Finite Group Databasebeta

← #34056081

Subgroups — #34056081

Order 19072.

342 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 113 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#23749909C212yesmaximal, complemented
3#23749908C212yesmaximal, complemented
4#23749883C211yesmaximal, characteristic
5#23749881C212yesmaximal
6#23749834C212yesmaximal, complemented
7#23749833C212yesmaximal, complemented
8#23749648C211yesmaximal, characteristic
9#470×C149C211yesmaximal, characteristic
10C2×Dic596C2211yescharacteristic
11C2×#14558726C2212yes—
12C2×#14558720C2211yescharacteristic
13#18011910C2212yes—
14#18011909C2212yes—
15#18011901—22no—
16#18011890C2212yes—
17#18011888—22no—
18Q8×Dic149C2212yes—
19#18011876—22no—
20#18011876C2212yes—
21#18011867—22no—
22C2×C4×Dic149C2211yescharacteristic
23#18011843C2211yescharacteristic
24#18011842C2212yes—
25#18011840C2212yes—
26#18011840C2212yes—
27#18011836C2212yes—
28#18011835C2212yes—
29#18011834C2212yes—
30C2×Q16×C149C2211yescharacteristic
31C2×M16×C149C2211yescharacteristic
32C22⋊Q8×C149C2212yes—
33#106×C149C2211yescharacteristic
34#103×C149C2212yes—
35C2×Dic298—22no—
36C2×Dic298C2312yes—
37C22×Dic149D412yes—
38Dic596—41no—
39#14558726—42no—
40#14558720—41no—
41C2×#11924746C2312yes—
42C4⋊Dic149—22no—
43C4⋊Dic149C2312yes—
44#14558715—22no—
45#14558715—22no—
46#14558715—22no—
47#14558715—22no—
48#14558715—22no—
49C22⋊Dic149—22no—
50C4×Dic149—22no—
51C4×Dic149—22no—
52C4×Dic149D411yescharacteristic
53C4×Dic149D411yescharacteristic
54C4×Dic149C2312yes—
55C2×Q8×C149C2312yes—
56C22×C4×C149C2311yescharacteristic
57Q16×C149—41no—
58M16×C149—41no—
59C2×C8×C149C2311yescharacteristic
60C2×C8×C149C2311yescharacteristic
61C4⋊C4×C149—22no—
62C4⋊C4×C149C2312yes—
63C22⋊C4×C149—22no—
64Dic298—22no—
65Dic298—22no—
66Dic298—44no—
67C2×Dic149—24no—
68C2×Dic149—22no—
69C2×Dic149—22no—
70C2×Dic149C2×D412yes—
71C2×Dic149C2×D412yes—
72#11924746—22no—
73C23×C149C2×D411yescharacteristic
74Q8×C149—22no—
75Q8×C149—22no—
76C2×C4×C149—21no—
77C2×C4×C149—21no—
78C2×C4×C149—22no—
79C2×C4×C149—22no—
80C2×C4×C149C2×D411yescharacteristic
81C2×C4×C149C2411yescharacteristic
82C8×C149—21no—
83C8×C149—21no—
84C22×C149—21no—
85C22×C149—22no—
86C22×C149C22×D411yescharacteristic
87C4×C149—21no—
88C4×C149—42no—
89C4×C149—42no—
90C4×C149H(5,𝔽2)11yescharacteristic
91C4×C1492−1+411yescharacteristic
92Dic149—22no—
93Dic149—42no—
94Dic149—42no—
95Dic149#13714yes—
96C2×C149—41no—
97C2×C149#53711yescharacteristic
98C2×C149C2×#13712yes—
99C149#325511yescharacteristic, complemented, Sylow
100#3255—1491nomaximal, Sylow
101#533—1492no—
102#475—1492no—
103#475—1492no—
104#470—1491no—
105#470—1492no—
106#470D14911yescharacteristic
107#462—1492no—
108#462—1492no—
109#423—1491no—
110C2×Q16—1492no—
111C2×Q16—1491no—
112C2×Q16C2×D14911yescharacteristic
113C2×M16—1491no—
114C2×M16C2×D14911yescharacteristic
115C4⋊Q8—1492no—
116C4⋊Q8—1492no—
117#125—2982no—
118C22⋊Q8—2982no—
119C22⋊Q8—1492no—
120C22⋊Q8C2×D14912yes—
121C4×Q8—2982no—
122C4×Q8—1492no—
123C4×Q8—1492no—
124#117—2982no—
125C2×C42—1491no—
126#106—1491no—
127#106—1492no—
128#106C2×D14911yescharacteristic
129C4⋊C8—1492no—
130C4⋊C8—1492no—
131#103—1492no—
132#103—1492no—
133#103—1492no—
134#103C2×D14912yes—
135C2×Q8—2982no—
136C2×Q8—1492no—
137C2×Q8C22×D14912yes—
138C22×C4—1492no—
139C22×C4C22×D14911yescharacteristic
140Q16—41no—
141Q16—5961no—
142Q16—5962no—
143M16—41no—
144M16—5961no—
145C2×C8—1492no—
146C2×C8C22×D14911yescharacteristic
147C2×C8C22×D14911yescharacteristic
148C4⋊C4—22no—
149C4⋊C4—2982no—
150C4⋊C4—2982no—
151C4⋊C4—2982no—
152C4⋊C4—2982no—
153C4⋊C4—2982no—
154C4⋊C4—2982no—
155C4⋊C4—1492no—
156C4⋊C4C22×D14912yes—
157C22⋊C4—22no—
158C22⋊C4—2982no—
159C42—2982no—
160C42—2982no—
161C42—1491no—
162C42—1491no—
163C42—1492no—
164C23D4×D14911yescharacteristic
165Q8—22no—
166Q8—22no—
167Q8—2982no—
168Q8—2982no—
169Q8—5964no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—2984no—
175C2×C4—2982no—
176C2×C4—2982no—
177C2×C4—1492no—
178C2×C4—1492no—
179C2×C4D4×D14911yescharacteristic
180C2×C4C23×D14911yescharacteristic
181C8—21no—
182C8—21no—
183C8—2982no—
184C22—22no—
185C22—21no—
186C22C2×D4×D14911yescharacteristic
187C4—21no—
188C4—42no—
189C4—42no—
190C4—2982no—
191C4—5962no—
192C4—5962no—
193C4—1494no—
194C4#1801195611yescharacteristic
195C4#1801195811yescharacteristic
196C2—41no—
197C2#2375020211yescharacteristic
198C2#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#3255
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. #23749909C2semidirect
3. #23749908C2semidirect
6. #23749834C2semidirect
7. #23749833C2semidirect
99. C149#3255semidirect

Maximal subgroups

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

subgroupindex
#237501772
#237499092
#237499082
#237498832
#237498812
#237498342
#237498332
#237496482
#470×C1492
#3255149