Finite Group Databasebeta

← #16938801

Subgroups — #16938801

Order 4352.

442 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14533820C211yesmaximal, characteristic
2#14529548C211yesmaximal, characteristic
3#14529543C211yesmaximal, characteristic
4#14528940C211yesmaximal, characteristic
5#14526623C211yesmaximal, characteristic
6#14526623C211yesmaximal, characteristic
7C17×#1296C211yesmaximal, characteristic
8C2×#10587576—21no—
9C2×#10587489—21no—
10C2×#10587488—21no—
11C2×#10587479—22no—
12C2×C4×#3622C2211yescharacteristic
13#11762742—22no—
14#11762708—21no—
15#11762705—21no—
16#11762679C2211yescharacteristic
17#11762678—21no—
18C4×C4⋊Dic17C2211yescharacteristic
19C4×C4⋊Dic17C2211yescharacteristic
20#11762572—21no—
21#11762572—21no—
22C2×C17×C4⋊C8C2211yescharacteristic
23C2×C17×C4⋊C8C2211yescharacteristic
24C17×#384C2211yescharacteristic
25C22×C8×C17—21no—
26C22×C8×C17—21no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17D412yes—
30C2×C42×C17C2311yescharacteristic
31C2×C4⋊Dic17—22no—
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17D411yescharacteristic
36C2×C4⋊Dic17D411yescharacteristic
37C2×C4⋊Dic17D411yescharacteristic
38C2×C4⋊Dic17D411yescharacteristic
39C2×#63225—22no—
40C2×#63225—22no—
41C2×C4×Dic17—21no—
42C2×C4×Dic17—21no—
43C22×#3622—21no—
44#10587576—42no—
45#10587576—42no—
46C17×C4⋊C8—21no—
47C17×C4⋊C8—21no—
48C17×C4⋊C8Q812yes—
49C17×C4⋊C8Q812yes—
50#10587502—22no—
51#10587502—21no—
52#10587502—21no—
53#10587489—42no—
54#10587488—42no—
55#10587479—44no—
56C4×#3622—21no—
57C4×#3622Q812yes—
58C22×C4×C17—22no—
59C22×C4×C17C2×D411yescharacteristic
60C22×C4×C17C2×D411yescharacteristic
61C22×C4×C17C2×D411yescharacteristic
62C22×Dic17—21no—
63C22×Dic17—21no—
64C22×Dic17—21no—
65C22×Dic17—21no—
66C22×Dic17—41no—
67C2×C8×C17—22no—
68C2×C8×C17—22no—
69C2×C8×C17—41no—
70C2×C8×C17—41no—
71C2×C8×C17—41no—
72C2×C8×C17—41no—
73C4⋊C4×C17—42no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17—41no—
77C4⋊C4×C17—41no—
78C42×C17C2×Q811yescharacteristic
79C42×C17C2×Q811yescharacteristic
80C42×C17C2×Q811yescharacteristic
81C42×C17#4111yescharacteristic
82C4⋊Dic17—21no—
83C4⋊Dic17—21no—
84C4⋊Dic17—21no—
85C4⋊Dic17—21no—
86C4⋊Dic17—21no—
87C4⋊Dic17—21no—
88C4⋊Dic17—44no—
89C4⋊Dic17—42no—
90C4⋊Dic17—41no—
91C4⋊Dic17—41no—
92C4⋊Dic17—41no—
93C4⋊Dic17—41no—
94C4⋊Dic17SD1612yes—
95C4⋊Dic17SD1612yes—
96#63225—44no—
97#63225—82no—
98C4×Dic17—41no—
99C4×Dic17—41no—
100C4×Dic17—41no—
101C4×Dic17—41no—
102C2×#3622—22no—
103C2×#3622—22no—
104C2×#3622—22no—
105#10580—171nomaximal, Sylow
106C23×C17#12011yescharacteristic
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—42no—
110C2×C4×C17—42no—
111C2×C4×C17—42no—
112C2×C4×C17C22⋊Q811yescharacteristic
113C2×C4×C17C22⋊Q811yescharacteristic
114C2×C4×C17C22⋊Q811yescharacteristic
115C2×C4×C17C4⋊Q811yescharacteristic
116C2×C4×C17C4⋊Q811yescharacteristic
117C2×C4×C17C4⋊Q811yescharacteristic
118C2×C4×C17C2×SD1611yescharacteristic
119C2×C4×C17C2×SD1611yescharacteristic
120C2×C4×C17#13511yescharacteristic
121C2×C4×C17#13511yescharacteristic
122C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C17#13711yescharacteristic
125C2×C4×C17#13711yescharacteristic
126C2×Dic17—22no—
127C2×Dic17—22no—
128C2×Dic17—41no—
129C2×Dic17—41no—
130C2×Dic17—41no—
131C2×Dic17—41no—
132C2×Dic17—41no—
133C2×Dic17—41no—
134C2×Dic17—41no—
135C2×Dic17—41no—
136C2×Dic17—41no—
137C2×Dic17—41no—
138C2×Dic17—81no—
139C2×Dic17—81no—
140C2×Dic17—81no—
141C8×C17—42no—
142C8×C17—42no—
143#3622—24no—
144#2552—171no—
145#1948—171no—
146#1947—171no—
147#1844—171no—
148#1296D1711yescharacteristic
149#1279—171no—
150#1279—171no—
151C22×C17#39511yescharacteristic
152C22×C17#44811yescharacteristic
153C22×C17#44911yescharacteristic
154C22×C17#45011yescharacteristic
155C22×C17#45211yescharacteristic
156C22×C17#45311yescharacteristic
157C22×C17#45611yescharacteristic
158C4×C17—21no—
159C4×C17—21no—
160C4×C17—82no—
161C4×C17#47511yescharacteristic
162C4×C17#47611yescharacteristic
163C4×C17#47811yescharacteristic
164C4×C17#47911yescharacteristic
165C4×C17#49811yescharacteristic
166C4×C17#49911yescharacteristic
167C4×C17#50111yescharacteristic
168C4×C17#50111yescharacteristic
169Dic17—42no—
170Dic17—42no—
171Dic17—81no—
172Dic17—81no—
173Dic17—161no—
174C2×#125—341no—
175C2×#107—341no—
176C2×#106—341no—
177C2×#106—342no—
178C2×C4⋊C8C2×D1711yescharacteristic
179C2×C4⋊C8C2×D1711yescharacteristic
180C2×C4×C8—171no—
181#398—342no—
182#389—341no—
183#389—341no—
184#384—171no—
185#384—341no—
186#384C2×D1711yescharacteristic
187C4×C4⋊C4—171no—
188C4×C4⋊C4—171no—
189#340—341no—
190#340—341no—
191C2×C17#162211yescharacteristic
192C2×C17#163111yescharacteristic
193C2×C17#165311yescharacteristic
194C2×C17#165411yescharacteristic
195C2×C17#205811yescharacteristic
196C2×C17#205911yescharacteristic
197C2×C17#206011yescharacteristic
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—341no—
201#125—682no—
202#125—682no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—171no—
206C2×C4⋊C4—171no—
207C2×C4⋊C4—171no—
208C2×C4⋊C4—171no—
209C2×C4⋊C4—342no—
210C2×C4⋊C4—342no—
211C2×C4⋊C4—341no—
212C2×C4⋊C4—341no—
213C2×C4⋊C4—341no—
214C2×C4⋊C4—342no—
215C2×C4⋊C4D6812yes—
216C2×C42—341no—
217C2×C42—341no—
218C2×C42C22×D1711yescharacteristic
219#107—682no—
220#106—684no—
221#106—682no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8Dic3412yes—
225C4⋊C8Dic3412yes—
226C4×C8—172no—
227C4×C8—341no—
228#95—342no—
229#95—341no—
230#95—341no—
231C17#1058011yescharacteristic, complemented, Sylow
232C22×C4—22no—
233C22×C4—341no—
234C22×C4—341no—
235C22×C4—341no—
236C22×C4—341no—
237C22×C4—681no—
238C22×C4C2×D6811yescharacteristic
239C22×C4D4×D1711yescharacteristic
240C22×C4D4×D1711yescharacteristic
241C2×C8—22no—
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—342no—
248C2×C8—342no—
249C2×C8—342no—
250C4⋊C4—42no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—172no—
256C4⋊C4—172no—
257C4⋊C4—341no—
258C4⋊C4—341no—
259C4⋊C4—341no—
260C4⋊C4—341no—
261C4⋊C4—341no—
262C4⋊C4—341no—
263C4⋊C4—682no—
264C4⋊C4—684no—
265C4⋊C4—684no—
266C4⋊C4—681no—
267C4⋊C4—681no—
268C4⋊C4—681no—
269C4⋊C4—681no—
270C4⋊C4—1362no—
271C42—681no—
272C42—681no—
273C42—681no—
274C42—681no—
275C42C2×Dic3411yescharacteristic
276C42C2×Dic3411yescharacteristic
277C42#6325411yescharacteristic
278C42Q8×D1711yescharacteristic
279C23#1058756811yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—342no—
286C2×C4—342no—
287C2×C4—681no—
288C2×C4—681no—
289C2×C4—681no—
290C2×C4—681no—
291C2×C4—681no—
292C2×C4—681no—
293C2×C4—681no—
294C2×C4—681no—
295C2×C4—681no—
296C2×C4—681no—
297C2×C4—1361no—
298C2×C4—1361no—
299C2×C4—1361no—
300C2×C4#1058755511yescharacteristic
301C2×C4#1058756411yescharacteristic
302C2×C4#1058756411yescharacteristic
303C2×C4#1058757411yescharacteristic
304C2×C4#1058757411yescharacteristic
305C2×C4#1058758311yescharacteristic
306C2×C4#1058759711yescharacteristic
307C2×C4#1058759811yescharacteristic
308C2×C4SD16×D1711yescharacteristic
309C2×C4SD16×D1711yescharacteristic
310C2×C4#1058760011yescharacteristic
311C2×C4#1058760111yescharacteristic
312C2×C4#1058760411yescharacteristic
313C2×C4#1058760511yescharacteristic
314C8—42no—
315C8—42no—
316C8—344no—
317C22#1176273011yescharacteristic
318C22#1176294911yescharacteristic
319C22#1176295711yescharacteristic
320C22#1176296111yescharacteristic
321C22#1176297211yescharacteristic
322C22#1176297911yescharacteristic
323C22#1176299411yescharacteristic
324C4—21no—
325C4—21no—
326C4—82no—
327C4—2721no—
328C4—682no—
329C4—682no—
330C4—1361no—
331C4—1361no—
332C4#1176309211yescharacteristic
333C4#1176309711yescharacteristic
334C4#1176310711yescharacteristic
335C4#1176311811yescharacteristic
336C4#1176320611yescharacteristic
337C4#1176321011yescharacteristic
338C4#1176321611yescharacteristic
339C4#1176321711yescharacteristic
340C2#1452785711yescharacteristic
341C2#1452791211yescharacteristic
342C2#1452806211yescharacteristic
343C2#1452806911yescharacteristic
344C2#1453011611yescharacteristic
345C2#1453012511yescharacteristic
346C2#1453013011yescharacteristic
subgroupG/H
centerC23#10587568
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1296C2
socle, prime radicalC23×C17#120
hypercenter#1296D17
hypocenterC17#10580
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
231. C17#10580semidirect

Maximal subgroups

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

subgroupindex
#145338202
#145295482
#145295432
#145289402
#145266232
C17×#12962
#1058017