Finite Group Databasebeta

← #34045823

Subgroups — #34045823

Order 19072.

430 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 75 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#23750187C211yesmaximal, characteristic
2C2×#18011895C212yesmaximal, complemented
3C2×#18011825C212yesmaximal, complemented
4#23749486C211yesmaximal, characteristic, complemented
5#342×C149C211yesmaximal, characteristic, complemented
6C22×C22⋊D149C2212yes—
7C23×Dic149C2211yescharacteristic
8#18011895—24no—
9#18011895—22no—
10#18011895—24no—
11#18011885—22no—
12#18011881—22no—
13C2×C4⋊Dic149—22no—
14C2×C22⋊Dic149C2211yescharacteristic
15C2×#14558713—22no—
16#18011825—24no—
17#18011818—22no—
18C2×C22⋊C4×C149C2211yescharacteristic
19C2×C22⋊C4×C149C2212yes—
20C23×D149D412yes—
21C2×D596—22no—
22C2×C22⋊D149—22no—
23C2×C22⋊D149—22no—
24C2×C22⋊D149—22no—
25C2×C22⋊D149—22no—
26C2×C22⋊D149—22no—
27C2×C22⋊D149—22no—
28C22×Dic149—21no—
29C22×Dic149—22no—
30C22×Dic149—22no—
31C22×Dic149—21no—
32C22×Dic149—21no—
33C22×Dic149D412yes—
34C22×Dic149D412yescomplemented
35C4⋊Dic149—28no—
36C4⋊Dic149—22no—
37C22⋊Dic149—22no—
38#14558713—28no—
39#14558713—24no—
40C24×C149C2311yescharacteristic
41C22×C4×C149—22no—
42C22×C4×C149D412yes—
43C22⋊C4×C149—22no—
44C22⋊C4×C149—22no—
45C22⋊C4×C149D414yescomplemented
46C22×D149—22no—
47C22×D149—22no—
48C22×D149—22no—
49C22×D149—44no—
50D596—82no—
51C22⋊D149—42no—
52C22⋊D149—42no—
53C22⋊D149—42no—
54C22⋊D149—42no—
55C2×Dic149—24no—
56C2×Dic149—22no—
57C2×Dic149—22no—
58C2×Dic149—22no—
59C2×Dic149—22no—
60C2×Dic149—41no—
61C2×Dic149—42no—
62C2×Dic149—41no—
63C2×Dic149—42no—
64C2×Dic149—41no—
65C23×C149—42no—
66C23×C149C2×D412yes—
67C23×C149C2×D411yescharacteristic
68C23×C149C2×D411yescharacteristic
69C23×C149C2×D412yes—
70C23×C149#4111yescharacteristic
71C2×C4×C149—22no—
72C2×C4×C149—24no—
73C2×C4×C149—44no—
74C2×C4×C149—42no—
75C22×C149—22no—
76C22×C149—24no—
77C22×C149—41no—
78C22×C149—42no—
79C22×C149—41no—
80C22×C149#12012yes—
81C22×C149#12011yescharacteristic
82C22×C149#12111yescharacteristic
83C22×C149#12112yes—
84C22×C149#12711yescharacteristic
85C2×D149—44no—
86C2×D149—42no—
87C2×D149—44no—
88C2×D149—82no—
89C4×C149—44no—
90C4×C149—42no—
91Dic149—42no—
92Dic149—42no—
93Dic149—81no—
94C2×C149—21no—
95C2×C149—22no—
96C2×C149—22no—
97C2×C149—21no—
98C2×C149#39211yescharacteristic
99C2×C149#45812yes—
100D149—82no—
101C149#202211yescharacteristic, complemented, Sylow
102#2022—1491nomaximal, Sylow
103#534—1491no—
104C2×#123—1492no—
105C2×#99—1492no—
106#381—1491no—
107#342D14911yescharacteristic, complemented
108C22×D4—1492no—
109C23×C4—1491no—
110#123—2984no—
111#123—2982no—
112#123—2984no—
113#121—2982no—
114#120—2982no—
115C2×C4⋊C4—2982no—
116C2×C22⋊C4—2982no—
117C2×C22⋊C4—1491no—
118C2×C22⋊C4C2×D14911yescharacteristic
119C2×C22⋊C4C2×D14912yes—
120#99—2984no—
121#95—2982no—
122C24—1492no—
123C24C22×D14911yescharacteristic
124C2×D4—2982no—
125C2×D4—2982no—
126C2×D4—2982no—
127C2×D4—2982no—
128C2×D4—2982no—
129C2×D4—2982no—
130C2×D4—2982no—
131C22×C4—22no—
132C22×C4—2982no—
133C22×C4—2981no—
134C22×C4—2982no—
135C22×C4—2981no—
136C22×C4—2981no—
137C22×C4—1492no—
138C22×C4—1492no—
139C22×C4D59612yes—
140C4⋊C4—2988no—
141C4⋊C4—2982no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—2988no—
145C22⋊C4—2984no—
146C22⋊C4—2982no—
147C22⋊C4D59614yescomplemented
148C23—42no—
149C23—2982no—
150C23—2982no—
151C23—2982no—
152C23—5964no—
153C23D4×D14912yes—
154C23D4×D14911yescharacteristic
155C23C2×D59611yescharacteristic
156C23C2×D59612yes—
157C23#1455873711yescharacteristic
158D4—5962no—
159D4—5962no—
160D4—5962no—
161D4—5962no—
162D4—11922no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—44no—
166C2×C4—42no—
167C2×C4—2984no—
168C2×C4—2982no—
169C2×C4—2982no—
170C2×C4—2982no—
171C2×C4—2982no—
172C2×C4—5961no—
173C2×C4—5961no—
174C2×C4—5962no—
175C2×C4—5962no—
176C2×C4—5961no—
177C22—22no—
178C22—24no—
179C22—41no—
180C22—42no—
181C22—41no—
182C22—5964no—
183C22—5962no—
184C22—5964no—
185C22—11922no—
186C22#1801188112yes—
187C22#1801188111yescharacteristic
188C22#1801188611yescharacteristic
189C22#1801188612yes—
190C22#1801190811yescharacteristic
191C4—44no—
192C4—42no—
193C4—5962no—
194C4—5962no—
195C4—11921no—
196C2—22no—
197C2—21no—
198C2—22no—
199C2—21no—
200C2—11922no—
201C2#2374953511yescharacteristic
202C2#2374981612yes—
subgroupG/H
centerC22#18011881
commutator, cosocleC24×C149C23
FrattiniC24C22×D149
Fitting#342×C149C2
socleC22×C149#120
prime radical#23750187C2
hypercenter#342D149
hypocenterC149#2022
LCSG ▷ C24×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×#18011895C2semidirect
3. C2×#18011825C2semidirect
4. #23749486C2semidirect
5. #342×C149C2semidirect
34. C22×Dic149D4semidirect
45. C22⋊C4×C149D4semidirect
101. C149#2022semidirect
107. #342D149semidirect
147. C22⋊C4D596semidirect

Maximal subgroups

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

subgroupindex
#237501872
C2×#180118952
C2×#180118252
#237494862
#342×C1492
#2022149