Finite Group Databasebeta

← #18070622

Subgroups — #18070622

Order 4864.

482 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
1#14566099C211yesmaximal, characteristic
2#14563778C211yesmaximal, characteristic, complemented
3#14561457C212yesmaximal, complemented
4#14561455C212yesmaximal
5C19×#1831C211yesmaximal, characteristic, complemented
6C2×C4×D76C411yescharacteristic
7C2×#10597318—21no—
8#11926446C411yescharacteristic
9#11926446C2211yescharacteristic
10#11926442C411yescharacteristic
11#11926442C2211yescharacteristic
12#11926435—21no—
13#11926435—21no—
14C4×C4⋊Dic19C411yescharacteristic
15C4×(C2×D19)⋊C4—21no—
16#11926299—21no—
17#11926299—21no—
18#11926299C2212yes—
19C2×C19×C4⋊C8—21no—
20C43×C19C2211yescharacteristic
21C19×#336—21no—
22C19×#336C2212yes—
23C22×D76C2×C411yescharacteristic
24C22×C4×D19—21no—
25C22×C8×C19—22no—
26C2×C42×C19C2×C411yescharacteristic
27C2×C42×C19C2×C411yescharacteristic
28C2×C42×C19D411yescharacteristic
29C2×C42×C19D411yescharacteristic
30C2×C42×C19D411yescharacteristic
31C2×C42×C19D411yescharacteristic
32C2×C42×C19C2311yescharacteristic
33C2×(C2×D19)⋊C4—21no—
34C2×(C2×D19)⋊C4—21no—
35C2×(C2×D19)⋊C4—21no—
36C2×(C2×D19)⋊C4—21no—
37C2×(C2×D19)⋊C4—21no—
38C2×C4⋊Dic19C2×C411yescharacteristic
39C2×C4⋊Dic19C2×C411yescharacteristic
40C2×C4⋊Dic19C2×C411yescharacteristic
41C2×Dic19⋊C4—21no—
42C2×Dic19⋊C4—21no—
43C2×C4×Dic19—21no—
44C22×C19⋊C8—22no—
45C4×D76—22no—
46C4×D76C814yescomplemented
47#10597318—44no—
48C19×C4⋊C8—42no—
49C19⋊#95—21no—
50C19⋊#95—21no—
51C19⋊#95—21no—
52C23×D19—21no—
53C22×C4×C19C22⋊C411yescharacteristic
54C22×C4×C19C22⋊C411yescharacteristic
55C22×C4×C19C22⋊C411yescharacteristic
56C22×C4×C19C22⋊C411yescharacteristic
57C22×C4×C19C22×C411yescharacteristic
58C22×C4×C19C2×D411yescharacteristic
59C22×C4×C19C2×D411yescharacteristic
60C22×Dic19—21no—
61C22×Dic19—21no—
62C22×Dic19—21no—
63C2×D76—21no—
64C2×D76—41no—
65C2×D76—41no—
66C2×D76C2×C812yes—
67C2×C4×D19—24no—
68C2×C4×D19—42no—
69C2×C4×D19—42no—
70C2×C8×C19—42no—
71C2×C8×C19—42no—
72C2×C8×C19—42no—
73C42×C19—21no—
74C42×C19—22no—
75C42×C19—21no—
76C42×C19—41no—
77C42×C19—41no—
78C42×C19—41no—
79C42×C19—41no—
80C42×C19C2×C812yes—
81C42×C19M1612yes—
82(C2×D19)⋊C4—24no—
83(C2×D19)⋊C4—42no—
84(C2×D19)⋊C4—42no—
85(C2×D19)⋊C4—42no—
86(C2×D19)⋊C4—41no—
87(C2×D19)⋊C4—41no—
88C4⋊Dic19—21no—
89C4⋊Dic19—41no—
90C4⋊Dic19—41no—
91C4⋊Dic19C2×C812yes—
92Dic19⋊C4—42no—
93Dic19⋊C4—42no—
94C4×Dic19—42no—
95C2×C19⋊C8—42no—
96C2×C19⋊C8—42no—
97C2×C19⋊C8—42no—
98#7594—191nomaximal, Sylow
99C23×C19C2×C22⋊C411yescharacteristic
100C22×D19—22no—
101C22×D19—41no—
102C22×D19—41no—
103C22×D19—41no—
104C22×D19—41no—
105C22×D19—41no—
106C22×D19—41no—
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19C22⋊C812yes—
124C2×C4×C19C22⋊C812yes—
125C2×C4×C19C22×C811yescharacteristic
126C2×C4×C19C2×M1611yescharacteristic
127C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C19AGL(1,ℤ/8)12yes—
129C2×C4×C19#13711yescharacteristic
130C2×Dic19—22no—
131C2×Dic19—41no—
132C2×Dic19—41no—
133C2×Dic19—41no—
134C2×Dic19—41no—
135C2×Dic19—41no—
136C2×Dic19—41no—
137C2×Dic19—41no—
138C2×Dic19—41no—
139D76—42no—
140D76—42no—
141C4×D19—48no—
142C8×C19—82no—
143C19⋊C8—82no—
144#2293—191no—
145#1839—191no—
146#1831D1911yescharacteristic, complemented
147#1271—192no—
148#1270—192no—
149C22×C19C2×C22⋊C811yescharacteristic
150C22×C19#41011yescharacteristic
151C22×C19#41311yescharacteristic
152C22×C19#41711yescharacteristic
153C22×C19#41811yescharacteristic
154C22×C19#42111yescharacteristic
155C22×C19#42111yescharacteristic
156C2×D19—42no—
157C2×D19—42no—
158C2×D19—42no—
159C2×D19—81no—
160C2×D19—81no—
161C2×D19—81no—
162C2×D19—81no—
163C4×C19—21no—
164C4×C19—21no—
165C4×C19—22no—
166C4×C19—22no—
167C4×C19—21no—
168C4×C19—21no—
169C4×C19—22no—
170C4×C19—41no—
171C4×C19—41no—
172Dic19—42no—
173Dic19—81no—
174Dic19—81no—
175C2×C4×D4—191no—
176C2×#117—381no—
177C2×C4⋊C8—21no—
178#390—191no—
179#390—191no—
180#389—191no—
181#389—191no—
182#388—381no—
183#388—381no—
184C4×C4⋊C4—191no—
185C4×C22⋊C4—381no—
186C43C2×D1911yescharacteristic
187#336—21no—
188#336—192no—
189#336—381no—
190#336—381no—
191#336C2×D1912yes—
192C2×C19#145811yescharacteristic
193C2×C19#147711yescharacteristic
194C2×C19#147811yescharacteristic
195C2×C19#151211yescharacteristic
196C2×C19#151411yescharacteristic
197C2×C19#153511yescharacteristic
198C2×C19#155711yescharacteristic
199D19—82no—
200C22×D4—191no—
201C23×C4—381no—
202C22×C8—22no—
203C22×C8—382no—
204C4×D4—194no—
205C4×D4—382no—
206#117—764no—
207C2×C4⋊C4—191no—
208C2×C4⋊C4—191no—
209C2×C4⋊C4—191no—
210C2×C4⋊C4—381no—
211C2×C4⋊C4—381no—
212C2×C22⋊C4—381no—
213C2×C22⋊C4—381no—
214C2×C22⋊C4—381no—
215C2×C22⋊C4—381no—
216C2×C22⋊C4—381no—
217C2×C42—381no—
218C2×C42C4×D1911yescharacteristic
219C2×C42C4×D1911yescharacteristic
220C2×C42D7611yescharacteristic
221C2×C42D7611yescharacteristic
222C2×C42C22⋊D1911yescharacteristic
223C2×C42C22⋊D1911yescharacteristic
224C2×C42C22×D1911yescharacteristic
225C4⋊C8—42no—
226#95—381no—
227#95—381no—
228#95—381no—
229C19#759411yescharacteristic, complemented, Sylow
230C24—381no—
231C2×D4—192no—
232C2×D4—381no—
233C2×D4—761no—
234C2×D4—761no—
235C22×C4—381no—
236C22×C4—384no—
237C22×C4—381no—
238C22×C4—381no—
239C22×C4—762no—
240C22×C4—762no—
241C22×C4(C2×D19)⋊C411yescharacteristic
242C22×C4(C2×D19)⋊C411yescharacteristic
243C22×C4(C2×D19)⋊C411yescharacteristic
244C22×C4(C2×D19)⋊C411yescharacteristic
245C22×C4C2×C4×D1911yescharacteristic
246C22×C4C2×D7611yescharacteristic
247C22×C4C2×C22⋊D1911yescharacteristic
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—762no—
252C2×C8—762no—
253C2×C8—762no—
254C4⋊C4—192no—
255C4⋊C4—381no—
256C4⋊C4—761no—
257C4⋊C4—761no—
258C4⋊C4—762no—
259C4⋊C4—762no—
260C22⋊C4—384no—
261C22⋊C4—762no—
262C22⋊C4—762no—
263C22⋊C4—761no—
264C22⋊C4—761no—
265C22⋊C4—762no—
266C42—21no—
267C42—21no—
268C42—22no—
269C42—41no—
270C42—41no—
271C42—41no—
272C42—41no—
273C42—762no—
274C42C8×D1912yes—
275C42#6451512yes—
276C23—382no—
277C23—761no—
278C23—761no—
279C23—761no—
280C23—761no—
281C23—761no—
282C23—761no—
283C23C2×(C2×D19)⋊C411yescharacteristic
284D4—762no—
285D4—762no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—382no—
303C2×C4—768no—
304C2×C4—761no—
305C2×C4—761no—
306C2×C4—761no—
307C2×C4—761no—
308C2×C4—761no—
309C2×C4—761no—
310C2×C4—761no—
311C2×C4—761no—
312C2×C4(C2×D19)⋊C812yes—
313C2×C4(C2×D19)⋊C812yes—
314C2×C4C2×C8×D1911yescharacteristic
315C2×C4C2×#6451511yescharacteristic
316C2×C4#1059735412yes—
317C2×C4#1059737811yescharacteristic
318C2×C4#1059738811yescharacteristic
319C8—82no—
320C8—1522no—
321C22—762no—
322C22—762no—
323C22—762no—
324C22—1521no—
325C22—1521no—
326C22—1521no—
327C22—1521no—
328C22C2×(C2×D19)⋊C811yescharacteristic
329C22#1192651711yescharacteristic
330C22#1192652611yescharacteristic
331C22#1192654311yescharacteristic
332C22#1192655011yescharacteristic
333C22#1192656011yescharacteristic
334C22#1192656211yescharacteristic
335C4—21no—
336C4—21no—
337C4—22no—
338C4—21no—
339C4—21no—
340C4—22no—
341C4—22no—
342C4—41no—
343C4—41no—
344C4—762no—
345C4—1521no—
346C4—1521no—
347C2—1522no—
348C2#1456194711yescharacteristic
349C2#1456202011yescharacteristic
350C2#1456202711yescharacteristic
351C2#1456217111yescharacteristic
352C2#1456218311yescharacteristic
353C2#1456226411yescharacteristic
354C2#1456235511yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC2×C4×C19C22×C8
FrattiniC2×C42C22×D19
FittingC19×#1831C2
socleC23×C19C2×C22⋊C4
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenter#1831D19
hypocenterC19#7594
LCSG ▷ C2×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C43 ◁ #1831

Complements

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

NH ≅ G/Ntype
2. #14563778C2semidirect
3. #14561457C2semidirect
5. C19×#1831C2semidirect
46. C4×D76C8semidirect
146. #1831D19semidirect
229. C19#7594semidirect

Maximal subgroups

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

subgroupindex
#145660992
#145637782
#145614572
#145614552
C19×#18312
#759419