Finite Group Databasebeta

← #32989478

Subgroups — #32989478

Order 18688.

386 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 91 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#22617999C211yesmaximal, characteristic
2#22610899C212yesmaximal
3C2×#17988328C212yesmaximal
4#22607812C211yesmaximal, characteristic
5C73×#1836C211yesmaximal, characteristic
6C2×#14556583C2212yes—
7C2×#14556502C2212yes—
8#17988527—22no—
9#17988519—22no—
10#17988517—22no—
11#17988349—22no—
12#17988349—22no—
13#17988328—24no—
14C2×#97×C73C2211yescharacteristic
15#384×C73C2211yescharacteristic
16#382×C73C2211yescharacteristic
17#340×C73—22no—
18C22×#10596831—22no—
19#14556583—22no—
20#14556583—22no—
21#14556583—22no—
22#14556583—22no—
23C2×C4⋊Dic73—22no—
24C2×C4⋊Dic73D412yes—
25C2×C4⋊Dic73D412yes—
26C2×#11924007—22no—
27C2×#11924007—22no—
28#14556502—22no—
29#14556502—22no—
30#14556498—24no—
31#14556498—22no—
32C22×C8×C73—21no—
33C2×C4⋊C4×C73—21no—
34C2×C4⋊C4×C73—22no—
35C2×C4⋊C4×C73D412yes—
36C2×C42×C73C2311yescharacteristic
37#97×C73—21no—
38#97×C73D412yes—
39#95×C73—22no—
40C22×Dic73—22no—
41C22×Dic73—22no—
42C2×#10596831—24no—
43C2×#10596831—42no—
44C2×#10596831—42no—
45C4⋊Dic73—22no—
46C4⋊Dic73—22no—
47C4⋊Dic73—22no—
48C4⋊Dic73—22no—
49C4⋊Dic73—82no—
50#11924007—42no—
51#11924007—42no—
52#11924007—42no—
53#11924007—42no—
54C22×C4×C73—22no—
55C22×C4×C73—41no—
56C22×C4×C73C2×D412yes—
57C22×C4×C73C2×D411yescharacteristic
58C2×C8×C73—22no—
59C2×C8×C73—41no—
60C2×C8×C73—41no—
61C4⋊C4×C73—42no—
62C4⋊C4×C73—42no—
63C4⋊C4×C73—44no—
64C42×C73C2×D411yescharacteristic
65C42×C73#4111yescharacteristic
66C42×C73#4112yes—
67C23×C73#12011yescharacteristic
68C2×C4×C73—21no—
69C2×C4×C73—22no—
70C2×C4×C73—21no—
71C2×C4×C73—22no—
72C2×C4×C73—42no—
73C2×C4×C73—42no—
74C2×C4×C73—42no—
75C2×C4×C73—82no—
76C2×C4×C73—81no—
77C2×C4×C73#12111yescharacteristic
78C2×C4×C73#12112yes—
79C2×C4×C73#12312yes—
80C2×C4×C73#12411yescharacteristic
81C2×Dic73—42no—
82C2×Dic73—42no—
83C2×Dic73—42no—
84C2×Dic73—42no—
85C2×Dic73—42no—
86C2×Dic73—42no—
87C8×C73—42no—
88#10596831—44no—
89C22×C73#39411yescharacteristic
90C22×C73#45412yes—
91C22×C73#45411yescharacteristic
92C22×C73#45511yescharacteristic
93C22×C73#45612yes—
94C4×C73—22no—
95C4×C73—22no—
96C4×C73—21no—
97C4×C73—21no—
98C4×C73—82no—
99C4×C73—161no—
100Dic73—82no—
101Dic73—82no—
102#10428—731nomaximal, Sylow
103C2×C73#165811yescharacteristic
104C2×C73#166311yescharacteristic
105C2×C73#166412yes—
106C2×C73#203812yes—
107C2×C73#204011yescharacteristic
108#2822—731no—
109#1992—732no—
110#1836D7311yescharacteristic
111C2×#330—732no—
112#1295—731no—
113C73#1042811yescharacteristic, complemented, Sylow
114C2×#125—732no—
115C2×#97—732no—
116C2×#97C2×D7311yescharacteristic
117#400—1462no—
118#398—1462no—
119#398—1462no—
120#384C2×D7311yescharacteristic
121#382C2×D7311yescharacteristic
122#340—22no—
123#340—1462no—
124#340—1462no—
125#330—1464no—
126C22×C8—21no—
127C22×C8—1462no—
128#125—1462no—
129#125—1462no—
130#125—1462no—
131#125—1462no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—732no—
135C2×C4⋊C4—732no—
136C2×C4⋊C4—1462no—
137C2×C4⋊C4—1462no—
138C2×C4⋊C4—1462no—
139C2×C4⋊C4C22⋊D7312yes—
140C2×C42C22×D7311yescharacteristic
141#97—21no—
142#97—1462no—
143#97—1462no—
144#97D29212yes—
145#95—22no—
146#95—1464no—
147#95—1462no—
148C22×C4—22no—
149C22×C4—41no—
150C22×C4—1462no—
151C22×C4—1462no—
152C22×C4D4×D7312yes—
153C22×C4C2×C22⋊D7311yescharacteristic
154C2×C8—22no—
155C2×C8—41no—
156C2×C8—41no—
157C2×C8—2922no—
158C2×C8—2922no—
159C2×C8—1464no—
160C4⋊C4—42no—
161C4⋊C4—44no—
162C4⋊C4—42no—
163C4⋊C4—2922no—
164C4⋊C4—2922no—
165C4⋊C4—2922no—
166C4⋊C4—2922no—
167C4⋊C4—5842no—
168C4⋊C4—1462no—
169C4⋊C4—1462no—
170C4⋊C4—1462no—
171C4⋊C4—1462no—
172C42C2×D29211yescharacteristic
173C42#1192402811yescharacteristic
174C42#1192402912yes—
175C23#1455655911yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—82no—
184C2×C4—81no—
185C2×C4—2922no—
186C2×C4—2922no—
187C2×C4—2922no—
188C2×C4—2922no—
189C2×C4—2922no—
190C2×C4—2922no—
191C2×C4#1455656511yescharacteristic
192C2×C4#1455656612yes—
193C2×C4#1455657612yes—
194C2×C4#1455658011yescharacteristic
195C8—42no—
196C8—2924no—
197C22#1798850411yescharacteristic
198C22#1798875812yes—
199C22#1798875911yescharacteristic
200C22#1798876411yescharacteristic
201C22#1798876812yes—
202C4—22no—
203C4—22no—
204C4—21no—
205C4—21no—
206C4—82no—
207C4—161no—
208C4—5842no—
209C4—5842no—
210C2#2260923211yescharacteristic
211C2#2260925711yescharacteristic
212C2#2260926412yes—
213C2#2261115012yes—
214C2#2261116011yescharacteristic
subgroupG/H
centerC23#14556559
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1836C2
socle, prime radicalC23×C73#120
hypercenter#1836D73
hypocenterC73#10428
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1836

Complements

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

NH ≅ G/Ntype
113. C73#10428semidirect

Maximal subgroups

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

subgroupindex
#226179992
#226108992
C2×#179883282
#226078122
C73×#18362
#1042873