Finite Group Databasebeta

← #16937834

Subgroups — #16937834

Order 4352.

614 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14533697C211yesmaximal, characteristic
2#14528912C211yesmaximal, characteristic, complemented
3#14528785C211yesmaximal, characteristic, complemented
4#14528784C211yesmaximal, characteristic, complemented
5C2×#11762538C211yesmaximal, characteristic, complemented
6#14526668C211yesmaximal, characteristic, complemented
7C2×C17×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#10587616—21no—
9C2×#10587624—21no—
10C2×C4×D68C2211yescharacteristic
11C2×C4⋊#3622C2211yescharacteristic
12C2×#10587492—21no—
13C2×#10587503—21no—
14#11762725—22no—
15#11762679C2211yescharacteristic
16#11762679C2211yescharacteristic
17#11762669—21no—
18#11762666—21no—
19#11762572—21no—
20#11762572—22no—
21#11762571—21no—
22#11762538—22no—
23C2×C4×D4×C17C2211yescharacteristic
24C2×C17×C4⋊C8C2211yescharacteristic
25C2×C4×C8×C17C2211yescharacteristic
26C17×D4⋊C8—22no—
27C22×D4×C17D411yescharacteristic
28C23×C4×C17—21no—
29C22×C22⋊D17—22no—
30C22×D68D411yescharacteristic
31C22×C4×D17—21no—
32C22×C8×C17—21no—
33C22×C8×C17—21no—
34C4×D4×C17—21no—
35C4×D4×C17—21no—
36C4×D4×C17—21no—
37C4×D4×C17—21no—
38C2×C4⋊C4×C17D411yescharacteristic
39C2×C22⋊C4×C17—21no—
40C2×C42×C17C2311yescharacteristic
41C2×C22⋊Dic17—22no—
42#10587624—42no—
43#10587624—42no—
44#10587616—42no—
45#10587616—42no—
46C2×#63227—22no—
47C2×#63227—21no—
48C2×C4⋊Dic17—21no—
49C2×C4⋊Dic17—21no—
50C2×C4⋊Dic17—21no—
51C2×C4⋊Dic17—21no—
52C2×C4⋊Dic17—21no—
53C2×C4⋊Dic17D411yescharacteristic
54C2×C4⋊Dic17D412yes—
55C22×#3622—21no—
56C4×D68—21no—
57C4×D68—21no—
58C4×D68—21no—
59C4×D68—21no—
60C17×C4⋊C8—21no—
61C17×C4⋊C8—21no—
62C4×C8×C17—21no—
63C4×C8×C17D412yescomplemented
64#10587503—42no—
65#10587502—22no—
66#10587492—42no—
67C4⋊#3622—21no—
68C4⋊#3622—21no—
69C24×C17—21no—
70C23×D17—21no—
71C2×D4×C17—21no—
72C2×D4×C17—21no—
73C2×D4×C17—21no—
74C2×D4×C17—21no—
75C2×D4×C17—21no—
76C2×D4×C17SD1612yes—
77C22×C4×C17—21no—
78C22×C4×C17—41no—
79C22×C4×C17—41no—
80C22×C4×C17—41no—
81C22×C4×C17—41no—
82C22×C4×C17—41no—
83C22×C4×C17—41no—
84C22×C4×C17C2×D411yescharacteristic
85C22×C4×C17C2×D411yescharacteristic
86C22×C4×C17C2×D411yescharacteristic
87C2×C22⋊D17—44no—
88C2×C22⋊D17—44no—
89C2×C22⋊D17—82no—
90C22×Dic17—21no—
91C22×Dic17—22no—
92C22×Dic17—41no—
93C2×D68—21no—
94C2×D68—21no—
95C2×D68—21no—
96C2×D68—21no—
97C2×D68—21no—
98C2×D68D812yes—
99C2×C4×D17—41no—
100C2×C4×D17—41no—
101C2×C4×D17—41no—
102C2×C4×D17—41no—
103C2×C4×D17—41no—
104C2×C4×D17—41no—
105C2×C8×C17—22no—
106C2×C8×C17—41no—
107C2×C8×C17—41no—
108C2×C8×C17—41no—
109C2×C8×C17—41no—
110C2×C8×C17—41no—
111C4⋊C4×C17—21no—
112C4⋊C4×C17—21no—
113C22⋊C4×C17—41no—
114C22⋊C4×C17—41no—
115C42×C17C2×D411yescharacteristic
116C42×C17#4111yescharacteristic
117C42×C17#4111yescharacteristic
118C42×C17#4111yescharacteristic
119C22⋊Dic17—44no—
120#63227—44no—
121#63227—41no—
122#63227—41no—
123C4⋊Dic17—21no—
124C4⋊Dic17—21no—
125C4⋊Dic17—41no—
126C4⋊Dic17—41no—
127C4⋊Dic17—41no—
128C4⋊Dic17—41no—
129C4⋊Dic17—42no—
130C4⋊Dic17—42no—
131C4⋊Dic17—41no—
132C4⋊Dic17—41no—
133C4⋊Dic17—41no—
134C4⋊Dic17—41no—
135C2×#3622—41no—
136C2×#3622—41no—
137C2×#3622—41no—
138#10431—171nomaximal, Sylow
139C23×C17—22no—
140C23×C17—41no—
141C23×C17—41no—
142C23×C17—41no—
143C23×C17—41no—
144C23×C17—41no—
145C23×C17—41no—
146C23×C17#12011yescharacteristic
147C22×D17—22no—
148C22×D17—41no—
149C22×D17—41no—
150C22×D17—41no—
151C22×D17—41no—
152C22×D17—41no—
153C22×D17—41no—
154D4×C17—22no—
155D4×C17—22no—
156D4×C17—41no—
157D4×C17—41no—
158C2×C4×C17—21no—
159C2×C4×C17—21no—
160C2×C4×C17—41no—
161C2×C4×C17—41no—
162C2×C4×C17—41no—
163C2×C4×C17—81no—
164C2×C4×C17—81no—
165C2×C4×C17—81no—
166C2×C4×C17—81no—
167C2×C4×C17#12111yescharacteristic
168C2×C4×C17#12111yescharacteristic
169C2×C4×C17#12111yescharacteristic
170C2×C4×C17#12311yescharacteristic
171C2×C4×C17#12311yescharacteristic
172C2×C4×C17#12411yescharacteristic
173C2×C4×C17C2×D811yescharacteristic
174C2×C4×C17C2×SD1611yescharacteristic
175C2×C4×C17#13511yescharacteristic
176C2×C4×C17#13511yescharacteristic
177C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C17#13711yescharacteristic
181C22⋊D17—88no—
182C2×Dic17—41no—
183C2×Dic17—42no—
184C2×Dic17—41no—
185C2×Dic17—41no—
186C2×Dic17—42no—
187C2×Dic17—42no—
188C2×Dic17—81no—
189C2×Dic17—81no—
190C2×Dic17—81no—
191D68—22no—
192D68—22no—
193D68—41no—
194D68—41no—
195C4×D17—81no—
196C4×D17—81no—
197C4×D17—81no—
198C4×D17—81no—
199C8×C17—42no—
200C8×C17—81no—
201#3622—81no—
202#2537—171no—
203#1834—171no—
204#1802—171no—
205#1802—171no—
206C2×D4⋊C8—171no—
207C2×D4⋊C8D1711yescharacteristic, complemented
208#1296—171no—
209C22×C17—42no—
210C22×C17—42no—
211C22×C17—42no—
212C22×C17—81no—
213C22×C17—81no—
214C22×C17—81no—
215C22×C17—81no—
216C22×C17#39411yescharacteristic
217C22×C17#44711yescharacteristic
218C22×C17#44911yescharacteristic
219C22×C17#45011yescharacteristic
220C22×C17#45211yescharacteristic
221C22×C17#45411yescharacteristic
222C22×C17#45511yescharacteristic
223C2×D17—42no—
224C2×D17—42no—
225C2×D17—42no—
226C2×D17—81no—
227C2×D17—81no—
228C2×D17—81no—
229C2×D17—81no—
230C4×C17—21no—
231C4×C17—21no—
232C4×C17—81no—
233C4×C17#46511yescharacteristic
234C4×C17#46611yescharacteristic
235C4×C17#46811yescharacteristic
236C4×C17#46911yescharacteristic
237C4×C17#48011yescharacteristic
238C4×C17#48111yescharacteristic
239C4×C17#48211yescharacteristic
240C4×C17#48211yescharacteristic
241Dic17—82no—
242Dic17—81no—
243Dic17—161no—
244C2×#121—341no—
245C2×#121—341no—
246C2×C4×D4—171no—
247C2×C4×D4C2×D1711yescharacteristic
248C2×C4⋊C8—171no—
249C2×C4⋊C8C2×D1711yescharacteristic
250C2×#102—341no—
251C2×#102—341no—
252C2×C4×C8C2×D1711yescharacteristic
253#394—342no—
254#384—171no—
255#384—171no—
256#380—341no—
257#380—341no—
258#340—341no—
259#340—342no—
260#340—341no—
261D4⋊C8—22no—
262D4⋊C8—342no—
263C2×C17—82no—
264C2×C17#162511yescharacteristic
265C2×C17#163511yescharacteristic
266C2×C17#163911yescharacteristic
267C2×C17#164611yescharacteristic
268C2×C17#203311yescharacteristic
269C2×C17#203411yescharacteristic
270C2×C17#204011yescharacteristic
271D17—82no—
272C22×D4—171no—
273C22×D4—342no—
274C22×D4D6811yescharacteristic
275C23×C4—21no—
276C23×C4—341no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—341no—
280#121—682no—
281#121—682no—
282#121—682no—
283#121—682no—
284C4×D4—21no—
285C4×D4—21no—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4—341no—
289C4×D4—341no—
290C4×D4—341no—
291C4×D4—341no—
292C2×C4⋊C4—171no—
293C2×C4⋊C4—172no—
294C2×C4⋊C4—341no—
295C2×C4⋊C4—341no—
296C2×C4⋊C4—341no—
297C2×C4⋊C4—341no—
298C2×C4⋊C4—341no—
299C2×C4⋊C4D6811yescharacteristic
300C2×C22⋊C4—21no—
301C2×C22⋊C4—342no—
302C2×C22⋊C4—342no—
303C2×C22⋊C4—341no—
304C2×C42C22×D1711yescharacteristic
305C4⋊C8—21no—
306C4⋊C8—21no—
307C4⋊C8—341no—
308C4⋊C8—341no—
309#102—682no—
310#102—682no—
311C4×C8—21no—
312C4×C8C22⋊D1712yescomplemented
313#95—342no—
314C17#1043111yescharacteristic, complemented, Sylow
315C24—21no—
316C24—341no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—172no—
323C2×D4—341no—
324C2×D4—341no—
325C2×D4—341no—
326C2×D4—341no—
327C2×D4—341no—
328C2×D4—684no—
329C2×D4—684no—
330C2×D4—1362no—
331C2×D4#6321912yes—
332C22×C4—21no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—341no—
340C22×C4—342no—
341C22×C4—681no—
342C22×C4—681no—
343C22×C4—681no—
344C22×C4—681no—
345C22×C4—681no—
346C22×C4—681no—
347C22×C4—681no—
348C22×C4C2×D6811yescharacteristic
349C22×C4D4×D1711yescharacteristic
350C22×C4D4×D1711yescharacteristic
351C2×C8—22no—
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—41no—
355C2×C8—41no—
356C2×C8—41no—
357C2×C8—681no—
358C2×C8—681no—
359C2×C8—681no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—341no—
363C4⋊C4—341no—
364C4⋊C4—682no—
365C4⋊C4—682no—
366C4⋊C4—681no—
367C4⋊C4—681no—
368C4⋊C4—681no—
369C4⋊C4—681no—
370C4⋊C4—681no—
371C4⋊C4—681no—
372C4⋊C4—681no—
373C4⋊C4—681no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C22⋊C4—684no—
377C22⋊C4—684no—
378C22⋊C4—681no—
379C22⋊C4—681no—
380C42#6325211yescharacteristic
381C42#6325411yescharacteristic
382C42#6325411yescharacteristic
383C42C2×C22⋊D1711yescharacteristic
384C23—22no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—342no—
392C23—681no—
393C23—681no—
394C23—681no—
395C23—681no—
396C23—681no—
397C23—681no—
398C23#1058756811yescharacteristic
399D4—22no—
400D4—22no—
401D4—41no—
402D4—41no—
403D4—342no—
404D4—342no—
405D4—681no—
406D4—681no—
407D4—1368no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—682no—
418C2×C4—681no—
419C2×C4—681no—
420C2×C4—682no—
421C2×C4—681no—
422C2×C4—682no—
423C2×C4—1361no—
424C2×C4—1361no—
425C2×C4—1361no—
426C2×C4—1361no—
427C2×C4—1361no—
428C2×C4—1361no—
429C2×C4—1361no—
430C2×C4#1058756911yescharacteristic
431C2×C4#1058757111yescharacteristic
432C2×C4#1058757211yescharacteristic
433C2×C4C2×#6321911yescharacteristic
434C2×C4#1058759011yescharacteristic
435C2×C4#1058759411yescharacteristic
436C2×C4#1058759411yescharacteristic
437C2×C4D8×D1711yescharacteristic
438C2×C4#1058759811yescharacteristic
439C2×C4#1058760011yescharacteristic
440C2×C4#1058760111yescharacteristic
441C2×C4#1058761611yescharacteristic
442C2×C4#1058762411yescharacteristic
443C2×C4#1058762511yescharacteristic
444C8—42no—
445C8—81no—
446C8—1361no—
447C22—42no—
448C22—42no—
449C22—42no—
450C22—81no—
451C22—81no—
452C22—81no—
453C22—81no—
454C22—682no—
455C22—682no—
456C22—682no—
457C22—1361no—
458C22—1361no—
459C22—1361no—
460C22—1361no—
461C22#1176272511yescharacteristic
462C22#1176294411yescharacteristic
463C22#1176295611yescharacteristic
464C22#1176296211yescharacteristic
465C22#1176297211yescharacteristic
466C22#1176298311yescharacteristic
467C22#1176298811yescharacteristic
468C4—21no—
469C4—21no—
470C4—81no—
471C4—2721no—
472C4—1361no—
473C4—1362no—
474C4#1176303811yescharacteristic
475C4#1176304211yescharacteristic
476C4#1176305211yescharacteristic
477C4#1176306211yescharacteristic
478C4#1176312111yescharacteristic
479C4#1176312811yescharacteristic
480C4#1176313111yescharacteristic
481C4#1176313411yescharacteristic
482C2—82no—
483C2—1362no—
484C2#1452787611yescharacteristic
485C2#1452793711yescharacteristic
486C2#1452796611yescharacteristic
487C2#1452801411yescharacteristic
488C2#1452996511yescharacteristic
489C2#1452997411yescharacteristic
490C2#1453001211yescharacteristic
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#10431
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
2. #14528912C2semidirect
3. #14528785C2semidirect
4. #14528784C2semidirect
5. C2×#11762538C2semidirect
6. #14526668C2semidirect
7. C2×C17×D4⋊C8C2semidirect
63. C4×C8×C17D4semidirect
207. C2×D4⋊C8D17semidirect
312. C4×C8C22⋊D17semidirect
314. C17#10431semidirect

Maximal subgroups

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

subgroupindex
#145336972
#145289122
#145287852
#145287842
C2×#117625382
#145266682
C2×C17×D4⋊C82
#1043117