Finite Group Databasebeta

← #18083151

Subgroups — #18083151

Order 4864.

716 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 83 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#14574410C211yesmaximal, characteristic, complemented
2#14572895C212yesmaximal
3#14561998C212yesmaximal, complemented
4#14561512C211yesmaximal, characteristic, complemented
5C19×#1780C211yesmaximal, characteristic
6C2×#10597397—22no—
7C2×#10597370C2212yes—
8#11926880—22no—
9#11926785—22no—
10#11926706—24no—
11#11926702—22no—
12#11926700—22no—
13#11926695—22no—
14#11926545—22no—
15#11926508C2212yes—
16#11926269—24no—
17C22×#41×C19C2211yescharacteristic
18C2×C19×C22⋊C8—22no—
19C2×C19×C22⋊C8C2211yescharacteristic
20C2×C19×C22⋊C8C2211yescharacteristic
21C2×#41×C19—22no—
22C2×#41×C19—22no—
23C2×#41×C19—44no—
24C22×Q8×C19D411yescharacteristic
25C22×D4×C19—21no—
26C22×D4×C19D411yescharacteristic
27C23×C4×C19—21no—
28C23×C4×C19C2311yescharacteristic
29C22×Dic38D412yes—
30C22×C8×C19—21no—
31C22×C8×C19D412yes—
32C2×C22⋊Dic19—22no—
33#10597397—48no—
34C2×#64528—24no—
35C2×#64526—24no—
36C2×C4⋊Dic19D412yes—
37#10597370—22no—
38#10597370—22no—
39#10597370—22no—
40#10597370—22no—
41C2×Dic19⋊C4—22no—
42C2×#64520—22no—
43C2×Dic76—22no—
44C19×C22⋊C8—22no—
45C19×C22⋊C8—22no—
46C19×C22⋊C8—44no—
47#10597292—24no—
48#10597289—24no—
49C22⋊(C19⋊C8)—22no—
50C22⋊(C19⋊C8)D414yes—
51#10597275—22no—
52#10597273—24no—
53C24×C19—21no—
54C24×C19#4111yescharacteristic
55#41×C19—28no—
56#41×C19—44no—
57#41×C19—44no—
58#41×C19—44no—
59C2×Q8×C19—22no—
60C2×Q8×C19—42no—
61C2×D4×C19—22no—
62C2×D4×C19—42no—
63C2×D4×C19—42no—
64C2×D4×C19—42no—
65C2×D4×C19—42no—
66C22×C4×C19—24no—
67C22×C4×C19—21no—
68C22×C4×C19—42no—
69C22×C4×C19—42no—
70C22×C4×C19—41no—
71C22×C4×C19—41no—
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19C2×D412yes—
74C22×C4×C19C2×D412yes—
75C22×C4×C19C2×D411yescharacteristic
76C22×Dic19—22no—
77C22×Dic19—22no—
78C2×Dic38—22no—
79C2×Dic38—22no—
80C2×Dic38—44no—
81C2×C8×C19—22no—
82C2×C8×C19—42no—
83C2×C8×C19—42no—
84C2×C8×C19—41no—
85C22⋊Dic19—42no—
86C22⋊Dic19—42no—
87#64528—48no—
88#64526—48no—
89C4⋊Dic19—22no—
90C4⋊Dic19—22no—
91Dic19⋊C4—42no—
92Dic19⋊C4—42no—
93#64520—44no—
94C2×C19⋊C8—24no—
95Dic76—82no—
96#9976—191nomaximal, Sylow
97C23×C19—22no—
98C23×C19—22no—
99C23×C19—41no—
100C23×C19—41no—
101C23×C19—41no—
102C23×C19—42no—
103C23×C19—41no—
104C23×C19—42no—
105C23×C19#12111yescharacteristic
106C23×C19#12112yes—
107Q8×C19—24no—
108Q8×C19—42no—
109D4×C19—24no—
110D4×C19—42no—
111D4×C19—48no—
112C2×C4×C19—24no—
113C2×C4×C19—22no—
114C2×C4×C19—22no—
115C2×C4×C19—41no—
116C2×C4×C19—42no—
117C2×C4×C19—44no—
118C2×C4×C19—41no—
119C2×C4×C19—41no—
120C2×C4×C19—44no—
121C2×C4×C19#12011yescharacteristic
122C2×C4×C19#12012yes—
123C2×C4×C19#12711yescharacteristic
124C2×Dic19—44no—
125C2×Dic19—42no—
126C2×Dic19—42no—
127C2×Dic19—82no—
128Dic38—44no—
129Dic38—44no—
130C8×C19—42no—
131C8×C19—81no—
132C19⋊C8—44no—
133#3189—191no—
134#3007—192no—
135#1780D1911yescharacteristic
136#1472—192no—
137#1293—191no—
138C22×C19—21no—
139C22×C19—21no—
140C22×C19—22no—
141C22×C19—22no—
142C22×C19—22no—
143C22×C19—44no—
144C22×C19—42no—
145C22×C19—82no—
146C22×C19—82no—
147C22×C19—81no—
148C22×C19—81no—
149C22×C19#39211yescharacteristic
150C22×C19#47312yes—
151C4×C19—22no—
152C4×C19—21no—
153C4×C19—42no—
154C4×C19B(4,𝔽2)12yes—
155Dic19—82no—
156Dic19—82no—
157C22×#41C2×D1911yescharacteristic
158C2×#137—382no—
159C2×C22⋊Q8—192no—
160#484—382no—
161#467—382no—
162#452—384no—
163#451—382no—
164#451—382no—
165#450—382no—
166#417—382no—
167#407—192no—
168C2×C22⋊C8—22no—
169C2×C22⋊C8C2×D1911yescharacteristic
170C2×C22⋊C8C2×D1911yescharacteristic
171#324—384no—
172C2×C19—22no—
173C2×C19—42no—
174C2×C19—82no—
175C2×C19#201711yescharacteristic
176C2×C19#202011yescharacteristic
177C2×C19#202111yescharacteristic
178C2×#41—22no—
179C2×#41—22no—
180C2×#41—44no—
181C22×Q8—192no—
182C22×Q8D7611yescharacteristic
183C22×D4—21no—
184C22×D4D7611yescharacteristic
185C23×C4—21no—
186C23×C4C22×D1911yescharacteristic
187#137—768no—
188C2×Q16—382no—
189C2×Q16—384no—
190C2×SD16—384no—
191C2×M16—382no—
192C22×C8—21no—
193C22×C8C22⋊D1912yes—
194C22⋊Q8—382no—
195C22⋊Q8—382no—
196C22⋊Q8—382no—
197C22⋊Q8—382no—
198C2×C4⋊C4—192no—
199C2×C4⋊C4—382no—
200C2×C22⋊C4—382no—
201#107—382no—
202#103—384no—
203#103—384no—
204#102—384no—
205C22⋊C8—22no—
206C22⋊C8—22no—
207C22⋊C8—44no—
208C22⋊C8—194no—
209C22⋊C8—382no—
210C19#997611yescharacteristic, complemented, Sylow
211C24—21no—
212C24#6454111yescharacteristic
213#41—28no—
214#41—44no—
215#41—44no—
216#41—44no—
217C2×Q8—22no—
218C2×Q8—42no—
219C2×Q8—382no—
220C2×Q8—382no—
221C2×Q8—764no—
222C2×D4—22no—
223C2×D4—42no—
224C2×D4—42no—
225C2×D4—42no—
226C2×D4—42no—
227C22×C4—24no—
228C22×C4—21no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—382no—
234C22×C4—382no—
235C22×C4C2×D7611yescharacteristic
236C22×C4D4×D1912yes—
237C22×C4D4×D1912yes—
238C22×C4C2×C22⋊D1911yescharacteristic
239Q16—768no—
240Q16—1522no—
241SD16—768no—
242M16—764no—
243C2×C8—22no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—41no—
247C2×C8—384no—
248C4⋊C4—382no—
249C4⋊C4—382no—
250C4⋊C4—762no—
251C4⋊C4—762no—
252C22⋊C4—762no—
253C22⋊C4—762no—
254C23—22no—
255C23—22no—
256C23—41no—
257C23—41no—
258C23—41no—
259C23—42no—
260C23—42no—
261C23—41no—
262C23#1059733012yes—
263C23#1059737611yescharacteristic
264Q8—24no—
265Q8—42no—
266Q8—764no—
267Q8—764no—
268D4—24no—
269D4—42no—
270D4—48no—
271C2×C4—22no—
272C2×C4—24no—
273C2×C4—22no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—44no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—44no—
280C2×C4—764no—
281C2×C4—762no—
282C2×C4—762no—
283C2×C4—1522no—
284C2×C4#1059732812yes—
285C2×C4#1059738311yescharacteristic
286C2×C4#1059738611yescharacteristic
287C8—42no—
288C8—81no—
289C8—764no—
290C22—21no—
291C22—21no—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—44no—
296C22—42no—
297C22—82no—
298C22—82no—
299C22—81no—
300C22—81no—
301C22#1192645311yescharacteristic
302C22#1192681912yes—
303C4—21no—
304C4—22no—
305C4—42no—
306C4—1522no—
307C4—1522no—
308C4#1192673012yes—
309C2—22no—
310C2—42no—
311C2—82no—
312C2#1456473911yescharacteristic
313C2#1456475611yescharacteristic
314C2#1456476111yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1780C2
socleC22×C19#392
prime radicalC22×#41×C19C22
hypercenter#1780D19
hypocenterC19#9976
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1780

Complements

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

NH ≅ G/Ntype
1. #14574410C2semidirect
3. #14561998C2semidirect
4. #14561512C2semidirect
210. C19#9976semidirect

Maximal subgroups

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

subgroupindex
#145744102
#145728952
#145619982
#145615122
C19×#17802
#997619