Finite Group Databasebeta

← #34060949

Subgroups — #34060949

Order 19072.

280 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 52 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, complemented
2D149⋊#99C211yesmaximal, characteristic, complemented
3#23750527C212yesmaximal, complemented
4#23750526C212yesmaximal, complemented
5#23750186C211yesmaximal, characteristic
6D149⋊M16—21no—
7C2×C22⋊#10597010—21no—
8#18011971—21no—
9#18011971C2212yes—
10#18011970—21no—
11#18011969C2212yes—
12C22×D596C411yescharacteristic, complemented
13C2×D4×D149C2211yescharacteristic
14#18011896—21no—
15#18011894C2211yescharacteristic
16#18011886—21no—
17#18011884—21no—
18#18011881—21no—
19#18011881C2211yescharacteristic
20#18011879C411yescharacteristic, complemented
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×D149C2×C411yescharacteristic, complemented
31C23×D149D411yescharacteristic
32C2×D596—21no—
33C2×D596—21no—
34C2×D596—21no—
35C2×D596—41no—
36C2×D596—41no—
37C2×D596D411yescharacteristic
38C2×C22⋊D149—21no—
39C2×C22⋊D149D411yescharacteristic
40C2×C22⋊D149C2311yescharacteristic
41D4×D149—41no—
42D4×D149—41no—
43C2×C4×D149—21no—
44C2×C4×D149D411yescharacteristic
45#14558715—21no—
46C22⋊Dic149C2×C411yescharacteristic, complemented
47#14558713—21no—
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—21no—
64C22×D149—41no—
65C22×D149—81no—
66C22×D149—81no—
67C22×D149—81no—
68C22×D149C22⋊C411yescharacteristic
69C22×D149C22⋊C411yescharacteristic
70C22×D149C2×D411yescharacteristic
71D596—41no—
72D596—42no—
73D596—41no—
74D596—41no—
75D596—81no—
76C22⋊D149—41no—
77C22⋊D149—41no—
78C22⋊D149—81no—
79C2×Dic149—21no—
80C2×Dic149C2×D411yescharacteristic
81C4×D149—21no—
82C4×D149—21no—
83C4×D149—81no—
84C23×C149C22⋊C411yescharacteristic
85C23×C149C22×C411yescharacteristic
86D4×C149—41no—
87C2×C4×C149—21no—
88C2×C4×C149—21no—
89C2×C4×C149—41no—
90C2×C4×C149C22⋊C411yescharacteristic
91C22×C149—21no—
92C22×C149—21no—
93C22×C149—41no—
94C22×C149—41no—
95C22×C149C2×C22⋊C411yescharacteristic
96C2×D149—21no—
97C2×D149—21no—
98C2×D149—41no—
99C2×D149—42no—
100C2×D149—41no—
101C2×D149—41no—
102C2×D149—41no—
103C2×D149—41no—
104C2×D149—41no—
105C2×D149—81no—
106C2×D149—81no—
107C2×D149—81no—
108C2×D149—82no—
109C2×D149#9911yescharacteristic
110C2×D149#9911yescharacteristic
111#10597010—82no—
112C4×C149—21no—
113C4×C149—41no—
114C4×C149—41no—
115Dic149—21no—
116Dic149—41no—
117C2×C149—21no—
118C2×C149—41no—
119C2×C149—41no—
120C2×C149C2×#9911yescharacteristic
121D149—21no—
122D149—21no—
123D149—41no—
124D149—41no—
125D149—81no—
126C149#212111yescharacteristic, complemented, Sylow
127#2121—1491nomaximal, Sylow
128#534—1491no—
129C2×#100—1491no—
130C2×#99—1491no—
131#352—1492no—
132AΣL(1,𝔽16)—1492no—
133C22×D4—1491no—
134C22×D4—1491no—
135C2×M16—2981no—
136#123—2981no—
137#123—1491no—
138#123#1059701011yescharacteristic, complemented
139#121—2981no—
140#121—2981no—
141#120—2981no—
142#120—1491no—
143#120—1491no—
144C2×C22⋊C4—2981no—
145C2×C22⋊C4—1491no—
146#100—2981no—
147#100—1492no—
148#99—2981no—
149#99—1492no—
150C24—1491no—
151C24—1491no—
152C24—1491no—
153C2×D4—2981no—
154C2×D4—2981no—
155C2×D4—2981no—
156C2×D4—2981no—
157C2×D4—5961no—
158C2×D4—5961no—
159C2×D4—5961no—
160C2×D4—5961no—
161C2×D4—1491no—
162C2×D4—1491no—
163C2×D4—1491no—
164C2×D4C2×#1059701011yescharacteristic
165C22×C4—2981no—
166C22×C4—5961no—
167C22×C4—1491no—
168C22×C4C2×#1059701011yescharacteristic, complemented
169M16—2982no—
170M16—5961no—
171C2×C8—5961no—
172C4⋊C4—21no—
173C4⋊C4—2981no—
174C22⋊C4—21no—
175C22⋊C4—2981no—
176C22⋊C4—2981no—
177C22⋊C4—2981no—
178C22⋊C4—2981no—
179C22⋊C4—2982no—
180C22⋊C4—5961no—
181C22⋊C4—1491no—
182C22⋊C4C2×#1059701011yescharacteristic, complemented
183C23—2981no—
184C23—2981no—
185C23—2981no—
186C23—2981no—
187C23—2981no—
188C23—5961no—
189C23—1491no—
190C23—1491no—
191C23—1491no—
192C23—11921no—
193C23—11921no—
194C23—11921no—
195C23C22⋊#1059701011yescharacteristic
196C23C22×#1059701011yescharacteristic
197D4—41no—
198D4—5961no—
199D4—5962no—
200D4—5961no—
201D4—5961no—
202D4—5961no—
203D4—5961no—
204D4—11921no—
205D4—11921no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—2981no—
210C2×C4—2981no—
211C2×C4—2981no—
212C2×C4—5962no—
213C2×C4—1491no—
214C2×C4—11921no—
215C2×C4—11922no—
216C2×C4C22⋊#1059701011yescharacteristic
217C8—5962no—
218C22—21no—
219C22—21no—
220C22—41no—
221C22—41no—
222C22—2981no—
223C22—2981no—
224C22—5961no—
225C22—5961no—
226C22—5961no—
227C22—5961no—
228C22—5961no—
229C22—5962no—
230C22—5961no—
231C22—1491no—
232C22—1491no—
233C22—11921no—
234C22—11921no—
235C22—11921no—
236C22—11922no—
237C22C2×C22⋊#1059701011yescharacteristic
238C4—21no—
239C4—41no—
240C4—41no—
241C4—2981no—
242C4—5961no—
243C4—11922no—
244C2—21no—
245C2—41no—
246C2—41no—
247C2—2981no—
248C2—2981no—
249C2—5961no—
250C2—5961no—
251C2—11921no—
252C2D149⋊#9911yescharacteristic
subgroupG/H
centerC2D149⋊#99
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
Fitting#123×C149C4
socleC2×C149C2×#99
prime radical#23750186C2
cosocleC2×C22⋊D149C23
hypercenter#123#10597010
hypocenterC149#2121
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
1. D149⋊#100C2semidirect
2. D149⋊#99C2semidirect
3. #23750527C2semidirect
4. #23750526C2semidirect
12. C22×D596C4semidirect
20. #18011879C4semidirect
21. C22⋊C4×D149C4semidirect
22. #123×C149C4semidirect
30. C23×D149C2×C4semidirect
46. C22⋊Dic149C2×C4semidirect
52. C22×C4×C149C2×C4semidirect
55. C22⋊C4×C149C2×C4semidirect
126. C149#2121semidirect
138. #123#10597010semidirect
168. C22×C4C2×#10597010semidirect
182. 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
#237505272
#237505262
#237501862
#2121149