Finite Group Databasebeta

← C2×#24915639 #35610779

Subgroups — C2×#24915639 #35610779

Order 21248.

1718 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24915639C2116yesmaximal, direct product factor
2C2×C83⋊#401C212yesmaximal
3C2×#19127643C212yesmaximal
4C2×#19127642C212yesmaximal
5C2×#19127640C211yesmaximal, characteristic
6C2×#19127635C212yesmaximal
7C2×#19127631C211yesmaximal, characteristic
8C2×#19127620C212yesmaximal
9C2×#19127585C212yesmaximal
10C2×#391×C83C211yesmaximal, characteristic
11C22×C4⋊Dic83C2211yescharacteristic
12C22×C4⋊Dic83C2211yescharacteristic
13C22×Dic83⋊C4C2212yes—
14C22×Dic83⋊C4C2212yes—
15C22×Dic83⋊C4C2212yes—
16C22×Dic83⋊C4C2212yes—
17C83⋊#401C22116yes—
18#19127643C22116yes—
19#19127642C22116yes—
20#19127640C2218yes—
21#19127635C22116yes—
22#19127631C2218yes—
23#19127620C22116yes—
24#19127585C22116yes—
25C2×C83⋊#95C2212yes—
26C2×C83⋊#95C2212yes—
27C2×C83⋊#95C2212yes—
28C2×C83⋊#95C2212yes—
29C2×C83⋊#95C2212yes—
30C2×C83⋊#95C2212yes—
31C2×C83⋊#95C2212yes—
32C2×C83⋊#95C2211yescharacteristic
33C2×C83⋊#95C2212yes—
34C2×C83⋊#95C2211yescharacteristic
35C23×Q8×C83C2211yescharacteristic
36C22×C4⋊C4×C83C2211yescharacteristic
37C22×C42×C83C2211yescharacteristic
38#391×C83C2218yes—
39C2×#95×C83C2212yes—
40C2×#95×C83C2212yes—
41C23×Dic83C2312yes—
42C23×Dic83C2312yes—
43C23×Dic83C2312yes—
44C23×Dic83C2312yes—
45C2×C4⋊Dic83—42no—
46C2×C4⋊Dic83—42no—
47C2×C4⋊Dic83C2314yes—
48C2×C4⋊Dic83C2314yes—
49C2×Dic83⋊C4—28no—
50C2×Dic83⋊C4—44no—
51C2×Dic83⋊C4—44no—
52C2×Dic83⋊C4—44no—
53C2×Dic83⋊C4C2318yes—
54C2×Dic83⋊C4C2318yes—
55C2×Dic83⋊C4C2318yes—
56C2×Dic83⋊C4C2318yes—
57C83⋊#95C2318yes—
58C83⋊#95C2318yes—
59C83⋊#95C2318yes—
60C83⋊#95C2318yes—
61C83⋊#95C2318yes—
62C83⋊#95C2318yes—
63C83⋊#95C2318yes—
64C83⋊#95C2314yes—
65C83⋊#95C2318yes—
66C83⋊#95C2314yes—
67C22×Q8×C83—24no—
68C22×Q8×C83—42no—
69C22×Q8×C83—42no—
70C22×Q8×C83C2314yes—
71C23×C4×C83C2312yes—
72C23×C4×C83C2311yescharacteristic
73C23×C4×C83C2311yescharacteristic
74C23×C4×C83C2312yes—
75C23×C4×C83C2311yescharacteristic
76C2×C4⋊C4×C83—42no—
77C2×C4⋊C4×C83C2314yes—
78C2×C42×C83—42no—
79C2×C42×C83C2314yes—
80#95×C83C2318yes—
81#95×C83C2318yes—
82C22×Dic83—24no—
83C22×Dic83—24no—
84C22×Dic83—24no—
85C22×Dic83—24no—
86C22×Dic83—24no—
87C22×Dic83—24no—
88C22×Dic83—24no—
89C22×Dic83—24no—
90C22×Dic83—24no—
91C22×Dic83—24no—
92C22×Dic83—28no—
93C22×Dic83C2414yes—
94C22×Dic83C2414yes—
95C22×Dic83C2414yes—
96C22×Dic83C2414yes—
97C4⋊Dic83—44no—
98C4⋊Dic83—44no—
99Dic83⋊C4—216no—
100Dic83⋊C4—48no—
101Dic83⋊C4—48no—
102Dic83⋊C4—48no—
103C24×C83C2411yescharacteristic
104C2×Q8×C83—28no—
105C2×Q8×C83—44no—
106C2×Q8×C83—44no—
107C2×Q8×C83—416no—
108C22×C4×C83—22no—
109C22×C4×C83—22no—
110C22×C4×C83—24no—
111C22×C4×C83—24no—
112C22×C4×C83—22no—
113C22×C4×C83—22no—
114C22×C4×C83—24no—
115C22×C4×C83—24no—
116C22×C4×C83—24no—
117C22×C4×C83—24no—
118C22×C4×C83—24no—
119C22×C4×C83—24no—
120C22×C4×C83#4114yes—
121C22×C4×C83C2414yes—
122C22×C4×C83C2412yes—
123C22×C4×C83C2412yes—
124C22×C4×C83C2414yes—
125C22×C4×C83C2412yes—
126C4⋊C4×C83—44no—
127C42×C83—44no—
128C23×C83C2×#4112yes—
129C23×C83H(5,𝔽2)12yes—
130C23×C83H(5,𝔽2)12yes—
131C23×C832−1+414yes—
132C23×C832−1+414yes—
133C23×C83C2511yescharacteristic
134Q8×C83—416no—
135C2×C4×C83—28no—
136C2×C4×C83—22no—
137C2×C4×C83—22no—
138C2×C4×C83—24no—
139C2×C4×C83—24no—
140C2×C4×C83—22no—
141C2×C4×C83—22no—
142C2×C4×C83—24no—
143C2×C4×C83—24no—
144C2×C4×C83—24no—
145C2×C4×C83—24no—
146C2×C4×C83—24no—
147C2×C4×C83—24no—
148C2×C4×C83—48no—
149C2×C4×C83—44no—
150C2×C4×C83—44no—
151C2×C4×C83—48no—
152C2×C4×C83C2×#4114yes—
153C2×Dic83—24no—
154C2×Dic83—24no—
155C2×Dic83—24no—
156C2×Dic83—24no—
157C2×Dic83—24no—
158C2×Dic83—24no—
159C2×Dic83—24no—
160C2×Dic83—24no—
161C2×Dic83—24no—
162C2×Dic83—24no—
163C2×Dic83—28no—
164C2×Dic83—48no—
165C2×Dic83—48no—
166C2×Dic83—48no—
167C2×Dic83—48no—
168C22×C83#53814yes—
169C22×C83#54118yes—
170C22×C83#56314yes—
171C22×C83#56314yes—
172C22×C83#56318yes—
173C22×C83C22×#4111yescharacteristic
174C22×C83C2×H(5,𝔽2)11yescharacteristic
175C22×C83C2×H(5,𝔽2)11yescharacteristic
176C22×C83C2×2−1+412yes—
177C22×C83C2×2−1+412yes—
178C4×C83—24no—
179C4×C83—44no—
180C4×C83—42no—
181C4×C83—42no—
182C4×C83—44no—
183Dic83—44no—
184Dic83—44no—
185Dic83—44no—
186Dic83—44no—
187C2×#2833—831nomaximal, Sylow
188C2×C83#283318yescomplemented
189C2×C83C2×#53811yescharacteristic
190C2×C83C2×#54112yes—
191C2×C83C2×#56311yescharacteristic
192C2×C83C2×#56311yescharacteristic
193C2×C83C2×#56312yes—
194#2833—8316no—
195C2×#401—832no—
196C2×#400—832no—
197C2×#400—832no—
198C2×#400—831no—
199C2×#398—832no—
200C2×#398—831no—
201C2×#395—832no—
202C2×#391D8311yescharacteristic
203C2×#387—832no—
204C83C2×#283311yescharacteristic, complemented, Sylow
205C23×Q8C2×D8311yescharacteristic
206C22×C4⋊C4—832no—
207C22×C4⋊C4—832no—
208C22×C4⋊C4—831no—
209C22×C4⋊C4—832no—
210C22×C4⋊C4—831no—
211C22×C4⋊C4—832no—
212C22×C4⋊C4C2×D8311yescharacteristic
213C22×C42C2×D8311yescharacteristic
214#401—8316no—
215#400—838no—
216#400—8316no—
217#400—8316no—
218#398—838no—
219#398—8316no—
220#395—8316no—
221#391C2×D8318yes—
222#387—8316no—
223C2×#95—832no—
224C2×#95—832no—
225C2×#95—832no—
226C2×#95—832no—
227C2×#95—832no—
228C2×#95—832no—
229C2×#95—831no—
230C2×#95—831no—
231C2×#95—832no—
232C2×#95—832no—
233C2×#95C2×D8312yes—
234C2×#95C2×D8312yes—
235C22×Q8—24no—
236C22×Q8—42no—
237C22×Q8—42no—
238C22×Q8C22×D8314yes—
239C23×C4—832no—
240C23×C4—832no—
241C23×C4—832no—
242C23×C4—832no—
243C23×C4C22×D8312yes—
244C23×C4C22×D8311yescharacteristic
245C23×C4C22×D8311yescharacteristic
246C23×C4C22×D8312yes—
247C23×C4C22×D8311yescharacteristic
248C2×C4⋊C4—42no—
249C2×C4⋊C4—3324no—
250C2×C4⋊C4—3324no—
251C2×C4⋊C4—3324no—
252C2×C4⋊C4—3322no—
253C2×C4⋊C4—3322no—
254C2×C4⋊C4—838no—
255C2×C4⋊C4—838no—
256C2×C4⋊C4—838no—
257C2×C4⋊C4—834no—
258C2×C4⋊C4—834no—
259C2×C4⋊C4—838no—
260C2×C4⋊C4—1668no—
261C2×C4⋊C4C22×D8314yes—
262C2×C42—42no—
263C2×C42C22×D8314yes—
264#95—838no—
265#95—838no—
266#95—838no—
267#95—838no—
268#95—838no—
269#95—838no—
270#95—838no—
271#95—838no—
272#95—834no—
273#95—834no—
274#95C22×D8318yes—
275#95C22×D8318yes—
276C24C23×D8311yescharacteristic
277C2×Q8—28no—
278C2×Q8—44no—
279C2×Q8—44no—
280C2×Q8—416no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—24no—
288C22×C4—24no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—24no—
293C22×C4—834no—
294C22×C4—834no—
295C22×C4—834no—
296C22×C4—834no—
297C22×C4—1664no—
298C22×C4—1664no—
299C22×C4—1664no—
300C22×C4—1664no—
301C22×C4—1664no—
302C22×C4—1664no—
303C22×C4—1664no—
304C22×C4—1664no—
305C22×C4—1668no—
306C22×C4—1664no—
307C22×C4—1664no—
308C22×C4#1305059014yes—
309C22×C4C23×D8314yes—
310C22×C4C23×D8312yes—
311C22×C4C23×D8312yes—
312C22×C4C23×D8314yes—
313C22×C4C23×D8312yes—
314C4⋊C4—44no—
315C4⋊C4—3328no—
316C4⋊C4—3328no—
317C4⋊C4—3328no—
318C4⋊C4—3324no—
319C4⋊C4—3324no—
320C4⋊C4—16616no—
321C42—44no—
322C23C2×#1305059012yes—
323C23#1458183712yes—
324C23#1458183712yes—
325C23#1458183914yes—
326C23#1458184014yes—
327C23C24×D8311yescharacteristic
328Q8—416no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—28no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—24no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—48no—
345C2×C4—48no—
346C2×C4—3328no—
347C2×C4—3328no—
348C2×C4—3328no—
349C2×C4—3328no—
350C2×C4—1664no—
351C2×C4—1664no—
352C2×C4—1664no—
353C2×C4—1664no—
354C2×C4—1664no—
355C2×C4—1664no—
356C2×C4—1664no—
357C2×C4—1664no—
358C2×C4—1668no—
359C2×C4—1664no—
360C2×C4—1664no—
361C2×C4C2×#1305059014yes—
362C22#1912828914yes—
363C22#1912830918yes—
364C22#1912845014yes—
365C22#1912845114yes—
366C22#1912845218yes—
367C22C22×#1305059011yescharacteristic
368C22C2×#1458183711yescharacteristic
369C22C2×#1458183711yescharacteristic
370C22C2×#1458183912yes—
371C22C2×#1458184012yes—
372C4—24no—
373C4—44no—
374C4—42no—
375C4—42no—
376C4—44no—
377C4—3324no—
378C4—3324no—
379C4—3324no—
380C4—3324no—
381C2#2491563918yesdirect product factor
382C2C2×#1912828911yescharacteristic
383C2C2×#1912830912yes—
384C2C2×#1912845011yescharacteristic
385C2C2×#1912845111yescharacteristic
386C2C2×#1912845212yes—
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#391×C83C2
socle, prime radicalC24×C83C24
hypercenterC2×#391D83
hypocenterC83C2×#2833
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
1. #24915639C2direct (N × H)
188. C2×C83#2833semidirect
204. C83C2×#2833semidirect
381. C2#24915639direct (N × H)

Maximal subgroups

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

subgroupindex
#249156392
C2×C83⋊#4012
C2×#191276432
C2×#191276422
C2×#191276402
C2×#191276352
C2×#191276312
C2×#191276202
C2×#191275852
C2×#391×C832
C2×#283383