Finite Group Databasebeta

← #18073376

Subgroups — #18073376

Order 4864.

538 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926622C211yesmaximal, characteristic
2#14563505C211yesmaximal, characteristic, complemented
3C4×#10597289C211yesmaximal, characteristic
4C2×#11926266C211yesmaximal, characteristic, complemented
5#14561475C211yesmaximal, characteristic, complemented
6#14561469C211yesmaximal, characteristic, complemented
7C2×C19×D4⋊C8C211yesmaximal, characteristic
8C22×#64520—21no—
9#11926622—22no—
10#11926622C414yescomplemented
11C2×C4⋊(C19⋊C8)C2211yescharacteristic
12C2×#10597289C412yes—
13C2×C22⋊(C19⋊C8)—21no—
14C2×#10597272—21no—
15C2×C4×C19⋊C8C2211yescharacteristic
16C2×C4×C19⋊C8C2211yescharacteristic
17C4×C4⋊Dic19C2211yescharacteristic
18#11926306C412yes—
19#11926298—21no—
20#11926266—22no—
21C2×C4×D4×C19C2211yescharacteristic
22C2×C19×C4⋊C8C2211yescharacteristic
23C2×C4×C8×C19C2211yescharacteristic
24C19×D4⋊C8C414yescomplemented
25C22×D4×C19C2×C411yescharacteristic
26C23×C4×C19—21no—
27C22×C8×C19—21no—
28C22×C8×C19—21no—
29C4×D4×C19—21no—
30C4×D4×C19—21no—
31C4×D4×C19C2×C412yes—
32C4×D4×C19C2×C412yes—
33C2×C4⋊C4×C19C2×C411yescharacteristic
34C2×C22⋊C4×C19—21no—
35C2×C42×C19C2311yescharacteristic
36C2×C4⋊Dic19C2×C412yes—
37C2×C4×Dic19—21no—
38C2×#64520—24no—
39C2×#64520—42no—
40C2×#64520—42no—
41C22×C19⋊C8—21no—
42C22×C19⋊C8C2×C412yes—
43C22×C19⋊C8D411yescharacteristic
44C22×C19⋊C8D411yescharacteristic
45C19×C4⋊C8—21no—
46C19×C4⋊C8C2×C412yes—
47C4×C8×C19—21no—
48C4×C8×C19C2×C412yes—
49#10597289—24no—
50C19⋊#95—21no—
51C22⋊(C19⋊C8)—24no—
52#10597272—42no—
53C4⋊(C19⋊C8)—21no—
54C4⋊(C19⋊C8)C2×C412yes—
55C4×C19⋊C8—21no—
56C4×C19⋊C8—21no—
57C4×C19⋊C8C2×C412yes—
58C4×C19⋊C8D412yes—
59C24×C19—21no—
60C2×D4×C19—21no—
61C2×D4×C19—22no—
62C2×D4×C19—22no—
63C2×D4×C19C4212yes—
64C22×C4×C19—21no—
65C22×C4×C19—22no—
66C22×C4×C19—22no—
67C22×C4×C19—41no—
68C22×C4×C19—41no—
69C22×C4×C19—41no—
70C22×C4×C19—41no—
71C22×C4×C19C22×C411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19#4111yescharacteristic
74C22×Dic19—22no—
75C2×C8×C19—22no—
76C2×C8×C19—22no—
77C2×C8×C19—42no—
78C2×C8×C19—41no—
79C2×C8×C19—41no—
80C4⋊C4×C19—21no—
81C4⋊C4×C19C4212yes—
82C22⋊C4×C19—22no—
83C22⋊C4×C19—22no—
84C42×C19C22×C411yescharacteristic
85C42×C19C22×C411yescharacteristic
86C42×C19C2×D411yescharacteristic
87C42×C19#4111yescharacteristic
88C4⋊Dic19—22no—
89C4⋊Dic19—22no—
90C4×Dic19—41no—
91C4×Dic19—41no—
92#64520—48no—
93C2×C19⋊C8—22no—
94C2×C19⋊C8—22no—
95C2×C19⋊C8—21no—
96C2×C19⋊C8—21no—
97C2×C19⋊C8—21no—
98C2×C19⋊C8—21no—
99C2×C19⋊C8—22no—
100C2×C19⋊C8—41no—
101C2×C19⋊C8—41no—
102C2×C19⋊C8C22⋊C412yes—
103C2×C19⋊C8C22⋊C412yes—
104C2×C19⋊C8M1614yescomplemented
105#8208—191nomaximal, Sylow
106C23×C19—22no—
107C23×C19—42no—
108C23×C19—41no—
109C23×C19—41no—
110C23×C19—42no—
111C23×C19C4×D411yescharacteristic
112D4×C19—22no—
113D4×C19—22no—
114D4×C19—42no—
115C2×C4×C19—22no—
116C2×C4×C19—22no—
117C2×C4×C19—41no—
118C2×C4×C19—41no—
119C2×C4×C19—42no—
120C2×C4×C19—42no—
121C2×C4×C19—42no—
122C2×C4×C19—42no—
123C2×C4×C19C2×C4211yescharacteristic
124C2×C4×C19C2×C22⋊C411yescharacteristic
125C2×C4×C19#11711yescharacteristic
126C2×C4×C19C4×D411yescharacteristic
127C2×C4×C19C4×D411yescharacteristic
128C2×C4×C19C4×D411yescharacteristic
129C2×C4×C19C2×M1612yes—
130C2×C4×C19#13112yes—
131C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C19#13711yescharacteristic
135C2×Dic19—42no—
136C2×Dic19—42no—
137C2×Dic19—42no—
138C8×C19—42no—
139C8×C19—42no—
140C19⋊C8—22no—
141C19⋊C8—22no—
142C19⋊C8—24no—
143C19⋊C8—42no—
144C2×#436—191no—
145#1770—191no—
146C4×#102—191no—
147C2×D4⋊C8D1911yescharacteristic
148C2×#322—191no—
149#1279—191no—
150#1277—191no—
151C22×C19—42no—
152C22×C19—42no—
153C22×C19—42no—
154C22×C19—82no—
155C22×C19—82no—
156C22×C19C4×C22⋊C411yescharacteristic
157C22×C19#43612yes—
158C22×C19#44011yescharacteristic
159C22×C19#44211yescharacteristic
160C22×C19#44412yes—
161C4×C19—21no—
162C4×C19—21no—
163C4×C19—42no—
164C4×C19C4×M1611yescharacteristic
165C4×C19#40511yescharacteristic
166C4×C19#41711yescharacteristic
167C4×C19#41811yescharacteristic
168C4×C19#43512yes—
169C4×C19#44011yescharacteristic
170C4×C19#44211yescharacteristic
171Dic19—82no—
172C22×M16—381no—
173C2×C4×D4C2×D1911yescharacteristic
174#436—194no—
175#436—382no—
176C2×C4⋊C8—191no—
177C2×C4⋊C8C2×D1911yescharacteristic
178C2×#102—192no—
179C2×C22⋊C8—381no—
180C2×#97—381no—
181C2×C4×C8—191no—
182C2×C4×C8—191no—
183C2×C4×C8C2×D1911yescharacteristic
184C4×C4⋊C4—191no—
185#340—192no—
186#336—381no—
187D4⋊C8Dic1914yescomplemented
188#322—382no—
189C2×C19—82no—
190C2×C19#159212yes—
191C2×C19#159412yes—
192C2×C19#175311yescharacteristic
193C2×C19#176211yescharacteristic
194C2×C19#176511yescharacteristic
195C22×D4C4×D1911yescharacteristic
196C23×C4—21no—
197C2×M16—384no—
198C2×M16—762no—
199C2×M16—762no—
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—192no—
203C22×C8—191no—
204C22×C8—191no—
205C22×C8—381no—
206C4×D4—21no—
207C4×D4—21no—
208C4×D4C4×D1912yes—
209C4×D4C2×Dic1912yes—
210C2×C4⋊C4—192no—
211C2×C4⋊C4C4×D1911yescharacteristic
212C2×C22⋊C4—21no—
213C2×C42—381no—
214C2×C42C22×D1911yescharacteristic
215C4⋊C8—21no—
216C4⋊C8—192no—
217C4⋊C8—381no—
218C4⋊C8C2×Dic1912yes—
219#102—384no—
220C22⋊C8—384no—
221#97—762no—
222C4×C8—21no—
223C4×C8—192no—
224C4×C8—192no—
225C4×C8—381no—
226C4×C8—381no—
227C4×C8C2×Dic1912yes—
228#95—381no—
229C19#820811yescharacteristic, complemented, Sylow
230C24—21no—
231C2×D4—21no—
232C2×D4—22no—
233C2×D4—22no—
234C2×D4C4×Dic1912yes—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—382no—
243C22×C4C2×C4×D1911yescharacteristic
244C22×C4D4×D1911yescharacteristic
245C22×C4#6454311yescharacteristic
246M16—768no—
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—42no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—192no—
253C2×C8—192no—
254C2×C8—194no—
255C2×C8—382no—
256C2×C8—382no—
257C2×C8—381no—
258C2×C8—381no—
259C2×C8—381no—
260C2×C8—381no—
261C2×C8—382no—
262C2×C8—761no—
263C2×C8—761no—
264C4⋊C4—21no—
265C4⋊C4—382no—
266C4⋊C4—382no—
267C4⋊C4C4×Dic1912yes—
268C22⋊C4—22no—
269C22⋊C4—22no—
270C42—761no—
271C42—761no—
272C42C2×C4×D1911yescharacteristic
273C42D4×D1911yescharacteristic
274C42#6454311yescharacteristic
275C42C22×Dic1911yescharacteristic
276C23—22no—
277C23—42no—
278C23—41no—
279C23—41no—
280C23—42no—
281C23(C22⋊D19)⋊C411yescharacteristic
282D4—22no—
283D4—22no—
284D4—42no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—762no—
294C2×C4—762no—
295C2×C4—762no—
296C2×C4#1059732311yescharacteristic
297C2×C4C22⋊C4×D1911yescharacteristic
298C2×C4(C22⋊D19)⋊C411yescharacteristic
299C2×C4#1059734712yes—
300C2×C4M16×D1912yes—
301C2×C4#1059735711yescharacteristic
302C2×C4#1059735711yescharacteristic
303C2×C4#1059736011yescharacteristic
304C2×C4#1059736111yescharacteristic
305C2×C4C2×C4×Dic1911yescharacteristic
306C2×C4D4×Dic1911yescharacteristic
307C2×C4D4×Dic1911yescharacteristic
308C8—42no—
309C8—42no—
310C8—382no—
311C8—382no—
312C8—384no—
313C8—762no—
314C22—42no—
315C22—42no—
316C22—42no—
317C22—82no—
318C22—82no—
319C22C22⋊C4×Dic1911yescharacteristic
320C22#1192661912yes—
321C22#1192664111yescharacteristic
322C22#1192665311yescharacteristic
323C22#1192666312yes—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—1522no—
328C4M16×Dic1911yescharacteristic
329C4#1192649911yescharacteristic
330C4#1192654211yescharacteristic
331C4#1192654711yescharacteristic
332C4#1192661812yes—
333C4#1192664511yescharacteristic
334C4#1192665611yescharacteristic
335C2—82no—
336C2#1456253412yes—
337C2#1456254612yes—
338C2#1456342111yescharacteristic
339C2#1456346211yescharacteristic
340C2#1456348011yescharacteristic
subgroupG/H
centerC22×C4D4×D19
commutatorC2×C4×C19C2×C42
FrattiniC2×C42C22×D19
FittingC2×C19×D4⋊C8C2
socleC23×C19C4×D4
prime radicalC22×D4×C19C2×C4
cosocleC2×C42×C19C23
hypercenterC2×D4⋊C8D19
hypocenterC19#8208
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #14563505C2semidirect
4. C2×#11926266C2semidirect
5. #14561475C2semidirect
6. #14561469C2semidirect
10. #11926622C4semidirect
24. C19×D4⋊C8C4semidirect
104. C2×C19⋊C8M16semidirect
187. D4⋊C8Dic19semidirect
229. C19#8208semidirect

Maximal subgroups

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

subgroupindex
C2×#119266222
#145635052
C4×#105972892
C2×#119262662
#145614752
#145614692
C2×C19×D4⋊C82
#820819