
328C22×C67#57712yes—
329C22×C67C23×D411yescharacteristic
330C2×D67—24no—
331C2×D67—24no—
332C2×D67—48no—
333C2×D67—48no—
334C2×D67—42no—
335C2×D67—42no—
336C2×D67—42no—
337C2×D67—42no—
338C4×C67—22no—
339C4×C67—22no—
340C4×C67—42no—
341C4×C67—42no—
342C4×C67—42no—
343C4×C67—42no—
344C4×C67D4×Q812yes—
345C4×C67C23×Q811yescharacteristic
346C4×C67C2×2−1+411yescharacteristic
347Dic67—22no—
348Dic67—22no—
349Dic67—22no—
350Dic67—42no—
351Dic67—42no—
352Dic67C2×AGL(1,ℤ/8)14yes—
353C2×#3384—671nomaximal, Sylow
354C2×C67#338414yescomplemented
355C2×C67C2×D4×Q811yescharacteristic
356C2×C67C22×AGL(1,ℤ/8)11yescharacteristic
357C2×C67C2×#57711yescharacteristic
358D67—44no—
359D67—44no—
360C2×#554—671no—
361C2×D4×Q8—671no—
362#3384—6716no—
363C2×#501—671no—
364C2×#501D6711yescharacteristic, complemented
365C2×#498—671no—
366C2×#478—671no—
367C2×#478—671no—
368C2×#476—671no—
369C2×#476—671no—
370C2×#476—671no—
371C2×#474—671no—
372C2×#446—671no—
373C2×#442—671no—
374C2×#442—671no—
375C2×C4×D8—671no—
376C67C2×#338411yescharacteristic, complemented, Sylow
377C23×Q8—1341no—
378C22×D8—671no—
379#554—678no—
380#554—1344no—
381D4×Q8—678no—
382D4×Q8—1344no—
383C2×C4⋊Q8—671no—
384C2×C4⋊Q8—671no—
385C2×C4⋊Q8—671no—
386C2×C4⋊Q8C2×D6711yescharacteristic
387C2×#125—671no—
388C2×#125C2×D6711yescharacteristic
389C2×C22⋊Q8—1341no—
390C2×C22⋊Q8—1341no—
391C2×C22⋊Q8—1341no—
392C2×C22⋊Q8—1341no—
393C2×C22⋊Q8—1341no—
394C2×C22⋊Q8—1341no—
395C2×C4×Q8—671no—
396C2×C4×D4—671no—
397C2×C4×D4—671no—
398C2×C4×D4—671no—
399C2×C4×D4—671no—
400C2×C4×D4—671no—
401C2×C4×D4—671no—
402C22×C4⋊C4—1341no—
403#501—678no—
404#501C2×D6718yescomplemented
405#498—678no—
406#478—678no—
407#478—678no—
408#476—678no—
409#476—678no—
410#476—678no—
411#474—678no—
412#446—678no—
413#442—678no—
414#442—678no—
415C4×D8—678no—
416C2×#107—671no—
417C2×#107C2×D6711yescharacteristic
418C2×#107C2×D6711yescharacteristic
419C2×#106—671no—
420C2×#106—671no—
421C2×#106—671no—
422C2×#106—671no—
423C2×#106C2×D6711yescharacteristic
424C2×#106C2×D6711yescharacteristic
425C2×C4⋊C8—671no—
426C2×C4⋊C8—671no—
427C2×C4⋊C8—671no—
428C2×#102—671no—
429C2×#102—671no—
430C2×#102—671no—
431C2×#102—671no—
432C2×#102—671no—
433C2×#102—671no—
434C2×#97—671no—
435C2×#97C2×D6711yescharacteristic
436C2×C4×C8—671no—
437C22×Q8—21no—
438C22×Q8—2688no—
439C22×Q8—671no—
440C22×Q8—1341no—
441C22×Q8—1341no—
442C22×Q8—1341no—
443C22×Q8—1348no—
444C22×D4—671no—
445C22×D4—671no—
446C23×C4—1341no—
447C23×C4—1341no—
448C23×C4—1341no—
449C23×C4—1341no—
450C23×C4—1341no—
451C23×C4—1341no—
452C2×D8—678no—
453C2×D8—674no—
454C22×C8—671no—
455C22×C8—671no—
456C22×C8C22×D6711yescharacteristic
457C22×C8C22×D6711yescharacteristic
458C4⋊Q8—22no—
459C4⋊Q8—674no—
460C4⋊Q8—674no—
461C4⋊Q8—674no—
462C4⋊Q8—1342no—
463C4⋊Q8—1342no—
464C4⋊Q8—1342no—
465C4⋊Q8C22×D6714yes—
466#125—22no—
467#125—674no—
468#125—1342no—
469#125C22×D6714yes—
470C22⋊Q8—1348no—
471C22⋊Q8—1348no—
472C22⋊Q8—1348no—
473C22⋊Q8—1348no—
474C22⋊Q8—1348no—
475C22⋊Q8—1348no—
476C4×Q8—674no—
477C4×Q8—674no—
478C4×D4—674no—
479C4×D4—674no—
480C4×D4—674no—
481C4×D4—674no—
482C4×D4—674no—
483C4×D4—674no—
484C4×D4—1342no—
485C4×D4—1342no—
486C4×D4—1342no—
487C4×D4—1342no—
488C4×D4—1342no—
489C4×D4—1342no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—671no—
494C2×C4⋊C4—671no—
495C2×C4⋊C4—671no—
496C2×C4⋊C4—671no—
497C2×C4⋊C4—671no—
498C2×C4⋊C4—1348no—
499C2×C4⋊C4—1341no—
500C2×C4⋊C4—1341no—
501C2×C4⋊C4—1341no—
502C2×C4⋊C4—1341no—
503C2×C4⋊C4—1341no—
504C2×C4⋊C4C22×D6711yescharacteristic
505C2×C4⋊C4C22×D6711yescharacteristic
506C2×C4⋊C4C22×D6711yescharacteristic
507C2×C4⋊C4C22×D6711yescharacteristic
508C2×C22⋊C4—1341no—
509C2×C22⋊C4—1341no—
510C2×C22⋊C4—1341no—
511C2×C22⋊C4—1341no—
512C2×C22⋊C4—1341no—
513C2×C22⋊C4—1341no—
514C2×C42—671no—
515C2×C42—671no—
516C2×C42C22×D6711yescharacteristic
517#107—674no—
518#107C22×D6714yes—
519#107C22×D6714yes—
520#106—674no—
521#106—674no—
522#106—674no—
523#106—674no—
524#106C22×D6714yes—
525#106C22×D6714yes—
526C4⋊C8—674no—
527C4⋊C8—674no—
528C4⋊C8—674no—
529#102—674no—
530#102—674no—
531#102—674no—
532#102—674no—
533#102—674no—
534#102—674no—
535#97—674no—
536#97C22×D6714yes—
537C4×C8—674no—
538C24—1341no—
539C24—1341no—
540C2×Q8—24no—
541C2×Q8—44no—
542C2×Q8—2684no—
543C2×Q8—2684no—
544C2×Q8—26832no—
545C2×Q8—5362no—
546C2×Q8—674no—
547C2×Q8—1344no—
548C2×Q8—1344no—
549C2×Q8—1344no—
550C2×Q8—1344no—
551C2×D4—674no—
552C2×D4—674no—
553C2×D4—672no—
554C2×D4—672no—
555C2×D4—1341no—
556C2×D4—1341no—
557C2×D4—1342no—
558C2×D4—1342no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—2684no—
564C22×C4—2684no—
565C22×C4—2684no—
566C22×C4—2684no—
567C22×C4—5362no—
568C22×C4—5362no—
569C22×C4—671no—
570C22×C4—671no—
571C22×C4—671no—
572C22×C4—671no—
573C22×C4—1344no—
574C22×C4—1344no—
575C22×C4—1344no—
576C22×C4—1344no—
577C22×C4—1341no—
578C22×C4—1341no—
579C22×C4—1344no—
580C22×C4—1344no—
581C22×C4D4×D6711yescharacteristic
582C22×C4D4×D6711yescharacteristic
583C22×C4C23×D6711yescharacteristic
584D8—6716no—
585C2×C8—22no—
586C2×C8—672no—
587C2×C8—672no—
588C2×C8—1342no—
589C2×C8—1342no—
590C2×C8Q8×D6714yescomplemented
591C2×C8C23×D6712yes—
592C2×C8C23×D6712yes—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—674no—
601C4⋊C4—674no—
602C4⋊C4—674no—
603C4⋊C4—672no—
604C4⋊C4—672no—
605C4⋊C4—1344no—
606C4⋊C4—1344no—
607C4⋊C4—1344no—
608C4⋊C4—1344no—
609C4⋊C4—1344no—
610C4⋊C4—1341no—
611C4⋊C4—1341no—
612C4⋊C4C23×D6712yes—
613C4⋊C4C23×D6712yes—
614C4⋊C4C23×D6712yes—
615C4⋊C4C23×D6712yes—
616C22⋊C4—1344no—
617C22⋊C4—1344no—
618C22⋊C4—1344no—
619C22⋊C4—1344no—
620C22⋊C4—1344no—
621C22⋊C4—1344no—
622C42—672no—
623C42—672no—
624C42—672no—
625C42—672no—
626C42D4×D6712yes—
627C42C23×D6712yes—
628C23—2682no—
629C23—2682no—
630C23—2682no—
631C23—2682no—
632C23—1344no—
633C23—1344no—
634C23—1342no—
635C23—1342no—
636C23C2×D4×D6711yescharacteristic
637Q8—48no—
638Q8—2688no—
639Q8—2688no—
640Q8—5364no—
641Q8—1348no—
642D4—674no—
643D4—674no—
644D4—1344no—
645D4—1344no—
646D4—1342no—
647D4—1342no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—2688no—
659C2×C4—2688no—
660C2×C4—2688no—
661C2×C4—2688no—
662C2×C4—2682no—
663C2×C4—2682no—
664C2×C4—5364no—
665C2×C4—5364no—
666C2×C4—674no—
667C2×C4—672no—
668C2×C4—672no—
669C2×C4—672no—
670C2×C4—672no—
671C2×C4—1342no—
672C2×C4—1342no—
673C2×C4—1342no—
674C2×C4—1342no—
675C2×C4—1342no—
676C2×C4C2×D4×D6712yes—
677C2×C4C2×D4×D6712yes—
678C2×C4C2×D4×D6711yescharacteristic
679C2×C4C2×Q8×D6712yes—
680C2×C4#1452409112yes—
681C2×C4C24×D6711yescharacteristic
682C8—22no—
683C8—1342no—
684C8—1342no—
685C8C2×Q8×D6714yescomplemented
686C22—2688no—
687C22—2688no—
688C22—2682no—
689C22—2682no—
690C22—2682no—
691C22—2682no—
692C22—1344no—
693C22—1344no—
694C22#1686406112yes—
695C22AGL(1,ℤ/8)×D6712yes—
696C22#1686420512yes—
697C22C22×D4×D6711yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—2682no—
705C4—2682no—
706C4—674no—
707C4—1342no—
708C4—1342no—
709C4—1342no—
710C4#1686406112yes—
711C4C22×Q8×D6711yescharacteristic
712C4C2×#1452409111yescharacteristic
713C2—2684no—
714C2—2684no—
715C2#2257310514yesdirect product factor
716C2C2×#1686406111yescharacteristic
717C2C2×AGL(1,ℤ/8)×D6711yescharacteristic
718C2C2×#1686420511yescharacteristic
subgroupG/H
centerC23C2×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#501×C67C2
socleC23×C67C22×D4
prime radicalC22×D536C22
hypercenterC2×#501D67
hypocenterC67C2×#3384
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#16864102C2semidirect
2. C2×#16864061C2semidirect
3. #22573105C2direct (N × H)
4. C2×#16863804C2semidirect
5. C2×#16863793C2semidirect
6. C2×#16863699C2semidirect
7. C2×#16863693C2semidirect
8. C2×#16863685C2semidirect
9. C2×#16863685C2semidirect
10. C2×#16863683C2semidirect
11. C2×#16863675C2semidirect
12. C2×#16863524C2semidirect
16. C2×#501×C67C2semidirect
20. #16864102C22semidirect
22. #16864061C22semidirect
41. #16863804C22semidirect
42. #16863793C22semidirect
43. #16863699C22semidirect
44. #16863693C22semidirect
45. #16863685C22semidirect
46. #16863685C22semidirect
47. #16863683C22semidirect
48. #16863675C22semidirect
49. #16863524C22semidirect
71. #501×C67C22semidirect
91. C2×D536Q8semidirect
194. C2×D268C2×Q8semidirect
215. D536C2×Q8semidirect
252. C2×C8×C67C2×Q8semidirect
311. D268C22×Q8semidirect
323. C8×C67C22×Q8semidirect
354. C2×C67#3384semidirect
364. C2×#501D67semidirect
376. C67C2×#3384semidirect
404. #501C2×D67semidirect
590. C2×C8Q8×D67semidirect
685. C8C2×Q8×D67semidirect
715. C2#22573105direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168641022
C2×#168640612
#225731052
C2×#168638042
C2×#168637932
C2×#168636992
C2×#168636932
C2×#168636852
C2×#168636832
C2×#168636752
C2×#168635242
C2×#168635092
C2×#168635072
C2×#168634782
C2×#501×C672
C2×#338467