Finite Group Databasebeta

← #34060100

Subgroups — #34060100

Order 19072.

274 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 58 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#23750596C211yesmaximal, characteristic
2#23750568C211yesmaximal, characteristic
3#23750479C212yesmaximal, complemented
4#23750478C212yesmaximal, complemented
5C22⋊Q8×D149C211yesmaximal, characteristic
6C2×#14558746—21no—
7C2×C22⋊#10597010—21no—
8#18011968C2212yes—
9C22⋊#11924753—21no—
10(C2×#10597010)⋊C4—21no—
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#14558746—42no—
25C2×#11924753—22no—
26C22⋊#10597010—42no—
27C23×D149D411yescharacteristic
28C2×Dic298—21no—
29C2×Dic298C2×C411yescharacteristic
30Q8×D149—42no—
31C22×Dic149D411yescharacteristic
32C2×C4×D149—21no—
33C2×C4×D149—21no—
34C2×C4×D149—42no—
35C2×C4×D149C2×C411yescharacteristic
36C2×C4×D149D411yescharacteristic
37C2×C4×D149D411yescharacteristic
38C2×C4×D149C2311yescharacteristic
39C4⋊Dic149—21no—
40C4⋊Dic149C2×C411yescharacteristic
41#14558715—21no—
42#14558715—21no—
43#14558715—21no—
44C22⋊Dic149—21no—
45#14558713—21no—
46#14558713—21no—
47C2×Q8×C149C2×C411yescharacteristic
48C22×C4×C149C2×C411yescharacteristic
49C4⋊C4×C149—21no—
50C4⋊C4×C149C2×C411yescharacteristic
51C22⋊C4×C149—21no—
52C2×#10597010—42no—
53C2×#10597010—42no—
54C2×#10597010—42no—
55#11924753—42no—
56C22×D149—22no—
57C22×D149—22no—
58C22×D149—41no—
59C22×D149C22⋊C411yescharacteristic
60C22×D149C2×D411yescharacteristic
61Dic298—42no—
62Dic298—41no—
63C2×Dic149—21no—
64C2×Dic149—21no—
65C2×Dic149—41no—
66C2×Dic149C22⋊C411yescharacteristic
67C2×Dic149C2×D411yescharacteristic
68C4×D149—22no—
69C4×D149—22no—
70C4×D149—41no—
71C4×D149—41no—
72C4×D149—42no—
73C4×D149—42no—
74C23×C149C22⋊C411yescharacteristic
75Q8×C149—41no—
76C2×C4×C149—21no—
77C2×C4×C149—21no—
78C2×C4×C149—41no—
79C2×C4×C149C22⋊C411yescharacteristic
80C2×C4×C149C22×C411yescharacteristic
81C22×C149—21no—
82C22×C149—21no—
83C22×C149—21no—
84C22×C149C2×C22⋊C411yescharacteristic
85C2×D149—21no—
86C2×D149—21no—
87C2×D149—21no—
88C2×D149—21no—
89C2×D149—44no—
90C2×D149#9912yes—
91C2×D149#13712yes—
92#10597010—82no—
93C4×C149—21no—
94C4×C149—21no—
95C4×C149—41no—
96C4×C149—41no—
97Dic149—21no—
98Dic149—21no—
99Dic149—41no—
100Dic149—41no—
101C2×C149—41no—
102C2×C149C2×#9911yescharacteristic
103C2×C149#41911yescharacteristic
104C2×C149#42111yescharacteristic
105D149—22no—
106D149—22no—
107C149#151111yescharacteristic, complemented, Sylow
108#1511—1491nomaximal, Sylow
109C2×C22⋊Q8—1491no—
110#407—1491no—
111#381—1491no—
112#328—1492no—
113#328—1492no—
114C22×Q8—1491no—
115C23×C4—1491no—
116C2×M16—2981no—
117C22⋊Q8—2981no—
118C22⋊Q8—2981no—
119C22⋊Q8—1491no—
120C22⋊Q8—1491no—
121C22⋊Q8—1491no—
122C22⋊Q8#1059701011yescharacteristic, complemented
123C2×C4⋊C4—2981no—
124C2×C4⋊C4—1491no—
125C2×C22⋊C4—2981no—
126C2×C22⋊C4—2981no—
127C22⋊C8—2981no—
128C22⋊C8—1492no—
129#95—2981no—
130#95—1492no—
131C24—1491no—
132C2×Q8—2981no—
133C2×Q8—5962no—
134C2×Q8—1491no—
135C2×Q8C2×#1059701011yescharacteristic
136C22×C4—2981no—
137C22×C4—2981no—
138C22×C4—2982no—
139C22×C4—5962no—
140C22×C4—1491no—
141C22×C4—1491no—
142C22×C4—1491no—
143C22×C4—1491no—
144C22×C4—1491no—
145C22×C4C2×#1059701011yescharacteristic
146M16—5962no—
147C2×C8—2982no—
148C4⋊C4—21no—
149C4⋊C4—2981no—
150C4⋊C4—2981no—
151C4⋊C4—2981no—
152C4⋊C4—2981no—
153C4⋊C4—1491no—
154C4⋊C4C2×#1059701011yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—2981no—
157C22⋊C4—2981no—
158C22⋊C4—2981no—
159C22⋊C4—5962no—
160C23—2982no—
161C23—2982no—
162C23—5961no—
163C23—1491no—
164C23—1491no—
165C23C22⋊#1059701011yescharacteristic
166Q8—41no—
167Q8—5961no—
168Q8—5962no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—2982no—
173C2×C4—2982no—
174C2×C4—2981no—
175C2×C4—2981no—
176C2×C4—5961no—
177C2×C4—5961no—
178C2×C4—5962no—
179C2×C4—5962no—
180C2×C4—5961no—
181C2×C4—5962no—
182C2×C4—5962no—
183C2×C4—5962no—
184C2×C4—1491no—
185C2×C4—1491no—
186C2×C4C22⋊#1059701011yescharacteristic
187C2×C4C22×#1059701011yescharacteristic
188C8—5962no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—2981no—
193C22—2981no—
194C22—2981no—
195C22—2981no—
196C22—5964no—
197C22—1492no—
198C22—1492no—
199C22C2×C22⋊#1059701011yescharacteristic
200C4—21no—
201C4—21no—
202C4—41no—
203C4—41no—
204C4—2981no—
205C4—2981no—
206C4—5961no—
207C4—5961no—
208C4—11922no—
209C2—41no—
210C2—2982no—
211C2—2982no—
212C2D149⋊#9911yescharacteristic
213C2#2375061811yescharacteristic
214C2#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#1511
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
107. C149#1511semidirect
122. C22⋊Q8#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505962
#237505682
#237504792
#237504782
C22⋊Q8×D1492
#1511149