Finite Group Databasebeta

← C2×#14534580 #17201394

Subgroups — C2×#14534580 #17201394

Order 4352.

2590 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587564C211yesmaximal, characteristic
2C22×#10587563C211yesmaximal, characteristic
3#14534580C2116yesmaximal, direct product factor
4C2×#11762751C211yesmaximal, characteristic, complemented
5C2×#11762750C211yesmaximal, characteristic, complemented
6C2×#11762743C211yesmaximal, characteristic, complemented
7C2×#11762742C211yesmaximal, characteristic, complemented
8C2×#11762737C211yesmaximal, characteristic
9C2×#11762737C211yesmaximal, characteristic
10C2×#11762734C211yesmaximal, characteristic
11C2×#11762713C211yesmaximal, characteristic, complemented
12C2×#11762713C211yesmaximal, characteristic, complemented
13C2×#11762706C211yesmaximal, characteristic, complemented
14C2×#11762704C211yesmaximal, characteristic, complemented
15C2×#11762667C211yesmaximal, characteristic
16C2×C17×#397C211yesmaximal, characteristic
17C23×Dic34C2211yescharacteristic
18C24×Dic17C2211yescharacteristic
19C2×#10587564—28no—
20C2×#10587564C2218yes—
21C2×#10587563—28no—
22C2×#10587563C2218yes—
23C22×C4⋊Dic17C2211yescharacteristic
24C22×C4⋊Dic17C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×#63225C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C22×#63225C2211yescharacteristic
29C22×#63225C2211yescharacteristic
30C22×#63225C2211yescharacteristic
31C22×#63225C2211yescharacteristic
32C22×#63225C2211yescharacteristic
33C22×C22⋊Dic17C2211yescharacteristic
34C22×C22⋊Dic17C2211yescharacteristic
35C22×C22⋊Dic17C2211yescharacteristic
36C22×C4×Dic17C2211yescharacteristic
37C22×C4×Dic17C2211yescharacteristic
38#11762751C2218yescomplemented
39#11762750C2218yescomplemented
40#11762743C2218yescomplemented
41#11762742C2218yescomplemented
42#11762737C2218yes—
43#11762737C2218yes—
44#11762734C2218yes—
45#11762713C2218yescomplemented
46#11762713C2218yescomplemented
47#11762706C2218yescomplemented
48#11762704C2218yescomplemented
49#11762667C2218yes—
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×C22⋊C4×C17C2211yescharacteristic
63C22×C22⋊C4×C17C2211yescharacteristic
64C22×C22⋊C4×C17C2211yescharacteristic
65C17×#397C2218yes—
66C2×C17×#95C2211yescharacteristic
67C2×C17×#95C2211yescharacteristic
68C2×C17×#95C2211yescharacteristic
69C25×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×Dic17—24no—
77C23×Dic17—24no—
78C23×Dic17D418yes—
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C23×Dic17C2311yescharacteristic
85C23×Dic17C2311yescharacteristic
86C23×Dic17C2314yes—
87C23×Dic17C2311yescharacteristic
88C22×Dic34—24no—
89C22×Dic34—24no—
90C22×Dic34—24no—
91C22×Dic34C2314yes—
92C2×C4⋊C4×C17—42no—
93C2×C4⋊C4×C17C2314yes—
94C2×C22⋊C4×C17—24no—
95C2×C22⋊C4×C17—24no—
96C2×C22⋊C4×C17—42no—
97C2×C22⋊C4×C17C2314yes—
98C2×C22⋊C4×C17C2314yes—
99C2×C22⋊C4×C17C2314yes—
100C2×C22⋊Dic17—24no—
101C2×C22⋊Dic17—24no—
102C2×C22⋊Dic17—42no—
103C2×C22⋊Dic17C2314yes—
104C2×C22⋊Dic17C2314yes—
105C2×C22⋊Dic17C2314yes—
106C2×C4⋊Dic17—24no—
107C2×C4⋊Dic17—42no—
108C2×C4⋊Dic17C2314yes—
109C2×C4⋊Dic17C2314yes—
110C2×#63225—24no—
111C2×#63225—24no—
112C2×#63225—24no—
113C2×#63225—24no—
114C2×#63225—24no—
115C2×#63225—24no—
116C2×#63225—42no—
117C2×#63225—42no—
118C2×#63225C2314yes—
119C2×#63225C2314yes—
120C2×#63225C2314yes—
121C2×#63225C2314yes—
122C2×#63225C2314yes—
123C2×#63225C2314yes—
124C2×#63225C2314yes—
125C2×#63225C2314yes—
126C2×C4×Dic17—24no—
127C2×C4×Dic17—24no—
128C2×C4×Dic17C2314yes—
129C2×C4×Dic17C2314yes—
130#10587564—232no—
131#10587563—232no—
132C17×#95C2314yes—
133C17×#95C2314yes—
134C17×#95C2314yes—
135#10587502C2314yes—
136#10587502C2314yes—
137#10587502C2314yes—
138#10587502C2314yes—
139#10587502C2314yes—
140#10587502C2314yes—
141#10587502C2314yes—
142#10587502C2314yes—
143#10587502C2314yes—
144#10587502C2314yes—
145#10587502C2314yes—
146C24×C17—22no—
147C24×C17—22no—
148C24×C17—22no—
149C24×C17—22no—
150C24×C17—22no—
151C24×C17—22no—
152C24×C17C2×D414yes—
153C24×C17C2412yes—
154C24×C17C2411yescharacteristic
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×C17C2412yes—
174C22×C4×C17C2412yes—
175C22×C4×C17C2412yes—
176C22×C4×C17C2412yes—
177C22×C4×C17C2412yes—
178C22×C4×C17C2412yes—
179C22×Dic17—22no—
180C22×Dic17—22no—
181C22×Dic17—232no—
182C22×Dic17—28no—
183C22×Dic17—28no—
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×D4116yes—
203C22×Dic17C2×D414yes—
204C22×Dic17C2×D414yes—
205C22×Dic17#4114yes—
206C22×Dic17#4114yes—
207C22×Dic17C2412yes—
208C22×Dic17C2412yes—
209C22×Dic17C2412yes—
210C22×Dic17C2412yes—
211C22×Dic17C2412yes—
212C22×Dic17C2412yes—
213C22×Dic17C2412yes—
214C22×Dic17C2412yes—
215C2×Dic34—28no—
216C2×Dic34—28no—
217C2×Dic34—28no—
218C2×Dic34—416no—
219C4⋊C4×C17—44no—
220C22⋊C4×C17—28no—
221C22⋊C4×C17—28no—
222C22⋊C4×C17—44no—
223C22⋊Dic17—28no—
224C22⋊Dic17—28no—
225C22⋊Dic17—44no—
226C4⋊Dic17—28no—
227C4⋊Dic17—44no—
228#63225—28no—
229#63225—28no—
230#63225—28no—
231#63225—28no—
232#63225—28no—
233#63225—28no—
234#63225—44no—
235#63225—44no—
236C4×Dic17—28no—
237C4×Dic17—28no—
238C2×#2625—171nomaximal, Sylow
239C23×C17—28no—
240C23×C17—28no—
241C23×C17—28no—
242C23×C17—22no—
243C23×C17—22no—
244C23×C17—22no—
245C23×C17—22no—
246C23×C17—22no—
247C23×C17—22no—
248C23×C17—44no—
249C23×C17—44no—
250C23×C17—44no—
251C23×C17—44no—
252C23×C17C22×D414yes—
253C23×C17C22×D412yes—
254C23×C17C2×#4112yes—
255C23×C17C2×#4112yes—
256C23×C17H(5,𝔽2)12yes—
257C23×C172−1+412yes—
258C23×C172−1+412yes—
259C23×C172−1+412yes—
260C23×C17C2511yescharacteristic
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—44no—
280C2×C4×C17—44no—
281C2×C4×C17—44no—
282C2×C4×C17—44no—
283C2×C4×C17—44no—
284C2×C4×C17—44no—
285C2×Dic17—28no—
286C2×Dic17—22no—
287C2×Dic17—22no—
288C2×Dic17—232no—
289C2×Dic17—22no—
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—44no—
308C2×Dic17—44no—
309C2×Dic17—44no—
310C2×Dic17—44no—
311C2×Dic17—44no—
312C2×Dic17—44no—
313C2×Dic17#123116yes—
314C2×Dic17C22×D414yes—
315C2×Dic17C22×D414yes—
316C2×Dic17C2×#4114yes—
317C2×Dic17C2×#4114yes—
318Dic34—416no—
319C22×C22⋊Q8—171no—
320C22×#117—171no—
321#2625—1716no—
322C2×#400—171no—
323C2×#400—171no—
324C2×#398—171no—
325C2×#398—171no—
326C2×#397—171no—
327C2×#397—171no—
328C2×#397—171no—
329C2×#397D1711yescharacteristic
330C2×#391—171no—
331C2×#391—171no—
332C2×#389—171no—
333C2×#389—171no—
334C2×#380—171no—
335C22×C17—24no—
336C22×C17—24no—
337C22×C17—24no—
338C22×C17—416no—
339C22×C17—42no—
340C22×C17—42no—
341C22×C17—42no—
342C22×C17—42no—
343C22×C17C2×#12314yes—
344C22×C17#53614yes—
345C22×C17#53714yes—
346C22×C17#54114yes—
347C22×C17#54114yes—
348C22×C17#54214yes—
349C22×C17#54214yes—
350C22×C17C23×D411yescharacteristic
351C22×C17C22×#4111yescharacteristic
352C22×C17C22×#4111yescharacteristic
353C22×C17C2×H(5,𝔽2)11yescharacteristic
354C22×C17C2×2−1+411yescharacteristic
355C22×C17C2×2−1+411yescharacteristic
356C22×C17C2×2−1+411yescharacteristic
357C4×C17—42no—
358C4×C17—42no—
359C4×C17—42no—
360C4×C17—42no—
361C4×C17—42no—
362C4×C17—42no—
363Dic17—24no—
364Dic17—42no—
365Dic17—42no—
366Dic17—42no—
367Dic17—42no—
368Dic17—42no—
369Dic17—42no—
370Dic17C2×#12318yes—
371C23×Q8—171no—
372C24×C4—171no—
373C2×C22⋊Q8—178no—
374C2×C22⋊Q8—348no—
375C2×#117—178no—
376C2×#117—348no—
377C22×C4⋊C4—171no—
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—171no—
387C22×C4⋊C4C2×D1711yescharacteristic
388C22×C22⋊C4—171no—
389C22×C22⋊C4—171no—
390C22×C22⋊C4—171no—
391C22×C22⋊C4C2×D1711yescharacteristic
392C22×C22⋊C4C2×D1711yescharacteristic
393C22×C22⋊C4C2×D1711yescharacteristic
394C22×C42—171no—
395C22×C42—171no—
396#400—178no—
397#400—178no—
398#398—178no—
399#398—178no—
400#397—178no—
401#397—178no—
402#397—178no—
403#397C2×D1718yes—
404#391—178no—
405#391—178no—
406#389—178no—
407#389—178no—
408#380—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×#95C2×D1711yescharacteristic
421C2×#95C2×D1711yescharacteristic
422C2×#95C2×D1711yescharacteristic
423C2×C17—44no—
424C2×C17#262518yescomplemented
425C2×C17C22×#12311yescharacteristic
426C2×C17C2×#53611yescharacteristic
427C2×C17C2×#53711yescharacteristic
428C2×C17C2×#54111yescharacteristic
429C2×C17C2×#54111yescharacteristic
430C2×C17C2×#54211yescharacteristic
431C2×C17C2×#54211yescharacteristic
432C25C22×D1711yescharacteristic
433C22×Q8—174no—
434C22×Q8—344no—
435C22×Q8—344no—
436C22×Q8—344no—
437C23×C4—171no—
438C23×C4—178no—
439C23×C4—174no—
440C23×C4—171no—
441C23×C4—171no—
442C23×C4—171no—
443C23×C4—171no—
444C23×C4—171no—
445C23×C4—171no—
446C23×C4—171no—
447C23×C4—344no—
448C23×C4—344no—
449C23×C4C22×D1711yescharacteristic
450C23×C4C22×D1711yescharacteristic
451C23×C4C22×D1711yescharacteristic
452C23×C4C22×D1711yescharacteristic
453C23×C4C22×D1711yescharacteristic
454C23×C4C22×D1711yescharacteristic
455C22⋊Q8—3432no—
456#117—3432no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—174no—
459C2×C4⋊C4—174no—
460C2×C4⋊C4—174no—
461C2×C4⋊C4—174no—
462C2×C4⋊C4—174no—
463C2×C4⋊C4—174no—
464C2×C4⋊C4—174no—
465C2×C4⋊C4—174no—
466C2×C4⋊C4—174no—
467C2×C4⋊C4—174no—
468C2×C4⋊C4—344no—
469C2×C4⋊C4—344no—
470C2×C4⋊C4—344no—
471C2×C4⋊C4—344no—
472C2×C4⋊C4—344no—
473C2×C4⋊C4—344no—
474C2×C4⋊C4—344no—
475C2×C4⋊C4—682no—
476C2×C4⋊C4—682no—
477C2×C4⋊C4—682no—
478C2×C4⋊C4C22×D1714yes—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—42no—
482C2×C22⋊C4—174no—
483C2×C22⋊C4—174no—
484C2×C22⋊C4—174no—
485C2×C22⋊C4—344no—
486C2×C22⋊C4—344no—
487C2×C22⋊C4—682no—
488C2×C22⋊C4C22×D1714yes—
489C2×C22⋊C4C22×D1714yes—
490C2×C22⋊C4C22×D1714yes—
491C2×C42—174no—
492C2×C42—174no—
493C2×C42—344no—
494C2×C42—344no—
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#95C22×D1714yes—
507#95C22×D1714yes—
508#95C22×D1714yes—
509C17C2×#262511yescharacteristic, complemented, Sylow
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24D4×D1714yes—
517C24C23×D1712yes—
518C24C23×D1711yescharacteristic
519C2×Q8—348no—
520C2×Q8—348no—
521C2×Q8—348no—
522C2×Q8—6816no—
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—22no—
541C22×C4—174no—
542C22×C4—174no—
543C22×C4—174no—
544C22×C4—172no—
545C22×C4—174no—
546C22×C4—1716no—
547C22×C4—172no—
548C22×C4—172no—
549C22×C4—172no—
550C22×C4—172no—
551C22×C4—172no—
552C22×C4—172no—
553C22×C4—172no—
554C22×C4—3432no—
555C22×C4—348no—
556C22×C4—348no—
557C22×C4—342no—
558C22×C4—342no—
559C22×C4—342no—
560C22×C4—342no—
561C22×C4—342no—
562C22×C4—342no—
563C22×C4—342no—
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×C4C23×D1712yes—
578C22×C4C23×D1712yes—
579C22×C4C23×D1712yes—
580C22×C4C23×D1712yes—
581C22×C4C23×D1712yes—
582C22×C4C23×D1712yes—
583C4⋊C4—44no—
584C4⋊C4—348no—
585C4⋊C4—348no—
586C4⋊C4—348no—
587C4⋊C4—348no—
588C4⋊C4—348no—
589C4⋊C4—348no—
590C4⋊C4—348no—
591C4⋊C4—684no—
592C4⋊C4—684no—
593C4⋊C4—684no—
594C22⋊C4—28no—
595C22⋊C4—28no—
596C22⋊C4—44no—
597C22⋊C4—348no—
598C22⋊C4—348no—
599C22⋊C4—684no—
600C42—348no—
601C42—348no—
602C23—28no—
603C23—22no—
604C23—22no—
605C23—28no—
606C23—22no—
607C23—28no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—44no—
612C23—44no—
613C23—44no—
614C23—44no—
615C23C2×D4×D1714yes—
616C23C2×D4×D1712yes—
617C23#1058769112yes—
618C23#41×D1712yes—
619C23#41×D1712yes—
620C23#1058769712yes—
621C23#1058769712yes—
622C23#1058769712yes—
623C23C24×D1711yescharacteristic
624Q8—6816no—
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—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—44no—
648C2×C4—44no—
649C2×C4—1716no—
650C2×C4—174no—
651C2×C4—174no—
652C2×C4—174no—
653C2×C4—174no—
654C2×C4—3432no—
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—342no—
669C2×C4—342no—
670C2×C4—342no—
671C2×C4—342no—
672C2×C4—342no—
673C2×C4—342no—
674C2×C4—342no—
675C2×C4—342no—
676C2×C4—684no—
677C2×C4—684no—
678C2×C4—684no—
679C2×C4—684no—
680C2×C4—684no—
681C2×C4—684no—
682C22—24no—
683C22—24no—
684C22—24no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—416no—
690C22#123×D1714yes—
691C22#1176338114yes—
692C22#1176338614yes—
693C22#1176341614yes—
694C22#1176341614yes—
695C22#1176342314yes—
696C22#1176342714yes—
697C22C22×D4×D1711yescharacteristic
698C22C2×#41×D1711yescharacteristic
699C22C2×#41×D1711yescharacteristic
700C22C2×#1058769111yescharacteristic
701C22C2×#1058769711yescharacteristic
702C22C2×#1058769711yescharacteristic
703C22C2×#1058769711yescharacteristic
704C4—42no—
705C4—42no—
706C4—42no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—178no—
711C4—344no—
712C4—682no—
713C4—682no—
714C4—682no—
715C4—682no—
716C4—682no—
717C4—682no—
718C2—44no—
719C2#1453458018yesdirect product factor
720C2C2×#123×D1711yescharacteristic
721C2C2×#1176338111yescharacteristic
722C2C2×#1176338611yescharacteristic
723C2C2×#1176341611yescharacteristic
724C2C2×#1176341611yescharacteristic
725C2C2×#1176342311yescharacteristic
726C2C2×#1176342711yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#397C2
socleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×#397D17
hypocenterC17C2×#2625
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
3. #14534580C2direct (N × H)
4. C2×#11762751C2semidirect
5. C2×#11762750C2semidirect
6. C2×#11762743C2semidirect
7. C2×#11762742C2semidirect
11. C2×#11762713C2semidirect
12. C2×#11762713C2semidirect
13. C2×#11762706C2semidirect
14. C2×#11762704C2semidirect
38. #11762751C22semidirect
39. #11762750C22semidirect
40. #11762743C22semidirect
41. #11762742C22semidirect
45. #11762713C22semidirect
46. #11762713C22semidirect
47. #11762706C22semidirect
48. #11762704C22semidirect
424. C2×C17#2625semidirect
509. C17C2×#2625semidirect
719. C2#14534580direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875642
C22×#105875632
#145345802
C2×#117627512
C2×#117627502
C2×#117627432
C2×#117627422
C2×#117627372
C2×#117627342
C2×#117627132
C2×#117627062
C2×#117627042
C2×#117626672
C2×C17×#3972
C2×#262517