Finite Group Databasebeta

← #32990492

Subgroups — #32990492

Order 18688.

382 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 97 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#22618206C211yesmaximal, characteristic
2#22610099C212yesmaximal
3#22610064C211yesmaximal, characteristic
4#22607813C212yesmaximal
5C73×#1295C211yesmaximal, characteristic
6C2×#14556525—22no—
7C2×#14556523—22no—
8C2×#14556502C2211yescharacteristic
9#17988521—22no—
10#17988520—22no—
11#17988519—22no—
12#17988457C2211yescharacteristic
13#17988453C2212yes—
14#17988349—22no—
15C2×#97×C73C2212yes—
16#382×C73C2211yescharacteristic
17C22×#10596831—21no—
18C2×C4⋊Dic73—22no—
19C2×C4⋊Dic73—22no—
20C2×C4⋊Dic73—21no—
21C2×C4⋊Dic73D412yes—
22C2×C4⋊Dic73D412yes—
23C2×#11924007—22no—
24C2×#11924007—22no—
25#14556525—44no—
26#14556523—44no—
27#14556502—21no—
28#14556502Q812yes—
29#14556498—22no—
30#14556498—22no—
31#14556498—22no—
32C22×C8×C73—22no—
33C2×C4⋊C4×C73D412yes—
34C2×C42×C73C2311yescharacteristic
35#97×C73—22no—
36#97×C73Q814yes—
37#95×C73—22no—
38C22×Dic73—22no—
39C22×Dic73—22no—
40C22×Dic73—41no—
41C2×#10596831—22no—
42C2×#10596831—41no—
43C2×#10596831—41no—
44C4⋊Dic73—42no—
45C4⋊Dic73—42no—
46C4⋊Dic73—42no—
47C4⋊Dic73—42no—
48C4⋊Dic73—42no—
49C4⋊Dic73—82no—
50#11924007—82no—
51#11924007—82no—
52C22×C4×C73—22no—
53C22×C4×C73C2×D412yes—
54C22×C4×C73C2×D411yescharacteristic
55C2×C8×C73—24no—
56C2×C8×C73—24no—
57C2×C8×C73—24no—
58C4⋊C4×C73—42no—
59C42×C73C2×Q811yescharacteristic
60C42×C73C2×Q812yes—
61C42×C73#4111yescharacteristic
62C23×C73#12011yescharacteristic
63C2×C4×C73—22no—
64C2×C4×C73—21no—
65C2×C4×C73—21no—
66C2×C4×C73—22no—
67C2×C4×C73—42no—
68C2×C4×C73—42no—
69C2×C4×C73—42no—
70C2×C4×C73C22⋊Q812yes—
71C2×C4×C73C22⋊Q811yescharacteristic
72C2×C4×C73C4⋊Q812yes—
73C2×C4×C73C4⋊Q811yescharacteristic
74C2×Dic73—42no—
75C2×Dic73—42no—
76C2×Dic73—42no—
77C2×Dic73—42no—
78C2×Dic73—42no—
79C2×Dic73—42no—
80C2×Dic73—82no—
81C2×Dic73—81no—
82C8×C73—28no—
83#10596831—42no—
84C22×C73#39511yescharacteristic
85C22×C73#45312yes—
86C22×C73#45411yescharacteristic
87C22×C73#45511yescharacteristic
88C22×C73#45612yes—
89C4×C73—22no—
90C4×C73—22no—
91C4×C73—21no—
92C4×C73—21no—
93C4×C73—82no—
94Dic73—82no—
95Dic73—82no—
96Dic73—161no—
97#10585—731nomaximal, Sylow
98C2×C73#165611yescharacteristic
99C2×C73#166112yes—
100C2×C73#166311yescharacteristic
101C2×C73#206012yes—
102C2×C73#206111yescharacteristic
103#2845—731no—
104#1847—732no—
105#1836—731no—
106#1295—732no—
107#1295D7311yescharacteristic
108C73#1058511yescharacteristic, complemented, Sylow
109C2×#107—1462no—
110C2×#106—1462no—
111C2×#97—731no—
112C2×#97C2×D7312yes—
113#398—1462no—
114#398—1462no—
115#398—1462no—
116#384—731no—
117#382—732no—
118#382C2×D7311yescharacteristic
119#340—1462no—
120C22×C8—22no—
121C22×C8—1461no—
122C2×C4⋊C4—732no—
123C2×C4⋊C4—732no—
124C2×C4⋊C4—1462no—
125C2×C4⋊C4—1461no—
126C2×C4⋊C4—1462no—
127C2×C4⋊C4—1462no—
128C2×C4⋊C4—1462no—
129C2×C4⋊C4D29212yes—
130C2×C42C22×D7311yescharacteristic
131#107—2924no—
132#106—2924no—
133#97—22no—
134#97—732no—
135#97—1461no—
136#97Dic14614yes—
137#95—22no—
138#95—1462no—
139#95—1462no—
140#95—1462no—
141C22×C4—22no—
142C22×C4—2921no—
143C22×C4—1462no—
144C22×C4—1462no—
145C22×C4D4×D7312yes—
146C22×C4C2×D29211yescharacteristic
147C2×C8—24no—
148C2×C8—24no—
149C2×C8—24no—
150C2×C8—2921no—
151C2×C8—2921no—
152C2×C8—1462no—
153C4⋊C4—42no—
154C4⋊C4—2922no—
155C4⋊C4—2922no—
156C4⋊C4—2922no—
157C4⋊C4—2922no—
158C4⋊C4—2922no—
159C4⋊C4—5842no—
160C4⋊C4—5842no—
161C4⋊C4—5842no—
162C42Q8×D7311yescharacteristic
163C42C2×Dic14612yes—
164C42#1192402711yescharacteristic
165C23#1455656111yescharacteristic
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—2922no—
174C2×C4—2922no—
175C2×C4—2922no—
176C2×C4—2922no—
177C2×C4—2922no—
178C2×C4—2922no—
179C2×C4—5842no—
180C2×C4—5841no—
181C2×C4#1455656812yes—
182C2×C4#1455657111yescharacteristic
183C2×C4#1455659012yes—
184C2×C4#1455659111yescharacteristic
185C8—28no—
186C8—2922no—
187C22#1798850811yescharacteristic
188C22#1798875612yes—
189C22#1798876211yescharacteristic
190C22#1798876711yescharacteristic
191C22#1798877112yes—
192C4—22no—
193C4—22no—
194C4—21no—
195C4—21no—
196C4—82no—
197C4—5842no—
198C4—5842no—
199C4—11681no—
200C2#2260922611yescharacteristic
201C2#2260925112yes—
202C2#2260926011yescharacteristic
203C2#2261127512yes—
204C2#2261128211yescharacteristic
subgroupG/H
centerC23#14556561
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1295C2
socle, prime radicalC23×C73#120
hypercenter#1295D73
hypocenterC73#10585
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
108. C73#10585semidirect

Maximal subgroups

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

subgroupindex
#226182062
#226100992
#226100642
#226078132
C73×#12952
#1058573