Finite Group Databasebeta

← #16929554

Subgroups — #16929554

Order 4352.

470 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537733C211yesmaximal, characteristic, complemented
2#14529704C211yesmaximal, characteristic
3#14527283C211yesmaximal, characteristic, complemented
4#14527183C211yesmaximal, characteristic
5#14526624C211yesmaximal, characteristic, complemented
6#14526621C211yesmaximal, characteristic, complemented
7C17×#3167C211yesmaximal, characteristic
8#11762940—22no—
9#11762940—21no—
10Q8×#3622—21no—
11#11762862C2211yescharacteristic
12#11762836—21no—
13C2×C4⋊#3622C2211yescharacteristic
14C2×#10587508—21no—
15C2×#10587508—21no—
16#11762765—21no—
17C4×#63223C2211yescharacteristic
18C4×C4⋊Dic17C2211yescharacteristic
19#11762546—22no—
20D4⋊#3622—21no—
21D4⋊#3622—21no—
22C17×#533C2211yescharacteristic
23C17×#532C2211yescharacteristic
24C17×#498C411yescharacteristic, complemented
25C17×#492C411yescharacteristic, complemented
26C17×#487C411yescharacteristic, complemented
27C17×#486C411yescharacteristic, complemented
28C17×#465—22no—
29C4×SD16×C17—22no—
30C2×C4×C8×C17C2211yescharacteristic
31C2×#41×C17—21no—
32C2×SD16×C17—22no—
33C22×C8×C17—21no—
34C17×C4⋊Q8C2×C411yescharacteristic
35C17×C4⋊Q8C2×C411yescharacteristic
36C17×C4⋊Q8C2×C411yescharacteristic
37C17×#127C2×C411yescharacteristic
38C17×#125—21no—
39C17×#124—21no—
40C17×C22⋊Q8—21no—
41C17×C22⋊Q8D412yes—
42C17×#121—21no—
43C17×#121—21no—
44C4×Q8×C17—21no—
45C4×Q8×C17D412yes—
46C4×D4×C17—21no—
47C4×D4×C17—21no—
48C17×#117—21no—
49C2×C42×C17C2311yescharacteristic
50C2×C4⋊Dic17—21no—
51C2×C4×Dic17—21no—
52C2×#63223D411yescharacteristic
53C2×#63223D411yescharacteristic
54C22×#3622—21no—
55C17×#106—22no—
56C17×#103—22no—
57C17×#102—22no—
58C4×C8×C17—21no—
59C4×C8×C17C2×C411yescharacteristic
60C4×C8×C17C2×C411yescharacteristic
61#10587508—42no—
62#10587508—42no—
63#10587502—21no—
64C22⋊#3622—21no—
65C4⋊#3622—22no—
66C4⋊#3622—22no—
67C4⋊#3622—21no—
68C4⋊#3622—21no—
69C4⋊#3622D411yescharacteristic
70C4⋊#3622D411yescharacteristic
71#10587474—22no—
72#10587474—21no—
73C4×#3622—22no—
74C4×#3622—21no—
75C4×#3622—21no—
76#41×C17—41no—
77#41×C17—41no—
78#41×C17—41no—
79#41×C17—41no—
80C2×Q8×C17—21no—
81C2×Q8×C17—21no—
82C2×Q8×C17C22⋊C412yes—
83C2×D4×C17—21no—
84C2×D4×C17—21no—
85C2×D4×C17—21no—
86C2×D4×C17—41no—
87C22×C4×C17—41no—
88C22×C4×C17C2×D411yescharacteristic
89C22×C4×C17C2×D411yescharacteristic
90C22×C4×C17#4111yescharacteristic
91C22×Dic17—41no—
92SD16×C17—44no—
93C2×C8×C17—21no—
94C2×C8×C17—21no—
95C2×C8×C17—42no—
96C4⋊C4×C17—21no—
97C4⋊C4×C17—21no—
98C4⋊C4×C17—21no—
99C4⋊C4×C17—22no—
100C4⋊C4×C17—22no—
101C4⋊C4×C17—21no—
102C4⋊C4×C17—21no—
103C4⋊C4×C17C22⋊C412yes—
104C22⋊C4×C17—22no—
105C22⋊C4×C17—41no—
106C22⋊C4×C17—41no—
107C42×C17—22no—
108C42×C17C22×C411yescharacteristic
109C42×C17C2×D411yescharacteristic
110C42×C17C2×D411yescharacteristic
111C42×C17#4111yescharacteristic
112C4⋊Dic17—22no—
113C4⋊Dic17—41no—
114C4×Dic17—41no—
115C4×Dic17—41no—
116#63223—21no—
117#63223—21no—
118#63223—21no—
119#63223SD1612yescomplemented
120C2×#3622—21no—
121C2×#3622—21no—
122C2×#3622—21no—
123C2×#3622—21no—
124C2×#3622—41no—
125C2×#3622—41no—
126C2×#3622—41no—
127#9054—171nomaximal, Sylow
128C23×C17—41no—
129C23×C17#12111yescharacteristic
130Q8×C17—42no—
131Q8×C17—41no—
132Q8×C17—41no—
133Q8×C17—41no—
134Q8×C17—41no—
135D4×C17—42no—
136D4×C17—41no—
137D4×C17—41no—
138D4×C17—41no—
139D4×C17—41no—
140D4×C17—81no—
141D4×C17—81no—
142C2×C4×C17—21no—
143C2×C4×C17—21no—
144C2×C4×C17—22no—
145C2×C4×C17—22no—
146C2×C4×C17—41no—
147C2×C4×C17—41no—
148C2×C4×C17—81no—
149C2×C4×C17—81no—
150C2×C4×C17C2×C22⋊C411yescharacteristic
151C2×C4×C17C4×D411yescharacteristic
152C2×C4×C17C4×D411yescharacteristic
153C2×C4×C17#12011yescharacteristic
154C2×C4×C17#12111yescharacteristic
155C2×C4×C17#12311yescharacteristic
156C2×C4×C17C2×SD1611yescharacteristic
157C2×C4×C17#13511yescharacteristic
158C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C17#13711yescharacteristic
160C2×Dic17—42no—
161C2×Dic17—81no—
162C2×Dic17—81no—
163C8×C17—22no—
164C8×C17—41no—
165#3622—22no—
166#3622—41no—
167#3622—41no—
168#3622—41no—
169#3622—81no—
170#3167D1711yescharacteristic
171#2962—171no—
172#1980—171no—
173#1503—171no—
174#1480—171no—
175#1279—171no—
176#1278—171no—
177C22×C17—21no—
178C22×C17—21no—
179C22×C17—81no—
180C22×C17—81no—
181C22×C17—81no—
182C22×C17#38611yescharacteristic
183C22×C17#46011yescharacteristic
184C22×C17#46411yescharacteristic
185C4×C17—21no—
186C4×C17—21no—
187C4×C17—21no—
188C4×C17—42no—
189C4×C17—42no—
190C4×C17—81no—
191C4×C17C4×SD1611yescharacteristic
192C4×C17#44011yescharacteristic
193C4×C17#44311yescharacteristic
194C4×C17#44411yescharacteristic
195C4×C17#44811yescharacteristic
196C4×C17#44911yescharacteristic
197Dic17—82no—
198#533C2×D1711yescharacteristic
199#532C2×D1711yescharacteristic
200#498Dic1711yescharacteristic, complemented
201#492Dic1711yescharacteristic, complemented
202#487Dic1711yescharacteristic, complemented
203#486Dic1711yescharacteristic, complemented
204#465—22no—
205#446—341no—
206#446—342no—
207C8×Q8—341no—
208C4×SD16—22no—
209#431—171no—
210#424—341no—
211C2×C4⋊C8—171no—
212C2×#104—341no—
213C2×#104—341no—
214#405—341no—
215C4×M16—171no—
216C2×C4×C8C2×D1711yescharacteristic
217C4×C4⋊C4—171no—
218#328—342no—
219D4⋊C8—341no—
220D4⋊C8—341no—
221C2×C17—21no—
222C2×C17—21no—
223C2×C17—161no—
224C2×C17#187611yescharacteristic
225C2×C17#188011yescharacteristic
226C2×C17#188411yescharacteristic
227C2×#41—21no—
228C2×SD16—22no—
229C2×M16—171no—
230C2×M16—171no—
231C22×C8—21no—
232C22×C8—341no—
233C4⋊Q8C2×Dic1711yescharacteristic
234C4⋊Q8C2×Dic1711yescharacteristic
235C4⋊Q8C2×Dic1711yescharacteristic
236#127C2×Dic1711yescharacteristic
237#125—21no—
238#124—21no—
239C22⋊Q8—21no—
240C22⋊Q8C22⋊D1712yes—
241#121—21no—
242#121—21no—
243C4×Q8—21no—
244C4×Q8C22⋊D1712yes—
245C4×D4—21no—
246C4×D4—21no—
247#117—21no—
248C2×C4⋊C4—341no—
249C2×C42—341no—
250C2×C42C22×D1711yescharacteristic
251#106—22no—
252C4⋊C8—171no—
253C4⋊C8—171no—
254C4⋊C8—342no—
255C4⋊C8—342no—
256C4⋊C8—341no—
257C4⋊C8—341no—
258#104—682no—
259#104—682no—
260#103—22no—
261#102—22no—
262C22⋊C8—341no—
263#97—342no—
264#97—341no—
265C4×C8—21no—
266C4×C8—342no—
267C4×C8—341no—
268C4×C8—341no—
269C4×C8C2×Dic1711yescharacteristic
270C4×C8C2×Dic1711yescharacteristic
271#95—341no—
272C17#905411yescharacteristic, complemented, Sylow
273#41—41no—
274#41—41no—
275#41—41no—
276#41—41no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8C22⋊Dic1712yes—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C22×C4—41no—
285C22×C4—681no—
286C22×C4D4×D1711yescharacteristic
287C22×C4#6325411yescharacteristic
288C22×C4C2×C22⋊D1711yescharacteristic
289SD16—44no—
290M16—172no—
291M16—341no—
292M16—341no—
293M16—341no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—42no—
297C2×C8—341no—
298C2×C8—341no—
299C2×C8—341no—
300C2×C8—341no—
301C2×C8—681no—
302C2×C8—681no—
303C2×C8—681no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—342no—
312C4⋊C4—681no—
313C4⋊C4C22⋊Dic1712yes—
314C22⋊C4—22no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C42—22no—
318C42—681no—
319C42—681no—
320C42D4×D1711yescharacteristic
321C42#6325411yescharacteristic
322C42C22×Dic1711yescharacteristic
323C42C2×C22⋊D1711yescharacteristic
324C23—41no—
325C23#1058762511yescharacteristic
326Q8—42no—
327Q8—41no—
328Q8—41no—
329Q8—41no—
330Q8—41no—
331D4—42no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—41no—
336D4—81no—
337D4—81no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—682no—
347C2×C4—1361no—
348C2×C4—1361no—
349C2×C4SD16×D1711yescharacteristic
350C2×C4#1058760011yescharacteristic
351C2×C4#1058760111yescharacteristic
352C2×C4#1058760211yescharacteristic
353C2×C4D4×Dic1711yescharacteristic
354C2×C4D4×Dic1711yescharacteristic
355C2×C4#1058762111yescharacteristic
356C2×C4#1058762311yescharacteristic
357C2×C4#1058762511yescharacteristic
358C2×C4C2×C22⋊Dic1711yescharacteristic
359C8—22no—
360C8—41no—
361C8—342no—
362C8—681no—
363C8—681no—
364C8—681no—
365C8—1361no—
366C22—21no—
367C22—21no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22#1176268911yescharacteristic
372C22#1176300711yescharacteristic
373C22#1176302911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—42no—
378C4—42no—
379C4—81no—
380C4—1362no—
381C4SD16×Dic1711yescharacteristic
382C4#1176291011yescharacteristic
383C4#1176292611yescharacteristic
384C4#1176293111yescharacteristic
385C4#1176294611yescharacteristic
386C4#1176295311yescharacteristic
387C2—21no—
388C2—21no—
389C2—161no—
390C2#1452911311yescharacteristic
391C2#1452914111yescharacteristic
392C2#1452916811yescharacteristic
subgroupG/H
centerC2×C4#10587623
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#3167C2
socleC22×C17#386
prime radicalC17×#532C22
cosocleC2×C42×C17C23
hypercenter#3167D17
hypocenterC17#9054
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
1. #14537733C2semidirect
3. #14527283C2semidirect
5. #14526624C2semidirect
6. #14526621C2semidirect
24. C17×#498C4semidirect
25. C17×#492C4semidirect
26. C17×#487C4semidirect
27. C17×#486C4semidirect
119. #63223SD16semidirect
200. #498Dic17semidirect
201. #492Dic17semidirect
202. #487Dic17semidirect
203. #486Dic17semidirect
272. C17#9054semidirect

Maximal subgroups

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

subgroupindex
#145377332
#145297042
#145272832
#145271832
#145266242
#145266212
C17×#31672
#905417