Finite Group Databasebeta

← C2×#14540889 #17910908

Subgroups — C2×#14540889 #17910908

Order 4352.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763468C211yesmaximal, characteristic
2#14540889C2116yesmaximal, direct product factor
3C2×#11763171C211yesmaximal, characteristic, complemented
4C2×#11763127C211yesmaximal, characteristic, complemented
5C2×#11763139C211yesmaximal, characteristic, complemented
6C2×#11763091C211yesmaximal, characteristic, complemented
7C2×#11763065C211yesmaximal, characteristic, complemented
8C2×#11763040C211yesmaximal, characteristic, complemented
9C2×#11763031C211yesmaximal, characteristic, complemented
10C2×#11762969C211yesmaximal, characteristic, complemented
11C2×#11762964C211yesmaximal, characteristic, complemented
12C2×#11762914C211yesmaximal, characteristic, complemented
13C2×#11762881C211yesmaximal, characteristic, complemented
14C2×#11762808C211yesmaximal, characteristic, complemented
15C22×#10587481C211yesmaximal, characteristic, complemented
16C2×C17×#554C211yesmaximal, characteristic, complemented
17C22×#63252C2211yescharacteristic
18C23×Dic34C2211yescharacteristic
19C22×#63231C2211yescharacteristic
20C22×#63231C2211yescharacteristic
21C22×#63230C2211yescharacteristic
22C22×#63223C2211yescharacteristic
23C23×#3622C2211yescharacteristic
24#11763468—24no—
25#11763468C2218yes—
26C2×#10587561C2211yescharacteristic
27C2×#10587571—21no—
28C2×#10587610C2211yescharacteristic
29C2×#10587582—21no—
30C2×#10587616C2211yescharacteristic
31C2×#10587625—21no—
32C2×C4×Dic34C2211yescharacteristic
33C2×#10587567—21no—
34#11763171C2218yescomplemented
35#11763139C2218yescomplemented
36#11763127C2218yescomplemented
37#11763091C2218yescomplemented
38#11763065C2218yescomplemented
39#11763040C2218yescomplemented
40#11763031C2218yescomplemented
41#11762969C2218yescomplemented
42#11762964C2218yescomplemented
43#11762914C2218yescomplemented
44#11762881C2218yescomplemented
45C2×#10587479C2211yescharacteristic
46C2×#10587479C2211yescharacteristic
47C2×#10587479C2211yescharacteristic
48C2×C4⋊#3622C2211yescharacteristic
49#11762808C2218yescomplemented
50C2×#10587506C2211yescharacteristic
51C2×#10587481C2211yescharacteristic
52C2×#10587481C2211yescharacteristic
53C2×#10587481C2211yescharacteristic
54C2×#10587481C2211yescharacteristic
55C2×#10587481C2211yescharacteristic
56C2×#10587481C2211yescharacteristic
57C2×#10587481C2218yescomplemented
58C2×#10587480C2211yescharacteristic
59C2×#10587480C2211yescharacteristic
60C2×#10587480C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×C22⋊#3622C2211yescharacteristic
63C2×#10587474C2211yescharacteristic
64C17×#554—24no—
65C17×#554C2218yescomplemented
66C2×C17×C4⋊Q8C2211yescharacteristic
67C2×C17×#125—21no—
68C2×C17×C22⋊Q8—21no—
69C2×C17×C22⋊Q8—21no—
70C2×C17×C22⋊Q8C2211yescharacteristic
71C2×C17×C22⋊Q8C2211yescharacteristic
72C2×C4×Q8×C17C2211yescharacteristic
73C2×C4×D4×C17—21no—
74C2×C4×D4×C17C2211yescharacteristic
75C22×C4⋊C4×C17C2211yescharacteristic
76C22×C4⋊C4×C17C2211yescharacteristic
77C22×Q8×C17—21no—
78C22×Q8×C17C2311yescharacteristic
79C22×D4×C17D411yescharacteristic
80C23×C4×C17—21no—
81C23×C4×C17—21no—
82C23×C4×C17C2311yescharacteristic
83C23×C4×C17C2311yescharacteristic
84C22×C22⋊D17—21no—
85C22×C22⋊D17—21no—
86C23×Dic17—21no—
87C2×#63252—22no—
88C2×#63252—24no—
89C2×#63252—42no—
90C2×#63252C2314yes—
91C22×D68C2311yescharacteristic
92C22×C4×D17—21no—
93C22×Dic34—24no—
94C22×Dic34—22no—
95C22×Dic34—21no—
96C22×Dic34—42no—
97C22×Dic34C2311yescharacteristic
98C22×Dic34C2314yes—
99C22×Dic34C2311yescharacteristic
100C17×C4⋊Q8—22no—
101C17×C4⋊Q8C2314yes—
102C17×#125—28no—
103C17×C22⋊Q8—22no—
104C17×C22⋊Q8—22no—
105C17×C22⋊Q8—28no—
106C17×C22⋊Q8—28no—
107C17×C22⋊Q8C2314yes—
108C17×C22⋊Q8C2314yes—
109C4×Q8×C17—22no—
110C4×Q8×C17C2314yes—
111C4×D4×C17—28no—
112C4×D4×C17D414yes—
113C4×D4×C17C2314yes—
114C2×C4⋊C4×C17—21no—
115C2×C4⋊C4×C17—21no—
116C2×C4⋊C4×C17—22no—
117C2×C4⋊C4×C17—22no—
118C2×C4⋊C4×C17—21no—
119C2×C4⋊C4×C17—21no—
120C2×C4⋊C4×C17—21no—
121C2×C4⋊C4×C17—21no—
122C2×C4⋊C4×C17D411yescharacteristic
123C2×C4⋊C4×C17C2311yescharacteristic
124C2×C4⋊C4×C17C2311yescharacteristic
125C2×C4⋊C4×C17C2311yescharacteristic
126C2×C4⋊C4×C17C2314yes—
127C2×C4⋊C4×C17C2314yes—
128C2×C22⋊C4×C17—21no—
129C2×C22⋊C4×C17—21no—
130C2×C22⋊C4×C17D411yescharacteristic
131C2×C22⋊C4×C17D411yescharacteristic
132C2×C42×C17—21no—
133C2×C42×C17C2311yescharacteristic
134C2×C22⋊Dic17—21no—
135C2×#63231—24no—
136C2×#63231—42no—
137C2×#63231C2314yes—
138C2×#63231C2314yes—
139C2×#63230—42no—
140C2×#63230C2314yes—
141#10587625—28no—
142#10587616—22no—
143#10587616C2314yes—
144C2×#63227—21no—
145C2×#63227—21no—
146C2×#63227—21no—
147C2×C4⋊Dic17C2311yescharacteristic
148#10587610—22no—
149#10587610C2314yes—
150C2×#63225—21no—
151C2×#63225—21no—
152C2×C4×Dic17—21no—
153C2×#63223—42no—
154C2×#63223C2314yes—
155C22×#3622—42no—
156C22×#3622C2311yescharacteristic
157C22×#3622C2311yescharacteristic
158C22×#3622C2311yescharacteristic
159C22×#3622C2311yescharacteristic
160C22×#3622C2314yes—
161#10587582—28no—
162#10587571—28no—
163#10587567—28no—
164#10587561—22no—
165#10587561C2314yes—
166C4×Dic34—22no—
167C4×Dic34C2314yes—
168#10587506C2314yes—
169C22⋊#3622C2314yes—
170C22⋊#3622C2314yes—
171#10587481C2314yes—
172#10587481C2314yes—
173#10587481C2314yes—
174#10587481C2314yes—
175#10587481C2314yes—
176#10587481C2314yes—
177#10587480C2314yes—
178#10587480C2314yes—
179#10587480C2314yes—
180#10587479C2314yes—
181#10587479C2314yes—
182#10587479C2314yes—
183C4⋊#3622C2314yes—
184#10587474C2314yes—
185C24×C17C2×D411yescharacteristic
186C24×C17C2×D411yescharacteristic
187C23×D17—21no—
188C2×Q8×C17—21no—
189C2×Q8×C17—24no—
190C2×Q8×C17—22no—
191C2×Q8×C17—22no—
192C2×Q8×C17—82no—
193C2×Q8×C17C2412yes—
194C2×D4×C17—24no—
195C2×D4×C17C2×D414yes—
196C22×C4×C17—22no—
197C22×C4×C17—22no—
198C22×C4×C17—22no—
199C22×C4×C17—22no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—24no—
205C22×C4×C17—24no—
206C22×C4×C17—82no—
207C22×C4×C17—82no—
208C22×C4×C17C2×D412yes—
209C22×C4×C17C2×D412yes—
210C22×C4×C17C2×D411yescharacteristic
211C22×C4×C17C2×D411yescharacteristic
212C22×C4×C17C2×D411yescharacteristic
213C22×C4×C17C2×D411yescharacteristic
214C22×C4×C17C2412yes—
215C22×C4×C17C2412yes—
216C22×C4×C17C2411yescharacteristic
217C2×C22⋊D17—24no—
218C2×C22⋊D17—24no—
219C2×C22⋊D17—44no—
220C2×C22⋊D17—44no—
221C22×Dic17—21no—
222C22×Dic17—24no—
223C22×Dic17—21no—
224C22×Dic17—21no—
225C22×Dic17—44no—
226#63252—28no—
227#63252—44no—
228#63252—48no—
229C2×D68—22no—
230C2×D68—22no—
231C2×D68—21no—
232C2×D68C2412yes—
233C2×C4×D17—24no—
234C2×C4×D17—44no—
235C2×Dic34—21no—
236C2×Dic34—22no—
237C2×Dic34—22no—
238C2×Dic34—22no—
239C2×Dic34—28no—
240C2×Dic34—21no—
241C2×Dic34—24no—
242C2×Dic34—44no—
243C2×Dic34—48no—
244C2×Dic34—44no—
245C2×Dic34#4114yes—
246C2×Dic34C2412yes—
247C2×Dic34C2412yes—
248C4⋊C4×C17—24no—
249C4⋊C4×C17—24no—
250C4⋊C4×C17—24no—
251C4⋊C4×C17—24no—
252C4⋊C4×C17—24no—
253C4⋊C4×C17—21no—
254C4⋊C4×C17—21no—
255C4⋊C4×C17—24no—
256C4⋊C4×C17—21no—
257C4⋊C4×C17C2×D414yes—
258C4⋊C4×C17C2412yes—
259C4⋊C4×C17C2412yes—
260C4⋊C4×C17C2412yes—
261C22⋊C4×C17—24no—
262C22⋊C4×C17—24no—
263C22⋊C4×C17C2×D414yes—
264C22⋊C4×C17C2×D414yes—
265C42×C17—24no—
266C42×C17C2×D412yes—
267C42×C17C2412yes—
268C22⋊Dic17—24no—
269#63231—28no—
270#63231—44no—
271#63230—44no—
272#63227—24no—
273#63227—24no—
274#63227—24no—
275C4⋊Dic17—21no—
276C4⋊Dic17C2412yes—
277#63225—24no—
278#63225—24no—
279C4×Dic17—24no—
280#63223—44no—
281C2×#3622—22no—
282C2×#3622—22no—
283C2×#3622—22no—
284C2×#3622—22no—
285C2×#3622—44no—
286C2×#3622C2412yes—
287C2×#3622C2412yes—
288C2×#3622C2412yes—
289C2×#3622C2412yes—
290C2×#3316—171nomaximal, Sylow
291C23×C17—22no—
292C23×C17—22no—
293C23×C17—22no—
294C23×C17—22no—
295C23×C17—22no—
296C23×C17#13714yes—
297C23×C17C22×D412yes—
298C23×C17C22×D412yes—
299C23×C17C22×D411yescharacteristic
300C22×D17—22no—
301C22×D17—42no—
302C22×D17—42no—
303C22×D17—42no—
304Q8×C17—22no—
305Q8×C17—22no—
306Q8×C17—42no—
307Q8×C17—84no—
308D4×C17—28no—
309C2×C4×C17—22no—
310C2×C4×C17—22no—
311C2×C4×C17—22no—
312C2×C4×C17—22no—
313C2×C4×C17—24no—
314C2×C4×C17—24no—
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—42no—
324C2×C4×C17—42no—
325C2×C4×C17—42no—
326C2×C4×C17—42no—
327C2×C4×C17—84no—
328C2×C4×C17—84no—
329C2×C4×C17C22×D412yes—
330C2×C4×C17C22×D412yes—
331C2×C4×C17C22×D412yes—
332C2×C4×C17C22×D412yes—
333C2×C4×C17C22×D411yescharacteristic
334C2×C4×C17C2×#4112yes—
335C2×C4×C17H(5,𝔽2)12yes—
336C2×C4×C17C2511yescharacteristic
337C22⋊D17—48no—
338C22⋊D17—48no—
339C2×Dic17—24no—
340C2×Dic17—22no—
341C2×Dic17—22no—
342C2×Dic17—22no—
343C2×Dic17—48no—
344C2×Dic17—42no—
345C2×Dic17—42no—
346D68—22no—
347D68—22no—
348D68—42no—
349C4×D17—48no—
350Dic34—24no—
351Dic34—22no—
352Dic34—22no—
353Dic34—22no—
354Dic34—48no—
355Dic34—42no—
356Dic34C2×#4114yes—
357#3622—22no—
358#3622—22no—
359#3622—22no—
360#3622—22no—
361C2×#554D1711yescharacteristic, complemented
362C2×#548—171no—
363#3316—1716no—
364C2×#489—171no—
365C2×#481—171no—
366C2×#483—171no—
367C2×#475—171no—
368C2×#470—171no—
369C2×#465—171no—
370C2×#464—171no—
371C2×#452—171no—
372C2×#451—171no—
373C2×#441—171no—
374C2×#435—171no—
375C2×#417—171no—
376C22×#103—171no—
377C22×C17—22no—
378C22×C17—28no—
379C22×C17—22no—
380C22×C17—22no—
381C22×C17—22no—
382C22×C17—22no—
383C22×C17—44no—
384C22×C17#54612yes—
385C22×C17C2×#13714yes—
386C22×C17C2×#13712yes—
387C22×C17#57712yes—
388C22×C17C23×D411yescharacteristic
389C2×D17—42no—
390C2×D17—42no—
391C2×D17—42no—
392C2×D17—84no—
393C4×C17—22no—
394C4×C17—22no—
395C4×C17—22no—
396C4×C17—22no—
397C4×C17—42no—
398C4×C17—42no—
399C4×C17—42no—
400C4×C17—42no—
401C4×C17#54612yes—
402C4×C17C22×#4111yescharacteristic
403C4×C17C2×H(5,𝔽2)11yescharacteristic
404Dic17—24no—
405Dic17—42no—
406Dic17—42no—
407C22×#41—171no—
408C23×Q8—171no—
409C22×Q16—171no—
410C22×Q16—171no—
411C22×SD16—171no—
412C22×M16—171no—
413C23×C8—171no—
414#554—24no—
415#554C2×D1718yescomplemented
416#548—178no—
417#548—344no—
418C2×C4⋊Q8C2×D1711yescharacteristic
419C2×#125—21no—
420C2×#124—171no—
421C2×#124—341no—
422C2×C22⋊Q8—21no—
423C2×C22⋊Q8—21no—
424C2×C22⋊Q8—171no—
425C2×C22⋊Q8—341no—
426C2×C22⋊Q8C2×D1711yescharacteristic
427C2×C22⋊Q8C2×D1711yescharacteristic
428C2×#121—171no—
429C2×#121—341no—
430C2×C4×Q8—171no—
431C2×C4×Q8C2×D1711yescharacteristic
432C2×C4×D4—21no—
433C2×C4×D4—341no—
434C2×C4×D4C2×D1711yescharacteristic
435C22×C4⋊C4C2×D1711yescharacteristic
436C22×C4⋊C4C2×D1711yescharacteristic
437#489—178no—
438#483—178no—
439#481—178no—
440#475—178no—
441#470—178no—
442#465—178no—
443#464—178no—
444#452—178no—
445#451—178no—
446#441—178no—
447#435—178no—
448C2×#106—171no—
449C2×#106—171no—
450C2×#106—171no—
451C2×C4⋊C8—171no—
452#417—178no—
453C2×#103—171no—
454C2×#103—171no—
455C2×#103—171no—
456C2×#103—171no—
457C2×#103—171no—
458C2×#103—171no—
459C2×#103—171no—
460C2×#103—178no—
461C2×#102—171no—
462C2×#102—171no—
463C2×#102—171no—
464C2×C22⋊C8—171no—
465C2×C22⋊C8—171no—
466C2×#97—171no—
467C2×C17—24no—
468C2×C17—42no—
469C2×C17#331614yescomplemented
470C2×C17C2×#54611yescharacteristic
471C2×C17C22×#13711yescharacteristic
472C2×C17C2×#57711yescharacteristic
473D17—82no—
474C2×#41—174no—
475C2×#41—344no—
476C2×#41—342no—
477C2×#41—682no—
478C22×Q8—21no—
479C22×Q8—171no—
480C22×Q8—171no—
481C22×Q8—174no—
482C22×Q8—344no—
483C22×Q8—341no—
484C22×Q8—342no—
485C22×Q8—682no—
486C22×Q8C22×D1711yescharacteristic
487C22×D4—171no—
488C22×D4—341no—
489C22×D4—341no—
490C22×D4C22⋊D1711yescharacteristic
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—341no—
494C23×C4—341no—
495C23×C4C22×D1711yescharacteristic
496C23×C4C22×D1711yescharacteristic
497C2×Q16—174no—
498C2×Q16—174no—
499C2×Q16—344no—
500C2×Q16—682no—
501C2×SD16—174no—
502C2×SD16—682no—
503C2×M16—174no—
504C2×M16—682no—
505C22×C8—171no—
506C22×C8—171no—
507C22×C8—171no—
508C22×C8—171no—
509C22×C8—174no—
510C22×C8—682no—
511C4⋊Q8—22no—
512C4⋊Q8C22×D1714yes—
513#125—28no—
514#124—174no—
515#124—348no—
516#124—342no—
517C22⋊Q8—22no—
518C22⋊Q8—22no—
519C22⋊Q8—28no—
520C22⋊Q8—28no—
521C22⋊Q8—174no—
522C22⋊Q8—342no—
523C22⋊Q8—348no—
524C22⋊Q8C22×D1714yes—
525C22⋊Q8C22×D1714yes—
526#121—174no—
527#121—348no—
528#121—342no—
529C4×Q8—22no—
530C4×Q8—174no—
531C4×Q8—342no—
532C4×Q8C22×D1714yes—
533C4×D4—28no—
534C4×D4—348no—
535C4×D4C22⋊D1714yes—
536C4×D4C22×D1714yes—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—22no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—171no—
546C2×C4⋊C4—341no—
547C2×C4⋊C4—341no—
548C2×C4⋊C4C22⋊D1711yescharacteristic
549C2×C4⋊C4C22×D1711yescharacteristic
550C2×C4⋊C4C22×D1711yescharacteristic
551C2×C4⋊C4C22×D1711yescharacteristic
552C2×C4⋊C4C22×D1714yes—
553C2×C4⋊C4C22×D1714yes—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—341no—
557C2×C22⋊C4—341no—
558C2×C22⋊C4—341no—
559C2×C22⋊C4—341no—
560C2×C22⋊C4C22⋊D1711yescharacteristic
561C2×C22⋊C4C22⋊D1711yescharacteristic
562C2×C42—21no—
563C2×C42—341no—
564C2×C42C22×D1711yescharacteristic
565#106—174no—
566#106—174no—
567#106—174no—
568C4⋊C8—174no—
569#103—174no—
570#103—174no—
571#103—174no—
572#103—174no—
573#103—174no—
574#103—174no—
575#103—174no—
576#102—174no—
577#102—174no—
578#102—174no—
579C22⋊C8—174no—
580C22⋊C8—174no—
581#97—174no—
582C17C2×#331611yescharacteristic, complemented, Sylow
583C24—341no—
584C24C2×C22⋊D1711yescharacteristic
585C24C2×C22⋊D1711yescharacteristic
586#41—348no—
587#41—684no—
588#41—688no—
589C2×Q8—21no—
590C2×Q8—24no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—82no—
594C2×Q8—174no—
595C2×Q8—172no—
596C2×Q8—172no—
597C2×Q8—348no—
598C2×Q8—342no—
599C2×Q8—341no—
600C2×Q8—344no—
601C2×Q8—341no—
602C2×Q8—342no—
603C2×Q8—342no—
604C2×Q8—684no—
605C2×Q8—684no—
606C2×Q8—688no—
607C2×Q8C23×D1712yes—
608C2×D4—24no—
609C2×D4—172no—
610C2×D4—344no—
611C2×D4—344no—
612C2×D4—342no—
613C2×D4—342no—
614C2×D4—341no—
615C2×D4—684no—
616C2×D4—684no—
617C2×D4C2×C22⋊D1714yes—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—24no—
627C22×C4—24no—
628C22×C4—82no—
629C22×C4—82no—
630C22×C4—341no—
631C22×C4—344no—
632C22×C4—341no—
633C22×C4—341no—
634C22×C4—344no—
635C22×C4—684no—
636C22×C4—684no—
637C22×C4C2×C22⋊D1712yes—
638C22×C4C2×C22⋊D1712yes—
639C22×C4C2×C22⋊D1711yescharacteristic
640C22×C4C2×C22⋊D1711yescharacteristic
641C22×C4C2×C22⋊D1711yescharacteristic
642C22×C4C2×C22⋊D1711yescharacteristic
643C22×C4C23×D1712yes—
644C22×C4C23×D1712yes—
645C22×C4C23×D1711yescharacteristic
646Q16—348no—
647Q16—684no—
648SD16—684no—
649M16—684no—
650C2×C8—172no—
651C2×C8—172no—
652C2×C8—172no—
653C2×C8—172no—
654C2×C8—342no—
655C2×C8—342no—
656C2×C8—342no—
657C2×C8—342no—
658C2×C8—684no—
659C4⋊C4—21no—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—24no—
665C4⋊C4—24no—
666C4⋊C4—24no—
667C4⋊C4—24no—
668C4⋊C4—172no—
669C4⋊C4—341no—
670C4⋊C4—344no—
671C4⋊C4—344no—
672C4⋊C4C2×C22⋊D1714yes—
673C4⋊C4C23×D1712yes—
674C4⋊C4C23×D1712yes—
675C4⋊C4C23×D1712yes—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—344no—
679C22⋊C4—344no—
680C22⋊C4—344no—
681C22⋊C4—344no—
682C22⋊C4C2×C22⋊D1714yes—
683C22⋊C4C2×C22⋊D1714yes—
684C42—24no—
685C42—344no—
686C42C2×C22⋊D1712yes—
687C42C23×D1712yes—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—342no—
694C23—682no—
695C23—682no—
696C23—682no—
697C23#1058762814yes—
698C23C22×C22⋊D1712yes—
699C23C22×C22⋊D1712yes—
700C23C22×C22⋊D1711yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—42no—
704Q8—84no—
705Q8—174no—
706Q8—342no—
707Q8—344no—
708Q8—342no—
709Q8—342no—
710Q8—688no—
711Q8—682no—
712D4—28no—
713D4—342no—
714D4—342no—
715D4—688no—
716D4—688no—
717D4—682no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—84no—
737C2×C4—84no—
738C2×C4—342no—
739C2×C4—344no—
740C2×C4—342no—
741C2×C4—342no—
742C2×C4—688no—
743C2×C4—688no—
744C2×C4—682no—
745C2×C4—682no—
746C2×C4#41×D1712yes—
747C2×C4#1058769612yes—
748C2×C4C22×C22⋊D1712yes—
749C2×C4C22×C22⋊D1712yes—
750C2×C4C22×C22⋊D1712yes—
751C2×C4C22×C22⋊D1712yes—
752C2×C4C22×C22⋊D1711yescharacteristic
753C2×C4C24×D1711yescharacteristic
754C8—342no—
755C8—342no—
756C8—342no—
757C8—342no—
758C22—28no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—682no—
766C22—682no—
767C22—682no—
768C22—1364no—
769C22#1176344712yes—
770C22C2×#1058762814yes—
771C22C2×#1058762812yes—
772C22#1176362012yes—
773C22C23×C22⋊D1711yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—344no—
783C4—682no—
784C4—682no—
785C4#1176344712yes—
786C4C2×#41×D1711yescharacteristic
787C4C2×#1058769611yescharacteristic
788C2—24no—
789C2—42no—
790C2—1362no—
791C2#1454088914yesdirect product factor
792C2C2×#1176344711yescharacteristic
793C2C22×#1058762811yescharacteristic
794C2C2×#1176362011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#554C2
socleC23×C17C22×D4
prime radicalC2×#11763468C2
hypercenterC2×#554D17
hypocenterC17C2×#3316
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #14540889C2direct (N × H)
3. C2×#11763171C2semidirect
4. C2×#11763127C2semidirect
5. C2×#11763139C2semidirect
6. C2×#11763091C2semidirect
7. C2×#11763065C2semidirect
8. C2×#11763040C2semidirect
9. C2×#11763031C2semidirect
10. C2×#11762969C2semidirect
11. C2×#11762964C2semidirect
12. C2×#11762914C2semidirect
13. C2×#11762881C2semidirect
14. C2×#11762808C2semidirect
15. C22×#10587481C2semidirect
16. C2×C17×#554C2semidirect
34. #11763171C22semidirect
35. #11763139C22semidirect
36. #11763127C22semidirect
37. #11763091C22semidirect
38. #11763065C22semidirect
39. #11763040C22semidirect
40. #11763031C22semidirect
41. #11762969C22semidirect
42. #11762964C22semidirect
43. #11762914C22semidirect
44. #11762881C22semidirect
49. #11762808C22semidirect
57. C2×#10587481C22semidirect
65. C17×#554C22semidirect
361. C2×#554D17semidirect
415. #554C2×D17semidirect
469. C2×C17#3316semidirect
582. C17C2×#3316semidirect
791. C2#14540889direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634682
#145408892
C2×#117631712
C2×#117631272
C2×#117631392
C2×#117630912
C2×#117630652
C2×#117630402
C2×#117630312
C2×#117629692
C2×#117629642
C2×#117629142
C2×#117628812
C2×#117628082
C22×#105874812
C2×C17×#5542
C2×#331617