Finite Group Databasebeta

← #18078297

Subgroups — #18078297

Order 4864.

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

normal subgroups only

This group has 630 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
1#14571974C211yesmaximal, characteristic
2C2×#11926410C211yesmaximal, characteristic
3C2×#11926282C212yesmaximal
4#14561515C212yesmaximal
5C19×#1817C211yesmaximal, characteristic
6C2×#10597370C2211yescharacteristic
7C22×C4⋊Dic19—21no—
8#11926450C412yescomplemented
9#11926442C412yescomplemented
10#11926428—22no—
11#11926417—21no—
12#11926410—24no—
13#11926407—21no—
14#11926404C2211yescharacteristic
15C2×C19⋊#95—21no—
16C2×C19⋊#95C2212yes—
17#11926282—24no—
18C22×C42×C19C2211yescharacteristic
19C2×C19×C22⋊C8C2212yes—
20C19×#336—22no—
21C23×C4×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19C2311yescharacteristic
24C23×Dic19—22no—
25C22×Dic38C2×C411yescharacteristic
26C22×C8×C19—22no—
27C2×C42×C19—22no—
28C2×C42×C19—22no—
29C2×C42×C19C2×C412yes—
30C2×C42×C19D412yes—
31C2×C22⋊Dic19—21no—
32C2×C22⋊Dic19—21no—
33C2×C4⋊Dic19—24no—
34C2×C4⋊Dic19—42no—
35C2×C4⋊Dic19—42no—
36C2×C4⋊Dic19C2×C411yescharacteristic
37C2×C4⋊Dic19C2×C412yes—
38#10597370—22no—
39#10597370—22no—
40C2×Dic19⋊C4—22no—
41C2×Dic19⋊C4—21no—
42C19×C22⋊C8—22no—
43C19×C22⋊C8—22no—
44C19⋊#95—24no—
45C19⋊#95—22no—
46C19⋊#95—22no—
47C19⋊#95—22no—
48C19⋊#95—22no—
49C19⋊#95—21no—
50C19⋊#95D414yes—
51C24×C19C2×D411yescharacteristic
52C22×C4×C19—21no—
53C22×C4×C19—21no—
54C22×C4×C19—21no—
55C22×C4×C19—21no—
56C22×C4×C19—21no—
57C22×C4×C19—21no—
58C22×C4×C19—42no—
59C22×C4×C19—42no—
60C22×C4×C19C22⋊C412yes—
61C22×C4×C19C22⋊C412yes—
62C22×C4×C19SD1612yes—
63C22×C4×C19Q1612yes—
64C22×C4×C19C22×C411yescharacteristic
65C22×C4×C19C2×D412yes—
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19#4112yes—
68C22×Dic19—21no—
69C22×Dic19—22no—
70C22×Dic19—21no—
71C22×Dic19—24no—
72C22×Dic19—44no—
73C22×Dic19—44no—
74C22×Dic19—42no—
75C22×Dic19—42no—
76C2×Dic38—22no—
77C2×Dic38—42no—
78C2×C8×C19—44no—
79C2×C8×C19—42no—
80C42×C19—24no—
81C42×C19—24no—
82C22⋊Dic19—41no—
83C22⋊Dic19—41no—
84C22⋊Dic19—41no—
85C22⋊Dic19—41no—
86C4⋊Dic19—22no—
87C4⋊Dic19—48no—
88C4⋊Dic19—42no—
89Dic19⋊C4—44no—
90Dic19⋊C4—42no—
91#9152—191nomaximal, Sylow
92C23×C19—22no—
93C23×C19—22no—
94C23×C19C2×C22⋊C411yescharacteristic
95C23×C19#12011yescharacteristic
96C23×C19#12311yescharacteristic
97C23×C19C2×SD1611yescharacteristic
98C23×C19C2×Q1611yescharacteristic
99C23×C19AGL(1,ℤ/8)11yescharacteristic
100C23×C19#13711yescharacteristic
101C2×C4×C19—22no—
102C2×C4×C19—22no—
103C2×C4×C19—22no—
104C2×C4×C19—22no—
105C2×C4×C19—22no—
106C2×C4×C19—22no—
107C2×C4×C19—22no—
108C2×C4×C19—22no—
109C2×C4×C19—22no—
110C2×C4×C19—22no—
111C2×C4×C19—22no—
112C2×C4×C19—42no—
113C2×C4×C19—42no—
114C2×C4×C19—42no—
115C2×C4×C19—42no—
116C2×C4×C19#10314yes—
117C2×C4×C19C4×D412yes—
118C2×C4×C19#12112yes—
119C2×Dic19—44no—
120C2×Dic19—44no—
121C2×Dic19—41no—
122C2×Dic19—41no—
123C2×Dic19—42no—
124C2×Dic19—42no—
125C2×Dic19—42no—
126C2×Dic19—42no—
127C2×Dic19—42no—
128C2×Dic19—44no—
129C2×Dic19—84no—
130C2×Dic19—84no—
131Dic38—82no—
132C8×C19—82no—
133#2855—191no—
134C2×#382—191no—
135#1817D1911yescharacteristic
136C2×#328—192no—
137#1294—192no—
138C22×C19—21no—
139C22×C19—21no—
140C22×C19—21no—
141C22×C19—21no—
142C22×C19—22no—
143C22×C19—22no—
144C22×C19—22no—
145C22×C19—22no—
146C22×C19#38611yescharacteristic
147C22×C19#41012yes—
148C22×C19C2×#10311yescharacteristic
149C22×C19#41711yescharacteristic
150C22×C19#42112yes—
151C22×C19#45011yescharacteristic
152C22×C19#45111yescharacteristic
153C22×C19#48311yescharacteristic
154C22×C19#48411yescharacteristic
155C4×C19—24no—
156C4×C19—22no—
157C4×C19—22no—
158C4×C19—42no—
159Dic19—84no—
160Dic19—81no—
161Dic19—81no—
162Dic19—82no—
163C2×C22⋊Q8—191no—
164C22×C4⋊C4—381no—
165C22×C42C2×D1911yescharacteristic
166C2×C22⋊C8C2×D1912yes—
167#391—192no—
168#389—192no—
169#387—382no—
170#385—381no—
171#382—384no—
172#381—381no—
173#380—191no—
174C2×#95—192no—
175C2×#95—381no—
176#336—22no—
177#328—384no—
178C2×C19—21no—
179C2×C19—21no—
180C2×C19—21no—
181C2×C19—21no—
182C2×C19#151212yes—
183C2×C19#151812yes—
184C2×C19#187211yescharacteristic
185C2×C19#189711yescharacteristic
186C2×C19#189911yescharacteristic
187C22×Q8—191no—
188C23×C4—382no—
189C23×C4D7611yescharacteristic
190C23×C4D7611yescharacteristic
191C23×C4C22×D1911yescharacteristic
192C22×C8—22no—
193C22⋊Q8—382no—
194C22⋊Q8—382no—
195C2×C4⋊C4—191no—
196C2×C4⋊C4—192no—
197C2×C4⋊C4—384no—
198C2×C4⋊C4—382no—
199C2×C4⋊C4—381no—
200C2×C4⋊C4—762no—
201C2×C4⋊C4—762no—
202C2×C22⋊C4—381no—
203C2×C22⋊C4—381no—
204C2×C42—22no—
205C2×C42—22no—
206C2×C42C4×D1912yes—
207C2×C42C22⋊D1912yes—
208C22⋊C8—22no—
209C22⋊C8—22no—
210#95—194no—
211#95—384no—
212#95—382no—
213#95—382no—
214#95—382no—
215#95—382no—
216#95—381no—
217C19#915211yescharacteristic, complemented, Sylow
218C24C2×D7611yescharacteristic
219C2×Q8—382no—
220C2×Q8—762no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—384no—
230C22×C4—382no—
231C22×C4—381no—
232C22×C4—381no—
233C22×C4—764no—
234C22×C4—764no—
235C22×C4—762no—
236C22×C4—762no—
237C22×C4#6451612yes—
238C22×C4Dic7612yes—
239C22×C4(C2×D19)⋊C412yes—
240C22×C4(C2×D19)⋊C412yes—
241C22×C4C2×C4×D1911yescharacteristic
242C22×C4D4×D1912yes—
243C22×C4#6454312yes—
244C22×C4C2×C22⋊D1911yescharacteristic
245C2×C8—44no—
246C2×C8—42no—
247C4⋊C4—382no—
248C4⋊C4—762no—
249C4⋊C4—764no—
250C4⋊C4—768no—
251C4⋊C4—762no—
252C22⋊C4—761no—
253C22⋊C4—761no—
254C22⋊C4—761no—
255C22⋊C4—761no—
256C42—24no—
257C42—24no—
258C23—22no—
259C23—22no—
260C23#1059732811yescharacteristic
261C23#1059733211yescharacteristic
262C23C2×#6451611yescharacteristic
263C23C2×Dic7611yescharacteristic
264C23#1059735411yescharacteristic
265C23#1059735511yescharacteristic
266C23C2×(C2×D19)⋊C411yescharacteristic
267Q8—1522no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—764no—
284C2×C4—764no—
285C2×C4—762no—
286C2×C4—762no—
287C2×C4—762no—
288C2×C4—761no—
289C2×C4—761no—
290C2×C4—764no—
291C2×C4—762no—
292C2×C4—762no—
293C2×C4—1524no—
294C2×C4—1524no—
295C2×C4#1059727314yes—
296C2×C4(C22⋊D19)⋊C412yes—
297C2×C4#1059738512yes—
298C8—82no—
299C22—22no—
300C22—22no—
301C22—22no—
302C22—22no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22#1192642111yescharacteristic
308C22#1192651712yes—
309C22C2×#1059727311yescharacteristic
310C22#1192654611yescharacteristic
311C22#1192656012yes—
312C22#1192669711yescharacteristic
313C22#1192670211yescharacteristic
314C22#1192687511yescharacteristic
315C22#1192688011yescharacteristic
316C4—24no—
317C4—22no—
318C4—22no—
319C4—42no—
320C4—1524no—
321C4—1522no—
322C4—1521no—
323C4—1521no—
324C2—21no—
325C2—21no—
326C2—21no—
327C2—21no—
328C2#1456217412yes—
329C2#1456220012yes—
330C2#1456394011yescharacteristic
331C2#1456408111yescharacteristic
332C2#1456409111yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1817C2
socleC23×C19C2×C22⋊C4
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#1817D19
hypocenterC19#9152
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
8. #11926450C4semidirect
9. #11926442C4semidirect
217. C19#9152semidirect

Maximal subgroups

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

subgroupindex
#145719742
C2×#119264102
C2×#119262822
#145615152
C19×#18172
#915219