Finite Group Databasebeta

← #34000355

Subgroups — #34000355

Order 18688.

304 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 68 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#22626160C211yesmaximal, characteristic
2C8×C22⋊#64408C211yesmaximal, characteristic
3C22⋊C16×D73C211yesmaximal, characteristic
4C2×#14556665C412yescomplemented
5#17989555C411yescharacteristic
6C2×C8×#64408—21no—
7C4×C22⋊#64408C411yescharacteristic
8#17989482—21no—
9#17989482—21no—
10#17989452—21no—
11C22×C8×D73C2211yescharacteristic
12C2×C16×D73—21no—
13C22⋊#11924003C411yescharacteristic, complemented
14#17988366—21no—
15C22⋊C16×C73C411yescharacteristic, complemented
16C2×#11924036—21no—
17C2×C22⋊#64408—21no—
18C2×C4×#64408—21no—
19#14556665—42no—
20C2×#11924031—22no—
21#14556648C812yes—
22C22⋊#10596833—21no—
23C8×#64408—42no—
24(C2×#64408)⋊C4C812yes—
25C22×C4×D73C2×C411yescharacteristic
26C22×#10596831C2×C411yescharacteristic
27C2×C8×D73—42no—
28C2×C8×D73D411yescharacteristic
29C2×C8×D73D411yescharacteristic
30C2×C8×D73D411yescharacteristic
31C2×C8×D73Q811yescharacteristic
32C2×#11924003—21no—
33C16×D73—42no—
34C22×C8×C73C2×C411yescharacteristic
35C2×C16×C73—21no—
36C22×#64408—22no—
37#11924036—41no—
38#11924036—41no—
39C2×#10596833—22no—
40C22⋊#64408—24no—
41C4×#64408—41no—
42C4×#64408—41no—
43#11924031—42no—
44C23×D73M1611yescharacteristic
45C22×Dic73M1611yescharacteristic
46C2×C4×D73—41no—
47C2×C4×D73—41no—
48C2×C4×D73C22⋊C411yescharacteristic
49C2×C4×D73C4⋊C411yescharacteristic
50C2×C4×D73C2×C811yescharacteristic
51C2×C4×D73C2×C811yescharacteristic
52C2×#10596831—22no—
53C2×#10596831C22⋊C411yescharacteristic
54C2×#10596831C4⋊C411yescharacteristic
55C8×D73—22no—
56C8×D73—22no—
57C8×D73—41no—
58C8×D73—41no—
59#11924003—41no—
60C22×C4×C73C4211yescharacteristic
61C2×C8×C73—41no—
62C2×C8×C73C22⋊C411yescharacteristic
63C2×C8×C73C4⋊C411yescharacteristic
64C16×C73—41no—
65C23×C73#9711yescharacteristic
66C22×D73—22no—
67C22×D73—22no—
68C22×D73—41no—
69C22×D73C22⋊C811yescharacteristic
70C22×D73C4⋊C811yescharacteristic
71C2×#64408—24no—
72C2×#64408—42no—
73C2×#64408—42no—
74C2×C4×C73—21no—
75C2×C4×C73—21no—
76C2×C4×C73#9511yescharacteristic
77C2×C4×C73C4×C811yescharacteristic
78C2×Dic73—41no—
79C2×Dic73C22⋊C811yescharacteristic
80C2×Dic73C4⋊C811yescharacteristic
81C4×D73—21no—
82C4×D73—21no—
83C4×D73—21no—
84C4×D73—21no—
85C4×D73—41no—
86C4×D73—41no—
87#10596833—42no—
88C8×C73—21no—
89C8×C73—21no—
90#10596831—21no—
91#10596831#9912yes—
92C22×C73—21no—
93C22×C73—21no—
94C22×C73—21no—
95C22×C73#33611yescharacteristic
96C2×D73—21no—
97C2×D73—21no—
98C2×D73—21no—
99C2×D73—21no—
100C2×D73—44no—
101C2×D73#35012yes—
102C2×D73#36412yes—
103#64408—44no—
104C4×C73—21no—
105C4×C73#34211yescharacteristic
106C4×C73#34411yescharacteristic
107Dic73—21no—
108Dic73—21no—
109#7202—731nomaximal, Sylow
110C2×C73—41no—
111C2×C73#128211yescharacteristic
112C2×C73#137611yescharacteristic
113C2×C73#137911yescharacteristic
114D73—22no—
115D73—22no—
116#2112—731no—
117C2×C22⋊C16—731no—
118C8×C22⋊C4—731no—
119C73#720211yescharacteristic, complemented, Sylow
120C23×C8—731no—
121C2×M32—732no—
122C22×C16—1461no—
123C2×C22⋊C8—731no—
124C2×C4×C8—1461no—
125C4×C22⋊C4—731no—
126C22⋊C16—731no—
127C22⋊C16—1461no—
128C22⋊C16—1461no—
129C22⋊C16—1461no—
130C22⋊C16#6440811yescharacteristic, complemented
131#336—1461no—
132C23×C4—731no—
133C22×C8—2922no—
134C22×C8—731no—
135C22×C8—731no—
136C22×C8—731no—
137C22×C8—731no—
138C22×C8—731no—
139C22×C8—1461no—
140C22×C8C2×#6440811yescharacteristic
141C2×C22⋊C4—1461no—
142C2×C42—1461no—
143M32—2922no—
144C2×C16—21no—
145C2×C16—2922no—
146C2×C16—1462no—
147C2×C16—1461no—
148C22⋊C8—732no—
149C22⋊C8—1461no—
150C4×C8—2922no—
151#95—732no—
152C24—731no—
153C22×C4—2921no—
154C22×C4—2921no—
155C22×C4—731no—
156C22×C4—731no—
157C22×C4—731no—
158C22×C4—731no—
159C22×C4—731no—
160C22×C4—1462no—
161C22×C4C4×#6440811yescharacteristic
162C2×C8—41no—
163C2×C8—2921no—
164C2×C8—2921no—
165C2×C8—2921no—
166C2×C8—2921no—
167C2×C8—731no—
168C2×C8—731no—
169C2×C8—1462no—
170C2×C8—1462no—
171C2×C8—1462no—
172C2×C8—1462no—
173C2×C8C22⋊#6440811yescharacteristic
174C2×C8C4⋊#6440811yescharacteristic
175C22⋊C4—1464no—
176C42—2921no—
177C42—2921no—
178C16—41no—
179C16—2921no—
180C16—2922no—
181C23—2921no—
182C23—731no—
183C23—731no—
184C23—1462no—
185C23—1462no—
186C23#1455664511yescharacteristic
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—2921no—
190C2×C4—2921no—
191C2×C4—2922no—
192C2×C4—2922no—
193C2×C4—2921no—
194C2×C4—731no—
195C2×C4—731no—
196C2×C4—1464no—
197C2×C4—1461no—
198C2×C4—1461no—
199C2×C4—1461no—
200C2×C4—1461no—
201C2×C4(C2×#64408)⋊C411yescharacteristic
202C2×C4C8×#6440811yescharacteristic
203C8—21no—
204C8—21no—
205C8—2922no—
206C8—732no—
207C8—1461no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—2924no—
212C22—732no—
213C22—732no—
214C22—1461no—
215C22—1461no—
216C22—1461no—
217C22—1461no—
218C22#1798945211yescharacteristic
219C4—21no—
220C4—2924no—
221C4—1461no—
222C4—1461no—
223C4#1798946411yescharacteristic
224C4#1798947011yescharacteristic
225C2—41no—
226C2—1462no—
227C2—1462no—
228C2#2262477211yescharacteristic
229C2#2262497411yescharacteristic
230C2#2262498411yescharacteristic
subgroupG/H
centerC2×C4(C2×#64408)⋊C4
commutatorC2×C4×C73C4×C8
FrattiniC22×C8C2×#64408
FittingC22⋊C16×C73C4
socleC22×C73#336
prime radicalC23×D73M16
cosocleC22×C8×D73C22
hypercenterC22⋊C16#64408
hypocenterC73#7202
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
4. C2×#14556665C4semidirect
13. C22⋊#11924003C4semidirect
15. C22⋊C16×C73C4semidirect
119. C73#7202semidirect
130. C22⋊C16#64408semidirect

Maximal subgroups

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

subgroupindex
#226261602
C8×C22⋊#644082
C22⋊C16×D732
#720273