Finite Group Databasebeta

← #18073402

Subgroups — #18073402

Order 4864.

550 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
2C4⋊C4×C19⋊C8C211yesmaximal, characteristic, complemented
3C2×D4⋊(C19⋊C8)C211yesmaximal, characteristic
4C2×#11926266C211yesmaximal, characteristic, complemented
5#14561476C211yesmaximal, characteristic, complemented
6#14561470C211yesmaximal, characteristic, complemented
7C4×C19×#102C211yesmaximal, characteristic
8C22×#64520—21no—
9#11926622—22no—
10#11926622C414yescomplemented
11C2×C4⋊(C19⋊C8)C2211yescharacteristic
12C2×C4⋊(C19⋊C8)C2211yescharacteristic
13C2×C22⋊(C19⋊C8)—21no—
14C2×C4×C19⋊C8—21no—
15C2×C4×C19⋊C8C2211yescharacteristic
16C2×C4×C19⋊C8C2211yescharacteristic
17#11926299—21no—
18D4⋊(C19⋊C8)C414yescomplemented
19#11926266—22no—
20C2×C4×D4×C19C2211yescharacteristic
21C2×C19×#102C412yes—
22C2×C4×C8×C19C2211yescharacteristic
23C4×C4⋊C4×C19C2211yescharacteristic
24C19×#340C412yes—
25C22×D4×C19C2×C411yescharacteristic
26C23×C4×C19—21no—
27C22×C8×C19C2×C412yes—
28C4×D4×C19—21no—
29C4×D4×C19—21no—
30C4×D4×C19C2×C412yes—
31C4×D4×C19C2×C412yes—
32C2×C4⋊C4×C19C2×C411yescharacteristic
33C2×C4⋊C4×C19C2×C412yes—
34C2×C22⋊C4×C19—21no—
35C2×C42×C19—21no—
36C2×C42×C19C2311yescharacteristic
37C2×#64520—24no—
38C2×#64520—42no—
39C2×#64520—42no—
40C22×C19⋊C8—21no—
41C22×C19⋊C8—21no—
42C22×C19⋊C8—21no—
43C22×C19⋊C8D411yescharacteristic
44C22×C19⋊C8D411yescharacteristic
45C19×#102—24no—
46C4×C8×C19—21no—
47C4×C8×C19—21no—
48C19×#95—21no—
49C22⋊(C19⋊C8)—24no—
50C4⋊(C19⋊C8)—21no—
51C4⋊(C19⋊C8)—21no—
52C4⋊(C19⋊C8)C2×C412yes—
53C4⋊(C19⋊C8)C2×C412yes—
54C4×C19⋊C8—21no—
55C4×C19⋊C8—42no—
56C4×C19⋊C8C2×C412yes—
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—22no—
65C22×C4×C19—21no—
66C22×C4×C19—22no—
67C22×C4×C19—22no—
68C22×C4×C19—41no—
69C22×C4×C19—41no—
70C22×C4×C19—41no—
71C22×C4×C19—41no—
72C22×C4×C19C22×C411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19#4111yescharacteristic
75C2×C8×C19—22no—
76C2×C8×C19—22no—
77C2×C8×C19—22no—
78C4⋊C4×C19—21no—
79C4⋊C4×C19—22no—
80C4⋊C4×C19C4212yes—
81C4⋊C4×C19M1614yescomplemented
82C22⋊C4×C19—22no—
83C22⋊C4×C19—22no—
84C42×C19—41no—
85C42×C19—41no—
86C42×C19C22×C411yescharacteristic
87C42×C19C22×C411yescharacteristic
88C42×C19C2×D411yescharacteristic
89C42×C19#4111yescharacteristic
90#64520—48no—
91C2×C19⋊C8—24no—
92C2×C19⋊C8—22no—
93C2×C19⋊C8—21no—
94C2×C19⋊C8—21no—
95C2×C19⋊C8—21no—
96C2×C19⋊C8—21no—
97C2×C19⋊C8—22no—
98C2×C19⋊C8—22no—
99C2×C19⋊C8—41no—
100C2×C19⋊C8—41no—
101C2×C19⋊C8—41no—
102C2×C19⋊C8—41no—
103C2×C19⋊C8C22⋊C412yes—
104C2×C19⋊C8C22⋊C412yes—
105#8212—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—24no—
118C2×C4×C19—41no—
119C2×C4×C19—42no—
120C2×C4×C19—41no—
121C2×C4×C19—42no—
122C2×C4×C19—42no—
123C2×C4×C19—42no—
124C2×C4×C19—42no—
125C2×C4×C19—42no—
126C2×C4×C19C2×C4211yescharacteristic
127C2×C4×C19C2×C22⋊C411yescharacteristic
128C2×C4×C19#11711yescharacteristic
129C2×C4×C19C4×D411yescharacteristic
130C2×C4×C19C4×D411yescharacteristic
131C2×C4×C19C4×D411yescharacteristic
132C2×C4×C19C2×M1612yes—
133C2×C4×C19#13112yes—
134C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C19#13711yescharacteristic
138C8×C19—42no—
139C19⋊C8—24no—
140C19⋊C8—22no—
141C19⋊C8—22no—
142C19⋊C8—42no—
143C19⋊C8—42no—
144C2×#436—191no—
145C8×C4⋊C4—191no—
146C4×#102D1911yescharacteristic
147C2×D4⋊C8—191no—
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#43512yes—
158C22×C19#44011yescharacteristic
159C22×C19#44211yescharacteristic
160C22×C19#44312yes—
161C4×C19—21no—
162C4×C19—21no—
163C4×C19—44no—
164C4×C19—42no—
165C4×C19C4×M1611yescharacteristic
166C4×C19#40511yescharacteristic
167C4×C19#41711yescharacteristic
168C4×C19#41811yescharacteristic
169C4×C19#43612yes—
170C4×C19#44011yescharacteristic
171C4×C19#44211yescharacteristic
172C22×M16—381no—
173C2×C4×D4C2×D1911yescharacteristic
174#436—194no—
175#436—382no—
176C2×C4⋊C8—191no—
177C2×C4⋊C8—191no—
178C2×#102Dic1912yes—
179C2×C22⋊C8—381no—
180C2×C4×C8—191no—
181C2×C4×C8—191no—
182C2×C4×C8—381no—
183C2×C4×C8C2×D1911yescharacteristic
184C4×C4⋊C4C2×D1911yescharacteristic
185#340Dic1912yes—
186#336—381no—
187D4⋊C8—194no—
188#322—382no—
189C2×C19—82no—
190C2×C19#158612yes—
191C2×C19#158812yes—
192C2×C19#175311yescharacteristic
193C2×C19#176211yescharacteristic
194C2×C19#176411yescharacteristic
195C22×D4C2×Dic1911yescharacteristic
196C23×C4—21no—
197C2×M16—384no—
198C2×M16—762no—
199C2×M16—762no—
200C22×C8—191no—
201C22×C8—191no—
202C22×C8—381no—
203C22×C8—381no—
204C22×C8—381no—
205C22×C8C2×Dic1912yes—
206C4×D4—21no—
207C4×D4—21no—
208C4×D4C4×D1912yes—
209C4×D4C4×D1912yes—
210C2×C4⋊C4C2×Dic1912yes—
211C2×C4⋊C4C2×Dic1911yescharacteristic
212C2×C22⋊C4—21no—
213C2×C42—21no—
214C2×C42C22×D1911yescharacteristic
215C4⋊C8—192no—
216C4⋊C8—192no—
217C4⋊C8—381no—
218C4⋊C8—381no—
219#102—24no—
220C22⋊C8—384no—
221C4×C8—21no—
222C4×C8—21no—
223C4×C8—192no—
224C4×C8—192no—
225C4×C8—192no—
226C4×C8—381no—
227C4×C8—762no—
228#95—21no—
229C19#821211yescharacteristic, complemented, Sylow
230C24—21no—
231C2×D4—21no—
232C2×D4—22no—
233C2×D4—22no—
234C2×D4C4×Dic1912yes—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4D4×D1911yescharacteristic
244C22×C4#6454311yescharacteristic
245C22×C4C22×Dic1911yescharacteristic
246M16—768no—
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—192no—
251C2×C8—192no—
252C2×C8—384no—
253C2×C8—382no—
254C2×C8—381no—
255C2×C8—381no—
256C2×C8—381no—
257C2×C8—381no—
258C2×C8—382no—
259C2×C8—382no—
260C2×C8—761no—
261C2×C8—761no—
262C2×C8—761no—
263C2×C8—761no—
264C4⋊C4—21no—
265C4⋊C4—22no—
266C4⋊C4#6452014yescomplemented
267C4⋊C4C4×Dic1912yes—
268C22⋊C4—22no—
269C22⋊C4—22no—
270C42—41no—
271C42—41no—
272C42C2×C4×D1911yescharacteristic
273C42C2×C4×D1911yescharacteristic
274C42D4×D1911yescharacteristic
275C42#6454311yescharacteristic
276C23—22no—
277C23—42no—
278C23—41no—
279C23—41no—
280C23—42no—
281C23D4×Dic1911yescharacteristic
282D4—22no—
283D4—22no—
284D4—42no—
285C2×C4—22no—
286C2×C4—24no—
287C2×C4—22no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4#1059732311yescharacteristic
297C2×C4C22⋊C4×D1911yescharacteristic
298C2×C4(C22⋊D19)⋊C411yescharacteristic
299C2×C4(C22⋊D19)⋊C411yescharacteristic
300C2×C4#1059735711yescharacteristic
301C2×C4#1059735711yescharacteristic
302C2×C4#1059736011yescharacteristic
303C2×C4#1059736111yescharacteristic
304C2×C4C2×#6452012yes—
305C2×C4C2×C4×Dic1911yescharacteristic
306C2×C4D4×Dic1911yescharacteristic
307C2×C4#1059739412yes—
308C8—42no—
309C8—384no—
310C8—382no—
311C8—382no—
312C8—762no—
313C8—762no—
314C22—42no—
315C22—42no—
316C22—42no—
317C22—82no—
318C22—82no—
319C22C22⋊C4×Dic1911yescharacteristic
320C22#1192661612yes—
321C22#1192664511yescharacteristic
322C22#1192665611yescharacteristic
323C22#1192666112yes—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—44no—
328C4C4×#6452011yescharacteristic
329C4#1192650011yescharacteristic
330C4#1192654211yescharacteristic
331C4#1192654711yescharacteristic
332C4#1192662212yes—
333C4#1192664111yescharacteristic
334C4#1192665311yescharacteristic
335C2—82no—
336C2#1456250012yes—
337C2#1456251412yes—
338C2#1456341911yescharacteristic
339C2#1456346211yescharacteristic
340C2#1456347511yescharacteristic
subgroupG/H
centerC22×C4D4×D19
commutatorC2×C4×C19C2×C42
FrattiniC2×C42C22×D19
FittingC4×C19×#102C2
socleC23×C19C4×D4
prime radicalC22×D4×C19C2×C4
cosocleC2×C42×C19C23
hypercenterC4×#102D19
hypocenterC19#8212
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C4⋊C4×C19⋊C8C2semidirect
4. C2×#11926266C2semidirect
5. #14561476C2semidirect
6. #14561470C2semidirect
10. #11926622C4semidirect
18. D4⋊(C19⋊C8)C4semidirect
81. C4⋊C4×C19M16semidirect
229. C19#8212semidirect
266. C4⋊C4#64520semidirect

Maximal subgroups

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

subgroupindex
C2×#119266222
C4⋊C4×C19⋊C82
C2×D4⋊(C19⋊C8)2
C2×#119262662
#145614762
#145614702
C4×C19×#1022
#821219