Finite Group Databasebeta

← #34005250

Subgroups — #34005250

Order 18688.

526 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 100 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#22625657C212yesmaximal
2#22624807C214yesmaximal, complemented
3#22612334C211yesmaximal, characteristic
4C2×C22⋊#10596833—22no—
5C2×#14556646C2214yes—
6#17989453—22no—
7C2×#14556550C411yescharacteristic
8C22×C4×Dic73C2211yescharacteristic
9#17988456C412yes—
10#17988452C2212yes—
11#17988445—22no—
12C4×#11924007—22no—
13C2×#117×C73C411yescharacteristic
14C22×#10596833—24no—
15C22⋊#10596833—28no—
16#14556646—28no—
17C23×Dic73D412yes—
18#14556550—42no—
19C2×C4⋊Dic73C2×C412yes—
20C2×#11924007—22no—
21C2×#11924007—22no—
22C2×C22⋊Dic73—21no—
23C2×C4×Dic73—24no—
24C2×C4×Dic73—21no—
25C2×C4×Dic73C2×C411yescharacteristic
26C2×C4×Dic73D412yes—
27C2×C4×Dic73C2311yescharacteristic
28#14556498—24no—
29C23×C4×C73C2×C411yescharacteristic
30#117×C73—42no—
31C2×C4⋊C4×C73C2×C412yes—
32C2×C22⋊C4×C73—21no—
33C2×C42×C73—21no—
34C2×#10596833—28no—
35C2×#10596833—44no—
36C2×#10596833—44no—
37C22×Dic73—24no—
38C22×Dic73—24no—
39C22×Dic73—22no—
40C22×Dic73—42no—
41C22×Dic73C22⋊C412yes—
42C22×Dic73C2×D412yes—
43C4⋊Dic73—42no—
44#11924007—44no—
45#11924007—44no—
46C22⋊Dic73—42no—
47C4×Dic73—22no—
48C4×Dic73—24no—
49C4×Dic73—42no—
50C4×Dic73#4114yes—
51C24×C73C22⋊C411yescharacteristic
52C22×C4×C73—22no—
53C22×C4×C73—22no—
54C22×C4×C73—22no—
55C22×C4×C73—22no—
56C22×C4×C73C22⋊C411yescharacteristic
57C22×C4×C73C22×C411yescharacteristic
58C4⋊C4×C73—42no—
59C22⋊C4×C73—42no—
60C42×C73—42no—
61C23×C73—21no—
62C23×C73—21no—
63C23×C73—22no—
64C23×C73—22no—
65C23×C73#10012yes—
66C23×C73C2×C22⋊C411yescharacteristic
67C2×C4×C73—28no—
68C2×C4×C73—21no—
69C2×C4×C73—21no—
70C2×C4×C73—21no—
71C2×C4×C73—21no—
72C2×C4×C73—42no—
73C2×C4×C73—42no—
74C2×C4×C73—42no—
75C2×C4×C73#10112yes—
76C2×C4×C73#11712yes—
77C2×Dic73—22no—
78C2×Dic73—22no—
79C2×Dic73—22no—
80C2×Dic73—22no—
81C2×Dic73—48no—
82C2×Dic73—42no—
83C2×Dic73—42no—
84C2×Dic73—42no—
85C2×Dic73#10414yes—
86C2×Dic73#12314yes—
87#10596833—48no—
88C22×C73—22no—
89C22×C73—24no—
90C22×C73—41no—
91C22×C73—42no—
92C22×C73—41no—
93C22×C73#38111yescharacteristic
94C22×C73C2×#10011yescharacteristic
95C22×C73C2×#10111yescharacteristic
96C22×C73C2×#10412yes—
97C22×C73#42112yes—
98C4×C73—22no—
99C4×C73—22no—
100C4×C73—82no—
101Dic73—24no—
102Dic73—24no—
103Dic73—82no—
104#8722—731nomaximal, Sylow
105C2×C73—42no—
106C2×C73#152611yescharacteristic
107C2×C73#153012yes—
108C2×C73#153711yescharacteristic
109C2×C73#182111yescharacteristic
110C2×C73#182612yes—
111#2285—731no—
112#1749—732no—
113#1295—734no—
114C73#872211yescharacteristic, complemented, Sylow
115C2×#117—731no—
116C2×#117#6440811yescharacteristic
117C22×C42—731no—
118C2×C22⋊C8—1462no—
119C2×#97—734no—
120#384—732no—
121#382—732no—
122#380—1462no—
123C4×C4⋊C4—1462no—
124#336—1462no—
125C23×C4—732no—
126C23×C4C2×#6440811yescharacteristic
127C22×C8—1464no—
128#117—42no—
129#117—2922no—
130C2×C4⋊C4—732no—
131C2×C4⋊C4—1462no—
132C2×C4⋊C4—1462no—
133C2×C4⋊C4C2×#6440812yes—
134C2×C22⋊C4—21no—
135C2×C22⋊C4—1461no—
136C2×C42—21no—
137C2×C42—731no—
138C2×C42—732no—
139C2×C42—731no—
140C2×C42—1461no—
141C2×C42—1464no—
142C22⋊C8—1468no—
143#97—1468no—
144#95—1464no—
145C24C22⋊#6440811yescharacteristic
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—2922no—
151C22×C4—732no—
152C22×C4—732no—
153C22×C4—1462no—
154C22×C4—1464no—
155C22×C4—1464no—
156C22×C4C22⋊#6440811yescharacteristic
157C22×C4C22×#6440811yescharacteristic
158C2×C8—2924no—
159C2×C8—2924no—
160C2×C8—1468no—
161C4⋊C4—42no—
162C4⋊C4—2922no—
163C4⋊C4—2924no—
164C4⋊C4—2924no—
165C22⋊C4—42no—
166C22⋊C4—2922no—
167C42—42no—
168C42—2922no—
169C42—734no—
170C42—1464no—
171C42—1462no—
172C23—21no—
173C23—21no—
174C23—22no—
175C23—22no—
176C23#1455665112yes—
177C23C2×C22⋊#6440811yescharacteristic
178C2×C4—28no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—2922no—
187C2×C4—2922no—
188C2×C4—2922no—
189C2×C4—2928no—
190C2×C4—734no—
191C2×C4—734no—
192C2×C4—1462no—
193C2×C4—1462no—
194C2×C4—1462no—
195C2×C4—1462no—
196C2×C4#1455665212yes—
197C2×C4#1455667012yes—
198C8—2928no—
199C22—22no—
200C22—24no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22#1798953011yescharacteristic
205C22C2×#1455665111yescharacteristic
206C22C2×#1455665211yescharacteristic
207C22D73⋊#10412yes—
208C22#1798958412yes—
209C4—22no—
210C4—22no—
211C4—82no—
212C4—5842no—
213C4—1464no—
214C4—1464no—
215C2—42no—
216C2#2262538811yescharacteristic
217C2#2262540012yes—
218C2#2262542211yescharacteristic
219C2#2262583011yescharacteristic
220C2#2262583912yes—
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
FittingC2×#117×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22⋊C4
cosocleC2×C4×Dic73C23
hypercenterC2×#117#64408
hypocenterC73#8722
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #22624807C2semidirect
114. C73#8722semidirect

Maximal subgroups

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

subgroupindex
#226256572
#226248072
#226123342
#872273