Finite Group Databasebeta

← #17044380

Subgroups — #17044380

Order 4352.

950 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531165C211yesmaximal, characteristic
2#14529400C211yesmaximal, characteristic, complemented
3#14529399C211yesmaximal, characteristic, complemented
4#14529398C211yesmaximal, characteristic, complemented
5#14529395C211yesmaximal, characteristic, complemented
6#14529390C211yesmaximal, characteristic, complemented
7#14529389C211yesmaximal, characteristic, complemented
8#14529387C211yesmaximal, characteristic, complemented
9#14528767C211yesmaximal, characteristic, complemented
10#14528765C211yesmaximal, characteristic, complemented
11#14528693C211yesmaximal, characteristic
12#14528693C211yesmaximal, characteristic
13#14528551C211yesmaximal, characteristic, complemented
14#14528549C211yesmaximal, characteristic, complemented
15C17×#1923C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17C2×#10587558C2211yescharacteristic
18C2×#10587558C2211yescharacteristic
19C2×C4⋊#3622C2211yescharacteristic, complemented
20C2×#10587485C2211yescharacteristic, complemented
21C2×#10587485C2211yescharacteristic, complemented
22C2×C22⋊#3622C2211yescharacteristic
23C2×C22⋊#3622C2211yescharacteristic
24C2×#10587491C2211yescharacteristic
25C2×#10587491C2211yescharacteristic
26C2×#10587491C2211yescharacteristic
27C2×#10587491C2211yescharacteristic
28C2×#10587491C2211yescharacteristic
29C2×#10587491C2211yescharacteristic
30C2×#10587491C2211yescharacteristic
31C2×#10587491C2211yescharacteristic
32C2×#10587474C2211yescharacteristic, complemented
33C2×#10587486C2211yescharacteristic, complemented
34C2×C8×Dic17C2211yescharacteristic, complemented
35#11762671C411yescharacteristic
36#11762671C411yescharacteristic
37#11762668C411yescharacteristic
38#11762668C411yescharacteristic
39#11762667C411yescharacteristic
40#11762667C411yescharacteristic
41#11762664C411yescharacteristic
42#11762664C411yescharacteristic
43C4×#63227C2211yescharacteristic
44C4×#63227C2211yescharacteristic
45C4×C22⋊Dic17C2211yescharacteristic
46#11762564C2211yescharacteristic, complemented
47#11762564C2211yescharacteristic, complemented
48#11762563C2211yescharacteristic, complemented
49#11762563C2211yescharacteristic, complemented
50#11762563C2211yescharacteristic, complemented
51#11762563C2211yescharacteristic, complemented
52C2×C17×C4⋊C8C2211yescharacteristic, complemented
53C2×C17×C22⋊C8C2211yescharacteristic
54C2×C17×C22⋊C8C2211yescharacteristic
55C2×C4×C8×C17C2211yescharacteristic, complemented
56C4×C22⋊C4×C17C2211yescharacteristic
57C17×#336C2211yescharacteristic, complemented
58C17×#336C2211yescharacteristic, complemented
59C24×D17C2×C411yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×Dic17C2×C411yescharacteristic
62C22×C4×D17—22no—
63C22×C4×D17—22no—
64C22×C4×D17—41no—
65C22×C4×D17—41no—
66C22×C4×D17—41no—
67C22×C4×D17—41no—
68C22×C4×D17C2×C411yescharacteristic
69C22×C4×D17C2×C411yescharacteristic
70C22×C4×D17C2311yescharacteristic
71C22×C4×D17C2311yescharacteristic
72C22×C8×C17C2311yescharacteristic
73C22×C8×C17C2311yescharacteristic
74C22×C8×C17C2311yescharacteristic
75C22×C8×C17C2311yescharacteristic
76C2×C22⋊C4×C17C2×C411yescharacteristic
77C2×C22⋊C4×C17C2×C411yescharacteristic
78C2×C42×C17C2311yescharacteristic
79C2×C42×C17C2311yescharacteristic
80C2×C22⋊Dic17C2×C411yescharacteristic
81C2×C22⋊Dic17C2×C411yescharacteristic
82C2×#63227C2×C411yescharacteristic
83C2×#63227C2×C411yescharacteristic
84C2×#63227C2×C411yescharacteristic
85C2×#63227C2×C411yescharacteristic
86C2×#63227C2×C411yescharacteristic
87C2×#63227C2×C411yescharacteristic
88C2×#63227C2×C411yescharacteristic
89C2×#63227C2×C411yescharacteristic
90C2×#63225C2×C411yescharacteristic
91C2×#63225C2×C411yescharacteristic
92C2×#63225C2×C411yescharacteristic
93C2×#63225C2×C411yescharacteristic
94C2×C4×Dic17C2311yescharacteristic
95C2×C4×Dic17C2311yescharacteristic
96C22×#3622C2311yescharacteristic
97C22×#3622C2311yescharacteristic
98C22×#3622C2311yescharacteristic
99C22×#3622C2311yescharacteristic
100#10587558—41no—
101#10587558—41no—
102#10587558—41no—
103#10587558—41no—
104C17×C4⋊C8—41no—
105C17×C22⋊C8—41no—
106C17×C22⋊C8—41no—
107C4×C8×C17—41no—
108C17×#95C2×C411yescharacteristic
109C17×#95C2×C411yescharacteristic
110#10587502C2×C411yescharacteristic
111#10587502C2×C411yescharacteristic
112#10587502C2×C411yescharacteristic
113#10587502C2×C411yescharacteristic
114#10587502C2×C411yescharacteristic
115#10587502C2×C411yescharacteristic
116C22⋊#3622—41no—
117C22⋊#3622—41no—
118#10587491—22no—
119#10587491—22no—
120#10587491—22no—
121#10587491—22no—
122#10587491—41no—
123#10587491—41no—
124#10587491—41no—
125#10587491—41no—
126#10587486—41no—
127#10587485—41no—
128#10587485—41no—
129C8×Dic17—41no—
130C4⋊#3622—41no—
131#10587474—41no—
132C24×C17C22×C411yescharacteristic
133C23×D17—22no—
134C23×D17—22no—
135C23×D17—22no—
136C23×D17—41no—
137C23×D17—41no—
138C23×D17—41no—
139C23×D17—41no—
140C23×D17C22×C411yescharacteristic
141C23×D17C22×C411yescharacteristic
142C22×C4×C17—21no—
143C22×C4×C17—21no—
144C22×C4×C17—21no—
145C22×C4×C17—21no—
146C22×C4×C17—21no—
147C22×C4×C17—21no—
148C22×C4×C17C22×C411yescharacteristic
149C22×C4×C17C22×C411yescharacteristic
150C22×C4×C17C22×C411yescharacteristic
151C22×C4×C17C22×C411yescharacteristic
152C22×C4×C17C22×C411yescharacteristic
153C22×C4×C17C2411yescharacteristic
154C22×Dic17—22no—
155C22×Dic17—41no—
156C22×Dic17—41no—
157C22×Dic17C22×C411yescharacteristic
158C22×Dic17C22×C411yescharacteristic
159C22×Dic17C22×C411yescharacteristic
160C22×Dic17C22×C411yescharacteristic
161C22×Dic17C22×C411yescharacteristic
162C22×Dic17C22×C411yescharacteristic
163C2×C4×D17—21no—
164C2×C4×D17—21no—
165C2×C4×D17—21no—
166C2×C4×D17—21no—
167C2×C4×D17—22no—
168C2×C4×D17—21no—
169C2×C4×D17—21no—
170C2×C4×D17—21no—
171C2×C4×D17—21no—
172C2×C4×D17—21no—
173C2×C4×D17—21no—
174C2×C4×D17—22no—
175C2×C4×D17—44no—
176C2×C4×D17—44no—
177C2×C4×D17—44no—
178C2×C4×D17—44no—
179C2×C4×D17—41no—
180C2×C4×D17—41no—
181C2×C4×D17—41no—
182C2×C4×D17—41no—
183C2×C4×D17#4112yes—
184C2×C4×D17#4112yes—
185C2×C8×C17—21no—
186C2×C8×C17—21no—
187C2×C8×C17—21no—
188C2×C8×C17—21no—
189C2×C8×C17—21no—
190C2×C8×C17—21no—
191C2×C8×C17—21no—
192C2×C8×C17—21no—
193C2×C8×C17—21no—
194C2×C8×C17—21no—
195C2×C8×C17—21no—
196C2×C8×C17—21no—
197C22⋊C4×C17—22no—
198C22⋊C4×C17—41no—
199C42×C17—21no—
200C42×C17—21no—
201C42×C17—21no—
202C42×C17—21no—
203C22⋊Dic17—22no—
204C22⋊Dic17—41no—
205#63227—22no—
206#63227—22no—
207#63227—41no—
208#63227—41no—
209#63227—41no—
210#63227—41no—
211#63227—41no—
212#63227—41no—
213#63225—41no—
214#63225—41no—
215#63225—41no—
216#63225—41no—
217C4×Dic17—21no—
218C4×Dic17—21no—
219C4×Dic17—21no—
220C4×Dic17—21no—
221C2×#3622—21no—
222C2×#3622—21no—
223C2×#3622—21no—
224C2×#3622—21no—
225C2×#3622—21no—
226C2×#3622—21no—
227C2×#3622—21no—
228C2×#3622—21no—
229C2×#3622—21no—
230C2×#3622—21no—
231C2×#3622—21no—
232C2×#3622—21no—
233#21908—171nomaximal, Sylow
234C23×C17—21no—
235C23×C17—21no—
236C23×C17—21no—
237C23×C17—21no—
238C23×C17—21no—
239C23×C17—21no—
240C23×C17#13112yes—
241C23×C17C23×C411yescharacteristic
242C22×D17—21no—
243C22×D17—21no—
244C22×D17—21no—
245C22×D17—21no—
246C22×D17—21no—
247C22×D17—21no—
248C22×D17—21no—
249C22×D17—21no—
250C22×D17—21no—
251C22×D17—21no—
252C22×D17—21no—
253C22×D17—21no—
254C22×D17—44no—
255C22×D17—44no—
256C22×D17—44no—
257C22×D17—44no—
258C22×D17—44no—
259C22×D17—44no—
260C22×D17—44no—
261C22×D17#11712yes—
262C22×D17#13112yes—
263C2×C4×C17—21no—
264C2×C4×C17—21no—
265C2×C4×C17—21no—
266C2×C4×C17—21no—
267C2×C4×C17—21no—
268C2×C4×C17—21no—
269C2×C4×C17—21no—
270C2×C4×C17—21no—
271C2×C4×C17—21no—
272C2×C4×C17—21no—
273C2×C4×C17—21no—
274C2×C4×C17—21no—
275C2×C4×C17—21no—
276C2×C4×C17—21no—
277C2×C4×C17—21no—
278C2×C4×C17—41no—
279C2×C4×C17—41no—
280C2×C4×C17—41no—
281C2×C4×C17—41no—
282C2×C4×C17C2×#4111yescharacteristic
283C2×C4×C17C2×#4111yescharacteristic
284C2×C4×C17H(5,𝔽2)11yescharacteristic
285C2×C4×C17H(5,𝔽2)11yescharacteristic
286C2×C4×C17H(5,𝔽2)11yescharacteristic
287C2×C4×C17H(5,𝔽2)11yescharacteristic
288C2×Dic17—21no—
289C2×Dic17—21no—
290C2×Dic17—21no—
291C2×Dic17—21no—
292C2×Dic17—21no—
293C2×Dic17—21no—
294C2×Dic17—21no—
295C2×Dic17—21no—
296C2×Dic17—21no—
297C2×Dic17—21no—
298C2×Dic17—21no—
299C2×Dic17—21no—
300C2×Dic17—21no—
301C2×Dic17—21no—
302C2×Dic17—21no—
303C2×Dic17—21no—
304C2×Dic17—21no—
305C2×Dic17—44no—
306C2×Dic17#11712yes—
307C4×D17—22no—
308C4×D17—22no—
309C4×D17—22no—
310C4×D17—22no—
311C4×D17—44no—
312C4×D17—44no—
313C4×D17—41no—
314C4×D17—41no—
315C4×D17—41no—
316C4×D17—41no—
317C8×C17—41no—
318C8×C17—41no—
319C8×C17—41no—
320C8×C17—41no—
321#3622—41no—
322#3622—41no—
323#3622—41no—
324#3622—41no—
325#2280—171no—
326#1924—171no—
327#1924—171no—
328#1924—171no—
329#1924—171no—
330#1923—171no—
331#1923—171no—
332#1923—171no—
333#1923D1711yescharacteristic, complemented
334#1798—171no—
335#1798—171no—
336#1779—171no—
337#1779—171no—
338#1750—171no—
339#1750—171no—
340C22×C17—22no—
341C22×C17—22no—
342C22×C17—22no—
343C22×C17—41no—
344C22×C17—41no—
345C22×C17—41no—
346C22×C17—41no—
347C22×C17C2×#11711yescharacteristic
348C22×C17#51811yescharacteristic
349C22×C17#51811yescharacteristic
350C22×C17C2×#13111yescharacteristic
351C22×C17C2×#13111yescharacteristic
352C22×C17#56811yescharacteristic
353C22×C17#56811yescharacteristic
354C2×D17—22no—
355C2×D17—22no—
356C2×D17—22no—
357C2×D17—22no—
358C2×D17—22no—
359C2×D17—22no—
360C2×D17—416no—
361C2×D17—41no—
362C2×D17—41no—
363C2×D17—41no—
364C2×D17—41no—
365C2×D17—41no—
366C2×D17—41no—
367C2×D17—41no—
368C2×D17—41no—
369C4×C17—41no—
370C4×C17—41no—
371C4×C17—41no—
372C4×C17—41no—
373C4×C17—41no—
374C4×C17#53811yescharacteristic
375C4×C17#53811yescharacteristic
376C4×C17#53811yescharacteristic
377C4×C17#53811yescharacteristic
378Dic17—22no—
379Dic17—41no—
380Dic17—41no—
381Dic17—41no—
382Dic17—41no—
383Dic17—41no—
384C24×C4—171no—
385C2×#117—171no—
386C2×#117—171no—
387C2×C4⋊C8—171no—
388C2×C4⋊C8—171no—
389C2×C4⋊C8—171no—
390C2×C4⋊C8C2×D1711yescharacteristic, complemented
391C2×C22⋊C8—171no—
392C2×C22⋊C8—171no—
393C2×C22⋊C8—171no—
394C2×C22⋊C8—171no—
395C2×C22⋊C8—171no—
396C2×C22⋊C8—171no—
397C2×C22⋊C8—171no—
398C2×C22⋊C8—171no—
399C2×C22⋊C8—171no—
400C2×C22⋊C8—171no—
401C2×C22⋊C8C2×D1711yescharacteristic
402C2×C22⋊C8C2×D1711yescharacteristic
403C2×#97—171no—
404C2×#97—171no—
405C2×C4×C8—171no—
406C2×C4×C8C2×D1711yescharacteristic, complemented
407#381—171no—
408#381—171no—
409#380—171no—
410#380—171no—
411#380—171no—
412#380—171no—
413#379—171no—
414#379—171no—
415C4×C22⋊C4—171no—
416C4×C22⋊C4—171no—
417C4×C22⋊C4—171no—
418C4×C22⋊C4C2×D1711yescharacteristic
419#336—171no—
420#336—171no—
421#336—171no—
422#336—171no—
423#336—171no—
424#336—171no—
425#336C2×D1711yescharacteristic, complemented
426#336C2×D1711yescharacteristic, complemented
427C2×C17—42no—
428C2×C17#231211yescharacteristic
429C2×C17#292411yescharacteristic
430C2×C17#292411yescharacteristic
431C2×C17#297611yescharacteristic
432C2×C17#297611yescharacteristic
433C2×C17#297711yescharacteristic
434C2×C17#297811yescharacteristic
435D17—42no—
436D17—42no—
437C25—171no—
438C23×C4—171no—
439C23×C4—171no—
440C23×C4—171no—
441C23×C4—171no—
442C23×C4—171no—
443C23×C4—342no—
444C23×C4—342no—
445C23×C4—681no—
446C23×C4—681no—
447C23×C4—681no—
448C23×C4—681no—
449C23×C4C22×D1711yescharacteristic
450C22×C8—171no—
451C22×C8—171no—
452C22×C8—171no—
453C22×C8—171no—
454C22×C8C22×D1711yescharacteristic
455C22×C8C22×D1711yescharacteristic
456C22×C8C22×D1711yescharacteristic
457C22×C8C22×D1711yescharacteristic
458#117—681no—
459#117—681no—
460#117—681no—
461#117—681no—
462C2×C4⋊C4—171no—
463C2×C4⋊C4—171no—
464C2×C4⋊C4—171no—
465C2×C4⋊C4—171no—
466C2×C22⋊C4—171no—
467C2×C22⋊C4—171no—
468C2×C22⋊C4—171no—
469C2×C22⋊C4—171no—
470C2×C22⋊C4—171no—
471C2×C22⋊C4—171no—
472C2×C22⋊C4—171no—
473C2×C22⋊C4—171no—
474C2×C22⋊C4—171no—
475C2×C22⋊C4—171no—
476C2×C22⋊C4C4×D1711yescharacteristic
477C2×C22⋊C4C4×D1711yescharacteristic
478C2×C42—171no—
479C2×C42—171no—
480C2×C42C22×D1711yescharacteristic
481C2×C42C22×D1711yescharacteristic
482C4⋊C8—41no—
483C4⋊C8—681no—
484C4⋊C8—681no—
485C4⋊C8—681no—
486C22⋊C8—41no—
487C22⋊C8—41no—
488C22⋊C8—342no—
489C22⋊C8—342no—
490C22⋊C8—342no—
491C22⋊C8—342no—
492C22⋊C8—681no—
493C22⋊C8—681no—
494C22⋊C8—681no—
495C22⋊C8—681no—
496C22⋊C8—681no—
497C22⋊C8—681no—
498#97—681no—
499#97—681no—
500C4×C8—41no—
501C4×C8—681no—
502#95—171no—
503#95—171no—
504#95—171no—
505#95—171no—
506#95—171no—
507#95—171no—
508#95C4×D1711yescharacteristic
509#95C4×D1711yescharacteristic
510C17#2190811yescharacteristic, complemented, Sylow
511C24—171no—
512C24—171no—
513C24—342no—
514C24—342no—
515C24—342no—
516C24—681no—
517C24—681no—
518C24—681no—
519C24—681no—
520C24C2×C4×D1711yescharacteristic
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—171no—
528C22×C4—172no—
529C22×C4—172no—
530C22×C4—171no—
531C22×C4—171no—
532C22×C4—171no—
533C22×C4—171no—
534C22×C4—171no—
535C22×C4—342no—
536C22×C4—342no—
537C22×C4—342no—
538C22×C4—341no—
539C22×C4—341no—
540C22×C4—341no—
541C22×C4—341no—
542C22×C4—341no—
543C22×C4—341no—
544C22×C4—341no—
545C22×C4—341no—
546C22×C4—341no—
547C22×C4—341no—
548C22×C4—681no—
549C22×C4—681no—
550C22×C4—681no—
551C22×C4—681no—
552C22×C4—684no—
553C22×C4—684no—
554C22×C4—684no—
555C22×C4—684no—
556C22×C4—681no—
557C22×C4—681no—
558C22×C4C2×C4×D1711yescharacteristic
559C22×C4C2×C4×D1711yescharacteristic
560C22×C4C2×C4×D1711yescharacteristic
561C22×C4C2×C4×D1711yescharacteristic
562C22×C4C2×C4×D1711yescharacteristic
563C22×C4C23×D1711yescharacteristic
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—341no—
577C2×C8—341no—
578C2×C8—341no—
579C2×C8—341no—
580C2×C8—341no—
581C2×C8—341no—
582C2×C8—341no—
583C2×C8—341no—
584C2×C8—341no—
585C2×C8—341no—
586C2×C8—341no—
587C2×C8—341no—
588C4⋊C4—681no—
589C4⋊C4—681no—
590C4⋊C4—681no—
591C4⋊C4—681no—
592C22⋊C4—22no—
593C22⋊C4—41no—
594C22⋊C4—342no—
595C22⋊C4—342no—
596C22⋊C4—342no—
597C22⋊C4—681no—
598C22⋊C4—681no—
599C22⋊C4—681no—
600C22⋊C4—681no—
601C22⋊C4—681no—
602C22⋊C4—681no—
603C22⋊C4—681no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—21no—
608C42—341no—
609C42—341no—
610C42—341no—
611C42—341no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—172no—
619C23—172no—
620C23—341no—
621C23—341no—
622C23—341no—
623C23—341no—
624C23—341no—
625C23—341no—
626C23—341no—
627C23—341no—
628C23—341no—
629C23—341no—
630C23—341no—
631C23—341no—
632C23—684no—
633C23—684no—
634C23—684no—
635C23—684no—
636C23—684no—
637C23—684no—
638C23—684no—
639C23#1058758712yes—
640C23C22×C4×D1711yescharacteristic
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—172no—
661C2×C4—341no—
662C2×C4—341no—
663C2×C4—342no—
664C2×C4—342no—
665C2×C4—342no—
666C2×C4—342no—
667C2×C4—341no—
668C2×C4—341no—
669C2×C4—341no—
670C2×C4—341no—
671C2×C4—341no—
672C2×C4—341no—
673C2×C4—341no—
674C2×C4—341no—
675C2×C4—341no—
676C2×C4—341no—
677C2×C4—341no—
678C2×C4—341no—
679C2×C4—341no—
680C2×C4—341no—
681C2×C4—341no—
682C2×C4—684no—
683C2×C4—684no—
684C2×C4—684no—
685C2×C4—681no—
686C2×C4—681no—
687C2×C4—681no—
688C2×C4—681no—
689C2×C4#1058769111yescharacteristic
690C2×C4#1058769111yescharacteristic
691C2×C4#41×D1711yescharacteristic
692C2×C4#41×D1711yescharacteristic
693C2×C4#1058769611yescharacteristic
694C2×C4#1058769611yescharacteristic
695C8—41no—
696C8—41no—
697C8—41no—
698C8—41no—
699C8—681no—
700C8—681no—
701C8—681no—
702C8—681no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—342no—
711C22—342no—
712C22—342no—
713C22—342no—
714C22—342no—
715C22—342no—
716C22—6816no—
717C22—681no—
718C22—681no—
719C22—681no—
720C22—681no—
721C22—681no—
722C22—681no—
723C22—681no—
724C22—681no—
725C22#117×D1711yescharacteristic
726C22#1176328111yescharacteristic
727C22#1176328111yescharacteristic
728C22#131×D1711yescharacteristic
729C22C2×#1058758711yescharacteristic
730C22#1176357411yescharacteristic
731C22#1176357511yescharacteristic
732C4—41no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—342no—
738C4—681no—
739C4—681no—
740C4—681no—
741C4—681no—
742C4—681no—
743C4#1176339111yescharacteristic
744C4#1176339311yescharacteristic
745C4#1176339511yescharacteristic
746C4#1176339811yescharacteristic
747C2—42no—
748C2—682no—
749C2—682no—
750C2#1453137811yescharacteristic
751C2#1453743711yescharacteristic
752C2#1453744011yescharacteristic
753C2#1453782611yescharacteristic
754C2#1453783111yescharacteristic
755C2#1453783711yescharacteristic
756C2#1453784111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
FittingC17×#1923C2
prime radicalC24×D17C2×C4
cosocleC22×C4×C17C24
hypercenter#1923D17
hypocenterC17#21908
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
2. #14529400C2semidirect
3. #14529399C2semidirect
4. #14529398C2semidirect
5. #14529395C2semidirect
6. #14529390C2semidirect
7. #14529389C2semidirect
8. #14529387C2semidirect
9. #14528767C2semidirect
10. #14528765C2semidirect
13. #14528551C2semidirect
14. #14528549C2semidirect
15. C17×#1923C2semidirect
19. C2×C4⋊#3622C22semidirect
20. C2×#10587485C22semidirect
21. C2×#10587485C22semidirect
32. C2×#10587474C22semidirect
33. C2×#10587486C22semidirect
34. C2×C8×Dic17C22semidirect
46. #11762564C22semidirect
47. #11762564C22semidirect
48. #11762563C22semidirect
49. #11762563C22semidirect
50. #11762563C22semidirect
51. #11762563C22semidirect
52. C2×C17×C4⋊C8C22semidirect
55. C2×C4×C8×C17C22semidirect
57. C17×#336C22semidirect
58. C17×#336C22semidirect
333. #1923D17semidirect
390. C2×C4⋊C8C2×D17semidirect
406. C2×C4×C8C2×D17semidirect
425. #336C2×D17semidirect
426. #336C2×D17semidirect
510. C17#21908semidirect

Maximal subgroups

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

subgroupindex
#145311652
#145294002
#145293992
#145293982
#145293952
#145293902
#145293892
#145293872
#145287672
#145287652
#145286932
#145285512
#145285492
C17×#19232
#2190817