Finite Group Databasebeta

← #16936640

Subgroups — #16936640

Order 4352.

728 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763090C211yesmaximal, characteristic, complemented
2C2×#11763014C211yesmaximal, characteristic, complemented
3#14533697C211yesmaximal, characteristic
4#14529745C211yesmaximal, characteristic, complemented
5C2×#11762538C211yesmaximal, characteristic, complemented
6#14526668C211yesmaximal, characteristic, complemented
7C2×C17×D4⋊C8C211yesmaximal, characteristic, complemented
8C22×#63229—21no—
9C2×#10587555C2211yescharacteristic
10C2×#10587616—21no—
11C2×#10587624—21no—
12C2×C4×D68C2211yescharacteristic
13#11763090—22no—
14#11763090—22no—
15#11763014—22no—
16#11763014—22no—
17C2×#10587489—21no—
18C2×C4⋊#3622C2211yescharacteristic
19C2×#10587481—21no—
20C2×#10587492—21no—
21#11762725—22no—
22#11762679C2211yescharacteristic
23#11762669—21no—
24#11762666—21no—
25#11762572—22no—
26#11762538—22no—
27C2×C4×D4×C17C2211yescharacteristic
28C2×C17×C4⋊C8C2211yescharacteristic
29C2×C4×C8×C17C2211yescharacteristic
30C17×D4⋊C8—22no—
31C22×D4×C17D411yescharacteristic
32C23×C4×C17—21no—
33C22×C22⋊D17—22no—
34C22×D68D411yescharacteristic
35C22×C4×D17—21no—
36C22×Dic34—21no—
37C22×C8×C17—21no—
38C22×C8×C17—21no—
39C4×D4×C17—21no—
40C4×D4×C17—21no—
41C4×D4×C17—21no—
42C4×D4×C17—21no—
43C2×C4⋊C4×C17D411yescharacteristic
44C2×C22⋊C4×C17—21no—
45C2×C42×C17C2311yescharacteristic
46C2×C22⋊Dic17—22no—
47#10587624—42no—
48#10587624—42no—
49C2×#63229—24no—
50C2×#63229—42no—
51C2×#63229—42no—
52#10587616—42no—
53#10587616—42no—
54C2×#63227—22no—
55C2×#63227—21no—
56C2×C4⋊Dic17—21no—
57C2×C4⋊Dic17—21no—
58C2×C4⋊Dic17—21no—
59C2×C4⋊Dic17—21no—
60C2×C4⋊Dic17D411yescharacteristic
61C2×C4⋊Dic17D412yes—
62C22×#3622—21no—
63C4×D68—21no—
64C4×D68—21no—
65C4×D68—21no—
66C4×D68—21no—
67#10587555—21no—
68#10587555—21no—
69#10587555—21no—
70#10587555D412yescomplemented
71C17×C4⋊C8—21no—
72C17×C4⋊C8D412yescomplemented
73C4×C8×C17—21no—
74C4×C8×C17—21no—
75#10587502—22no—
76#10587492—24no—
77#10587489—24no—
78#10587481—24no—
79C4⋊#3622—21no—
80C4⋊#3622D412yescomplemented
81C24×C17—21no—
82C23×D17—21no—
83C2×D4×C17—21no—
84C2×D4×C17—21no—
85C2×D4×C17—21no—
86C2×D4×C17—21no—
87C2×D4×C17—21no—
88C2×D4×C17D812yes—
89C22×C4×C17—21no—
90C22×C4×C17—41no—
91C22×C4×C17—41no—
92C22×C4×C17—41no—
93C22×C4×C17—41no—
94C22×C4×C17—41no—
95C22×C4×C17—41no—
96C22×C4×C17C2×D411yescharacteristic
97C22×C4×C17C2×D411yescharacteristic
98C22×C4×C17C2×D411yescharacteristic
99C2×C22⋊D17—44no—
100C2×C22⋊D17—44no—
101C2×C22⋊D17—82no—
102C22×Dic17—21no—
103C22×Dic17—22no—
104C22×Dic17—41no—
105C2×D68—21no—
106C2×D68—21no—
107C2×D68—21no—
108C2×D68—21no—
109C2×D68—21no—
110C2×D68SD1612yescomplemented
111C2×C4×D17—41no—
112C2×C4×D17—41no—
113C2×C4×D17—41no—
114C2×C4×D17—41no—
115C2×C4×D17—41no—
116C2×C4×D17—41no—
117C2×Dic34—22no—
118C2×Dic34—41no—
119C2×Dic34—41no—
120C2×Dic34—41no—
121C2×Dic34—41no—
122C2×Dic34—41no—
123C2×C8×C17—22no—
124C2×C8×C17—22no—
125C2×C8×C17—41no—
126C2×C8×C17—41no—
127C2×C8×C17—41no—
128C2×C8×C17—41no—
129C4⋊C4×C17—21no—
130C4⋊C4×C17—21no—
131C22⋊C4×C17—41no—
132C22⋊C4×C17—41no—
133C42×C17C2×D411yescharacteristic
134C42×C17C2×D411yescharacteristic
135C42×C17C2×D411yescharacteristic
136C42×C17#4111yescharacteristic
137C22⋊Dic17—44no—
138#63229—48no—
139#63227—44no—
140#63227—41no—
141#63227—41no—
142C4⋊Dic17—21no—
143C4⋊Dic17—22no—
144C4⋊Dic17—22no—
145C4⋊Dic17—21no—
146C4⋊Dic17—41no—
147C4⋊Dic17—41no—
148C4⋊Dic17—41no—
149C4⋊Dic17—41no—
150C4⋊Dic17—41no—
151C4⋊Dic17—41no—
152C4⋊Dic17—42no—
153C2×#3622—22no—
154C2×#3622—41no—
155C2×#3622—41no—
156#10231—171nomaximal, Sylow
157C23×C17—22no—
158C23×C17—41no—
159C23×C17—41no—
160C23×C17—41no—
161C23×C17—41no—
162C23×C17—41no—
163C23×C17—41no—
164C23×C17#12011yescharacteristic
165C22×D17—22no—
166C22×D17—41no—
167C22×D17—41no—
168C22×D17—41no—
169C22×D17—41no—
170C22×D17—41no—
171C22×D17—41no—
172D4×C17—22no—
173D4×C17—22no—
174D4×C17—41no—
175D4×C17—41no—
176C2×C4×C17—21no—
177C2×C4×C17—21no—
178C2×C4×C17—41no—
179C2×C4×C17—41no—
180C2×C4×C17—41no—
181C2×C4×C17—81no—
182C2×C4×C17—81no—
183C2×C4×C17—81no—
184C2×C4×C17—81no—
185C2×C4×C17#12011yescharacteristic
186C2×C4×C17#12011yescharacteristic
187C2×C4×C17#12111yescharacteristic
188C2×C4×C17#12111yescharacteristic
189C2×C4×C17#12111yescharacteristic
190C2×C4×C17#12711yescharacteristic
191C2×C4×C17C2×D811yescharacteristic
192C2×C4×C17C2×SD1611yescharacteristic
193C2×C4×C17#13511yescharacteristic
194C2×C4×C17#13511yescharacteristic
195C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
196C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
197C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
198C2×C4×C17#13711yescharacteristic
199C22⋊D17—88no—
200C2×Dic17—42no—
201C2×Dic17—41no—
202C2×Dic17—41no—
203C2×Dic17—42no—
204C2×Dic17—41no—
205C2×Dic17—42no—
206C2×Dic17—42no—
207C2×Dic17—81no—
208C2×Dic17—81no—
209D68—22no—
210D68—22no—
211D68—41no—
212D68—41no—
213C4×D17—81no—
214C4×D17—81no—
215C4×D17—81no—
216C4×D17—81no—
217Dic34—42no—
218Dic34—42no—
219Dic34—81no—
220Dic34—81no—
221C8×C17—42no—
222C8×C17—42no—
223#3622—42no—
224C2×#474—171no—
225C2×#461—171no—
226#2537—171no—
227#1990—171no—
228C2×D4⋊C8—171no—
229C2×D4⋊C8D1711yescharacteristic, complemented
230#1296—171no—
231C22×C17—42no—
232C22×C17—42no—
233C22×C17—42no—
234C22×C17—81no—
235C22×C17—81no—
236C22×C17—81no—
237C22×C17—81no—
238C22×C17#39211yescharacteristic
239C22×C17#44711yescharacteristic
240C22×C17#44911yescharacteristic
241C22×C17#45011yescharacteristic
242C22×C17#45211yescharacteristic
243C22×C17#45511yescharacteristic
244C22×C17#45611yescharacteristic
245C2×D17—42no—
246C2×D17—42no—
247C2×D17—42no—
248C2×D17—81no—
249C2×D17—81no—
250C2×D17—81no—
251C2×D17—81no—
252C4×C17—21no—
253C4×C17—21no—
254C4×C17—81no—
255C4×C17#44711yescharacteristic
256C4×C17#44811yescharacteristic
257C4×C17#44911yescharacteristic
258C4×C17#44911yescharacteristic
259C4×C17#46511yescharacteristic
260C4×C17#46611yescharacteristic
261C4×C17#46811yescharacteristic
262C4×C17#46911yescharacteristic
263Dic17—82no—
264Dic17—82no—
265Dic17—81no—
266C22×SD16—341no—
267C2×C4⋊Q8—171no—
268C2×#121—341no—
269C2×#121—341no—
270C2×C4×D4—171no—
271C2×C4×D4C2×D1711yescharacteristic
272#474—342no—
273#474—342no—
274#461—342no—
275#461—342no—
276C2×#107—341no—
277C2×C4⋊C8—171no—
278C2×C4⋊C8C2×D1711yescharacteristic
279C2×#103—341no—
280C2×#102—341no—
281C2×C4×C8C2×D1711yescharacteristic
282#394—342no—
283#384—171no—
284#380—341no—
285#380—341no—
286#340—342no—
287D4⋊C8—22no—
288D4⋊C8—342no—
289C2×C17—82no—
290C2×C17#163911yescharacteristic
291C2×C17#164611yescharacteristic
292C2×C17#164711yescharacteristic
293C2×C17#165411yescharacteristic
294C2×C17#199911yescharacteristic
295C2×C17#200011yescharacteristic
296C2×C17#200711yescharacteristic
297D17—82no—
298C22×Q8—341no—
299C22×D4—171no—
300C22×D4—342no—
301C22×D4D6811yescharacteristic
302C23×C4—21no—
303C23×C4—341no—
304C2×SD16—344no—
305C2×SD16—682no—
306C2×SD16—682no—
307C22×C8—21no—
308C22×C8—21no—
309C22×C8—341no—
310C4⋊Q8—172no—
311C4⋊Q8—341no—
312C4⋊Q8—341no—
313C4⋊Q8—341no—
314#121—682no—
315#121—682no—
316#121—682no—
317#121—682no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4—341no—
323C4×D4—341no—
324C4×D4—341no—
325C4×D4—341no—
326C2×C4⋊C4—171no—
327C2×C4⋊C4—172no—
328C2×C4⋊C4—341no—
329C2×C4⋊C4—341no—
330C2×C4⋊C4—341no—
331C2×C4⋊C4—341no—
332C2×C4⋊C4D6811yescharacteristic
333C2×C22⋊C4—21no—
334C2×C22⋊C4—342no—
335C2×C22⋊C4—342no—
336C2×C22⋊C4—341no—
337C2×C42C22×D1711yescharacteristic
338#107—344no—
339C4⋊C8—21no—
340C4⋊C8—172no—
341C4⋊C8—341no—
342C4⋊C8C22⋊D1712yescomplemented
343#103—344no—
344#102—344no—
345C4×C8—21no—
346C4×C8—21no—
347#95—342no—
348C17#1023111yescharacteristic, complemented, Sylow
349C24—21no—
350C24—341no—
351C2×Q8—342no—
352C2×Q8—681no—
353C2×Q8—681no—
354C2×Q8—681no—
355C2×Q8—681no—
356C2×Q8—681no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—172no—
363C2×D4—341no—
364C2×D4—341no—
365C2×D4—341no—
366C2×D4—341no—
367C2×D4—341no—
368C2×D4—684no—
369C2×D4—684no—
370C2×D4—1362no—
371C2×D4D13612yes—
372C22×C4—21no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—341no—
380C22×C4—342no—
381C22×C4—681no—
382C22×C4—681no—
383C22×C4—681no—
384C22×C4—681no—
385C22×C4—681no—
386C22×C4—681no—
387C22×C4—681no—
388C22×C4C2×D6811yescharacteristic
389C22×C4D4×D1711yescharacteristic
390C22×C4D4×D1711yescharacteristic
391SD16—688no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—41no—
395C2×C8—41no—
396C2×C8—41no—
397C2×C8—41no—
398C2×C8—342no—
399C2×C8—681no—
400C2×C8—681no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—341no—
404C4⋊C4—342no—
405C4⋊C4—342no—
406C4⋊C4—341no—
407C4⋊C4—682no—
408C4⋊C4—681no—
409C4⋊C4—681no—
410C4⋊C4—681no—
411C4⋊C4—681no—
412C4⋊C4—681no—
413C4⋊C4—681no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—684no—
417C22⋊C4—684no—
418C22⋊C4—681no—
419C22⋊C4—681no—
420C42#6325211yescharacteristic
421C42D4×D1711yescharacteristic
422C42D4×D1711yescharacteristic
423C42C2×C22⋊D1711yescharacteristic
424C23—22no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—342no—
432C23—681no—
433C23—681no—
434C23—681no—
435C23—681no—
436C23—681no—
437C23—681no—
438C23#1058756811yescharacteristic
439Q8—682no—
440Q8—682no—
441Q8—1361no—
442Q8—1361no—
443D4—22no—
444D4—22no—
445D4—41no—
446D4—41no—
447D4—342no—
448D4—342no—
449D4—681no—
450D4—681no—
451D4—1368no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—81no—
461C2×C4—681no—
462C2×C4—682no—
463C2×C4—681no—
464C2×C4—682no—
465C2×C4—681no—
466C2×C4—682no—
467C2×C4—682no—
468C2×C4—1361no—
469C2×C4—1361no—
470C2×C4—1361no—
471C2×C4—1361no—
472C2×C4—1361no—
473C2×C4—1361no—
474C2×C4#1058756811yescharacteristic
475C2×C4#1058757011yescharacteristic
476C2×C4#1058757011yescharacteristic
477C2×C4C2×D13611yescharacteristic
478C2×C4#1058759011yescharacteristic
479C2×C4#1058759411yescharacteristic
480C2×C4#1058759411yescharacteristic
481C2×C4#1058759711yescharacteristic
482C2×C4#1058759811yescharacteristic
483C2×C4SD16×D1711yescharacteristic
484C2×C4#1058760111yescharacteristic
485C2×C4#1058761611yescharacteristic
486C2×C4#1058762311yescharacteristic
487C2×C4#1058762611yescharacteristic
488C8—42no—
489C8—42no—
490C8—682no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—682no—
499C22—682no—
500C22—682no—
501C22—1361no—
502C22—1361no—
503C22—1361no—
504C22—1361no—
505C22#1176271811yescharacteristic
506C22#1176294511yescharacteristic
507C22#1176295611yescharacteristic
508C22#1176296111yescharacteristic
509C22#1176297211yescharacteristic
510C22#1176298811yescharacteristic
511C22#1176299311yescharacteristic
512C4—21no—
513C4—21no—
514C4—81no—
515C4—1362no—
516C4—1361no—
517C4—1362no—
518C4#1176294511yescharacteristic
519C4#1176294611yescharacteristic
520C4#1176295111yescharacteristic
521C4#1176295611yescharacteristic
522C4#1176303711yescharacteristic
523C4#1176304511yescharacteristic
524C4#1176305411yescharacteristic
525C4#1176306211yescharacteristic
526C2—82no—
527C2—1362no—
528C2#1452796511yescharacteristic
529C2#1452801411yescharacteristic
530C2#1452802111yescharacteristic
531C2#1452807011yescharacteristic
532C2#1452978211yescharacteristic
533C2#1452978811yescharacteristic
534C2#1452983211yescharacteristic
subgroupG/H
centerC23#10587568
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC2×C17×D4⋊C8C2
socleC23×C17#120
prime radical#14533697C2
hypercenterC2×D4⋊C8D17
hypocenterC17#10231
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#11763090C2semidirect
2. C2×#11763014C2semidirect
4. #14529745C2semidirect
5. C2×#11762538C2semidirect
6. #14526668C2semidirect
7. C2×C17×D4⋊C8C2semidirect
70. #10587555D4semidirect
72. C17×C4⋊C8D4semidirect
80. C4⋊#3622D4semidirect
110. C2×D68SD16semidirect
229. C2×D4⋊C8D17semidirect
342. C4⋊C8C22⋊D17semidirect
348. C17#10231semidirect

Maximal subgroups

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

subgroupindex
C2×#117630902
C2×#117630142
#145336972
#145297452
C2×#117625382
#145266682
C2×C17×D4⋊C82
#1023117