Finite Group Databasebeta

← #34060223

Subgroups — #34060223

Order 19072.

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

normal subgroups only

This group has 246 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#23750645C211yesmaximal, characteristic, complemented
2#23750628C211yesmaximal, characteristic, complemented
3#23750484C212yesmaximal, complemented
4#23750483C212yesmaximal, complemented
5#23750170C211yesmaximal, characteristic
6C2×#14558745—21no—
7#18011978C2212yes—
8#18011978C2212yes—
9C4⋊#11924753—21no—
10C22⋊#11924753—21no—
11#18011966—21no—
12C2×#14558735—21no—
13#18011910C2211yescharacteristic
14#18011907C2211yescharacteristic
15#18011897—21no—
16#18011885C411yescharacteristic
17#18011883—21no—
18D4×Dic149C411yescharacteristic
19#18011873C411yescharacteristic
20#18011871—21no—
21C2×C4×Dic149C2211yescharacteristic
22#121×C149C411yescharacteristic
23#14558745—42no—
24C2×#11924753—22no—
25C2×#11924753—22no—
26#14558735—44no—
27C2×Dic298—21no—
28C2×D596C2×C411yescharacteristic
29C2×C22⋊D149—21no—
30C2×C22⋊D149—21no—
31C2×C22⋊D149—21no—
32C22×Dic149—21no—
33C22×Dic149D411yescharacteristic
34C22×Dic149D411yescharacteristic
35C2×C4×D149—21no—
36C4⋊Dic149C2×C411yescharacteristic
37#14558715—21no—
38C22⋊Dic149—21no—
39#14558713—21no—
40#14558713—21no—
41C4×Dic149C2×C411yescharacteristic
42C4×Dic149D411yescharacteristic
43C4×Dic149D411yescharacteristic
44C4×Dic149C2311yescharacteristic
45C2×D4×C149—21no—
46C2×D4×C149C2×C411yescharacteristic
47C22×C4×C149C2×C411yescharacteristic
48C4⋊C4×C149C2×C411yescharacteristic
49C22⋊C4×C149—21no—
50#11924753—42no—
51#11924753—42no—
52C22×D149—21no—
53Dic298—42no—
54D596—41no—
55C22⋊D149—42no—
56C22⋊D149—41no—
57C22⋊D149—42no—
58C22⋊D149—41no—
59C2×Dic149—22no—
60C2×Dic149—21no—
61C2×Dic149—21no—
62C2×Dic149—21no—
63C2×Dic149—42no—
64C2×Dic149C22⋊C411yescharacteristic
65C2×Dic149C22⋊C411yescharacteristic
66C2×Dic149C2×D411yescharacteristic
67C2×Dic149C2×D411yescharacteristic
68C4×D149—42no—
69C23×C149—21no—
70C23×C149C22⋊C411yescharacteristic
71D4×C149—41no—
72D4×C149—42no—
73C2×C4×C149—21no—
74C2×C4×C149—41no—
75C2×C4×C149C22⋊C411yescharacteristic
76C2×C4×C149C22×C411yescharacteristic
77C22×C149—21no—
78C22×C149—21no—
79C22×C149—21no—
80C22×C149—41no—
81C22×C149—41no—
82C22×C149—41no—
83C22×C149C2×C22⋊C411yescharacteristic
84C2×D149—41no—
85C2×D149—41no—
86C2×D149—41no—
87C4×C149—21no—
88C4×C149—21no—
89C4×C149—41no—
90Dic149—21no—
91Dic149—21no—
92Dic149—41no—
93Dic149AGL(1,ℤ/8)11yescharacteristic
94Dic149AGL(1,ℤ/8)12yes—
95Dic149#13711yescharacteristic
96C2×C149—41no—
97C2×C149—81no—
98C2×C149#41311yescharacteristic
99C2×C149#41711yescharacteristic
100C2×C149#41811yescharacteristic
101D149—81no—
102C149#155711yescharacteristic, complemented, Sylow
103#1557—1491nomaximal, Sylow
104#532—1491no—
105#432—1491no—
106#423—1491no—
107#332—1492no—
108#331—1492no—
109C2×#41—2981no—
110C2×M16—2981no—
111C4⋊Q8—1491no—
112#127—1491no—
113#124—2981no—
114#121—2981no—
115#121—1491no—
116#121#1059701011yescharacteristic
117C4×D4—2981no—
118C4×D4—1491no—
119C4×D4—1491no—
120C2×C42—1491no—
121C4⋊C8—2981no—
122C4⋊C8—1492no—
123C4⋊C8—1492no—
124C22⋊C8—2981no—
125#97—2981no—
126#41—5964no—
127C2×Q8—2981no—
128C2×D4—21no—
129C2×D4—2981no—
130C2×D4—2981no—
131C2×D4—2981no—
132C2×D4—1491no—
133C2×D4C2×#1059701011yescharacteristic
134C22×C4—2981no—
135C22×C4—2981no—
136C22×C4—1491no—
137C22×C4—1491no—
138C22×C4C2×#1059701011yescharacteristic
139M16—5962no—
140C2×C8—2982no—
141C2×C8—2982no—
142C4⋊C4—2981no—
143C4⋊C4—1491no—
144C4⋊C4C2×#1059701011yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—2981no—
147C22⋊C4—2981no—
148C22⋊C4—2981no—
149C42—1491no—
150C42—1491no—
151C42—1491no—
152C42—1491no—
153C23—21no—
154C23—2981no—
155C23C22⋊#1059701011yescharacteristic
156Q8—5962no—
157D4—41no—
158D4—42no—
159D4—5961no—
160D4—5962no—
161D4—5961no—
162D4—5961no—
163D4—5962no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—2981no—
167C2×C4—2981no—
168C2×C4—2982no—
169C2×C4—2981no—
170C2×C4—5962no—
171C2×C4—5962no—
172C2×C4—1491no—
173C2×C4—1491no—
174C2×C4—1491no—
175C2×C4—1491no—
176C2×C4C22⋊#1059701011yescharacteristic
177C2×C4C22×#1059701011yescharacteristic
178C8—5962no—
179C8—5962no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—41no—
184C22—41no—
185C22—41no—
186C22—5961no—
187C22—5961no—
188C22—5961no—
189C22C2×C22⋊#1059701011yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—2981no—
194C4—2981no—
195C4—5961no—
196C4—1491no—
197C4—1491no—
198C4—1492no—
199C2—41no—
200C2—81no—
201C2—11921no—
202C2#2375061211yescharacteristic
203C2#2375061611yescharacteristic
204C2#2375061711yescharacteristic
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#1557
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #23750645C2semidirect
2. #23750628C2semidirect
3. #23750484C2semidirect
4. #23750483C2semidirect
102. C149#1557semidirect

Maximal subgroups

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

subgroupindex
#237506452
#237506282
#237504842
#237504832
#237501702
#1557149