Finite Group Databasebeta

← #34043707

Subgroups — #34043707

Order 19072.

232 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 49 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#23750213C211yesmaximal, characteristic
2#23749956C211yesmaximal, characteristic, complemented
3#23749939C211yesmaximal, characteristic, complemented
4#23749550C211yesmaximal, characteristic, complemented
5#23749363C211yesmaximal, characteristic, complemented
6#23749360C211yesmaximal, characteristic, complemented
7#323×C149C211yesmaximal, characteristic, complemented
8#18011904—21no—
9#18011897—21no—
10#18011893—21no—
11#18011890C2211yescharacteristic
12#18011885C2211yescharacteristic
13#18011884—21no—
14#18011880—21no—
15C4×C22⋊D149—21no—
16C2×C4⋊Dic149C2211yescharacteristic
17C2×C22⋊Dic149—21no—
18#18011845—21no—
19#18011843—21no—
20#18011836—21no—
21#18011833—21no—
22#18011818—21no—
23#18011818C2211yescharacteristic
24C2×C22⋊C4×C149C2211yescharacteristic
25C22⋊C8×C149C2211yescharacteristic
26C22⋊C8×C149C2211yescharacteristic
27C2×Dic298D411yescharacteristic
28C2×D596D411yescharacteristic
29C2×C22⋊D149—21no—
30C2×C22⋊D149—21no—
31C2×C22⋊D149—21no—
32C22×Dic149—21no—
33C22×Dic149—21no—
34C2×C4×D149—21no—
35C4⋊Dic149—21no—
36C4⋊Dic149—21no—
37C4⋊Dic149D411yescharacteristic
38C4⋊Dic149D411yescharacteristic
39#14558715—21no—
40#14558715—21no—
41C22⋊Dic149—21no—
42C22⋊Dic149—21no—
43C22⋊Dic149—21no—
44C22⋊Dic149—42no—
45#14558713—21no—
46#14558713—21no—
47C4×Dic149—21no—
48C24×C149D411yescharacteristic
49C22×C4×C149D411yescharacteristic
50C22×C4×C149C2311yescharacteristic
51C2×C8×C149—21no—
52C2×C8×C149—21no—
53C22⋊C4×C149—21no—
54C22⋊C4×C149—21no—
55C22×D149—21no—
56Dic298—41no—
57D596—41no—
58C22⋊D149—41no—
59C22⋊D149—41no—
60C22⋊D149—81no—
61C22⋊D149—81no—
62C2×Dic149—21no—
63C2×Dic149—21no—
64C2×Dic149—21no—
65C2×Dic149—41no—
66C2×Dic149—41no—
67C2×Dic149—41no—
68C2×Dic149—41no—
69C2×Dic149—41no—
70C2×Dic149—41no—
71C4×D149—81no—
72C23×C149—21no—
73C23×C149—21no—
74C23×C149—21no—
75C23×C149—41no—
76C23×C149—41no—
77C23×C149C2×D411yescharacteristic
78C2×C4×C149—21no—
79C2×C4×C149—41no—
80C2×C4×C149—41no—
81C2×C4×C149C2×D411yescharacteristic
82C2×C4×C149C2×D411yescharacteristic
83C8×C149—41no—
84C8×C149—41no—
85C22×C149—21no—
86C22×C149—21no—
87C22×C149—42no—
88C22×C149—41no—
89C22×C149—41no—
90C22×C149—41no—
91C22×C149—81no—
92C22×C149#12011yescharacteristic
93C22×C149#13511yescharacteristic
94C22×C149AGL(1,ℤ/8)11yescharacteristic
95C2×D149—41no—
96C2×D149—41no—
97C2×D149—41no—
98C4×C149—21no—
99C4×C149—21no—
100C4×C149—41no—
101Dic149—41no—
102Dic149—41no—
103Dic149—41no—
104Dic149—81no—
105Dic149—81no—
106C2×C149—21no—
107C2×C149—21no—
108C2×C149—81no—
109C2×C149#44911yescharacteristic
110C2×C149#45511yescharacteristic
111C2×C149#45811yescharacteristic
112D149—81no—
113C149#161211yescharacteristic, complemented, Sylow
114#1612—1491nomaximal, Sylow
115#538—1491no—
116#483—1491no—
117#480—1491no—
118#397—1491no—
119#328—1491no—
120#327—1491no—
121#323D14911yescharacteristic, complemented
122#126—2981no—
123#124—2981no—
124#123—2981no—
125C22⋊Q8—1491no—
126#121—2981no—
127#121—1491no—
128#120—2981no—
129C4×D4—2981no—
130C2×C4⋊C4—1491no—
131C2×C22⋊C4—2981no—
132C2×C22⋊C4C2×D14911yescharacteristic
133#107—2981no—
134#106—2981no—
135#103—2981no—
136#102—2981no—
137C22⋊C8C2×D14911yescharacteristic
138C22⋊C8C2×D14911yescharacteristic
139#95—2981no—
140#95—1491no—
141C24D59611yescharacteristic
142C2×Q8—1491no—
143C2×D4—2981no—
144C2×D4—2981no—
145C2×D4—2981no—
146C2×D4—1491no—
147C22×C4—2981no—
148C22×C4—2981no—
149C22×C4—2981no—
150C22×C4D59611yescharacteristic
151C22×C4C22×D14911yescharacteristic
152C2×C8—21no—
153C2×C8—21no—
154C4⋊C4—2981no—
155C4⋊C4—2981no—
156C4⋊C4—2981no—
157C4⋊C4—2981no—
158C4⋊C4—1491no—
159C4⋊C4—1491no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—2981no—
163C22⋊C4—2981no—
164C22⋊C4—2981no—
165C22⋊C4—2981no—
166C22⋊C4—2981no—
167C22⋊C4—5962no—
168C42—2981no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—2981no—
175C23C2×D59611yescharacteristic
176Q8—5961no—
177D4—5961no—
178D4—5961no—
179D4—5961no—
180D4—11921no—
181D4—11921no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—2981no—
186C2×C4—2981no—
187C2×C4—2981no—
188C2×C4—5961no—
189C2×C4—5961no—
190C2×C4—5961no—
191C2×C4—5961no—
192C2×C4—5961no—
193C2×C4—5961no—
194C2×C4—11921no—
195C2×C4D4×D14911yescharacteristic
196C2×C4D4×D14911yescharacteristic
197C8—41no—
198C8—41no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—81no—
206C22—5961no—
207C22—5961no—
208C22—5961no—
209C22#1801188111yescharacteristic
210C22#1801193311yescharacteristic
211C22#1801193911yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—5961no—
216C4—5961no—
217C4—5961no—
218C4—11921no—
219C4—11921no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—11921no—
224C2#2374977211yescharacteristic
225C2#2374980511yescharacteristic
226C2#2374981611yescharacteristic
subgroupG/H
centerC22#18011881
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#323×C149C2
socleC22×C149#120
prime radical#23750213C2
hypercenter#323D149
hypocenterC149#1612
LCSG ▷ C22×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #23749956C2semidirect
3. #23749939C2semidirect
4. #23749550C2semidirect
5. #23749363C2semidirect
6. #23749360C2semidirect
7. #323×C149C2semidirect
113. C149#1612semidirect
121. #323D149semidirect

Maximal subgroups

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

subgroupindex
#237502132
#237499562
#237499392
#237495502
#237493632
#237493602
#323×C1492
#1612149