Finite Group Databasebeta

← #34010112

Subgroups — #34010112

Order 18688.

418 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 80 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#22625182C211yesmaximal, characteristic
2#22625182C211yesmaximal, characteristic
3#22624875C214yesmaximal
4#22612554C211yesmaximal, characteristic
5#17989607—21no—
6#17989607—21no—
7#17989432—21no—
8#17989432—21no—
9#17989430C2212yes—
10#17989430C2212yes—
11C2×#14556550C2211yescharacteristic
12C22×C4⋊Dic73C411yescharacteristic
13#17988486—21no—
14#17988486—21no—
15#17988462C412yes—
16#17988462C2212yes—
17#17988457—21no—
18#17988453—21no—
19C2×#117×C73C411yescharacteristic
20#14556658—41no—
21#14556658—41no—
22C22⋊#10596833—22no—
23C22⋊#10596833—22no—
24#14556646—41no—
25#14556646—41no—
26C23×Dic73C2×C412yes—
27#14556550—41no—
28#14556550—41no—
29C2×C4⋊Dic73—22no—
30C2×C4⋊Dic73—22no—
31C2×C4⋊Dic73—21no—
32C2×C4⋊Dic73—21no—
33C2×C4⋊Dic73—41no—
34C2×C4⋊Dic73—41no—
35C2×C4⋊Dic73D411yescharacteristic
36C2×C4⋊Dic73D411yescharacteristic
37C2×C22⋊Dic73C2×C411yescharacteristic
38C2×C22⋊Dic73C2311yescharacteristic
39C2×C4×Dic73D411yescharacteristic
40C2×C4×Dic73D411yescharacteristic
41#14556498—22no—
42#14556498—22no—
43C23×C4×C73C2×C411yescharacteristic
44#117×C73—24no—
45C2×C4⋊C4×C73—21no—
46C2×C22⋊C4×C73C2×C412yes—
47C2×C42×C73—21no—
48C2×#10596833—42no—
49C2×#10596833—42no—
50C22×Dic73—22no—
51C22×Dic73—42no—
52C22×Dic73—82no—
53C22×Dic73C22⋊C411yescharacteristic
54C22×Dic73C22⋊C411yescharacteristic
55C22×Dic73C2×D411yescharacteristic
56C22×Dic73C2×D411yescharacteristic
57C4⋊Dic73—41no—
58C4⋊Dic73—41no—
59C4⋊Dic73—42no—
60C4⋊Dic73—41no—
61C4⋊Dic73—41no—
62C4⋊Dic73—82no—
63C4⋊Dic73—82no—
64C22⋊Dic73—41no—
65C22⋊Dic73—41no—
66C4×Dic73—21no—
67C4×Dic73—21no—
68C4×Dic73—21no—
69C4×Dic73—21no—
70C24×C73C22×C411yescharacteristic
71C22×C4×C73—22no—
72C22×C4×C73—21no—
73C22×C4×C73—21no—
74C22×C4×C73—22no—
75C22×C4×C73—22no—
76C22×C4×C73C22⋊C411yescharacteristic
77C22×C4×C73C22⋊C411yescharacteristic
78C4⋊C4×C73—24no—
79C22⋊C4×C73—22no—
80C22⋊C4×C73M1614yes—
81C42×C73—24no—
82C23×C73—21no—
83C23×C73—21no—
84C23×C73—41no—
85C23×C73—41no—
86C23×C73C2×C22⋊C411yescharacteristic
87C23×C73C2×M1612yes—
88C2×C4×C73—24no—
89C2×C4×C73—24no—
90C2×C4×C73—21no—
91C2×C4×C73—21no—
92C2×C4×C73—21no—
93C2×C4×C73—21no—
94C2×C4×C73—24no—
95C2×C4×C73—42no—
96C2×C4×C73—42no—
97C2×C4×C73#9911yescharacteristic
98C2×C4×C73#9911yescharacteristic
99C2×C4×C73#10112yes—
100C2×Dic73—21no—
101C2×Dic73—21no—
102C2×Dic73—21no—
103C2×Dic73—21no—
104C2×Dic73—41no—
105C2×Dic73—41no—
106C2×Dic73—41no—
107C2×Dic73—41no—
108C2×Dic73—42no—
109C2×Dic73—42no—
110C2×Dic73—42no—
111C2×Dic73—84no—
112#10596833—82no—
113#10596833—82no—
114C22×C73—21no—
115C22×C73—21no—
116C22×C73—22no—
117C22×C73—42no—
118C22×C73—42no—
119C22×C73—41no—
120C22×C73—41no—
121C22×C73#40711yescharacteristic
122C22×C73C2×#9911yescharacteristic
123C22×C73C2×#10111yescharacteristic
124C4×C73—21no—
125C4×C73—21no—
126C4×C73—22no—
127C4×C73—44no—
128Dic73—41no—
129Dic73—41no—
130Dic73—41no—
131Dic73—41no—
132Dic73—82no—
133#11520—731nomaximal, Sylow
134C2×C73—21no—
135C2×C73—21no—
136C2×C73—42no—
137C2×C73#146311yescharacteristic
138C2×C73#212211yescharacteristic
139C2×C73#212311yescharacteristic
140#2317—731no—
141#1464—731no—
142#1464—731no—
143#1326—734no—
144C73#1152011yescharacteristic, complemented, Sylow
145C2×#117—731no—
146C2×#117#6440811yescharacteristic
147C22×C4⋊C4—731no—
148#432—1461no—
149#432—1461no—
150#389—1461no—
151#389—1461no—
152#385—732no—
153#385—732no—
154#384—1461no—
155#382—1461no—
156#324—1461no—
157#324—1461no—
158#323—732no—
159#323—732no—
160C23×C4—732no—
161C23×C4C2×#6440811yescharacteristic
162#117—24no—
163#117—2921no—
164#117—2921no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—2921no—
167C2×C4⋊C4—2921no—
168C2×C4⋊C4—731no—
169C2×C4⋊C4—731no—
170C2×C4⋊C4—1461no—
171C2×C4⋊C4—1461no—
172C2×C4⋊C4—1462no—
173C2×C4⋊C4—1462no—
174C2×C22⋊C4—731no—
175C2×C22⋊C4—731no—
176C2×C22⋊C4C2×#6440812yes—
177C2×C42—21no—
178C2×C42—731no—
179C2×C42—731no—
180C4⋊C8—2921no—
181C4⋊C8—2921no—
182C22⋊C8—1462no—
183C22⋊C8—1462no—
184#97—2921no—
185#97—2921no—
186#95—1462no—
187#95—1462no—
188C24C22×#6440811yescharacteristic
189C22×C4—22no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—2922no—
195C22×C4—5842no—
196C22×C4—731no—
197C22×C4—731no—
198C22×C4—731no—
199C22×C4—731no—
200C22×C4—1462no—
201C22×C4C22⋊#6440811yescharacteristic
202C22×C4C22⋊#6440811yescharacteristic
203C2×C8—2922no—
204C2×C8—2922no—
205C4⋊C4—24no—
206C4⋊C4—2922no—
207C4⋊C4—2921no—
208C4⋊C4—2921no—
209C4⋊C4—2921no—
210C4⋊C4—2921no—
211C4⋊C4—5842no—
212C4⋊C4—5842no—
213C22⋊C4—22no—
214C22⋊C4—2921no—
215C22⋊C4—2921no—
216C22⋊C4#1192403714yes—
217C42—24no—
218C42—1461no—
219C42—1461no—
220C42—1461no—
221C42—1461no—
222C23—21no—
223C23—21no—
224C23—41no—
225C23—41no—
226C23C2×C22⋊#6440811yescharacteristic
227C23C2×#1192403712yes—
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—24no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—2921no—
238C2×C4—2921no—
239C2×C4—2921no—
240C2×C4—2921no—
241C2×C4—2922no—
242C2×C4—2922no—
243C2×C4—2922no—
244C2×C4—5844no—
245C2×C4—1461no—
246C2×C4—1461no—
247C2×C4—1461no—
248C2×C4—1461no—
249C2×C4#1455665011yescharacteristic
250C2×C4#1455665011yescharacteristic
251C2×C4#1455665212yes—
252C8—5842no—
253C8—5842no—
254C22—21no—
255C22—21no—
256C22—22no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22#1798955711yescharacteristic
262C22C2×#1455665011yescharacteristic
263C22C2×#1455665211yescharacteristic
264C4—21no—
265C4—21no—
266C4—22no—
267C4—44no—
268C4—2921no—
269C4—2921no—
270C4—2921no—
271C4—2921no—
272C4—5842no—
273C2—21no—
274C2—21no—
275C2—42no—
276C2#2262517911yescharacteristic
277C2#2262619211yescharacteristic
278C2#2262619511yescharacteristic
subgroupG/H
centerC22C2×#14556650
commutator, prime radicalC24×C73C22×C4
FrattiniC24C22×#64408
FittingC2×#117×C73C4
socleC22×C73C2×#99
cosocleC2×C22⋊Dic73C23
hypercenterC2×#117#64408
hypocenterC73#11520
LCSG ▷ C24×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
144. C73#11520semidirect

Maximal subgroups

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

subgroupindex
#226251822
#226248752
#226125542
#1152073