Finite Group Databasebeta

← #34060129

Subgroups — #34060129

Order 19072.

288 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C2×#18011968C211yesmaximal, characteristic
2#23750567C211yesmaximal, characteristic
3#23750479C212yesmaximal, complemented
4#23750478C212yesmaximal, complemented
5C22⋊Q8×D149C211yesmaximal, characteristic
6C22×#11924753—21no—
7C2×C4⋊#10597010—21no—
8C2×C22⋊#10597010—21no—
9#18011968—21no—
10#18011968C2212yes—
11(C2×#10597010)⋊C4C2212yes—
12C2×Q8×D149C411yescharacteristic, complemented
13C22×C4×D149C2211yescharacteristic
14#18011891C2211yescharacteristic
15#18011890C411yescharacteristic, complemented
16#18011889—21no—
17#18011888—21no—
18#18011887C2211yescharacteristic
19C4⋊C4×D149—21no—
20C4⋊C4×D149C411yescharacteristic, complemented
21C22⋊C4×D149—21no—
22C22⋊Q8×C149C411yescharacteristic, complemented
23C22×#10597010—22no—
24C2×#11924753—22no—
25C2×#11924753—42no—
26C4⋊#10597010—42no—
27C22⋊#10597010—42no—
28C23×D149D411yescharacteristic
29C2×Dic298—21no—
30C2×Dic298C2×C411yescharacteristic
31Q8×D149—42no—
32C22×Dic149D411yescharacteristic
33C2×C4×D149—21no—
34C2×C4×D149—21no—
35C2×C4×D149—42no—
36C2×C4×D149C2×C411yescharacteristic
37C2×C4×D149D411yescharacteristic
38C2×C4×D149D411yescharacteristic
39C2×C4×D149C2311yescharacteristic
40C4⋊Dic149—21no—
41C4⋊Dic149C2×C411yescharacteristic
42#14558715—21no—
43#14558715—21no—
44#14558715—21no—
45C22⋊Dic149—21no—
46#14558713—21no—
47#14558713—21no—
48C2×Q8×C149C2×C411yescharacteristic
49C22×C4×C149C2×C411yescharacteristic
50C4⋊C4×C149—21no—
51C4⋊C4×C149C2×C411yescharacteristic
52C22⋊C4×C149—21no—
53C2×#10597010—42no—
54C2×#10597010—42no—
55C2×#10597010—42no—
56#11924753—42no—
57C22×D149—41no—
58C22×D149—41no—
59C22×D149C22⋊C411yescharacteristic
60C22×D149SD1612yes—
61C22×D149Q1612yes—
62C22×D149C2×D411yescharacteristic
63Dic298—42no—
64Dic298—41no—
65C2×Dic149—22no—
66C2×Dic149—21no—
67C2×Dic149—21no—
68C2×Dic149C22⋊C411yescharacteristic
69C2×Dic149C2×D411yescharacteristic
70C4×D149—22no—
71C4×D149—22no—
72C4×D149—41no—
73C4×D149—41no—
74C4×D149—42no—
75C4×D149—42no—
76C23×C149C22⋊C411yescharacteristic
77Q8×C149—41no—
78C2×C4×C149—21no—
79C2×C4×C149—21no—
80C2×C4×C149—41no—
81C2×C4×C149C22⋊C411yescharacteristic
82C2×C4×C149C22×C411yescharacteristic
83C22×C149—21no—
84C22×C149—21no—
85C22×C149#10312yes—
86C22×C149C2×C22⋊C411yescharacteristic
87C2×D149—21no—
88C2×D149—21no—
89C2×D149—21no—
90C2×D149—21no—
91C2×D149—42no—
92C2×D149—42no—
93C2×D149#10312yes—
94C2×D149C2×SD1611yescharacteristic
95C2×D149C2×Q1611yescharacteristic
96#10597010—82no—
97C4×C149—21no—
98C4×C149—21no—
99C4×C149—41no—
100C4×C149—41no—
101Dic149—21no—
102Dic149—41no—
103Dic149—41no—
104Dic149#9912yes—
105C2×C149—22no—
106C2×C149C2×#9911yescharacteristic
107C2×C149C2×#10311yescharacteristic
108C2×C149#42111yescharacteristic
109D149—21no—
110D149—22no—
111D149—21no—
112C149#152011yescharacteristic, complemented, Sylow
113#1520—1491nomaximal, Sylow
114C2×C22⋊Q8—1491no—
115C2×C22⋊C8—1491no—
116#380—1491no—
117#328—1492no—
118#328—1492no—
119C22×Q8—1491no—
120C23×C4—1491no—
121C22×C8—2981no—
122C22⋊Q8—2981no—
123C22⋊Q8—2981no—
124C22⋊Q8—1491no—
125C22⋊Q8—1491no—
126C22⋊Q8—1491no—
127C22⋊Q8#1059701011yescharacteristic, complemented
128C2×C4⋊C4—2981no—
129C2×C4⋊C4—2981no—
130C2×C4⋊C4—1491no—
131C2×C22⋊C4—2981no—
132C2×C22⋊C4—2981no—
133C22⋊C8—2981no—
134C22⋊C8—1492no—
135#95—1492no—
136C24—1491no—
137C2×Q8—2981no—
138C2×Q8—5962no—
139C2×Q8—1491no—
140C2×Q8C2×#1059701011yescharacteristic
141C22×C4—2981no—
142C22×C4—2981no—
143C22×C4—2982no—
144C22×C4—5962no—
145C22×C4—1491no—
146C22×C4—1491no—
147C22×C4—1491no—
148C22×C4—1491no—
149C22×C4—1491no—
150C22×C4C2×#1059701011yescharacteristic
151C2×C8—2982no—
152C2×C8—5962no—
153C4⋊C4—21no—
154C4⋊C4—2981no—
155C4⋊C4—2981no—
156C4⋊C4—2981no—
157C4⋊C4—2981no—
158C4⋊C4—5962no—
159C4⋊C4—1491no—
160C4⋊C4C2×#1059701011yescharacteristic
161C22⋊C4—21no—
162C22⋊C4—2981no—
163C22⋊C4—2981no—
164C22⋊C4—2981no—
165C22⋊C4—5962no—
166C23—5961no—
167C23—5961no—
168C23—1491no—
169C23—1491no—
170C23—1492no—
171C23—1492no—
172C23C22⋊#1059701011yescharacteristic
173Q8—41no—
174Q8—5961no—
175Q8—5962no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—2982no—
180C2×C4—2982no—
181C2×C4—2982no—
182C2×C4—2981no—
183C2×C4—2981no—
184C2×C4—5961no—
185C2×C4—5961no—
186C2×C4—5962no—
187C2×C4—5962no—
188C2×C4—5962no—
189C2×C4—5962no—
190C2×C4—5962no—
191C2×C4—1491no—
192C2×C4—1491no—
193C2×C4C22⋊#1059701011yescharacteristic
194C2×C4C22×#1059701011yescharacteristic
195C8—5962no—
196C22—21no—
197C22—21no—
198C22—2981no—
199C22—2981no—
200C22—2981no—
201C22—2981no—
202C22—5962no—
203C22—5962no—
204C22—1491no—
205C22—1492no—
206C22—1491no—
207C22#1801197412yes—
208C22C2×C22⋊#1059701011yescharacteristic
209C4—21no—
210C4—21no—
211C4—41no—
212C4—41no—
213C4—2981no—
214C4—5961no—
215C4—5961no—
216C4—1492no—
217C4—11922no—
218C2—22no—
219C2—2981no—
220C2—2982no—
221C2—2981no—
222C2D149⋊#9911yescharacteristic
223C2C2×#1801197411yescharacteristic
224C2#2375062211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC22⋊Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC23×D149D4
cosocleC2×C4×D149C23
hypercenterC22⋊Q8#10597010
hypocenterC149#1520
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #23750479C2semidirect
4. #23750478C2semidirect
12. C2×Q8×D149C4semidirect
15. #18011890C4semidirect
20. C4⋊C4×D149C4semidirect
22. C22⋊Q8×C149C4semidirect
112. C149#1520semidirect
127. C22⋊Q8#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×#180119682
#237505672
#237504792
#237504782
C22⋊Q8×D1492
#1520149