Finite Group Databasebeta

← #17091375

Subgroups — #17091375

Order 4352.

1206 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
1C2×#11763087C211yesmaximal, characteristic, complemented
2#14532480C211yesmaximal, characteristic, complemented
3D4×C22⋊Dic17C211yesmaximal, characteristic
4#14530310C211yesmaximal, characteristic, complemented
5#14530170C211yesmaximal, characteristic, complemented
6#14530168C211yesmaximal, characteristic, complemented
7#14529918C211yesmaximal, characteristic, complemented
8#14529033C211yesmaximal, characteristic, complemented
9#14529029C211yesmaximal, characteristic, complemented
10#14528972C211yesmaximal, characteristic, complemented
11#14528962C211yesmaximal, characteristic, complemented
12#14528813C211yesmaximal, characteristic, complemented
13#14528782C211yesmaximal, characteristic, complemented
14#14528715C211yesmaximal, characteristic
15C22×C17×#102C211yesmaximal, characteristic
16C2×#10587574C2211yescharacteristic, complemented
17C2×#10587610—21no—
18C2×D4×Dic17C2211yescharacteristic
19C2×D4×Dic17C2211yescharacteristic
20C22×C22⋊Dic17—21no—
21#11763087—24no—
22C2×#10587489C2211yescharacteristic, complemented
23C2×#10587489C2211yescharacteristic, complemented
24C2×#10587478C2211yescharacteristic, complemented
25C2×#10587478C2211yescharacteristic, complemented
26C2×#10587485C2211yescharacteristic, complemented
27C2×#10587485C2211yescharacteristic, complemented
28C2×#10587503C2211yescharacteristic
29C2×#10587503C2211yescharacteristic
30C2×#10587503C2211yescharacteristic
31C2×#10587503C2211yescharacteristic
32C2×C22⋊#3622C2211yescharacteristic
33#11762742—21no—
34#11762729—21no—
35#11762712C2211yescharacteristic
36#11762712C2211yescharacteristic
37#11762708C2211yescharacteristic, complemented
38#11762705C2211yescharacteristic, complemented
39#11762689—21no—
40#11762689—21no—
41#11762682—21no—
42#11762678C2211yescharacteristic, complemented
43#11762669C2211yescharacteristic
44#11762669C2211yescharacteristic
45#11762665—21no—
46C4×C22⋊Dic17C2211yescharacteristic
47#11762572C2211yescharacteristic, complemented
48#11762572C2211yescharacteristic, complemented
49#11762571C2211yescharacteristic, complemented
50#11762571C2211yescharacteristic, complemented
51#11762563C2211yescharacteristic, complemented
52#11762563C2211yescharacteristic, complemented
53C23×D4×C17C2211yescharacteristic
54C23×C8×C17C2211yescharacteristic
55C22×C4⋊C4×C17C2211yescharacteristic
56C2×C17×#102—24no—
57C2×C17×#102C2211yescharacteristic
58C2×C17×#102C2211yescharacteristic
59C2×C17×#102C2211yescharacteristic
60C2×C17×#102C2211yescharacteristic
61C25×C17—21no—
62C22×D4×C17—22no—
63C22×D4×C17—22no—
64C22×D4×C17—21no—
65C22×D4×C17—22no—
66C22×D4×C17—41no—
67C22×D4×C17—41no—
68C22×D4×C17Q814yescomplemented
69C22×D4×C17C2311yescharacteristic
70C22×D4×C17C2311yescharacteristic
71C23×C4×C17—21no—
72C23×C4×C17C2311yescharacteristic
73C23×Dic17—21no—
74C23×Dic17—21no—
75C22×Dic34—21no—
76C22×C8×C17—22no—
77C22×C8×C17—22no—
78C22×C8×C17—41no—
79C22×C8×C17C2311yescharacteristic
80C22×C8×C17C2311yescharacteristic
81C2×C4⋊C4×C17—22no—
82C2×C4⋊C4×C17—21no—
83C2×C4⋊C4×C17—41no—
84C2×C4⋊C4×C17C2311yescharacteristic
85C2×C4⋊C4×C17C2311yescharacteristic
86C2×C22⋊Dic17—21no—
87C2×C22⋊Dic17—21no—
88C2×C22⋊Dic17—21no—
89C2×C22⋊Dic17—21no—
90C2×C22⋊Dic17—21no—
91C2×C22⋊Dic17—21no—
92C2×C22⋊Dic17—21no—
93C2×C22⋊Dic17—21no—
94C2×C22⋊Dic17—44no—
95C2×C22⋊Dic17D411yescharacteristic
96C2×C22⋊Dic17D411yescharacteristic
97D4×Dic17—22no—
98D4×Dic17—22no—
99D4×Dic17—41no—
100D4×Dic17—41no—
101C2×C4⋊Dic17—21no—
102C2×C4⋊Dic17C2311yescharacteristic
103C2×C4⋊Dic17C2311yescharacteristic
104C2×C4⋊Dic17C2311yescharacteristic
105C2×C4⋊Dic17C2311yescharacteristic
106#10587610—44no—
107C2×#63225—21no—
108C2×#63225—21no—
109C2×#63225—21no—
110C2×#63225—21no—
111C2×C4×Dic17C2311yescharacteristic
112C2×C4×Dic17C2311yescharacteristic
113C22×#3622C2311yescharacteristic
114C22×#3622C2311yescharacteristic
115#10587574—22no—
116#10587574—41no—
117C17×#102—22no—
118C17×#102—22no—
119C17×#102—22no—
120C17×#102D414yes—
121#10587503—22no—
122#10587503—22no—
123#10587503—41no—
124#10587503—41no—
125#10587502—21no—
126#10587502—21no—
127#10587502—21no—
128#10587502—21no—
129#10587502D411yescharacteristic
130#10587502D411yescharacteristic
131C22⋊#3622—22no—
132#10587489—22no—
133#10587489—41no—
134#10587485—22no—
135#10587485—41no—
136#10587478—22no—
137#10587478—41no—
138C24×C17—21no—
139C24×C17—21no—
140C24×C17—24no—
141C24×C17—42no—
142C24×C17—42no—
143C24×C17—42no—
144C24×C17—42no—
145C24×C17—81no—
146C24×C17—81no—
147C24×C17C2×D411yescharacteristic
148C2×D4×C17—28no—
149C2×D4×C17—24no—
150C2×D4×C17—21no—
151C2×D4×C17—21no—
152C2×D4×C17—21no—
153C2×D4×C17—21no—
154C2×D4×C17—21no—
155C2×D4×C17—21no—
156C2×D4×C17—21no—
157C2×D4×C17—21no—
158C2×D4×C17—44no—
159C2×D4×C17—44no—
160C2×D4×C17—44no—
161C2×D4×C17—42no—
162C2×D4×C17—42no—
163C2×D4×C17C2×D412yes—
164C2×D4×C17C2×Q812yes—
165C2×D4×C17C2×Q812yes—
166C2×D4×C17#4112yes—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—42no—
174C22×C4×C17—42no—
175C22×C4×C17—81no—
176C22×C4×C17C2×D411yescharacteristic
177C22×C4×C17C2×Q812yes—
178C22×C4×C17#4112yes—
179C22×C4×C17C2411yescharacteristic
180C22×Dic17—21no—
181C22×Dic17—21no—
182C22×Dic17—21no—
183C22×Dic17—21no—
184C22×Dic17—42no—
185C22×Dic17—42no—
186C22×Dic17—42no—
187C22×Dic17—42no—
188C22×Dic17—81no—
189C22×Dic17—81no—
190C22×Dic17C2×D411yescharacteristic
191C22×Dic17C2×D411yescharacteristic
192C22×Dic17C2×D411yescharacteristic
193C22×Dic17C2×D411yescharacteristic
194C2×Dic34—42no—
195C2×Dic34—42no—
196C2×Dic34—81no—
197C2×C8×C17—21no—
198C2×C8×C17—21no—
199C2×C8×C17—21no—
200C2×C8×C17—21no—
201C2×C8×C17—21no—
202C2×C8×C17—44no—
203C2×C8×C17C2×D412yes—
204C4⋊C4×C17—21no—
205C4⋊C4×C17—21no—
206C4⋊C4×C17—21no—
207C4⋊C4×C17—42no—
208C4⋊C4×C17C2×D412yes—
209C22⋊Dic17—22no—
210C22⋊Dic17—42no—
211C22⋊Dic17—42no—
212C22⋊Dic17—42no—
213C22⋊Dic17—42no—
214C22⋊Dic17—42no—
215C22⋊Dic17—42no—
216C22⋊Dic17—81no—
217C22⋊Dic17—81no—
218C22⋊Dic17D814yes—
219C4⋊Dic17—21no—
220C4⋊Dic17—21no—
221C4⋊Dic17—21no—
222C4⋊Dic17—21no—
223C4⋊Dic17—21no—
224C4⋊Dic17—21no—
225C4⋊Dic17—21no—
226C4⋊Dic17—21no—
227C4⋊Dic17—42no—
228#63225—42no—
229#63225—42no—
230#63225—42no—
231#63225—81no—
232C4×Dic17—21no—
233C4×Dic17—21no—
234C4×Dic17—21no—
235C4×Dic17—21no—
236C2×#3622—21no—
237C2×#3622—21no—
238C2×#3622—21no—
239C2×#3622—21no—
240C2×#3622—21no—
241C2×#3622—21no—
242#25950—171nomaximal, Sylow
243C23×C17—21no—
244C23×C17—21no—
245C23×C17—21no—
246C23×C17—21no—
247C23×C17—22no—
248C23×C17—22no—
249C23×C17—22no—
250C23×C17—22no—
251C23×C17—48no—
252C23×C17—41no—
253C23×C17—41no—
254C23×C17—41no—
255C23×C17—41no—
256C23×C17—41no—
257C23×C17—41no—
258C23×C17—41no—
259C23×C17—41no—
260C23×C17—41no—
261C23×C17—41no—
262C23×C17—48no—
263C23×C17—84no—
264C23×C17—84no—
265C23×C17—84no—
266C23×C17—84no—
267C23×C17—84no—
268C23×C17C22⋊Q812yes—
269C23×C17C2×D812yes—
270C23×C17#13712yes—
271C23×C17C22×D411yescharacteristic
272D4×C17—22no—
273D4×C17—22no—
274D4×C17—22no—
275D4×C17—22no—
276D4×C17—22no—
277D4×C17—48no—
278D4×C17—41no—
279D4×C17—41no—
280D4×C17C22⋊Q814yescomplemented
281C2×C4×C17—21no—
282C2×C4×C17—21no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—41no—
289C2×C4×C17—41no—
290C2×C4×C17—41no—
291C2×C4×C17—41no—
292C2×C4×C17—41no—
293C2×C4×C17—84no—
294C2×C4×C17C22⋊Q812yes—
295C2×C4×C17C22×D411yescharacteristic
296C2×C4×C17C22×Q811yescharacteristic
297C2×C4×C17C2×#4111yescharacteristic
298C2×C4×C17C2×#4111yescharacteristic
299C2×C4×C17H(5,𝔽2)11yescharacteristic
300C2×C4×C17H(5,𝔽2)11yescharacteristic
301C2×Dic17—21no—
302C2×Dic17—21no—
303C2×Dic17—21no—
304C2×Dic17—21no—
305C2×Dic17—21no—
306C2×Dic17—21no—
307C2×Dic17—21no—
308C2×Dic17—21no—
309C2×Dic17—21no—
310C2×Dic17—21no—
311C2×Dic17—41no—
312C2×Dic17—41no—
313C2×Dic17—41no—
314C2×Dic17—41no—
315C2×Dic17—41no—
316C2×Dic17—41no—
317C2×Dic17—41no—
318C2×Dic17—41no—
319C2×Dic17—41no—
320C2×Dic17—41no—
321C2×Dic17—41no—
322C2×Dic17—41no—
323C2×Dic17—84no—
324C2×Dic17—84no—
325C2×Dic17C2×D812yes—
326C2×Dic17C2×D812yes—
327Dic34—84no—
328C8×C17—22no—
329C8×C17—41no—
330#3622—41no—
331#3622—41no—
332C2×#474—171no—
333C22×#102D1711yescharacteristic
334#2440—171no—
335D4×C22⋊C4—171no—
336#2093—171no—
337#2067—171no—
338#2067—171no—
339#2023—171no—
340#1862—171no—
341#1862—171no—
342#1852—171no—
343#1850—171no—
344#1808—171no—
345#1802—171no—
346#1786—171no—
347C22×C17—22no—
348C22×C17—22no—
349C22×C17—22no—
350C22×C17—22no—
351C22×C17—22no—
352C22×C17—22no—
353C22×C17—24no—
354C22×C17—42no—
355C22×C17—42no—
356C22×C17—42no—
357C22×C17—42no—
358C22×C17—42no—
359C22×C17—42no—
360C22×C17—42no—
361C22×C17—42no—
362C22×C17—42no—
363C22×C17—816no—
364C22×C17—81no—
365C22×C17—81no—
366C22×C17—81no—
367C22×C17—81no—
368C22×C17#47414yescomplemented
369C22×C17C2×C22⋊Q811yescharacteristic
370C22×C17D4211yescharacteristic
371C22×C17#54611yescharacteristic
372C22×C17C22×D811yescharacteristic
373C22×C17C2×#13711yescharacteristic
374C22×C17#57611yescharacteristic
375C22×C17#57711yescharacteristic
376C4×C17—22no—
377C4×C17—42no—
378C4×C17—81no—
379C4×C17C2×C22⋊Q811yescharacteristic
380C4×C17#54311yescharacteristic
381C4×C17#54611yescharacteristic
382C4×C17#55111yescharacteristic
383Dic17—22no—
384Dic17—22no—
385Dic17—41no—
386Dic17—41no—
387Dic17—81no—
388Dic17—81no—
389Dic17—81no—
390Dic17—81no—
391C23×D4C2×D1711yescharacteristic
392C23×C8C2×D1711yescharacteristic
393C2×C4⋊Q8—171no—
394C2×C22⋊Q8—341no—
395C2×C4×D4—171no—
396C2×C4×D4—171no—
397C22×C4⋊C4C2×D1711yescharacteristic
398C22×C22⋊C4—341no—
399#474—344no—
400C2×#107—171no—
401C2×#107—171no—
402C2×#107—171no—
403C2×#107—171no—
404C2×C4⋊C8—171no—
405C2×C4⋊C8—171no—
406C2×#102—24no—
407C2×#102—171no—
408C2×#102—171no—
409C2×#102—171no—
410C2×#102—171no—
411C2×#102C2×D1711yescharacteristic
412C2×#102C2×D1711yescharacteristic
413C2×#102C2×D1711yescharacteristic
414C2×#102C2×D1711yescharacteristic
415C2×C22⋊C8—171no—
416#398—341no—
417#395—341no—
418#390—171no—
419#390—171no—
420#389—171no—
421#389—171no—
422#386—341no—
423#386—341no—
424#385—341no—
425#384—171no—
426#380—171no—
427#380—171no—
428#379—341no—
429C4×C22⋊C4—171no—
430#340—171no—
431#340—171no—
432#340—171no—
433#340—171no—
434#336—171no—
435#336—171no—
436C2×C17—24no—
437C2×C17—44no—
438C2×C17—82no—
439C2×C17#243711yescharacteristic
440C2×C17C2×#47411yescharacteristic
441C2×C17#308111yescharacteristic
442C2×C17#326611yescharacteristic
443C2×C17D4×D811yescharacteristic
444C2×C17#329411yescharacteristic
445C2×C17#331411yescharacteristic
446C25—21no—
447C22×Q8—341no—
448C22×D4—22no—
449C22×D4—22no—
450C22×D4—21no—
451C22×D4—22no—
452C22×D4—41no—
453C22×D4—41no—
454C22×D4Dic3414yescomplemented
455C22×D4C22×D1711yescharacteristic
456C22×D4C22×D1711yescharacteristic
457C23×C4—21no—
458C23×C4—341no—
459C23×C4—341no—
460C23×C4C22×D1711yescharacteristic
461C22×C8—22no—
462C22×C8—22no—
463C22×C8—41no—
464C22×C8—171no—
465C22×C8—171no—
466C22×C8C22×D1711yescharacteristic
467C22×C8C22×D1711yescharacteristic
468C4⋊Q8—342no—
469C4⋊Q8—681no—
470C22⋊Q8—684no—
471C4×D4—342no—
472C4×D4—342no—
473C4×D4—681no—
474C4×D4—681no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—41no—
478C2×C4⋊C4—171no—
479C2×C4⋊C4—171no—
480C2×C4⋊C4—171no—
481C2×C4⋊C4—171no—
482C2×C4⋊C4—341no—
483C2×C4⋊C4—341no—
484C2×C4⋊C4—341no—
485C2×C4⋊C4—341no—
486C2×C4⋊C4—341no—
487C2×C4⋊C4C22×D1711yescharacteristic
488C2×C4⋊C4C22×D1711yescharacteristic
489C2×C22⋊C4—171no—
490C2×C22⋊C4—171no—
491C2×C22⋊C4—341no—
492C2×C22⋊C4—341no—
493C2×C22⋊C4—341no—
494C2×C22⋊C4—341no—
495C2×C22⋊C4—341no—
496C2×C22⋊C4—341no—
497C2×C22⋊C4—341no—
498C2×C22⋊C4—341no—
499C2×C22⋊C4—684no—
500C2×C42—171no—
501C2×C42—171no—
502#107—342no—
503#107—342no—
504#107—681no—
505#107—681no—
506C4⋊C8—342no—
507C4⋊C8—681no—
508#102—22no—
509#102—22no—
510#102—22no—
511#102—342no—
512#102—342no—
513#102—681no—
514#102—681no—
515#102C22⋊D1714yes—
516C22⋊C8—342no—
517#95—171no—
518#95—171no—
519#95—341no—
520#95—341no—
521#95—341no—
522#95—341no—
523C17#2595011yescharacteristic, complemented, Sylow
524C24—21no—
525C24—21no—
526C24—24no—
527C24—42no—
528C24—42no—
529C24—42no—
530C24—42no—
531C24—81no—
532C24—81no—
533C24D4×D1711yescharacteristic
534C2×Q8—682no—
535C2×Q8—682no—
536C2×Q8—1361no—
537C2×D4—28no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—24no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4C2×Dic3412yes—
553C2×D4C2×Dic3412yes—
554C2×D4#6325212yes—
555C2×D4C2×C22⋊D1712yes—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—81no—
565C22×C4—171no—
566C22×C4—171no—
567C22×C4—171no—
568C22×C4—171no—
569C22×C4—341no—
570C22×C4—341no—
571C22×C4—341no—
572C22×C4—341no—
573C22×C4—682no—
574C22×C4—682no—
575C22×C4—682no—
576C22×C4—682no—
577C22×C4—1361no—
578C22×C4—1361no—
579C22×C4C2×Dic3412yes—
580C22×C4D4×D1711yescharacteristic
581C22×C4#6325412yes—
582C22×C4C23×D1711yescharacteristic
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—44no—
589C2×C8—341no—
590C2×C8—341no—
591C2×C8—341no—
592C2×C8—341no—
593C2×C8—341no—
594C2×C8—341no—
595C2×C8C2×C22⋊D1712yes—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—42no—
600C4⋊C4—341no—
601C4⋊C4—341no—
602C4⋊C4—341no—
603C4⋊C4—341no—
604C4⋊C4—341no—
605C4⋊C4—341no—
606C4⋊C4—341no—
607C4⋊C4—341no—
608C4⋊C4—682no—
609C4⋊C4—682no—
610C4⋊C4—682no—
611C4⋊C4—682no—
612C4⋊C4—1361no—
613C4⋊C4C2×C22⋊D1712yes—
614C22⋊C4—174no—
615C22⋊C4—342no—
616C22⋊C4—682no—
617C22⋊C4—682no—
618C22⋊C4—682no—
619C22⋊C4—682no—
620C22⋊C4—682no—
621C22⋊C4—682no—
622C22⋊C4—1361no—
623C22⋊C4—1361no—
624C42—341no—
625C42—341no—
626C42—341no—
627C42—341no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—48no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—48no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23#1058756412yes—
654C23D8×D1712yes—
655C23#1058760112yes—
656C23C2×D4×D1711yescharacteristic
657Q8—1364no—
658D4—22no—
659D4—22no—
660D4—22no—
661D4—22no—
662D4—22no—
663D4—48no—
664D4—41no—
665D4—41no—
666D4#1058761014yescomplemented
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—84no—
680C2×C4—172no—
681C2×C4—172no—
682C2×C4—341no—
683C2×C4—341no—
684C2×C4—341no—
685C2×C4—341no—
686C2×C4—341no—
687C2×C4—341no—
688C2×C4—341no—
689C2×C4—341no—
690C2×C4—341no—
691C2×C4—341no—
692C2×C4—681no—
693C2×C4—681no—
694C2×C4—681no—
695C2×C4—681no—
696C2×C4—681no—
697C2×C4—681no—
698C2×C4—681no—
699C2×C4—681no—
700C2×C4—681no—
701C2×C4—681no—
702C2×C4—681no—
703C2×C4—681no—
704C2×C4—1364no—
705C2×C4—1364no—
706C2×C4#1058756412yes—
707C2×C4C22×Dic3411yescharacteristic
708C2×C4C2×#6325211yescharacteristic
709C2×C4C2×#6325411yescharacteristic
710C2×C4#1058769111yescharacteristic
711C2×C4#1058769111yescharacteristic
712C2×C4C22×C22⋊D1711yescharacteristic
713C8—22no—
714C8—41no—
715C8—681no—
716C8—681no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—24no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—816no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22#1176308714yescomplemented
739C22C2×#1058756411yescharacteristic
740C22D4×C22⋊D1711yescharacteristic
741C22#1176344911yescharacteristic
742C22C2×D8×D1711yescharacteristic
743C22C2×#1058760111yescharacteristic
744C22#1176361011yescharacteristic
745C22#1176361511yescharacteristic
746C4—22no—
747C4—42no—
748C4—81no—
749C4—342no—
750C4—342no—
751C4—681no—
752C4—681no—
753C4—1361no—
754C4—1361no—
755C4—1361no—
756C4—1361no—
757C4C2×#1058761011yescharacteristic
758C4#1176343511yescharacteristic
759C4#1176345311yescharacteristic
760C4#1176348511yescharacteristic
761C2—24no—
762C2—44no—
763C2—82no—
764C2#1453244511yescharacteristic
765C2C2×#1176308711yescharacteristic
766C2#1453861111yescharacteristic
767C2#1454029411yescharacteristic
768C2D8×C22⋊D1711yescharacteristic
769C2#1454059311yescharacteristic
770C2#1454086111yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC22×C17×#102C2
socleC23×C17C22×D4
prime radicalC23×D4×C17C22
hypercenterC22×#102D17
hypocenterC17#25950
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
1. C2×#11763087C2semidirect
2. #14532480C2semidirect
4. #14530310C2semidirect
5. #14530170C2semidirect
6. #14530168C2semidirect
7. #14529918C2semidirect
8. #14529033C2semidirect
9. #14529029C2semidirect
10. #14528972C2semidirect
11. #14528962C2semidirect
12. #14528813C2semidirect
13. #14528782C2semidirect
16. C2×#10587574C22semidirect
22. C2×#10587489C22semidirect
23. C2×#10587489C22semidirect
24. C2×#10587478C22semidirect
25. C2×#10587478C22semidirect
26. C2×#10587485C22semidirect
27. C2×#10587485C22semidirect
37. #11762708C22semidirect
38. #11762705C22semidirect
42. #11762678C22semidirect
47. #11762572C22semidirect
48. #11762572C22semidirect
49. #11762571C22semidirect
50. #11762571C22semidirect
51. #11762563C22semidirect
52. #11762563C22semidirect
68. C22×D4×C17Q8semidirect
280. D4×C17C22⋊Q8semidirect
368. C22×C17#474semidirect
454. C22×D4Dic34semidirect
523. C17#25950semidirect
666. D4#10587610semidirect
738. C22#11763087semidirect

Maximal subgroups

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

subgroupindex
C2×#117630872
#145324802
D4×C22⋊Dic172
#145303102
#145301702
#145301682
#145299182
#145290332
#145290292
#145289722
#145289622
#145288132
#145287822
#145287152
C22×C17×#1022
#2595017