Finite Group Databasebeta

← C2×#22570736 #31725451

Subgroups — C2×#22570736 #31725451

Order 17152.

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×#16864026C211yesmaximal, characteristic
2C2×#16864023C211yesmaximal, characteristic
3#22570736C2116yesmaximal, direct product factor
4C2×#16863805C211yesmaximal, characteristic, complemented
5C2×#16863804C211yesmaximal, characteristic, complemented
6C2×#16863803C211yesmaximal, characteristic, complemented
7C2×#16863797C211yesmaximal, characteristic, complemented
8C2×#16863795C211yesmaximal, characteristic, complemented
9C2×#16863793C211yesmaximal, characteristic, complemented
10C2×#16863792C211yesmaximal, characteristic, complemented
11C2×#16863437C211yesmaximal, characteristic
12C2×#16863435C211yesmaximal, characteristic
13C2×#16863433C211yesmaximal, characteristic
14C2×#106×D67C211yesmaximal, characteristic
15C2×#16863353C211yesmaximal, characteristic
16C2×#501×C67C211yesmaximal, characteristic, complemented
17C22×#11761611C2211yescharacteristic
18C22×C8×D67C2211yescharacteristic
19#16864026—24no—
20#16864026C2218yes—
21#16864023—24no—
22#16864023C2218yes—
23C2×#14524043C2211yescharacteristic
24C2×#14524042—21no—
25C2×#14524042C2211yescharacteristic
26C2×#14524042C2211yescharacteristic
27C2×#14524041—21no—
28C2×#14524035C2211yescharacteristic
29C2×#14524034C2211yescharacteristic
30C2×#14524034C2211yescharacteristic
31C2×#14524033—21no—
32C2×#14524033—21no—
33C2×#14524023—21no—
34C2×#14524021—21no—
35C2×#14524021—21no—
36C2×#14524019—21no—
37C2×#14524001C2211yescharacteristic
38C2×#14524001C2211yescharacteristic
39C2×#14524000C2211yescharacteristic
40C2×C4⋊C4×D67C2211yescharacteristic
41C2×C4⋊C4×D67C2211yescharacteristic
42#16863805C2218yescomplemented
43#16863804C2218yescomplemented
44#16863803C2218yescomplemented
45#16863797C2218yescomplemented
46#16863795C2218yescomplemented
47#16863793C2218yescomplemented
48#16863792C2218yescomplemented
49#16863437C2218yes—
50#16863435C2218yes—
51#16863433C2218yes—
52C2×#14523977C2211yescharacteristic
53C2×#14523977C2211yescharacteristic
54C2×#14523976C2211yescharacteristic
55C2×#14523976C2211yescharacteristic
56C2×#14523975C2211yescharacteristic
57C2×#14523975C2211yescharacteristic
58C2×#14523974C2211yescharacteristic
59C2×#14523974C2211yescharacteristic
60C2×#14523974C2211yescharacteristic
61C2×#14523974C2211yescharacteristic
62C2×#14523974C2211yescharacteristic
63C2×#14523974C2211yescharacteristic
64#106×D67C2218yes—
65#16863353C2218yes—
66C2×#14523953C2211yescharacteristic
67C2×C4×C67⋊C8C2211yescharacteristic
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×C4×D67—21no—
81C22×C4×D67—21no—
82C22×C4×D67C2311yescharacteristic
83C2×#11761611Q818yescomplemented
84C2×#11761611C2314yes—
85C22×C67⋊C8C2311yescharacteristic
86C22×C67⋊C8C2311yescharacteristic
87C2×C8×D67Q818yescomplemented
88C2×C8×D67C2314yes—
89#14524043—22no—
90#14524043C2314yes—
91#14524042—28no—
92#14524042—22no—
93#14524042—22no—
94#14524042C2314yes—
95#14524042C2314yes—
96#14524041—28no—
97#14524035—22no—
98#14524035C2314yes—
99#14524034—22no—
100#14524034—22no—
101#14524034C2314yes—
102#14524034C2314yes—
103#14524033—28no—
104#14524033—28no—
105#14524023—28no—
106#14524021—28no—
107#14524021—28no—
108#14524019—28no—
109#14524001—22no—
110#14524001—22no—
111#14524001C2314yes—
112#14524001C2314yes—
113#14524000D414yes—
114#14524000C2314yes—
115C2×C4⋊Dic67—21no—
116C2×C4⋊Dic67—21no—
117C2×C4⋊Dic67—21no—
118C2×C4⋊Dic67C2311yescharacteristic
119C2×C4⋊Dic67C2311yescharacteristic
120C2×C4⋊Dic67C2311yescharacteristic
121C2×C4⋊Dic67C2311yescharacteristic
122C2×Dic67⋊C4—21no—
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—22no—
133C4⋊C4×D67—22no—
134C4⋊C4×D67C2314yes—
135C4⋊C4×D67C2314yes—
136C2×(C2×D67)⋊C4—21no—
137C2×(C2×D67)⋊C4—21no—
138C2×(C2×D67)⋊C4D411yescharacteristic
139C2×(C2×D67)⋊C4D411yescharacteristic
140C2×C4×Dic67—21no—
141C2×C4×Dic67—21no—
142C2×C4×Dic67C2311yescharacteristic
143#14523977C2314yes—
144#14523977C2314yes—
145#14523976C2314yes—
146#14523976C2314yes—
147#14523975C2314yes—
148#14523975C2314yes—
149#14523974C2314yes—
150#14523974C2314yes—
151#14523974C2314yes—
152#14523974C2314yes—
153#14523974C2314yes—
154#14523974C2314yes—
155#14523953C2314yes—
156C4×C67⋊C8C2314yes—
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×D67C2×D411yescharacteristic
179C2×Dic134—24no—
180C2×Dic134—24no—
181C2×Dic134—24no—
182C2×Dic134—82no—
183C2×Dic134—82no—
184C2×Dic134—82no—
185C22×Dic67—21no—
186C22×Dic67—21no—
187C22×Dic67—21no—
188C22×Dic67—21no—
189C22×Dic67C2×D411yescharacteristic
190C22×Dic67C2×D411yescharacteristic
191C22×Dic67C2×D411yescharacteristic
192C2×C4×D67—24no—
193C2×C4×D67—24no—
194C2×C4×D67—82no—
195C2×C4×D67—82no—
196C2×C4×D67C2×D412yes—
197C2×C4×D67C2×Q814yes—
198C2×C4×D67C2×Q814yes—
199C2×C4×D67C2412yes—
200#11761611C2×Q8116yescomplemented
201C2×C67⋊C8C2×Q814yes—
202C2×C67⋊C8C2×Q814yes—
203C2×C67⋊C8C2412yes—
204C2×C67⋊C8C2412yes—
205C8×D67C2×Q8116yescomplemented
206C4⋊Dic67—21no—
207C4⋊Dic67—21no—
208C4⋊Dic67—24no—
209C4⋊Dic67—21no—
210C4⋊Dic67—21no—
211C4⋊Dic67—24no—
212C4⋊Dic67—24no—
213C4⋊Dic67C2412yes—
214C4⋊Dic67C2412yes—
215C4⋊Dic67C2412yes—
216C4⋊Dic67C2412yes—
217Dic67⋊C4—24no—
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)⋊C4C2×D414yes—
230(C2×D67)⋊C4C2×D414yes—
231C4×Dic67—24no—
232C4×Dic67—24no—
233C4×Dic67C2×D412yes—
234C4×Dic67C2412yes—
235C2×Q8×C67—24no—
236C2×Q8×C67—82no—
237C22×C4×C67—21no—
238C22×C4×C67—21no—
239C22×C4×C67—21no—
240C22×C4×C67—21no—
241C22×C4×C67C2×D411yescharacteristic
242C22×C4×C67C2×D411yescharacteristic
243C22×C4×C67C2411yescharacteristic
244C2×C8×C67C2×Q814yes—
245C2×C8×C67C2×Q814yes—
246C2×C8×C67C2412yes—
247C2×C8×C67C2412yes—
248C4⋊C4×C67—24no—
249C4⋊C4×C67—24no—
250C4⋊C4×C67—24no—
251C4⋊C4×C67—21no—
252C4⋊C4×C67—21no—
253C4⋊C4×C67—21no—
254C4⋊C4×C67—21no—
255C4⋊C4×C67C2412yes—
256C4⋊C4×C67C2412yes—
257C4⋊C4×C67C2412yes—
258C4⋊C4×C67C2412yes—
259C42×C67C2×D412yes—
260C42×C67C2412yes—
261C23×C67C22×D411yescharacteristic
262C22×D67—22no—
263C22×D67—22no—
264C22×D67C4⋊Q814yes—
265C22×D67C22×D412yes—
266Q8×C67—84no—
267C2×C4×C67—22no—
268C2×C4×C67—22no—
269C2×C4×C67—22no—
270C2×C4×C67—22no—
271C2×C4×C67—22no—
272C2×C4×C67—22no—
273C2×C4×C67—42no—
274C2×C4×C67—42no—
275C2×C4×C67—42no—
276C2×C4×C67—42no—
277C2×C4×C67C22×D412yes—
278C2×C4×C67C22×D412yes—
279C2×C4×C67C22×D411yescharacteristic
280C2×C4×C67C22×Q812yes—
281C2×C4×C67C22×Q812yes—
282C2×C4×C67C2511yescharacteristic
283C2×Dic67—22no—
284C2×Dic67—22no—
285C2×Dic67—22no—
286C2×Dic67—22no—
287C2×Dic67—22no—
288C2×Dic67—22no—
289C2×Dic67—42no—
290C2×Dic67—42no—
291C2×Dic67—42no—
292C2×Dic67—42no—
293C2×Dic67C4⋊Q814yes—
294C2×Dic67C22×D412yes—
295C2×Dic67C22×D412yes—
296C2×Dic67C22×D412yes—
297C4×D67—84no—
298C4×D67—84no—
299C4×D67C4⋊Q818yes—
300C4×D67C22×Q814yes—
301C4×D67C22×Q814yes—
302Dic134—84no—
303Dic134—84no—
304Dic134—84no—
305C8×C67C22×Q814yes—
306C8×C67C22×Q814yes—
307C67⋊C8C22×Q814yes—
308C67⋊C8C22×Q814yes—
309C22×C67C2×C4⋊Q812yes—
310C22×C67#57712yes—
311C22×C67#57712yes—
312C22×C67C23×D411yescharacteristic
313C2×D67—28no—
314C2×D67—22no—
315C2×D67—22no—
316C2×D67C2×C4⋊Q814yes—
317C4×C67—22no—
318C4×C67—22no—
319C4×C67—42no—
320C4×C67—42no—
321C4×C67—42no—
322C4×C67—42no—
323C4×C67C2×C4⋊Q812yes—
324C4×C67C23×Q811yescharacteristic
325C4×C67C23×Q811yescharacteristic
326Dic67—22no—
327Dic67—22no—
328Dic67—42no—
329Dic67—42no—
330Dic67—42no—
331Dic67—42no—
332Dic67C2×C4⋊Q814yes—
333C2×#3163—671nomaximal, Sylow
334C2×C67#316314yescomplemented
335C2×C67C22×C4⋊Q811yescharacteristic
336C2×C67C2×#57711yescharacteristic
337C2×C67C2×#57711yescharacteristic
338D67—24no—
339C2×#544—671no—
340C2×#544—671no—
341#3163—6716no—
342C2×#501—671no—
343C2×#501—671no—
344C2×#501—671no—
345C2×#501D6711yescharacteristic, complemented
346C2×#499—671no—
347C2×#499—671no—
348C2×#498—671no—
349C2×#498—671no—
350C2×#428—671no—
351C2×#428—671no—
352C2×#427—671no—
353C22×#106—671no—
354C2×#405—671no—
355C67C2×#316311yescharacteristic, complemented, Sylow
356C22×M16—671no—
357C23×C8—671no—
358#544—678no—
359#544—678no—
360#544—1344no—
361#544—1344no—
362C2×C4⋊Q8—671no—
363C2×C4⋊Q8—671no—
364C2×C4⋊Q8—671no—
365C2×C4⋊Q8—1341no—
366C2×C4⋊Q8—1341no—
367C2×C4⋊Q8C2×D6711yescharacteristic
368C2×#125—671no—
369C2×#125—671no—
370C2×#125—671no—
371C2×#125—1341no—
372C2×#125—1341no—
373C2×#125C2×D6711yescharacteristic
374C2×C22⋊Q8—1341no—
375C2×C22⋊Q8—1341no—
376C2×C22⋊Q8—1341no—
377C2×C22⋊Q8—1341no—
378C2×#117—671no—
379C2×#117—671no—
380C2×#117—671no—
381C22×C4⋊C4—671no—
382C22×C4⋊C4—671no—
383#501—678no—
384#501—678no—
385#501—678no—
386#501C2×D6718yescomplemented
387#499—678no—
388#499—678no—
389#498—678no—
390#498—678no—
391#428—678no—
392#428—678no—
393#427—678no—
394C2×#107—671no—
395C2×#107—671no—
396C2×#107—671no—
397C2×#107—671no—
398C2×#107C2×D6711yescharacteristic
399C2×#107C2×D6711yescharacteristic
400C2×#106—671no—
401C2×#106—671no—
402C2×#106—671no—
403C2×#106—671no—
404C2×#106—671no—
405C2×#106—671no—
406C2×#106—671no—
407C2×#106—671no—
408C2×#106—678no—
409C2×#106C2×D6711yescharacteristic
410C2×#106C2×D6711yescharacteristic
411#405—678no—
412C2×#97—671no—
413C2×#97C2×D6711yescharacteristic
414C2×C4×C8—671no—
415C2×C4×C8—671no—
416C22×Q8—21no—
417C22×Q8—1341no—
418C22×Q8—1341no—
419C22×Q8—1341no—
420C23×C4—671no—
421C23×C4—1341no—
422C23×C4—1341no—
423C2×M16—678no—
424C2×M16—674no—
425C22×C8—671no—
426C22×C8—671no—
427C22×C8—678no—
428C22×C8—674no—
429C22×C8C22×D6711yescharacteristic
430C22×C8C22×D6711yescharacteristic
431C4⋊Q8—22no—
432C4⋊Q8—674no—
433C4⋊Q8—674no—
434C4⋊Q8—674no—
435C4⋊Q8—1342no—
436C4⋊Q8—1342no—
437C4⋊Q8—1348no—
438C4⋊Q8—1348no—
439C4⋊Q8—1342no—
440C4⋊Q8C22×D6714yes—
441#125—22no—
442#125—674no—
443#125—674no—
444#125—674no—
445#125—1342no—
446#125—1342no—
447#125—1348no—
448#125—1348no—
449#125—1342no—
450#125C22×D6714yes—
451C22⋊Q8—1348no—
452C22⋊Q8—1348no—
453C22⋊Q8—1348no—
454C22⋊Q8—1348no—
455#117—674no—
456#117—674no—
457#117—674no—
458#117—674no—
459#117—1342no—
460#117—1342no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—671no—
465C2×C4⋊C4—671no—
466C2×C4⋊C4—671no—
467C2×C4⋊C4—671no—
468C2×C4⋊C4—671no—
469C2×C4⋊C4—671no—
470C2×C4⋊C4—674no—
471C2×C4⋊C4—674no—
472C2×C4⋊C4—1342no—
473C2×C4⋊C4—1342no—
474C2×C4⋊C4—1341no—
475C2×C4⋊C4—1341no—
476C2×C4⋊C4—1341no—
477C2×C4⋊C4—1341no—
478C2×C4⋊C4—1341no—
479C2×C4⋊C4—1341no—
480C2×C4⋊C4—1341no—
481C2×C4⋊C4—1341no—
482C2×C4⋊C4—1341no—
483C2×C4⋊C4—1341no—
484C2×C4⋊C4—1341no—
485C2×C4⋊C4C22×D6711yescharacteristic
486C2×C4⋊C4C22×D6711yescharacteristic
487C2×C4⋊C4C22×D6711yescharacteristic
488C2×C4⋊C4C22×D6711yescharacteristic
489C2×C22⋊C4—671no—
490C2×C22⋊C4—671no—
491C2×C22⋊C4—1341no—
492C2×C22⋊C4—1341no—
493C2×C42—671no—
494C2×C42—1341no—
495C2×C42—1341no—
496C2×C42C22×D6711yescharacteristic
497#107—674no—
498#107—674no—
499#107—674no—
500#107—674no—
501#107C22×D6714yes—
502#107C22×D6714yes—
503#106—674no—
504#106—674no—
505#106—674no—
506#106—674no—
507#106—674no—
508#106—674no—
509#106—674no—
510#106—674no—
511#106C22×D6714yes—
512#106C22×D6714yes—
513#97—674no—
514#97C22×D6714yes—
515C4×C8—674no—
516C4×C8—674no—
517C24—671no—
518C2×Q8—24no—
519C2×Q8—82no—
520C2×Q8—5362no—
521C2×Q8—5362no—
522C2×Q8—5362no—
523C2×Q8—1344no—
524C2×Q8—1344no—
525C2×Q8—1344no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—5362no—
531C22×C4—5362no—
532C22×C4—671no—
533C22×C4—672no—
534C22×C4—674no—
535C22×C4—674no—
536C22×C4—672no—
537C22×C4—671no—
538C22×C4—671no—
539C22×C4—1344no—
540C22×C4—1344no—
541C22×C4—1341no—
542C22×C4—1341no—
543C22×C4—1341no—
544C22×C4—1341no—
545C22×C4D4×D6711yescharacteristic
546C22×C4D4×D6711yescharacteristic
547C22×C4C23×D6711yescharacteristic
548M16—6716no—
549C2×C8—674no—
550C2×C8—674no—
551C2×C8—672no—
552C2×C8—672no—
553C2×C8—6716no—
554C2×C8Q8×D6714yes—
555C2×C8Q8×D6714yes—
556C2×C8C23×D6712yes—
557C2×C8C23×D6712yes—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—674no—
566C4⋊C4—674no—
567C4⋊C4—672no—
568C4⋊C4—672no—
569C4⋊C4—672no—
570C4⋊C4—672no—
571C4⋊C4—1344no—
572C4⋊C4—1344no—
573C4⋊C4—1344no—
574C4⋊C4—1344no—
575C4⋊C4—1344no—
576C4⋊C4—1344no—
577C4⋊C4—1344no—
578C4⋊C4—1344no—
579C4⋊C4—1341no—
580C4⋊C4—1341no—
581C4⋊C4—1341no—
582C4⋊C4—1341no—
583C4⋊C4—1344no—
584C4⋊C4—1344no—
585C4⋊C4—1344no—
586C4⋊C4C23×D6712yes—
587C4⋊C4C23×D6712yes—
588C4⋊C4C23×D6712yes—
589C4⋊C4C23×D6712yes—
590C22⋊C4—674no—
591C22⋊C4—674no—
592C22⋊C4—1344no—
593C22⋊C4—1344no—
594C42—672no—
595C42—672no—
596C42—1344no—
597C42—1344no—
598C42D4×D6712yes—
599C42C23×D6712yes—
600C23—674no—
601C23—672no—
602C23—1342no—
603C23—1342no—
604C23C2×D4×D6711yescharacteristic
605Q8—84no—
606Q8—5364no—
607Q8—5364no—
608Q8—5364no—
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—2682no—
620C2×C4—2682no—
621C2×C4—2682no—
622C2×C4—2682no—
623C2×C4—5364no—
624C2×C4—5364no—
625C2×C4—674no—
626C2×C4—672no—
627C2×C4—678no—
628C2×C4—674no—
629C2×C4—674no—
630C2×C4—672no—
631C2×C4—672no—
632C2×C4—1342no—
633C2×C4—1342no—
634C2×C4—1342no—
635C2×C4—1342no—
636C2×C4—1342no—
637C2×C4—1342no—
638C2×C4C2×D4×D6712yes—
639C2×C4C2×D4×D6712yes—
640C2×C4C2×D4×D6711yescharacteristic
641C2×C4C2×Q8×D6712yes—
642C2×C4C2×Q8×D6712yes—
643C2×C4C24×D6711yescharacteristic
644C8—674no—
645C8—674no—
646C8C2×Q8×D6714yes—
647C8C2×Q8×D6714yes—
648C22—674no—
649C22—1342no—
650C22—1342no—
651C22—1348no—
652C22C4⋊Q8×D6712yes—
653C22#1686420512yes—
654C22#1686420612yes—
655C22C22×D4×D6711yescharacteristic
656C4—22no—
657C4—22no—
658C4—42no—
659C4—42no—
660C4—42no—
661C4—42no—
662C4—2682no—
663C4—2682no—
664C4—2682no—
665C4—2682no—
666C4—674no—
667C4—1342no—
668C4—1342no—
669C4C4⋊Q8×D6712yes—
670C4C22×Q8×D6711yescharacteristic
671C4C22×Q8×D6711yescharacteristic
672C2—1344no—
673C2#2257073614yesdirect product factor
674C2C2×C4⋊Q8×D6711yescharacteristic
675C2C2×#1686420511yescharacteristic
676C2C2×#1686420611yescharacteristic
subgroupG/H
centerC23C2×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#501×C67C2
socleC23×C67C22×D4
prime radicalC23×D67C2×D4
hypercenterC2×#501D67
hypocenterC67C2×#3163
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
3. #22570736C2direct (N × H)
4. C2×#16863805C2semidirect
5. C2×#16863804C2semidirect
6. C2×#16863803C2semidirect
7. C2×#16863797C2semidirect
8. C2×#16863795C2semidirect
9. C2×#16863793C2semidirect
10. C2×#16863792C2semidirect
16. C2×#501×C67C2semidirect
42. #16863805C22semidirect
43. #16863804C22semidirect
44. #16863803C22semidirect
45. #16863797C22semidirect
46. #16863795C22semidirect
47. #16863793C22semidirect
48. #16863792C22semidirect
71. #501×C67C22semidirect
83. C2×#11761611Q8semidirect
87. C2×C8×D67Q8semidirect
200. #11761611C2×Q8semidirect
205. C8×D67C2×Q8semidirect
334. C2×C67#3163semidirect
345. C2×#501D67semidirect
355. C67C2×#3163semidirect
386. #501C2×D67semidirect
673. C2#22570736direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640262
C2×#168640232
#225707362
C2×#168638052
C2×#168638042
C2×#168638032
C2×#168637972
C2×#168637952
C2×#168637932
C2×#168637922
C2×#168634372
C2×#168634352
C2×#168634332
C2×#106×D672
C2×#168633532
C2×#501×C672
C2×#316367