Finite Group Databasebeta

← C2×#14534199 #17204607

Subgroups — C2×#14534199 #17204607

Order 4352.

2270 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14534199C2116yesmaximal, direct product factor
2C2×#11762751C211yesmaximal, characteristic, complemented
3C2×#11762743C211yesmaximal, characteristic, complemented
4C2×#11762732C211yesmaximal, characteristic
5C2×#11762732C211yesmaximal, characteristic
6C2×#11762707C211yesmaximal, characteristic, complemented
7C2×#11762707C211yesmaximal, characteristic, complemented
8C2×#11762706C211yesmaximal, characteristic, complemented
9C2×#11762702C211yesmaximal, characteristic
10C2×#11762702C211yesmaximal, characteristic
11C2×#11762696C211yesmaximal, characteristic, complemented
12C2×#11762693C211yesmaximal, characteristic, complemented
13C2×#11762682C211yesmaximal, characteristic
14C2×#11762682C211yesmaximal, characteristic
15C2×C4×#63225C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C17C211yesmaximal, characteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×C4⋊Dic17C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×#63225C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C22×#63225C2211yescharacteristic
29C22×C22⋊Dic17C2211yescharacteristic
30C22×C22⋊Dic17C2211yescharacteristic
31C22×C22⋊Dic17C2211yescharacteristic
32C22×C22⋊Dic17C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35#11762751C2218yescomplemented
36#11762743C2218yescomplemented
37#11762732C2218yes—
38#11762732C2218yes—
39#11762707C2218yescomplemented
40#11762707C2218yescomplemented
41#11762706C2218yescomplemented
42#11762702C2218yes—
43#11762702C2218yes—
44#11762696C2218yescomplemented
45#11762693C2218yescomplemented
46#11762682C2218yes—
47#11762682C2218yes—
48C4×#63225C2218yescomplemented
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
53C2×#10587502C2211yescharacteristic
54C2×#10587502C2211yescharacteristic
55C2×#10587502C2211yescharacteristic
56C2×#10587502C2211yescharacteristic
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59C24×C4×C17C2211yescharacteristic
60C22×C22⋊C4×C17C2211yescharacteristic
61C22×C22⋊C4×C17C2211yescharacteristic
62C22×C42×C17C2211yescharacteristic
63C22×C42×C17C2211yescharacteristic
64C4×C22⋊C4×C17C2218yes—
65C2×C17×#95C2211yescharacteristic
66C2×C17×#95C2211yescharacteristic
67C25×C17C2311yescharacteristic
68C23×C4×C17—24no—
69C23×C4×C17—42no—
70C23×C4×C17—42no—
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C23×C4×C17C2314yes—
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C23×Dic17C2311yescharacteristic
85C23×Dic17C2311yescharacteristic
86C2×C22⋊C4×C17—24no—
87C2×C22⋊C4×C17Q818yes—
88C2×C22⋊C4×C17C2314yes—
89C2×C22⋊C4×C17C2314yes—
90C2×C42×C17—42no—
91C2×C42×C17—42no—
92C2×C42×C17C2314yes—
93C2×C42×C17C2314yes—
94C2×C22⋊Dic17—24no—
95C2×C22⋊Dic17—24no—
96C2×C22⋊Dic17—42no—
97C2×C22⋊Dic17—42no—
98C2×C22⋊Dic17C2314yes—
99C2×C22⋊Dic17C2314yes—
100C2×C22⋊Dic17C2314yes—
101C2×C22⋊Dic17C2314yes—
102C2×C4⋊Dic17—24no—
103C2×C4⋊Dic17—24no—
104C2×C4⋊Dic17—42no—
105C2×C4⋊Dic17—42no—
106C2×C4⋊Dic17C2314yes—
107C2×C4⋊Dic17C2314yes—
108C2×C4⋊Dic17C2314yes—
109C2×C4⋊Dic17C2314yes—
110C2×#63225—24no—
111C2×#63225—24no—
112C2×#63225—24no—
113C2×#63225—24no—
114C2×#63225—24no—
115C2×#63225—42no—
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—42no—
128C2×C4×Dic17C2314yes—
129C2×C4×Dic17C2314yes—
130C17×#95C2314yes—
131C17×#95C2314yes—
132#10587502C2314yes—
133#10587502C2314yes—
134#10587502C2314yes—
135#10587502C2314yes—
136#10587502C2314yes—
137#10587502C2314yes—
138#10587502C2314yes—
139#10587502C2314yes—
140#10587502C2314yes—
141#10587502C2314yes—
142C24×C17—22no—
143C24×C17—22no—
144C24×C17—22no—
145C24×C17—22no—
146C24×C17—22no—
147C24×C17—22no—
148C24×C17C2×Q814yes—
149C24×C17C2412yes—
150C24×C17C2411yescharacteristic
151C22×C4×C17—22no—
152C22×C4×C17—22no—
153C22×C4×C17—22no—
154C22×C4×C17—22no—
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—28no—
166C22×C4×C17—44no—
167C22×C4×C17—44no—
168C22×C4×C17—416no—
169C22×C4×C17C2×Q814yes—
170C22×C4×C17C2×Q814yes—
171C22×C4×C17#4114yes—
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×Dic17—22no—
201C22×Dic17#4114yes—
202C22×Dic17#4114yes—
203C22×Dic17C2412yes—
204C22×Dic17C2412yes—
205C22×Dic17C2412yes—
206C22×Dic17C2412yes—
207C22×Dic17C2412yes—
208C22×Dic17C2412yes—
209C22×Dic17C2412yes—
210C22×Dic17C2412yes—
211C22⋊C4×C17—28no—
212C22⋊C4×C17C2×Q8116yes—
213C42×C17—44no—
214C42×C17—44no—
215C22⋊Dic17—28no—
216C22⋊Dic17—28no—
217C22⋊Dic17—44no—
218C22⋊Dic17—44no—
219C4⋊Dic17—28no—
220C4⋊Dic17—28no—
221C4⋊Dic17—44no—
222C4⋊Dic17—44no—
223#63225—28no—
224#63225—28no—
225#63225—28no—
226#63225—28no—
227#63225—28no—
228#63225—44no—
229#63225—44no—
230#63225—44no—
231C4×Dic17—28no—
232C4×Dic17—44no—
233C2×#2587—171nomaximal, Sylow
234C23×C17—28no—
235C23×C17—28no—
236C23×C17—28no—
237C23×C17—22no—
238C23×C17—22no—
239C23×C17—22no—
240C23×C17—22no—
241C23×C17—22no—
242C23×C17—22no—
243C23×C17—44no—
244C23×C17—44no—
245C23×C17—44no—
246C23×C17—44no—
247C23×C17C22×Q814yes—
248C23×C17C22×Q812yes—
249C23×C17C2×#4112yes—
250C23×C17C2×#4112yes—
251C23×C17C2×#4112yes—
252C23×C17C2×#4112yes—
253C23×C17H(5,𝔽2)12yes—
254C23×C17H(5,𝔽2)12yes—
255C23×C17C2511yescharacteristic
256C2×C4×C17—28no—
257C2×C4×C17—28no—
258C2×C4×C17—28no—
259C2×C4×C17—28no—
260C2×C4×C17—22no—
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—416no—
275C2×C4×C17—44no—
276C2×C4×C17—44no—
277C2×C4×C17C22×Q814yes—
278C2×C4×C17C22×Q814yes—
279C2×C4×C17C2×#4114yes—
280C2×C4×C17C2×#4114yes—
281C2×Dic17—28no—
282C2×Dic17—28no—
283C2×Dic17—22no—
284C2×Dic17—22no—
285C2×Dic17—22no—
286C2×Dic17—22no—
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—44no—
306C2×Dic17—44no—
307C2×Dic17—44no—
308C2×Dic17—44no—
309C2×Dic17—44no—
310C2×Dic17—44no—
311C2×Dic17C2×#4114yes—
312C2×Dic17C2×#4114yes—
313#2587—1716no—
314C2×#400—171no—
315C2×#398—171no—
316C2×#396—171no—
317C2×#396—171no—
318C2×#389—171no—
319C2×#389—171no—
320C2×#389—171no—
321C2×#388—171no—
322C2×#388—171no—
323C2×#387—171no—
324C2×#387—171no—
325C2×#385—171no—
326C2×#385—171no—
327C2×C4×C4⋊C4—171no—
328C2×C4×C22⋊C4D1711yescharacteristic
329C22×C17—24no—
330C22×C17—24no—
331C22×C17—24no—
332C22×C17—416no—
333C22×C17—42no—
334C22×C17—42no—
335C22×C17—42no—
336C22×C17—42no—
337C22×C17#52914yes—
338C22×C17#53314yes—
339C22×C17#53814yes—
340C22×C17#55314yes—
341C22×C17#55314yes—
342C22×C17#55414yes—
343C22×C17#55414yes—
344C22×C17C23×Q811yescharacteristic
345C22×C17C22×#4111yescharacteristic
346C22×C17C22×#4111yescharacteristic
347C22×C17C22×#4111yescharacteristic
348C22×C17C22×#4111yescharacteristic
349C22×C17C2×H(5,𝔽2)11yescharacteristic
350C22×C17C2×H(5,𝔽2)11yescharacteristic
351C4×C17—24no—
352C4×C17—24no—
353C4×C17—24no—
354C4×C17—24no—
355C4×C17—42no—
356C4×C17—42no—
357Dic17—24no—
358Dic17—24no—
359Dic17—42no—
360Dic17—42no—
361Dic17—42no—
362Dic17—42no—
363Dic17—42no—
364Dic17—42no—
365C24×C4C2×D1711yescharacteristic
366C22×C4⋊C4—171no—
367C22×C4⋊C4—171no—
368C22×C4⋊C4—171no—
369C22×C4⋊C4—171no—
370C22×C4⋊C4—171no—
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×C22⋊C4—171no—
379C22×C22⋊C4—171no—
380C22×C22⋊C4—171no—
381C22×C22⋊C4—171no—
382C22×C22⋊C4C2×D1711yescharacteristic
383C22×C22⋊C4C2×D1711yescharacteristic
384C22×C42—171no—
385C22×C42—171no—
386C22×C42C2×D1711yescharacteristic
387C22×C42C2×D1711yescharacteristic
388#400—178no—
389#398—178no—
390#396—178no—
391#396—178no—
392#389—178no—
393#389—178no—
394#389—178no—
395#388—178no—
396#388—178no—
397#387—178no—
398#387—178no—
399#385—178no—
400#385—178no—
401C4×C4⋊C4—178no—
402C4×C22⋊C4C2×D1718yes—
403C2×#95—171no—
404C2×#95—171no—
405C2×#95—171no—
406C2×#95—171no—
407C2×#95—171no—
408C2×#95—171no—
409C2×#95—171no—
410C2×#95—171no—
411C2×#95—171no—
412C2×#95—171no—
413C2×#95C2×D1711yescharacteristic
414C2×#95C2×D1711yescharacteristic
415C2×C17—44no—
416C2×C17#258718yescomplemented
417C2×C17C2×#52911yescharacteristic
418C2×C17C2×#53311yescharacteristic
419C2×C17C2×#53811yescharacteristic
420C2×C17C2×#55311yescharacteristic
421C2×C17C2×#55311yescharacteristic
422C2×C17C2×#55411yescharacteristic
423C2×C17C2×#55411yescharacteristic
424C25C22×D1711yescharacteristic
425C23×C4—24no—
426C23×C4—42no—
427C23×C4—42no—
428C23×C4—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×D1714yes—
443C2×C4⋊C4—174no—
444C2×C4⋊C4—174no—
445C2×C4⋊C4—174no—
446C2×C4⋊C4—174no—
447C2×C4⋊C4—174no—
448C2×C4⋊C4—174no—
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—344no—
456C2×C4⋊C4—344no—
457C2×C4⋊C4—344no—
458C2×C4⋊C4—344no—
459C2×C4⋊C4—344no—
460C2×C4⋊C4—344no—
461C2×C4⋊C4—344no—
462C2×C4⋊C4—682no—
463C2×C4⋊C4—682no—
464C2×C4⋊C4—682no—
465C2×C4⋊C4—682no—
466C2×C4⋊C4—682no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—174no—
469C2×C22⋊C4—174no—
470C2×C22⋊C4—174no—
471C2×C22⋊C4—174no—
472C2×C22⋊C4—344no—
473C2×C22⋊C4—344no—
474C2×C22⋊C4—682no—
475C2×C22⋊C4—682no—
476C2×C22⋊C4Dic3418yes—
477C2×C22⋊C4C22×D1714yes—
478C2×C22⋊C4C22×D1714yes—
479C2×C42—42no—
480C2×C42—42no—
481C2×C42—174no—
482C2×C42—174no—
483C2×C42—344no—
484C2×C42—682no—
485C2×C42C22×D1714yes—
486C2×C42C22×D1714yes—
487#95—174no—
488#95—174no—
489#95—174no—
490#95—174no—
491#95—174no—
492#95—174no—
493#95—174no—
494#95—174no—
495#95—174no—
496#95—174no—
497#95C22×D1714yes—
498#95C22×D1714yes—
499C17C2×#258711yescharacteristic, complemented, Sylow
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24C2×Dic3414yes—
507C24C23×D1712yes—
508C24C23×D1711yescharacteristic
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
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—28no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—416no—
527C22×C4—174no—
528C22×C4—174no—
529C22×C4—172no—
530C22×C4—172no—
531C22×C4—172no—
532C22×C4—172no—
533C22×C4—172no—
534C22×C4—172no—
535C22×C4—172no—
536C22×C4—172no—
537C22×C4—342no—
538C22×C4—342no—
539C22×C4—342no—
540C22×C4—342no—
541C22×C4—342no—
542C22×C4—342no—
543C22×C4—342no—
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×C4C2×Dic3414yes—
560C22×C4C2×Dic3414yes—
561C22×C4#6325214yes—
562C22×C4#6325214yes—
563C22×C4C23×D1712yes—
564C22×C4C23×D1712yes—
565C22×C4C23×D1712yes—
566C22×C4C23×D1712yes—
567C22×C4C23×D1712yes—
568C22×C4C23×D1712yes—
569C4⋊C4—348no—
570C4⋊C4—348no—
571C4⋊C4—348no—
572C4⋊C4—348no—
573C4⋊C4—348no—
574C4⋊C4—348no—
575C4⋊C4—348no—
576C4⋊C4—684no—
577C4⋊C4—684no—
578C4⋊C4—684no—
579C4⋊C4—684no—
580C4⋊C4—684no—
581C22⋊C4—28no—
582C22⋊C4—348no—
583C22⋊C4—348no—
584C22⋊C4—684no—
585C22⋊C4—684no—
586C22⋊C4C2×Dic34116yes—
587C42—44no—
588C42—44no—
589C42—348no—
590C42—684no—
591C23—28no—
592C23—28no—
593C23—28no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—44no—
601C23—44no—
602C23—44no—
603C23—44no—
604C23C22×Dic3414yes—
605C23C22×Dic3412yes—
606C23C2×#6325212yes—
607C23C2×#6325212yes—
608C23#1058769112yes—
609C23#1058769112yes—
610C23#41×D1712yes—
611C23#41×D1712yes—
612C23C24×D1711yescharacteristic
613C2×C4—28no—
614C2×C4—28no—
615C2×C4—28no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—28no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—416no—
632C2×C4—44no—
633C2×C4—44no—
634C2×C4—174no—
635C2×C4—174no—
636C2×C4—348no—
637C2×C4—348no—
638C2×C4—342no—
639C2×C4—342no—
640C2×C4—342no—
641C2×C4—342no—
642C2×C4—342no—
643C2×C4—342no—
644C2×C4—342no—
645C2×C4—342no—
646C2×C4—342no—
647C2×C4—342no—
648C2×C4—342no—
649C2×C4—342no—
650C2×C4—342no—
651C2×C4—342no—
652C2×C4—342no—
653C2×C4—342no—
654C2×C4—342no—
655C2×C4—342no—
656C2×C4—342no—
657C2×C4—342no—
658C2×C4—342no—
659C2×C4—342no—
660C2×C4—684no—
661C2×C4—684no—
662C2×C4—684no—
663C2×C4—684no—
664C2×C4—684no—
665C2×C4—684no—
666C2×C4C22×Dic3414yes—
667C2×C4C22×Dic3414yes—
668C2×C4C2×#6325214yes—
669C2×C4C2×#6325214yes—
670C22—24no—
671C22—24no—
672C22—24no—
673C22—42no—
674C22—416no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22#1176333714yes—
679C22#1176336614yes—
680C22#1176339714yes—
681C22#1176350814yes—
682C22#1176350914yes—
683C22#1176351814yes—
684C22#1176351814yes—
685C22C23×Dic3411yescharacteristic
686C22C2×#41×D1711yescharacteristic
687C22C2×#41×D1711yescharacteristic
688C22C22×#6325211yescharacteristic
689C22C22×#6325211yescharacteristic
690C22C2×#1058769111yescharacteristic
691C22C2×#1058769111yescharacteristic
692C4—24no—
693C4—24no—
694C4—24no—
695C4—24no—
696C4—42no—
697C4—42no—
698C4—344no—
699C4—344no—
700C4—682no—
701C4—682no—
702C4—682no—
703C4—682no—
704C4—682no—
705C4—682no—
706C2—44no—
707C2#1453419918yesdirect product factor
708C2C2×#1176333711yescharacteristic
709C2C2×#1176336611yescharacteristic
710C2C2×#1176339711yescharacteristic
711C2C2×#1176350811yescharacteristic
712C2C2×#1176350911yescharacteristic
713C2C2×#1176351811yescharacteristic
714C2C2×#1176351811yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C4×C22⋊C4×C17C2
socleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×C4×C22⋊C4D17
hypocenterC17C2×#2587
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #14534199C2direct (N × H)
2. C2×#11762751C2semidirect
3. C2×#11762743C2semidirect
6. C2×#11762707C2semidirect
7. C2×#11762707C2semidirect
8. C2×#11762706C2semidirect
11. C2×#11762696C2semidirect
12. C2×#11762693C2semidirect
15. C2×C4×#63225C2semidirect
35. #11762751C22semidirect
36. #11762743C22semidirect
39. #11762707C22semidirect
40. #11762707C22semidirect
41. #11762706C22semidirect
44. #11762696C22semidirect
45. #11762693C22semidirect
48. C4×#63225C22semidirect
416. C2×C17#2587semidirect
499. C17C2×#2587semidirect
707. C2#14534199direct (N × H)

Maximal subgroups

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

subgroupindex
#145341992
C2×#117627512
C2×#117627432
C2×#117627322
C2×#117627072
C2×#117627062
C2×#117627022
C2×#117626962
C2×#117626932
C2×#117626822
C2×C4×#632252
C2×C4×C22⋊C4×C172
C2×#258717