Finite Group Databasebeta

← #32990078

Subgroups — #32990078

Order 18688.

364 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 79 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#22621276C211yesmaximal, characteristic
2#22608629C212yesmaximal
3#22608442C212yesmaximal
4#22607801C211yesmaximal, characteristic
5C73×#1843C211yesmaximal, characteristic
6#17989144C2212yes—
7#17988883—22no—
8#17988828—22no—
9#17988798—22no—
10#17988644C2212yes—
11#17988334—22no—
12#17988332—22no—
13#17988323—24no—
14C2×C4⋊C8×C73—22no—
15C2×C4⋊C8×C73C2211yescharacteristic
16C2×C4⋊C8×C73C2211yescharacteristic
17#376×C73C2211yescharacteristic
18C2×Dic292—22no—
19#14556591D412yes—
20#14556591D412yes—
21#14556583—22no—
22#14556570—22no—
23#14556570—22no—
24C4×Dic146—22no—
25C4×Dic146—22no—
26#14556550—22no—
27#14556525—22no—
28C4⋊#10596831—22no—
29#14556516—24no—
30C22⋊#10596831—22no—
31#14556502—22no—
32C22×C8×C73—21no—
33C22×C8×C73D412yes—
34C2×C42×C73—21no—
35C2×C42×C73C2311yescharacteristic
36C4⋊C8×C73—22no—
37C4⋊C8×C73—22no—
38C4⋊C8×C73—44no—
39#95×C73—21no—
40#95×C73D412yes—
41C2×Dic146—22no—
42C2×Dic146—22no—
43Dic292—82no—
44C2×#10596831—42no—
45C4⋊Dic73—22no—
46C4⋊Dic73—22no—
47C4⋊Dic73—22no—
48C4⋊Dic73—22no—
49#11924007—42no—
50#11924007—42no—
51C22⋊Dic73—42no—
52C4×Dic73—42no—
53C22×C4×C73—22no—
54C22×C4×C73C2×D411yescharacteristic
55C22×C4×C73C2×D411yescharacteristic
56C22×C4×C73#4111yescharacteristic
57C2×C8×C73—22no—
58C2×C8×C73—42no—
59C2×C8×C73—42no—
60C2×C8×C73—41no—
61C42×C73—22no—
62C42×C73—22no—
63C42×C73C2×D412yes—
64C42×C73#4112yes—
65C23×C73#12111yescharacteristic
66C2×C4×C73—22no—
67C2×C4×C73—21no—
68C2×C4×C73—21no—
69C2×C4×C73—24no—
70C2×C4×C73—41no—
71C2×C4×C73—42no—
72C2×C4×C73—42no—
73C2×C4×C73#12011yescharacteristic
74C2×C4×C73#12112yes—
75C2×C4×C73#12312yes—
76C2×C4×C73#12411yescharacteristic
77C2×Dic73—42no—
78C2×Dic73—42no—
79Dic146—42no—
80Dic146—42no—
81Dic146—82no—
82C8×C73—42no—
83C8×C73—81no—
84#10596831—82no—
85C22×C73—21no—
86C22×C73—21no—
87C22×C73#39411yescharacteristic
88C22×C73#47312yes—
89C4×C73—22no—
90C4×C73—21no—
91C4×C73—22no—
92C4×C73—44no—
93C4×C73#45311yescharacteristic
94C4×C73#45611yescharacteristic
95Dic73—82no—
96Dic73—82no—
97#10516—731nomaximal, Sylow
98C2×C73—22no—
99C2×C73#203911yescharacteristic
100C2×C73#204711yescharacteristic
101C2×C73#205311yescharacteristic
102#3249—731no—
103#1843D7311yescharacteristic
104#1552—732no—
105#1506—732no—
106#1290—731no—
107C73#1051611yescharacteristic, complemented, Sylow
108#533—732no—
109#477—1462no—
110#467—1462no—
111#462—1462no—
112#432—732no—
113C2×C4⋊C8—22no—
114C2×C4⋊C8C2×D7311yescharacteristic
115C2×C4⋊C8C2×D7311yescharacteristic
116#376C2×D7311yescharacteristic
117#332—1462no—
118#332—1462no—
119#328—1464no—
120C2×Q16—1462no—
121C22×C8—21no—
122C22×C8C22⋊D7312yes—
123C4⋊Q8—732no—
124C4⋊Q8—732no—
125#125—1462no—
126C22⋊Q8—1462no—
127C22⋊Q8—1462no—
128C4×Q8—1462no—
129C4×Q8—1462no—
130#117—1462no—
131C2×C42—21no—
132C2×C42C22×D7311yescharacteristic
133#107—1462no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—44no—
137C4⋊C8—1462no—
138#103—1464no—
139C22⋊C8—1462no—
140#97—1462no—
141#95—21no—
142#95D29212yes—
143C2×Q8—1462no—
144C2×Q8—1462no—
145C22×C4—22no—
146C22×C4C2×C22⋊D7311yescharacteristic
147C22×C4C2×D29211yescharacteristic
148C22×C4#1192402811yescharacteristic
149Q16—5842no—
150C2×C8—22no—
151C2×C8—42no—
152C2×C8—42no—
153C2×C8—41no—
154C2×C8—2922no—
155C4⋊C4—2922no—
156C4⋊C4—2922no—
157C4⋊C4—1462no—
158C4⋊C4—1462no—
159C4⋊C4—1462no—
160C4⋊C4—1462no—
161C22⋊C4—2922no—
162C42—22no—
163C42—22no—
164C42—2922no—
165C42D4×D7312yes—
166C42#1192402912yes—
167C23#1455656511yescharacteristic
168Q8—2922no—
169Q8—2922no—
170Q8—5842no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—24no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—2922no—
179C2×C4—2922no—
180C2×C4#1455655911yescharacteristic
181C2×C4#1455656612yes—
182C2×C4#1455657612yes—
183C2×C4#1455658011yescharacteristic
184C8—42no—
185C8—81no—
186C8—5842no—
187C22—21no—
188C22—21no—
189C22#1798850411yescharacteristic
190C22#1798886212yes—
191C4—22no—
192C4—21no—
193C4—22no—
194C4—44no—
195C4—5842no—
196C4—5842no—
197C4#1798875411yescharacteristic
198C4#1798876911yescharacteristic
199C2—22no—
200C2#2261115511yescharacteristic
201C2#2261119911yescharacteristic
202C2#2261123711yescharacteristic
subgroupG/H
centerC22#17988504
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1843C2
socleC22×C73#394
prime radicalC23×C73#121
hypercenter#1843D73
hypocenterC73#10516
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1843

Complements

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

NH ≅ G/Ntype
107. C73#10516semidirect

Maximal subgroups

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

subgroupindex
#226212762
#226086292
#226084422
#226078012
C73×#18432
#1051673