Finite Group Databasebeta

← C2×#14532490 #17202808

Subgroups — C2×#14532490 #17202808

Order 4352.

2726 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587575C211yesmaximal, characteristic, complemented
2C22×#10587563C211yesmaximal, characteristic
3#14532490C2116yesmaximal, direct product factor
4C2×#11762745C211yesmaximal, characteristic
5C2×#11762732C211yesmaximal, characteristic
6C2×#11762732C211yesmaximal, characteristic
7C2×#11762706C211yesmaximal, characteristic, complemented
8C2×#11762705C211yesmaximal, characteristic, complemented
9C2×#11762704C211yesmaximal, characteristic, complemented
10C2×#11762704C211yesmaximal, characteristic, complemented
11C2×#11762695C211yesmaximal, characteristic, complemented
12C2×#11762694C211yesmaximal, characteristic, complemented
13C2×#11762678C211yesmaximal, characteristic, complemented
14C2×#11762667C211yesmaximal, characteristic
15C2×C22⋊C4×Dic17C211yesmaximal, characteristic
16C2×C17×#399C211yesmaximal, characteristic
17C24×Dic17C2211yescharacteristic
18C2×#10587575—28no—
19C2×#10587575C2218yescomplemented
20C2×#10587563—28no—
21C2×#10587563C2218yes—
22C22×C4⋊Dic17C2211yescharacteristic
23C22×C4⋊Dic17C2211yescharacteristic
24C22×C4⋊Dic17C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×#63225C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C22×#63225C2211yescharacteristic
29C22×#63225C2211yescharacteristic
30C22×#63225C2211yescharacteristic
31C22×#63225C2211yescharacteristic
32C22×#63225C2211yescharacteristic
33C22×#63225C2211yescharacteristic
34C22×#63225C2211yescharacteristic
35C22×C22⋊Dic17C2211yescharacteristic
36C22×C22⋊Dic17C2211yescharacteristic
37C22×C22⋊Dic17C2211yescharacteristic
38C22×C4×Dic17C2211yescharacteristic
39C22×C4×Dic17C2211yescharacteristic
40C22×C4×Dic17C2211yescharacteristic
41C22×C4×Dic17C2211yescharacteristic
42#11762745C2218yes—
43#11762732C2218yes—
44#11762732C2218yes—
45#11762706C2218yescomplemented
46#11762705C2218yescomplemented
47#11762704C2218yescomplemented
48#11762704C2218yescomplemented
49#11762695C2218yescomplemented
50#11762694C2218yescomplemented
51#11762678C2218yescomplemented
52#11762667C2218yes—
53C22⋊C4×Dic17C2218yes—
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×#399C2218yes—
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×Dic17Q818yes—
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C23×Dic17C2311yescharacteristic
85C23×Dic17C2314yes—
86C23×Dic17C2311yescharacteristic
87C23×Dic17C2311yescharacteristic
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—42no—
103C2×C22⋊Dic17C2314yes—
104C2×C22⋊Dic17C2314yes—
105C2×C22⋊Dic17C2314yes—
106C2×C4⋊Dic17—24no—
107C2×C4⋊Dic17—24no—
108C2×C4⋊Dic17—24no—
109C2×C4⋊Dic17C2314yes—
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—42no—
119C2×#63225—42no—
120C2×#63225—42no—
121C2×#63225D418yes—
122C2×#63225C2314yes—
123C2×#63225C2314yes—
124C2×#63225C2314yes—
125C2×#63225C2314yes—
126C2×#63225C2314yes—
127C2×#63225C2314yes—
128C2×#63225C2314yes—
129C2×#63225C2314yes—
130C2×#63225C2314yes—
131C2×#63225C2314yes—
132C2×C4×Dic17—24no—
133C2×C4×Dic17—24no—
134C2×C4×Dic17—24no—
135C2×C4×Dic17—24no—
136C2×C4×Dic17C2314yes—
137C2×C4×Dic17C2314yes—
138C2×C4×Dic17C2314yes—
139C2×C4×Dic17C2314yes—
140#10587575—232no—
141#10587563—232no—
142C17×#95C2314yes—
143#10587502C2314yes—
144#10587502C2314yes—
145#10587502C2314yes—
146#10587502C2314yes—
147#10587502C2314yes—
148#10587502C2314yes—
149#10587502C2314yes—
150C24×C17—22no—
151C24×C17—22no—
152C24×C17—22no—
153C24×C17—22no—
154C24×C17—22no—
155C24×C17—22no—
156C24×C17C2×Q814yes—
157C24×C17C2412yes—
158C24×C17C2411yescharacteristic
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×C17—22no—
175C22×C4×C17C2×D414yes—
176C22×C4×C17#4114yes—
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—232no—
190C22×Dic17—28no—
191C22×Dic17—28no—
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×Dic17—22no—
203C22×Dic17—22no—
204C22×Dic17C2×D414yes—
205C22×Dic17C2×D414yes—
206C22×Dic17C2×Q814yes—
207C22×Dic17C2×Q8116yes—
208C22×Dic17C2×Q814yes—
209C22×Dic17#4114yes—
210C22×Dic17#4114yes—
211C22×Dic17C2412yes—
212C22×Dic17C2412yes—
213C22×Dic17C2412yes—
214C22×Dic17C2412yes—
215C22×Dic17C2412yes—
216C22×Dic17C2412yes—
217C22×Dic17C2412yes—
218C22×Dic17C2412yes—
219C4⋊C4×C17—28no—
220C4⋊C4×C17—28no—
221C4⋊C4×C17—44no—
222C22⋊C4×C17—28no—
223C22⋊C4×C17—28no—
224C22⋊C4×C17—44no—
225C22⋊Dic17—28no—
226C22⋊Dic17—28no—
227C22⋊Dic17—44no—
228C4⋊Dic17—28no—
229C4⋊Dic17—28no—
230C4⋊Dic17—28no—
231#63225—28no—
232#63225—28no—
233#63225—28no—
234#63225—28no—
235#63225—28no—
236#63225—28no—
237#63225—44no—
238#63225—44no—
239#63225—44no—
240#63225C2×D4116yes—
241C4×Dic17—28no—
242C4×Dic17—28no—
243C4×Dic17—28no—
244C4×Dic17—28no—
245C2×#2441—171nomaximal, Sylow
246C23×C17—28no—
247C23×C17—28no—
248C23×C17—28no—
249C23×C17—22no—
250C23×C17—22no—
251C23×C17—22no—
252C23×C17—22no—
253C23×C17—22no—
254C23×C17—22no—
255C23×C17—44no—
256C23×C17—44no—
257C23×C17—44no—
258C23×C17—44no—
259C23×C17C22×D412yes—
260C23×C17C22×Q814yes—
261C23×C17C22×Q812yes—
262C23×C17C2×#4112yes—
263C23×C17C2×#4112yes—
264C23×C17C2×#4112yes—
265C23×C17H(5,𝔽2)12yes—
266C23×C172−1+412yes—
267C23×C17C2511yescharacteristic
268C2×C4×C17—28no—
269C2×C4×C17—28no—
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—22no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17—44no—
287C2×C4×C17—44no—
288C2×C4×C17—44no—
289C2×C4×C17—44no—
290C2×C4×C17C22×D414yes—
291C2×C4×C17C2×#4114yes—
292C2×Dic17—28no—
293C2×Dic17—28no—
294C2×Dic17—28no—
295C2×Dic17—22no—
296C2×Dic17—22no—
297C2×Dic17—22no—
298C2×Dic17—22no—
299C2×Dic17—22no—
300C2×Dic17—22no—
301C2×Dic17—232no—
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—22no—
312C2×Dic17—22no—
313C2×Dic17—22no—
314C2×Dic17—44no—
315C2×Dic17—44no—
316C2×Dic17—44no—
317C2×Dic17—44no—
318C2×Dic17C22⋊Q8116yes—
319C2×Dic17C22×D414yes—
320C2×Dic17C22×D414yes—
321C2×Dic17C22×Q814yes—
322C2×Dic17C22×Q814yes—
323C2×Dic17C2×#4114yes—
324C2×Dic17C2×#4114yes—
325C22×#125—171no—
326C22×#117—171no—
327#2441—1716no—
328C2×#399—171no—
329C2×#399D1711yescharacteristic
330C2×#396—171no—
331C2×#396—171no—
332C2×#389—171no—
333C2×#389—171no—
334C2×#389—171no—
335C2×#389—171no—
336C2×#387—171no—
337C2×#387—171no—
338C2×#384—171no—
339C2×#380—171no—
340C2×C4×C22⋊C4—171no—
341C22×C17—24no—
342C22×C17—24no—
343C22×C17—24no—
344C22×C17—42no—
345C22×C17—416no—
346C22×C17—42no—
347C22×C17—42no—
348C22×C17—42no—
349C22×C17C2×C22⋊Q814yes—
350C22×C17#53314yes—
351C22×C17#54414yes—
352C22×C17#54714yes—
353C22×C17#55014yes—
354C22×C17#55214yes—
355C22×C17#55314yes—
356C22×C17C23×D411yescharacteristic
357C22×C17C23×Q811yescharacteristic
358C22×C17C22×#4111yescharacteristic
359C22×C17C22×#4111yescharacteristic
360C22×C17C22×#4111yescharacteristic
361C22×C17C2×H(5,𝔽2)11yescharacteristic
362C22×C17C2×2−1+411yescharacteristic
363C4×C17—24no—
364C4×C17—24no—
365C4×C17—42no—
366C4×C17—42no—
367C4×C17—42no—
368C4×C17—42no—
369Dic17—24no—
370Dic17—24no—
371Dic17—24no—
372Dic17—42no—
373Dic17—42no—
374Dic17—42no—
375Dic17—42no—
376Dic17C2×C22⋊Q818yes—
377C24×C4—171no—
378C2×#125—178no—
379C2×#125—348no—
380C2×#117—178no—
381C2×#117—348no—
382C22×C4⋊C4—171no—
383C22×C4⋊C4—171no—
384C22×C4⋊C4—171no—
385C22×C4⋊C4—171no—
386C22×C4⋊C4—171no—
387C22×C4⋊C4—171no—
388C22×C4⋊C4—171no—
389C22×C4⋊C4—171no—
390C22×C4⋊C4—171no—
391C22×C4⋊C4—171no—
392C22×C4⋊C4—171no—
393C22×C4⋊C4—171no—
394C22×C4⋊C4—171no—
395C22×C4⋊C4C2×D1711yescharacteristic
396C22×C4⋊C4C2×D1711yescharacteristic
397C22×C4⋊C4C2×D1711yescharacteristic
398C22×C22⋊C4—171no—
399C22×C22⋊C4—171no—
400C22×C22⋊C4—171no—
401C22×C22⋊C4C2×D1711yescharacteristic
402C22×C22⋊C4C2×D1711yescharacteristic
403C22×C22⋊C4C2×D1711yescharacteristic
404C22×C42—171no—
405C22×C42—171no—
406C22×C42—171no—
407C22×C42—171no—
408#399—178no—
409#399C2×D1718yes—
410#396—178no—
411#396—178no—
412#389—178no—
413#389—178no—
414#389—178no—
415#389—178no—
416#387—178no—
417#387—178no—
418#384—178no—
419#380—178no—
420C4×C22⋊C4—178no—
421C2×#95—171no—
422C2×#95—171no—
423C2×#95—171no—
424C2×#95—171no—
425C2×#95—171no—
426C2×#95—171no—
427C2×#95—171no—
428C2×#95C2×D1711yescharacteristic
429C2×C17—44no—
430C2×C17#244118yescomplemented
431C2×C17C22×C22⋊Q811yescharacteristic
432C2×C17C2×#53311yescharacteristic
433C2×C17C2×#54411yescharacteristic
434C2×C17C2×#54711yescharacteristic
435C2×C17C2×#55011yescharacteristic
436C2×C17C2×#55211yescharacteristic
437C2×C17C2×#55311yescharacteristic
438C25C22×D1711yescharacteristic
439C23×C4—171no—
440C23×C4—178no—
441C23×C4—174no—
442C23×C4—171no—
443C23×C4—171no—
444C23×C4—171no—
445C23×C4—171no—
446C23×C4—171no—
447C23×C4—171no—
448C23×C4—171no—
449C23×C4—344no—
450C23×C4—344no—
451C23×C4C22×D1711yescharacteristic
452C23×C4C22×D1711yescharacteristic
453C23×C4C22×D1711yescharacteristic
454C23×C4C22×D1711yescharacteristic
455C23×C4C22×D1711yescharacteristic
456C23×C4C22×D1711yescharacteristic
457#125—3432no—
458#117—3432no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—178no—
463C2×C4⋊C4—174no—
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—174no—
473C2×C4⋊C4—174no—
474C2×C4⋊C4—174no—
475C2×C4⋊C4—174no—
476C2×C4⋊C4—344no—
477C2×C4⋊C4—344no—
478C2×C4⋊C4—344no—
479C2×C4⋊C4—344no—
480C2×C4⋊C4—344no—
481C2×C4⋊C4—344no—
482C2×C4⋊C4—344no—
483C2×C4⋊C4—344no—
484C2×C4⋊C4—344no—
485C2×C4⋊C4—682no—
486C2×C4⋊C4—682no—
487C2×C4⋊C4—682no—
488C2×C4⋊C4C22×D1714yes—
489C2×C4⋊C4C22×D1714yes—
490C2×C4⋊C4C22×D1714yes—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—174no—
495C2×C22⋊C4—174no—
496C2×C22⋊C4—174no—
497C2×C22⋊C4—344no—
498C2×C22⋊C4—344no—
499C2×C22⋊C4—682no—
500C2×C22⋊C4C22×D1714yes—
501C2×C22⋊C4C22×D1714yes—
502C2×C22⋊C4C22×D1714yes—
503C2×C42—174no—
504C2×C42—174no—
505C2×C42—174no—
506C2×C42—174no—
507C2×C42—344no—
508C2×C42—344no—
509C2×C42—344no—
510C2×C42—344no—
511#95—174no—
512#95—174no—
513#95—174no—
514#95—174no—
515#95—174no—
516#95—174no—
517#95—174no—
518#95C22×D1714yes—
519C17C2×#244111yescharacteristic, complemented, Sylow
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24Q8×D1714yes—
527C24C23×D1712yes—
528C24C23×D1711yescharacteristic
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—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—174no—
546C22×C4—174no—
547C22×C4—174no—
548C22×C4—172no—
549C22×C4—174no—
550C22×C4—1716no—
551C22×C4—174no—
552C22×C4—174no—
553C22×C4—172no—
554C22×C4—172no—
555C22×C4—172no—
556C22×C4—172no—
557C22×C4—172no—
558C22×C4—172no—
559C22×C4—172no—
560C22×C4—348no—
561C22×C4—3432no—
562C22×C4—348no—
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×C4—342no—
578C22×C4—342no—
579C22×C4—342no—
580C22×C4—342no—
581C22×C4D4×D1714yes—
582C22×C4#6325414yes—
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—44no—
592C4⋊C4—1716no—
593C4⋊C4—348no—
594C4⋊C4—348no—
595C4⋊C4—348no—
596C4⋊C4—348no—
597C4⋊C4—348no—
598C4⋊C4—348no—
599C4⋊C4—348no—
600C4⋊C4—348no—
601C4⋊C4—348no—
602C4⋊C4—684no—
603C4⋊C4—684no—
604C4⋊C4—684no—
605C22⋊C4—28no—
606C22⋊C4—28no—
607C22⋊C4—44no—
608C22⋊C4—348no—
609C22⋊C4—348no—
610C22⋊C4—684no—
611C42—348no—
612C42—348no—
613C42—348no—
614C42—348no—
615C23—28no—
616C23—28no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—28no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23C2×D4×D1712yes—
629C23C2×#6325412yes—
630C23#1058769112yes—
631C23C2×Q8×D1714yes—
632C23C2×Q8×D1712yes—
633C23#41×D1712yes—
634C23#41×D1712yes—
635C23#1058769712yes—
636C23C24×D1711yescharacteristic
637C2×C4—28no—
638C2×C4—28no—
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—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—44no—
656C2×C4—44no—
657C2×C4—44no—
658C2×C4—44no—
659C2×C4—1716no—
660C2×C4—174no—
661C2×C4—174no—
662C2×C4—174no—
663C2×C4—174no—
664C2×C4—174no—
665C2×C4—174no—
666C2×C4—3432no—
667C2×C4—348no—
668C2×C4—348no—
669C2×C4—348no—
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—342no—
679C2×C4—342no—
680C2×C4—342no—
681C2×C4—342no—
682C2×C4—342no—
683C2×C4—342no—
684C2×C4—342no—
685C2×C4—342no—
686C2×C4—342no—
687C2×C4—342no—
688C2×C4—684no—
689C2×C4—684no—
690C2×C4—684no—
691C2×C4—684no—
692C2×C4C2×D4×D1714yes—
693C2×C4C2×#6325414yes—
694C22—24no—
695C22—24no—
696C22—24no—
697C22—416no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22C22⋊Q8×D1714yes—
703C22#1176336114yes—
704C22#1176343814yes—
705C22#1176345714yes—
706C22#1176347914yes—
707C22#1176349614yes—
708C22#1176350414yes—
709C22C22×D4×D1711yescharacteristic
710C22C22×Q8×D1711yescharacteristic
711C22C2×#41×D1711yescharacteristic
712C22C2×#41×D1711yescharacteristic
713C22C22×#6325411yescharacteristic
714C22C2×#1058769111yescharacteristic
715C22C2×#1058769711yescharacteristic
716C4—24no—
717C4—24no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—178no—
723C4—344no—
724C4—344no—
725C4—344no—
726C4—682no—
727C4—682no—
728C4—682no—
729C4—682no—
730C2—44no—
731C2#1453249018yesdirect product factor
732C2C2×C22⋊Q8×D1711yescharacteristic
733C2C2×#1176336111yescharacteristic
734C2C2×#1176343811yescharacteristic
735C2C2×#1176345711yescharacteristic
736C2C2×#1176347911yescharacteristic
737C2C2×#1176349611yescharacteristic
738C2C2×#1176350411yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#399C2
socleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×#399D17
hypocenterC17C2×#2441
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#10587575C2semidirect
3. #14532490C2direct (N × H)
7. C2×#11762706C2semidirect
8. C2×#11762705C2semidirect
9. C2×#11762704C2semidirect
10. C2×#11762704C2semidirect
11. C2×#11762695C2semidirect
12. C2×#11762694C2semidirect
13. C2×#11762678C2semidirect
19. C2×#10587575C22semidirect
45. #11762706C22semidirect
46. #11762705C22semidirect
47. #11762704C22semidirect
48. #11762704C22semidirect
49. #11762695C22semidirect
50. #11762694C22semidirect
51. #11762678C22semidirect
430. C2×C17#2441semidirect
519. C17C2×#2441semidirect
731. C2#14532490direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875752
C22×#105875632
#145324902
C2×#117627452
C2×#117627322
C2×#117627062
C2×#117627052
C2×#117627042
C2×#117626952
C2×#117626942
C2×#117626782
C2×#117626672
C2×C22⋊C4×Dic172
C2×C17×#3992
C2×#244117