Finite Group Databasebeta

← #34055410

Subgroups — #34055410

Order 19072.

402 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 129 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#23750175C211yesmaximal, characteristic
2#23750028C211yesmaximal, characteristic, complemented
3#23749999C211yesmaximal, characteristic, complemented
4#23749975C211yesmaximal, characteristic, complemented
5#23749973C211yesmaximal, characteristic, complemented
6#23749873C214yesmaximal, complemented
7#23749723C214yesmaximal, complemented
8C4×#14558720C211yesmaximal, characteristic, complemented
9#533×C149C211yesmaximal, characteristic, complemented
10C2×#14558736—21no—
11C2×#14558723C2214yes—
12C2×#14558720C2212yes—
13#18011911C2211yescharacteristic
14#18011908C2211yescharacteristic
15#18011899—21no—
16#18011885—21no—
17#18011885C2212yes—
18C4×D596—21no—
19C4×D596C2212yes—
20#18011844C2214yes—
21#18011835C2214yes—
22#18011831C2214yes—
23#18011822C2212yes—
24C4×#11924746C2211yescharacteristic
25C4×#11924746C2211yescharacteristic
26C4⋊Q8×C149C2211yescharacteristic
27C4⋊Q8×C149C2211yescharacteristic
28#125×C149—21no—
29C22⋊Q8×C149—21no—
30C22⋊Q8×C149C2212yes—
31C4×Q8×C149—21no—
32C4×Q8×C149C2212yes—
33#117×C149—21no—
34C2×C42×C149C2211yescharacteristic
35#14558736—44no—
36C2×Dic298—21no—
37C2×D596—21no—
38C2×D596—21no—
39C2×D596C2312yes—
40C2×C22⋊D149—22no—
41C2×C4×D149—22no—
42#14558723—28no—
43#14558720—24no—
44C2×#11924746C2312yes—
45C2×#11924746C2312yes—
46C4⋊Dic149—21no—
47C4⋊Dic149C2312yes—
48#14558713—22no—
49#14558713—22no—
50C2×Q8×C149—21no—
51C2×Q8×C149C2312yes—
52C22×C4×C149D411yescharacteristic
53C22×C4×C149D411yescharacteristic
54C22×C4×C149C2311yescharacteristic
55C4⋊C4×C149—21no—
56C4⋊C4×C149—21no—
57C4⋊C4×C149—21no—
58C4⋊C4×C149—22no—
59C4⋊C4×C149—22no—
60C4⋊C4×C149C2312yes—
61C22⋊C4×C149—22no—
62C42×C149—22no—
63C42×C149D411yescharacteristic
64C42×C149D411yescharacteristic
65C42×C149C2311yescharacteristic
66C42×C149C2311yescharacteristic
67C22×D149—22no—
68Dic298—42no—
69D596—24no—
70D596—42no—
71D596—42no—
72C22⋊D149—44no—
73C2×Dic149—22no—
74C4×D149—44no—
75#11924746—22no—
76#11924746#4114yescomplemented
77C23×C149C2×D411yescharacteristic
78Q8×C149—24no—
79Q8×C149—42no—
80C2×C4×C149—22no—
81C2×C4×C149—22no—
82C2×C4×C149—22no—
83C2×C4×C149—22no—
84C2×C4×C149—22no—
85C2×C4×C149C2×D411yescharacteristic
86C2×C4×C149C2×D411yescharacteristic
87C2×C4×C149C2×D411yescharacteristic
88C2×C4×C149C2×D411yescharacteristic
89C2×C4×C149C2×D411yescharacteristic
90C2×C4×C149C2411yescharacteristic
91C22×C149—21no—
92C22×C149—21no—
93C22×C149—21no—
94C22×C149C22×D411yescharacteristic
95C2×D149—42no—
96C2×D149—42no—
97C2×D149—42no—
98C4×C149—21no—
99C4×C149—21no—
100C4×C149—21no—
101C4×C149—42no—
102C4×C149—42no—
103C4×C149AGL(1,ℤ/8)12yes—
104C4×C149#13712yes—
105C4×C149C2×#4112yes—
106Dic149—42no—
107C2×C149—41no—
108C2×C149#53211yescharacteristic
109C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
110C2×C149C2×#13711yescharacteristic
111D149—82no—
112C149#318211yescharacteristic, complemented, Sylow
113#3182—1491nomaximal, Sylow
114#533D14911yescharacteristic, complemented
115#532—1491no—
116#500—1491no—
117#492—1491no—
118#487—1491no—
119#486—1491no—
120#468—1494no—
121#440—1494no—
122C4×M16—1491no—
123C2×#41—2981no—
124C2×SD16—1494no—
125C2×M16—1492no—
126C4⋊Q8—1491no—
127C4⋊Q8C2×D14911yescharacteristic
128C4⋊Q8C2×D14911yescharacteristic
129#127—1491no—
130#125—21no—
131#124—2981no—
132C22⋊Q8—21no—
133C22⋊Q8C2×D14912yes—
134#121—2981no—
135#121—1492no—
136C4×Q8—21no—
137C4×Q8C2×D14912yes—
138C4×D4—2981no—
139C4×D4—1492no—
140#117—21no—
141C2×C42C2×D14911yescharacteristic
142#107—1494no—
143#103—1494no—
144#102—1494no—
145#97—1492no—
146C4×C8—1491no—
147C4×C8—1491no—
148#41—5964no—
149C2×Q8—21no—
150C2×Q8—2981no—
151C2×Q8C22×D14912yes—
152C2×D4—2982no—
153C2×D4—2981no—
154C2×D4—2981no—
155C2×D4—1492no—
156C22×C4—2982no—
157C22×C4C22⋊D14911yescharacteristic
158C22×C4C22⋊D14911yescharacteristic
159C22×C4C22×D14911yescharacteristic
160SD16—2988no—
161M16—2984no—
162C2×C8—1492no—
163C2×C8—1492no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—22no—
168C4⋊C4—22no—
169C4⋊C4—2981no—
170C4⋊C4—1492no—
171C4⋊C4C22×D14912yes—
172C22⋊C4—22no—
173C22⋊C4—2982no—
174C22⋊C4—2982no—
175C42—22no—
176C42C22⋊D14911yescharacteristic
177C42C22⋊D14911yescharacteristic
178C42C22×D14911yescharacteristic
179C42C22×D14911yescharacteristic
180C23—2982no—
181C23C2×C22⋊D14911yescharacteristic
182Q8—24no—
183Q8—42no—
184Q8—5962no—
185D4—2984no—
186D4—5964no—
187D4—5962no—
188D4—5962no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—2982no—
195C2×C4—5964no—
196C2×C4C2×C22⋊D14911yescharacteristic
197C2×C4C2×C22⋊D14911yescharacteristic
198C2×C4C2×C22⋊D14911yescharacteristic
199C2×C4C2×C22⋊D14911yescharacteristic
200C2×C4C2×C22⋊D14911yescharacteristic
201C2×C4C23×D14911yescharacteristic
202C8—2982no—
203C8—1494no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—5962no—
208C22—5962no—
209C22—5962no—
210C22C22×C22⋊D14911yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—42no—
216C4—5962no—
217C4#1801193612yes—
218C4#1801194212yes—
219C4#41×D14912yes—
220C2—41no—
221C2—11922no—
222C2#2375017111yescharacteristic
223C2C2×#1801193611yescharacteristic
224C2C2×#1801194211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#533×C149C2
socleC22×C149C22×D4
prime radical#23750175C2
hypercenter#533D149
hypocenterC149#3182
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #23750028C2semidirect
3. #23749999C2semidirect
4. #23749975C2semidirect
5. #23749973C2semidirect
6. #23749873C2semidirect
7. #23749723C2semidirect
8. C4×#14558720C2semidirect
9. #533×C149C2semidirect
76. #11924746#41semidirect
112. C149#3182semidirect
114. #533D149semidirect

Maximal subgroups

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

subgroupindex
#237501752
#237500282
#237499992
#237499752
#237499732
#237498732
#237497232
C4×#145587202
#533×C1492
#3182149