Finite Group Databasebeta

← #18070973

Subgroups — #18070973

Order 4864.

458 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C4⋊(C19⋊C8)C211yesmaximal, characteristic, complemented
2#14563384C211yesmaximal, characteristic, complemented
3#14561461C212yesmaximal, complemented
4#14561456C212yesmaximal
5C19×#2861C211yesmaximal, characteristic
6C2×C4⋊(C19⋊C8)—21no—
7C2×#10597260—21no—
8C2×C4×C19⋊C8—21no—
9#11926299—21no—
10#11926299C2212yes—
11#11926299C2212yes—
12C2×C19×#125C411yescharacteristic
13C2×C19×#124C411yescharacteristic
14C19×#391C411yescharacteristic
15C19×#391C2211yescharacteristic
16C19×#390C411yescharacteristic
17C19×#390C2211yescharacteristic
18C19×#388—21no—
19C19×#388—21no—
20C19×#388—21no—
21C19×#388—21no—
22C43×C19C2211yescharacteristic
23C22×Q8×C19C2×C411yescharacteristic
24C22×D4×C19C2×C411yescharacteristic
25C19×#125—42no—
26C19×#124—42no—
27C2×C4⋊C4×C19—21no—
28C2×C4⋊C4×C19—21no—
29C2×C4⋊C4×C19C2×C411yescharacteristic
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C22⋊C4×C19—21no—
32C2×C22⋊C4×C19—21no—
33C2×C22⋊C4×C19—21no—
34C2×C22⋊C4×C19—21no—
35C2×C22⋊C4×C19—21no—
36C2×C22⋊C4×C19—21no—
37C2×C42×C19C2×C411yescharacteristic
38C2×C42×C19C2×C411yescharacteristic
39C2×C42×C19D411yescharacteristic
40C2×C42×C19D411yescharacteristic
41C2×C42×C19D411yescharacteristic
42C2×C42×C19D411yescharacteristic
43C2×C42×C19C2311yescharacteristic
44C22×C19⋊C8—22no—
45C22×C19⋊C8—22no—
46C19×#95—21no—
47C19×#95—21no—
48C19×#95—21no—
49C19×#95—21no—
50C4⋊(C19⋊C8)—24no—
51#10597260—24no—
52C4×C19⋊C8—42no—
53C24×C19—21no—
54C2×Q8×C19—22no—
55C2×Q8×C19—41no—
56C2×Q8×C19—41no—
57C2×D4×C19—22no—
58C2×D4×C19—41no—
59C2×D4×C19—41no—
60C22×C4×C19—21no—
61C22×C4×C19—21no—
62C22×C4×C19—21no—
63C22×C4×C19C22⋊C411yescharacteristic
64C22×C4×C19C22⋊C411yescharacteristic
65C22×C4×C19C22⋊C411yescharacteristic
66C22×C4×C19C22⋊C411yescharacteristic
67C22×C4×C19C22×C411yescharacteristic
68C22×C4×C19C2×D411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C4⋊C4×C19—41no—
71C4⋊C4×C19—41no—
72C4⋊C4×C19—42no—
73C4⋊C4×C19—42no—
74C22⋊C4×C19—42no—
75C22⋊C4×C19—42no—
76C22⋊C4×C19—42no—
77C22⋊C4×C19—42no—
78C22⋊C4×C19—42no—
79C22⋊C4×C19—41no—
80C22⋊C4×C19—41no—
81C42×C19—22no—
82C42×C19—22no—
83C42×C19—22no—
84C42×C19—22no—
85C42×C19—22no—
86C42×C19—21no—
87C42×C19—21no—
88C42×C19—41no—
89C2×C19⋊C8—24no—
90C2×C19⋊C8—24no—
91C2×C19⋊C8—42no—
92C2×C19⋊C8—42no—
93C2×C19⋊C8—42no—
94C2×C19⋊C8—42no—
95#7676—191nomaximal, Sylow
96C23×C19—41no—
97C23×C19—41no—
98C23×C19—41no—
99C23×C19—41no—
100C23×C19—41no—
101C23×C19—41no—
102C23×C19—41no—
103C23×C19C2×C22⋊C411yescharacteristic
104Q8×C19—82no—
105D4×C19—82no—
106C2×C4×C19—21no—
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—41no—
122C2×C4×C19—41no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19#10012yes—
131C2×C4×C19#10412yes—
132C2×C4×C19#10412yes—
133C2×C4×C19#13112yes—
134C2×C4×C19#13512yes—
135C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C19#13711yescharacteristic
137C19⋊C8—44no—
138C19⋊C8—44no—
139#2861D1911yescharacteristic
140C4×C4⋊C8—191no—
141#1745—191no—
142#1272—192no—
143#1270—192no—
144C22×C19—81no—
145C22×C19—81no—
146C22×C19—81no—
147C22×C19—81no—
148C22×C19—81no—
149C22×C19—81no—
150C22×C19—81no—
151C22×C19#40811yescharacteristic
152C22×C19#41011yescharacteristic
153C22×C19C2×#10011yescharacteristic
154C22×C19#41611yescharacteristic
155C22×C19#41711yescharacteristic
156C22×C19C2×#10411yescharacteristic
157C22×C19C2×#10411yescharacteristic
158C4×C19—22no—
159C4×C19—22no—
160C4×C19—22no—
161C4×C19—22no—
162C4×C19—22no—
163C4×C19—21no—
164C4×C19—21no—
165C4×C19—41no—
166C4×C19—81no—
167C4×C19—81no—
168C4×C19—81no—
169C2×#125Dic1911yescharacteristic
170C2×#124Dic1911yescharacteristic
171C2×C4⋊C8—381no—
172C2×#97—381no—
173C2×C4×C8—381no—
174#391Dic1911yescharacteristic
175#391C2×D1911yescharacteristic
176#390Dic1911yescharacteristic
177#390C2×D1911yescharacteristic
178#388—21no—
179#388—21no—
180#388—21no—
181#388—21no—
182C43C2×D1911yescharacteristic
183#336—192no—
184#336—192no—
185#336—381no—
186C2×C19—161no—
187C2×C19#146911yescharacteristic
188C2×C19#148311yescharacteristic
189C2×C19#149411yescharacteristic
190C2×C19#150011yescharacteristic
191C2×C19#150911yescharacteristic
192C2×C19#152511yescharacteristic
193C2×C19#155111yescharacteristic
194C22×Q8C2×Dic1911yescharacteristic
195C22×D4C2×Dic1911yescharacteristic
196C22×C8—382no—
197C22×C8—382no—
198#125—42no—
199#124—42no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4C2×Dic1911yescharacteristic
203C2×C4⋊C4C2×Dic1911yescharacteristic
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C42C2×Dic1911yescharacteristic
211C2×C42C2×Dic1911yescharacteristic
212C2×C42C22⋊D1911yescharacteristic
213C2×C42C22⋊D1911yescharacteristic
214C2×C42C22⋊D1911yescharacteristic
215C2×C42C22⋊D1911yescharacteristic
216C2×C42C22×D1911yescharacteristic
217C4⋊C8—384no—
218#97—384no—
219C4×C8—762no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224C19#767611yescharacteristic, complemented, Sylow
225C24—21no—
226C2×Q8—22no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×D4—22no—
230C2×D4—41no—
231C2×D4—41no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4C22⋊Dic1911yescharacteristic
236C22×C4C22⋊Dic1911yescharacteristic
237C22×C4C22⋊Dic1911yescharacteristic
238C22×C4C22⋊Dic1911yescharacteristic
239C22×C4C22×Dic1911yescharacteristic
240C22×C4C2×C22⋊D1911yescharacteristic
241C22×C4C2×C22⋊D1911yescharacteristic
242C2×C8—384no—
243C2×C8—384no—
244C2×C8—762no—
245C2×C8—762no—
246C2×C8—762no—
247C2×C8—762no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C22⋊C4—42no—
253C22⋊C4—41no—
254C22⋊C4—42no—
255C22⋊C4—41no—
256C22⋊C4—42no—
257C22⋊C4—42no—
258C22⋊C4—42no—
259C42—22no—
260C42—21no—
261C42—22no—
262C42—21no—
263C42—22no—
264C42—22no—
265C42—22no—
266C42—41no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23C2×C22⋊Dic1911yescharacteristic
275Q8—82no—
276D4—82no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4#1059729012yes—
302C2×C4#1059729412yes—
303C2×C4#1059729412yes—
304C2×C4#1059739412yes—
305C2×C4#1059739511yescharacteristic
306C2×C4#1059739612yes—
307C2×C4#1059739711yescharacteristic
308C8—764no—
309C8—764no—
310C22—81no—
311C22—81no—
312C22—81no—
313C22—81no—
314C22—81no—
315C22—81no—
316C22—81no—
317C22#1192651111yescharacteristic
318C22#1192651811yescharacteristic
319C22C2×#1059729011yescharacteristic
320C22#1192654011yescharacteristic
321C22#1192654511yescharacteristic
322C22C2×#1059729411yescharacteristic
323C22C2×#1059729411yescharacteristic
324C4—22no—
325C4—22no—
326C4—22no—
327C4—22no—
328C4—21no—
329C4—21no—
330C4—22no—
331C4—41no—
332C4—81no—
333C4—81no—
334C4—81no—
335C2—161no—
336C2#1456198711yescharacteristic
337C2#1456204811yescharacteristic
338C2#1456209511yescharacteristic
339C2#1456212111yescharacteristic
340C2#1456216011yescharacteristic
341C2#1456222711yescharacteristic
342C2#1456233011yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2861C2
socleC23×C19C2×C22⋊C4
prime radicalC22×D4×C19C2×C4
cosocleC2×C42×C19C23
hypercenter#2861D19
hypocenterC19#7676
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C43 ◁ #2861

Complements

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

NH ≅ G/Ntype
1. C4×C4⋊(C19⋊C8)C2semidirect
2. #14563384C2semidirect
3. #14561461C2semidirect
224. C19#7676semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊(C19⋊C8)2
#145633842
#145614612
#145614562
C19×#28612
#767619