Finite Group Databasebeta

← #2859×D83 #35610379

Subgroups — #2859×D83 #35610379

Order 21248.

2558 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D83C212yesmaximal
2#24915826C211yesmaximal, characteristic, complemented
3#24915825C212yesmaximal, complemented
4#24915824C212yesmaximal, complemented
5#24915823C212yesmaximal, complemented
6#24915822C218yesmaximal, complemented
7#389×D83C218yesmaximal
8#384×D83C212yesmaximal
9#382×D83C212yesmaximal
10C43×D83C211yesmaximal, characteristic
11C83×#2859C211yesmaximal, characteristic, complemented
12C2×#14581784C2212yes—
13C2×#14581783C2214yes—
14C2×#14581782C2218yes—
15#125×D83—216no—
16C2×C4⋊C4×D83C2214yes—
17C2×C4⋊C4×D83C2218yes—
18C2×C4⋊C4×D83C2218yes—
19C2×C42×D83C2214yes—
20C2×C42×D83C2211yescharacteristic
21C2×C42×D83C2211yescharacteristic
22C2×C42×D83C2211yescharacteristic
23#19127600C2218yes—
24#19127599C2218yes—
25#19127598C22116yes—
26#19127597C2218yes—
27#19127596C22116yes—
28#19127571C2212yes—
29#19127570C2218yes—
30#19127570C2214yes—
31#19127567C2212yes—
32#19127566C2214yes—
33#19127565C2218yes—
34#95×D83C2218yes—
35C42×Dic83C2214yes—
36C42×Dic83C2211yescharacteristic
37C42×Dic83C2211yescharacteristic
38C42×Dic83C2211yescharacteristic
39C2×#125×C83C2212yes—
40#389×C83C2218yes—
41#384×C83C2212yes—
42#382×C83C2212yes—
43C43×C83C2211yescharacteristic
44C22×C4×D83C2318yes—
45C22×C4×D83C2312yes—
46C22×C4×D83C2312yes—
47C22×C4×D83C2311yescharacteristic
48C22×C4×D83C2312yes—
49#14581784—28no—
50#14581783—216no—
51#14581782—232no—
52C2×C4⋊Dic83C2314yes—
53C2×C4⋊Dic83C2318yes—
54C2×C4⋊Dic83C2318yes—
55C2×Dic83⋊C4C2318yes—
56C2×Dic83⋊C4C23116yes—
57C2×Dic83⋊C4C2318yes—
58C2×Dic83⋊C4C2318yes—
59C4⋊C4×D83—232no—
60C4⋊C4×D83—216no—
61C4⋊C4×D83—232no—
62C2×C4×Dic83C2314yes—
63C2×C4×Dic83C2314yes—
64C2×C4×Dic83C2314yes—
65C2×C4×Dic83C2312yes—
66C2×C4×Dic83C2311yescharacteristic
67C2×C4×Dic83C2312yes—
68C2×C4×Dic83C2311yescharacteristic
69C2×C4×Dic83C2311yescharacteristic
70C2×C4×Dic83C2312yes—
71C42×D83—216no—
72C42×D83D418yes—
73C42×D83Q818yes—
74C42×D83Q818yes—
75C83⋊#95C23116yes—
76C83⋊#95C2318yes—
77#125×C83—28no—
78C2×C4⋊C4×C83C2314yes—
79C2×C4⋊C4×C83C2318yes—
80C2×C4⋊C4×C83C2318yes—
81C2×C42×C83C2314yes—
82C2×C42×C83C2311yescharacteristic
83C2×C42×C83C2311yescharacteristic
84C2×C42×C83C2311yescharacteristic
85#95×C83C2318yes—
86C23×D83C2411yescharacteristic
87C22×Dic83C2418yes—
88C22×Dic83C2412yes—
89C22×Dic83C2412yes—
90C22×Dic83C2411yescharacteristic
91C22×Dic83C2412yes—
92C2×C4×D83—28no—
93C2×C4×D83—28no—
94C2×C4×D83—216no—
95C2×C4×D83—232no—
96C2×C4×D83C2×D418yes—
97C2×C4×D83C2×D414yes—
98C2×C4×D83C2×Q818yes—
99C2×C4×D83C2×Q818yes—
100C2×C4×D83C2×Q814yes—
101C2×C4×D83C2×Q814yes—
102C2×C4×D83#41116yes—
103C4⋊Dic83—28no—
104C4⋊Dic83—216no—
105C4⋊Dic83—216no—
106Dic83⋊C4—216no—
107Dic83⋊C4—216no—
108Dic83⋊C4—216no—
109Dic83⋊C4—232no—
110C4×Dic83—28no—
111C4×Dic83—28no—
112C4×Dic83—28no—
113C4×Dic83C2×D418yes—
114C4×Dic83C2×D414yes—
115C4×Dic83C2×Q814yes—
116C4×Dic83C2×Q818yes—
117C4×Dic83C2×Q814yes—
118C4×Dic83C2×Q818yes—
119C22×C4×C83C2418yes—
120C22×C4×C83C2412yes—
121C22×C4×C83C2412yes—
122C22×C4×C83C2411yescharacteristic
123C22×C4×C83C2412yes—
124C4⋊C4×C83—216no—
125C4⋊C4×C83—28no—
126C4⋊C4×C83—216no—
127C42×C83—28no—
128C42×C83C2×D414yes—
129C42×C83C2×Q814yes—
130C42×C83C2×Q814yes—
131C23×C83C2511yescharacteristic
132C22×D83C22×D412yes—
133C22×D83C22×Q812yes—
134C22×D83C22×Q812yes—
135C22×D83C2×#4118yes—
136C2×C4×C83—24no—
137C2×C4×C83—24no—
138C2×C4×C83—28no—
139C2×C4×C83—216no—
140C2×C4×C83C22×D414yes—
141C2×C4×C83C22×D412yes—
142C2×C4×C83C22×Q814yes—
143C2×C4×C83C22×Q814yes—
144C2×C4×C83C22×Q812yes—
145C2×C4×C83C22×Q812yes—
146C2×C4×C83C2×#4118yes—
147C2×Dic83—24no—
148C2×Dic83—24no—
149C2×Dic83—28no—
150C2×Dic83—216no—
151C2×Dic83C22×D414yes—
152C2×Dic83C22×D412yes—
153C2×Dic83C22×Q814yes—
154C2×Dic83C22×Q814yes—
155C2×Dic83C22×Q812yes—
156C2×Dic83C22×Q812yes—
157C2×Dic83C2×#4118yes—
158C4×D83—216no—
159C4×D83—216no—
160C4×D83—432no—
161C4×D83#125132yescomplemented
162C4×D83C4⋊Q8116yes—
163C22×C83C23×D411yescharacteristic
164C22×C83C23×Q811yescharacteristic
165C22×C83C23×Q811yescharacteristic
166C22×C83C22×#4114yes—
167C2×D83C2×#12518yes—
168C2×D83C2×C4⋊Q814yes—
169C2×D83#53218yes—
170C2×D83#53318yes—
171C4×C83—24no—
172C4×C83—24no—
173C4×C83—48no—
174C4×C83C2×#12518yescomplemented
175C4×C83C2×C4⋊Q814yes—
176Dic83—24no—
177Dic83—24no—
178Dic83—48no—
179Dic83C2×#12518yescomplemented
180Dic83C2×C4⋊Q814yes—
181C2×#2859—831nomaximal, Sylow
182C2×C83C22×#12512yes—
183C2×C83C22×C4⋊Q811yescharacteristic
184C2×C83C2×#53212yes—
185C2×C83C2×#53312yes—
186D83#285918yesdirect product factor
187C22×#125—832no—
188#2859—838no—
189#2859—832no—
190#2859—832no—
191#2859—831no—
192#2859—832no—
193#2859D8311yescharacteristic, direct product factor
194C2×#389—838no—
195C2×#384—832no—
196C2×#382—832no—
197C2×C43—831no—
198C83C2×#285911yescharacteristic, complemented, Sylow
199C2×#125—838no—
200C2×#125—834no—
201C2×#125—832no—
202C2×#125—16616no—
203C2×#125C2×D8312yes—
204C22×C4⋊C4—834no—
205C22×C4⋊C4—838no—
206C22×C4⋊C4—838no—
207C22×C42—831no—
208C22×C42—831no—
209C22×C42—831no—
210C22×C42—834no—
211#389—8316no—
212#389—838no—
213#389—838no—
214#389—838no—
215#389—8316no—
216#389C2×D8318yes—
217#384—838no—
218#384—834no—
219#384—832no—
220#384C2×D8312yes—
221#382—834no—
222#382—832no—
223#382—838no—
224#382C2×D8312yes—
225C2×#95—838no—
226C43—834no—
227C43—831no—
228C43—831no—
229C43—831no—
230C43C2×D8311yescharacteristic
231C23×C4—831no—
232C23×C4—832no—
233C23×C4—832no—
234C23×C4—832no—
235C23×C4—838no—
236#125—28no—
237#125—16632no—
238#125—16616no—
239#125—1668no—
240C2×C4⋊C4—838no—
241C2×C4⋊C4—834no—
242C2×C4⋊C4—838no—
243C2×C4⋊C4—838no—
244C2×C4⋊C4—838no—
245C2×C4⋊C4—8316no—
246C2×C4⋊C4—838no—
247C2×C4⋊C4—16616no—
248C2×C4⋊C4—16632no—
249C2×C4⋊C4—16632no—
250C2×C4⋊C4C22×D8314yes—
251C2×C4⋊C4C22×D8318yes—
252C2×C4⋊C4C22×D8318yes—
253C2×C42—832no—
254C2×C42—831no—
255C2×C42—832no—
256C2×C42—831no—
257C2×C42—831no—
258C2×C42—832no—
259C2×C42—838no—
260C2×C42—838no—
261C2×C42—838no—
262C2×C42—834no—
263C2×C42—834no—
264C2×C42—834no—
265C2×C42—16616no—
266C2×C42C22×D8314yes—
267C2×C42C22×D8311yescharacteristic
268C2×C42C22×D8311yescharacteristic
269C2×C42C22×D8311yescharacteristic
270#95—8316no—
271#95—838no—
272#95C22×D8318yes—
273C24—831no—
274C22×C4—831no—
275C22×C4—832no—
276C22×C4—834no—
277C22×C4—838no—
278C22×C4—834no—
279C22×C4—834no—
280C22×C4—8316no—
281C22×C4—832no—
282C22×C4—832no—
283C22×C4—838no—
284C22×C4—838no—
285C22×C4—838no—
286C22×C4—16616no—
287C22×C4—16632no—
288C22×C4—1668no—
289C22×C4—1668no—
290C22×C4C23×D8318yes—
291C22×C4C23×D8312yes—
292C22×C4C23×D8312yes—
293C22×C4C23×D8311yescharacteristic
294C22×C4C23×D8312yes—
295C4⋊C4—216no—
296C4⋊C4—28no—
297C4⋊C4—216no—
298C4⋊C4—16616no—
299C4⋊C4—16616no—
300C4⋊C4—16616no—
301C4⋊C4—16632no—
302C4⋊C4—16616no—
303C4⋊C4—1668no—
304C4⋊C4—16616no—
305C42—28no—
306C42—838no—
307C42—834no—
308C42—838no—
309C42—834no—
310C42—838no—
311C42—834no—
312C42—1668no—
313C42—1668no—
314C42—1668no—
315C42D4×D8314yes—
316C42Q8×D8314yes—
317C42Q8×D8314yes—
318C23—832no—
319C23—832no—
320C23—832no—
321C23—838no—
322C23C24×D8311yescharacteristic
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—28no—
326C2×C4—216no—
327C2×C4—33232no—
328C2×C4—832no—
329C2×C4—834no—
330C2×C4—832no—
331C2×C4—832no—
332C2×C4—838no—
333C2×C4—8332no—
334C2×C4—8316no—
335C2×C4—834no—
336C2×C4—834no—
337C2×C4—16616no—
338C2×C4—16616no—
339C2×C4—1668no—
340C2×C4—16616no—
341C2×C4—1664no—
342C2×C4—1664no—
343C2×C4C2×D4×D8314yes—
344C2×C4C2×D4×D8312yes—
345C2×C4C2×Q8×D8314yes—
346C2×C4C2×Q8×D8314yes—
347C2×C4C2×Q8×D8312yes—
348C2×C4C2×Q8×D8312yes—
349C2×C4#41×D8318yes—
350C22—838no—
351C22—834no—
352C22—838no—
353C22—838no—
354C22C22×D4×D8311yescharacteristic
355C22C22×Q8×D8311yescharacteristic
356C22C22×Q8×D8311yescharacteristic
357C22C2×#41×D8314yes—
358C4—24no—
359C4—24no—
360C4—48no—
361C4—3328no—
362C4—838no—
363C4—834no—
364C4—1664no—
365C4—1664no—
366C4#125×D8318yescomplemented
367C4C4⋊Q8×D8314yes—
368C2—838no—
369C2C2×#125×D8312yes—
370C2C2×C4⋊Q8×D8311yescharacteristic
371C2#532×D8312yes—
372C2#533×D8312yes—
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC83×#2859C2
prime radicalC23×D83C24
hypercenter#2859D83
hypocenterC83C2×#2859
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2859

Complements

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

NH ≅ G/Ntype
2. #24915826C2semidirect
3. #24915825C2semidirect
4. #24915824C2semidirect
5. #24915823C2semidirect
6. #24915822C2semidirect
11. C83×#2859C2semidirect
161. C4×D83#125semidirect
174. C4×C83C2×#125semidirect
179. Dic83C2×#125semidirect
186. D83#2859direct (N × H)
193. #2859D83direct (N × H)
198. C83C2×#2859semidirect
366. C4#125×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#125×D832
#249158262
#249158252
#249158242
#249158232
#249158222
#389×D832
#384×D832
#382×D832
C43×D832
C83×#28592
C2×#285983