Finite Group Databasebeta

← #34000689

Subgroups — #34000689

Order 18688.

484 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 54 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#22625760C212yesmaximal
2#22609842C211yesmaximal, characteristic
3C2×#14556650—22no—
4C2×#14556649C414yescomplemented
5#17989530—22no—
6C22×#11924028C2211yescharacteristic
7C2×C22⋊#10596831C411yescharacteristic, complemented
8C2×#14556503—22no—
9C2×C22⋊C8×C73C411yescharacteristic, complemented
10C2×C22⋊#64408—24no—
11#14556650—44no—
12#14556649—44no—
13(C2×#64408)⋊C4—42no—
14(C2×#64408)⋊C4—42no—
15C2×#11924028—41no—
16C2×#11924028—41no—
17C2×#11924028—44no—
18C22×Dic146Q811yescharacteristic
19C22×D292D411yescharacteristic
20C22×C22⋊D73C2×C412yes—
21C22×C4×D73D412yes—
22C22×#10596831—21no—
23C22⋊#10596831—41no—
24#14556503—44no—
25C23×C4×C73C2×C411yescharacteristic
26C22×C8×C73—21no—
27C22⋊C8×C73—41no—
28C22×#64408—44no—
29C22⋊#64408—44no—
30C22⋊#64408—44no—
31C23×D73C22⋊C412yes—
32#11924028—48no—
33#11924028—48no—
34C2×Dic146—41no—
35C2×Dic146—42no—
36C2×D292—24no—
37C2×D292—41no—
38C2×C22⋊D73—24no—
39C2×C22⋊D73—42no—
40C2×C22⋊D73—42no—
41C22×Dic73C4⋊C412yes—
42C2×C4×D73—24no—
43C2×C4×D73—22no—
44C2×C4×D73—22no—
45C2×C4×D73—42no—
46C2×#10596831—42no—
47C2×#10596831—41no—
48C24×C73C4211yescharacteristic
49C22×C4×C73—21no—
50C22×C4×C73—21no—
51C22×C4×C73—42no—
52C22×C4×C73C22⋊C411yescharacteristic
53C22×C4×C73C4⋊C411yescharacteristic
54C2×C8×C73—42no—
55C2×C8×C73—41no—
56C23×C73—21no—
57C23×C73—22no—
58C23×C73—41no—
59C23×C73—41no—
60C23×C73#9511yescharacteristic
61C22×D73—22no—
62C22×D73—22no—
63C22×D73—42no—
64C22×D73—42no—
65C22×D73#9914yes—
66C2×#64408—84no—
67C2×#64408—84no—
68C2×#64408—84no—
69C2×C4×C73—22no—
70C2×C4×C73—21no—
71C2×C4×C73—22no—
72C2×C4×C73—42no—
73C2×C4×C73—42no—
74C2×C4×C73#9911yescharacteristic
75C2×C4×C73#9911yescharacteristic
76C22⋊D73—48no—
77C2×Dic73—22no—
78C2×Dic73—22no—
79C2×Dic73—22no—
80D292—44no—
81C4×D73—44no—
82C4×D73—44no—
83Dic146—44no—
84C8×C73—81no—
85#10596831—81no—
86C22×C73—21no—
87C22×C73—21no—
88C22×C73—41no—
89C22×C73—41no—
90C22×C73—41no—
91C22×C73—82no—
92C22×C73#34212yes—
93C22×C73#34211yescharacteristic
94C2×D73—24no—
95C2×D73—42no—
96C2×D73—42no—
97C2×D73—44no—
98C2×D73—82no—
99#64408—164no—
100C4×C73—21no—
101C4×C73—21no—
102C4×C73—41no—
103Dic73—42no—
104#7305—731nomaximal, Sylow
105C2×C73—22no—
106C2×C73—81no—
107C2×C73#130411yescharacteristic
108C2×C73#139111yescharacteristic
109C2×C73#139111yescharacteristic
110D73—44no—
111#1782—732no—
112#1780—731no—
113C73#730511yescharacteristic, complemented, Sylow
114C22×#41—731no—
115C2×#99—734no—
116C2×#99—1462no—
117C2×C22⋊C8—731no—
118C2×C22⋊C8—1462no—
119C2×C22⋊C8#6440811yescharacteristic, complemented
120#381—1462no—
121C2×#41—2921no—
122C2×#41—2921no—
123C2×#41—2924no—
124C22×Q8—731no—
125C22×D4—732no—
126C22×D4—731no—
127C23×C4—732no—
128C23×C4C2×#6440811yescharacteristic
129C22×C8—21no—
130C22×C8—1461no—
131C2×C22⋊C4—1464no—
132#99—2924no—
133#99—2924no—
134C22⋊C8—41no—
135C22⋊C8—2924no—
136C22⋊C8—2921no—
137#95—2922no—
138#95—2922no—
139C24—732no—
140C24C4×#6440811yescharacteristic
141#41—2928no—
142#41—2928no—
143C2×Q8—2922no—
144C2×Q8—2921no—
145C2×D4—2921no—
146C2×D4—2922no—
147C2×D4—2922no—
148C2×D4—1464no—
149C2×D4—1464no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—42no—
153C22×C4—2922no—
154C22×C4—2924no—
155C22×C4—732no—
156C22×C4—1464no—
157C22×C4—1462no—
158C22×C4—1462no—
159C22×C4C22⋊#6440811yescharacteristic
160C22×C4C4⋊#6440811yescharacteristic
161C2×C8—42no—
162C2×C8—41no—
163C2×C8—2922no—
164C2×C8—2921no—
165C22⋊C4—2924no—
166C22⋊C4—2924no—
167C23—21no—
168C23—22no—
169C23—41no—
170C23—41no—
171C23—2922no—
172C23—2922no—
173C23—734no—
174C23—1462no—
175C23—1462no—
176C23(C2×#64408)⋊C411yescharacteristic
177Q8—2924no—
178D4—2924no—
179D4—2928no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—2924no—
186C2×C4—2924no—
187C2×C4—5844no—
188C2×C4—5844no—
189C2×C4—5844no—
190C2×C4—1462no—
191C2×C4—1462no—
192C2×C4—1462no—
193C2×C4#1455664911yescharacteristic
194C2×C4#1455665011yescharacteristic
195C8—81no—
196C8—5841no—
197C22—21no—
198C22—21no—
199C22—41no—
200C22—41no—
201C22—41no—
202C22—82no—
203C22—2924no—
204C22—2922no—
205C22—2922no—
206C22—5842no—
207C22—1464no—
208C22#1798946412yes—
209C22#1798946511yescharacteristic
210C4—21no—
211C4—21no—
212C4—41no—
213C4—2922no—
214C4—11684no—
215C2—22no—
216C2—81no—
217C2—2924no—
218C2#2262483011yescharacteristic
219C2#2262501911yescharacteristic
220C2#2262502011yescharacteristic
subgroupG/H
centerC22#17989465
commutatorC24×C73C42
FrattiniC23×C4C2×#64408
FittingC2×C22⋊C8×C73C4
socleC22×C73#342
prime radical, cosocleC22×#11924028C22
hypercenterC2×C22⋊C8#64408
hypocenterC73#7305
LCSG ▷ C24×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
4. C2×#14556649C4semidirect
7. C2×C22⋊#10596831C4semidirect
9. C2×C22⋊C8×C73C4semidirect
113. C73#7305semidirect
119. C2×C22⋊C8#64408semidirect

Maximal subgroups

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

subgroupindex
#226257602
#226098422
#730573