Finite Group Databasebeta

← D149⋊#352 #34060940

Subgroups — D149⋊#352 #34060940

Order 19072.

278 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 54 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
1D149⋊#100C211yesmaximal, characteristic
2D149⋊#99C211yesmaximal, characteristic
3#23750528C212yesmaximal, complemented
4#23750527C212yesmaximal, complemented
5#123×D149C211yesmaximal, characteristic
6D149⋊M16—21no—
7C2×C22⋊#10597010—21no—
8#18011971—21no—
9#18011971C2212yes—
10#18011970—21no—
11#18011969C2212yes—
12C2×D4×D149C2211yescharacteristic
13C22×C4×D149C411yescharacteristic, complemented
14#18011896—21no—
15#18011895C2211yescharacteristic
16#18011894C2211yescharacteristic
17#18011893—21no—
18#18011892C411yescharacteristic, complemented
19C4⋊C4×D149—21no—
20C22⋊C4×D149—21no—
21C22⋊C4×D149C411yescharacteristic, complemented
22#123×C149C411yescharacteristic, complemented
23C22×#10597010—41no—
24#14558746—41no—
25#14558745—22no—
26D149⋊C8—41no—
27C22⋊#10597010—22no—
28C22⋊#10597010—41no—
29C23×D149C2×C411yescharacteristic
30C23×D149D411yescharacteristic
31C2×D596D411yescharacteristic
32C2×C22⋊D149D411yescharacteristic
33C2×C22⋊D149C2311yescharacteristic
34D4×D149—41no—
35D4×D149—41no—
36C22×Dic149C2×C411yescharacteristic, complemented
37C2×C4×D149—21no—
38C2×C4×D149—21no—
39C2×C4×D149—21no—
40C2×C4×D149—41no—
41C2×C4×D149—41no—
42C2×C4×D149D411yescharacteristic
43C4⋊Dic149—21no—
44#14558715—21no—
45#14558715—21no—
46C22⋊Dic149—21no—
47C22⋊Dic149C2×C411yescharacteristic, complemented
48#14558713—21no—
49#14558713—21no—
50#14558713—21no—
51C2×D4×C149C2×C411yescharacteristic
52C22×C4×C149C2×C411yescharacteristic, complemented
53C4⋊C4×C149—21no—
54C22⋊C4×C149—21no—
55C22⋊C4×C149C2×C411yescharacteristic, complemented
56C2×#10597010—42no—
57C2×#10597010—82no—
58#11924753—42no—
59C22×D149—21no—
60C22×D149—21no—
61C22×D149—21no—
62C22×D149—21no—
63C22×D149—42no—
64C22×D149—42no—
65C22×D149C22⋊C411yescharacteristic
66C22×D149C22⋊C411yescharacteristic
67C22×D149C2×D411yescharacteristic
68D596—41no—
69C22⋊D149—41no—
70C22⋊D149—41no—
71C2×Dic149—21no—
72C2×Dic149—21no—
73C2×Dic149—41no—
74C2×Dic149C2×D411yescharacteristic
75C4×D149—21no—
76C4×D149—21no—
77C4×D149—42no—
78C4×D149—42no—
79C4×D149—41no—
80C4×D149—41no—
81C23×C149C22⋊C411yescharacteristic
82C23×C149C22×C411yescharacteristic
83D4×C149—41no—
84C2×C4×C149—21no—
85C2×C4×C149—21no—
86C2×C4×C149—41no—
87C2×C4×C149C22⋊C411yescharacteristic
88C22×C149—21no—
89C22×C149—21no—
90C22×C149—41no—
91C22×C149—41no—
92C22×C149C2×C22⋊C411yescharacteristic
93C2×D149—22no—
94C2×D149—21no—
95C2×D149—21no—
96C2×D149—42no—
97C2×D149—42no—
98C2×D149—42no—
99C2×D149—41no—
100C2×D149—41no—
101C2×D149—81no—
102C2×D149#9911yescharacteristic
103C2×D149#9911yescharacteristic
104#10597010—82no—
105C4×C149—21no—
106C4×C149—41no—
107C4×C149—41no—
108Dic149—21no—
109Dic149—41no—
110Dic149—41no—
111C2×C149—21no—
112C2×C149—41no—
113C2×C149—41no—
114C2×C149C2×#9911yescharacteristic
115D149—21no—
116D149—41no—
117D149—41no—
118D149#35212yescomplemented
119C149C2×#35211yescharacteristic, complemented, Sylow
120C2×#352—1491nomaximal, Sylow
121C2×#123—1491no—
122C2×#100—1491no—
123C2×#99—1491no—
124#352—1492no—
125#352—1492no—
126C22×D4—1491no—
127C23×C4—1491no—
128C2×M16—2981no—
129#123—2981no—
130#123—2981no—
131#123—1491no—
132#123—1491no—
133#123—1491no—
134#123#1059701011yescharacteristic, complemented
135C2×C4⋊C4—2981no—
136C2×C22⋊C4—2981no—
137C2×C22⋊C4—2981no—
138C2×C22⋊C4—1491no—
139#100—2981no—
140#100—1492no—
141#99—2981no—
142#99—1492no—
143C24—1491no—
144C24—1491no—
145C2×D4—5961no—
146C2×D4—5961no—
147C2×D4—1491no—
148C2×D4—1491no—
149C2×D4—1491no—
150C2×D4C2×#1059701011yescharacteristic
151C22×C4—2981no—
152C22×C4—2981no—
153C22×C4—2981no—
154C22×C4—5961no—
155C22×C4—5961no—
156C22×C4—5961no—
157C22×C4—1491no—
158C22×C4—1491no—
159C22×C4C2×#1059701011yescharacteristic, complemented
160M16—2982no—
161M16—5961no—
162C2×C8—5961no—
163C4⋊C4—21no—
164C4⋊C4—2981no—
165C4⋊C4—2981no—
166C4⋊C4—2981no—
167C22⋊C4—21no—
168C22⋊C4—2981no—
169C22⋊C4—2981no—
170C22⋊C4—2981no—
171C22⋊C4—2981no—
172C22⋊C4—2982no—
173C22⋊C4—5961no—
174C22⋊C4—1491no—
175C22⋊C4C2×#1059701011yescharacteristic, complemented
176C23—2981no—
177C23—2981no—
178C23—2981no—
179C23—2981no—
180C23—5962no—
181C23—5962no—
182C23—1491no—
183C23—1491no—
184C23—1491no—
185C23C22⋊#1059701011yescharacteristic
186C23C22×#1059701011yescharacteristic
187D4—41no—
188D4—5961no—
189D4—5961no—
190D4—5961no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—2981no—
195C2×C4—2981no—
196C2×C4—2981no—
197C2×C4—2981no—
198C2×C4—5962no—
199C2×C4—5962no—
200C2×C4—5961no—
201C2×C4—5961no—
202C2×C4—5961no—
203C2×C4—5962no—
204C2×C4—1491no—
205C2×C4—11922no—
206C2×C4C22⋊#1059701011yescharacteristic
207C8—5962no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—2982no—
213C22—2981no—
214C22—2981no—
215C22—5961no—
216C22—5961no—
217C22—5962no—
218C22—5962no—
219C22—5962no—
220C22—1491no—
221C22—1491no—
222C22—11921no—
223C22C2×C22⋊#1059701011yescharacteristic
224C4—21no—
225C4—41no—
226C4—41no—
227C4—2981no—
228C4—5961no—
229C4—5961no—
230C4—11922no—
231C2—21no—
232C2—41no—
233C2—41no—
234C2—2981no—
235C2—5961no—
236C2—5961no—
237C2—1492no—
238C2D149⋊#9911yescharacteristic
subgroupG/H
centerC2D149⋊#99
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
Fitting#123×C149C4
socleC2×C149C2×#99
prime radicalC2×D4×D149C22
cosocleC2×C22⋊D149C23
hypercenter#123#10597010
hypocenterC149C2×#352
LCSG ▷ C23×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #123

Complements

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

NH ≅ G/Ntype
3. #23750528C2semidirect
4. #23750527C2semidirect
13. C22×C4×D149C4semidirect
18. #18011892C4semidirect
21. C22⋊C4×D149C4semidirect
22. #123×C149C4semidirect
36. C22×Dic149C2×C4semidirect
47. C22⋊Dic149C2×C4semidirect
52. C22×C4×C149C2×C4semidirect
55. C22⋊C4×C149C2×C4semidirect
118. D149#352semidirect
119. C149C2×#352semidirect
134. #123#10597010semidirect
159. C22×C4C2×#10597010semidirect
175. C22⋊C4C2×#10597010semidirect

Maximal subgroups

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

subgroupindex
D149⋊#1002
D149⋊#992
#237505282
#237505272
#123×D1492
C2×#352149