Finite Group Databasebeta

← C2×#14533069 #17204139

Subgroups — C2×#14533069 #17204139

Order 4352.

2918 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587558C211yesmaximal, characteristic
2C22×C4⋊C4×D17C211yesmaximal, characteristic
3#14533069C2116yesmaximal, direct product factor
4C2×#11762751C211yesmaximal, characteristic, complemented
5C2×#11762750C211yesmaximal, characteristic, complemented
6C2×#11762743C211yesmaximal, characteristic, complemented
7C2×#11762742C211yesmaximal, characteristic, complemented
8C2×#11762694C211yesmaximal, characteristic, complemented
9C2×#11762693C211yesmaximal, characteristic, complemented
10C2×#11762690C211yesmaximal, characteristic, complemented
11C2×#11762683C211yesmaximal, characteristic
12C2×#11762680C211yesmaximal, characteristic
13C2×#11762671C211yesmaximal, characteristic
14C2×#11762671C211yesmaximal, characteristic
15C2×#11762671C211yesmaximal, characteristic
16C2×C17×#387C211yesmaximal, characteristic, complemented
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C2×#10587558—28no—
21C2×#10587558C2218yes—
22C22×C4⋊Dic17C2211yescharacteristic
23C22×C4⋊Dic17C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×#63225C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C22×#63225C2211yescharacteristic
29C22×#63225C2211yescharacteristic
30C2×C4⋊C4×D17—28no—
31C2×C4⋊C4×D17C2218yes—
32C22×#63227C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34C22×#63227C2211yescharacteristic
35C22×#63227C2211yescharacteristic
36C22×C4×Dic17C2211yescharacteristic
37#11762751C2218yescomplemented
38#11762750C2218yescomplemented
39#11762743C2218yescomplemented
40#11762742C2218yescomplemented
41#11762694C2218yescomplemented
42#11762693C2218yescomplemented
43#11762690C2218yescomplemented
44#11762683C2218yes—
45#11762680C2218yes—
46#11762671C2218yes—
47#11762671C2218yes—
48#11762671C2218yes—
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
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×C42×C17C2211yescharacteristic
64C17×#387C2218yescomplemented
65C2×C17×#95C2211yescharacteristic
66C2×C17×#95C2211yescharacteristic
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
84C22×C4×D17—24no—
85C22×C4×D17—24no—
86C22×C4×D17—24no—
87C22×C4×D17—24no—
88C22×C4×D17—24no—
89C22×C4×D17—24no—
90C22×C4×D17—24no—
91C22×C4×D17—24no—
92C22×C4×D17D418yes—
93C22×C4×D17C2314yes—
94C22×C4×D17C2314yes—
95C22×C4×D17C2314yes—
96C2×C4⋊C4×C17—24no—
97C2×C4⋊C4×C17—24no—
98C2×C4⋊C4×C17C2314yes—
99C2×C4⋊C4×C17C2314yes—
100C2×C42×C17—24no—
101C2×C42×C17C2314yes—
102C2×#63227—24no—
103C2×#63227—24no—
104C2×#63227—24no—
105C2×#63227—24no—
106C2×#63227C2314yes—
107C2×#63227C2314yes—
108C2×#63227C2314yes—
109C2×#63227C2314yes—
110C2×C4⋊Dic17—24no—
111C2×C4⋊Dic17—24no—
112C2×C4⋊Dic17C2314yes—
113C2×C4⋊Dic17C2314yes—
114C2×#63225—24no—
115C2×#63225—24no—
116C2×#63225—24no—
117C2×#63225—24no—
118C2×#63225—24no—
119C2×#63225—24no—
120C2×#63225C2314yes—
121C2×#63225C2314yes—
122C2×#63225C2314yes—
123C2×#63225C2314yes—
124C2×#63225C2314yes—
125C2×#63225C2314yes—
126C2×C4×Dic17—24no—
127C2×C4×Dic17C2314yes—
128C4⋊C4×D17—232no—
129#10587558—232no—
130C17×#95C2314yes—
131C17×#95C2314yes—
132C17×#95C2314yes—
133C17×#95C2314yes—
134#10587502C2314yes—
135#10587502C2314yes—
136#10587502C2314yes—
137#10587502C2314yes—
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×D17C2×D414yes—
152C23×D17#4114yes—
153C23×D17#4114yes—
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×Dic17—22no—
202C22×Dic17C2×D414yes—
203C22×Dic17#4114yes—
204C22×Dic17C2412yes—
205C22×Dic17C2412yes—
206C22×Dic17C2412yes—
207C22×Dic17C2412yes—
208C22×Dic17C2412yes—
209C22×Dic17C2412yes—
210C22×Dic17C2412yes—
211C2×C4×D17—232no—
212C2×C4×D17—232no—
213C2×C4×D17—28no—
214C2×C4×D17—28no—
215C2×C4×D17—28no—
216C2×C4×D17—28no—
217C2×C4×D17—28no—
218C2×C4×D17—28no—
219C2×C4×D17—28no—
220C2×C4×D17—28no—
221C2×C4×D17—416no—
222C2×C4×D17C2×D4116yes—
223C4⋊C4×C17—28no—
224C4⋊C4×C17—28no—
225C42×C17—28no—
226#63227—28no—
227#63227—28no—
228#63227—28no—
229#63227—28no—
230C4⋊Dic17—28no—
231C4⋊Dic17—28no—
232#63225—28no—
233#63225—28no—
234#63225—28no—
235#63225—28no—
236#63225—28no—
237#63225—28no—
238C4×Dic17—28no—
239C2×#2484—171nomaximal, Sylow
240C23×C17C22×D412yes—
241C23×C17C2×#4112yes—
242C23×C17C2×#4112yes—
243C23×C17C2×#4112yes—
244C23×C17C2×#4112yes—
245C23×C172−1+412yes—
246C23×C172−1+412yes—
247C23×C17C2511yescharacteristic
248C22×D17—28no—
249C22×D17—28no—
250C22×D17—28no—
251C22×D17—28no—
252C22×D17—28no—
253C22×D17—28no—
254C22×D17—22no—
255C22×D17—22no—
256C22×D17—22no—
257C22×D17—22no—
258C22×D17#123116yes—
259C22×D17C22×D414yes—
260C22×D17C2×#4114yes—
261C22×D17C2×#4114yes—
262C2×C4×C17—28no—
263C2×C4×C17—28no—
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—22no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—44no—
284C2×C4×C17—44no—
285C2×C4×C17—44no—
286C2×C4×C17—44no—
287C2×C4×C17—44no—
288C2×C4×C17C22×D414yes—
289C2×C4×C17C2×#4114yes—
290C2×Dic17—28no—
291C2×Dic17—28no—
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—22no—
309C2×Dic17—22no—
310C2×Dic17—22no—
311C2×Dic17—44no—
312C2×Dic17—44no—
313C2×Dic17—44no—
314C2×Dic17—44no—
315C2×Dic17—44no—
316C2×Dic17C22×D414yes—
317C2×Dic17C2×#4114yes—
318C4×D17—232no—
319C4×D17—232no—
320C4×D17—416no—
321C22×#117—171no—
322C23×C4⋊C4—171no—
323#2484—1716no—
324C2×#400—171no—
325C2×#400—171no—
326C2×#398—171no—
327C2×#398—171no—
328C2×#387—171no—
329C2×#387—171no—
330C2×#387—171no—
331C2×#387D1711yescharacteristic, complemented
332C2×#385—171no—
333C2×#385—171no—
334C2×#381—171no—
335C2×#381—171no—
336C2×#381—171no—
337C22×C17C2×#12314yes—
338C22×C17#52514yes—
339C22×C17#53614yes—
340C22×C17#55214yes—
341C22×C17#55214yes—
342C22×C17#55214yes—
343C22×C17#55214yes—
344C22×C17C23×D411yescharacteristic
345C22×C17C22×#4111yescharacteristic
346C22×C17C22×#4111yescharacteristic
347C22×C17C22×#4111yescharacteristic
348C22×C17C22×#4111yescharacteristic
349C22×C17C2×2−1+411yescharacteristic
350C22×C17C2×2−1+411yescharacteristic
351C2×D17—24no—
352C2×D17—24no—
353C2×D17—24no—
354C2×D17—24no—
355C2×D17—24no—
356C2×D17—24no—
357C2×D17—232no—
358C2×D17C2×#12318yes—
359C4×C17—24no—
360C4×C17—24no—
361C4×C17—42no—
362C4×C17—42no—
363C4×C17—42no—
364C4×C17—42no—
365C4×C17—42no—
366Dic17—24no—
367Dic17—24no—
368Dic17—42no—
369Dic17—42no—
370Dic17—42no—
371Dic17—42no—
372Dic17—42no—
373C24×C4—171no—
374C24×C4—171no—
375C24×C4—171no—
376C2×#117—178no—
377C2×#117—348no—
378C22×C4⋊C4—171no—
379C22×C4⋊C4—171no—
380C22×C4⋊C4—171no—
381C22×C4⋊C4—171no—
382C22×C4⋊C4—171no—
383C22×C4⋊C4—171no—
384C22×C4⋊C4—171no—
385C22×C4⋊C4—171no—
386C22×C4⋊C4—178no—
387C22×C4⋊C4—348no—
388C22×C4⋊C4C2×D1711yescharacteristic
389C22×C4⋊C4C2×D1711yescharacteristic
390C22×C22⋊C4—171no—
391C22×C22⋊C4—171no—
392C22×C22⋊C4—171no—
393C22×C22⋊C4—171no—
394C22×C42—171no—
395C22×C42C2×D1711yescharacteristic
396#400—178no—
397#400—178no—
398#398—178no—
399#398—178no—
400#387—178no—
401#387—178no—
402#387—178no—
403#387C2×D1718yescomplemented
404#385—178no—
405#385—178no—
406#381—178no—
407#381—178no—
408#381—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×#95—171no—
418C2×#95—171no—
419C2×#95—171no—
420C2×#95—171no—
421C2×#95C2×D1711yescharacteristic
422C2×#95C2×D1711yescharacteristic
423C2×#95C2×D1711yescharacteristic
424C2×#95C2×D1711yescharacteristic
425C2×C17#248418yescomplemented
426C2×C17C22×#12311yescharacteristic
427C2×C17C2×#52511yescharacteristic
428C2×C17C2×#53611yescharacteristic
429C2×C17C2×#55211yescharacteristic
430C2×C17C2×#55211yescharacteristic
431C2×C17C2×#55211yescharacteristic
432C2×C17C2×#55211yescharacteristic
433D17—28no—
434C25—171no—
435C23×C4—171no—
436C23×C4—171no—
437C23×C4—178no—
438C23×C4—174no—
439C23×C4—171no—
440C23×C4—171no—
441C23×C4—171no—
442C23×C4—171no—
443C23×C4—171no—
444C23×C4—174no—
445C23×C4—174no—
446C23×C4—344no—
447C23×C4—344no—
448C23×C4—344no—
449C23×C4—344no—
450C23×C4—344no—
451C23×C4—344no—
452C23×C4—344no—
453C23×C4—344no—
454C23×C4C22×D1711yescharacteristic
455C23×C4C22×D1711yescharacteristic
456C23×C4C22×D1711yescharacteristic
457C23×C4C22×D1711yescharacteristic
458C23×C4C22×D1711yescharacteristic
459C23×C4C22×D1711yescharacteristic
460C23×C4C22×D1711yescharacteristic
461#117—3432no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—174no—
465C2×C4⋊C4—174no—
466C2×C4⋊C4—174no—
467C2×C4⋊C4—174no—
468C2×C4⋊C4—174no—
469C2×C4⋊C4—174no—
470C2×C4⋊C4—174no—
471C2×C4⋊C4—174no—
472C2×C4⋊C4—3432no—
473C2×C4⋊C4—344no—
474C2×C4⋊C4—344no—
475C2×C4⋊C4—344no—
476C2×C4⋊C4—344no—
477C2×C4⋊C4—344no—
478C2×C4⋊C4—344no—
479C2×C4⋊C4—344no—
480C2×C4⋊C4—344no—
481C2×C4⋊C4C22×D1714yes—
482C2×C4⋊C4C22×D1714yes—
483C2×C22⋊C4—174no—
484C2×C22⋊C4—174no—
485C2×C22⋊C4—174no—
486C2×C22⋊C4—174no—
487C2×C22⋊C4—344no—
488C2×C22⋊C4—344no—
489C2×C22⋊C4—344no—
490C2×C22⋊C4—344no—
491C2×C42—24no—
492C2×C42—174no—
493C2×C42—344no—
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#95—174no—
504#95—174no—
505#95—174no—
506#95—174no—
507#95C22×D1714yes—
508#95C22×D1714yes—
509#95C22×D1714yes—
510#95C22×D1714yes—
511C17C2×#248411yescharacteristic, complemented, Sylow
512C24—174no—
513C24—174no—
514C24—174no—
515C24—172no—
516C24—342no—
517C24—342no—
518C24—342no—
519C24—342no—
520C24C23×D1711yescharacteristic
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—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—174no—
541C22×C4—174no—
542C22×C4—172no—
543C22×C4—172no—
544C22×C4—1716no—
545C22×C4—172no—
546C22×C4—172no—
547C22×C4—172no—
548C22×C4—172no—
549C22×C4—172no—
550C22×C4—348no—
551C22×C4—348no—
552C22×C4—3432no—
553C22×C4—348no—
554C22×C4—348no—
555C22×C4—3432no—
556C22×C4—348no—
557C22×C4—348no—
558C22×C4—348no—
559C22×C4—342no—
560C22×C4—342no—
561C22×C4—342no—
562C22×C4—342no—
563C22×C4—348no—
564C22×C4—342no—
565C22×C4—342no—
566C22×C4—342no—
567C22×C4—342no—
568C22×C4—342no—
569C22×C4—342no—
570C22×C4—342no—
571C22×C4—342no—
572C22×C4—342no—
573C22×C4—342no—
574C22×C4—342no—
575C22×C4—342no—
576C22×C4—342no—
577C22×C4—342no—
578C22×C4—342no—
579C22×C4—6816no—
580C22×C4#6325214yes—
581C22×C4D4×D1714yes—
582C22×C4C23×D1712yes—
583C22×C4C23×D1712yes—
584C22×C4C23×D1712yes—
585C22×C4C23×D1712yes—
586C22×C4C23×D1712yes—
587C22×C4C23×D1712yes—
588C22×C4C23×D1712yes—
589C4⋊C4—28no—
590C4⋊C4—28no—
591C4⋊C4—348no—
592C4⋊C4—348no—
593C4⋊C4—348no—
594C4⋊C4—348no—
595C4⋊C4—348no—
596C4⋊C4—348no—
597C4⋊C4—348no—
598C4⋊C4—348no—
599C22⋊C4—348no—
600C22⋊C4—348no—
601C22⋊C4—348no—
602C22⋊C4—348no—
603C42—28no—
604C42—348no—
605C23—1716no—
606C23—174no—
607C23—174no—
608C23—174no—
609C23—348no—
610C23—348no—
611C23—348no—
612C23—348no—
613C23—348no—
614C23—342no—
615C23—342no—
616C23—348no—
617C23—342no—
618C23—342no—
619C23C2×#6325212yes—
620C23C2×D4×D1712yes—
621C23#1058769412yes—
622C23#41×D1712yes—
623C23#41×D1712yes—
624C23#41×D1712yes—
625C23#1058769712yes—
626C23C24×D1711yescharacteristic
627C2×C4—28no—
628C2×C4—28no—
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—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—44no—
649C2×C4—44no—
650C2×C4—44no—
651C2×C4—44no—
652C2×C4—44no—
653C2×C4—174no—
654C2×C4—174no—
655C2×C4—3432no—
656C2×C4—3432no—
657C2×C4—348no—
658C2×C4—348no—
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—342no—
669C2×C4—342no—
670C2×C4—342no—
671C2×C4—342no—
672C2×C4—342no—
673C2×C4—342no—
674C2×C4—342no—
675C2×C4—342no—
676C2×C4—342no—
677C2×C4—342no—
678C2×C4—6816no—
679C2×C4—684no—
680C2×C4—684no—
681C2×C4—684no—
682C2×C4—684no—
683C2×C4—684no—
684C2×C4C2×#6325214yes—
685C2×C4C2×D4×D1714yes—
686C22—178no—
687C22—344no—
688C22—344no—
689C22—3432no—
690C22—344no—
691C22—344no—
692C22—344no—
693C22—344no—
694C22#123×D1714yes—
695C22#1176331814yes—
696C22#1176338214yes—
697C22#1176349114yes—
698C22#1176349514yes—
699C22#1176349814yes—
700C22#1176350014yes—
701C22C22×D4×D1711yescharacteristic
702C22C2×#41×D1711yescharacteristic
703C22C2×#41×D1711yescharacteristic
704C22C2×#41×D1711yescharacteristic
705C22C22×#6325211yescharacteristic
706C22C2×#1058769711yescharacteristic
707C22C2×#1058769411yescharacteristic
708C4—24no—
709C4—24no—
710C4—42no—
711C4—42no—
712C4—42no—
713C4—42no—
714C4—42no—
715C4—344no—
716C4—344no—
717C4—682no—
718C4—682no—
719C4—682no—
720C4—682no—
721C4—682no—
722C2—348no—
723C2#1453306918yesdirect product factor
724C2C2×#123×D1711yescharacteristic
725C2C2×#1176331811yescharacteristic
726C2C2×#1176338211yescharacteristic
727C2C2×#1176349111yescharacteristic
728C2C2×#1176349511yescharacteristic
729C2C2×#1176349811yescharacteristic
730C2C2×#1176350011yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#387C2
socleC24×C17C24
prime radicalC24×D17C23
hypercenterC2×#387D17
hypocenterC17C2×#2484
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. #14533069C2direct (N × H)
4. C2×#11762751C2semidirect
5. C2×#11762750C2semidirect
6. C2×#11762743C2semidirect
7. C2×#11762742C2semidirect
8. C2×#11762694C2semidirect
9. C2×#11762693C2semidirect
10. C2×#11762690C2semidirect
16. C2×C17×#387C2semidirect
37. #11762751C22semidirect
38. #11762750C22semidirect
39. #11762743C22semidirect
40. #11762742C22semidirect
41. #11762694C22semidirect
42. #11762693C22semidirect
43. #11762690C22semidirect
64. C17×#387C22semidirect
331. C2×#387D17semidirect
403. #387C2×D17semidirect
425. C2×C17#2484semidirect
511. C17C2×#2484semidirect
723. C2#14533069direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875582
C22×C4⋊C4×D172
#145330692
C2×#117627512
C2×#117627502
C2×#117627432
C2×#117627422
C2×#117626942
C2×#117626932
C2×#117626902
C2×#117626832
C2×#117626802
C2×#117626712
C2×C17×#3872
C2×#248417