Finite Group Databasebeta

← #34043695

Subgroups — #34043695

Order 19072.

254 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 51 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#23750202C211yesmaximal, characteristic
2#23749939C211yesmaximal, characteristic, complemented
3#23749936C211yesmaximal, characteristic, complemented
4#23749557C211yesmaximal, characteristic, complemented
5#23749358C211yesmaximal, characteristic, complemented
6#23749350C211yesmaximal, characteristic, complemented
7#327×C149C211yesmaximal, characteristic, complemented
8C2×#14558735—21no—
9#18011889—21no—
10#18011888—21no—
11#18011885C2211yescharacteristic
12#18011884—21no—
13#18011883—21no—
14#18011883—21no—
15C2×C4⋊Dic149—21no—
16C2×C4⋊Dic149C2211yescharacteristic
17C2×#14558715C2211yescharacteristic
18#18011845—21no—
19#18011844—21no—
20#18011833—21no—
21#18011832—21no—
22C22⋊#11924746C2211yescharacteristic
23#18011818—21no—
24#121×C149C2211yescharacteristic
25C22⋊C8×C149C2211yescharacteristic
26#95×C149C2211yescharacteristic
27#14558735—42no—
28#14558735—42no—
29C2×Dic298—21no—
30C2×D596D411yescharacteristic
31C2×C22⋊D149—21no—
32C2×C22⋊D149—21no—
33C2×C22⋊D149—21no—
34C22×Dic149—21no—
35C22×Dic149—21no—
36C22×Dic149D411yescharacteristic
37C22×Dic149D411yescharacteristic
38C2×C4×D149—21no—
39C2×#11924746—21no—
40C4⋊Dic149—21no—
41C4⋊Dic149—21no—
42C4⋊Dic149—42no—
43C4⋊Dic149D411yescharacteristic
44#14558715—21no—
45#14558715—21no—
46#14558715—21no—
47C22⋊Dic149—21no—
48#14558713—21no—
49#14558713—21no—
50C2×D4×C149—21no—
51C2×D4×C149D411yescharacteristic
52C22×C4×C149—21no—
53C22×C4×C149C2311yescharacteristic
54C2×C8×C149—21no—
55C4⋊C4×C149D411yescharacteristic
56C22⋊C4×C149—21no—
57C22×D149—21no—
58Dic298—42no—
59D596—41no—
60C22⋊D149—42no—
61C22⋊D149—41no—
62C22⋊D149—41no—
63C22⋊D149—81no—
64C2×Dic149—21no—
65C2×Dic149—21no—
66C2×Dic149—21no—
67C2×Dic149—21no—
68C2×Dic149—42no—
69C2×Dic149—41no—
70C2×Dic149—41no—
71C2×Dic149—41no—
72C2×Dic149—41no—
73C2×Dic149D812yes—
74C4×D149—42no—
75#11924746—41no—
76C23×C149—21no—
77C23×C149C2×D411yescharacteristic
78D4×C149—41no—
79D4×C149—41no—
80D4×C149—41no—
81C2×C4×C149—22no—
82C2×C4×C149—21no—
83C2×C4×C149—41no—
84C2×C4×C149—41no—
85C2×C4×C149—41no—
86C2×C4×C149C2×D411yescharacteristic
87C2×C4×C149C2×D411yescharacteristic
88C8×C149—41no—
89C22×C149—21no—
90C22×C149—21no—
91C22×C149—41no—
92C22×C149—41no—
93C22×C149—41no—
94C22×C149#12011yescharacteristic
95C22×C149C2×D811yescharacteristic
96C22×C149AGL(1,ℤ/8)11yescharacteristic
97C2×D149—41no—
98C2×D149—41no—
99C2×D149—41no—
100C4×C149—21no—
101C4×C149—21no—
102C4×C149—42no—
103C4×C149—41no—
104Dic149—22no—
105Dic149—41no—
106Dic149—41no—
107Dic149—81no—
108C2×C149—21no—
109C2×C149—21no—
110C2×C149—81no—
111C2×C149#44711yescharacteristic
112C2×C149#45611yescharacteristic
113C2×C149#45811yescharacteristic
114D149—81no—
115C149#161011yescharacteristic, complemented, Sylow
116#1610—1491nomaximal, Sylow
117#537—1491no—
118#480—1491no—
119#480—1491no—
120#398—1491no—
121#327—1491no—
122#327D14911yescharacteristic, complemented
123#324—1491no—
124C2×#41—2981no—
125C22⋊Q8—2981no—
126C22⋊Q8—2981no—
127#121—2981no—
128#121—2981no—
129#121—2981no—
130#121—1491no—
131#121C2×D14911yescharacteristic
132C2×C4⋊C4—2981no—
133C2×C4⋊C4—1491no—
134C2×C4⋊C4—1491no—
135#107—2981no—
136#107—2981no—
137#102—2981no—
138#102—2981no—
139C22⋊C8—1491no—
140C22⋊C8C2×D14911yescharacteristic
141#95—2981no—
142#95C2×D14911yescharacteristic
143#41—5962no—
144#41—5962no—
145C2×Q8—2981no—
146C2×D4—21no—
147C2×D4—2981no—
148C2×D4—2981no—
149C2×D4—2981no—
150C2×D4—1491no—
151C2×D4D59611yescharacteristic
152C22×C4—21no—
153C22×C4—2981no—
154C22×C4—2981no—
155C22×C4—2981no—
156C22×C4—1491no—
157C22×C4—1491no—
158C22×C4C22×D14911yescharacteristic
159C2×C8—21no—
160C2×C8—2981no—
161C4⋊C4—2981no—
162C4⋊C4—2981no—
163C4⋊C4—2981no—
164C4⋊C4—2981no—
165C4⋊C4—2981no—
166C4⋊C4—5962no—
167C4⋊C4—1491no—
168C4⋊C4D59611yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—2981no—
171C22⋊C4—2981no—
172C22⋊C4—2981no—
173C23—21no—
174C23—2981no—
175C23D4×D14911yescharacteristic
176Q8—5962no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—5961no—
181D4—5962no—
182D4—5961no—
183D4—5961no—
184D4—11921no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—2981no—
191C2×C4—2981no—
192C2×C4—2981no—
193C2×C4—2981no—
194C2×C4—5962no—
195C2×C4—5962no—
196C2×C4—5961no—
197C2×C4—5961no—
198C2×C4—5961no—
199C2×C4—5961no—
200C2×C4—1492no—
201C2×C4D4×D14911yescharacteristic
202C2×C4C2×D59611yescharacteristic
203C8—41no—
204C8—5961no—
205C22—21no—
206C22—21no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—5961no—
211C22—5961no—
212C22—5961no—
213C22#1801188111yescharacteristic
214C22D8×D14911yescharacteristic
215C22#1801193811yescharacteristic
216C4—21no—
217C4—21no—
218C4—42no—
219C4—41no—
220C4—2982no—
221C4—5961no—
222C4—5961no—
223C4—11921no—
224C2—21no—
225C2—21no—
226C2—81no—
227C2—11921no—
228C2#2374976011yescharacteristic
229C2#2374980911yescharacteristic
230C2#2374981611yescharacteristic
subgroupG/H
centerC22#18011881
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#327×C149C2
socleC22×C149#120
prime radical#23750202C2
hypercenter#327D149
hypocenterC149#1610
LCSG ▷ C22×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #23749939C2semidirect
3. #23749936C2semidirect
4. #23749557C2semidirect
5. #23749358C2semidirect
6. #23749350C2semidirect
7. #327×C149C2semidirect
115. C149#1610semidirect
122. #327D149semidirect

Maximal subgroups

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

subgroupindex
#237502022
#237499392
#237499362
#237495572
#237493582
#237493502
#327×C1492
#1610149