Finite Group Databasebeta

← #32995493

Subgroups — #32995493

Order 18688.

262 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 71 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#22618868C211yesmaximal, characteristic
2#22611744C212yesmaximal
3#22607883C212yesmaximal
4#22607882C211yesmaximal, characteristic
5C73×#1327C211yesmaximal, characteristic
6#17989144C411yescharacteristic
7#17988716—22no—
8#17988716—22no—
9#17988615C411yescharacteristic
10#17988615C2211yescharacteristic
11#17988545C411yescharacteristic
12#17988545C2211yescharacteristic
13C2×#14556502C411yescharacteristic
14#17988407—22no—
15#17988369C2212yes—
16#17988364—22no—
17#423×C73C2211yescharacteristic
18#349×C73C2212yes—
19C22×#10596831C2×C411yescharacteristic
20C22×#10596831C2×C411yescharacteristic
21#14556591—21no—
22#14556583—21no—
23#14556570—22no—
24C4×Dic146—22no—
25#14556550C2×C411yescharacteristic
26#14556550C2×C411yescharacteristic
27#14556531—22no—
28#14556520—22no—
29#14556520—22no—
30#14556502—21no—
31#14556502—21no—
32#14556501—21no—
33#14556501D412yes—
34C8×Dic73—21no—
35C8×Dic73D412yes—
36C2×M16×C73C2×C411yescharacteristic
37C2×M16×C73C2311yescharacteristic
38C2×C42×C73C2×C411yescharacteristic
39M32×C73—22no—
40C4⋊C8×C73—22no—
41C2×Dic146—22no—
42C2×#10596831—22no—
43C2×#10596831—21no—
44C2×#10596831—41no—
45C2×#10596831C22⋊C411yescharacteristic
46C2×#10596831C22⋊C411yescharacteristic
47C4⋊Dic73—22no—
48C4⋊Dic73—21no—
49C4⋊Dic73—21no—
50#11924007—24no—
51C22⋊Dic73—21no—
52C22⋊Dic73M1612yes—
53C4×Dic73—21no—
54C4×Dic73C22⋊C412yes—
55#11924003—42no—
56C22×C4×C73—21no—
57C22×C4×C73C22×C411yescharacteristic
58M16×C73—41no—
59M16×C73—41no—
60C2×C8×C73—21no—
61C2×C8×C73C2×D412yes—
62C42×C73—21no—
63C42×C73M1611yescharacteristic
64C42×C73M1611yescharacteristic
65C16×C73—42no—
66C23×C73C2×M1611yescharacteristic
67C2×C4×C73—21no—
68C2×C4×C73—21no—
69C2×C4×C73—21no—
70C2×C4×C73—21no—
71C2×C4×C73—81no—
72C2×C4×C73C2×C22⋊C411yescharacteristic
73C2×C4×C73C2×M1611yescharacteristic
74C2×Dic73—22no—
75C2×Dic73—22no—
76Dic146—82no—
77C8×C73—22no—
78C8×C73—41no—
79#10596831—21no—
80#10596831—41no—
81#10596831#10112yes—
82C22×C73—21no—
83C22×C73—41no—
84C22×C73#40711yescharacteristic
85C4×C73—21no—
86C4×C73—41no—
87C4×C73—41no—
88C4×C73#41011yescharacteristic
89C4×C73C2×#10111yescharacteristic
90Dic73—42no—
91Dic73—42no—
92#11540—731nomaximal, Sylow
93C2×C73—21no—
94C2×C73—41no—
95C2×C73#146711yescharacteristic
96#2961—731no—
97#2166—732no—
98#1328—732no—
99#1327—731no—
100#1327D7311yescharacteristic
101C73#1154011yescharacteristic, complemented, Sylow
102#533—731no—
103#446—1462no—
104#446—1462no—
105#424—731no—
106#424—731no—
107#423C2×D7311yescharacteristic
108#405—731no—
109#405—731no—
110C2×#97—731no—
111#364—1462no—
112#349—732no—
113#349C2×D7312yes—
114#347—1462no—
115C2×M16C4×D7311yescharacteristic
116C2×M16C22×D7311yescharacteristic
117C22×C8—731no—
118C22×C8—731no—
119C4⋊Q8—1461no—
120#125—1461no—
121C22⋊Q8—1462no—
122C4×Q8—1462no—
123#117—731no—
124#117—731no—
125C2×C42C4×D7311yescharacteristic
126M32—22no—
127M32—1462no—
128C4⋊C8—22no—
129C4⋊C8—1462no—
130C4⋊C8—1462no—
131#97—732no—
132#97—1461no—
133#97—1461no—
134#97—1461no—
135C4×C8—732no—
136C4×C8—1461no—
137C2×Q8—1462no—
138C22×C4—21no—
139C22×C4C2×C4×D7311yescharacteristic
140M16—41no—
141M16—41no—
142C2×C8—21no—
143C2×C8—2921no—
144C2×C8—731no—
145C2×C8—731no—
146C2×C8—1461no—
147C2×C8—1462no—
148C2×C8D4×D7312yes—
149C4⋊C4—1464no—
150C4⋊C4—1462no—
151C4⋊C4—1461no—
152C4⋊C4—1461no—
153C22⋊C4—732no—
154C22⋊C4—1461no—
155C42—21no—
156C42—732no—
157C42—1461no—
158C42#1192401111yescharacteristic
159C42#1192401111yescharacteristic
160C16—42no—
161C16—2922no—
162C23M16×D7311yescharacteristic
163Q8—5842no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—81no—
169C2×C4—1462no—
170C2×C4—1462no—
171C2×C4C22⋊C4×D7311yescharacteristic
172C2×C4C2×#1192401111yescharacteristic
173C8—22no—
174C8—41no—
175C8—2921no—
176C8—732no—
177C8—1461no—
178C22—21no—
179C22—41no—
180C22#1798854911yescharacteristic
181C4—21no—
182C4—41no—
183C4—41no—
184C4—2922no—
185C4—2922no—
186C4#1798855911yescharacteristic
187C4#101×D7311yescharacteristic
188C2—21no—
189C2—41no—
190C2#2260827311yescharacteristic
subgroupG/H
centerC4#17988559
commutatorC22×C4×C73C22×C4
FrattiniC2×M16C22×D73
FittingC73×#1327C2
socleC2×C73#1467
prime radicalC23×C73C2×M16
cosocleC2×M16×C73C23
hypercenter#1327D73
hypocenterC73#11540
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
101. C73#11540semidirect

Maximal subgroups

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

subgroupindex
#226188682
#226117442
#226078832
#226078822
C73×#13272
#1154073