Finite Group Databasebeta

← C2×#22598875 #32867081

Subgroups — C2×#22598875 #32867081

Order 18176.

1854 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986629C211yesmaximal, characteristic
2C2×#17986626C211yesmaximal, characteristic
3#22598875C2116yesmaximal, direct product factor
4C2×#17986408C211yesmaximal, characteristic, complemented
5C2×#17986407C211yesmaximal, characteristic, complemented
6C2×#17986406C211yesmaximal, characteristic, complemented
7C2×#17986403C211yesmaximal, characteristic, complemented
8C2×#17986402C211yesmaximal, characteristic, complemented
9C2×#17986399C211yesmaximal, characteristic, complemented
10C2×#17986398C211yesmaximal, characteristic, complemented
11C2×#17986040C211yesmaximal, characteristic
12C2×#17986038C211yesmaximal, characteristic
13C2×#17986034C211yesmaximal, characteristic
14C2×#107×D71C211yesmaximal, characteristic
15C2×#17985956C211yesmaximal, characteristic
16C2×#501×C71C211yesmaximal, characteristic, complemented
17C22×#11765848C2211yescharacteristic
18C22×C8×D71C2211yescharacteristic
19#17986629—24no—
20#17986629C2218yes—
21#17986626—24no—
22#17986626C2218yes—
23C2×#14556128C2211yescharacteristic
24C2×#14556127—21no—
25C2×#14556127C2211yescharacteristic
26C2×#14556127C2211yescharacteristic
27C2×#14556126—21no—
28C2×#14556120C2211yescharacteristic
29C2×#14556119C2211yescharacteristic
30C2×#14556119C2211yescharacteristic
31C2×#14556118—21no—
32C2×#14556118—21no—
33C2×#14556108—21no—
34C2×#14556106—21no—
35C2×#14556106—21no—
36C2×#14556104—21no—
37C2×#14556086C2211yescharacteristic
38C2×#14556086C2211yescharacteristic
39C2×#14556085C2211yescharacteristic
40C2×C4⋊C4×D71C2211yescharacteristic
41C2×C4⋊C4×D71C2211yescharacteristic
42#17986408C2218yescomplemented
43#17986407C2218yescomplemented
44#17986406C2218yescomplemented
45#17986403C2218yescomplemented
46#17986402C2218yescomplemented
47#17986399C2218yescomplemented
48#17986398C2218yescomplemented
49#17986040C2218yes—
50#17986038C2218yes—
51#17986034C2218yes—
52C2×#14556062C2211yescharacteristic
53C2×#14556062C2211yescharacteristic
54C2×#14556061C2211yescharacteristic
55C2×#14556061C2211yescharacteristic
56C2×#14556061C2211yescharacteristic
57C2×#14556061C2211yescharacteristic
58C2×#14556061C2211yescharacteristic
59C2×#14556061C2211yescharacteristic
60#107×D71C2218yes—
61C2×#14556060C2211yescharacteristic
62C2×#14556060C2211yescharacteristic
63C2×#14556059C2211yescharacteristic
64C2×#14556059C2211yescharacteristic
65#17985956C2218yes—
66C2×#14556038C2211yescharacteristic
67C2×C4×C71⋊C8C2211yescharacteristic
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×C4×D71—21no—
81C22×C4×D71—21no—
82C22×C4×D71C2311yescharacteristic
83C2×#11765848Q818yescomplemented
84C2×#11765848C2314yes—
85C22×C71⋊C8C2311yescharacteristic
86C22×C71⋊C8C2311yescharacteristic
87C2×C8×D71Q818yescomplemented
88C2×C8×D71C2314yes—
89#14556128—22no—
90#14556128C2314yes—
91#14556127—28no—
92#14556127—22no—
93#14556127—22no—
94#14556127C2314yes—
95#14556127C2314yes—
96#14556126—28no—
97#14556120—22no—
98#14556120C2314yes—
99#14556119—22no—
100#14556119—22no—
101#14556119C2314yes—
102#14556119C2314yes—
103#14556118—28no—
104#14556118—28no—
105#14556108—28no—
106#14556106—28no—
107#14556106—28no—
108#14556104—28no—
109#14556086—22no—
110#14556086—22no—
111#14556086C2314yes—
112#14556086C2314yes—
113#14556085D414yes—
114#14556085C2314yes—
115C2×C4⋊Dic71—21no—
116C2×C4⋊Dic71—21no—
117C2×C4⋊Dic71—21no—
118C2×C4⋊Dic71C2311yescharacteristic
119C2×C4⋊Dic71C2311yescharacteristic
120C2×C4⋊Dic71C2311yescharacteristic
121C2×C4⋊Dic71C2311yescharacteristic
122C2×Dic71⋊C4—21no—
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—22no—
133C4⋊C4×D71—22no—
134C4⋊C4×D71C2314yes—
135C4⋊C4×D71C2314yes—
136C2×(C2×D71)⋊C4—21no—
137C2×(C2×D71)⋊C4—21no—
138C2×(C2×D71)⋊C4D411yescharacteristic
139C2×(C2×D71)⋊C4D411yescharacteristic
140C2×C4×Dic71—21no—
141C2×C4×Dic71—21no—
142C2×C4×Dic71C2311yescharacteristic
143#14556062C2314yes—
144#14556062C2314yes—
145#14556061C2314yes—
146#14556061C2314yes—
147#14556061C2314yes—
148#14556061C2314yes—
149#14556061C2314yes—
150#14556061C2314yes—
151#14556060C2314yes—
152#14556060C2314yes—
153#14556059C2314yes—
154#14556059C2314yes—
155#14556038C2314yes—
156C4×C71⋊C8C2314yes—
157C8×Dic71C2314yes—
158C22×Q8×C71—21no—
159C22×C8×C71C2311yescharacteristic
160C22×C8×C71C2311yescharacteristic
161C4⋊Q8×C71—22no—
162C4⋊Q8×C71C2314yes—
163#125×C71—22no—
164#125×C71C2314yes—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71—21no—
167C2×C4⋊C4×C71—21no—
168C2×C4⋊C4×C71C2311yescharacteristic
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C42×C71C2311yescharacteristic
173#107×C71C2314yes—
174#107×C71C2314yes—
175#106×C71C2314yes—
176#106×C71C2314yes—
177#97×C71C2314yes—
178C23×D71C2×D411yescharacteristic
179C2×Dic142—24no—
180C2×Dic142—24no—
181C2×Dic142—24no—
182C2×Dic142—82no—
183C2×Dic142—82no—
184C2×Dic142—82no—
185C22×Dic71—21no—
186C22×Dic71—21no—
187C22×Dic71—21no—
188C22×Dic71—21no—
189C22×Dic71C2×D411yescharacteristic
190C22×Dic71C2×D411yescharacteristic
191C22×Dic71C2×D411yescharacteristic
192C2×C4×D71—24no—
193C2×C4×D71—24no—
194C2×C4×D71—82no—
195C2×C4×D71—82no—
196C2×C4×D71C2×D412yes—
197C2×C4×D71C2×Q814yes—
198C2×C4×D71C2×Q814yes—
199C2×C4×D71C2412yes—
200#11765848C2×Q8116yescomplemented
201C2×C71⋊C8C2×Q814yes—
202C2×C71⋊C8C2×Q814yes—
203C2×C71⋊C8C2412yes—
204C2×C71⋊C8C2412yes—
205C8×D71C2×Q8116yescomplemented
206C4⋊Dic71—21no—
207C4⋊Dic71—21no—
208C4⋊Dic71—24no—
209C4⋊Dic71—21no—
210C4⋊Dic71—21no—
211C4⋊Dic71—24no—
212C4⋊Dic71—24no—
213C4⋊Dic71C2412yes—
214C4⋊Dic71C2412yes—
215C4⋊Dic71C2412yes—
216C4⋊Dic71C2412yes—
217Dic71⋊C4—24no—
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)⋊C4C2×D414yes—
230(C2×D71)⋊C4C2×D414yes—
231C4×Dic71—24no—
232C4×Dic71—24no—
233C4×Dic71C2×D412yes—
234C4×Dic71C2412yes—
235C2×Q8×C71—24no—
236C2×Q8×C71—82no—
237C22×C4×C71—21no—
238C22×C4×C71—21no—
239C22×C4×C71—21no—
240C22×C4×C71—21no—
241C22×C4×C71C2×D411yescharacteristic
242C22×C4×C71C2×D411yescharacteristic
243C22×C4×C71C2411yescharacteristic
244C2×C8×C71C2×Q814yes—
245C2×C8×C71C2×Q814yes—
246C2×C8×C71C2412yes—
247C2×C8×C71C2412yes—
248C4⋊C4×C71—24no—
249C4⋊C4×C71—24no—
250C4⋊C4×C71—24no—
251C4⋊C4×C71—21no—
252C4⋊C4×C71—21no—
253C4⋊C4×C71—21no—
254C4⋊C4×C71—21no—
255C4⋊C4×C71C2412yes—
256C4⋊C4×C71C2412yes—
257C4⋊C4×C71C2412yes—
258C4⋊C4×C71C2412yes—
259C42×C71C2×D412yes—
260C42×C71C2412yes—
261C23×C71C22×D411yescharacteristic
262C22×D71—22no—
263C22×D71—22no—
264C22×D71C4⋊Q814yes—
265C22×D71C22×D412yes—
266Q8×C71—84no—
267C2×C4×C71—22no—
268C2×C4×C71—22no—
269C2×C4×C71—22no—
270C2×C4×C71—22no—
271C2×C4×C71—22no—
272C2×C4×C71—22no—
273C2×C4×C71—42no—
274C2×C4×C71—42no—
275C2×C4×C71—42no—
276C2×C4×C71—42no—
277C2×C4×C71C22×D412yes—
278C2×C4×C71C22×D412yes—
279C2×C4×C71C22×D411yescharacteristic
280C2×C4×C71C22×Q812yes—
281C2×C4×C71C22×Q812yes—
282C2×C4×C71C2511yescharacteristic
283C2×Dic71—22no—
284C2×Dic71—22no—
285C2×Dic71—22no—
286C2×Dic71—22no—
287C2×Dic71—22no—
288C2×Dic71—22no—
289C2×Dic71—42no—
290C2×Dic71—42no—
291C2×Dic71—42no—
292C2×Dic71—42no—
293C2×Dic71C4⋊Q814yes—
294C2×Dic71C22×D412yes—
295C2×Dic71C22×D412yes—
296C2×Dic71C22×D412yes—
297C4×D71—84no—
298C4×D71—84no—
299C4×D71C4⋊Q818yes—
300C4×D71C22×Q814yes—
301C4×D71C22×Q814yes—
302Dic142—84no—
303Dic142—84no—
304Dic142—84no—
305C8×C71C22×Q814yes—
306C8×C71C22×Q814yes—
307C71⋊C8C22×Q814yes—
308C71⋊C8C22×Q814yes—
309C22×C71C2×C4⋊Q812yes—
310C22×C71#57612yes—
311C22×C71#57812yes—
312C22×C71C23×D411yescharacteristic
313C2×D71—28no—
314C2×D71—22no—
315C2×D71—22no—
316C2×D71C2×C4⋊Q814yes—
317C4×C71—22no—
318C4×C71—22no—
319C4×C71—42no—
320C4×C71—42no—
321C4×C71—42no—
322C4×C71—42no—
323C4×C71C2×C4⋊Q812yes—
324C4×C71C23×Q811yescharacteristic
325C4×C71C23×Q811yescharacteristic
326Dic71—22no—
327Dic71—22no—
328Dic71—42no—
329Dic71—42no—
330Dic71—42no—
331Dic71—42no—
332Dic71C2×C4⋊Q814yes—
333C2×#3164—711nomaximal, Sylow
334C2×C71#316414yescomplemented
335C2×C71C22×C4⋊Q811yescharacteristic
336C2×C71C2×#57611yescharacteristic
337C2×C71C2×#57811yescharacteristic
338D71—24no—
339C2×#544—711no—
340C2×#544—711no—
341#3164—7116no—
342C2×#501—711no—
343C2×#501—711no—
344C2×#501—711no—
345C2×#501D7111yescharacteristic, complemented
346C2×#500—711no—
347C2×#500—711no—
348C2×#499—711no—
349C2×#499—711no—
350C2×#428—711no—
351C2×#428—711no—
352C2×#427—711no—
353C22×#107—711no—
354C2×#405—711no—
355C71C2×#316411yescharacteristic, complemented, Sylow
356C22×M16—711no—
357C23×C8—711no—
358#544—718no—
359#544—718no—
360#544—1424no—
361#544—1424no—
362C2×C4⋊Q8—711no—
363C2×C4⋊Q8—711no—
364C2×C4⋊Q8—711no—
365C2×C4⋊Q8—1421no—
366C2×C4⋊Q8—1421no—
367C2×C4⋊Q8C2×D7111yescharacteristic
368C2×#125—711no—
369C2×#125—711no—
370C2×#125—711no—
371C2×#125—1421no—
372C2×#125—1421no—
373C2×#125C2×D7111yescharacteristic
374C2×C22⋊Q8—1421no—
375C2×C22⋊Q8—1421no—
376C2×C22⋊Q8—1421no—
377C2×C22⋊Q8—1421no—
378C2×#117—711no—
379C2×#117—711no—
380C2×#117—711no—
381C22×C4⋊C4—711no—
382C22×C4⋊C4—711no—
383#501—718no—
384#501—718no—
385#501—718no—
386#501C2×D7118yescomplemented
387#500—718no—
388#500—718no—
389#499—718no—
390#499—718no—
391#428—718no—
392#428—718no—
393#427—718no—
394C2×#107—711no—
395C2×#107—711no—
396C2×#107—711no—
397C2×#107—711no—
398C2×#107—711no—
399C2×#107—711no—
400C2×#107—711no—
401C2×#107—711no—
402C2×#107—718no—
403C2×#107C2×D7111yescharacteristic
404C2×#107C2×D7111yescharacteristic
405C2×#106—711no—
406C2×#106—711no—
407C2×#106—711no—
408C2×#106—711no—
409C2×#106C2×D7111yescharacteristic
410C2×#106C2×D7111yescharacteristic
411#405—718no—
412C2×#97—711no—
413C2×#97C2×D7111yescharacteristic
414C2×C4×C8—711no—
415C2×C4×C8—711no—
416C22×Q8—21no—
417C22×Q8—1421no—
418C22×Q8—1421no—
419C22×Q8—1421no—
420C23×C4—711no—
421C23×C4—1421no—
422C23×C4—1421no—
423C2×M16—718no—
424C2×M16—714no—
425C22×C8—711no—
426C22×C8—711no—
427C22×C8—718no—
428C22×C8—714no—
429C22×C8C22×D7111yescharacteristic
430C22×C8C22×D7111yescharacteristic
431C4⋊Q8—22no—
432C4⋊Q8—714no—
433C4⋊Q8—714no—
434C4⋊Q8—714no—
435C4⋊Q8—1422no—
436C4⋊Q8—1422no—
437C4⋊Q8—1428no—
438C4⋊Q8—1428no—
439C4⋊Q8—1422no—
440C4⋊Q8C22×D7114yes—
441#125—22no—
442#125—714no—
443#125—714no—
444#125—714no—
445#125—1422no—
446#125—1422no—
447#125—1428no—
448#125—1428no—
449#125—1422no—
450#125C22×D7114yes—
451C22⋊Q8—1428no—
452C22⋊Q8—1428no—
453C22⋊Q8—1428no—
454C22⋊Q8—1428no—
455#117—714no—
456#117—714no—
457#117—714no—
458#117—714no—
459#117—1422no—
460#117—1422no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—711no—
465C2×C4⋊C4—711no—
466C2×C4⋊C4—711no—
467C2×C4⋊C4—711no—
468C2×C4⋊C4—711no—
469C2×C4⋊C4—711no—
470C2×C4⋊C4—714no—
471C2×C4⋊C4—714no—
472C2×C4⋊C4—1422no—
473C2×C4⋊C4—1422no—
474C2×C4⋊C4—1421no—
475C2×C4⋊C4—1421no—
476C2×C4⋊C4—1421no—
477C2×C4⋊C4—1421no—
478C2×C4⋊C4—1421no—
479C2×C4⋊C4—1421no—
480C2×C4⋊C4—1421no—
481C2×C4⋊C4—1421no—
482C2×C4⋊C4—1421no—
483C2×C4⋊C4—1421no—
484C2×C4⋊C4—1421no—
485C2×C4⋊C4C22×D7111yescharacteristic
486C2×C4⋊C4C22×D7111yescharacteristic
487C2×C4⋊C4C22×D7111yescharacteristic
488C2×C4⋊C4C22×D7111yescharacteristic
489C2×C22⋊C4—711no—
490C2×C22⋊C4—711no—
491C2×C22⋊C4—1421no—
492C2×C22⋊C4—1421no—
493C2×C42—711no—
494C2×C42—1421no—
495C2×C42—1421no—
496C2×C42C22×D7111yescharacteristic
497#107—714no—
498#107—714no—
499#107—714no—
500#107—714no—
501#107—714no—
502#107—714no—
503#107—714no—
504#107—714no—
505#107C22×D7114yes—
506#107C22×D7114yes—
507#106—714no—
508#106—714no—
509#106—714no—
510#106—714no—
511#106C22×D7114yes—
512#106C22×D7114yes—
513#97—714no—
514#97C22×D7114yes—
515C4×C8—714no—
516C4×C8—714no—
517C24—711no—
518C2×Q8—24no—
519C2×Q8—82no—
520C2×Q8—5682no—
521C2×Q8—5682no—
522C2×Q8—5682no—
523C2×Q8—1424no—
524C2×Q8—1424no—
525C2×Q8—1424no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—5682no—
531C22×C4—5682no—
532C22×C4—711no—
533C22×C4—712no—
534C22×C4—714no—
535C22×C4—714no—
536C22×C4—712no—
537C22×C4—711no—
538C22×C4—711no—
539C22×C4—1424no—
540C22×C4—1424no—
541C22×C4—1421no—
542C22×C4—1421no—
543C22×C4—1421no—
544C22×C4—1421no—
545C22×C4D4×D7111yescharacteristic
546C22×C4D4×D7111yescharacteristic
547C22×C4C23×D7111yescharacteristic
548M16—7116no—
549C2×C8—714no—
550C2×C8—714no—
551C2×C8—712no—
552C2×C8—712no—
553C2×C8—7116no—
554C2×C8Q8×D7114yes—
555C2×C8Q8×D7114yes—
556C2×C8C23×D7112yes—
557C2×C8C23×D7112yes—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—714no—
566C4⋊C4—714no—
567C4⋊C4—712no—
568C4⋊C4—712no—
569C4⋊C4—712no—
570C4⋊C4—712no—
571C4⋊C4—1424no—
572C4⋊C4—1424no—
573C4⋊C4—1424no—
574C4⋊C4—1424no—
575C4⋊C4—1424no—
576C4⋊C4—1424no—
577C4⋊C4—1424no—
578C4⋊C4—1424no—
579C4⋊C4—1424no—
580C4⋊C4—1424no—
581C4⋊C4—1421no—
582C4⋊C4—1421no—
583C4⋊C4—1421no—
584C4⋊C4—1421no—
585C4⋊C4—1424no—
586C4⋊C4C23×D7112yes—
587C4⋊C4C23×D7112yes—
588C4⋊C4C23×D7112yes—
589C4⋊C4C23×D7112yes—
590C22⋊C4—714no—
591C22⋊C4—714no—
592C22⋊C4—1424no—
593C22⋊C4—1424no—
594C42—712no—
595C42—712no—
596C42—1424no—
597C42—1424no—
598C42D4×D7112yes—
599C42C23×D7112yes—
600C23—712no—
601C23—714no—
602C23—1422no—
603C23—1422no—
604C23C2×D4×D7111yescharacteristic
605Q8—84no—
606Q8—5684no—
607Q8—5684no—
608Q8—5684no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—2842no—
620C2×C4—2842no—
621C2×C4—2842no—
622C2×C4—2842no—
623C2×C4—5684no—
624C2×C4—5684no—
625C2×C4—712no—
626C2×C4—714no—
627C2×C4—714no—
628C2×C4—714no—
629C2×C4—718no—
630C2×C4—712no—
631C2×C4—712no—
632C2×C4—1422no—
633C2×C4—1422no—
634C2×C4—1422no—
635C2×C4—1422no—
636C2×C4—1422no—
637C2×C4—1422no—
638C2×C4C2×D4×D7112yes—
639C2×C4C2×D4×D7112yes—
640C2×C4C2×D4×D7111yescharacteristic
641C2×C4C2×Q8×D7112yes—
642C2×C4C2×Q8×D7112yes—
643C2×C4C24×D7111yescharacteristic
644C8—714no—
645C8—714no—
646C8C2×Q8×D7114yes—
647C8C2×Q8×D7114yes—
648C22—714no—
649C22—1422no—
650C22—1422no—
651C22—1428no—
652C22C4⋊Q8×D7112yes—
653C22#1798680312yes—
654C22#1798681512yes—
655C22C22×D4×D7111yescharacteristic
656C4—22no—
657C4—22no—
658C4—42no—
659C4—42no—
660C4—42no—
661C4—42no—
662C4—2842no—
663C4—2842no—
664C4—2842no—
665C4—2842no—
666C4—714no—
667C4—1422no—
668C4—1422no—
669C4C4⋊Q8×D7112yes—
670C4C22×Q8×D7111yescharacteristic
671C4C22×Q8×D7111yescharacteristic
672C2—1424no—
673C2#2259887514yesdirect product factor
674C2C2×C4⋊Q8×D7111yescharacteristic
675C2C2×#1798680311yescharacteristic
676C2C2×#1798681511yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#501×C71C2
socleC23×C71C22×D4
prime radicalC23×D71C2×D4
hypercenterC2×#501D71
hypocenterC71C2×#3164
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
3. #22598875C2direct (N × H)
4. C2×#17986408C2semidirect
5. C2×#17986407C2semidirect
6. C2×#17986406C2semidirect
7. C2×#17986403C2semidirect
8. C2×#17986402C2semidirect
9. C2×#17986399C2semidirect
10. C2×#17986398C2semidirect
16. C2×#501×C71C2semidirect
42. #17986408C22semidirect
43. #17986407C22semidirect
44. #17986406C22semidirect
45. #17986403C22semidirect
46. #17986402C22semidirect
47. #17986399C22semidirect
48. #17986398C22semidirect
71. #501×C71C22semidirect
83. C2×#11765848Q8semidirect
87. C2×C8×D71Q8semidirect
200. #11765848C2×Q8semidirect
205. C8×D71C2×Q8semidirect
334. C2×C71#3164semidirect
345. C2×#501D71semidirect
355. C71C2×#3164semidirect
386. #501C2×D71semidirect
673. C2#22598875direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866292
C2×#179866262
#225988752
C2×#179864082
C2×#179864072
C2×#179864062
C2×#179864032
C2×#179864022
C2×#179863992
C2×#179863982
C2×#179860402
C2×#179860382
C2×#179860342
C2×#107×D712
C2×#179859562
C2×#501×C712
C2×#316471