Finite Group Databasebeta

← #34001667

Subgroups — #34001667

Order 18688.

426 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 120 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#22625848C211yesmaximal, characteristic
2C4×#14556658C211yesmaximal, characteristic
3#22624750C214yesmaximal
4#22618292C211yesmaximal, characteristic
5C2×#14556658—21no—
6C2×C4⋊#10596833—21no—
7C2×C4×#10596833—21no—
8#17989453—21no—
9#17989453C2212yes—
10#17989453C2212yes—
11C2×#14556582—21no—
12#17988486—21no—
13#17988486C412yes—
14#17988483—21no—
15#17988483C2212yes—
16#17988457C411yescharacteristic
17#17988452—21no—
18C42×Dic73C2211yescharacteristic
19#384×C73C411yescharacteristic
20C22×#10596833—22no—
21C22×#10596833—22no—
22#14556658—24no—
23C4⋊#10596833—42no—
24C4×#10596833—42no—
25#14556582—42no—
26#14556582—42no—
27C2×C4⋊Dic73—22no—
28C2×C4⋊Dic73—21no—
29C2×C4⋊Dic73—21no—
30C2×C4⋊Dic73C2×C412yes—
31C2×#11924007—22no—
32C2×C4×Dic73C2×C411yescharacteristic
33C2×C4×Dic73D411yescharacteristic
34C2×C4×Dic73D411yescharacteristic
35C2×C4×Dic73D411yescharacteristic
36C2×C4×Dic73D411yescharacteristic
37C2×C4×Dic73C2311yescharacteristic
38#14556498—22no—
39#14556498—22no—
40C2×C4⋊C4×C73—21no—
41C2×C4⋊C4×C73—21no—
42C2×C4⋊C4×C73C2×C412yes—
43C2×C42×C73C2×C411yescharacteristic
44C2×#10596833—24no—
45C2×#10596833—42no—
46C2×#10596833—42no—
47C2×#10596833—42no—
48C2×#10596833—42no—
49C2×#10596833—42no—
50C22×Dic73—22no—
51C22×Dic73C22⋊C411yescharacteristic
52C22×Dic73C22⋊C411yescharacteristic
53C22×Dic73C2×D411yescharacteristic
54C22×Dic73C2×D411yescharacteristic
55C4⋊Dic73—24no—
56C4⋊Dic73—42no—
57C4⋊Dic73—42no—
58C4⋊Dic73—44no—
59#11924007—42no—
60#11924007—42no—
61C4×Dic73—22no—
62C4×Dic73—22no—
63C4×Dic73—41no—
64C4×Dic73—41no—
65C4×Dic73D812yes—
66C4×Dic73SD1612yes—
67C4×Dic73SD1612yes—
68C4×Dic73Q1612yes—
69C22×C4×C73—22no—
70C22×C4×C73C22⋊C411yescharacteristic
71C22×C4×C73C22⋊C411yescharacteristic
72C22×C4×C73C22×C411yescharacteristic
73C4⋊C4×C73—42no—
74C4⋊C4×C73—42no—
75C4⋊C4×C73—42no—
76C42×C73—22no—
77C23×C73C2×C22⋊C411yescharacteristic
78C2×C4×C73—21no—
79C2×C4×C73—21no—
80C2×C4×C73—21no—
81C2×C4×C73—21no—
82C2×C4×C73—42no—
83C2×C4×C73—42no—
84C2×C4×C73—42no—
85C2×C4×C73#10112yes—
86C2×C4×C73#10212yes—
87C2×C4×C73#10312yes—
88C2×C4×C73#10412yes—
89C2×C4×C73#13112yes—
90C2×Dic73—21no—
91C2×Dic73—21no—
92C2×Dic73—21no—
93C2×Dic73—21no—
94C2×Dic73—21no—
95C2×Dic73—21no—
96C2×Dic73—21no—
97C2×Dic73—21no—
98C2×Dic73—42no—
99C2×Dic73—42no—
100C2×Dic73—42no—
101C2×Dic73#10212yes—
102C2×Dic73#10312yes—
103C2×Dic73C2×D811yescharacteristic
104C2×Dic73C2×SD1611yescharacteristic
105C2×Dic73C2×SD1611yescharacteristic
106C2×Dic73C2×Q1611yescharacteristic
107#10596833—44no—
108#10596833—82no—
109C22×C73#40811yescharacteristic
110C22×C73#41011yescharacteristic
111C22×C73C2×#10111yescharacteristic
112C22×C73C2×#10211yescharacteristic
113C22×C73C2×#10311yescharacteristic
114C22×C73C2×#10411yescharacteristic
115C22×C73#42111yescharacteristic
116C4×C73—22no—
117C4×C73—22no—
118C4×C73—82no—
119C4×C73#33214yes—
120Dic73—22no—
121Dic73—22no—
122Dic73—21no—
123Dic73—21no—
124Dic73—21no—
125Dic73—21no—
126Dic73—82no—
127#7663—731nomaximal, Sylow
128C2×C73#147011yescharacteristic
129C2×C73#148011yescharacteristic
130C2×C73#149311yescharacteristic
131C2×C73#150211yescharacteristic
132C2×C73#151811yescharacteristic
133C2×C73#152811yescharacteristic
134C2×C73C2×#33211yescharacteristic
135#2859—731no—
136#1831—731no—
137C4×C4⋊C8—731no—
138#1271—734no—
139C73#766311yescharacteristic, complemented, Sylow
140C2×#125—1461no—
141C2×C4⋊C8—1461no—
142C2×C4⋊C8—1461no—
143C2×C4×C8—1461no—
144#389—732no—
145#389—732no—
146#389—1461no—
147#389—1461no—
148#384—731no—
149#384#6440811yescharacteristic
150#382—1461no—
151C43—731no—
152#336—732no—
153#336—732no—
154#336—1461no—
155C22×C8—1462no—
156C22×C8—1462no—
157#125—2922no—
158#125—2922no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—732no—
162C2×C4⋊C4—1462no—
163C2×C4⋊C4—1462no—
164C2×C4⋊C4—1461no—
165C2×C4⋊C4—1461no—
166C2×C4⋊C4C2×#6440812yes—
167C2×C42—731no—
168C2×C42—731no—
169C2×C42—731no—
170C2×C42—731no—
171C2×C42—731no—
172C2×C42—731no—
173C2×C42C2×#6440811yescharacteristic
174C4⋊C8—2922no—
175C4⋊C8—1464no—
176C4×C8—2922no—
177#95—1462no—
178#95—1462no—
179C22×C4—22no—
180C22×C4—731no—
181C22×C4—731no—
182C22×C4—731no—
183C22×C4—731no—
184C22×C4—1462no—
185C22×C4C22⋊#6440811yescharacteristic
186C22×C4C22⋊#6440811yescharacteristic
187C22×C4C22×#6440811yescharacteristic
188C2×C8—2922no—
189C2×C8—2922no—
190C2×C8—2922no—
191C2×C8—2922no—
192C2×C8—2922no—
193C2×C8—1464no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—2922no—
198C4⋊C4—2922no—
199C4⋊C4—2922no—
200C4⋊C4—2924no—
201C4⋊C4—2922no—
202C4⋊C4—1464no—
203C42—22no—
204C42—2921no—
205C42—2921no—
206C42—732no—
207C42—732no—
208C42—732no—
209C42—732no—
210C42—1462no—
211C42—1462no—
212C23C2×C22⋊#6440811yescharacteristic
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—2922no—
221C2×C4—2922no—
222C2×C4—2922no—
223C2×C4—731no—
224C2×C4—732no—
225C2×C4—731no—
226C2×C4—731no—
227C2×C4—732no—
228C2×C4—731no—
229C2×C4—1461no—
230C2×C4—1461no—
231C2×C4—1461no—
232C2×C4—1461no—
233C2×C4—1461no—
234C2×C4—1461no—
235C2×C4—1461no—
236C2×C4—1461no—
237C2×C4#1455665212yes—
238C2×C4#1455665312yes—
239C2×C4#1455665412yes—
240C2×C4#1455665512yes—
241C2×C4#1455667912yes—
242C8—2924no—
243C8—5842no—
244C22#1798956211yescharacteristic
245C22#1798956711yescharacteristic
246C22C2×#1455665211yescharacteristic
247C22C2×#1455665311yescharacteristic
248C22C2×#1455665411yescharacteristic
249C22C2×#1455665511yescharacteristic
250C22#1798958611yescharacteristic
251C4—22no—
252C4—22no—
253C4—82no—
254C4—5842no—
255C4—1462no—
256C4—1461no—
257C4—1461no—
258C4—1461no—
259C4—1461no—
260C4—1462no—
261C4#1798944614yes—
262C2#2262520511yescharacteristic
263C2#2262523811yescharacteristic
264C2#2262528111yescharacteristic
265C2#2262531111yescharacteristic
266C2#2262536511yescharacteristic
267C2#2262539311yescharacteristic
268C2C2×#1798944611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
Fitting#384×C73C4
socle, prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4×Dic73C23
hypercenter#384#64408
hypocenterC73#7663
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
139. C73#7663semidirect

Maximal subgroups

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

subgroupindex
#226258482
C4×#145566582
#226247502
#226182922
#766373