Finite Group Databasebeta

← #34045136

Subgroups — #34045136

Order 19072.

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

normal subgroups only

This group has 358 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#23750132C211yesmaximal, characteristic
2C2×#18011868C211yesmaximal, characteristic, complemented
3C2×#18011838C211yesmaximal, characteristic, complemented
4#23749588C211yesmaximal, characteristic, complemented
5#23749386C211yesmaximal, characteristic, complemented
6#23749385C211yesmaximal, characteristic, complemented
7C2×#104×C149C211yesmaximal, characteristic, complemented
8C22×C4×D149C2211yescharacteristic
9C2×#14558720C2211yescharacteristic
10#18011892—21no—
11#18011887C412yescomplemented
12#18011882C412yescomplemented
13#18011879—21no—
14C4×C22⋊D149—22no—
15#18011870C2211yescharacteristic
16#18011868—22no—
17#18011868—22no—
18C2×#14558715—21no—
19C2×#14558713—21no—
20C2×C4×Dic149C2211yescharacteristic
21#18011838—22no—
22#18011823—22no—
23C2×#41×C149C2211yescharacteristic
24C2×M16×C149C2211yescharacteristic
25C2×C42×C149C2211yescharacteristic
26#104×C149—22no—
27C23×D149D411yescharacteristic
28C2×C22⋊D149—22no—
29C22×Dic149—21no—
30C22×Dic149D411yescharacteristic
31C2×C4×D149—21no—
32C2×C4×D149—21no—
33C2×C4×D149—21no—
34C2×C4×D149—21no—
35C2×C4×D149C2×C412yes—
36C2×C4×D149D412yes—
37#14558720—21no—
38#14558720—21no—
39C2×#11924746—21no—
40C4⋊Dic149C2×C412yes—
41#14558715—24no—
42#14558715—22no—
43C22⋊Dic149—22no—
44C22⋊Dic149—21no—
45#14558713—24no—
46#14558713—22no—
47C4×Dic149—21no—
48C4×Dic149—21no—
49C4×Dic149D412yescomplemented
50#41×C149—21no—
51#41×C149—21no—
52#41×C149—21no—
53#41×C149—21no—
54C2×Q8×C149C2×C411yescharacteristic
55C2×D4×C149—21no—
56C2×D4×C149C2×C411yescharacteristic
57C22×C4×C149—21no—
58C22×C4×C149—21no—
59C22×C4×C149C2311yescharacteristic
60M16×C149—21no—
61M16×C149—21no—
62C2×C8×C149—21no—
63C42×C149—21no—
64C42×C149D412yescomplemented
65C22×D149—21no—
66C22×D149—21no—
67C22×D149—42no—
68C22×D149C22⋊C412yes—
69C22⋊D149—44no—
70C2×Dic149—21no—
71C2×Dic149—21no—
72C2×Dic149—22no—
73C2×Dic149—22no—
74C2×Dic149—42no—
75C2×Dic149C22⋊C412yes—
76C4×D149—22no—
77C4×D149—22no—
78C4×D149—22no—
79C4×D149—22no—
80#11924746—41no—
81C23×C149—21no—
82C23×C149C2×D411yescharacteristic
83Q8×C149—21no—
84Q8×C149—21no—
85D4×C149—21no—
86D4×C149—21no—
87D4×C149—41no—
88D4×C149—41no—
89C2×C4×C149—21no—
90C2×C4×C149—22no—
91C2×C4×C149—42no—
92C2×C4×C149—41no—
93C2×C4×C149—41no—
94C2×C4×C149C22×C411yescharacteristic
95C2×C4×C149C2×D411yescharacteristic
96C2×C4×C149C2×D411yescharacteristic
97C2×C4×C149C2×D411yescharacteristic
98C2×C4×C149#4111yescharacteristic
99C2×C4×C149#4111yescharacteristic
100C8×C149—41no—
101C22×C149—22no—
102C22×C149—41no—
103C22×C149—42no—
104C22×C149C2×C22⋊C411yescharacteristic
105C22×C149#12011yescharacteristic
106C22×C149#12311yescharacteristic
107C2×D149—22no—
108C2×D149—22no—
109C2×D149—22no—
110C2×D149—42no—
111C2×D149—42no—
112C4×C149—42no—
113C4×C149—41no—
114C4×C149C4×D411yescharacteristic
115C4×C149C4×D411yescharacteristic
116C4×C149#12111yescharacteristic
117C4×C149#12111yescharacteristic
118Dic149—22no—
119Dic149—42no—
120Dic149—42no—
121C2×C149—21no—
122C2×C149—21no—
123C2×C149—81no—
124C2×C149#38611yescharacteristic
125C2×C149#42112yes—
126D149—42no—
127C149#189711yescharacteristic, complemented, Sylow
128#1897—1491nomaximal, Sylow
129#525—1491no—
130C2×#117—1491no—
131C2×#104—1491no—
132C2×#104D14911yescharacteristic, complemented
133#407—1491no—
134#339—1491no—
135#339—1491no—
136C2×#41C2×D14911yescharacteristic
137C23×C4—1491no—
138C2×M16—1491no—
139C2×M16C2×D14911yescharacteristic
140#123—2981no—
141C22⋊Q8—1492no—
142#121—1492no—
143#120—2981no—
144C4×D4—2982no—
145#117—2982no—
146#117—2982no—
147#117—1491no—
148C2×C4⋊C4—2981no—
149C2×C22⋊C4—2981no—
150C2×C42—1491no—
151C2×C42C2×D14911yescharacteristic
152#104—22no—
153#104—2982no—
154C22⋊C8—2982no—
155C24—1491no—
156#41—21no—
157#41—21no—
158#41—21no—
159#41—21no—
160C2×Q8C4×D14911yescharacteristic
161C2×D4—21no—
162C2×D4—2982no—
163C2×D4C4×D14911yescharacteristic
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—2981no—
167C22×C4—2981no—
168C22×C4—2981no—
169C22×C4—2981no—
170C22×C4—2981no—
171C22×C4—1491no—
172C22×C4—1492no—
173C22×C4—1492no—
174C22×C4C22×D14911yescharacteristic
175M16—21no—
176M16—21no—
177M16—2981no—
178M16—2981no—
179C2×C8—21no—
180C2×C8—2981no—
181C4⋊C4—2984no—
182C4⋊C4—2982no—
183C4⋊C4—1492no—
184C22⋊C4—2984no—
185C22⋊C4—2982no—
186C22⋊C4—2981no—
187C22⋊C4—2982no—
188C42—21no—
189C42—2981no—
190C42—2981no—
191C42—1492no—
192C42C22⋊D14912yescomplemented
193C23—21no—
194C23—2981no—
195C23—2981no—
196C23—5962no—
197C23—1492no—
198C23D4×D14911yescharacteristic
199Q8—21no—
200Q8—21no—
201D4—21no—
202D4—21no—
203D4—41no—
204D4—41no—
205D4—5964no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—2981no—
212C2×C4—2981no—
213C2×C4—2982no—
214C2×C4—2982no—
215C2×C4—2982no—
216C2×C4—2982no—
217C2×C4—2982no—
218C2×C4—2982no—
219C2×C4—5962no—
220C2×C4—1492no—
221C2×C4C2×C4×D14911yescharacteristic
222C2×C4D4×D14911yescharacteristic
223C2×C4D4×D14911yescharacteristic
224C2×C4C2×C22⋊D14911yescharacteristic
225C2×C4#1455873511yescharacteristic
226C2×C4#1455873611yescharacteristic
227C8—41no—
228C8—5961no—
229C22—22no—
230C22—42no—
231C22—41no—
232C22—2982no—
233C22—2982no—
234C22—2982no—
235C22—5962no—
236C22—5962no—
237C22C22⋊C4×D14911yescharacteristic
238C22#1801187911yescharacteristic
239C22#1801189311yescharacteristic
240C4—42no—
241C4—41no—
242C4—2982no—
243C4—5962no—
244C4—5962no—
245C4#1801187111yescharacteristic
246C4C4×C22⋊D14911yescharacteristic
247C4#1801188211yescharacteristic
248C4#1801188411yescharacteristic
249C2—21no—
250C2—21no—
251C2—81no—
252C2—5962no—
253C2#2374950111yescharacteristic
254C2#2374964012yes—
subgroupG/H
centerC2×C4D4×D149
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
FittingC2×#104×C149C2
socleC22×C149C2×C22⋊C4
prime radical#23750132C2
cosocleC22×C4×C149C23
hypercenterC2×#104D149
hypocenterC149#1897
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#18011868C2semidirect
3. C2×#18011838C2semidirect
4. #23749588C2semidirect
5. #23749386C2semidirect
6. #23749385C2semidirect
7. C2×#104×C149C2semidirect
11. #18011887C4semidirect
12. #18011882C4semidirect
49. C4×Dic149D4semidirect
64. C42×C149D4semidirect
127. C149#1897semidirect
132. C2×#104D149semidirect
192. C42C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
#237501322
C2×#180118682
C2×#180118382
#237495882
#237493862
#237493852
C2×#104×C1492
#1897149