Finite Group Databasebeta

← #34032810

Subgroups — #34032810

Order 18688.

268 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 47 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#22627007C212yesmaximal, complemented
2#22626057C211yesmaximal, characteristic
3C2×#14556687—22no—
4C2×#14556658C411yescharacteristic
5C2×#14556648—22no—
6C2×#14556646C2211yescharacteristic
7C2×#14556553C411yescharacteristic
8#14556687—24no—
9#14556687—42no—
10C2×#11924040—42no—
11C22×#10596833—21no—
12C22×#10596833D412yes—
13#14556658—41no—
14#14556648—42no—
15#14556648—42no—
16#14556646—41no—
17C22×D292C811yescharacteristic
18C22×C4×D73—21no—
19#14556553—41no—
20#14556553—41no—
21C2×#11924005—21no—
22C2×C4×Dic73C2×C411yescharacteristic
23C2×C4⋊C4×C73C811yescharacteristic
24#11924040—44no—
25C2×#10596833—22no—
26C2×#10596833—22no—
27C2×#10596833—41no—
28C2×#10596833—42no—
29C2×#10596833D812yes—
30C2×#10596833SD1612yes—
31C23×D73—21no—
32C2×D292—41no—
33C2×D292—42no—
34C22×Dic73C22⋊C411yescharacteristic
35C22×Dic73M1611yescharacteristic
36C2×C4×D73—41no—
37C2×C4×D73—41no—
38C2×C4×D73—42no—
39C2×C4×D73—42no—
40#11924005—42no—
41C4×Dic73—21no—
42C4×Dic73—21no—
43C22×C4×C73—21no—
44C22×C4×C73C2×C811yescharacteristic
45C4⋊C4×C73—41no—
46C23×C73C22⋊C811yescharacteristic
47C22×D73—22no—
48C22×D73—41no—
49C22×D73—42no—
50C22×D73—41no—
51C22×D73—42no—
52C2×C4×C73—21no—
53C2×C4×C73—41no—
54C2×C4×C73—41no—
55C2×C4×C73—42no—
56C2×Dic73—21no—
57C2×Dic73—41no—
58C2×Dic73#9911yescharacteristic
59C2×Dic73#10011yescharacteristic
60C2×Dic73#10212yes—
61C2×Dic73#10412yes—
62D292—42no—
63D292—42no—
64C4×D73—82no—
65C4×D73—81no—
66C4×D73—81no—
67#10596833—22no—
68#10596833—22no—
69#10596833—81no—
70C22×C73—21no—
71C22×C73—21no—
72C22×C73#32311yescharacteristic
73C22×C73D4⋊C812yes—
74C2×D73—44no—
75C2×D73—42no—
76C2×D73—82no—
77C2×D73—81no—
78C2×D73—81no—
79C4×C73—41no—
80C4×C73—81no—
81Dic73—41no—
82Dic73#32712yes—
83Dic73#32911yescharacteristic
84Dic73#33111yescharacteristic
85#7105—731nomaximal, Sylow
86C2×C73—22no—
87C2×C73#127011yescharacteristic
88C2×C73#132011yescharacteristic
89C2×C73#132111yescharacteristic
90D73—82no—
91#1955—731no—
92#1377—732no—
93C73#710511yescharacteristic, complemented, Sylow
94C2×C4×D4—731no—
95C2×M32—1462no—
96C2×C4⋊C8—731no—
97C2×C22⋊C8—1462no—
98C2×#97—731no—
99C22×D4—731no—
100C23×C4—1461no—
101C22×C8—732no—
102C22×C8—1461no—
103C4×D4—2921no—
104C4×D4—2921no—
105C2×C4⋊C4#1059684211yescharacteristic
106C2×C22⋊C4—1461no—
107C2×C42—731no—
108M32—2922no—
109M32—1464no—
110C2×C16—2922no—
111C4⋊C8—2921no—
112C22⋊C8—2922no—
113C22⋊C8—2922no—
114#97—2921no—
115C24—1461no—
116C2×D4—2921no—
117C2×D4—2922no—
118C22×C4—21no—
119C22×C4—2922no—
120C22×C4—2921no—
121C22×C4—2921no—
122C22×C4—2922no—
123C22×C4—731no—
124C22×C4—731no—
125C22×C4C2×#1059684211yescharacteristic
126C2×C8—2922no—
127C2×C8—2921no—
128C2×C8—732no—
129C2×C8—732no—
130C2×C8—1462no—
131C2×C8—1462no—
132C4⋊C4—41no—
133C22⋊C4—2922no—
134C42—1461no—
135C42—1461no—
136C16—2924no—
137C23—2921no—
138C23—2922no—
139C23—2921no—
140C23—2922no—
141C23—1462no—
142C23C22⋊#1059684211yescharacteristic
143D4—2922no—
144D4—2922no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—42no—
149C2×C4—2921no—
150C2×C4—5841no—
151C2×C4—5842no—
152C2×C4—5841no—
153C2×C4—731no—
154C2×C4—731no—
155C2×C4—732no—
156C2×C4—732no—
157C2×C4—1461no—
158C8—5841no—
159C8—1462no—
160C8—1462no—
161C22—21no—
162C22—21no—
163C22—2924no—
164C22—2922no—
165C22—5842no—
166C22—5841no—
167C22—5841no—
168C22#1798967211yescharacteristic
169C22D4⋊#1059684212yes—
170C4—41no—
171C4—81no—
172C4—2921no—
173C4—731no—
174C4—732no—
175C4—731no—
176C2—22no—
177C2—5842no—
178C2#2262693011yescharacteristic
179C2#2262696111yescharacteristic
180C2#2262696311yescharacteristic
subgroupG/H
centerC22#17989672
commutatorC22×C4×C73C2×C8
FrattiniC22×C4C2×#10596842
FittingC2×C4⋊C4×C73C8
socleC22×C73#323
prime radicalC22×D292C8
cosocleC2×#14556646C22
hypercenterC2×C4⋊C4#10596842
hypocenterC73#7105
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #22627007C2semidirect
93. C73#7105semidirect

Maximal subgroups

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

subgroupindex
#226270072
#226260572
#710573