Finite Group Databasebeta

← C2×#22569993 #31723328

Subgroups — C2×#22569993 #31723328

Order 17152.

2162 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863949C211yesmaximal, characteristic, complemented
2C2×#41×Dic67C211yesmaximal, characteristic
3#22569993C2116yesmaximal, direct product factor
4C2×#16863705C211yesmaximal, characteristic, complemented
5C2×#16863701C211yesmaximal, characteristic, complemented
6C2×#16863689C211yesmaximal, characteristic, complemented
7C2×#16863679C211yesmaximal, characteristic, complemented
8C2×#16863698C211yesmaximal, characteristic, complemented
9C2×#16863694C211yesmaximal, characteristic, complemented
10C2×#16863684C211yesmaximal, characteristic, complemented
11C2×#16863674C211yesmaximal, characteristic, complemented
12C2×#16863434C211yesmaximal, characteristic, complemented
13C2×#16863432C211yesmaximal, characteristic, complemented
14C22×Dic67⋊C8C211yesmaximal, characteristic, complemented
15C2×#16863392C211yesmaximal, characteristic
16C2×#416×C67C211yesmaximal, characteristic
17C23×C67⋊C8C2211yescharacteristic
18#16863949—24no—
19#16863949C2218yescomplemented
20C2×#14524042C2211yescharacteristic
21C2×#14524042C2211yescharacteristic
22C2×#14524034C2211yescharacteristic
23C2×#14524034C2211yescharacteristic
24C2×#14524020—21no—
25C2×#14524020—21no—
26#41×Dic67—24no—
27#41×Dic67C2218yes—
28C2×Q8×Dic67C2211yescharacteristic
29C2×Q8×Dic67C2211yescharacteristic
30C2×C4×Dic134—21no—
31C2×C4×Dic134—21no—
32C2×D4×Dic67—21no—
33C2×D4×Dic67—21no—
34C2×D4×Dic67C2211yescharacteristic
35C2×D4×Dic67C2211yescharacteristic
36C2×#14524002—21no—
37C2×#14524002C2211yescharacteristic
38C2×#14524002C2211yescharacteristic
39C22×C4×Dic67—21no—
40C22×C4×Dic67C2211yescharacteristic
41#16863705C2218yescomplemented
42#16863701C2218yescomplemented
43#16863698C2218yescomplemented
44#16863694C2218yescomplemented
45#16863689C2218yescomplemented
46#16863684C2218yescomplemented
47#16863679C2218yescomplemented
48#16863674C2218yescomplemented
49#16863434C2218yescomplemented
50#16863432C2218yescomplemented
51C2×#14523977C2211yescharacteristic
52C2×#14523977C2211yescharacteristic
53C2×#14523976C2211yescharacteristic
54C2×#14523976C2211yescharacteristic
55C2×#14523975C2211yescharacteristic
56C2×#14523975C2211yescharacteristic
57C2×#14523974C2211yescharacteristic
58C2×#14523974C2211yescharacteristic
59C2×Dic67⋊C8C2211yescharacteristic
60C2×Dic67⋊C8C2211yescharacteristic
61C2×Dic67⋊C8C2211yescharacteristic
62C2×Dic67⋊C8C2211yescharacteristic
63C2×Dic67⋊C8C2218yescomplemented
64#16863392C2218yes—
65C2×#14523967C2211yescharacteristic
66C2×#14523967C2211yescharacteristic
67C2×#14523964C2211yescharacteristic
68C2×#14523964C2211yescharacteristic
69C22×#41×C67C2211yescharacteristic
70C23×C8×C67C2211yescharacteristic
71C2×#117×C67C2211yescharacteristic
72#416×C67C2218yes—
73C2×#103×C67C2211yescharacteristic
74C2×#103×C67C2211yescharacteristic
75C2×#102×C67C2211yescharacteristic
76C2×#102×C67C2211yescharacteristic
77C22×Dic134—21no—
78C22×Dic134—21no—
79C23×Dic67—21no—
80C23×Dic67—21no—
81C23×Dic67D411yescharacteristic
82C23×Dic67D411yescharacteristic
83C22×C67⋊C8—24no—
84C22×C67⋊C8C2311yescharacteristic
85C22×C67⋊C8C2311yescharacteristic
86C22×C67⋊C8C2314yes—
87#14524042—22no—
88#14524042—22no—
89#14524042C2314yes—
90#14524042C2314yes—
91#14524034—22no—
92#14524034—22no—
93#14524034C2314yes—
94#14524034C2314yes—
95#14524020—28no—
96#14524020—28no—
97Q8×Dic67—22no—
98Q8×Dic67—22no—
99Q8×Dic67C2314yes—
100Q8×Dic67C2314yes—
101C4×Dic134—28no—
102C4×Dic134—28no—
103D4×Dic67—28no—
104D4×Dic67—28no—
105D4×Dic67—22no—
106D4×Dic67—22no—
107D4×Dic67C2314yes—
108D4×Dic67C2314yes—
109#14524002—28no—
110#14524002—22no—
111#14524002—22no—
112#14524002C2314yes—
113#14524002C2314yes—
114C2×C4⋊Dic67—21no—
115C2×C4⋊Dic67—21no—
116C2×C4⋊Dic67—21no—
117C2×C4⋊Dic67—21no—
118C2×C4⋊Dic67C2311yescharacteristic
119C2×C4⋊Dic67C2311yescharacteristic
120C2×C4⋊Dic67C2311yescharacteristic
121C2×C4⋊Dic67C2311yescharacteristic
122C2×Dic67⋊C4—21no—
123C2×Dic67⋊C4—21no—
124C2×Dic67⋊C4—21no—
125C2×Dic67⋊C4—21no—
126C2×C22⋊Dic67—21no—
127C2×C22⋊Dic67—21no—
128C2×C22⋊Dic67—21no—
129C2×C22⋊Dic67—21no—
130C2×C4×Dic67—21no—
131C2×C4×Dic67—21no—
132C2×C4×Dic67—28no—
133C2×C4×Dic67—21no—
134C2×C4×Dic67—21no—
135C2×C4×Dic67D411yescharacteristic
136C2×C4×Dic67D411yescharacteristic
137C2×C4×Dic67D414yes—
138C2×C4×Dic67C2311yescharacteristic
139C2×C4×Dic67C2311yescharacteristic
140C2×C4×Dic67C2314yes—
141#14523977C2314yes—
142#14523977C2314yes—
143#14523976C2314yes—
144#14523976C2314yes—
145#14523975C2314yes—
146#14523975C2314yes—
147#14523974C2314yes—
148#14523974C2314yes—
149Dic67⋊C8C2314yes—
150Dic67⋊C8C2314yes—
151Dic67⋊C8C2314yes—
152Dic67⋊C8C2314yes—
153#14523967C2314yes—
154#14523967C2314yes—
155#14523964C2314yes—
156#14523964C2314yes—
157C2×#41×C67—22no—
158C2×#41×C67—24no—
159C2×#41×C67Q818yescomplemented
160C2×#41×C67C2314yes—
161C22×Q8×C67C2311yescharacteristic
162C22×D4×C67—21no—
163C22×D4×C67C2311yescharacteristic
164C23×C4×C67—21no—
165C23×C4×C67C2311yescharacteristic
166C22×C8×C67—24no—
167C22×C8×C67C2311yescharacteristic
168C22×C8×C67C2311yescharacteristic
169C22×C8×C67C2314yes—
170#117×C67—22no—
171#117×C67C2314yes—
172C2×C4⋊C4×C67C2311yescharacteristic
173C2×C4⋊C4×C67C2311yescharacteristic
174C2×C22⋊C4×C67—21no—
175C2×C42×C67—21no—
176#103×C67C2314yes—
177#103×C67C2314yes—
178#102×C67C2314yes—
179#102×C67C2314yes—
180C2×Dic134—24no—
181C2×Dic134—24no—
182C2×Dic134—44no—
183C2×Dic134—44no—
184C22×Dic67—24no—
185C22×Dic67—21no—
186C22×Dic67—21no—
187C22×Dic67—21no—
188C22×Dic67—21no—
189C22×Dic67—24no—
190C22×Dic67—24no—
191C22×Dic67—42no—
192C22×Dic67—44no—
193C22×Dic67—44no—
194C22×Dic67C2×D411yescharacteristic
195C22×Dic67C2×D411yescharacteristic
196C22×Dic67C2×D411yescharacteristic
197C22×Dic67C2×D414yes—
198C22×Dic67C2×D414yes—
199C22×Dic67C2×D411yescharacteristic
200C2×C67⋊C8—22no—
201C2×C67⋊C8—22no—
202C2×C67⋊C8—28no—
203C2×C67⋊C8C2412yes—
204C2×C67⋊C8C2412yes—
205C4⋊Dic67—21no—
206C4⋊Dic67—21no—
207C4⋊Dic67—21no—
208C4⋊Dic67—21no—
209C4⋊Dic67—24no—
210C4⋊Dic67—24no—
211C4⋊Dic67—24no—
212C4⋊Dic67—24no—
213C4⋊Dic67C2412yes—
214C4⋊Dic67C2412yes—
215C4⋊Dic67C2412yes—
216C4⋊Dic67C2412yes—
217Dic67⋊C4—24no—
218Dic67⋊C4—24no—
219Dic67⋊C4—24no—
220Dic67⋊C4—24no—
221C22⋊Dic67—24no—
222C22⋊Dic67—24no—
223C22⋊Dic67—24no—
224C22⋊Dic67—24no—
225C4×Dic67—24no—
226C4×Dic67—24no—
227C4×Dic67—24no—
228C4×Dic67—24no—
229C4×Dic67C2×D414yes—
230C4×Dic67C2×D414yes—
231C4×Dic67C2×D412yes—
232C4×Dic67C2×D412yes—
233C4×Dic67C2412yes—
234C4×Dic67C2412yes—
235C24×C67—21no—
236C24×C67C2×D411yescharacteristic
237#41×C67—216no—
238#41×C67—28no—
239#41×C67C2×Q8116yescomplemented
240C2×Q8×C67—21no—
241C2×Q8×C67—22no—
242C2×Q8×C67C2×Q814yes—
243C2×Q8×C67C2412yes—
244C2×D4×C67—28no—
245C2×D4×C67—24no—
246C2×D4×C67—21no—
247C2×D4×C67—22no—
248C2×D4×C67C2×Q814yes—
249C2×D4×C67C2412yes—
250C22×C4×C67—21no—
251C22×C4×C67—28no—
252C22×C4×C67—24no—
253C22×C4×C67—21no—
254C22×C4×C67—21no—
255C22×C4×C67C2×D412yes—
256C22×C4×C67C2×D411yescharacteristic
257C22×C4×C67C2×Q814yes—
258C22×C4×C67#4114yes—
259C22×C4×C67C2411yescharacteristic
260C22×C4×C67C2412yes—
261C2×C8×C67—22no—
262C2×C8×C67—22no—
263C2×C8×C67—28no—
264C2×C8×C67C2412yes—
265C2×C8×C67C2412yes—
266C4⋊C4×C67—21no—
267C4⋊C4×C67—21no—
268C4⋊C4×C67C2412yes—
269C4⋊C4×C67C2412yes—
270C22⋊C4×C67—24no—
271C42×C67—24no—
272C23×C67—22no—
273C23×C67—22no—
274C23×C67—24no—
275C23×C67—22no—
276C23×C67—42no—
277C23×C67—42no—
278C23×C67C22⋊Q814yes—
279C23×C67C22×D412yes—
280C23×C67C22×D411yescharacteristic
281Q8×C67—24no—
282Q8×C67—22no—
283Q8×C67C22×Q814yes—
284D4×C67—216no—
285D4×C67—24no—
286D4×C67—22no—
287D4×C67C22×Q814yes—
288C2×C4×C67—24no—
289C2×C4×C67—22no—
290C2×C4×C67—216no—
291C2×C4×C67—22no—
292C2×C4×C67—22no—
293C2×C4×C67—42no—
294C2×C4×C67—42no—
295C2×C4×C67C22⋊Q814yes—
296C2×C4×C67C22⋊Q818yes—
297C2×C4×C67C22×D412yes—
298C2×C4×C67C22×D411yescharacteristic
299C2×C4×C67C22×Q812yes—
300C2×C4×C67C22×Q814yes—
301C2×C4×C67C2×#4112yes—
302C2×C4×C67C2×#4114yes—
303C2×C4×C67C2511yescharacteristic
304C2×Dic67—22no—
305C2×Dic67—22no—
306C2×Dic67—22no—
307C2×Dic67—28no—
308C2×Dic67—22no—
309C2×Dic67—22no—
310C2×Dic67—22no—
311C2×Dic67—22no—
312C2×Dic67—44no—
313C2×Dic67—48no—
314C2×Dic67—42no—
315C2×Dic67—42no—
316C2×Dic67—42no—
317C2×Dic67—42no—
318C2×Dic67—48no—
319C2×Dic67#13514yes—
320C2×Dic67C22×D412yes—
321C2×Dic67C22×D412yes—
322C2×Dic67C22×D412yes—
323C2×Dic67C22×D412yes—
324Dic134—48no—
325Dic134—48no—
326C8×C67—22no—
327C8×C67—22no—
328C67⋊C8—22no—
329C67⋊C8—22no—
330C22×C67—28no—
331C22×C67—22no—
332C22×C67—22no—
333C22×C67—24no—
334C22×C67—48no—
335C22×C67—42no—
336C22×C67—42no—
337C22×C67C2×C22⋊Q814yes—
338C22×C67C2×C22⋊Q812yes—
339C22×C67C2×#13512yes—
340C22×C67#57512yes—
341C22×C67C23×D411yescharacteristic
342C4×C67—24no—
343C4×C67—42no—
344C4×C67—42no—
345C4×C67C2×C22⋊Q814yes—
346C4×C67C2×C22⋊Q812yes—
347C4×C67C23×Q811yescharacteristic
348C4×C67C22×#4111yescharacteristic
349Dic67—22no—
350Dic67—22no—
351Dic67—22no—
352Dic67—42no—
353Dic67—42no—
354Dic67—42no—
355Dic67—42no—
356Dic67C2×#13514yes—
357C2×#3076—671nomaximal, Sylow
358C2×C67—24no—
359C2×C67—44no—
360C2×C67#307614yescomplemented
361C2×C67C22×C22⋊Q811yescharacteristic
362C2×C67C22×#13511yescharacteristic
363C2×C67C2×#57511yescharacteristic
364C2×#533—671no—
365C2×C4×#41—671no—
366#3076—6716no—
367C2×#479—671no—
368C2×#479—671no—
369C2×#477—671no—
370C2×#475—671no—
371C2×#478—671no—
372C2×#478—671no—
373C2×#476—671no—
374C2×#474—671no—
375C2×#427—671no—
376C2×#427—671no—
377C22×C4⋊C8—671no—
378C2×#416—671no—
379C2×#416D6711yescharacteristic
380C67C2×#307611yescharacteristic, complemented, Sylow
381C22×#41C2×D6711yescharacteristic
382C23×C8—671no—
383C23×C8C2×D6711yescharacteristic
384#533—678no—
385#533—1344no—
386C2×C4⋊Q8—671no—
387C2×C4⋊Q8—671no—
388C2×#125—671no—
389C2×#125—671no—
390C2×C22⋊Q8—1341no—
391C2×C22⋊Q8—1341no—
392C4×#41—678no—
393C4×#41—1344no—
394C2×C4×Q8—671no—
395C2×C4×Q8—671no—
396C2×C4×Q8—1341no—
397C2×C4×Q8—1341no—
398C2×C4×D4—671no—
399C2×C4×D4—671no—
400C2×C4×D4—1341no—
401C2×C4×D4—1341no—
402C2×#117—671no—
403C2×#117—671no—
404C2×#117—1341no—
405C2×#117C2×D6711yescharacteristic
406C22×C42—671no—
407C22×C42—1341no—
408#479—678no—
409#479—678no—
410#478—678no—
411#478—678no—
412#477—678no—
413#476—678no—
414#475—678no—
415#474—678no—
416#427—678no—
417#427—678no—
418C2×#107—671no—
419C2×#107—671no—
420C2×#107—671no—
421C2×#107—671no—
422C2×#106—671no—
423C2×#106—671no—
424C2×#106—671no—
425C2×#106—671no—
426C2×C4⋊C8—671no—
427C2×C4⋊C8—671no—
428C2×C4⋊C8—671no—
429C2×C4⋊C8—671no—
430C2×C4⋊C8—678no—
431#416—678no—
432#416C2×D6718yes—
433C2×#103—671no—
434C2×#103—671no—
435C2×#103C2×D6711yescharacteristic
436C2×#103C2×D6711yescharacteristic
437C2×#102—671no—
438C2×#102—671no—
439C2×#102C2×D6711yescharacteristic
440C2×#102C2×D6711yescharacteristic
441C2×#41—22no—
442C2×#41—24no—
443C2×#41Dic13418yescomplemented
444C2×#41C22×D6714yes—
445C22×Q8—1341no—
446C22×Q8—1341no—
447C22×Q8C22×D6711yescharacteristic
448C22×D4—21no—
449C22×D4C22×D6711yescharacteristic
450C23×C4—21no—
451C23×C4—671no—
452C23×C4—671no—
453C23×C4—1341no—
454C23×C4—1341no—
455C23×C4C22×D6711yescharacteristic
456C22×C8—24no—
457C22×C8—671no—
458C22×C8—671no—
459C22×C8—674no—
460C22×C8—1344no—
461C22×C8C22×D6711yescharacteristic
462C22×C8C22×D6711yescharacteristic
463C22×C8C22×D6714yes—
464C4⋊Q8—674no—
465C4⋊Q8—674no—
466C4⋊Q8—1342no—
467C4⋊Q8—1342no—
468#125—674no—
469#125—674no—
470#125—1342no—
471#125—1342no—
472C22⋊Q8—1348no—
473C22⋊Q8—1348no—
474C4×Q8—674no—
475C4×Q8—674no—
476C4×Q8—1348no—
477C4×Q8—1348no—
478C4×Q8—1342no—
479C4×Q8—1342no—
480C4×D4—674no—
481C4×D4—674no—
482C4×D4—1342no—
483C4×D4—1342no—
484C4×D4—1348no—
485C4×D4—1348no—
486#117—22no—
487#117—674no—
488#117—674no—
489#117—1348no—
490#117—1342no—
491#117—1342no—
492#117C22×D6714yes—
493C2×C4⋊C4—671no—
494C2×C4⋊C4—671no—
495C2×C4⋊C4—671no—
496C2×C4⋊C4—671no—
497C2×C4⋊C4—1341no—
498C2×C4⋊C4—1341no—
499C2×C4⋊C4—1341no—
500C2×C4⋊C4—1341no—
501C2×C4⋊C4—1341no—
502C2×C4⋊C4—1341no—
503C2×C4⋊C4—1341no—
504C2×C4⋊C4—1341no—
505C2×C4⋊C4C22×D6711yescharacteristic
506C2×C4⋊C4C22×D6711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1341no—
509C2×C22⋊C4—1341no—
510C2×C22⋊C4—1341no—
511C2×C22⋊C4—1341no—
512C2×C42—21no—
513C2×C42—674no—
514C2×C42—671no—
515C2×C42—671no—
516C2×C42—671no—
517C2×C42—671no—
518C2×C42—674no—
519C2×C42—1348no—
520C2×C42—1341no—
521C2×C42—1341no—
522C2×C42—1341no—
523C2×C42—1341no—
524#107—674no—
525#107—674no—
526#107—674no—
527#107—674no—
528#106—674no—
529#106—674no—
530#106—674no—
531#106—674no—
532C4⋊C8—674no—
533C4⋊C8—674no—
534C4⋊C8—674no—
535C4⋊C8—674no—
536#103—674no—
537#103—674no—
538#103C22×D6714yes—
539#103C22×D6714yes—
540#102—674no—
541#102—674no—
542#102C22×D6714yes—
543#102C22×D6714yes—
544C24—21no—
545C24D4×D6711yescharacteristic
546#41—216no—
547#41—28no—
548#41C2×Dic134116yescomplemented
549C2×Q8—21no—
550C2×Q8—22no—
551C2×Q8—2684no—
552C2×Q8—2684no—
553C2×Q8—1344no—
554C2×Q8—1344no—
555C2×Q8C2×Dic13414yes—
556C2×Q8C23×D6712yes—
557C2×D4—28no—
558C2×D4—24no—
559C2×D4—21no—
560C2×D4—22no—
561C2×D4C2×Dic13414yes—
562C2×D4C23×D6712yes—
563C22×C4—21no—
564C22×C4—28no—
565C22×C4—24no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—2684no—
569C22×C4—2684no—
570C22×C4—2682no—
571C22×C4—674no—
572C22×C4—671no—
573C22×C4—671no—
574C22×C4—671no—
575C22×C4—671no—
576C22×C4—674no—
577C22×C4—1344no—
578C22×C4—1344no—
579C22×C4—1341no—
580C22×C4—1341no—
581C22×C4—1341no—
582C22×C4—1341no—
583C22×C4—1344no—
584C22×C4D4×D6712yes—
585C22×C4D4×D6711yescharacteristic
586C22×C4C2×Dic13414yes—
587C22×C4#1176162714yes—
588C22×C4C23×D6711yescharacteristic
589C22×C4C23×D6712yes—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—28no—
593C2×C8—672no—
594C2×C8—672no—
595C2×C8—1342no—
596C2×C8—1342no—
597C2×C8—1348no—
598C2×C8C23×D6712yes—
599C2×C8C23×D6712yes—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—672no—
603C4⋊C4—672no—
604C4⋊C4—672no—
605C4⋊C4—672no—
606C4⋊C4—1344no—
607C4⋊C4—1344no—
608C4⋊C4—1344no—
609C4⋊C4—1344no—
610C4⋊C4—1344no—
611C4⋊C4—1344no—
612C4⋊C4—1344no—
613C4⋊C4—1344no—
614C4⋊C4—1341no—
615C4⋊C4—1341no—
616C4⋊C4—1341no—
617C4⋊C4—1341no—
618C4⋊C4C23×D6712yes—
619C4⋊C4C23×D6712yes—
620C22⋊C4—24no—
621C22⋊C4—1344no—
622C22⋊C4—1344no—
623C22⋊C4—1344no—
624C22⋊C4—1344no—
625C42—24no—
626C42—674no—
627C42—674no—
628C42—672no—
629C42—672no—
630C42—672no—
631C42—672no—
632C42—1344no—
633C42—1344no—
634C42—1344no—
635C42—1344no—
636C23—22no—
637C23—22no—
638C23—24no—
639C23—22no—
640C23—42no—
641C23—42no—
642C23#1452402014yes—
643C23C2×D4×D6712yes—
644C23C2×D4×D6711yescharacteristic
645Q8—24no—
646Q8—22no—
647Q8—2688no—
648Q8—2688no—
649Q8C22×Dic13414yes—
650D4—216no—
651D4—24no—
652D4—22no—
653D4C22×Dic13414yes—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—216no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—2682no—
662C2×C4—2682no—
663C2×C4—2682no—
664C2×C4—2682no—
665C2×C4—2688no—
666C2×C4—2688no—
667C2×C4—2684no—
668C2×C4—674no—
669C2×C4—672no—
670C2×C4—672no—
671C2×C4—672no—
672C2×C4—672no—
673C2×C4—1342no—
674C2×C4—1342no—
675C2×C4—1342no—
676C2×C4—1342no—
677C2×C4—1348no—
678C2×C4—1342no—
679C2×C4—1342no—
680C2×C4—1342no—
681C2×C4#1452402014yes—
682C2×C4#1452402018yes—
683C2×C4C2×D4×D6712yes—
684C2×C4C2×D4×D6711yescharacteristic
685C2×C4C22×Dic13412yes—
686C2×C4C22×Dic13414yes—
687C2×C4C2×#1176162712yes—
688C2×C4C2×#1176162714yes—
689C2×C4C24×D6711yescharacteristic
690C8—22no—
691C8—22no—
692C8—1342no—
693C8—1342no—
694C22—28no—
695C22—22no—
696C22—22no—
697C22—24no—
698C22—48no—
699C22—42no—
700C22—42no—
701C22C2×#1452402014yes—
702C22C2×#1452402012yes—
703C22#135×D6712yes—
704C22#1686419312yes—
705C22C22×D4×D6711yescharacteristic
706C4—24no—
707C4—42no—
708C4—42no—
709C4—2682no—
710C4—2682no—
711C4—2682no—
712C4—2682no—
713C4—674no—
714C4—1342no—
715C4—1342no—
716C4—1342no—
717C4C2×#1452402014yes—
718C4C2×#1452402012yes—
719C4C23×Dic13411yescharacteristic
720C4C22×#1176162711yescharacteristic
721C2—24no—
722C2—44no—
723C2#2256999314yesdirect product factor
724C2C22×#1452402011yescharacteristic
725C2C2×#135×D6711yescharacteristic
726C2C2×#1686419311yescharacteristic
subgroupG/H
centerC22×C4D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#416×C67C2
socleC23×C67C22×D4
prime radicalC22×#41×C67C22
hypercenterC2×#416D67
hypocenterC67C2×#3076
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#16863949C2semidirect
3. #22569993C2direct (N × H)
4. C2×#16863705C2semidirect
5. C2×#16863701C2semidirect
6. C2×#16863689C2semidirect
7. C2×#16863679C2semidirect
8. C2×#16863698C2semidirect
9. C2×#16863694C2semidirect
10. C2×#16863684C2semidirect
11. C2×#16863674C2semidirect
12. C2×#16863434C2semidirect
13. C2×#16863432C2semidirect
14. C22×Dic67⋊C8C2semidirect
19. #16863949C22semidirect
41. #16863705C22semidirect
42. #16863701C22semidirect
43. #16863698C22semidirect
44. #16863694C22semidirect
45. #16863689C22semidirect
46. #16863684C22semidirect
47. #16863679C22semidirect
48. #16863674C22semidirect
49. #16863434C22semidirect
50. #16863432C22semidirect
63. C2×Dic67⋊C8C22semidirect
159. C2×#41×C67Q8semidirect
239. #41×C67C2×Q8semidirect
360. C2×C67#3076semidirect
380. C67C2×#3076semidirect
443. C2×#41Dic134semidirect
548. #41C2×Dic134semidirect
723. C2#22569993direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168639492
C2×#41×Dic672
#225699932
C2×#168637052
C2×#168637012
C2×#168636892
C2×#168636792
C2×#168636982
C2×#168636942
C2×#168636842
C2×#168636742
C2×#168634342
C2×#168634322
C22×Dic67⋊C82
C2×#168633922
C2×#416×C672
C2×#307667