Finite Group Databasebeta

← #34060020

Subgroups — #34060020

Order 19072.

248 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 76 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#23750644C211yesmaximal, characteristic
2#23750629C211yesmaximal, characteristic
3#23750475C212yesmaximal, complemented
4Q8⋊#11924753C212yesmaximal, complemented
5C4×Q8×D149C211yesmaximal, characteristic
6C2×#14558746—21no—
7C4⋊#11924753—21no—
8C4⋊#11924753—21no—
9C4⋊#11924753C2212yes—
10#18011968—21no—
11C4×#11924753C2212yes—
12C2×Q8×D149C411yescharacteristic
13Q8×Dic149C2211yescharacteristic
14C4×Dic298—21no—
15C4×Dic298C411yescharacteristic
16#18011876—21no—
17#18011876C2211yescharacteristic
18C4⋊C4×D149—21no—
19C4⋊C4×D149C411yescharacteristic
20C42×D149—21no—
21C42×D149C2211yescharacteristic
22C4×Q8×C149C411yescharacteristic
23#14558746—42no—
24C2×#11924753—22no—
25C2×#11924753—22no—
26C2×Dic298—21no—
27C2×Dic298C2×C411yescharacteristic
28Q8×D149—22no—
29Q8×D149—22no—
30C2×C4×D149—21no—
31C2×C4×D149—21no—
32C2×C4×D149C2×C411yescharacteristic
33C2×C4×D149D411yescharacteristic
34C2×C4×D149D411yescharacteristic
35C4⋊Dic149—21no—
36C4⋊Dic149C2×C411yescharacteristic
37#14558715—21no—
38#14558715—21no—
39#14558715—21no—
40C4×Dic149—21no—
41C4×Dic149—21no—
42C4×Dic149—21no—
43C4×Dic149D411yescharacteristic
44C4×Dic149D411yescharacteristic
45C4×Dic149C2311yescharacteristic
46C2×Q8×C149C2×C411yescharacteristic
47C4⋊C4×C149—21no—
48C4⋊C4×C149C2×C411yescharacteristic
49C42×C149—21no—
50C42×C149C2×C411yescharacteristic
51#11924753—42no—
52#11924753—42no—
53C22×D149C22⋊C411yescharacteristic
54Dic298—24no—
55Dic298—21no—
56Dic298M1612yescomplemented
57C2×Dic149—21no—
58C2×Dic149—21no—
59C2×Dic149C22⋊C411yescharacteristic
60C2×Dic149C2×D411yescharacteristic
61C2×Dic149C2×D411yescharacteristic
62C4×D149—24no—
63C4×D149—21no—
64C4×D149—21no—
65C4×D149—41no—
66C4×D149—42no—
67C4×D149SD1612yes—
68C4×D149Q1612yes—
69Q8×C149—21no—
70Q8×C149M1612yescomplemented
71C2×C4×C149—21no—
72C2×C4×C149—21no—
73C2×C4×C149C22⋊C411yescharacteristic
74C2×C4×C149C22⋊C411yescharacteristic
75C2×C4×C149C22×C411yescharacteristic
76C22×C149C2×C22⋊C411yescharacteristic
77C2×D149—21no—
78C2×D149—21no—
79C2×D149#10312yes—
80C4×C149—22no—
81C4×C149—21no—
82C4×C149—41no—
83C4×C149#10312yes—
84C4×C149C2×M1611yescharacteristic
85C4×C149C2×M1611yescharacteristic
86Dic149—22no—
87Dic149—21no—
88Dic149—21no—
89Dic149—41no—
90Dic149C2×SD1611yescharacteristic
91Dic149C2×Q1611yescharacteristic
92C2×C149#40711yescharacteristic
93C2×C149C2×#10311yescharacteristic
94C2×C149#42111yescharacteristic
95D149—22no—
96C149#148711yescharacteristic, complemented, Sylow
97#1487—1491nomaximal, Sylow
98C2×C4×Q8—1491no—
99#431—1491no—
100#423—1491no—
101Q8⋊C8—1492no—
102Q8⋊C8—1492no—
103C22×Q8—1491no—
104C2×M16—2981no—
105C4×Q8—2981no—
106C4×Q8—2981no—
107C4×Q8—1491no—
108C4×Q8—1491no—
109C4×Q8—1491no—
110C4×Q8#1059701011yescharacteristic
111C2×C4⋊C4—2981no—
112C2×C4⋊C4—1491no—
113C2×C42—2981no—
114C2×C42—1491no—
115C4⋊C8—2981no—
116C4⋊C8—2981no—
117C4⋊C8—1492no—
118C22⋊C8—2981no—
119C4×C8—1492no—
120C2×Q8—2981no—
121C2×Q8—2982no—
122C2×Q8—2982no—
123C2×Q8—1491no—
124C2×Q8C2×#1059701011yescharacteristic
125C22×C4—2981no—
126C22×C4—2981no—
127C22×C4—1491no—
128C22×C4—1491no—
129C22×C4—1491no—
130M16—5962no—
131C2×C8—2982no—
132C2×C8—2982no—
133C4⋊C4—21no—
134C4⋊C4—2981no—
135C4⋊C4—2981no—
136C4⋊C4—2981no—
137C4⋊C4—2981no—
138C4⋊C4—1491no—
139C4⋊C4C2×#1059701011yescharacteristic
140C42—21no—
141C42—2981no—
142C42—2981no—
143C42—2981no—
144C42—1491no—
145C42—1491no—
146C42—1491no—
147C42C2×#1059701011yescharacteristic
148C23—1491no—
149Q8—21no—
150Q8—2984no—
151Q8—2981no—
152Q8—1492no—
153Q8#1455874612yescomplemented
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—2984no—
157C2×C4—2981no—
158C2×C4—2981no—
159C2×C4—2981no—
160C2×C4—2981no—
161C2×C4—5961no—
162C2×C4—5962no—
163C2×C4—1491no—
164C2×C4—1491no—
165C2×C4—1491no—
166C2×C4—1492no—
167C2×C4—1492no—
168C2×C4C22⋊#1059701011yescharacteristic
169C2×C4C22⋊#1059701011yescharacteristic
170C2×C4C22×#1059701011yescharacteristic
171C8—5962no—
172C8—5962no—
173C22—2981no—
174C22—2981no—
175C22—1492no—
176C22C2×C22⋊#1059701011yescharacteristic
177C4—22no—
178C4—21no—
179C4—41no—
180C4—2982no—
181C4—2981no—
182C4—2981no—
183C4—5961no—
184C4—1491no—
185C4—1491no—
186C4#1801197412yes—
187C4D149⋊M1611yescharacteristic
188C4C2×#1455874611yescharacteristic
189C2—2982no—
190C2#2375059611yescharacteristic
191C2C2×#1801197411yescharacteristic
192C2#2375062211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4×Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C22⋊C4
cosocleC4×Dic149C23
hypercenterC4×Q8#10597010
hypocenterC149#1487
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. #23750475C2semidirect
4. Q8⋊#11924753C2semidirect
56. Dic298M16semidirect
70. Q8×C149M16semidirect
96. C149#1487semidirect
153. Q8#14558746semidirect

Maximal subgroups

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

subgroupindex
#237506442
#237506292
#237504752
Q8⋊#119247532
C4×Q8×D1492
#1487149