Finite Group Databasebeta

← C2×#22573120 #31736321

Subgroups — C2×#22573120 #31736321

Order 17152.

1854 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×Dic134C211yesmaximal, characteristic, complemented
2C2×#16864105C211yesmaximal, characteristic
3#22573120C2116yesmaximal, direct product factor
4C2×#16863805C211yesmaximal, characteristic, complemented
5C2×#16863804C211yesmaximal, characteristic, complemented
6C2×#16863800C211yesmaximal, characteristic, complemented
7C2×#16863703C211yesmaximal, characteristic, complemented
8C2×#16863701C211yesmaximal, characteristic, complemented
9C2×#16863689C211yesmaximal, characteristic, complemented
10C2×#16863684C211yesmaximal, characteristic
11C2×#16863676C211yesmaximal, characteristic
12C2×#16863674C211yesmaximal, characteristic
13C2×#16863524C211yesmaximal, characteristic, complemented
14C2×#16863497C211yesmaximal, characteristic
15C2×SD16×Dic67C211yesmaximal, characteristic
16C2×#440×C67C211yesmaximal, characteristic
17Q8×Dic134—24no—
18Q8×Dic134C2218yescomplemented
19#16864105—24no—
20#16864105C2218yes—
21C2×#14524043—21no—
22C2×#14524043C2211yescharacteristic
23C2×#14524042—21no—
24C2×#14524042—21no—
25C2×#14524042C2211yescharacteristic
26C2×#14524042C2211yescharacteristic
27C2×#14524042C2211yescharacteristic
28C2×#14524035C2211yescharacteristic
29C2×#14524034C2211yescharacteristic
30C2×#14524022—21no—
31C2×#14524020—21no—
32C2×#14524020—21no—
33C2×Q8×Dic67C2211yescharacteristic
34C2×Q8×Dic67C2211yescharacteristic
35C2×C4×Dic134—21no—
36C2×C4×Dic134C2211yescharacteristic
37C2×D4×Dic67C2211yescharacteristic
38C2×D4×Dic67C2211yescharacteristic
39C22×Dic67⋊C4—21no—
40#16863805C2218yescomplemented
41#16863804C2218yescomplemented
42#16863800C2218yescomplemented
43#16863703C2218yescomplemented
44#16863701C2218yescomplemented
45#16863689C2218yescomplemented
46#16863684C2218yes—
47#16863676C2218yes—
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—21no—
78C22×Dic134—21no—
79C22×Dic134—21no—
80C22×Dic134—21no—
81C22×Dic134D411yescharacteristic
82C23×Dic67—21no—
83C23×Dic67—21no—
84C22×C67⋊C8C2311yescharacteristic
85C22×C67⋊C8C2311yescharacteristic
86#14524043—28no—
87#14524043—22no—
88#14524043C2314yes—
89#14524042—28no—
90#14524042—28no—
91#14524042—22no—
92#14524042—22no—
93#14524042—22no—
94#14524042C2314yes—
95#14524042C2314yes—
96#14524042C2314yes—
97#14524035—22no—
98#14524035C2314yes—
99#14524034—22no—
100#14524034C2314yes—
101#14524022—28no—
102#14524020—28no—
103#14524020—28no—
104Q8×Dic67—22no—
105Q8×Dic67—22no—
106Q8×Dic67C2314yes—
107Q8×Dic67C2314yes—
108C4×Dic134—28no—
109C4×Dic134D414yes—
110C4×Dic134C2314yes—
111D4×Dic67—22no—
112D4×Dic67—22no—
113D4×Dic67C2314yes—
114D4×Dic67C2314yes—
115C2×C4⋊Dic67—21no—
116C2×C4⋊Dic67—21no—
117C2×C4⋊Dic67—21no—
118C2×C4⋊Dic67—21no—
119C2×C4⋊Dic67D411yescharacteristic
120C2×C4⋊Dic67C2311yescharacteristic
121C2×C4⋊Dic67C2311yescharacteristic
122C2×C4⋊Dic67C2311yescharacteristic
123C2×C4⋊Dic67C2311yescharacteristic
124C2×Dic67⋊C4—21no—
125C2×Dic67⋊C4—21no—
126C2×Dic67⋊C4—21no—
127C2×Dic67⋊C4—21no—
128C2×Dic67⋊C4—28no—
129C2×Dic67⋊C4—21no—
130C2×Dic67⋊C4—21no—
131C2×Dic67⋊C4D411yescharacteristic
132C2×Dic67⋊C4D411yescharacteristic
133C2×C22⋊Dic67—21no—
134C2×C22⋊Dic67—21no—
135C2×C4×Dic67—21no—
136C2×C4×Dic67—21no—
137C2×C4×Dic67C2311yescharacteristic
138C2×C4×Dic67C2311yescharacteristic
139#14523977C2314yes—
140#14523977C2314yes—
141#14523976C2314yes—
142#14523976C2314yes—
143#14523976C2314yes—
144#14523975C2314yes—
145#14523975C2314yes—
146#14523974C2314yes—
147C4⋊(C67⋊C8)C2314yes—
148Dic67⋊C8C2314yes—
149Dic67⋊C8C2314yes—
150#14523967C2314yes—
151#14523967C2314yes—
152#14523964C2314yes—
153#14523964C2314yes—
154#14523953C2314yes—
155C8×Dic67C2314yes—
156C22×Q8×C67C2311yescharacteristic
157C22×D4×C67C2311yescharacteristic
158C23×C4×C67—21no—
159C2×SD16×C67Q818yescomplemented
160C2×SD16×C67C2314yes—
161C22×C8×C67C2311yescharacteristic
162C22×C8×C67C2311yescharacteristic
163C4×Q8×C67—22no—
164C4×Q8×C67C2314yes—
165C4×D4×C67—22no—
166C4×D4×C67C2314yes—
167C2×C4⋊C4×C67—21no—
168C2×C4⋊C4×C67C2311yescharacteristic
169C2×C4⋊C4×C67C2311yescharacteristic
170C2×C22⋊C4×C67—21no—
171C2×C42×C67—21no—
172C2×C42×C67C2311yescharacteristic
173#107×C67C2314yes—
174#103×C67C2314yes—
175#102×C67C2314yes—
176#97×C67C2314yes—
177C2×Dic134—24no—
178C2×Dic134—24no—
179C2×Dic134—24no—
180C2×Dic134—24no—
181C2×Dic134—24no—
182C2×Dic134—82no—
183C2×Dic134—82no—
184C2×Dic134—82no—
185C2×Dic134—82no—
186C2×Dic134C2×D414yes—
187C22×Dic67—21no—
188C22×Dic67—21no—
189C22×Dic67—21no—
190C22×Dic67—21no—
191C22×Dic67—24no—
192C22×Dic67—24no—
193C22×Dic67—44no—
194C22×Dic67—82no—
195C22×Dic67C2×D411yescharacteristic
196C22×Dic67C2×D411yescharacteristic
197C22×Dic67C2×D411yescharacteristic
198C22×Dic67C2×D411yescharacteristic
199C2×C67⋊C8—22no—
200C2×C67⋊C8—22no—
201C2×C67⋊C8C2412yes—
202C2×C67⋊C8C2412yes—
203C4⋊Dic67—24no—
204C4⋊Dic67—21no—
205C4⋊Dic67—21no—
206C4⋊Dic67—21no—
207C4⋊Dic67—21no—
208C4⋊Dic67—24no—
209C4⋊Dic67—24no—
210C4⋊Dic67—24no—
211C4⋊Dic67C2×D414yes—
212C4⋊Dic67C2412yes—
213C4⋊Dic67C2412yes—
214C4⋊Dic67C2412yes—
215C4⋊Dic67C2412yes—
216Dic67⋊C4—24no—
217Dic67⋊C4—24no—
218Dic67⋊C4—24no—
219Dic67⋊C4—24no—
220Dic67⋊C4—24no—
221Dic67⋊C4—24no—
222Dic67⋊C4C2×D414yes—
223Dic67⋊C4C2×D414yes—
224C22⋊Dic67—24no—
225C22⋊Dic67—24no—
226C4×Dic67—24no—
227C4×Dic67—24no—
228C4×Dic67C2×D412yes—
229C4×Dic67C2×D412yes—
230C4×Dic67C2412yes—
231C4×Dic67C2412yes—
232C24×C67—21no—
233C2×Q8×C67—21no—
234C2×Q8×C67—22no—
235C2×Q8×C67C2×Q814yes—
236C2×Q8×C67C2412yes—
237C2×D4×C67—21no—
238C2×D4×C67—22no—
239C2×D4×C67C2×Q814yes—
240C2×D4×C67C2412yes—
241C22×C4×C67—21no—
242C22×C4×C67—21no—
243C22×C4×C67—21no—
244C22×C4×C67—24no—
245C22×C4×C67—82no—
246C22×C4×C67C2×D411yescharacteristic
247C22×C4×C67C2×D411yescharacteristic
248C22×C4×C67C2411yescharacteristic
249SD16×C67C2×Q8116yescomplemented
250C2×C8×C67—22no—
251C2×C8×C67C2×Q814yes—
252C2×C8×C67C2412yes—
253C2×C8×C67C2412yes—
254C4⋊C4×C67—24no—
255C4⋊C4×C67—21no—
256C4⋊C4×C67—21no—
257C4⋊C4×C67C2412yes—
258C4⋊C4×C67C2412yes—
259C22⋊C4×C67—24no—
260C42×C67—24no—
261C42×C67C2×D412yes—
262C42×C67C2412yes—
263C23×C67—24no—
264C23×C67—22no—
265C23×C67—42no—
266C23×C67—42no—
267C23×C67C22×D411yescharacteristic
268Q8×C67—24no—
269Q8×C67—22no—
270Q8×C67C22×Q814yes—
271D4×C67—24no—
272D4×C67—22no—
273D4×C67C22×Q814yes—
274C2×C4×C67—24no—
275C2×C4×C67—22no—
276C2×C4×C67—22no—
277C2×C4×C67—22no—
278C2×C4×C67—22no—
279C2×C4×C67—22no—
280C2×C4×C67—42no—
281C2×C4×C67—42no—
282C2×C4×C67—84no—
283C2×C4×C67C22×D412yes—
284C2×C4×C67C22×D412yes—
285C2×C4×C67C22×D411yescharacteristic
286C2×C4×C67C22×Q812yes—
287C2×C4×C672−1+412yes—
288C2×C4×C67C2511yescharacteristic
289C2×Dic67—22no—
290C2×Dic67—22no—
291C2×Dic67—22no—
292C2×Dic67—22no—
293C2×Dic67—22no—
294C2×Dic67—22no—
295C2×Dic67—22no—
296C2×Dic67—42no—
297C2×Dic67—42no—
298C2×Dic67—42no—
299C2×Dic67—42no—
300C2×Dic67—48no—
301C2×Dic67—84no—
302C2×Dic67#13714yes—
303C2×Dic67C22×D412yes—
304C2×Dic67C22×D412yes—
305C2×Dic67C22×D412yes—
306C2×Dic67C22×D412yes—
307Dic134—28no—
308Dic134—84no—
309Dic134—84no—
310Dic134—84no—
311Dic134—84no—
312C8×C67—22no—
313C8×C67C22×Q814yes—
314C67⋊C8—22no—
315C67⋊C8—22no—
316C22×C67—24no—
317C22×C67—48no—
318C22×C67—42no—
319C22×C67—42no—
320C22×C67D4×Q812yes—
321C22×C67C2×#13712yes—
322C22×C67#57612yes—
323C22×C67C23×D411yescharacteristic
324C4×C67—24no—
325C4×C67—22no—
326C4×C67—22no—
327C4×C67—42no—
328C4×C67—42no—
329C4×C67D4×Q812yes—
330C4×C67C23×Q811yescharacteristic
331C4×C67C2×2−1+411yescharacteristic
332Dic67—22no—
333Dic67—22no—
334Dic67—22no—
335Dic67—42no—
336Dic67—42no—
337Dic67—42no—
338Dic67—42no—
339Dic67C2×#13714yes—
340C2×#3385—671nomaximal, Sylow
341C2×C67—44no—
342C2×C67#338514yescomplemented
343C2×C67C2×D4×Q811yescharacteristic
344C2×C67C22×#13711yescharacteristic
345C2×C67C2×#57611yescharacteristic
346C2×Q82—671no—
347C2×#554—671no—
348#3385—6716no—
349C2×#501—671no—
350C2×#501—671no—
351C2×#500—671no—
352C2×#479—671no—
353C2×#479—671no—
354C2×#477—671no—
355C2×#476—671no—
356C2×#474—671no—
357C2×#474—671no—
358C2×#446—671no—
359C2×#440—671no—
360C2×#440D6711yescharacteristic
361C2×C4×SD16—671no—
362C67C2×#338511yescharacteristic, complemented, Sylow
363C22×SD16C2×D6711yescharacteristic
364Q82—678no—
365Q82—1344no—
366#554—678no—
367#554—1344no—
368C2×C4⋊Q8—671no—
369C2×C4⋊Q8—671no—
370C2×C4⋊Q8—671no—
371C2×C4⋊Q8—671no—
372C2×C4⋊Q8—1341no—
373C2×C4⋊Q8—1341no—
374C2×C4⋊Q8—1341no—
375C2×#125—671no—
376C2×#125—671no—
377C2×C22⋊Q8—1341no—
378C2×C22⋊Q8—1341no—
379C2×C22⋊Q8—1341no—
380C2×C4×Q8—671no—
381C2×C4×Q8—671no—
382C2×C4×Q8—671no—
383C2×C4×Q8—1341no—
384C2×C4×Q8C2×D6711yescharacteristic
385C2×C4×D4—671no—
386C2×C4×D4—671no—
387C2×C4×D4C2×D6711yescharacteristic
388C22×C4⋊C4—1341no—
389#501—678no—
390#501—678no—
391#500—678no—
392#479—678no—
393#479—678no—
394#477—678no—
395#476—678no—
396#474—678no—
397#474—678no—
398#446—678no—
399#440—678no—
400#440C2×D6718yes—
401C4×SD16—678no—
402C2×#107—671no—
403C2×#107—671no—
404C2×#107—671no—
405C2×#107—671no—
406C2×#107—671no—
407C2×#107C2×D6711yescharacteristic
408C2×#106—671no—
409C2×#106—671no—
410C2×#106—671no—
411C2×C4⋊C8—671no—
412C2×C4⋊C8—671no—
413C2×C4⋊C8—671no—
414C2×#103—671no—
415C2×#103—671no—
416C2×#103C2×D6711yescharacteristic
417C2×#102—671no—
418C2×#102—671no—
419C2×#102C2×D6711yescharacteristic
420C2×#97—671no—
421C2×#97C2×D6711yescharacteristic
422C2×C4×C8—671no—
423C22×Q8—671no—
424C22×Q8—1341no—
425C22×Q8—1341no—
426C22×Q8—1341no—
427C22×Q8—1341no—
428C22×Q8C22×D6711yescharacteristic
429C22×D4C22×D6711yescharacteristic
430C23×C4—21no—
431C23×C4—1341no—
432C23×C4—1341no—
433C2×SD16Dic13418yescomplemented
434C2×SD16C22×D6714yes—
435C22×C8—671no—
436C22×C8—671no—
437C22×C8C22×D6711yescharacteristic
438C22×C8C22×D6711yescharacteristic
439C4⋊Q8—674no—
440C4⋊Q8—674no—
441C4⋊Q8—674no—
442C4⋊Q8—674no—
443C4⋊Q8—1348no—
444C4⋊Q8—1342no—
445C4⋊Q8—1342no—
446C4⋊Q8—1342no—
447C4⋊Q8—1348no—
448C4⋊Q8—1348no—
449C4⋊Q8—1342no—
450#125—674no—
451#125—674no—
452#125—1342no—
453#125—1342no—
454C22⋊Q8—1348no—
455C22⋊Q8—1348no—
456C22⋊Q8—1348no—
457C4×Q8—22no—
458C4×Q8—674no—
459C4×Q8—674no—
460C4×Q8—674no—
461C4×Q8—674no—
462C4×Q8—1348no—
463C4×Q8—1342no—
464C4×Q8—1342no—
465C4×Q8C22×D6714yes—
466C4×D4—22no—
467C4×D4—674no—
468C4×D4—674no—
469C4×D4—1342no—
470C4×D4—1342no—
471C4×D4C22×D6714yes—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—671no—
474C2×C4⋊C4—671no—
475C2×C4⋊C4—671no—
476C2×C4⋊C4—671no—
477C2×C4⋊C4—671no—
478C2×C4⋊C4—671no—
479C2×C4⋊C4—671no—
480C2×C4⋊C4—1348no—
481C2×C4⋊C4—1341no—
482C2×C4⋊C4—1341no—
483C2×C4⋊C4—1341no—
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⋊C4C22×D6711yescharacteristic
492C2×C4⋊C4C22×D6711yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—1341no—
495C2×C22⋊C4—1341no—
496C2×C42—21no—
497C2×C42—671no—
498C2×C42—671no—
499C2×C42—1341no—
500C2×C42—1341no—
501C2×C42C22×D6711yescharacteristic
502#107—674no—
503#107—674no—
504#107—674no—
505#107—674no—
506#107—674no—
507#107C22×D6714yes—
508#106—674no—
509#106—674no—
510#106—674no—
511C4⋊C8—674no—
512C4⋊C8—674no—
513C4⋊C8—674no—
514#103—674no—
515#103—674no—
516#103C22×D6714yes—
517#102—674no—
518#102—674no—
519#102C22×D6714yes—
520#97—674no—
521#97C22×D6714yes—
522C4×C8—674no—
523C24—21no—
524C2×Q8—21no—
525C2×Q8—22no—
526C2×Q8—5362no—
527C2×Q8—5362no—
528C2×Q8—5362no—
529C2×Q8—5362no—
530C2×Q8—674no—
531C2×Q8—1344no—
532C2×Q8—1344no—
533C2×Q8—1344no—
534C2×Q8—1344no—
535C2×Q8—1344no—
536C2×Q8C2×Dic13414yes—
537C2×Q8C23×D6712yes—
538C2×D4—21no—
539C2×D4—22no—
540C2×D4C2×Dic13414yes—
541C2×D4C23×D6712yes—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—24no—
546C22×C4—82no—
547C22×C4—2684no—
548C22×C4—5362no—
549C22×C4—671no—
550C22×C4—671no—
551C22×C4—671no—
552C22×C4—671no—
553C22×C4—1344no—
554C22×C4—1341no—
555C22×C4—1341no—
556C22×C4—1341no—
557C22×C4—1341no—
558C22×C4—1344no—
559C22×C4D4×D6711yescharacteristic
560C22×C4D4×D6711yescharacteristic
561C22×C4C23×D6711yescharacteristic
562SD16C2×Dic134116yescomplemented
563C2×C8—22no—
564C2×C8—672no—
565C2×C8—672no—
566C2×C8—1342no—
567C2×C8—1342no—
568C2×C8C2×Dic13414yes—
569C2×C8C23×D6712yes—
570C2×C8C23×D6712yes—
571C4⋊C4—24no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—674no—
575C4⋊C4—674no—
576C4⋊C4—674no—
577C4⋊C4—672no—
578C4⋊C4—672no—
579C4⋊C4—672no—
580C4⋊C4—672no—
581C4⋊C4—1344no—
582C4⋊C4—1344no—
583C4⋊C4—1344no—
584C4⋊C4—1344no—
585C4⋊C4—1344no—
586C4⋊C4—1344no—
587C4⋊C4—1344no—
588C4⋊C4—1341no—
589C4⋊C4—1341no—
590C4⋊C4—1341no—
591C4⋊C4—1341no—
592C4⋊C4—1344no—
593C4⋊C4—1344no—
594C4⋊C4—1344no—
595C4⋊C4C23×D6712yes—
596C4⋊C4C23×D6712yes—
597C22⋊C4—24no—
598C22⋊C4—1344no—
599C22⋊C4—1344no—
600C42—24no—
601C42—672no—
602C42—672no—
603C42—672no—
604C42—672no—
605C42—1344no—
606C42—1344no—
607C42D4×D6712yes—
608C42C23×D6712yes—
609C23—24no—
610C23—22no—
611C23—42no—
612C23—42no—
613C23C2×D4×D6711yescharacteristic
614Q8—24no—
615Q8—22no—
616Q8—5364no—
617Q8—5364no—
618Q8—5364no—
619Q8—5364no—
620Q8—1348no—
621Q8C22×Dic13414yes—
622D4—24no—
623D4—22no—
624D4C22×Dic13414yes—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—84no—
634C2×C4—2682no—
635C2×C4—2682no—
636C2×C4—2682no—
637C2×C4—2682no—
638C2×C4—2688no—
639C2×C4—5364no—
640C2×C4—674no—
641C2×C4—672no—
642C2×C4—672no—
643C2×C4—672no—
644C2×C4—672no—
645C2×C4—1342no—
646C2×C4—1342no—
647C2×C4—1342no—
648C2×C4—1342no—
649C2×C4—1342no—
650C2×C4—1342no—
651C2×C4—1342no—
652C2×C4C2×D4×D6712yes—
653C2×C4C2×D4×D6712yes—
654C2×C4C2×D4×D6711yescharacteristic
655C2×C4C22×Dic13412yes—
656C2×C4#1452409012yes—
657C2×C4C24×D6711yescharacteristic
658C8—22no—
659C8—1342no—
660C8—1342no—
661C8C22×Dic13414yes—
662C22—24no—
663C22—48no—
664C22—42no—
665C22—42no—
666C22D4×Dic13412yes—
667C22#137×D6712yes—
668C22#1686420012yes—
669C22C22×D4×D6711yescharacteristic
670C4—22no—
671C4—22no—
672C4—24no—
673C4—42no—
674C4—42no—
675C4—2682no—
676C4—2682no—
677C4—2682no—
678C4—2682no—
679C4—674no—
680C4—1342no—
681C4—1342no—
682C4—1342no—
683C4D4×Dic13412yes—
684C4C23×Dic13411yescharacteristic
685C4C2×#1452409011yescharacteristic
686C2—44no—
687C2#2257312014yesdirect product factor
688C2C2×D4×Dic13411yescharacteristic
689C2C2×#137×D6711yescharacteristic
690C2C2×#1686420011yescharacteristic
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×#3385
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×Q8×Dic134C2semidirect
3. #22573120C2direct (N × H)
4. C2×#16863805C2semidirect
5. C2×#16863804C2semidirect
6. C2×#16863800C2semidirect
7. C2×#16863703C2semidirect
8. C2×#16863701C2semidirect
9. C2×#16863689C2semidirect
13. C2×#16863524C2semidirect
18. Q8×Dic134C22semidirect
40. #16863805C22semidirect
41. #16863804C22semidirect
42. #16863800C22semidirect
43. #16863703C22semidirect
44. #16863701C22semidirect
45. #16863689C22semidirect
49. #16863524C22semidirect
159. C2×SD16×C67Q8semidirect
249. SD16×C67C2×Q8semidirect
342. C2×C67#3385semidirect
362. C67C2×#3385semidirect
433. C2×SD16Dic134semidirect
562. SD16C2×Dic134semidirect
687. C2#22573120direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×Dic1342
C2×#168641052
#225731202
C2×#168638052
C2×#168638042
C2×#168638002
C2×#168637032
C2×#168637012
C2×#168636892
C2×#168636842
C2×#168636762
C2×#168636742
C2×#168635242
C2×#168634972
C2×SD16×Dic672
C2×#440×C672
C2×#338567