Finite Group Databasebeta

← C2×#14530347 #17064232

Subgroups — C2×#14530347 #17064232

Order 4352.

998 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762679C211yesmaximal, characteristic
2#14530347C218yesmaximal, direct product factor
3C2×#11762571C212yesmaximal
4C2×#11762571C212yesmaximal
5C2×#11762564C211yesmaximal, characteristic
6C2×C17×#389C211yesmaximal, characteristic
7C23×#3622C2212yes—
8C22×C4⋊Dic17—21no—
9C22×C4⋊Dic17—21no—
10C22×C4⋊Dic17C2212yes—
11#11762679—22no—
12#11762679C2214yes—
13#11762571C2218yes—
14#11762571C2218yes—
15#11762564C2214yes—
16C22×C4⋊C4×C17—21no—
17C22×C4⋊C4×C17C2211yescharacteristic
18C22×C4⋊C4×C17C2211yescharacteristic
19C22×C42×C17C2211yescharacteristic
20C17×#389—22no—
21C17×#389C2214yes—
22C2×C17×#95—21no—
23C23×C4×C17—21no—
24C23×C4×C17—21no—
25C23×C4×C17D411yescharacteristic
26C23×C4×C17D411yescharacteristic
27C23×C4×C17C2311yescharacteristic
28C23×Dic17—22no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—22no—
31C2×C4⋊C4×C17—24no—
32C2×C4⋊C4×C17—24no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17—44no—
35C2×C4⋊C4×C17Q814yes—
36C2×C4⋊C4×C17C2312yes—
37C2×C4⋊C4×C17C2312yes—
38C2×C42×C17—24no—
39C2×C42×C17D412yes—
40C2×C42×C17C2312yes—
41C2×C4⋊Dic17—24no—
42C2×C4⋊Dic17—24no—
43C2×C4⋊Dic17—22no—
44C2×C4⋊Dic17—28no—
45C2×C4⋊Dic17—44no—
46C2×C4⋊Dic17—44no—
47C2×C4⋊Dic17C2314yes—
48C22×#3622—24no—
49C22×#3622—24no—
50C22×#3622—24no—
51C22×#3622C2314yes—
52C17×#95—24no—
53C24×C17C2×D411yescharacteristic
54C22×C4×C17—22no—
55C22×C4×C17—22no—
56C22×C4×C17—22no—
57C22×C4×C17—22no—
58C22×C4×C17—24no—
59C22×C4×C17—22no—
60C22×C4×C17—22no—
61C22×C4×C17—42no—
62C22×C4×C17—42no—
63C22×C4×C17—42no—
64C22×C4×C17—42no—
65C22×C4×C17—42no—
66C22×C4×C17SD1614yes—
67C22×C4×C17Q1614yes—
68C22×C4×C17C2×D412yes—
69C22×C4×C17C2×D412yes—
70C22×C4×C17C2×D411yescharacteristic
71C22×C4×C17C2×Q812yes—
72C22×C4×C17#4112yes—
73C22×C4×C17#4114yes—
74C22×C4×C17#4114yes—
75C22×C4×C17C2411yescharacteristic
76C22×Dic17—24no—
77C22×Dic17—44no—
78C22×Dic17—44no—
79C22×Dic17—44no—
80C4⋊C4×C17—24no—
81C4⋊C4×C17—22no—
82C4⋊C4×C17—24no—
83C4⋊C4×C17—42no—
84C4⋊C4×C17—48no—
85C4⋊C4×C17C2×Q814yes—
86C42×C17—24no—
87C42×C17—24no—
88C4⋊Dic17—28no—
89C4⋊Dic17—48no—
90C4⋊Dic17—48no—
91C4⋊Dic17—44no—
92C2×#3622—24no—
93C2×#3622—24no—
94C2×#3622—24no—
95C2×#3622—48no—
96C2×#2100—171nomaximal, Sylow
97C23×C17C22⋊Q812yes—
98C23×C17#12312yes—
99C23×C17#12412yes—
100C23×C17C2×SD1612yes—
101C23×C17C2×Q1612yes—
102C23×C17AGL(1,ℤ/8)12yes—
103C23×C17AGL(1,ℤ/8)12yes—
104C23×C17C22×D411yescharacteristic
105C2×C4×C17—22no—
106C2×C4×C17—22no—
107C2×C4×C17—22no—
108C2×C4×C17—22no—
109C2×C4×C17—28no—
110C2×C4×C17—28no—
111C2×C4×C17—24no—
112C2×C4×C17—42no—
113C2×C4×C17—42no—
114C2×C4×C17—48no—
115C2×C4×C17—42no—
116C2×C4×C17—42no—
117C2×C4×C17—42no—
118C2×C4×C17—84no—
119C2×C4×C17C22⋊Q812yes—
120C2×C4×C17#12312yes—
121C2×C4×C17#12412yes—
122C2×C4×C17#12518yes—
123C2×C4×C17#12618yes—
124C2×C4×C17C2×SD1614yes—
125C2×C4×C17C2×Q1614yes—
126C2×C4×C17C22×Q811yescharacteristic
127C2×C4×C17C2×#4111yescharacteristic
128C2×C4×C17C2×#4112yes—
129C2×C4×C17C2×#4112yes—
130C2×Dic17—44no—
131C2×Dic17—44no—
132C2×Dic17—44no—
133C2×Dic17—88no—
134#3622—44no—
135C2×#389D1711yescharacteristic
136C2×#384—171no—
137#2100—178no—
138C2×#340—172no—
139C2×#340—172no—
140C2×#336—171no—
141C22×C17#40014yes—
142C22×C17#47614yes—
143C22×C17#47714yes—
144C22×C17#48114yes—
145C22×C17#48414yes—
146C22×C17#48714yes—
147C22×C17#49014yes—
148C22×C17C2×C22⋊Q811yescharacteristic
149C22×C17C2×#12311yescharacteristic
150C22×C17C2×#12411yescharacteristic
151C22×C17C22×SD1611yescharacteristic
152C22×C17C22×Q1611yescharacteristic
153C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
154C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
155C4×C17—24no—
156C4×C17—24no—
157C4×C17—44no—
158C4×C17—82no—
159C4×C17#40014yes—
160C4×C17C2×#12512yes—
161C4×C17C2×#12612yes—
162Dic17—84no—
163C23×C8—172no—
164C22×C4⋊C4—21no—
165C22×C4⋊C4—172no—
166C22×C4⋊C4—341no—
167C22×C4⋊C4—341no—
168C22×C4⋊C4C2×D1711yescharacteristic
169C22×C4⋊C4C2×D1711yescharacteristic
170C22×C42C2×D1711yescharacteristic
171#389—22no—
172#389C2×D1714yes—
173#384—174no—
174#384—342no—
175C2×#95—21no—
176#340—178no—
177#340—178no—
178#336—174no—
179C2×C17#210018yescomplemented
180C2×C17C2×#40011yescharacteristic
181C2×C17C2×#47611yescharacteristic
182C2×C17C2×#47711yescharacteristic
183C2×C17C2×#48111yescharacteristic
184C2×C17C2×#48411yescharacteristic
185C2×C17C2×#48711yescharacteristic
186C2×C17C2×#49011yescharacteristic
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—342no—
190C23×C4C22⋊D1711yescharacteristic
191C23×C4C22⋊D1711yescharacteristic
192C23×C4C22×D1711yescharacteristic
193C22×C8—174no—
194C22×C8—344no—
195C22×C8—344no—
196C22×C8—344no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—24no—
200C2×C4⋊C4—24no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—44no—
203C2×C4⋊C4—174no—
204C2×C4⋊C4—348no—
205C2×C4⋊C4—342no—
206C2×C4⋊C4—344no—
207C2×C4⋊C4—344no—
208C2×C4⋊C4—684no—
209C2×C4⋊C4—684no—
210C2×C4⋊C4Dic3414yes—
211C2×C4⋊C4C22×D1712yes—
212C2×C4⋊C4C22×D1712yes—
213C2×C42—24no—
214C2×C42C22⋊D1712yes—
215C2×C42C22×D1712yes—
216#95—24no—
217C17C2×#210011yescharacteristic, complemented, Sylow
218C24C2×C22⋊D1711yescharacteristic
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—24no—
225C22×C4—22no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—344no—
232C22×C4—684no—
233C22×C4—684no—
234C22×C4—684no—
235C22×C4#6322914yes—
236C22×C4#6323114yes—
237C22×C4C2×Dic3412yes—
238C22×C4#6325212yes—
239C22×C4#6325414yes—
240C22×C4#6325614yes—
241C22×C4C2×C22⋊D1712yes—
242C22×C4C2×C22⋊D1712yes—
243C22×C4C2×C22⋊D1711yescharacteristic
244C22×C4C23×D1711yescharacteristic
245C2×C8—344no—
246C2×C8—344no—
247C2×C8—344no—
248C2×C8—688no—
249C4⋊C4—22no—
250C4⋊C4—24no—
251C4⋊C4—24no—
252C4⋊C4—48no—
253C4⋊C4—42no—
254C4⋊C4—348no—
255C4⋊C4—688no—
256C4⋊C4—688no—
257C4⋊C4—684no—
258C4⋊C4C2×Dic3414yes—
259C42—24no—
260C42—24no—
261C23#1058761012yes—
262C23C2×#6322912yes—
263C23#1058762112yes—
264C23C2×#6323112yes—
265C23#1058763312yes—
266C23#1058763512yes—
267C23#1058763512yes—
268C23C22×C22⋊D1711yescharacteristic
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—28no—
274C2×C4—28no—
275C2×C4—24no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—48no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—84no—
283C2×C4—684no—
284C2×C4—684no—
285C2×C4—684no—
286C2×C4—1368no—
287C2×C4#1058757618yes—
288C2×C4#1058758418yes—
289C2×C4#1058761012yes—
290C2×C4C2×#6322914yes—
291C2×C4#1058762112yes—
292C2×C4C2×#6323114yes—
293C2×C4#1058763312yes—
294C2×C4C22×Dic3411yescharacteristic
295C2×C4C2×#6325211yescharacteristic
296C2×C4C2×#6325412yes—
297C2×C4C2×#6325612yes—
298C8—684no—
299C22#1176274814yes—
300C22#1176309914yes—
301C22#1176310414yes—
302C22#1176312514yes—
303C22#1176314214yes—
304C22#1176316114yes—
305C22#1176317514yes—
306C22C2×#1058761011yescharacteristic
307C22C2×#1058762111yescharacteristic
308C22C2×#1058763311yescharacteristic
309C22C22×#6322911yescharacteristic
310C22C22×#6323111yescharacteristic
311C22C2×#1058763511yescharacteristic
312C22C2×#1058763511yescharacteristic
313C4—24no—
314C4—24no—
315C4—44no—
316C4—82no—
317C4—1364no—
318C4#1176274814yes—
319C4C2×#1058757612yes—
320C4C2×#1058758412yes—
321C2#1453034718yesdirect product factor
322C2C2×#1176274811yescharacteristic
323C2C2×#1176309911yescharacteristic
324C2C2×#1176310411yescharacteristic
325C2C2×#1176312511yescharacteristic
326C2C2×#1176314211yescharacteristic
327C2C2×#1176316111yescharacteristic
328C2C2×#1176317511yescharacteristic
subgroupG/H
centerC24C2×C22⋊D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC2×C17×#389C2
socle, prime radicalC24×C17C2×D4
hypercenterC2×#389D17
hypocenterC17C2×#2100
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. #14530347C2direct (N × H)
179. C2×C17#2100semidirect
217. C17C2×#2100semidirect
321. C2#14530347direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117626792
#145303472
C2×#117625712
C2×#117625642
C2×C17×#3892
C2×#210017