Finite Group Databasebeta

← C2×#24907035 #35386974

Subgroups — C2×#24907035 #35386974

Order 21248.

694 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127988C211yesmaximal, characteristic
2C2×#19127978C211yesmaximal, characteristic
3C2×#19127780C211yesmaximal, characteristic
4#24907035C218yesmaximal, direct product factor
5C2×#19127452C211yesmaximal, characteristic, complemented
6C2×#19127450C211yesmaximal, characteristic, complemented
7C2×#19127447C211yesmaximal, characteristic, complemented
8C2×#487×C83C211yesmaximal, characteristic, complemented
9C22×#13050573—21no—
10C2×C4×D332C2211yescharacteristic
11#19127988—22no—
12#19127988C2214yes—
13#19127978—22no—
14#19127978C2214yes—
15#19127780—22no—
16#19127780C2214yes—
17C2×#14581725—21no—
18C2×#14581723—21no—
19C2×C4⋊(C83⋊C8)C2211yescharacteristic
20C2×C4⋊(C83⋊C8)C2211yescharacteristic
21C2×C4⋊(C83⋊C8)C2211yescharacteristic
22C2×#14581712—21no—
23C2×#14581712—21no—
24C2×(C2×D83)⋊C8—21no—
25#19127452C2214yescomplemented
26#19127450C2214yescomplemented
27#19127447C2214yescomplemented
28C2×C4⋊Q8×C83C2211yescharacteristic
29C2×C4⋊Q8×C83C2211yescharacteristic
30#487×C83—22no—
31#487×C83C2214yescomplemented
32C2×#103×C83—21no—
33C2×#103×C83—21no—
34C2×C4×C8×C83C2211yescharacteristic
35C22×D332D411yescharacteristic
36C22×C4×D83—21no—
37C2×#13050573—24no—
38C2×#13050573—44no—
39C22×C83⋊C8—21no—
40C22×C83⋊C8—21no—
41C22×C83⋊C8—21no—
42C4×D332—21no—
43C4×D332—21no—
44C4×D332D412yes—
45C4×D332C2312yes—
46C2×C4⋊Dic83D411yescharacteristic
47C2×(C2×D83)⋊C4—21no—
48#14581725—24no—
49#14581723—24no—
50C4⋊(C83⋊C8)—21no—
51C4⋊(C83⋊C8)—21no—
52C4⋊(C83⋊C8)—21no—
53C4⋊(C83⋊C8)C2312yes—
54C4⋊(C83⋊C8)C2312yes—
55C4⋊(C83⋊C8)C2312yes—
56#14581712—24no—
57#14581712—24no—
58(C2×D83)⋊C8—24no—
59C22×Q8×C83—21no—
60C22×Q8×C83—21no—
61C22×C8×C83D411yescharacteristic
62C22×C8×C83D411yescharacteristic
63C4⋊Q8×C83—21no—
64C4⋊Q8×C83—21no—
65C4⋊Q8×C83—21no—
66C4⋊Q8×C83—21no—
67C4⋊Q8×C83—21no—
68C4⋊Q8×C83—21no—
69C4⋊Q8×C83C2312yes—
70C4⋊Q8×C83C2312yes—
71C2×C4⋊C4×C83—21no—
72C2×C4⋊C4×C83—21no—
73C2×C4⋊C4×C83—21no—
74C2×C4⋊C4×C83—21no—
75C2×C42×C83C2311yescharacteristic
76#103×C83—24no—
77#103×C83—24no—
78C4×C8×C83D412yes—
79C4×C8×C83C2312yes—
80C23×D83—21no—
81C2×D332—22no—
82C2×D332—22no—
83C2×D332—21no—
84C2×D332C2×D412yes—
85C22×Dic83—21no—
86C2×C4×D83—22no—
87C2×C4×D83—22no—
88C2×C4×D83—42no—
89C2×C4×D83—42no—
90#13050573—48no—
91C2×C83⋊C8—22no—
92C2×C83⋊C8—22no—
93C2×C83⋊C8—22no—
94C2×C83⋊C8—42no—
95C2×C83⋊C8—42no—
96C2×C83⋊C8—42no—
97C4⋊Dic83—21no—
98C4⋊Dic83C2×D412yes—
99(C2×D83)⋊C4—22no—
100(C2×D83)⋊C4—22no—
101C2×Q8×C83—22no—
102C2×Q8×C83—22no—
103C2×Q8×C83—41no—
104C2×Q8×C83—41no—
105C2×Q8×C83—42no—
106C2×Q8×C83—42no—
107C2×Q8×C83—82no—
108C22×C4×C83—41no—
109C22×C4×C83—41no—
110C22×C4×C83C2×D411yescharacteristic
111C22×C4×C83C2×D411yescharacteristic
112C22×C4×C83#4111yescharacteristic
113C2×C8×C83—22no—
114C2×C8×C83—22no—
115C2×C8×C83C2×D412yes—
116C2×C8×C83C2×D412yes—
117C4⋊C4×C83—22no—
118C4⋊C4×C83—22no—
119C4⋊C4×C83—22no—
120C4⋊C4×C83—22no—
121C4⋊C4×C83—41no—
122C4⋊C4×C83—41no—
123C4⋊C4×C83—41no—
124C4⋊C4×C83—41no—
125C42×C83C2×D411yescharacteristic
126C42×C83C2×D411yescharacteristic
127C42×C83#4111yescharacteristic
128C42×C83C2411yescharacteristic
129C23×C83#12111yescharacteristic
130C22×D83—22no—
131C22×D83—42no—
132C22×D83—42no—
133C22×D83—42no—
134Q8×C83—42no—
135Q8×C83—42no—
136Q8×C83—82no—
137Q8×C83—82no—
138Q8×C83—82no—
139C2×C4×C83—22no—
140C2×C4×C83—42no—
141C2×C4×C83—42no—
142C2×C4×C83—82no—
143C2×C4×C83—82no—
144C2×C4×C83#12111yescharacteristic
145C2×C4×C83#12111yescharacteristic
146C2×C4×C83#12111yescharacteristic
147C2×C4×C83#13512yes—
148C2×C4×C83AGL(1,ℤ/8)12yes—
149C2×C4×C83#13712yes—
150C2×C4×C83#13712yes—
151C2×C4×C83C22×D411yescharacteristic
152C2×C4×C83C22×D411yescharacteristic
153C2×C4×C83C2×#4111yescharacteristic
154C2×Dic83—22no—
155C2×Dic83—42no—
156D332—22no—
157D332—22no—
158D332—42no—
159C4×D83—42no—
160C4×D83—42no—
161C4×D83—44no—
162C8×C83—22no—
163C8×C83—22no—
164C83⋊C8—42no—
165C83⋊C8—42no—
166C83⋊C8—42no—
167C22×C83#46312yes—
168C22×C83#47012yes—
169C22×C83#47112yes—
170C22×C83C2×#12111yescharacteristic
171C2×D83—42no—
172C2×D83—42no—
173C2×D83—42no—
174C2×D83—84no—
175C4×C83—21no—
176C4×C83—21no—
177C4×C83—82no—
178C4×C83—82no—
179C4×C83#46312yes—
180C4×C83#47012yes—
181C4×C83C2×#13511yescharacteristic
182C4×C83C2×AGL(1,ℤ/8)11yescharacteristic
183C4×C83C2×#13711yescharacteristic
184C4×C83C2×#13711yescharacteristic
185Dic83—42no—
186C2×#1703—831nomaximal, Sylow
187C2×C83#170314yescomplemented
188C2×C83C2×#46311yescharacteristic
189C2×C83C2×#47011yescharacteristic
190C2×C83C2×#47111yescharacteristic
191D83—82no—
192C2×#487D8311yescharacteristic, complemented
193C2×#476—831no—
194C2×#474—831no—
195C2×#436—831no—
196#1703—838no—
197C2×#334—831no—
198C2×#333—831no—
199C2×#332—831no—
200C83C2×#170311yescharacteristic, complemented, Sylow
201C22×M16—1661no—
202C2×C4⋊Q8C2×D8311yescharacteristic
203C2×C4⋊Q8C2×D8311yescharacteristic
204C2×C4×D4—831no—
205#487—22no—
206#487C2×D8314yescomplemented
207#476—834no—
208#476—1662no—
209#474—834no—
210#474—1662no—
211#436—834no—
212#436—1662no—
213C2×#107—1661no—
214C2×#106—1661no—
215C2×C4⋊C8—831no—
216C2×C4⋊C8—831no—
217C2×C4⋊C8—831no—
218C2×#103—21no—
219C2×#103—21no—
220C2×#102—1661no—
221C2×#102—1661no—
222C2×C22⋊C8—1661no—
223C2×C4×C8C2×D8311yescharacteristic
224#334—834no—
225#333—834no—
226#332—834no—
227C22×Q8—21no—
228C22×Q8—21no—
229C22×D4—831no—
230C23×C4—1661no—
231C2×M16—3324no—
232C2×M16—1664no—
233C22×C8—1661no—
234C22×C8—1661no—
235C22×C8—1661no—
236C22×C8C22⋊D8311yescharacteristic
237C22×C8C22⋊D8311yescharacteristic
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8C22×D8312yes—
245C4⋊Q8C22×D8312yes—
246C4×D4—832no—
247C4×D4—832no—
248C4×D4—1661no—
249C4×D4—1661no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—831no—
255C2×C22⋊C4—1661no—
256C2×C42C22×D8311yescharacteristic
257#107—1664no—
258#106—1664no—
259C4⋊C8—832no—
260C4⋊C8—832no—
261C4⋊C8—832no—
262C4⋊C8—1661no—
263C4⋊C8—1661no—
264C4⋊C8—1661no—
265#103—24no—
266#103—24no—
267#102—1664no—
268#102—1664no—
269C22⋊C8—1664no—
270C4×C8C22⋊D8312yes—
271C4×C8C22×D8312yes—
272C24—1661no—
273C2×Q8—22no—
274C2×Q8—22no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—42no—
278C2×Q8—42no—
279C2×Q8—82no—
280C2×D4—832no—
281C2×D4—1661no—
282C2×D4—1662no—
283C2×D4—1662no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—3322no—
287C22×C4—3322no—
288C22×C4—1661no—
289C22×C4—1662no—
290C22×C4—1662no—
291C22×C4D4×D8311yescharacteristic
292C22×C4C2×C22⋊D8311yescharacteristic
293C22×C4#1305058911yescharacteristic
294M16—3328no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—3322no—
298C2×C8—3322no—
299C2×C8—3322no—
300C2×C8—1662no—
301C2×C8—1662no—
302C2×C8—1662no—
303C2×C8C2×C22⋊D8312yes—
304C2×C8C2×C22⋊D8312yes—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—832no—
314C4⋊C4—1661no—
315C22⋊C4—1662no—
316C22⋊C4—1662no—
317C42D4×D8311yescharacteristic
318C42C2×C22⋊D8311yescharacteristic
319C42#1305058911yescharacteristic
320C42C23×D8311yescharacteristic
321C23—3322no—
322C23—3322no—
323C23—3322no—
324C23—1662no—
325C23#1458176311yescharacteristic
326Q8—42no—
327Q8—42no—
328Q8—82no—
329Q8—82no—
330Q8—82no—
331D4—3322no—
332D4—1662no—
333D4—1662no—
334C2×C4—22no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—3322no—
340C2×C4—3324no—
341C2×C4—3322no—
342C2×C4—3322no—
343C2×C4—1662no—
344C2×C4#1458176311yescharacteristic
345C2×C4#1458176311yescharacteristic
346C2×C4#1458176311yescharacteristic
347C2×C4#1458181212yes—
348C2×C4#1458181712yes—
349C2×C4#1458182412yes—
350C2×C4#1458182412yes—
351C2×C4C2×D4×D8311yescharacteristic
352C2×C4C22×C22⋊D8311yescharacteristic
353C2×C4C2×#1305058911yescharacteristic
354C8—22no—
355C8—22no—
356C8—3322no—
357C8—3322no—
358C8—3322no—
359C22—3322no—
360C22—3322no—
361C22—3322no—
362C22—6644no—
363C22#1912791312yes—
364C22#1912795612yes—
365C22#1912796112yes—
366C22C2×#1458176311yescharacteristic
367C4—21no—
368C4—21no—
369C4—82no—
370C4—82no—
371C4—3322no—
372C4#1912791312yes—
373C4#1912795612yes—
374C4C2×#1458181211yescharacteristic
375C4C2×#1458181711yescharacteristic
376C4C2×#1458182411yescharacteristic
377C4C2×#1458182411yescharacteristic
378C2—6642no—
379C2#2490703514yesdirect product factor
380C2C2×#1912791311yescharacteristic
381C2C2×#1912795611yescharacteristic
382C2C2×#1912796111yescharacteristic
subgroupG/H
centerC23#14581763
commutator, cosocleC42×C83C24
FrattiniC42C23×D83
FittingC2×#487×C83C2
socleC23×C83#121
prime radicalC22×D332D4
hypercenterC2×#487D83
hypocenterC83C2×#1703
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
4. #24907035C2direct (N × H)
5. C2×#19127452C2semidirect
6. C2×#19127450C2semidirect
7. C2×#19127447C2semidirect
8. C2×#487×C83C2semidirect
25. #19127452C22semidirect
26. #19127450C22semidirect
27. #19127447C22semidirect
31. #487×C83C22semidirect
187. C2×C83#1703semidirect
192. C2×#487D83semidirect
200. C83C2×#1703semidirect
206. #487C2×D83semidirect
379. C2#24907035direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191279882
C2×#191279782
C2×#191277802
#249070352
C2×#191274522
C2×#191274502
C2×#191274472
C2×#487×C832
C2×#170383