Finite Group Databasebeta

← C2×#14531784 #17193836

Subgroups — C2×#14531784 #17193836

Order 4352.

3614 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587564C211yesmaximal, characteristic
2C22×#10587573C211yesmaximal, characteristic, complemented
3C23×#63225C211yesmaximal, characteristic
4#14531784C2116yesmaximal, direct product factor
5C2×#11762713C211yesmaximal, characteristic, complemented
6C2×#11762705C211yesmaximal, characteristic, complemented
7C2×#11762704C211yesmaximal, characteristic, complemented
8C2×#11762704C211yesmaximal, characteristic, complemented
9C2×#11762694C211yesmaximal, characteristic, complemented
10C2×#11762691C211yesmaximal, characteristic, complemented
11C2×#11762681C211yesmaximal, characteristic
12C2×#11762660C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic17C211yesmaximal, characteristic
14C2×C22⋊C4×Dic17C211yesmaximal, characteristic
15C2×C4×C22⋊Dic17C211yesmaximal, characteristic
16C2×C17×#385C211yesmaximal, characteristic
17C23×Dic34C2211yescharacteristic
18C24×Dic17C2211yescharacteristic
19C24×Dic17C2211yescharacteristic
20C2×#10587564C4116yescomplemented
21C2×#10587564C2218yes—
22C2×#10587573—28no—
23C2×#10587573C2218yescomplemented
24C22×C4⋊Dic17C2211yescharacteristic
25C22×#63225—28no—
26C22×#63225C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C22×#63225C2211yescharacteristic
29C22×#63225C2218yes—
30C22×#63225C2211yescharacteristic
31C22×#63225C2211yescharacteristic
32C22×#63225C2211yescharacteristic
33C22×#63225C2211yescharacteristic
34C22×#63225C2211yescharacteristic
35C22×C22⋊Dic17C2211yescharacteristic
36C22×C22⋊Dic17C2211yescharacteristic
37C22×C4×Dic17C2211yescharacteristic
38C22×C4×Dic17C2211yescharacteristic
39C22×C4×Dic17C2211yescharacteristic
40C22×C4×Dic17C2211yescharacteristic
41C22×C4×Dic17C2211yescharacteristic
42C22×C4×Dic17C2211yescharacteristic
43#11762713C2218yescomplemented
44#11762705C2218yescomplemented
45#11762704C2218yescomplemented
46#11762704C2218yescomplemented
47#11762694C2218yescomplemented
48#11762691C2218yescomplemented
49#11762681C2218yes—
50#11762660C2218yescomplemented
51C22⋊C4×Dic17C2218yes—
52C22⋊C4×Dic17C2218yes—
53C4×C22⋊Dic17C2218yes—
54C2×#10587502C2211yescharacteristic
55C2×#10587502C2211yescharacteristic
56C2×#10587502C2211yescharacteristic
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59C2×#10587502C2211yescharacteristic
60C2×#10587502C2211yescharacteristic
61C2×#10587502C2211yescharacteristic
62C24×C4×C17C2211yescharacteristic
63C22×C4⋊C4×C17C2211yescharacteristic
64C22×C4⋊C4×C17C2211yescharacteristic
65C22×C22⋊C4×C17C2211yescharacteristic
66C22×C22⋊C4×C17C2211yescharacteristic
67C17×#385C2218yes—
68C2×C17×#95C2211yescharacteristic
69C2×C17×#95C2211yescharacteristic
70C25×C17C2311yescharacteristic
71C23×C4×C17—24no—
72C23×C4×C17—24no—
73C23×C4×C17—42no—
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C23×C4×C17C2314yes—
78C23×C4×C17C2311yescharacteristic
79C23×C4×C17C2311yescharacteristic
80C23×C4×C17C2311yescharacteristic
81C23×Dic17—24no—
82C23×Dic17—24no—
83C23×Dic17—24no—
84C23×Dic17—24no—
85C23×Dic17—42no—
86C23×Dic17C2×C418yes—
87C23×Dic17C2311yescharacteristic
88C23×Dic17C2314yes—
89C23×Dic17C2311yescharacteristic
90C23×Dic17C2311yescharacteristic
91C23×Dic17C2311yescharacteristic
92C23×Dic17C2314yes—
93C23×Dic17C2311yescharacteristic
94C23×Dic17C2311yescharacteristic
95C23×Dic17C2311yescharacteristic
96C23×Dic17C2311yescharacteristic
97C22×Dic34—24no—
98C22×Dic34—24no—
99C22×Dic34C2×C418yescomplemented
100C22×Dic34C2314yes—
101C2×C4⋊C4×C17—24no—
102C2×C4⋊C4×C17—42no—
103C2×C4⋊C4×C17C2314yes—
104C2×C4⋊C4×C17C2314yes—
105C2×C22⋊C4×C17—24no—
106C2×C22⋊C4×C17C2×C418yes—
107C2×C22⋊C4×C17C2314yes—
108C2×C22⋊C4×C17C2314yes—
109C2×C22⋊Dic17C2×C418yes—
110C2×C22⋊Dic17Q818yescomplemented
111C2×C22⋊Dic17C2314yes—
112C2×C22⋊Dic17C2314yes—
113C2×C4⋊Dic17C2×C418yescomplemented
114C2×C4⋊Dic17C2314yes—
115C2×#63225—232no—
116C2×#63225—24no—
117C2×#63225—24no—
118C2×#63225—24no—
119C2×#63225—24no—
120C2×#63225—42no—
121C2×#63225C2×C418yescomplemented
122C2×#63225C2×C418yescomplemented
123C2×#63225D418yes—
124C2×#63225C2314yes—
125C2×#63225C2314yes—
126C2×#63225C2314yes—
127C2×#63225C2314yes—
128C2×#63225C2314yes—
129C2×#63225C2314yes—
130C2×#63225C2314yes—
131C2×#63225C2314yes—
132C2×C4×Dic17—24no—
133C2×C4×Dic17—24no—
134C2×C4×Dic17—24no—
135C2×C4×Dic17—24no—
136C2×C4×Dic17—42no—
137C2×C4×Dic17—42no—
138C2×C4×Dic17C2314yes—
139C2×C4×Dic17C2314yes—
140C2×C4×Dic17C2314yes—
141C2×C4×Dic17C2314yes—
142C2×C4×Dic17C2314yes—
143C2×C4×Dic17C2314yes—
144#10587573—232no—
145#10587564C2×C4164yescomplemented
146C17×#95C2314yes—
147C17×#95C2314yes—
148#10587502C2314yes—
149#10587502C2314yes—
150#10587502C2314yes—
151#10587502C2314yes—
152#10587502C2314yes—
153#10587502C2314yes—
154#10587502C2314yes—
155#10587502C2314yes—
156C24×C17—22no—
157C24×C17—22no—
158C24×C17—22no—
159C24×C17—22no—
160C24×C17C22×C414yes—
161C24×C17C2×Q814yes—
162C24×C17#4114yes—
163C24×C17C2412yes—
164C24×C17C2411yescharacteristic
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—28no—
174C22×C4×C17—22no—
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—28no—
182C22×C4×C17—44no—
183C22×C4×C17—416no—
184C22×C4×C17C22×C414yes—
185C22×C4×C17C22×C414yes—
186C22×C4×C17C2×D414yes—
187C22×C4×C17C2412yes—
188C22×C4×C17C2412yes—
189C22×C4×C17C2412yes—
190C22×C4×C17C2412yes—
191C22×C4×C17C2412yes—
192C22×C4×C17C2412yes—
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×Dic17—22no—
205C22×Dic17—232no—
206C22×Dic17—28no—
207C22×Dic17—28no—
208C22×Dic17—22no—
209C22×Dic17—28no—
210C22×Dic17—22no—
211C22×Dic17—22no—
212C22×Dic17—28no—
213C22×Dic17—44no—
214C22×Dic17—416no—
215C22×Dic17C22×C414yes—
216C22×Dic17C22×C4116yes—
217C22×Dic17C22×C414yes—
218C22×Dic17C22×C414yes—
219C22×Dic17C22×C414yes—
220C22×Dic17C2×D414yes—
221C22×Dic17C2×D414yes—
222C22×Dic17C2×Q814yes—
223C22×Dic17C2×Q814yes—
224C22×Dic17#4114yes—
225C22×Dic17C2412yes—
226C22×Dic17C2412yes—
227C22×Dic17C2412yes—
228C22×Dic17C2412yes—
229C22×Dic17C2412yes—
230C22×Dic17C2412yes—
231C22×Dic17C2412yes—
232C22×Dic17C2412yes—
233C2×Dic34—232no—
234C2×Dic34—28no—
235C2×Dic34—28no—
236C2×Dic34C22×C4116yescomplemented
237C4⋊C4×C17—28no—
238C4⋊C4×C17—44no—
239C22⋊C4×C17—28no—
240C22⋊C4×C17C22×C4116yes—
241C22⋊Dic17C22×C4116yes—
242C22⋊Dic17C2×Q8116yescomplemented
243C4⋊Dic17C22×C4116yescomplemented
244#63225—28no—
245#63225—28no—
246#63225—28no—
247#63225—28no—
248#63225—44no—
249#63225C22×C4116yescomplemented
250#63225C22×C4116yescomplemented
251#63225C2×D4116yes—
252C4×Dic17—28no—
253C4×Dic17—28no—
254C4×Dic17—28no—
255C4×Dic17—28no—
256C4×Dic17—44no—
257C4×Dic17—44no—
258C2×#2360—171nomaximal, Sylow
259C23×C17—28no—
260C23×C17—28no—
261C23×C17—28no—
262C23×C17—28no—
263C23×C17—28no—
264C23×C17—28no—
265C23×C17—22no—
266C23×C17—22no—
267C23×C17—22no—
268C23×C17—22no—
269C23×C17C4×Q8116yescomplemented
270C23×C17C23×C414yes—
271C23×C17C23×C412yes—
272C23×C17C22×D412yes—
273C23×C17C22×Q814yes—
274C23×C17C22×Q812yes—
275C23×C17C2×#4114yes—
276C23×C17C2×#4112yes—
277C23×C17C2×#4112yes—
278C23×C17H(5,𝔽2)12yes—
279C23×C172−1+412yes—
280C23×C17C2511yescharacteristic
281C2×C4×C17—28no—
282C2×C4×C17—28no—
283C2×C4×C17—28no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
295C2×C4×C17—22no—
296C2×C4×C17—22no—
297C2×C4×C17—22no—
298C2×C4×C17—22no—
299C2×C4×C17—416no—
300C2×C4×C17—44no—
301C2×C4×C17—44no—
302C2×C4×C17—44no—
303C2×C4×C17C23×C414yes—
304C2×C4×C17C23×C414yes—
305C2×C4×C17C22×D414yes—
306C2×Dic17—28no—
307C2×Dic17—28no—
308C2×Dic17—28no—
309C2×Dic17—28no—
310C2×Dic17—28no—
311C2×Dic17—28no—
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—22no—
322C2×Dic17—22no—
323C2×Dic17—22no—
324C2×Dic17—232no—
325C2×Dic17—22no—
326C2×Dic17—22no—
327C2×Dic17—22no—
328C2×Dic17—416no—
329C2×Dic17—44no—
330C2×Dic17C4×D4116yes—
331C2×Dic17C23×C414yes—
332C2×Dic17C23×C414yes—
333C2×Dic17C23×C414yes—
334C2×Dic17C23×C414yes—
335C2×Dic17C22×D414yes—
336C2×Dic17C22×D414yes—
337C2×Dic17C22×Q814yes—
338C2×Dic17C22×Q814yes—
339C2×Dic17C2×#4114yes—
340Dic34—232no—
341C22×C22⋊Q8—171no—
342C22×C4×Q8—171no—
343C23×C4⋊C4—171no—
344#2360—1716no—
345C2×#391—171no—
346C2×#389—171no—
347C2×#389—171no—
348C2×#389—171no—
349C2×#387—171no—
350C2×#387—171no—
351C2×#385—171no—
352C2×#385D1711yescharacteristic
353C2×C4×C4⋊C4—171no—
354C2×C4×C22⋊C4—171no—
355C2×C4×C22⋊C4—171no—
356C2×C4×C22⋊C4—171no—
357C22×C17—232no—
358C22×C17—24no—
359C22×C17—24no—
360C22×C17—24no—
361C22×C17—24no—
362C22×C17—24no—
363C22×C17—24no—
364C22×C17C2×C4×D414yes—
365C22×C17C2×C4×Q814yes—
366C22×C17C2×C4×Q818yescomplemented
367C22×C17#52014yes—
368C22×C17#54614yes—
369C22×C17D4×Q814yes—
370C22×C17#55214yes—
371C22×C17#55414yes—
372C22×C17C24×C411yescharacteristic
373C22×C17C23×D411yescharacteristic
374C22×C17C23×Q811yescharacteristic
375C22×C17C22×#4111yescharacteristic
376C22×C17C22×#4111yescharacteristic
377C22×C17C2×H(5,𝔽2)11yescharacteristic
378C22×C17C2×2−1+411yescharacteristic
379C4×C17—24no—
380C4×C17—24no—
381C4×C17—24no—
382C4×C17—42no—
383C4×C17—42no—
384C4×C17—42no—
385Dic17—24no—
386Dic17—24no—
387Dic17—24no—
388Dic17—24no—
389Dic17—24no—
390Dic17—24no—
391Dic17—42no—
392Dic17C2×C4×D418yes—
393C23×Q8—171no—
394C24×C4—171no—
395C24×C4—171no—
396C24×C4C2×D1711yescharacteristic
397C2×C22⋊Q8—1716no—
398C2×C22⋊Q8—178no—
399C2×C4×Q8—178no—
400C2×C4×Q8—348no—
401C22×C4⋊C4—171no—
402C22×C4⋊C4—171no—
403C22×C4⋊C4—171no—
404C22×C4⋊C4—171no—
405C22×C4⋊C4—178no—
406C22×C4⋊C4—171no—
407C22×C4⋊C4—171no—
408C22×C4⋊C4—171no—
409C22×C4⋊C4—171no—
410C22×C4⋊C4—171no—
411C22×C4⋊C4—348no—
412C22×C4⋊C4C2×D1711yescharacteristic
413C22×C4⋊C4C2×D1711yescharacteristic
414C22×C22⋊C4—171no—
415C22×C22⋊C4—171no—
416C22×C22⋊C4C2×D1711yescharacteristic
417C22×C22⋊C4C2×D1711yescharacteristic
418C22×C42—171no—
419C22×C42—171no—
420C22×C42—171no—
421C22×C42—171no—
422C22×C42—171no—
423C22×C42—171no—
424#391—178no—
425#389—178no—
426#389—178no—
427#389—178no—
428#387—178no—
429#387—178no—
430#385—178no—
431#385C2×D1718yes—
432C4×C4⋊C4—178no—
433C4×C22⋊C4—178no—
434C4×C22⋊C4—178no—
435C4×C22⋊C4—178no—
436C2×#95—171no—
437C2×#95—171no—
438C2×#95—171no—
439C2×#95—171no—
440C2×#95—171no—
441C2×#95—171no—
442C2×#95—171no—
443C2×#95—171no—
444C2×#95C2×D1711yescharacteristic
445C2×#95C2×D1711yescharacteristic
446C2×C17—28no—
447C2×C17#236018yescomplemented
448C2×C17C22×C4×D411yescharacteristic
449C2×C17C22×C4×Q811yescharacteristic
450C2×C17C2×#52011yescharacteristic
451C2×C17C2×#54611yescharacteristic
452C2×C17C2×D4×Q811yescharacteristic
453C2×C17C2×#55211yescharacteristic
454C2×C17C2×#55411yescharacteristic
455C25C22×D1711yescharacteristic
456C22×Q8—178no—
457C22×Q8—174no—
458C22×Q8—344no—
459C22×Q8—344no—
460C23×C4—24no—
461C23×C4—24no—
462C23×C4—42no—
463C23×C4—171no—
464C23×C4—178no—
465C23×C4—174no—
466C23×C4—171no—
467C23×C4—171no—
468C23×C4—171no—
469C23×C4—171no—
470C23×C4—171no—
471C23×C4—171no—
472C23×C4—171no—
473C23×C4—174no—
474C23×C4—344no—
475C23×C4—344no—
476C23×C4—344no—
477C23×C4—344no—
478C23×C4—682no—
479C23×C4C22×D1711yescharacteristic
480C23×C4C22×D1711yescharacteristic
481C23×C4C22×D1711yescharacteristic
482C23×C4C22×D1714yes—
483C23×C4C22×D1711yescharacteristic
484C23×C4C22×D1711yescharacteristic
485C23×C4C22×D1711yescharacteristic
486C22⋊Q8—1764no—
487C4×Q8—3432no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—42no—
490C2×C4⋊C4—178no—
491C2×C4⋊C4—178no—
492C2×C4⋊C4—178no—
493C2×C4⋊C4—178no—
494C2×C4⋊C4—174no—
495C2×C4⋊C4—174no—
496C2×C4⋊C4—174no—
497C2×C4⋊C4—174no—
498C2×C4⋊C4—174no—
499C2×C4⋊C4—174no—
500C2×C4⋊C4—174no—
501C2×C4⋊C4—174no—
502C2×C4⋊C4—174no—
503C2×C4⋊C4—3432no—
504C2×C4⋊C4—344no—
505C2×C4⋊C4—344no—
506C2×C4⋊C4—344no—
507C2×C4⋊C4—344no—
508C2×C4⋊C4—682no—
509C2×C4⋊C4C22×D1714yes—
510C2×C4⋊C4C22×D1714yes—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—178no—
513C2×C22⋊C4—178no—
514C2×C22⋊C4—174no—
515C2×C22⋊C4—174no—
516C2×C22⋊C4C4×D1718yes—
517C2×C22⋊C4C22×D1714yes—
518C2×C22⋊C4C22×D1714yes—
519C2×C42—174no—
520C2×C42—174no—
521C2×C42—174no—
522C2×C42—174no—
523C2×C42—174no—
524C2×C42—174no—
525C2×C42—344no—
526C2×C42—344no—
527C2×C42—344no—
528C2×C42—344no—
529C2×C42—682no—
530C2×C42—682no—
531#95—174no—
532#95—174no—
533#95—174no—
534#95—174no—
535#95—174no—
536#95—174no—
537#95—174no—
538#95—174no—
539#95C22×D1714yes—
540#95C22×D1714yes—
541C17C2×#236011yescharacteristic, complemented, Sylow
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24C2×C4×D1714yes—
547C24#6325414yes—
548C24Q8×D1714yes—
549C24C23×D1712yes—
550C24C23×D1711yescharacteristic
551C2×Q8—1716no—
552C2×Q8—348no—
553C2×Q8—3432no—
554C2×Q8—348no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—28no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—28no—
572C22×C4—44no—
573C22×C4—416no—
574C22×C4—174no—
575C22×C4—174no—
576C22×C4—174no—
577C22×C4—172no—
578C22×C4—174no—
579C22×C4—174no—
580C22×C4—174no—
581C22×C4—1716no—
582C22×C4—174no—
583C22×C4—174no—
584C22×C4—174no—
585C22×C4—172no—
586C22×C4—172no—
587C22×C4—172no—
588C22×C4—172no—
589C22×C4—172no—
590C22×C4—172no—
591C22×C4—172no—
592C22×C4—348no—
593C22×C4—3432no—
594C22×C4—348no—
595C22×C4—348no—
596C22×C4—342no—
597C22×C4—342no—
598C22×C4—342no—
599C22×C4—342no—
600C22×C4—342no—
601C22×C4—342no—
602C22×C4—342no—
603C22×C4—342no—
604C22×C4—342no—
605C22×C4—342no—
606C22×C4—342no—
607C22×C4—342no—
608C22×C4—342no—
609C22×C4—348no—
610C22×C4—342no—
611C22×C4—342no—
612C22×C4—684no—
613C22×C4—6816no—
614C22×C4C2×C4×D1714yes—
615C22×C4C2×C4×D1714yes—
616C22×C4D4×D1714yes—
617C22×C4C23×D1712yes—
618C22×C4C23×D1712yes—
619C22×C4C23×D1712yes—
620C22×C4C23×D1712yes—
621C22×C4C23×D1712yes—
622C22×C4C23×D1712yes—
623C4⋊C4—28no—
624C4⋊C4—44no—
625C4⋊C4—1716no—
626C4⋊C4—1716no—
627C4⋊C4—1716no—
628C4⋊C4—1716no—
629C4⋊C4—348no—
630C4⋊C4—348no—
631C4⋊C4—348no—
632C4⋊C4—348no—
633C4⋊C4—684no—
634C22⋊C4—28no—
635C22⋊C4—1716no—
636C22⋊C4—1716no—
637C22⋊C4C2×C4×D17116yes—
638C42—348no—
639C42—348no—
640C42—348no—
641C42—348no—
642C42—684no—
643C42—684no—
644C23—28no—
645C23—28no—
646C23—28no—
647C23—28no—
648C23—28no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—28no—
654C23#10587573116yescomplemented
655C23C22×C4×D1714yes—
656C23C22×C4×D1712yes—
657C23C2×D4×D1712yes—
658C23C2×#6325414yes—
659C23C2×#6325412yes—
660C23#1058769112yes—
661C23C2×Q8×D1714yes—
662C23C2×Q8×D1712yes—
663C23#41×D1712yes—
664C23#1058769712yes—
665C23C24×D1711yescharacteristic
666Q8—3432no—
667C2×C4—28no—
668C2×C4—28no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—28no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—416no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—1716no—
690C2×C4—174no—
691C2×C4—174no—
692C2×C4—174no—
693C2×C4—174no—
694C2×C4—174no—
695C2×C4—174no—
696C2×C4—174no—
697C2×C4—174no—
698C2×C4—174no—
699C2×C4—3432no—
700C2×C4—348no—
701C2×C4—348no—
702C2×C4—348no—
703C2×C4—348no—
704C2×C4—348no—
705C2×C4—342no—
706C2×C4—342no—
707C2×C4—342no—
708C2×C4—342no—
709C2×C4—342no—
710C2×C4—342no—
711C2×C4—342no—
712C2×C4—342no—
713C2×C4—342no—
714C2×C4—342no—
715C2×C4—342no—
716C2×C4—342no—
717C2×C4—348no—
718C2×C4—342no—
719C2×C4—342no—
720C2×C4—342no—
721C2×C4—6816no—
722C2×C4—684no—
723C2×C4C22×C4×D1714yes—
724C2×C4C22×C4×D1714yes—
725C2×C4C2×D4×D1714yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—232no—
731C22—24no—
732C22—24no—
733C22C4×D4×D1714yes—
734C22C2×#1058757314yes—
735C22C2×#1058757318yescomplemented
736C22#1176328814yes—
737C22#1176344614yes—
738C22#1176347214yes—
739C22#1176349614yes—
740C22#1176351314yes—
741C22C23×C4×D1711yescharacteristic
742C22C22×D4×D1711yescharacteristic
743C22C22×Q8×D1711yescharacteristic
744C22C2×#41×D1711yescharacteristic
745C22C22×#6325411yescharacteristic
746C22C2×#1058769111yescharacteristic
747C22C2×#1058769711yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—178no—
755C4—344no—
756C4—344no—
757C4—344no—
758C4—344no—
759C4—344no—
760C4—344no—
761C4—682no—
762C2—28no—
763C2#1453178418yesdirect product factor
764C2C2×C4×D4×D1711yescharacteristic
765C2C22×#1058757311yescharacteristic
766C2C2×#1176328811yescharacteristic
767C2C2×#1176344611yescharacteristic
768C2C2×#1176347211yescharacteristic
769C2C2×#1176349611yescharacteristic
770C2C2×#1176351311yescharacteristic
subgroupG/H
centerC24C23×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC2×C17×#385C2
socleC24×C17C24
prime radicalC25×C17C23
cosocleC23×C17C25
hypercenterC2×#385D17
hypocenterC17C2×#2360
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#10587573C2semidirect
4. #14531784C2direct (N × H)
5. C2×#11762713C2semidirect
6. C2×#11762705C2semidirect
7. C2×#11762704C2semidirect
8. C2×#11762704C2semidirect
9. C2×#11762694C2semidirect
10. C2×#11762691C2semidirect
12. C2×#11762660C2semidirect
20. C2×#10587564C4semidirect
23. C2×#10587573C22semidirect
43. #11762713C22semidirect
44. #11762705C22semidirect
45. #11762704C22semidirect
46. #11762704C22semidirect
47. #11762694C22semidirect
48. #11762691C22semidirect
50. #11762660C22semidirect
99. C22×Dic34C2×C4semidirect
110. C2×C22⋊Dic17Q8semidirect
113. C2×C4⋊Dic17C2×C4semidirect
121. C2×#63225C2×C4semidirect
122. C2×#63225C2×C4semidirect
145. #10587564C2×C4semidirect
236. C2×Dic34C22×C4semidirect
242. C22⋊Dic17C2×Q8semidirect
243. C4⋊Dic17C22×C4semidirect
249. #63225C22×C4semidirect
250. #63225C22×C4semidirect
269. C23×C17C4×Q8semidirect
366. C22×C17C2×C4×Q8semidirect
447. C2×C17#2360semidirect
541. C17C2×#2360semidirect
654. C23#10587573semidirect
735. C22C2×#10587573semidirect
763. C2#14531784direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875642
C22×#105875732
C23×#632252
#145317842
C2×#117627132
C2×#117627052
C2×#117627042
C2×#117626942
C2×#117626912
C2×#117626812
C2×#117626602
C2×C22⋊C4×Dic172
C2×C4×C22⋊Dic172
C2×C17×#3852
C2×#236017