Finite Group Databasebeta

← #34032814

Subgroups — #34032814

Order 18688.

242 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 45 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#22627005C212yesmaximal
2#22626058C211yesmaximal, characteristic
3#17989706—22no—
4C2×#14556654—22no—
5C4×#11924036C2211yescharacteristic
6#17989533C411yescharacteristic
7C4⋊Q8×D73C411yescharacteristic
8#14556688—24no—
9#14556687—42no—
10#14556686—42no—
11C2×#11924036D412yes—
12C2×C4⋊#64408—21no—
13C2×C4⋊#64408—41no—
14#14556654—42no—
15#14556654—42no—
16C4×#10596833—41no—
17C2×Q8×D73—21no—
18#14556591C811yescharacteristic
19#14556590—41no—
20#14556589—21no—
21C4⋊C4×D73—41no—
22C42×D73C2×C411yescharacteristic
23C4⋊Q8×C73C811yescharacteristic
24#11924040—44no—
25C22×#64408—41no—
26#11924036—22no—
27#11924036D812yes—
28#11924036SD1612yes—
29C2×#10596833—22no—
30C4⋊#64408—42no—
31C4⋊#64408—82no—
32C2×Dic146—21no—
33C2×Dic146—41no—
34Q8×D73—42no—
35Q8×D73—42no—
36C2×C4×D73—21no—
37C2×C4×D73—41no—
38C2×C4×D73C22⋊C411yescharacteristic
39C4⋊Dic73—41no—
40#11924007—42no—
41C4×Dic73—21no—
42C4×Dic73M1611yescharacteristic
43C2×Q8×C73—21no—
44C4⋊C4×C73—41no—
45C42×C73C2×C811yescharacteristic
46C22×D73#10011yescharacteristic
47C2×#64408—82no—
48C2×#64408—81no—
49Q8×C73—42no—
50C2×C4×C73—21no—
51C2×C4×C73—41no—
52C2×C4×C73C22⋊C811yescharacteristic
53C2×Dic73—21no—
54C2×Dic73—41no—
55C2×Dic73#9911yescharacteristic
56C4×D73—22no—
57C4×D73—22no—
58C4×D73—81no—
59C4×D73—81no—
60C4×D73#10212yes—
61C4×D73#10412yes—
62Dic146—42no—
63Dic146—82no—
64#10596833—22no—
65#10596833—22no—
66C22×C73#32311yescharacteristic
67C2×D73—21no—
68C2×D73—21no—
69C2×D73#32911yescharacteristic
70C2×D73#33111yescharacteristic
71#64408—161no—
72C4×C73—22no—
73C4×C73—81no—
74C4×C73D4⋊C812yes—
75Dic73—22no—
76Dic73—81no—
77Dic73#32712yes—
78#7108—731nomaximal, Sylow
79C2×C73—21no—
80C2×C73#127011yescharacteristic
81D73—21no—
82D73#135811yescharacteristic
83D73#135911yescharacteristic
84#1956—731no—
85#1376—732no—
86C73#710811yescharacteristic, complemented, Sylow
87C2×C4⋊Q8—731no—
88C2×M32—1462no—
89C2×#103—1462no—
90C2×C4×C8—731no—
91#384—731no—
92C22×Q8—1461no—
93C22×C8—732no—
94C4⋊Q8—2921no—
95C4⋊Q8—731no—
96C4⋊Q8—1461no—
97C4⋊Q8#1059684211yescharacteristic
98C2×C4⋊C4—2921no—
99C2×C4⋊C4—2921no—
100C2×C4⋊C4—1461no—
101C2×C42—731no—
102M32—2922no—
103M32—1464no—
104C2×C16—2922no—
105#103—2922no—
106#103—2922no—
107C4×C8—2921no—
108C2×Q8—21no—
109C2×Q8—2921no—
110C2×Q8—2922no—
111C2×Q8—2922no—
112C2×Q8—1461no—
113C22×C4—2921no—
114C22×C4—2921no—
115C22×C4—731no—
116C22×C4—1461no—
117C2×C8—732no—
118C2×C8—732no—
119C2×C8—1462no—
120C2×C8—1462no—
121C4⋊C4—41no—
122C4⋊C4—2921no—
123C4⋊C4—2922no—
124C4⋊C4—2922no—
125C4⋊C4—5842no—
126C42—731no—
127C42—1461no—
128C42C2×#1059684211yescharacteristic
129C16—2924no—
130C23—731no—
131Q8—42no—
132Q8—2922no—
133Q8—5842no—
134C2×C4—21no—
135C2×C4—41no—
136C2×C4—2921no—
137C2×C4—5841no—
138C2×C4—5841no—
139C2×C4—5841no—
140C2×C4—5842no—
141C2×C4—731no—
142C2×C4—732no—
143C2×C4—732no—
144C2×C4—1462no—
145C2×C4—1462no—
146C2×C4—1461no—
147C2×C4C22⋊#1059684211yescharacteristic
148C8—1462no—
149C8—1462no—
150C22—731no—
151C22—731no—
152C22—1461no—
153C22—1461no—
154C22#1798967211yescharacteristic
155C4—22no—
156C4—81no—
157C4—5841no—
158C4—732no—
159C4—11681no—
160C4—1462no—
161C4D4⋊#1059684212yes—
162C2—21no—
163C2—731no—
164C2—731no—
165C2—1461no—
166C2#2262693011yescharacteristic
subgroupG/H
centerC2#22626930
commutatorC42×C73C2×C8
FrattiniC42C2×#10596842
FittingC4⋊Q8×C73C8
socleC2×C73#1270
prime radicalC22×D73#100
cosocleC4×#11924036C22
hypercenterC4⋊Q8#10596842
hypocenterC73#7108
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
86. C73#7108semidirect

Maximal subgroups

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

subgroupindex
#226270052
#226260582
#710873