Finite Group Databasebeta

← C2×#14531769 #17193820

Subgroups — C2×#14531769 #17193820

Order 4352.

3830 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587580C211yesmaximal, characteristic
2C22×#10587579C211yesmaximal, characteristic
3C22×#10587558C211yesmaximal, characteristic, complemented
4#14531769C2116yesmaximal, direct product factor
5C2×#11762704C211yesmaximal, characteristic, complemented
6C2×#11762698C211yesmaximal, characteristic, complemented
7C2×#11762698C211yesmaximal, characteristic, complemented
8C2×#11762691C211yesmaximal, characteristic, complemented
9C2×#11762687C211yesmaximal, characteristic
10C2×#11762683C211yesmaximal, characteristic, complemented
11C2×#11762683C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×Dic17C211yesmaximal, characteristic, complemented
13C2×C4×#63227C211yesmaximal, characteristic, complemented
14C2×#11762656C211yesmaximal, characteristic, complemented
15C2×#95×D17C211yesmaximal, characteristic, complemented
16C2×C17×#387C211yesmaximal, characteristic, complemented
17C23×D68C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C23×C4×D17C2211yescharacteristic
21C23×C4×D17C2211yescharacteristic
22C2×#10587580C4116yescomplemented
23C2×#10587580C2218yes—
24C2×#10587579—28no—
25C2×#10587579C2218yes—
26C2×#10587558—28no—
27C2×#10587558C2218yescomplemented
28C22×C4⋊Dic17C2211yescharacteristic
29C22×#63225C2211yescharacteristic
30C22×#63225C2211yescharacteristic
31C22×#63225C2211yescharacteristic
32C22×#63225C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34C22×#63227C2211yescharacteristic
35C22×#63227C2211yescharacteristic
36C22×#63227C2211yescharacteristic
37C22×#63227C2211yescharacteristic
38C22×#63227C2211yescharacteristic
39C22×#63227C2211yescharacteristic
40C22×#63227C2211yescharacteristic
41C22×C4×Dic17C2211yescharacteristic
42C22×C4×Dic17C2211yescharacteristic
43C22×C4×Dic17C2211yescharacteristic
44C22×C4×Dic17C2211yescharacteristic
45#11762704C2218yescomplemented
46#11762698C2218yescomplemented
47#11762698C2218yescomplemented
48#11762691C2218yescomplemented
49#11762687C2218yes—
50#11762683C2218yescomplemented
51#11762683C2218yescomplemented
52C4⋊C4×Dic17C2218yescomplemented
53C4×#63227C2218yescomplemented
54#11762656C2218yescomplemented
55C2×#10587502C2211yescharacteristic
56C2×#10587502C2211yescharacteristic
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59C2×#10587502C2211yescharacteristic
60C2×#10587502C2211yescharacteristic
61#95×D17C2218yescomplemented
62C22×C4⋊C4×C17C2211yescharacteristic
63C22×C4⋊C4×C17C2211yescharacteristic
64C22×C42×C17C2211yescharacteristic
65C17×#387C2218yescomplemented
66C2×C17×#95C2211yescharacteristic
67C2×C17×#95C2211yescharacteristic
68C2×C17×#95C2211yescharacteristic
69C2×C17×#95C2211yescharacteristic
70C24×D17C2311yescharacteristic
71C24×D17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C23×C4×C17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C23×Dic17C2311yescharacteristic
85C22×D68—24no—
86C22×D68—24no—
87C22×D68C2×C418yes—
88C22×D68C2314yes—
89C22×C4×D17—24no—
90C22×C4×D17—24no—
91C22×C4×D17—24no—
92C22×C4×D17—24no—
93C22×C4×D17—24no—
94C22×C4×D17—24no—
95C22×C4×D17—24no—
96C22×C4×D17—24no—
97C22×C4×D17—42no—
98C22×C4×D17—42no—
99C22×C4×D17—42no—
100C22×C4×D17C2×C418yescomplemented
101C22×C4×D17C2314yes—
102C22×C4×D17C2314yes—
103C22×C4×D17C2314yes—
104C22×C4×D17C2314yes—
105C2×C4⋊C4×C17—24no—
106C2×C4⋊C4×C17C2×C418yescomplemented
107C2×C4⋊C4×C17C2314yes—
108C2×C4⋊C4×C17C2314yes—
109C2×C42×C17—24no—
110C2×C42×C17C2314yes—
111C2×#63227—24no—
112C2×#63227—24no—
113C2×#63227—24no—
114C2×#63227—42no—
115C2×#63227C2×C418yescomplemented
116C2×#63227C2×C418yescomplemented
117C2×#63227C2×C418yescomplemented
118C2×#63227D418yes—
119C2×#63227C2314yes—
120C2×#63227C2314yes—
121C2×#63227C2314yes—
122C2×#63227C2314yes—
123C2×#63227C2314yes—
124C2×#63227C2314yes—
125C2×#63227C2314yes—
126C2×#63227C2314yes—
127C2×C4⋊Dic17—24no—
128C2×C4⋊Dic17C2314yes—
129C2×#63225—24no—
130C2×#63225—24no—
131C2×#63225—42no—
132C2×#63225C2×C418yescomplemented
133C2×#63225C2314yes—
134C2×#63225C2314yes—
135C2×#63225C2314yes—
136C2×#63225C2314yes—
137C2×C4×Dic17—24no—
138C2×C4×Dic17—24no—
139C2×C4×Dic17—24no—
140C2×C4×Dic17—42no—
141C2×C4×Dic17C2314yes—
142C2×C4×Dic17C2314yes—
143C2×C4×Dic17C2314yes—
144C2×C4×Dic17C2314yes—
145#10587580C2×C4164yescomplemented
146#10587579—232no—
147#10587558—232no—
148C17×#95C2314yes—
149C17×#95C2314yes—
150C17×#95C2314yes—
151C17×#95C2314yes—
152#10587502C2314yes—
153#10587502C2314yes—
154#10587502C2314yes—
155#10587502C2314yes—
156#10587502C2314yes—
157#10587502C2314yes—
158C24×C17C2411yescharacteristic
159C23×D17—22no—
160C23×D17—22no—
161C23×D17—22no—
162C23×D17—22no—
163C23×D17—22no—
164C23×D17—22no—
165C23×D17—22no—
166C23×D17—22no—
167C23×D17—22no—
168C23×D17—22no—
169C23×D17C22×C414yes—
170C23×D17C22×C414yes—
171C23×D17C2×D414yes—
172C23×D17#4114yes—
173C23×D17C2412yes—
174C23×D17C2412yes—
175C22×C4×C17—22no—
176C22×C4×C17—22no—
177C22×C4×C17—22no—
178C22×C4×C17—22no—
179C22×C4×C17—22no—
180C22×C4×C17—22no—
181C22×C4×C17—22no—
182C22×C4×C17—22no—
183C22×C4×C17—22no—
184C22×C4×C17—22no—
185C22×C4×C17—22no—
186C22×C4×C17—22no—
187C22×C4×C17—22no—
188C22×C4×C17—22no—
189C22×C4×C17—22no—
190C22×C4×C17—22no—
191C22×C4×C17—22no—
192C22×C4×C17C22×C414yes—
193C22×C4×C17C22×C414yes—
194C22×C4×C17C22×C414yes—
195C22×C4×C17C2×D414yes—
196C22×C4×C17C2412yes—
197C22×C4×C17C2412yes—
198C22×C4×C17C2412yes—
199C22×C4×C17C2412yes—
200C22×C4×C17C2412yes—
201C22×C4×C17C2412yes—
202C22×C4×C17C2412yes—
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×Dic17C22×C414yes—
217C22×Dic17C22×C414yes—
218C22×Dic17C2×D414yes—
219C22×Dic17#4114yes—
220C22×Dic17#4114yes—
221C22×Dic17C2412yes—
222C22×Dic17C2412yes—
223C22×Dic17C2412yes—
224C22×Dic17C2412yes—
225C22×Dic17C2412yes—
226C22×Dic17C2412yes—
227C2×D68—232no—
228C2×D68—28no—
229C2×D68—28no—
230C2×D68C22×C4116yes—
231C2×C4×D17—232no—
232C2×C4×D17—28no—
233C2×C4×D17—28no—
234C2×C4×D17—28no—
235C2×C4×D17—28no—
236C2×C4×D17—28no—
237C2×C4×D17—28no—
238C2×C4×D17—28no—
239C2×C4×D17—28no—
240C2×C4×D17—44no—
241C2×C4×D17—44no—
242C2×C4×D17—44no—
243C2×C4×D17—416no—
244C2×C4×D17—416no—
245C2×C4×D17—416no—
246C2×C4×D17C22×C4116yescomplemented
247C4⋊C4×C17—28no—
248C4⋊C4×C17C22×C4116yescomplemented
249C42×C17—28no—
250#63227—28no—
251#63227—28no—
252#63227—28no—
253#63227—44no—
254#63227C22×C4116yescomplemented
255#63227C22×C4116yescomplemented
256#63227C22×C4116yescomplemented
257#63227C2×D4116yes—
258C4⋊Dic17—28no—
259#63225—28no—
260#63225—28no—
261#63225—44no—
262#63225C22×C4116yescomplemented
263C4×Dic17—28no—
264C4×Dic17—28no—
265C4×Dic17—28no—
266C4×Dic17—44no—
267C2×#2359—171nomaximal, Sylow
268C23×C17C23×C412yes—
269C23×C17C22×D412yes—
270C23×C17C2×#4112yes—
271C23×C17C2×#4112yes—
272C23×C17C2×#4112yes—
273C23×C17H(5,𝔽2)12yes—
274C23×C172−1+412yes—
275C23×C17C2511yescharacteristic
276C22×D17—28no—
277C22×D17—28no—
278C22×D17—28no—
279C22×D17—28no—
280C22×D17—28no—
281C22×D17—28no—
282C22×D17—22no—
283C22×D17—22no—
284C22×D17—22no—
285C22×D17—22no—
286C22×D17—28no—
287C22×D17—28no—
288C22×D17—28no—
289C22×D17—22no—
290C22×D17—22no—
291C22×D17—22no—
292C22×D17—22no—
293C22×D17—22no—
294C22×D17—22no—
295C22×D17—44no—
296C22×D17—44no—
297C22×D17—44no—
298C22×D17—44no—
299C22×D17C4×D4116yes—
300C22×D17C23×C414yes—
301C22×D17C23×C414yes—
302C22×D17C22×D414yes—
303C22×D17C2×#4114yes—
304C2×C4×C17—28no—
305C2×C4×C17—28no—
306C2×C4×C17—28no—
307C2×C4×C17—28no—
308C2×C4×C17—22no—
309C2×C4×C17—22no—
310C2×C4×C17—22no—
311C2×C4×C17—22no—
312C2×C4×C17—22no—
313C2×C4×C17—22no—
314C2×C4×C17—22no—
315C2×C4×C17—22no—
316C2×C4×C17—22no—
317C2×C4×C17—22no—
318C2×C4×C17—22no—
319C2×C4×C17—22no—
320C2×C4×C17—22no—
321C2×C4×C17—22no—
322C2×C4×C17—22no—
323C2×C4×C17—22no—
324C2×C4×C17—22no—
325C2×C4×C17—44no—
326C2×C4×C17—44no—
327C2×C4×C17—44no—
328C2×C4×C17C23×C414yes—
329C2×C4×C17C23×C414yes—
330C2×C4×C17C23×C414yes—
331C2×C4×C17C22×D414yes—
332C2×Dic17—28no—
333C2×Dic17—28no—
334C2×Dic17—28no—
335C2×Dic17—28no—
336C2×Dic17—28no—
337C2×Dic17—22no—
338C2×Dic17—22no—
339C2×Dic17—22no—
340C2×Dic17—22no—
341C2×Dic17—22no—
342C2×Dic17—22no—
343C2×Dic17—22no—
344C2×Dic17—22no—
345C2×Dic17—22no—
346C2×Dic17—22no—
347C2×Dic17—22no—
348C2×Dic17—22no—
349C2×Dic17—22no—
350C2×Dic17—44no—
351C2×Dic17C23×C414yes—
352C2×Dic17C23×C414yes—
353C2×Dic17C22×D414yes—
354C2×Dic17C2×#4114yes—
355C2×Dic17C2×#4114yes—
356D68—232no—
357C4×D17—232no—
358C4×D17—416no—
359C4×D17—416no—
360C4×D17—416no—
361C22×#123—171no—
362C22×C4×D4—171no—
363C22×#117—171no—
364#2359—1716no—
365C2×#389—171no—
366C2×#388—171no—
367C2×#388—171no—
368C2×#387—171no—
369C2×#387D1711yescharacteristic, complemented
370C2×#386—171no—
371C2×#385—171no—
372C2×#385—171no—
373C2×C4×C4⋊C4—171no—
374C2×C4×C22⋊C4—171no—
375C2×C4×C22⋊C4—171no—
376C22×#95—171no—
377C22×C17C2×C4×D414yes—
378C22×C17C4×#4114yes—
379C22×C17#52014yes—
380C22×C17#54614yes—
381C22×C17#54714yes—
382C22×C17#55114yes—
383C22×C17#55214yes—
384C22×C17C24×C411yescharacteristic
385C22×C17C23×D411yescharacteristic
386C22×C17C22×#4111yescharacteristic
387C22×C17C22×#4111yescharacteristic
388C22×C17C22×#4111yescharacteristic
389C22×C17C2×H(5,𝔽2)11yescharacteristic
390C22×C17C2×2−1+411yescharacteristic
391C2×D17—232no—
392C2×D17—24no—
393C2×D17—24no—
394C2×D17—24no—
395C2×D17—24no—
396C2×D17—24no—
397C2×D17—24no—
398C2×D17—24no—
399C2×D17—24no—
400C2×D17—24no—
401C2×D17—416no—
402C2×D17—42no—
403C2×D17—42no—
404C2×D17—42no—
405C2×D17—42no—
406C2×D17C2×C4×D418yes—
407C4×C17—24no—
408C4×C17—24no—
409C4×C17—24no—
410C4×C17—24no—
411C4×C17—42no—
412C4×C17—42no—
413C4×C17—42no—
414Dic17—24no—
415Dic17—24no—
416Dic17—24no—
417Dic17—24no—
418Dic17—24no—
419Dic17—42no—
420C23×D4—171no—
421C24×C4—171no—
422C24×C4—171no—
423C24×C4—171no—
424C24×C4—171no—
425C2×#123—1716no—
426C2×#123—178no—
427C2×C4×D4—178no—
428C2×C4×D4—348no—
429C2×#117—178no—
430C2×#117—348no—
431C22×C4⋊C4—171no—
432C22×C4⋊C4—171no—
433C22×C4⋊C4—171no—
434C22×C4⋊C4—171no—
435C22×C4⋊C4—171no—
436C22×C4⋊C4C2×D1711yescharacteristic
437C22×C4⋊C4C2×D1711yescharacteristic
438C22×C22⋊C4—171no—
439C22×C22⋊C4—171no—
440C22×C22⋊C4—171no—
441C22×C22⋊C4—171no—
442C22×C22⋊C4—171no—
443C22×C22⋊C4—171no—
444C22×C22⋊C4—171no—
445C22×C22⋊C4—171no—
446C22×C42—171no—
447C22×C42—171no—
448C22×C42—171no—
449C22×C42—171no—
450C22×C42C2×D1711yescharacteristic
451#389—178no—
452#388—178no—
453#388—178no—
454#387—178no—
455#387C2×D1718yescomplemented
456#386—178no—
457#385—178no—
458#385—178no—
459C4×C4⋊C4—178no—
460C4×C22⋊C4—178no—
461C4×C22⋊C4—178no—
462C2×#95—171no—
463C2×#95—171no—
464C2×#95—171no—
465C2×#95—171no—
466C2×#95—171no—
467C2×#95—171no—
468C2×#95—178no—
469C2×#95C2×D1711yescharacteristic
470C2×#95C2×D1711yescharacteristic
471C2×#95C2×D1711yescharacteristic
472C2×#95C2×D1711yescharacteristic
473C2×C17#235918yescomplemented
474C2×C17C22×C4×D411yescharacteristic
475C2×C17C2×C4×#4111yescharacteristic
476C2×C17C2×#52011yescharacteristic
477C2×C17C2×#54611yescharacteristic
478C2×C17C2×#54711yescharacteristic
479C2×C17C2×#55111yescharacteristic
480C2×C17C2×#55211yescharacteristic
481D17—28no—
482D17—44no—
483C25—171no—
484C25—171no—
485C22×D4—178no—
486C22×D4—174no—
487C22×D4—344no—
488C22×D4—344no—
489C23×C4—171no—
490C23×C4—171no—
491C23×C4—171no—
492C23×C4—171no—
493C23×C4—171no—
494C23×C4—178no—
495C23×C4—174no—
496C23×C4—171no—
497C23×C4—174no—
498C23×C4—174no—
499C23×C4—174no—
500C23×C4—344no—
501C23×C4—344no—
502C23×C4—344no—
503C23×C4—344no—
504C23×C4—344no—
505C23×C4—344no—
506C23×C4—344no—
507C23×C4—344no—
508C23×C4—682no—
509C23×C4—682no—
510C23×C4—682no—
511C23×C4C22×D1711yescharacteristic
512C23×C4C22×D1711yescharacteristic
513C23×C4C22×D1711yescharacteristic
514C23×C4C22×D1711yescharacteristic
515C23×C4C22×D1711yescharacteristic
516C23×C4C22×D1711yescharacteristic
517C23×C4C22×D1711yescharacteristic
518#123—1764no—
519C4×D4—3432no—
520#117—3432no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—178no—
523C2×C4⋊C4—174no—
524C2×C4⋊C4—174no—
525C2×C4⋊C4—174no—
526C2×C4⋊C4—174no—
527C2×C4⋊C4—174no—
528C2×C4⋊C4—344no—
529C2×C4⋊C4—344no—
530C2×C4⋊C4—344no—
531C2×C4⋊C4—682no—
532C2×C4⋊C4C4×D1718yescomplemented
533C2×C4⋊C4C22×D1714yes—
534C2×C4⋊C4C22×D1714yes—
535C2×C22⋊C4—178no—
536C2×C22⋊C4—178no—
537C2×C22⋊C4—178no—
538C2×C22⋊C4—178no—
539C2×C22⋊C4—174no—
540C2×C22⋊C4—174no—
541C2×C22⋊C4—174no—
542C2×C22⋊C4—174no—
543C2×C22⋊C4—174no—
544C2×C22⋊C4—174no—
545C2×C22⋊C4—174no—
546C2×C22⋊C4—174no—
547C2×C22⋊C4—344no—
548C2×C22⋊C4—344no—
549C2×C22⋊C4—344no—
550C2×C22⋊C4—682no—
551C2×C42—24no—
552C2×C42—174no—
553C2×C42—174no—
554C2×C42—174no—
555C2×C42—174no—
556C2×C42—344no—
557C2×C42—344no—
558C2×C42—344no—
559C2×C42—682no—
560C2×C42C22×D1714yes—
561#95—174no—
562#95—174no—
563#95—174no—
564#95—174no—
565#95—174no—
566#95—174no—
567#95C22×D1714yes—
568#95C22×D1714yes—
569#95C22×D1714yes—
570#95C22×D1714yes—
571C17C2×#235911yescharacteristic, complemented, Sylow
572C24—174no—
573C24—174no—
574C24—174no—
575C24—172no—
576C24—174no—
577C24—172no—
578C24—342no—
579C24—342no—
580C24—342no—
581C24—342no—
582C24—342no—
583C24—342no—
584C24—342no—
585C24—342no—
586C24—342no—
587C24—342no—
588C24C23×D1711yescharacteristic
589C2×D4—1716no—
590C2×D4—348no—
591C2×D4—3432no—
592C2×D4—348no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—174no—
611C22×C4—174no—
612C22×C4—174no—
613C22×C4—174no—
614C22×C4—174no—
615C22×C4—172no—
616C22×C4—172no—
617C22×C4—172no—
618C22×C4—172no—
619C22×C4—172no—
620C22×C4—1716no—
621C22×C4—172no—
622C22×C4—348no—
623C22×C4—348no—
624C22×C4—348no—
625C22×C4—348no—
626C22×C4—3432no—
627C22×C4—348no—
628C22×C4—348no—
629C22×C4—348no—
630C22×C4—342no—
631C22×C4—342no—
632C22×C4—342no—
633C22×C4—342no—
634C22×C4—342no—
635C22×C4—342no—
636C22×C4—342no—
637C22×C4—342no—
638C22×C4—342no—
639C22×C4—342no—
640C22×C4—342no—
641C22×C4—342no—
642C22×C4—342no—
643C22×C4—348no—
644C22×C4—684no—
645C22×C4—684no—
646C22×C4—684no—
647C22×C4—6816no—
648C22×C4—6816no—
649C22×C4—6816no—
650C22×C4C2×C4×D1714yes—
651C22×C4C2×C4×D1714yes—
652C22×C4C2×C4×D1714yes—
653C22×C4D4×D1714yes—
654C22×C4C23×D1712yes—
655C22×C4C23×D1712yes—
656C22×C4C23×D1712yes—
657C22×C4C23×D1712yes—
658C22×C4C23×D1712yes—
659C22×C4C23×D1712yes—
660C22×C4C23×D1712yes—
661C4⋊C4—28no—
662C4⋊C4—1716no—
663C4⋊C4—348no—
664C4⋊C4—348no—
665C4⋊C4—348no—
666C4⋊C4—684no—
667C4⋊C4C2×C4×D17116yescomplemented
668C22⋊C4—1716no—
669C22⋊C4—1716no—
670C22⋊C4—1716no—
671C22⋊C4—1716no—
672C22⋊C4—348no—
673C22⋊C4—348no—
674C22⋊C4—348no—
675C22⋊C4—684no—
676C42—28no—
677C42—348no—
678C42—348no—
679C42—348no—
680C42—684no—
681C23—1716no—
682C23—174no—
683C23—174no—
684C23—174no—
685C23—174no—
686C23—348no—
687C23—348no—
688C23—348no—
689C23—348no—
690C23—348no—
691C23—342no—
692C23—342no—
693C23—342no—
694C23—342no—
695C23—348no—
696C23—348no—
697C23—348no—
698C23—348no—
699C23—342no—
700C23—342no—
701C23—342no—
702C23—342no—
703C23—342no—
704C23—342no—
705C23—684no—
706C23—684no—
707C23—684no—
708C23—684no—
709C23C22×C4×D1712yes—
710C23C2×D4×D1712yes—
711C23#1058769412yes—
712C23#41×D1712yes—
713C23#41×D1712yes—
714C23#41×D1712yes—
715C23#1058769612yes—
716C23C24×D1711yescharacteristic
717D4—3432no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—28no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—174no—
743C2×C4—174no—
744C2×C4—174no—
745C2×C4—174no—
746C2×C4—174no—
747C2×C4—3432no—
748C2×C4—348no—
749C2×C4—348no—
750C2×C4—348no—
751C2×C4—348no—
752C2×C4—342no—
753C2×C4—342no—
754C2×C4—342no—
755C2×C4—342no—
756C2×C4—342no—
757C2×C4—342no—
758C2×C4—342no—
759C2×C4—342no—
760C2×C4—342no—
761C2×C4—342no—
762C2×C4—348no—
763C2×C4—342no—
764C2×C4—342no—
765C2×C4—342no—
766C2×C4—6816no—
767C2×C4—6816no—
768C2×C4—6816no—
769C2×C4—684no—
770C2×C4C22×C4×D1714yes—
771C2×C4C22×C4×D1714yes—
772C2×C4C22×C4×D1714yes—
773C2×C4C2×D4×D1714yes—
774C22—178no—
775C22—344no—
776C22—344no—
777C22—344no—
778C22—344no—
779C22—3432no—
780C22—344no—
781C22—344no—
782C22—344no—
783C22—344no—
784C22—344no—
785C22—682no—
786C22—682no—
787C22—6816no—
788C22—682no—
789C22—682no—
790C22C4×D4×D1714yes—
791C22#1176327714yes—
792C22#1176329114yes—
793C22#1176345114yes—
794C22#1176346114yes—
795C22#1176348414yes—
796C22#1176349114yes—
797C22C23×C4×D1711yescharacteristic
798C22C22×D4×D1711yescharacteristic
799C22C2×#41×D1711yescharacteristic
800C22C2×#41×D1711yescharacteristic
801C22C2×#41×D1711yescharacteristic
802C22C2×#1058769611yescharacteristic
803C22C2×#1058769411yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—344no—
812C4—344no—
813C4—344no—
814C4—344no—
815C4—344no—
816C4—682no—
817C2—348no—
818C2—684no—
819C2#1453176918yesdirect product factor
820C2C2×C4×D4×D1711yescharacteristic
821C2C2×#1176327711yescharacteristic
822C2C2×#1176329111yescharacteristic
823C2C2×#1176345111yescharacteristic
824C2C2×#1176346111yescharacteristic
825C2C2×#1176348411yescharacteristic
826C2C2×#1176349111yescharacteristic
subgroupG/H
centerC24C23×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC2×C17×#387C2
socleC24×C17C24
prime radicalC23×D68C22
cosocleC23×C17C25
hypercenterC2×#387D17
hypocenterC17C2×#2359
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. C22×#10587558C2semidirect
4. #14531769C2direct (N × H)
5. C2×#11762704C2semidirect
6. C2×#11762698C2semidirect
7. C2×#11762698C2semidirect
8. C2×#11762691C2semidirect
10. C2×#11762683C2semidirect
11. C2×#11762683C2semidirect
12. C2×C4⋊C4×Dic17C2semidirect
13. C2×C4×#63227C2semidirect
14. C2×#11762656C2semidirect
15. C2×#95×D17C2semidirect
16. C2×C17×#387C2semidirect
22. C2×#10587580C4semidirect
27. C2×#10587558C22semidirect
45. #11762704C22semidirect
46. #11762698C22semidirect
47. #11762698C22semidirect
48. #11762691C22semidirect
50. #11762683C22semidirect
51. #11762683C22semidirect
52. C4⋊C4×Dic17C22semidirect
53. C4×#63227C22semidirect
54. #11762656C22semidirect
61. #95×D17C22semidirect
65. C17×#387C22semidirect
100. C22×C4×D17C2×C4semidirect
106. C2×C4⋊C4×C17C2×C4semidirect
115. C2×#63227C2×C4semidirect
116. C2×#63227C2×C4semidirect
117. C2×#63227C2×C4semidirect
132. C2×#63225C2×C4semidirect
145. #10587580C2×C4semidirect
246. C2×C4×D17C22×C4semidirect
248. C4⋊C4×C17C22×C4semidirect
254. #63227C22×C4semidirect
255. #63227C22×C4semidirect
256. #63227C22×C4semidirect
262. #63225C22×C4semidirect
369. C2×#387D17semidirect
455. #387C2×D17semidirect
473. C2×C17#2359semidirect
532. C2×C4⋊C4C4×D17semidirect
571. C17C2×#2359semidirect
667. C4⋊C4C2×C4×D17semidirect
819. C2#14531769direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875802
C22×#105875792
C22×#105875582
#145317692
C2×#117627042
C2×#117626982
C2×#117626912
C2×#117626872
C2×#117626832
C2×C4⋊C4×Dic172
C2×C4×#632272
C2×#117626562
C2×#95×D172
C2×C17×#3872
C2×#235917