Finite Group Databasebeta

← #17044351

Subgroups — #17044351

Order 4352.

894 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531270C211yesmaximal, characteristic
2#14529393C211yesmaximal, characteristic, complemented
3#14529392C211yesmaximal, characteristic, complemented
4#14529391C211yesmaximal, characteristic, complemented
5#14529390C211yesmaximal, characteristic, complemented
6#14529389C211yesmaximal, characteristic, complemented
7#14529388C211yesmaximal, characteristic, complemented
8#14529387C211yesmaximal, characteristic, complemented
9#14528767C211yesmaximal, characteristic, complemented
10#14528765C211yesmaximal, characteristic, complemented
11#14528695C211yesmaximal, characteristic
12#14528695C211yesmaximal, characteristic
13C4×#10587491C211yesmaximal, characteristic, complemented
14#14528541C211yesmaximal, characteristic, complemented
15C17×#1923C211yesmaximal, characteristic, complemented
16C22×#63252C2211yescharacteristic
17C2×#10587558C2211yescharacteristic
18C2×C42×D17C2211yescharacteristic
19C2×C4⋊#3622C2211yescharacteristic
20C2×#10587485C2211yescharacteristic
21C2×#10587485C2211yescharacteristic
22C2×C22⋊#3622C2211yescharacteristic
23C2×C22⋊#3622C2211yescharacteristic
24C2×#10587491C2211yescharacteristic
25C2×#10587491C2211yescharacteristic
26C2×#10587491C2211yescharacteristic
27C2×#10587491C2211yescharacteristic
28C2×#10587491C2211yescharacteristic
29C2×#10587491C2211yescharacteristic
30C2×#10587491C2211yescharacteristic
31C2×#10587491C2211yescharacteristic
32C2×C4×#3622C2211yescharacteristic
33C2×C8×Dic17C2211yescharacteristic
34C2×C8×Dic17C2211yescharacteristic
35#11762713C411yescharacteristic
36#11762713C411yescharacteristic
37#11762709C411yescharacteristic
38#11762709C411yescharacteristic
39#11762687C411yescharacteristic
40#11762687C411yescharacteristic
41#11762685C411yescharacteristic
42#11762685C411yescharacteristic
43C4×#63227C2211yescharacteristic
44C4×#63227C2211yescharacteristic
45C4×C22⋊Dic17C2211yescharacteristic
46#11762564C2211yescharacteristic
47#11762564C2211yescharacteristic
48#11762563C2211yescharacteristic
49#11762563C2211yescharacteristic
50#11762563C2211yescharacteristic
51#11762563C2211yescharacteristic
52C2×C17×C4⋊C8C2211yescharacteristic
53C2×C17×C22⋊C8C2211yescharacteristic
54C2×C17×C22⋊C8C2211yescharacteristic
55C2×C4×C8×C17C2211yescharacteristic
56C4×C22⋊C4×C17C2211yescharacteristic
57C17×#336C2211yescharacteristic
58C17×#336C2211yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C22×C22⋊D17C2×C411yescharacteristic
61C22×C22⋊D17C2×C411yescharacteristic
62C2×#63252—22no—
63C2×#63252—22no—
64C2×#63252—41no—
65C2×#63252—41no—
66C2×#63252—41no—
67C2×#63252—41no—
68C22×D68C2×C411yescharacteristic
69C22×C4×D17C2×C411yescharacteristic
70C22×C4×D17C2×C411yescharacteristic
71C22×C4×D17C2311yescharacteristic
72C22×C4×D17C2311yescharacteristic
73C22×Dic34C2×C411yescharacteristic
74C22×C8×C17C2311yescharacteristic
75C22×C8×C17C2311yescharacteristic
76C22×C8×C17C2311yescharacteristic
77C22×C8×C17C2311yescharacteristic
78C2×C22⋊C4×C17C2×C411yescharacteristic
79C2×C22⋊C4×C17C2×C411yescharacteristic
80C2×C42×C17C2311yescharacteristic
81C2×C42×C17C2311yescharacteristic
82C2×C22⋊Dic17C2×C411yescharacteristic
83C2×C22⋊Dic17C2×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×C4×Dic17C2×C411yescharacteristic
93C2×C4×Dic17C2×C411yescharacteristic
94C2×C4×Dic17C2311yescharacteristic
95C2×C4×Dic17C2311yescharacteristic
96C22×#3622C2311yescharacteristic
97C22×#3622C2311yescharacteristic
98C22×#3622C2311yescharacteristic
99C22×#3622C2311yescharacteristic
100#10587558—41no—
101#10587558—41no—
102C42×D17—41no—
103C42×D17—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#10587485—41no—
127#10587485—41no—
128C8×Dic17—41no—
129C8×Dic17—41no—
130C4⋊#3622—41no—
131C4×#3622—41no—
132C24×C17C22×C411yescharacteristic
133C23×D17C22×C411yescharacteristic
134C23×D17C22×C411yescharacteristic
135C22×C4×C17—21no—
136C22×C4×C17—21no—
137C22×C4×C17—21no—
138C22×C4×C17—21no—
139C22×C4×C17—21no—
140C22×C4×C17—21no—
141C22×C4×C17C22×C411yescharacteristic
142C22×C4×C17C22×C411yescharacteristic
143C22×C4×C17C22×C411yescharacteristic
144C22×C4×C17C22×C411yescharacteristic
145C22×C4×C17C22×C411yescharacteristic
146C22×C4×C17C2411yescharacteristic
147C2×C22⋊D17—22no—
148C2×C22⋊D17—22no—
149C2×C22⋊D17—41no—
150C2×C22⋊D17—41no—
151C2×C22⋊D17—41no—
152C2×C22⋊D17—41no—
153C22×Dic17C22×C411yescharacteristic
154C22×Dic17C22×C411yescharacteristic
155C22×Dic17C22×C411yescharacteristic
156C22×Dic17C22×C411yescharacteristic
157C22×Dic17C22×C411yescharacteristic
158C22×Dic17C22×C411yescharacteristic
159#63252—44no—
160#63252—44no—
161#63252—44no—
162#63252—44no—
163C2×D68—22no—
164C2×D68—41no—
165C2×D68—41no—
166C2×C4×D17—21no—
167C2×C4×D17—21no—
168C2×C4×D17—21no—
169C2×C4×D17—21no—
170C2×C4×D17—22no—
171C2×C4×D17—22no—
172C2×C4×D17—21no—
173C2×C4×D17—21no—
174C2×C4×D17—21no—
175C2×C4×D17—21no—
176C2×C4×D17—21no—
177C2×C4×D17—21no—
178C2×C4×D17—22no—
179C2×C4×D17—22no—
180C2×C4×D17—41no—
181C2×C4×D17—41no—
182C2×C4×D17#4112yes—
183C2×C4×D17#4112yes—
184C2×Dic34—22no—
185C2×Dic34—41no—
186C2×Dic34—41no—
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—
197C2×C8×C17—21no—
198C2×C8×C17—21no—
199C22⋊C4×C17—22no—
200C22⋊C4×C17—22no—
201C42×C17—21no—
202C42×C17—21no—
203C42×C17—21no—
204C42×C17—21no—
205C22⋊Dic17—22no—
206C22⋊Dic17—22no—
207#63227—22no—
208#63227—22no—
209#63227—22no—
210#63227—22no—
211#63227—41no—
212#63227—41no—
213#63225—41no—
214#63225—41no—
215C4×Dic17—21no—
216C4×Dic17—21no—
217C4×Dic17—21no—
218C4×Dic17—21no—
219C4×Dic17—41no—
220C4×Dic17—41no—
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#21903—171nomaximal, Sylow
234C23×C17—21no—
235C23×C17—21no—
236C23×C17—21no—
237C23×C17—21no—
238C23×C17—21no—
239C23×C17—21no—
240C23×C17—21no—
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—21no—
255C22×D17#11712yes—
256C2×C4×C17—21no—
257C2×C4×C17—21no—
258C2×C4×C17—21no—
259C2×C4×C17—21no—
260C2×C4×C17—21no—
261C2×C4×C17—21no—
262C2×C4×C17—21no—
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—41no—
270C2×C4×C17—41no—
271C2×C4×C17—41no—
272C2×C4×C17—41no—
273C2×C4×C17#13112yes—
274C2×C4×C17#13112yes—
275C2×C4×C17C2×#4111yescharacteristic
276C2×C4×C17C2×#4111yescharacteristic
277C2×C4×C17H(5,𝔽2)11yescharacteristic
278C2×C4×C17H(5,𝔽2)11yescharacteristic
279C2×C4×C17H(5,𝔽2)11yescharacteristic
280C2×C4×C17H(5,𝔽2)11yescharacteristic
281C22⋊D17—44no—
282C22⋊D17—44no—
283C2×Dic17—21no—
284C2×Dic17—21no—
285C2×Dic17—21no—
286C2×Dic17—21no—
287C2×Dic17—21no—
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#11712yes—
299C2×Dic17#13112yes—
300C2×Dic17#13112yes—
301D68—44no—
302C4×D17—22no—
303C4×D17—22no—
304C4×D17—22no—
305C4×D17—22no—
306C4×D17—44no—
307C4×D17—44no—
308C4×D17—41no—
309C4×D17—41no—
310C4×D17—41no—
311C4×D17—41no—
312Dic34—44no—
313C8×C17—41no—
314C8×C17—41no—
315C8×C17—41no—
316C8×C17—41no—
317#3622—41no—
318#3622—41no—
319#3622—41no—
320#3622—41no—
321#2297—171no—
322#1923—171no—
323#1923—171no—
324#1923—171no—
325#1923—171no—
326#1923—171no—
327#1923—171no—
328#1923—171no—
329#1923D1711yescharacteristic, complemented
330#1798—171no—
331#1798—171no—
332#1780—171no—
333#1780—171no—
334C4×C22⋊C8—171no—
335C4×C22⋊C8—171no—
336C22×C17—41no—
337C22×C17—41no—
338C22×C17—41no—
339C22×C17—41no—
340C22×C17—41no—
341C22×C17—41no—
342C22×C17—41no—
343C22×C17C2×#11711yescharacteristic
344C22×C17#51811yescharacteristic
345C22×C17#51811yescharacteristic
346C22×C17C2×#13111yescharacteristic
347C22×C17C2×#13111yescharacteristic
348C22×C17C2×#13111yescharacteristic
349C22×C17C2×#13111yescharacteristic
350C2×D17—22no—
351C2×D17—22no—
352C2×D17—22no—
353C2×D17—41no—
354C2×D17—41no—
355C2×D17—41no—
356C2×D17—41no—
357C2×D17—41no—
358C2×D17—41no—
359C2×D17—41no—
360C2×D17—41no—
361C2×D17—41no—
362C2×D17—41no—
363C2×D17—41no—
364C4×C17—22no—
365C4×C17—22no—
366C4×C17—41no—
367C4×C17—41no—
368C4×C17—41no—
369C4×C17#53811yescharacteristic
370C4×C17#53811yescharacteristic
371C4×C17#53811yescharacteristic
372C4×C17#53811yescharacteristic
373Dic17—22no—
374Dic17—22no—
375Dic17—22no—
376Dic17—41no—
377Dic17—41no—
378Dic17—41no—
379C22×#41—171no—
380C2×#117—171no—
381C22×C42—171no—
382C2×C4⋊C8—171no—
383C2×C4⋊C8—171no—
384C2×C4⋊C8—171no—
385C2×C4⋊C8C2×D1711yescharacteristic
386C2×C22⋊C8—171no—
387C2×C22⋊C8—171no—
388C2×C22⋊C8—171no—
389C2×C22⋊C8—171no—
390C2×C22⋊C8—171no—
391C2×C22⋊C8—171no—
392C2×C22⋊C8—171no—
393C2×C22⋊C8—171no—
394C2×C22⋊C8—171no—
395C2×C22⋊C8—171no—
396C2×C22⋊C8C2×D1711yescharacteristic
397C2×C22⋊C8C2×D1711yescharacteristic
398C2×C4×C8—171no—
399C2×C4×C8—171no—
400C2×C4×C8—171no—
401C2×C4×C8C2×D1711yescharacteristic
402#391—171no—
403#391—171no—
404#390—171no—
405#390—171no—
406#386—171no—
407#386—171no—
408#386—171no—
409#386—171no—
410C4×C22⋊C4—171no—
411C4×C22⋊C4—171no—
412C4×C22⋊C4—171no—
413C4×C22⋊C4C2×D1711yescharacteristic
414#336—171no—
415#336—171no—
416#336—171no—
417#336—171no—
418#336—171no—
419#336—171no—
420#336C2×D1711yescharacteristic
421#336C2×D1711yescharacteristic
422C2×C17—81no—
423C2×C17#231211yescharacteristic
424C2×C17#292211yescharacteristic
425C2×C17#292211yescharacteristic
426C2×C17#297711yescharacteristic
427C2×C17#297711yescharacteristic
428C2×C17#297911yescharacteristic
429C2×C17#297911yescharacteristic
430D17—42no—
431D17—81no—
432C2×#41—342no—
433C2×#41—342no—
434C2×#41—681no—
435C2×#41—681no—
436C2×#41—681no—
437C2×#41—681no—
438C22×Q8—171no—
439C22×D4—171no—
440C22×D4—171no—
441C22×D4—171no—
442C23×C4—171no—
443C23×C4—171no—
444C23×C4—171no—
445C23×C4—171no—
446C23×C4C22×D1711yescharacteristic
447C22×C8—171no—
448C22×C8—171no—
449C22×C8—171no—
450C22×C8—171no—
451C22×C8C22×D1711yescharacteristic
452C22×C8C22×D1711yescharacteristic
453C22×C8C22×D1711yescharacteristic
454C22×C8C22×D1711yescharacteristic
455#117—681no—
456#117—681no—
457C2×C4⋊C4—171no—
458C2×C4⋊C4—171no—
459C2×C22⋊C4—171no—
460C2×C22⋊C4—171no—
461C2×C22⋊C4—171no—
462C2×C22⋊C4—171no—
463C2×C22⋊C4—171no—
464C2×C22⋊C4—171no—
465C2×C22⋊C4—171no—
466C2×C22⋊C4—171no—
467C2×C22⋊C4C4×D1711yescharacteristic
468C2×C22⋊C4C4×D1711yescharacteristic
469C2×C42—171no—
470C2×C42—171no—
471C2×C42—171no—
472C2×C42—171no—
473C2×C42—681no—
474C2×C42—681no—
475C2×C42C22×D1711yescharacteristic
476C2×C42C22×D1711yescharacteristic
477C4⋊C8—41no—
478C4⋊C8—681no—
479C4⋊C8—681no—
480C4⋊C8—681no—
481C22⋊C8—41no—
482C22⋊C8—41no—
483C22⋊C8—342no—
484C22⋊C8—342no—
485C22⋊C8—342no—
486C22⋊C8—342no—
487C22⋊C8—681no—
488C22⋊C8—681no—
489C22⋊C8—681no—
490C22⋊C8—681no—
491C22⋊C8—681no—
492C22⋊C8—681no—
493C4×C8—41no—
494C4×C8—681no—
495C4×C8—681no—
496C4×C8—681no—
497#95—171no—
498#95—171no—
499#95—171no—
500#95—171no—
501#95—171no—
502#95—171no—
503#95C4×D1711yescharacteristic
504#95C4×D1711yescharacteristic
505C17#2190311yescharacteristic, complemented, Sylow
506C24—171no—
507C24—171no—
508C24C2×C4×D1711yescharacteristic
509#41—684no—
510#41—684no—
511#41—684no—
512#41—684no—
513C2×Q8—342no—
514C2×Q8—681no—
515C2×Q8—681no—
516C2×D4—342no—
517C2×D4—342no—
518C2×D4—342no—
519C2×D4—681no—
520C2×D4—681no—
521C2×D4—681no—
522C2×D4—681no—
523C2×D4—681no—
524C2×D4—681no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—171no—
532C22×C4—171no—
533C22×C4—171no—
534C22×C4—172no—
535C22×C4—172no—
536C22×C4—171no—
537C22×C4—171no—
538C22×C4—171no—
539C22×C4—342no—
540C22×C4—342no—
541C22×C4—341no—
542C22×C4—341no—
543C22×C4—341no—
544C22×C4—341no—
545C22×C4—341no—
546C22×C4—341no—
547C22×C4—341no—
548C22×C4—341no—
549C22×C4—341no—
550C22×C4—341no—
551C22×C4—342no—
552C22×C4—342no—
553C22×C4—681no—
554C22×C4—681no—
555C22×C4C2×C4×D1711yescharacteristic
556C22×C4C2×C4×D1711yescharacteristic
557C22×C4C2×C4×D1711yescharacteristic
558C22×C4C2×C4×D1711yescharacteristic
559C22×C4C2×C4×D1711yescharacteristic
560C22×C4C23×D1711yescharacteristic
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
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—341no—
574C2×C8—341no—
575C2×C8—341no—
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—
585C4⋊C4—681no—
586C4⋊C4—681no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—342no—
590C22⋊C4—342no—
591C22⋊C4—342no—
592C22⋊C4—342no—
593C22⋊C4—342no—
594C22⋊C4—342no—
595C22⋊C4—681no—
596C22⋊C4—681no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—341no—
602C42—341no—
603C42—341no—
604C42—341no—
605C42—681no—
606C42—681no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—172no—
615C23—341no—
616C23—341no—
617C23—341no—
618C23—341no—
619C23—341no—
620C23—341no—
621C23—341no—
622C23—341no—
623C23—341no—
624C23—341no—
625C23—341no—
626C23—341no—
627C23—341no—
628C23C22×C4×D1711yescharacteristic
629Q8—684no—
630D4—684no—
631D4—684no—
632D4—684no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—172no—
651C2×C4—172no—
652C2×C4—172no—
653C2×C4—341no—
654C2×C4—341no—
655C2×C4—341no—
656C2×C4—341no—
657C2×C4—341no—
658C2×C4—341no—
659C2×C4—342no—
660C2×C4—342no—
661C2×C4—342no—
662C2×C4—342no—
663C2×C4—341no—
664C2×C4—341no—
665C2×C4—341no—
666C2×C4—341no—
667C2×C4—341no—
668C2×C4—341no—
669C2×C4—341no—
670C2×C4—341no—
671C2×C4—341no—
672C2×C4—684no—
673C2×C4—684no—
674C2×C4—681no—
675C2×C4—681no—
676C2×C4—681no—
677C2×C4—681no—
678C2×C4#1058758712yes—
679C2×C4#1058759312yes—
680C2×C4#1058769111yescharacteristic
681C2×C4#1058769111yescharacteristic
682C2×C4#41×D1711yescharacteristic
683C2×C4#41×D1711yescharacteristic
684C2×C4#1058769611yescharacteristic
685C2×C4#1058769611yescharacteristic
686C8—41no—
687C8—41no—
688C8—41no—
689C8—41no—
690C8—681no—
691C8—681no—
692C8—681no—
693C8—681no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—342no—
702C22—342no—
703C22—342no—
704C22—681no—
705C22—681no—
706C22—681no—
707C22—681no—
708C22—681no—
709C22—681no—
710C22—681no—
711C22—681no—
712C22—681no—
713C22—681no—
714C22—681no—
715C22#117×D1711yescharacteristic
716C22#1176328111yescharacteristic
717C22#1176328111yescharacteristic
718C22#131×D1711yescharacteristic
719C22#131×D1711yescharacteristic
720C22C2×#1058758711yescharacteristic
721C22C2×#1058759311yescharacteristic
722C4—22no—
723C4—22no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—342no—
728C4—342no—
729C4—342no—
730C4—681no—
731C4—681no—
732C4—681no—
733C4#1176339111yescharacteristic
734C4#1176339311yescharacteristic
735C4#1176339511yescharacteristic
736C4#1176339811yescharacteristic
737C2—81no—
738C2—682no—
739C2—1361no—
740C2#1453137811yescharacteristic
741C2#1453742311yescharacteristic
742C2#1453742511yescharacteristic
743C2#1453783511yescharacteristic
744C2#1453783711yescharacteristic
745C2#1453784711yescharacteristic
746C2#1453784911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
FittingC17×#1923C2
prime radicalC22×#63252C22
cosocleC22×C4×C17C24
hypercenter#1923D17
hypocenterC17#21903
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
2. #14529393C2semidirect
3. #14529392C2semidirect
4. #14529391C2semidirect
5. #14529390C2semidirect
6. #14529389C2semidirect
7. #14529388C2semidirect
8. #14529387C2semidirect
9. #14528767C2semidirect
10. #14528765C2semidirect
13. C4×#10587491C2semidirect
14. #14528541C2semidirect
15. C17×#1923C2semidirect
329. #1923D17semidirect
505. C17#21903semidirect

Maximal subgroups

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

subgroupindex
#145312702
#145293932
#145293922
#145293912
#145293902
#145293892
#145293882
#145293872
#145287672
#145287652
#145286952
C4×#105874912
#145285412
C17×#19232
#2190317