Finite Group Databasebeta

← #18080363

Subgroups — #18080363

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#14566970C211yesmaximal, characteristic
2#14563580C212yesmaximal
3#14561965C211yesmaximal, characteristic, complemented
4#14561488C212yesmaximal, complemented
5C19×#2313C211yesmaximal, characteristic, complemented
6C22×#64541C2211yescharacteristic
7C2×#10597375—21no—
8C2×#10597262—24no—
9#11926508C2212yes—
10#11926464C412yescomplemented
11#11926461C412yescomplemented
12#11926423—21no—
13#11926415—22no—
14#11926407C2211yescharacteristic
15#11926270—22no—
16C22×C4⋊C4×C19C2211yescharacteristic
17C19×#387—24no—
18C19×#381—21no—
19C19×#380—21no—
20C4×C22⋊C4×C19C2212yes—
21C23×C4×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19C2311yescharacteristic
24C22×C22⋊D19—21no—
25C2×#64541—22no—
26C2×#64541—22no—
27C2×#64541—44no—
28C22×D76C2×C411yescharacteristic
29C22×C4×D19—21no—
30C22×Dic38C2×C411yescharacteristic
31C2×C4⋊C4×C19—22no—
32C2×C4⋊C4×C19—22no—
33C2×C4⋊C4×C19—22no—
34C2×C4⋊C4×C19C2×C412yes—
35C2×C4⋊C4×C19D412yes—
36C2×C22⋊C4×C19—22no—
37C2×C42×C19D414yes—
38C2×C22⋊Dic19—21no—
39#10597375—44no—
40C2×(C2×D19)⋊C4—22no—
41C2×(C2×D19)⋊C4—22no—
42C2×Dic19⋊C4—22no—
43C2×#64520—22no—
44C19×#95—22no—
45C19×#95—24no—
46C19×#95—22no—
47C19⋊#95—22no—
48C19⋊#95—21no—
49C19⋊#95C2×C412yes—
50C22⋊(C19⋊C8)—22no—
51C22⋊(C19⋊C8)—22no—
52#10597262—48no—
53C24×C19C2×D411yescharacteristic
54C23×D19—21no—
55C22×C4×C19—21no—
56C22×C4×C19—21no—
57C22×C4×C19—21no—
58C22×C4×C19—21no—
59C22×C4×C19—24no—
60C22×C4×C19—42no—
61C22×C4×C19—42no—
62C22×C4×C19—42no—
63C22×C4×C19C22⋊C412yes—
64C22×C4×C19C22⋊C412yes—
65C22×C4×C19C22×C411yescharacteristic
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19C2×D412yes—
68C22×C4×C19#4112yes—
69C2×C22⋊D19—24no—
70C2×C22⋊D19—42no—
71C2×C22⋊D19—41no—
72C2×C22⋊D19—41no—
73C22×Dic19—21no—
74C22×Dic19—22no—
75#64541—28no—
76#64541—44no—
77#64541—44no—
78#64541—44no—
79C2×D76—22no—
80C2×D76—42no—
81C2×C4×D19—42no—
82C2×C4×D19—42no—
83C2×C4×D19—42no—
84C2×Dic38—22no—
85C2×Dic38—42no—
86C4⋊C4×C19—24no—
87C4⋊C4×C19—24no—
88C4⋊C4×C19—82no—
89C22⋊C4×C19—44no—
90C42×C19—44no—
91C22⋊Dic19—42no—
92(C2×D19)⋊C4—44no—
93(C2×D19)⋊C4—44no—
94Dic19⋊C4—44no—
95#64520—44no—
96C2×C19⋊C8—42no—
97#9480—191nomaximal, Sylow
98C23×C19—22no—
99C23×C19—22no—
100C23×C19—41no—
101C23×C19C2×C22⋊C411yescharacteristic
102C23×C19#12011yescharacteristic
103C23×C19#12311yescharacteristic
104C22×D19—22no—
105C22×D19—41no—
106C22×D19—42no—
107C22×D19—41no—
108C22×D19—42no—
109C2×C4×C19—24no—
110C2×C4×C19—22no—
111C2×C4×C19—22no—
112C2×C4×C19—22no—
113C2×C4×C19—22no—
114C2×C4×C19—41no—
115C2×C4×C19—41no—
116C2×C4×C19—42no—
117C2×C4×C19—42no—
118C2×C4×C19—42no—
119C2×C4×C19—42no—
120C2×C4×C19—42no—
121C2×C4×C19—44no—
122C2×C4×C19—44no—
123C2×C4×C19—44no—
124C2×C4×C19—81no—
125C2×C4×C19C4×D412yes—
126C2×C4×C19#12112yes—
127C22⋊D19—44no—
128C22⋊D19—44no—
129C2×Dic19—22no—
130C2×Dic19—41no—
131C2×Dic19—41no—
132C2×Dic19—42no—
133C2×Dic19—42no—
134C2×Dic19—42no—
135D76—24no—
136D76—42no—
137C4×D19—48no—
138Dic38—24no—
139Dic38—42no—
140C19⋊C8—82no—
141#2406—191no—
142#2313D1911yescharacteristic, complemented
143#1789—192no—
144#1463—191no—
145#1284—192no—
146C22×C19—21no—
147C22×C19—21no—
148C22×C19—21no—
149C22×C19—21no—
150C22×C19—21no—
151C22×C19—21no—
152C22×C19—21no—
153C22×C19—44no—
154C22×C19#38611yescharacteristic
155C22×C19#42112yes—
156C22×C19B(4,𝔽2)12yes—
157C2×D19—44no—
158C2×D19—42no—
159C2×D19—82no—
160C2×D19—81no—
161C2×D19—81no—
162C4×C19—22no—
163C4×C19—22no—
164C4×C19—42no—
165C4×C19—42no—
166C4×C19—84no—
167Dic19—42no—
168Dic19—82no—
169C22×#41—191no—
170C2×#123—381no—
171C22×C4⋊C4C2×D1911yescharacteristic
172C2×#104—384no—
173#407—192no—
174#395—192no—
175#394—192no—
176#387—24no—
177#386—381no—
178#385—382no—
179#381—21no—
180#381—191no—
181#380—21no—
182C4×C22⋊C4C2×D1912yes—
183#324—382no—
184C2×C19—22no—
185C2×C19—22no—
186C2×C19—41no—
187C2×C19#188911yescharacteristic
188C2×C19#189711yescharacteristic
189C2×C19#191211yescharacteristic
190D19—82no—
191C2×#41—382no—
192C2×#41—382no—
193C2×#41—764no—
194C22×Q8—191no—
195C22×D4—191no—
196C22×D4—381no—
197C23×C4—381no—
198C23×C4C22⋊D1911yescharacteristic
199C23×C4C22⋊D1911yescharacteristic
200C23×C4C22×D1911yescharacteristic
201C2×M16—382no—
202#123—764no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—382no—
207C2×C4⋊C4C4×D1912yes—
208C2×C4⋊C4D7612yes—
209C2×C22⋊C4—22no—
210C2×C22⋊C4—381no—
211C2×C22⋊C4—382no—
212C2×C22⋊C4—382no—
213C2×C42C22⋊D1914yes—
214#104—768no—
215C22⋊C8—382no—
216C22⋊C8—382no—
217#95—22no—
218#95—24no—
219#95—22no—
220#95—192no—
221#95—382no—
222#95—381no—
223C19#948011yescharacteristic, complemented, Sylow
224C24—381no—
225C24C2×C22⋊D1911yescharacteristic
226#41—388no—
227#41—764no—
228#41—764no—
229#41—764no—
230C2×Q8—382no—
231C2×Q8—762no—
232C2×D4—384no—
233C2×D4—382no—
234C2×D4—762no—
235C2×D4—762no—
236C2×D4—761no—
237C2×D4—761no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—24no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—381no—
247C22×C4—382no—
248C22×C4—762no—
249C22×C4—762no—
250C22×C4—762no—
251C22×C4(C2×D19)⋊C412yes—
252C22×C4(C2×D19)⋊C412yes—
253C22×C4C2×C4×D1911yescharacteristic
254C22×C4C2×D7611yescharacteristic
255C22×C4#6454112yes—
256C22×C4C2×C22⋊D1912yes—
257M16—764no—
258C2×C8—762no—
259C4⋊C4—24no—
260C4⋊C4—24no—
261C4⋊C4—82no—
262C4⋊C4—764no—
263C22⋊C4—44no—
264C22⋊C4—764no—
265C22⋊C4—764no—
266C22⋊C4—762no—
267C42—44no—
268C23—22no—
269C23—22no—
270C23—41no—
271C23—382no—
272C23—761no—
273C23—762no—
274C23—762no—
275C23—761no—
276C23C2×(C2×D19)⋊C411yescharacteristic
277C23#1059737511yescharacteristic
278C23#1059739911yescharacteristic
279Q8—384no—
280Q8—762no—
281D4—384no—
282D4—762no—
283D4—764no—
284D4—764no—
285C2×C4—24no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4—81no—
301C2×C4—382no—
302C2×C4—768no—
303C2×C4—761no—
304C2×C4—761no—
305C2×C4—762no—
306C2×C4—762no—
307C2×C4—762no—
308C2×C4C4×C22⋊D1912yes—
309C2×C4#1059737612yes—
310C8—1522no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—44no—
319C22—764no—
320C22—762no—
321C22—1522no—
322C22—1521no—
323C22—1521no—
324C22#1192642311yescharacteristic
325C22#1192656212yes—
326C22#1192673112yes—
327C4—22no—
328C4—22no—
329C4—42no—
330C4—42no—
331C4—84no—
332C4—762no—
333C4—1522no—
334C2—22no—
335C2—22no—
336C2—41no—
337C2—1522no—
338C2#1456404311yescharacteristic
339C2#1456408311yescharacteristic
340C2#1456417211yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2313C2
socleC22×C19#386
prime radicalC22×#64541C22
cosocleC23×C4×C19C23
hypercenter#2313D19
hypocenterC19#9480
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2313

Complements

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

NH ≅ G/Ntype
3. #14561965C2semidirect
4. #14561488C2semidirect
5. C19×#2313C2semidirect
10. #11926464C4semidirect
11. #11926461C4semidirect
142. #2313D19semidirect
223. C19#9480semidirect

Maximal subgroups

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

subgroupindex
#145669702
#145635802
#145619652
#145614882
C19×#23132
#948019