Finite Group Databasebeta

← C2×#14531775 #17193826

Subgroups — C2×#14531775 #17193826

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×#10587569C211yesmaximal, characteristic
2C22×#10587567C211yesmaximal, characteristic
3C22×#10587578C211yesmaximal, characteristic, complemented
4#14531775C2116yesmaximal, direct product factor
5C2×#11762706C211yesmaximal, characteristic, complemented
6C2×#11762697C211yesmaximal, characteristic, complemented
7C2×#11762692C211yesmaximal, characteristic, complemented
8C2×#11762690C211yesmaximal, characteristic, complemented
9C2×#11762685C211yesmaximal, characteristic
10C2×#11762684C211yesmaximal, characteristic, complemented
11C2×#11762683C211yesmaximal, characteristic, complemented
12C2×C4×C4⋊Dic17C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic17C211yesmaximal, characteristic, complemented
14C2×C4×#63227C211yesmaximal, characteristic, complemented
15C2×#95×D17C211yesmaximal, characteristic, complemented
16C2×C17×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D17C2211yescharacteristic
18C24×Dic17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C23×C4×D17C2211yescharacteristic
21C23×C4×D17C2211yescharacteristic
22C2×#10587569C4116yescomplemented
23C2×#10587569C2218yes—
24C2×#10587567—28no—
25C2×#10587567C2218yes—
26C2×#10587578—28no—
27C2×#10587578C2218yescomplemented
28C22×C4⋊Dic17C2211yescharacteristic
29C22×C4⋊Dic17C2211yescharacteristic
30C22×C4⋊Dic17C2211yescharacteristic
31C22×#63225C2211yescharacteristic
32C22×#63225C2211yescharacteristic
33C22×#63225C2211yescharacteristic
34C22×C22⋊Dic17C2211yescharacteristic
35C22×C22⋊Dic17C2211yescharacteristic
36C22×#63227C2211yescharacteristic
37C22×#63227C2211yescharacteristic
38C22×#63227C2211yescharacteristic
39C22×C4×Dic17C2211yescharacteristic
40C22×C4×Dic17C2211yescharacteristic
41C22×C4×Dic17C2211yescharacteristic
42C22×C4×Dic17C2211yescharacteristic
43#11762706C2218yescomplemented
44#11762697C2218yescomplemented
45#11762692C2218yescomplemented
46#11762690C2218yescomplemented
47#11762685C2218yes—
48#11762684C2218yescomplemented
49#11762683C2218yescomplemented
50C4×C4⋊Dic17C2218yescomplemented
51C22⋊C4×Dic17C2218yescomplemented
52C4×#63227C2218yescomplemented
53C2×#10587502C2211yescharacteristic
54C2×#10587502C2211yescharacteristic
55C2×#10587502C2211yescharacteristic
56C2×#10587502C2211yescharacteristic
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59C2×#10587502C2211yescharacteristic
60C2×#10587502C2211yescharacteristic
61#95×D17C2218yescomplemented
62C22×C4⋊C4×C17C2211yescharacteristic
63C22×C22⋊C4×C17C2211yescharacteristic
64C22×C22⋊C4×C17C2211yescharacteristic
65C22×C22⋊C4×C17C2211yescharacteristic
66C22×C42×C17C2211yescharacteristic
67C17×#388C2218yescomplemented
68C2×C17×#95C2211yescharacteristic
69C2×C17×#95C2211yescharacteristic
70C25×C17C2311yescharacteristic
71C24×D17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C22×C22⋊D17—24no—
79C22×C22⋊D17—24no—
80C22×C22⋊D17C2×C418yes—
81C22×C22⋊D17C2314yes—
82C23×Dic17—24no—
83C23×Dic17—24no—
84C23×Dic17—42no—
85C23×Dic17C2311yescharacteristic
86C23×Dic17C2311yescharacteristic
87C23×Dic17C2314yes—
88C23×Dic17C2311yescharacteristic
89C23×Dic17C2311yescharacteristic
90C23×Dic17C2311yescharacteristic
91C23×Dic17C2311yescharacteristic
92C23×Dic17C2311yescharacteristic
93C22×C4×D17—24no—
94C22×C4×D17—24no—
95C22×C4×D17—24no—
96C22×C4×D17—24no—
97C22×C4×D17—24no—
98C22×C4×D17—24no—
99C22×C4×D17—42no—
100C22×C4×D17—42no—
101C22×C4×D17C2×C418yescomplemented
102C22×C4×D17C2314yes—
103C22×C4×D17C2314yes—
104C22×C4×D17C2314yes—
105C2×C4⋊C4×C17—24no—
106C2×C4⋊C4×C17C2314yes—
107C2×C22⋊C4×C17—24no—
108C2×C22⋊C4×C17—24no—
109C2×C22⋊C4×C17C2×C418yescomplemented
110C2×C22⋊C4×C17C2314yes—
111C2×C22⋊C4×C17C2314yes—
112C2×C22⋊C4×C17C2314yes—
113C2×C42×C17—24no—
114C2×C42×C17C2314yes—
115C2×C22⋊Dic17—42no—
116C2×C22⋊Dic17C2×C418yescomplemented
117C2×C22⋊Dic17C2314yes—
118C2×C22⋊Dic17C2314yes—
119C2×#63227—24no—
120C2×#63227C2×C418yescomplemented
121C2×#63227D418yes—
122C2×#63227C2314yes—
123C2×#63227C2314yes—
124C2×#63227C2314yes—
125C2×C4⋊Dic17—24no—
126C2×C4⋊Dic17—24no—
127C2×C4⋊Dic17C2×C418yescomplemented
128C2×C4⋊Dic17C2314yes—
129C2×C4⋊Dic17C2314yes—
130C2×C4⋊Dic17C2314yes—
131C2×#63225—24no—
132C2×#63225—42no—
133C2×#63225C2×C418yescomplemented
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#10587578—232no—
146#10587569C2×C4164yescomplemented
147#10587567—232no—
148C17×#95C2314yes—
149C17×#95C2314yes—
150#10587502C2314yes—
151#10587502C2314yes—
152#10587502C2314yes—
153#10587502C2314yes—
154#10587502C2314yes—
155#10587502C2314yes—
156#10587502C2314yes—
157#10587502C2314yes—
158C24×C17—22no—
159C24×C17—22no—
160C24×C17—22no—
161C24×C17—22no—
162C24×C17—22no—
163C24×C17—22no—
164C24×C17C22×C414yes—
165C24×C17C2412yes—
166C24×C17C2411yescharacteristic
167C23×D17—22no—
168C23×D17—22no—
169C23×D17—22no—
170C23×D17—22no—
171C23×D17C22×C414yes—
172C23×D17C2×D414yes—
173C23×D17#4114yes—
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×C17C22×C414yes—
190C22×C4×C17C22×C414yes—
191C22×C4×C17C2×D414yes—
192C22×C4×C17#4114yes—
193C22×C4×C17C2412yes—
194C22×C4×C17C2412yes—
195C22×C4×C17C2412yes—
196C22×C4×C17C2412yes—
197C22×C4×C17C2412yes—
198C22×C4×C17C2412yes—
199C2×C22⋊D17—232no—
200C2×C22⋊D17—28no—
201C2×C22⋊D17—28no—
202C2×C22⋊D17C22×C4116yes—
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×Dic17—22no—
218C22×Dic17—22no—
219C22×Dic17—28no—
220C22×Dic17—28no—
221C22×Dic17—44no—
222C22×Dic17—416no—
223C22×Dic17C22×C414yes—
224C22×Dic17C22×C414yes—
225C22×Dic17C22×C414yes—
226C22×Dic17C2×D414yes—
227C22×Dic17#4114yes—
228C22×Dic17C2412yes—
229C22×Dic17C2412yes—
230C22×Dic17C2412yes—
231C22×Dic17C2412yes—
232C22×Dic17C2412yes—
233C22×Dic17C2412yes—
234C22×Dic17C2412yes—
235C2×C4×D17—232no—
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—44no—
243C2×C4×D17—44no—
244C2×C4×D17—416no—
245C2×C4×D17—416no—
246C2×C4×D17C22×C4116yescomplemented
247C4⋊C4×C17—28no—
248C22⋊C4×C17—28no—
249C22⋊C4×C17—28no—
250C22⋊C4×C17C22×C4116yescomplemented
251C42×C17—28no—
252C22⋊Dic17—44no—
253C22⋊Dic17C22×C4116yescomplemented
254#63227—28no—
255#63227C22×C4116yescomplemented
256#63227C2×D4116yes—
257C4⋊Dic17—28no—
258C4⋊Dic17—28no—
259C4⋊Dic17C22×C4116yescomplemented
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×C17—28no—
269C23×C17—28no—
270C23×C17—28no—
271C23×C17—22no—
272C23×C17—22no—
273C23×C17—22no—
274C23×C17—22no—
275C23×C17—22no—
276C23×C17—22no—
277C23×C17—44no—
278C23×C17—44no—
279C23×C17—44no—
280C23×C17—44no—
281C23×C17C23×C414yes—
282C23×C17C23×C412yes—
283C23×C17C22×D412yes—
284C23×C17C2×#4112yes—
285C23×C17C2×#4112yes—
286C23×C17C2×#4112yes—
287C23×C17H(5,𝔽2)12yes—
288C23×C172−1+412yes—
289C23×C17C2511yescharacteristic
290C22×D17—28no—
291C22×D17—28no—
292C22×D17—28no—
293C22×D17—28no—
294C22×D17—28no—
295C22×D17—28no—
296C22×D17—22no—
297C22×D17—22no—
298C22×D17—22no—
299C22×D17—22no—
300C22×D17C4×D4116yes—
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—44no—
323C2×C4×C17—44no—
324C2×C4×C17C23×C414yes—
325C2×C4×C17C23×C414yes—
326C2×C4×C17C22×D414yes—
327C2×C4×C17C2×#4114yes—
328C22⋊D17—232no—
329C2×Dic17—28no—
330C2×Dic17—28no—
331C2×Dic17—28no—
332C2×Dic17—28no—
333C2×Dic17—28no—
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—416no—
351C2×Dic17—44no—
352C2×Dic17—44no—
353C2×Dic17C23×C414yes—
354C2×Dic17C23×C414yes—
355C2×Dic17C23×C414yes—
356C2×Dic17C22×D414yes—
357C2×Dic17C2×#4114yes—
358C4×D17—232no—
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×#388D1711yescharacteristic, complemented
368C2×#387—171no—
369C2×#387—171no—
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×C17—24no—
378C22×C17—24no—
379C22×C17—24no—
380C22×C17—416no—
381C22×C17—42no—
382C22×C17—42no—
383C22×C17—42no—
384C22×C17—42no—
385C22×C17C2×C4×D414yes—
386C22×C17C4×#4114yes—
387C22×C17#52014yes—
388C22×C17#54614yes—
389C22×C17#54714yes—
390C22×C17#55114yes—
391C22×C17#55214yes—
392C22×C17C24×C411yescharacteristic
393C22×C17C23×D411yescharacteristic
394C22×C17C22×#4111yescharacteristic
395C22×C17C22×#4111yescharacteristic
396C22×C17C22×#4111yescharacteristic
397C22×C17C2×H(5,𝔽2)11yescharacteristic
398C22×C17C2×2−1+411yescharacteristic
399C2×D17—232no—
400C2×D17—24no—
401C2×D17—24no—
402C2×D17—24no—
403C2×D17—24no—
404C2×D17—24no—
405C2×D17—24no—
406C2×D17C2×C4×D418yes—
407C4×C17—24no—
408C4×C17—24no—
409C4×C17—24no—
410C4×C17—24no—
411C4×C17—42no—
412C4×C17—42no—
413Dic17—24no—
414Dic17—24no—
415Dic17—24no—
416Dic17—24no—
417Dic17—24no—
418Dic17—42no—
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⋊C4—171no—
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⋊C4C2×D1711yescharacteristic
444C22×C22⋊C4C2×D1711yescharacteristic
445C22×C22⋊C4C2×D1711yescharacteristic
446C22×C42—171no—
447C22×C42—171no—
448C22×C42—171no—
449C22×C42—171no—
450C22×C42C2×D1711yescharacteristic
451#389—178no—
452#388—178no—
453#388C2×D1718yescomplemented
454#387—178no—
455#387—178no—
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—171no—
469C2×#95—171no—
470C2×#95—178no—
471C2×#95C2×D1711yescharacteristic
472C2×#95C2×D1711yescharacteristic
473C2×C17—44no—
474C2×C17#235918yescomplemented
475C2×C17C22×C4×D411yescharacteristic
476C2×C17C2×C4×#4111yescharacteristic
477C2×C17C2×#52011yescharacteristic
478C2×C17C2×#54611yescharacteristic
479C2×C17C2×#54711yescharacteristic
480C2×C17C2×#55111yescharacteristic
481C2×C17C2×#55211yescharacteristic
482D17—28no—
483C25—171no—
484C25C22×D1711yescharacteristic
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—171no—
498C23×C4—174no—
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×C4—682no—
510C23×C4—682no—
511C23×C4—682no—
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—178no—
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—344no—
531C2×C4⋊C4—344no—
532C2×C4⋊C4—344no—
533C2×C4⋊C4—682no—
534C2×C4⋊C4C22×D1714yes—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—178no—
538C2×C22⋊C4—174no—
539C2×C22⋊C4—178no—
540C2×C22⋊C4—178no—
541C2×C22⋊C4—174no—
542C2×C22⋊C4—174no—
543C2×C22⋊C4—174no—
544C2×C22⋊C4—174no—
545C2×C22⋊C4—344no—
546C2×C22⋊C4—682no—
547C2×C22⋊C4C4×D1718yescomplemented
548C2×C22⋊C4C22×D1714yes—
549C2×C22⋊C4C22×D1714yes—
550C2×C22⋊C4C22×D1714yes—
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#95—174no—
568#95—174no—
569#95C22×D1714yes—
570#95C22×D1714yes—
571C17C2×#235911yescharacteristic, complemented, Sylow
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—174no—
579C24—174no—
580C24—174no—
581C24—172no—
582C24—342no—
583C24—342no—
584C24—342no—
585C24—342no—
586C24C2×C4×D1714yes—
587C24C23×D1712yes—
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—174no—
608C22×C4—174no—
609C22×C4—174no—
610C22×C4—174no—
611C22×C4—174no—
612C22×C4—172no—
613C22×C4—172no—
614C22×C4—172no—
615C22×C4—172no—
616C22×C4—172no—
617C22×C4—1716no—
618C22×C4—172no—
619C22×C4—172no—
620C22×C4—348no—
621C22×C4—348no—
622C22×C4—3432no—
623C22×C4—348no—
624C22×C4—348no—
625C22×C4—348no—
626C22×C4—348no—
627C22×C4—348no—
628C22×C4—342no—
629C22×C4—342no—
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—342no—
644C22×C4—348no—
645C22×C4—684no—
646C22×C4—684no—
647C22×C4—6816no—
648C22×C4—6816no—
649C22×C4—684no—
650C22×C4—6816no—
651C22×C4C2×C4×D1714yes—
652C22×C4C2×C4×D1714yes—
653C22×C4D4×D1714yes—
654C22×C4#6325414yes—
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—1716no—
664C4⋊C4—348no—
665C4⋊C4—348no—
666C4⋊C4—348no—
667C4⋊C4—684no—
668C22⋊C4—28no—
669C22⋊C4—28no—
670C22⋊C4—1716no—
671C22⋊C4—1716no—
672C22⋊C4—1716no—
673C22⋊C4—348no—
674C22⋊C4—684no—
675C22⋊C4C2×C4×D17116yescomplemented
676C42—28no—
677C42—348no—
678C42—348no—
679C42—348no—
680C42—684no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—1716no—
695C23—174no—
696C23—174no—
697C23—174no—
698C23—348no—
699C23—348no—
700C23—348no—
701C23—348no—
702C23—348no—
703C23—342no—
704C23—342no—
705C23—342no—
706C23—342no—
707C23—348no—
708C23C22×C4×D1714yes—
709C23C22×C4×D1712yes—
710C23C2×D4×D1712yes—
711C23C2×#6325412yes—
712C23#41×D1712yes—
713C23#41×D1712yes—
714C23#1058769612yes—
715C23#1058769712yes—
716C23C24×D1711yescharacteristic
717D4—3432no—
718C2×C4—28no—
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—44no—
737C2×C4—44no—
738C2×C4—174no—
739C2×C4—174no—
740C2×C4—174no—
741C2×C4—174no—
742C2×C4—174no—
743C2×C4—3432no—
744C2×C4—348no—
745C2×C4—348no—
746C2×C4—348no—
747C2×C4—342no—
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—348no—
758C2×C4—348no—
759C2×C4—342no—
760C2×C4—342no—
761C2×C4—342no—
762C2×C4—342no—
763C2×C4—342no—
764C2×C4—342no—
765C2×C4—6816no—
766C2×C4—6816no—
767C2×C4—6816no—
768C2×C4—684no—
769C2×C4—684no—
770C2×C4C22×C4×D1714yes—
771C2×C4C22×C4×D1714yes—
772C2×C4C2×D4×D1714yes—
773C2×C4C2×#6325414yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—42no—
778C22—42no—
779C22—416no—
780C22—42no—
781C22—42no—
782C22—178no—
783C22—344no—
784C22—344no—
785C22—344no—
786C22—344no—
787C22—3432no—
788C22—344no—
789C22—344no—
790C22C4×D4×D1714yes—
791C22C4×#6325414yes—
792C22#1176328914yes—
793C22#1176345214yes—
794C22#1176345914yes—
795C22#1176348214yes—
796C22#1176349514yes—
797C22C23×C4×D1711yescharacteristic
798C22C22×D4×D1711yescharacteristic
799C22C2×#41×D1711yescharacteristic
800C22C2×#41×D1711yescharacteristic
801C22C22×#6325411yescharacteristic
802C22C2×#1058769611yescharacteristic
803C22C2×#1058769711yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—42no—
809C4—42no—
810C4—344no—
811C4—344no—
812C4—344no—
813C4—344no—
814C4—344no—
815C4—682no—
816C4—682no—
817C2—44no—
818C2—348no—
819C2#1453177518yesdirect product factor
820C2C2×C4×D4×D1711yescharacteristic
821C2C2×C4×#6325411yescharacteristic
822C2C2×#1176328911yescharacteristic
823C2C2×#1176345211yescharacteristic
824C2C2×#1176345911yescharacteristic
825C2C2×#1176348211yescharacteristic
826C2C2×#1176349511yescharacteristic
subgroupG/H
centerC24C23×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC2×C17×#388C2
socleC24×C17C24
prime radicalC23×C22⋊D17C22
cosocleC23×C17C25
hypercenterC2×#388D17
hypocenterC17C2×#2359
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C22×#10587578C2semidirect
4. #14531775C2direct (N × H)
5. C2×#11762706C2semidirect
6. C2×#11762697C2semidirect
7. C2×#11762692C2semidirect
8. C2×#11762690C2semidirect
10. C2×#11762684C2semidirect
11. C2×#11762683C2semidirect
12. C2×C4×C4⋊Dic17C2semidirect
13. C2×C22⋊C4×Dic17C2semidirect
14. C2×C4×#63227C2semidirect
15. C2×#95×D17C2semidirect
16. C2×C17×#388C2semidirect
22. C2×#10587569C4semidirect
27. C2×#10587578C22semidirect
43. #11762706C22semidirect
44. #11762697C22semidirect
45. #11762692C22semidirect
46. #11762690C22semidirect
48. #11762684C22semidirect
49. #11762683C22semidirect
50. C4×C4⋊Dic17C22semidirect
51. C22⋊C4×Dic17C22semidirect
52. C4×#63227C22semidirect
61. #95×D17C22semidirect
67. C17×#388C22semidirect
101. C22×C4×D17C2×C4semidirect
109. C2×C22⋊C4×C17C2×C4semidirect
116. C2×C22⋊Dic17C2×C4semidirect
120. C2×#63227C2×C4semidirect
127. C2×C4⋊Dic17C2×C4semidirect
133. C2×#63225C2×C4semidirect
146. #10587569C2×C4semidirect
246. C2×C4×D17C22×C4semidirect
250. C22⋊C4×C17C22×C4semidirect
253. C22⋊Dic17C22×C4semidirect
255. #63227C22×C4semidirect
259. C4⋊Dic17C22×C4semidirect
262. #63225C22×C4semidirect
367. C2×#388D17semidirect
453. #388C2×D17semidirect
474. C2×C17#2359semidirect
547. C2×C22⋊C4C4×D17semidirect
571. C17C2×#2359semidirect
675. C22⋊C4C2×C4×D17semidirect
819. C2#14531775direct (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×#105875672
C22×#105875782
#145317752
C2×#117627062
C2×#117626972
C2×#117626922
C2×#117626902
C2×#117626852
C2×#117626842
C2×#117626832
C2×C4×C4⋊Dic172
C2×C22⋊C4×Dic172
C2×C4×#632272
C2×#95×D172
C2×C17×#3882
C2×#235917