Finite Group Databasebeta

← #32980946

Subgroups — #32980946

Order 18688.

398 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 95 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#22620279C211yesmaximal, characteristic
2#22619037C211yesmaximal, characteristic, complemented
3#22608401C212yesmaximal
4#22607831C212yesmaximal, complemented
5C73×#1544C211yesmaximal, characteristic, complemented
6#17989137C2211yescharacteristic
7#17988957C412yes—
8#17988953C412yes—
9#17988949—22no—
10#17988718—24no—
11#17988648—22no—
12#17988644C2212yes—
13#17988581—22no—
14C2×#14556502C2211yescharacteristic
15#17988316—24no—
16#533×C73C2211yescharacteristic
17#431×C73C2212yes—
18#332×C73—22no—
19C2×#11924028—21no—
20C22×#10596831—21no—
21#14556591C2×C411yescharacteristic
22#14556588C2×C411yescharacteristic
23#14556579—21no—
24#14556565—22no—
25C4×D292—22no—
26C4⋊#10596831—24no—
27C4⋊#10596831D414yes—
28#14556514—24no—
29#14556511—24no—
30C22⋊#10596831—22no—
31#14556502—22no—
32#14556502—22no—
33#14556502—21no—
34#14556502C2×C412yes—
35C4×#10596831—22no—
36C4⋊Q8×C73D412yes—
37#125×C73C2×C412yes—
38C22⋊Q8×C73—22no—
39C4×Q8×C73—22no—
40#117×C73D412yes—
41C2×C42×C73C2311yescharacteristic
42C4⋊C8×C73—22no—
43C22⋊C8×C73—22no—
44C4×C8×C73—22no—
45#11924028—44no—
46C2×Dic146—21no—
47C2×D292—21no—
48C2×D292—22no—
49C2×C22⋊D73—41no—
50C2×C4×D73—41no—
51C2×#10596831—22no—
52C2×#10596831—24no—
53C2×#10596831—42no—
54C4⋊Dic73—22no—
55#11924005—42no—
56C2×Q8×C73—22no—
57C22×C4×C73C2×D411yescharacteristic
58C22×C4×C73#4112yes—
59C2×C8×C73—42no—
60C4⋊C4×C73—24no—
61C4⋊C4×C73—22no—
62C4⋊C4×C73C22⋊C414yes—
63C22⋊C4×C73—22no—
64C42×C73—22no—
65C42×C73C22×C411yescharacteristic
66C42×C73C2×D412yes—
67C42×C73C2×D411yescharacteristic
68C23×C73#12311yescharacteristic
69C22×D73—41no—
70Q8×C73—82no—
71C2×C4×C73—22no—
72C2×C4×C73—24no—
73C2×C4×C73—42no—
74C2×C4×C73C2×C22⋊C411yescharacteristic
75C2×C4×C73C4×D412yes—
76C2×C4×C73#12011yescharacteristic
77C2×C4×C73#12112yes—
78C22⋊D73—82no—
79C2×Dic73—41no—
80D292—44no—
81D292—42no—
82C4×D73—82no—
83Dic146—42no—
84C8×C73—82no—
85#10596831—42no—
86#10596831—44no—
87C22×C73—22no—
88C22×C73—21no—
89C22×C73#38611yescharacteristic
90C2×D73—82no—
91C2×D73—81no—
92C4×C73—22no—
93C4×C73—22no—
94C4×C73—21no—
95C4×C73—44no—
96C4×C73#45412yes—
97Dic73—81no—
98#9008—731nomaximal, Sylow
99C2×C73—41no—
100C2×C73#188112yes—
101C2×C73#188811yescharacteristic
102D73—161no—
103#3135—731no—
104#2987—731no—
105#1544D7311yescharacteristic, complemented
106#1496—732no—
107#1302—732no—
108C73#900811yescharacteristic, complemented, Sylow
109#533C2×D7311yescharacteristic
110#532—731no—
111#491—732no—
112#490—732no—
113#489—1462no—
114#446—1464no—
115#433—1462no—
116#432—732no—
117#431C2×D7312yes—
118#416—1462no—
119C2×#97—731no—
120#332—22no—
121D4⋊C8—1464no—
122C2×#41—1461no—
123C22×C8—1461no—
124C4⋊Q8—731no—
125C4⋊Q8C22⋊D7312yes—
126#127—731no—
127#125C4×D7312yes—
128#124—1461no—
129C22⋊Q8—22no—
130#121—1462no—
131C4×Q8—22no—
132C4×D4—1462no—
133#117D29212yes—
134C2×C42C22×D7311yescharacteristic
135C4⋊C8—22no—
136C4⋊C8—734no—
137C4⋊C8—1464no—
138#103—1464no—
139#102—1464no—
140C22⋊C8—22no—
141C22⋊C8—1462no—
142#97—732no—
143#97—1462no—
144#97—1462no—
145#97—1461no—
146C4×C8—22no—
147C4×C8—1462no—
148#41—2924no—
149C2×Q8—22no—
150C2×Q8—1461no—
151C2×D4—2921no—
152C2×D4—1461no—
153C2×D4—1462no—
154C22×C4—2921no—
155C22×C4C2×D29211yescharacteristic
156C22×C4#1192402712yes—
157C2×C8—42no—
158C2×C8—2922no—
159C2×C8—1462no—
160C2×C8—1464no—
161C4⋊C4—24no—
162C4⋊C4—22no—
163C4⋊C4—1462no—
164C4⋊C4#1192400514yes—
165C22⋊C4—22no—
166C22⋊C4—2922no—
167C42—22no—
168C42C2×C4×D7311yescharacteristic
169C42D4×D7312yes—
170C42C2×C22⋊D7311yescharacteristic
171C23—2921no—
172C23#1455657511yescharacteristic
173Q8—82no—
174Q8—2922no—
175D4—2922no—
176D4—2924no—
177D4—5842no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—42no—
181C2×C4—2921no—
182C2×C4—5842no—
183C2×C4C2×#1192400511yescharacteristic
184C2×C4#1455655112yes—
185C2×C4#1455656111yescharacteristic
186C2×C4#1455656312yes—
187C8—82no—
188C8—2922no—
189C8—2924no—
190C22—22no—
191C22—21no—
192C22—5842no—
193C22—5841no—
194C22#1798846411yescharacteristic
195C4—22no—
196C4—22no—
197C4—21no—
198C4—44no—
199C4—5841no—
200C4#1798876212yes—
201C2—41no—
202C2—11681no—
203C2#2261029112yes—
204C2#2261033211yescharacteristic
subgroupG/H
centerC2×C4#14556561
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1544C2
socleC22×C73#386
prime radical#17989137C22
cosocleC2×C42×C73C23
hypercenter#1544D73
hypocenterC73#9008
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1544

Complements

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

NH ≅ G/Ntype
2. #22619037C2semidirect
4. #22607831C2semidirect
5. C73×#1544C2semidirect
105. #1544D73semidirect
108. C73#9008semidirect

Maximal subgroups

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

subgroupindex
#226202792
#226190372
#226084012
#226078312
C73×#15442
#900873