Finite Group Databasebeta

← #32989089

Subgroups — #32989089

Order 18688.

402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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#22610759C211yesmaximal, characteristic
2#22608490C212yesmaximal
3#22607789C212yesmaximal, complemented
4#22607764C211yesmaximal, characteristic, complemented
5C73×#2864C211yesmaximal, characteristic, complemented
6#17989137C2211yescharacteristic
7#17988640C2212yes—
8#17988611C2211yescharacteristic
9C2×#14556519—22no—
10#17988320—24no—
11#389×C73—22no—
12#387×C73—24no—
13#382×C73C2212yes—
14C43×C73C2211yescharacteristic
15C2×#11924028—21no—
16C2×#11924012—21no—
17#14556591Q811yescharacteristic
18#14556588Q811yescharacteristic
19#14556579—21no—
20#14556565—22no—
21C4×D292—22no—
22C4⋊#10596831—22no—
23C4⋊#10596831—22no—
24#14556519—44no—
25C22⋊#10596831—22no—
26C4×#10596831—22no—
27C2×C4⋊C4×C73—24no—
28C2×C4⋊C4×C73—22no—
29C2×C42×C73—22no—
30C2×C42×C73D412yes—
31C2×C42×C73C2311yescharacteristic
32#95×C73—24no—
33#95×C73—22no—
34#95×C73D414yes—
35#11924028—42no—
36#11924028—42no—
37C2×Dic146—21no—
38C2×D292—21no—
39C2×D292—22no—
40C2×C22⋊D73—41no—
41C2×C4×D73—41no—
42#11924012—42no—
43C2×#10596831—42no—
44C2×#10596831—41no—
45C4⋊Dic73—22no—
46#11924005—42no—
47C22×C4×C73—22no—
48C22×C4×C73—24no—
49C22×C4×C73C2×D412yes—
50C22×C4×C73C2×D411yescharacteristic
51C4⋊C4×C73—48no—
52C4⋊C4×C73—42no—
53C4⋊C4×C73—42no—
54C42×C73—22no—
55C42×C73—22no—
56C42×C73—44no—
57C42×C73C2×Q811yescharacteristic
58C42×C73#4111yescharacteristic
59C42×C73#4112yes—
60C23×C73#12011yescharacteristic
61C22×D73—41no—
62C2×C4×C73—24no—
63C2×C4×C73—42no—
64C2×C4×C73—42no—
65C2×C4×C73—42no—
66C2×C4×C73—48no—
67C2×C4×C73—44no—
68C2×C4×C73C22⋊Q812yes—
69C2×C4×C73C22⋊Q811yescharacteristic
70C2×C4×C73#12412yes—
71C2×C4×C73#12411yescharacteristic
72C2×C4×C73#13512yes—
73C2×C4×C73AGL(1,ℤ/8)12yes—
74C22⋊D73—82no—
75C2×Dic73—41no—
76D292—42no—
77D292—82no—
78C4×D73—81no—
79C4×D73—81no—
80Dic146—42no—
81#10596831—82no—
82#10596831—81no—
83C22×C73—22no—
84C22×C73#39311yescharacteristic
85C22×C73#44912yes—
86C2×D73—81no—
87C2×D73—82no—
88C4×C73—22no—
89C4×C73—22no—
90C4×C73—44no—
91C4×C73—84no—
92C4×C73#47812yes—
93C4×C73#48811yescharacteristic
94C4×C73#49011yescharacteristic
95Dic73—81no—
96#10366—731nomaximal, Sylow
97C2×C73—22no—
98C2×C73#202511yescharacteristic
99C2×C73#203112yes—
100D73—161no—
101#2864D7311yescharacteristic, complemented
102#1962—731no—
103#1517—732no—
104#1286—732no—
105#1276—731no—
106C73#1036611yescharacteristic, complemented, Sylow
107#532—731no—
108#431—732no—
109#423—731no—
110C2×#104—1462no—
111#389—22no—
112#387—24no—
113#382C2×D7312yes—
114C43C2×D7311yescharacteristic
115#327—1464no—
116C2×#41—1461no—
117C2×M16—1461no—
118C4⋊Q8—731no—
119#127—731no—
120#124—1461no—
121#121—1462no—
122C4×D4—1462no—
123C2×C4⋊C4—24no—
124C2×C4⋊C4—22no—
125C2×C42—22no—
126C2×C42C22⋊D7312yes—
127C2×C42C22×D7311yescharacteristic
128C4⋊C8—1462no—
129C4⋊C8—1462no—
130#104—2924no—
131C22⋊C8—1462no—
132C4×C8—1462no—
133#95—24no—
134#95—22no—
135#95C22⋊D7314yes—
136#41—2922no—
137#41—2922no—
138C2×Q8—1461no—
139C2×D4—2921no—
140C2×D4—1461no—
141C2×D4—1462no—
142C22×C4—22no—
143C22×C4—24no—
144C22×C4—2921no—
145C22×C4C2×C22⋊D7312yes—
146C22×C4C2×C22⋊D7311yescharacteristic
147M16—2922no—
148C2×C8—2922no—
149C2×C8—2921no—
150C4⋊C4—48no—
151C4⋊C4—42no—
152C4⋊C4—42no—
153C4⋊C4—1462no—
154C22⋊C4—2922no—
155C42—22no—
156C42—22no—
157C42—44no—
158C42Q8×D7311yescharacteristic
159C42#1192402911yescharacteristic
160C42#1192402912yes—
161C23—2921no—
162C23#1455656011yescharacteristic
163Q8—2922no—
164D4—2922no—
165D4—5842no—
166D4—5842no—
167C2×C4—24no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—48no—
172C2×C4—44no—
173C2×C4—2921no—
174C2×C4—5841no—
175C2×C4—5841no—
176C2×C4#1455656712yes—
177C2×C4#1455656711yescharacteristic
178C2×C4#1455658012yes—
179C2×C4#1455658011yescharacteristic
180C2×C4#1455661112yes—
181C2×C4#1455661612yes—
182C8—5842no—
183C8—5841no—
184C22—22no—
185C22—5841no—
186C22—5842no—
187C22#1798849811yescharacteristic
188C22#1798873212yes—
189C4—22no—
190C4—22no—
191C4—44no—
192C4—84no—
193C4—5841no—
194C4#1798888412yes—
195C4#1798894411yescharacteristic
196C4#1798895311yescharacteristic
197C2—22no—
198C2—11681no—
199C2#2261107411yescharacteristic
200C2#2261110012yes—
subgroupG/H
centerC22#17988498
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#2864C2
socleC22×C73#393
prime radical#17989137C22
hypercenter#2864D73
hypocenterC73#10366
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2864

Complements

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

NH ≅ G/Ntype
3. #22607789C2semidirect
4. #22607764C2semidirect
5. C73×#2864C2semidirect
101. #2864D73semidirect
106. C73#10366semidirect

Maximal subgroups

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

subgroupindex
#226107592
#226084902
#226077892
#226077642
C73×#28642
#1036673