Finite Group Databasebeta

← C2×#14534947 #17201121

Subgroups — C2×#14534947 #17201121

Order 4352.

2354 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587584C211yesmaximal, characteristic
2C22×#10587575C211yesmaximal, characteristic, complemented
3#14534947C2116yesmaximal, direct product factor
4C2×#11762751C211yesmaximal, characteristic, complemented
5C2×#11762744C211yesmaximal, characteristic
6C2×#11762743C211yesmaximal, characteristic, complemented
7C2×#11762742C211yesmaximal, characteristic, complemented
8C2×#11762740C211yesmaximal, characteristic, complemented
9C2×#11762738C211yesmaximal, characteristic
10C2×#11762733C211yesmaximal, characteristic
11C2×#11762731C211yesmaximal, characteristic
12C2×#11762704C211yesmaximal, characteristic, complemented
13C2×#11762700C211yesmaximal, characteristic
14C2×#11762699C211yesmaximal, characteristic
15C2×C4×#63225C211yesmaximal, characteristic, complemented
16C2×C17×#389C211yesmaximal, characteristic, complemented
17C2×#10587584—28no—
18C2×#10587584C2218yes—
19C2×#10587575—28no—
20C2×#10587575C2218yescomplemented
21C22×C4⋊Dic17C2211yescharacteristic
22C22×C4⋊Dic17C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×#63225C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C22×#63225C2211yescharacteristic
29C22×#63225C2211yescharacteristic
30C22×#63225C2211yescharacteristic
31C22×#63225C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34C22×#63227C2211yescharacteristic
35C22×#63227C2211yescharacteristic
36C22×#63227C2211yescharacteristic
37C22×#63227C2211yescharacteristic
38C22×#63227C2211yescharacteristic
39C22×C4×Dic17C2211yescharacteristic
40C22×C4×Dic17C2211yescharacteristic
41#11762751C2218yescomplemented
42#11762744C2218yes—
43#11762743C2218yescomplemented
44#11762742C2218yescomplemented
45#11762740C2218yescomplemented
46#11762738C2218yes—
47#11762733C2218yes—
48#11762731C2218yes—
49#11762704C2218yescomplemented
50#11762700C2218yes—
51#11762699C2218yes—
52C4×#63225C2218yescomplemented
53C2×#10587502C2211yescharacteristic
54C2×#10587502C2211yescharacteristic
55C2×#10587502C2211yescharacteristic
56C2×#10587502C2211yescharacteristic
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59C2×#10587502C2211yescharacteristic
60C2×#10587502C2211yescharacteristic
61C22×C4⋊C4×C17C2211yescharacteristic
62C22×C4⋊C4×C17C2211yescharacteristic
63C22×C4⋊C4×C17C2211yescharacteristic
64C22×C4⋊C4×C17C2211yescharacteristic
65C22×C42×C17C2211yescharacteristic
66C17×#389C2218yescomplemented
67C2×C17×#95C2211yescharacteristic
68C2×C17×#95C2211yescharacteristic
69C24×D17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C2×C4⋊C4×C17—24no—
85C2×C4⋊C4×C17—24no—
86C2×C4⋊C4×C17—24no—
87C2×C4⋊C4×C17—42no—
88C2×C4⋊C4×C17C2314yes—
89C2×C4⋊C4×C17C2314yes—
90C2×C4⋊C4×C17C2314yes—
91C2×C4⋊C4×C17C2314yes—
92C2×C42×C17—42no—
93C2×C42×C17C2314yes—
94C2×#63227—24no—
95C2×#63227—24no—
96C2×#63227—24no—
97C2×#63227—24no—
98C2×#63227—24no—
99C2×#63227—42no—
100C2×#63227—42no—
101C2×#63227C2314yes—
102C2×#63227C2314yes—
103C2×#63227C2314yes—
104C2×#63227C2314yes—
105C2×#63227C2314yes—
106C2×#63227C2314yes—
107C2×#63227C2314yes—
108C2×C4⋊Dic17—24no—
109C2×C4⋊Dic17—24no—
110C2×C4⋊Dic17C2314yes—
111C2×C4⋊Dic17C2314yes—
112C2×#63225—24no—
113C2×#63225—24no—
114C2×#63225—24no—
115C2×#63225—24no—
116C2×#63225—24no—
117C2×#63225—24no—
118C2×#63225—24no—
119C2×#63225—24no—
120C2×#63225—42no—
121C2×#63225C2314yes—
122C2×#63225C2314yes—
123C2×#63225C2314yes—
124C2×#63225C2314yes—
125C2×#63225C2314yes—
126C2×#63225C2314yes—
127C2×#63225C2314yes—
128C2×#63225C2314yes—
129C2×#63225C2314yes—
130C2×C4×Dic17—42no—
131C2×C4×Dic17D418yes—
132C2×C4×Dic17C2314yes—
133C2×C4×Dic17C2314yes—
134#10587584—232no—
135#10587575—232no—
136C17×#95C2314yes—
137C17×#95C2314yes—
138#10587502C2314yes—
139#10587502C2314yes—
140#10587502C2314yes—
141#10587502C2314yes—
142#10587502C2314yes—
143#10587502C2314yes—
144#10587502C2314yes—
145#10587502C2314yes—
146C24×C17C2411yescharacteristic
147C23×D17—22no—
148C23×D17—22no—
149C23×D17—22no—
150C23×D17—22no—
151C23×D17—22no—
152C23×D17—22no—
153C23×D17—22no—
154C23×D17C2412yes—
155C22×C4×C17—22no—
156C22×C4×C17—22no—
157C22×C4×C17—22no—
158C22×C4×C17—22no—
159C22×C4×C17—22no—
160C22×C4×C17—22no—
161C22×C4×C17—22no—
162C22×C4×C17—22no—
163C22×C4×C17—22no—
164C22×C4×C17—22no—
165C22×C4×C17—22no—
166C22×C4×C17—22no—
167C22×C4×C17—22no—
168C22×C4×C17—22no—
169C22×C4×C17—22no—
170C22×C4×C17—22no—
171C22×C4×C17—22no—
172C22×C4×C17—22no—
173C22×C4×C17—22no—
174C22×C4×C17C2×D414yes—
175C22×C4×C17#4114yes—
176C22×C4×C17C2412yes—
177C22×C4×C17C2412yes—
178C22×C4×C17C2412yes—
179C22×C4×C17C2412yes—
180C22×C4×C17C2412yes—
181C22×C4×C17C2412yes—
182C22×C4×C17C2412yes—
183C22×Dic17—22no—
184C22×Dic17—22no—
185C22×Dic17—22no—
186C22×Dic17—22no—
187C22×Dic17—22no—
188C22×Dic17—22no—
189C22×Dic17—22no—
190C22×Dic17—22no—
191C22×Dic17—22no—
192C22×Dic17—22no—
193C22×Dic17—22no—
194C22×Dic17—22no—
195C22×Dic17—22no—
196C22×Dic17—22no—
197C22×Dic17—22no—
198C22×Dic17—22no—
199C22×Dic17—22no—
200C22×Dic17—22no—
201C22×Dic17C2×D414yes—
202C22×Dic17C2×D414yes—
203C22×Dic17#4114yes—
204C22×Dic17C2412yes—
205C22×Dic17C2412yes—
206C22×Dic17C2412yes—
207C22×Dic17C2412yes—
208C22×Dic17C2412yes—
209C22×Dic17C2412yes—
210C22×Dic17C2412yes—
211C4⋊C4×C17—28no—
212C4⋊C4×C17—28no—
213C4⋊C4×C17—28no—
214C4⋊C4×C17—44no—
215C42×C17—44no—
216#63227—28no—
217#63227—28no—
218#63227—28no—
219#63227—28no—
220#63227—28no—
221#63227—44no—
222#63227—44no—
223C4⋊Dic17—28no—
224C4⋊Dic17—28no—
225#63225—28no—
226#63225—28no—
227#63225—28no—
228#63225—28no—
229#63225—28no—
230#63225—28no—
231#63225—28no—
232#63225—28no—
233#63225—44no—
234C4×Dic17—44no—
235C4×Dic17C2×D4116yes—
236C2×#2664—171nomaximal, Sylow
237C23×C17C22×D412yes—
238C23×C17C2×#4112yes—
239C23×C17C2×#4112yes—
240C23×C17H(5,𝔽2)12yes—
241C23×C172−1+412yes—
242C23×C172−1+412yes—
243C23×C172−1+412yes—
244C23×C17C2511yescharacteristic
245C22×D17—22no—
246C22×D17—22no—
247C22×D17—22no—
248C22×D17—22no—
249C22×D17—22no—
250C22×D17—22no—
251C22×D17—22no—
252C22×D17—44no—
253C22×D17—44no—
254C22×D17—44no—
255C22×D17—44no—
256C22×D17—44no—
257C22×D17—44no—
258C22×D17—44no—
259C2×C4×C17—28no—
260C2×C4×C17—28no—
261C2×C4×C17—22no—
262C2×C4×C17—22no—
263C2×C4×C17—22no—
264C2×C4×C17—22no—
265C2×C4×C17—22no—
266C2×C4×C17—22no—
267C2×C4×C17—22no—
268C2×C4×C17—22no—
269C2×C4×C17—22no—
270C2×C4×C17—22no—
271C2×C4×C17—22no—
272C2×C4×C17—22no—
273C2×C4×C17—22no—
274C2×C4×C17—22no—
275C2×C4×C17—22no—
276C2×C4×C17—22no—
277C2×C4×C17—22no—
278C2×C4×C17—22no—
279C2×C4×C17—22no—
280C2×C4×C17—44no—
281C2×C4×C17—44no—
282C2×C4×C17—44no—
283C2×C4×C17—44no—
284C2×C4×C17—44no—
285C2×C4×C17C22×D414yes—
286C2×C4×C17C2×#4114yes—
287C2×Dic17—28no—
288C2×Dic17—28no—
289C2×Dic17—28no—
290C2×Dic17—22no—
291C2×Dic17—22no—
292C2×Dic17—22no—
293C2×Dic17—22no—
294C2×Dic17—22no—
295C2×Dic17—22no—
296C2×Dic17—22no—
297C2×Dic17—22no—
298C2×Dic17—22no—
299C2×Dic17—22no—
300C2×Dic17—22no—
301C2×Dic17—22no—
302C2×Dic17—22no—
303C2×Dic17—22no—
304C2×Dic17—22no—
305C2×Dic17—22no—
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17—44no—
309C2×Dic17—44no—
310C2×Dic17—44no—
311C2×Dic17—44no—
312C2×Dic17C22×D414yes—
313C2×Dic17C22×D414yes—
314C2×Dic17C2×#4114yes—
315C22×#126—171no—
316C22×#125—171no—
317#2664—1716no—
318C2×#400—171no—
319C2×#399—171no—
320C2×#398—171no—
321C2×#398—171no—
322C2×#398—171no—
323C2×#397—171no—
324C2×#396—171no—
325C2×#396—171no—
326C2×#389—171no—
327C2×#389D1711yescharacteristic, complemented
328C2×#388—171no—
329C2×#388—171no—
330C2×C4×C4⋊C4—171no—
331C22×C17#53214yes—
332C22×C17#53614yes—
333C22×C17#53714yes—
334C22×C17#53914yes—
335C22×C17#53914yes—
336C22×C17#54114yes—
337C22×C17#54114yes—
338C22×C17C23×D411yescharacteristic
339C22×C17C22×#4111yescharacteristic
340C22×C17C22×#4111yescharacteristic
341C22×C17C2×H(5,𝔽2)11yescharacteristic
342C22×C17C2×2−1+411yescharacteristic
343C22×C17C2×2−1+411yescharacteristic
344C22×C17C2×2−1+411yescharacteristic
345C2×D17—42no—
346C2×D17—42no—
347C2×D17—42no—
348C2×D17—42no—
349C2×D17—42no—
350C2×D17—42no—
351C2×D17—42no—
352C2×D17—88no—
353C4×C17—24no—
354C4×C17—24no—
355C4×C17—42no—
356C4×C17—42no—
357C4×C17—42no—
358C4×C17—42no—
359C4×C17—42no—
360Dic17—24no—
361Dic17—24no—
362Dic17—24no—
363Dic17—42no—
364Dic17—42no—
365Dic17—42no—
366Dic17—42no—
367C2×#126—178no—
368C2×#126—348no—
369C2×#125—178no—
370C2×#125—348no—
371C22×C4⋊C4—171no—
372C22×C4⋊C4—171no—
373C22×C4⋊C4—171no—
374C22×C4⋊C4—171no—
375C22×C4⋊C4—171no—
376C22×C4⋊C4—171no—
377C22×C4⋊C4—171no—
378C22×C4⋊C4—171no—
379C22×C4⋊C4—171no—
380C22×C4⋊C4—171no—
381C22×C4⋊C4—171no—
382C22×C4⋊C4C2×D1711yescharacteristic
383C22×C4⋊C4C2×D1711yescharacteristic
384C22×C4⋊C4C2×D1711yescharacteristic
385C22×C4⋊C4C2×D1711yescharacteristic
386C22×C22⋊C4—171no—
387C22×C22⋊C4—171no—
388C22×C22⋊C4—171no—
389C22×C22⋊C4—171no—
390C22×C22⋊C4—171no—
391C22×C22⋊C4—171no—
392C22×C22⋊C4—171no—
393C22×C42—171no—
394C22×C42—171no—
395C22×C42C2×D1711yescharacteristic
396#400—178no—
397#399—178no—
398#398—178no—
399#398—178no—
400#398—178no—
401#397—178no—
402#396—178no—
403#396—178no—
404#389—178no—
405#389C2×D1718yescomplemented
406#388—178no—
407#388—178no—
408C4×C4⋊C4—178no—
409C2×#95—171no—
410C2×#95—171no—
411C2×#95—171no—
412C2×#95—171no—
413C2×#95—171no—
414C2×#95—171no—
415C2×#95—171no—
416C2×#95—171no—
417C2×#95C2×D1711yescharacteristic
418C2×#95C2×D1711yescharacteristic
419C2×C17#266418yescomplemented
420C2×C17C2×#53211yescharacteristic
421C2×C17C2×#53611yescharacteristic
422C2×C17C2×#53711yescharacteristic
423C2×C17C2×#53911yescharacteristic
424C2×C17C2×#53911yescharacteristic
425C2×C17C2×#54111yescharacteristic
426C2×C17C2×#54111yescharacteristic
427D17—82no—
428C25—171no—
429C23×C4—171no—
430C23×C4—171no—
431C23×C4—171no—
432C23×C4—171no—
433C23×C4—171no—
434C23×C4—171no—
435C23×C4—171no—
436C23×C4C22×D1711yescharacteristic
437C23×C4C22×D1711yescharacteristic
438C23×C4C22×D1711yescharacteristic
439C23×C4C22×D1711yescharacteristic
440C23×C4C22×D1711yescharacteristic
441C23×C4C22×D1711yescharacteristic
442C23×C4C22×D1711yescharacteristic
443#126—3432no—
444#125—3432no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—174no—
450C2×C4⋊C4—174no—
451C2×C4⋊C4—174no—
452C2×C4⋊C4—174no—
453C2×C4⋊C4—174no—
454C2×C4⋊C4—174no—
455C2×C4⋊C4—174no—
456C2×C4⋊C4—174no—
457C2×C4⋊C4—174no—
458C2×C4⋊C4—174no—
459C2×C4⋊C4—174no—
460C2×C4⋊C4—344no—
461C2×C4⋊C4—344no—
462C2×C4⋊C4—344no—
463C2×C4⋊C4—344no—
464C2×C4⋊C4—344no—
465C2×C4⋊C4—344no—
466C2×C4⋊C4—344no—
467C2×C4⋊C4—344no—
468C2×C4⋊C4—344no—
469C2×C4⋊C4—344no—
470C2×C4⋊C4—682no—
471C2×C4⋊C4C22×D1714yes—
472C2×C4⋊C4C22×D1714yes—
473C2×C4⋊C4C22×D1714yes—
474C2×C4⋊C4C22×D1714yes—
475C2×C22⋊C4—174no—
476C2×C22⋊C4—174no—
477C2×C22⋊C4—174no—
478C2×C22⋊C4—174no—
479C2×C22⋊C4—174no—
480C2×C22⋊C4—174no—
481C2×C22⋊C4—174no—
482C2×C22⋊C4—344no—
483C2×C22⋊C4—344no—
484C2×C22⋊C4—344no—
485C2×C22⋊C4—344no—
486C2×C22⋊C4—344no—
487C2×C22⋊C4—682no—
488C2×C22⋊C4—682no—
489C2×C42—42no—
490C2×C42—178no—
491C2×C42—174no—
492C2×C42—174no—
493C2×C42—682no—
494C2×C42C22×D1714yes—
495#95—174no—
496#95—174no—
497#95—174no—
498#95—174no—
499#95—174no—
500#95—174no—
501#95—174no—
502#95—174no—
503#95C22×D1714yes—
504#95C22×D1714yes—
505C17C2×#266411yescharacteristic, complemented, Sylow
506C24—172no—
507C24—342no—
508C24—342no—
509C24—342no—
510C24—342no—
511C24—342no—
512C24—342no—
513C24—342no—
514C24C23×D1711yescharacteristic
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—174no—
535C22×C4—174no—
536C22×C4—174no—
537C22×C4—172no—
538C22×C4—172no—
539C22×C4—172no—
540C22×C4—172no—
541C22×C4—172no—
542C22×C4—172no—
543C22×C4—172no—
544C22×C4—342no—
545C22×C4—342no—
546C22×C4—342no—
547C22×C4—342no—
548C22×C4—342no—
549C22×C4—342no—
550C22×C4—342no—
551C22×C4—342no—
552C22×C4—342no—
553C22×C4—342no—
554C22×C4—342no—
555C22×C4—342no—
556C22×C4—342no—
557C22×C4—342no—
558C22×C4—342no—
559C22×C4—342no—
560C22×C4—342no—
561C22×C4—342no—
562C22×C4#6325214yes—
563C22×C4D4×D1714yes—
564C22×C4C23×D1712yes—
565C22×C4C23×D1712yes—
566C22×C4C23×D1712yes—
567C22×C4C23×D1712yes—
568C22×C4C23×D1712yes—
569C22×C4C23×D1712yes—
570C22×C4C23×D1712yes—
571C4⋊C4—28no—
572C4⋊C4—28no—
573C4⋊C4—28no—
574C4⋊C4—44no—
575C4⋊C4—348no—
576C4⋊C4—348no—
577C4⋊C4—348no—
578C4⋊C4—348no—
579C4⋊C4—348no—
580C4⋊C4—348no—
581C4⋊C4—348no—
582C4⋊C4—348no—
583C4⋊C4—348no—
584C4⋊C4—348no—
585C4⋊C4—684no—
586C22⋊C4—348no—
587C22⋊C4—348no—
588C22⋊C4—348no—
589C22⋊C4—348no—
590C22⋊C4—348no—
591C22⋊C4—684no—
592C22⋊C4—684no—
593C42—44no—
594C42—1716no—
595C42—684no—
596C23—342no—
597C23—342no—
598C23—342no—
599C23—342no—
600C23—342no—
601C23—342no—
602C23—342no—
603C23—684no—
604C23—684no—
605C23—684no—
606C23—684no—
607C23—684no—
608C23—684no—
609C23—684no—
610C23C2×#6325212yes—
611C23C2×D4×D1712yes—
612C23#1058769112yes—
613C23#1058769412yes—
614C23#1058769412yes—
615C23#41×D1712yes—
616C23#1058769712yes—
617C23C24×D1711yescharacteristic
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—28no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—28no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—174no—
645C2×C4—174no—
646C2×C4—174no—
647C2×C4—348no—
648C2×C4—342no—
649C2×C4—342no—
650C2×C4—342no—
651C2×C4—348no—
652C2×C4—342no—
653C2×C4—342no—
654C2×C4—342no—
655C2×C4—348no—
656C2×C4—342no—
657C2×C4—342no—
658C2×C4—342no—
659C2×C4—342no—
660C2×C4—342no—
661C2×C4—342no—
662C2×C4—342no—
663C2×C4—342no—
664C2×C4—342no—
665C2×C4—342no—
666C2×C4—342no—
667C2×C4—342no—
668C2×C4—684no—
669C2×C4—684no—
670C2×C4—684no—
671C2×C4—684no—
672C2×C4C2×#6325214yes—
673C2×C4C2×D4×D1714yes—
674C22—682no—
675C22—682no—
676C22—682no—
677C22—682no—
678C22—682no—
679C22—682no—
680C22—682no—
681C22—1368no—
682C22#1176335614yes—
683C22#1176338414yes—
684C22#1176338614yes—
685C22#1176340514yes—
686C22#1176340614yes—
687C22#1176341714yes—
688C22#1176341814yes—
689C22C22×D4×D1711yescharacteristic
690C22C2×#41×D1711yescharacteristic
691C22C22×#6325211yescharacteristic
692C22C2×#1058769111yescharacteristic
693C22C2×#1058769711yescharacteristic
694C22C2×#1058769411yescharacteristic
695C22C2×#1058769411yescharacteristic
696C4—24no—
697C4—24no—
698C4—42no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—344no—
704C4—344no—
705C4—344no—
706C4—682no—
707C4—682no—
708C4—682no—
709C4—682no—
710C2—1362no—
711C2#1453494718yesdirect product factor
712C2C2×#1176335611yescharacteristic
713C2C2×#1176338411yescharacteristic
714C2C2×#1176338611yescharacteristic
715C2C2×#1176340511yescharacteristic
716C2C2×#1176340611yescharacteristic
717C2C2×#1176341711yescharacteristic
718C2C2×#1176341811yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#389C2
socleC24×C17C24
prime radicalC24×D17C23
hypercenterC2×#389D17
hypocenterC17C2×#2664
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C22×#10587575C2semidirect
3. #14534947C2direct (N × H)
4. C2×#11762751C2semidirect
6. C2×#11762743C2semidirect
7. C2×#11762742C2semidirect
8. C2×#11762740C2semidirect
12. C2×#11762704C2semidirect
15. C2×C4×#63225C2semidirect
16. C2×C17×#389C2semidirect
20. C2×#10587575C22semidirect
41. #11762751C22semidirect
43. #11762743C22semidirect
44. #11762742C22semidirect
45. #11762740C22semidirect
49. #11762704C22semidirect
52. C4×#63225C22semidirect
66. C17×#389C22semidirect
327. C2×#389D17semidirect
405. #389C2×D17semidirect
419. C2×C17#2664semidirect
505. C17C2×#2664semidirect
711. C2#14534947direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875842
C22×#105875752
#145349472
C2×#117627512
C2×#117627442
C2×#117627432
C2×#117627422
C2×#117627402
C2×#117627382
C2×#117627332
C2×#117627312
C2×#117627042
C2×#117627002
C2×#117626992
C2×C4×#632252
C2×C17×#3892
C2×#266417