Finite Group Databasebeta

← #18078540

Subgroups — #18078540

Order 4864.

504 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 127 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#14572199C211yesmaximal, characteristic
2#14569456C211yesmaximal, characteristic
3#14562315C212yesmaximal, complemented
4#14561494C212yesmaximal, complemented
5C19×#1458C211yesmaximal, characteristic
6C22×#64520—21no—
7C2×#10597315C2211yescharacteristic
8#11926571—24no—
9#11926568—21no—
10#11926568C2212yes—
11#11926483—21no—
12#11926480—21no—
13#11926464C412yes—
14#11926456C412yes—
15#11926442—21no—
16#11926410C2211yescharacteristic
17#11926404—21no—
18#11926292—24no—
19C2×C19×#117C2211yescharacteristic
20C19×#431C2212yes—
21C19×#324—21no—
22C19×#323—21no—
23C23×C4×C19D411yescharacteristic
24C22×Dic38C2×C412yes—
25C19×#117—22no—
26C19×#117—22no—
27C2×C4⋊C4×C19C2×C411yescharacteristic
28C2×C4⋊C4×C19D411yescharacteristic
29C2×C22⋊C4×C19C2×C411yescharacteristic
30C2×C22⋊C4×C19D411yescharacteristic
31C2×C42×C19D411yescharacteristic
32C2×C42×C19C2311yescharacteristic
33C2×C22⋊Dic19—22no—
34C2×C4⋊Dic19—21no—
35C2×C4⋊Dic19—21no—
36C2×C4⋊Dic19—21no—
37C2×Dic19⋊C4—22no—
38C2×#64520—22no—
39C2×#64520—22no—
40C2×#64520—42no—
41C2×#64520—42no—
42C22×C19⋊C8—22no—
43#10597315—22no—
44#10597315—22no—
45C19×C4⋊C8—22no—
46C19×C22⋊C8—22no—
47C4×C8×C19—22no—
48C19⋊#95—22no—
49C19⋊#95—22no—
50C19⋊#95—21no—
51C19⋊#95C2×C412yes—
52C4⋊(C19⋊C8)—24no—
53C4⋊(C19⋊C8)—22no—
54C4⋊(C19⋊C8)D414yes—
55C24×C19C22⋊C411yescharacteristic
56C22×C4×C19—21no—
57C22×C4×C19—21no—
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19C22⋊C411yescharacteristic
61C22×C4×C19C22⋊C411yescharacteristic
62C22×C4×C19C22⋊C411yescharacteristic
63C22×C4×C19SD1612yes—
64C22×C4×C19Q1612yes—
65C22×C4×C19C22×C411yescharacteristic
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19C2×D411yescharacteristic
68C22×Dic19—22no—
69C22×Dic19—22no—
70C2×Dic38—24no—
71C2×Dic38—82no—
72C2×C8×C19—42no—
73C4⋊C4×C19—22no—
74C4⋊C4×C19—22no—
75C22⋊C4×C19—22no—
76C22⋊C4×C19—22no—
77C42×C19—21no—
78C42×C19—21no—
79C42×C19C2×D412yes—
80C42×C19#4112yes—
81C22⋊Dic19—82no—
82C4⋊Dic19—41no—
83C4⋊Dic19—42no—
84C4⋊Dic19—41no—
85C4⋊Dic19—41no—
86C4⋊Dic19—41no—
87Dic19⋊C4—82no—
88#64520—44no—
89#64520—42no—
90#64520—42no—
91C2×C19⋊C8—24no—
92C2×C19⋊C8—44no—
93#9191—191nomaximal, Sylow
94C23×C19—21no—
95C23×C19—21no—
96C23×C19—41no—
97C23×C19—41no—
98C23×C19#10312yes—
99C23×C19C2×C22⋊C411yescharacteristic
100C2×C4×C19—21no—
101C2×C4×C19—21no—
102C2×C4×C19—22no—
103C2×C4×C19—22no—
104C2×C4×C19—22no—
105C2×C4×C19—22no—
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—41no—
109C2×C4×C19—41no—
110C2×C4×C19—41no—
111C2×C4×C19—41no—
112C2×C4×C19#10312yes—
113C2×C4×C19C4×D412yes—
114C2×C4×C19#12011yescharacteristic
115C2×C4×C19#12112yes—
116C2×C4×C19#12311yescharacteristic
117C2×C4×C19C2×SD1611yescharacteristic
118C2×C4×C19C2×Q1611yescharacteristic
119C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C19#13711yescharacteristic
121C2×Dic19—42no—
122C2×Dic19—42no—
123C2×Dic19—42no—
124C2×Dic19—42no—
125C2×Dic19—42no—
126C2×Dic19—42no—
127Dic38—84no—
128C8×C19—82no—
129C19⋊C8—44no—
130#2905—191no—
131#2628—191no—
132#1548—192no—
133#1458D1911yescharacteristic
134#1286—192no—
135C22×C19—21no—
136C22×C19—21no—
137C22×C19—22no—
138C22×C19—42no—
139C22×C19—41no—
140C22×C19—41no—
141C22×C19—81no—
142C22×C19#38611yescharacteristic
143C22×C19C2×#10311yescharacteristic
144C22×C19#41711yescharacteristic
145C4×C19—22no—
146C4×C19—22no—
147C4×C19—22no—
148C4×C19—41no—
149C4×C19—41no—
150C4×C19#45011yescharacteristic
151C4×C19#45111yescharacteristic
152C4×C19#48311yescharacteristic
153C4×C19#48411yescharacteristic
154Dic19—82no—
155Dic19—82no—
156C22×M16—381no—
157C2×C4⋊Q8—191no—
158C2×#117C2×D1911yescharacteristic
159#431C2×D1912yes—
160#424—384no—
161#423—192no—
162#423—381no—
163#400—381no—
164#399—381no—
165#395—192no—
166#393—192no—
167#389—381no—
168#382—191no—
169#380—381no—
170#333—384no—
171#324—21no—
172#323—21no—
173C2×C19—21no—
174C2×C19—21no—
175C2×C19—42no—
176C2×C19#187211yescharacteristic
177C2×C19#190911yescharacteristic
178C2×C19#191411yescharacteristic
179C22×Q8—192no—
180C23×C4D7611yescharacteristic
181C2×M16—382no—
182C2×M16—382no—
183C2×M16—762no—
184C2×M16—762no—
185C22×C8—382no—
186C4⋊Q8—382no—
187C4⋊Q8—382no—
188#117—22no—
189#117—22no—
190C2×C4⋊C4—381no—
191C2×C4⋊C4—381no—
192C2×C4⋊C4—381no—
193C2×C4⋊C4—382no—
194C2×C4⋊C4C4×D1911yescharacteristic
195C2×C4⋊C4C22⋊D1911yescharacteristic
196C2×C22⋊C4—382no—
197C2×C22⋊C4C4×D1911yescharacteristic
198C2×C22⋊C4C22⋊D1911yescharacteristic
199C2×C42D7611yescharacteristic
200C2×C42C22×D1911yescharacteristic
201C4⋊C8—22no—
202C4⋊C8—194no—
203C4⋊C8—384no—
204C4⋊C8—382no—
205C22⋊C8—22no—
206C4×C8—22no—
207#95—192no—
208#95—382no—
209#95—382no—
210#95—381no—
211C19#919111yescharacteristic, complemented, Sylow
212C24(C2×D19)⋊C411yescharacteristic
213C2×Q8—384no—
214C2×Q8—1522no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—382no—
220C22×C4—382no—
221C22×C4#6451612yes—
222C22×C4Dic7612yes—
223C22×C4(C2×D19)⋊C411yescharacteristic
224C22×C4(C2×D19)⋊C411yescharacteristic
225C22×C4(C2×D19)⋊C411yescharacteristic
226C22×C4C2×C4×D1911yescharacteristic
227C22×C4C2×D7611yescharacteristic
228C22×C4C2×C22⋊D1911yescharacteristic
229M16—764no—
230M16—762no—
231M16—762no—
232C2×C8—42no—
233C2×C8—384no—
234C2×C8—764no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—762no—
238C4⋊C4—761no—
239C4⋊C4—761no—
240C4⋊C4—761no—
241C4⋊C4—761no—
242C4⋊C4—1522no—
243C22⋊C4—22no—
244C22⋊C4—22no—
245C22⋊C4—1522no—
246C42—21no—
247C42—21no—
248C42D4×D1912yes—
249C42#6454312yes—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23#1059727312yes—
255C23C2×(C2×D19)⋊C411yescharacteristic
256Q8—1524no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—762no—
270C2×C4—762no—
271C2×C4—762no—
272C2×C4—762no—
273C2×C4—762no—
274C2×C4—762no—
275C2×C4#1059727312yes—
276C2×C4(C22⋊D19)⋊C412yes—
277C2×C4#1059732811yescharacteristic
278C2×C4#1059733211yescharacteristic
279C2×C4C2×#6451611yescharacteristic
280C2×C4C2×Dic7611yescharacteristic
281C2×C4#1059735411yescharacteristic
282C2×C4#1059735511yescharacteristic
283C2×C4#1059738512yes—
284C8—82no—
285C8—764no—
286C22—21no—
287C22—21no—
288C22—22no—
289C22—42no—
290C22—41no—
291C22—41no—
292C22—81no—
293C22#1192642111yescharacteristic
294C22C2×#1059727311yescharacteristic
295C22#1192654611yescharacteristic
296C4—22no—
297C4—22no—
298C4—22no—
299C4—41no—
300C4—41no—
301C4—1522no—
302C4—1522no—
303C4#1192669711yescharacteristic
304C4#1192670211yescharacteristic
305C4#1192687511yescharacteristic
306C4#1192688011yescharacteristic
307C2—21no—
308C2—21no—
309C2—42no—
310C2#1456394011yescharacteristic
311C2#1456415511yescharacteristic
312C2#1456418011yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1458C2
socleC22×C19#386
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1458D19
hypocenterC19#9191
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
3. #14562315C2semidirect
4. #14561494C2semidirect
211. C19#9191semidirect

Maximal subgroups

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

subgroupindex
#145721992
#145694562
#145623152
#145614942
C19×#14582
#919119