Finite Group Databasebeta

← #34060550

Subgroups — #34060550

Order 19072.

312 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 92 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×#18011978C211yesmaximal, characteristic, complemented
2C2×C4⋊#11924753C211yesmaximal, characteristic, complemented
3C2×#18011968C212yesmaximal
4#23750491C212yesmaximal, complemented
5C2×#18011869C211yesmaximal, characteristic
6C22×#11924753C2212yes—
7C22×#11924753C2212yes—
8#18011978—22no—
9C4⋊#11924753—22no—
10#18011968—24no—
11C22×C4×D149C2211yescharacteristic
12#18011869—22no—
13#18011869—22no—
14C2×C4⋊Dic149C411yescharacteristic
15C2×#14558713C411yescharacteristic
16C2×#14558713C411yescharacteristic
17C2×C4×Dic149C2211yescharacteristic
18C2×C4×Dic149C2211yescharacteristic
19C2×C4⋊C4×C149C411yescharacteristic
20C2×#11924753—22no—
21C2×#11924753—22no—
22C2×#11924753—22no—
23C2×#11924753—22no—
24C2×#11924753—22no—
25C2×#11924753—22no—
26C23×D149C2×C411yescharacteristic
27C22×Dic149C2×C411yescharacteristic
28C22×Dic149C2×C411yescharacteristic
29C22×Dic149C2311yescharacteristic
30C2×C4×D149—21no—
31C2×C4×D149—21no—
32C2×C4×D149—21no—
33C2×C4×D149—21no—
34C2×C4×D149D412yes—
35C2×C4×D149Q812yes—
36C4⋊Dic149—22no—
37#14558713—22no—
38#14558713—22no—
39C4×Dic149—21no—
40C4×Dic149—21no—
41C4×Dic149D412yes—
42C4×Dic149D412yes—
43C22×C4×C149C2×C411yescharacteristic
44C22×C4×C149C2×C411yescharacteristic
45C22×C4×C149C2×C411yescharacteristic
46C4⋊C4×C149—22no—
47#11924753—42no—
48#11924753—42no—
49C22×D149—21no—
50C22×D149—21no—
51C22×D149—22no—
52C22×D149—22no—
53C22×D149C4⋊C412yes—
54C2×Dic149—22no—
55C2×Dic149—21no—
56C2×Dic149—22no—
57C2×Dic149C22⋊C412yes—
58C2×Dic149C2×D411yescharacteristic
59C2×Dic149C2×D411yescharacteristic
60C2×Dic149C2×D411yescharacteristic
61C2×Dic149C2×Q811yescharacteristic
62C2×Dic149#4111yescharacteristic
63C2×Dic149#4111yescharacteristic
64C4×D149—22no—
65C4×D149—22no—
66C4×D149—22no—
67C4×D149—22no—
68C23×C149C22×C411yescharacteristic
69C2×C4×C149—21no—
70C2×C4×C149—21no—
71C2×C4×C149—22no—
72C2×C4×C149—21no—
73C2×C4×C149—22no—
74C2×C4×C149C22⋊C412yes—
75C2×C4×C149C4⋊C412yes—
76C22×C149C2×C22⋊C411yescharacteristic
77C22×C149C2×C4⋊C411yescharacteristic
78C22×C149#11711yescharacteristic
79C22×C149#13112yes—
80C22×C149#13112yes—
81C2×D149—22no—
82C2×D149—24no—
83C2×D149—41no—
84C2×D149—41no—
85C2×D149—42no—
86C4×C149—22no—
87C4×C149—22no—
88C4×C149—41no—
89Dic149—22no—
90Dic149—41no—
91Dic149#12111yescharacteristic
92Dic149#12111yescharacteristic
93Dic149C22⋊Q811yescharacteristic
94Dic149C22⋊Q811yescharacteristic
95C2×C149#38011yescharacteristic
96C2×C149#40811yescharacteristic
97C2×C149#40811yescharacteristic
98C2×C149#42412yes—
99C2×C149#43312yes—
100D149—42no—
101C149#179811yescharacteristic, complemented, Sylow
102#1798—1491nomaximal, Sylow
103C2×#117—1491no—
104C2×C4⋊C8—1491no—
105C2×C4⋊C8—1491no—
106C2×C22⋊C8—1492no—
107#336—1492no—
108C23×C4—1491no—
109C22×C8—1492no—
110C22×C8—1492no—
111#117—2982no—
112#117—2982no—
113C2×C4⋊C4—1491no—
114C2×C4⋊C4#1059701011yescharacteristic
115C2×C22⋊C4—1491no—
116C2×C22⋊C4—1491no—
117C2×C42—1491no—
118C2×C42—1491no—
119C4⋊C8—2982no—
120C4⋊C8—2982no—
121C22⋊C8—2984no—
122C24—1491no—
123C22×C4—2981no—
124C22×C4—2981no—
125C22×C4—2981no—
126C22×C4—2981no—
127C22×C4—1491no—
128C22×C4—1491no—
129C22×C4—1492no—
130C22×C4—1492no—
131C22×C4—1491no—
132C22×C4C2×#1059701011yescharacteristic
133C22×C4C2×#1059701011yescharacteristic
134C22×C4C2×#1059701011yescharacteristic
135C2×C8—2982no—
136C2×C8—2982no—
137C2×C8—2982no—
138C2×C8—2982no—
139C2×C8—2982no—
140C2×C8—2982no—
141C4⋊C4—22no—
142C4⋊C4—2982no—
143C22⋊C4—2982no—
144C22⋊C4—2982no—
145C42—2981no—
146C42—2981no—
147C42—1492no—
148C42—1492no—
149C23—2981no—
150C23—2981no—
151C23—2982no—
152C23—2982no—
153C23—1492no—
154C23C22×#1059701011yescharacteristic
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—2982no—
161C2×C4—2982no—
162C2×C4—2982no—
163C2×C4—2982no—
164C2×C4—2982no—
165C2×C4—2981no—
166C2×C4—2982no—
167C2×C4—1492no—
168C2×C4—1491no—
169C2×C4—1491no—
170C2×C4—1491no—
171C2×C4—1491no—
172C2×C4—1491no—
173C2×C4—1491no—
174C2×C4C22⋊#1059701012yes—
175C2×C4C4⋊#1059701012yes—
176C8—5962no—
177C8—5962no—
178C22—2982no—
179C22—2984no—
180C22—5961no—
181C22—5961no—
182C22—5962no—
183C22C2×C22⋊#1059701011yescharacteristic
184C22C2×C4⋊#1059701011yescharacteristic
185C22#1801199011yescharacteristic
186C22#1801199812yes—
187C22#1801199912yes—
188C4—22no—
189C4—22no—
190C4—41no—
191C4—2982no—
192C4—5961no—
193C4—1491no—
194C4—1491no—
195C4—1491no—
196C4—1491no—
197C2—5962no—
198C2#2375056711yescharacteristic
199C2#2375059811yescharacteristic
200C2#2375060011yescharacteristic
201C2#2375063212yes—
202C2#2375065012yes—
subgroupG/H
center, FrattiniC23C22×#10597010
commutator, socleC23×C149C22×C4
FittingC2×C4⋊C4×C149C4
prime radicalC23×D149C2×C4
cosocleC22×Dic149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1798
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#18011978C2semidirect
2. C2×C4⋊#11924753C2semidirect
4. #23750491C2semidirect
101. C149#1798semidirect

Maximal subgroups

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

subgroupindex
C2×#180119782
C2×C4⋊#119247532
C2×#180119682
#237504912
C2×#180118692
#1798149