Finite Group Databasebeta

← #32989074

Subgroups — #32989074

Order 18688.

416 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 101 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#22610908C211yesmaximal, characteristic
2#22608494C212yesmaximal
3#22607789C212yesmaximal
4#22607764C211yesmaximal, characteristic
5C73×#2862C211yesmaximal, characteristic
6#17989144C2211yescharacteristic
7#17988640C2212yes—
8#17988611C2211yescharacteristic
9#17988347—21no—
10#17988347—21no—
11#17988323—24no—
12C2×C4⋊Q8×C73—21no—
13#391×C73—24no—
14#382×C73—21no—
15#382×C73C2212yes—
16C43×C73C2211yescharacteristic
17C2×#11924012—21no—
18#14556591Q812yescomplemented
19#14556583—21no—
20#14556570—22no—
21C4×Dic146—22no—
22#14556550—21no—
23C4⋊#10596831—22no—
24C4⋊#10596831—22no—
25C22⋊#10596831—22no—
26C4×#10596831—22no—
27C22×Q8×C73—22no—
28C4⋊Q8×C73—42no—
29C4⋊Q8×C73—42no—
30C2×C4⋊C4×C73—22no—
31C2×C4⋊C4×C73—22no—
32C2×C42×C73—22no—
33C2×C42×C73D411yescharacteristic
34C2×C42×C73D411yescharacteristic
35C2×C42×C73C2311yescharacteristic
36#95×C73—24no—
37#95×C73—22no—
38#95×C73D414yes—
39C2×Dic146—22no—
40#11924012—41no—
41#11924012—41no—
42C2×#10596831—42no—
43C2×#10596831—41no—
44C4⋊Dic73—22no—
45C4⋊Dic73—22no—
46#11924007—42no—
47C22⋊Dic73—41no—
48C4×Dic73—41no—
49C2×Q8×C73—44no—
50C2×Q8×C73—48no—
51C22×C4×C73—21no—
52C22×C4×C73—21no—
53C22×C4×C73—24no—
54C22×C4×C73C2×D412yes—
55C22×C4×C73C2×D411yescharacteristic
56C4⋊C4×C73—44no—
57C4⋊C4×C73—42no—
58C4⋊C4×C73—42no—
59C42×C73—21no—
60C42×C73—21no—
61C42×C73—44no—
62C42×C73SD1612yes—
63C42×C73Q1612yes—
64C42×C73C2×Q811yescharacteristic
65C42×C73#4111yescharacteristic
66C42×C73#4112yes—
67C23×C73#12011yescharacteristic
68Q8×C73—88no—
69C2×C4×C73—24no—
70C2×C4×C73—22no—
71C2×C4×C73—22no—
72C2×C4×C73—42no—
73C2×C4×C73—42no—
74C2×C4×C73—48no—
75C2×C4×C73—44no—
76C2×C4×C73C22⋊Q812yes—
77C2×C4×C73C22⋊Q811yescharacteristic
78C2×C4×C73#12412yes—
79C2×C4×C73#12411yescharacteristic
80C2×C4×C73C2×SD1611yescharacteristic
81C2×C4×C73C2×Q1611yescharacteristic
82C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
83C2×C4×C73#13711yescharacteristic
84C2×Dic73—42no—
85Dic146—82no—
86#10596831—82no—
87#10596831—81no—
88C22×C73—22no—
89C22×C73#39311yescharacteristic
90C22×C73#45011yescharacteristic
91C22×C73#45111yescharacteristic
92C4×C73—24no—
93C4×C73—22no—
94C4×C73—22no—
95C4×C73—42no—
96C4×C73—84no—
97C4×C73#47511yescharacteristic
98C4×C73#47711yescharacteristic
99C4×C73#48711yescharacteristic
100C4×C73#48911yescharacteristic
101Dic73—82no—
102#10363—731nomaximal, Sylow
103C2×C73—21no—
104C2×C73—21no—
105C2×C73#202411yescharacteristic
106C2×C73#203112yes—
107#2862D7311yescharacteristic
108#1994—731no—
109#1518—732no—
110#1286—732no—
111#1276—731no—
112C73#1036311yescharacteristic, complemented, Sylow
113#533—731no—
114C2×C4⋊Q8—21no—
115#431—732no—
116#423—731no—
117#391—24no—
118#382—21no—
119#382C2×D7312yes—
120C43C2×D7311yescharacteristic
121#339—1461no—
122#339—1461no—
123#328—1464no—
124C22×Q8—22no—
125C2×M16—1461no—
126C4⋊Q8—42no—
127C4⋊Q8—42no—
128C4⋊Q8—732no—
129#125—1461no—
130C22⋊Q8—1462no—
131C4×Q8—1462no—
132#117—1461no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C42—22no—
136C2×C42C22⋊D7311yescharacteristic
137C2×C42C22⋊D7311yescharacteristic
138C2×C42C22×D7311yescharacteristic
139C4⋊C8—1462no—
140C4⋊C8—1462no—
141C22⋊C8—1462no—
142C4×C8—1462no—
143#95—24no—
144#95—22no—
145#95C22⋊D7314yes—
146C2×Q8—44no—
147C2×Q8—48no—
148C2×Q8—1462no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—24no—
152C22×C4C2×C22⋊D7312yes—
153C22×C4C2×C22⋊D7311yescharacteristic
154M16—2921no—
155M16—2921no—
156C2×C8—2922no—
157C2×C8—2921no—
158C4⋊C4—44no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C4⋊C4—2922no—
162C4⋊C4—1462no—
163C4⋊C4—1462no—
164C22⋊C4—2921no—
165C42—21no—
166C42—21no—
167C42—44no—
168C42—2921no—
169C42#1192401612yes—
170C42#1192401812yes—
171C42Q8×D7311yescharacteristic
172C42#1192402911yescharacteristic
173C42#1192402912yes—
174C23#1455656011yescharacteristic
175Q8—88no—
176Q8—5842no—
177C2×C4—24no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—48no—
183C2×C4—44no—
184C2×C4—2922no—
185C2×C4#1455656712yes—
186C2×C4#1455656711yescharacteristic
187C2×C4#1455658012yes—
188C2×C4#1455658011yescharacteristic
189C2×C4C2×#1192401611yescharacteristic
190C2×C4C2×#1192401811yescharacteristic
191C2×C4#1455661711yescharacteristic
192C2×C4#1455662211yescharacteristic
193C8—5842no—
194C8—5841no—
195C22—22no—
196C22#1798849811yescharacteristic
197C22#1798873811yescharacteristic
198C22#1798874311yescharacteristic
199C4—24no—
200C4—22no—
201C4—22no—
202C4—42no—
203C4—84no—
204C4—5842no—
205C4#1798886911yescharacteristic
206C4#1798887911yescharacteristic
207C4#1798893911yescharacteristic
208C4#1798894911yescharacteristic
209C2—21no—
210C2—21no—
211C2#2261106911yescharacteristic
212C2#2261110012yes—
subgroupG/H
centerC22#17988498
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#2862C2
socleC22×C73#393
prime radicalC23×C73#120
hypercenter#2862D73
hypocenterC73#10363
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2862

Complements

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

NH ≅ G/Ntype
18. #14556591Q8semidirect
112. C73#10363semidirect

Maximal subgroups

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

subgroupindex
#226109082
#226084942
#226077892
#226077642
C73×#28622
#1036373