Finite Group Databasebeta

← #16950821

Subgroups — #16950821

Order 4352.

486 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#107×D17C211yesmaximal, characteristic
2C2×#11762634C211yesmaximal, characteristic, complemented
3C2×#11762588C211yesmaximal, characteristic
4#14528810C211yesmaximal, characteristic
5#14526876C211yesmaximal, characteristic, complemented
6#14526875C211yesmaximal, characteristic, complemented
7C2×C17×#366C211yesmaximal, characteristic, complemented
8C22×C8×D17C2211yescharacteristic
9C2×C4⋊C4×D17—21no—
10C22×#63214C2211yescharacteristic
11C2×#10587489C2211yescharacteristic
12C2×#10587489C2211yescharacteristic
13C2×#10587478—21no—
14#107×D17—22no—
15#107×D17—22no—
16#11762666—21no—
17#11762634—22no—
18#11762588C414yescomplemented
19#11762571—21no—
20C22×C16×C17C2211yescharacteristic
21C2×C17×#107C2211yescharacteristic
22C2×C17×#107C2211yescharacteristic
23C17×#366—22no—
24C22×C4×D17—41no—
25C22×C4×D17D411yescharacteristic
26C22×C8×C17C2311yescharacteristic
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17—21no—
29C2×#63227—41no—
30C2×C4⋊Dic17—21no—
31C2×C4⋊Dic17—21no—
32C2×#63225—41no—
33C22×#3622D411yescharacteristic
34C2×C8×D17—21no—
35C2×C8×D17—21no—
36C2×C8×D17—21no—
37C2×C8×D17—21no—
38C2×C8×D17C2×C412yes—
39C2×C8×D17Q812yes—
40C4⋊C4×D17—24no—
41C4⋊C4×D17—42no—
42C2×C16×C17—21no—
43C2×C16×C17—21no—
44C2×C16×C17C2×C412yescomplemented
45C17×#107—21no—
46C17×#107—21no—
47C17×#107—21no—
48C17×#107D412yes—
49#10587502—41no—
50#10587489—21no—
51#10587489—21no—
52#10587489—21no—
53#10587489D412yes—
54C2×#63214—21no—
55C2×#63214—21no—
56C2×#63214C2×C412yescomplemented
57#10587478—24no—
58C23×D17D811yescharacteristic
59C22×C4×C17—41no—
60C22×C4×C17—41no—
61C22×C4×C17C2×D411yescharacteristic
62C22×Dic17—41no—
63C22×Dic17—41no—
64C22×Dic17D811yescharacteristic
65C2×C4×D17—21no—
66C2×C4×D17—21no—
67C2×C4×D17—21no—
68C2×C4×D17—21no—
69C2×C4×D17—44no—
70C2×C4×D17—82no—
71C2×C4×D17—82no—
72C2×C4×D17C4⋊C412yes—
73C2×C4×D17Q1612yes—
74C2×C8×C17C22×C411yescharacteristic
75C2×C8×C17C2×D411yescharacteristic
76C2×C8×C17C2×D411yescharacteristic
77C2×C8×C17C2×Q811yescharacteristic
78C2×C8×C17#4111yescharacteristic
79C2×C8×C17#4111yescharacteristic
80C4⋊C4×C17—22no—
81C4⋊C4×C17—41no—
82C4⋊C4×C17—41no—
83C4⋊C4×C17—41no—
84#63227—82no—
85C4⋊Dic17—22no—
86C4⋊Dic17—41no—
87C4⋊Dic17—41no—
88C4⋊Dic17—41no—
89#63225—44no—
90C2×#3622—21no—
91C2×#3622—21no—
92C2×#3622C4⋊C412yes—
93C8×D17—22no—
94C8×D17—22no—
95C8×D17—22no—
96C8×D17—22no—
97C16×C17—22no—
98#63214—22no—
99#12919—171nomaximal, Sylow
100C23×C17C2×D811yescharacteristic
101C22×D17—21no—
102C22×D17—21no—
103C22×D17—21no—
104C22×D17—21no—
105C22×D17#10712yes—
106C22×D17D1612yes—
107C22×D17Q3212yes—
108C2×C4×C17—42no—
109C2×C4×C17—81no—
110C2×C4×C17—81no—
111C2×C4×C17—81no—
112C2×C4×C17—81no—
113C2×C4×C17—81no—
114C2×C4×C17C2×C4⋊C411yescharacteristic
115C2×C4×C17#12011yescharacteristic
116C2×C4×C17#12311yescharacteristic
117C2×C4×C17C2×Q1611yescharacteristic
118C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C17#13711yescharacteristic
120C2×Dic17—21no—
121C2×Dic17—21no—
122C2×Dic17—42no—
123C2×Dic17—81no—
124C2×Dic17—81no—
125C2×Dic17—81no—
126C2×Dic17—81no—
127C2×Dic17—81no—
128C2×Dic17#10712yes—
129C4×D17—22no—
130C4×D17—22no—
131C4×D17—22no—
132C4×D17—22no—
133C4×D17—88no—
134C8×C17C4×D411yescharacteristic
135C8×C17C4×D411yescharacteristic
136C8×C17C22⋊Q811yescharacteristic
137C8×C17C22⋊Q811yescharacteristic
138#3622—22no—
139C22×#107—171no—
140C2×#366—171no—
141C2×#366D1711yescharacteristic, complemented
142C2×C22⋊C16—171no—
143#1808—171no—
144#1380—171no—
145#1380—171no—
146C22×C17C2×#10711yescharacteristic
147C22×C17#44711yescharacteristic
148C22×C17#48011yescharacteristic
149C22×C17C2×D1611yescharacteristic
150C22×C17C2×Q3211yescharacteristic
151C22×C17#50911yescharacteristic
152C22×C17#51011yescharacteristic
153C2×D17—22no—
154C2×D17—22no—
155C2×D17—22no—
156C2×D17—22no—
157C2×D17—22no—
158C2×D17—22no—
159C2×D17#36614yescomplemented
160C4×C17—82no—
161C4×C17—161no—
162C4×C17#38511yescharacteristic
163C4×C17#42811yescharacteristic
164C4×C17#45111yescharacteristic
165C4×C17#48411yescharacteristic
166Dic17—22no—
167Dic17—82no—
168Dic17—161no—
169C23×C8—171no—
170C22×C4⋊C4—341no—
171C22×C16—171no—
172C22×C16C2×D1711yescharacteristic
173C2×#107—171no—
174C2×#107—171no—
175C2×#107—342no—
176C2×#107—341no—
177C2×#107—342no—
178C2×#107C2×D1711yescharacteristic
179C2×#107C2×D1711yescharacteristic
180#380—341no—
181#366—22no—
182#366—342no—
183C22⋊C16—174no—
184#340—341no—
185C2×C17#185211yescharacteristic
186C2×C17C2×#36611yescharacteristic
187C2×C17#215911yescharacteristic
188C2×C17#218411yescharacteristic
189C2×C17#218811yescharacteristic
190C2×C17#223211yescharacteristic
191C2×C17#223611yescharacteristic
192D17—24no—
193C23×C4—171no—
194C23×C4—681no—
195C22×C8—171no—
196C22×C8—172no—
197C22×C8—172no—
198C22×C8—341no—
199C22×C8—341no—
200C22×C8—341no—
201C22×C8—341no—
202C22×C8C22×D1711yescharacteristic
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—344no—
206C2×C4⋊C4—341no—
207C2×C4⋊C4—341no—
208C2×C4⋊C4—682no—
209C2×C4⋊C4—681no—
210C2×C22⋊C4—681no—
211C2×C16—21no—
212C2×C16—21no—
213C2×C16—172no—
214C2×C16—341no—
215C2×C16—341no—
216C2×C16C4×D1712yescomplemented
217#107—21no—
218#107—21no—
219#107—21no—
220#107—172no—
221#107—344no—
222#107—341no—
223#107—341no—
224#107—341no—
225#107C22⋊D1712yes—
226#95—681no—
227C17#1291911yescharacteristic, complemented, Sylow
228C24—171no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—171no—
232C22×C4—172no—
233C22×C4—172no—
234C22×C4—341no—
235C22×C4—341no—
236C22×C4—341no—
237C22×C4—341no—
238C22×C4—684no—
239C22×C4—681no—
240C22×C4—681no—
241C22×C4—1362no—
242C22×C4—1362no—
243C22×C4D4×D1711yescharacteristic
244C2×C8—172no—
245C2×C8—341no—
246C2×C8—341no—
247C2×C8—342no—
248C2×C8—342no—
249C2×C8—342no—
250C2×C8—342no—
251C2×C8C2×C4×D1711yescharacteristic
252C2×C8#6325211yescharacteristic
253C2×C8D4×D1711yescharacteristic
254C2×C8Q8×D1711yescharacteristic
255C2×C8#6325611yescharacteristic
256C2×C8C2×C22⋊D1711yescharacteristic
257C4⋊C4—22no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—342no—
262C4⋊C4—684no—
263C4⋊C4—681no—
264C4⋊C4—681no—
265C4⋊C4—681no—
266C22⋊C4—1362no—
267C16—22no—
268C16—342no—
269C23—172no—
270C23—172no—
271C23—172no—
272C23—341no—
273C23—341no—
274C23—341no—
275C23—341no—
276C23D8×D1711yescharacteristic
277C2×C4—42no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—172no—
284C2×C4—341no—
285C2×C4—341no—
286C2×C4—342no—
287C2×C4—342no—
288C2×C4—342no—
289C2×C4—342no—
290C2×C4—682no—
291C2×C4—1368no—
292C2×C4—1361no—
293C2×C4—1361no—
294C2×C4—1361no—
295C2×C4—1361no—
296C2×C4—1361no—
297C2×C4C4⋊C4×D1711yescharacteristic
298C2×C4#1058758011yescharacteristic
299C2×C4#1058759711yescharacteristic
300C2×C4Q16×D1711yescharacteristic
301C2×C4#1058760411yescharacteristic
302C2×C4#1058762311yescharacteristic
303C8—342no—
304C8#1058757911yescharacteristic
305C8#1058758211yescharacteristic
306C8C4×C22⋊D1711yescharacteristic
307C8#1058763211yescharacteristic
308C22—174no—
309C22—342no—
310C22—342no—
311C22—342no—
312C22—342no—
313C22—342no—
314C22—342no—
315C22#107×D1711yescharacteristic
316C22#1176294111yescharacteristic
317C22#1176312411yescharacteristic
318C22D16×D1711yescharacteristic
319C22Q32×D1711yescharacteristic
320C22#1176324311yescharacteristic
321C22#1176325111yescharacteristic
322C4—82no—
323C4—161no—
324C4—2721no—
325C4—342no—
326C4—1362no—
327C4#1176268011yescharacteristic
328C4#1176285011yescharacteristic
329C4#1176296311yescharacteristic
330C4#1176314611yescharacteristic
331C2—344no—
332C2#1452897011yescharacteristic
333C2D17×#36611yescharacteristic
334C2#1453056911yescharacteristic
335C2#1453069411yescharacteristic
336C2#1453071611yescharacteristic
337C2#1453096611yescharacteristic
338C2#1453098811yescharacteristic
subgroupG/H
centerC23D8×D17
commutatorC2×C8×C17C22×C4
FrattiniC22×C8C22×D17
FittingC2×C17×#366C2
socleC23×C17C2×D8
prime radicalC23×D17D8
cosocleC22×C8×C17C23
hypercenterC2×#366D17
hypocenterC17#12919
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#366

Complements

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

NH ≅ G/Ntype
2. C2×#11762634C2semidirect
5. #14526876C2semidirect
6. #14526875C2semidirect
7. C2×C17×#366C2semidirect
18. #11762588C4semidirect
44. C2×C16×C17C2×C4semidirect
56. C2×#63214C2×C4semidirect
141. C2×#366D17semidirect
159. C2×D17#366semidirect
216. C2×C16C4×D17semidirect
227. C17#12919semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D172
C2×#117626342
C2×#117625882
#145288102
#145268762
#145268752
C2×C17×#3662
#1291917