Finite Group Databasebeta

← #32980486

Subgroups — #32980486

Order 18688.

412 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 103 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#22618998C211yesmaximal, characteristic
2#22608722C212yesmaximal, complemented
3#22608593C211yesmaximal, characteristic
4#22607764C212yesmaximal, complemented
5C73×#1962C211yesmaximal, characteristic
6#17988665—22no—
7D4×#10596831—22no—
8#17988640C2212yes—
9#17988640C2212yes—
10#17988554—22no—
11#17988339—22no—
12#17988337—22no—
13#17988336C412yescomplemented
14#17988331C411yescharacteristic, complemented
15#17988331C411yescharacteristic, complemented
16#532×C73C2211yescharacteristic
17#423×C73C2211yescharacteristic
18C2×#104×C73—22no—
19C43×C73C2211yescharacteristic
20C2×#11924012—22no—
21C22×#10596831—22no—
22C4⋊#10596831C2×C412yes—
23C4⋊#10596831C2×C412yes—
24C4⋊#10596831D412yes—
25C4⋊#10596831D412yes—
26C22⋊#10596831—24no—
27C22⋊#10596831—22no—
28C22⋊#10596831—22no—
29C4×#10596831—22no—
30C4×#10596831—22no—
31C2×#41×C73D412yes—
32C2×M16×C73—21no—
33C4⋊Q8×C73C2×C411yescharacteristic
34#127×C73C2×C411yescharacteristic
35#124×C73Q812yes—
36#121×C73—22no—
37C4×D4×C73—22no—
38C2×C42×C73—21no—
39C2×C42×C73—22no—
40C2×C42×C73C2311yescharacteristic
41C4⋊C8×C73—22no—
42#104×C73—44no—
43#11924012—82no—
44C2×#10596831—22no—
45C2×#10596831—22no—
46C2×#10596831—22no—
47C2×#10596831—22no—
48C2×#10596831—82no—
49#41×C73—42no—
50#41×C73—42no—
51C2×Q8×C73C4⋊C412yes—
52C2×D4×C73—22no—
53C2×D4×C73—22no—
54C2×D4×C73C4⋊C412yes—
55C22×C4×C73—22no—
56C22×C4×C73—41no—
57C22×C4×C73C2×D411yescharacteristic
58C22×C4×C73#4112yes—
59M16×C73—42no—
60C2×C8×C73—41no—
61C4⋊C4×C73—22no—
62C22⋊C4×C73—24no—
63C42×C73—22no—
64C42×C73—24no—
65C42×C73—42no—
66C42×C73—41no—
67C42×C73C22×C411yescharacteristic
68C42×C73C2×D412yes—
69C42×C73C2×Q811yescharacteristic
70C23×C73—22no—
71C23×C73#12311yescharacteristic
72Q8×C73—42no—
73D4×C73—42no—
74D4×C73—42no—
75D4×C73—42no—
76D4×C73—82no—
77C2×C4×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73—21no—
80C2×C4×C73—21no—
81C2×C4×C73—22no—
82C2×C4×C73—42no—
83C2×C4×C73—44no—
84C2×C4×C73—42no—
85C2×C4×C73—42no—
86C2×C4×C73C2×C4⋊C411yescharacteristic
87C2×C4×C73C4×D412yes—
88C2×C4×C73#12011yescharacteristic
89C2×C4×C73C22⋊Q812yes—
90C8×C73—81no—
91#10596831—42no—
92#10596831—42no—
93#10596831—42no—
94#10596831—42no—
95C22×C73—21no—
96C22×C73—22no—
97C22×C73—42no—
98C22×C73—44no—
99C22×C73#38511yescharacteristic
100C4×C73—21no—
101C4×C73—22no—
102C4×C73—44no—
103C4×C73—42no—
104C4×C73#44312yes—
105C4×C73#44412yes—
106C4×C73#45311yescharacteristic
107C4×C73#45511yescharacteristic
108#8934—731nomaximal, Sylow
109C2×C73—41no—
110C2×C73—82no—
111C2×C73#185611yescharacteristic
112C2×C73#186612yes—
113#2979—731no—
114#1962D7311yescharacteristic
115#1574—732no—
116#1543—731no—
117#1276—732no—
118C73#893411yescharacteristic, complemented, Sylow
119#532C2×D7311yescharacteristic
120#436—1462no—
121C8×D4—1462no—
122#431—732no—
123#431—732no—
124#423C2×D7311yescharacteristic
125C2×#104—22no—
126#408—1462no—
127C43C2×D7311yescharacteristic
128#335—1462no—
129#334—1462no—
130#333—732no—
131#331—731no—
132#331—731no—
133C2×#41C22⋊D7312yes—
134C2×M16—21no—
135C2×M16—1462no—
136C22×C8—1462no—
137C4⋊Q8C4×D7311yescharacteristic
138#127C4×D7311yescharacteristic
139#124Dic14612yes—
140#121—22no—
141C4×D4—22no—
142C2×C42—21no—
143C2×C42—22no—
144C2×C42C22×D7311yescharacteristic
145C4⋊C8—22no—
146C4⋊C8—732no—
147C4⋊C8—732no—
148C4⋊C8—732no—
149C4⋊C8—732no—
150#104—44no—
151C22⋊C8—1464no—
152C22⋊C8—1462no—
153C22⋊C8—1462no—
154C4×C8—1462no—
155C4×C8—1462no—
156#41—42no—
157#41—42no—
158C2×Q8#1192400712yes—
159C2×D4—22no—
160C2×D4—22no—
161C2×D4#1192400712yes—
162C22×C4—22no—
163C22×C4—41no—
164C22×C4C2×C22⋊D7311yescharacteristic
165C22×C4#1192402712yes—
166M16—42no—
167M16—5842no—
168C2×C8—41no—
169C2×C8—5842no—
170C2×C8—1462no—
171C2×C8—1462no—
172C2×C8—1462no—
173C2×C8—1462no—
174C4⋊C4—22no—
175C22⋊C4—24no—
176C42—22no—
177C42—24no—
178C42—42no—
179C42—41no—
180C42C2×C4×D7311yescharacteristic
181C42D4×D7312yes—
182C42C2×Dic14611yescharacteristic
183C23—22no—
184C23#1455657211yescharacteristic
185Q8—42no—
186D4—42no—
187D4—42no—
188D4—42no—
189D4—82no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—44no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4C2×#1192400711yescharacteristic
200C2×C4#1455655112yes—
201C2×C4#1455655911yescharacteristic
202C2×C4#1455656812yes—
203C8—81no—
204C8—2922no—
205C8—2922no—
206C8—2922no—
207C8—2922no—
208C22—22no—
209C22—21no—
210C22—44no—
211C22—42no—
212C22#1798845911yescharacteristic
213C4—22no—
214C4—21no—
215C4—44no—
216C4—42no—
217C4#1798870112yes—
218C4#1798870612yes—
219C4#1798875411yescharacteristic
220C4#1798876411yescharacteristic
221C2—41no—
222C2—82no—
223C2#2261014011yescharacteristic
224C2#2261020412yes—
subgroupG/H
centerC2×C4#14556559
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1962C2
socleC22×C73#385
prime radical#532×C73C22
cosocleC2×C42×C73C23
hypercenter#1962D73
hypocenterC73#8934
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1962

Complements

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

NH ≅ G/Ntype
2. #22608722C2semidirect
4. #22607764C2semidirect
13. #17988336C4semidirect
14. #17988331C4semidirect
15. #17988331C4semidirect
118. C73#8934semidirect

Maximal subgroups

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

subgroupindex
#226189982
#226087222
#226085932
#226077642
C73×#19622
#893473