Finite Group Databasebeta

← #34060036

Subgroups — #34060036

Order 19072.

276 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 72 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#23750628C211yesmaximal, characteristic, complemented
2C2×C4×#11924753C211yesmaximal, characteristic, complemented
3#23750473C212yesmaximal, complemented
4D4⋊#11924753C212yesmaximal, complemented
5#23750170C211yesmaximal, characteristic
6C2×#14558745—21no—
7C22×#11924753—21no—
8#18011978—21no—
9C4⋊#11924753C2212yes—
10C4×#11924753—21no—
11C4×#11924753C2212yes—
12C2×#14558735—21no—
13#18011910C411yescharacteristic
14#18011907C411yescharacteristic
15#18011897—21no—
16#18011885C411yescharacteristic
17#18011883—21no—
18D4×Dic149C2211yescharacteristic
19#18011873C2211yescharacteristic
20#18011871—21no—
21C2×C4×Dic149C2211yescharacteristic
22#121×C149C411yescharacteristic
23#14558745—42no—
24C2×#11924753—24no—
25C2×#11924753—22no—
26C2×#11924753—22no—
27#14558735—42no—
28#14558735—42no—
29C2×Dic298—21no—
30C2×D596C2×C411yescharacteristic
31C2×C22⋊D149—21no—
32C2×C22⋊D149—21no—
33C2×C22⋊D149—21no—
34C22×Dic149—21no—
35C22×Dic149D411yescharacteristic
36C22×Dic149D411yescharacteristic
37C2×C4×D149—21no—
38C4⋊Dic149C2×C411yescharacteristic
39#14558715—21no—
40C22⋊Dic149—21no—
41#14558713—21no—
42#14558713—21no—
43C4×Dic149C2×C411yescharacteristic
44C4×Dic149D411yescharacteristic
45C4×Dic149D411yescharacteristic
46C4×Dic149C2311yescharacteristic
47C2×D4×C149—21no—
48C2×D4×C149C2×C411yescharacteristic
49C22×C4×C149C2×C411yescharacteristic
50C4⋊C4×C149C2×C411yescharacteristic
51C22⋊C4×C149—21no—
52#11924753—24no—
53#11924753—42no—
54C22×D149—21no—
55Dic298—42no—
56D596—22no—
57C22⋊D149—42no—
58C22⋊D149—42no—
59C22⋊D149—42no—
60C2×Dic149—22no—
61C2×Dic149—21no—
62C2×Dic149—41no—
63C2×Dic149—41no—
64C2×Dic149C22⋊C411yescharacteristic
65C2×Dic149C22⋊C411yescharacteristic
66C2×Dic149D812yes—
67C2×Dic149SD1612yes—
68C2×Dic149C2×D411yescharacteristic
69C2×Dic149C2×D411yescharacteristic
70C4×D149—41no—
71C4×D149—41no—
72C23×C149—21no—
73C23×C149C22⋊C411yescharacteristic
74D4×C149—22no—
75D4×C149—42no—
76C2×C4×C149—22no—
77C2×C4×C149—21no—
78C2×C4×C149C22⋊C411yescharacteristic
79C2×C4×C149C22×C411yescharacteristic
80C22×C149—21no—
81C22×C149—21no—
82C22×C149—41no—
83C22×C149—41no—
84C22×C149—41no—
85C22×C149#10212yes—
86C22×C149C2×C22⋊C411yescharacteristic
87C2×D149—41no—
88C2×D149—41no—
89C2×D149—41no—
90C4×C149—21no—
91C4×C149—41no—
92C4×C149#13112yes—
93Dic149—21no—
94Dic149—41no—
95Dic149#10212yes—
96Dic149#10412yes—
97Dic149C2×D811yescharacteristic
98Dic149C2×SD1611yescharacteristic
99C2×C149—22no—
100C2×C149—81no—
101C2×C149#40811yescharacteristic
102C2×C149C2×#10211yescharacteristic
103C2×C149C2×#10411yescharacteristic
104D149—81no—
105C149#149211yescharacteristic, complemented, Sylow
106#1492—1491nomaximal, Sylow
107#532—1491no—
108#423—1491no—
109C2×C4×C8—1491no—
110D4⋊C8—1492no—
111D4⋊C8—1492no—
112C2×#41—2981no—
113C2×M16—2981no—
114C22×C8—2981no—
115C4⋊Q8—1491no—
116#127—1491no—
117#124—2981no—
118#121—2981no—
119#121—1491no—
120#121#1059701011yescharacteristic
121C4×D4—2981no—
122C4×D4—1491no—
123C4×D4—1491no—
124C2×C42—1491no—
125C4⋊C8—2981no—
126C4⋊C8—1492no—
127C4×C8—2981no—
128C4×C8—1492no—
129#41—5962no—
130#41—5962no—
131C2×Q8—2981no—
132C2×D4—21no—
133C2×D4—2981no—
134C2×D4—2981no—
135C2×D4—2981no—
136C2×D4—1491no—
137C2×D4C2×#1059701011yescharacteristic
138C22×C4—2981no—
139C22×C4—2981no—
140C22×C4—1491no—
141C22×C4—1491no—
142C22×C4C2×#1059701011yescharacteristic
143M16—5962no—
144C2×C8—2984no—
145C2×C8—2982no—
146C2×C8—2982no—
147C4⋊C4—2981no—
148C4⋊C4—1491no—
149C4⋊C4C2×#1059701011yescharacteristic
150C22⋊C4—21no—
151C22⋊C4—2981no—
152C22⋊C4—2981no—
153C22⋊C4—2981no—
154C42—1491no—
155C42—1491no—
156C42—1491no—
157C42—1491no—
158C23—21no—
159C23—2981no—
160C23C22⋊#1059701011yescharacteristic
161Q8—5962no—
162D4—22no—
163D4—42no—
164D4—2982no—
165D4—5962no—
166D4—5962no—
167D4—5962no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—2982no—
171C2×C4—2981no—
172C2×C4—5961no—
173C2×C4—5961no—
174C2×C4—5961no—
175C2×C4—5961no—
176C2×C4—1491no—
177C2×C4—1492no—
178C2×C4—1492no—
179C2×C4—1491no—
180C2×C4—1491no—
181C2×C4—1491no—
182C2×C4C22⋊#1059701011yescharacteristic
183C2×C4C22×#1059701011yescharacteristic
184C8—2984no—
185C8—5962no—
186C22—21no—
187C22—21no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22—5961no—
192C22—5961no—
193C22—5961no—
194C22#1801197312yes—
195C22C2×C22⋊#1059701011yescharacteristic
196C4—21no—
197C4—41no—
198C4—2981no—
199C4—5961no—
200C4—1491no—
201C4—1491no—
202C4—1492no—
203C4—1492no—
204C4#1801199812yes—
205C2—22no—
206C2—81no—
207C2—11921no—
208C2#2375059811yescharacteristic
209C2C2×#1801197311yescharacteristic
210C2D149⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#121×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750170C2
cosocleC4×Dic149C23
hypercenter#121#10597010
hypocenterC149#1492
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #23750628C2semidirect
2. C2×C4×#11924753C2semidirect
3. #23750473C2semidirect
4. D4⋊#11924753C2semidirect
105. C149#1492semidirect

Maximal subgroups

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

subgroupindex
#237506282
C2×C4×#119247532
#237504732
D4⋊#119247532
#237501702
#1492149