Finite Group Databasebeta

← #18080901

Subgroups — #18080901

Order 4864.

382 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564596C211yesmaximal, characteristic
2#14564583C211yesmaximal, characteristic
3#14564393C211yesmaximal, characteristic
4C2×#11926292C211yesmaximal, characteristic
5#14561519C211yesmaximal, characteristic
6#14561470C211yesmaximal, characteristic
7C8×C4⋊C4×C19C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9C2×#10597264—21no—
10C2×C4⋊(C19⋊C8)C2211yescharacteristic
11C2×C4⋊(C19⋊C8)C2211yescharacteristic
12#11926414C2211yescharacteristic
13#11926307—21no—
14#11926307—21no—
15#11926306—21no—
16#11926306—21no—
17#11926306—21no—
18#11926292C414yescomplemented
19C2×C19×C4⋊C8C2211yescharacteristic
20C2×C4×C8×C19—21no—
21C2×C4×C8×C19C2211yescharacteristic
22C4×C4⋊C4×C19C2211yescharacteristic
23C19×#336—21no—
24C22×Dic38—21no—
25C22×C8×C19—21no—
26C22×C8×C19D411yescharacteristic
27C22×C8×C19D411yescharacteristic
28C2×C4⋊C4×C19D411yescharacteristic
29C2×C4⋊C4×C19D411yescharacteristic
30C2×C42×C19—21no—
31C2×C42×C19C2311yescharacteristic
32C2×C4⋊Dic19—21no—
33C2×C4⋊Dic19—21no—
34C2×C4⋊Dic19—21no—
35C2×C4⋊Dic19—21no—
36C2×C4⋊Dic19—21no—
37C22×C19⋊C8—21no—
38C22×C19⋊C8—21no—
39#10597315—21no—
40#10597315—21no—
41#10597315—21no—
42#10597315C2×C412yes—
43C19×C4⋊C8—21no—
44C19×C4⋊C8C2×C412yes—
45C4×C8×C19—21no—
46C4×C8×C19—21no—
47C4×C8×C19—42no—
48C19×#95—21no—
49#10597264—42no—
50C4⋊(C19⋊C8)—21no—
51C4⋊(C19⋊C8)—21no—
52C4⋊(C19⋊C8)—21no—
53C4⋊(C19⋊C8)C2×C412yes—
54C22×C4×C19—21no—
55C22×C4×C19—21no—
56C22×C4×C19C2×D411yescharacteristic
57C22×C4×C19C2×D411yescharacteristic
58C22×C4×C19#4111yescharacteristic
59C22×Dic19—41no—
60C22×Dic19—41no—
61C2×Dic38—22no—
62C2×Dic38—41no—
63C2×Dic38—81no—
64C2×Dic38—81no—
65C2×C8×C19—21no—
66C2×C8×C19—21no—
67C2×C8×C19—22no—
68C2×C8×C19—21no—
69C2×C8×C19—21no—
70C2×C8×C19—21no—
71C2×C8×C19—41no—
72C2×C8×C19—41no—
73C2×C8×C19Q1612yes—
74C4⋊C4×C19—21no—
75C4⋊C4×C19—21no—
76C4⋊C4×C19SD1612yes—
77C4⋊C4×C19Q1612yes—
78C42×C19—41no—
79C42×C19—41no—
80C42×C19C22×C411yescharacteristic
81C42×C19#4111yescharacteristic
82C42×C19#4111yescharacteristic
83C42×C19#4111yescharacteristic
84C4⋊Dic19—22no—
85C4⋊Dic19—22no—
86C4⋊Dic19—41no—
87C4⋊Dic19—41no—
88C4⋊Dic19—41no—
89C4⋊Dic19—41no—
90C4⋊Dic19—41no—
91C4⋊Dic19—41no—
92C4⋊Dic19—81no—
93C2×C19⋊C8—22no—
94C2×C19⋊C8—41no—
95C2×C19⋊C8—41no—
96C2×C19⋊C8—41no—
97C2×C19⋊C8—41no—
98C2×C19⋊C8—41no—
99#9568—191nomaximal, Sylow
100C23×C19#12111yescharacteristic
101C2×C4×C19—21no—
102C2×C4×C19—21no—
103C2×C4×C19—22no—
104C2×C4×C19—22no—
105C2×C4×C19—41no—
106C2×C4×C19—41no—
107C2×C4×C19—41no—
108C2×C4×C19—41no—
109C2×C4×C19#11711yescharacteristic
110C2×C4×C19C4×D411yescharacteristic
111C2×C4×C19C4×D411yescharacteristic
112C2×C4×C19#12311yescharacteristic
113C2×C4×C19#12411yescharacteristic
114C2×C4×C19#12611yescharacteristic
115C2×C4×C19C2×SD1611yescharacteristic
116C2×C4×C19C2×Q1611yescharacteristic
117C2×C4×C19C2×Q1611yescharacteristic
118C2×C4×C19#13511yescharacteristic
119C2×C4×C19#13511yescharacteristic
120C2×C4×C19#13511yescharacteristic
121C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C19#13711yescharacteristic
123C2×Dic19—42no—
124C2×Dic19—81no—
125C2×Dic19—81no—
126C2×Dic19—81no—
127C2×Dic19—81no—
128C2×Dic19—81no—
129Dic38—82no—
130Dic38—82no—
131C8×C19—22no—
132C8×C19—42no—
133C8×C19—41no—
134C19⋊C8—42no—
135C19⋊C8—81no—
136#1990—191no—
137#1987—191no—
138#1947—191no—
139C8×C4⋊C4D1911yescharacteristic
140C2×#333—191no—
141#1296—191no—
142#1277—191no—
143C22×C19#38811yescharacteristic
144C22×C19#46211yescharacteristic
145C22×C19#46311yescharacteristic
146C22×C19#46511yescharacteristic
147C22×C19#46711yescharacteristic
148C22×C19#47111yescharacteristic
149C22×C19#47211yescharacteristic
150C4×C19—21no—
151C4×C19—21no—
152C4×C19—42no—
153C4×C19—42no—
154C4×C19C4×SD1611yescharacteristic
155C4×C19C4×Q1611yescharacteristic
156C4×C19C4×Q1611yescharacteristic
157C4×C19#44011yescharacteristic
158C4×C19#48411yescharacteristic
159C4×C19#48511yescharacteristic
160C4×C19#48711yescharacteristic
161C4×C19#48811yescharacteristic
162Dic19—82no—
163Dic19—161no—
164C2×C4⋊Q8—191no—
165C2×#107—381no—
166C2×C4⋊C8—191no—
167C2×C4⋊C8—191no—
168C2×C4⋊C8C2×D1911yescharacteristic
169C2×C4×C8—21no—
170C2×C4×C8C2×D1911yescharacteristic
171#384—191no—
172C4×C4⋊C4C2×D1911yescharacteristic
173#340—381no—
174#340—381no—
175#340—381no—
176#340—381no—
177#340—381no—
178#336—21no—
179#333—194no—
180C2×C19#167211yescharacteristic
181C2×C19#167611yescharacteristic
182C2×C19#167711yescharacteristic
183C2×C19#168311yescharacteristic
184C2×C19#192811yescharacteristic
185C2×C19#193111yescharacteristic
186C2×C19#193311yescharacteristic
187C22×Q8—381no—
188C22×C8—21no—
189C22×C8—381no—
190C22×C8—381no—
191C22×C8C22⋊D1911yescharacteristic
192C22×C8C22⋊D1911yescharacteristic
193C4⋊Q8—192no—
194C4⋊Q8—381no—
195C4⋊Q8—381no—
196C4⋊Q8—381no—
197C2×C4⋊C4—381no—
198C2×C4⋊C4—381no—
199C2×C4⋊C4—381no—
200C2×C4⋊C4—381no—
201C2×C4⋊C4—381no—
202C2×C4⋊C4D7611yescharacteristic
203C2×C4⋊C4D7611yescharacteristic
204C2×C42—21no—
205C2×C42C22×D1911yescharacteristic
206#107—762no—
207C4⋊C8—21no—
208C4⋊C8—192no—
209C4⋊C8—381no—
210C4⋊C8—381no—
211C4⋊C8—381no—
212C4⋊C8C4×D1912yes—
213C4×C8—21no—
214C4×C8—21no—
215C4×C8—42no—
216#95—21no—
217C19#956811yescharacteristic, complemented, Sylow
218C2×Q8—382no—
219C2×Q8—761no—
220C2×Q8—1521no—
221C2×Q8—1521no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—761no—
225C22×C4—761no—
226C22×C4C2×D7611yescharacteristic
227C22×C4#6454111yescharacteristic
228C22×C4C2×C22⋊D1911yescharacteristic
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—22no—
234C2×C8—21no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—382no—
238C2×C8—761no—
239C2×C8—761no—
240C2×C8—761no—
241C2×C8—761no—
242C2×C8—761no—
243C2×C8#6452812yes—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—382no—
247C4⋊C4—382no—
248C4⋊C4—761no—
249C4⋊C4—761no—
250C4⋊C4—761no—
251C4⋊C4—761no—
252C4⋊C4—761no—
253C4⋊C4—761no—
254C4⋊C4—1521no—
255C4⋊C4#6451612yes—
256C4⋊C4Dic7612yes—
257C42—41no—
258C42—41no—
259C42C2×C4×D1911yescharacteristic
260C42#6454111yescharacteristic
261C42#6454111yescharacteristic
262C42#6454111yescharacteristic
263C23#1059737611yescharacteristic
264Q8—1522no—
265Q8—1522no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—762no—
275C2×C4—1521no—
276C2×C4—1521no—
277C2×C4—1521no—
278C2×C4—1521no—
279C2×C4—1521no—
280C2×C4#1059731811yescharacteristic
281C2×C4C4×D7611yescharacteristic
282C2×C4#1059732111yescharacteristic
283C2×C4#1059732211yescharacteristic
284C2×C4C2×#6451611yescharacteristic
285C2×C4#1059735011yescharacteristic
286C2×C4#1059735011yescharacteristic
287C2×C4C2×Dic7611yescharacteristic
288C2×C4C4×C22⋊D1911yescharacteristic
289C2×C4#1059737511yescharacteristic
290C2×C4#1059737811yescharacteristic
291C2×C4C2×#6452811yescharacteristic
292C2×C4#1059739611yescharacteristic
293C2×C4#1059739711yescharacteristic
294C8—22no—
295C8—41no—
296C8—42no—
297C8—762no—
298C8—1521no—
299C22#1192643511yescharacteristic
300C22#1192675411yescharacteristic
301C22#1192675911yescharacteristic
302C22#1192677311yescharacteristic
303C22#1192678511yescharacteristic
304C22#1192680711yescharacteristic
305C22#1192681411yescharacteristic
306C4—21no—
307C4—21no—
308C4—42no—
309C4—42no—
310C4—3041no—
311C4—1522no—
312C4C4×#6451611yescharacteristic
313C4C4×#6452811yescharacteristic
314C4C4×Dic7611yescharacteristic
315C4#1192664411yescharacteristic
316C4#1192687911yescharacteristic
317C4#1192688511yescharacteristic
318C4#1192689511yescharacteristic
319C4#1192689911yescharacteristic
320C2#1456301711yescharacteristic
321C2#1456303911yescharacteristic
322C2#1456304411yescharacteristic
323C2#1456308611yescharacteristic
324C2#1456427611yescharacteristic
325C2#1456429711yescharacteristic
326C2#1456431111yescharacteristic
subgroupG/H
centerC23#10597376
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC8×C4⋊C4×C19C2
socle, prime radicalC23×C19#121
cosocleC2×C42×C19C23
hypercenterC8×C4⋊C4D19
hypocenterC19#9568
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C8×C4⋊C4

Complements

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

NH ≅ G/Ntype
18. #11926292C4semidirect
217. C19#9568semidirect

Maximal subgroups

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

subgroupindex
#145645962
#145645832
#145643932
C2×#119262922
#145615192
#145614702
C8×C4⋊C4×C192
#956819