Finite Group Databasebeta

← C2×#14528392 #17021995

Subgroups — C2×#14528392 #17021995

Order 4352.

750 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763212C211yesmaximal, characteristic
2C2×#11763212C211yesmaximal, characteristic
3C2×#11763161C211yesmaximal, characteristic
4C2×#11763160C211yesmaximal, characteristic
5C2×#11763159C211yesmaximal, characteristic
6#14528392C218yesmaximal, direct product factor
7C2×C8×#3622C211yesmaximal, characteristic
8C2×C17×#487C211yesmaximal, characteristic
9C2×#10587555C2211yescharacteristic
10C2×#10587555C2211yescharacteristic
11#11763212—22no—
12#11763212—22no—
13#11763212C2214yes—
14#11763212C2214yes—
15#11763161—22no—
16#11763161C2214yes—
17#11763160—22no—
18#11763160C2214yes—
19#11763159—22no—
20#11763159C2214yes—
21C2×#10587478—22no—
22C2×#10587478—22no—
23C2×#10587487—22no—
24C2×#10587506—22no—
25C2×#10587481—22no—
26C2×C4×#3622C2211yescharacteristic
27C2×C4×#3622C2211yescharacteristic
28C8×#3622C2214yes—
29C2×C17×C4⋊Q8C2211yescharacteristic
30C2×C17×C4⋊Q8C2211yescharacteristic
31C17×#487—22no—
32C17×#487C2214yes—
33C2×C17×#103—22no—
34C2×C4×C8×C17C2211yescharacteristic
35C22×Q8×C17—21no—
36C22×Q8×C17—21no—
37C22×Dic34—21no—
38C22×Dic34—21no—
39C22×C8×C17D412yes—
40C17×C4⋊Q8—21no—
41C17×C4⋊Q8—21no—
42C17×C4⋊Q8—21no—
43C17×C4⋊Q8—21no—
44C17×C4⋊Q8—21no—
45C17×C4⋊Q8—21no—
46C17×C4⋊Q8C2312yes—
47C17×C4⋊Q8C2312yes—
48C2×C4⋊C4×C17—21no—
49C2×C4⋊C4×C17—21no—
50C2×C4⋊C4×C17—21no—
51C2×C4⋊C4×C17—21no—
52C2×C42×C17C2311yescharacteristic
53C2×C4⋊Dic17—21no—
54C2×C4⋊Dic17—21no—
55C2×C4⋊Dic17—21no—
56C2×C4⋊Dic17—21no—
57C22×#3622D412yes—
58C22×#3622D412yes—
59#10587555—21no—
60#10587555—21no—
61#10587555—21no—
62#10587555—21no—
63#10587555—21no—
64#10587555—21no—
65#10587555C2312yes—
66#10587555C2312yes—
67C17×#103—28no—
68C4×C8×C17D412yes—
69C4×C8×C17C2312yes—
70#10587506—28no—
71#10587487—28no—
72#10587481—28no—
73#10587478—28no—
74#10587478—28no—
75C4×#3622D412yes—
76C4×#3622D412yes—
77C4×#3622C2312yes—
78C4×#3622C2312yes—
79C2×Q8×C17—22no—
80C2×Q8×C17—22no—
81C2×Q8×C17—41no—
82C2×Q8×C17—41no—
83C2×Q8×C17—44no—
84C2×Q8×C17—44no—
85C22×C4×C17—41no—
86C22×C4×C17—41no—
87C22×C4×C17C2×D411yescharacteristic
88C22×C4×C17C2×D411yescharacteristic
89C22×C4×C17C2×D411yescharacteristic
90C22×Dic17—41no—
91C22×Dic17—41no—
92C2×Dic34—22no—
93C2×Dic34—22no—
94C2×Dic34—44no—
95C2×Dic34—44no—
96C2×Dic34—41no—
97C2×Dic34—41no—
98C2×C8×C17—24no—
99C2×C8×C17C2×D414yes—
100C4⋊C4×C17—22no—
101C4⋊C4×C17—22no—
102C4⋊C4×C17—22no—
103C4⋊C4×C17—22no—
104C4⋊C4×C17—41no—
105C4⋊C4×C17—41no—
106C4⋊C4×C17—41no—
107C4⋊C4×C17—41no—
108C42×C17C2×D411yescharacteristic
109C42×C17C2×D411yescharacteristic
110C42×C17C2×D411yescharacteristic
111C42×C17C2411yescharacteristic
112C4⋊Dic17—22no—
113C4⋊Dic17—22no—
114C4⋊Dic17—22no—
115C4⋊Dic17—22no—
116C4⋊Dic17—41no—
117C4⋊Dic17—41no—
118C4⋊Dic17—41no—
119C4⋊Dic17—41no—
120C2×#3622—24no—
121C2×#3622Q1618yes—
122C2×#3622C2×D414yes—
123C2×#3622C2×D414yes—
124C2×#1710—171nomaximal, Sylow
125C23×C17#12711yescharacteristic
126Q8×C17—44no—
127Q8×C17—44no—
128Q8×C17—82no—
129Q8×C17—82no—
130C2×C4×C17—42no—
131C2×C4×C17—42no—
132C2×C4×C17—82no—
133C2×C4×C17—82no—
134C2×C4×C17#12711yescharacteristic
135C2×C4×C17#12711yescharacteristic
136C2×C4×C17#12711yescharacteristic
137C2×C4×C17C2×Q1614yes—
138C2×C4×C17#13514yes—
139C2×C4×C17#13514yes—
140C2×C4×C17C22×D411yescharacteristic
141C2×C4×C17C22×D411yescharacteristic
142C2×C4×C17C22×D411yescharacteristic
143C2×Dic17—42no—
144C2×Dic17—42no—
145C2×Dic17—82no—
146C2×Dic17—82no—
147Dic34—44no—
148Dic34—44no—
149Dic34—82no—
150Dic34—82no—
151C8×C17—24no—
152#3622—24no—
153#3622C2×Q1618yes—
154C2×#500—171no—
155C2×#500—171no—
156C2×#487—171no—
157C2×#487—171no—
158C2×#487—171no—
159C2×#487D1711yescharacteristic
160#1710—178no—
161C2×C82—171no—
162C22×C17#49412yes—
163C22×C17#49512yes—
164C22×C17#49512yes—
165C22×C17C2×#12711yescharacteristic
166C4×C17—82no—
167C4×C17—82no—
168C4×C17#49412yes—
169C4×C17#49512yes—
170C4×C17#49512yes—
171C4×C17C22×Q1612yes—
172C4×C17C2×#13512yes—
173C4×C17C2×#13512yes—
174Dic17—82no—
175Dic17—82no—
176C2×C4⋊Q8—171no—
177C2×C4⋊Q8—171no—
178C2×C4⋊Q8C2×D1711yescharacteristic
179C2×C4⋊Q8C2×D1711yescharacteristic
180#500—174no—
181#500—174no—
182#500—342no—
183#500—342no—
184#487—22no—
185#487—174no—
186#487—174no—
187#487—174no—
188#487—342no—
189#487—342no—
190#487—342no—
191#487C2×D1714yes—
192C2×#107—342no—
193C2×#107—342no—
194C2×#103—22no—
195C2×#103—342no—
196C2×#103—342no—
197C2×#103—342no—
198C2×C4×C8—171no—
199C2×C4×C8—171no—
200C2×C4×C8C2×D1711yescharacteristic
201C82—174no—
202C2×C17#171014yescomplemented
203C2×C17C2×#49411yescharacteristic
204C2×C17C2×#49511yescharacteristic
205C2×C17C2×#49511yescharacteristic
206C22×Q8—21no—
207C22×Q8—21no—
208C22×Q8—341no—
209C22×Q8—341no—
210C22×C8—172no—
211C22×C8—172no—
212C22×C8C22⋊D1712yes—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—172no—
220C4⋊Q8—172no—
221C4⋊Q8—341no—
222C4⋊Q8—341no—
223C4⋊Q8—341no—
224C4⋊Q8—341no—
225C4⋊Q8—341no—
226C4⋊Q8—341no—
227C4⋊Q8C22×D1712yes—
228C4⋊Q8C22×D1712yes—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—341no—
234C2×C4⋊C4—341no—
235C2×C4⋊C4—341no—
236C2×C4⋊C4—341no—
237C2×C42C22×D1711yescharacteristic
238#107—348no—
239#107—348no—
240#103—28no—
241#103—348no—
242#103—348no—
243#103—348no—
244C4×C8—172no—
245C4×C8—172no—
246C4×C8—172no—
247C4×C8—172no—
248C4×C8C22⋊D1712yes—
249C4×C8C22×D1712yes—
250C17C2×#171011yescharacteristic, complemented, Sylow
251C2×Q8—22no—
252C2×Q8—22no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—44no—
256C2×Q8—44no—
257C2×Q8—342no—
258C2×Q8—342no—
259C2×Q8—681no—
260C2×Q8—681no—
261C2×Q8—684no—
262C2×Q8—684no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—681no—
266C22×C4—681no—
267C22×C4D4×D1711yescharacteristic
268C22×C4D4×D1711yescharacteristic
269C22×C4C2×C22⋊D1711yescharacteristic
270C2×C8—24no—
271C2×C8—174no—
272C2×C8—178no—
273C2×C8—174no—
274C2×C8—344no—
275C2×C8C2×C22⋊D1714yes—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—342no—
285C4⋊C4—342no—
286C4⋊C4—342no—
287C4⋊C4—342no—
288C4⋊C4—681no—
289C4⋊C4—681no—
290C4⋊C4—681no—
291C4⋊C4—681no—
292C42D4×D1711yescharacteristic
293C42D4×D1711yescharacteristic
294C42C2×C22⋊D1711yescharacteristic
295C42C23×D1711yescharacteristic
296C23#1058762611yescharacteristic
297Q8—44no—
298Q8—44no—
299Q8—82no—
300Q8—82no—
301Q8—684no—
302Q8—684no—
303Q8—1362no—
304Q8—1362no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—82no—
308C2×C4—82no—
309C2×C4—682no—
310C2×C4—682no—
311C2×C4—1362no—
312C2×C4—1362no—
313C2×C4#1058760214yes—
314C2×C4Q16×D1714yes—
315C2×C4#1058762611yescharacteristic
316C2×C4#1058762611yescharacteristic
317C2×C4#1058762611yescharacteristic
318C2×C4#1058763614yes—
319C2×C4C2×D4×D1711yescharacteristic
320C2×C4C2×D4×D1711yescharacteristic
321C2×C4C22×C22⋊D1711yescharacteristic
322C8—24no—
323C8—178no—
324C8—344no—
325C22#1176318712yes—
326C22#1176319012yes—
327C22#1176319112yes—
328C22C2×#1058762611yescharacteristic
329C4—82no—
330C4—82no—
331C4—1362no—
332C4—1362no—
333C4#1176318712yes—
334C4#1176319012yes—
335C4#1176319112yes—
336C4C2×Q16×D1712yes—
337C4C2×#1058763612yes—
338C4C2×#1058760212yes—
339C2#1452839214yesdirect product factor
340C2C2×#1176318711yescharacteristic
341C2C2×#1176319011yescharacteristic
342C2C2×#1176319111yescharacteristic
subgroupG/H
centerC23#10587626
commutator, cosocleC42×C17C24
FrattiniC42C23×D17
FittingC2×C17×#487C2
socle, prime radicalC23×C17#127
hypercenterC2×#487D17
hypocenterC17C2×#1710
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
6. #14528392C2direct (N × H)
202. C2×C17#1710semidirect
250. C17C2×#1710semidirect
339. C2#14528392direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117632122
C2×#117631612
C2×#117631602
C2×#117631592
#145283922
C2×C8×#36222
C2×C17×#4872
C2×#171017