Finite Group Databasebeta

← #16936664

Subgroups — #16936664

Order 4352.

712 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763096C211yesmaximal, characteristic, complemented
2#14533697C211yesmaximal, characteristic
3#14529587C211yesmaximal, characteristic, complemented
4C2×D4⋊#3622C211yesmaximal, characteristic, complemented
5C2×#11762536C211yesmaximal, characteristic, complemented
6#14526668C211yesmaximal, characteristic, complemented
7C2×C17×#476C211yesmaximal, characteristic, complemented
8C2×#10587616—21no—
9C2×#10587624—21no—
10C2×C4×D68C2211yescharacteristic
11#11763096—22no—
12#11763096—22no—
13C2×#10587479—21no—
14C2×C4⋊#3622C2211yescharacteristic
15C2×#10587506—22no—
16C2×#10587480—21no—
17C2×C4×#3622C2211yescharacteristic
18#11762725—22no—
19#11762679C2211yescharacteristic
20#11762669—21no—
21#11762666—21no—
22D4⋊#3622—22no—
23#11762536—22no—
24C2×C17×C4⋊Q8C2211yescharacteristic
25C2×C4×D4×C17C2211yescharacteristic
26C17×#476—22no—
27C17×#476—22no—
28C2×C17×#106—21no—
29C2×C17×C4⋊C8C2211yescharacteristic
30C2×C17×#102—21no—
31C22×Q8×C17—21no—
32C22×D4×C17D411yescharacteristic
33C23×C4×C17—21no—
34C22×C22⋊D17—22no—
35C22×D68D411yescharacteristic
36C22×C4×D17—21no—
37C22×C8×C17—21no—
38C17×C4⋊Q8—21no—
39C17×C4⋊Q8—21no—
40C17×C4⋊Q8—21no—
41C17×C4⋊Q8D412yescomplemented
42C4×D4×C17—21no—
43C4×D4×C17—21no—
44C4×D4×C17—21no—
45C4×D4×C17—21no—
46C2×C4⋊C4×C17—21no—
47C2×C4⋊C4×C17—21no—
48C2×C4⋊C4×C17D411yescharacteristic
49C2×C22⋊C4×C17—21no—
50C2×C42×C17C2311yescharacteristic
51C2×C22⋊Dic17—22no—
52#10587624—42no—
53#10587624—42no—
54#10587616—42no—
55#10587616—42no—
56C2×#63227—22no—
57C2×#63227—21no—
58C2×C4⋊Dic17—21no—
59C2×C4⋊Dic17—21no—
60C2×C4⋊Dic17D411yescharacteristic
61C2×C4⋊Dic17D412yes—
62C22×#3622—21no—
63C22×#3622—21no—
64C4×D68—21no—
65C4×D68—21no—
66C4×D68—21no—
67C4×D68—21no—
68C17×#106—24no—
69C17×C4⋊C8—21no—
70C17×C4⋊C8D412yescomplemented
71C17×#102—24no—
72#10587506—44no—
73#10587502—22no—
74#10587480—24no—
75#10587479—24no—
76C4⋊#3622—21no—
77C4⋊#3622D412yescomplemented
78C4×#3622—21no—
79C4×#3622—21no—
80C24×C17—21no—
81C23×D17—21no—
82C2×Q8×C17—22no—
83C2×Q8×C17—42no—
84C2×Q8×C17—42no—
85C2×Q8×C17—41no—
86C2×D4×C17—21no—
87C2×D4×C17—21no—
88C2×D4×C17—21no—
89C2×D4×C17—21no—
90C2×D4×C17—21no—
91C2×D4×C17SD1612yes—
92C22×C4×C17—21no—
93C22×C4×C17—41no—
94C22×C4×C17—41no—
95C22×C4×C17—41no—
96C22×C4×C17—41no—
97C22×C4×C17—41no—
98C22×C4×C17—41no—
99C22×C4×C17—41no—
100C22×C4×C17C2×D411yescharacteristic
101C22×C4×C17C2×D411yescharacteristic
102C22×C4×C17C2×D411yescharacteristic
103C2×C22⋊D17—44no—
104C2×C22⋊D17—44no—
105C2×C22⋊D17—82no—
106C22×Dic17—21no—
107C22×Dic17—22no—
108C2×D68—21no—
109C2×D68—21no—
110C2×D68—21no—
111C2×D68—21no—
112C2×D68—21no—
113C2×D68SD1612yes—
114C2×C4×D17—41no—
115C2×C4×D17—41no—
116C2×C4×D17—41no—
117C2×C4×D17—41no—
118C2×C4×D17—41no—
119C2×C4×D17—41no—
120C2×C8×C17—22no—
121C2×C8×C17—41no—
122C2×C8×C17—41no—
123C4⋊C4×C17—22no—
124C4⋊C4×C17—22no—
125C4⋊C4×C17—21no—
126C4⋊C4×C17—21no—
127C4⋊C4×C17—41no—
128C4⋊C4×C17—41no—
129C22⋊C4×C17—41no—
130C22⋊C4×C17—41no—
131C42×C17C2×D411yescharacteristic
132C42×C17C2×D411yescharacteristic
133C42×C17C2×D411yescharacteristic
134C42×C17#4111yescharacteristic
135C22⋊Dic17—44no—
136#63227—44no—
137#63227—41no—
138#63227—41no—
139C4⋊Dic17—21no—
140C4⋊Dic17—21no—
141C4⋊Dic17—41no—
142C4⋊Dic17—41no—
143C4⋊Dic17—41no—
144C4⋊Dic17—41no—
145C4⋊Dic17—42no—
146C2×#3622—22no—
147C2×#3622—22no—
148C2×#3622—41no—
149C2×#3622—41no—
150C2×#3622—41no—
151C2×#3622—41no—
152#10235—171nomaximal, Sylow
153C23×C17—22no—
154C23×C17—41no—
155C23×C17—41no—
156C23×C17—41no—
157C23×C17—41no—
158C23×C17—41no—
159C23×C17—41no—
160C23×C17#12011yescharacteristic
161C22×D17—22no—
162C22×D17—41no—
163C22×D17—41no—
164C22×D17—41no—
165C22×D17—41no—
166C22×D17—41no—
167C22×D17—41no—
168Q8×C17—44no—
169Q8×C17—82no—
170D4×C17—22no—
171D4×C17—22no—
172D4×C17—41no—
173D4×C17—41no—
174C2×C4×C17—21no—
175C2×C4×C17—21no—
176C2×C4×C17—41no—
177C2×C4×C17—42no—
178C2×C4×C17—41no—
179C2×C4×C17—41no—
180C2×C4×C17—81no—
181C2×C4×C17—81no—
182C2×C4×C17—81no—
183C2×C4×C17—81no—
184C2×C4×C17—81no—
185C2×C4×C17—81no—
186C2×C4×C17#12011yescharacteristic
187C2×C4×C17#12011yescharacteristic
188C2×C4×C17#12111yescharacteristic
189C2×C4×C17#12111yescharacteristic
190C2×C4×C17#12111yescharacteristic
191C2×C4×C17#12711yescharacteristic
192C2×C4×C17C2×SD1611yescharacteristic
193C2×C4×C17C2×SD1611yescharacteristic
194C2×C4×C17#13511yescharacteristic
195C2×C4×C17#13511yescharacteristic
196C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
197C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
198C2×C4×C17#13711yescharacteristic
199C2×C4×C17#13711yescharacteristic
200C22⋊D17—88no—
201C2×Dic17—41no—
202C2×Dic17—41no—
203C2×Dic17—42no—
204C2×Dic17—42no—
205C2×Dic17—41no—
206C2×Dic17—42no—
207D68—22no—
208D68—22no—
209D68—41no—
210D68—41no—
211C4×D17—81no—
212C4×D17—81no—
213C4×D17—81no—
214C4×D17—81no—
215C8×C17—42no—
216#3622—42no—
217#3622—42no—
218C2×#476—171no—
219C2×#476D1711yescharacteristic, complemented
220#2537—171no—
221#1956—171no—
222C2×D4⋊C8—171no—
223C2×D4⋊C8—171no—
224#1296—171no—
225C22×C17—42no—
226C22×C17—42no—
227C22×C17—42no—
228C22×C17—81no—
229C22×C17—81no—
230C22×C17—81no—
231C22×C17—81no—
232C22×C17#39211yescharacteristic
233C22×C17#45011yescharacteristic
234C22×C17#45011yescharacteristic
235C22×C17#45211yescharacteristic
236C22×C17#45211yescharacteristic
237C22×C17#45311yescharacteristic
238C22×C17#45411yescharacteristic
239C2×D17—42no—
240C2×D17—42no—
241C2×D17—42no—
242C2×D17—81no—
243C2×D17—81no—
244C2×D17—81no—
245C2×D17—81no—
246C4×C17—21no—
247C4×C17—21no—
248C4×C17—81no—
249C4×C17—82no—
250C4×C17#44811yescharacteristic
251C4×C17#44811yescharacteristic
252C4×C17#44911yescharacteristic
253C4×C17#44911yescharacteristic
254C4×C17#46511yescharacteristic
255C4×C17#46511yescharacteristic
256C4×C17#46811yescharacteristic
257C4×C17#46811yescharacteristic
258Dic17—82no—
259Dic17—81no—
260C2×C4⋊Q8C2×D1711yescharacteristic
261C2×#121—341no—
262C2×#121—341no—
263C2×C4×D4—171no—
264C2×C4×D4C2×D1711yescharacteristic
265#476—22no—
266#476—22no—
267#476—342no—
268#476—342no—
269C2×#106—21no—
270C2×#106—341no—
271C2×C4⋊C8—171no—
272C2×C4⋊C8C2×D1711yescharacteristic
273C2×#103—342no—
274C2×#102—21no—
275C2×#102—341no—
276C2×C4×C8—171no—
277#394—342no—
278#384—171no—
279#380—341no—
280#380—341no—
281D4⋊C8—342no—
282D4⋊C8—342no—
283C2×C17—82no—
284C2×C17#162911yescharacteristic
285C2×C17#163411yescharacteristic
286C2×C17#163511yescharacteristic
287C2×C17#163511yescharacteristic
288C2×C17#200011yescharacteristic
289C2×C17#200011yescharacteristic
290C2×C17#200611yescharacteristic
291D17—82no—
292C22×Q8—21no—
293C22×D4—171no—
294C22×D4—342no—
295C22×D4C22⋊D1711yescharacteristic
296C23×C4—21no—
297C23×C4—341no—
298C22×C8—21no—
299C22×C8—341no—
300C22×C8—341no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8C22⋊D1712yescomplemented
305#121—682no—
306#121—682no—
307#121—682no—
308#121—682no—
309C4×D4—21no—
310C4×D4—21no—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—341no—
314C4×D4—341no—
315C4×D4—341no—
316C4×D4—341no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—171no—
320C2×C4⋊C4—172no—
321C2×C4⋊C4—341no—
322C2×C4⋊C4—341no—
323C2×C4⋊C4C22⋊D1711yescharacteristic
324C2×C22⋊C4—21no—
325C2×C22⋊C4—342no—
326C2×C22⋊C4—342no—
327C2×C22⋊C4—341no—
328C2×C42C22×D1711yescharacteristic
329#106—24no—
330#106—344no—
331C4⋊C8—21no—
332C4⋊C8—172no—
333C4⋊C8—341no—
334C4⋊C8C22⋊D1712yescomplemented
335#103—684no—
336#102—24no—
337#102—344no—
338C4×C8—341no—
339C4×C8—341no—
340#95—342no—
341C17#1023511yescharacteristic, complemented, Sylow
342C24—21no—
343C24—341no—
344C2×Q8—22no—
345C2×Q8—42no—
346C2×Q8—42no—
347C2×Q8—41no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—172no—
354C2×D4—341no—
355C2×D4—341no—
356C2×D4—341no—
357C2×D4—341no—
358C2×D4—341no—
359C2×D4—684no—
360C2×D4—684no—
361C2×D4—1362no—
362C2×D4#6323012yes—
363C22×C4—21no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—341no—
372C22×C4—342no—
373C22×C4—681no—
374C22×C4—681no—
375C22×C4—681no—
376C22×C4—681no—
377C22×C4—681no—
378C22×C4—681no—
379C22×C4D4×D1711yescharacteristic
380C22×C4D4×D1711yescharacteristic
381C22×C4C2×C22⋊D1711yescharacteristic
382C2×C8—22no—
383C2×C8—41no—
384C2×C8—41no—
385C2×C8—342no—
386C2×C8—342no—
387C2×C8—681no—
388C2×C8—681no—
389C2×C8—681no—
390C2×C8—681no—
391C4⋊C4—22no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—21no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—341no—
398C4⋊C4—341no—
399C4⋊C4—682no—
400C4⋊C4—681no—
401C4⋊C4—681no—
402C4⋊C4—681no—
403C4⋊C4—681no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—684no—
407C22⋊C4—684no—
408C22⋊C4—681no—
409C22⋊C4—681no—
410C42D4×D1711yescharacteristic
411C42#6325411yescharacteristic
412C42C2×C22⋊D1711yescharacteristic
413C42C2×C22⋊D1711yescharacteristic
414C23—22no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—342no—
422C23—681no—
423C23—681no—
424C23—681no—
425C23—681no—
426C23—681no—
427C23—681no—
428C23#1058762311yescharacteristic
429Q8—44no—
430Q8—82no—
431D4—22no—
432D4—22no—
433D4—41no—
434D4—41no—
435D4—342no—
436D4—342no—
437D4—681no—
438D4—681no—
439D4—1368no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4—81no—
450C2×C4—81no—
451C2×C4—81no—
452C2×C4—682no—
453C2×C4—681no—
454C2×C4—682no—
455C2×C4—681no—
456C2×C4—681no—
457C2×C4—682no—
458C2×C4—1361no—
459C2×C4—1361no—
460C2×C4—1361no—
461C2×C4—1361no—
462C2×C4SD16×D1711yescharacteristic
463C2×C4#1058760011yescharacteristic
464C2×C4#1058760111yescharacteristic
465C2×C4#1058760211yescharacteristic
466C2×C4#1058762311yescharacteristic
467C2×C4#1058762411yescharacteristic
468C2×C4#1058762511yescharacteristic
469C2×C4#1058762511yescharacteristic
470C2×C4#1058762611yescharacteristic
471C2×C4C2×#6323011yescharacteristic
472C2×C4#1058762811yescharacteristic
473C2×C4#1058763511yescharacteristic
474C2×C4#1058763611yescharacteristic
475C2×C4#1058763911yescharacteristic
476C8—42no—
477C8—682no—
478C8—682no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22—682no—
487C22—682no—
488C22—682no—
489C22—1361no—
490C22—1361no—
491C22—1361no—
492C22—1361no—
493C22#1176271711yescharacteristic
494C22#1176295811yescharacteristic
495C22#1176295911yescharacteristic
496C22#1176296811yescharacteristic
497C22#1176296911yescharacteristic
498C22#1176297511yescharacteristic
499C22#1176298011yescharacteristic
500C4—21no—
501C4—21no—
502C4—82no—
503C4—81no—
504C4—1362no—
505C4—1361no—
506C4#1176294611yescharacteristic
507C4#1176294811yescharacteristic
508C4#1176295311yescharacteristic
509C4#1176295411yescharacteristic
510C4#1176303511yescharacteristic
511C4#1176304011yescharacteristic
512C4#1176305211yescharacteristic
513C4#1176305711yescharacteristic
514C2—82no—
515C2—1362no—
516C2#1452789911yescharacteristic
517C2#1452792811yescharacteristic
518C2#1452793311yescharacteristic
519C2#1452793411yescharacteristic
520C2#1452978411yescharacteristic
521C2#1452978511yescharacteristic
522C2#1452982411yescharacteristic
subgroupG/H
centerC23#10587623
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC2×C17×#476C2
socleC23×C17#120
prime radical#14533697C2
hypercenterC2×#476D17
hypocenterC17#10235
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#11763096C2semidirect
3. #14529587C2semidirect
4. C2×D4⋊#3622C2semidirect
5. C2×#11762536C2semidirect
6. #14526668C2semidirect
7. C2×C17×#476C2semidirect
41. C17×C4⋊Q8D4semidirect
70. C17×C4⋊C8D4semidirect
77. C4⋊#3622D4semidirect
219. C2×#476D17semidirect
304. C4⋊Q8C22⋊D17semidirect
334. C4⋊C8C22⋊D17semidirect
341. C17#10235semidirect

Maximal subgroups

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

subgroupindex
C2×#117630962
#145336972
#145295872
C2×D4⋊#36222
C2×#117625362
#145266682
C2×C17×#4762
#1023517