Finite Group Databasebeta

← #34047331

Subgroups — #34047331

Order 19072.

540 conjugacy classes of subgroups.

The subgroup lattice has 270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D149C211yesmaximal, characteristic
2#23749525C212yesmaximal
3#23749522C212yesmaximal, complemented
4#23749519C212yesmaximal, complemented
5#23749517C212yesmaximal, complemented
6#23749487C211yesmaximal, characteristic, complemented
7#23749485C211yesmaximal, characteristic, complemented
8#23749484C211yesmaximal, characteristic, complemented
9#23749476C211yesmaximal, characteristic, complemented
10#23749470C211yesmaximal, characteristic, complemented
11#381×C149C211yesmaximal, characteristic, complemented
12C22×C22⋊D149C2211yescharacteristic
13C22×C4×D149C2211yescharacteristic
14C4×C22⋊D149C418yescomplemented
15C2×C4⋊Dic149C2212yes—
16C2×#14558715C2212yes—
17C2×#14558715C2212yes—
18C2×#14558715C2211yescharacteristic
19C2×C22⋊Dic149C2212yes—
20C2×C22⋊Dic149C2211yescharacteristic
21C2×#14558713C2212yes—
22C2×#14558713C2212yes—
23C2×#14558713C2211yescharacteristic
24C2×C4×Dic149C2212yes—
25C2×C4×Dic149C2212yes—
26C2×C4×Dic149C2211yescharacteristic
27#18011818C2211yescharacteristic
28#18011818C2212yes—
29#18011818C2211yescharacteristic
30#18011818C2212yes—
31C23×C4×C149C2211yescharacteristic
32C2×C22⋊C4×C149C2212yes—
33#95×C149C2211yescharacteristic
34#95×C149C2211yescharacteristic
35#95×C149C2212yes—
36C23×D149C2311yescharacteristic
37C2×C22⋊D149—24no—
38C2×C22⋊D149C2×C414yes—
39C22×Dic149C2312yes—
40C22×Dic149C2312yes—
41C22×Dic149C2311yescharacteristic
42C22×Dic149C2311yescharacteristic
43C22×Dic149C2311yescharacteristic
44C2×C4×D149—42no—
45C2×C4×D149C2×C414yes—
46C4⋊Dic149—42no—
47#14558715—24no—
48#14558715—42no—
49#14558715C2×C414yes—
50C22⋊Dic149—42no—
51C22⋊Dic149C2×C414yes—
52#14558713—42no—
53#14558713—42no—
54#14558713C2×C414yes—
55C4×Dic149—24no—
56C4×Dic149—42no—
57C4×Dic149C2×C414yes—
58C24×C149C2311yescharacteristic
59C22×C4×C149—42no—
60C22×C4×C149C2×C414yes—
61C22×C4×C149C2312yes—
62C22×C4×C149C2312yes—
63C22×C4×C149C2311yescharacteristic
64C22×C4×C149C2311yescharacteristic
65C22⋊C4×C149—42no—
66C22×D149—22no—
67C22×D149—22no—
68C22×D149—21no—
69C22×D149—21no—
70C22×D149C22×C412yes—
71C22⋊D149—28no—
72C2×Dic149—22no—
73C2×Dic149—21no—
74C2×Dic149—21no—
75C2×Dic149—22no—
76C2×Dic149—22no—
77C2×Dic149—22no—
78C2×Dic149—22no—
79C2×Dic149—22no—
80C2×Dic149—22no—
81C2×Dic149C22×C412yes—
82C2×Dic149C22×C412yes—
83C2×Dic149C22×C412yes—
84C2×Dic149#4114yes—
85C4×D149—44no—
86C23×C149—22no—
87C23×C149—22no—
88C23×C149—21no—
89C23×C149—21no—
90C23×C149C22×C412yes—
91C23×C149C2411yescharacteristic
92C2×C4×C149—22no—
93C2×C4×C149—22no—
94C2×C4×C149—22no—
95C2×C4×C149—22no—
96C2×C4×C149—22no—
97C2×C4×C149—22no—
98C2×C4×C149—22no—
99C2×C4×C149—22no—
100C2×C4×C149—44no—
101C2×C4×C149C22×C412yes—
102C2×C4×C149C22×C412yes—
103C22×C149—22no—
104C22×C149—22no—
105C22×C149—22no—
106C22×C149—42no—
107C22×C149—42no—
108C22×C149C23×C411yescharacteristic
109C22×C149C2×#4112yes—
110C22×C149H(5,𝔽2)12yes—
111C22×C149H(5,𝔽2)11yescharacteristic
112C22×C1492−1+411yescharacteristic
113C2×D149—22no—
114C2×D149—22no—
115C2×D149—22no—
116C2×D149—42no—
117C2×D149—42no—
118C4×C149—22no—
119C4×C149—22no—
120C4×C149—42no—
121C4×C149—42no—
122Dic149—22no—
123Dic149—22no—
124Dic149—42no—
125Dic149—42no—
126Dic149#11714yes—
127C2×C149—42no—
128C2×C149C2×#11711yescharacteristic
129C2×C149#51811yescharacteristic
130C2×C149#52011yescharacteristic
131C2×C149#54012yes—
132C2×C149#54212yes—
133D149—42no—
134C149#231911yescharacteristic, complemented, Sylow
135#2319—1491nomaximal, Sylow
136C2×C4×D4—1491no—
137#390—1492no—
138#389—1492no—
139#388—1492no—
140#388—1492no—
141#381—1491no—
142#381D14911yescharacteristic, complemented
143#380—1491no—
144#380—1491no—
145C4×C4⋊C4—1491no—
146#376—1491no—
147C22×D4—1491no—
148C23×C4—1491no—
149C23×C4C2×D14911yescharacteristic
150C4×D4—1498no—
151C2×C4⋊C4—1492no—
152C2×C4⋊C4—1492no—
153C2×C4⋊C4—1492no—
154C2×C4⋊C4—1491no—
155C2×C22⋊C4—1492no—
156C2×C22⋊C4—1492no—
157C2×C22⋊C4—1492no—
158C2×C22⋊C4—1491no—
159C2×C22⋊C4—1491no—
160C2×C22⋊C4C2×D14912yes—
161C2×C42—1492no—
162C2×C42—1492no—
163C2×C42—1491no—
164#95—1491no—
165#95—1492no—
166#95—1491no—
167#95—1492no—
168#95C2×D14911yescharacteristic
169#95C2×D14911yescharacteristic
170#95C2×D14912yes—
171C24—1491no—
172C24C22×D14911yescharacteristic
173C2×D4—2984no—
174C2×D4—1494no—
175C22×C4—42no—
176C22×C4—5962no—
177C22×C4—1492no—
178C22×C4—1492no—
179C22×C4—1491no—
180C22×C4—1491no—
181C22×C4—1494no—
182C22×C4—1491no—
183C22×C4C4×D14914yes—
184C22×C4C22×D14912yes—
185C22×C4C22×D14912yes—
186C22×C4C22×D14911yescharacteristic
187C22×C4C22×D14911yescharacteristic
188C4⋊C4—2984no—
189C4⋊C4—5962no—
190C4⋊C4—5962no—
191C4⋊C4—1494no—
192C22⋊C4—42no—
193C22⋊C4—5962no—
194C22⋊C4—5962no—
195C22⋊C4—5962no—
196C22⋊C4—1494no—
197C22⋊C4—1494no—
198C42—2984no—
199C42—5962no—
200C42—1494no—
201C23—22no—
202C23—22no—
203C23—21no—
204C23—21no—
205C23—2982no—
206C23—2982no—
207C23—2981no—
208C23—2981no—
209C23—1492no—
210C23C2×C4×D14912yes—
211C23C23×D14911yescharacteristic
212D4—2988no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—44no—
222C2×C4—2982no—
223C2×C4—2981no—
224C2×C4—2981no—
225C2×C4—2982no—
226C2×C4—2982no—
227C2×C4—2982no—
228C2×C4—2982no—
229C2×C4—2982no—
230C2×C4—2982no—
231C2×C4—5964no—
232C2×C4—1492no—
233C2×C4—1492no—
234C2×C4—1492no—
235C2×C4—1494no—
236C2×C4C2×C4×D14912yes—
237C2×C4C2×C4×D14912yes—
238C22—22no—
239C22—22no—
240C22—22no—
241C22—42no—
242C22—42no—
243C22—2982no—
244C22—2982no—
245C22—2982no—
246C22—5962no—
247C22—5962no—
248C22C22×C4×D14911yescharacteristic
249C22#41×D14912yes—
250C22#1801195612yes—
251C22#1801195711yescharacteristic
252C22#1801195811yescharacteristic
253C4—22no—
254C4—22no—
255C4—42no—
256C4—42no—
257C4—2982no—
258C4—2982no—
259C4—5962no—
260C4—5962no—
261C4—1494no—
262C2—42no—
263C2—5962no—
264C2#117×D14911yescharacteristic
265C2#2375009811yescharacteristic
266C2#2375010511yescharacteristic
267C2#2375022712yes—
268C2#2375024312yes—
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#381×C149C2
socle, cosocleC23×C149C24
prime radicalC22×C22⋊D149C22
hypercenter#381D149
hypocenterC149#2319
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
3. #23749522C2semidirect
4. #23749519C2semidirect
5. #23749517C2semidirect
6. #23749487C2semidirect
7. #23749485C2semidirect
8. #23749484C2semidirect
9. #23749476C2semidirect
10. #23749470C2semidirect
11. #381×C149C2semidirect
14. C4×C22⋊D149C4semidirect
134. C149#2319semidirect
142. #381D149semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D1492
#237495252
#237495222
#237495192
#237495172
#237494872
#237494852
#237494842
#237494762
#237494702
#381×C1492
#2319149