Finite Group Databasebeta

← C2×#22573116 #31736317

Subgroups — C2×#22573116 #31736317

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×#16864126C211yesmaximal, characteristic, complemented
2C2×#16864102C211yesmaximal, characteristic
3#22573116C2116yesmaximal, direct product factor
4C2×#16863803C211yesmaximal, characteristic, complemented
5C2×#16863800C211yesmaximal, characteristic, complemented
6C2×#16863706C211yesmaximal, characteristic, complemented
7C2×#16863700C211yesmaximal, characteristic, complemented
8C2×#16863690C211yesmaximal, characteristic, complemented
9C2×#16863685C211yesmaximal, characteristic
10C2×#16863675C211yesmaximal, characteristic
11C2×#16863673C211yesmaximal, characteristic
12C2×#16863524C211yesmaximal, characteristic, complemented
13C2×#16863498C211yesmaximal, characteristic
14C2×#16863495C211yesmaximal, characteristic
15C2×#16863483C211yesmaximal, characteristic
16C2×#501×C67C211yesmaximal, characteristic, complemented
17C22×#11761617C2211yescharacteristic
18#16864126—24no—
19#16864126C2218yescomplemented
20#16864102—24no—
21#16864102C2218yes—
22C2×#14524042—21no—
23C2×#14524042C2211yescharacteristic
24C2×#14524042C2211yescharacteristic
25C2×#14524042C2211yescharacteristic
26C2×#14524041—21no—
27C2×#14524041—21no—
28C2×#14524034C2211yescharacteristic
29C2×#14524023—21no—
30C2×#14524021—21no—
31C2×#14524021—21no—
32C2×C4×Dic134C2211yescharacteristic
33C2×C4×Dic134C2211yescharacteristic
34C2×#14524008—21no—
35C2×#14524008C2211yescharacteristic
36C2×#14524008C2211yescharacteristic
37C2×C4×D268C2211yescharacteristic
38C2×#14524005C2211yescharacteristic
39C2×#14524005C2211yescharacteristic
40C2×C4⋊C4×D67—21no—
41#16863803C2218yescomplemented
42#16863800C2218yescomplemented
43#16863706C2218yescomplemented
44#16863700C2218yescomplemented
45#16863690C2218yescomplemented
46#16863685C2218yes—
47#16863675C2218yes—
48#16863673C2218yes—
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
82C22×D268C2311yescharacteristic
83C22×C4×D67—21no—
84C22×C4×D67—21no—
85C22×C4×D67—21no—
86C2×#11761617Q818yescomplemented
87C2×#11761617C2314yes—
88C22×C67⋊C8C2311yescharacteristic
89C22×C67⋊C8C2311yescharacteristic
90#14524042—28no—
91#14524042—22no—
92#14524042—22no—
93#14524042—22no—
94#14524042C2314yes—
95#14524042C2314yes—
96#14524042C2314yes—
97#14524041—28no—
98#14524041—28no—
99#14524034—22no—
100#14524034C2314yes—
101#14524023—28no—
102#14524021—28no—
103#14524021—28no—
104C4×Dic134—22no—
105C4×Dic134D414yes—
106C4×Dic134C2314yes—
107C4×Dic134C2314yes—
108#14524008—28no—
109#14524008—22no—
110#14524008—22no—
111#14524008C2314yes—
112#14524008C2314yes—
113C4×D268—22no—
114C4×D268C2314yes—
115#14524005—22no—
116#14524005—22no—
117#14524005C2314yes—
118#14524005C2314yes—
119C2×C4⋊Dic67—21no—
120C2×C4⋊Dic67D411yescharacteristic
121C2×C4⋊Dic67C2311yescharacteristic
122C2×C4⋊Dic67C2311yescharacteristic
123C2×Dic67⋊C4—21no—
124C2×Dic67⋊C4—21no—
125C2×Dic67⋊C4—21no—
126C2×Dic67⋊C4—21no—
127C2×Dic67⋊C4—21no—
128C2×Dic67⋊C4—21no—
129C2×Dic67⋊C4—21no—
130C2×Dic67⋊C4D411yescharacteristic
131C2×Dic67⋊C4D411yescharacteristic
132C4⋊C4×D67—28no—
133C2×(C2×D67)⋊C4—21no—
134C2×(C2×D67)⋊C4—21no—
135C2×(C2×D67)⋊C4—21no—
136C2×C4×Dic67—21no—
137C2×C4×Dic67—21no—
138C2×C4×Dic67—21no—
139C2×C4×Dic67C2311yescharacteristic
140C2×C4×Dic67C2311yescharacteristic
141#14523977C2314yes—
142#14523976C2314yes—
143#14523976C2314yes—
144#14523976C2314yes—
145#14523974C2314yes—
146C4⋊(C67⋊C8)C2314yes—
147Dic67⋊C8C2314yes—
148Dic67⋊C8C2314yes—
149#14523968C2314yes—
150#14523966C2314yes—
151#14523966C2314yes—
152#14523965C2314yes—
153#14523963C2314yes—
154#14523963C2314yes—
155#14523953C2314yes—
156C8×Dic67C2314yes—
157C22×Q8×C67—21no—
158C22×C8×C67C2311yescharacteristic
159C22×C8×C67C2311yescharacteristic
160C4⋊Q8×C67—22no—
161C4⋊Q8×C67C2314yes—
162#125×C67—22no—
163#125×C67C2314yes—
164C2×C4⋊C4×C67—21no—
165C2×C4⋊C4×C67—21no—
166C2×C4⋊C4×C67—21no—
167C2×C4⋊C4×C67C2311yescharacteristic
168C2×C4⋊C4×C67C2311yescharacteristic
169C2×C4⋊C4×C67C2311yescharacteristic
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C42×C67C2311yescharacteristic
172#107×C67C2314yes—
173#107×C67C2314yes—
174#106×C67C2314yes—
175#106×C67C2314yes—
176#97×C67C2314yes—
177C23×D67—21no—
178C2×Dic134—21no—
179C2×Dic134—22no—
180C2×Dic134—24no—
181C2×Dic134—24no—
182C2×Dic134—24no—
183C2×Dic134—24no—
184C2×Dic134—82no—
185C2×Dic134—82no—
186C2×Dic134—82no—
187C2×Dic134C2×D414yes—
188C2×Dic134C2×Q814yes—
189C2×Dic134C2412yes—
190C2×D268—21no—
191C2×D268—22no—
192C2×D268C2×Q814yes—
193C2×D268C2412yes—
194C22×Dic67—21no—
195C22×Dic67—21no—
196C22×Dic67—21no—
197C22×Dic67C2×D411yescharacteristic
198C22×Dic67C2×D411yescharacteristic
199C22×Dic67C2×D411yescharacteristic
200C22×Dic67C2×D411yescharacteristic
201C2×C4×D67—24no—
202C2×C4×D67—24no—
203C2×C4×D67—24no—
204C2×C4×D67—44no—
205C2×C4×D67—82no—
206C2×C4×D67—82no—
207#11761617C2×Q8116yescomplemented
208C2×C67⋊C8—22no—
209C2×C67⋊C8—22no—
210C2×C67⋊C8C2412yes—
211C2×C67⋊C8C2412yes—
212C4⋊Dic67—21no—
213C4⋊Dic67—21no—
214C4⋊Dic67—24no—
215C4⋊Dic67C2×D414yes—
216C4⋊Dic67C2412yes—
217C4⋊Dic67C2412yes—
218Dic67⋊C4—24no—
219Dic67⋊C4—24no—
220Dic67⋊C4—24no—
221Dic67⋊C4—24no—
222Dic67⋊C4—24no—
223Dic67⋊C4—24no—
224Dic67⋊C4—24no—
225Dic67⋊C4C2×D414yes—
226Dic67⋊C4C2×D414yes—
227(C2×D67)⋊C4—24no—
228(C2×D67)⋊C4—24no—
229(C2×D67)⋊C4—24no—
230C4×Dic67—24no—
231C4×Dic67—24no—
232C4×Dic67—24no—
233C4×Dic67C2×D412yes—
234C4×Dic67C2×D412yes—
235C4×Dic67C2412yes—
236C4×Dic67C2412yes—
237C2×Q8×C67—24no—
238C2×Q8×C67—82no—
239C22×C4×C67—21no—
240C22×C4×C67—21no—
241C22×C4×C67—21no—
242C22×C4×C67—21no—
243C22×C4×C67C2×D411yescharacteristic
244C22×C4×C67C2×D411yescharacteristic
245C22×C4×C67C2411yescharacteristic
246C2×C8×C67—22no—
247C2×C8×C67C2×Q814yes—
248C2×C8×C67C2412yes—
249C2×C8×C67C2412yes—
250C4⋊C4×C67—24no—
251C4⋊C4×C67—24no—
252C4⋊C4×C67—24no—
253C4⋊C4×C67—21no—
254C4⋊C4×C67—21no—
255C4⋊C4×C67—21no—
256C4⋊C4×C67—21no—
257C4⋊C4×C67C2412yes—
258C4⋊C4×C67C2412yes—
259C4⋊C4×C67C2412yes—
260C4⋊C4×C67C2412yes—
261C42×C67C2×D412yes—
262C42×C67C2412yes—
263C23×C67C22×D411yescharacteristic
264C22×D67—24no—
265C22×D67—22no—
266C22×D67—42no—
267C22×D67—42no—
268Q8×C67—84no—
269C2×C4×C67—22no—
270C2×C4×C67—22no—
271C2×C4×C67—22no—
272C2×C4×C67—22no—
273C2×C4×C67—22no—
274C2×C4×C67—22no—
275C2×C4×C67—42no—
276C2×C4×C67—42no—
277C2×C4×C67—42no—
278C2×C4×C67—42no—
279C2×C4×C67C22×D412yes—
280C2×C4×C67C22×D412yes—
281C2×C4×C67C22×D411yescharacteristic
282C2×C4×C67C22×Q812yes—
283C2×C4×C672−1+412yes—
284C2×C4×C67C2511yescharacteristic
285C2×Dic67—24no—
286C2×Dic67—22no—
287C2×Dic67—22no—
288C2×Dic67—22no—
289C2×Dic67—22no—
290C2×Dic67—22no—
291C2×Dic67—22no—
292C2×Dic67—42no—
293C2×Dic67—42no—
294C2×Dic67#13714yes—
295C2×Dic67C22×D412yes—
296C2×Dic67C22×D412yes—
297C2×Dic67C22×D412yes—
298C2×Dic67C22×D412yes—
299D268—24no—
300D268—22no—
301D268C22×Q814yes—
302C4×D67—48no—
303C4×D67—84no—
304C4×D67—84no—
305Dic134—24no—
306Dic134—22no—
307Dic134—28no—
308Dic134—84no—
309Dic134—84no—
310Dic134—84no—
311Dic134C22×Q814yes—
312C8×C67—22no—
313C8×C67C22×Q814yes—
314C67⋊C8—22no—
315C67⋊C8—22no—
316C22×C67D4×Q812yes—
317C22×C67C2×#13712yes—
318C22×C67#57612yes—
319C22×C67C23×D411yescharacteristic
320C2×D67—24no—
321C2×D67—48no—
322C2×D67—42no—
323C2×D67—42no—
324C4×C67—22no—
325C4×C67—22no—
326C4×C67—42no—
327C4×C67—42no—
328C4×C67—42no—
329C4×C67—42no—
330C4×C67D4×Q812yes—
331C4×C67C23×Q811yescharacteristic
332C4×C67C2×2−1+411yescharacteristic
333Dic67—24no—
334Dic67—22no—
335Dic67—22no—
336Dic67—22no—
337Dic67—42no—
338Dic67—42no—
339Dic67C2×#13714yes—
340C2×#3385—671nomaximal, Sylow
341C2×C67#338514yescomplemented
342C2×C67C2×D4×Q811yescharacteristic
343C2×C67C22×#13711yescharacteristic
344C2×C67C2×#57611yescharacteristic
345D67—44no—
346C2×Q82—671no—
347C2×#554—671no—
348#3385—6716no—
349C2×#501—671no—
350C2×#501D6711yescharacteristic, complemented
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×#440—671no—
361C2×C4×SD16—671no—
362C67C2×#338511yescharacteristic, complemented, Sylow
363C22×SD16—671no—
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—1341no—
372C2×C4⋊Q8—1341no—
373C2×C4⋊Q8—1341no—
374C2×C4⋊Q8C2×D6711yescharacteristic
375C2×#125—671no—
376C2×#125C2×D6711yescharacteristic
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—671no—
384C2×C4×Q8—1341no—
385C2×C4×D4—671no—
386C2×C4×D4—671no—
387C2×C4×D4—671no—
388C22×C4⋊C4—1341no—
389#501—678no—
390#501C2×D6718yescomplemented
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#440—678no—
401C4×SD16—678no—
402C2×#107—671no—
403C2×#107—671no—
404C2×#107—671no—
405C2×#107—671no—
406C2×#107C2×D6711yescharacteristic
407C2×#107C2×D6711yescharacteristic
408C2×#106—671no—
409C2×#106C2×D6711yescharacteristic
410C2×#106C2×D6711yescharacteristic
411C2×C4⋊C8—671no—
412C2×C4⋊C8—671no—
413C2×C4⋊C8—671no—
414C2×#103—671no—
415C2×#103—671no—
416C2×#103—671no—
417C2×#102—671no—
418C2×#102—671no—
419C2×#102—671no—
420C2×#97—671no—
421C2×#97C2×D6711yescharacteristic
422C2×C4×C8—671no—
423C22×Q8—21no—
424C22×Q8—671no—
425C22×Q8—671no—
426C22×Q8—1341no—
427C22×Q8—1341no—
428C22×Q8—1341no—
429C22×D4—671no—
430C23×C4—1341no—
431C23×C4—1341no—
432C23×C4—1341no—
433C2×SD16—678no—
434C2×SD16—674no—
435C22×C8—671no—
436C22×C8—671no—
437C22×C8C22×D6711yescharacteristic
438C22×C8C22×D6711yescharacteristic
439C4⋊Q8—22no—
440C4⋊Q8—674no—
441C4⋊Q8—674no—
442C4⋊Q8—674no—
443C4⋊Q8—1342no—
444C4⋊Q8—1342no—
445C4⋊Q8—1342no—
446C4⋊Q8—1348no—
447C4⋊Q8—1348no—
448C4⋊Q8—1348no—
449C4⋊Q8C22×D6714yes—
450#125—22no—
451#125—674no—
452#125—1342no—
453#125C22×D6714yes—
454C22⋊Q8—1348no—
455C22⋊Q8—1348no—
456C22⋊Q8—1348no—
457C4×Q8—674no—
458C4×Q8—674no—
459C4×Q8—674no—
460C4×Q8—674no—
461C4×Q8—674no—
462C4×Q8—1342no—
463C4×Q8—1342no—
464C4×Q8—1348no—
465C4×Q8—1342no—
466C4×D4—674no—
467C4×D4—674no—
468C4×D4—674no—
469C4×D4—1342no—
470C4×D4—1342no—
471C4×D4—1342no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
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⋊C4C22×D6711yescharacteristic
490C2×C4⋊C4C22×D6711yescharacteristic
491C2×C4⋊C4C22×D6711yescharacteristic
492C2×C4⋊C4C22×D6711yescharacteristic
493C2×C22⋊C4—1341no—
494C2×C22⋊C4—1341no—
495C2×C22⋊C4—1341no—
496C2×C42—671no—
497C2×C42—671no—
498C2×C42—1341no—
499C2×C42—1341no—
500C2×C42—1341no—
501C2×C42C22×D6711yescharacteristic
502#107—674no—
503#107—674no—
504#107—674no—
505#107—674no—
506#107C22×D6714yes—
507#107C22×D6714yes—
508#106—674no—
509#106C22×D6714yes—
510#106C22×D6714yes—
511C4⋊C8—674no—
512C4⋊C8—674no—
513C4⋊C8—674no—
514#103—674no—
515#103—674no—
516#103—674no—
517#102—674no—
518#102—674no—
519#102—674no—
520#97—674no—
521#97C22×D6714yes—
522C4×C8—674no—
523C24—1341no—
524C2×Q8—24no—
525C2×Q8—82no—
526C2×Q8—5362no—
527C2×Q8—5362no—
528C2×Q8—5362no—
529C2×Q8—674no—
530C2×Q8—674no—
531C2×Q8—672no—
532C2×Q8—1344no—
533C2×Q8—1344no—
534C2×Q8—1344no—
535C2×Q8—1344no—
536C2×Q8—1341no—
537C2×Q8—1342no—
538C2×D4—674no—
539C2×D4—672no—
540C2×D4—1341no—
541C2×D4—1342no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—2684no—
547C22×C4—5362no—
548C22×C4—5362no—
549C22×C4—671no—
550C22×C4—671no—
551C22×C4—671no—
552C22×C4—671no—
553C22×C4—1344no—
554C22×C4—1344no—
555C22×C4—1341no—
556C22×C4—1341no—
557C22×C4—1344no—
558C22×C4—1341no—
559C22×C4D4×D6711yescharacteristic
560C22×C4D4×D6711yescharacteristic
561C22×C4C23×D6711yescharacteristic
562SD16—6716no—
563C2×C8—22no—
564C2×C8—672no—
565C2×C8—672no—
566C2×C8—1342no—
567C2×C8—1342no—
568C2×C8Q8×D6714yes—
569C2×C8C23×D6712yes—
570C2×C8C23×D6712yes—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—674no—
579C4⋊C4—674no—
580C4⋊C4—674no—
581C4⋊C4—672no—
582C4⋊C4—672no—
583C4⋊C4—1344no—
584C4⋊C4—1344no—
585C4⋊C4—1344no—
586C4⋊C4—1344no—
587C4⋊C4—1344no—
588C4⋊C4—1344no—
589C4⋊C4—1344no—
590C4⋊C4—1341no—
591C4⋊C4—1341no—
592C4⋊C4—1344no—
593C4⋊C4C23×D6712yes—
594C4⋊C4C23×D6712yes—
595C4⋊C4C23×D6712yes—
596C4⋊C4C23×D6712yes—
597C22⋊C4—1344no—
598C22⋊C4—1344no—
599C22⋊C4—1344no—
600C42—672no—
601C42—672no—
602C42—672no—
603C42—672no—
604C42—1344no—
605C42—1344no—
606C42—1344no—
607C42D4×D6712yes—
608C42C23×D6712yes—
609C23—2682no—
610C23—2682no—
611C23—1344no—
612C23—1342no—
613C23C2×D4×D6711yescharacteristic
614Q8—84no—
615Q8—5364no—
616Q8—5364no—
617Q8—5364no—
618Q8—674no—
619Q8—1348no—
620Q8—1344no—
621Q8—1342no—
622D4—674no—
623D4—1344no—
624D4—1342no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—2688no—
636C2×C4—2682no—
637C2×C4—2682no—
638C2×C4—5364no—
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—1344no—
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×C4C2×Q8×D6712yes—
656C2×C4#1452409112yes—
657C2×C4C24×D6711yescharacteristic
658C8—22no—
659C8—1342no—
660C8—1342no—
661C8C2×Q8×D6714yes—
662C22—2688no—
663C22—2682no—
664C22—2682no—
665C22—1344no—
666C22#1686406112yes—
667C22#137×D6712yes—
668C22#1686420012yes—
669C22C22×D4×D6711yescharacteristic
670C4—22no—
671C4—22no—
672C4—42no—
673C4—42no—
674C4—42no—
675C4—42no—
676C4—2682no—
677C4—2682no—
678C4—674no—
679C4—1342no—
680C4—1342no—
681C4—1342no—
682C4—1344no—
683C4#1686406112yes—
684C4C22×Q8×D6711yescharacteristic
685C4C2×#1452409111yescharacteristic
686C2—2684no—
687C2#2257311614yesdirect product factor
688C2C2×#1686406111yescharacteristic
689C2C2×#137×D6711yescharacteristic
690C2C2×#1686420011yescharacteristic
subgroupG/H
centerC23C2×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#501×C67C2
socleC23×C67C22×D4
prime radicalC22×D268C23
hypercenterC2×#501D67
hypocenterC67C2×#3385
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×#16864126C2semidirect
3. #22573116C2direct (N × H)
4. C2×#16863803C2semidirect
5. C2×#16863800C2semidirect
6. C2×#16863706C2semidirect
7. C2×#16863700C2semidirect
8. C2×#16863690C2semidirect
12. C2×#16863524C2semidirect
16. C2×#501×C67C2semidirect
19. #16864126C22semidirect
41. #16863803C22semidirect
42. #16863800C22semidirect
43. #16863706C22semidirect
44. #16863700C22semidirect
45. #16863690C22semidirect
49. #16863524C22semidirect
71. #501×C67C22semidirect
86. C2×#11761617Q8semidirect
207. #11761617C2×Q8semidirect
341. C2×C67#3385semidirect
350. C2×#501D67semidirect
362. C67C2×#3385semidirect
390. #501C2×D67semidirect
687. C2#22573116direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168641262
C2×#168641022
#225731162
C2×#168638032
C2×#168638002
C2×#168637062
C2×#168637002
C2×#168636902
C2×#168636852
C2×#168636752
C2×#168636732
C2×#168635242
C2×#168634982
C2×#168634952
C2×#168634832
C2×#501×C672
C2×#338567