Finite Group Databasebeta

← #34055348

Subgroups — #34055348

Order 19072.

338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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#23750233C212yesmaximal
2#23750025C211yesmaximal, characteristic, complemented
3#23750003C211yesmaximal, characteristic, complemented
4#23749992C212yesmaximal, complemented
5#23749884C211yesmaximal, characteristic
6#23749880C211yesmaximal, characteristic
7#23749865C212yesmaximal
8#23749733C211yesmaximal, characteristic, complemented
9C4×#14558726C212yesmaximal, complemented
10#23749582C211yesmaximal, characteristic
11#441×C149C211yesmaximal, characteristic, complemented
12C2×Dic596C2211yescharacteristic
13C2×#14558726C2212yes—
14C2×#14558719C2211yescharacteristic
15C2×C8×D149C2211yescharacteristic
16#18011909C2212yes—
17#18011906—22no—
18#18011905—22no—
19#18011903—22no—
20#18011902C2212yes—
21#18011901—22no—
22#18011891C2212yes—
23#18011887C2212yes—
24C4×Dic298C2212yes—
25#18011868C2211yescharacteristic
26#18011844C2212yes—
27#18011843C2211yescharacteristic
28#18011836C2212yes—
29#18011835C2212yes—
30#18011834C2212yes—
31#18011821C2211yescharacteristic
32C4×#11924746C2211yescharacteristic
33C8×Dic149C2211yescharacteristic
34C2×Q16×C149C2211yescharacteristic
35C4×Q8×C149C2212yes—
36#106×C149C2211yescharacteristic
37#103×C149C2212yes—
38#97×C149C2211yescharacteristic
39C2×Dic298C2312yes—
40C2×C4×D149C2311yescharacteristic
41Dic596—22no—
42#14558726—24no—
43#14558719—22no—
44C2×#11924746C2311yescharacteristic
45C2×#11924746C2311yescharacteristic
46C8×D149—22no—
47C4⋊Dic149—22no—
48C4⋊Dic149—22no—
49C4⋊Dic149C2312yes—
50#14558715—22no—
51#14558715—22no—
52#14558715—22no—
53#14558715—22no—
54#14558715—22no—
55#14558715D412yes—
56#14558713—22no—
57#14558713—22no—
58#14558713D412yes—
59C4×Dic149—22no—
60C4×Dic149C2311yescharacteristic
61C2×Q8×C149C2312yes—
62Q16×C149—22no—
63C2×C8×C149C2311yescharacteristic
64C2×C8×C149C2311yescharacteristic
65C4⋊C4×C149—22no—
66C4⋊C4×C149C2312yes—
67C42×C149—22no—
68C42×C149C2311yescharacteristic
69C22×D149C2×D411yescharacteristic
70Dic298—22no—
71Dic298—22no—
72C2×Dic149—22no—
73C2×Dic149—22no—
74C2×Dic149C2×D411yescharacteristic
75C2×Dic149C2×D412yes—
76C4×D149—21no—
77C4×D149—21no—
78#11924746—21no—
79#11924746#4112yes—
80Q8×C149—22no—
81Q8×C149—22no—
82C2×C4×C149—22no—
83C2×C4×C149—22no—
84C2×C4×C149C2×D412yes—
85C2×C4×C149C2411yescharacteristic
86C8×C149—21no—
87C8×C149#4112yes—
88C22×C149C22×D411yescharacteristic
89C2×D149—21no—
90C2×D149—22no—
91C4×C149—22no—
92C4×C149—42no—
93C4×C149—42no—
94C4×C149C2×#4111yescharacteristic
95C4×C149C2×#4111yescharacteristic
96Dic149—21no—
97Dic149—22no—
98Dic149—42no—
99Dic149—42no—
100C2×C149#53211yescharacteristic
101C2×C149#57812yes—
102D149—41no—
103C149#317711yescharacteristic, complemented, Sylow
104#3177—1491nomaximal, Sylow
105#541—1492no—
106#499—1491no—
107#494—1491no—
108#491—1492no—
109#470—1491no—
110#470—1491no—
111#467—1492no—
112#441—1491no—
113#441D14911yescharacteristic, complemented
114C4×Q16—1492no—
115#405—1491no—
116C2×Q16—1492no—
117C2×Q16—1491no—
118C2×Q16C2×D14911yescharacteristic
119C2×M16—1491no—
120C22×C8—1491no—
121C4⋊Q8—1492no—
122#126—2982no—
123#126—2982no—
124#125—2982no—
125#125—2982no—
126#125—1492no—
127C22⋊Q8—1492no—
128C22⋊Q8—1492no—
129C4×Q8—1492no—
130C4×Q8C2×D14912yes—
131#117—1491no—
132#107—1492no—
133#106—1491no—
134#106C2×D14911yescharacteristic
135#103—1492no—
136#103—1492no—
137#103—1492no—
138#103C2×D14912yes—
139#97—1491no—
140#97C2×D14911yescharacteristic
141C4×C8—1491no—
142C4×C8—1491no—
143C2×Q8—1492no—
144C2×Q8C22×D14912yes—
145C22×C4—1491no—
146Q16—22no—
147Q16—2984no—
148Q16—2982no—
149M16—2982no—
150C2×C8—2982no—
151C2×C8—1491no—
152C2×C8—1491no—
153C2×C8C22×D14911yescharacteristic
154C2×C8C22×D14911yescharacteristic
155C4⋊C4—22no—
156C4⋊C4—2982no—
157C4⋊C4—2982no—
158C4⋊C4—2982no—
159C4⋊C4—2982no—
160C4⋊C4—2982no—
161C4⋊C4—2982no—
162C4⋊C4—2982no—
163C4⋊C4—1492no—
164C4⋊C4—1492no—
165C4⋊C4C22×D14912yes—
166C22⋊C4—2982no—
167C22⋊C4—2982no—
168C22⋊C4—1492no—
169C42—22no—
170C42—2982no—
171C42—1491no—
172C42C22×D14911yescharacteristic
173C23—1491no—
174Q8—22no—
175Q8—22no—
176Q8—2982no—
177Q8—2982no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—2981no—
181C2×C4—2981no—
182C2×C4—2982no—
183C2×C4—2982no—
184C2×C4—1492no—
185C2×C4—1491no—
186C2×C4D4×D14912yes—
187C2×C4C23×D14911yescharacteristic
188C8—21no—
189C8—2981no—
190C8—1492no—
191C8#1455873612yes—
192C22—2981no—
193C22—2982no—
194C22C2×D4×D14911yescharacteristic
195C4—22no—
196C4—42no—
197C4—42no—
198C4—2981no—
199C4—2982no—
200C4—5962no—
201C4—5962no—
202C4#41×D14911yescharacteristic
203C4C2×#1455873611yescharacteristic
204C2—5961no—
205C2#2375017211yescharacteristic
206C2#2375044112yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#441×C149C2
socleC22×C149C22×D4
prime radicalC22×D149C2×D4
hypercenter#441D149
hypocenterC149#3177
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
2. #23750025C2semidirect
3. #23750003C2semidirect
4. #23749992C2semidirect
8. #23749733C2semidirect
9. C4×#14558726C2semidirect
11. #441×C149C2semidirect
103. C149#3177semidirect
113. #441D149semidirect

Maximal subgroups

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

subgroupindex
#237502332
#237500252
#237500032
#237499922
#237498842
#237498802
#237498652
#237497332
C4×#145587262
#237495822
#441×C1492
#3177149