Finite Group Databasebeta

← #32995389

Subgroups — #32995389

Order 18688.

434 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 77 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#22612556C211yesmaximal, characteristic
2#22608259C212yesmaximal
3#22607876C212yesmaximal, complemented
4#22607875C211yesmaximal, characteristic, complemented
5C73×#1324C211yesmaximal, characteristic, complemented
6C2×#14556549C411yescharacteristic
7C2×#14556548C411yescharacteristic
8C2×C4⋊C4×D73C2211yescharacteristic
9#17988549—22no—
10#17988484—22no—
11#17988461—22no—
12#17988457C411yescharacteristic
13#17988456C2211yescharacteristic
14#17988452C411yescharacteristic
15#17988313C2212yes—
16#17988312—22no—
17#382×C73C2211yescharacteristic
18#324×C73C2212yes—
19C22×C4×D73C2×C411yescharacteristic
20C22×C4×D73D412yes—
21C2×#11924011—42no—
22#14556549—42no—
23#14556548—22no—
24#14556548—22no—
25C2×C4⋊Dic73—22no—
26C2×C4⋊Dic73C2×C411yescharacteristic
27C2×C4⋊Dic73C2×C411yescharacteristic
28C2×#11924007—21no—
29C2×#11924007—22no—
30C2×#11924007D412yes—
31C4⋊C4×D73—42no—
32C2×#11924005—21no—
33C2×#11924005—21no—
34C2×C4×Dic73—21no—
35C2×C4×Dic73C2×C411yescharacteristic
36C22⋊#10596831—22no—
37#14556503—42no—
38#14556498—22no—
39C2×C4⋊C4×C73C2×C411yescharacteristic
40C2×C4⋊C4×C73C2311yescharacteristic
41C2×C42×C73C2×C411yescharacteristic
42C22⋊C8×C73—22no—
43#95×C73—22no—
44C23×D73C22⋊C411yescharacteristic
45C22×Dic73—21no—
46C22×Dic73—21no—
47C22×Dic73C22⋊C411yescharacteristic
48C22×Dic73C22⋊C412yes—
49C2×C4×D73—22no—
50C2×C4×D73—21no—
51C2×C4×D73—21no—
52C2×C4×D73—22no—
53C2×C4×D73—22no—
54C2×C4×D73—22no—
55C2×C4×D73—82no—
56#11924011—84no—
57C2×#10596831—42no—
58C4⋊Dic73—41no—
59C4⋊Dic73—41no—
60C4⋊Dic73—82no—
61#11924007—24no—
62#11924007—42no—
63#11924007—82no—
64#11924005—24no—
65#11924005—42no—
66C4×Dic73—21no—
67C4×Dic73—42no—
68C4×Dic73M1612yescomplemented
69C22×C4×C73—21no—
70C22×C4×C73—21no—
71C22×C4×C73C22×C411yescharacteristic
72C22×C4×C73C2×D412yes—
73C2×C8×C73—42no—
74C4⋊C4×C73—41no—
75C4⋊C4×C73—41no—
76C42×C73—21no—
77C42×C73M1612yescomplemented
78C23×C73C2×C22⋊C411yescharacteristic
79C22×D73—21no—
80C22×D73—21no—
81C22×D73—41no—
82C22×D73—41no—
83C22×D73#9912yes—
84C2×C4×C73—21no—
85C2×C4×C73—21no—
86C2×C4×C73—22no—
87C2×C4×C73—22no—
88C2×C4×C73—41no—
89C2×C4×C73—41no—
90C2×C4×C73—42no—
91C2×C4×C73—42no—
92C2×C4×C73—41no—
93C2×C4×C73C2×M1611yescharacteristic
94C2×C4×C73C2×M1611yescharacteristic
95C2×Dic73—21no—
96C2×Dic73—21no—
97C2×Dic73—22no—
98C2×Dic73—22no—
99C2×Dic73—41no—
100C2×Dic73—41no—
101C2×Dic73—42no—
102C2×Dic73—42no—
103C2×Dic73—41no—
104C2×Dic73#10112yes—
105C4×D73—24no—
106C4×D73—24no—
107C4×D73—44no—
108C4×D73—82no—
109C8×C73—82no—
110#10596831—82no—
111C22×C73—21no—
112C22×C73—21no—
113C22×C73#40711yescharacteristic
114C22×C73C2×#9911yescharacteristic
115C22×C73C2×#10111yescharacteristic
116C2×D73—22no—
117C2×D73—22no—
118C2×D73—22no—
119C2×D73—42no—
120C2×D73—42no—
121C4×C73—21no—
122C4×C73—21no—
123C4×C73—42no—
124C4×C73—42no—
125C4×C73—81no—
126Dic73—22no—
127Dic73—42no—
128Dic73—42no—
129Dic73—81no—
130#11514—731nomaximal, Sylow
131C2×C73—21no—
132C2×C73—21no—
133C2×C73#146311yescharacteristic
134C2×C73#212711yescharacteristic
135C2×C73#213311yescharacteristic
136D73—42no—
137#2317—731no—
138#1463—732no—
139#1325—732no—
140#1324—731no—
141#1324D7311yescharacteristic, complemented
142C73#1151411yescharacteristic, complemented, Sylow
143C2×#117—731no—
144C2×#117—731no—
145C22×C4⋊C4—731no—
146#407—1462no—
147#389—1462no—
148#385—1462no—
149#384—731no—
150#384—731no—
151#382—731no—
152#382C2×D7311yescharacteristic
153#324—732no—
154#324—1462no—
155#324C2×D7312yes—
156C23×C4—732no—
157C23×C4—731no—
158C2×M16—2922no—
159#117—2922no—
160#117—1462no—
161#117—1462no—
162C2×C4⋊C4—2922no—
163C2×C4⋊C4—731no—
164C2×C4⋊C4—732no—
165C2×C4⋊C4—731no—
166C2×C4⋊C4—1462no—
167C2×C4⋊C4—1462no—
168C2×C4⋊C4—1461no—
169C2×C4⋊C4C4×D7311yescharacteristic
170C2×C4⋊C4C22×D7311yescharacteristic
171C2×C22⋊C4—1461no—
172C2×C22⋊C4—1461no—
173C2×C42—731no—
174C2×C42—1461no—
175C2×C42C4×D7311yescharacteristic
176C22⋊C8—22no—
177C22⋊C8—2922no—
178C22⋊C8—1462no—
179#95—22no—
180#95—1462no—
181C24—731no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—5842no—
185C22×C4—732no—
186C22×C4—731no—
187C22×C4—1462no—
188C22×C4—1462no—
189C22×C4—1462no—
190C22×C4—1462no—
191C22×C4—1461no—
192C22×C4—1461no—
193C22×C4—1461no—
194C22×C4—1461no—
195C22×C4C2×C4×D7311yescharacteristic
196C22×C4D4×D7312yes—
197M16—5844no—
198C2×C8—42no—
199C2×C8—2922no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—2921no—
203C4⋊C4—2922no—
204C4⋊C4—2921no—
205C4⋊C4—5842no—
206C4⋊C4—5842no—
207C4⋊C4—1464no—
208C22⋊C4—2922no—
209C22⋊C4—1464no—
210C42—21no—
211C42—2922no—
212C42—732no—
213C42—1461no—
214C42#1192401112yescomplemented
215C23—2921no—
216C23—2921no—
217C23—732no—
218C23—1461no—
219C23—1461no—
220C23C22⋊C4×D7311yescharacteristic
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—41no—
230C2×C4—2924no—
231C2×C4—2921no—
232C2×C4—2921no—
233C2×C4—2922no—
234C2×C4—2922no—
235C2×C4—2921no—
236C2×C4—5842no—
237C2×C4—732no—
238C2×C4—1464no—
239C2×C4—1464no—
240C2×C4—1462no—
241C2×C4—1462no—
242C2×C4—1461no—
243C2×C4—1461no—
244C2×C4M16×D7311yescharacteristic
245C2×C4C2×#1192401111yescharacteristic
246C8—82no—
247C8—5842no—
248C22—21no—
249C22—21no—
250C22—2922no—
251C22—2922no—
252C22—1462no—
253C22—1462no—
254C22—1462no—
255C22#1798854911yescharacteristic
256C22#99×D7311yescharacteristic
257C22#101×D7311yescharacteristic
258C4—21no—
259C4—21no—
260C4—42no—
261C4—42no—
262C4—81no—
263C4—2922no—
264C4—2922no—
265C4—5841no—
266C4—1462no—
267C2—21no—
268C2—21no—
269C2—2922no—
270C2#2260825911yescharacteristic
271C2#2261159911yescharacteristic
272C2#2261161711yescharacteristic
subgroupG/H
centerC22#99×D73
commutatorC22×C4×C73C22×C4
FrattiniC2×C4⋊C4C22×D73
FittingC73×#1324C2
socleC22×C73C2×#99
prime radicalC23×D73C22⋊C4
cosocleC2×C4⋊C4×C73C23
hypercenter#1324D73
hypocenterC73#11514
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
3. #22607876C2semidirect
4. #22607875C2semidirect
5. C73×#1324C2semidirect
68. C4×Dic73M16semidirect
77. C42×C73M16semidirect
141. #1324D73semidirect
142. C73#11514semidirect
214. C42#11924011semidirect

Maximal subgroups

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

subgroupindex
#226125562
#226082592
#226078762
#226078752
C73×#13242
#1151473