Finite Group Databasebeta

← #34043828

Subgroups — #34043828

Order 19072.

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

normal subgroups only

This group has 214 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#23750335C211yesmaximal, characteristic
2#23750005C211yesmaximal, characteristic, complemented
3#23749920C211yesmaximal, characteristic, complemented
4#23749916C211yesmaximal, characteristic
5#23749373C211yesmaximal, characteristic, complemented
6#23749354C211yesmaximal, characteristic
7Q8⋊C8×C149C211yesmaximal, characteristic, complemented
8C2×Dic596—22no—
9#18011911C2211yescharacteristic
10#18011911C2211yescharacteristic
11#18011903—21no—
12#18011889—22no—
13#18011887—21no—
14C4×D596—21no—
15C4×D596C2211yescharacteristic
16C4⋊C4×D149—21no—
17#18011844—21no—
18#18011843—21no—
19C4⋊#11924746C2211yescharacteristic
20#18011835—21no—
21#18011833—21no—
22C4×Q8×C149C2211yescharacteristic
23C4⋊C8×C149C2211yescharacteristic
24C4×C8×C149C2211yescharacteristic
25C2×Dic298—21no—
26C2×Dic298D412yes—
27C2×D596D411yescharacteristic
28C2×C4×D149—22no—
29C2×C4×D149—21no—
30Dic596—44no—
31C2×#11924746—21no—
32C4⋊Dic149—21no—
33C4⋊Dic149—21no—
34C4⋊Dic149—21no—
35C4⋊Dic149—21no—
36C4⋊Dic149D411yescharacteristic
37#14558715—22no—
38#14558715—22no—
39#14558713—22no—
40#14558713—21no—
41C2×Q8×C149D411yescharacteristic
42C2×C8×C149—21no—
43C2×C8×C149—21no—
44C4⋊C4×C149—21no—
45C4⋊C4×C149D411yescharacteristic
46C42×C149—21no—
47C42×C149C2311yescharacteristic
48C22×D149—21no—
49Dic298—42no—
50Dic298—42no—
51D596—21no—
52D596Q1612yescomplemented
53C2×Dic149—22no—
54C2×Dic149—21no—
55C2×Dic149—41no—
56C4×D149—41no—
57C4×D149—41no—
58C4×D149—82no—
59#11924746—41no—
60Q8×C149—21no—
61Q8×C149—21no—
62C2×C4×C149—21no—
63C2×C4×C149—21no—
64C2×C4×C149C2×D411yescharacteristic
65C2×C4×C149C2×D411yescharacteristic
66C2×C4×C149C2×D411yescharacteristic
67C8×C149—22no—
68C8×C149—41no—
69C22×C149#12011yescharacteristic
70C2×D149—22no—
71C2×D149—41no—
72C2×D149—41no—
73C4×C149—21no—
74C4×C149—41no—
75C4×C149—41no—
76C4×C149C2×Q1611yescharacteristic
77C4×C149#13511yescharacteristic
78C4×C149#13711yescharacteristic
79C4×C149#13711yescharacteristic
80Dic149—41no—
81Dic149—42no—
82Dic149—81no—
83C2×C149#45111yescharacteristic
84C2×C149#45211yescharacteristic
85C2×C149#45311yescharacteristic
86D149—42no—
87C149#163211yescharacteristic, complemented, Sylow
88#1632—1491nomaximal, Sylow
89#554—1491no—
90#494—1491no—
91#477—1491no—
92#476—1491no—
93#333—1491no—
94Q8⋊C8D14911yescharacteristic, complemented
95D4⋊C8—1491no—
96C2×Q16—2982no—
97C4⋊Q8—1491no—
98C4⋊Q8—1491no—
99#125—2981no—
100C22⋊Q8—2982no—
101C22⋊Q8—2981no—
102C4×Q8C2×D14911yescharacteristic
103C4×D4—2981no—
104C4×D4—1491no—
105C2×C4⋊C4—2981no—
106#107—2981no—
107#106—2981no—
108C4⋊C8—1491no—
109C4⋊C8C2×D14911yescharacteristic
110#103—2981no—
111#102—2981no—
112C4×C8C2×D14911yescharacteristic
113C2×Q8—2981no—
114C2×Q8—1492no—
115C2×Q8D59611yescharacteristic
116C2×D4—1491no—
117C22×C4—2982no—
118C22×C4—2981no—
119Q16—5964no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—2981no—
123C4⋊C4—21no—
124C4⋊C4—2982no—
125C4⋊C4—2982no—
126C4⋊C4—2981no—
127C4⋊C4—2981no—
128C4⋊C4—2981no—
129C4⋊C4—2981no—
130C4⋊C4—1491no—
131C4⋊C4D59611yescharacteristic
132C22⋊C4—2982no—
133C22⋊C4—2981no—
134C42—21no—
135C42C22×D14911yescharacteristic
136C23—2981no—
137Q8—21no—
138Q8—21no—
139Q8—5962no—
140Q8—5962no—
141D4—2981no—
142D4—1492no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—2981no—
146C2×C4—2982no—
147C2×C4—5961no—
148C2×C4—5961no—
149C2×C4—5961no—
150C2×C4—11922no—
151C2×C4D4×D14911yescharacteristic
152C2×C4D4×D14911yescharacteristic
153C2×C4C2×D59611yescharacteristic
154C8—22no—
155C8—41no—
156C8—5961no—
157C22—2982no—
158C22—5961no—
159C22—5961no—
160C22#1801188111yescharacteristic
161C4—21no—
162C4—41no—
163C4—41no—
164C4—5961no—
165C4—5962no—
166C4—11921no—
167C4Q16×D14911yescharacteristic
168C4#1801193311yescharacteristic
169C4#1801194011yescharacteristic
170C4#1801194411yescharacteristic
171C2—5962no—
172C2#2374978211yescharacteristic
173C2#2374978911yescharacteristic
174C2#2374979411yescharacteristic
subgroupG/H
centerC22#18011881
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
FittingQ8⋊C8×C149C2
socleC22×C149#120
prime radicalC2×D596D4
hypercenterQ8⋊C8D149
hypocenterC149#1632
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #23750005C2semidirect
3. #23749920C2semidirect
5. #23749373C2semidirect
7. Q8⋊C8×C149C2semidirect
52. D596Q16semidirect
87. C149#1632semidirect
94. Q8⋊C8D149semidirect

Maximal subgroups

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

subgroupindex
#237503352
#237500052
#237499202
#237499162
#237493732
#237493542
Q8⋊C8×C1492
#1632149