Finite Group Databasebeta

← C2×#14532190 #17203024

Subgroups — C2×#14532190 #17203024

Order 4352.

3570 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×#10587569C211yesmaximal, characteristic
2C22×#10587569C211yesmaximal, characteristic
3C22×#10587558C211yesmaximal, characteristic, complemented
4C22×C4⋊C4×D17C211yesmaximal, characteristic, complemented
5#14532190C2116yesmaximal, direct product factor
6C2×#11762743C211yesmaximal, characteristic, complemented
7C2×#11762741C211yesmaximal, characteristic, complemented
8C2×#11762732C211yesmaximal, characteristic, complemented
9C2×#11762732C211yesmaximal, characteristic, complemented
10C2×#11762707C211yesmaximal, characteristic, complemented
11C2×#11762704C211yesmaximal, characteristic, complemented
12C2×#11762703C211yesmaximal, characteristic, complemented
13C2×#11762685C211yesmaximal, characteristic
14C2×#11762683C211yesmaximal, characteristic, complemented
15C2×#11762671C211yesmaximal, characteristic, complemented
16C2×C17×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C23×C4×D17C2211yescharacteristic
21C2×#10587569—28no—
22C2×#10587569—28no—
23C2×#10587569C2218yes—
24C2×#10587569C2218yes—
25C2×#10587558—28no—
26C2×#10587558C2218yescomplemented
27C22×C4⋊Dic17C2211yescharacteristic
28C22×C4⋊Dic17C2211yescharacteristic
29C22×C4⋊Dic17C2211yescharacteristic
30C22×C4⋊Dic17C2211yescharacteristic
31C22×#63225C2211yescharacteristic
32C22×#63225C2211yescharacteristic
33C22×#63225C2211yescharacteristic
34C22×#63225C2211yescharacteristic
35C22×#63225C2211yescharacteristic
36C22×#63225C2211yescharacteristic
37C22×#63225C2211yescharacteristic
38C2×C4⋊C4×D17—28no—
39C2×C4⋊C4×D17C2218yescomplemented
40C22×C22⋊Dic17C2211yescharacteristic
41C22×C22⋊Dic17C2211yescharacteristic
42C22×C22⋊Dic17C2211yescharacteristic
43C22×#63227C2211yescharacteristic
44C22×#63227C2211yescharacteristic
45C22×#63227C2211yescharacteristic
46C22×C4×Dic17C2211yescharacteristic
47#11762743C2218yescomplemented
48#11762741C2218yescomplemented
49#11762732C2218yescomplemented
50#11762732C2218yescomplemented
51#11762707C2218yescomplemented
52#11762704C2218yescomplemented
53#11762703C2218yescomplemented
54#11762685C2218yes—
55#11762683C2218yescomplemented
56#11762671C2218yescomplemented
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59C2×#10587502C2211yescharacteristic
60C2×#10587502C2211yescharacteristic
61C2×#10587502C2211yescharacteristic
62C2×#10587502C2211yescharacteristic
63C22×C4⋊C4×C17C2211yescharacteristic
64C22×C22⋊C4×C17C2211yescharacteristic
65C22×C22⋊C4×C17C2211yescharacteristic
66C22×C22⋊C4×C17C2211yescharacteristic
67C22×C42×C17C2211yescharacteristic
68C17×#388C2218yescomplemented
69C2×C17×#95C2211yescharacteristic
70C2×C17×#95C2211yescharacteristic
71C25×C17C2311yescharacteristic
72C24×D17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C23×C4×C17C2311yescharacteristic
79C22×C22⋊D17—24no—
80C22×C22⋊D17—24no—
81C22×C22⋊D17—24no—
82C22×C22⋊D17C2314yes—
83C23×Dic17C2311yescharacteristic
84C23×Dic17C2311yescharacteristic
85C23×Dic17C2311yescharacteristic
86C23×Dic17C2311yescharacteristic
87C23×Dic17C2311yescharacteristic
88C23×Dic17C2311yescharacteristic
89C23×Dic17C2311yescharacteristic
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—24no—
98C22×C4×D17D418yes—
99C22×C4×D17C2314yes—
100C22×C4×D17C2314yes—
101C22×C4×D17C2314yes—
102C2×C4⋊C4×C17—24no—
103C2×C4⋊C4×C17C2314yes—
104C2×C22⋊C4×C17—24no—
105C2×C22⋊C4×C17—24no—
106C2×C22⋊C4×C17—24no—
107C2×C22⋊C4×C17C2314yes—
108C2×C22⋊C4×C17C2314yes—
109C2×C22⋊C4×C17C2314yes—
110C2×C42×C17—24no—
111C2×C42×C17C2314yes—
112C2×C22⋊Dic17—24no—
113C2×C22⋊Dic17—24no—
114C2×C22⋊Dic17—24no—
115C2×C22⋊Dic17C2314yes—
116C2×C22⋊Dic17C2314yes—
117C2×C22⋊Dic17C2314yes—
118C2×#63227—24no—
119C2×#63227—24no—
120C2×#63227D418yes—
121C2×#63227C2314yes—
122C2×#63227C2314yes—
123C2×#63227C2314yes—
124C2×C4⋊Dic17—24no—
125C2×C4⋊Dic17—24no—
126C2×C4⋊Dic17—24no—
127C2×C4⋊Dic17—24no—
128C2×C4⋊Dic17C2314yes—
129C2×C4⋊Dic17C2314yes—
130C2×C4⋊Dic17C2314yes—
131C2×C4⋊Dic17C2314yes—
132C2×#63225—24no—
133C2×#63225—24no—
134C2×#63225—24no—
135C2×#63225—24no—
136C2×#63225—24no—
137C2×#63225—24no—
138C2×#63225—24no—
139C2×#63225C2314yes—
140C2×#63225C2314yes—
141C2×#63225C2314yes—
142C2×#63225C2314yes—
143C2×#63225C2314yes—
144C2×#63225C2314yes—
145C2×#63225C2314yes—
146C2×C4×Dic17—24no—
147C2×C4×Dic17C2314yes—
148C4⋊C4×D17—232no—
149#10587569—232no—
150#10587569—232no—
151#10587558—232no—
152C17×#95C2314yes—
153C17×#95C2314yes—
154#10587502C2314yes—
155#10587502C2314yes—
156#10587502C2314yes—
157#10587502C2314yes—
158#10587502C2314yes—
159#10587502C2314yes—
160C24×C17—22no—
161C24×C17—22no—
162C24×C17—22no—
163C24×C17—22no—
164C24×C17—22no—
165C24×C17—22no—
166C24×C17—22no—
167C24×C17C2412yes—
168C24×C17C2411yescharacteristic
169C23×D17—22no—
170C23×D17—22no—
171C23×D17—22no—
172C23×D17—22no—
173C23×D17C2×D414yes—
174C23×D17C2×D414yes—
175C23×D17#4114yes—
176C23×D17C2412yes—
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×C17C2×D414yes—
193C22×C4×C17C2×D414yes—
194C22×C4×C17#4114yes—
195C22×C4×C17C2412yes—
196C22×C4×C17C2412yes—
197C22×C4×C17C2412yes—
198C22×C4×C17C2412yes—
199C22×C4×C17C2412yes—
200C22×C4×C17C2412yes—
201C2×C22⋊D17—28no—
202C2×C22⋊D17—28no—
203C2×C22⋊D17—28no—
204C2×C22⋊D17—416no—
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×Dic17—22no—
218C22×Dic17—22no—
219C22×Dic17—22no—
220C22×Dic17—22no—
221C22×Dic17—22no—
222C22×Dic17—22no—
223C22×Dic17C2×D414yes—
224C22×Dic17C2×D414yes—
225C22×Dic17#4114yes—
226C22×Dic17C2412yes—
227C22×Dic17C2412yes—
228C22×Dic17C2412yes—
229C22×Dic17C2412yes—
230C22×Dic17C2412yes—
231C22×Dic17C2412yes—
232C22×Dic17C2412yes—
233C2×C4×D17—232no—
234C2×C4×D17—232no—
235C2×C4×D17—28no—
236C2×C4×D17—28no—
237C2×C4×D17—28no—
238C2×C4×D17—28no—
239C2×C4×D17—28no—
240C2×C4×D17—28no—
241C2×C4×D17—28no—
242C2×C4×D17—28no—
243C2×C4×D17—416no—
244C2×C4×D17C2×D4116yes—
245C4⋊C4×C17—28no—
246C22⋊C4×C17—28no—
247C22⋊C4×C17—28no—
248C22⋊C4×C17—28no—
249C42×C17—28no—
250C22⋊Dic17—28no—
251C22⋊Dic17—28no—
252C22⋊Dic17—28no—
253#63227—28no—
254#63227—28no—
255#63227C2×D4116yes—
256C4⋊Dic17—28no—
257C4⋊Dic17—28no—
258C4⋊Dic17—28no—
259C4⋊Dic17—28no—
260#63225—28no—
261#63225—28no—
262#63225—28no—
263#63225—28no—
264#63225—28no—
265#63225—28no—
266#63225—28no—
267C4×Dic17—28no—
268C2×#2413—171nomaximal, Sylow
269C23×C17—22no—
270C23×C17—22no—
271C23×C17—22no—
272C23×C17—22no—
273C23×C17—22no—
274C23×C17—22no—
275C23×C17—22no—
276C23×C17—44no—
277C23×C17—44no—
278C23×C17—44no—
279C23×C17—44no—
280C23×C17—44no—
281C23×C17—44no—
282C23×C17—44no—
283C23×C17C22×D412yes—
284C23×C17C22×D412yes—
285C23×C17C2×#4112yes—
286C23×C17C2×#4112yes—
287C23×C17C2×#4112yes—
288C23×C172−1+412yes—
289C23×C172−1+412yes—
290C23×C17C2511yescharacteristic
291C22×D17—28no—
292C22×D17—28no—
293C22×D17—28no—
294C22×D17—28no—
295C22×D17—28no—
296C22×D17—28no—
297C22×D17—22no—
298C22×D17—22no—
299C22×D17—22no—
300C22×D17—22no—
301C22×D17#121116yes—
302C22×D17C22×D414yes—
303C22×D17C22×D414yes—
304C22×D17C2×#4114yes—
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—44no—
324C2×C4×C17—44no—
325C2×C4×C17—44no—
326C2×C4×C17C22×D414yes—
327C2×C4×C17C22×D414yes—
328C2×C4×C17C2×#4114yes—
329C22⋊D17—416no—
330C2×Dic17—28no—
331C2×Dic17—28no—
332C2×Dic17—28no—
333C2×Dic17—22no—
334C2×Dic17—22no—
335C2×Dic17—22no—
336C2×Dic17—22no—
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—22no—
351C2×Dic17—44no—
352C2×Dic17—44no—
353C2×Dic17—44no—
354C2×Dic17—44no—
355C2×Dic17C22×D414yes—
356C2×Dic17C22×D414yes—
357C2×Dic17C2×#4114yes—
358C4×D17—232no—
359C4×D17—232no—
360C4×D17—416no—
361C22×#123—171no—
362C22×#123—171no—
363C22×#117—171no—
364C23×C4⋊C4—171no—
365#2413—1716no—
366C2×#398—171no—
367C2×#398—171no—
368C2×#396—171no—
369C2×#396—171no—
370C2×#389—171no—
371C2×#389—171no—
372C2×#388—171no—
373C2×#388D1711yescharacteristic, complemented
374C2×#386—171no—
375C2×#385—171no—
376C2×#381—171no—
377C22×C17—42no—
378C22×C17—42no—
379C22×C17—42no—
380C22×C17—42no—
381C22×C17—42no—
382C22×C17—42no—
383C22×C17—42no—
384C22×C17—88no—
385C22×C17C2×#12114yes—
386C22×C17#52514yes—
387C22×C17#53614yes—
388C22×C17#54714yes—
389C22×C17#54714yes—
390C22×C17#55214yes—
391C22×C17#55214yes—
392C22×C17C23×D411yescharacteristic
393C22×C17C23×D411yescharacteristic
394C22×C17C22×#4111yescharacteristic
395C22×C17C22×#4111yescharacteristic
396C22×C17C22×#4111yescharacteristic
397C22×C17C2×2−1+411yescharacteristic
398C22×C17C2×2−1+411yescharacteristic
399C2×D17—24no—
400C2×D17—232no—
401C2×D17—24no—
402C2×D17—24no—
403C2×D17—24no—
404C2×D17—24no—
405C2×D17—24no—
406C2×D17C2×#12118yes—
407C4×C17—24no—
408C4×C17—24no—
409C4×C17—24no—
410C4×C17—42no—
411C4×C17—42no—
412C4×C17—42no—
413Dic17—24no—
414Dic17—24no—
415Dic17—24no—
416Dic17—42no—
417Dic17—42no—
418Dic17—42no—
419Dic17—42no—
420C23×D4—171no—
421C24×C4—171no—
422C24×C4—171no—
423C24×C4—171no—
424C2×#123—178no—
425C2×#123—178no—
426C2×#123—348no—
427C2×#123—348no—
428C2×#117—178no—
429C2×#117—348no—
430C22×C4⋊C4—171no—
431C22×C4⋊C4—171no—
432C22×C4⋊C4—171no—
433C22×C4⋊C4—171no—
434C22×C4⋊C4—171no—
435C22×C4⋊C4—171no—
436C22×C4⋊C4—171no—
437C22×C4⋊C4—171no—
438C22×C4⋊C4—171no—
439C22×C4⋊C4—171no—
440C22×C4⋊C4—171no—
441C22×C4⋊C4—178no—
442C22×C4⋊C4—348no—
443C22×C4⋊C4C2×D1711yescharacteristic
444C22×C22⋊C4—171no—
445C22×C22⋊C4—171no—
446C22×C22⋊C4—171no—
447C22×C22⋊C4—171no—
448C22×C22⋊C4—171no—
449C22×C22⋊C4—171no—
450C22×C22⋊C4C2×D1711yescharacteristic
451C22×C22⋊C4C2×D1711yescharacteristic
452C22×C22⋊C4C2×D1711yescharacteristic
453C22×C42—171no—
454C22×C42C2×D1711yescharacteristic
455#398—178no—
456#398—178no—
457#396—178no—
458#396—178no—
459#389—178no—
460#389—178no—
461#388—178no—
462#388C2×D1718yescomplemented
463#386—178no—
464#385—178no—
465#381—178no—
466C2×#95—171no—
467C2×#95—171no—
468C2×#95—171no—
469C2×#95—171no—
470C2×#95—171no—
471C2×#95—171no—
472C2×#95C2×D1711yescharacteristic
473C2×#95C2×D1711yescharacteristic
474C2×C17—82no—
475C2×C17#241318yescomplemented
476C2×C17C22×#12111yescharacteristic
477C2×C17C2×#52511yescharacteristic
478C2×C17C2×#53611yescharacteristic
479C2×C17C2×#54711yescharacteristic
480C2×C17C2×#54711yescharacteristic
481C2×C17C2×#55211yescharacteristic
482C2×C17C2×#55211yescharacteristic
483D17—28no—
484C25—171no—
485C25C22×D1711yescharacteristic
486C22×D4—174no—
487C22×D4—344no—
488C22×D4—344no—
489C22×D4—344no—
490C23×C4—171no—
491C23×C4—171no—
492C23×C4—171no—
493C23×C4—178no—
494C23×C4—174no—
495C23×C4—171no—
496C23×C4—171no—
497C23×C4—171no—
498C23×C4—171no—
499C23×C4—174no—
500C23×C4—174no—
501C23×C4—344no—
502C23×C4—344no—
503C23×C4—344no—
504C23×C4—344no—
505C23×C4—344no—
506C23×C4—344no—
507C23×C4—344no—
508C23×C4—344no—
509C23×C4C22×D1711yescharacteristic
510C23×C4C22×D1711yescharacteristic
511C23×C4C22×D1711yescharacteristic
512C23×C4C22×D1711yescharacteristic
513C23×C4C22×D1711yescharacteristic
514C23×C4C22×D1711yescharacteristic
515#123—3432no—
516#123—3432no—
517#117—3432no—
518C2×C4⋊C4—24no—
519C2×C4⋊C4—174no—
520C2×C4⋊C4—174no—
521C2×C4⋊C4—174no—
522C2×C4⋊C4—174no—
523C2×C4⋊C4—174no—
524C2×C4⋊C4—174no—
525C2×C4⋊C4—174no—
526C2×C4⋊C4—174no—
527C2×C4⋊C4—174no—
528C2×C4⋊C4—174no—
529C2×C4⋊C4—174no—
530C2×C4⋊C4—3432no—
531C2×C4⋊C4—344no—
532C2×C4⋊C4—344no—
533C2×C4⋊C4—344no—
534C2×C4⋊C4—344no—
535C2×C4⋊C4—344no—
536C2×C4⋊C4—344no—
537C2×C4⋊C4—344no—
538C2×C4⋊C4—344no—
539C2×C4⋊C4—344no—
540C2×C4⋊C4—344no—
541C2×C4⋊C4—344no—
542C2×C4⋊C4C22×D1714yes—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—178no—
547C2×C22⋊C4—174no—
548C2×C22⋊C4—174no—
549C2×C22⋊C4—174no—
550C2×C22⋊C4—174no—
551C2×C22⋊C4—174no—
552C2×C22⋊C4—174no—
553C2×C22⋊C4—344no—
554C2×C22⋊C4—344no—
555C2×C22⋊C4—344no—
556C2×C22⋊C4—344no—
557C2×C22⋊C4—344no—
558C2×C22⋊C4C22×D1714yes—
559C2×C22⋊C4C22×D1714yes—
560C2×C22⋊C4C22×D1714yes—
561C2×C42—24no—
562C2×C42—174no—
563C2×C42—344no—
564C2×C42C22×D1714yes—
565#95—174no—
566#95—174no—
567#95—174no—
568#95—174no—
569#95—174no—
570#95—174no—
571#95C22×D1714yes—
572#95C22×D1714yes—
573C17C2×#241311yescharacteristic, complemented, Sylow
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—174no—
582C24—174no—
583C24—174no—
584C24—172no—
585C24—342no—
586C24—342no—
587C24—342no—
588C24—342no—
589C24C23×D1712yes—
590C24C23×D1711yescharacteristic
591C2×D4—348no—
592C2×D4—348no—
593C2×D4—348no—
594C2×D4—6816no—
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—172no—
614C22×C4—172no—
615C22×C4—172no—
616C22×C4—1716no—
617C22×C4—172no—
618C22×C4—172no—
619C22×C4—172no—
620C22×C4—172no—
621C22×C4—348no—
622C22×C4—348no—
623C22×C4—348no—
624C22×C4—3432no—
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—348no—
637C22×C4—342no—
638C22×C4—342no—
639C22×C4—342no—
640C22×C4—342no—
641C22×C4—342no—
642C22×C4—342no—
643C22×C4—342no—
644C22×C4—342no—
645C22×C4—342no—
646C22×C4—342no—
647C22×C4—342no—
648C22×C4—342no—
649C22×C4—6816no—
650C22×C4#6325214yes—
651C22×C4D4×D1714yes—
652C22×C4D4×D1714yes—
653C22×C4C23×D1712yes—
654C22×C4C23×D1712yes—
655C22×C4C23×D1712yes—
656C22×C4C23×D1712yes—
657C22×C4C23×D1712yes—
658C22×C4C23×D1712yes—
659C4⋊C4—28no—
660C4⋊C4—348no—
661C4⋊C4—348no—
662C4⋊C4—348no—
663C4⋊C4—348no—
664C4⋊C4—348no—
665C4⋊C4—348no—
666C4⋊C4—348no—
667C4⋊C4—348no—
668C4⋊C4—348no—
669C4⋊C4—348no—
670C4⋊C4—348no—
671C22⋊C4—28no—
672C22⋊C4—28no—
673C22⋊C4—28no—
674C22⋊C4—1716no—
675C22⋊C4—348no—
676C22⋊C4—348no—
677C22⋊C4—348no—
678C22⋊C4—348no—
679C22⋊C4—348no—
680C42—28no—
681C42—348no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—1716no—
697C23—174no—
698C23—174no—
699C23—174no—
700C23—348no—
701C23—348no—
702C23—348no—
703C23—348no—
704C23—348no—
705C23—342no—
706C23—348no—
707C23—342no—
708C23—342no—
709C23—342no—
710C23C2×#6325212yes—
711C23C2×D4×D1712yes—
712C23C2×D4×D1712yes—
713C23#41×D1712yes—
714C23#41×D1712yes—
715C23#1058769712yes—
716C23#1058769712yes—
717C23C24×D1711yescharacteristic
718D4—6816no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—174no—
741C2×C4—174no—
742C2×C4—174no—
743C2×C4—3432no—
744C2×C4—3432no—
745C2×C4—348no—
746C2×C4—348no—
747C2×C4—348no—
748C2×C4—342no—
749C2×C4—342no—
750C2×C4—342no—
751C2×C4—342no—
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—342no—
763C2×C4—342no—
764C2×C4—342no—
765C2×C4—342no—
766C2×C4—6816no—
767C2×C4—684no—
768C2×C4—684no—
769C2×C4—684no—
770C2×C4—684no—
771C2×C4C2×#6325214yes—
772C2×C4C2×D4×D1714yes—
773C2×C4C2×D4×D1714yes—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—88no—
782C22—178no—
783C22—344no—
784C22—3432no—
785C22—344no—
786C22—344no—
787C22—344no—
788C22—344no—
789C22—344no—
790C22#121×D1714yes—
791C22#1176331814yes—
792C22#1176337914yes—
793C22#1176345714yes—
794C22#1176346414yes—
795C22#1176349514yes—
796C22#1176349814yes—
797C22C22×D4×D1711yescharacteristic
798C22C22×D4×D1711yescharacteristic
799C22C2×#41×D1711yescharacteristic
800C22C2×#41×D1711yescharacteristic
801C22C22×#6325211yescharacteristic
802C22C2×#1058769711yescharacteristic
803C22C2×#1058769711yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—344no—
811C4—344no—
812C4—344no—
813C4—682no—
814C4—682no—
815C4—682no—
816C4—682no—
817C2—82no—
818C2—348no—
819C2#1453219018yesdirect product factor
820C2C2×#121×D1711yescharacteristic
821C2C2×#1176331811yescharacteristic
822C2C2×#1176337911yescharacteristic
823C2C2×#1176345711yescharacteristic
824C2C2×#1176346411yescharacteristic
825C2C2×#1176349511yescharacteristic
826C2C2×#1176349811yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#388C2
socleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC2×#388D17
hypocenterC17C2×#2413
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C22×#10587558C2semidirect
4. C22×C4⋊C4×D17C2semidirect
5. #14532190C2direct (N × H)
6. C2×#11762743C2semidirect
7. C2×#11762741C2semidirect
8. C2×#11762732C2semidirect
9. C2×#11762732C2semidirect
10. C2×#11762707C2semidirect
11. C2×#11762704C2semidirect
12. C2×#11762703C2semidirect
14. C2×#11762683C2semidirect
15. C2×#11762671C2semidirect
16. C2×C17×#388C2semidirect
26. C2×#10587558C22semidirect
39. C2×C4⋊C4×D17C22semidirect
47. #11762743C22semidirect
48. #11762741C22semidirect
49. #11762732C22semidirect
50. #11762732C22semidirect
51. #11762707C22semidirect
52. #11762704C22semidirect
53. #11762703C22semidirect
55. #11762683C22semidirect
56. #11762671C22semidirect
68. C17×#388C22semidirect
373. C2×#388D17semidirect
462. #388C2×D17semidirect
475. C2×C17#2413semidirect
573. C17C2×#2413semidirect
819. C2#14532190direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875692
C22×#105875582
C22×C4⋊C4×D172
#145321902
C2×#117627432
C2×#117627412
C2×#117627322
C2×#117627072
C2×#117627042
C2×#117627032
C2×#117626852
C2×#117626832
C2×#117626712
C2×C17×#3882
C2×#241317