Finite Group Databasebeta

← #34043876

Subgroups — #34043876

Order 19072.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#23750360C211yesmaximal, characteristic
2#23749973C211yesmaximal, characteristic
3#23749832C211yesmaximal, characteristic, complemented
4#23749368C211yesmaximal, characteristic
5Q8⋊#11924746C211yesmaximal, characteristic, complemented
6#23749355C211yesmaximal, characteristic, complemented
7#475×C149C211yesmaximal, characteristic, complemented
8C2×#14558726—21no—
9#18011908C2211yescharacteristic
10#18011900—21no—
11#18011899—21no—
12#18011896—22no—
13C4×Dic298C2211yescharacteristic
14C4×D596—21no—
15#18011873—21no—
16C4⋊#11924746C2211yescharacteristic
17#18011835—21no—
18#18011831—22no—
19C4×#11924746C2211yescharacteristic
20C4⋊Q8×C149C2211yescharacteristic
21C4×Q8×C149C2211yescharacteristic
22#106×C149—21no—
23C4⋊C8×C149C2211yescharacteristic
24#103×C149—21no—
25C2×Dic298D411yescharacteristic
26C2×D596—21no—
27C2×D596—21no—
28C2×D596D412yes—
29C2×C4×D149—22no—
30#14558726—42no—
31C2×#11924746—21no—
32C2×#11924746—21no—
33C4⋊Dic149D411yescharacteristic
34#14558715—21no—
35#14558713—22no—
36#14558713—22no—
37#14558713—22no—
38C4×Dic149—21no—
39C2×Q8×C149—21no—
40C2×Q8×C149D411yescharacteristic
41C2×C8×C149—21no—
42C4⋊C4×C149—21no—
43C4⋊C4×C149—21no—
44C4⋊C4×C149—21no—
45C4⋊C4×C149D411yescharacteristic
46C42×C149—21no—
47C42×C149C2311yescharacteristic
48C22×D149—22no—
49Dic298—21no—
50Dic298—21no—
51D596—42no—
52D596—41no—
53D596—41no—
54D596—41no—
55D596—41no—
56C2×Dic149—21no—
57C2×Dic149—21no—
58C4×D149—82no—
59#11924746—41no—
60#11924746—41no—
61Q8×C149—21no—
62Q8×C149—21no—
63Q8×C149—41no—
64Q8×C149—41no—
65C2×C4×C149—21no—
66C2×C4×C149—21no—
67C2×C4×C149—41no—
68C2×C4×C149C2×D411yescharacteristic
69C2×C4×C149C2×D411yescharacteristic
70C2×C4×C149C2×D411yescharacteristic
71C8×C149—41no—
72C22×C149#12011yescharacteristic
73C2×D149—42no—
74C2×D149—42no—
75C2×D149—42no—
76C4×C149—21no—
77C4×C149—41no—
78C4×C149—41no—
79C4×C149—81no—
80C4×C149#13511yescharacteristic
81C4×C149#13511yescharacteristic
82C4×C149AGL(1,ℤ/8)11yescharacteristic
83C4×C149#13711yescharacteristic
84Dic149—41no—
85Dic149—41no—
86C2×C149#44911yescharacteristic
87C2×C149#45211yescharacteristic
88C2×C149#45511yescharacteristic
89D149—82no—
90C149#164011yescharacteristic, complemented, Sylow
91#1640—1491nomaximal, Sylow
92#559—1491no—
93#486—1491no—
94#475D14911yescharacteristic, complemented
95#462—1491no—
96#331—1491no—
97Q8⋊C8—1491no—
98Q8⋊C8—1491no—
99C2×Q16—2981no—
100C4⋊Q8C2×D14911yescharacteristic
101#127—1491no—
102#124—2981no—
103#124—2981no—
104#123—2982no—
105C4×Q8—1491no—
106C4×Q8C2×D14911yescharacteristic
107C4×D4—2981no—
108C4×D4—2981no—
109#106—21no—
110C4⋊C8—1491no—
111C4⋊C8C2×D14911yescharacteristic
112#103—21no—
113#103—2981no—
114#102—2982no—
115C4×C8—1491no—
116C2×Q8—21no—
117C2×Q8—1491no—
118C2×Q8C22⋊D14911yescharacteristic
119C2×D4—2981no—
120C2×D4—2981no—
121C2×D4—1492no—
122C22×C4—2982no—
123Q16—5962no—
124C2×C8—21no—
125C2×C8—2981no—
126C2×C8—2981no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—2981no—
131C4⋊C4—1491no—
132C4⋊C4C22⋊D14911yescharacteristic
133C22⋊C4—2982no—
134C22⋊C4—2982no—
135C22⋊C4—2982no—
136C42—21no—
137C42—2981no—
138C42C22×D14911yescharacteristic
139C23—2982no—
140Q8—21no—
141Q8—21no—
142Q8—41no—
143Q8—41no—
144Q8—2981no—
145Q8—2981no—
146D4—5962no—
147D4—5961no—
148D4—5961no—
149D4—5961no—
150D4—5961no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—2981no—
155C2×C4—2981no—
156C2×C4—11922no—
157C2×C4D4×D14911yescharacteristic
158C2×C4D4×D14911yescharacteristic
159C2×C4C2×C22⋊D14911yescharacteristic
160C8—41no—
161C8—5961no—
162C8—5961no—
163C22—5962no—
164C22—5962no—
165C22—5962no—
166C22#1801187911yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—81no—
171C4—5961no—
172C4—5961no—
173C4#1801193111yescharacteristic
174C4#1801193211yescharacteristic
175C4#1801193811yescharacteristic
176C4#1801194211yescharacteristic
177C2—11922no—
178C2#2374976911yescharacteristic
179C2#2374978511yescharacteristic
180C2#2374980111yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
Fitting#475×C149C2
socleC22×C149#120
prime radical#18011908C22
hypercenter#475D149
hypocenterC149#1640
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. #23749832C2semidirect
5. Q8⋊#11924746C2semidirect
6. #23749355C2semidirect
7. #475×C149C2semidirect
90. C149#1640semidirect
94. #475D149semidirect

Maximal subgroups

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

subgroupindex
#237503602
#237499732
#237498322
#237493682
Q8⋊#119247462
#237493552
#475×C1492
#1640149