Finite Group Databasebeta

← #34054496

Subgroups — #34054496

Order 19072.

376 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 153 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#23750182C211yesmaximal, characteristic
2#23749932C214yesmaximal, complemented
3#23749920C212yesmaximal, complemented
4#23749910C212yesmaximal, complemented
5#23749665C212yesmaximal
6#23749649C211yesmaximal, characteristic
7#23749634C212yesmaximal
8C2×C4×Q8×C149C211yesmaximal, characteristic
9C2×#14558720C2212yes—
10#18011911C2211yescharacteristic
11#18011911C2211yescharacteristic
12#18011903C2212yes—
13#18011890—21no—
14#18011890—21no—
15C4×Dic298—21no—
16C4×Dic298—21no—
17#18011870C2212yes—
18#18011844C2214yes—
19#18011842C2214yes—
20C4⋊#11924746C2212yes—
21C4⋊#11924746C2212yes—
22#18011835C2214yes—
23#18011835C2214yes—
24C22×Q8×C149C2211yescharacteristic
25C4×Q8×C149—21no—
26C4×Q8×C149—21no—
27C4×Q8×C149C2212yes—
28C4×Q8×C149C2212yes—
29C2×C4⋊C4×C149—21no—
30C2×C4⋊C4×C149C2211yescharacteristic
31C2×C42×C149—21no—
32C2×C42×C149C2211yescharacteristic
33C2×Dic298—21no—
34C2×Dic298—21no—
35#14558720—24no—
36C2×#11924746C2314yes—
37C4⋊Dic149—21no—
38C4⋊Dic149—21no—
39C4⋊Dic149C2312yes—
40C4⋊Dic149C2312yes—
41#14558715—22no—
42#14558715—22no—
43C22⋊Dic149—22no—
44C4×Dic149—22no—
45C2×Q8×C149—21no—
46C2×Q8×C149—22no—
47C2×Q8×C149Q814yescomplemented
48C2×Q8×C149C2312yes—
49C22×C4×C149—21no—
50C22×C4×C149—21no—
51C22×C4×C149D411yescharacteristic
52C22×C4×C149D411yescharacteristic
53C22×C4×C149C2311yescharacteristic
54C4⋊C4×C149—22no—
55C4⋊C4×C149—22no—
56C4⋊C4×C149—21no—
57C4⋊C4×C149C2312yes—
58C42×C149—22no—
59C42×C149—22no—
60C42×C149D411yescharacteristic
61C42×C149D411yescharacteristic
62C42×C149C2311yescharacteristic
63C42×C149C2311yescharacteristic
64Dic298—42no—
65Dic298—42no—
66C2×Dic149—22no—
67C2×Dic149—22no—
68#11924746—24no—
69C23×C149C2×D411yescharacteristic
70Q8×C149—24no—
71Q8×C149—22no—
72Q8×C149C2×Q814yes—
73C2×C4×C149—24no—
74C2×C4×C149—22no—
75C2×C4×C149—22no—
76C2×C4×C149—22no—
77C2×C4×C149—41no—
78C2×C4×C149—42no—
79C2×C4×C149C2×D411yescharacteristic
80C2×C4×C149C2×D411yescharacteristic
81C2×C4×C149C2×D411yescharacteristic
82C2×C4×C149C2×D411yescharacteristic
83C2×C4×C149C2×D411yescharacteristic
84C2×C4×C149C2×Q812yes—
85C2×C4×C149#4112yes—
86C2×C4×C149C2411yescharacteristic
87C22×C149—21no—
88C22×C149—21no—
89C22×C149C22⋊Q812yes—
90C22×C149C22×D411yescharacteristic
91C4×C149—24no—
92C4×C149—21no—
93C4×C149—21no—
94C4×C149—21no—
95C4×C149—42no—
96C4×C149C22⋊Q812yes—
97C4×C149#13712yes—
98C4×C149C22×Q811yescharacteristic
99C4×C149C2×#4111yescharacteristic
100Dic149—42no—
101Dic149—42no—
102C2×C149—22no—
103C2×C149C2×C22⋊Q811yescharacteristic
104C2×C149C2×#13711yescharacteristic
105C2×C149#57511yescharacteristic
106C149#307811yescharacteristic, complemented, Sylow
107#3078—1491nomaximal, Sylow
108#533—1491no—
109C2×C4×Q8D14911yescharacteristic
110#479—1494no—
111#477—1492no—
112#475—1492no—
113#428—1492no—
114#423—1491no—
115#419—1492no—
116C22×Q8C2×D14911yescharacteristic
117C2×M16—1492no—
118C4⋊Q8—1491no—
119C4⋊Q8—1491no—
120#125—1492no—
121C22⋊Q8—2981no—
122C22⋊Q8—2981no—
123C4×Q8—21no—
124C4×Q8—21no—
125C4×Q8—2981no—
126C4×Q8—2981no—
127C4×Q8C2×D14912yes—
128C4×Q8C2×D14912yes—
129#117—1492no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4C2×D14911yescharacteristic
132C2×C42—21no—
133C2×C42C2×D14911yescharacteristic
134#107—1494no—
135#106—1494no—
136C4⋊C8—1492no—
137C4⋊C8—1492no—
138#103—1494no—
139#103—1494no—
140C2×Q8—21no—
141C2×Q8—22no—
142C2×Q8—2981no—
143C2×Q8—2981no—
144C2×Q8Dic29814yescomplemented
145C2×Q8C22×D14912yes—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4C22⋊D14911yescharacteristic
149C22×C4C22⋊D14911yescharacteristic
150C22×C4C22×D14911yescharacteristic
151M16—2984no—
152C2×C8—1494no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—21no—
156C4⋊C4—2982no—
157C4⋊C4—2982no—
158C4⋊C4—2981no—
159C4⋊C4—2981no—
160C4⋊C4—1492no—
161C4⋊C4—1492no—
162C4⋊C4C22×D14912yes—
163C22⋊C4—2982no—
164C42—22no—
165C42—22no—
166C42—2982no—
167C42C22⋊D14911yescharacteristic
168C42C22⋊D14911yescharacteristic
169C42C22×D14911yescharacteristic
170C42C22×D14911yescharacteristic
171C23C2×C22⋊D14911yescharacteristic
172Q8—22no—
173Q8—24no—
174Q8—5962no—
175Q8—5962no—
176Q8C2×Dic29814yes—
177C2×C4—22no—
178C2×C4—24no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—41no—
182C2×C4—42no—
183C2×C4—2982no—
184C2×C4—2982no—
185C2×C4C2×C22⋊D14911yescharacteristic
186C2×C4C2×C22⋊D14911yescharacteristic
187C2×C4C2×C22⋊D14911yescharacteristic
188C2×C4C2×C22⋊D14911yescharacteristic
189C2×C4C2×C22⋊D14911yescharacteristic
190C2×C4C2×Dic29812yes—
191C2×C4#1455873612yes—
192C2×C4C23×D14911yescharacteristic
193C8—2984no—
194C22—21no—
195C22—21no—
196C22#1801189012yes—
197C22C22×C22⋊D14911yescharacteristic
198C4—21no—
199C4—21no—
200C4—21no—
201C4—24no—
202C4—42no—
203C4—5962no—
204C4—5962no—
205C4#1801189012yes—
206C4#1801194212yes—
207C4C22×Dic29811yescharacteristic
208C4C2×#1455873611yescharacteristic
209C2—22no—
210C2C2×#1801189011yescharacteristic
211C2C2×#1801194211yescharacteristic
212C2#2375042311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×C4×Q8×C149C2
socleC22×C149C22×D4
prime radicalC23×C149C2×D4
hypercenterC2×C4×Q8D149
hypocenterC149#3078
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #23749932C2semidirect
3. #23749920C2semidirect
4. #23749910C2semidirect
47. C2×Q8×C149Q8semidirect
106. C149#3078semidirect
144. C2×Q8Dic298semidirect

Maximal subgroups

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

subgroupindex
#237501822
#237499322
#237499202
#237499102
#237496652
#237496492
#237496342
C2×C4×Q8×C1492
#3078149