Finite Group Databasebeta

← #34056086

Subgroups — #34056086

Order 19072.

354 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 109 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#23750156C212yesmaximal, complemented
2#23749935C212yesmaximal, complemented
3#23749927C212yesmaximal, complemented
4#23749883C211yesmaximal, characteristic, complemented
5#23749869C212yesmaximal, complemented
6#23749846C212yesmaximal, complemented
7#23749838C212yesmaximal, complemented
8#23749648C211yesmaximal, characteristic, complemented
9#469×C149C211yesmaximal, characteristic
10C2×Dic596C2211yescharacteristic
11C2×#14558724C2212yes—
12C2×#14558720C2211yescharacteristic
13#18011904—22no—
14#18011902C2212yes—
15#18011898C2212yes—
16#18011892—22no—
17#18011890C2212yes—
18#18011876C2212yes—
19D4×Dic149—22no—
20D4×Dic149C2212yes—
21#18011867—22no—
22C2×C4×Dic149C2211yescharacteristic
23#18011844C2212yes—
24#18011843C2211yescharacteristic
25#18011840C2212yes—
26#18011840C2212yes—
27#18011836C2212yes—
28#18011834C2212yes—
29#18011832C2212yes—
30C2×D8×C149C2211yescharacteristic
31C2×M16×C149C2211yescharacteristic
32#121×C149C2212yes—
33#106×C149C2211yescharacteristic
34#102×C149C2212yes—
35C2×Dic298C2312yes—
36C22×Dic149—22no—
37C22×Dic149D412yes—
38Dic596—41no—
39#14558724—42no—
40#14558720—41no—
41C2×#11924746C2312yes—
42C4⋊Dic149—22no—
43C4⋊Dic149C2312yes—
44#14558715—22no—
45#14558715—22no—
46#14558715—22no—
47C22⋊Dic149—22no—
48C22⋊Dic149—22no—
49C22⋊Dic149—22no—
50C22⋊Dic149—22no—
51C4×Dic149—22no—
52C4×Dic149D411yescharacteristic
53C4×Dic149D411yescharacteristic
54C4×Dic149C2312yes—
55C2×D4×C149—22no—
56C2×D4×C149C2312yes—
57C22×C4×C149C2311yescharacteristic
58D8×C149—41no—
59M16×C149—41no—
60C2×C8×C149C2311yescharacteristic
61C2×C8×C149C2311yescharacteristic
62C4⋊C4×C149C2312yes—
63C22⋊C4×C149—22no—
64Dic298—22no—
65Dic298—22no—
66C2×Dic149—22no—
67C2×Dic149—22no—
68C2×Dic149—42no—
69C2×Dic149—44no—
70C2×Dic149C2×D412yes—
71C2×Dic149C2×D412yes—
72#11924746—22no—
73C23×C149—22no—
74C23×C149C2×D411yescharacteristic
75D4×C149—22no—
76D4×C149—22no—
77D4×C149—44no—
78C2×C4×C149—21no—
79C2×C4×C149—21no—
80C2×C4×C149—22no—
81C2×C4×C149C2×D411yescharacteristic
82C2×C4×C149C2411yescharacteristic
83C8×C149—21no—
84C8×C149—21no—
85C22×C149—21no—
86C22×C149—22no—
87C22×C149—42no—
88C22×C149—42no—
89C22×C149—42no—
90C22×C149C22×D411yescharacteristic
91C4×C149—21no—
92C4×C149—42no—
93C4×C149H(5,𝔽2)11yescharacteristic
94C4×C1492−1+411yescharacteristic
95Dic149—22no—
96Dic149—22no—
97Dic149—42no—
98Dic149—42no—
99C2×C149—41no—
100C2×C149—82no—
101C2×C149#53711yescharacteristic
102C2×C149#57512yes—
103C149#325611yescharacteristic, complemented, Sylow
104#3256—1491nomaximal, Sylow
105#529—1492no—
106#479—1492no—
107#478—1492no—
108#470—1491no—
109#469D14911yescharacteristic
110#468—1492no—
111#464—1492no—
112#463—1492no—
113#423—1491no—
114C2×Q16—1491no—
115C2×SD16—1492no—
116C2×D8C2×D14911yescharacteristic
117C2×M16—1491no—
118C2×M16C2×D14911yescharacteristic
119#126—2982no—
120#125—1492no—
121#124—1492no—
122#123—2982no—
123C22⋊Q8—1492no—
124#121C2×D14912yes—
125C4×Q8—1492no—
126C4×D4—2982no—
127C4×D4—1492no—
128#117—2982no—
129C2×C42—1491no—
130#107—1492no—
131#106—1491no—
132#106C2×D14911yescharacteristic
133C4⋊C8—1492no—
134C4⋊C8—1492no—
135#103—1492no—
136#103—1492no—
137#102—1492no—
138#102C2×D14912yes—
139C2×Q8—1492no—
140C2×D4—22no—
141C2×D4C22×D14912yes—
142C22×C4—2982no—
143C22×C4—1492no—
144C22×C4C22×D14911yescharacteristic
145Q16—5961no—
146SD16—5962no—
147D8—41no—
148M16—41no—
149M16—5961no—
150C2×C8—1492no—
151C2×C8C22×D14911yescharacteristic
152C2×C8C22×D14911yescharacteristic
153C4⋊C4—2982no—
154C4⋊C4—2982no—
155C4⋊C4—2982no—
156C4⋊C4—2982no—
157C4⋊C4—1492no—
158C4⋊C4C22×D14912yes—
159C22⋊C4—22no—
160C22⋊C4—2982no—
161C22⋊C4—2982no—
162C22⋊C4—2982no—
163C22⋊C4—2982no—
164C42—2982no—
165C42—1491no—
166C42—1491no—
167C42—1492no—
168C23—22no—
169C23D4×D14911yescharacteristic
170Q8—2982no—
171Q8—2982no—
172D4—22no—
173D4—22no—
174D4—44no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—2982no—
179C2×C4—2982no—
180C2×C4—5962no—
181C2×C4—5964no—
182C2×C4—1492no—
183C2×C4—1492no—
184C2×C4D4×D14911yescharacteristic
185C2×C4C23×D14911yescharacteristic
186C8—21no—
187C8—21no—
188C8—2982no—
189C22—22no—
190C22—21no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22C2×D4×D14911yescharacteristic
195C4—21no—
196C4—42no—
197C4—2982no—
198C4—2982no—
199C4—5962no—
200C4—5962no—
201C4#1801195611yescharacteristic
202C4#1801195811yescharacteristic
203C2—41no—
204C2—82no—
205C2#2375020211yescharacteristic
206C2#2375042112yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting, prime radical#469×C149C2
socleC22×C149C22×D4
hypercenter#469D149
hypocenterC149#3256
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #23750156C2semidirect
2. #23749935C2semidirect
3. #23749927C2semidirect
4. #23749883C2semidirect
5. #23749869C2semidirect
6. #23749846C2semidirect
7. #23749838C2semidirect
8. #23749648C2semidirect
103. C149#3256semidirect

Maximal subgroups

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

subgroupindex
#237501562
#237499352
#237499272
#237498832
#237498692
#237498462
#237498382
#237496482
#469×C1492
#3256149