Finite Group Databasebeta

← #18080243

Subgroups — #18080243

Order 4864.

432 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 107 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#14568847C211yesmaximal, characteristic
2#14562353C212yesmaximal
3#14561979C211yesmaximal, characteristic
4#14561492C212yesmaximal
5C19×#2983C211yesmaximal, characteristic
6C2×#10597315C2211yescharacteristic
7#11926601C2212yes—
8#11926483—21no—
9#11926483—21no—
10#11926451C412yes—
11#11926450—21no—
12#11926450—21no—
13#11926409C412yes—
14C4×C4⋊Dic19C2211yescharacteristic
15#11926291—24no—
16#11926270—21no—
17#11926270—21no—
18C2×C4×Q8×C19C2211yescharacteristic
19C19×#446—24no—
20C19×#432—21no—
21C19×#432C2212yes—
22C19×#431—21no—
23C22×Q8×C19C2×C411yescharacteristic
24C22×Dic38—21no—
25C4×Q8×C19—22no—
26C4×Q8×C19—22no—
27C2×C4⋊C4×C19C2×C411yescharacteristic
28C2×C4⋊C4×C19D411yescharacteristic
29C2×C4⋊C4×C19D411yescharacteristic
30C2×C42×C19D411yescharacteristic
31C2×C42×C19D411yescharacteristic
32C2×C42×C19C2311yescharacteristic
33C2×C4⋊Dic19—21no—
34C2×C4⋊Dic19—21no—
35C2×C4⋊Dic19C2×C412yes—
36C2×C4×Dic19C2×C412yes—
37#10597315—22no—
38#10597315—22no—
39C19×C4⋊C8—22no—
40C19×C4⋊C8—22no—
41C19×C4⋊C8D414yes—
42C19×C22⋊C8—22no—
43C19×#97—22no—
44C19×#97—22no—
45C4×C8×C19—22no—
46C19⋊#95—22no—
47C19⋊#95—22no—
48C19⋊#95—22no—
49C19⋊#95—22no—
50C19⋊#95—21no—
51C22⋊(C19⋊C8)—22no—
52C4⋊(C19⋊C8)—22no—
53#10597260—22no—
54C2×Q8×C19—22no—
55C2×Q8×C19—22no—
56C2×Q8×C19—41no—
57C22×C4×C19C22⋊C411yescharacteristic
58C22×C4×C19C22⋊C411yescharacteristic
59C22×C4×C19C22⋊C411yescharacteristic
60C22×C4×C19C22⋊C411yescharacteristic
61C22×C4×C19C22×C411yescharacteristic
62C22×C4×C19C2×D411yescharacteristic
63C22×C4×C19C2×D411yescharacteristic
64C22×Dic19—22no—
65C22×Dic19—22no—
66C2×Dic38—44no—
67C2×Dic38—41no—
68C2×Dic38—41no—
69C2×C8×C19—24no—
70C4⋊C4×C19—22no—
71C4⋊C4×C19—22no—
72C4⋊C4×C19—22no—
73C42×C19—21no—
74C42×C19—21no—
75C42×C19—21no—
76C42×C19—21no—
77C42×C19C2×D412yes—
78C42×C19#4112yes—
79C4⋊Dic19—24no—
80C4⋊Dic19—42no—
81C4⋊Dic19—42no—
82C4×Dic19—42no—
83C2×C19⋊C8—42no—
84#9456—191nomaximal, Sylow
85C23×C19C2×C22⋊C411yescharacteristic
86Q8×C19—44no—
87C2×C4×C19—21no—
88C2×C4×C19—21no—
89C2×C4×C19—21no—
90C2×C4×C19—21no—
91C2×C4×C19—22no—
92C2×C4×C19—21no—
93C2×C4×C19—21no—
94C2×C4×C19—21no—
95C2×C4×C19—21no—
96C2×C4×C19—21no—
97C2×C4×C19—41no—
98C2×C4×C19—41no—
99C2×C4×C19—41no—
100C2×C4×C19#10112yes—
101C2×C4×C19C4×D412yes—
102C2×C4×C19#12011yescharacteristic
103C2×C4×C19#12112yes—
104C2×C4×C19#12311yescharacteristic
105C2×Dic19—42no—
106C2×Dic19—44no—
107C2×Dic19—42no—
108C2×Dic19—42no—
109C2×Dic19—42no—
110Dic38—82no—
111Dic38—82no—
112C8×C19—44no—
113C19⋊C8—82no—
114#2983D1911yescharacteristic
115#2568—191no—
116#1556—192no—
117#1467—191no—
118#1285—192no—
119C22×C19—21no—
120C22×C19—21no—
121C22×C19#38611yescharacteristic
122C22×C19C2×#10111yescharacteristic
123C22×C19#41311yescharacteristic
124C4×C19—21no—
125C4×C19—22no—
126C4×C19—22no—
127C4×C19—22no—
128C4×C19—41no—
129C4×C19—41no—
130C4×C19—41no—
131C4×C19#45412yes—
132Dic19—82no—
133Dic19—82no—
134C2×C4⋊Q8—191no—
135C2×C4×Q8C2×D1911yescharacteristic
136#446—24no—
137#432—21no—
138#432—192no—
139#432C2×D1912yes—
140#431—21no—
141#400—381no—
142#400—381no—
143#391—192no—
144#391—381no—
145#391—381no—
146#382—192no—
147C4×C4⋊C4—191no—
148#332—384no—
149#324—381no—
150#324—381no—
151C2×C19—21no—
152C2×C19—21no—
153C2×C19#188811yescharacteristic
154C2×C19#190111yescharacteristic
155C2×C19#190911yescharacteristic
156C22×Q8—381no—
157C22×Q8C4×D1911yescharacteristic
158C4⋊Q8—382no—
159C4⋊Q8—382no—
160C4×Q8—22no—
161C4×Q8—22no—
162C2×C4⋊C4—192no—
163C2×C4⋊C4—381no—
164C2×C4⋊C4—381no—
165C2×C4⋊C4C4×D1911yescharacteristic
166C2×C4⋊C4D7611yescharacteristic
167C2×C4⋊C4D7611yescharacteristic
168C2×C42—192no—
169C2×C42C22⋊D1911yescharacteristic
170C2×C42C22⋊D1911yescharacteristic
171C2×C42C22×D1911yescharacteristic
172C4⋊C8—22no—
173C4⋊C8—22no—
174C4⋊C8—382no—
175C4⋊C8C22⋊D1914yes—
176C22⋊C8—22no—
177C22⋊C8—382no—
178#97—22no—
179#97—22no—
180#97—382no—
181C4×C8—22no—
182#95—382no—
183#95—382no—
184#95—382no—
185#95—382no—
186#95—381no—
187C19#945611yescharacteristic, complemented, Sylow
188C2×Q8—22no—
189C2×Q8—22no—
190C2×Q8—41no—
191C2×Q8—764no—
192C2×Q8—761no—
193C2×Q8—761no—
194C22×C4—382no—
195C22×C4—382no—
196C22×C4(C2×D19)⋊C411yescharacteristic
197C22×C4(C2×D19)⋊C411yescharacteristic
198C22×C4(C2×D19)⋊C411yescharacteristic
199C22×C4(C2×D19)⋊C411yescharacteristic
200C22×C4C2×C4×D1911yescharacteristic
201C22×C4C2×D7611yescharacteristic
202C22×C4C2×C22⋊D1911yescharacteristic
203C2×C8—24no—
204C2×C8—762no—
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—384no—
209C4⋊C4—762no—
210C4⋊C4—762no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—762no—
216C42#6454112yes—
217C42C2×C22⋊D1912yes—
218C23C2×(C2×D19)⋊C411yescharacteristic
219Q8—44no—
220Q8—1522no—
221Q8—1522no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—762no—
236C2×C4—764no—
237C2×C4—762no—
238C2×C4—762no—
239C2×C4—762no—
240C2×C4#1059728112yes—
241C2×C4C4×C22⋊D1912yes—
242C2×C4#1059737511yescharacteristic
243C2×C4#1059737612yes—
244C2×C4#1059739911yescharacteristic
245C8—44no—
246C8—1522no—
247C22—21no—
248C22—21no—
249C22#1192642311yescharacteristic
250C22C2×#1059728111yescharacteristic
251C22#1192652611yescharacteristic
252C4—22no—
253C4—22no—
254C4—22no—
255C4—21no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—1522no—
260C4—1522no—
261C4#1192671712yes—
262C2—21no—
263C2—21no—
264C2#1456403811yescharacteristic
265C2#1456410311yescharacteristic
266C2#1456415711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2983C2
socleC22×C19#386
prime radicalC23×C19C2×C22⋊C4
cosocleC2×C42×C19C23
hypercenter#2983D19
hypocenterC19#9456
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
187. C19#9456semidirect

Maximal subgroups

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

subgroupindex
#145688472
#145623532
#145619792
#145614922
C19×#29832
#945619