Finite Group Databasebeta

← C2×#14532919 #17201914

Subgroups — C2×#14532919 #17201914

Order 4352.

2942 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587575C211yesmaximal, characteristic, complemented
2#14532919C2116yesmaximal, direct product factor
3C2×#11762747C211yesmaximal, characteristic, complemented
4C2×#11762742C211yesmaximal, characteristic, complemented
5C2×#11762740C211yesmaximal, characteristic, complemented
6C2×#11762739C211yesmaximal, characteristic, complemented
7C2×#11762704C211yesmaximal, characteristic, complemented
8C2×#11762695C211yesmaximal, characteristic, complemented
9C2×#11762690C211yesmaximal, characteristic, complemented
10C2×#11762682C211yesmaximal, characteristic
11C2×#11762682C211yesmaximal, characteristic
12C2×#11762682C211yesmaximal, characteristic
13C2×#11762682C211yesmaximal, characteristic
14C2×#11762669C211yesmaximal, characteristic
15C2×C4×C22⋊Dic17C211yesmaximal, characteristic
16C23×C4⋊C4×C17C211yesmaximal, characteristic
17C2×#10587575—28no—
18C2×#10587575C2218yescomplemented
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#11762747C2218yescomplemented
36#11762742C2218yescomplemented
37#11762740C2218yescomplemented
38#11762739C2218yescomplemented
39#11762704C2218yescomplemented
40#11762695C2218yescomplemented
41#11762690C2218yescomplemented
42#11762682C2218yes—
43#11762682C2218yes—
44#11762682C2218yes—
45#11762682C2218yes—
46#11762669C2218yes—
47C4×C22⋊Dic17C2218yes—
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
53C2×#10587502C2211yescharacteristic
54C2×#10587502C2211yescharacteristic
55C2×#10587502C2211yescharacteristic
56C2×#10587502C2211yescharacteristic
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59C2×#10587502C2211yescharacteristic
60C24×C4×C17C2211yescharacteristic
61C24×C4×C17C2211yescharacteristic
62C24×C4×C17C2211yescharacteristic
63C22×C4⋊C4×C17—28no—
64C22×C4⋊C4×C17C2218yes—
65C22×C4⋊C4×C17C2211yescharacteristic
66C22×C4⋊C4×C17C2211yescharacteristic
67C22×C4⋊C4×C17C2211yescharacteristic
68C22×C4⋊C4×C17C2211yescharacteristic
69C25×C17C2311yescharacteristic
70C23×C4×C17—24no—
71C23×C4×C17—24no—
72C23×C4×C17—24no—
73C23×C4×C17—24no—
74C23×C4×C17—24no—
75C23×C4×C17—24no—
76C23×C4×C17—24no—
77C23×C4×C17—42no—
78C23×C4×C17—42no—
79C23×C4×C17C2311yescharacteristic
80C23×C4×C17C2311yescharacteristic
81C23×C4×C17C2314yes—
82C23×C4×C17C2314yes—
83C23×C4×C17C2314yes—
84C23×C4×C17C2311yescharacteristic
85C23×C4×C17C2311yescharacteristic
86C23×C4×C17C2311yescharacteristic
87C23×C4×C17C2311yescharacteristic
88C23×Dic17C2311yescharacteristic
89C23×Dic17C2311yescharacteristic
90C23×Dic17C2311yescharacteristic
91C23×Dic17C2311yescharacteristic
92C23×Dic17C2311yescharacteristic
93C23×Dic17C2311yescharacteristic
94C23×Dic17C2311yescharacteristic
95C23×Dic17C2311yescharacteristic
96C2×C4⋊C4×C17—24no—
97C2×C4⋊C4×C17—24no—
98C2×C4⋊C4×C17—24no—
99C2×C4⋊C4×C17—232no—
100C2×C4⋊C4×C17D418yes—
101C2×C4⋊C4×C17C2314yes—
102C2×C4⋊C4×C17C2314yes—
103C2×C4⋊C4×C17C2314yes—
104C2×C4⋊C4×C17C2314yes—
105C2×C22⋊Dic17—24no—
106C2×C22⋊Dic17—24no—
107C2×C22⋊Dic17—24no—
108C2×C22⋊Dic17Q818yes—
109C2×C22⋊Dic17C2314yes—
110C2×C22⋊Dic17C2314yes—
111C2×C22⋊Dic17C2314yes—
112C2×C22⋊Dic17C2314yes—
113C2×C4⋊Dic17—24no—
114C2×C4⋊Dic17—42no—
115C2×C4⋊Dic17C2314yes—
116C2×C4⋊Dic17C2314yes—
117C2×#63225—24no—
118C2×#63225—24no—
119C2×#63225—24no—
120C2×#63225—24no—
121C2×#63225—24no—
122C2×#63225—24no—
123C2×#63225—42no—
124C2×#63225—42no—
125C2×#63225C2314yes—
126C2×#63225C2314yes—
127C2×#63225C2314yes—
128C2×#63225C2314yes—
129C2×#63225C2314yes—
130C2×#63225C2314yes—
131C2×#63225C2314yes—
132C2×#63225C2314yes—
133C2×C4×Dic17—24no—
134C2×C4×Dic17—42no—
135C2×C4×Dic17C2314yes—
136C2×C4×Dic17C2314yes—
137#10587575—232no—
138#10587502C2314yes—
139#10587502C2314yes—
140#10587502C2314yes—
141#10587502C2314yes—
142#10587502C2314yes—
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×C17C2×Q814yes—
155C24×C17#4114yes—
156C24×C17#4114yes—
157C24×C17C2412yes—
158C24×C17C2411yescharacteristic
159C22×C4×C17—232no—
160C22×C4×C17—22no—
161C22×C4×C17—28no—
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—28no—
170C22×C4×C17—28no—
171C22×C4×C17—22no—
172C22×C4×C17—22no—
173C22×C4×C17—28no—
174C22×C4×C17—28no—
175C22×C4×C17—22no—
176C22×C4×C17—22no—
177C22×C4×C17—22no—
178C22×C4×C17—22no—
179C22×C4×C17—28no—
180C22×C4×C17—28no—
181C22×C4×C17—44no—
182C22×C4×C17—44no—
183C22×C4×C17—416no—
184C22×C4×C17—416no—
185C22×C4×C17C2×D414yes—
186C22×C4×C17C2×D414yes—
187C22×C4×C17C2×D414yes—
188C22×C4×C17#4114yes—
189C22×C4×C17C2412yes—
190C22×C4×C17C2412yes—
191C22×C4×C17C2412yes—
192C22×C4×C17C2412yes—
193C22×C4×C17C2412yes—
194C22×C4×C17C2412yes—
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×Dic17—22no—
205C22×Dic17—22no—
206C22×Dic17—22no—
207C22×Dic17—22no—
208C22×Dic17—22no—
209C22×Dic17—22no—
210C22×Dic17—22no—
211C22×Dic17—22no—
212C22×Dic17—22no—
213C22×Dic17—22no—
214C22×Dic17—22no—
215C22×Dic17—22no—
216C22×Dic17—22no—
217C22×Dic17C2×Q814yes—
218C22×Dic17C2×Q814yes—
219C22×Dic17C2412yes—
220C22×Dic17C2412yes—
221C22×Dic17C2412yes—
222C22×Dic17C2412yes—
223C22×Dic17C2412yes—
224C22×Dic17C2412yes—
225C22×Dic17C2412yes—
226C22×Dic17C2412yes—
227C4⋊C4×C17—28no—
228C4⋊C4×C17—28no—
229C4⋊C4×C17—28no—
230C4⋊C4×C17C2×D4116yes—
231C22⋊Dic17—28no—
232C22⋊Dic17—28no—
233C22⋊Dic17—28no—
234C22⋊Dic17C2×Q8116yes—
235C4⋊Dic17—28no—
236C4⋊Dic17—44no—
237#63225—28no—
238#63225—28no—
239#63225—28no—
240#63225—28no—
241#63225—28no—
242#63225—28no—
243#63225—44no—
244#63225—44no—
245C4×Dic17—28no—
246C4×Dic17—44no—
247C2×#2473—171nomaximal, Sylow
248C23×C17—28no—
249C23×C17—28no—
250C23×C17—28no—
251C23×C17—28no—
252C23×C17—28no—
253C23×C17—28no—
254C23×C17—22no—
255C23×C17—22no—
256C23×C17—22no—
257C23×C17—22no—
258C23×C17#125116yescomplemented
259C23×C17C22×D412yes—
260C23×C17C22×Q814yes—
261C23×C17C22×Q812yes—
262C23×C17C2×#4114yes—
263C23×C17C2×#4112yes—
264C23×C17C2×#4112yes—
265C23×C17C2×#4114yes—
266C23×C17C2×#4112yes—
267C23×C17H(5,𝔽2)12yes—
268C23×C172−1+412yes—
269C23×C17C2511yescharacteristic
270C2×C4×C17—232no—
271C2×C4×C17—28no—
272C2×C4×C17—28no—
273C2×C4×C17—28no—
274C2×C4×C17—28no—
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—22no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—416no—
290C2×C4×C17—416no—
291C2×C4×C17—44no—
292C2×C4×C17—44no—
293C2×C4×C17C22×D414yes—
294C2×C4×C17C22×D414yes—
295C2×C4×C17C22×D414yes—
296C2×C4×C17C2×#4114yes—
297C2×Dic17—28no—
298C2×Dic17—28no—
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—22no—
312C2×Dic17—22no—
313C2×Dic17—22no—
314C2×Dic17—22no—
315C2×Dic17—22no—
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—22no—
320C2×Dic17—22no—
321C2×Dic17—44no—
322C2×Dic17—44no—
323C2×Dic17—44no—
324C2×Dic17—44no—
325C2×Dic17—44no—
326C2×Dic17—44no—
327C2×Dic17C22×Q814yes—
328C2×Dic17C22×Q814yes—
329C22×#125—171no—
330C23×C4⋊C4D1711yescharacteristic
331#2473—1716no—
332C2×#400—171no—
333C2×#398—171no—
334C2×#398—171no—
335C2×#398—171no—
336C2×#389—171no—
337C2×#387—171no—
338C2×#387—171no—
339C2×#385—171no—
340C2×#385—171no—
341C2×#385—171no—
342C2×#385—171no—
343C2×#380—171no—
344C2×C4×C22⋊C4—171no—
345C22×C17—24no—
346C22×C17—24no—
347C22×C17—24no—
348C22×C17—24no—
349C22×C17—24no—
350C22×C17—24no—
351C22×C17—232no—
352C22×C17#52514yes—
353C22×C17C2×#12514yes—
354C22×C17C2×#12518yescomplemented
355C22×C17#53914yes—
356C22×C17#54614yes—
357C22×C17D4×Q814yes—
358C22×C17#55214yes—
359C22×C17#55414yes—
360C22×C17C23×D411yescharacteristic
361C22×C17C23×Q811yescharacteristic
362C22×C17C22×#4111yescharacteristic
363C22×C17C22×#4111yescharacteristic
364C22×C17C22×#4111yescharacteristic
365C22×C17C2×H(5,𝔽2)11yescharacteristic
366C22×C17C2×2−1+411yescharacteristic
367C4×C17—24no—
368C4×C17—24no—
369C4×C17—24no—
370C4×C17—24no—
371C4×C17—42no—
372C4×C17—42no—
373Dic17—24no—
374Dic17—24no—
375Dic17—42no—
376Dic17—42no—
377Dic17—42no—
378Dic17—42no—
379Dic17—42no—
380Dic17—42no—
381C24×C4C2×D1711yescharacteristic
382C24×C4C2×D1711yescharacteristic
383C24×C4C2×D1711yescharacteristic
384C2×#125—178no—
385C2×#125—348no—
386C22×C4⋊C4—28no—
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⋊C4—171no—
396C22×C4⋊C4—171no—
397C22×C4⋊C4C2×D1711yescharacteristic
398C22×C4⋊C4C2×D1711yescharacteristic
399C22×C4⋊C4C2×D1718yes—
400C22×C4⋊C4C2×D1711yescharacteristic
401C22×C4⋊C4C2×D1711yescharacteristic
402C22×C22⋊C4—171no—
403C22×C22⋊C4—171no—
404C22×C22⋊C4—171no—
405C22×C22⋊C4—171no—
406C22×C42—171no—
407C22×C42—171no—
408#400—178no—
409#398—178no—
410#398—178no—
411#398—178no—
412#389—178no—
413#387—178no—
414#387—178no—
415#385—178no—
416#385—178no—
417#385—178no—
418#385—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×#95—171no—
429C2×#95—171no—
430C2×#95—171no—
431C2×#95—171no—
432C2×#95—171no—
433C2×C17—28no—
434C2×C17#247318yescomplemented
435C2×C17C2×#52511yescharacteristic
436C2×C17C22×#12511yescharacteristic
437C2×C17C2×#53911yescharacteristic
438C2×C17C2×#54611yescharacteristic
439C2×C17C2×D4×Q811yescharacteristic
440C2×C17C2×#55211yescharacteristic
441C2×C17C2×#55411yescharacteristic
442C25C22×D1711yescharacteristic
443C23×C4—24no—
444C23×C4—24no—
445C23×C4—24no—
446C23×C4—24no—
447C23×C4—24no—
448C23×C4—24no—
449C23×C4—24no—
450C23×C4—42no—
451C23×C4—42no—
452C23×C4—171no—
453C23×C4—171no—
454C23×C4—171no—
455C23×C4—171no—
456C23×C4—171no—
457C23×C4—171no—
458C23×C4—171no—
459C23×C4—171no—
460C23×C4C22×D1714yes—
461C23×C4C22×D1711yescharacteristic
462C23×C4C22×D1711yescharacteristic
463C23×C4C22×D1714yes—
464C23×C4C22×D1714yes—
465C23×C4C22×D1711yescharacteristic
466C23×C4C22×D1711yescharacteristic
467C23×C4C22×D1711yescharacteristic
468C23×C4C22×D1711yescharacteristic
469#125—3432no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—232no—
474C2×C4⋊C4—174no—
475C2×C4⋊C4—174no—
476C2×C4⋊C4—174no—
477C2×C4⋊C4—174no—
478C2×C4⋊C4—174no—
479C2×C4⋊C4—174no—
480C2×C4⋊C4—174no—
481C2×C4⋊C4—174no—
482C2×C4⋊C4—174no—
483C2×C4⋊C4—174no—
484C2×C4⋊C4—344no—
485C2×C4⋊C4—344no—
486C2×C4⋊C4—344no—
487C2×C4⋊C4—344no—
488C2×C4⋊C4—344no—
489C2×C4⋊C4—344no—
490C2×C4⋊C4—344no—
491C2×C4⋊C4—682no—
492C2×C4⋊C4—682no—
493C2×C4⋊C4—682no—
494C2×C4⋊C4C22⋊D1718yes—
495C2×C4⋊C4C22×D1714yes—
496C2×C4⋊C4C22×D1714yes—
497C2×C4⋊C4C22×D1714yes—
498C2×C4⋊C4C22×D1714yes—
499C2×C22⋊C4—178no—
500C2×C22⋊C4—174no—
501C2×C22⋊C4—174no—
502C2×C22⋊C4—174no—
503C2×C22⋊C4—174no—
504C2×C22⋊C4—344no—
505C2×C22⋊C4—344no—
506C2×C22⋊C4—344no—
507C2×C42—174no—
508C2×C42—174no—
509C2×C42—344no—
510C2×C42—682no—
511#95—174no—
512#95—174no—
513#95—174no—
514#95—174no—
515#95—174no—
516#95—174no—
517#95—174no—
518#95—174no—
519#95—174no—
520#95—174no—
521#95—174no—
522#95—174no—
523C17C2×#247311yescharacteristic, complemented, Sylow
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24#6325214yes—
529C24#6325414yes—
530C24Q8×D1714yes—
531C24C23×D1712yes—
532C24C23×D1711yescharacteristic
533C22×C4—232no—
534C22×C4—28no—
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—28no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—416no—
558C22×C4—416no—
559C22×C4—174no—
560C22×C4—174no—
561C22×C4—172no—
562C22×C4—172no—
563C22×C4—172no—
564C22×C4—172no—
565C22×C4—172no—
566C22×C4—172no—
567C22×C4—172no—
568C22×C4—172no—
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×C4—342no—
582C22×C4—342no—
583C22×C4—342no—
584C22×C4—342no—
585C22×C4—342no—
586C22×C4—342no—
587C22×C4—342no—
588C22×C4—342no—
589C22×C4—342no—
590C22×C4—342no—
591C22×C4#6325214yes—
592C22×C4C2×C22⋊D1714yes—
593C22×C4C2×C22⋊D1714yes—
594C22×C4C2×C22⋊D1714yes—
595C22×C4C23×D1712yes—
596C22×C4C23×D1712yes—
597C22×C4C23×D1712yes—
598C22×C4C23×D1712yes—
599C22×C4C23×D1712yes—
600C22×C4C23×D1712yes—
601C4⋊C4—28no—
602C4⋊C4—28no—
603C4⋊C4—28no—
604C4⋊C4—348no—
605C4⋊C4—348no—
606C4⋊C4—348no—
607C4⋊C4—348no—
608C4⋊C4—348no—
609C4⋊C4—348no—
610C4⋊C4—348no—
611C4⋊C4—684no—
612C4⋊C4—684no—
613C4⋊C4—684no—
614C4⋊C4C2×C22⋊D17116yes—
615C22⋊C4—1716no—
616C22⋊C4—348no—
617C22⋊C4—348no—
618C22⋊C4—348no—
619C42—348no—
620C42—684no—
621C23—28no—
622C23—28no—
623C23—28no—
624C23—28no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—28no—
630C23—28no—
631C23#10587575116yescomplemented
632C23C2×#6325214yes—
633C23C2×#6325212yes—
634C23C2×#6325212yes—
635C23C2×#6325414yes—
636C23C2×#6325412yes—
637C23#1058769112yes—
638C23C2×Q8×D1714yes—
639C23C2×Q8×D1712yes—
640C23#1058769412yes—
641C23C22×C22⋊D1712yes—
642C23C24×D1711yescharacteristic
643C2×C4—232no—
644C2×C4—28no—
645C2×C4—28no—
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—28no—
655C2×C4—28no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—416no—
663C2×C4—416no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—174no—
667C2×C4—174no—
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—342no—
689C2×C4—342no—
690C2×C4—342no—
691C2×C4—342no—
692C2×C4—684no—
693C2×C4—684no—
694C2×C4—684no—
695C2×C4—684no—
696C2×C4—684no—
697C2×C4—684no—
698C2×C4C2×#6325214yes—
699C2×C4C22×C22⋊D1714yes—
700C2×C4C22×C22⋊D1714yes—
701C2×C4C22×C22⋊D1714yes—
702C22—232no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—24no—
709C22#1176332014yes—
710C22C2×#1058757514yes—
711C22C2×#1058757518yescomplemented
712C22#1176340614yes—
713C22#1176345314yes—
714C22Q8×C22⋊D1714yes—
715C22#1176349414yes—
716C22#1176351414yes—
717C22C23×C22⋊D1711yescharacteristic
718C22C22×Q8×D1711yescharacteristic
719C22C22×#6325411yescharacteristic
720C22C22×#6325211yescharacteristic
721C22C22×#6325211yescharacteristic
722C22C2×#1058769111yescharacteristic
723C22C2×#1058769411yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—344no—
731C4—344no—
732C4—682no—
733C4—682no—
734C4—682no—
735C4—682no—
736C4—682no—
737C4—682no—
738C2—28no—
739C2#1453291918yesdirect product factor
740C2C2×#1176332011yescharacteristic
741C2C22×#1058757511yescharacteristic
742C2C2×#1176340611yescharacteristic
743C2C2×#1176345311yescharacteristic
744C2C2×Q8×C22⋊D1711yescharacteristic
745C2C2×#1176349411yescharacteristic
746C2C2×#1176351411yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC23×C4⋊C4×C17C2
socleC24×C17C24
prime radicalC25×C17C23
hypercenterC23×C4⋊C4D17
hypocenterC17C2×#2473
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#10587575C2semidirect
2. #14532919C2direct (N × H)
3. C2×#11762747C2semidirect
4. C2×#11762742C2semidirect
5. C2×#11762740C2semidirect
6. C2×#11762739C2semidirect
7. C2×#11762704C2semidirect
8. C2×#11762695C2semidirect
9. C2×#11762690C2semidirect
18. C2×#10587575C22semidirect
35. #11762747C22semidirect
36. #11762742C22semidirect
37. #11762740C22semidirect
38. #11762739C22semidirect
39. #11762704C22semidirect
40. #11762695C22semidirect
41. #11762690C22semidirect
258. C23×C17#125semidirect
354. C22×C17C2×#125semidirect
434. C2×C17#2473semidirect
523. C17C2×#2473semidirect
631. C23#10587575semidirect
711. C22C2×#10587575semidirect
739. C2#14532919direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875752
#145329192
C2×#117627472
C2×#117627422
C2×#117627402
C2×#117627392
C2×#117627042
C2×#117626952
C2×#117626902
C2×#117626822
C2×#117626692
C2×C4×C22⋊Dic172
C23×C4⋊C4×C172
C2×#247317