Finite Group Databasebeta

← #34060089

Subgroups — #34060089

Order 19072.

294 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 60 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#23750597C211yesmaximal, characteristic
2C4×C22⋊#10597010C211yesmaximal, characteristic
3#23750479C212yesmaximal, complemented
4#23750478C212yesmaximal, complemented
5C22⋊Q8×D149C211yesmaximal, characteristic
6C2×#14558745—21no—
7C2×C22⋊#10597010—21no—
8C2×C4×#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—
24#14558745—42no—
25C2×#11924753—22no—
26C22⋊#10597010—24no—
27C4×#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—24no—
54C2×#10597010—42no—
55C2×#10597010—42no—
56#11924753—42no—
57C22×D149—22no—
58C22×D149—22no—
59C22×D149—41no—
60C22×D149C22⋊C411yescharacteristic
61C22×D149C2×D411yescharacteristic
62Dic298—42no—
63Dic298—41no—
64C2×Dic149—22no—
65C2×Dic149—21no—
66C2×Dic149—21no—
67C2×Dic149C22⋊C411yescharacteristic
68C2×Dic149C2×D411yescharacteristic
69C4×D149—22no—
70C4×D149—22no—
71C4×D149—41no—
72C4×D149—41no—
73C4×D149—42no—
74C4×D149—42no—
75C23×C149C22⋊C411yescharacteristic
76Q8×C149—41no—
77C2×C4×C149—21no—
78C2×C4×C149—21no—
79C2×C4×C149—41no—
80C2×C4×C149C22⋊C411yescharacteristic
81C2×C4×C149C22×C411yescharacteristic
82C22×C149—21no—
83C22×C149—21no—
84C22×C149—21no—
85C22×C149C2×C22⋊C411yescharacteristic
86C2×D149—21no—
87C2×D149—21no—
88C2×D149—21no—
89C2×D149—21no—
90C2×D149—44no—
91C2×D149#10412yes—
92C2×D149#13712yes—
93#10597010—44no—
94C4×C149—21no—
95C4×C149—21no—
96C4×C149—41no—
97C4×C149—41no—
98Dic149—21no—
99Dic149—41no—
100Dic149—41no—
101Dic149#9912yes—
102C2×C149—41no—
103C2×C149C2×#9911yescharacteristic
104C2×C149#41911yescharacteristic
105C2×C149C2×#10411yescharacteristic
106D149—22no—
107D149—22no—
108C149#150811yescharacteristic, complemented, Sylow
109#1508—1491nomaximal, Sylow
110C2×C22⋊Q8—1491no—
111#407—1491no—
112C4×C22⋊C4—1491no—
113#328—1492no—
114#328—1492no—
115C22×Q8—1491no—
116C23×C4—1491no—
117C2×M16—2981no—
118C22⋊Q8—2981no—
119C22⋊Q8—2981no—
120C22⋊Q8—1491no—
121C22⋊Q8—1491no—
122C22⋊Q8—1491no—
123C22⋊Q8#1059701011yescharacteristic, complemented
124C2×C4⋊C4—2981no—
125C2×C4⋊C4—1491no—
126C2×C22⋊C4—2981no—
127C2×C22⋊C4—2981no—
128C2×C42—2981no—
129C22⋊C8—2981no—
130C22⋊C8—1492no—
131#95—1492no—
132C24—1491no—
133C2×Q8—2981no—
134C2×Q8—5962no—
135C2×Q8—1491no—
136C2×Q8C2×#1059701011yescharacteristic
137C22×C4—2981no—
138C22×C4—2981no—
139C22×C4—2982no—
140C22×C4—5962no—
141C22×C4—1491no—
142C22×C4—1491no—
143C22×C4—1491no—
144C22×C4—1491no—
145C22×C4—1491no—
146C22×C4C2×#1059701011yescharacteristic
147M16—5962no—
148C2×C8—2982no—
149C4⋊C4—21no—
150C4⋊C4—2981no—
151C4⋊C4—2981no—
152C4⋊C4—2981no—
153C4⋊C4—2981no—
154C4⋊C4—1491no—
155C4⋊C4C2×#1059701011yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—2981no—
158C22⋊C4—2981no—
159C22⋊C4—2984no—
160C22⋊C4—2981no—
161C42—5962no—
162C23—2982no—
163C23—2982no—
164C23—5961no—
165C23—1491no—
166C23—1491no—
167C23C22⋊#1059701011yescharacteristic
168Q8—41no—
169Q8—5961no—
170Q8—5962no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—41no—
174C2×C4—2982no—
175C2×C4—2982no—
176C2×C4—2982no—
177C2×C4—2984no—
178C2×C4—2981no—
179C2×C4—2981no—
180C2×C4—5961no—
181C2×C4—5961no—
182C2×C4—5962no—
183C2×C4—5962no—
184C2×C4—5962no—
185C2×C4—5962no—
186C2×C4—1491no—
187C2×C4—1491no—
188C2×C4C22⋊#1059701011yescharacteristic
189C2×C4C22×#1059701011yescharacteristic
190C8—5962no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—2981no—
195C22—2981no—
196C22—2981no—
197C22—2981no—
198C22—5964no—
199C22—1492no—
200C22—1492no—
201C22C2×C22⋊#1059701011yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—41no—
206C4—2981no—
207C4—5964no—
208C4—5961no—
209C4—5961no—
210C4—1492no—
211C2—41no—
212C2—2982no—
213C2—2982no—
214C2D149⋊#9911yescharacteristic
215C2#2375061811yescharacteristic
216C2D149⋊#10411yescharacteristic
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#1508
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
108. C149#1508semidirect
123. C22⋊Q8#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505972
C4×C22⋊#105970102
#237504792
#237504782
C22⋊Q8×D1492
#1508149