Finite Group Databasebeta

← #16951403

Subgroups — #16951403

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×#11762903C211yesmaximal, characteristic
3C2×#11762612C211yesmaximal, characteristic
4C2×#11762612C211yesmaximal, characteristic
5#14529643C211yesmaximal, characteristic
6#14526861C211yesmaximal, characteristic
7C17×#1380C211yesmaximal, characteristic
8C22×Dic68C2211yescharacteristic
9C22×Dic68C2211yescharacteristic
10C2×#10587573—21no—
11C2×Dic136—22no—
12C2×Dic136—22no—
13C2×Dic136C414yescomplemented
14C22×#63214C2211yescharacteristic
15#11762903—22no—
16#11762903—22no—
17C2×#10587481—21no—
18C2×#10587481—21no—
19C2×C8×Dic17C2211yescharacteristic
20#11762714—21no—
21#11762612—22no—
22#11762612—22no—
23C22×C16×C17C2211yescharacteristic
24C2×C17×#107C2211yescharacteristic
25C2×C17×#107C2211yescharacteristic
26C22×Dic34—21no—
27C22×Dic34—21no—
28C22×C8×C17C2311yescharacteristic
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—21no—
31C2×#63225—41no—
32C2×C4×Dic17—41no—
33C2×C4×Dic17D411yescharacteristic
34C22×#3622D411yescharacteristic
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—
47#10587573—24no—
48#10587573—42no—
49C2×C16×C17—21no—
50C2×C16×C17—21no—
51C2×C16×C17C2×C412yes—
52C17×#107—21no—
53C17×#107—21no—
54C17×#107—21no—
55C17×#107D412yes—
56#10587502—41no—
57#10587502—41no—
58C8×Dic17—21no—
59C8×Dic17—21no—
60C2×#63214—21no—
61C2×#63214—21no—
62C2×#63214—21no—
63#10587481—24no—
64#10587481—42no—
65Dic136—28no—
66C22×C4×C17—41no—
67C22×C4×C17—41no—
68C22×C4×C17C2×D411yescharacteristic
69C22×Dic17—41no—
70C22×Dic17—41no—
71C22×Dic17D811yescharacteristic
72C22×Dic17D811yescharacteristic
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×C17C22×C411yescharacteristic
86C2×C8×C17C2×D411yescharacteristic
87C2×C8×C17C2×D411yescharacteristic
88C2×C8×C17C2×D411yescharacteristic
89C2×C8×C17#4111yescharacteristic
90C2×C8×C17#4111yescharacteristic
91C4⋊C4×C17—22no—
92C4⋊C4×C17—41no—
93C4⋊C4×C17—41no—
94C4⋊C4×C17—41no—
95#63225—44no—
96C4×Dic17—21no—
97C4×Dic17—21no—
98C4×Dic17—44no—
99C2×#3622—21no—
100C2×#3622—21no—
101C2×#3622—21no—
102Dic68—22no—
103Dic68—22no—
104Dic68—22no—
105Dic68—22no—
106Dic68—22no—
107Dic68—41no—
108Dic68—41no—
109Dic68C22⋊C414yes—
110C16×C17—22no—
111#63214—41no—
112#13015—171nomaximal, Sylow
113C23×C17C2×D811yescharacteristic
114C2×C4×C17—42no—
115C2×C4×C17—81no—
116C2×C4×C17—81no—
117C2×C4×C17—81no—
118C2×C4×C17—81no—
119C2×C4×C17—81no—
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—21no—
127C2×Dic17—21no—
128C2×Dic17—21no—
129C2×Dic17—21no—
130C2×Dic17—21no—
131C2×Dic17—42no—
132C2×Dic17—42no—
133C2×Dic17—42no—
134C2×Dic17—42no—
135C2×Dic17—81no—
136C2×Dic17—81no—
137C2×Dic17Q3212yescomplemented
138Dic34—24no—
139Dic34—42no—
140Dic34—42no—
141Dic34—42no—
142Dic34—42no—
143Dic34—42no—
144Dic34—81no—
145Dic34—81no—
146C8×C17C2×C22⋊C411yescharacteristic
147C8×C17C4×D411yescharacteristic
148C8×C17#12111yescharacteristic
149C8×C17#12311yescharacteristic
150#3622—41no—
151C22×Q32—171no—
152C2×C4×Q16—171no—
153C2×#358—171no—
154C2×#358—171no—
155#1969—171no—
156#1380D1711yescharacteristic
157#1374—171no—
158C22×C17C4×D811yescharacteristic
159C22×C17#44711yescharacteristic
160C22×C17#45911yescharacteristic
161C22×C17C2×Q3211yescharacteristic
162C22×C17#50811yescharacteristic
163C22×C17#51011yescharacteristic
164C22×C17#51011yescharacteristic
165C4×C17—82no—
166C4×C17—161no—
167C4×C17#38611yescharacteristic
168C4×C17#44211yescharacteristic
169C4×C17#44911yescharacteristic
170C4×C17#46311yescharacteristic
171Dic17—22no—
172Dic17—44no—
173Dic17—41no—
174Dic17—82no—
175C22×Q16—171no—
176C22×Q16—171no—
177C2×C4×Q8—341no—
178C2×Q32—174no—
179C2×Q32—342no—
180C2×Q32—342no—
181C22×C16—171no—
182C22×C16C2×D1711yescharacteristic
183C4×Q16—342no—
184C4×Q16—342no—
185C2×#107C2×D1711yescharacteristic
186C2×#107C2×D1711yescharacteristic
187C2×#103—341no—
188C2×#103—341no—
189C2×C4×C8—171no—
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×C8—171no—
215C22×C8C22×D1711yescharacteristic
216C4×Q8—344no—
217C4×Q8—682no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—681no—
221C2×C42—171no—
222C2×C42—681no—
223Q32—348no—
224C2×C16—21no—
225C2×C16—21no—
226C2×C16—341no—
227C2×C16—341no—
228C2×C16—341no—
229C2×C16C4×D1712yes—
230#107—21no—
231#107—21no—
232#107—21no—
233#107D6812yes—
234#103—344no—
235#103—682no—
236C4×C8—341no—
237C4×C8—341no—
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—41no—
254C22×C4—41no—
255C22×C4—171no—
256C22×C4—171no—
257C22×C4—681no—
258C22×C4—681no—
259C22×C4D4×D1711yescharacteristic
260Q16—174no—
261Q16—342no—
262Q16—342no—
263Q16—342no—
264Q16—342no—
265Q16—342no—
266Q16—681no—
267Q16—681no—
268C2×C8—341no—
269C2×C8—341no—
270C2×C8—341no—
271C2×C8C2×C4×D1711yescharacteristic
272C2×C8C2×D6811yescharacteristic
273C2×C8#6325211yescharacteristic
274C2×C8D4×D1711yescharacteristic
275C2×C8D4×D1711yescharacteristic
276C2×C8#6325611yescharacteristic
277C4⋊C4—22no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—684no—
282C42—341no—
283C42—341no—
284C42—684no—
285C16—22no—
286C16—681no—
287C23D8×D1711yescharacteristic
288Q8—344no—
289Q8—682no—
290Q8—682no—
291Q8—682no—
292Q8—682no—
293Q8—682no—
294Q8—1361no—
295Q8—1361no—
296C2×C4—42no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—172no—
303C2×C4—341no—
304C2×C4—341no—
305C2×C4—341no—
306C2×C4—341no—
307C2×C4—341no—
308C2×C4—682no—
309C2×C4—682no—
310C2×C4—682no—
311C2×C4—682no—
312C2×C4—1361no—
313C2×C4—1361no—
314C2×C4#1058756811yescharacteristic
315C2×C4#1058757011yescharacteristic
316C2×C4#1058757911yescharacteristic
317C2×C4#1058760011yescharacteristic
318C2×C4#1058760011yescharacteristic
319C2×C4#1058760511yescharacteristic
320C8—681no—
321C8C4×D6811yescharacteristic
322C8C22⋊C4×D1711yescharacteristic
323C8#1058758011yescharacteristic
324C8#1058758111yescharacteristic
325C22#1176289111yescharacteristic
326C22#1176294411yescharacteristic
327C22#1176300311yescharacteristic
328C22Q32×D1711yescharacteristic
329C22#1176323811yescharacteristic
330C22#1176324811yescharacteristic
331C22#1176324811yescharacteristic
332C4—82no—
333C4—161no—
334C4—342no—
335C4—684no—
336C4—681no—
337C4—1362no—
338C4#1176268711yescharacteristic
339C4#1176292011yescharacteristic
340C4#1176295711yescharacteristic
341C4#1176302711yescharacteristic
342C2#1452913311yescharacteristic
343C2#1453064211yescharacteristic
344C2#1453065411yescharacteristic
345C2#1453071911yescharacteristic
346C2#1453072511yescharacteristic
347C2#1453083311yescharacteristic
348C2#1453084511yescharacteristic
subgroupG/H
centerC23D8×D17
commutatorC2×C8×C17C22×C4
FrattiniC22×C8C22×D17
FittingC17×#1380C2
socle, prime radicalC23×C17C2×D8
cosocleC22×C8×C17C23
hypercenter#1380D17
hypocenterC17#13015
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
13. C2×Dic136C4semidirect
137. C2×Dic17Q32semidirect
240. C17#13015semidirect

Maximal subgroups

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

subgroupindex
C22×Dic1362
C2×#117629032
C2×#117626122
#145296432
#145268612
C17×#13802
#1301517