Finite Group Databasebeta

← C2×#22573127 #31736329

Subgroups — C2×#22573127 #31736329

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×#16864123C211yesmaximal, characteristic, complemented
2C2×#16864061C211yesmaximal, characteristic
3#22573127C2116yesmaximal, direct product factor
4C2×#16863803C211yesmaximal, characteristic, complemented
5C2×#16863800C211yesmaximal, characteristic, complemented
6C2×#16863690C211yesmaximal, characteristic, complemented
7C2×#16863688C211yesmaximal, characteristic, complemented
8C2×#16863680C211yesmaximal, characteristic, complemented
9C2×#16863695C211yesmaximal, characteristic
10C2×#16863693C211yesmaximal, characteristic
11C2×#16863675C211yesmaximal, characteristic
12C2×#16863524C211yesmaximal, characteristic, complemented
13C2×#16863498C211yesmaximal, characteristic
14C2×#16863495C211yesmaximal, characteristic
15C2×#16863483C211yesmaximal, characteristic
16C2×#501×C67C211yesmaximal, characteristic, complemented
17C22×Q8×D67—21no—
18C22×#11761617C2211yescharacteristic
19#16864123—24no—
20#16864123C2218yescomplemented
21#16864061—24no—
22#16864061C2218yes—
23C2×#14524042—21no—
24C2×#14524042C2211yescharacteristic
25C2×#14524042C2211yescharacteristic
26C2×#14524042C2211yescharacteristic
27C2×#14524034C2211yescharacteristic
28C2×#14524033—21no—
29C2×#14524033—21no—
30C2×#14524021—21no—
31C2×#14524021—21no—
32C2×#14524019—21no—
33C2×C4×Dic134C2211yescharacteristic
34C2×C4×Dic134C2211yescharacteristic
35C2×#14524008—21no—
36C2×#14524008C2211yescharacteristic
37C2×#14524008C2211yescharacteristic
38C2×C4×D268C2211yescharacteristic
39C2×#14524005C2211yescharacteristic
40C2×#14524005C2211yescharacteristic
41#16863803C2218yescomplemented
42#16863800C2218yescomplemented
43#16863695C2218yes—
44#16863693C2218yes—
45#16863690C2218yescomplemented
46#16863688C2218yescomplemented
47#16863680C2218yescomplemented
48#16863675C2218yes—
49#16863524C2218yescomplemented
50#16863498C2218yes—
51#16863495C2218yes—
52#16863483C2218yes—
53C2×#14523977C2211yescharacteristic
54C2×#14523976C2211yescharacteristic
55C2×#14523976C2211yescharacteristic
56C2×#14523976C2211yescharacteristic
57C2×#14523974C2211yescharacteristic
58C2×C4⋊(C67⋊C8)C2211yescharacteristic
59C2×Dic67⋊C8C2211yescharacteristic
60C2×Dic67⋊C8C2211yescharacteristic
61C2×#14523968C2211yescharacteristic
62C2×#14523966C2211yescharacteristic
63C2×#14523966C2211yescharacteristic
64C2×#14523965C2211yescharacteristic
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
81C22×Dic134C2311yescharacteristic
82C2×Q8×D67—28no—
83C2×Q8×D67—48no—
84C22×D268C2311yescharacteristic
85C22×C4×D67—21no—
86C22×C4×D67—21no—
87C22×C4×D67—21no—
88C2×#11761617Q818yescomplemented
89C2×#11761617C2314yes—
90C22×C67⋊C8C2311yescharacteristic
91C22×C67⋊C8C2311yescharacteristic
92#14524042—28no—
93#14524042—22no—
94#14524042—22no—
95#14524042—22no—
96#14524042C2314yes—
97#14524042C2314yes—
98#14524042C2314yes—
99#14524034—22no—
100#14524034C2314yes—
101#14524033—28no—
102#14524033—28no—
103#14524021—28no—
104#14524021—28no—
105#14524019—28no—
106C4×Dic134—22no—
107C4×Dic134D414yes—
108C4×Dic134C2314yes—
109C4×Dic134C2314yes—
110#14524008—28no—
111#14524008—22no—
112#14524008—22no—
113#14524008C2314yes—
114#14524008C2314yes—
115C4×D268—22no—
116C4×D268C2314yes—
117#14524005—22no—
118#14524005—22no—
119#14524005C2314yes—
120#14524005C2314yes—
121C2×C4⋊Dic67—21no—
122C2×C4⋊Dic67D411yescharacteristic
123C2×C4⋊Dic67C2311yescharacteristic
124C2×C4⋊Dic67C2311yescharacteristic
125C2×Dic67⋊C4—21no—
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×(C2×D67)⋊C4—21no—
135C2×(C2×D67)⋊C4—21no—
136C2×(C2×D67)⋊C4—21no—
137C2×C4×Dic67—21no—
138C2×C4×Dic67—21no—
139C2×C4×Dic67—21no—
140C2×C4×Dic67C2311yescharacteristic
141C2×C4×Dic67C2311yescharacteristic
142#14523977C2314yes—
143#14523976C2314yes—
144#14523976C2314yes—
145#14523976C2314yes—
146#14523974C2314yes—
147C4⋊(C67⋊C8)C2314yes—
148Dic67⋊C8C2314yes—
149Dic67⋊C8C2314yes—
150#14523968C2314yes—
151#14523966C2314yes—
152#14523966C2314yes—
153#14523965C2314yes—
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—
179C2×Dic134—21no—
180C2×Dic134—22no—
181C2×Dic134—24no—
182C2×Dic134—24no—
183C2×Dic134—24no—
184C2×Dic134—24no—
185C2×Dic134—44no—
186C2×Dic134—44no—
187C2×Dic134—44no—
188C2×Dic134C2×D414yes—
189C2×Dic134C2×Q814yescomplemented
190C2×Dic134C2412yes—
191Q8×D67—432no—
192C2×D268—21no—
193C2×D268—22no—
194C2×D268C2×Q814yes—
195C2×D268C2412yes—
196C22×Dic67—21no—
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—44no—
207C2×C4×D67—44no—
208C2×C4×D67—44no—
209#11761617C2×Q8116yescomplemented
210C2×C67⋊C8—22no—
211C2×C67⋊C8—22no—
212C2×C67⋊C8C2412yes—
213C2×C67⋊C8C2412yes—
214C4⋊Dic67—21no—
215C4⋊Dic67—21no—
216C4⋊Dic67—24no—
217C4⋊Dic67C2×D414yes—
218C4⋊Dic67C2412yes—
219C4⋊Dic67C2412yes—
220Dic67⋊C4—24no—
221Dic67⋊C4—24no—
222Dic67⋊C4—24no—
223Dic67⋊C4—24no—
224Dic67⋊C4—24no—
225Dic67⋊C4—24no—
226Dic67⋊C4—24no—
227Dic67⋊C4C2×D414yes—
228Dic67⋊C4C2×D414yes—
229(C2×D67)⋊C4—24no—
230(C2×D67)⋊C4—24no—
231(C2×D67)⋊C4—24no—
232C4×Dic67—24no—
233C4×Dic67—24no—
234C4×Dic67—24no—
235C4×Dic67C2×D412yes—
236C4×Dic67C2×D412yes—
237C4×Dic67C2412yes—
238C4×Dic67C2412yes—
239C2×Q8×C67—24no—
240C2×Q8×C67—44no—
241C22×C4×C67—21no—
242C22×C4×C67—21no—
243C22×C4×C67—21no—
244C22×C4×C67—21no—
245C22×C4×C67C2×D411yescharacteristic
246C22×C4×C67C2×D411yescharacteristic
247C22×C4×C67C2411yescharacteristic
248C2×C8×C67—22no—
249C2×C8×C67C2×Q814yescomplemented
250C2×C8×C67C2412yes—
251C2×C8×C67C2412yes—
252C4⋊C4×C67—24no—
253C4⋊C4×C67—24no—
254C4⋊C4×C67—24no—
255C4⋊C4×C67—21no—
256C4⋊C4×C67—21no—
257C4⋊C4×C67—21no—
258C4⋊C4×C67—21no—
259C4⋊C4×C67C2412yes—
260C4⋊C4×C67C2412yes—
261C4⋊C4×C67C2412yes—
262C4⋊C4×C67C2412yes—
263C42×C67C2×D412yes—
264C42×C67C2412yes—
265C23×C67C22×D411yescharacteristic
266C22×D67—24no—
267C22×D67—22no—
268C22×D67—42no—
269C22×D67—42no—
270Q8×C67—48no—
271C2×C4×C67—22no—
272C2×C4×C67—22no—
273C2×C4×C67—22no—
274C2×C4×C67—22no—
275C2×C4×C67—22no—
276C2×C4×C67—22no—
277C2×C4×C67—42no—
278C2×C4×C67—42no—
279C2×C4×C67—42no—
280C2×C4×C67—42no—
281C2×C4×C67C22×D412yes—
282C2×C4×C67C22×D412yes—
283C2×C4×C67C22×D411yescharacteristic
284C2×C4×C67C22×Q812yes—
285C2×C4×C672−1+412yes—
286C2×C4×C67C2511yescharacteristic
287C2×Dic67—24no—
288C2×Dic67—22no—
289C2×Dic67—22no—
290C2×Dic67—22no—
291C2×Dic67—22no—
292C2×Dic67—22no—
293C2×Dic67—22no—
294C2×Dic67—42no—
295C2×Dic67—42no—
296C2×Dic67AGL(1,ℤ/8)14yes—
297C2×Dic67C22×D412yes—
298C2×Dic67C22×D412yes—
299C2×Dic67C22×D412yes—
300C2×Dic67C22×D412yes—
301D268—24no—
302D268—22no—
303D268C22×Q814yes—
304C4×D67—48no—
305C4×D67—48no—
306C4×D67—48no—
307Dic134—24no—
308Dic134—22no—
309Dic134—28no—
310Dic134—48no—
311Dic134—48no—
312Dic134—48no—
313Dic134C22×Q814yescomplemented
314C8×C67—22no—
315C8×C67C22×Q814yescomplemented
316C67⋊C8—22no—
317C67⋊C8—22no—
318C22×C67D4×Q812yes—
319C22×C67C2×AGL(1,ℤ/8)12yes—
320C22×C67#57812yes—
321C22×C67C23×D411yescharacteristic
322C2×D67—24no—
323C2×D67—48no—
324C2×D67—42no—
325C2×D67—42no—
326C4×C67—22no—
327C4×C67—22no—
328C4×C67—42no—
329C4×C67—42no—
330C4×C67—42no—
331C4×C67—42no—
332C4×C67D4×Q812yes—
333C4×C67C23×Q811yescharacteristic
334C4×C67C2×2−1+411yescharacteristic
335Dic67—24no—
336Dic67—22no—
337Dic67—22no—
338Dic67—22no—
339Dic67—42no—
340Dic67—42no—
341Dic67C2×AGL(1,ℤ/8)14yes—
342C2×#3386—671nomaximal, Sylow
343C2×C67#338614yescomplemented
344C2×C67C2×D4×Q811yescharacteristic
345C2×C67C22×AGL(1,ℤ/8)11yescharacteristic
346C2×C67C2×#57811yescharacteristic
347D67—44no—
348C2×#557—671no—
349C2×D4×Q8—671no—
350#3386—6716no—
351C2×#501—671no—
352C2×#501D6711yescharacteristic, complemented
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×#440—671no—
363C2×C4×SD16—671no—
364C67C2×#338611yescharacteristic, complemented, Sylow
365C23×Q8—1341no—
366C22×SD16—671no—
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—1341no—
375C2×C4⋊Q8C2×D6711yescharacteristic
376C2×#125—671no—
377C2×#125—1341no—
378C2×#125—1341no—
379C2×#125C2×D6711yescharacteristic
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—671no—
387C2×C4×Q8—1341no—
388C2×C4×D4—671no—
389C2×C4×D4—671no—
390C2×C4×D4—671no—
391#501—678no—
392#501C2×D6718yescomplemented
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#440—678no—
403C4×SD16—678no—
404C2×#107—671no—
405C2×#107—671no—
406C2×#107—671no—
407C2×#107—671no—
408C2×#107C2×D6711yescharacteristic
409C2×#107C2×D6711yescharacteristic
410C2×#106—671no—
411C2×#106C2×D6711yescharacteristic
412C2×#106C2×D6711yescharacteristic
413C2×C4⋊C8—671no—
414C2×C4⋊C8—671no—
415C2×C4⋊C8—671no—
416C2×#103—671no—
417C2×#103—671no—
418C2×#103—671no—
419C2×#102—671no—
420C2×#102—671no—
421C2×#102—671no—
422C2×#97—671no—
423C2×#97C2×D6711yescharacteristic
424C2×C4×C8—671no—
425C22×Q8—21no—
426C22×Q8—2688no—
427C22×Q8—671no—
428C22×Q8—671no—
429C22×Q8—1341no—
430C22×Q8—1341no—
431C22×Q8—1341no—
432C22×Q8—1348no—
433C22×D4—671no—
434C23×C4—1341no—
435C23×C4—1341no—
436C23×C4—1341no—
437C2×SD16—678no—
438C2×SD16—674no—
439C22×C8—671no—
440C22×C8—671no—
441C22×C8C22×D6711yescharacteristic
442C22×C8C22×D6711yescharacteristic
443C4⋊Q8—22no—
444C4⋊Q8—674no—
445C4⋊Q8—674no—
446C4⋊Q8—674no—
447C4⋊Q8—1342no—
448C4⋊Q8—1342no—
449C4⋊Q8—1342no—
450C4⋊Q8—1348no—
451C4⋊Q8C22×D6714yes—
452#125—22no—
453#125—674no—
454#125—1342no—
455#125—1348no—
456#125—1348no—
457#125C22×D6714yes—
458C22⋊Q8—1348no—
459C22⋊Q8—1348no—
460C22⋊Q8—1348no—
461C4×Q8—674no—
462C4×Q8—674no—
463C4×Q8—674no—
464C4×Q8—674no—
465C4×Q8—674no—
466C4×Q8—1342no—
467C4×Q8—1342no—
468C4×Q8—1348no—
469C4×Q8—1342no—
470C4×D4—674no—
471C4×D4—674no—
472C4×D4—674no—
473C4×D4—1342no—
474C4×D4—1342no—
475C4×D4—1342no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
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⋊C4C22×D6711yescharacteristic
493C2×C4⋊C4C22×D6711yescharacteristic
494C2×C4⋊C4C22×D6711yescharacteristic
495C2×C4⋊C4C22×D6711yescharacteristic
496C2×C22⋊C4—1341no—
497C2×C22⋊C4—1341no—
498C2×C22⋊C4—1341no—
499C2×C42—671no—
500C2×C42—671no—
501C2×C42—1341no—
502C2×C42—1341no—
503C2×C42—1341no—
504C2×C42C22×D6711yescharacteristic
505#107—674no—
506#107—674no—
507#107—674no—
508#107—674no—
509#107C22×D6714yes—
510#107C22×D6714yes—
511#106—674no—
512#106C22×D6714yes—
513#106C22×D6714yes—
514C4⋊C8—674no—
515C4⋊C8—674no—
516C4⋊C8—674no—
517#103—674no—
518#103—674no—
519#103—674no—
520#102—674no—
521#102—674no—
522#102—674no—
523#97—674no—
524#97C22×D6714yes—
525C4×C8—674no—
526C24—1341no—
527C2×Q8—24no—
528C2×Q8—44no—
529C2×Q8—2684no—
530C2×Q8—2684no—
531C2×Q8—2684no—
532C2×Q8—26832no—
533C2×Q8—674no—
534C2×Q8—674no—
535C2×Q8—672no—
536C2×Q8—1344no—
537C2×Q8—1344no—
538C2×Q8—1344no—
539C2×Q8—1344no—
540C2×Q8—1341no—
541C2×Q8—1342no—
542C2×D4—674no—
543C2×D4—672no—
544C2×D4—1341no—
545C2×D4—1342no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—2684no—
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—1344no—
562C22×C4—1341no—
563C22×C4D4×D6711yescharacteristic
564C22×C4D4×D6711yescharacteristic
565C22×C4C23×D6711yescharacteristic
566SD16—6716no—
567C2×C8—22no—
568C2×C8—672no—
569C2×C8—672no—
570C2×C8—1342no—
571C2×C8—1342no—
572C2×C8Q8×D6714yescomplemented
573C2×C8C23×D6712yes—
574C2×C8C23×D6712yes—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—674no—
583C4⋊C4—674no—
584C4⋊C4—674no—
585C4⋊C4—672no—
586C4⋊C4—672no—
587C4⋊C4—1344no—
588C4⋊C4—1344no—
589C4⋊C4—1344no—
590C4⋊C4—1344no—
591C4⋊C4—1344no—
592C4⋊C4—1344no—
593C4⋊C4—1344no—
594C4⋊C4—1341no—
595C4⋊C4—1341no—
596C4⋊C4—1344no—
597C4⋊C4C23×D6712yes—
598C4⋊C4C23×D6712yes—
599C4⋊C4C23×D6712yes—
600C4⋊C4C23×D6712yes—
601C22⋊C4—1344no—
602C22⋊C4—1344no—
603C22⋊C4—1344no—
604C42—672no—
605C42—672no—
606C42—672no—
607C42—672no—
608C42—1344no—
609C42—1344no—
610C42—1344no—
611C42D4×D6712yes—
612C42C23×D6712yes—
613C23—2682no—
614C23—2682no—
615C23—1344no—
616C23—1342no—
617C23C2×D4×D6711yescharacteristic
618Q8—48no—
619Q8—2688no—
620Q8—2688no—
621Q8—2688no—
622Q8—674no—
623Q8—1348no—
624Q8—1344no—
625Q8—1342no—
626D4—674no—
627D4—1344no—
628D4—1342no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—2688no—
640C2×C4—2688no—
641C2×C4—2688no—
642C2×C4—2682no—
643C2×C4—2682no—
644C2×C4—674no—
645C2×C4—672no—
646C2×C4—672no—
647C2×C4—672no—
648C2×C4—672no—
649C2×C4—1342no—
650C2×C4—1342no—
651C2×C4—1344no—
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×C4C2×Q8×D6712yes—
660C2×C4#1452409112yes—
661C2×C4C24×D6711yescharacteristic
662C8—22no—
663C8—1342no—
664C8—1342no—
665C8C2×Q8×D6714yescomplemented
666C22—2688no—
667C22—2682no—
668C22—2682no—
669C22—1344no—
670C22#1686406112yes—
671C22AGL(1,ℤ/8)×D6712yes—
672C22#1686421212yes—
673C22C22×D4×D6711yescharacteristic
674C4—22no—
675C4—22no—
676C4—42no—
677C4—42no—
678C4—42no—
679C4—42no—
680C4—2682no—
681C4—2682no—
682C4—674no—
683C4—1342no—
684C4—1344no—
685C4—1342no—
686C4—1342no—
687C4#1686406112yes—
688C4C22×Q8×D6711yescharacteristic
689C4C2×#1452409111yescharacteristic
690C2—2684no—
691C2#2257312714yesdirect product factor
692C2C2×#1686406111yescharacteristic
693C2C2×AGL(1,ℤ/8)×D6711yescharacteristic
694C2C2×#1686421211yescharacteristic
subgroupG/H
centerC23C2×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#501×C67C2
socleC23×C67C22×D4
prime radicalC22×D268C23
hypercenterC2×#501D67
hypocenterC67C2×#3386
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×#16864123C2semidirect
3. #22573127C2direct (N × H)
4. C2×#16863803C2semidirect
5. C2×#16863800C2semidirect
6. C2×#16863690C2semidirect
7. C2×#16863688C2semidirect
8. C2×#16863680C2semidirect
12. C2×#16863524C2semidirect
16. C2×#501×C67C2semidirect
20. #16864123C22semidirect
41. #16863803C22semidirect
42. #16863800C22semidirect
45. #16863690C22semidirect
46. #16863688C22semidirect
47. #16863680C22semidirect
49. #16863524C22semidirect
71. #501×C67C22semidirect
88. C2×#11761617Q8semidirect
189. C2×Dic134C2×Q8semidirect
209. #11761617C2×Q8semidirect
249. C2×C8×C67C2×Q8semidirect
313. Dic134C22×Q8semidirect
315. C8×C67C22×Q8semidirect
343. C2×C67#3386semidirect
352. C2×#501D67semidirect
364. C67C2×#3386semidirect
392. #501C2×D67semidirect
572. C2×C8Q8×D67semidirect
665. C8C2×Q8×D67semidirect
691. C2#22573127direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168641232
C2×#168640612
#225731272
C2×#168638032
C2×#168638002
C2×#168636902
C2×#168636882
C2×#168636802
C2×#168636952
C2×#168636932
C2×#168636752
C2×#168635242
C2×#168634982
C2×#168634952
C2×#168634832
C2×#501×C672
C2×#338667