Finite Group Databasebeta

← #34047255

Subgroups — #34047255

Order 19072.

924 conjugacy classes of subgroups; only the 237 normal subgroups are shown.

normal subgroups only

This group has 924 conjugacy classes of subgroups — too many to draw. Only its 237 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
1C2×#18011907C211yesmaximal, characteristic
2C2×D4×Dic149C211yesmaximal, characteristic, complemented
3C2×#18011873C211yesmaximal, characteristic, complemented
4C2×#18011871C214yesmaximal, complemented
5#23749527C211yesmaximal, characteristic, complemented
6#23749525C214yesmaximal, complemented
7#23749494C211yesmaximal, characteristic, complemented
8C42×Dic149C211yesmaximal, characteristic, complemented
9#390×C149C211yesmaximal, characteristic, complemented
10C22×D596C2211yescharacteristic
11C22×C22⋊D149C2214yes—
12C23×Dic149C2212yes—
13C22×C4×D149C2212yes—
14#18011907C418yescomplemented
15D4×Dic149—24no—
16#18011873—24no—
17#18011871—216no—
18C2×C4⋊Dic149C2211yescharacteristic
19C2×#14558715C2214yes—
20C2×C22⋊Dic149C2212yes—
21C2×#14558713C2212yes—
22C2×#14558713C2214yes—
23C2×C4×Dic149C2212yes—
24C2×C4×Dic149C2211yescharacteristic
25C2×C4×Dic149C2212yes—
26C2×C4×Dic149C2211yescharacteristic
27C22×D4×C149C2211yescharacteristic
28C2×C4⋊C4×C149C2211yescharacteristic
29C2×C22⋊C4×C149C2214yes—
30C2×C42×C149C2211yescharacteristic
31C23×D149C2312yes—
32C2×D596—22no—
33C2×D596—22no—
34C2×D596C2×C414yescomplemented
35C2×C22⋊D149—28no—
36C2×C22⋊D149—28no—
37C2×C22⋊D149C2×C4116yescomplemented
38C22×Dic149—28no—
39C22×Dic149—24no—
40C22×Dic149C2312yes—
41C22×Dic149C2311yescharacteristic
42C22×Dic149C2312yes—
43C22×Dic149C2311yescharacteristic
44C2×C4×D149—28no—
45C2×C4×D149—24no—
46C4⋊Dic149—22no—
47#14558715—28no—
48C22⋊Dic149—24no—
49#14558713—24no—
50#14558713—28no—
51C4×Dic149—24no—
52C4×Dic149C2×C414yescomplemented
53C4×Dic149D418yescomplemented
54C4×Dic149D414yescomplemented
55C24×C149C2312yes—
56C2×D4×C149—22no—
57C2×D4×C149—22no—
58C2×D4×C149C2×C414yescomplemented
59C22×C4×C149C2312yes—
60C22×C4×C149C2312yes—
61C22×C4×C149C2311yescharacteristic
62C4⋊C4×C149—22no—
63C22⋊C4×C149—28no—
64C42×C149—22no—
65C22×D149—24no—
66C22×D149—22no—
67C22×D149—24no—
68C22×D149—22no—
69C22×D149C22×C414yes—
70D596—28no—
71C22⋊D149—232no—
72C2×Dic149—22no—
73C2×Dic149—24no—
74C2×Dic149—22no—
75C2×Dic149—48no—
76C2×Dic149C22×C414yes—
77C2×Dic149C2×D412yes—
78C2×Dic149C2×D414yes—
79C2×Dic149C2×D414yes—
80C2×Dic149C2×D412yes—
81C2×Dic149#4114yes—
82C4×D149—48no—
83C23×C149—24no—
84C23×C149—22no—
85C23×C149—24no—
86C23×C149—22no—
87C23×C149C22×C414yes—
88C23×C149C2411yescharacteristic
89D4×C149—28no—
90C2×C4×C149—22no—
91C2×C4×C149—22no—
92C2×C4×C149—24no—
93C2×C4×C149—22no—
94C2×C4×C149C22×C412yes—
95C2×C4×C149C2×D414yes—
96C2×C4×C149C2×D412yes—
97C2×C4×C149#4112yes—
98C22×C149—24no—
99C22×C149—28no—
100C22×C149—42no—
101C22×C149—44no—
102C22×C149—42no—
103C22×C149C23×C411yescharacteristic
104C22×C149C22×D412yes—
105C22×C149C22×D411yescharacteristic
106C22×C149C2×#4112yes—
107C22×C149C2×#4111yescharacteristic
108C2×D149—28no—
109C2×D149—24no—
110C2×D149—42no—
111C2×D149—44no—
112C2×D149—42no—
113C4×C149—24no—
114C4×C149—42no—
115C4×C149C4×D414yescomplemented
116Dic149—22no—
117Dic149—42no—
118Dic149C4×D418yescomplemented
119Dic149#12714yescomplemented
120C2×C149—44no—
121C2×C149C2×C4×D412yes—
122C2×C149C2×C4×D411yescharacteristic
123C2×C149C2×#12711yescharacteristic
124C2×C149#53212yes—
125C2×C149#53211yescharacteristic
126D149—44no—
127C149C4×#12711yescharacteristic, complemented, Sylow
128C4×#127—1491nomaximal, Sylow
129C2×#127—1491no—
130C2×C4×D4—1491no—
131C2×C4×D4—1491no—
132C2×C4×D4—1494no—
133#390—1494no—
134#390—1491no—
135#390D14911yescharacteristic, complemented
136#384—1491no—
137C43—1491no—
138C22×D4—1494no—
139C22×D4—1491no—
140C22×D4C2×D14911yescharacteristic
141C23×C4—1492no—
142C23×C4—1492no—
143#127—1498no—
144C4×D4—29816no—
145C4×D4—2984no—
146C4×D4—2984no—
147C2×C4⋊C4—1494no—
148C2×C4⋊C4—1491no—
149C2×C4⋊C4C2×D14911yescharacteristic
150C2×C22⋊C4—1492no—
151C2×C22⋊C4—1492no—
152C2×C22⋊C4—1494no—
153C2×C22⋊C4C2×D14914yes—
154C2×C42—1492no—
155C2×C42—1491no—
156C2×C42—1492no—
157C2×C42—1491no—
158C2×C42C2×D14911yescharacteristic
159C24—1492no—
160C24C22×D14912yes—
161C2×D4—22no—
162C2×D4—22no—
163C2×D4—2988no—
164C2×D4—2988no—
165C2×D4—2982no—
166C2×D4—2982no—
167C2×D4—14916no—
168C2×D4—1494no—
169C2×D4C4×D14914yescomplemented
170C22×C4—2988no—
171C22×C4—2984no—
172C22×C4—2988no—
173C22×C4—2984no—
174C22×C4—1492no—
175C22×C4—1491no—
176C22×C4—1492no—
177C22×C4—1491no—
178C22×C4C22×D14912yes—
179C22×C4C22×D14912yes—
180C22×C4C22×D14911yescharacteristic
181C4⋊C4—22no—
182C4⋊C4—2988no—
183C4⋊C4—2982no—
184C22⋊C4—28no—
185C22⋊C4—2984no—
186C22⋊C4—2984no—
187C22⋊C4—2988no—
188C42—22no—
189C42—2984no—
190C42—1494no—
191C42—1494no—
192C42—1498no—
193C23—24no—
194C23—22no—
195C23—24no—
196C23—22no—
197C23—2984no—
198C23—2982no—
199C23—2984no—
200C23—2982no—
201C23—1494no—
202C23C2×C4×D14914yes—
203C23C23×D14911yescharacteristic
204D4—28no—
205D4—29832no—
206D4—2988no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—2982no—
212C2×C4—2984no—
213C2×C4—2982no—
214C2×C4—5968no—
215C2×C4—5968no—
216C2×C4—1492no—
217C2×C4—1494no—
218C2×C4—1494no—
219C2×C4—1494no—
220C2×C4—1492no—
221C2×C4—1494no—
222C2×C4C2×C4×D14912yes—
223C2×C4D4×D14914yes—
224C2×C4D4×D14912yes—
225C2×C4#1455873512yes—
226C22—28no—
227C22—24no—
228C22—42no—
229C22—44no—
230C22—42no—
231C22—2988no—
232C22—2984no—
233C22—5962no—
234C22—5964no—
235C22—5962no—
236C22C22×C4×D14911yescharacteristic
237C22C2×D4×D14912yes—
238C22C2×D4×D14911yescharacteristic
239C22#41×D14912yes—
240C22C2×#1455873511yescharacteristic
241C4—24no—
242C4—42no—
243C4—2982no—
244C4—5962no—
245C4—1494no—
246C4—1498no—
247C4#1801187114yescomplemented
248C2—44no—
249C2—5964no—
250C2C4×D4×D14912yes—
251C2C2×#1801187111yescharacteristic
252C2#127×D14911yescharacteristic
253C2#2375017012yes—
254C2#2375017411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#390×C149C2
socle, cosocleC23×C149C24
prime radicalC2×#18011907C2
hypercenter#390D149
hypocenterC149C4×#127
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic149C2semidirect
3. C2×#18011873C2semidirect
4. C2×#18011871C2semidirect
5. #23749527C2semidirect
6. #23749525C2semidirect
7. #23749494C2semidirect
8. C42×Dic149C2semidirect
9. #390×C149C2semidirect
14. #18011907C4semidirect
34. C2×D596C2×C4semidirect
37. C2×C22⋊D149C2×C4semidirect
52. C4×Dic149C2×C4semidirect
53. C4×Dic149D4semidirect
54. C4×Dic149D4semidirect
58. C2×D4×C149C2×C4semidirect
115. C4×C149C4×D4semidirect
118. Dic149C4×D4semidirect
119. Dic149#127semidirect
127. C149C4×#127semidirect
135. #390D149semidirect
169. C2×D4C4×D149semidirect
247. C4#18011871semidirect

Maximal subgroups

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

subgroupindex
C2×#180119072
C2×D4×Dic1492
C2×#180118732
C2×#180118712
#237495272
#237495252
#237494942
C42×Dic1492
#390×C1492
C4×#127149