Finite Group Databasebeta

← #18077576

Subgroups — #18077576

Order 4864.

616 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 143 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×#11926483C211yesmaximal, characteristic
2#14566253C211yesmaximal, characteristic
3#14563726C212yesmaximal
4#14561515C212yesmaximal
5C2×C19×#324C211yesmaximal, characteristic
6C2×#10597372—21no—
7C22×C4⋊Dic19C2211yescharacteristic
8#11926483—22no—
9#11926483C414yescomplemented
10#11926443—24no—
11#11926404—21no—
12#11926404C2212yes—
13C2×C19⋊#95—21no—
14C2×C19⋊#95—21no—
15C2×C19⋊#95C2211yescharacteristic
16#11926307—24no—
17C22×C4⋊C4×C19C2211yescharacteristic
18C2×C19×C22⋊C8C2212yes—
19C19×#324—22no—
20C23×C4×C19D411yescharacteristic
21C23×C4×C19D411yescharacteristic
22C23×C4×C19C2311yescharacteristic
23C23×Dic19—21no—
24C23×Dic19—21no—
25C22×C8×C19—22no—
26C2×C4⋊C4×C19—22no—
27C2×C4⋊C4×C19—22no—
28C2×C4⋊C4×C19C2×C412yes—
29C2×C4⋊C4×C19D412yes—
30C2×C22⋊Dic19—22no—
31#10597372—42no—
32#10597372—42no—
33C2×C4⋊Dic19—22no—
34C2×C4⋊Dic19—22no—
35C2×C4⋊Dic19—22no—
36C2×C4⋊Dic19—21no—
37C2×C4⋊Dic19—22no—
38C2×C4⋊Dic19C2×C412yes—
39C2×C4⋊Dic19D414yes—
40C2×C4×Dic19—22no—
41C19×C22⋊C8—22no—
42C19×C22⋊C8—22no—
43C19⋊#95—22no—
44C19⋊#95—24no—
45C19⋊#95—24no—
46C19⋊#95—21no—
47C19⋊#95—22no—
48C19⋊#95C2×C412yes—
49C24×C19C2×D411yescharacteristic
50C22×C4×C19—21no—
51C22×C4×C19—21no—
52C22×C4×C19—21no—
53C22×C4×C19—21no—
54C22×C4×C19—21no—
55C22×C4×C19—21no—
56C22×C4×C19—42no—
57C22×C4×C19—42no—
58C22×C4×C19C22⋊C412yes—
59C22×C4×C19C22⋊C412yes—
60C22×C4×C19SD1612yes—
61C22×C4×C19Q1612yes—
62C22×C4×C19C22×C411yescharacteristic
63C22×C4×C19C2×D412yes—
64C22×C4×C19C2×D411yescharacteristic
65C22×C4×C19#4112yes—
66C22×Dic19—22no—
67C22×Dic19—22no—
68C22×Dic19—24no—
69C22×Dic19—42no—
70C22×Dic19—42no—
71C22×Dic19—44no—
72C22×Dic19—41no—
73C22×Dic19—41no—
74C22×Dic19—41no—
75C22×Dic19—41no—
76C2×C8×C19—44no—
77C2×C8×C19—42no—
78C4⋊C4×C19—24no—
79C4⋊C4×C19—24no—
80C22⋊Dic19—42no—
81C22⋊Dic19—42no—
82C4⋊Dic19—24no—
83C4⋊Dic19—44no—
84C4⋊Dic19—42no—
85C4⋊Dic19—44no—
86C4⋊Dic19—82no—
87C4×Dic19—44no—
88#9023—191nomaximal, Sylow
89C23×C19—22no—
90C23×C19—22no—
91C23×C19C2×C22⋊C411yescharacteristic
92C23×C19#12011yescharacteristic
93C23×C19#12311yescharacteristic
94C23×C19C2×SD1611yescharacteristic
95C23×C19C2×Q1611yescharacteristic
96C23×C19AGL(1,ℤ/8)11yescharacteristic
97C23×C19#13711yescharacteristic
98C2×C4×C19—22no—
99C2×C4×C19—22no—
100C2×C4×C19—22no—
101C2×C4×C19—22no—
102C2×C4×C19—24no—
103C2×C4×C19—22no—
104C2×C4×C19—22no—
105C2×C4×C19—22no—
106C2×C4×C19—41no—
107C2×C4×C19—41no—
108C2×C4×C19—42no—
109C2×C4×C19—42no—
110C2×C4×C19—42no—
111C2×C4×C19—81no—
112C2×C4×C19#10314yes—
113C2×C4×C19C4×D412yes—
114C2×C4×C19#12112yes—
115C2×Dic19—42no—
116C2×Dic19—42no—
117C2×Dic19—44no—
118C2×Dic19—42no—
119C2×Dic19—42no—
120C2×Dic19—44no—
121C2×Dic19—44no—
122C2×Dic19—44no—
123C2×Dic19—82no—
124C2×Dic19—82no—
125C2×Dic19—82no—
126C2×Dic19—82no—
127C8×C19—82no—
128C2×#400—191no—
129#2316—191no—
130#1824—192no—
131C2×#324D1911yescharacteristic
132#1294—192no—
133C22×C19—22no—
134C22×C19—22no—
135C22×C19—22no—
136C22×C19—22no—
137C22×C19—21no—
138C22×C19—21no—
139C22×C19—21no—
140C22×C19—21no—
141C22×C19#38611yescharacteristic
142C22×C19C2×#10311yescharacteristic
143C22×C19#41711yescharacteristic
144C22×C19#45011yescharacteristic
145C22×C19#45111yescharacteristic
146C22×C19#45412yes—
147C22×C19#45812yes—
148C22×C19#48311yescharacteristic
149C22×C19#48411yescharacteristic
150C4×C19—24no—
151C4×C19—22no—
152C4×C19—22no—
153C4×C19—42no—
154Dic19—82no—
155Dic19—84no—
156Dic19—82no—
157C2×#117—381no—
158C22×C4⋊C4—191no—
159C22×C4⋊C4C2×D1911yescharacteristic
160C2×C22⋊C8C2×D1912yes—
161#400—194no—
162#400—382no—
163#389—384no—
164#380—192no—
165#380—381no—
166C2×#95—191no—
167C2×#95—381no—
168C2×#95—381no—
169#340—384no—
170#324—22no—
171C2×C19—21no—
172C2×C19—21no—
173C2×C19—21no—
174C2×C19—21no—
175C2×C19#161612yes—
176C2×C19#161712yes—
177C2×C19#187211yescharacteristic
178C2×C19#188811yescharacteristic
179C2×C19#189011yescharacteristic
180C23×C4—381no—
181C23×C4—381no—
182C23×C4D7611yescharacteristic
183C23×C4D7611yescharacteristic
184C23×C4C22×D1911yescharacteristic
185C22×C8—22no—
186#117—762no—
187#117—762no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—192no—
191C2×C4⋊C4—194no—
192C2×C4⋊C4—382no—
193C2×C4⋊C4—382no—
194C2×C4⋊C4—382no—
195C2×C4⋊C4—381no—
196C2×C4⋊C4—382no—
197C2×C4⋊C4C4×D1912yes—
198C2×C4⋊C4C22⋊D1912yes—
199C2×C22⋊C4—382no—
200C2×C42—382no—
201C22⋊C8—22no—
202C22⋊C8—22no—
203#95—192no—
204#95—382no—
205#95—384no—
206#95—384no—
207#95—382no—
208#95—381no—
209C19#902311yescharacteristic, complemented, Sylow
210C24C2×D7611yescharacteristic
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—384no—
220C22×C4—382no—
221C22×C4—382no—
222C22×C4—762no—
223C22×C4—762no—
224C22×C4—764no—
225C22×C4—761no—
226C22×C4—761no—
227C22×C4—761no—
228C22×C4—761no—
229C22×C4#6451612yes—
230C22×C4Dic7612yes—
231C22×C4(C2×D19)⋊C412yes—
232C22×C4(C2×D19)⋊C412yes—
233C22×C4C2×C4×D1911yescharacteristic
234C22×C4D4×D1912yes—
235C22×C4#6454312yes—
236C22×C4C2×C22⋊D1911yescharacteristic
237C2×C8—44no—
238C2×C8—42no—
239C4⋊C4—24no—
240C4⋊C4—24no—
241C4⋊C4—384no—
242C4⋊C4—764no—
243C4⋊C4—764no—
244C4⋊C4—762no—
245C4⋊C4—1522no—
246C22⋊C4—762no—
247C22⋊C4—762no—
248C42—764no—
249C23—22no—
250C23—22no—
251C23#1059732811yescharacteristic
252C23#1059733211yescharacteristic
253C23C2×#6451611yescharacteristic
254C23C2×Dic7611yescharacteristic
255C23#1059735411yescharacteristic
256C23#1059735511yescharacteristic
257C23C2×(C2×D19)⋊C411yescharacteristic
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—24no—
265C2×C4—22no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—81no—
272C2×C4—762no—
273C2×C4—762no—
274C2×C4—764no—
275C2×C4—762no—
276C2×C4—762no—
277C2×C4—764no—
278C2×C4—764no—
279C2×C4—764no—
280C2×C4—1522no—
281C2×C4—1522no—
282C2×C4—1522no—
283C2×C4—1522no—
284C2×C4#1059727314yes—
285C2×C4(C22⋊D19)⋊C412yes—
286C2×C4#1059738512yes—
287C8—82no—
288C22—22no—
289C22—22no—
290C22—22no—
291C22—22no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22#1192642111yescharacteristic
297C22C2×#1059727311yescharacteristic
298C22#1192654611yescharacteristic
299C22#1192669711yescharacteristic
300C22#1192670211yescharacteristic
301C22#1192671912yes—
302C22#1192673512yes—
303C22#1192687511yescharacteristic
304C22#1192688011yescharacteristic
305C4—24no—
306C4—22no—
307C4—22no—
308C4—42no—
309C4—1522no—
310C4—1524no—
311C4—1522no—
312C2—21no—
313C2—21no—
314C2—21no—
315C2—21no—
316C2#1456267412yes—
317C2#1456267912yes—
318C2#1456394011yescharacteristic
319C2#1456403611yescharacteristic
320C2#1456404611yescharacteristic
subgroupG/H
centerC23#10597328
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#324C2
socleC23×C19#120
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenterC2×#324D19
hypocenterC19#9023
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
9. #11926483C4semidirect
209. C19#9023semidirect

Maximal subgroups

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

subgroupindex
C2×#119264832
#145662532
#145637262
#145615152
C2×C19×#3242
#902319