Finite Group Databasebeta

← C2×#22570564 #31725068

Subgroups — C2×#22570564 #31725068

Order 17152.

2262 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864026C211yesmaximal, characteristic, complemented
2C2×#16863959C211yesmaximal, characteristic
3#22570564C2116yesmaximal, direct product factor
4C2×#16863759C211yesmaximal, characteristic, complemented
5C2×#16863756C211yesmaximal, characteristic, complemented
6C2×#16863754C211yesmaximal, characteristic, complemented
7C2×#16863753C211yesmaximal, characteristic, complemented
8C2×#16863749C211yesmaximal, characteristic, complemented
9C2×#16863742C211yesmaximal, characteristic, complemented
10C2×#16863741C211yesmaximal, characteristic, complemented
11C2×#16863394C211yesmaximal, characteristic, complemented
12C2×#16863399C211yesmaximal, characteristic, complemented
13C2×#16863389C211yesmaximal, characteristic, complemented
14C2×#102×D67C211yesmaximal, characteristic, complemented
15C2×#16863353C211yesmaximal, characteristic, complemented
16C2×#490×C67C211yesmaximal, characteristic, complemented
17C22×#11761627C2211yescharacteristic
18C22×D4×D67C2211yescharacteristic
19C22×#11761611C2211yescharacteristic
20C22×C8×D67C2211yescharacteristic
21#16864026—24no—
22#16864026C2218yescomplemented
23#16863959—24no—
24#16863959C2218yes—
25C2×#14524043C2211yescharacteristic, complemented
26C2×#14524042—21no—
27C2×#14524042C2211yescharacteristic, complemented
28C2×#14524039C2211yescharacteristic
29C2×#14524034C2211yescharacteristic, complemented
30C2×#14524033—21no—
31C2×#14524031C2211yescharacteristic
32C2×#14524030C2211yescharacteristic
33C2×#14524023—21no—
34C2×#14524021—21no—
35C2×#14524015—21no—
36C2×#14524015—21no—
37C2×#14524011—21no—
38C2×#14524011—21no—
39C2×#14524001C2211yescharacteristic
40C2×#14524000C2211yescharacteristic
41C2×C4⋊C4×D67C2211yescharacteristic
42#16863759C2218yescomplemented
43#16863756C2218yescomplemented
44#16863754C2218yescomplemented
45#16863753C2218yescomplemented
46#16863749C2218yescomplemented
47#16863742C2218yescomplemented
48#16863741C2218yescomplemented
49#16863399C2218yescomplemented
50#16863394C2218yescomplemented
51#16863389C2218yescomplemented
52C2×#14523968C2211yescharacteristic, complemented
53C2×#14523968C2211yescharacteristic, complemented
54C2×#14523966C2211yescharacteristic, complemented
55C2×#14523966C2211yescharacteristic, complemented
56C2×#14523965C2211yescharacteristic
57C2×#14523965C2211yescharacteristic
58C2×#14523964C2211yescharacteristic
59C2×#14523964C2211yescharacteristic
60C2×#14523964C2211yescharacteristic, complemented
61C2×#14523964C2211yescharacteristic, complemented
62C2×#14523963C2211yescharacteristic
63C2×#14523963C2211yescharacteristic
64#102×D67C2218yescomplemented
65#16863353C2218yescomplemented
66C2×#14523953C2211yescharacteristic, complemented
67C2×C4×C67⋊C8C2211yescharacteristic, complemented
68C2×C8×Dic67C2211yescharacteristic, complemented
69C2×#127×C67C2211yescharacteristic
70C2×#125×C67C2211yescharacteristic, complemented
71#490×C67C2218yescomplemented
72C2×#102×C67C2211yescharacteristic
73C2×#102×C67C2211yescharacteristic
74C2×#102×C67C2211yescharacteristic, complemented
75C2×#102×C67C2211yescharacteristic, complemented
76C2×#97×C67C2211yescharacteristic, complemented
77C24×D67—21no—
78C2×#11761627—22no—
79C2×#11761627—24no—
80C2×#11761627—24no—
81C2×#11761627C2314yes—
82C22×Dic134—21no—
83C22×Dic134—21no—
84C22×Dic134C2311yescharacteristic
85C22×D268C2311yescharacteristic
86C22×C22⋊D67—21no—
87C22×C22⋊D67—21no—
88C22×C22⋊D67—21no—
89C22×C22⋊D67—21no—
90C2×D4×D67—22no—
91C2×D4×D67—24no—
92C2×D4×D67—24no—
93C2×D4×D67C2314yes—
94C23×Dic67—21no—
95C22×C4×D67—21no—
96C22×C4×D67C2311yescharacteristic
97C2×#11761611—24no—
98C2×#11761611C2314yes—
99C22×C67⋊C8C2311yescharacteristic
100C22×C67⋊C8C2311yescharacteristic
101C2×C8×D67—24no—
102C2×C8×D67C2314yes—
103#14524043—22no—
104#14524043C2314yescomplemented
105#14524042—28no—
106#14524042—22no—
107#14524042C2314yescomplemented
108#14524039—22no—
109#14524039C2314yes—
110#14524034—22no—
111#14524034C2314yescomplemented
112#14524033—28no—
113#14524031—22no—
114#14524031C2314yes—
115#14524030—22no—
116#14524030C2314yes—
117#14524023—28no—
118#14524021—28no—
119#14524015—28no—
120#14524015—28no—
121#14524011—28no—
122#14524011—28no—
123#14524001—22no—
124#14524001C2314yes—
125#14524000D414yes—
126#14524000C2314yes—
127C2×C4⋊Dic67—21no—
128C2×C4⋊Dic67—21no—
129C2×C4⋊Dic67C2311yescharacteristic
130C2×C4⋊Dic67C2311yescharacteristic
131C2×Dic67⋊C4—21no—
132C2×Dic67⋊C4—21no—
133C2×Dic67⋊C4—21no—
134C2×Dic67⋊C4D411yescharacteristic
135C2×Dic67⋊C4D411yescharacteristic
136C4⋊C4×D67—22no—
137C4⋊C4×D67C2314yes—
138C2×C22⋊Dic67—21no—
139C2×C22⋊Dic67—21no—
140C2×(C2×D67)⋊C4—21no—
141C2×(C2×D67)⋊C4—21no—
142C2×(C2×D67)⋊C4—21no—
143C2×(C2×D67)⋊C4D411yescharacteristic
144C2×(C2×D67)⋊C4D411yescharacteristic
145C2×C4×Dic67—21no—
146C2×C4×Dic67C2311yescharacteristic
147#14523968C2314yescomplemented
148#14523968C2314yescomplemented
149#14523966C2314yescomplemented
150#14523966C2314yescomplemented
151#14523965C2314yes—
152#14523965C2314yes—
153#14523964C2314yes—
154#14523964C2314yes—
155#14523964C2314yescomplemented
156#14523964C2314yescomplemented
157#14523963C2314yes—
158#14523963C2314yes—
159#14523953C2314yescomplemented
160C4×C67⋊C8C2314yescomplemented
161C8×Dic67C2314yescomplemented
162C22×D4×C67—21no—
163C22×D4×C67—21no—
164C22×D4×C67C2311yescharacteristic
165C22×D4×C67C2311yescharacteristic
166C22×C8×C67C2311yescharacteristic
167C22×C8×C67C2311yescharacteristic
168#127×C67—22no—
169#127×C67C2314yes—
170#125×C67—22no—
171#125×C67C2314yescomplemented
172C2×C4⋊C4×C67—21no—
173C2×C4⋊C4×C67—21no—
174C2×C4⋊C4×C67C2311yescharacteristic
175C2×C4⋊C4×C67C2311yescharacteristic
176C2×C42×C67C2311yescharacteristic
177#102×C67C2314yes—
178#102×C67C2314yes—
179#102×C67C2314yescomplemented
180#102×C67C2314yescomplemented
181#97×C67C2314yescomplemented
182C23×D67—21no—
183C23×D67—24no—
184C23×D67—44no—
185C23×D67—82no—
186C23×D67—82no—
187C23×D67C2×D411yescharacteristic
188#11761627—28no—
189#11761627—28no—
190#11761627—48no—
191C2×Dic134—22no—
192C2×Dic134—22no—
193C2×Dic134—21no—
194C2×Dic134—24no—
195C2×Dic134—24no—
196C2×Dic134—82no—
197C2×Dic134—82no—
198C2×Dic134C2412yes—
199C2×D268—22no—
200C2×D268—22no—
201C2×D268—21no—
202C2×D268C2412yes—
203C2×C22⋊D67—24no—
204C2×C22⋊D67—24no—
205C2×C22⋊D67—24no—
206C2×C22⋊D67—24no—
207C2×C22⋊D67—44no—
208C2×C22⋊D67—44no—
209C2×C22⋊D67—82no—
210C2×C22⋊D67—82no—
211D4×D67—28no—
212D4×D67—28no—
213D4×D67—48no—
214C22×Dic67—21no—
215C22×Dic67—21no—
216C22×Dic67—21no—
217C22×Dic67—24no—
218C22×Dic67—44no—
219C22×Dic67C2×D411yescharacteristic
220C22×Dic67C2×D411yescharacteristic
221C22×Dic67C2×D411yescharacteristic
222C2×C4×D67—24no—
223C2×C4×D67—82no—
224C2×C4×D67C2×D412yes—
225C2×C4×D67#4114yes—
226C2×C4×D67#4114yes—
227C2×C4×D67C2412yes—
228#11761611—28no—
229C2×C67⋊C8—22no—
230C2×C67⋊C8—22no—
231C2×C67⋊C8C2412yes—
232C2×C67⋊C8C2412yes—
233C8×D67—28no—
234C4⋊Dic67—21no—
235C4⋊Dic67—24no—
236C4⋊Dic67—21no—
237C4⋊Dic67—24no—
238C4⋊Dic67C2412yes—
239C4⋊Dic67C2412yes—
240Dic67⋊C4—24no—
241Dic67⋊C4—24no—
242Dic67⋊C4—24no—
243Dic67⋊C4C2×D414yes—
244Dic67⋊C4C2×D414yes—
245C22⋊Dic67—24no—
246C22⋊Dic67—24no—
247(C2×D67)⋊C4—24no—
248(C2×D67)⋊C4—24no—
249(C2×D67)⋊C4—24no—
250(C2×D67)⋊C4C2×D414yes—
251(C2×D67)⋊C4C2×D414yes—
252C4×Dic67—24no—
253C4×Dic67C2×D412yes—
254C4×Dic67C2412yes—
255C24×C67—21no—
256C24×C67—21no—
257C2×D4×C67—21no—
258C2×D4×C67—21no—
259C2×D4×C67—24no—
260C2×D4×C67—24no—
261C2×D4×C67—22no—
262C2×D4×C67—22no—
263C2×D4×C67—22no—
264C2×D4×C67—22no—
265C2×D4×C67—82no—
266C2×D4×C67—82no—
267C2×D4×C67C2412yes—
268C2×D4×C67C2412yes—
269C22×C4×C67—21no—
270C22×C4×C67—21no—
271C22×C4×C67C2×D411yescharacteristic
272C22×C4×C67C2×D411yescharacteristic
273C22×C4×C67C2411yescharacteristic
274C2×C8×C67—22no—
275C2×C8×C67—22no—
276C2×C8×C67C2412yes—
277C2×C8×C67C2412yes—
278C4⋊C4×C67—24no—
279C4⋊C4×C67—24no—
280C4⋊C4×C67—21no—
281C4⋊C4×C67—21no—
282C4⋊C4×C67C2412yes—
283C4⋊C4×C67C2412yes—
284C42×C67C2×D412yes—
285C42×C67C2412yes—
286C23×C67—22no—
287C23×C67—22no—
288C23×C67—42no—
289C23×C67—42no—
290C23×C67—42no—
291C23×C67—42no—
292C23×C67—42no—
293C23×C67—42no—
294C23×C67C22×D411yescharacteristic
295C22×D67—22no—
296C22×D67—22no—
297C22×D67—22no—
298C22×D67—42no—
299C22×D67—42no—
300C22×D67—42no—
301C22×D67—48no—
302C22×D67—84no—
303C22×D67—84no—
304C22×D67—816no—
305C22×D67#12414yes—
306C22×D67C22×D412yes—
307D4×C67—22no—
308D4×C67—22no—
309D4×C67—22no—
310D4×C67—22no—
311D4×C67—42no—
312D4×C67—42no—
313D4×C67—84no—
314D4×C67—84no—
315C2×C4×C67—22no—
316C2×C4×C67—22no—
317C2×C4×C67—22no—
318C2×C4×C67—22no—
319C2×C4×C67—42no—
320C2×C4×C67—42no—
321C2×C4×C67C22×D412yes—
322C2×C4×C67C22×D412yes—
323C2×C4×C67C22×D411yescharacteristic
324C2×C4×C67C2×#4112yes—
325C2×C4×C67C2×#4112yes—
326C2×C4×C67C2511yescharacteristic
327C22⋊D67—48no—
328C22⋊D67—48no—
329C22⋊D67—84no—
330C22⋊D67—84no—
331C2×Dic67—22no—
332C2×Dic67—22no—
333C2×Dic67—22no—
334C2×Dic67—22no—
335C2×Dic67—22no—
336C2×Dic67—42no—
337C2×Dic67—42no—
338C2×Dic67—42no—
339C2×Dic67—48no—
340C2×Dic67#12414yes—
341C2×Dic67C22×D412yes—
342C2×Dic67C22×D412yes—
343C2×Dic67C22×D412yes—
344D268—22no—
345D268—22no—
346D268—42no—
347C4×D67—84no—
348C4×D67#12418yes—
349C4×D67C2×#4114yes—
350C4×D67C2×#4114yes—
351Dic134—22no—
352Dic134—22no—
353Dic134—42no—
354Dic134—84no—
355Dic134—84no—
356C8×C67—22no—
357C8×C67—22no—
358C67⋊C8—22no—
359C67⋊C8—22no—
360C22×C67—42no—
361C22×C67—42no—
362C22×C67—42no—
363C22×C67—42no—
364C22×C67—42no—
365C22×C67—42no—
366C22×C67—84no—
367C22×C67—84no—
368C22×C67C2×#12412yes—
369C22×C67#57612yes—
370C22×C67#57712yes—
371C22×C67C23×D411yescharacteristic
372C2×D67—28no—
373C2×D67—22no—
374C2×D67—22no—
375C2×D67—42no—
376C2×D67—42no—
377C2×D67—42no—
378C2×D67—816no—
379C2×D67—84no—
380C2×D67C2×#12414yes—
381C4×C67—22no—
382C4×C67—22no—
383C4×C67—42no—
384C4×C67—42no—
385C4×C67C2×#12412yes—
386C4×C67C22×#4111yescharacteristic
387C4×C67C22×#4111yescharacteristic
388Dic67—22no—
389Dic67—22no—
390Dic67—42no—
391Dic67—42no—
392Dic67—42no—
393Dic67C2×#12414yes—
394C2×#3136—671nomaximal, Sylow
395C2×C67—82no—
396C2×C67—82no—
397C2×C67#313614yescomplemented
398C2×C67C22×#12411yescharacteristic
399C2×C67C2×#57611yescharacteristic
400C2×C67C2×#57711yescharacteristic
401D67—24no—
402D67—82no—
403C2×#544—671no—
404C2×#535—671no—
405#3136—6716no—
406C2×#490—671no—
407C2×#490D6711yescharacteristic, complemented
408C2×#489—671no—
409C2×#489—671no—
410C2×#488—671no—
411C2×#488—671no—
412C2×#486—671no—
413C2×#486—671no—
414C2×#417—671no—
415C2×#418—671no—
416C2×#416—671no—
417C22×#102—671no—
418C2×#405—671no—
419C67C2×#313611yescharacteristic, complemented, Sylow
420C22×#41—671no—
421C23×D4—671no—
422C22×M16—671no—
423C23×C8—671no—
424#544—678no—
425#544—1344no—
426#535—678no—
427#535—1344no—
428C2×C4⋊Q8—671no—
429C2×C4⋊Q8—671no—
430C2×C4⋊Q8—1341no—
431C2×#127—671no—
432C2×#127C2×D6711yescharacteristic
433C2×#125—671no—
434C2×#125—1341no—
435C2×#125C2×D6711yescharacteristic, complemented
436C2×#124—671no—
437C2×#124—671no—
438C2×C22⋊Q8—1341no—
439C2×C22⋊Q8—1341no—
440C2×#121—1341no—
441C2×#121—1341no—
442C2×#120—1341no—
443C2×#120—1341no—
444C2×#117—671no—
445C2×#117—671no—
446C22×C4⋊C4—671no—
447#490—678no—
448#490C2×D6718yescomplemented
449#489—678no—
450#489—678no—
451#488—678no—
452#488—678no—
453#486—678no—
454#486—678no—
455#418—678no—
456#417—678no—
457#416—678no—
458C2×#103—671no—
459C2×#103—671no—
460C2×#103—671no—
461C2×#103—671no—
462C2×#102—671no—
463C2×#102—671no—
464C2×#102—671no—
465C2×#102—671no—
466C2×#102—671no—
467C2×#102—671no—
468C2×#102—671no—
469C2×#102—671no—
470C2×#102—678no—
471C2×#102C2×D6711yescharacteristic
472C2×#102C2×D6711yescharacteristic
473C2×#102C2×D6711yescharacteristic, complemented
474C2×#102C2×D6711yescharacteristic, complemented
475#405—678no—
476C2×#97—671no—
477C2×#97C2×D6711yescharacteristic, complemented
478C2×C4×C8—671no—
479C2×C4×C8—671no—
480C25—1341no—
481C2×#41—674no—
482C2×#41—1344no—
483C2×#41—1344no—
484C2×#41—1342no—
485C22×Q8—671no—
486C22×Q8—1341no—
487C22×Q8—1341no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—674no—
491C22×D4—671no—
492C22×D4—1342no—
493C22×D4—1344no—
494C22×D4—1344no—
495C22×D4—1341no—
496C22×D4—1341no—
497C22×D4—1341no—
498C22×D4—1341no—
499C22×D4C22×D6711yescharacteristic
500C22×D4C22×D6711yescharacteristic
501C23×C4—671no—
502C23×C4—1341no—
503C23×C4—1341no—
504C2×M16—674no—
505C2×M16—1344no—
506C22×C8—671no—
507C22×C8—671no—
508C22×C8—674no—
509C22×C8—1344no—
510C22×C8C22×D6711yescharacteristic
511C22×C8C22×D6711yescharacteristic
512C4⋊Q8—674no—
513C4⋊Q8—674no—
514C4⋊Q8—1342no—
515C4⋊Q8—1348no—
516C4⋊Q8—1342no—
517#127—22no—
518#127—674no—
519#127—1342no—
520#127C22×D6714yes—
521#125—22no—
522#125—674no—
523#125—1342no—
524#125—1348no—
525#125C22×D6714yescomplemented
526#124—674no—
527#124—674no—
528#124—1342no—
529#124—1342no—
530C22⋊Q8—1348no—
531C22⋊Q8—1348no—
532#121—1348no—
533#121—1348no—
534#120—1348no—
535#120—1348no—
536#117—674no—
537#117—674no—
538#117—674no—
539#117—1342no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—671no—
543C2×C4⋊C4—671no—
544C2×C4⋊C4—671no—
545C2×C4⋊C4—671no—
546C2×C4⋊C4—674no—
547C2×C4⋊C4—1342no—
548C2×C4⋊C4—1341no—
549C2×C4⋊C4—1341no—
550C2×C4⋊C4—1341no—
551C2×C4⋊C4—1341no—
552C2×C4⋊C4—1341no—
553C2×C4⋊C4C22×D6711yescharacteristic
554C2×C4⋊C4C22×D6711yescharacteristic
555C2×C22⋊C4—671no—
556C2×C22⋊C4—671no—
557C2×C22⋊C4—1341no—
558C2×C22⋊C4—1341no—
559C2×C22⋊C4—1341no—
560C2×C22⋊C4—1341no—
561C2×C22⋊C4—1341no—
562C2×C42—671no—
563C2×C42—1341no—
564C2×C42C22×D6711yescharacteristic
565#103—674no—
566#103—674no—
567#103—674no—
568#103—674no—
569#102—674no—
570#102—674no—
571#102—674no—
572#102—674no—
573#102—674no—
574#102—674no—
575#102—674no—
576#102—674no—
577#102C22×D6714yes—
578#102C22×D6714yes—
579#102C22×D6714yescomplemented
580#102C22×D6714yescomplemented
581#97—674no—
582#97C22×D6714yescomplemented
583C4×C8—674no—
584C4×C8—674no—
585C24—21no—
586C24—21no—
587C24—2684no—
588C24—5362no—
589C24—5362no—
590C24—671no—
591C24—1344no—
592C24—1341no—
593#41—2688no—
594#41—1348no—
595#41—1348no—
596C2×Q8—5362no—
597C2×Q8—5362no—
598C2×Q8—672no—
599C2×Q8—1344no—
600C2×Q8—1342no—
601C2×Q8—1342no—
602C2×Q8—1341no—
603C2×Q8—1344no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—24no—
607C2×D4—24no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—82no—
613C2×D4—82no—
614C2×D4—2684no—
615C2×D4—2688no—
616C2×D4—2684no—
617C2×D4—5362no—
618C2×D4—5362no—
619C2×D4—672no—
620C2×D4—1348no—
621C2×D4—1348no—
622C2×D4—1344no—
623C2×D4—1344no—
624C2×D4—1344no—
625C2×D4—1344no—
626C2×D4—1341no—
627C2×D4—1342no—
628C2×D4—1342no—
629C2×D4C23×D6712yes—
630C2×D4C23×D6712yes—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—2684no—
634C22×C4—5362no—
635C22×C4—671no—
636C22×C4—672no—
637C22×C4—674no—
638C22×C4—674no—
639C22×C4—672no—
640C22×C4—671no—
641C22×C4—671no—
642C22×C4—1344no—
643C22×C4—1344no—
644C22×C4—1341no—
645C22×C4—1341no—
646C22×C4—1341no—
647C22×C4D4×D6711yescharacteristic
648C22×C4D4×D6711yescharacteristic
649C22×C4C23×D6711yescharacteristic
650M16—1348no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—672no—
654C2×C8—672no—
655C2×C8—1348no—
656C2×C8—1342no—
657C2×C8—1342no—
658C2×C8C23×D6712yes—
659C2×C8C23×D6712yes—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—674no—
665C4⋊C4—674no—
666C4⋊C4—672no—
667C4⋊C4—672no—
668C4⋊C4—1344no—
669C4⋊C4—1344no—
670C4⋊C4—1344no—
671C4⋊C4—1344no—
672C4⋊C4—1341no—
673C4⋊C4—1341no—
674C4⋊C4—1344no—
675C4⋊C4C23×D6712yes—
676C4⋊C4C23×D6712yes—
677C22⋊C4—674no—
678C22⋊C4—674no—
679C22⋊C4—1344no—
680C22⋊C4—1344no—
681C22⋊C4—1344no—
682C22⋊C4—1344no—
683C22⋊C4—1344no—
684C42—672no—
685C42—672no—
686C42—1344no—
687C42D4×D6712yes—
688C42C23×D6712yes—
689C23—22no—
690C23—22no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—2688no—
698C23—2682no—
699C23—2682no—
700C23—2682no—
701C23—5364no—
702C23—5364no—
703C23—53616no—
704C23—674no—
705C23—672no—
706C23—1342no—
707C23—1342no—
708C23—1342no—
709C23C2×D4×D6711yescharacteristic
710Q8—2682no—
711Q8—5364no—
712Q8—5364no—
713Q8—1342no—
714Q8—1342no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—42no—
720D4—42no—
721D4—84no—
722D4—84no—
723D4—2688no—
724D4—2688no—
725D4—2682no—
726D4—5364no—
727D4—5364no—
728D4—1342no—
729D4—1342no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—2682no—
737C2×C4—2682no—
738C2×C4—2682no—
739C2×C4—2688no—
740C2×C4—5364no—
741C2×C4—674no—
742C2×C4—672no—
743C2×C4—678no—
744C2×C4—674no—
745C2×C4—674no—
746C2×C4—672no—
747C2×C4—672no—
748C2×C4—1342no—
749C2×C4—1342no—
750C2×C4—1342no—
751C2×C4—1342no—
752C2×C4—1342no—
753C2×C4C2×D4×D6712yes—
754C2×C4C2×D4×D6712yes—
755C2×C4C2×D4×D6711yescharacteristic
756C2×C4#41×D6712yes—
757C2×C4#41×D6712yes—
758C2×C4C24×D6711yescharacteristic
759C8—22no—
760C8—22no—
761C8—1342no—
762C8—1342no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—84no—
770C22—84no—
771C22—2682no—
772C22—2682no—
773C22—2682no—
774C22—53616no—
775C22—5364no—
776C22—674no—
777C22—1348no—
778C22—1342no—
779C22—1342no—
780C22#124×D6712yes—
781C22#1686420012yes—
782C22#1686420612yes—
783C22C22×D4×D6711yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—2682no—
789C4—2682no—
790C4—2682no—
791C4—674no—
792C4—1342no—
793C4—1342no—
794C4#124×D6712yes—
795C4C2×#41×D6711yescharacteristic
796C4C2×#41×D6711yescharacteristic
797C2—82no—
798C2—82no—
799C2—5362no—
800C2—1344no—
801C2#2257056414yesdirect product factor
802C2C2×#124×D6711yescharacteristic
803C2C2×#1686420011yescharacteristic
804C2C2×#1686420611yescharacteristic
subgroupG/H
centerC23C2×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#490×C67C2
socleC23×C67C22×D4
prime radicalC2×#16863959C2
hypercenterC2×#490D67
hypocenterC67C2×#3136
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. C2×#16864026C2semidirect
3. #22570564C2direct (N × H)
4. C2×#16863759C2semidirect
5. C2×#16863756C2semidirect
6. C2×#16863754C2semidirect
7. C2×#16863753C2semidirect
8. C2×#16863749C2semidirect
9. C2×#16863742C2semidirect
10. C2×#16863741C2semidirect
11. C2×#16863394C2semidirect
12. C2×#16863399C2semidirect
13. C2×#16863389C2semidirect
14. C2×#102×D67C2semidirect
15. C2×#16863353C2semidirect
16. C2×#490×C67C2semidirect
22. #16864026C22semidirect
25. C2×#14524043C22semidirect
27. C2×#14524042C22semidirect
29. C2×#14524034C22semidirect
42. #16863759C22semidirect
43. #16863756C22semidirect
44. #16863754C22semidirect
45. #16863753C22semidirect
46. #16863749C22semidirect
47. #16863742C22semidirect
48. #16863741C22semidirect
49. #16863399C22semidirect
50. #16863394C22semidirect
51. #16863389C22semidirect
52. C2×#14523968C22semidirect
53. C2×#14523968C22semidirect
54. C2×#14523966C22semidirect
55. C2×#14523966C22semidirect
60. C2×#14523964C22semidirect
61. C2×#14523964C22semidirect
64. #102×D67C22semidirect
65. #16863353C22semidirect
66. C2×#14523953C22semidirect
67. C2×C4×C67⋊C8C22semidirect
68. C2×C8×Dic67C22semidirect
70. C2×#125×C67C22semidirect
71. #490×C67C22semidirect
74. C2×#102×C67C22semidirect
75. C2×#102×C67C22semidirect
76. C2×#97×C67C22semidirect
104. #14524043C23semidirect
107. #14524042C23semidirect
111. #14524034C23semidirect
147. #14523968C23semidirect
148. #14523968C23semidirect
149. #14523966C23semidirect
150. #14523966C23semidirect
155. #14523964C23semidirect
156. #14523964C23semidirect
159. #14523953C23semidirect
160. C4×C67⋊C8C23semidirect
161. C8×Dic67C23semidirect
171. #125×C67C23semidirect
179. #102×C67C23semidirect
180. #102×C67C23semidirect
181. #97×C67C23semidirect
397. C2×C67#3136semidirect
407. C2×#490D67semidirect
419. C67C2×#3136semidirect
435. C2×#125C2×D67semidirect
448. #490C2×D67semidirect
473. C2×#102C2×D67semidirect
474. C2×#102C2×D67semidirect
477. C2×#97C2×D67semidirect
525. #125C22×D67semidirect
579. #102C22×D67semidirect
580. #102C22×D67semidirect
582. #97C22×D67semidirect
801. C2#22570564direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640262
C2×#168639592
#225705642
C2×#168637592
C2×#168637562
C2×#168637542
C2×#168637532
C2×#168637492
C2×#168637422
C2×#168637412
C2×#168633942
C2×#168633992
C2×#168633892
C2×#102×D672
C2×#168633532
C2×#490×C672
C2×#313667