Finite Group Databasebeta

← #34043839

Subgroups — #34043839

Order 19072.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#23750278C211yesmaximal, characteristic
2#23749912C211yesmaximal, characteristic, complemented
3#23749912C211yesmaximal, characteristic, complemented
4#23749371C211yesmaximal, characteristic, complemented
5#23749354C211yesmaximal, characteristic, complemented
6#23749354C211yesmaximal, characteristic, complemented
7#487×C149C211yesmaximal, characteristic, complemented
8C2×#14558737—21no—
9#18011896—22no—
10#18011887—21no—
11#18011886—21no—
12C4×D596C2211yescharacteristic
13C4×D596C2211yescharacteristic
14C4⋊C4×D149—21no—
15#18011842—21no—
16#18011842—21no—
17C4⋊#11924746C2211yescharacteristic
18C4⋊#11924746C2211yescharacteristic
19#18011831—21no—
20#18011831—21no—
21C4⋊Q8×C149C2211yescharacteristic
22C4⋊Q8×C149C2211yescharacteristic
23#103×C149—22no—
24C4×C8×C149C2211yescharacteristic
25#14558737—42no—
26#14558737—42no—
27C2×D596—22no—
28C2×D596D411yescharacteristic
29C2×D596D411yescharacteristic
30C2×C4×D149—22no—
31C2×C4×D149—21no—
32C2×C4×D149—21no—
33C2×#11924746—21no—
34C2×#11924746—21no—
35C4⋊Dic149D411yescharacteristic
36C4⋊Dic149D411yescharacteristic
37#14558715—22no—
38#14558713—22no—
39#14558713—21no—
40#14558713—21no—
41C2×Q8×C149—21no—
42C2×Q8×C149—21no—
43C2×C8×C149—21no—
44C4⋊C4×C149—21no—
45C4⋊C4×C149—21no—
46C4⋊C4×C149—21no—
47C4⋊C4×C149D412yes—
48C42×C149C2311yescharacteristic
49C22×D149—21no—
50C22×D149—21no—
51D596—21no—
52D596—21no—
53D596—21no—
54D596—44no—
55D596SD1612yes—
56C2×Dic149—21no—
57C2×Dic149—21no—
58C4×D149—44no—
59C4×D149—41no—
60C4×D149—41no—
61C4×D149—41no—
62C4×D149—41no—
63#11924746—41no—
64#11924746—41no—
65Q8×C149—42no—
66Q8×C149—41no—
67Q8×C149—41no—
68C2×C4×C149—22no—
69C2×C4×C149—41no—
70C2×C4×C149C2×D411yescharacteristic
71C2×C4×C149C2×D411yescharacteristic
72C2×C4×C149C2×D411yescharacteristic
73C8×C149—41no—
74C22×C149#12011yescharacteristic
75C2×D149—22no—
76C2×D149—41no—
77C2×D149—41no—
78C2×D149—41no—
79C2×D149—41no—
80C2×D149—41no—
81C4×C149—21no—
82C4×C149—42no—
83C4×C149—81no—
84C4×C149C2×SD1611yescharacteristic
85C4×C149#13511yescharacteristic
86C4×C149AGL(1,ℤ/8)11yescharacteristic
87C4×C149#13711yescharacteristic
88Dic149—41no—
89Dic149—41no—
90C2×C149#45011yescharacteristic
91C2×C149#45211yescharacteristic
92C2×C149#45411yescharacteristic
93D149—42no—
94D149—81no—
95C149#163511yescharacteristic, complemented, Sylow
96#1635—1491nomaximal, Sylow
97#547—1491no—
98#487D14911yescharacteristic, complemented
99#476—1491no—
100#476—1491no—
101#332—1491no—
102D4⋊C8—1491no—
103D4⋊C8—1491no—
104C2×#41—2981no—
105C4⋊Q8C2×D14911yescharacteristic
106C4⋊Q8C2×D14911yescharacteristic
107#123—2982no—
108C22⋊Q8—2981no—
109#121—2981no—
110C4×D4—1491no—
111C4×D4—1491no—
112C2×C4⋊C4—2981no—
113#106—2981no—
114#106—2981no—
115C4⋊C8—1491no—
116C4⋊C8—1491no—
117#103—22no—
118#102—2981no—
119#102—2981no—
120C4×C8C2×D14911yescharacteristic
121#41—5962no—
122#41—5962no—
123C2×Q8—21no—
124C2×Q8—21no—
125C2×D4—2982no—
126C2×D4—1491no—
127C2×D4—1491no—
128C22×C4—2982no—
129C22×C4—2981no—
130C22×C4—2981no—
131C2×C8—21no—
132C2×C8—2981no—
133C2×C8—2981no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—2982no—
138C4⋊C4—1491no—
139C4⋊C4—1491no—
140C4⋊C4C22⋊D14912yes—
141C22⋊C4—2982no—
142C22⋊C4—2981no—
143C22⋊C4—2981no—
144C42C22×D14911yescharacteristic
145C23—2981no—
146C23—2981no—
147Q8—42no—
148Q8—41no—
149Q8—41no—
150D4—2981no—
151D4—2981no—
152D4—2981no—
153D4—5964no—
154D4—1492no—
155C2×C4—22no—
156C2×C4—41no—
157C2×C4—2981no—
158C2×C4—2981no—
159C2×C4—5964no—
160C2×C4—5961no—
161C2×C4—5961no—
162C2×C4—5961no—
163C2×C4—5961no—
164C2×C4D4×D14911yescharacteristic
165C2×C4D4×D14911yescharacteristic
166C2×C4C2×C22⋊D14911yescharacteristic
167C8—41no—
168C8—5961no—
169C8—5961no—
170C22—2982no—
171C22—5961no—
172C22—5961no—
173C22—5961no—
174C22—5961no—
175C22—5961no—
176C22#1801187911yescharacteristic
177C4—21no—
178C4—42no—
179C4—81no—
180C4—5961no—
181C4—5961no—
182C4SD16×D14911yescharacteristic
183C4#1801193411yescharacteristic
184C4#1801193811yescharacteristic
185C4#1801194311yescharacteristic
186C2—5962no—
187C2—11921no—
188C2#2374977411yescharacteristic
189C2#2374978611yescharacteristic
190C2#2374979711yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
Fitting#487×C149C2
socleC22×C149#120
prime radical#23750278C2
hypercenter#487D149
hypocenterC149#1635
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #23749912C2semidirect
3. #23749912C2semidirect
4. #23749371C2semidirect
5. #23749354C2semidirect
6. #23749354C2semidirect
7. #487×C149C2semidirect
95. C149#1635semidirect
98. #487D149semidirect

Maximal subgroups

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

subgroupindex
#237502782
#237499122
#237493712
#237493542
#487×C1492
#1635149