Finite Group Databasebeta

← C2×#24920445 #36285306

Subgroups — C2×#24920445 #36285306

Order 21248.

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×#19128430C211yesmaximal, characteristic, complemented
2C2×#19128373C211yesmaximal, characteristic
3#24920445C2116yesmaximal, direct product factor
4C2×#19128074C213yesmaximal, complemented
5C2×#19127902C213yesmaximal, complemented
6C2×#19127907C213yesmaximal, complemented
7C2×C4×#13050579C213yesmaximal, complemented
8C2×C8×Q8×C83C211yesmaximal, characteristic, complemented
9C22×#13050591—21no—
10C22×#13050579C2213yes—
11C22×#13050579C2216yes—
12#19128430—24no—
13#19128430C2218yescomplemented
14#19128373—24no—
15#19128373C2218yes—
16C2×#14581792C2213yes—
17C2×#14581789C2213yes—
18C2×#14581783—23no—
19C2×#14581767—23no—
20C2×Q8×Dic83—21no—
21C2×C4×Dic166C2213yes—
22C2×C4×D332C2213yes—
23#19128074C22124yescomplemented
24#19127907C22124yescomplemented
25#19127902C22124yescomplemented
26C4×#13050579C22124yescomplemented
27C2×#14581724C2211yescharacteristic
28C2×#14581717C2213yes—
29C2×#14581714C2213yes—
30C2×C4×Q8×C83C2211yescharacteristic
31C8×Q8×C83C2218yescomplemented
32C2×C4⋊C8×C83C2213yes—
33C2×C4×C8×C83C2213yes—
34C2×#13050591—28no—
35C2×#13050591—48no—
36C22×Dic166C2313yes—
37C22×D332—23no—
38C22×D332—23no—
39C22×D332C2313yes—
40C22×C4×D83—23no—
41C2×#13050579—212no—
42C2×#13050579—412no—
43C2×#13050579C23112yes—
44C2×#13050579C23124yes—
45#14581792—26no—
46#14581792C23112yes—
47#14581789—26no—
48#14581789C23112yes—
49#14581783—224no—
50#14581767—224no—
51Q8×Dic83—28no—
52C4×Dic166—26no—
53C4×Dic166C23112yes—
54C4×D332—26no—
55C4×D332C23112yes—
56C2×C4⋊Dic83—23no—
57C2×C4⋊Dic83—23no—
58C2×C4⋊Dic83C2311yescharacteristic
59C2×C4⋊Dic83C2311yescharacteristic
60C2×Dic83⋊C4—23no—
61C2×(C2×D83)⋊C4—23no—
62C2×C4×Dic83—23no—
63#14581724C2314yes—
64#14581717C23112yes—
65#14581714C23112yes—
66C22×Q8×C83D411yescharacteristic
67C22×C8×C83C2313yes—
68C22×C8×C83C2311yescharacteristic
69C4×Q8×C83D414yes—
70C4×Q8×C83C2314yes—
71C2×C4⋊C4×C83D413yes—
72C2×C42×C83C2313yes—
73C4⋊C8×C83C23112yes—
74C4×C8×C83C23112yes—
75C23×D83—23no—
76#13050591—432no—
77C2×Dic166—26no—
78C2×Dic166—26no—
79C2×Dic166—23no—
80C2×Dic166C2416yes—
81C2×D332—26no—
82C2×D332—26no—
83C2×D332—212no—
84C2×D332—23no—
85C2×D332—212no—
86C2×D332—412no—
87C2×D332—86no—
88C2×D332C2416yes—
89C22×Dic83—21no—
90C22×Dic83—23no—
91C22×Dic83—21no—
92C2×C4×D83—212no—
93C2×C4×D83—412no—
94#13050579—224no—
95#13050579—424no—
96C4⋊Dic83—212no—
97C4⋊Dic83—212no—
98C4⋊Dic83—21no—
99C4⋊Dic83—21no—
100C4⋊Dic83C2412yes—
101C4⋊Dic83C2412yes—
102Dic83⋊C4—212no—
103(C2×D83)⋊C4—212no—
104C4×Dic83—212no—
105C2×Q8×C83SD1618yescomplemented
106C2×Q8×C83C2×D414yes—
107C22×C4×C83C2×D413yes—
108C22×C4×C83C2×D413yes—
109C22×C4×C83C2411yescharacteristic
110C2×C8×C83—26no—
111C2×C8×C83#4114yescomplemented
112C2×C8×C83C2416yes—
113C2×C8×C83C2412yes—
114C4⋊C4×C83C2×D4112yes—
115C42×C83C2×D416yes—
116C42×C83C2416yes—
117C23×C83C22×D411yescharacteristic
118C22×D83—26no—
119C22×D83—46no—
120C22×D83—46no—
121C22×D83—46no—
122Q8×C83C2×SD16116yescomplemented
123C2×C4×C83—26no—
124C2×C4×C83C2×SD16112yes—
125C2×C4×C83C22×D416yes—
126C2×C4×C83C22×D411yescharacteristic
127C2×C4×C83C22×D416yes—
128C2×C4×C83C2×#4112yes—
129C2×C4×C83H(5,𝔽2)12yes—
130C2×C4×C83C2511yescharacteristic
131C2×Dic83—22no—
132C2×Dic83—26no—
133C2×Dic83—22no—
134C2×Dic83—46no—
135C2×Dic83—42no—
136C2×Dic83—42no—
137D332—26no—
138D332—26no—
139D332—46no—
140D332—424no—
141D332—812no—
142C4×D83—424no—
143Dic166—26no—
144Dic166—26no—
145Dic166—46no—
146C8×C83—26no—
147C8×C83C2×#4114yescomplemented
148C22×C83#55012yes—
149C22×C83C22×SD1612yes—
150C22×C83#57712yes—
151C22×C83C23×D411yescharacteristic
152C2×D83—46no—
153C2×D83—46no—
154C2×D83—46no—
155C2×D83—812no—
156C4×C83—26no—
157C4×C83#55012yes—
158C4×C83C22×SD16112yes—
159C4×C83C22×#4111yescharacteristic
160C4×C83C2×H(5,𝔽2)11yescharacteristic
161Dic83—46no—
162Dic83—42no—
163Dic83—42no—
164C2×#3392—831nomaximal, Sylow
165C2×C83#339214yescomplemented
166C2×C83C2×#55011yescharacteristic
167C2×C83C23×SD1611yescharacteristic
168C2×C83C2×#57711yescharacteristic
169D83—86no—
170C2×#557—831no—
171C2×#550—831no—
172#3392—8316no—
173C2×#492—833no—
174C2×#460—833no—
175C2×#461—833no—
176C2×C8×Q8D8311yescharacteristic, complemented
177C2×C4×SD16—833no—
178C83C2×#339211yescharacteristic, complemented, Sylow
179C22×#41—1661no—
180C22×SD16—836no—
181C22×SD16—833no—
182#557—838no—
183#557—1664no—
184#550—838no—
185#550—1664no—
186C2×C4⋊Q8—833no—
187C2×#127—833no—
188C2×#125—1663no—
189C2×#121—1663no—
190C2×C4×Q8—833no—
191C2×C4×Q8—1661no—
192C2×C4×Q8C2×D8311yescharacteristic
193C2×C4×D4—833no—
194#492—8324no—
195#461—8324no—
196#460—8324no—
197C8×Q8C2×D8318yescomplemented
198C4×SD16—8324no—
199C2×#106—831no—
200C2×C4⋊C8C2×D8313yes—
201C2×#103—833no—
202C2×#102—833no—
203C2×C4×C8C2×D8313yes—
204C2×#41—3328no—
205C2×#41—1668no—
206C22×Q8—833no—
207C22×Q8D33211yescharacteristic
208C22×D4—833no—
209C22×D4—1663no—
210C22×D4—1663no—
211C23×C4—1663no—
212C2×SD16—33212no—
213C2×SD16—8324no—
214C2×SD16—8312no—
215C2×SD16—16612no—
216C22×C8C22×D8313yes—
217C22×C8C22×D8311yescharacteristic
218C4⋊Q8—8312no—
219C4⋊Q8—1666no—
220#127—8312no—
221#127—1666no—
222#125—16624no—
223#121—16624no—
224C4×Q8—8312no—
225C4×Q8—1668no—
226C4×Q8—1666no—
227C4×Q8D33214yes—
228C4×Q8C22×D8314yes—
229C4×D4—8312no—
230C4×D4—1666no—
231C2×C4⋊C4—831no—
232C2×C4⋊C4—831no—
233C2×C4⋊C4—1663no—
234C2×C4⋊C4—1663no—
235C2×C4⋊C4—1663no—
236C2×C4⋊C4D33213yes—
237C2×C22⋊C4—1663no—
238C2×C42—1663no—
239C2×C42C22×D8313yes—
240#106—834no—
241C4⋊C8C22×D83112yes—
242#103—8312no—
243#102—8312no—
244C4×C8C22×D83112yes—
245C24—1663no—
246#41—33232no—
247C2×Q8—836no—
248C2×Q8—1666no—
249C2×Q8—1666no—
250C2×Q8—1663no—
251C2×Q8#1305057918yescomplemented
252C2×Q8C2×D33214yes—
253C2×D4—33212no—
254C2×D4—836no—
255C2×D4—6646no—
256C2×D4—1663no—
257C2×D4—16612no—
258C2×D4—16612no—
259C2×D4—1666no—
260C2×D4—1666no—
261C22×C4—33212no—
262C22×C4—1661no—
263C22×C4—1663no—
264C22×C4—1661no—
265C22×C4—16612no—
266C22×C4C2×D33213yes—
267C22×C4C2×D33213yes—
268C22×C4C23×D8311yescharacteristic
269SD16—33224no—
270SD16—16624no—
271C2×C8—26no—
272C2×C8#1305059114yescomplemented
273C2×C8C23×D8316yes—
274C2×C8C23×D8312yes—
275C4⋊C4—832no—
276C4⋊C4—832no—
277C4⋊C4—1661no—
278C4⋊C4—1661no—
279C4⋊C4—16612no—
280C4⋊C4—16612no—
281C4⋊C4—16612no—
282C4⋊C4C2×D332112yes—
283C22⋊C4—16612no—
284C42—16612no—
285C42C2×D33216yes—
286C42C23×D8316yes—
287C23—3326no—
288C23—3326no—
289C23—3326no—
290C23—1666no—
291C23C22×D33211yescharacteristic
292Q8—3326no—
293Q8—1666no—
294Q8—1666no—
295Q8C2×#13050579116yescomplemented
296D4—3326no—
297D4—33224no—
298D4—66412no—
299D4—1666no—
300D4—1666no—
301C2×C4—26no—
302C2×C4—3326no—
303C2×C4—3322no—
304C2×C4—3322no—
305C2×C4—33224no—
306C2×C4—1662no—
307C2×C4—1666no—
308C2×C4—1662no—
309C2×C4C2×#13050579112yes—
310C2×C4C22×D33216yes—
311C2×C4C22×D33211yescharacteristic
312C2×C4C22×D33216yes—
313C2×C4C2×#1305059112yes—
314C2×C4#1458183812yes—
315C2×C4C24×D8311yescharacteristic
316C8—26no—
317C8C2×#1305059114yescomplemented
318C22—3326no—
319C22—3326no—
320C22—3326no—
321C22—66412no—
322C22#1912837312yes—
323C22C22×#1305057912yes—
324C22#1912851312yes—
325C22C23×D33211yescharacteristic
326C4—26no—
327C4—3322no—
328C4—3326no—
329C4—3322no—
330C4#1912837312yes—
331C4C22×#13050579112yes—
332C4C22×#1305059111yescharacteristic
333C4C2×#1458183811yescharacteristic
334C2—6646no—
335C2#2492044514yesdirect product factor
336C2C2×#1912837311yescharacteristic
337C2C23×#1305057911yescharacteristic
338C2C2×#1912851311yescharacteristic
subgroupG/H
centerC23C22×D332
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×C8×Q8×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128373C2
hypercenterC2×C8×Q8D83
hypocenterC83C2×#3392
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#19128430C2semidirect
3. #24920445C2direct (N × H)
4. C2×#19128074C2semidirect
5. C2×#19127902C2semidirect
6. C2×#19127907C2semidirect
7. C2×C4×#13050579C2semidirect
8. C2×C8×Q8×C83C2semidirect
13. #19128430C22semidirect
23. #19128074C22semidirect
24. #19127907C22semidirect
25. #19127902C22semidirect
26. C4×#13050579C22semidirect
31. C8×Q8×C83C22semidirect
105. C2×Q8×C83SD16semidirect
111. C2×C8×C83#41semidirect
122. Q8×C83C2×SD16semidirect
147. C8×C83C2×#41semidirect
165. C2×C83#3392semidirect
176. C2×C8×Q8D83semidirect
178. C83C2×#3392semidirect
197. C8×Q8C2×D83semidirect
251. C2×Q8#13050579semidirect
272. C2×C8#13050591semidirect
295. Q8C2×#13050579semidirect
317. C8C2×#13050591semidirect
335. C2#24920445direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284302
C2×#191283732
#249204452
C2×#191280742
C2×#191279022
C2×#191279072
C2×C4×#130505792
C2×C8×Q8×C832
C2×#339283