Finite Group Databasebeta

← #18071375

Subgroups — #18071375

Order 4864.

456 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 87 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#14571628C211yesmaximal, characteristic
2#14564773C212yesmaximal
3#14561461C211yesmaximal, characteristic
4#14561460C212yesmaximal
5C19×#2016C211yesmaximal, characteristic
6C2×#10597267—22no—
7#11926465—22no—
8#11926464—21no—
9#11926451—21no—
10#11926450C2212yes—
11#11926448—22no—
12#11926306—22no—
13#11926299C2212yes—
14C22×Q16×C19—21no—
15C2×C19×C4⋊Q8C2211yescharacteristic
16C2×C19×#103—21no—
17C19×#391C2211yescharacteristic
18C19×#336C2211yescharacteristic
19C22×Q8×C19—21no—
20C22×Q8×C19D411yescharacteristic
21C22×Dic38—21no—
22C22×Dic38D412yes—
23C2×Q16×C19—42no—
24C2×Q16×C19—42no—
25C2×Q16×C19—42no—
26C22×C8×C19—21no—
27C19×C4⋊Q8—42no—
28C2×C4⋊C4×C19—22no—
29C2×C4⋊C4×C19D411yescharacteristic
30C2×C42×C19C2311yescharacteristic
31C2×C4⋊Dic19—21no—
32C2×C4⋊Dic19D412yes—
33C2×Dic19⋊C4—22no—
34C2×C4×Dic19—21no—
35C22×C19⋊C8—22no—
36C19×#103—42no—
37C19×#95—22no—
38C19⋊#95—21no—
39C19⋊#95—22no—
40C19⋊#95—22no—
41C19⋊#95—22no—
42#10597267—44no—
43C2×Q8×C19—21no—
44C2×Q8×C19—22no—
45C2×Q8×C19—41no—
46C2×Q8×C19—41no—
47C2×Q8×C19—41no—
48C2×Q8×C19—41no—
49C2×Q8×C19—41no—
50C2×Q8×C19—41no—
51C2×Q8×C19—41no—
52C2×Q8×C19SD1612yes—
53C22×C4×C19—21no—
54C22×C4×C19—21no—
55C22×C4×C19—41no—
56C22×C4×C19C2×D412yes—
57C22×C4×C19C2×D411yescharacteristic
58C22×Dic19—22no—
59C22×Dic19—22no—
60C2×Dic38—22no—
61C2×Dic38—42no—
62C2×Dic38—42no—
63C2×Dic38—81no—
64C2×Dic38—82no—
65C2×Dic38Q1614yescomplemented
66Q16×C19—48no—
67C2×C8×C19—22no—
68C2×C8×C19—41no—
69C2×C8×C19—41no—
70C4⋊C4×C19—24no—
71C4⋊C4×C19—41no—
72C4⋊C4×C19—42no—
73C42×C19—41no—
74C4⋊Dic19—42no—
75C4⋊Dic19—81no—
76Dic19⋊C4—82no—
77C4×Dic19—81no—
78C2×C19⋊C8—42no—
79C2×C19⋊C8—42no—
80C2×C19⋊C8—42no—
81#7759—191nomaximal, Sylow
82C23×C19#12011yescharacteristic
83Q8×C19—42no—
84Q8×C19—42no—
85Q8×C19—42no—
86Q8×C19—81no—
87Q8×C19—81no—
88Q8×C19—81no—
89C2×C4×C19—21no—
90C2×C4×C19—22no—
91C2×C4×C19—22no—
92C2×C4×C19—21no—
93C2×C4×C19—22no—
94C2×C4×C19—41no—
95C2×C4×C19—41no—
96C2×C4×C19—41no—
97C2×C4×C19—42no—
98C2×C4×C19—42no—
99C2×C4×C19—81no—
100C2×C4×C19—81no—
101C2×C4×C19C2×SD1611yescharacteristic
102C2×C4×C19C2×Q1612yes—
103C2×C4×C19#13711yescharacteristic
104C2×C4×C19#13712yes—
105C2×Dic19—24no—
106C2×Dic19—42no—
107C2×Dic19—42no—
108C2×Dic19—42no—
109C2×Dic19—42no—
110C2×Dic19—42no—
111Dic38—44no—
112Dic38—82no—
113Dic38—84no—
114C8×C19—42no—
115C19⋊C8—82no—
116#2811—191no—
117#2024—192no—
118#2016D1911yescharacteristic
119#1272—191no—
120#1272—192no—
121C22×C19#44811yescharacteristic
122C22×C19#45112yes—
123C22×C19#45311yescharacteristic
124C22×C19#45512yes—
125C22×C19B(4,𝔽2)11yescharacteristic
126C4×C19—21no—
127C4×C19—21no—
128C4×C19—22no—
129C4×C19—22no—
130C4×C19—42no—
131C4×C19—82no—
132C4×C19—81no—
133Dic19—44no—
134Dic19—82no—
135C22×Q16—21no—
136C2×C4⋊Q8C2×D1911yescharacteristic
137C2×#103—21no—
138C2×#103—382no—
139#395—382no—
140#395—381no—
141#391—192no—
142#391—382no—
143#391—381no—
144#391C2×D1911yescharacteristic
145#340—382no—
146#336—192no—
147#336C2×D1911yescharacteristic
148C2×C19#159611yescharacteristic
149C2×C19#160212yes—
150C2×C19#163311yescharacteristic
151C2×C19#164512yes—
152C2×C19#165911yescharacteristic
153C22×Q8—21no—
154C22×Q8—192no—
155C22×Q8—381no—
156C22×Q8C22⋊D1911yescharacteristic
157C2×Q16—42no—
158C2×Q16—42no—
159C2×Q16—42no—
160C22×C8—21no—
161C22×C8—382no—
162C4⋊Q8—42no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—192no—
165C2×C4⋊C4—382no—
166C2×C4⋊C4—381no—
167C2×C4⋊C4C22⋊D1911yescharacteristic
168C2×C42—381no—
169C2×C42C22×D1911yescharacteristic
170#103—42no—
171#103—764no—
172#95—22no—
173#95—382no—
174#95—381no—
175#95—382no—
176#95—382no—
177C19#775911yescharacteristic, complemented, Sylow
178C2×Q8—21no—
179C2×Q8—22no—
180C2×Q8—41no—
181C2×Q8—41no—
182C2×Q8—41no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8—41no—
187C2×Q8—194no—
188C2×Q8—382no—
189C2×Q8—762no—
190C2×Q8—762no—
191C2×Q8—1521no—
192C2×Q8—1522no—
193C2×Q8#6452612yes—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—41no—
197C22×C4—382no—
198C22×C4—382no—
199C22×C4D4×D1912yes—
200C22×C4C2×C22⋊D1911yescharacteristic
201Q16—48no—
202C2×C8—22no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—762no—
206C2×C8—762no—
207C2×C8—762no—
208C4⋊C4—24no—
209C4⋊C4—41no—
210C4⋊C4—42no—
211C4⋊C4—762no—
212C4⋊C4—1522no—
213C4⋊C4—1521no—
214C42—41no—
215C42—1521no—
216C23#1059738311yescharacteristic
217Q8—42no—
218Q8—42no—
219Q8—42no—
220Q8—81no—
221Q8—81no—
222Q8—81no—
223Q8—764no—
224Q8—1522no—
225Q8—1524no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—81no—
237C2×C4—81no—
238C2×C4—384no—
239C2×C4—762no—
240C2×C4—762no—
241C2×C4—762no—
242C2×C4—762no—
243C2×C4—762no—
244C2×C4Q16×D1912yes—
245C2×C4#1059736412yes—
246C2×C4C2×#6452611yescharacteristic
247C2×C4#1059739711yescharacteristic
248C8—42no—
249C8—1522no—
250C22#1192668211yescharacteristic
251C22#1192669812yes—
252C22#1192671111yescharacteristic
253C22#1192672012yes—
254C22#1192673011yescharacteristic
255C4—22no—
256C4—22no—
257C4—21no—
258C4—21no—
259C4—42no—
260C4—81no—
261C4—82no—
262C4—764no—
263C4—1522no—
264C2#1456255711yescharacteristic
265C2#1456259012yes—
266C2#1456277311yescharacteristic
267C2#1456285412yes—
268C2#1456293911yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2016C2
socle, prime radicalC23×C19#120
hypercenter#2016D19
hypocenterC19#7759
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2016

Complements

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

NH ≅ G/Ntype
65. C2×Dic38Q16semidirect
177. C19#7759semidirect

Maximal subgroups

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

subgroupindex
#145716282
#145647732
#145614612
#145614602
C19×#20162
#775919