Finite Group Databasebeta

← #17091381

Subgroups — #17091381

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×#11763089C211yesmaximal, characteristic, complemented
2C22×#10587503C211yesmaximal, characteristic
3#14532486C211yesmaximal, characteristic, complemented
4#14530312C211yesmaximal, characteristic, complemented
5#14530172C211yesmaximal, characteristic, complemented
6#14530172C211yesmaximal, characteristic, complemented
7#14529920C211yesmaximal, characteristic, complemented
8#14529031C211yesmaximal, characteristic, complemented
9#14529031C211yesmaximal, characteristic, complemented
10#14528971C211yesmaximal, characteristic, complemented
11#14528964C211yesmaximal, characteristic, complemented
12#14528811C211yesmaximal, characteristic, complemented
13#14528784C211yesmaximal, characteristic, complemented
14#14528715C211yesmaximal, characteristic
15D4×C22⋊C4×C17C211yesmaximal, characteristic
16C23×#3622C2211yescharacteristic
17C2×#10587555C2211yescharacteristic, complemented
18C2×#10587564—21no—
19C22×C4⋊Dic17C2211yescharacteristic
20#11763089—24no—
21C2×#10587478C2211yescharacteristic, complemented
22C2×#10587478C2211yescharacteristic, complemented
23C2×#10587478C2211yescharacteristic, complemented
24C2×#10587478C2211yescharacteristic, complemented
25C2×C4⋊#3622C2211yescharacteristic, complemented
26C2×C4⋊#3622C2211yescharacteristic, complemented
27C2×#10587503—24no—
28C2×#10587503C2211yescharacteristic
29C2×#10587503C2211yescharacteristic
30C2×#10587503C2211yescharacteristic
31C2×#10587503C2211yescharacteristic
32C2×#10587503C2211yescharacteristic
33C2×#10587503C2211yescharacteristic
34C2×#10587503C2211yescharacteristic
35C2×#10587503C2211yescharacteristic
36C2×C22⋊#3622C2211yescharacteristic
37#11762741—21no—
38#11762730—21no—
39#11762707C2211yescharacteristic, complemented
40#11762707C2211yescharacteristic, complemented
41#11762684—21no—
42#11762679C2211yescharacteristic, complemented
43#11762669C2211yescharacteristic
44#11762571C2211yescharacteristic, complemented
45#11762571C2211yescharacteristic, complemented
46#11762571C2211yescharacteristic, complemented
47#11762571C2211yescharacteristic, complemented
48#11762564C2211yescharacteristic, complemented
49#11762564C2211yescharacteristic, complemented
50C23×D4×C17C2211yescharacteristic
51C2×C4×D4×C17C2211yescharacteristic
52C2×C4×D4×C17C2211yescharacteristic
53C22×C22⋊C4×C17—21no—
54C17×#390C2211yescharacteristic
55C17×#390C2211yescharacteristic
56C17×#386—21no—
57C17×#386—21no—
58C17×#380C2211yescharacteristic
59C17×#379—21no—
60C4×C22⋊C4×C17C2211yescharacteristic
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×C17—21no—
73C23×C4×C17C2311yescharacteristic
74C23×Dic17—21no—
75C22×Dic34—21no—
76C4×D4×C17—22no—
77C4×D4×C17—22no—
78C4×D4×C17—41no—
79C4×D4×C17—41no—
80C2×C4⋊C4×C17C2311yescharacteristic
81C2×C4⋊C4×C17C2311yescharacteristic
82C2×C22⋊C4×C17—21no—
83C2×C22⋊C4×C17—21no—
84C2×C22⋊C4×C17—21no—
85C2×C22⋊C4×C17—21no—
86C2×C22⋊C4×C17—21no—
87C2×C22⋊C4×C17—21no—
88C2×C22⋊C4×C17—21no—
89C2×C22⋊C4×C17—44no—
90C2×C22⋊C4×C17D411yescharacteristic
91C2×C22⋊C4×C17D411yescharacteristic
92C2×C42×C17C2311yescharacteristic
93C2×C42×C17C2311yescharacteristic
94C2×C22⋊Dic17—21no—
95C2×C4⋊Dic17—21no—
96C2×C4⋊Dic17—21no—
97C2×C4⋊Dic17—21no—
98C2×C4⋊Dic17—21no—
99C2×C4⋊Dic17—22no—
100C2×C4⋊Dic17—41no—
101C2×C4⋊Dic17C2311yescharacteristic
102C2×C4⋊Dic17C2311yescharacteristic
103C2×C4⋊Dic17C2311yescharacteristic
104C2×C4⋊Dic17C2311yescharacteristic
105C2×#63225—21no—
106C2×#63225—21no—
107C22×#3622—22no—
108C22×#3622—22no—
109C22×#3622—41no—
110C22×#3622C2311yescharacteristic
111C22×#3622C2311yescharacteristic
112C22×#3622C2311yescharacteristic
113C22×#3622C2311yescharacteristic
114#10587564—44no—
115#10587555—22no—
116#10587555—41no—
117C17×#95—21no—
118C17×#95D411yescharacteristic
119C17×#95D411yescharacteristic
120#10587503—22no—
121#10587503—22no—
122#10587503—22no—
123#10587503—22no—
124#10587503—22no—
125#10587503—41no—
126#10587503—41no—
127#10587503D414yes—
128#10587502—21no—
129#10587502—21no—
130#10587502—21no—
131C22⋊#3622—22no—
132#10587478—22no—
133#10587478—22no—
134#10587478—41no—
135#10587478—41no—
136C4⋊#3622—22no—
137C4⋊#3622—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—42no—
176C22×C4×C17—42no—
177C22×C4×C17—81no—
178C22×C4×C17—81no—
179C22×C4×C17C2×D411yescharacteristic
180C22×C4×C17C2×D411yescharacteristic
181C22×C4×C17C2×D411yescharacteristic
182C22×C4×C17C2×D411yescharacteristic
183C22×C4×C17C2×D411yescharacteristic
184C22×C4×C17C2×Q812yes—
185C22×C4×C17#4112yes—
186C22×C4×C17C2411yescharacteristic
187C22×Dic17—21no—
188C22×Dic17—21no—
189C22×Dic17—21no—
190C22×Dic17—21no—
191C22×Dic17—42no—
192C22×Dic17—42no—
193C22×Dic17—81no—
194C2×Dic34—42no—
195C2×Dic34—42no—
196C2×Dic34—81no—
197C4⋊C4×C17—21no—
198C4⋊C4×C17—21no—
199C4⋊C4×C17—21no—
200C4⋊C4×C17—21no—
201C22⋊C4×C17—22no—
202C22⋊C4×C17—42no—
203C22⋊C4×C17—42no—
204C22⋊C4×C17—42no—
205C22⋊C4×C17—42no—
206C22⋊C4×C17—42no—
207C22⋊C4×C17—81no—
208C22⋊C4×C17—81no—
209C22⋊C4×C17D814yes—
210C42×C17—21no—
211C42×C17—21no—
212C42×C17—21no—
213C42×C17—21no—
214C22⋊Dic17—42no—
215C4⋊Dic17—21no—
216C4⋊Dic17—21no—
217C4⋊Dic17—21no—
218C4⋊Dic17—21no—
219C4⋊Dic17—21no—
220C4⋊Dic17—21no—
221C4⋊Dic17—21no—
222C4⋊Dic17—42no—
223C4⋊Dic17—42no—
224C4⋊Dic17—42no—
225C4⋊Dic17—81no—
226C4⋊Dic17C2×D412yes—
227#63225—42no—
228#63225—42no—
229C2×#3622—21no—
230C2×#3622—21no—
231C2×#3622—21no—
232C2×#3622—21no—
233C2×#3622—21no—
234C2×#3622—21no—
235C2×#3622—21no—
236C2×#3622—21no—
237C2×#3622—21no—
238C2×#3622—21no—
239C2×#3622—21no—
240C2×#3622—44no—
241C2×#3622C2×D412yes—
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—21no—
284C2×C4×C17—21no—
285C2×C4×C17—21no—
286C2×C4×C17—21no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—21no—
292C2×C4×C17—21no—
293C2×C4×C17—21no—
294C2×C4×C17—21no—
295C2×C4×C17—21no—
296C2×C4×C17—21no—
297C2×C4×C17—41no—
298C2×C4×C17—41no—
299C2×C4×C17—41no—
300C2×C4×C17—41no—
301C2×C4×C17—41no—
302C2×C4×C17—41no—
303C2×C4×C17—84no—
304C2×C4×C17—84no—
305C2×C4×C17C22⋊Q812yes—
306C2×C4×C17C2×D812yes—
307C2×C4×C17C2×D812yes—
308C2×C4×C17C22×D411yescharacteristic
309C2×C4×C17C22×Q811yescharacteristic
310C2×C4×C17C2×#4111yescharacteristic
311C2×C4×C17C2×#4111yescharacteristic
312C2×C4×C17H(5,𝔽2)11yescharacteristic
313C2×C4×C17H(5,𝔽2)11yescharacteristic
314C2×Dic17—22no—
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—41no—
324C2×Dic17—41no—
325C2×Dic17—41no—
326C2×Dic17—84no—
327Dic34—84no—
328#3622—22no—
329#3622—41no—
330#3622—41no—
331#3622—41no—
332C2×#474—171no—
333C22×#102—171no—
334#2440—171no—
335D4×C22⋊C4D1711yescharacteristic
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—22no—
378C4×C17—22no—
379C4×C17—41no—
380C4×C17—41no—
381C4×C17—81no—
382C4×C17—81no—
383C4×C17C2×C22⋊Q811yescharacteristic
384C4×C17#54311yescharacteristic
385C4×C17#54611yescharacteristic
386C4×C17#55111yescharacteristic
387Dic17—42no—
388Dic17—81no—
389Dic17—81no—
390Dic17—81no—
391C23×D4C2×D1711yescharacteristic
392C23×C8—171no—
393C2×C4⋊Q8—171no—
394C2×C22⋊Q8—341no—
395C2×C4×D4C2×D1711yescharacteristic
396C2×C4×D4C2×D1711yescharacteristic
397C22×C4⋊C4—171no—
398C22×C22⋊C4—21no—
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—171no—
407C2×#102—171no—
408C2×#102—171no—
409C2×#102—171no—
410C2×#102—171no—
411C2×#102—171no—
412C2×#102—171no—
413C2×#102—171no—
414C2×#102—344no—
415C2×C22⋊C8—171no—
416#398—341no—
417#395—341no—
418#390C2×D1711yescharacteristic
419#390C2×D1711yescharacteristic
420#389—171no—
421#389—171no—
422#386—21no—
423#386—21no—
424#385—341no—
425#384—171no—
426#380—171no—
427#380C2×D1711yescharacteristic
428#379—21no—
429C4×C22⋊C4C2×D1711yescharacteristic
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—22no—
451C22×D4—21no—
452C22×D4—41no—
453C22×D4—41no—
454C22×D4Dic3414yescomplemented
455C22×D4C22×D1711yescharacteristic
456C22×D4C22×D1711yescharacteristic
457C23×C4—21no—
458C23×C4—21no—
459C23×C4—341no—
460C23×C4C22×D1711yescharacteristic
461C22×C8—171no—
462C22×C8—171no—
463C22×C8—171no—
464C22×C8—171no—
465C22×C8—342no—
466C22×C8—342no—
467C22×C8—681no—
468C4⋊Q8—342no—
469C4⋊Q8—681no—
470C22⋊Q8—684no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—41no—
474C4×D4—41no—
475C2×C4⋊C4—171no—
476C2×C4⋊C4—171no—
477C2×C4⋊C4—171no—
478C2×C4⋊C4—171no—
479C2×C4⋊C4—342no—
480C2×C4⋊C4—341no—
481C2×C4⋊C4—341no—
482C2×C4⋊C4—341no—
483C2×C4⋊C4—341no—
484C2×C4⋊C4—341no—
485C2×C4⋊C4—341no—
486C2×C4⋊C4—681no—
487C2×C4⋊C4C22×D1711yescharacteristic
488C2×C4⋊C4C22×D1711yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—44no—
497C2×C22⋊C4—341no—
498C2×C22⋊C4C22⋊D1711yescharacteristic
499C2×C22⋊C4C22⋊D1711yescharacteristic
500C2×C42C22×D1711yescharacteristic
501C2×C42C22×D1711yescharacteristic
502#107—342no—
503#107—342no—
504#107—681no—
505#107—681no—
506C4⋊C8—342no—
507C4⋊C8—681no—
508#102—174no—
509#102—342no—
510#102—342no—
511#102—342no—
512#102—342no—
513#102—342no—
514#102—681no—
515#102—681no—
516C22⋊C8—342no—
517#95—21no—
518#95—341no—
519#95—341no—
520#95—341no—
521#95C22⋊D1711yescharacteristic
522#95C22⋊D1711yescharacteristic
523C17#2595011yescharacteristic, complemented, Sylow
524C24—21no—
525C24—21no—
526C24—24no—
527C24—42no—
528C24—42no—
529C24—42no—
530C24—42no—
531C24—81no—
532C24—81no—
533C24C2×C22⋊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×D4D4×D1712yes—
555C2×D4#6325412yes—
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—42no—
565C22×C4—42no—
566C22×C4—81no—
567C22×C4—81no—
568C22×C4—341no—
569C22×C4—341no—
570C22×C4—341no—
571C22×C4—341no—
572C22×C4—682no—
573C22×C4—682no—
574C22×C4—1361no—
575C22×C4C2×Dic3412yes—
576C22×C4#6325212yes—
577C22×C4C2×C22⋊D1711yescharacteristic
578C22×C4C2×C22⋊D1711yescharacteristic
579C22×C4C2×C22⋊D1711yescharacteristic
580C22×C4C2×C22⋊D1711yescharacteristic
581C22×C4C2×C22⋊D1711yescharacteristic
582C22×C4C23×D1711yescharacteristic
583C2×C8—172no—
584C2×C8—341no—
585C2×C8—341no—
586C2×C8—341no—
587C2×C8—341no—
588C2×C8—341no—
589C2×C8—341no—
590C2×C8—341no—
591C2×C8—341no—
592C2×C8—341no—
593C2×C8—341no—
594C2×C8—341no—
595C2×C8—684no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—172no—
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—682no—
613C4⋊C4—1361no—
614C22⋊C4—22no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—81no—
621C22⋊C4—81no—
622C22⋊C4—682no—
623C22⋊C4#6322814yes—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
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#1058761012yes—
654C23C2×#6322812yes—
655C23#1058763712yes—
656C23C22×C22⋊D1711yescharacteristic
657Q8—1364no—
658D4—22no—
659D4—22no—
660D4—22no—
661D4—22no—
662D4—22no—
663D4—48no—
664D4—41no—
665D4—41no—
666D4#1058756414yescomplemented
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—84no—
690C2×C4—84no—
691C2×C4—342no—
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—1364no—
704C2×C4#1058761012yes—
705C2×C4C2×#6322812yes—
706C2×C4C2×#6322812yes—
707C2×C4C22×Dic3411yescharacteristic
708C2×C4C2×#6325211yescharacteristic
709C2×C4C2×D4×D1711yescharacteristic
710C2×C4C2×#6325411yescharacteristic
711C2×C4#1058769111yescharacteristic
712C2×C4#1058769111yescharacteristic
713C8—342no—
714C8—681no—
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#1176308914yescomplemented
739C22C2×#1058761011yescharacteristic
740C22D4×C22⋊D1711yescharacteristic
741C22#1176345311yescharacteristic
742C22C22×#6322811yescharacteristic
743C22C2×#1058763711yescharacteristic
744C22#1176361211yescharacteristic
745C22#1176362011yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—41no—
751C4—81no—
752C4—81no—
753C4—682no—
754C4—1361no—
755C4—1361no—
756C4—1361no—
757C4C2×#1058756411yescharacteristic
758C4#1176343511yescharacteristic
759C4#1176344911yescharacteristic
760C4#1176348511yescharacteristic
761C2—24no—
762C2—44no—
763C2—82no—
764C2#1453244511yescharacteristic
765C2C2×#1176308911yescharacteristic
766C2#1453861511yescharacteristic
767C2#1454029011yescharacteristic
768C2D4×#6322811yescharacteristic
769C2#1454059711yescharacteristic
770C2#1454086511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingD4×C22⋊C4×C17C2
socleC23×C17C22×D4
prime radicalC23×D4×C17C22
hypercenterD4×C22⋊C4D17
hypocenterC17#25950
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11763089C2semidirect
3. #14532486C2semidirect
4. #14530312C2semidirect
5. #14530172C2semidirect
6. #14530172C2semidirect
7. #14529920C2semidirect
8. #14529031C2semidirect
9. #14529031C2semidirect
10. #14528971C2semidirect
11. #14528964C2semidirect
12. #14528811C2semidirect
13. #14528784C2semidirect
17. C2×#10587555C22semidirect
21. C2×#10587478C22semidirect
22. C2×#10587478C22semidirect
23. C2×#10587478C22semidirect
24. C2×#10587478C22semidirect
25. C2×C4⋊#3622C22semidirect
26. C2×C4⋊#3622C22semidirect
39. #11762707C22semidirect
40. #11762707C22semidirect
42. #11762679C22semidirect
44. #11762571C22semidirect
45. #11762571C22semidirect
46. #11762571C22semidirect
47. #11762571C22semidirect
48. #11762564C22semidirect
49. #11762564C22semidirect
68. C22×D4×C17Q8semidirect
280. D4×C17C22⋊Q8semidirect
368. C22×C17#474semidirect
454. C22×D4Dic34semidirect
523. C17#25950semidirect
666. D4#10587564semidirect
738. C22#11763089semidirect

Maximal subgroups

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

subgroupindex
C2×#117630892
C22×#105875032
#145324862
#145303122
#145301722
#145299202
#145290312
#145289712
#145289642
#145288112
#145287842
#145287152
D4×C22⋊C4×C172
#2595017