Finite Group Databasebeta

← C2×#24915774 #35610276

Subgroups — C2×#24915774 #35610276

Order 21248.

3182 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581784C211yesmaximal, characteristic, complemented
2C22×C42×D83C211yesmaximal, characteristic
3#24915774C2116yesmaximal, direct product factor
4C2×#19127600C212yesmaximal, complemented
5C2×#19127586C214yesmaximal, complemented
6C2×#19127575C214yesmaximal
7C2×#19127558C212yesmaximal
8C2×#382×C83C211yesmaximal, characteristic, complemented
9C23×C4×D83C2212yes—
10C23×C4×D83C2211yescharacteristic
11C2×#14581784—28no—
12C2×#14581784C2218yescomplemented
13C22×C4⋊Dic83C2212yes—
14C22×C4⋊Dic83C2214yes—
15C22×Dic83⋊C4C2214yes—
16C22×(C2×D83)⋊C4C2214yes—
17C22×C4×Dic83C2212yes—
18C22×C4×Dic83C2211yescharacteristic
19C2×C42×D83—28no—
20C2×C42×D83C2218yes—
21#19127600C22116yescomplemented
22#19127586C22132yescomplemented
23#19127575C22132yes—
24#19127558C22116yes—
25C2×C83⋊#95C2214yes—
26C2×C83⋊#95C2214yes—
27C22×C4⋊C4×C83C2212yes—
28C22×C42×C83C2211yescharacteristic
29#382×C83C2218yescomplemented
30C2×#95×C83C2214yes—
31C24×D83C2311yescharacteristic
32C23×Dic83C2314yes—
33C23×Dic83C2311yescharacteristic
34C23×Dic83C2312yes—
35C22×C4×D83—28no—
36C22×C4×D83—28no—
37C22×C4×D83—28no—
38C22×C4×D83—24no—
39C22×C4×D83—24no—
40C22×C4×D83Q818yes—
41C22×C4×D83C2318yes—
42C22×C4×D83C2314yes—
43#14581784—232no—
44C2×C4⋊Dic83—216no—
45C2×C4⋊Dic83—28no—
46C2×C4⋊Dic83C2318yes—
47C2×C4⋊Dic83C23116yes—
48C2×Dic83⋊C4—216no—
49C2×Dic83⋊C4C23116yes—
50C2×(C2×D83)⋊C4—216no—
51C2×(C2×D83)⋊C4C23116yes—
52C2×C4×Dic83—28no—
53C2×C4×Dic83—24no—
54C2×C4×Dic83C2318yes—
55C2×C4×Dic83C2314yes—
56C42×D83—232no—
57C83⋊#95C23116yes—
58C83⋊#95C23116yes—
59C23×C4×C83C2314yes—
60C23×C4×C83C2312yes—
61C23×C4×C83C2311yescharacteristic
62C2×C4⋊C4×C83—28no—
63C2×C4⋊C4×C83C2318yes—
64C2×C42×C83D418yes—
65C2×C42×C83C2314yes—
66#95×C83C23116yes—
67C23×D83—22no—
68C23×D83—24no—
69C23×D83—22no—
70C23×D83C2×Q814yes—
71C23×D83#4118yes—
72C23×D83C2412yes—
73C22×Dic83—22no—
74C22×Dic83—24no—
75C22×Dic83—24no—
76C22×Dic83—22no—
77C22×Dic83—28no—
78C22×Dic83—28no—
79C22×Dic83—28no—
80C22×Dic83C2×Q814yes—
81C22×Dic83#4118yes—
82C22×Dic83C2418yes—
83C22×Dic83C2412yes—
84C22×Dic83C2414yes—
85C2×C4×D83—264no—
86C2×C4×D83—216no—
87C2×C4×D83—232no—
88C2×C4×D83—216no—
89C2×C4×D83—28no—
90C2×C4×D83—28no—
91C2×C4×D83—216no—
92C2×C4×D83C2×Q8116yes—
93C4⋊Dic83—216no—
94C4⋊Dic83—232no—
95Dic83⋊C4—232no—
96(C2×D83)⋊C4—232no—
97C4×Dic83—216no—
98C4×Dic83—28no—
99C24×C83C2411yescharacteristic
100C22×C4×C83—24no—
101C22×C4×C83—24no—
102C22×C4×C83—28no—
103C22×C4×C83—28no—
104C22×C4×C83—28no—
105C22×C4×C83C2×D418yes—
106C22×C4×C83C2×D414yes—
107C22×C4×C83C2×Q814yes—
108C22×C4×C83#4114yes—
109C22×C4×C83C2418yes—
110C22×C4×C83C2414yes—
111C22×C4×C83C2412yes—
112C4⋊C4×C83—216no—
113C42×C83C2×D4116yes—
114C23×C83C22×D412yes—
115C23×C83C22×Q812yes—
116C23×C83C2×#4114yes—
117C23×C83C2×#4114yes—
118C23×C83C2×#4112yes—
119C23×C83C2511yescharacteristic
120C22×D83—28no—
121C22×D83—216no—
122C22×D83—216no—
123C22×D83—28no—
124C22×D83—22no—
125C22×D83—24no—
126C22×D83—22no—
127C22×D83#125116yescomplemented
128C22×D83C22×Q814yes—
129C22×D83C2×#4118yes—
130C2×C4×C83—216no—
131C2×C4×C83—24no—
132C2×C4×C83—24no—
133C2×C4×C83—28no—
134C2×C4×C83—28no—
135C2×C4×C83—28no—
136C2×C4×C83—416no—
137C2×C4×C83C22⋊Q8116yes—
138C2×C4×C83C22×D418yes—
139C2×C4×C83C22×D414yes—
140C2×C4×C83C22×Q814yes—
141C2×C4×C83C2×#4114yes—
142C2×Dic83—28no—
143C2×Dic83—216no—
144C2×Dic83—22no—
145C2×Dic83—24no—
146C2×Dic83—24no—
147C2×Dic83—22no—
148C2×Dic83—28no—
149C2×Dic83—28no—
150C2×Dic83—28no—
151C2×Dic83—416no—
152C2×Dic83C22×Q814yes—
153C2×Dic83C2×#4118yes—
154C4×D83—264no—
155C4×D83—232no—
156C22×C83C2×C22⋊Q814yes—
157C22×C83#52518yes—
158C22×C83C2×#12514yes—
159C22×C83#52918yes—
160C22×C83#53314yes—
161C22×C83C23×D411yescharacteristic
162C22×C83C23×Q811yescharacteristic
163C22×C83C22×#4112yes—
164C22×C83C22×#4112yes—
165C22×C83C22×#4111yescharacteristic
166C2×D83—232no—
167C2×D83—24no—
168C2×D83—28no—
169C2×D83—28no—
170C2×D83—24no—
171C2×D83C2×#12518yescomplemented
172C4×C83—28no—
173C4×C83—48no—
174C4×C83C2×C22⋊Q818yes—
175Dic83—24no—
176Dic83—28no—
177Dic83—48no—
178C2×#2851—831nomaximal, Sylow
179C2×C83#285118yescomplemented
180C2×C83C22×C22⋊Q811yescharacteristic
181C2×C83C2×#52512yes—
182C2×C83C22×#12511yescharacteristic
183C2×C83C2×#52912yes—
184C2×C83C2×#53311yescharacteristic
185D83—28no—
186C22×#125—831no—
187C23×C42—831no—
188#2851—8316no—
189C2×#389—832no—
190C2×#387—834no—
191C2×#385—834no—
192C2×#382D8311yescharacteristic, complemented
193C2×#380—832no—
194C83C2×#285111yescharacteristic, complemented, Sylow
195C24×C4—831no—
196C24×C4—832no—
197C2×#125—838no—
198C2×#125—1668no—
199C22×C4⋊C4—834no—
200C22×C4⋊C4—832no—
201C22×C4⋊C4—834no—
202C22×C4⋊C4C2×D8312yes—
203C22×C22⋊C4—834no—
204C22×C42—832no—
205C22×C42—831no—
206C22×C42—838no—
207C22×C42—1668no—
208C22×C42C2×D8311yescharacteristic
209#389—8316no—
210#387—8332no—
211#385—8332no—
212#382C2×D8318yescomplemented
213#380—8316no—
214C2×#95—834no—
215C2×#95—834no—
216C2×#95C2×D8314yes—
217C25—831no—
218C23×C4—832no—
219C23×C4—831no—
220C23×C4—838no—
221C23×C4—834no—
222C23×C4—834no—
223C23×C4—838no—
224C23×C4—1668no—
225C23×C4—1668no—
226C23×C4—1668no—
227C23×C4—1664no—
228C23×C4—1664no—
229C23×C4C22×D8314yes—
230C23×C4C22×D8312yes—
231C23×C4C22×D8311yescharacteristic
232#125—16632no—
233C2×C4⋊C4—28no—
234C2×C4⋊C4—838no—
235C2×C4⋊C4—8316no—
236C2×C4⋊C4—8316no—
237C2×C4⋊C4—16616no—
238C2×C4⋊C4—16616no—
239C2×C4⋊C4—1668no—
240C2×C4⋊C4C22×D8318yes—
241C2×C22⋊C4—8316no—
242C2×C22⋊C4—16616no—
243C2×C42—838no—
244C2×C42—834no—
245C2×C42—1668no—
246C2×C42—1664no—
247C2×C42—16632no—
248C2×C42D33218yes—
249C2×C42C22×D8314yes—
250#95—8316no—
251#95—8316no—
252#95C22×D83116yes—
253C24—834no—
254C24—838no—
255C24—832no—
256C24—1662no—
257C24—1664no—
258C24—1662no—
259C24C23×D8311yescharacteristic
260C22×C4—24no—
261C22×C4—24no—
262C22×C4—28no—
263C22×C4—28no—
264C22×C4—28no—
265C22×C4—834no—
266C22×C4—838no—
267C22×C4—832no—
268C22×C4—834no—
269C22×C4—8316no—
270C22×C4—838no—
271C22×C4—16616no—
272C22×C4—16616no—
273C22×C4—16664no—
274C22×C4—1668no—
275C22×C4—1668no—
276C22×C4—1668no—
277C22×C4—1662no—
278C22×C4—1664no—
279C22×C4—1664no—
280C22×C4—1662no—
281C22×C4—16632no—
282C22×C4—16616no—
283C22×C4—1668no—
284C22×C4—1668no—
285C22×C4C2×D33218yes—
286C22×C4C2×D33214yes—
287C22×C4Q8×D8314yes—
288C22×C4#1305058914yes—
289C22×C4C23×D8318yes—
290C22×C4C23×D8314yes—
291C22×C4C23×D8312yes—
292C4⋊C4—216no—
293C4⋊C4—16632no—
294C4⋊C4—16632no—
295C4⋊C4—16616no—
296C22⋊C4—16632no—
297C42—16616no—
298C42—1668no—
299C42C2×D332116yes—
300C23—8316no—
301C23—834no—
302C23—838no—
303C23—1668no—
304C23—16616no—
305C23—16616no—
306C23—1668no—
307C23—1662no—
308C23—1664no—
309C23—1662no—
310C23C22×D33212yes—
311C23C2×Q8×D8312yes—
312C23#41×D8314yes—
313C23#41×D8314yes—
314C23C2×#1305058912yes—
315C23C24×D8311yescharacteristic
316C2×C4—216no—
317C2×C4—24no—
318C2×C4—24no—
319C2×C4—28no—
320C2×C4—28no—
321C2×C4—28no—
322C2×C4—416no—
323C2×C4—33216no—
324C2×C4—834no—
325C2×C4—838no—
326C2×C4—16664no—
327C2×C4—1668no—
328C2×C4—1668no—
329C2×C4—1668no—
330C2×C4—1668no—
331C2×C4—16616no—
332C2×C4—1662no—
333C2×C4—1664no—
334C2×C4—1664no—
335C2×C4—1662no—
336C2×C4—16632no—
337C2×C4#14581772116yes—
338C2×C4C22×D33218yes—
339C2×C4C22×D33214yes—
340C2×C4C2×Q8×D8314yes—
341C2×C4C2×#1305058914yes—
342C22—838no—
343C22—16632no—
344C22—1664no—
345C22—1668no—
346C22—1668no—
347C22—1664no—
348C22C2×#1458177214yes—
349C22#1912821318yes—
350C22#125×D8314yes—
351C22#1912823018yes—
352C22#1912825714yes—
353C22C23×D33211yescharacteristic
354C22C22×Q8×D8311yescharacteristic
355C22C2×#41×D8312yes—
356C22C2×#41×D8312yes—
357C22C22×#1305058911yescharacteristic
358C4—28no—
359C4—48no—
360C4—3328no—
361C4—1664no—
362C4—1668no—
363C4C2×#1458177218yes—
364C2—1668no—
365C2#2491577418yesdirect product factor
366C2C22×#1458177211yescharacteristic
367C2C2×#1912821312yes—
368C2C2×#125×D8311yescharacteristic
369C2C2×#1912823012yes—
370C2C2×#1912825711yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#382×C83C2
socleC24×C83C24
prime radicalC24×D83C23
hypercenterC2×#382D83
hypocenterC83C2×#2851
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
1. C22×#14581784C2semidirect
3. #24915774C2direct (N × H)
4. C2×#19127600C2semidirect
5. C2×#19127586C2semidirect
8. C2×#382×C83C2semidirect
12. C2×#14581784C22semidirect
21. #19127600C22semidirect
22. #19127586C22semidirect
29. #382×C83C22semidirect
127. C22×D83#125semidirect
171. C2×D83C2×#125semidirect
179. C2×C83#2851semidirect
192. C2×#382D83semidirect
194. C83C2×#2851semidirect
212. #382C2×D83semidirect
365. C2#24915774direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817842
C22×C42×D832
#249157742
C2×#191276002
C2×#191275862
C2×#191275752
C2×#191275582
C2×#382×C832
C2×#285183