Finite Group Databasebeta

← #16951401

Subgroups — #16951401

Order 4352.

490 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic136C211yesmaximal, characteristic
2C2×C4×Dic68C211yesmaximal, characteristic
3C2×#11762614C211yesmaximal, characteristic
4C2×#11762614C211yesmaximal, characteristic
5#14529645C211yesmaximal, characteristic
6#14526876C211yesmaximal, characteristic
7C17×#1374C211yesmaximal, characteristic
8C22×Dic68C2211yescharacteristic
9C22×Dic68C2211yescharacteristic
10C2×C4×Dic34—21no—
11C2×Dic136—22no—
12C2×Dic136—22no—
13C2×Dic136C414yescomplemented
14C4×Dic68—22no—
15C4×Dic68—22no—
16C2×#10587489C2211yescharacteristic
17C2×#10587489C2211yescharacteristic
18C2×#10587487—21no—
19C2×#10587487—21no—
20#11762715—21no—
21#11762614—22no—
22#11762614—22no—
23C22×C16×C17C2211yescharacteristic
24C22×C16×C17C2211yescharacteristic
25C2×C4×C8×C17C2211yescharacteristic
26C22×Dic34—21no—
27C22×Dic34—21no—
28C22×C8×C17D411yescharacteristic
29C22×C8×C17C2311yescharacteristic
30C2×C42×C17D411yescharacteristic
31C2×C4⋊Dic17—21no—
32C2×C4⋊Dic17—21no—
33C2×#63225—41no—
34C2×C4×Dic17—41no—
35C2×Dic68—21no—
36C2×Dic68—21no—
37C2×Dic68—21no—
38C2×Dic68—21no—
39C2×Dic68—21no—
40C2×Dic68—21no—
41C2×Dic68—21no—
42C2×Dic68—21no—
43C2×Dic68C2×C412yes—
44C2×Dic68C2×C412yes—
45C2×Dic68D412yes—
46C2×Dic68D412yes—
47C4×Dic34—24no—
48C4×Dic34—42no—
49C2×C16×C17—21no—
50C2×C16×C17—21no—
51C2×C16×C17—21no—
52C2×C16×C17—21no—
53C2×C16×C17—21no—
54C2×C16×C17C2×C412yes—
55C4×C8×C17—21no—
56C4×C8×C17—21no—
57#10587502—41no—
58#10587502—41no—
59#10587489—21no—
60#10587489—21no—
61#10587489—21no—
62#10587489D412yes—
63#10587487—24no—
64#10587487—42no—
65Dic136—28no—
66C22×C4×C17D811yescharacteristic
67C22×C4×C17D811yescharacteristic
68C22×C4×C17C2×D411yescharacteristic
69C22×Dic17—41no—
70C22×Dic17—41no—
71C22×Dic17—41no—
72C22×Dic17—41no—
73C2×Dic34—22no—
74C2×Dic34—22no—
75C2×Dic34—22no—
76C2×Dic34—22no—
77C2×Dic34—41no—
78C2×Dic34—41no—
79C2×Dic34—41no—
80C2×Dic34—41no—
81C2×Dic34—41no—
82C2×Dic34—41no—
83C2×Dic34—41no—
84C2×Dic34—41no—
85C2×C8×C17—21no—
86C2×C8×C17—21no—
87C2×C8×C17—21no—
88C2×C8×C17C22×C411yescharacteristic
89C2×C8×C17C2×D411yescharacteristic
90C2×C8×C17C2×D411yescharacteristic
91C2×C8×C17C2×D411yescharacteristic
92C2×C8×C17#4111yescharacteristic
93C2×C8×C17#4111yescharacteristic
94C42×C17—21no—
95C42×C17—21no—
96C4⋊Dic17—22no—
97C4⋊Dic17—41no—
98C4⋊Dic17—41no—
99C4⋊Dic17—41no—
100#63225—44no—
101C4×Dic17—44no—
102Dic68—22no—
103Dic68—22no—
104Dic68—22no—
105Dic68—22no—
106Dic68—22no—
107Dic68—41no—
108Dic68—41no—
109Dic68C22⋊C414yes—
110C16×C17—22no—
111C16×C17—41no—
112#13015—171nomaximal, Sylow
113C23×C17C2×D811yescharacteristic
114C2×C4×C17—21no—
115C2×C4×C17—21no—
116C2×C4×C17—21no—
117C2×C4×C17—21no—
118C2×C4×C17—21no—
119C2×C4×C17Q3212yescomplemented
120C2×C4×C17C4×D411yescharacteristic
121C2×C4×C17#12011yescharacteristic
122C2×C4×C17#12111yescharacteristic
123C2×C4×C17#13511yescharacteristic
124C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
126C2×Dic17—42no—
127C2×Dic17—42no—
128C2×Dic17—42no—
129C2×Dic17—42no—
130C2×Dic17—42no—
131C2×Dic17—81no—
132C2×Dic17—81no—
133C2×Dic17—81no—
134C2×Dic17—81no—
135C2×Dic17—81no—
136C2×Dic17—81no—
137C2×Dic17—81no—
138Dic34—24no—
139Dic34—42no—
140Dic34—42no—
141Dic34—42no—
142Dic34—42no—
143Dic34—42no—
144Dic34—81no—
145Dic34—81no—
146C8×C17—41no—
147C8×C17C2×C22⋊C411yescharacteristic
148C8×C17C4×D411yescharacteristic
149C8×C17#12111yescharacteristic
150C8×C17#12311yescharacteristic
151C22×Q32—171no—
152C2×C4×Q16—171no—
153C2×#358—171no—
154C2×#358—171no—
155#1969—171no—
156#1380—171no—
157#1374D1711yescharacteristic
158C22×C17C4×D811yescharacteristic
159C22×C17#44711yescharacteristic
160C22×C17#45911yescharacteristic
161C22×C17C2×Q3211yescharacteristic
162C22×C17#50811yescharacteristic
163C22×C17#51011yescharacteristic
164C22×C17#51011yescharacteristic
165C4×C17—22no—
166C4×C17—41no—
167C4×C17#38611yescharacteristic
168C4×C17#44211yescharacteristic
169C4×C17#44911yescharacteristic
170C4×C17#46311yescharacteristic
171Dic17—44no—
172Dic17—82no—
173Dic17—82no—
174Dic17—161no—
175C22×Q16—171no—
176C22×Q16—171no—
177C2×C4×Q8—341no—
178C2×Q32—174no—
179C2×Q32—342no—
180C2×Q32—342no—
181C22×C16C2×D1711yescharacteristic
182C22×C16C2×D1711yescharacteristic
183C4×Q16—342no—
184C4×Q16—342no—
185C2×#107—171no—
186C2×#107—171no—
187C2×#103—341no—
188C2×#103—341no—
189C2×C4×C8C2×D1711yescharacteristic
190#391—341no—
191#358—342no—
192#358—342no—
193C2×C17#187911yescharacteristic
194C2×C17C4×Q3211yescharacteristic
195C2×C17#217611yescharacteristic
196C2×C17#218811yescharacteristic
197C2×C17#218911yescharacteristic
198C2×C17#220911yescharacteristic
199C2×C17#221111yescharacteristic
200C22×Q8—341no—
201C22×Q8—341no—
202C2×Q16—172no—
203C2×Q16—172no—
204C2×Q16—172no—
205C2×Q16—172no—
206C2×Q16—341no—
207C2×Q16—341no—
208C2×Q16—341no—
209C2×Q16—341no—
210C2×Q16—341no—
211C2×Q16—341no—
212C2×Q16—341no—
213C2×Q16—341no—
214C22×C8D6811yescharacteristic
215C22×C8C22×D1711yescharacteristic
216C4×Q8—344no—
217C4×Q8—682no—
218C2×C4⋊C4—341no—
219C2×C4⋊C4—341no—
220C2×C4⋊C4—681no—
221C2×C42—681no—
222C2×C42D6811yescharacteristic
223Q32—348no—
224C2×C16—21no—
225C2×C16—21no—
226C2×C16—21no—
227C2×C16—21no—
228C2×C16—21no—
229C2×C16C4×D1712yes—
230#107—172no—
231#107—341no—
232#107—341no—
233#107—341no—
234#103—344no—
235#103—682no—
236C4×C8—21no—
237C4×C8—21no—
238#95—681no—
239#95—681no—
240C17#1301511yescharacteristic, complemented, Sylow
241C2×Q8—342no—
242C2×Q8—342no—
243C2×Q8—342no—
244C2×Q8—342no—
245C2×Q8—681no—
246C2×Q8—681no—
247C2×Q8—681no—
248C2×Q8—681no—
249C2×Q8—681no—
250C2×Q8—681no—
251C2×Q8—681no—
252C2×Q8—681no—
253C22×C4—681no—
254C22×C4—681no—
255C22×C4—681no—
256C22×C4—681no—
257C22×C4D13611yescharacteristic
258C22×C4D13611yescharacteristic
259C22×C4C2×D6811yescharacteristic
260Q16—174no—
261Q16—342no—
262Q16—342no—
263Q16—342no—
264Q16—342no—
265Q16—342no—
266Q16—681no—
267Q16—681no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8C2×C4×D1711yescharacteristic
272C2×C8#6325211yescharacteristic
273C2×C8D4×D1711yescharacteristic
274C2×C8D4×D1711yescharacteristic
275C2×C8D4×D1711yescharacteristic
276C2×C8#6325611yescharacteristic
277C4⋊C4—342no—
278C4⋊C4—684no—
279C4⋊C4—681no—
280C4⋊C4—681no—
281C4⋊C4—681no—
282C42—21no—
283C42—21no—
284C42—684no—
285C16—22no—
286C16—41no—
287C23C2×D13611yescharacteristic
288Q8—344no—
289Q8—682no—
290Q8—682no—
291Q8—682no—
292Q8—682no—
293Q8—682no—
294Q8—1361no—
295Q8—1361no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—682no—
302C2×C4—682no—
303C2×C4—682no—
304C2×C4—682no—
305C2×C4—682no—
306C2×C4—1361no—
307C2×C4—1361no—
308C2×C4—1361no—
309C2×C4—1361no—
310C2×C4—1361no—
311C2×C4—1361no—
312C2×C4—1361no—
313C2×C4Dic13612yescomplemented
314C2×C4C4×D6811yescharacteristic
315C2×C4#1058756811yescharacteristic
316C2×C4#1058758111yescharacteristic
317C2×C4#1058759011yescharacteristic
318C2×C4#1058759411yescharacteristic
319C2×C4#1058759411yescharacteristic
320C8—41no—
321C8C22⋊C4×D1711yescharacteristic
322C8#1058757011yescharacteristic
323C8#1058757911yescharacteristic
324C8#1058758011yescharacteristic
325C22C4×D13611yescharacteristic
326C22#1176294511yescharacteristic
327C22#1176300511yescharacteristic
328C22C2×Dic13611yescharacteristic
329C22#1176324111yescharacteristic
330C22#1176325211yescharacteristic
331C22#1176325211yescharacteristic
332C4—22no—
333C4—41no—
334C4—2721no—
335C4—684no—
336C4—1362no—
337C4—1362no—
338C4#1176268711yescharacteristic
339C4#1176292211yescharacteristic
340C4#1176295611yescharacteristic
341C4#1176302511yescharacteristic
342C2#1452913111yescharacteristic
343C2C4×Dic13611yescharacteristic
344C2#1453065611yescharacteristic
345C2#1453072011yescharacteristic
346C2#1453072611yescharacteristic
347C2#1453083511yescharacteristic
348C2#1453084711yescharacteristic
subgroupG/H
centerC23C2×D136
commutatorC2×C8×C17C22×C4
FrattiniC22×C8C22×D17
FittingC17×#1374C2
socle, prime radicalC23×C17C2×D8
cosocleC22×C8×C17C23
hypercenter#1374D17
hypocenterC17#13015
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1374

Complements

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

NH ≅ G/Ntype
13. C2×Dic136C4semidirect
119. C2×C4×C17Q32semidirect
240. C17#13015semidirect
313. C2×C4Dic136semidirect

Maximal subgroups

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

subgroupindex
C22×Dic1362
C2×C4×Dic682
C2×#117626142
#145296452
#145268762
C17×#13742
#1301517