Finite Group Databasebeta

← #34055431

Subgroups — #34055431

Order 19072.

358 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 119 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#23750177C212yesmaximal
2#23750022C211yesmaximal, characteristic, complemented
3#23750003C211yesmaximal, characteristic, complemented
4#23749974C212yesmaximal, complemented
5#23749883C211yesmaximal, characteristic
6#23749881C212yesmaximal
7#23749732C211yesmaximal, characteristic, complemented
8#23749731C211yesmaximal, characteristic, complemented
9#23749729C212yesmaximal, complemented
10M16×Dic149C211yesmaximal, characteristic
11#470×C149C211yesmaximal, characteristic
12C2×Dic596C2211yescharacteristic
13C2×#14558726C2212yes—
14C2×#14558720C2211yescharacteristic
15#18011910C2212yes—
16#18011909C2212yes—
17#18011901—22no—
18#18011890C2212yes—
19#18011888—22no—
20Q8×Dic149C2212yes—
21#18011876—22no—
22#18011876C2212yes—
23#18011867—22no—
24C2×C4×Dic149C2211yescharacteristic
25#18011843C2211yescharacteristic
26#18011842C2212yes—
27#18011836C2212yes—
28#18011835C2212yes—
29#18011834C2212yes—
30#18011821C2211yescharacteristic
31#18011821C2211yescharacteristic
32C8×Dic149C2211yescharacteristic
33C8×Dic149C2211yescharacteristic
34C2×Q16×C149C2211yescharacteristic
35C2×M16×C149C2211yescharacteristic
36C22⋊Q8×C149C2212yes—
37#106×C149C2211yescharacteristic
38#103×C149C2212yes—
39C2×Dic298—22no—
40C2×Dic298C2312yes—
41C22×Dic149D412yes—
42Dic596—22no—
43#14558726—24no—
44#14558720—22no—
45C2×#11924746C2311yescharacteristic
46C2×#11924746C2311yescharacteristic
47C4⋊Dic149—22no—
48C4⋊Dic149C2312yes—
49#14558715—22no—
50#14558715—22no—
51#14558715—22no—
52#14558715—22no—
53#14558715—22no—
54C22⋊Dic149—22no—
55C4×Dic149—22no—
56C4×Dic149—22no—
57C4×Dic149D412yes—
58C4×Dic149C2311yescharacteristic
59C4×Dic149C2311yescharacteristic
60C2×Q8×C149C2312yes—
61C22×C4×C149C2311yescharacteristic
62Q16×C149—22no—
63M16×C149—22no—
64C2×C8×C149C2311yescharacteristic
65C2×C8×C149C2311yescharacteristic
66C4⋊C4×C149—22no—
67C4⋊C4×C149C2312yes—
68C22⋊C4×C149—22no—
69Dic298—22no—
70Dic298—22no—
71Dic298—44no—
72C2×Dic149—24no—
73C2×Dic149—22no—
74C2×Dic149—22no—
75C2×Dic149C2×D412yes—
76C2×Dic149C2×D412yes—
77#11924746—21no—
78#11924746#4112yes—
79C23×C149C2×D411yescharacteristic
80Q8×C149—22no—
81Q8×C149—22no—
82C2×C4×C149—21no—
83C2×C4×C149—21no—
84C2×C4×C149—22no—
85C2×C4×C149—22no—
86C2×C4×C149C2×D411yescharacteristic
87C2×C4×C149C2411yescharacteristic
88C8×C149—21no—
89C8×C149#4112yes—
90C22×C149—21no—
91C22×C149—22no—
92C22×C149C22×D411yescharacteristic
93C4×C149—21no—
94C4×C149—42no—
95C4×C149—42no—
96C4×C149C2×#4111yescharacteristic
97C4×C149C2×#4111yescharacteristic
98Dic149—22no—
99Dic149—42no—
100Dic149—42no—
101Dic149#13714yes—
102C2×C149—41no—
103C2×C149#53211yescharacteristic
104C2×C149C2×#13712yes—
105C149#318511yescharacteristic, complemented, Sylow
106#3185—1491nomaximal, Sylow
107#533—1492no—
108#498—1491no—
109#494—1491no—
110#487—1492no—
111#470—1491no—
112#470—1492no—
113#470D14911yescharacteristic
114#441—1491no—
115#441—1491no—
116#441—1492no—
117C4×M16—1491no—
118C2×Q16—1492no—
119C2×Q16—1491no—
120C2×Q16C2×D14911yescharacteristic
121C2×M16—1491no—
122C2×M16C2×D14911yescharacteristic
123C4⋊Q8—1492no—
124C4⋊Q8—1492no—
125#125—2982no—
126C22⋊Q8—2982no—
127C22⋊Q8—1492no—
128C22⋊Q8C2×D14912yes—
129C4×Q8—2982no—
130C4×Q8—1492no—
131C4×Q8—1492no—
132#117—2982no—
133C2×C42—1491no—
134#106—1491no—
135#106—1492no—
136#106C2×D14911yescharacteristic
137#103—1492no—
138#103—1492no—
139#103—1492no—
140#103C2×D14912yes—
141#97—1491no—
142#97—1491no—
143C4×C8—1491no—
144C4×C8—1491no—
145C2×Q8—2982no—
146C2×Q8—1492no—
147C2×Q8C22×D14912yes—
148C22×C4—1492no—
149C22×C4C22×D14911yescharacteristic
150Q16—22no—
151Q16—2984no—
152Q16—2982no—
153M16—22no—
154M16—2982no—
155C2×C8—1491no—
156C2×C8—1491no—
157C2×C8C22×D14911yescharacteristic
158C2×C8C22×D14911yescharacteristic
159C4⋊C4—22no—
160C4⋊C4—2982no—
161C4⋊C4—2982no—
162C4⋊C4—2982no—
163C4⋊C4—2982no—
164C4⋊C4—2982no—
165C4⋊C4—2982no—
166C4⋊C4—1492no—
167C4⋊C4C22×D14912yes—
168C22⋊C4—22no—
169C22⋊C4—2982no—
170C42—2982no—
171C42—2982no—
172C42—1492no—
173C42—1491no—
174C42—1491no—
175C23D4×D14911yescharacteristic
176Q8—22no—
177Q8—22no—
178Q8—2982no—
179Q8—2982no—
180Q8—5964no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—2984no—
186C2×C4—2982no—
187C2×C4—2982no—
188C2×C4—1492no—
189C2×C4—1492no—
190C2×C4D4×D14911yescharacteristic
191C2×C4C23×D14911yescharacteristic
192C8—21no—
193C8—2981no—
194C8—1492no—
195C8#1455873512yes—
196C22—22no—
197C22—21no—
198C22C2×D4×D14911yescharacteristic
199C4—21no—
200C4—42no—
201C4—42no—
202C4—2982no—
203C4—5962no—
204C4—5962no—
205C4—1494no—
206C4#41×D14911yescharacteristic
207C4C2×#1455873511yescharacteristic
208C2—41no—
209C2#2375017011yescharacteristic
210C2#137×D14912yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#470×C149C2
socleC22×C149C22×D4
prime radicalC23×C149C2×D4
hypercenter#470D149
hypocenterC149#3185
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #23750022C2semidirect
3. #23750003C2semidirect
4. #23749974C2semidirect
7. #23749732C2semidirect
8. #23749731C2semidirect
9. #23749729C2semidirect
105. C149#3185semidirect

Maximal subgroups

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

subgroupindex
#237501772
#237500222
#237500032
#237499742
#237498832
#237498812
#237497322
#237497312
#237497292
M16×Dic1492
#470×C1492
#3185149