Finite Group Databasebeta

← #34046702

Subgroups — #34046702

Order 19072.

226 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 41 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#23750378C211yesmaximal, characteristic, complemented
2#23749815C211yesmaximal, characteristic
3#23749803C211yesmaximal, characteristic
4#23749419C211yesmaximal, characteristic, complemented
5#23749415C211yesmaximal, characteristic, complemented
6#23749414C211yesmaximal, characteristic, complemented
7#458×C149C211yesmaximal, characteristic
8#18011941—21no—
9#18011910—21no—
10#18011904—21no—
11#18011904—21no—
12#18011901—21no—
13#18011898C2211yescharacteristic
14#18011892—21no—
15#18011892C2211yescharacteristic
16#18011890—21no—
17#18011888—21no—
18#18011838—21no—
19#18011828C2211yescharacteristic
20#18011826—21no—
21#18011826C2211yescharacteristic
22H(5,𝔽2)×C149C2211yescharacteristic
23#123×C149—21no—
24#123×C149C2211yescharacteristic
25#99×C149—21no—
26#99×C149C2211yescharacteristic
27C2×Dic298—21no—
28C2×Dic298D411yescharacteristic
29C22×Dic149D411yescharacteristic
30#14558726—41no—
31#14558724—41no—
32#14558720—21no—
33C4⋊Dic149—21no—
34C4⋊Dic149—21no—
35#14558715—21no—
36#14558715—21no—
37#14558715—21no—
38#14558715—21no—
39#14558715—21no—
40#14558715—41no—
41C22⋊Dic149—21no—
42C22⋊Dic149—21no—
43C22⋊Dic149—21no—
44C22⋊Dic149—21no—
45C22⋊Dic149—41no—
46C22⋊Dic149D411yescharacteristic
47C4×Dic149—21no—
48C4×Dic149D411yescharacteristic
49#41×C149—21no—
50#41×C149—41no—
51C2×D4×C149—21no—
52C2×D4×C149—21no—
53C2×D4×C149—41no—
54C2×D4×C149C2311yescharacteristic
55C22×C4×C149D411yescharacteristic
56C4⋊C4×C149—21no—
57C4⋊C4×C149—41no—
58C22⋊C4×C149—21no—
59C22⋊C4×C149—21no—
60C22⋊C4×C149—41no—
61C22⋊C4×C149D411yescharacteristic
62Dic298—41no—
63Dic298—81no—
64C2×Dic149—21no—
65C2×Dic149—21no—
66C2×Dic149—21no—
67C2×Dic149—21no—
68C2×Dic149—41no—
69C2×Dic149—41no—
70#11924746—41no—
71C23×C149—21no—
72C23×C149—21no—
73C23×C149C2×D411yescharacteristic
74C23×C149C2×D411yescharacteristic
75Q8×C149—21no—
76D4×C149—21no—
77D4×C149—41no—
78D4×C149—41no—
79D4×C149—41no—
80D4×C149—41no—
81C2×C4×C149—21no—
82C2×C4×C149—21no—
83C2×C4×C149—21no—
84C2×C4×C149—21no—
85C2×C4×C149—41no—
86C2×C4×C149—41no—
87C2×C4×C149—41no—
88C2×C4×C149C2×D411yescharacteristic
89C22×C149—21no—
90C22×C149—21no—
91C22×C149—41no—
92C22×C149—41no—
93C22×C149—41no—
94C22×C149—81no—
95C22×C149—81no—
96C22×C149#12011yescharacteristic
97C4×C149—21no—
98C4×C149—41no—
99C4×C149—41no—
100C4×C149—41no—
101C4×C149—81no—
102Dic149—41no—
103Dic149—41no—
104Dic149—41no—
105Dic149—41no—
106Dic149—81no—
107C2×C149—21no—
108C2×C149—41no—
109C2×C149—41no—
110C2×C149—81no—
111C2×C149B(4,𝔽2)11yescharacteristic
112C149#220111yescharacteristic, complemented, Sylow
113#2201—1491nomaximal, Sylow
114#563—1491no—
115#458—1491no—
116#458D14911yescharacteristic
117#455—1491no—
118#354—1491no—
119#352—1491no—
120#352—1491no—
121H(5,𝔽2)C2×D14911yescharacteristic
122#137—2981no—
123C4⋊Q8—2981no—
124#126—2981no—
125#126—2981no—
126#125—2981no—
127#124—1491no—
128#123—21no—
129#123—2981no—
130#123—1491no—
131#123C2×D14911yescharacteristic
132C22⋊Q8—2981no—
133C22⋊Q8—2981no—
134#104—2981no—
135#100—1491no—
136#99—21no—
137#99—2981no—
138#99—1491no—
139#99C2×D14911yescharacteristic
140#41—21no—
141#41—41no—
142C2×Q8—2981no—
143C2×Q8—1491no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—41no—
147C2×D4C22×D14911yescharacteristic
148C22×C4—1491no—
149C22×C4C22⋊D14911yescharacteristic
150Q16—5961no—
151SD16—5961no—
152M16—2981no—
153C4⋊C4—21no—
154C4⋊C4—41no—
155C4⋊C4—2981no—
156C4⋊C4—2981no—
157C4⋊C4—2981no—
158C4⋊C4—2981no—
159C4⋊C4—2981no—
160C4⋊C4—2981no—
161C4⋊C4—2981no—
162C4⋊C4—5961no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—41no—
166C22⋊C4—2981no—
167C22⋊C4—2981no—
168C22⋊C4—2981no—
169C22⋊C4—2981no—
170C22⋊C4—5961no—
171C22⋊C4—1491no—
172C22⋊C4C22⋊D14911yescharacteristic
173C42—2981no—
174C42—1491no—
175C23—21no—
176C23—21no—
177C23D4×D14911yescharacteristic
178C23C2×C22⋊D14911yescharacteristic
179Q8—21no—
180Q8—5961no—
181Q8—11921no—
182D4—21no—
183D4—41no—
184D4—41no—
185D4—41no—
186D4—41no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—2981no—
195C2×C4—2981no—
196C2×C4—2981no—
197C2×C4—2981no—
198C2×C4—5961no—
199C2×C4—5961no—
200C2×C4D4×D14911yescharacteristic
201C8—5961no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—81no—
208C22—81no—
209C22#1801187911yescharacteristic
210C4—21no—
211C4—41no—
212C4—41no—
213C4—41no—
214C4—81no—
215C4—5961no—
216C4—5961no—
217C4—5961no—
218C4—5961no—
219C4—11921no—
220C2—21no—
221C2—41no—
222C2—41no—
223C2—81no—
224C2#2374981111yescharacteristic
subgroupG/H
centerC2#23749811
commutator, cosocleC2×D4×C149C23
FrattiniC2×D4C22×D149
Fitting#458×C149C2
socleC2×C149B(4,𝔽2)
prime radicalH(5,𝔽2)×C149C22
hypercenter#458D149
hypocenterC149#2201
LCSG ▷ C2×D4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #458

Complements

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

NH ≅ G/Ntype
1. #23750378C2semidirect
4. #23749419C2semidirect
5. #23749415C2semidirect
6. #23749414C2semidirect
112. C149#2201semidirect

Maximal subgroups

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

subgroupindex
#237503782
#237498152
#237498032
#237494192
#237494152
#237494142
#458×C1492
#2201149