Finite Group Databasebeta

← #18085402

Subgroups — #18085402

Order 4864.

726 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 726 conjugacy classes of subgroups — too many to draw. Only its 103 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#14574386C211yesmaximal, characteristic
2#14571966C212yesmaximal, complemented
3#14562204C212yesmaximal, complemented
4#14561503C211yesmaximal, characteristic, complemented
5C19×#1817C211yesmaximal, characteristic, complemented
6C2×#10597375—22no—
7C2×#10597376C2212yes—
8#11926858—22no—
9#11926780—22no—
10#11926680—22no—
11#11926446—22no—
12#11926442—22no—
13#11926435—24no—
14#11926423—22no—
15#11926404C2212yes—
16#11926279—24no—
17C22×C42×C19C2211yescharacteristic
18C2×C19×C22⋊C8C2211yescharacteristic
19C2×C19×C22⋊C8C2211yescharacteristic
20C19×#336—22no—
21C23×C4×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19C2311yescharacteristic
24C22×C22⋊D19—22no—
25C22×D76D412yes—
26C22×C8×C19—21no—
27C22×C8×C19D412yes—
28C2×C42×C19—22no—
29C2×C42×C19—22no—
30C2×C42×C19—21no—
31C2×C42×C19—21no—
32C2×C22⋊Dic19—22no—
33#10597376—22no—
34#10597376—22no—
35#10597376—22no—
36#10597376—22no—
37#10597375—44no—
38#10597375—44no—
39C2×(C2×D19)⋊C4—24no—
40C2×(C2×D19)⋊C4—24no—
41C2×(C2×D19)⋊C4—22no—
42C2×C4⋊Dic19—22no—
43C2×C4⋊Dic19D412yes—
44C2×Dic19⋊C4—24no—
45C2×D152—22no—
46C19×C22⋊C8—22no—
47C19×C22⋊C8—22no—
48C19⋊#95—24no—
49C19⋊#95D414yes—
50#10597278—24no—
51#10597275—22no—
52C24×C19C2×D411yescharacteristic
53C23×D19—22no—
54C22×C4×C19—22no—
55C22×C4×C19—22no—
56C22×C4×C19—21no—
57C22×C4×C19—21no—
58C22×C4×C19—21no—
59C22×C4×C19—22no—
60C22×C4×C19—42no—
61C22×C4×C19—42no—
62C22×C4×C19D812yescomplemented
63C22×C4×C19C2×D412yes—
64C22×C4×C19C2×D412yes—
65C22×C4×C19C2×D411yescharacteristic
66C22×C4×C19#4111yescharacteristic
67C2×C22⋊D19—42no—
68C2×C22⋊D19—42no—
69C2×C22⋊D19—42no—
70C2×C22⋊D19—42no—
71C2×C22⋊D19—42no—
72C2×C22⋊D19—42no—
73C22×Dic19—24no—
74C22×Dic19—22no—
75C2×D76—22no—
76C2×D76—22no—
77C2×D76—44no—
78C2×C8×C19—22no—
79C2×C8×C19—42no—
80C2×C8×C19—42no—
81C2×C8×C19—41no—
82C42×C19—41no—
83C42×C19—42no—
84C42×C19—41no—
85C22⋊Dic19—42no—
86C22⋊Dic19—42no—
87(C2×D19)⋊C4—48no—
88(C2×D19)⋊C4—48no—
89(C2×D19)⋊C4—42no—
90(C2×D19)⋊C4—42no—
91C4⋊Dic19—22no—
92C4⋊Dic19—22no—
93C4⋊Dic19—44no—
94Dic19⋊C4—48no—
95D152—82no—
96#10321—191nomaximal, Sylow
97C23×C19—41no—
98C23×C19—41no—
99C23×C19#12012yes—
100C23×C19#12111yescharacteristic
101C23×C19C2×D811yescharacteristic
102C23×C19#13511yescharacteristic
103C23×C19AGL(1,ℤ/8)12yes—
104C22×D19—44no—
105C22×D19—44no—
106C22×D19—42no—
107C22×D19—42no—
108C22×D19—42no—
109C2×C4×C19—24no—
110C2×C4×C19—22no—
111C2×C4×C19—24no—
112C2×C4×C19—22no—
113C2×C4×C19—24no—
114C2×C4×C19—22no—
115C2×C4×C19—42no—
116C2×C4×C19—41no—
117C2×C4×C19—42no—
118C2×C4×C19—41no—
119C2×C4×C19—41no—
120C2×C4×C19—41no—
121C2×C4×C19—42no—
122C2×C4×C19—41no—
123C2×C4×C19#12011yescharacteristic
124C2×C4×C19#12112yes—
125C2×C4×C19#12711yescharacteristic
126C22⋊D19—82no—
127C22⋊D19—82no—
128C22⋊D19—82no—
129C22⋊D19—82no—
130C2×Dic19—44no—
131C2×Dic19—44no—
132C2×Dic19—42no—
133C2×Dic19—42no—
134C2×Dic19—44no—
135C2×Dic19—42no—
136D76—44no—
137D76—82no—
138C8×C19—42no—
139C8×C19—81no—
140#3186—191no—
141#2854—192no—
142#1817D1911yescharacteristic, complemented
143#1519—192no—
144#1289—191no—
145C22×C19—22no—
146C22×C19—21no—
147C22×C19—22no—
148C22×C19—21no—
149C22×C19—41no—
150C22×C19—41no—
151C22×C19—42no—
152C22×C19#39211yescharacteristic
153C22×C19#44712yes—
154C22×C19#44912yes—
155C22×C19#46611yescharacteristic
156C22×C19#46911yescharacteristic
157C2×D19—84no—
158C2×D19—84no—
159C2×D19—82no—
160C2×D19—82no—
161C2×D19—82no—
162C4×C19—21no—
163C4×C19—22no—
164C4×C19—42no—
165C4×C19—42no—
166C4×C19#45812yes—
167Dic19—84no—
168Dic19—82no—
169C2×#123—382no—
170C2×#121—192no—
171C22×C42C2×D1911yescharacteristic
172#480—382no—
173#466—382no—
174#447—382no—
175C2×C22⋊C8C2×D1911yescharacteristic
176C2×C22⋊C8C2×D1911yescharacteristic
177#390—382no—
178#389—382no—
179#388—384no—
180#386—382no—
181#380—192no—
182#336—22no—
183#327—384no—
184C2×C19—22no—
185C2×C19—22no—
186C2×C19—21no—
187C2×C19—21no—
188C2×C19#199911yescharacteristic
189C2×C19#201011yescharacteristic
190C2×C19#202211yescharacteristic
191D19—162no—
192C22×D4—192no—
193C22×D4—382no—
194C23×C4D7611yescharacteristic
195C23×C4D7611yescharacteristic
196C23×C4C22×D1911yescharacteristic
197C2×D8—382no—
198C22×C8—21no—
199C22×C8C22⋊D1912yes—
200#123—764no—
201#123—764no—
202#121—382no—
203#121—382no—
204#121—382no—
205#121—382no—
206C2×C4⋊C4—192no—
207C2×C4⋊C4—384no—
208C2×C4⋊C4—382no—
209C2×C22⋊C4—384no—
210C2×C22⋊C4—384no—
211C2×C22⋊C4—382no—
212C2×C22⋊C4—382no—
213C2×C42—21no—
214C2×C42—22no—
215C2×C42—22no—
216C2×C42—21no—
217#107—382no—
218#102—384no—
219C22⋊C8—22no—
220C22⋊C8—22no—
221#95—194no—
222#95—384no—
223C19#1032111yescharacteristic, complemented, Sylow
224C24—382no—
225C24C2×D7611yescharacteristic
226C2×D4—382no—
227C2×D4—382no—
228C2×D4—764no—
229C2×D4—762no—
230C2×D4—762no—
231C2×D4—762no—
232C2×D4—762no—
233C2×D4—762no—
234C2×D4—762no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—384no—
244C22×C4—382no—
245C22×C4D15212yescomplemented
246C22×C4#6454111yescharacteristic
247C22×C4D4×D1912yes—
248C22×C4D4×D1912yes—
249C22×C4C2×C22⋊D1911yescharacteristic
250D8—1522no—
251C2×C8—22no—
252C2×C8—42no—
253C2×C8—42no—
254C2×C8—41no—
255C4⋊C4—382no—
256C4⋊C4—382no—
257C4⋊C4—768no—
258C4⋊C4—764no—
259C22⋊C4—768no—
260C22⋊C4—768no—
261C22⋊C4—762no—
262C22⋊C4—762no—
263C22⋊C4—762no—
264C22⋊C4—762no—
265C42—41no—
266C42—41no—
267C42—42no—
268C23—41no—
269C23—41no—
270C23—764no—
271C23—764no—
272C23—762no—
273C23—762no—
274C23—762no—
275C23#1059732812yes—
276C23C2×D15211yescharacteristic
277C23#1059735011yescharacteristic
278C23#1059735412yes—
279C23#1059737611yescharacteristic
280D4—764no—
281D4—1522no—
282D4—1522no—
283D4—1522no—
284D4—1522no—
285D4—1522no—
286C2×C4—24no—
287C2×C4—22no—
288C2×C4—24no—
289C2×C4—22no—
290C2×C4—24no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—764no—
301C2×C4—764no—
302C2×C4—764no—
303C2×C4—762no—
304C2×C4—762no—
305C2×C4—762no—
306C2×C4#1059733012yes—
307C2×C4#1059738311yescharacteristic
308C2×C4#1059738611yescharacteristic
309C8—42no—
310C8—81no—
311C22—22no—
312C22—21no—
313C22—22no—
314C22—21no—
315C22—41no—
316C22—41no—
317C22—42no—
318C22—1524no—
319C22—1524no—
320C22—1522no—
321C22—1522no—
322C22—1522no—
323C22#1192645311yescharacteristic
324C22#1192668012yes—
325C22#1192669112yes—
326C22#1192678011yescharacteristic
327C22#1192679711yescharacteristic
328C4—21no—
329C4—22no—
330C4—42no—
331C4—42no—
332C4—1524no—
333C4—1522no—
334C4#1192673312yes—
335C2—22no—
336C2—22no—
337C2—21no—
338C2—21no—
339C2—3042no—
340C2#1456463311yescharacteristic
341C2#1456470211yescharacteristic
342C2#1456476611yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1817C2
socleC22×C19#392
prime radical#14574386C2
hypercenter#1817D19
hypocenterC19#10321
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1817

Complements

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

NH ≅ G/Ntype
2. #14571966C2semidirect
3. #14562204C2semidirect
4. #14561503C2semidirect
5. C19×#1817C2semidirect
62. C22×C4×C19D8semidirect
142. #1817D19semidirect
223. C19#10321semidirect
245. C22×C4D152semidirect

Maximal subgroups

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

subgroupindex
#145743862
#145719662
#145622042
#145615032
C19×#18172
#1032119