Finite Group Databasebeta

← #32990495

Subgroups — #32990495

Order 18688.

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

normal subgroups only

This group has 350 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#22610065C212yesmaximal
3#22610064C211yesmaximal, characteristic
4#22607813C212yesmaximal
5C73×#1295C211yesmaximal, characteristic
6C2×#14556502C2211yescharacteristic
7#17988521—22no—
8#17988520—22no—
9#17988519—22no—
10#17988457C2211yescharacteristic
11#17988453C2212yes—
12#17988350—22no—
13#17988350—22no—
14#17988349—22no—
15C2×#97×C73C2212yes—
16#382×C73C2211yescharacteristic
17C22×#10596831—21no—
18C2×C4⋊Dic73—22no—
19C2×C4⋊Dic73—21no—
20C2×C4⋊Dic73—22no—
21C2×C4⋊Dic73D412yes—
22C2×C4⋊Dic73D412yes—
23C2×#11924007—22no—
24C2×#11924007—22no—
25#14556502—21no—
26#14556502Q812yes—
27#14556498—22no—
28#14556498—22no—
29#14556498—22no—
30C22×C8×C73—22no—
31C2×C4⋊C4×C73D412yes—
32C2×C42×C73C2311yescharacteristic
33#97×C73—22no—
34#97×C73Q814yes—
35#95×C73—22no—
36C22×Dic73—22no—
37C22×Dic73—22no—
38C22×Dic73—41no—
39C2×#10596831—22no—
40C2×#10596831—41no—
41C2×#10596831—41no—
42C4⋊Dic73—42no—
43C4⋊Dic73—42no—
44C4⋊Dic73—44no—
45C4⋊Dic73—42no—
46C4⋊Dic73—82no—
47#11924007—82no—
48#11924007—82no—
49C22×C4×C73—22no—
50C22×C4×C73C2×D412yes—
51C22×C4×C73C2×D411yescharacteristic
52C2×C8×C73—24no—
53C2×C8×C73—42no—
54C2×C8×C73—42no—
55C4⋊C4×C73—42no—
56C42×C73C2×Q811yescharacteristic
57C42×C73C2×Q812yes—
58C42×C73#4111yescharacteristic
59C23×C73#12011yescharacteristic
60C2×C4×C73—22no—
61C2×C4×C73—21no—
62C2×C4×C73—21no—
63C2×C4×C73—22no—
64C2×C4×C73—42no—
65C2×C4×C73—42no—
66C2×C4×C73—42no—
67C2×C4×C73C22⋊Q812yes—
68C2×C4×C73C22⋊Q811yescharacteristic
69C2×C4×C73C4⋊Q812yes—
70C2×C4×C73C4⋊Q811yescharacteristic
71C2×Dic73—42no—
72C2×Dic73—42no—
73C2×Dic73—42no—
74C2×Dic73—42no—
75C2×Dic73—42no—
76C2×Dic73—42no—
77C2×Dic73—82no—
78C2×Dic73—81no—
79C8×C73—44no—
80#10596831—42no—
81C22×C73#39511yescharacteristic
82C22×C73#45412yes—
83C22×C73#45411yescharacteristic
84C22×C73#45512yes—
85C22×C73#45511yescharacteristic
86C4×C73—21no—
87C4×C73—22no—
88C4×C73—22no—
89C4×C73—21no—
90C4×C73—82no—
91Dic73—82no—
92Dic73—82no—
93Dic73—161no—
94#10586—731nomaximal, Sylow
95C2×C73#165811yescharacteristic
96C2×C73#166211yescharacteristic
97C2×C73#166212yes—
98C2×C73#206112yes—
99C2×C73#206111yescharacteristic
100#2845—731no—
101#1836—732no—
102#1836—731no—
103#1295—732no—
104#1295D7311yescharacteristic
105C73#1058611yescharacteristic, complemented, Sylow
106C2×#97—731no—
107C2×#97C2×D7312yes—
108#398—1462no—
109#398—1462no—
110#398—1462no—
111#384—731no—
112#382—732no—
113#382C2×D7311yescharacteristic
114#340—1462no—
115#340—1462no—
116#340—1462no—
117C22×C8—22no—
118C22×C8—1461no—
119C2×C4⋊C4—732no—
120C2×C4⋊C4—732no—
121C2×C4⋊C4—1462no—
122C2×C4⋊C4—1461no—
123C2×C4⋊C4—1462no—
124C2×C4⋊C4—1462no—
125C2×C4⋊C4—1462no—
126C2×C4⋊C4D29212yes—
127C2×C42C22×D7311yescharacteristic
128#97—22no—
129#97—732no—
130#97—1461no—
131#97Dic14614yes—
132#95—22no—
133#95—1462no—
134#95—1462no—
135#95—1462no—
136C22×C4—22no—
137C22×C4—2921no—
138C22×C4—1462no—
139C22×C4—1462no—
140C22×C4D4×D7312yes—
141C22×C4C2×D29211yescharacteristic
142C2×C8—24no—
143C2×C8—42no—
144C2×C8—42no—
145C2×C8—2921no—
146C2×C8—2921no—
147C2×C8—1462no—
148C4⋊C4—42no—
149C4⋊C4—2922no—
150C4⋊C4—2922no—
151C4⋊C4—2924no—
152C4⋊C4—2922no—
153C4⋊C4—5842no—
154C4⋊C4—5842no—
155C4⋊C4—5842no—
156C42Q8×D7311yescharacteristic
157C42C2×Dic14612yes—
158C42#1192402711yescharacteristic
159C23#1455656111yescharacteristic
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—2922no—
168C2×C4—2922no—
169C2×C4—2922no—
170C2×C4—2922no—
171C2×C4—2922no—
172C2×C4—2922no—
173C2×C4—5842no—
174C2×C4—5841no—
175C2×C4#1455656812yes—
176C2×C4#1455657111yescharacteristic
177C2×C4#1455659012yes—
178C2×C4#1455659111yescharacteristic
179C8—44no—
180C8—2922no—
181C22#1798850811yescharacteristic
182C22#1798876112yes—
183C22#1798876211yescharacteristic
184C22#1798876612yes—
185C22#1798876711yescharacteristic
186C4—22no—
187C4—22no—
188C4—21no—
189C4—21no—
190C4—82no—
191C4—5842no—
192C4—5842no—
193C4—11681no—
194C2#2260923411yescharacteristic
195C2#2260925511yescharacteristic
196C2#2260925612yes—
197C2#2261128012yes—
198C2#2261128211yescharacteristic
subgroupG/H
centerC23#14556561
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1295C2
socle, prime radicalC23×C73#120
hypercenter#1295D73
hypocenterC73#10586
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
105. C73#10586semidirect

Maximal subgroups

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

subgroupindex
#226182062
#226100652
#226100642
#226078132
C73×#12952
#1058673