Finite Group Databasebeta

← #16937857

Subgroups — #16937857

Order 4352.

546 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14533702C211yesmaximal, characteristic
2#14528940C211yesmaximal, characteristic, complemented
3#14528781C211yesmaximal, characteristic
4C2×Q8⋊#3622C211yesmaximal, characteristic, complemented
5C2×#11762536C211yesmaximal, characteristic
6#14526668C211yesmaximal, characteristic, complemented
7C17×#1803C211yesmaximal, characteristic, complemented
8C2×#10587632—21no—
9C2×C4×D68C2211yescharacteristic
10C2×#10587479—22no—
11C2×C4⋊#3622C2211yescharacteristic
12C2×#10587480—21no—
13C2×C4×#3622C2211yescharacteristic
14#11762731—22no—
15#11762711—21no—
16#11762707—21no—
17#11762679C2211yescharacteristic
18#11762666—21no—
19#11762571—21no—
20Q8⋊#3622—22no—
21#11762536—22no—
22C2×C4×Q8×C17C2211yescharacteristic
23C2×C17×C4⋊C8C2211yescharacteristic
24C2×C17×#103—21no—
25C17×#384C2211yescharacteristic
26C17×#340—21no—
27C22×Q8×C17D411yescharacteristic
28C22×D68D411yescharacteristic
29C22×C4×D17—21no—
30C22×C8×C17—21no—
31C4×Q8×C17—21no—
32C4×Q8×C17—21no—
33C4×Q8×C17—21no—
34C4×Q8×C17—21no—
35C2×C4⋊C4×C17—21no—
36C2×C4⋊C4×C17—21no—
37C2×C4⋊C4×C17—21no—
38C2×C4⋊C4×C17—21no—
39C2×C4⋊C4×C17D411yescharacteristic
40C2×C42×C17—21no—
41C2×C42×C17C2311yescharacteristic
42#10587632—42no—
43#10587632—42no—
44C2×#63227—22no—
45C2×#63227—22no—
46C2×#63227—21no—
47C2×C4⋊Dic17—21no—
48C2×C4⋊Dic17—21no—
49C2×C4⋊Dic17D411yescharacteristic
50C2×C4⋊Dic17D412yes—
51C2×#63225—22no—
52C22×#3622—21no—
53C22×#3622—21no—
54C4×D68—21no—
55C4×D68—21no—
56C4×D68—21no—
57C4×D68—21no—
58C17×C4⋊C8—21no—
59C17×C4⋊C8—21no—
60C17×#103—42no—
61#10587502—22no—
62#10587480—42no—
63#10587479—44no—
64C4⋊#3622—21no—
65C4⋊#3622—21no—
66C4×#3622—21no—
67C4×#3622D412yes—
68C23×D17—21no—
69C2×Q8×C17—21no—
70C2×Q8×C17—21no—
71C2×Q8×C17—21no—
72C2×Q8×C17—21no—
73C2×Q8×C17—21no—
74C2×Q8×C17SD1612yes—
75C22×C4×C17—21no—
76C22×C4×C17—21no—
77C22×C4×C17—41no—
78C22×C4×C17C2×D411yescharacteristic
79C22×C4×C17C2×D411yescharacteristic
80C22×C4×C17C2×D411yescharacteristic
81C22×Dic17—21no—
82C22×Dic17—22no—
83C2×D68—21no—
84C2×D68—21no—
85C2×D68—21no—
86C2×D68—21no—
87C2×D68—21no—
88C2×D68SD1612yes—
89C2×C4×D17—41no—
90C2×C4×D17—41no—
91C2×C4×D17—41no—
92C2×C4×D17—41no—
93C2×C4×D17—41no—
94C2×C4×D17—41no—
95C2×C8×C17—41no—
96C2×C8×C17—41no—
97C2×C8×C17—41no—
98C4⋊C4×C17—21no—
99C4⋊C4×C17—21no—
100C4⋊C4×C17—42no—
101C4⋊C4×C17—41no—
102C4⋊C4×C17—41no—
103C4⋊C4×C17—41no—
104C4⋊C4×C17—41no—
105C4⋊C4×C17—41no—
106C4⋊C4×C17—41no—
107C42×C17—41no—
108C42×C17—41no—
109C42×C17C2×D411yescharacteristic
110C42×C17#4111yescharacteristic
111C42×C17#4111yescharacteristic
112C42×C17#4111yescharacteristic
113#63227—44no—
114#63227—41no—
115#63227—41no—
116#63227—82no—
117C4⋊Dic17—21no—
118C4⋊Dic17—21no—
119C4⋊Dic17—41no—
120C4⋊Dic17—41no—
121C4⋊Dic17—41no—
122C4⋊Dic17—41no—
123C4⋊Dic17—42no—
124#63225—44no—
125C2×#3622—22no—
126C2×#3622—22no—
127C2×#3622—22no—
128C2×#3622—41no—
129C2×#3622—41no—
130C2×#3622—41no—
131#10435—171nomaximal, Sylow
132C23×C17#12011yescharacteristic
133C22×D17—22no—
134C22×D17—41no—
135C22×D17—41no—
136C22×D17—41no—
137C22×D17—41no—
138C22×D17—41no—
139C22×D17—41no—
140Q8×C17—22no—
141Q8×C17—22no—
142Q8×C17—41no—
143Q8×C17—41no—
144C2×C4×C17—21no—
145C2×C4×C17—21no—
146C2×C4×C17—22no—
147C2×C4×C17—41no—
148C2×C4×C17—41no—
149C2×C4×C17—41no—
150C2×C4×C17—41no—
151C2×C4×C17—41no—
152C2×C4×C17—81no—
153C2×C4×C17—81no—
154C2×C4×C17—81no—
155C2×C4×C17#12111yescharacteristic
156C2×C4×C17#12111yescharacteristic
157C2×C4×C17#12111yescharacteristic
158C2×C4×C17#12311yescharacteristic
159C2×C4×C17#12311yescharacteristic
160C2×C4×C17#12411yescharacteristic
161C2×C4×C17C2×SD1611yescharacteristic
162C2×C4×C17C2×SD1611yescharacteristic
163C2×C4×C17#13511yescharacteristic
164C2×C4×C17#13511yescharacteristic
165C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C17#13711yescharacteristic
168C2×C4×C17#13711yescharacteristic
169C2×Dic17—41no—
170C2×Dic17—41no—
171C2×Dic17—41no—
172C2×Dic17—42no—
173C2×Dic17—42no—
174C2×Dic17—42no—
175D68—22no—
176D68—22no—
177D68—41no—
178D68—41no—
179C4×D17—81no—
180C4×D17—81no—
181C4×D17—81no—
182C4×D17—81no—
183C8×C17—81no—
184#3622—24no—
185#3622—81no—
186#2538—171no—
187#1844—171no—
188#1803D1711yescharacteristic, complemented
189#1802—171no—
190C2×Q8⋊C8—171no—
191C2×D4⋊C8—171no—
192#1296—171no—
193C22×C17#39411yescharacteristic
194C22×C17#44811yescharacteristic
195C22×C17#44911yescharacteristic
196C22×C17#45011yescharacteristic
197C22×C17#45211yescharacteristic
198C22×C17#45311yescharacteristic
199C22×C17#45611yescharacteristic
200C2×D17—42no—
201C2×D17—42no—
202C2×D17—42no—
203C2×D17—81no—
204C2×D17—81no—
205C2×D17—81no—
206C2×D17—81no—
207C4×C17—21no—
208C4×C17—21no—
209C4×C17—42no—
210C4×C17—81no—
211C4×C17—161no—
212C4×C17#46511yescharacteristic
213C4×C17#46511yescharacteristic
214C4×C17#46911yescharacteristic
215C4×C17#47011yescharacteristic
216C4×C17#48111yescharacteristic
217C4×C17#48211yescharacteristic
218C4×C17#48311yescharacteristic
219C4×C17#48511yescharacteristic
220Dic17—82no—
221Dic17—81no—
222C2×C22⋊Q8—341no—
223C2×C4×Q8C2×D1711yescharacteristic
224C2×C4×D4—171no—
225C2×#106—342no—
226C2×C4⋊C8—171no—
227C2×C4⋊C8C2×D1711yescharacteristic
228C2×#103—21no—
229C2×#102—341no—
230C2×C4×C8—171no—
231#396—342no—
232#390—341no—
233#389—341no—
234#384—171no—
235#384C2×D1711yescharacteristic
236#380—341no—
237#340—21no—
238#340—341no—
239Q8⋊C8—342no—
240D4⋊C8—342no—
241C2×C17#162211yescharacteristic
242C2×C17#163111yescharacteristic
243C2×C17#165111yescharacteristic
244C2×C17#165211yescharacteristic
245C2×C17#203411yescharacteristic
246C2×C17#203511yescharacteristic
247C2×C17#203911yescharacteristic
248D17—82no—
249C22×Q8C22⋊D1711yescharacteristic
250C22×D4—171no—
251C23×C4—341no—
252C22×C8—21no—
253C22×C8—341no—
254C22×C8—341no—
255C22⋊Q8—682no—
256C22⋊Q8—682no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×D4—341no—
262C4×D4—341no—
263C4×D4—341no—
264C4×D4—341no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—171no—
270C2×C4⋊C4—172no—
271C2×C4⋊C4—342no—
272C2×C4⋊C4—341no—
273C2×C4⋊C4—341no—
274C2×C4⋊C4C22⋊D1711yescharacteristic
275C2×C22⋊C4—342no—
276C2×C22⋊C4—341no—
277C2×C22⋊C4—342no—
278C2×C42—21no—
279C2×C42C22×D1711yescharacteristic
280#106—684no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283C4⋊C8—341no—
284C4⋊C8—341no—
285#103—42no—
286#102—682no—
287C4×C8—172no—
288C4×C8—341no—
289#95—342no—
290C17#1043511yescharacteristic, complemented, Sylow
291C24—341no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8#6323012yes—
298C2×D4—172no—
299C2×D4—341no—
300C2×D4—341no—
301C2×D4—341no—
302C2×D4—341no—
303C2×D4—341no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—41no—
307C22×C4—341no—
308C22×C4—342no—
309C22×C4—681no—
310C22×C4—681no—
311C22×C4—681no—
312C22×C4—681no—
313C22×C4—681no—
314C22×C4—681no—
315C22×C4D4×D1711yescharacteristic
316C22×C4D4×D1711yescharacteristic
317C22×C4C2×C22⋊D1711yescharacteristic
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—342no—
322C2×C8—342no—
323C2×C8—342no—
324C2×C8—681no—
325C2×C8—681no—
326C2×C8—681no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—42no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—341no—
337C4⋊C4—341no—
338C4⋊C4—682no—
339C4⋊C4—684no—
340C4⋊C4—681no—
341C4⋊C4—681no—
342C4⋊C4—681no—
343C4⋊C4—681no—
344C22⋊C4—684no—
345C22⋊C4—681no—
346C22⋊C4—681no—
347C22⋊C4—1362no—
348C42—41no—
349C42—41no—
350C42#6325211yescharacteristic
351C42#6325211yescharacteristic
352C42D4×D1711yescharacteristic
353C42#6325411yescharacteristic
354C23—342no—
355C23—681no—
356C23—681no—
357C23—681no—
358C23—681no—
359C23—681no—
360C23—681no—
361C23#1058762311yescharacteristic
362Q8—22no—
363Q8—22no—
364Q8—41no—
365Q8—41no—
366D4—342no—
367D4—342no—
368D4—681no—
369D4—681no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—681no—
382C2×C4—682no—
383C2×C4—681no—
384C2×C4—682no—
385C2×C4—682no—
386C2×C4—681no—
387C2×C4—1361no—
388C2×C4—1361no—
389C2×C4—1361no—
390C2×C4—1361no—
391C2×C4#1058756911yescharacteristic
392C2×C4#1058757011yescharacteristic
393C2×C4#1058757011yescharacteristic
394C2×C4#1058757111yescharacteristic
395C2×C4SD16×D1711yescharacteristic
396C2×C4#1058760111yescharacteristic
397C2×C4#1058760411yescharacteristic
398C2×C4#1058760511yescharacteristic
399C2×C4#1058761511yescharacteristic
400C2×C4#1058761811yescharacteristic
401C2×C4#1058762511yescharacteristic
402C2×C4C2×#6323011yescharacteristic
403C2×C4#1058763511yescharacteristic
404C2×C4#1058763611yescharacteristic
405C8—81no—
406C8—344no—
407C8—1361no—
408C22—682no—
409C22—682no—
410C22—682no—
411C22—1361no—
412C22—1361no—
413C22—1361no—
414C22—1361no—
415C22#1176272411yescharacteristic
416C22#1176294611yescharacteristic
417C22#1176295211yescharacteristic
418C22#1176295911yescharacteristic
419C22#1176297011yescharacteristic
420C22#1176297511yescharacteristic
421C22#1176299011yescharacteristic
422C4—21no—
423C4—21no—
424C4—42no—
425C4—81no—
426C4—161no—
427C4—1362no—
428C4—1361no—
429C4#1176304011yescharacteristic
430C4#1176304111yescharacteristic
431C4#1176306011yescharacteristic
432C4#1176306611yescharacteristic
433C4#1176312711yescharacteristic
434C4#1176313311yescharacteristic
435C4#1176313811yescharacteristic
436C4#1176314911yescharacteristic
437C2—1362no—
438C2#1452785511yescharacteristic
439C2#1452790911yescharacteristic
440C2#1452804611yescharacteristic
441C2#1452805211yescharacteristic
442C2#1452997311yescharacteristic
443C2#1452997811yescharacteristic
444C2#1453000611yescharacteristic
subgroupG/H
centerC23#10587623
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1803C2
socleC23×C17#120
prime radicalC22×D68D4
hypercenter#1803D17
hypocenterC17#10435
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. #14528940C2semidirect
4. C2×Q8⋊#3622C2semidirect
6. #14526668C2semidirect
7. C17×#1803C2semidirect
188. #1803D17semidirect
290. C17#10435semidirect

Maximal subgroups

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

subgroupindex
#145337022
#145289402
#145287812
C2×Q8⋊#36222
C2×#117625362
#145266682
C17×#18032
#1043517