Finite Group Databasebeta

← C2×#14541761 #17915221

Subgroups — C2×#14541761 #17915221

Order 4352.

2238 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×#11763481C211yesmaximal, characteristic
2#14541761C2116yesmaximal, direct product factor
3C2×#11763183C213yesmaximal, complemented
4C2×#11763009C213yesmaximal, complemented
5C2×#11763011C213yesmaximal, complemented
6C2×Q8×#3622C211yesmaximal, characteristic, complemented
7C2×C4×#63230C213yesmaximal, complemented
8C2×C17×#557C211yesmaximal, characteristic, complemented
9C22×#63256—21no—
10C22×#63230C2213yes—
11C22×#63230C2216yes—
12#11763481—24no—
13#11763481C2218yes—
14C2×#10587560C2213yes—
15C2×#10587581—23no—
16C2×C4×D68C2213yes—
17#11763183C22124yescomplemented
18#11763011C22124yescomplemented
19#11763009C22124yescomplemented
20Q8×#3622C2218yescomplemented
21C4×#63230C22124yescomplemented
22C2×#10587479C2211yescharacteristic
23C2×C4⋊#3622C2213yes—
24C2×#10587506C2213yes—
25C2×#10587480C2213yes—
26C2×C4×#3622C2213yes—
27C17×#557—24no—
28C17×#557C2218yescomplemented
29C2×C17×C4⋊Q8C2213yes—
30C2×C17×#125—23no—
31C2×C4×Q8×C17—21no—
32C2×C4×Q8×C17C2213yes—
33C2×C4×Q8×C17C2211yescharacteristic
34C22×Q8×C17D411yescharacteristic
35C22×Q8×C17C2313yes—
36C2×#63256—28no—
37C2×#63256—48no—
38C22×D68—23no—
39C22×D68—23no—
40C22×D68C2313yes—
41C22×C4×D17—23no—
42C17×C4⋊Q8—26no—
43C17×C4⋊Q8C23112yes—
44C17×#125—224no—
45C4×Q8×C17—28no—
46C4×Q8×C17—26no—
47C4×Q8×C17D414yes—
48C4×Q8×C17C23112yes—
49C4×Q8×C17C2314yes—
50C2×C4⋊C4×C17—23no—
51C2×C4⋊C4×C17—23no—
52C2×C4⋊C4×C17—23no—
53C2×C4⋊C4×C17D413yes—
54C2×C4⋊C4×C17C2311yescharacteristic
55C2×C42×C17—23no—
56C2×C42×C17C2313yes—
57C2×#63230—212no—
58C2×#63230—412no—
59C2×#63230C23112yes—
60C2×#63230C23124yes—
61C2×#63227—23no—
62C2×C4⋊Dic17C2311yescharacteristic
63C22×#3622C2313yes—
64C22×#3622C2311yescharacteristic
65#10587581—224no—
66#10587560—26no—
67#10587560C23112yes—
68C4×D68—26no—
69C4×D68C23112yes—
70#10587506C23112yes—
71#10587480C23112yes—
72#10587479C2314yes—
73C4⋊#3622C23112yes—
74C4×#3622C23112yes—
75C23×D17—23no—
76C2×Q8×C17—23no—
77C2×Q8×C17—26no—
78C2×Q8×C17—26no—
79C2×Q8×C17SD1618yescomplemented
80C2×Q8×C17C2×D414yes—
81C2×Q8×C17C2416yes—
82C22×C4×C17—23no—
83C22×C4×C17—21no—
84C22×C4×C17C2×D413yes—
85C22×C4×C17C2×D413yes—
86C22×C4×C17C2411yescharacteristic
87C22×Dic17—21no—
88#63256—432no—
89C2×D68—26no—
90C2×D68—26no—
91C2×D68—212no—
92C2×D68—23no—
93C2×D68—212no—
94C2×D68—412no—
95C2×D68—86no—
96C2×D68C2416yes—
97C2×C4×D17—212no—
98C2×C4×D17—412no—
99C4⋊C4×C17—212no—
100C4⋊C4×C17—212no—
101C4⋊C4×C17—212no—
102C4⋊C4×C17—21no—
103C4⋊C4×C17C2×D4112yes—
104C4⋊C4×C17C2412yes—
105C42×C17—212no—
106C42×C17C2×D416yes—
107C42×C17C2416yes—
108#63230—224no—
109#63230—424no—
110#63227—212no—
111C4⋊Dic17—21no—
112C4⋊Dic17C2412yes—
113C2×#3622—26no—
114C2×#3622#4114yescomplemented
115C2×#3622C2416yes—
116C2×#3622C2412yes—
117C2×#3392—171nomaximal, Sylow
118C23×C17C22×D411yescharacteristic
119C22×D17—26no—
120C22×D17—46no—
121C22×D17—46no—
122C22×D17—46no—
123Q8×C17—26no—
124Q8×C17—26no—
125Q8×C17—46no—
126Q8×C17C2×SD16116yescomplemented
127C2×C4×C17—26no—
128C2×C4×C17—22no—
129C2×C4×C17—26no—
130C2×C4×C17—46no—
131C2×C4×C17—42no—
132C2×C4×C17C2×SD16112yes—
133C2×C4×C17C22×D416yes—
134C2×C4×C17C22×D411yescharacteristic
135C2×C4×C17C22×D416yes—
136C2×C4×C17C2×#4112yes—
137C2×C4×C17H(5,𝔽2)12yes—
138C2×C4×C17C2511yescharacteristic
139C2×Dic17—22no—
140C2×Dic17—42no—
141D68—26no—
142D68—26no—
143D68—46no—
144D68—424no—
145D68—812no—
146C4×D17—424no—
147#3622—26no—
148#3622C2×#4114yescomplemented
149C2×#557D1711yescharacteristic, complemented
150C2×#550—171no—
151#3392—1716no—
152C2×#492—173no—
153C2×#460—173no—
154C2×#461—173no—
155C2×C8×Q8—171no—
156C2×C4×SD16—173no—
157C22×C17#55012yes—
158C22×C17C22×SD1612yes—
159C22×C17#57712yes—
160C22×C17C23×D411yescharacteristic
161C2×D17—46no—
162C2×D17—46no—
163C2×D17—46no—
164C2×D17—812no—
165C4×C17—26no—
166C4×C17—46no—
167C4×C17—42no—
168C4×C17#55012yes—
169C4×C17C22×SD16112yes—
170C4×C17C22×#4111yescharacteristic
171C4×C17C2×H(5,𝔽2)11yescharacteristic
172Dic17—42no—
173C22×#41—341no—
174C22×SD16—173no—
175C22×SD16—176no—
176#557—24no—
177#557C2×D1718yescomplemented
178#550—178no—
179#550—344no—
180C2×C4⋊Q8C2×D1713yes—
181C2×#127—173no—
182C2×#125—23no—
183C2×#121—343no—
184C2×C4×Q8—21no—
185C2×C4×Q8C2×D1713yes—
186C2×C4×Q8C2×D1711yescharacteristic
187C2×C4×D4—173no—
188#492—1724no—
189#461—1724no—
190#460—1724no—
191C8×Q8—178no—
192C4×SD16—1724no—
193C2×#106—171no—
194C2×C4⋊C8—173no—
195C2×#103—173no—
196C2×#102—173no—
197C2×C4×C8—173no—
198C2×C17#339214yescomplemented
199C2×C17C2×#55011yescharacteristic
200C2×C17C23×SD1611yescharacteristic
201C2×C17C2×#57711yescharacteristic
202D17—86no—
203C2×#41—348no—
204C2×#41—688no—
205C22×Q8C22⋊D1711yescharacteristic
206C22×Q8C22×D1713yes—
207C22×D4—173no—
208C22×D4—343no—
209C22×D4—343no—
210C23×C4—343no—
211C2×SD16—1712no—
212C2×SD16—1724no—
213C2×SD16—3412no—
214C2×SD16—6812no—
215C22×C8—171no—
216C22×C8—173no—
217C4⋊Q8—26no—
218C4⋊Q8C22×D17112yes—
219#127—1712no—
220#127—346no—
221#125—224no—
222#121—3424no—
223C4×Q8—28no—
224C4×Q8—26no—
225C4×Q8C22⋊D1714yes—
226C4×Q8C22×D17112yes—
227C4×Q8C22×D1714yes—
228C4×D4—1712no—
229C4×D4—346no—
230C2×C4⋊C4—23no—
231C2×C4⋊C4—23no—
232C2×C4⋊C4—23no—
233C2×C4⋊C4—171no—
234C2×C4⋊C4C22⋊D1713yes—
235C2×C4⋊C4C22×D1711yescharacteristic
236C2×C22⋊C4—343no—
237C2×C42—23no—
238C2×C42C22×D1713yes—
239#106—174no—
240C4⋊C8—1712no—
241#103—1712no—
242#102—1712no—
243C4×C8—1712no—
244C17C2×#339211yescharacteristic, complemented, Sylow
245C24—343no—
246#41—6832no—
247C2×Q8—23no—
248C2×Q8—26no—
249C2×Q8—26no—
250C2×Q8#6323018yescomplemented
251C2×Q8C2×C22⋊D1714yes—
252C2×Q8C23×D1716yes—
253C2×D4—176no—
254C2×D4—346no—
255C2×D4—346no—
256C2×D4—343no—
257C2×D4—3412no—
258C2×D4—3412no—
259C2×D4—6812no—
260C2×D4—1366no—
261C22×C4—21no—
262C22×C4—23no—
263C22×C4—341no—
264C22×C4—3412no—
265C22×C4—6812no—
266C22×C4C2×C22⋊D1713yes—
267C22×C4C2×C22⋊D1713yes—
268C22×C4C23×D1711yescharacteristic
269SD16—3424no—
270SD16—6824no—
271C2×C8—174no—
272C2×C8—172no—
273C2×C8—176no—
274C2×C8—346no—
275C4⋊C4—212no—
276C4⋊C4—212no—
277C4⋊C4—212no—
278C4⋊C4—21no—
279C4⋊C4—172no—
280C4⋊C4—341no—
281C4⋊C4C2×C22⋊D17112yes—
282C4⋊C4C23×D1712yes—
283C22⋊C4—3412no—
284C42—212no—
285C42C2×C22⋊D1716yes—
286C42C23×D1716yes—
287C23—346no—
288C23—686no—
289C23—686no—
290C23—686no—
291C23C22×C22⋊D1711yescharacteristic
292Q8—26no—
293Q8—26no—
294Q8—46no—
295Q8C2×#63230116yescomplemented
296D4—346no—
297D4—346no—
298D4—686no—
299D4—6824no—
300D4—13612no—
301C2×C4—26no—
302C2×C4—22no—
303C2×C4—26no—
304C2×C4—46no—
305C2×C4—42no—
306C2×C4—342no—
307C2×C4—682no—
308C2×C4—6824no—
309C2×C4C2×#63230112yes—
310C2×C4#41×D1712yes—
311C2×C4#1058769612yes—
312C2×C4C22×C22⋊D1716yes—
313C2×C4C22×C22⋊D1711yescharacteristic
314C2×C4C22×C22⋊D1716yes—
315C2×C4C24×D1711yescharacteristic
316C8—174no—
317C8—346no—
318C22—686no—
319C22—686no—
320C22—686no—
321C22—13612no—
322C22#1176347812yes—
323C22C22×#6323012yes—
324C22#1176361712yes—
325C22C23×C22⋊D1711yescharacteristic
326C4—26no—
327C4—42no—
328C4—46no—
329C4—682no—
330C4#1176347812yes—
331C4C22×#63230112yes—
332C4C2×#41×D1711yescharacteristic
333C4C2×#1058769611yescharacteristic
334C2—1366no—
335C2#1454176114yesdirect product factor
336C2C2×#1176347811yescharacteristic
337C2C23×#6323011yescharacteristic
338C2C2×#1176361711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#557C2
socleC23×C17C22×D4
prime radicalC2×#11763481C2
hypercenterC2×#557D17
hypocenterC17C2×#3392
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #14541761C2direct (N × H)
3. C2×#11763183C2semidirect
4. C2×#11763009C2semidirect
5. C2×#11763011C2semidirect
6. C2×Q8×#3622C2semidirect
7. C2×C4×#63230C2semidirect
8. C2×C17×#557C2semidirect
17. #11763183C22semidirect
18. #11763011C22semidirect
19. #11763009C22semidirect
20. Q8×#3622C22semidirect
21. C4×#63230C22semidirect
28. C17×#557C22semidirect
79. C2×Q8×C17SD16semidirect
114. C2×#3622#41semidirect
126. Q8×C17C2×SD16semidirect
148. #3622C2×#41semidirect
149. C2×#557D17semidirect
177. #557C2×D17semidirect
198. C2×C17#3392semidirect
244. C17C2×#3392semidirect
250. C2×Q8#63230semidirect
295. Q8C2×#63230semidirect
335. C2#14541761direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634812
#145417612
C2×#117631832
C2×#117630092
C2×#117630112
C2×Q8×#36222
C2×C4×#632302
C2×C17×#5572
C2×#339217