Finite Group Databasebeta

← #16928396

Subgroups — #16928396

Order 4352.

658 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531487C211yesmaximal, characteristic
2#14529099C211yesmaximal, characteristic
3#14528974C211yesmaximal, characteristic, complemented
4C2×#11762544C211yesmaximal, characteristic
5#14527040C211yesmaximal, characteristic, complemented
6#14526664C211yesmaximal, characteristic, complemented
7C17×#1280C211yesmaximal, characteristic, complemented
8C2×#10587616C2211yescharacteristic
9C2×C4×C22⋊D17—21no—
10C22×C4⋊Dic17C2211yescharacteristic
11C2×#10587489—21no—
12C2×#10587492—21no—
13#11762701—21no—
14#11762694—21no—
15#11762688—21no—
16#11762687—21no—
17#11762683—21no—
18#11762669C2211yescharacteristic
19C2×#10587502—21no—
20C2×#10587502—21no—
21C2×#10587502C2211yescharacteristic
22#11762572—21no—
23#11762572—21no—
24#11762544C414yescomplemented
25C2×C17×C22⋊C8C2211yescharacteristic
26C2×C17×C22⋊C8C2211yescharacteristic
27C2×C17×#95C2211yescharacteristic
28C23×C4×C17D411yescharacteristic
29C23×C4×C17D411yescharacteristic
30C23×C4×C17C2311yescharacteristic
31C22×C22⋊D17—21no—
32C23×Dic17—21no—
33C23×Dic17—21no—
34C22×D68D411yescharacteristic
35C22×C4×D17—21no—
36C22×C8×C17—21no—
37C22×C8×C17—21no—
38C2×C22⋊Dic17—21no—
39#10587616—21no—
40#10587616—21no—
41#10587616C2×C412yes—
42#10587616Q812yes—
43C4×C22⋊D17—42no—
44C4×C22⋊D17—42no—
45C2×#63227—21no—
46C2×#63227—21no—
47C2×#63227—21no—
48C2×#63227—21no—
49C2×C4⋊Dic17—21no—
50C2×C4⋊Dic17—21no—
51C2×C4⋊Dic17—42no—
52C2×C4⋊Dic17D411yescharacteristic
53C2×C4⋊Dic17D411yescharacteristic
54C2×C4⋊Dic17D411yescharacteristic
55C2×#63225—21no—
56C2×C4×Dic17—21no—
57C17×C22⋊C8—21no—
58C17×C22⋊C8—21no—
59C17×C22⋊C8—21no—
60C17×C22⋊C8C2×C412yescomplemented
61C17×#95—21no—
62C17×#95—21no—
63#10587502—21no—
64#10587502—21no—
65#10587502—21no—
66#10587502—21no—
67#10587502—42no—
68#10587502—42no—
69#10587502C2×C412yescomplemented
70#10587492—42no—
71#10587489—42no—
72C24×C17C2×D411yescharacteristic
73C23×D17—21no—
74C22×C4×C17—21no—
75C22×C4×C17—21no—
76C22×C4×C17—21no—
77C22×C4×C17—21no—
78C22×C4×C17—21no—
79C22×C4×C17—41no—
80C22×C4×C17—41no—
81C22×C4×C17—41no—
82C22×C4×C17—41no—
83C22×C4×C17—41no—
84C22×C4×C17—41no—
85C22×C4×C17D812yes—
86C22×C4×C17C22×C411yescharacteristic
87C22×C4×C17C2×D411yescharacteristic
88C22×C4×C17C2×D411yescharacteristic
89C22×C4×C17C2×Q811yescharacteristic
90C22×C4×C17#4111yescharacteristic
91C22×C4×C17#4111yescharacteristic
92C2×C22⋊D17—22no—
93C2×C22⋊D17—22no—
94C2×C22⋊D17—41no—
95C2×C22⋊D17—41no—
96C2×C22⋊D17—41no—
97C2×C22⋊D17—41no—
98C22×Dic17—21no—
99C22×Dic17—22no—
100C22×Dic17—22no—
101C22×Dic17—21no—
102C22×Dic17—21no—
103C22×Dic17—41no—
104C22×Dic17—41no—
105C22×Dic17—41no—
106C22×Dic17—41no—
107C22×Dic17—41no—
108C22×Dic17—41no—
109C22×Dic17—41no—
110C22×Dic17—41no—
111C22×Dic17—41no—
112C22×Dic17—41no—
113C22×Dic17—41no—
114C22×Dic17—41no—
115C2×D68—21no—
116C2×D68—41no—
117C2×D68—41no—
118C2×D68C4⋊C412yes—
119C2×C4×D17—42no—
120C2×C4×D17—81no—
121C2×C4×D17—81no—
122C2×C8×C17—22no—
123C2×C8×C17—41no—
124C2×C8×C17—41no—
125C2×C8×C17—41no—
126C2×C8×C17—41no—
127C2×C8×C17—41no—
128C22⋊Dic17—41no—
129C22⋊Dic17—41no—
130#63227—22no—
131#63227—22no—
132#63227—42no—
133#63227—81no—
134#63227—81no—
135C4⋊Dic17—21no—
136C4⋊Dic17—22no—
137C4⋊Dic17—22no—
138C4⋊Dic17—41no—
139C4⋊Dic17—41no—
140C4⋊Dic17—41no—
141C4⋊Dic17—41no—
142C4⋊Dic17C4⋊C412yes—
143#63225—42no—
144C4×Dic17—42no—
145#8869—171nomaximal, Sylow
146C23×C17—21no—
147C23×C17—21no—
148C23×C17—21no—
149C23×C17—21no—
150C23×C17C4×D411yescharacteristic
151C23×C17#12011yescharacteristic
152C23×C17C22⋊Q811yescharacteristic
153C23×C17C2×D811yescharacteristic
154C23×C17#13511yescharacteristic
155C23×C17AGL(1,ℤ/8)11yescharacteristic
156C23×C17#13711yescharacteristic
157C22×D17—22no—
158C22×D17—41no—
159C22×D17—41no—
160C22×D17—41no—
161C22×D17—41no—
162C22×D17—41no—
163C22×D17—41no—
164C2×C4×C17—21no—
165C2×C4×C17—21no—
166C2×C4×C17—21no—
167C2×C4×C17—21no—
168C2×C4×C17—22no—
169C2×C4×C17—41no—
170C2×C4×C17—41no—
171C2×C4×C17—41no—
172C2×C4×C17—41no—
173C2×C4×C17—41no—
174C2×C4×C17—41no—
175C2×C4×C17—42no—
176C2×C4×C17—42no—
177C2×C4×C17—41no—
178C2×C4×C17—41no—
179C2×C4×C17—41no—
180C2×C4×C17—81no—
181C2×C4×C17—81no—
182C2×C4×C17C2×C4⋊C411yescharacteristic
183C2×C4×C17C4×D411yescharacteristic
184C2×C4×C17C22⋊Q811yescharacteristic
185C2×C4×C17#12311yescharacteristic
186C22⋊D17—42no—
187C22⋊D17—42no—
188C22⋊D17—42no—
189C22⋊D17—42no—
190C2×Dic17—22no—
191C2×Dic17—41no—
192C2×Dic17—41no—
193C2×Dic17—42no—
194C2×Dic17—42no—
195C2×Dic17—42no—
196C2×Dic17—42no—
197C2×Dic17—42no—
198C2×Dic17—41no—
199C2×Dic17—41no—
200C2×Dic17—41no—
201C2×Dic17—41no—
202C2×Dic17—42no—
203C2×Dic17—41no—
204C2×Dic17—41no—
205C2×Dic17—81no—
206C2×Dic17—81no—
207C2×Dic17—81no—
208C2×Dic17—81no—
209C2×Dic17—81no—
210C2×Dic17—81no—
211C2×Dic17—81no—
212C2×Dic17—81no—
213D68—42no—
214D68—81no—
215C4×D17—84no—
216C8×C17—42no—
217C8×C17—81no—
218#2325—171no—
219#1874—171no—
220#1852—171no—
221C2×#327—171no—
222#1442—171no—
223#1294—171no—
224#1280D1711yescharacteristic, complemented
225C22×C17—21no—
226C22×C17—21no—
227C22×C17—21no—
228C22×C17—21no—
229C22×C17—21no—
230C22×C17—21no—
231C22×C17—21no—
232C22×C17—21no—
233C22×C17—21no—
234C22×C17—21no—
235C22×C17—21no—
236C22×C17—21no—
237C22×C17#38511yescharacteristic
238C22×C17C4×D811yescharacteristic
239C22×C17#44011yescharacteristic
240C22×C17#44711yescharacteristic
241C22×C17#45211yescharacteristic
242C22×C17#45411yescharacteristic
243C22×C17#45511yescharacteristic
244C22×C17B(4,𝔽2)11yescharacteristic
245C22×C17#45811yescharacteristic
246C22×C17#47411yescharacteristic
247C22×C17#47811yescharacteristic
248C2×D17—42no—
249C2×D17—42no—
250C2×D17—42no—
251C2×D17—81no—
252C2×D17—81no—
253C2×D17—81no—
254C2×D17—81no—
255C4×C17—21no—
256C4×C17—21no—
257C4×C17—21no—
258C4×C17—21no—
259C4×C17—42no—
260C4×C17—81no—
261Dic17—42no—
262Dic17—82no—
263Dic17—81no—
264Dic17—82no—
265Dic17—81no—
266C2×#121—171no—
267C2×C4×D4—341no—
268C22×C4⋊C4—171no—
269C2×#107—341no—
270C2×#102—341no—
271C2×C22⋊C8C2×D1711yescharacteristic
272C2×C22⋊C8C2×D1711yescharacteristic
273#388—341no—
274#387—341no—
275#386—341no—
276#386—341no—
277#385—341no—
278#380—171no—
279C2×#95—171no—
280C2×#95—341no—
281C2×#95—341no—
282C2×#95C2×D1711yescharacteristic
283#340—341no—
284#340—341no—
285#327—174no—
286C2×C17—21no—
287C2×C17—21no—
288C2×C17—21no—
289C2×C17—21no—
290C2×C17#159811yescharacteristic
291C2×C17#160611yescharacteristic
292C2×C17#160711yescharacteristic
293C2×C17#161511yescharacteristic
294C2×C17#186011yescharacteristic
295C2×C17#186211yescharacteristic
296C2×C17#186711yescharacteristic
297D17—82no—
298C22×D4—171no—
299C22×D4—341no—
300C23×C4—341no—
301C23×C4—341no—
302C23×C4—341no—
303C23×C4D6811yescharacteristic
304C23×C4D6811yescharacteristic
305C23×C4C22×D1711yescharacteristic
306C22×C8—21no—
307C22×C8—21no—
308#121—172no—
309#121—172no—
310#121—341no—
311#121—341no—
312C4×D4—682no—
313C4×D4—682no—
314C2×C4⋊C4—171no—
315C2×C4⋊C4—171no—
316C2×C4⋊C4—171no—
317C2×C4⋊C4—341no—
318C2×C4⋊C4—341no—
319C2×C4⋊C4—341no—
320C2×C4⋊C4—682no—
321C2×C22⋊C4—341no—
322C2×C22⋊C4—341no—
323C2×C22⋊C4—341no—
324C2×C22⋊C4—341no—
325C2×C22⋊C4—341no—
326C2×C42—341no—
327#107—682no—
328#102—682no—
329C22⋊C8—21no—
330C22⋊C8—21no—
331C22⋊C8—21no—
332C22⋊C8C4×D1712yescomplemented
333#95—21no—
334#95—21no—
335#95—172no—
336#95—341no—
337#95—341no—
338#95—341no—
339#95—341no—
340#95—682no—
341#95—682no—
342C17#886911yescharacteristic, complemented, Sylow
343C24—341no—
344C24C2×D6811yescharacteristic
345C2×D4—172no—
346C2×D4—342no—
347C2×D4—342no—
348C2×D4—341no—
349C2×D4—681no—
350C2×D4—681no—
351C2×D4—681no—
352C2×D4—681no—
353C2×D4—681no—
354C2×D4—681no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—341no—
367C22×C4—342no—
368C22×C4—342no—
369C22×C4—341no—
370C22×C4—341no—
371C22×C4—682no—
372C22×C4—681no—
373C22×C4—681no—
374C22×C4—681no—
375C22×C4—681no—
376C22×C4—681no—
377C22×C4—681no—
378C22×C4—681no—
379C22×C4—681no—
380C22×C4—681no—
381C22×C4—681no—
382C22×C4—681no—
383C22×C4—681no—
384C22×C4—1361no—
385C22×C4—1361no—
386C22×C4D13612yes—
387C22×C4C2×C4×D1711yescharacteristic
388C22×C4#6325211yescharacteristic
389C22×C4D4×D1711yescharacteristic
390C22×C4D4×D1711yescharacteristic
391C22×C4#6325411yescharacteristic
392C22×C4Q8×D1711yescharacteristic
393C2×C8—22no—
394C2×C8—41no—
395C2×C8—41no—
396C2×C8—41no—
397C2×C8—41no—
398C2×C8—41no—
399C4⋊C4—172no—
400C4⋊C4—342no—
401C4⋊C4—342no—
402C4⋊C4—341no—
403C4⋊C4—681no—
404C4⋊C4—681no—
405C4⋊C4—681no—
406C4⋊C4—681no—
407C4⋊C4—682no—
408C22⋊C4—342no—
409C22⋊C4—342no—
410C22⋊C4—682no—
411C22⋊C4—681no—
412C22⋊C4—681no—
413C22⋊C4—1361no—
414C22⋊C4—1361no—
415C42—682no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—342no—
421C23—681no—
422C23—681no—
423C23—681no—
424C23—681no—
425C23—681no—
426C23—681no—
427C23C4×D6811yescharacteristic
428C23#1058756811yescharacteristic
429C23#1058758311yescharacteristic
430C23C2×D13611yescharacteristic
431C23#1058759011yescharacteristic
432C23#1058759411yescharacteristic
433C23#1058759511yescharacteristic
434D4—682no—
435D4—682no—
436D4—682no—
437D4—682no—
438D4—682no—
439D4—1361no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—81no—
457C2×C4—81no—
458C2×C4—342no—
459C2×C4—681no—
460C2×C4—681no—
461C2×C4—682no—
462C2×C4—682no—
463C2×C4—682no—
464C2×C4—682no—
465C2×C4—681no—
466C2×C4—681no—
467C2×C4—681no—
468C2×C4—681no—
469C2×C4—681no—
470C2×C4—682no—
471C2×C4—681no—
472C2×C4—682no—
473C2×C4—1364no—
474C2×C4—1361no—
475C2×C4—1361no—
476C2×C4—1361no—
477C2×C4—1361no—
478C2×C4—1361no—
479C2×C4—1361no—
480C2×C4—1361no—
481C2×C4—1361no—
482C2×C4#1058756711yescharacteristic
483C2×C4#1058756911yescharacteristic
484C2×C4C4⋊C4×D1711yescharacteristic
485C2×C4#1058758211yescharacteristic
486C8—42no—
487C8—81no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—682no—
501C22—682no—
502C22—682no—
503C22—1361no—
504C22—1361no—
505C22—1361no—
506C22—1361no—
507C22#1176268311yescharacteristic
508C22C4×D13611yescharacteristic
509C22#1176291111yescharacteristic
510C22#1176294511yescharacteristic
511C22#1176297311yescharacteristic
512C22#1176298411yescharacteristic
513C22#1176298911yescharacteristic
514C22#1176299711yescharacteristic
515C22#1176300011yescharacteristic
516C22#1176309011yescharacteristic
517C22#1176311011yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—81no—
524C4—682no—
525C4—1362no—
526C4—1361no—
527C4—1362no—
528C4—1361no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—21no—
533C2—1362no—
534C2#1452772111yescharacteristic
535C2#1452776611yescharacteristic
536C2#1452777211yescharacteristic
537C2#1452781711yescharacteristic
538C2#1452902011yescharacteristic
539C2#1452903411yescharacteristic
540C2#1452906611yescharacteristic
subgroupG/H
centerC23#10587568
commutatorC22×C4×C17C22×C4
FrattiniC23×C4C22×D17
FittingC17×#1280C2
socleC23×C17#120
prime radicalC2×#10587616C22
cosocleC23×C4×C17C23
hypercenter#1280D17
hypocenterC17#8869
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
3. #14528974C2semidirect
5. #14527040C2semidirect
6. #14526664C2semidirect
7. C17×#1280C2semidirect
24. #11762544C4semidirect
60. C17×C22⋊C8C2×C4semidirect
69. #10587502C2×C4semidirect
224. #1280D17semidirect
332. C22⋊C8C4×D17semidirect
342. C17#8869semidirect

Maximal subgroups

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

subgroupindex
#145314872
#145290992
#145289742
C2×#117625442
#145270402
#145266642
C17×#12802
#886917