Finite Group Databasebeta

← #34055418

Subgroups — #34055418

Order 19072.

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

normal subgroups only

This group has 370 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#23750157C212yesmaximal, complemented
2#23750025C211yesmaximal, characteristic, complemented
3#23750008C211yesmaximal, characteristic, complemented
4#23749978C212yesmaximal, complemented
5#23749884C211yesmaximal, characteristic, complemented
6#23749875C211yesmaximal, characteristic
7#23749870C212yesmaximal, complemented
8#23749733C211yesmaximal, characteristic, complemented
9#23749725C212yesmaximal, complemented
10#23749577C211yesmaximal, characteristic, complemented
11#442×C149C211yesmaximal, characteristic, complemented
12C2×Dic596C2211yescharacteristic
13C2×#14558724C2212yes—
14C2×#14558719C2211yescharacteristic
15C2×#14558719C2211yescharacteristic
16#18011904—22no—
17#18011902C2212yes—
18#18011898C2212yes—
19#18011893—22no—
20#18011891C2212yes—
21#18011882C2212yes—
22C4×Dic298C2212yes—
23C4×C22⋊D149—22no—
24#18011870—22no—
25C42×D149C2211yescharacteristic
26#18011844C2212yes—
27#18011843C2211yescharacteristic
28#18011836C2212yes—
29#18011834C2212yes—
30#18011832C2212yes—
31#18011822C2211yescharacteristic
32C8×Dic149C2211yescharacteristic
33C8×Dic149C2211yescharacteristic
34C2×D8×C149C2211yescharacteristic
35C4×D4×C149C2212yes—
36#106×C149C2211yescharacteristic
37#102×C149C2212yes—
38#97×C149C2211yescharacteristic
39C2×Dic298C2312yes—
40C2×C22⋊D149—22no—
41C2×C4×D149D412yes—
42C2×C4×D149C2311yescharacteristic
43Dic596—22no—
44#14558724—24no—
45#14558719—22no—
46#14558719—22no—
47C2×#11924746C2311yescharacteristic
48C2×#11924746C2311yescharacteristic
49C4⋊Dic149—22no—
50C4⋊Dic149—22no—
51C4⋊Dic149C2312yes—
52#14558715—22no—
53#14558715—22no—
54C22⋊Dic149—22no—
55C22⋊Dic149—22no—
56C22⋊Dic149—22no—
57#14558713—22no—
58C4×Dic149—22no—
59C4×Dic149D412yes—
60C4×Dic149C2311yescharacteristic
61C2×D4×C149C2312yes—
62C22×C4×C149—22no—
63D8×C149—22no—
64C2×C8×C149C2311yescharacteristic
65C2×C8×C149C2311yescharacteristic
66C4⋊C4×C149C2312yes—
67C22⋊C4×C149—22no—
68C42×C149C2311yescharacteristic
69C22×D149C2×D411yescharacteristic
70Dic298—22no—
71Dic298—22no—
72C22⋊D149—44no—
73C2×Dic149—22no—
74C2×Dic149—22no—
75C2×Dic149C2×D412yes—
76C2×Dic149C2×D411yescharacteristic
77C4×D149—21no—
78C4×D149—21no—
79C4×D149—42no—
80#11924746—21no—
81#11924746#4112yes—
82C23×C149—22no—
83D4×C149—22no—
84D4×C149—22no—
85C2×C4×C149—22no—
86C2×C4×C149—44no—
87C2×C4×C149C2×D412yes—
88C2×C4×C149C2411yescharacteristic
89C8×C149—21no—
90C8×C149#4112yes—
91C22×C149—42no—
92C22×C149—42no—
93C22×C149—42no—
94C22×C149C22×D411yescharacteristic
95C2×D149—21no—
96C2×D149—22no—
97C4×C149—22no—
98C4×C149—42no—
99C4×C149C2×#4111yescharacteristic
100C4×C149C2×#4111yescharacteristic
101Dic149—21no—
102Dic149—22no—
103Dic149—42no—
104Dic149—42no—
105C2×C149—82no—
106C2×C149#53211yescharacteristic
107C2×C149#57512yes—
108D149—41no—
109C149#318311yescharacteristic, complemented, Sylow
110#3183—1491nomaximal, Sylow
111#529—1492no—
112#499—1491no—
113#495—1491no—
114#488—1492no—
115#470—1491no—
116#469—1491no—
117#468—1492no—
118#442D14911yescharacteristic, complemented
119#441—1491no—
120#440—1492no—
121C4×M16—1491no—
122C2×Q16—1491no—
123C2×SD16—1492no—
124C2×D8C2×D14911yescharacteristic
125C2×M16—1491no—
126C2×M16—1491no—
127#126—2982no—
128#125—1492no—
129#124—1492no—
130#123—2982no—
131C22⋊Q8—1492no—
132#121—1492no—
133C4×Q8—1492no—
134C4×D4—2982no—
135C4×D4C2×D14912yes—
136#117—2982no—
137C2×C42—1491no—
138#107—1492no—
139#106—1491no—
140#106C2×D14911yescharacteristic
141#103—1492no—
142#103—1492no—
143#102—1492no—
144#102C2×D14912yes—
145#97—1491no—
146#97C2×D14911yescharacteristic
147C4×C8—1491no—
148C4×C8—1491no—
149C2×Q8—1492no—
150C2×D4—2982no—
151C2×D4C22×D14912yes—
152C22×C4—22no—
153C22×C4—1491no—
154C22×C4—1492no—
155Q16—2982no—
156SD16—2984no—
157D8—22no—
158M16—2982no—
159M16—2982no—
160C2×C8—1491no—
161C2×C8—1491no—
162C2×C8C22×D14911yescharacteristic
163C2×C8C22×D14911yescharacteristic
164C4⋊C4—2982no—
165C4⋊C4—2982no—
166C4⋊C4—2982no—
167C4⋊C4—2982no—
168C4⋊C4—1492no—
169C4⋊C4C22×D14912yes—
170C22⋊C4—22no—
171C22⋊C4—2982no—
172C22⋊C4—2982no—
173C22⋊C4—2982no—
174C22⋊C4—2982no—
175C42—2982no—
176C42—1492no—
177C42—1491no—
178C42C22×D14911yescharacteristic
179C23—22no—
180C23—1491no—
181Q8—2982no—
182Q8—2982no—
183D4—22no—
184D4—22no—
185D4—5964no—
186C2×C4—22no—
187C2×C4—44no—
188C2×C4—2981no—
189C2×C4—2981no—
190C2×C4—2982no—
191C2×C4—2982no—
192C2×C4—5962no—
193C2×C4—1492no—
194C2×C4—1491no—
195C2×C4D4×D14912yes—
196C2×C4C23×D14911yescharacteristic
197C8—21no—
198C8—2981no—
199C8—1492no—
200C8#1455873612yes—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—2982no—
205C22—2981no—
206C22C2×D4×D14911yescharacteristic
207C4—22no—
208C4—42no—
209C4—2982no—
210C4—2981no—
211C4—5962no—
212C4—5962no—
213C4#41×D14911yescharacteristic
214C4C2×#1455873611yescharacteristic
215C2—82no—
216C2—5961no—
217C2#2375017211yescharacteristic
218C2#2375042112yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#442×C149C2
socleC22×C149C22×D4
prime radical#23749875C2
hypercenter#442D149
hypocenterC149#3183
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #23750157C2semidirect
2. #23750025C2semidirect
3. #23750008C2semidirect
4. #23749978C2semidirect
5. #23749884C2semidirect
7. #23749870C2semidirect
8. #23749733C2semidirect
9. #23749725C2semidirect
10. #23749577C2semidirect
11. #442×C149C2semidirect
109. C149#3183semidirect
118. #442D149semidirect

Maximal subgroups

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

subgroupindex
#237501572
#237500252
#237500082
#237499782
#237498842
#237498752
#237498702
#237497332
#237497252
#237495772
#442×C1492
#3183149