Finite Group Databasebeta

← C2×#22601247 #32877938

Subgroups — C2×#22601247 #32877938

Order 18176.

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×#17986729C211yesmaximal, characteristic, complemented
2C2×#17986705C211yesmaximal, characteristic
3#22601247C2116yesmaximal, direct product factor
4C2×#17986406C211yesmaximal, characteristic, complemented
5C2×#17986403C211yesmaximal, characteristic, complemented
6C2×#17986309C211yesmaximal, characteristic, complemented
7C2×#17986303C211yesmaximal, characteristic, complemented
8C2×#17986293C211yesmaximal, characteristic, complemented
9C2×#17986288C211yesmaximal, characteristic
10C2×#17986278C211yesmaximal, characteristic
11C2×#17986276C211yesmaximal, characteristic
12C2×#17986127C211yesmaximal, characteristic, complemented
13C2×#17986101C211yesmaximal, characteristic
14C2×#17986098C211yesmaximal, characteristic
15C2×#17986086C211yesmaximal, characteristic
16C2×#501×C71C211yesmaximal, characteristic, complemented
17C22×#11765854C2211yescharacteristic
18#17986729—24no—
19#17986729C2218yescomplemented
20#17986705—24no—
21#17986705C2218yes—
22C2×#14556127—21no—
23C2×#14556127C2211yescharacteristic
24C2×#14556127C2211yescharacteristic
25C2×#14556127C2211yescharacteristic
26C2×#14556126—21no—
27C2×#14556126—21no—
28C2×#14556119C2211yescharacteristic
29C2×#14556108—21no—
30C2×#14556106—21no—
31C2×#14556106—21no—
32C2×C4×Dic142C2211yescharacteristic
33C2×C4×Dic142C2211yescharacteristic
34C2×#14556093—21no—
35C2×#14556093C2211yescharacteristic
36C2×#14556093C2211yescharacteristic
37C2×C4×D284C2211yescharacteristic
38C2×#14556090C2211yescharacteristic
39C2×#14556090C2211yescharacteristic
40C2×C4⋊C4×D71—21no—
41#17986406C2218yescomplemented
42#17986403C2218yescomplemented
43#17986309C2218yescomplemented
44#17986303C2218yescomplemented
45#17986293C2218yescomplemented
46#17986288C2218yes—
47#17986278C2218yes—
48#17986276C2218yes—
49#17986127C2218yescomplemented
50#17986101C2218yes—
51#17986098C2218yes—
52#17986086C2218yes—
53C2×#14556062C2211yescharacteristic
54C2×#14556061C2211yescharacteristic
55C2×#14556061C2211yescharacteristic
56C2×#14556061C2211yescharacteristic
57C2×#14556059C2211yescharacteristic
58C2×C4⋊(C71⋊C8)C2211yescharacteristic
59C2×Dic71⋊C8C2211yescharacteristic
60C2×Dic71⋊C8C2211yescharacteristic
61C2×#14556053C2211yescharacteristic
62C2×#14556051C2211yescharacteristic
63C2×#14556051C2211yescharacteristic
64C2×#14556050C2211yescharacteristic
65C2×#14556048C2211yescharacteristic
66C2×#14556048C2211yescharacteristic
67C2×#14556038C2211yescharacteristic
68C2×C8×Dic71C2211yescharacteristic
69C2×C4⋊Q8×C71C2211yescharacteristic
70C2×#125×C71C2211yescharacteristic
71#501×C71C2218yescomplemented
72C2×#107×C71C2211yescharacteristic
73C2×#107×C71C2211yescharacteristic
74C2×#106×C71C2211yescharacteristic
75C2×#106×C71C2211yescharacteristic
76C2×#97×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142—21no—
79C22×Dic142—21no—
80C22×Dic142D411yescharacteristic
81C22×Dic142C2311yescharacteristic
82C22×D284C2311yescharacteristic
83C22×C4×D71—21no—
84C22×C4×D71—21no—
85C22×C4×D71—21no—
86C2×#11765854Q818yescomplemented
87C2×#11765854C2314yes—
88C22×C71⋊C8C2311yescharacteristic
89C22×C71⋊C8C2311yescharacteristic
90#14556127—28no—
91#14556127—22no—
92#14556127—22no—
93#14556127—22no—
94#14556127C2314yes—
95#14556127C2314yes—
96#14556127C2314yes—
97#14556126—28no—
98#14556126—28no—
99#14556119—22no—
100#14556119C2314yes—
101#14556108—28no—
102#14556106—28no—
103#14556106—28no—
104C4×Dic142—22no—
105C4×Dic142D414yes—
106C4×Dic142C2314yes—
107C4×Dic142C2314yes—
108#14556093—28no—
109#14556093—22no—
110#14556093—22no—
111#14556093C2314yes—
112#14556093C2314yes—
113C4×D284—22no—
114C4×D284C2314yes—
115#14556090—22no—
116#14556090—22no—
117#14556090C2314yes—
118#14556090C2314yes—
119C2×C4⋊Dic71—21no—
120C2×C4⋊Dic71D411yescharacteristic
121C2×C4⋊Dic71C2311yescharacteristic
122C2×C4⋊Dic71C2311yescharacteristic
123C2×Dic71⋊C4—21no—
124C2×Dic71⋊C4—21no—
125C2×Dic71⋊C4—21no—
126C2×Dic71⋊C4—21no—
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C2×Dic71⋊C4—21no—
130C2×Dic71⋊C4D411yescharacteristic
131C2×Dic71⋊C4D411yescharacteristic
132C4⋊C4×D71—28no—
133C2×(C2×D71)⋊C4—21no—
134C2×(C2×D71)⋊C4—21no—
135C2×(C2×D71)⋊C4—21no—
136C2×C4×Dic71—21no—
137C2×C4×Dic71—21no—
138C2×C4×Dic71—21no—
139C2×C4×Dic71C2311yescharacteristic
140C2×C4×Dic71C2311yescharacteristic
141#14556062C2314yes—
142#14556061C2314yes—
143#14556061C2314yes—
144#14556061C2314yes—
145#14556059C2314yes—
146C4⋊(C71⋊C8)C2314yes—
147Dic71⋊C8C2314yes—
148Dic71⋊C8C2314yes—
149#14556053C2314yes—
150#14556051C2314yes—
151#14556051C2314yes—
152#14556050C2314yes—
153#14556048C2314yes—
154#14556048C2314yes—
155#14556038C2314yes—
156C8×Dic71C2314yes—
157C22×Q8×C71—21no—
158C22×C8×C71C2311yescharacteristic
159C22×C8×C71C2311yescharacteristic
160C4⋊Q8×C71—22no—
161C4⋊Q8×C71C2314yes—
162#125×C71—22no—
163#125×C71C2314yes—
164C2×C4⋊C4×C71—21no—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71—21no—
167C2×C4⋊C4×C71C2311yescharacteristic
168C2×C4⋊C4×C71C2311yescharacteristic
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C42×C71C2311yescharacteristic
172#107×C71C2314yes—
173#107×C71C2314yes—
174#106×C71C2314yes—
175#106×C71C2314yes—
176#97×C71C2314yes—
177C23×D71—21no—
178C2×Dic142—21no—
179C2×Dic142—22no—
180C2×Dic142—24no—
181C2×Dic142—24no—
182C2×Dic142—24no—
183C2×Dic142—24no—
184C2×Dic142—82no—
185C2×Dic142—82no—
186C2×Dic142—82no—
187C2×Dic142C2×D414yes—
188C2×Dic142C2×Q814yes—
189C2×Dic142C2412yes—
190C2×D284—21no—
191C2×D284—22no—
192C2×D284C2×Q814yes—
193C2×D284C2412yes—
194C22×Dic71—21no—
195C22×Dic71—21no—
196C22×Dic71—21no—
197C22×Dic71C2×D411yescharacteristic
198C22×Dic71C2×D411yescharacteristic
199C22×Dic71C2×D411yescharacteristic
200C22×Dic71C2×D411yescharacteristic
201C2×C4×D71—24no—
202C2×C4×D71—24no—
203C2×C4×D71—24no—
204C2×C4×D71—44no—
205C2×C4×D71—82no—
206C2×C4×D71—82no—
207#11765854C2×Q8116yescomplemented
208C2×C71⋊C8—22no—
209C2×C71⋊C8—22no—
210C2×C71⋊C8C2412yes—
211C2×C71⋊C8C2412yes—
212C4⋊Dic71—21no—
213C4⋊Dic71—21no—
214C4⋊Dic71—24no—
215C4⋊Dic71C2×D414yes—
216C4⋊Dic71C2412yes—
217C4⋊Dic71C2412yes—
218Dic71⋊C4—24no—
219Dic71⋊C4—24no—
220Dic71⋊C4—24no—
221Dic71⋊C4—24no—
222Dic71⋊C4—24no—
223Dic71⋊C4—24no—
224Dic71⋊C4—24no—
225Dic71⋊C4C2×D414yes—
226Dic71⋊C4C2×D414yes—
227(C2×D71)⋊C4—24no—
228(C2×D71)⋊C4—24no—
229(C2×D71)⋊C4—24no—
230C4×Dic71—24no—
231C4×Dic71—24no—
232C4×Dic71—24no—
233C4×Dic71C2×D412yes—
234C4×Dic71C2×D412yes—
235C4×Dic71C2412yes—
236C4×Dic71C2412yes—
237C2×Q8×C71—24no—
238C2×Q8×C71—82no—
239C22×C4×C71—21no—
240C22×C4×C71—21no—
241C22×C4×C71—21no—
242C22×C4×C71—21no—
243C22×C4×C71C2×D411yescharacteristic
244C22×C4×C71C2×D411yescharacteristic
245C22×C4×C71C2411yescharacteristic
246C2×C8×C71—22no—
247C2×C8×C71C2×Q814yes—
248C2×C8×C71C2412yes—
249C2×C8×C71C2412yes—
250C4⋊C4×C71—24no—
251C4⋊C4×C71—24no—
252C4⋊C4×C71—24no—
253C4⋊C4×C71—21no—
254C4⋊C4×C71—21no—
255C4⋊C4×C71—21no—
256C4⋊C4×C71—21no—
257C4⋊C4×C71C2412yes—
258C4⋊C4×C71C2412yes—
259C4⋊C4×C71C2412yes—
260C4⋊C4×C71C2412yes—
261C42×C71C2×D412yes—
262C42×C71C2412yes—
263C23×C71C22×D411yescharacteristic
264C22×D71—24no—
265C22×D71—22no—
266C22×D71—42no—
267C22×D71—42no—
268Q8×C71—84no—
269C2×C4×C71—22no—
270C2×C4×C71—22no—
271C2×C4×C71—22no—
272C2×C4×C71—22no—
273C2×C4×C71—22no—
274C2×C4×C71—22no—
275C2×C4×C71—42no—
276C2×C4×C71—42no—
277C2×C4×C71—42no—
278C2×C4×C71—42no—
279C2×C4×C71C22×D412yes—
280C2×C4×C71C22×D412yes—
281C2×C4×C71C22×D411yescharacteristic
282C2×C4×C71C22×Q812yes—
283C2×C4×C712−1+412yes—
284C2×C4×C71C2511yescharacteristic
285C2×Dic71—24no—
286C2×Dic71—22no—
287C2×Dic71—22no—
288C2×Dic71—22no—
289C2×Dic71—22no—
290C2×Dic71—22no—
291C2×Dic71—22no—
292C2×Dic71—42no—
293C2×Dic71—42no—
294C2×Dic71#13714yes—
295C2×Dic71C22×D412yes—
296C2×Dic71C22×D412yes—
297C2×Dic71C22×D412yes—
298C2×Dic71C22×D412yes—
299D284—24no—
300D284—22no—
301D284C22×Q814yes—
302C4×D71—48no—
303C4×D71—84no—
304C4×D71—84no—
305Dic142—24no—
306Dic142—22no—
307Dic142—28no—
308Dic142—84no—
309Dic142—84no—
310Dic142—84no—
311Dic142C22×Q814yes—
312C8×C71—22no—
313C8×C71C22×Q814yes—
314C71⋊C8—22no—
315C71⋊C8—22no—
316C22×C71D4×Q812yes—
317C22×C71C2×#13712yes—
318C22×C71#57612yes—
319C22×C71C23×D411yescharacteristic
320C2×D71—24no—
321C2×D71—48no—
322C2×D71—42no—
323C2×D71—42no—
324C4×C71—22no—
325C4×C71—22no—
326C4×C71—42no—
327C4×C71—42no—
328C4×C71—42no—
329C4×C71—42no—
330C4×C71D4×Q812yes—
331C4×C71C23×Q811yescharacteristic
332C4×C71C2×2−1+411yescharacteristic
333Dic71—24no—
334Dic71—22no—
335Dic71—22no—
336Dic71—22no—
337Dic71—42no—
338Dic71—42no—
339Dic71C2×#13714yes—
340C2×#3385—711nomaximal, Sylow
341C2×C71#338514yescomplemented
342C2×C71C2×D4×Q811yescharacteristic
343C2×C71C22×#13711yescharacteristic
344C2×C71C2×#57611yescharacteristic
345D71—44no—
346C2×Q82—711no—
347C2×#554—711no—
348#3385—7116no—
349C2×#501—711no—
350C2×#501D7111yescharacteristic, complemented
351C2×#500—711no—
352C2×#479—711no—
353C2×#479—711no—
354C2×#477—711no—
355C2×#476—711no—
356C2×#474—711no—
357C2×#474—711no—
358C2×#446—711no—
359C2×#440—711no—
360C2×#440—711no—
361C2×C4×SD16—711no—
362C71C2×#338511yescharacteristic, complemented, Sylow
363C22×SD16—711no—
364Q82—718no—
365Q82—1424no—
366#554—718no—
367#554—1424no—
368C2×C4⋊Q8—711no—
369C2×C4⋊Q8—711no—
370C2×C4⋊Q8—711no—
371C2×C4⋊Q8—1421no—
372C2×C4⋊Q8—1421no—
373C2×C4⋊Q8—1421no—
374C2×C4⋊Q8C2×D7111yescharacteristic
375C2×#125—711no—
376C2×#125C2×D7111yescharacteristic
377C2×C22⋊Q8—1421no—
378C2×C22⋊Q8—1421no—
379C2×C22⋊Q8—1421no—
380C2×C4×Q8—711no—
381C2×C4×Q8—711no—
382C2×C4×Q8—711no—
383C2×C4×Q8—711no—
384C2×C4×Q8—1421no—
385C2×C4×D4—711no—
386C2×C4×D4—711no—
387C2×C4×D4—711no—
388C22×C4⋊C4—1421no—
389#501—718no—
390#501C2×D7118yescomplemented
391#500—718no—
392#479—718no—
393#479—718no—
394#477—718no—
395#476—718no—
396#474—718no—
397#474—718no—
398#446—718no—
399#440—718no—
400#440—718no—
401C4×SD16—718no—
402C2×#107—711no—
403C2×#107—711no—
404C2×#107—711no—
405C2×#107—711no—
406C2×#107C2×D7111yescharacteristic
407C2×#107C2×D7111yescharacteristic
408C2×#106—711no—
409C2×#106C2×D7111yescharacteristic
410C2×#106C2×D7111yescharacteristic
411C2×C4⋊C8—711no—
412C2×C4⋊C8—711no—
413C2×C4⋊C8—711no—
414C2×#103—711no—
415C2×#103—711no—
416C2×#103—711no—
417C2×#102—711no—
418C2×#102—711no—
419C2×#102—711no—
420C2×#97—711no—
421C2×#97C2×D7111yescharacteristic
422C2×C4×C8—711no—
423C22×Q8—21no—
424C22×Q8—711no—
425C22×Q8—711no—
426C22×Q8—1421no—
427C22×Q8—1421no—
428C22×Q8—1421no—
429C22×D4—711no—
430C23×C4—1421no—
431C23×C4—1421no—
432C23×C4—1421no—
433C2×SD16—718no—
434C2×SD16—714no—
435C22×C8—711no—
436C22×C8—711no—
437C22×C8C22×D7111yescharacteristic
438C22×C8C22×D7111yescharacteristic
439C4⋊Q8—22no—
440C4⋊Q8—714no—
441C4⋊Q8—714no—
442C4⋊Q8—714no—
443C4⋊Q8—1422no—
444C4⋊Q8—1422no—
445C4⋊Q8—1422no—
446C4⋊Q8—1428no—
447C4⋊Q8—1428no—
448C4⋊Q8—1428no—
449C4⋊Q8C22×D7114yes—
450#125—22no—
451#125—714no—
452#125—1422no—
453#125C22×D7114yes—
454C22⋊Q8—1428no—
455C22⋊Q8—1428no—
456C22⋊Q8—1428no—
457C4×Q8—714no—
458C4×Q8—714no—
459C4×Q8—714no—
460C4×Q8—714no—
461C4×Q8—714no—
462C4×Q8—1422no—
463C4×Q8—1422no—
464C4×Q8—1428no—
465C4×Q8—1422no—
466C4×D4—714no—
467C4×D4—714no—
468C4×D4—714no—
469C4×D4—1422no—
470C4×D4—1422no—
471C4×D4—1422no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—711no—
476C2×C4⋊C4—711no—
477C2×C4⋊C4—711no—
478C2×C4⋊C4—711no—
479C2×C4⋊C4—711no—
480C2×C4⋊C4—1428no—
481C2×C4⋊C4—1421no—
482C2×C4⋊C4—1421no—
483C2×C4⋊C4—1421no—
484C2×C4⋊C4—1421no—
485C2×C4⋊C4—1421no—
486C2×C4⋊C4—1421no—
487C2×C4⋊C4—1421no—
488C2×C4⋊C4—1421no—
489C2×C4⋊C4C22×D7111yescharacteristic
490C2×C4⋊C4C22×D7111yescharacteristic
491C2×C4⋊C4C22×D7111yescharacteristic
492C2×C4⋊C4C22×D7111yescharacteristic
493C2×C22⋊C4—1421no—
494C2×C22⋊C4—1421no—
495C2×C22⋊C4—1421no—
496C2×C42—711no—
497C2×C42—711no—
498C2×C42—1421no—
499C2×C42—1421no—
500C2×C42—1421no—
501C2×C42C22×D7111yescharacteristic
502#107—714no—
503#107—714no—
504#107—714no—
505#107—714no—
506#107C22×D7114yes—
507#107C22×D7114yes—
508#106—714no—
509#106C22×D7114yes—
510#106C22×D7114yes—
511C4⋊C8—714no—
512C4⋊C8—714no—
513C4⋊C8—714no—
514#103—714no—
515#103—714no—
516#103—714no—
517#102—714no—
518#102—714no—
519#102—714no—
520#97—714no—
521#97C22×D7114yes—
522C4×C8—714no—
523C24—1421no—
524C2×Q8—24no—
525C2×Q8—82no—
526C2×Q8—5682no—
527C2×Q8—5682no—
528C2×Q8—5682no—
529C2×Q8—714no—
530C2×Q8—714no—
531C2×Q8—712no—
532C2×Q8—1424no—
533C2×Q8—1424no—
534C2×Q8—1424no—
535C2×Q8—1424no—
536C2×Q8—1421no—
537C2×Q8—1422no—
538C2×D4—714no—
539C2×D4—712no—
540C2×D4—1421no—
541C2×D4—1422no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—2844no—
547C22×C4—5682no—
548C22×C4—5682no—
549C22×C4—711no—
550C22×C4—711no—
551C22×C4—711no—
552C22×C4—711no—
553C22×C4—1424no—
554C22×C4—1424no—
555C22×C4—1421no—
556C22×C4—1421no—
557C22×C4—1424no—
558C22×C4—1421no—
559C22×C4D4×D7111yescharacteristic
560C22×C4D4×D7111yescharacteristic
561C22×C4C23×D7111yescharacteristic
562SD16—7116no—
563C2×C8—22no—
564C2×C8—712no—
565C2×C8—712no—
566C2×C8—1422no—
567C2×C8—1422no—
568C2×C8Q8×D7114yes—
569C2×C8C23×D7112yes—
570C2×C8C23×D7112yes—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—714no—
579C4⋊C4—714no—
580C4⋊C4—714no—
581C4⋊C4—712no—
582C4⋊C4—712no—
583C4⋊C4—1424no—
584C4⋊C4—1424no—
585C4⋊C4—1424no—
586C4⋊C4—1424no—
587C4⋊C4—1424no—
588C4⋊C4—1424no—
589C4⋊C4—1424no—
590C4⋊C4—1424no—
591C4⋊C4—1421no—
592C4⋊C4—1421no—
593C4⋊C4C23×D7112yes—
594C4⋊C4C23×D7112yes—
595C4⋊C4C23×D7112yes—
596C4⋊C4C23×D7112yes—
597C22⋊C4—1424no—
598C22⋊C4—1424no—
599C22⋊C4—1424no—
600C42—712no—
601C42—712no—
602C42—712no—
603C42—712no—
604C42—1424no—
605C42—1424no—
606C42—1424no—
607C42D4×D7112yes—
608C42C23×D7112yes—
609C23—2842no—
610C23—2842no—
611C23—1422no—
612C23—1424no—
613C23C2×D4×D7111yescharacteristic
614Q8—84no—
615Q8—5684no—
616Q8—5684no—
617Q8—5684no—
618Q8—714no—
619Q8—1428no—
620Q8—1422no—
621Q8—1424no—
622D4—714no—
623D4—1422no—
624D4—1424no—
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—2848no—
636C2×C4—2842no—
637C2×C4—2842no—
638C2×C4—5684no—
639C2×C4—5684no—
640C2×C4—712no—
641C2×C4—714no—
642C2×C4—712no—
643C2×C4—712no—
644C2×C4—712no—
645C2×C4—1422no—
646C2×C4—1422no—
647C2×C4—1422no—
648C2×C4—1424no—
649C2×C4—1422no—
650C2×C4—1422no—
651C2×C4—1422no—
652C2×C4C2×D4×D7112yes—
653C2×C4C2×D4×D7112yes—
654C2×C4C2×D4×D7111yescharacteristic
655C2×C4C2×Q8×D7112yes—
656C2×C4#1455617612yes—
657C2×C4C24×D7111yescharacteristic
658C8—22no—
659C8—1422no—
660C8—1422no—
661C8C2×Q8×D7114yes—
662C22—2848no—
663C22—2842no—
664C22—2842no—
665C22—1424no—
666C22#1798666412yes—
667C22#137×D7112yes—
668C22#1798680312yes—
669C22C22×D4×D7111yescharacteristic
670C4—22no—
671C4—22no—
672C4—42no—
673C4—42no—
674C4—42no—
675C4—42no—
676C4—2842no—
677C4—2842no—
678C4—714no—
679C4—1422no—
680C4—1422no—
681C4—1422no—
682C4—1424no—
683C4#1798666412yes—
684C4C22×Q8×D7111yescharacteristic
685C4C2×#1455617611yescharacteristic
686C2—2844no—
687C2#2260124714yesdirect product factor
688C2C2×#1798666411yescharacteristic
689C2C2×#137×D7111yescharacteristic
690C2C2×#1798680311yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#501×C71C2
socleC23×C71C22×D4
prime radicalC22×D284C23
hypercenterC2×#501D71
hypocenterC71C2×#3385
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#17986729C2semidirect
3. #22601247C2direct (N × H)
4. C2×#17986406C2semidirect
5. C2×#17986403C2semidirect
6. C2×#17986309C2semidirect
7. C2×#17986303C2semidirect
8. C2×#17986293C2semidirect
12. C2×#17986127C2semidirect
16. C2×#501×C71C2semidirect
19. #17986729C22semidirect
41. #17986406C22semidirect
42. #17986403C22semidirect
43. #17986309C22semidirect
44. #17986303C22semidirect
45. #17986293C22semidirect
49. #17986127C22semidirect
71. #501×C71C22semidirect
86. C2×#11765854Q8semidirect
207. #11765854C2×Q8semidirect
341. C2×C71#3385semidirect
350. C2×#501D71semidirect
362. C71C2×#3385semidirect
390. #501C2×D71semidirect
687. C2#22601247direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867292
C2×#179867052
#226012472
C2×#179864062
C2×#179864032
C2×#179863092
C2×#179863032
C2×#179862932
C2×#179862882
C2×#179862782
C2×#179862762
C2×#179861272
C2×#179861012
C2×#179860982
C2×#179860862
C2×#501×C712
C2×#338571