Finite Group Databasebeta

← C2×#22573131 #31736333

Subgroups — C2×#22573131 #31736333

Order 17152.

2006 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864122C211yesmaximal, characteristic, complemented
2C2×D4×Dic134C211yesmaximal, characteristic
3#22573131C2116yesmaximal, direct product factor
4C2×#16863805C211yesmaximal, characteristic, complemented
5C2×#16863804C211yesmaximal, characteristic, complemented
6C2×#16863800C211yesmaximal, characteristic, complemented
7C2×#16863691C211yesmaximal, characteristic, complemented
8C2×#16863689C211yesmaximal, characteristic, complemented
9C2×#16863679C211yesmaximal, characteristic, complemented
10C2×#16863698C211yesmaximal, characteristic
11C2×#16863696C211yesmaximal, characteristic
12C2×#16863674C211yesmaximal, characteristic
13C2×#16863524C211yesmaximal, characteristic, complemented
14C2×#16863497C211yesmaximal, characteristic
15C2×SD16×Dic67C211yesmaximal, characteristic
16C2×#440×C67C211yesmaximal, characteristic
17C23×Dic134—21no—
18#16864122—24no—
19#16864122C2218yescomplemented
20D4×Dic134—24no—
21D4×Dic134C2218yes—
22C2×#14524043C2211yescharacteristic
23C2×#14524042—21no—
24C2×#14524042C2211yescharacteristic
25C2×#14524042C2211yescharacteristic
26C2×#14524042C2211yescharacteristic
27C2×#14524035—21no—
28C2×#14524035C2211yescharacteristic
29C2×#14524034—21no—
30C2×#14524034C2211yescharacteristic
31C2×#14524022—21no—
32C2×#14524020—21no—
33C2×#14524020—21no—
34C2×Q8×Dic67C2211yescharacteristic
35C2×Q8×Dic67C2211yescharacteristic
36C2×C4×Dic134—21no—
37C2×C4×Dic134C2211yescharacteristic
38C2×D4×Dic67C2211yescharacteristic
39C2×D4×Dic67C2211yescharacteristic
40#16863805C2218yescomplemented
41#16863804C2218yescomplemented
42#16863800C2218yescomplemented
43#16863698C2218yes—
44#16863696C2218yes—
45#16863691C2218yescomplemented
46#16863689C2218yescomplemented
47#16863679C2218yescomplemented
48#16863674C2218yes—
49#16863524C2218yescomplemented
50#16863497C2218yes—
51SD16×Dic67C2218yes—
52C2×#14523977C2211yescharacteristic
53C2×#14523977C2211yescharacteristic
54C2×#14523976C2211yescharacteristic
55C2×#14523976C2211yescharacteristic
56C2×#14523976C2211yescharacteristic
57C2×#14523975C2211yescharacteristic
58C2×#14523975C2211yescharacteristic
59C2×#14523974C2211yescharacteristic
60C2×C4⋊(C67⋊C8)C2211yescharacteristic
61C2×Dic67⋊C8C2211yescharacteristic
62C2×Dic67⋊C8C2211yescharacteristic
63C2×#14523967C2211yescharacteristic
64C2×#14523967C2211yescharacteristic
65C2×#14523964C2211yescharacteristic
66C2×#14523964C2211yescharacteristic
67C2×#14523953C2211yescharacteristic
68C2×C8×Dic67C2211yescharacteristic
69C22×SD16×C67C2211yescharacteristic
70C2×C4×Q8×C67C2211yescharacteristic
71C2×C4×D4×C67C2211yescharacteristic
72#440×C67C2218yes—
73C2×#107×C67C2211yescharacteristic
74C2×#103×C67C2211yescharacteristic
75C2×#102×C67C2211yescharacteristic
76C2×#97×C67C2211yescharacteristic
77C22×Dic134—28no—
78C22×Dic134—21no—
79C22×Dic134—21no—
80C22×Dic134—21no—
81C22×Dic134—21no—
82C22×Dic134—48no—
83C22×Dic134D411yescharacteristic
84C23×Dic67—21no—
85C23×Dic67—21no—
86C22×C67⋊C8C2311yescharacteristic
87C22×C67⋊C8C2311yescharacteristic
88#14524043—22no—
89#14524043C2314yes—
90#14524042—28no—
91#14524042—22no—
92#14524042—22no—
93#14524042—22no—
94#14524042C2314yes—
95#14524042C2314yes—
96#14524042C2314yes—
97#14524035—28no—
98#14524035—22no—
99#14524035C2314yes—
100#14524034—28no—
101#14524034—22no—
102#14524034C2314yes—
103#14524022—28no—
104#14524020—28no—
105#14524020—28no—
106Q8×Dic67—22no—
107Q8×Dic67—22no—
108Q8×Dic67C2314yes—
109Q8×Dic67C2314yes—
110C4×Dic134—28no—
111C4×Dic134D414yes—
112C4×Dic134C2314yes—
113D4×Dic67—22no—
114D4×Dic67—22no—
115D4×Dic67C2314yes—
116D4×Dic67C2314yes—
117C2×C4⋊Dic67—21no—
118C2×C4⋊Dic67—21no—
119C2×C4⋊Dic67—21no—
120C2×C4⋊Dic67—21no—
121C2×C4⋊Dic67D411yescharacteristic
122C2×C4⋊Dic67C2311yescharacteristic
123C2×C4⋊Dic67C2311yescharacteristic
124C2×C4⋊Dic67C2311yescharacteristic
125C2×C4⋊Dic67C2311yescharacteristic
126C2×Dic67⋊C4—21no—
127C2×Dic67⋊C4—21no—
128C2×Dic67⋊C4—21no—
129C2×Dic67⋊C4—21no—
130C2×Dic67⋊C4—21no—
131C2×Dic67⋊C4—21no—
132C2×Dic67⋊C4D411yescharacteristic
133C2×Dic67⋊C4D411yescharacteristic
134C2×C22⋊Dic67—21no—
135C2×C22⋊Dic67—21no—
136C2×C4×Dic67—21no—
137C2×C4×Dic67—21no—
138C2×C4×Dic67C2311yescharacteristic
139C2×C4×Dic67C2311yescharacteristic
140#14523977C2314yes—
141#14523977C2314yes—
142#14523976C2314yes—
143#14523976C2314yes—
144#14523976C2314yes—
145#14523975C2314yes—
146#14523975C2314yes—
147#14523974C2314yes—
148C4⋊(C67⋊C8)C2314yes—
149Dic67⋊C8C2314yes—
150Dic67⋊C8C2314yes—
151#14523967C2314yes—
152#14523967C2314yes—
153#14523964C2314yes—
154#14523964C2314yes—
155#14523953C2314yes—
156C8×Dic67C2314yes—
157C22×Q8×C67C2311yescharacteristic
158C22×D4×C67C2311yescharacteristic
159C23×C4×C67—21no—
160C2×SD16×C67Q818yescomplemented
161C2×SD16×C67C2314yes—
162C22×C8×C67C2311yescharacteristic
163C22×C8×C67C2311yescharacteristic
164C4×Q8×C67—22no—
165C4×Q8×C67C2314yes—
166C4×D4×C67—22no—
167C4×D4×C67C2314yes—
168C2×C4⋊C4×C67—21no—
169C2×C4⋊C4×C67C2311yescharacteristic
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C22⋊C4×C67—21no—
172C2×C42×C67—21no—
173C2×C42×C67C2311yescharacteristic
174#107×C67C2314yes—
175#103×C67C2314yes—
176#102×C67C2314yes—
177#97×C67C2314yes—
178C2×Dic134—24no—
179C2×Dic134—24no—
180C2×Dic134—24no—
181C2×Dic134—24no—
182C2×Dic134—24no—
183C2×Dic134—432no—
184C2×Dic134—44no—
185C2×Dic134—44no—
186C2×Dic134—44no—
187C2×Dic134—44no—
188C2×Dic134C2×D414yes—
189C22×Dic67—21no—
190C22×Dic67—21no—
191C22×Dic67—21no—
192C22×Dic67—21no—
193C22×Dic67—24no—
194C22×Dic67—24no—
195C22×Dic67—44no—
196C22×Dic67—44no—
197C22×Dic67C2×D411yescharacteristic
198C22×Dic67C2×D411yescharacteristic
199C22×Dic67C2×D411yescharacteristic
200C22×Dic67C2×D411yescharacteristic
201C2×C67⋊C8—22no—
202C2×C67⋊C8—22no—
203C2×C67⋊C8C2412yes—
204C2×C67⋊C8C2412yes—
205C4⋊Dic67—24no—
206C4⋊Dic67—21no—
207C4⋊Dic67—21no—
208C4⋊Dic67—21no—
209C4⋊Dic67—21no—
210C4⋊Dic67—24no—
211C4⋊Dic67—24no—
212C4⋊Dic67—24no—
213C4⋊Dic67C2×D414yes—
214C4⋊Dic67C2412yes—
215C4⋊Dic67C2412yes—
216C4⋊Dic67C2412yes—
217C4⋊Dic67C2412yes—
218Dic67⋊C4—24no—
219Dic67⋊C4—24no—
220Dic67⋊C4—24no—
221Dic67⋊C4—24no—
222Dic67⋊C4—24no—
223Dic67⋊C4—24no—
224Dic67⋊C4C2×D414yes—
225Dic67⋊C4C2×D414yes—
226C22⋊Dic67—24no—
227C22⋊Dic67—24no—
228C4×Dic67—24no—
229C4×Dic67—24no—
230C4×Dic67C2×D412yes—
231C4×Dic67C2×D412yes—
232C4×Dic67C2412yes—
233C4×Dic67C2412yes—
234C24×C67—21no—
235C2×Q8×C67—21no—
236C2×Q8×C67—22no—
237C2×Q8×C67C2×Q814yescomplemented
238C2×Q8×C67C2412yes—
239C2×D4×C67—21no—
240C2×D4×C67—22no—
241C2×D4×C67C2×Q814yes—
242C2×D4×C67C2412yes—
243C22×C4×C67—21no—
244C22×C4×C67—21no—
245C22×C4×C67—21no—
246C22×C4×C67—24no—
247C22×C4×C67—44no—
248C22×C4×C67C2×D411yescharacteristic
249C22×C4×C67C2×D411yescharacteristic
250C22×C4×C67C2411yescharacteristic
251SD16×C67C2×Q8116yescomplemented
252C2×C8×C67—22no—
253C2×C8×C67C2×Q814yescomplemented
254C2×C8×C67C2412yes—
255C2×C8×C67C2412yes—
256C4⋊C4×C67—24no—
257C4⋊C4×C67—21no—
258C4⋊C4×C67—21no—
259C4⋊C4×C67C2412yes—
260C4⋊C4×C67C2412yes—
261C22⋊C4×C67—24no—
262C42×C67—24no—
263C42×C67C2×D412yes—
264C42×C67C2412yes—
265C23×C67—24no—
266C23×C67—22no—
267C23×C67—42no—
268C23×C67—42no—
269C23×C67C22×D411yescharacteristic
270Q8×C67—24no—
271Q8×C67—22no—
272Q8×C67C22×Q814yescomplemented
273D4×C67—24no—
274D4×C67—22no—
275D4×C67C22×Q814yes—
276C2×C4×C67—24no—
277C2×C4×C67—22no—
278C2×C4×C67—22no—
279C2×C4×C67—22no—
280C2×C4×C67—22no—
281C2×C4×C67—22no—
282C2×C4×C67—48no—
283C2×C4×C67—42no—
284C2×C4×C67—42no—
285C2×C4×C67C22×D412yes—
286C2×C4×C67C22×D412yes—
287C2×C4×C67C22×D411yescharacteristic
288C2×C4×C67C22×Q812yes—
289C2×C4×C672−1+412yes—
290C2×C4×C67C2511yescharacteristic
291C2×Dic67—22no—
292C2×Dic67—22no—
293C2×Dic67—22no—
294C2×Dic67—22no—
295C2×Dic67—22no—
296C2×Dic67—22no—
297C2×Dic67—22no—
298C2×Dic67—48no—
299C2×Dic67—42no—
300C2×Dic67—42no—
301C2×Dic67—42no—
302C2×Dic67—42no—
303C2×Dic67—48no—
304C2×Dic67AGL(1,ℤ/8)14yes—
305C2×Dic67C22×D412yes—
306C2×Dic67C22×D412yes—
307C2×Dic67C22×D412yes—
308C2×Dic67C22×D412yes—
309Dic134—28no—
310Dic134—48no—
311Dic134—48no—
312Dic134—48no—
313Dic134—48no—
314C8×C67—22no—
315C8×C67C22×Q814yescomplemented
316C67⋊C8—22no—
317C67⋊C8—22no—
318C22×C67—24no—
319C22×C67—48no—
320C22×C67—42no—
321C22×C67—42no—
322C22×C67D4×Q812yes—
323C22×C67C2×AGL(1,ℤ/8)12yes—
324C22×C67#57812yes—
325C22×C67C23×D411yescharacteristic
326C4×C67—24no—
327C4×C67—22no—
328C4×C67—22no—
329C4×C67—42no—
330C4×C67—42no—
331C4×C67D4×Q812yes—
332C4×C67C23×Q811yescharacteristic
333C4×C67C2×2−1+411yescharacteristic
334Dic67—22no—
335Dic67—22no—
336Dic67—22no—
337Dic67—42no—
338Dic67—42no—
339Dic67—42no—
340Dic67—42no—
341Dic67C2×AGL(1,ℤ/8)14yes—
342C2×#3386—671nomaximal, Sylow
343C2×C67—44no—
344C2×C67#338614yescomplemented
345C2×C67C2×D4×Q811yescharacteristic
346C2×C67C22×AGL(1,ℤ/8)11yescharacteristic
347C2×C67C2×#57811yescharacteristic
348C2×#557—671no—
349C2×D4×Q8—671no—
350#3386—6716no—
351C2×#501—671no—
352C2×#501—671no—
353C2×#500—671no—
354C2×#477—671no—
355C2×#477—671no—
356C2×#475—671no—
357C2×#478—671no—
358C2×#478—671no—
359C2×#474—671no—
360C2×#446—671no—
361C2×#440—671no—
362C2×#440D6711yescharacteristic
363C2×C4×SD16—671no—
364C67C2×#338611yescharacteristic, complemented, Sylow
365C23×Q8—1341no—
366C22×SD16C2×D6711yescharacteristic
367#557—678no—
368#557—1344no—
369D4×Q8—678no—
370D4×Q8—1344no—
371C2×C4⋊Q8—671no—
372C2×C4⋊Q8—671no—
373C2×C4⋊Q8—671no—
374C2×C4⋊Q8—671no—
375C2×C4⋊Q8—1341no—
376C2×#125—671no—
377C2×#125—671no—
378C2×#125—1341no—
379C2×#125—1341no—
380C2×C22⋊Q8—1341no—
381C2×C22⋊Q8—1341no—
382C2×C22⋊Q8—1341no—
383C2×C4×Q8—671no—
384C2×C4×Q8—671no—
385C2×C4×Q8—671no—
386C2×C4×Q8—1341no—
387C2×C4×Q8C2×D6711yescharacteristic
388C2×C4×D4—671no—
389C2×C4×D4—671no—
390C2×C4×D4C2×D6711yescharacteristic
391#501—678no—
392#501—678no—
393#500—678no—
394#478—678no—
395#478—678no—
396#477—678no—
397#477—678no—
398#475—678no—
399#474—678no—
400#446—678no—
401#440—678no—
402#440C2×D6718yes—
403C4×SD16—678no—
404C2×#107—671no—
405C2×#107—671no—
406C2×#107—671no—
407C2×#107—671no—
408C2×#107—671no—
409C2×#107C2×D6711yescharacteristic
410C2×#106—671no—
411C2×#106—671no—
412C2×#106—671no—
413C2×C4⋊C8—671no—
414C2×C4⋊C8—671no—
415C2×C4⋊C8—671no—
416C2×#103—671no—
417C2×#103—671no—
418C2×#103C2×D6711yescharacteristic
419C2×#102—671no—
420C2×#102—671no—
421C2×#102C2×D6711yescharacteristic
422C2×#97—671no—
423C2×#97C2×D6711yescharacteristic
424C2×C4×C8—671no—
425C22×Q8—2688no—
426C22×Q8—671no—
427C22×Q8—1341no—
428C22×Q8—1341no—
429C22×Q8—1341no—
430C22×Q8—1348no—
431C22×Q8—1341no—
432C22×Q8C22×D6711yescharacteristic
433C22×D4C22×D6711yescharacteristic
434C23×C4—21no—
435C23×C4—1341no—
436C23×C4—1341no—
437C2×SD16Dic13418yescomplemented
438C2×SD16C22×D6714yes—
439C22×C8—671no—
440C22×C8—671no—
441C22×C8C22×D6711yescharacteristic
442C22×C8C22×D6711yescharacteristic
443C4⋊Q8—674no—
444C4⋊Q8—674no—
445C4⋊Q8—674no—
446C4⋊Q8—674no—
447C4⋊Q8—1342no—
448C4⋊Q8—1342no—
449C4⋊Q8—1342no—
450C4⋊Q8—1348no—
451C4⋊Q8—1342no—
452#125—674no—
453#125—674no—
454#125—1348no—
455#125—1342no—
456#125—1348no—
457#125—1342no—
458C22⋊Q8—1348no—
459C22⋊Q8—1348no—
460C22⋊Q8—1348no—
461C4×Q8—22no—
462C4×Q8—674no—
463C4×Q8—674no—
464C4×Q8—674no—
465C4×Q8—674no—
466C4×Q8—1348no—
467C4×Q8—1342no—
468C4×Q8—1342no—
469C4×Q8C22×D6714yes—
470C4×D4—22no—
471C4×D4—674no—
472C4×D4—674no—
473C4×D4—1342no—
474C4×D4—1342no—
475C4×D4C22×D6714yes—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—671no—
478C2×C4⋊C4—671no—
479C2×C4⋊C4—671no—
480C2×C4⋊C4—671no—
481C2×C4⋊C4—671no—
482C2×C4⋊C4—671no—
483C2×C4⋊C4—671no—
484C2×C4⋊C4—1341no—
485C2×C4⋊C4—1341no—
486C2×C4⋊C4—1341no—
487C2×C4⋊C4—1341no—
488C2×C4⋊C4—1341no—
489C2×C4⋊C4—1341no—
490C2×C4⋊C4—1341no—
491C2×C4⋊C4—1341no—
492C2×C4⋊C4—1341no—
493C2×C4⋊C4—1341no—
494C2×C4⋊C4C22×D6711yescharacteristic
495C2×C4⋊C4C22×D6711yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—1341no—
498C2×C22⋊C4—1341no—
499C2×C42—21no—
500C2×C42—671no—
501C2×C42—671no—
502C2×C42—1341no—
503C2×C42—1341no—
504C2×C42C22×D6711yescharacteristic
505#107—674no—
506#107—674no—
507#107—674no—
508#107—674no—
509#107—674no—
510#107C22×D6714yes—
511#106—674no—
512#106—674no—
513#106—674no—
514C4⋊C8—674no—
515C4⋊C8—674no—
516C4⋊C8—674no—
517#103—674no—
518#103—674no—
519#103C22×D6714yes—
520#102—674no—
521#102—674no—
522#102C22×D6714yes—
523#97—674no—
524#97C22×D6714yes—
525C4×C8—674no—
526C24—21no—
527C2×Q8—21no—
528C2×Q8—22no—
529C2×Q8—2684no—
530C2×Q8—26832no—
531C2×Q8—2684no—
532C2×Q8—2684no—
533C2×Q8—2684no—
534C2×Q8—674no—
535C2×Q8—1344no—
536C2×Q8—1344no—
537C2×Q8—1344no—
538C2×Q8—1344no—
539C2×Q8—1344no—
540C2×Q8C2×Dic13414yescomplemented
541C2×Q8C23×D6712yes—
542C2×D4—21no—
543C2×D4—22no—
544C2×D4C2×Dic13414yes—
545C2×D4C23×D6712yes—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—24no—
550C22×C4—44no—
551C22×C4—2684no—
552C22×C4—2684no—
553C22×C4—671no—
554C22×C4—671no—
555C22×C4—671no—
556C22×C4—671no—
557C22×C4—1344no—
558C22×C4—1344no—
559C22×C4—1341no—
560C22×C4—1341no—
561C22×C4—1341no—
562C22×C4—1341no—
563C22×C4D4×D6711yescharacteristic
564C22×C4D4×D6711yescharacteristic
565C22×C4C23×D6711yescharacteristic
566SD16C2×Dic134116yescomplemented
567C2×C8—22no—
568C2×C8—672no—
569C2×C8—672no—
570C2×C8—1342no—
571C2×C8—1342no—
572C2×C8C2×Dic13414yescomplemented
573C2×C8C23×D6712yes—
574C2×C8C23×D6712yes—
575C4⋊C4—24no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—674no—
579C4⋊C4—674no—
580C4⋊C4—674no—
581C4⋊C4—672no—
582C4⋊C4—672no—
583C4⋊C4—672no—
584C4⋊C4—672no—
585C4⋊C4—1344no—
586C4⋊C4—1344no—
587C4⋊C4—1344no—
588C4⋊C4—1344no—
589C4⋊C4—1344no—
590C4⋊C4—1344no—
591C4⋊C4—1344no—
592C4⋊C4—1341no—
593C4⋊C4—1341no—
594C4⋊C4—1341no—
595C4⋊C4—1341no—
596C4⋊C4—1344no—
597C4⋊C4—1344no—
598C4⋊C4—1344no—
599C4⋊C4C23×D6712yes—
600C4⋊C4C23×D6712yes—
601C22⋊C4—24no—
602C22⋊C4—1344no—
603C22⋊C4—1344no—
604C42—24no—
605C42—672no—
606C42—672no—
607C42—672no—
608C42—672no—
609C42—1344no—
610C42—1344no—
611C42D4×D6712yes—
612C42C23×D6712yes—
613C23—24no—
614C23—22no—
615C23—42no—
616C23—42no—
617C23C2×D4×D6711yescharacteristic
618Q8—24no—
619Q8—22no—
620Q8—2688no—
621Q8—2688no—
622Q8—2688no—
623Q8—2688no—
624Q8—1348no—
625Q8C22×Dic13414yescomplemented
626D4—24no—
627D4—22no—
628D4C22×Dic13414yes—
629C2×C4—24no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—48no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—2682no—
639C2×C4—2682no—
640C2×C4—2682no—
641C2×C4—2682no—
642C2×C4—2688no—
643C2×C4—2688no—
644C2×C4—674no—
645C2×C4—672no—
646C2×C4—672no—
647C2×C4—672no—
648C2×C4—672no—
649C2×C4—1342no—
650C2×C4—1342no—
651C2×C4—1342no—
652C2×C4—1342no—
653C2×C4—1342no—
654C2×C4—1342no—
655C2×C4—1342no—
656C2×C4C2×D4×D6712yes—
657C2×C4C2×D4×D6712yes—
658C2×C4C2×D4×D6711yescharacteristic
659C2×C4C22×Dic13412yes—
660C2×C4#1452409012yes—
661C2×C4C24×D6711yescharacteristic
662C8—22no—
663C8—1342no—
664C8—1342no—
665C8C22×Dic13414yescomplemented
666C22—24no—
667C22—48no—
668C22—42no—
669C22—42no—
670C22D4×Dic13412yes—
671C22AGL(1,ℤ/8)×D6712yes—
672C22#1686421212yes—
673C22C22×D4×D6711yescharacteristic
674C4—22no—
675C4—24no—
676C4—22no—
677C4—42no—
678C4—42no—
679C4—2682no—
680C4—2682no—
681C4—2682no—
682C4—2682no—
683C4—674no—
684C4—1342no—
685C4—1342no—
686C4—1342no—
687C4D4×Dic13412yes—
688C4C23×Dic13411yescharacteristic
689C4C2×#1452409011yescharacteristic
690C2—44no—
691C2#2257313114yesdirect product factor
692C2C2×D4×Dic13411yescharacteristic
693C2C2×AGL(1,ℤ/8)×D6711yescharacteristic
694C2C2×#1686421211yescharacteristic
subgroupG/H
centerC23C2×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#440×C67C2
socleC23×C67C22×D4
prime radicalC22×D4×C67C23
hypercenterC2×#440D67
hypocenterC67C2×#3386
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#16864122C2semidirect
3. #22573131C2direct (N × H)
4. C2×#16863805C2semidirect
5. C2×#16863804C2semidirect
6. C2×#16863800C2semidirect
7. C2×#16863691C2semidirect
8. C2×#16863689C2semidirect
9. C2×#16863679C2semidirect
13. C2×#16863524C2semidirect
19. #16864122C22semidirect
40. #16863805C22semidirect
41. #16863804C22semidirect
42. #16863800C22semidirect
45. #16863691C22semidirect
46. #16863689C22semidirect
47. #16863679C22semidirect
49. #16863524C22semidirect
160. C2×SD16×C67Q8semidirect
237. C2×Q8×C67C2×Q8semidirect
251. SD16×C67C2×Q8semidirect
253. C2×C8×C67C2×Q8semidirect
272. Q8×C67C22×Q8semidirect
315. C8×C67C22×Q8semidirect
344. C2×C67#3386semidirect
364. C67C2×#3386semidirect
437. C2×SD16Dic134semidirect
540. C2×Q8C2×Dic134semidirect
566. SD16C2×Dic134semidirect
572. C2×C8C2×Dic134semidirect
625. Q8C22×Dic134semidirect
665. C8C22×Dic134semidirect
691. C2#22573131direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168641222
C2×D4×Dic1342
#225731312
C2×#168638052
C2×#168638042
C2×#168638002
C2×#168636912
C2×#168636892
C2×#168636792
C2×#168636982
C2×#168636962
C2×#168636742
C2×#168635242
C2×#168634972
C2×SD16×Dic672
C2×#440×C672
C2×#338667