Finite Group Databasebeta

← C2×#24907009 #35386960

Subgroups — C2×#24907009 #35386960

Order 21248.

726 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128051C211yesmaximal, characteristic, complemented
2C2×#19127978C211yesmaximal, characteristic
3C2×#19127907C211yesmaximal, characteristic
4C2×#19127778C211yesmaximal, characteristic
5#24907009C218yesmaximal, direct product factor
6C2×#19127453C211yesmaximal, characteristic, complemented
7C2×#19127446C211yesmaximal, characteristic, complemented
8C2×#332×C83C211yesmaximal, characteristic, complemented
9C22×#13050579—21no—
10C22×#13050573—21no—
11C2×#14581792C2211yescharacteristic
12C2×C4×D332C2211yescharacteristic
13#19128051—22no—
14#19128051C2214yescomplemented
15#19127978—22no—
16#19127978C2214yes—
17#19127907—22no—
18#19127907C2214yes—
19#19127778—22no—
20#19127778C2214yes—
21C2×#14581725—21no—
22C2×C4⋊(C83⋊C8)C2211yescharacteristic
23C2×#14581717—21no—
24C2×#14581716—21no—
25C2×#14581716—21no—
26C2×#14581712—21no—
27C2×(C2×D83)⋊C8—21no—
28C2×C4×C83⋊C8C2211yescharacteristic
29#19127453C2214yescomplemented
30#19127446C2214yescomplemented
31C2×C4⋊Q8×C83C2211yescharacteristic
32C2×C4⋊C8×C83C2211yescharacteristic
33C2×C4⋊C8×C83C2211yescharacteristic
34#332×C83C2214yescomplemented
35C22×Dic166—21no—
36C22×D332D411yescharacteristic
37C22×C4×D83—21no—
38C2×#13050579—24no—
39C2×#13050579—44no—
40C2×#13050573—24no—
41C2×#13050573—44no—
42C22×C83⋊C8—21no—
43C22×C83⋊C8D411yescharacteristic
44C22×C83⋊C8D411yescharacteristic
45#14581792—21no—
46#14581792—21no—
47#14581792—21no—
48#14581792C2312yes—
49C4×D332—21no—
50C4×D332—21no—
51C4×D332D412yes—
52C4×D332C2312yes—
53C2×C4⋊Dic83—21no—
54C2×C4⋊Dic83—21no—
55C2×C4⋊Dic83D411yescharacteristic
56C2×(C2×D83)⋊C4—21no—
57#14581725—24no—
58C4⋊(C83⋊C8)—21no—
59C4⋊(C83⋊C8)C2312yes—
60#14581717—24no—
61#14581716—24no—
62#14581716—24no—
63#14581712—24no—
64(C2×D83)⋊C8—24no—
65C4×C83⋊C8D412yes—
66C4×C83⋊C8C2312yes—
67C22×Q8×C83—21no—
68C22×C8×C83—21no—
69C22×C8×C83—21no—
70C4⋊Q8×C83—21no—
71C4⋊Q8×C83—21no—
72C4⋊Q8×C83—21no—
73C4⋊Q8×C83C2312yes—
74C2×C4⋊C4×C83—21no—
75C2×C4⋊C4×C83—21no—
76C2×C42×C83C2311yescharacteristic
77C4⋊C8×C83—21no—
78C4⋊C8×C83—21no—
79C4⋊C8×C83C2312yes—
80C4⋊C8×C83C2312yes—
81C23×D83—21no—
82C2×Dic166—22no—
83C2×Dic166—42no—
84C2×Dic166—42no—
85C2×Dic166—41no—
86C2×D332—22no—
87C2×D332—22no—
88C2×D332—21no—
89C2×D332C2×D412yes—
90C22×Dic83—21no—
91C22×Dic83—41no—
92C2×C4×D83—22no—
93C2×C4×D83—22no—
94C2×C4×D83—42no—
95C2×C4×D83—42no—
96#13050579—48no—
97#13050573—48no—
98C2×C83⋊C8—22no—
99C2×C83⋊C8—22no—
100C2×C83⋊C8—22no—
101C2×C83⋊C8—42no—
102C2×C83⋊C8C2×D412yes—
103C2×C83⋊C8C2×D412yes—
104C4⋊Dic83—21no—
105C4⋊Dic83—22no—
106C4⋊Dic83—22no—
107C4⋊Dic83—41no—
108C4⋊Dic83—41no—
109C4⋊Dic83C2×D412yes—
110(C2×D83)⋊C4—22no—
111(C2×D83)⋊C4—22no—
112C2×Q8×C83—22no—
113C2×Q8×C83—41no—
114C2×Q8×C83—42no—
115C2×Q8×C83—42no—
116C22×C4×C83—41no—
117C22×C4×C83C2×D411yescharacteristic
118C22×C4×C83C2×D411yescharacteristic
119C22×C4×C83#4111yescharacteristic
120C2×C8×C83—22no—
121C2×C8×C83—22no—
122C2×C8×C83—42no—
123C2×C8×C83—42no—
124C4⋊C4×C83—22no—
125C4⋊C4×C83—22no—
126C4⋊C4×C83—41no—
127C4⋊C4×C83—41no—
128C42×C83C2×D411yescharacteristic
129C42×C83C2×D411yescharacteristic
130C42×C83#4111yescharacteristic
131C42×C83C2411yescharacteristic
132C23×C83#12111yescharacteristic
133C22×D83—22no—
134C22×D83—42no—
135C22×D83—42no—
136C22×D83—42no—
137Q8×C83—42no—
138Q8×C83—42no—
139Q8×C83—82no—
140C2×C4×C83—22no—
141C2×C4×C83—42no—
142C2×C4×C83—82no—
143C2×C4×C83#12111yescharacteristic
144C2×C4×C83#12111yescharacteristic
145C2×C4×C83#12111yescharacteristic
146C2×C4×C83#13512yes—
147C2×C4×C83AGL(1,ℤ/8)12yes—
148C2×C4×C83AGL(1,ℤ/8)12yes—
149C2×C4×C83#13712yes—
150C2×C4×C83C22×D411yescharacteristic
151C2×C4×C83C22×D411yescharacteristic
152C2×C4×C83C2×#4111yescharacteristic
153C2×Dic83—22no—
154C2×Dic83—42no—
155C2×Dic83—42no—
156C2×Dic83—82no—
157D332—22no—
158D332—22no—
159D332—42no—
160C4×D83—42no—
161C4×D83—42no—
162C4×D83—44no—
163Dic166—42no—
164Dic166—42no—
165Dic166—82no—
166C8×C83—42no—
167C8×C83—42no—
168C83⋊C8—22no—
169C83⋊C8—22no—
170C83⋊C8—42no—
171C22×C83#46312yes—
172C22×C83#46812yes—
173C22×C83#47312yes—
174C22×C83C2×#12111yescharacteristic
175C2×D83—42no—
176C2×D83—42no—
177C2×D83—42no—
178C2×D83—84no—
179C4×C83—21no—
180C4×C83—21no—
181C4×C83—82no—
182C4×C83#46312yes—
183C4×C83#46812yes—
184C4×C83C2×#13511yescharacteristic
185C4×C83C2×AGL(1,ℤ/8)11yescharacteristic
186C4×C83C2×AGL(1,ℤ/8)11yescharacteristic
187C4×C83C2×#13711yescharacteristic
188Dic83—42no—
189Dic83—82no—
190C2×#1699—831nomaximal, Sylow
191C2×C83#169914yescomplemented
192C2×C83C2×#46311yescharacteristic
193C2×C83C2×#46811yescharacteristic
194C2×C83C2×#47311yescharacteristic
195D83—82no—
196C2×#487—831no—
197C2×#474—831no—
198C2×#461—831no—
199C2×#436—831no—
200#1699—838no—
201C2×#335—831no—
202C2×#332—831no—
203C2×#332D8311yescharacteristic, complemented
204C83C2×#169911yescharacteristic, complemented, Sylow
205C22×SD16—1661no—
206C22×M16—1661no—
207C2×C4⋊Q8—831no—
208C2×C4⋊Q8C2×D8311yescharacteristic
209C2×C4×D4—831no—
210#487—834no—
211#487—1662no—
212#474—834no—
213#474—1662no—
214#461—834no—
215#461—1662no—
216#436—834no—
217#436—1662no—
218C2×#107—1661no—
219C2×C4⋊C8—831no—
220C2×C4⋊C8C2×D8311yescharacteristic
221C2×C4⋊C8C2×D8311yescharacteristic
222C2×#103—1661no—
223C2×#103—1661no—
224C2×#103—1661no—
225C2×#102—1661no—
226C2×C22⋊C8—1661no—
227C2×C4×C8—831no—
228#335—834no—
229#332—834no—
230#332C2×D8314yescomplemented
231C22×Q8—21no—
232C22×Q8—1661no—
233C22×D4—831no—
234C23×C4—1661no—
235C2×SD16—3324no—
236C2×SD16—1664no—
237C2×M16—3324no—
238C2×M16—1664no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—831no—
242C22×C8—831no—
243C22×C8—1661no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—832no—
248C4⋊Q8—1661no—
249C4⋊Q8—1661no—
250C4⋊Q8—1661no—
251C4⋊Q8C22×D8312yes—
252C4×D4—832no—
253C4×D4—832no—
254C4×D4—1661no—
255C4×D4—1661no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—831no—
259C2×C4⋊C4—1661no—
260C2×C4⋊C4—1661no—
261C2×C22⋊C4—1661no—
262C2×C42C22×D8311yescharacteristic
263#107—1664no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—832no—
267C4⋊C8—1661no—
268C4⋊C8C22×D8312yes—
269C4⋊C8C22×D8312yes—
270#103—1664no—
271#103—1664no—
272#103—1664no—
273#102—1664no—
274C22⋊C8—1664no—
275C4×C8—832no—
276C4×C8—832no—
277C24—1661no—
278C2×Q8—22no—
279C2×Q8—41no—
280C2×Q8—42no—
281C2×Q8—42no—
282C2×Q8—3321no—
283C2×Q8—3322no—
284C2×Q8—3322no—
285C2×Q8—1662no—
286C2×D4—832no—
287C2×D4—1661no—
288C2×D4—1662no—
289C2×D4—1662no—
290C22×C4—41no—
291C22×C4—3322no—
292C22×C4—3322no—
293C22×C4—3321no—
294C22×C4—1661no—
295C22×C4—1662no—
296C22×C4—1662no—
297C22×C4D4×D8311yescharacteristic
298C22×C4D4×D8311yescharacteristic
299C22×C4#1305059011yescharacteristic
300SD16—3328no—
301M16—3328no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—42no—
305C2×C8—42no—
306C2×C8—3322no—
307C2×C8—832no—
308C2×C8—832no—
309C2×C8—1662no—
310C2×C8—1662no—
311C2×C8—1662no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—3321no—
317C4⋊C4—3321no—
318C4⋊C4—832no—
319C4⋊C4—1662no—
320C4⋊C4—1662no—
321C4⋊C4—1661no—
322C22⋊C4—1662no—
323C22⋊C4—1662no—
324C42D4×D8311yescharacteristic
325C42D4×D8311yescharacteristic
326C42#1305059011yescharacteristic
327C42C23×D8311yescharacteristic
328C23—3322no—
329C23—3322no—
330C23—3322no—
331C23—1662no—
332C23#1458176511yescharacteristic
333Q8—42no—
334Q8—42no—
335Q8—82no—
336Q8—3322no—
337Q8—3322no—
338Q8—6642no—
339D4—3322no—
340D4—1662no—
341D4—1662no—
342C2×C4—22no—
343C2×C4—42no—
344C2×C4—82no—
345C2×C4—3322no—
346C2×C4—3324no—
347C2×C4—3322no—
348C2×C4—3322no—
349C2×C4—3322no—
350C2×C4—6642no—
351C2×C4—1662no—
352C2×C4#1458176511yescharacteristic
353C2×C4#1458176511yescharacteristic
354C2×C4#1458176511yescharacteristic
355C2×C4#1458181312yes—
356C2×C4#1458181612yes—
357C2×C4#1458181912yes—
358C2×C4#1458182412yes—
359C2×C4C2×D4×D8311yescharacteristic
360C2×C4C2×D4×D8311yescharacteristic
361C2×C4C2×#1305059011yescharacteristic
362C8—42no—
363C8—42no—
364C8—3322no—
365C8—1662no—
366C8—1662no—
367C22—3322no—
368C22—3322no—
369C22—3322no—
370C22—6644no—
371C22#1912791512yes—
372C22#1912795012yes—
373C22#1912797512yes—
374C22C2×#1458176511yescharacteristic
375C4—21no—
376C4—21no—
377C4—82no—
378C4—3322no—
379C4—6642no—
380C4#1912791512yes—
381C4#1912795012yes—
382C4C2×#1458181311yescharacteristic
383C4C2×#1458181611yescharacteristic
384C4C2×#1458181911yescharacteristic
385C4C2×#1458182411yescharacteristic
386C2—6642no—
387C2#2490700914yesdirect product factor
388C2C2×#1912791511yescharacteristic
389C2C2×#1912795011yescharacteristic
390C2C2×#1912797511yescharacteristic
subgroupG/H
centerC23#14581765
commutator, cosocleC42×C83C24
FrattiniC42C23×D83
FittingC2×#332×C83C2
socleC23×C83#121
prime radicalC22×D332D4
hypercenterC2×#332D83
hypocenterC83C2×#1699
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
1. C2×#19128051C2semidirect
5. #24907009C2direct (N × H)
6. C2×#19127453C2semidirect
7. C2×#19127446C2semidirect
8. C2×#332×C83C2semidirect
14. #19128051C22semidirect
29. #19127453C22semidirect
30. #19127446C22semidirect
34. #332×C83C22semidirect
191. C2×C83#1699semidirect
203. C2×#332D83semidirect
204. C83C2×#1699semidirect
230. #332C2×D83semidirect
387. C2#24907009direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191280512
C2×#191279782
C2×#191279072
C2×#191277782
#249070092
C2×#191274532
C2×#191274462
C2×#332×C832
C2×#169983