Finite Group Databasebeta

← C2×#14534697 #17201259

Subgroups — C2×#14534697 #17201259

Order 4352.

2482 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587565C211yesmaximal, characteristic
2C22×#10587573C211yesmaximal, characteristic, complemented
3#14534697C2116yesmaximal, direct product factor
4C2×#11762743C211yesmaximal, characteristic, complemented
5C2×#11762742C211yesmaximal, characteristic, complemented
6C2×#11762739C211yesmaximal, characteristic, complemented
7C2×#11762737C211yesmaximal, characteristic
8C2×#11762732C211yesmaximal, characteristic
9C2×#11762729C211yesmaximal, characteristic, complemented
10C2×#11762721C211yesmaximal, characteristic
11C2×#11762703C211yesmaximal, characteristic
12C2×#11762702C211yesmaximal, characteristic
13C2×#11762696C211yesmaximal, characteristic, complemented
14C2×#11762695C211yesmaximal, characteristic, complemented
15C2×#11762674C211yesmaximal, characteristic, complemented
16C2×C17×#396C211yesmaximal, characteristic
17C23×Dic34C2211yescharacteristic
18C2×#10587565—28no—
19C2×#10587565C2218yes—
20C2×#10587573—28no—
21C2×#10587573C2218yescomplemented
22C22×C4⋊Dic17C2211yescharacteristic
23C22×C4⋊Dic17C2211yescharacteristic
24C22×C4⋊Dic17C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×#63225C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C22×#63225C2211yescharacteristic
29C22×#63225C2211yescharacteristic
30C22×#63225C2211yescharacteristic
31C22×C22⋊Dic17C2211yescharacteristic
32C22×C22⋊Dic17C2211yescharacteristic
33C22×C22⋊Dic17C2211yescharacteristic
34C22×C22⋊Dic17C2211yescharacteristic
35C22×C4×Dic17C2211yescharacteristic
36C22×C4×Dic17C2211yescharacteristic
37C22×C4×Dic17C2211yescharacteristic
38#11762743C2218yescomplemented
39#11762742C2218yescomplemented
40#11762739C2218yescomplemented
41#11762737C2218yes—
42#11762732C2218yes—
43#11762729C2218yescomplemented
44#11762721C2218yes—
45#11762703C2218yes—
46#11762702C2218yes—
47#11762696C2218yescomplemented
48#11762695C2218yescomplemented
49#11762674C2218yescomplemented
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×C4⋊C4×C17C2211yescharacteristic
64C22×C22⋊C4×C17C2211yescharacteristic
65C22×C22⋊C4×C17C2211yescharacteristic
66C22×C22⋊C4×C17C2211yescharacteristic
67C17×#396C2218yes—
68C2×C17×#95C2211yescharacteristic
69C25×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C22×Dic34—24no—
85C22×Dic34—24no—
86C22×Dic34—24no—
87C22×Dic34C2314yes—
88C2×C4⋊C4×C17—24no—
89C2×C4⋊C4×C17—24no—
90C2×C4⋊C4×C17—42no—
91C2×C4⋊C4×C17C2314yes—
92C2×C4⋊C4×C17C2314yes—
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—24no—
103C2×C22⋊Dic17—42no—
104C2×C22⋊Dic17C2314yes—
105C2×C22⋊Dic17C2314yes—
106C2×C22⋊Dic17C2314yes—
107C2×C22⋊Dic17C2314yes—
108C2×C4⋊Dic17—24no—
109C2×C4⋊Dic17—42no—
110C2×C4⋊Dic17—42no—
111C2×C4⋊Dic17C2314yes—
112C2×C4⋊Dic17C2314yes—
113C2×C4⋊Dic17C2314yes—
114C2×#63225—24no—
115C2×#63225—24no—
116C2×#63225—24no—
117C2×#63225—24no—
118C2×#63225—24no—
119C2×#63225—42no—
120C2×#63225C2314yes—
121C2×#63225C2314yes—
122C2×#63225C2314yes—
123C2×#63225C2314yes—
124C2×#63225C2314yes—
125C2×#63225C2314yes—
126C2×C4×Dic17—24no—
127C2×C4×Dic17—24no—
128C2×C4×Dic17D418yes—
129C2×C4×Dic17C2314yes—
130C2×C4×Dic17C2314yes—
131C2×C4×Dic17C2314yes—
132#10587573—232no—
133#10587565—232no—
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×C17—22no—
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×C17C2×D414yes—
172C22×C4×C17#4114yes—
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—22no—
182C22×Dic17—22no—
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×Dic17C2×D414yes—
201C22×Dic17C2×D414yes—
202C22×Dic17#4114yes—
203C22×Dic17C2412yes—
204C22×Dic17C2412yes—
205C22×Dic17C2412yes—
206C22×Dic17C2412yes—
207C22×Dic17C2412yes—
208C22×Dic17C2412yes—
209C22×Dic17C2412yes—
210C22×Dic17C2412yes—
211C2×Dic34—232no—
212C2×Dic34—28no—
213C2×Dic34—28no—
214C2×Dic34—28no—
215C4⋊C4×C17—28no—
216C4⋊C4×C17—28no—
217C4⋊C4×C17—44no—
218C22⋊C4×C17—28no—
219C22⋊C4×C17—28no—
220C22⋊C4×C17—44no—
221C22⋊Dic17—28no—
222C22⋊Dic17—28no—
223C22⋊Dic17—28no—
224C22⋊Dic17—44no—
225C4⋊Dic17—28no—
226C4⋊Dic17—44no—
227C4⋊Dic17—44no—
228#63225—28no—
229#63225—28no—
230#63225—28no—
231#63225—28no—
232#63225—28no—
233#63225—44no—
234C4×Dic17—28no—
235C4×Dic17—28no—
236C4×Dic17C2×D4116yes—
237C2×#2637—171nomaximal, Sylow
238C23×C17—22no—
239C23×C17—22no—
240C23×C17—22no—
241C23×C17—22no—
242C23×C17—22no—
243C23×C17—22no—
244C23×C17—22no—
245C23×C17—44no—
246C23×C17—44no—
247C23×C17—44no—
248C23×C17—44no—
249C23×C17—44no—
250C23×C17—44no—
251C23×C17—44no—
252C23×C17C22×D412yes—
253C23×C17C2×#4112yes—
254C23×C17C2×#4112yes—
255C23×C17H(5,𝔽2)12yes—
256C23×C172−1+412yes—
257C23×C172−1+412yes—
258C23×C172−1+412yes—
259C23×C17C2511yescharacteristic
260C2×C4×C17—28no—
261C2×C4×C17—28no—
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—44no—
279C2×C4×C17—44no—
280C2×C4×C17—44no—
281C2×C4×C17—44no—
282C2×C4×C17C22×D414yes—
283C2×C4×C17C2×#4114yes—
284C2×Dic17—28no—
285C2×Dic17—28no—
286C2×Dic17—28no—
287C2×Dic17—22no—
288C2×Dic17—22no—
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—22no—
308C2×Dic17—44no—
309C2×Dic17—44no—
310C2×Dic17—44no—
311C2×Dic17—44no—
312C2×Dic17—44no—
313C2×Dic17C22×D414yes—
314C2×Dic17C22×D414yes—
315C2×Dic17C2×#4114yes—
316Dic34—232no—
317C22×#126—171no—
318C22×C4×Q8—171no—
319#2637—1716no—
320C2×#398—171no—
321C2×#398—171no—
322C2×#398—171no—
323C2×#397—171no—
324C2×#396—171no—
325C2×#396D1711yescharacteristic
326C2×#395—171no—
327C2×#393—171no—
328C2×#388—171no—
329C2×#388—171no—
330C2×#387—171no—
331C2×#387—171no—
332C2×#382—171no—
333C22×C17—42no—
334C22×C17—42no—
335C22×C17—42no—
336C22×C17—42no—
337C22×C17—42no—
338C22×C17—42no—
339C22×C17—42no—
340C22×C17—88no—
341C22×C17#52514yes—
342C22×C17#53614yes—
343C22×C17#53714yes—
344C22×C17#54114yes—
345C22×C17#54114yes—
346C22×C17#54214yes—
347C22×C17#54214yes—
348C22×C17C23×D411yescharacteristic
349C22×C17C22×#4111yescharacteristic
350C22×C17C22×#4111yescharacteristic
351C22×C17C2×H(5,𝔽2)11yescharacteristic
352C22×C17C2×2−1+411yescharacteristic
353C22×C17C2×2−1+411yescharacteristic
354C22×C17C2×2−1+411yescharacteristic
355C4×C17—24no—
356C4×C17—24no—
357C4×C17—42no—
358C4×C17—42no—
359C4×C17—42no—
360C4×C17—42no—
361Dic17—24no—
362Dic17—24no—
363Dic17—24no—
364Dic17—42no—
365Dic17—42no—
366Dic17—42no—
367Dic17—42no—
368Dic17—42no—
369C23×Q8—171no—
370C2×#126—178no—
371C2×#126—348no—
372C2×C4×Q8—178no—
373C2×C4×Q8—348no—
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⋊C4—171no—
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⋊C4C2×D1711yescharacteristic
391C22×C22⋊C4C2×D1711yescharacteristic
392C22×C22⋊C4C2×D1711yescharacteristic
393C22×C42—171no—
394C22×C42—171no—
395C22×C42—171no—
396#398—178no—
397#398—178no—
398#398—178no—
399#397—178no—
400#396—178no—
401#396C2×D1718yes—
402#395—178no—
403#393—178no—
404#388—178no—
405#388—178no—
406#387—178no—
407#387—178no—
408#382—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×C17—82no—
422C2×C17#263718yescomplemented
423C2×C17C2×#52511yescharacteristic
424C2×C17C2×#53611yescharacteristic
425C2×C17C2×#53711yescharacteristic
426C2×C17C2×#54111yescharacteristic
427C2×C17C2×#54111yescharacteristic
428C2×C17C2×#54211yescharacteristic
429C2×C17C2×#54211yescharacteristic
430C25C22×D1711yescharacteristic
431C22×Q8—174no—
432C22×Q8—344no—
433C22×Q8—344no—
434C22×Q8—344no—
435C23×C4—171no—
436C23×C4—171no—
437C23×C4—171no—
438C23×C4—171no—
439C23×C4—171no—
440C23×C4—171no—
441C23×C4—171no—
442C23×C4—171no—
443C23×C4C22×D1711yescharacteristic
444C23×C4C22×D1711yescharacteristic
445C23×C4C22×D1711yescharacteristic
446C23×C4C22×D1711yescharacteristic
447C23×C4C22×D1711yescharacteristic
448C23×C4C22×D1711yescharacteristic
449#126—3432no—
450C4×Q8—3432no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—42no—
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—174no—
461C2×C4⋊C4—174no—
462C2×C4⋊C4—174no—
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—682no—
470C2×C4⋊C4—682no—
471C2×C4⋊C4—682no—
472C2×C4⋊C4C22×D1714yes—
473C2×C4⋊C4C22×D1714yes—
474C2×C4⋊C4C22×D1714yes—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—42no—
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—682no—
486C2×C22⋊C4C22×D1714yes—
487C2×C22⋊C4C22×D1714yes—
488C2×C22⋊C4C22×D1714yes—
489C2×C42—178no—
490C2×C42—174no—
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—
507C17C2×#263711yescharacteristic, complemented, Sylow
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24C23×D1712yes—
516C24C23×D1711yescharacteristic
517C2×Q8—348no—
518C2×Q8—348no—
519C2×Q8—3432no—
520C2×Q8—348no—
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—174no—
538C22×C4—174no—
539C22×C4—174no—
540C22×C4—172no—
541C22×C4—172no—
542C22×C4—172no—
543C22×C4—172no—
544C22×C4—172no—
545C22×C4—172no—
546C22×C4—172no—
547C22×C4—172no—
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—342no—
563C22×C4—342no—
564C22×C4—342no—
565C22×C4—342no—
566C22×C4—342no—
567C22×C4—342no—
568C22×C4—342no—
569C22×C4D4×D1714yes—
570C22×C4#6325414yes—
571C22×C4C23×D1712yes—
572C22×C4C23×D1712yes—
573C22×C4C23×D1712yes—
574C22×C4C23×D1712yes—
575C22×C4C23×D1712yes—
576C22×C4C23×D1712yes—
577C4⋊C4—28no—
578C4⋊C4—28no—
579C4⋊C4—44no—
580C4⋊C4—348no—
581C4⋊C4—348no—
582C4⋊C4—348no—
583C4⋊C4—348no—
584C4⋊C4—348no—
585C4⋊C4—348no—
586C4⋊C4—684no—
587C4⋊C4—684no—
588C4⋊C4—684no—
589C22⋊C4—28no—
590C22⋊C4—28no—
591C22⋊C4—44no—
592C22⋊C4—348no—
593C22⋊C4—348no—
594C22⋊C4—348no—
595C22⋊C4—684no—
596C42—1716no—
597C42—348no—
598C42—348no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—44no—
607C23—44no—
608C23—44no—
609C23—44no—
610C23—44no—
611C23—44no—
612C23—44no—
613C23C2×D4×D1712yes—
614C23C2×#6325412yes—
615C23#1058769112yes—
616C23#1058769412yes—
617C23#41×D1712yes—
618C23#1058769712yes—
619C23#1058769712yes—
620C23C24×D1711yescharacteristic
621Q8—3432no—
622C2×C4—28no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—28no—
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—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—174no—
645C2×C4—174no—
646C2×C4—174no—
647C2×C4—348no—
648C2×C4—348no—
649C2×C4—342no—
650C2×C4—342no—
651C2×C4—342no—
652C2×C4—342no—
653C2×C4—348no—
654C2×C4—342no—
655C2×C4—342no—
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—684no—
672C2×C4—684no—
673C2×C4—684no—
674C2×C4—684no—
675C2×C4—684no—
676C2×C4C2×D4×D1714yes—
677C2×C4C2×#6325414yes—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—88no—
686C22#1176331914yes—
687C22#1176338214yes—
688C22#1176338614yes—
689C22#1176341614yes—
690C22#1176341914yes—
691C22#1176342614yes—
692C22#1176342914yes—
693C22C22×D4×D1711yescharacteristic
694C22C2×#41×D1711yescharacteristic
695C22C22×#6325411yescharacteristic
696C22C2×#1058769111yescharacteristic
697C22C2×#1058769711yescharacteristic
698C22C2×#1058769711yescharacteristic
699C22C2×#1058769411yescharacteristic
700C4—24no—
701C4—24no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—344no—
707C4—344no—
708C4—344no—
709C4—682no—
710C4—682no—
711C4—682no—
712C4—682no—
713C4—682no—
714C2—82no—
715C2#1453469718yesdirect product factor
716C2C2×#1176331911yescharacteristic
717C2C2×#1176338211yescharacteristic
718C2C2×#1176338611yescharacteristic
719C2C2×#1176341611yescharacteristic
720C2C2×#1176341911yescharacteristic
721C2C2×#1176342611yescharacteristic
722C2C2×#1176342911yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#396C2
socleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×#396D17
hypocenterC17C2×#2637
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
2. C22×#10587573C2semidirect
3. #14534697C2direct (N × H)
4. C2×#11762743C2semidirect
5. C2×#11762742C2semidirect
6. C2×#11762739C2semidirect
9. C2×#11762729C2semidirect
13. C2×#11762696C2semidirect
14. C2×#11762695C2semidirect
15. C2×#11762674C2semidirect
21. C2×#10587573C22semidirect
38. #11762743C22semidirect
39. #11762742C22semidirect
40. #11762739C22semidirect
43. #11762729C22semidirect
47. #11762696C22semidirect
48. #11762695C22semidirect
49. #11762674C22semidirect
422. C2×C17#2637semidirect
507. C17C2×#2637semidirect
715. C2#14534697direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875652
C22×#105875732
#145346972
C2×#117627432
C2×#117627422
C2×#117627392
C2×#117627372
C2×#117627322
C2×#117627292
C2×#117627212
C2×#117627032
C2×#117627022
C2×#117626962
C2×#117626952
C2×#117626742
C2×C17×#3962
C2×#263717