Finite Group Databasebeta

← #34043201

Subgroups — #34043201

Order 19072.

228 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 63 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#23750177C211yesmaximal, characteristic
2#23749679C211yesmaximal, characteristic
3#23749470C211yesmaximal, characteristic
4#23749363C211yesmaximal, characteristic
5#23749362C211yesmaximal, characteristic
6#23749361C211yesmaximal, characteristic
7#328×C149C211yesmaximal, characteristic
8#18011910C411yescharacteristic, complemented
9#18011909C411yescharacteristic, complemented
10#18011901—21no—
11#18011890C2211yescharacteristic
12#18011888—21no—
13Q8×Dic149C411yescharacteristic, complemented
14#18011876—21no—
15#18011876C411yescharacteristic, complemented
16#18011867—21no—
17C2×C4×Dic149—21no—
18C2×C4×Dic149C2211yescharacteristic
19#18011840—21no—
20C22⋊#11924746C2211yescharacteristic
21#18011821—21no—
22#18011818—21no—
23#18011818C2211yescharacteristic
24C22⋊Q8×C149C2211yescharacteristic
25C22⋊C8×C149C2211yescharacteristic
26#95×C149C2211yescharacteristic
27C2×Dic298—21no—
28C2×Dic298C2×C411yescharacteristic
29C22×Dic149—21no—
30C22×Dic149D411yescharacteristic
31C22×Dic149D411yescharacteristic
32C2×#11924746—21no—
33C4⋊Dic149—21no—
34C4⋊Dic149C2×C411yescharacteristic
35#14558715—21no—
36#14558715—21no—
37#14558715—21no—
38#14558715—21no—
39#14558715—21no—
40C22⋊Dic149—21no—
41C4×Dic149—24no—
42C4×Dic149—21no—
43C4×Dic149—21no—
44C4×Dic149C2×C411yescharacteristic
45C4×Dic149C2×C411yescharacteristic
46C4×Dic149D411yescharacteristic
47C4×Dic149D411yescharacteristic
48C2×Q8×C149C2×C411yescharacteristic
49C22×C4×C149—21no—
50C22×C4×C149C2311yescharacteristic
51C2×C8×C149—21no—
52C4⋊C4×C149—21no—
53C4⋊C4×C149C2×C411yescharacteristic
54C22⋊C4×C149—21no—
55Dic298—42no—
56Dic298—41no—
57C2×Dic149—21no—
58C2×Dic149—21no—
59C2×Dic149—22no—
60C2×Dic149—22no—
61C2×Dic149—21no—
62C2×Dic149—21no—
63C2×Dic149—41no—
64C2×Dic149—41no—
65C2×Dic149C22⋊C411yescharacteristic
66C2×Dic149C22⋊C411yescharacteristic
67C2×Dic149C22⋊C411yescharacteristic
68C2×Dic149C22⋊C411yescharacteristic
69#11924746—41no—
70C23×C149C2×D411yescharacteristic
71Q8×C149—41no—
72C2×C4×C149—22no—
73C2×C4×C149—21no—
74C2×C4×C149—21no—
75C2×C4×C149—41no—
76C2×C4×C149—41no—
77C2×C4×C149—41no—
78C2×C4×C149C22×C411yescharacteristic
79C2×C4×C149C2×D411yescharacteristic
80C8×C149—41no—
81C22×C149—21no—
82C22×C149—21no—
83C22×C149C2×C22⋊C411yescharacteristic
84C22×C149#13711yescharacteristic
85C22×C149#13711yescharacteristic
86C4×C149—21no—
87C4×C149—21no—
88C4×C149—42no—
89C4×C149—41no—
90C4×C149—41no—
91Dic149—21no—
92Dic149—21no—
93Dic149—21no—
94Dic149—42no—
95Dic149—41no—
96Dic149—41no—
97Dic149#10412yes—
98C2×C149—21no—
99C2×C149—21no—
100C2×C149#41011yescharacteristic
101C2×C149#41911yescharacteristic
102C2×C149C2×#10411yescharacteristic
103C149#150611yescharacteristic, complemented, Sylow
104#1506—1491nomaximal, Sylow
105#533—1491no—
106#432—1491no—
107#376—1491no—
108#328—1491no—
109#328—1491no—
110#328—1491no—
111#328D14911yescharacteristic
112C4⋊Q8—1491no—
113C4⋊Q8—1491no—
114#125—2981no—
115C22⋊Q8—2981no—
116C22⋊Q8—1491no—
117C22⋊Q8C2×D14911yescharacteristic
118C4×Q8—2981no—
119C4×Q8—1491no—
120C4×Q8—1491no—
121#117—2981no—
122C2×C42—2981no—
123C2×C42—1491no—
124C4⋊C8—2981no—
125C22⋊C8—1491no—
126C22⋊C8C2×D14911yescharacteristic
127#97—2981no—
128#95—2981no—
129#95—1491no—
130#95C2×D14911yescharacteristic
131C2×Q8—2981no—
132C2×Q8—1491no—
133C2×Q8C4×D14911yescharacteristic
134C22×C4—21no—
135C22×C4—2981no—
136C22×C4—1491no—
137C22×C4—1491no—
138C22×C4C22×D14911yescharacteristic
139C2×C8—21no—
140C2×C8—2981no—
141C4⋊C4—21no—
142C4⋊C4—2981no—
143C4⋊C4—2981no—
144C4⋊C4—2981no—
145C4⋊C4—2981no—
146C4⋊C4—2981no—
147C4⋊C4—2981no—
148C4⋊C4—1491no—
149C4⋊C4C4×D14911yescharacteristic
150C22⋊C4—21no—
151C22⋊C4—2981no—
152C42—2984no—
153C42—2981no—
154C42—2981no—
155C42—1491no—
156C42—1491no—
157C42—1491no—
158C42—1491no—
159C23D4×D14911yescharacteristic
160Q8—41no—
161Q8—5961no—
162Q8—5962no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—2981no—
170C2×C4—2981no—
171C2×C4—2982no—
172C2×C4—2982no—
173C2×C4—2981no—
174C2×C4—2981no—
175C2×C4—5961no—
176C2×C4—5961no—
177C2×C4—1491no—
178C2×C4—1491no—
179C2×C4—1491no—
180C2×C4—1491no—
181C2×C4C2×C4×D14911yescharacteristic
182C2×C4D4×D14911yescharacteristic
183C8—41no—
184C8—5961no—
185C22—21no—
186C22—21no—
187C22C22⋊C4×D14911yescharacteristic
188C22#1801194011yescharacteristic
189C22#1801194311yescharacteristic
190C4—21no—
191C4—21no—
192C4—42no—
193C4—41no—
194C4—41no—
195C4—2981no—
196C4—2981no—
197C4—2981no—
198C4—5962no—
199C4—5961no—
200C4—5961no—
201C4—1492no—
202C2—21no—
203C2—21no—
204C2#2374959711yescharacteristic
205C2#2374963211yescharacteristic
206C2#104×D14911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D149
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
Fitting#328×C149C2
socleC22×C149C2×C22⋊C4
prime radicalC23×C149C2×D4
cosocleC22×C4×C149C23
hypercenter#328D149
hypocenterC149#1506
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #18011910C4semidirect
9. #18011909C4semidirect
13. Q8×Dic149C4semidirect
15. #18011876C4semidirect
103. C149#1506semidirect

Maximal subgroups

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

subgroupindex
#237501772
#237496792
#237494702
#237493632
#237493622
#237493612
#328×C1492
#1506149