Finite Group Databasebeta

← C2×#22573156 #31736360

Subgroups — C2×#22573156 #31736360

Order 17152.

1822 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864124C211yesmaximal, characteristic, complemented
2C2×#16864106C211yesmaximal, characteristic
3#22573156C2116yesmaximal, direct product factor
4C2×#16863805C211yesmaximal, characteristic, complemented
5C2×#16863805C211yesmaximal, characteristic, complemented
6C2×#16863798C211yesmaximal, characteristic, complemented
7C2×#16863704C211yesmaximal, characteristic, complemented
8C2×#16863704C211yesmaximal, characteristic, complemented
9C2×#16863682C211yesmaximal, characteristic, complemented
10C2×#16863697C211yesmaximal, characteristic
11C2×#16863697C211yesmaximal, characteristic
12C2×#16863687C211yesmaximal, characteristic
13C2×#16863498C211yesmaximal, characteristic
14C2×#16863498C211yesmaximal, characteristic
15C2×C4×#11761617C211yesmaximal, characteristic
16C2×#446×C67C211yesmaximal, characteristic, complemented
17C22×#11761617C2211yescharacteristic
18#16864124—24no—
19#16864124C2218yescomplemented
20#16864106—24no—
21#16864106C2218yes—
22C2×#14524043C2211yescharacteristic
23C2×#14524043C2211yescharacteristic
24C2×#14524041—21no—
25C2×#14524035C2211yescharacteristic
26C2×#14524035C2211yescharacteristic
27C2×#14524035C2211yescharacteristic
28C2×#14524035C2211yescharacteristic
29C2×#14524033—21no—
30C2×#14524033—21no—
31C2×#14524021—21no—
32C2×#14524021—21no—
33C2×#14524019—21no—
34C2×C4×Dic134C2211yescharacteristic
35C2×C4×Dic134C2211yescharacteristic
36C2×C4×Dic134C2211yescharacteristic
37C2×#14524008—21no—
38C2×C4×D268C2211yescharacteristic
39C2×C4×D268C2211yescharacteristic
40C2×C4×D268C2211yescharacteristic
41C2×C4⋊C4×D67—21no—
42#16863805C2218yescomplemented
43#16863805C2218yescomplemented
44#16863798C2218yescomplemented
45#16863704C2218yescomplemented
46#16863704C2218yescomplemented
47#16863697C2218yes—
48#16863697C2218yes—
49#16863687C2218yes—
50#16863682C2218yescomplemented
51#16863498C2218yes—
52#16863498C2218yes—
53C4×#11761617C2218yes—
54C2×#14523977C2211yescharacteristic
55C2×#14523977C2211yescharacteristic
56C2×#14523977C2211yescharacteristic
57C2×#14523977C2211yescharacteristic
58C2×#14523975C2211yescharacteristic
59C2×#14523975C2211yescharacteristic
60C2×#14523975C2211yescharacteristic
61C2×#14523975C2211yescharacteristic
62C2×#14523975C2211yescharacteristic
63C2×#14523968C2211yescharacteristic
64C2×#14523968C2211yescharacteristic
65C2×#14523968C2211yescharacteristic
66C2×#14523965C2211yescharacteristic
67C2×#14523965C2211yescharacteristic
68C2×#14523965C2211yescharacteristic
69C2×C4×Q8×C67C2211yescharacteristic
70#446×C67C2218yescomplemented
71C2×C4⋊C8×C67C2211yescharacteristic
72C2×C4⋊C8×C67C2211yescharacteristic
73C2×C4⋊C8×C67C2211yescharacteristic
74C2×#97×C67C2211yescharacteristic
75C2×#97×C67C2211yescharacteristic
76C2×C4×C8×C67C2211yescharacteristic
77C22×Dic134—21no—
78C22×Dic134—21no—
79C22×Dic134C2311yescharacteristic
80C22×D268C2311yescharacteristic
81C22×C4×D67—21no—
82C22×C4×D67—21no—
83C22×C4×D67—21no—
84C2×#11761617Q818yescomplemented
85C2×#11761617C2314yes—
86#14524043—22no—
87#14524043—22no—
88#14524043C2314yes—
89#14524043C2314yes—
90#14524041—28no—
91#14524035—22no—
92#14524035—22no—
93#14524035—22no—
94#14524035—22no—
95#14524035C2314yes—
96#14524035C2314yes—
97#14524035C2314yes—
98#14524035C2314yes—
99#14524033—28no—
100#14524033—28no—
101#14524021—28no—
102#14524021—28no—
103#14524019—28no—
104C4×Dic134—22no—
105C4×Dic134—22no—
106C4×Dic134—22no—
107C4×Dic134C2314yes—
108C4×Dic134C2314yes—
109C4×Dic134C2314yes—
110#14524008—28no—
111C4×D268—22no—
112C4×D268—22no—
113C4×D268—22no—
114C4×D268C2314yes—
115C4×D268C2314yes—
116C4×D268C2314yes—
117C2×C4⋊Dic67—21no—
118C2×C4⋊Dic67—21no—
119C2×C4⋊Dic67C2311yescharacteristic
120C2×C4⋊Dic67C2311yescharacteristic
121C2×C4⋊Dic67C2311yescharacteristic
122C2×C4⋊Dic67C2311yescharacteristic
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⋊C4—21no—
133C2×Dic67⋊C4—21no—
134C2×Dic67⋊C4—21no—
135C2×Dic67⋊C4—21no—
136C4⋊C4×D67—28no—
137C2×(C2×D67)⋊C4—21no—
138C2×(C2×D67)⋊C4—21no—
139C2×(C2×D67)⋊C4—21no—
140C2×C4×Dic67—21no—
141C2×C4×Dic67—21no—
142C2×C4×Dic67—21no—
143#14523977C2314yes—
144#14523977C2314yes—
145#14523977C2314yes—
146#14523977C2314yes—
147#14523975C2314yes—
148#14523975C2314yes—
149#14523975C2314yes—
150#14523975C2314yes—
151#14523975C2314yes—
152#14523968C2314yes—
153#14523968C2314yes—
154#14523968C2314yes—
155#14523965C2314yes—
156#14523965C2314yes—
157#14523965C2314yes—
158C22×Q8×C67D411yescharacteristic
159C22×C8×C67C2311yescharacteristic
160C22×C8×C67C2311yescharacteristic
161C22×C8×C67C2311yescharacteristic
162C22×C8×C67C2311yescharacteristic
163C4×Q8×C67D414yes—
164C4×Q8×C67C2314yes—
165C2×C4⋊C4×C67D411yescharacteristic
166C2×C4⋊C4×C67D411yescharacteristic
167C2×C4⋊C4×C67D411yescharacteristic
168C2×C42×C67C2311yescharacteristic
169C2×C42×C67C2311yescharacteristic
170C2×C42×C67C2311yescharacteristic
171C4⋊C8×C67C2314yes—
172C4⋊C8×C67C2314yes—
173C4⋊C8×C67C2314yes—
174#97×C67C2314yes—
175#97×C67C2314yes—
176C4×C8×C67C2314yes—
177C23×D67—21no—
178C2×Dic134—21no—
179C2×Dic134—22no—
180C2×Dic134—24no—
181C2×Dic134—24no—
182C2×Dic134—44no—
183C2×Dic134—82no—
184C2×Dic134C2×Q814yes—
185C2×Dic134C2412yes—
186C2×D268—21no—
187C2×D268—22no—
188C2×D268C2×Q814yes—
189C2×D268C2412yes—
190C22×Dic67—21no—
191C22×Dic67—21no—
192C22×Dic67—21no—
193C22×Dic67—21no—
194C22×Dic67—21no—
195C22×Dic67—21no—
196C22×Dic67—21no—
197C2×C4×D67—24no—
198C2×C4×D67—24no—
199C2×C4×D67—24no—
200C2×C4×D67—44no—
201C2×C4×D67—82no—
202C2×C4×D67—82no—
203#11761617C2×Q8116yescomplemented
204C4⋊Dic67—24no—
205C4⋊Dic67—24no—
206C4⋊Dic67—21no—
207C4⋊Dic67—21no—
208C4⋊Dic67—21no—
209C4⋊Dic67—21no—
210C4⋊Dic67—21no—
211C4⋊Dic67—21no—
212C4⋊Dic67C2412yes—
213C4⋊Dic67C2412yes—
214C4⋊Dic67C2412yes—
215C4⋊Dic67C2412yes—
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⋊C4—24no—
226Dic67⋊C4—24no—
227Dic67⋊C4—24no—
228Dic67⋊C4—24no—
229(C2×D67)⋊C4—24no—
230(C2×D67)⋊C4—24no—
231(C2×D67)⋊C4—24no—
232C4×Dic67—24no—
233C4×Dic67—24no—
234C4×Dic67—24no—
235C2×Q8×C67—42no—
236C2×Q8×C67C2×D414yes—
237C22×C4×C67C2×D411yescharacteristic
238C22×C4×C67C2×D411yescharacteristic
239C22×C4×C67C2×D411yescharacteristic
240C22×C4×C67C2×D411yescharacteristic
241C22×C4×C67C2×D411yescharacteristic
242C22×C4×C67C2×D411yescharacteristic
243C22×C4×C67C2411yescharacteristic
244C2×C8×C67—22no—
245C2×C8×C67—22no—
246C2×C8×C67—22no—
247C2×C8×C67C2×Q814yes—
248C2×C8×C67C2412yes—
249C2×C8×C67C2412yes—
250C2×C8×C67C2412yes—
251C2×C8×C67C2412yes—
252C4⋊C4×C67C2×D414yes—
253C4⋊C4×C67C2×D414yes—
254C4⋊C4×C67C2×D414yes—
255C42×C67C2×D412yes—
256C42×C67C2×D412yes—
257C42×C67C2×D412yes—
258C42×C67C2412yes—
259C42×C67C2412yes—
260C42×C67C2412yes—
261C23×C67C22×D411yescharacteristic
262C22×D67—24no—
263C22×D67—22no—
264C22×D67—42no—
265C22×D67—42no—
266Q8×C67—44no—
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×C67C22×D412yes—
274C2×C4×C67C22×D412yes—
275C2×C4×C67C22×D412yes—
276C2×C4×C67C22×D412yes—
277C2×C4×C67C22×D412yes—
278C2×C4×C67C22×D412yes—
279C2×C4×C67C22×D411yescharacteristic
280C2×C4×C67C22×Q812yes—
281C2×C4×C672−1+412yes—
282C2×C4×C67C2511yescharacteristic
283C2×Dic67—24no—
284C2×Dic67—22no—
285C2×Dic67—22no—
286C2×Dic67—22no—
287C2×Dic67—22no—
288C2×Dic67—22no—
289C2×Dic67—22no—
290C2×Dic67—22no—
291C2×Dic67—42no—
292C2×Dic67—42no—
293C2×Dic67—42no—
294C2×Dic67—42no—
295C2×Dic67—42no—
296C2×Dic67—42no—
297D268—24no—
298D268—22no—
299D268C22×Q814yes—
300C4×D67—48no—
301C4×D67—84no—
302C4×D67—84no—
303Dic134—24no—
304Dic134—22no—
305Dic134—48no—
306Dic134—84no—
307Dic134C22×Q814yes—
308C8×C67—22no—
309C8×C67—22no—
310C8×C67—22no—
311C8×C67C22×Q814yes—
312C22×C67D4×Q812yes—
313C22×C67#57512yes—
314C22×C67#57712yes—
315C22×C67C23×D411yescharacteristic
316C2×D67—24no—
317C2×D67—48no—
318C2×D67—42no—
319C2×D67—42no—
320C4×C67—22no—
321C4×C67—22no—
322C4×C67—22no—
323C4×C67—22no—
324C4×C67—22no—
325C4×C67—22no—
326C4×C67D4×Q812yes—
327C4×C67C23×Q811yescharacteristic
328C4×C67C2×2−1+411yescharacteristic
329Dic67—24no—
330Dic67—42no—
331Dic67—42no—
332Dic67—42no—
333Dic67—42no—
334Dic67—42no—
335Dic67—42no—
336C2×#3388—671nomaximal, Sylow
337C2×C67#338814yescomplemented
338C2×C67C2×D4×Q811yescharacteristic
339C2×C67C2×#57511yescharacteristic
340C2×C67C2×#57711yescharacteristic
341D67—44no—
342C2×#557—671no—
343C2×#554—671no—
344#3388—6716no—
345C2×#501—671no—
346C2×#501—671no—
347C2×#499—671no—
348C2×#479—671no—
349C2×#479—671no—
350C2×#475—671no—
351C2×#478—671no—
352C2×#478—671no—
353C2×#476—671no—
354C2×#446D6711yescharacteristic, complemented
355C2×#440—671no—
356C2×#440—671no—
357C2×C4×SD16—671no—
358C67C2×#338811yescharacteristic, complemented, Sylow
359C22×SD16—671no—
360#557—678no—
361#557—1344no—
362#554—678no—
363#554—1344no—
364C2×C4⋊Q8—671no—
365C2×C4⋊Q8—671no—
366C2×C4⋊Q8—1341no—
367C2×#125—671no—
368C2×#125—671no—
369C2×#125—671no—
370C2×#125—671no—
371C2×#125—1341no—
372C2×#125—1341no—
373C2×C22⋊Q8—1341no—
374C2×C22⋊Q8—1341no—
375C2×C22⋊Q8—1341no—
376C2×C4×Q8—671no—
377C2×C4×Q8—671no—
378C2×C4×Q8—671no—
379C2×C4×Q8—1341no—
380C2×C4×Q8C2×D6711yescharacteristic
381C2×C4×D4—671no—
382C2×C4×D4—671no—
383C2×C4×D4—671no—
384C22×C4⋊C4—1341no—
385#501—678no—
386#501—678no—
387#499—678no—
388#479—678no—
389#479—678no—
390#478—678no—
391#478—678no—
392#476—678no—
393#475—678no—
394#446C2×D6718yescomplemented
395#440—678no—
396#440—678no—
397C4×SD16—678no—
398C2×#107—671no—
399C2×#107—671no—
400C2×#107—671no—
401C2×#107—671no—
402C2×#106—671no—
403C2×#106—671no—
404C2×#106—671no—
405C2×#106—671no—
406C2×#106—671no—
407C2×C4⋊C8C2×D6711yescharacteristic
408C2×C4⋊C8C2×D6711yescharacteristic
409C2×C4⋊C8C2×D6711yescharacteristic
410C2×#103—671no—
411C2×#103—671no—
412C2×#103—671no—
413C2×#102—671no—
414C2×#102—671no—
415C2×#102—671no—
416C2×#97C2×D6711yescharacteristic
417C2×#97C2×D6711yescharacteristic
418C2×C4×C8C2×D6711yescharacteristic
419C22×Q8—671no—
420C22×Q8—1341no—
421C22×Q8—1341no—
422C22×Q8D26811yescharacteristic
423C22×D4—671no—
424C23×C4—1341no—
425C23×C4—1341no—
426C23×C4—1341no—
427C2×SD16—678no—
428C2×SD16—674no—
429C22×C8C22×D6711yescharacteristic
430C22×C8C22×D6711yescharacteristic
431C22×C8C22×D6711yescharacteristic
432C22×C8C22×D6711yescharacteristic
433C4⋊Q8—674no—
434C4⋊Q8—674no—
435C4⋊Q8—1348no—
436C4⋊Q8—1342no—
437C4⋊Q8—1342no—
438#125—674no—
439#125—674no—
440#125—674no—
441#125—674no—
442#125—1348no—
443#125—1348no—
444#125—1342no—
445#125—1342no—
446#125—1342no—
447#125—1342no—
448C22⋊Q8—1348no—
449C22⋊Q8—1348no—
450C22⋊Q8—1348no—
451C4×Q8—674no—
452C4×Q8—674no—
453C4×Q8—674no—
454C4×Q8—1348no—
455C4×Q8—1342no—
456C4×Q8—1342no—
457C4×Q8—1342no—
458C4×Q8D26814yes—
459C4×Q8C22×D6714yes—
460C4×D4—674no—
461C4×D4—674no—
462C4×D4—674no—
463C4×D4—1342no—
464C4×D4—1342no—
465C4×D4—1342no—
466C2×C4⋊C4—671no—
467C2×C4⋊C4—671no—
468C2×C4⋊C4—671no—
469C2×C4⋊C4—671no—
470C2×C4⋊C4—671no—
471C2×C4⋊C4—671no—
472C2×C4⋊C4—1341no—
473C2×C4⋊C4—1341no—
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⋊C4—1348no—
486C2×C4⋊C4D26811yescharacteristic
487C2×C4⋊C4D26811yescharacteristic
488C2×C4⋊C4D26811yescharacteristic
489C2×C22⋊C4—1341no—
490C2×C22⋊C4—1341no—
491C2×C22⋊C4—1341no—
492C2×C42—1341no—
493C2×C42—1341no—
494C2×C42—1341no—
495C2×C42C22×D6711yescharacteristic
496C2×C42C22×D6711yescharacteristic
497C2×C42C22×D6711yescharacteristic
498#107—674no—
499#107—674no—
500#107—674no—
501#107—674no—
502#106—674no—
503#106—674no—
504#106—674no—
505#106—674no—
506#106—674no—
507C4⋊C8C22×D6714yes—
508C4⋊C8C22×D6714yes—
509C4⋊C8C22×D6714yes—
510#103—674no—
511#103—674no—
512#103—674no—
513#102—674no—
514#102—674no—
515#102—674no—
516#97C22×D6714yes—
517#97C22×D6714yes—
518C4×C8C22×D6714yes—
519C24—1341no—
520C2×Q8—42no—
521C2×Q8—2684no—
522C2×Q8—5362no—
523C2×Q8—674no—
524C2×Q8—672no—
525C2×Q8—1344no—
526C2×Q8—1344no—
527C2×Q8—1341no—
528C2×Q8—1342no—
529C2×Q8C2×D26814yes—
530C2×D4—674no—
531C2×D4—672no—
532C2×D4—1341no—
533C2×D4—1342no—
534C22×C4—2684no—
535C22×C4—5362no—
536C22×C4—5362no—
537C22×C4—1341no—
538C22×C4—1341no—
539C22×C4—1341no—
540C22×C4—1341no—
541C22×C4—1341no—
542C22×C4—1341no—
543C22×C4—1344no—
544C22×C4—1344no—
545C22×C4—1344no—
546C22×C4—1341no—
547C22×C4C2×D26811yescharacteristic
548C22×C4C2×D26811yescharacteristic
549C22×C4C2×D26811yescharacteristic
550C22×C4C2×D26811yescharacteristic
551C22×C4C2×D26811yescharacteristic
552C22×C4C2×D26811yescharacteristic
553C22×C4C23×D6711yescharacteristic
554SD16—6716no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8Q8×D6714yes—
559C2×C8C23×D6712yes—
560C2×C8C23×D6712yes—
561C2×C8C23×D6712yes—
562C2×C8C23×D6712yes—
563C4⋊C4—672no—
564C4⋊C4—672no—
565C4⋊C4—672no—
566C4⋊C4—672no—
567C4⋊C4—672no—
568C4⋊C4—672no—
569C4⋊C4—1341no—
570C4⋊C4—1341no—
571C4⋊C4—1341no—
572C4⋊C4—1341no—
573C4⋊C4—1341no—
574C4⋊C4—1341no—
575C4⋊C4—1344no—
576C4⋊C4—1344no—
577C4⋊C4—1344no—
578C4⋊C4—1344no—
579C4⋊C4—1344no—
580C4⋊C4—1344no—
581C4⋊C4—1344no—
582C4⋊C4—1344no—
583C4⋊C4—1344no—
584C4⋊C4—1344no—
585C4⋊C4—1344no—
586C4⋊C4—1344no—
587C4⋊C4—1344no—
588C4⋊C4C2×D26814yes—
589C4⋊C4C2×D26814yes—
590C4⋊C4C2×D26814yes—
591C22⋊C4—1344no—
592C22⋊C4—1344no—
593C22⋊C4—1344no—
594C42—1344no—
595C42—1344no—
596C42—1344no—
597C42C2×D26812yes—
598C42C2×D26812yes—
599C42C2×D26812yes—
600C42C23×D6712yes—
601C42C23×D6712yes—
602C42C23×D6712yes—
603C23—2682no—
604C23—2682no—
605C23—1344no—
606C23—1342no—
607C23C22×D26811yescharacteristic
608Q8—44no—
609Q8—2688no—
610Q8—5364no—
611Q8—674no—
612Q8—1344no—
613Q8—1342no—
614D4—674no—
615D4—1344no—
616D4—1342no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—2688no—
624C2×C4—2682no—
625C2×C4—2682no—
626C2×C4—2682no—
627C2×C4—2682no—
628C2×C4—2682no—
629C2×C4—2682no—
630C2×C4—5364no—
631C2×C4—5364no—
632C2×C4—1342no—
633C2×C4—1342no—
634C2×C4—1342no—
635C2×C4—1342no—
636C2×C4—1342no—
637C2×C4—1342no—
638C2×C4—1344no—
639C2×C4—1342no—
640C2×C4C22×D26812yes—
641C2×C4C22×D26812yes—
642C2×C4C22×D26812yes—
643C2×C4C22×D26812yes—
644C2×C4C22×D26812yes—
645C2×C4C22×D26812yes—
646C2×C4C22×D26811yescharacteristic
647C2×C4C2×Q8×D6712yes—
648C2×C4#1452409012yes—
649C2×C4C24×D6711yescharacteristic
650C8—22no—
651C8—22no—
652C8—22no—
653C8C2×Q8×D6714yes—
654C22—2688no—
655C22—2682no—
656C22—2682no—
657C22—1344no—
658C22Q8×D26812yes—
659C22#1686419612yes—
660C22#1686420812yes—
661C22C23×D26811yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—22no—
666C4—22no—
667C4—22no—
668C4—2682no—
669C4—2682no—
670C4—2682no—
671C4—2682no—
672C4—2682no—
673C4—2682no—
674C4—1344no—
675C4Q8×D26812yes—
676C4C22×Q8×D6711yescharacteristic
677C4C2×#1452409011yescharacteristic
678C2—2684no—
679C2#2257315614yesdirect product factor
680C2C2×Q8×D26811yescharacteristic
681C2C2×#1686419611yescharacteristic
682C2C2×#1686420811yescharacteristic
subgroupG/H
centerC23C22×D268
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#446×C67C2
socleC23×C67C22×D4
prime radicalC22×D268C23
hypercenterC2×#446D67
hypocenterC67C2×#3388
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
1. C2×#16864124C2semidirect
3. #22573156C2direct (N × H)
4. C2×#16863805C2semidirect
5. C2×#16863805C2semidirect
6. C2×#16863798C2semidirect
7. C2×#16863704C2semidirect
8. C2×#16863704C2semidirect
9. C2×#16863682C2semidirect
16. C2×#446×C67C2semidirect
19. #16864124C22semidirect
42. #16863805C22semidirect
43. #16863805C22semidirect
44. #16863798C22semidirect
45. #16863704C22semidirect
46. #16863704C22semidirect
50. #16863682C22semidirect
70. #446×C67C22semidirect
84. C2×#11761617Q8semidirect
203. #11761617C2×Q8semidirect
337. C2×C67#3388semidirect
354. C2×#446D67semidirect
358. C67C2×#3388semidirect
394. #446C2×D67semidirect
679. C2#22573156direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168641242
C2×#168641062
#225731562
C2×#168638052
C2×#168637982
C2×#168637042
C2×#168636822
C2×#168636972
C2×#168636872
C2×#168634982
C2×C4×#117616172
C2×#446×C672
C2×#338867