Finite Group Databasebeta

← C2×#14534616 #17201388

Subgroups — C2×#14534616 #17201388

Order 4352.

2614 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×#10587578C211yesmaximal, characteristic
3#14534616C2116yesmaximal, direct product factor
4C2×#11762743C211yesmaximal, characteristic, complemented
5C2×#11762742C211yesmaximal, characteristic, complemented
6C2×#11762741C211yesmaximal, characteristic, complemented
7C2×#11762733C211yesmaximal, characteristic
8C2×#11762731C211yesmaximal, characteristic
9C2×#11762731C211yesmaximal, characteristic
10C2×#11762731C211yesmaximal, characteristic
11C2×#11762706C211yesmaximal, characteristic, complemented
12C2×#11762704C211yesmaximal, characteristic, complemented
13C2×#11762678C211yesmaximal, characteristic, complemented
14C2×#11762668C211yesmaximal, characteristic
15C2×#11762668C211yesmaximal, characteristic
16C2×C17×#398C211yesmaximal, characteristic, complemented
17C23×C4×D17C2211yescharacteristic
18C2×#10587575—28no—
19C2×#10587575C2218yescomplemented
20C2×#10587578—28no—
21C2×#10587578C2218yes—
22C22×C4⋊Dic17C2211yescharacteristic
23C22×C4⋊Dic17C2211yescharacteristic
24C22×C4⋊Dic17C2211yescharacteristic
25C22×C4⋊Dic17C2211yescharacteristic
26C22×#63225C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C22×#63225C2211yescharacteristic
29C22×#63225C2211yescharacteristic
30C22×#63225C2211yescharacteristic
31C22×#63225C2211yescharacteristic
32C22×#63225C2211yescharacteristic
33C22×#63225C2211yescharacteristic
34C22×#63225C2211yescharacteristic
35C22×#63225C2211yescharacteristic
36C22×#63227C2211yescharacteristic
37C22×#63227C2211yescharacteristic
38C22×#63227C2211yescharacteristic
39C22×#63227C2211yescharacteristic
40C22×#63227C2211yescharacteristic
41C22×#63227C2211yescharacteristic
42C22×C4×Dic17C2211yescharacteristic
43C22×C4×Dic17C2211yescharacteristic
44#11762743C2218yescomplemented
45#11762742C2218yescomplemented
46#11762741C2218yescomplemented
47#11762733C2218yes—
48#11762731C2218yes—
49#11762731C2218yes—
50#11762731C2218yes—
51#11762706C2218yescomplemented
52#11762704C2218yescomplemented
53#11762678C2218yescomplemented
54#11762668C2218yes—
55#11762668C2218yes—
56C2×#10587502C2211yescharacteristic
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59C2×#10587502C2211yescharacteristic
60C2×#10587502C2211yescharacteristic
61C22×C4⋊C4×C17C2211yescharacteristic
62C22×C4⋊C4×C17C2211yescharacteristic
63C22×C4⋊C4×C17C2211yescharacteristic
64C22×C4⋊C4×C17C2211yescharacteristic
65C17×#398C2218yescomplemented
66C2×C17×#95C2211yescharacteristic
67C2×C17×#95C2211yescharacteristic
68C2×C17×#95C2211yescharacteristic
69C24×D17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C22×C4×D17—24no—
85C22×C4×D17—24no—
86C22×C4×D17Q818yes—
87C22×C4×D17C2314yes—
88C2×C4⋊C4×C17—24no—
89C2×C4⋊C4×C17—24no—
90C2×C4⋊C4×C17—42no—
91C2×C4⋊C4×C17—42no—
92C2×C4⋊C4×C17C2314yes—
93C2×C4⋊C4×C17C2314yes—
94C2×C4⋊C4×C17C2314yes—
95C2×C4⋊C4×C17C2314yes—
96C2×#63227—24no—
97C2×#63227—24no—
98C2×#63227—42no—
99C2×#63227—42no—
100C2×#63227—42no—
101C2×#63227—42no—
102C2×#63227C2314yes—
103C2×#63227C2314yes—
104C2×#63227C2314yes—
105C2×#63227C2314yes—
106C2×#63227C2314yes—
107C2×#63227C2314yes—
108C2×C4⋊Dic17—24no—
109C2×C4⋊Dic17—24no—
110C2×C4⋊Dic17—42no—
111C2×C4⋊Dic17—42no—
112C2×C4⋊Dic17C2314yes—
113C2×C4⋊Dic17C2314yes—
114C2×C4⋊Dic17C2314yes—
115C2×C4⋊Dic17C2314yes—
116C2×#63225—24no—
117C2×#63225—24no—
118C2×#63225—24no—
119C2×#63225—24no—
120C2×#63225—24no—
121C2×#63225—24no—
122C2×#63225—42no—
123C2×#63225—42no—
124C2×#63225—42no—
125C2×#63225—42no—
126C2×#63225C2314yes—
127C2×#63225C2314yes—
128C2×#63225C2314yes—
129C2×#63225C2314yes—
130C2×#63225C2314yes—
131C2×#63225C2314yes—
132C2×#63225C2314yes—
133C2×#63225C2314yes—
134C2×#63225C2314yes—
135C2×#63225C2314yes—
136C2×C4×Dic17—24no—
137C2×C4×Dic17D418yes—
138C2×C4×Dic17C2314yes—
139C2×C4×Dic17C2314yes—
140#10587578—232no—
141#10587575—232no—
142C17×#95C2314yes—
143C17×#95C2314yes—
144C17×#95C2314yes—
145#10587502C2314yes—
146#10587502C2314yes—
147#10587502C2314yes—
148#10587502C2314yes—
149#10587502C2314yes—
150C24×C17C2411yescharacteristic
151C23×D17—22no—
152C23×D17—22no—
153C23×D17—22no—
154C23×D17—22no—
155C23×D17—22no—
156C23×D17—22no—
157C23×D17C2×Q814yes—
158C23×D17C2412yes—
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×C17—22no—
176C22×C4×C17—22no—
177C22×C4×C17—22no—
178C22×C4×C17C2×D414yes—
179C22×C4×C17C2×Q814yes—
180C22×C4×C17C2412yes—
181C22×C4×C17C2412yes—
182C22×C4×C17C2412yes—
183C22×C4×C17C2412yes—
184C22×C4×C17C2412yes—
185C22×C4×C17C2412yes—
186C22×C4×C17C2412yes—
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×Dic17—22no—
203C22×Dic17—22no—
204C22×Dic17C2×D414yes—
205C22×Dic17C2×D414yes—
206C22×Dic17C2×Q814yes—
207C22×Dic17#4114yes—
208C22×Dic17C2412yes—
209C22×Dic17C2412yes—
210C22×Dic17C2412yes—
211C22×Dic17C2412yes—
212C22×Dic17C2412yes—
213C22×Dic17C2412yes—
214C22×Dic17C2412yes—
215C2×C4×D17—232no—
216C2×C4×D17—28no—
217C2×C4×D17—28no—
218C2×C4×D17C2×Q8116yes—
219C4⋊C4×C17—28no—
220C4⋊C4×C17—28no—
221C4⋊C4×C17—44no—
222C4⋊C4×C17—44no—
223#63227—28no—
224#63227—28no—
225#63227—44no—
226#63227—44no—
227#63227—44no—
228#63227—44no—
229C4⋊Dic17—28no—
230C4⋊Dic17—28no—
231C4⋊Dic17—44no—
232C4⋊Dic17—44no—
233#63225—28no—
234#63225—28no—
235#63225—28no—
236#63225—28no—
237#63225—28no—
238#63225—28no—
239#63225—44no—
240#63225—44no—
241#63225—44no—
242#63225—44no—
243C4×Dic17—28no—
244C4×Dic17C2×D4116yes—
245C2×#2629—171nomaximal, Sylow
246C23×C17C22×D412yes—
247C23×C17C22×Q812yes—
248C23×C17C2×#4112yes—
249C23×C17H(5,𝔽2)12yes—
250C23×C17H(5,𝔽2)12yes—
251C23×C172−1+412yes—
252C23×C172−1+412yes—
253C23×C17C2511yescharacteristic
254C22×D17—28no—
255C22×D17—28no—
256C22×D17—28no—
257C22×D17—22no—
258C22×D17—22no—
259C22×D17—22no—
260C22×D17—22no—
261C22×D17—22no—
262C22×D17—22no—
263C22×D17—44no—
264C22×D17—44no—
265C22×D17—44no—
266C22×D17—44no—
267C22×D17C22×Q814yes—
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—22no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—44no—
290C2×C4×C17—44no—
291C2×C4×C17—44no—
292C2×C4×C17—44no—
293C2×C4×C17—44no—
294C2×C4×C17C22×D414yes—
295C2×C4×C17C22×Q814yes—
296C2×Dic17—28no—
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—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×Dic17—44no—
319C2×Dic17C22⋊Q8116yes—
320C2×Dic17C22×D414yes—
321C2×Dic17C22×D414yes—
322C2×Dic17C22×Q814yes—
323C2×Dic17C2×#4114yes—
324C4×D17—232no—
325C22×#125—171no—
326C22×#117—171no—
327#2629—1716no—
328C2×#398—171no—
329C2×#398—171no—
330C2×#398—171no—
331C2×#398D1711yescharacteristic, complemented
332C2×#396—171no—
333C2×#396—171no—
334C2×#396—171no—
335C2×#396—171no—
336C2×#389—171no—
337C2×#389—171no—
338C2×#384—171no—
339C2×#380—171no—
340C2×#380—171no—
341C22×C17C2×C22⋊Q814yes—
342C22×C17#53714yes—
343C22×C17#53714yes—
344C22×C17#54014yes—
345C22×C17#54114yes—
346C22×C17#54414yes—
347C22×C17#54414yes—
348C22×C17C23×D411yescharacteristic
349C22×C17C23×Q811yescharacteristic
350C22×C17C22×#4111yescharacteristic
351C22×C17C2×H(5,𝔽2)11yescharacteristic
352C22×C17C2×H(5,𝔽2)11yescharacteristic
353C22×C17C2×2−1+411yescharacteristic
354C22×C17C2×2−1+411yescharacteristic
355C2×D17—24no—
356C2×D17—24no—
357C2×D17—24no—
358C2×D17—416no—
359C2×D17—42no—
360C2×D17—42no—
361C2×D17—42no—
362C2×D17—42no—
363C4×C17—24no—
364C4×C17—24no—
365C4×C17—42no—
366C4×C17—42no—
367C4×C17—42no—
368C4×C17—42no—
369C4×C17—42no—
370Dic17—24no—
371Dic17—42no—
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⋊C4—171no—
396C22×C4⋊C4C2×D1711yescharacteristic
397C22×C4⋊C4C2×D1711yescharacteristic
398C22×C4⋊C4C2×D1711yescharacteristic
399C22×C4⋊C4C2×D1711yescharacteristic
400C22×C22⋊C4—171no—
401C22×C22⋊C4—171no—
402C22×C22⋊C4—171no—
403C22×C22⋊C4—171no—
404C22×C22⋊C4—171no—
405C22×C22⋊C4—171no—
406C22×C42—171no—
407C22×C42—171no—
408#398—178no—
409#398—178no—
410#398—178no—
411#398C2×D1718yescomplemented
412#396—178no—
413#396—178no—
414#396—178no—
415#396—178no—
416#389—178no—
417#389—178no—
418#384—178no—
419#380—178no—
420#380—178no—
421C2×#95—171no—
422C2×#95—171no—
423C2×#95—171no—
424C2×#95—171no—
425C2×#95—171no—
426C2×#95C2×D1711yescharacteristic
427C2×#95C2×D1711yescharacteristic
428C2×#95C2×D1711yescharacteristic
429C2×C17#262918yescomplemented
430C2×C17C22×C22⋊Q811yescharacteristic
431C2×C17C2×#53711yescharacteristic
432C2×C17C2×#53711yescharacteristic
433C2×C17C2×#54011yescharacteristic
434C2×C17C2×#54111yescharacteristic
435C2×C17C2×#54411yescharacteristic
436C2×C17C2×#54411yescharacteristic
437D17—44no—
438C25—171no—
439C23×C4—171no—
440C23×C4—171no—
441C23×C4—178no—
442C23×C4—174no—
443C23×C4—171no—
444C23×C4—171no—
445C23×C4—171no—
446C23×C4—171no—
447C23×C4—171no—
448C23×C4—344no—
449C23×C4—344no—
450C23×C4C22×D1711yescharacteristic
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—42no—
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—174no—
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⋊C4—682no—
489C2×C4⋊C4—682no—
490C2×C4⋊C4—682no—
491C2×C4⋊C4C22×D1714yes—
492C2×C4⋊C4C22×D1714yes—
493C2×C4⋊C4C22×D1714yes—
494C2×C4⋊C4C22×D1714yes—
495C2×C22⋊C4—174no—
496C2×C22⋊C4—174no—
497C2×C22⋊C4—174no—
498C2×C22⋊C4—174no—
499C2×C22⋊C4—174no—
500C2×C22⋊C4—174no—
501C2×C22⋊C4—344no—
502C2×C22⋊C4—344no—
503C2×C22⋊C4—682no—
504C2×C22⋊C4—682no—
505C2×C22⋊C4—682no—
506C2×C22⋊C4—682no—
507C2×C42—178no—
508C2×C42—174no—
509C2×C42—174no—
510C2×C42—344no—
511#95—174no—
512#95—174no—
513#95—174no—
514#95—174no—
515#95—174no—
516#95C22×D1714yes—
517#95C22×D1714yes—
518#95C22×D1714yes—
519C17C2×#262911yescharacteristic, complemented, Sylow
520C24—174no—
521C24—172no—
522C24—342no—
523C24—342no—
524C24—342no—
525C24—342no—
526C24—342no—
527C24—342no—
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—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—174no—
549C22×C4—174no—
550C22×C4—174no—
551C22×C4—172no—
552C22×C4—174no—
553C22×C4—172no—
554C22×C4—1716no—
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×C4D4×D1714yes—
581C22×C4Q8×D1714yes—
582C22×C4C23×D1712yes—
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—44no—
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—684no—
602C4⋊C4—684no—
603C4⋊C4—684no—
604C4⋊C4—684no—
605C4⋊C4—684no—
606C4⋊C4—684no—
607C22⋊C4—348no—
608C22⋊C4—348no—
609C22⋊C4—684no—
610C22⋊C4—684no—
611C22⋊C4—684no—
612C22⋊C4—684no—
613C42—1716no—
614C42—348no—
615C23—174no—
616C23—348no—
617C23—342no—
618C23—342no—
619C23—342no—
620C23—342no—
621C23—342no—
622C23—342no—
623C23—348no—
624C23—348no—
625C23—684no—
626C23—684no—
627C23—684no—
628C23—684no—
629C23C2×D4×D1712yes—
630C23#1058769112yes—
631C23C2×Q8×D1712yes—
632C23#1058769412yes—
633C23#41×D1712yes—
634C23#1058769612yes—
635C23#1058769712yes—
636C23C24×D1711yescharacteristic
637C2×C4—28no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—28no—
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—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4—1716no—
664C2×C4—174no—
665C2×C4—174no—
666C2×C4—174no—
667C2×C4—174no—
668C2×C4—3432no—
669C2×C4—342no—
670C2×C4—342no—
671C2×C4—348no—
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—684no—
688C2×C4—684no—
689C2×C4—684no—
690C2×C4—684no—
691C2×C4—684no—
692C2×C4C2×D4×D1714yes—
693C2×C4C2×Q8×D1714yes—
694C22—344no—
695C22—344no—
696C22—344no—
697C22—682no—
698C22—682no—
699C22—682no—
700C22—682no—
701C22—6816no—
702C22C22⋊Q8×D1714yes—
703C22#1176338614yes—
704C22#1176338914yes—
705C22#1176341114yes—
706C22#1176341814yes—
707C22#1176343614yes—
708C22#1176343914yes—
709C22C22×D4×D1711yescharacteristic
710C22C22×Q8×D1711yescharacteristic
711C22C2×#41×D1711yescharacteristic
712C22C2×#1058769111yescharacteristic
713C22C2×#1058769611yescharacteristic
714C22C2×#1058769711yescharacteristic
715C22C2×#1058769411yescharacteristic
716C4—24no—
717C4—24no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—178no—
724C4—344no—
725C4—682no—
726C4—682no—
727C4—682no—
728C4—682no—
729C4—682no—
730C2—684no—
731C2#1453461618yesdirect product factor
732C2C2×C22⋊Q8×D1711yescharacteristic
733C2C2×#1176338611yescharacteristic
734C2C2×#1176338911yescharacteristic
735C2C2×#1176341111yescharacteristic
736C2C2×#1176341811yescharacteristic
737C2C2×#1176343611yescharacteristic
738C2C2×#1176343911yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#398C2
socleC24×C17C24
prime radicalC24×D17C23
hypercenterC2×#398D17
hypocenterC17C2×#2629
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#10587575C2semidirect
3. #14534616C2direct (N × H)
4. C2×#11762743C2semidirect
5. C2×#11762742C2semidirect
6. C2×#11762741C2semidirect
11. C2×#11762706C2semidirect
12. C2×#11762704C2semidirect
13. C2×#11762678C2semidirect
16. C2×C17×#398C2semidirect
19. C2×#10587575C22semidirect
44. #11762743C22semidirect
45. #11762742C22semidirect
46. #11762741C22semidirect
51. #11762706C22semidirect
52. #11762704C22semidirect
53. #11762678C22semidirect
65. C17×#398C22semidirect
331. C2×#398D17semidirect
411. #398C2×D17semidirect
429. C2×C17#2629semidirect
519. C17C2×#2629semidirect
731. C2#14534616direct (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×#105875782
#145346162
C2×#117627432
C2×#117627422
C2×#117627412
C2×#117627332
C2×#117627312
C2×#117627062
C2×#117627042
C2×#117626782
C2×#117626682
C2×C17×#3982
C2×#262917