Finite Group Databasebeta

← #32973579

Subgroups — #32973579

Order 18688.

206 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 41 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#22611092C211yesmaximal, characteristic
2#22608058C211yesmaximal, characteristic
3C73×#1272C211yesmaximal, characteristic
4#17989218C411yescharacteristic
5#17988596—21no—
6C2×#14556510—21no—
7#17988356C411yescharacteristic
8#17988347—21no—
9#391×C73C2211yescharacteristic
10#336×C73—21no—
11C2×#11924012—21no—
12C2×#11924012—41no—
13#14556590—41no—
14#14556582—41no—
15#14556570—41no—
16#14556550—21no—
17#14556515—41no—
18#14556515—41no—
19#14556510—22no—
20#14556510—41no—
21C22×Q8×C73D411yescharacteristic
22C22×C8×C73—41no—
23C2×C4⋊C4×C73C2×C411yescharacteristic
24C2×C42×C73D411yescharacteristic
25#95×C73—41no—
26C2×Dic146—41no—
27#11924012—42no—
28#11924012—41no—
29#11924012—41no—
30#11924012—81no—
31C2×#10596831—41no—
32C2×#10596831—81no—
33C4⋊Dic73—21no—
34C4⋊Dic73—21no—
35C4⋊Dic73—41no—
36#11924007—42no—
37C22⋊Dic73—41no—
38C4×Dic73—41no—
39C2×Q8×C73—21no—
40C2×Q8×C73—41no—
41C2×Q8×C73—41no—
42C2×Q8×C73SD1611yescharacteristic
43C2×Q8×C73Q1611yescharacteristic
44C22×C4×C73—21no—
45C22×C4×C73—21no—
46C22×C4×C73—21no—
47C22×C4×C73C22⋊C411yescharacteristic
48C2×C8×C73—42no—
49C2×C8×C73—81no—
50C2×C8×C73—81no—
51C4⋊C4×C73—41no—
52C42×C73—41no—
53C23×C73#9911yescharacteristic
54Q8×C73—41no—
55Q8×C73—41no—
56Q8×C73—81no—
57C2×C4×C73—21no—
58C2×C4×C73—21no—
59C2×C4×C73—21no—
60C2×C4×C73—21no—
61C2×C4×C73—21no—
62C2×C4×C73—21no—
63C2×C4×C73—41no—
64C2×C4×C73—41no—
65C2×C4×C73—41no—
66C2×C4×C73—41no—
67C2×C4×C73—41no—
68C2×C4×C73—81no—
69C2×C4×C73#10311yescharacteristic
70C2×C4×C73#10411yescharacteristic
71C2×Dic73—41no—
72C2×Dic73—41no—
73Dic146—161no—
74C8×C73—82no—
75#10596831—81no—
76#10596831—82no—
77C22×C73—21no—
78C22×C73—21no—
79C22×C73#32811yescharacteristic
80C22×C73AΣL(1,𝔽16)11yescharacteristic
81C22×C73#35411yescharacteristic
82C4×C73—21no—
83C4×C73—21no—
84C4×C73—41no—
85C4×C73—41no—
86C4×C73—41no—
87C4×C73—41no—
88C4×C73—81no—
89Dic73—81no—
90Dic73—81no—
91#7431—731nomaximal, Sylow
92C2×C73—21no—
93C2×C73—21no—
94C2×C73#135111yescharacteristic
95C2×C73#140311yescharacteristic
96C2×C73#140511yescharacteristic
97#2028—731no—
98#1394—731no—
99#1272D7311yescharacteristic
100C73#743111yescharacteristic, complemented, Sylow
101#544—731no—
102#419—1461no—
103C2×#101—1461no—
104#391C2×D7311yescharacteristic
105#343—731no—
106#339—1461no—
107#336—21no—
108C22×Q8D29211yescharacteristic
109C2×M16—2921no—
110C2×M16—1461no—
111C22×C8—41no—
112C4⋊Q8—2921no—
113#125—2921no—
114C22⋊Q8—2921no—
115#117—1461no—
116C2×C4⋊C4C4×D7311yescharacteristic
117C2×C42C22⋊D7311yescharacteristic
118#103—2921no—
119#103—2921no—
120#101—2921no—
121#101—1462no—
122#95—41no—
123C2×Q8—21no—
124C2×Q8—41no—
125C2×Q8—41no—
126C2×Q8—2921no—
127C2×Q8#1192401711yescharacteristic
128C2×Q8Dic29211yescharacteristic
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4#1192400511yescharacteristic
133M16—2922no—
134M16—2921no—
135M16—2921no—
136M16—5841no—
137C2×C8—42no—
138C2×C8—81no—
139C2×C8—81no—
140C2×C8—2921no—
141C2×C8—5841no—
142C4⋊C4—41no—
143C4⋊C4—2921no—
144C4⋊C4—2922no—
145C4⋊C4—1461no—
146C4⋊C4—1461no—
147C22⋊C4—2921no—
148C42—41no—
149C42—2921no—
150C23#1455650511yescharacteristic
151Q8—41no—
152Q8—41no—
153Q8—81no—
154Q8—11681no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—81no—
167C2×C4—2921no—
168C2×C4—2921no—
169C2×C4#1455651611yescharacteristic
170C2×C4#1455651711yescharacteristic
171C8—82no—
172C8—5841no—
173C8—5842no—
174C22—21no—
175C22—21no—
176C22#1798832511yescharacteristic
177C22#1798837511yescharacteristic
178C22#1798838111yescharacteristic
179C4—21no—
180C4—21no—
181C4—41no—
182C4—41no—
183C4—41no—
184C4—41no—
185C4—81no—
186C4—5841no—
187C4—5841no—
188C2—21no—
189C2—21no—
190C2#2260795311yescharacteristic
191C2#2260808011yescharacteristic
192C2#2260808611yescharacteristic
subgroupG/H
centerC22#17988375
commutatorC2×C4⋊C4×C73C2×C4
Frattini#391C2×D73
FittingC73×#1272C2
socleC22×C73AΣL(1,𝔽16)
prime radicalC23×C73#99
cosocle#391×C73C22
hypercenter#1272D73
hypocenterC73#7431
LCSG ▷ C2×C4⋊C4×C73 ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #391 ◁ #1272

Complements

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

NH ≅ G/Ntype
100. C73#7431semidirect

Maximal subgroups

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

subgroupindex
#226110922
#226080582
C73×#12722
#743173