Finite Group Databasebeta

← #18076204

Subgroups — #18076204

Order 4864.

378 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14563786C211yesmaximal, characteristic
2#14563751C211yesmaximal, characteristic
3C4×#10597272C211yesmaximal, characteristic
4#14561470C211yesmaximal, characteristic
5#14561469C211yesmaximal, characteristic
6#14561469C211yesmaximal, characteristic
7C19×#1277C211yesmaximal, characteristic
8C2×C4⋊(C19⋊C8)C2211yescharacteristic
9C2×C4⋊(C19⋊C8)C2211yescharacteristic
10C2×Dic19⋊C8—21no—
11C2×Dic19⋊C8—21no—
12C2×#10597272C411yescharacteristic
13C2×#10597272C411yescharacteristic
14C2×#10597272C411yescharacteristic
15C2×#10597272C411yescharacteristic
16C2×C4×C19⋊C8C2211yescharacteristic
17C42×Dic19C2211yescharacteristic
18#11926298—21no—
19#11926298—21no—
20C2×C19×C4⋊C8C2211yescharacteristic
21C2×C19×C4⋊C8C2211yescharacteristic
22C2×C4×C8×C19C2211yescharacteristic
23C22×C8×C19—21no—
24C22×C8×C19—21no—
25C22×C8×C19C2×C411yescharacteristic
26C22×C8×C19C2×C411yescharacteristic
27C2×C42×C19C2311yescharacteristic
28C2×C4×Dic19C2×C411yescharacteristic
29C2×C4×Dic19C2×C411yescharacteristic
30C2×C4×Dic19D411yescharacteristic
31C2×C4×Dic19D411yescharacteristic
32C2×C4×Dic19Q811yescharacteristic
33C2×C4×Dic19Q811yescharacteristic
34C22×C19⋊C8—21no—
35C22×C19⋊C8—21no—
36C22×C19⋊C8C2×C411yescharacteristic
37C22×C19⋊C8C2×C411yescharacteristic
38C19×C4⋊C8—21no—
39C19×C4⋊C8—21no—
40C19×C4⋊C8—21no—
41C19×C4⋊C8—21no—
42C4×C8×C19—21no—
43C4×C8×C19—21no—
44#10597272—22no—
45#10597272—22no—
46#10597272—22no—
47#10597272C814yescomplemented
48Dic19⋊C8—42no—
49Dic19⋊C8—42no—
50C4⋊(C19⋊C8)—21no—
51C4⋊(C19⋊C8)—21no—
52C4⋊(C19⋊C8)—21no—
53C4⋊(C19⋊C8)—21no—
54C4×C19⋊C8—21no—
55C4×C19⋊C8—21no—
56C22×C4×C19C22×C411yescharacteristic
57C22×C4×C19C2×D411yescharacteristic
58C22×C4×C19C2×Q811yescharacteristic
59C22×Dic19C4⋊C411yescharacteristic
60C22×Dic19C4⋊C411yescharacteristic
61C22×Dic19C4⋊C411yescharacteristic
62C22×Dic19C4⋊C411yescharacteristic
63C2×C8×C19—21no—
64C2×C8×C19—21no—
65C2×C8×C19—21no—
66C2×C8×C19—21no—
67C2×C8×C19—41no—
68C2×C8×C19—41no—
69C2×C8×C19—41no—
70C2×C8×C19—41no—
71C2×C8×C19—41no—
72C2×C8×C19—41no—
73C2×C8×C19C2×C812yes—
74C2×C8×C19M1612yes—
75C42×C19#4111yescharacteristic
76C42×C19#4111yescharacteristic
77C42×C19#4111yescharacteristic
78C42×C19#4111yescharacteristic
79C4×Dic19—21no—
80C4×Dic19—21no—
81C4×Dic19—21no—
82C4×Dic19—21no—
83C4×Dic19—21no—
84C4×Dic19—21no—
85C4×Dic19—41no—
86C4×Dic19—41no—
87C4×Dic19C2×C812yes—
88C4×Dic19M1612yes—
89C2×C19⋊C8—21no—
90C2×C19⋊C8—21no—
91C2×C19⋊C8—21no—
92C2×C19⋊C8—21no—
93C2×C19⋊C8—41no—
94C2×C19⋊C8—41no—
95C2×C19⋊C8—41no—
96C2×C19⋊C8—41no—
97C2×C19⋊C8—41no—
98C2×C19⋊C8—41no—
99C2×C19⋊C8C2×C812yes—
100C2×C19⋊C8M1612yes—
101#8786—191nomaximal, Sylow
102C23×C19C2×C4⋊C411yescharacteristic
103C2×C4×C19—21no—
104C2×C4×C19—21no—
105C2×C4×C19#11711yescharacteristic
106C2×C4×C19#11711yescharacteristic
107C2×C4×C19#12411yescharacteristic
108C2×C4×C19#12411yescharacteristic
109C2×C4×C19#12511yescharacteristic
110C2×C4×C19#12511yescharacteristic
111C2×C4×C19C22×C811yescharacteristic
112C2×C4×C19C2×M1611yescharacteristic
113C2×C4×C19C2×M1611yescharacteristic
114C2×C4×C19C2×M1611yescharacteristic
115C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C19#13711yescharacteristic
118C2×C4×C19#13711yescharacteristic
119C2×Dic19—21no—
120C2×Dic19—21no—
121C2×Dic19—21no—
122C2×Dic19—21no—
123C2×Dic19—21no—
124C2×Dic19—21no—
125C2×Dic19—21no—
126C2×Dic19—21no—
127C2×Dic19—21no—
128C2×Dic19—21no—
129C2×Dic19C4⋊C812yes—
130C2×Dic19C4⋊C812yes—
131C8×C19—22no—
132C8×C19—22no—
133C8×C19—81no—
134C8×C19—81no—
135C19⋊C8—22no—
136C19⋊C8—22no—
137C19⋊C8—81no—
138C19⋊C8—81no—
139#1842—191no—
140#1831—191no—
141C4×#97—191no—
142#1277—191no—
143#1277—191no—
144#1277—191no—
145#1277D1911yescharacteristic
146C22×C19#38211yescharacteristic
147C22×C19C2×C4⋊C811yescharacteristic
148C22×C19#42311yescharacteristic
149C22×C19#42811yescharacteristic
150C22×C19#42811yescharacteristic
151C22×C19#43011yescharacteristic
152C22×C19#43011yescharacteristic
153C4×C19—21no—
154C4×C19—21no—
155C4×C19#43111yescharacteristic
156C4×C19#43111yescharacteristic
157C4×C19#43211yescharacteristic
158C4×C19#43211yescharacteristic
159C4×C19#48911yescharacteristic
160C4×C19#48911yescharacteristic
161C4×C19#49011yescharacteristic
162C4×C19#49111yescharacteristic
163Dic19—22no—
164Dic19—22no—
165Dic19—41no—
166Dic19—41no—
167C2×C4⋊C8—191no—
168C2×C4⋊C8—191no—
169C2×C4⋊C8—381no—
170C2×C4⋊C8—381no—
171C2×C4⋊C8C2×D1911yescharacteristic
172C2×C4⋊C8C2×D1911yescharacteristic
173C2×#97—191no—
174C2×#97—191no—
175C2×#97—191no—
176C2×#97—191no—
177C2×C4×C8—191no—
178C2×C4×C8C2×D1911yescharacteristic
179C43—191no—
180#336—381no—
181#336—381no—
182C2×C19#156511yescharacteristic
183C2×C19#156511yescharacteristic
184C2×C19#156911yescharacteristic
185C2×C19#156911yescharacteristic
186C2×C19#183111yescharacteristic
187C2×C19#183611yescharacteristic
188C2×C19#183811yescharacteristic
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—191no—
192C22×C8—191no—
193C22×C8—381no—
194C22×C8—381no—
195C22×C8C4×D1911yescharacteristic
196C22×C8C4×D1911yescharacteristic
197C2×C42—191no—
198C2×C42—191no—
199C2×C42—191no—
200C2×C42—191no—
201C2×C42—191no—
202C2×C42—191no—
203C2×C42C22×D1911yescharacteristic
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—381no—
209C4⋊C8—381no—
210C4⋊C8—381no—
211C4⋊C8—381no—
212C4⋊C8—762no—
213C4⋊C8—762no—
214#97—194no—
215#97—382no—
216#97—382no—
217#97—382no—
218C4×C8—21no—
219C4×C8—21no—
220C4×C8—381no—
221C4×C8—381no—
222C19#878611yescharacteristic, complemented, Sylow
223C22×C4—191no—
224C22×C4—191no—
225C22×C4—191no—
226C22×C4—191no—
227C22×C4C2×C4×D1911yescharacteristic
228C22×C4D4×D1911yescharacteristic
229C22×C4Q8×D1911yescharacteristic
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—192no—
241C2×C8—192no—
242C2×C8—381no—
243C2×C8—381no—
244C2×C8—381no—
245C2×C8—381no—
246C2×C8—761no—
247C2×C8—761no—
248C2×C8—761no—
249C2×C8—761no—
250C2×C8—761no—
251C2×C8—761no—
252C2×C8C8×D1912yes—
253C2×C8#6451512yes—
254C42—192no—
255C42—192no—
256C42—381no—
257C42—381no—
258C42—381no—
259C42—381no—
260C42—381no—
261C42—381no—
262C42—761no—
263C42—761no—
264C42#6454111yescharacteristic
265C42#6454111yescharacteristic
266C42#6454311yescharacteristic
267C42#6454311yescharacteristic
268C23C4⋊C4×D1911yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—192no—
272C2×C4—192no—
273C2×C4—381no—
274C2×C4—381no—
275C2×C4—381no—
276C2×C4—381no—
277C2×C4—381no—
278C2×C4—381no—
279C2×C4—381no—
280C2×C4—381no—
281C2×C4—381no—
282C2×C4—381no—
283C2×C4#1059731811yescharacteristic
284C2×C4#1059732311yescharacteristic
285C2×C4#1059733111yescharacteristic
286C2×C4#1059733111yescharacteristic
287C2×C4#1059733511yescharacteristic
288C2×C4#1059733511yescharacteristic
289C2×C4C2×C8×D1911yescharacteristic
290C2×C4C2×#6451511yescharacteristic
291C2×C4M16×D1911yescharacteristic
292C2×C4M16×D1911yescharacteristic
293C2×C4#1059735711yescharacteristic
294C2×C4#1059736011yescharacteristic
295C2×C4#1059736111yescharacteristic
296C2×C4#1059736411yescharacteristic
297C8—22no—
298C8—22no—
299C8—81no—
300C8—81no—
301C8—382no—
302C8—382no—
303C8—1521no—
304C8—1521no—
305C22#1192640811yescharacteristic
306C22C4⋊C8×D1911yescharacteristic
307C22#1192656611yescharacteristic
308C22#1192658311yescharacteristic
309C22#1192658511yescharacteristic
310C22#1192659111yescharacteristic
311C22#1192659111yescharacteristic
312C4—21no—
313C4—21no—
314C4—382no—
315C4—382no—
316C4—761no—
317C4—761no—
318C4#1192659411yescharacteristic
319C4#1192659511yescharacteristic
320C4#1192659811yescharacteristic
321C4#1192659911yescharacteristic
322C4#1192690211yescharacteristic
323C4#1192690511yescharacteristic
324C4#1192690711yescharacteristic
325C4#1192691111yescharacteristic
326C2#1456238411yescharacteristic
327C2#1456238611yescharacteristic
328C2#1456239911yescharacteristic
329C2#1456240111yescharacteristic
330C2#1456375011yescharacteristic
331C2#1456376711yescharacteristic
332C2#1456377411yescharacteristic
subgroupG/H
centerC22×C4D4×D19
commutatorC2×C4×C19C22×C8
FrattiniC2×C42C22×D19
FittingC19×#1277C2
socle, prime radicalC23×C19C2×C4⋊C4
cosocleC2×C42×C19C23
hypercenter#1277D19
hypocenterC19#8786
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
47. #10597272C8semidirect
222. C19#8786semidirect

Maximal subgroups

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

subgroupindex
#145637862
#145637512
C4×#105972722
#145614702
#145614692
C19×#12772
#878619