Finite Group Databasebeta

← #34043653

Subgroups — #34043653

Order 19072.

244 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 49 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#23750224C211yesmaximal, characteristic
2#23749764C211yesmaximal, characteristic
3#23749544C211yesmaximal, characteristic, complemented
4#23749362C211yesmaximal, characteristic, complemented
5#23749360C211yesmaximal, characteristic
6#23749350C211yesmaximal, characteristic, complemented
7#451×C149C211yesmaximal, characteristic, complemented
8C2×#14558723—21no—
9#18011906—21no—
10#18011902—21no—
11#18011896—21no—
12#18011895—21no—
13#18011887—21no—
14#18011885C2211yescharacteristic
15#18011871—21no—
16C2×#14558715—21no—
17C2×#14558715C2211yescharacteristic
18#18011835—21no—
19C22⋊#11924746C2211yescharacteristic
20#18011818—21no—
21#18011818C2211yescharacteristic
22C22×Q8×C149C2211yescharacteristic
23C2×Q16×C149—21no—
24C22⋊Q8×C149C2211yescharacteristic
25#103×C149—21no—
26C22⋊C8×C149C2211yescharacteristic
27C2×D596D411yescharacteristic
28C2×C22⋊D149—21no—
29C22×Dic149—21no—
30C22×Dic149D411yescharacteristic
31C22×Dic149D411yescharacteristic
32C2×C4×D149—21no—
33#14558723—42no—
34C2×#11924746—21no—
35C4⋊Dic149—21no—
36C4⋊Dic149—21no—
37C4⋊Dic149D411yescharacteristic
38#14558715—21no—
39#14558715—21no—
40#14558715—21no—
41#14558715—42no—
42#14558713—21no—
43#14558713—21no—
44#14558713—21no—
45#14558713—21no—
46C4×Dic149—21no—
47C2×Q8×C149—21no—
48C2×Q8×C149—21no—
49C2×Q8×C149—42no—
50C2×Q8×C149D411yescharacteristic
51C22×C4×C149—21no—
52C22×C4×C149C2311yescharacteristic
53Q16×C149—42no—
54C2×C8×C149—21no—
55C4⋊C4×C149—21no—
56C4⋊C4×C149D411yescharacteristic
57C22⋊C4×C149—21no—
58C22×D149—21no—
59D596—41no—
60C22⋊D149—41no—
61C22⋊D149—41no—
62C2×Dic149—22no—
63C2×Dic149—21no—
64C2×Dic149—21no—
65C2×Dic149—21no—
66C2×Dic149—21no—
67C2×Dic149—21no—
68C2×Dic149—41no—
69C2×Dic149—41no—
70C2×Dic149—41no—
71C4×D149—81no—
72#11924746—41no—
73C23×C149C2×D411yescharacteristic
74Q8×C149—22no—
75Q8×C149—22no—
76Q8×C149—41no—
77Q8×C149—41no—
78Q8×C149—41no—
79C2×C4×C149—22no—
80C2×C4×C149—21no—
81C2×C4×C149—21no—
82C2×C4×C149—41no—
83C2×C4×C149—41no—
84C2×C4×C149—41no—
85C2×C4×C149C2×D411yescharacteristic
86C2×C4×C149C2×D411yescharacteristic
87C8×C149—41no—
88C22×C149—21no—
89C22×C149—21no—
90C22×C149#12011yescharacteristic
91C22×C149#13511yescharacteristic
92C22×C149#13711yescharacteristic
93C2×D149—41no—
94C2×D149—41no—
95C2×D149—41no—
96C4×C149—21no—
97C4×C149—21no—
98C4×C149—41no—
99C4×C149—42no—
100C4×C149—41no—
101Dic149—42no—
102Dic149—41no—
103Dic149—41no—
104Dic149—41no—
105C2×C149—21no—
106C2×C149—21no—
107C2×C149#45211yescharacteristic
108C2×C149#45611yescharacteristic
109C2×C149B(4,𝔽2)11yescharacteristic
110D149—81no—
111C149#160311yescharacteristic, complemented, Sylow
112#1603—1491nomaximal, Sylow
113#539—1491no—
114#451D14911yescharacteristic, complemented
115#448—1491no—
116#395—1491no—
117#328—1491no—
118#327—1491no—
119#324—1491no—
120C22×Q8C2×D14911yescharacteristic
121C2×Q16—21no—
122C2×SD16—2981no—
123#126—2981no—
124#125—2981no—
125#123—2981no—
126#123—2981no—
127C22⋊Q8—2981no—
128C22⋊Q8C2×D14911yescharacteristic
129#121—1491no—
130C4×D4—2981no—
131C2×C4⋊C4—2981no—
132C2×C4⋊C4—1491no—
133#103—21no—
134#103—2981no—
135C22⋊C8—1491no—
136C22⋊C8C2×D14911yescharacteristic
137#95—2981no—
138#95—1491no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—42no—
142C2×Q8C22⋊D14911yescharacteristic
143C2×D4—2981no—
144C2×D4—1491no—
145C22×C4—21no—
146C22×C4—2981no—
147C22×C4—2981no—
148C22×C4—1491no—
149C22×C4—1491no—
150C22×C4C22×D14911yescharacteristic
151Q16—42no—
152SD16—5962no—
153C2×C8—21no—
154C2×C8—2981no—
155C4⋊C4—21no—
156C4⋊C4—2981no—
157C4⋊C4—2981no—
158C4⋊C4—2981no—
159C4⋊C4—2981no—
160C4⋊C4—2981no—
161C4⋊C4—5962no—
162C4⋊C4—1491no—
163C4⋊C4C22⋊D14911yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—2981no—
166C22⋊C4—2981no—
167C22⋊C4—2981no—
168C22⋊C4—2981no—
169C42—2981no—
170C23—2981no—
171C23D4×D14911yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—41no—
175Q8—41no—
176Q8—41no—
177D4—5961no—
178D4—5961no—
179D4—5961no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—2982no—
187C2×C4—2981no—
188C2×C4—2981no—
189C2×C4—2981no—
190C2×C4—2981no—
191C2×C4—2981no—
192C2×C4—5961no—
193C2×C4—5961no—
194C2×C4—5961no—
195C2×C4—11921no—
196C2×C4D4×D14911yescharacteristic
197C2×C4C2×C22⋊D14911yescharacteristic
198C8—41no—
199C8—5961no—
200C22—21no—
201C22—21no—
202C22—5961no—
203C22—5961no—
204C22—5961no—
205C22#1801187911yescharacteristic
206C22#1801193411yescharacteristic
207C22#1801194311yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—42no—
212C4—41no—
213C4—5962no—
214C4—5961no—
215C4—5961no—
216C4—5961no—
217C2—21no—
218C2—21no—
219C2—11921no—
220C2#2374978611yescharacteristic
221C2#2374980611yescharacteristic
222C2#2374981111yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#451×C149C2
socleC22×C149#120
prime radical#18011885C22
hypercenter#451D149
hypocenterC149#1603
LCSG ▷ C22×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #23749544C2semidirect
4. #23749362C2semidirect
6. #23749350C2semidirect
7. #451×C149C2semidirect
111. C149#1603semidirect
114. #451D149semidirect

Maximal subgroups

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

subgroupindex
#237502242
#237497642
#237495442
#237493622
#237493602
#237493502
#451×C1492
#1603149