Finite Group Databasebeta

← #382×Dic59 #28509919

Subgroups — #382×Dic59 #28509919

Order 15104.

1742 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837268C211yesmaximal, characteristic
2C2×C4⋊C4×Dic59C212yesmaximal
3C2×C42×Dic59C211yesmaximal, characteristic
4#21422325C212yesmaximal
5#21422321C214yesmaximal
6#95×Dic59C214yesmaximal
7C2×C59×#382C211yesmaximal, characteristic
8C22×C4⋊Dic59C2212yes—
9C22×C4×Dic59C2214yes—
10C22×C4×Dic59C2212yes—
11C22×C4×Dic59C2212yes—
12C22×C4×Dic59C2211yescharacteristic
13C22×C4×Dic59C2211yescharacteristic
14#16837268C418yescomplemented
15C4⋊C4×Dic59—28no—
16C2×C59⋊#95C2214yes—
17C2×C59⋊#95C2218yes—
18C2×C59⋊#95C2214yes—
19C42×Dic59C418yescomplemented
20C22×C4⋊C4×C59C2212yes—
21C22×C42×C59C2211yescharacteristic
22C59×#382C418yescomplemented
23C2×#95×C59C2214yes—
24C23×Dic59C2314yes—
25C23×Dic59C2311yescharacteristic
26C23×Dic59C2312yes—
27C23×Dic59C2311yescharacteristic
28C2×C4⋊Dic59—24no—
29C2×C4⋊Dic59—24no—
30C2×C4⋊Dic59C2×C418yes—
31C2×C4×Dic59—22no—
32C2×C4×Dic59—22no—
33C2×C4×Dic59—28no—
34C2×C4×Dic59—28no—
35C2×C4×Dic59—28no—
36C2×C4×Dic59—216no—
37C2×C4×Dic59C2×C414yes—
38C2×C4×Dic59C2×C418yes—
39C2×C4×Dic59C2×C418yes—
40C2×C4×Dic59C2×C414yes—
41C2×C4×Dic59D414yes—
42C2×C4×Dic59Q814yes—
43C59⋊#95—28no—
44C59⋊#95—216no—
45C59⋊#95C2×C4116yes—
46C23×C4×C59C2314yes—
47C23×C4×C59C2312yes—
48C23×C4×C59C2311yescharacteristic
49C2×C4⋊C4×C59—24no—
50C2×C4⋊C4×C59—24no—
51C2×C4⋊C4×C59C2×C418yes—
52C2×C42×C59C2×C414yes—
53C2×C42×C59C2×C414yes—
54C2×C42×C59C2×C414yes—
55#95×C59C2×C4116yes—
56C24×C59C2411yescharacteristic
57C22×C4×C59—24no—
58C22×C4×C59—24no—
59C22×C4×C59—24no—
60C22×C4×C59—24no—
61C22×C4×C59—28no—
62C22×C4×C59—28no—
63C22×C4×C59C22×C418yes—
64C22×C4×C59C22×C414yes—
65C22×C4×C59C22×C414yes—
66C22×C4×C59C22×C414yes—
67C22×C4×C59C22×C412yes—
68C22×C4×C59C22×C412yes—
69C22×C4×C59C22×C412yes—
70C22×C4×C59C2×D412yes—
71C22×C4×C59C2×Q812yes—
72C22×C4×C59#4112yes—
73C22×C4×C59#4112yes—
74C22×Dic59—24no—
75C22×Dic59—22no—
76C22×Dic59—22no—
77C22×Dic59—24no—
78C22×Dic59—24no—
79C22×Dic59—28no—
80C22×Dic59—28no—
81C22×Dic59—24no—
82C22×Dic59C22×C418yes—
83C22×Dic59C22×C412yes—
84C22×Dic59C22×C414yes—
85C22×Dic59C22×C412yes—
86C22×Dic59C2×D412yes—
87C22×Dic59C2×D412yes—
88C22×Dic59C2×Q812yes—
89C22×Dic59C2×Q812yes—
90C22×Dic59#4118yes—
91C22×Dic59#4118yes—
92C4⋊C4×C59—216no—
93C42×C59C42116yescomplemented
94C4⋊Dic59—216no—
95C4×Dic59—28no—
96C4×Dic59—216no—
97C4×Dic59—216no—
98C4×Dic59—416no—
99C4×Dic59C4⋊C4116yes—
100C23×C59C23×C411yescharacteristic
101C23×C59C23×C411yescharacteristic
102C23×C59C23×C411yescharacteristic
103C23×C59C22×D411yescharacteristic
104C23×C59C22×Q811yescharacteristic
105C23×C59C2×#4114yes—
106C23×C59C2×#4114yes—
107C23×C59C2×#4111yescharacteristic
108C23×C59C2×#4111yescharacteristic
109C2×C4×C59—24no—
110C2×C4×C59—24no—
111C2×C4×C59—28no—
112C2×C4×C59—28no—
113C2×C4×C59—28no—
114C2×C4×C59—216no—
115C2×C4×C59—44no—
116C2×C4×C59—48no—
117C2×C4×C59—44no—
118C2×C4×C59C2×C4218yes—
119C2×C4×C59C2×C4214yes—
120C2×C4×C59C2×C4⋊C414yes—
121C2×C4×C59#11714yes—
122C2×C4×C59C4×D414yes—
123C2×C4×C59C4×D414yes—
124C2×C4×C59C4×Q814yes—
125C2×C4×C59C4×Q814yes—
126C2×Dic59—24no—
127C2×Dic59—24no—
128C2×Dic59—24no—
129C2×Dic59—28no—
130C2×Dic59—28no—
131C2×Dic59—24no—
132C2×Dic59—24no—
133C2×Dic59—28no—
134C2×Dic59—216no—
135C2×Dic59—44no—
136C2×Dic59—48no—
137C2×Dic59—44no—
138C2×Dic59C2×C4⋊C414yes—
139C2×Dic59C2×C4⋊C414yes—
140C2×Dic59#11718yes—
141C2×Dic59#11718yes—
142C2×Dic59#12418yes—
143C2×Dic59#12518yes—
144C4×#382—591nomaximal, Sylow
145C22×C59C22×C4211yescharacteristic
146C22×C59C22×C4⋊C411yescharacteristic
147C22×C59C2×#11712yes—
148C22×C59C2×#11712yes—
149C22×C59C2×#11711yescharacteristic
150C22×C59C2×C4×D411yescharacteristic
151C22×C59C2×C4×D411yescharacteristic
152C22×C59C2×C4×Q811yescharacteristic
153C22×C59C2×C4×Q811yescharacteristic
154C22×C59C4×#4114yes—
155C22×C59C4×#4114yes—
156C22×C59C2×#12412yes—
157C22×C59C2×#12512yes—
158C22×C59#52914yes—
159C22×C59#52914yes—
160C22×C59#53212yes—
161C22×C59#53312yes—
162C4×C59—28no—
163C4×C59—48no—
164C4×C59C4×C4⋊C418yes—
165Dic59—28no—
166Dic59—24no—
167Dic59—48no—
168Dic59#38218yesdirect product factor
169C2×#382—591no—
170C2×#382D5911yescharacteristic
171C2×C4×C4⋊C4—592no—
172C2×C43—591no—
173C4⋊#95—592no—
174#1434—594no—
175C4×#95—594no—
176C2×C59C2×C4×C4⋊C411yescharacteristic
177C2×C59C4×#11712yes—
178C2×C59C2×#38211yescharacteristic
179C2×C59#228312yes—
180C2×C59#228511yescharacteristic
181C2×C59C4×#12412yes—
182C2×C59C4×#12412yes—
183C2×C59C4×#12512yes—
184C2×C59C4×#12512yes—
185C22×C4⋊C4—592no—
186C22×C4⋊C4C2×D5912yes—
187C22×C42—591no—
188C22×C42—592no—
189C22×C42—592no—
190C22×C42—591no—
191C22×C42—594no—
192C22×C42C2×D5911yescharacteristic
193#382—598no—
194#382Dic5918yesdirect product factor
195C4×C4⋊C4—1188no—
196C2×#95—594no—
197C2×#95—598no—
198C2×#95—594no—
199C2×#95C2×D5914yes—
200C43—598no—
201C59C4×#38211yescharacteristic, complemented, Sylow
202C23×C4—591no—
203C23×C4—591no—
204C23×C4—592no—
205C23×C4—594no—
206C23×C4C22×D5914yes—
207C23×C4C22×D5912yes—
208C23×C4C22×D5911yescharacteristic
209C2×C4⋊C4—24no—
210C2×C4⋊C4—24no—
211C2×C4⋊C4—598no—
212C2×C4⋊C4—1184no—
213C2×C4⋊C4—1184no—
214C2×C4⋊C4C2×Dic5918yes—
215C2×C42—594no—
216C2×C42—594no—
217C2×C42—594no—
218C2×C42—598no—
219C2×C42—598no—
220C2×C42—594no—
221C2×C42—1188no—
222C2×C42—1188no—
223C2×C42—1182no—
224C2×C42—1182no—
225C2×C42—1188no—
226C2×C42—11816no—
227C2×C42C4×D5914yes—
228C2×C42C4×D5914yes—
229C2×C42C2×Dic5914yes—
230#95—5916no—
231#95—11816no—
232#95—1188no—
233#95C2×Dic59116yes—
234C24C23×D5911yescharacteristic
235C22×C4—24no—
236C22×C4—24no—
237C22×C4—24no—
238C22×C4—28no—
239C22×C4—28no—
240C22×C4—24no—
241C22×C4—592no—
242C22×C4—592no—
243C22×C4—592no—
244C22×C4—598no—
245C22×C4—592no—
246C22×C4—594no—
247C22×C4—592no—
248C22×C4—592no—
249C22×C4—598no—
250C22×C4—598no—
251C22×C4—1184no—
252C22×C4—1184no—
253C22×C4—1182no—
254C22×C4—1182no—
255C22×C4—1184no—
256C22×C4—1188no—
257C22×C4—1188no—
258C22×C4—1184no—
259C22×C4C2×C4×D5914yes—
260C22×C4C2×C4×D5914yes—
261C22×C4C2×C4×D5912yes—
262C22×C4C2×C4×D5912yes—
263C22×C4D4×D5912yes—
264C22×C4#1174568712yes—
265C22×C4Q8×D5912yes—
266C22×C4#1174568912yes—
267C22×C4C22×Dic5918yes—
268C22×C4C22×Dic5914yes—
269C22×C4C22×Dic5912yes—
270C4⋊C4—216no—
271C4⋊C4—11816no—
272C42—5916no—
273C42—11816no—
274C42—11816no—
275C42—1188no—
276C42—23616no—
277C42C4×Dic59116yescomplemented
278C23C22×C4×D5911yescharacteristic
279C23C22×C4×D5911yescharacteristic
280C23C23×Dic5911yescharacteristic
281C23C2×D4×D5911yescharacteristic
282C23C2×Q8×D5911yescharacteristic
283C23#41×D5914yes—
284C23#41×D5914yes—
285C23C2×#1174568711yescharacteristic
286C23C2×#1174568911yescharacteristic
287C2×C4—24no—
288C2×C4—24no—
289C2×C4—28no—
290C2×C4—28no—
291C2×C4—28no—
292C2×C4—216no—
293C2×C4—44no—
294C2×C4—48no—
295C2×C4—44no—
296C2×C4—598no—
297C2×C4—598no—
298C2×C4—594no—
299C2×C4—598no—
300C2×C4—594no—
301C2×C4—598no—
302C2×C4—1188no—
303C2×C4—1188no—
304C2×C4—1184no—
305C2×C4—1184no—
306C2×C4—1184no—
307C2×C4—1184no—
308C2×C4—1184no—
309C2×C4—1188no—
310C2×C4—11816no—
311C2×C4—2364no—
312C2×C4—2368no—
313C2×C4—2364no—
314C2×C4C2×C4×Dic5918yes—
315C2×C4C2×C4×Dic5914yes—
316C2×C4C4⋊C4×D5914yes—
317C2×C4#1427368514yes—
318C2×C4#1427368914yes—
319C2×C4D4×Dic5914yes—
320C2×C4#1427369214yes—
321C2×C4Q8×Dic5914yes—
322C22C22×C4×Dic5911yescharacteristic
323C22C2×C4⋊C4×D5911yescharacteristic
324C22#117×D5912yes—
325C22#117×D5912yes—
326C22C2×#1427368511yescharacteristic
327C22C2×#1427368911yescharacteristic
328C22C2×D4×Dic5911yescharacteristic
329C22C2×#1427369211yescharacteristic
330C22C2×Q8×Dic5911yescharacteristic
331C22#1683787014yes—
332C22#41×Dic5914yes—
333C22#124×D5912yes—
334C22#125×D5912yes—
335C22#1683793114yes—
336C22#1683793714yes—
337C22#1683795112yes—
338C22#1683795812yes—
339C4—28no—
340C4—48no—
341C4—598no—
342C4—1188no—
343C4—1184no—
344C4—2368no—
345C4C4⋊C4×Dic5918yes—
346C2C2×C4⋊C4×Dic5911yescharacteristic
347C2#117×Dic5912yes—
348C2#382×D5911yescharacteristic
349C2#2142648912yes—
350C2#2142650211yescharacteristic
351C2#2142663512yes—
352C2#124×Dic5912yes—
353C2#2142665112yes—
354C2#125×Dic5912yes—
subgroupG/H
center, FrattiniC24C23×D59
commutatorC22×C59C22×C42
FittingC2×C59×#382C2
socle, prime radical, cosocleC24×C59C24
hypercenterC2×#382D59
hypocenterC59C4×#382
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
14. #16837268C4semidirect
19. C42×Dic59C4semidirect
22. C59×#382C4semidirect
93. C42×C59C42semidirect
168. Dic59#382direct (N × H)
194. #382Dic59direct (N × H)
201. C59C4×#382semidirect
277. C42C4×Dic59semidirect

Maximal subgroups

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

subgroupindex
C2×#168372682
C2×C4⋊C4×Dic592
C2×C42×Dic592
#214223252
#214223212
#95×Dic592
C2×C59×#3822
C4×#38259