Finite Group Databasebeta

← #18074007

Subgroups — #18074007

Order 4864.

826 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 826 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D19C211yesmaximal, characteristic
2#14563398C212yesmaximal
3C2×#11926286C211yesmaximal, characteristic, complemented
4C2×#11926285C212yesmaximal, complemented
5C2×C19×#330C211yesmaximal, characteristic, complemented
6C2×#10597316C2211yescharacteristic
7C2×#10597336C412yes—
8C2×#10597335—22no—
9#125×D19—24no—
10#125×D19—22no—
11#125×D19—22no—
12C2×C4⋊C4×D19—22no—
13C2×C4⋊C4×D19C412yes—
14C2×C42×D19C2211yescharacteristic
15C2×(C2×D19)⋊C8—22no—
16C2×#10597260C2212yes—
17#11926298—22no—
18#11926286—22no—
19#11926285—24no—
20C2×C19×#125C2211yescharacteristic
21C2×C19×#97C2212yes—
22C19×#330—22no—
23C22×C4×D19—22no—
24C22×C4×D19C2×C411yescharacteristic
25C22×C4×D19D412yes—
26C22×C8×C19—22no—
27C19×#125—22no—
28C19×#125D412yes—
29C19×#125D412yes—
30C2×C4⋊C4×C19—22no—
31C2×C4⋊C4×C19C2×C412yes—
32C2×C42×C19C2311yescharacteristic
33C2×C4⋊Dic19—22no—
34C2×C4⋊Dic19C2×C412yes—
35C2×Dic19⋊C4—22no—
36C2×Dic19⋊C4—22no—
37C2×Dic19⋊C4—22no—
38C2×C4×Dic19C2×C411yescharacteristic
39C2×C4×Dic19D412yes—
40C22×C19⋊C8—22no—
41C4⋊C4×D19—28no—
42C4⋊C4×D19—28no—
43C4⋊C4×D19—24no—
44C4⋊C4×D19—24no—
45#10597336—24no—
46#10597336—24no—
47#10597335—28no—
48#10597335—28no—
49C42×D19—21no—
50C42×D19—22no—
51C42×D19—21no—
52#10597316—21no—
53#10597316—21no—
54#10597316D414yes—
55C19×#97—22no—
56C19×#97—22no—
57(C2×D19)⋊C8—28no—
58#10597260—22no—
59#10597260—22no—
60C23×D19C22⋊C411yescharacteristic
61C22×C4×C19—22no—
62C22×C4×C19C22×C411yescharacteristic
63C22×C4×C19C2×D412yes—
64C22×Dic19—22no—
65C22×Dic19C22⋊C412yes—
66C22×Dic19C22⋊C411yescharacteristic
67C2×C4×D19—22no—
68C2×C4×D19—21no—
69C2×C4×D19—21no—
70C2×C4×D19—22no—
71C2×C4×D19—28no—
72C2×C4×D19—24no—
73C2×C4×D19—22no—
74C2×C4×D19—22no—
75C2×C4×D19—42no—
76C2×C4×D19—44no—
77C2×C4×D19—44no—
78C2×C8×C19—24no—
79C2×C8×C19—42no—
80C2×C8×C19—42no—
81C4⋊C4×C19—22no—
82C4⋊C4×C19—24no—
83C4⋊C4×C19—24no—
84C4⋊C4×C19C22⋊C414yes—
85C42×C19C2×D411yescharacteristic
86C42×C19C2×D412yes—
87C42×C19C2×D411yescharacteristic
88C4⋊Dic19—28no—
89C4⋊Dic19—22no—
90C4⋊Dic19C22⋊C414yes—
91Dic19⋊C4—28no—
92Dic19⋊C4—28no—
93Dic19⋊C4—24no—
94Dic19⋊C4—24no—
95C4×Dic19—21no—
96C4×Dic19—21no—
97C4×Dic19—22no—
98C4×Dic19—22no—
99C2×C19⋊C8—24no—
100C2×C19⋊C8—42no—
101C2×C19⋊C8—42no—
102#8335—191nomaximal, Sylow
103C23×C19C2×C22⋊C411yescharacteristic
104C22×D19—21no—
105C22×D19—21no—
106C22×D19—22no—
107C22×D19#10112yes—
108C22×D19#10414yes—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—22no—
112C2×C4×C19—22no—
113C2×C4×C19—24no—
114C2×C4×C19—42no—
115C2×C4×C19—42no—
116C2×C4×C19C2×C22⋊C411yescharacteristic
117C2×C4×C19C2×C22⋊C411yescharacteristic
118C2×C4×C19#12012yes—
119C2×C4×C19#12012yes—
120C2×Dic19—21no—
121C2×Dic19—21no—
122C2×Dic19—22no—
123C2×Dic19—24no—
124C2×Dic19—22no—
125C2×Dic19—22no—
126C2×Dic19—42no—
127C2×Dic19—42no—
128C2×Dic19#10112yes—
129C4×D19—24no—
130C4×D19—24no—
131C4×D19—44no—
132C4×D19—44no—
133C4×D19—416no—
134C8×C19—44no—
135C19⋊C8—44no—
136C22×#125—191no—
137#1749—192no—
138C2×#330—192no—
139C2×#330—191no—
140C2×#330D1911yescharacteristic, complemented
141C22×C19#37911yescharacteristic
142C22×C19C2×#10111yescharacteristic
143C22×C19C2×#10111yescharacteristic
144C22×C19C2×#10412yes—
145C22×C19#42112yes—
146C2×D19—24no—
147C2×D19—22no—
148C2×D19—24no—
149C2×D19—22no—
150C2×D19#33014yescomplemented
151C4×C19—21no—
152C4×C19—21no—
153C4×C19—22no—
154C4×C19—22no—
155C4×C19—44no—
156Dic19—22no—
157Dic19—42no—
158Dic19—44no—
159C2×#125—192no—
160C2×#125—191no—
161C2×#125—382no—
162C2×#125—384no—
163C2×#125—382no—
164C2×#125—382no—
165C2×#125C2×D1911yescharacteristic
166C22×C4⋊C4—192no—
167C22×C4⋊C4—382no—
168C22×C42—191no—
169C2×C22⋊C8—382no—
170C2×#97—192no—
171C2×#97C2×D1912yes—
172#336—382no—
173#330—22no—
174#330—384no—
175#330—382no—
176C2×C19C2×#33011yescharacteristic
177C2×C19#152812yes—
178C2×C19#153411yescharacteristic
179C2×C19#178411yescharacteristic
180C2×C19#178912yes—
181D19—24no—
182C23×C4—191no—
183C23×C4—192no—
184C23×C4—382no—
185C22×C8—22no—
186C22×C8—382no—
187#125—22no—
188#125—194no—
189#125—384no—
190#125—388no—
191#125—388no—
192#125—384no—
193#125—381no—
194#125—381no—
195#125D7612yes—
196#125C22⋊D1912yes—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—192no—
199C2×C4⋊C4—384no—
200C2×C4⋊C4—388no—
201C2×C4⋊C4—388no—
202C2×C4⋊C4—382no—
203C2×C4⋊C4—382no—
204C2×C4⋊C4—382no—
205C2×C4⋊C4—382no—
206C2×C4⋊C4—384no—
207C2×C4⋊C4C4×D1912yes—
208C2×C42—191no—
209C2×C42—192no—
210C2×C42—381no—
211C2×C42—382no—
212C2×C42—381no—
213C2×C42C22×D1911yescharacteristic
214C22⋊C8—388no—
215#97—22no—
216#97—22no—
217#97—382no—
218#97—382no—
219C19#833511yescharacteristic, complemented, Sylow
220C24—191no—
221C22×C4—22no—
222C22×C4—191no—
223C22×C4—192no—
224C22×C4—382no—
225C22×C4—382no—
226C22×C4—384no—
227C22×C4—388no—
228C22×C4—381no—
229C22×C4—381no—
230C22×C4—382no—
231C22×C4—382no—
232C22×C4—382no—
233C22×C4—762no—
234C22×C4—764no—
235C22×C4—764no—
236C22×C4C2×C4×D1911yescharacteristic
237C22×C4D4×D1912yes—
238C2×C8—24no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—384no—
242C2×C8—762no—
243C2×C8—762no—
244C4⋊C4—24no—
245C4⋊C4—22no—
246C4⋊C4—24no—
247C4⋊C4—194no—
248C4⋊C4—388no—
249C4⋊C4—388no—
250C4⋊C4—388no—
251C4⋊C4—384no—
252C4⋊C4—384no—
253C4⋊C4—382no—
254C4⋊C4(C2×D19)⋊C414yes—
255C42—382no—
256C42—381no—
257C42—382no—
258C42—381no—
259C42C2×D7611yescharacteristic
260C42D4×D1912yes—
261C42C2×C22⋊D1911yescharacteristic
262C23—194no—
263C23—192no—
264C23—382no—
265C23—381no—
266C23—381no—
267C23C22⋊C4×D1911yescharacteristic
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—24no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—192no—
276C2×C4—384no—
277C2×C4—384no—
278C2×C4—381no—
279C2×C4—381no—
280C2×C4—382no—
281C2×C4—382no—
282C2×C4—382no—
283C2×C4—384no—
284C2×C4—764no—
285C2×C4—764no—
286C2×C4—7616no—
287C2×C4—762no—
288C2×C4—762no—
289C2×C4C22⋊C4×D1911yescharacteristic
290C2×C4#1059732812yes—
291C2×C4C2×(C2×D19)⋊C411yescharacteristic
292C2×C4#1059738312yes—
293C8—44no—
294C8—764no—
295C22—194no—
296C22—384no—
297C22—382no—
298C22—382no—
299C22—384no—
300C22#1192639911yescharacteristic
301C22#101×D1911yescharacteristic
302C22#101×D1911yescharacteristic
303C22#104×D1912yes—
304C22#1192655912yes—
305C4—21no—
306C4—21no—
307C4—22no—
308C4—22no—
309C4—44no—
310C4—382no—
311C4—762no—
312C4—764no—
313C2—384no—
314C2D19×#33011yescharacteristic
315C2#1456223512yes—
316C2#1456226011yescharacteristic
317C2#1456355711yescharacteristic
318C2#1456357712yes—
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC2×C19×#330C2
socleC23×C19C2×C22⋊C4
prime radicalC23×D19C22⋊C4
cosocleC2×C42×C19C23
hypercenterC2×#330D19
hypocenterC19#8335
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
3. C2×#11926286C2semidirect
4. C2×#11926285C2semidirect
5. C2×C19×#330C2semidirect
140. C2×#330D19semidirect
150. C2×D19#330semidirect
219. C19#8335semidirect

Maximal subgroups

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

subgroupindex
C2×#125×D192
#145633982
C2×#119262862
C2×#119262852
C2×C19×#3302
#833519