Finite Group Databasebeta

← #34047779

Subgroups — #34047779

Order 19072.

496 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 209 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×#18011909C211yesmaximal, characteristic
2#23749532C211yesmaximal, characteristic
3#23749529C212yesmaximal
4#23749522C212yesmaximal
5#23749520C212yesmaximal
6C4×#14558715C212yesmaximal
7#23749476C212yesmaximal
8#23749476C212yesmaximal
9#391×C149C211yesmaximal, characteristic
10C22×Dic298C2211yescharacteristic
11#18011909C418yescomplemented
12C2×C4⋊Dic149C2211yescharacteristic
13C2×#14558715C2212yes—
14C2×#14558715C2212yes—
15C2×#14558715C2212yes—
16C2×#14558715C2212yes—
17C2×#14558715C2212yes—
18C2×C4×Dic149C2212yes—
19C2×C4×Dic149C2212yes—
20C2×C4×Dic149C2211yescharacteristic
21C2×C4×Dic149C2212yes—
22C2×C4×Dic149C2211yescharacteristic
23#18011818C2212yes—
24#18011818C2212yes—
25#18011818C2212yes—
26#18011818C2212yes—
27C22×Q8×C149C2211yescharacteristic
28C2×C4⋊C4×C149C2211yescharacteristic
29C2×C42×C149C2211yescharacteristic
30#95×C149C2212yes—
31#95×C149C2212yes—
32C2×Dic298—41no—
33C2×Dic298—41no—
34C2×Dic298C2×C414yes—
35C22×Dic149C2312yes—
36C22×Dic149C2312yes—
37C22×Dic149C2312yes—
38C22×Dic149C2312yes—
39C4⋊Dic149—41no—
40#14558715—24no—
41#14558715—42no—
42#14558715C2×C418yes—
43#14558715C2×C418yes—
44#14558715Q818yescomplemented
45C4×Dic149—24no—
46C4×Dic149—24no—
47C4×Dic149—42no—
48C4×Dic149—41no—
49C4×Dic149C2×C414yes—
50C2×Q8×C149—41no—
51C2×Q8×C149—41no—
52C2×Q8×C149C2×C414yes—
53C22×C4×C149C2312yes—
54C22×C4×C149C2311yescharacteristic
55C22×C4×C149C2311yescharacteristic
56C22×C4×C149C2311yescharacteristic
57C22×C4×C149C2312yes—
58C4⋊C4×C149—41no—
59C42×C149—41no—
60Dic298—44no—
61C2×Dic149—22no—
62C2×Dic149—22no—
63C2×Dic149—22no—
64C2×Dic149—22no—
65C2×Dic149—22no—
66C2×Dic149—22no—
67C2×Dic149—22no—
68C2×Dic149C22×C414yes—
69C2×Dic149C22×C414yes—
70C2×Dic149C2×Q814yes—
71C2×Dic149C2×Q814yes—
72C2×Dic149#4114yes—
73C23×C149C2411yescharacteristic
74Q8×C149—44no—
75C2×C4×C149—22no—
76C2×C4×C149—21no—
77C2×C4×C149—21no—
78C2×C4×C149—21no—
79C2×C4×C149—22no—
80C2×C4×C149—21no—
81C2×C4×C149—21no—
82C2×C4×C149—21no—
83C2×C4×C149—22no—
84C2×C4×C149—22no—
85C2×C4×C149—22no—
86C2×C4×C149C22×C412yes—
87C2×C4×C149C22×C412yes—
88C2×C4×C149C22×C412yes—
89C2×C4×C149C2×Q814yes—
90C22×C149C23×C411yescharacteristic
91C22×C149C22×Q812yes—
92C22×C149C2×#4112yes—
93C22×C149H(5,𝔽2)11yescharacteristic
94C22×C149H(5,𝔽2)11yescharacteristic
95C4×C149—22no—
96C4×C149—22no—
97C4×C149—22no—
98C4×C149—24no—
99C4×C149—42no—
100Dic149—24no—
101Dic149—24no—
102Dic149—42no—
103Dic149C4×Q818yes—
104C2×C149C2×C4×Q812yes—
105C2×C149#51811yescharacteristic
106C2×C149#55412yes—
107C2×C149#55511yescharacteristic
108C2×C149Q8211yescharacteristic
109C149#236911yescharacteristic, complemented, Sylow
110#2369—1491nomaximal, Sylow
111C2×C4⋊Q8—1491no—
112#391—1491no—
113#391—1492no—
114#391D14911yescharacteristic
115#389—1492no—
116#389—1492no—
117C4×C4⋊C4—1492no—
118C4×C4⋊C4—1492no—
119C4×C4⋊C4—1492no—
120C22×Q8—1491no—
121C22×Q8C2×D14911yescharacteristic
122C4⋊Q8—1498no—
123C2×C4⋊C4—1492no—
124C2×C4⋊C4—1492no—
125C2×C4⋊C4—1491no—
126C2×C4⋊C4—1492no—
127C2×C4⋊C4—1492no—
128C2×C4⋊C4—1492no—
129C2×C4⋊C4C2×D14911yescharacteristic
130C2×C42—1492no—
131C2×C42—1492no—
132C2×C42—1491no—
133C2×C42—1492no—
134C2×C42—1491no—
135C2×C42C2×D14911yescharacteristic
136#95—1492no—
137#95—1492no—
138#95—1492no—
139#95—1492no—
140#95C2×D14912yes—
141#95C2×D14912yes—
142C2×Q8—41no—
143C2×Q8—41no—
144C2×Q8—5961no—
145C2×Q8—5961no—
146C2×Q8—1494no—
147C2×Q8C4×D14914yes—
148C22×C4—1492no—
149C22×C4—1492no—
150C22×C4—1492no—
151C22×C4—1492no—
152C22×C4C22×D14912yes—
153C22×C4C22×D14911yescharacteristic
154C22×C4C22×D14911yescharacteristic
155C22×C4C22×D14911yescharacteristic
156C22×C4C22×D14912yes—
157C4⋊C4—41no—
158C4⋊C4—2984no—
159C4⋊C4—5962no—
160C4⋊C4—5961no—
161C4⋊C4—1498no—
162C4⋊C4—1498no—
163C4⋊C4—1498no—
164C42—41no—
165C42—2984no—
166C42—2984no—
167C42—5962no—
168C42—5961no—
169C42—1494no—
170C23C23×D14911yescharacteristic
171Q8—44no—
172Q8—5964no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—2982no—
185C2×C4—2982no—
186C2×C4—2982no—
187C2×C4—2982no—
188C2×C4—2982no—
189C2×C4—2982no—
190C2×C4—2982no—
191C2×C4—1494no—
192C2×C4—1494no—
193C2×C4—1494no—
194C2×C4—1494no—
195C2×C4—1494no—
196C2×C4C2×C4×D14912yes—
197C2×C4C2×C4×D14912yes—
198C2×C4C2×C4×D14912yes—
199C2×C4Q8×D14914yes—
200C22C22×C4×D14911yescharacteristic
201C22C2×Q8×D14912yes—
202C22#41×D14912yes—
203C22#1801195611yescharacteristic
204C22#1801195611yescharacteristic
205C4—24no—
206C4—22no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—2984no—
211C4—2984no—
212C4—5962no—
213C4—1498no—
214C2C4×Q8×D14912yes—
215C2#2375009811yescharacteristic
216C2#2375032912yes—
217C2#2375033711yescharacteristic
218C2#2375035511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#391×C149C2
socle, prime radical, cosocleC23×C149C24
hypercenter#391D149
hypocenterC149#2369
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
11. #18011909C4semidirect
44. #14558715Q8semidirect
109. C149#2369semidirect

Maximal subgroups

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

subgroupindex
C2×#180119092
#237495322
#237495292
#237495222
#237495202
C4×#145587152
#237494762
#391×C1492
#2369149