Finite Group Databasebeta

← #34052752

Subgroups — #34052752

Order 19072.

430 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 133 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×#18011911C211yesmaximal, characteristic, complemented
2C2×#18011905C211yesmaximal, characteristic
3#23749565C212yesmaximal, complemented
4#23749562C212yesmaximal
5#23749557C212yesmaximal, complemented
6#23749552C212yesmaximal
7#23749546C212yesmaximal, complemented
8#23749538C212yesmaximal
9#383×C149C211yesmaximal, characteristic, complemented
10C22×Dic298C2212yes—
11#18011911—24no—
12#18011905—24no—
13C2×C4⋊Dic149C2212yes—
14C2×C4⋊Dic149C2212yes—
15C2×C4⋊Dic149C2214yes—
16C2×#14558715C2211yescharacteristic
17C2×#14558715C2211yescharacteristic
18C2×#14558715C2211yescharacteristic
19C2×#14558713C2211yescharacteristic
20C2×#14558713C2211yescharacteristic
21C2×#14558713C2211yescharacteristic
22C2×#14558713C2214yes—
23#18011818C2214yes—
24#18011818C2214yes—
25C2×C42×C149C2211yescharacteristic
26#95×C149C2212yes—
27#95×C149C2212yes—
28#95×C149C2212yes—
29C23×D149C2311yescharacteristic
30C2×Dic298—24no—
31C2×Dic298—44no—
32C22×Dic149C2314yes—
33C22×Dic149C2311yescharacteristic
34C22×Dic149C2311yescharacteristic
35C22×Dic149C2311yescharacteristic
36C4⋊Dic149—24no—
37C4⋊Dic149—24no—
38C4⋊Dic149—44no—
39#14558715—22no—
40#14558715—22no—
41#14558715—22no—
42#14558713—22no—
43#14558713—22no—
44#14558713—22no—
45#14558713—44no—
46C22×C4×C149C2314yes—
47C22×C4×C149C2311yescharacteristic
48C22×C4×C149C2311yescharacteristic
49C22×C4×C149C2311yescharacteristic
50C42×C149D414yes—
51C22×D149—21no—
52C22×D149—22no—
53C22×D149—22no—
54C22×D149—22no—
55Dic298—48no—
56C2×Dic149—24no—
57C2×Dic149—21no—
58C2×Dic149—21no—
59C2×Dic149—21no—
60C2×Dic149—24no—
61C2×Dic149—24no—
62C2×Dic149—22no—
63C2×Dic149—22no—
64C2×Dic149—22no—
65C23×C149C2411yescharacteristic
66C2×C4×C149—22no—
67C2×C4×C149—22no—
68C2×C4×C149—22no—
69C2×C4×C149—24no—
70C2×C4×C149—24no—
71C2×C4×C149—24no—
72C2×C4×C149C2×D412yes—
73C2×C4×C149C2×D412yes—
74C2×C4×C149C2×D412yes—
75C22×C149C22×D411yescharacteristic
76C22×C149H(5,𝔽2)12yes—
77C22×C1492−1+412yes—
78C22×C1492−1+412yes—
79C2×D149—41no—
80C2×D149—41no—
81C2×D149—41no—
82C2×D149—44no—
83C4×C149—22no—
84C4×C149—22no—
85C4×C149—22no—
86C4×C149—44no—
87Dic149—41no—
88Dic149—44no—
89Dic149—41no—
90Dic149—41no—
91C2×C149#53511yescharacteristic
92C2×C149#53611yescharacteristic
93C2×C149#53611yescharacteristic
94C2×C149#56314yes—
95D149—81no—
96C149#282111yescharacteristic, complemented, Sylow
97#2821—1491nomaximal, Sylow
98C2×C4⋊Q8—1491no—
99C2×#126—1491no—
100#400—1492no—
101#399—1492no—
102#398—1492no—
103#397—1492no—
104#395—1492no—
105#393—1492no—
106#383D14911yescharacteristic, complemented
107C22×Q8—1492no—
108C4⋊Q8—2984no—
109#126—2984no—
110C2×C4⋊C4—1491no—
111C2×C4⋊C4—1491no—
112C2×C4⋊C4—1491no—
113C2×C4⋊C4—1492no—
114C2×C4⋊C4—1492no—
115C2×C4⋊C4—1494no—
116C2×C22⋊C4—1491no—
117C2×C22⋊C4—1491no—
118C2×C22⋊C4—1491no—
119C2×C22⋊C4—1494no—
120C2×C42C2×D14911yescharacteristic
121#95—1494no—
122#95—1494no—
123#95C2×D14912yes—
124#95C2×D14912yes—
125#95C2×D14912yes—
126C24—1491no—
127C2×Q8—2984no—
128C2×Q8—5964no—
129C22×C4—1491no—
130C22×C4—1491no—
131C22×C4—1494no—
132C22×C4—1491no—
133C22×C4C22×D14914yes—
134C22×C4C22×D14911yescharacteristic
135C22×C4C22×D14911yescharacteristic
136C22×C4C22×D14911yescharacteristic
137C4⋊C4—2982no—
138C4⋊C4—2982no—
139C4⋊C4—2982no—
140C4⋊C4—2984no—
141C4⋊C4—2984no—
142C4⋊C4—5964no—
143C22⋊C4—2982no—
144C22⋊C4—2982no—
145C22⋊C4—2982no—
146C22⋊C4—5964no—
147C42D59614yes—
148C23—2981no—
149C23—2982no—
150C23—2982no—
151C23—2982no—
152C23C23×D14911yescharacteristic
153Q8—5968no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—2981no—
161C2×C4—2981no—
162C2×C4—2981no—
163C2×C4—2984no—
164C2×C4—2984no—
165C2×C4—2982no—
166C2×C4—2984no—
167C2×C4—2982no—
168C2×C4—2982no—
169C2×C4C2×D59612yes—
170C2×C4C2×D59612yes—
171C2×C4C2×D59612yes—
172C22—5961no—
173C22—5961no—
174C22—5961no—
175C22—5964no—
176C22C22×D59611yescharacteristic
177C22#1801195712yes—
178C22#1801195812yes—
179C22#1801195812yes—
180C4—22no—
181C4—22no—
182C4—22no—
183C4—44no—
184C4—5964no—
185C4—5961no—
186C4—5961no—
187C4—5961no—
188C2—11921no—
189C2#2375019411yescharacteristic
190C2#2375020111yescharacteristic
191C2#2375020111yescharacteristic
192C2#2375037714yes—
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
Fitting#383×C149C2
prime radicalC23×D149C23
hypercenter#383D149
hypocenterC149#2821
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
1. C2×#18011911C2semidirect
3. #23749565C2semidirect
5. #23749557C2semidirect
7. #23749546C2semidirect
9. #383×C149C2semidirect
96. C149#2821semidirect
106. #383D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119112
C2×#180119052
#237495652
#237495622
#237495572
#237495522
#237495462
#237495382
#383×C1492
#2821149