Finite Group Databasebeta

← #32983666

Subgroups — #32983666

Order 18688.

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

normal subgroups only

This group has 468 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#22619016C211yesmaximal, characteristic
2#22614916C211yesmaximal, characteristic
3#22608656C212yesmaximal
4#22607786C212yesmaximal
5C73×#1467C211yesmaximal, characteristic
6C2×#14556591C2211yescharacteristic
7C2×#14556589C412yes—
8#17988718—24no—
9#17988644—21no—
10#17988644C2212yes—
11#17988640—21no—
12#17988517—21no—
13#17988517—21no—
14#17988492C412yes—
15#17988485—21no—
16#17988485—21no—
17C4×C4⋊Dic73C2211yescharacteristic
18#17988335—24no—
19C2×C4×Q8×C73C2211yescharacteristic
20#432×C73C2212yes—
21#324×C73—21no—
22#324×C73—21no—
23C22×Dic146C2×C412yes—
24#14556591—22no—
25#14556591—22no—
26#14556589—44no—
27C2×C4⋊Dic73—21no—
28C2×C4⋊Dic73—21no—
29C2×C4⋊Dic73—21no—
30C2×#11924007—22no—
31C2×#11924007—22no—
32C2×C4×Dic73C2×C412yes—
33C4⋊#10596831—22no—
34C4⋊#10596831—22no—
35C4⋊#10596831D414yes—
36C22⋊#10596831—22no—
37#14556502—22no—
38#14556502—22no—
39C4×#10596831—22no—
40#14556498—22no—
41#14556498—22no—
42#14556498—21no—
43C22×Q8×C73C2×C411yescharacteristic
44C4×Q8×C73—22no—
45C4×Q8×C73—22no—
46C2×C4⋊C4×C73C2×C411yescharacteristic
47C2×C4⋊C4×C73D411yescharacteristic
48C2×C4⋊C4×C73D411yescharacteristic
49C2×C42×C73D411yescharacteristic
50C2×C42×C73D411yescharacteristic
51C2×C42×C73C2311yescharacteristic
52C4⋊C8×C73—22no—
53C22⋊C8×C73—22no—
54#97×C73—22no—
55C2×Dic146—24no—
56C2×Dic146—42no—
57C2×Dic146—42no—
58C22×Dic73—22no—
59C22×Dic73—22no—
60C2×#10596831—24no—
61C4⋊Dic73—24no—
62C4⋊Dic73—41no—
63C4⋊Dic73—42no—
64C4⋊Dic73—41no—
65#11924007—44no—
66#11924007—44no—
67C4×Dic73—42no—
68C2×Q8×C73—22no—
69C2×Q8×C73—22no—
70C2×Q8×C73—41no—
71C22×C4×C73C22⋊C411yescharacteristic
72C22×C4×C73C22⋊C411yescharacteristic
73C22×C4×C73C22⋊C411yescharacteristic
74C22×C4×C73C22⋊C411yescharacteristic
75C22×C4×C73C22×C411yescharacteristic
76C22×C4×C73C2×D411yescharacteristic
77C22×C4×C73C2×D411yescharacteristic
78C2×C8×C73—42no—
79C4⋊C4×C73—22no—
80C4⋊C4×C73—22no—
81C4⋊C4×C73—22no—
82C42×C73—21no—
83C42×C73—21no—
84C42×C73—21no—
85C42×C73—21no—
86C42×C73C2×D412yes—
87C42×C73#4112yes—
88C23×C73C2×C22⋊C411yescharacteristic
89Q8×C73—44no—
90C2×C4×C73—21no—
91C2×C4×C73—21no—
92C2×C4×C73—21no—
93C2×C4×C73—21no—
94C2×C4×C73—22no—
95C2×C4×C73—21no—
96C2×C4×C73—21no—
97C2×C4×C73—21no—
98C2×C4×C73—21no—
99C2×C4×C73—21no—
100C2×C4×C73—41no—
101C2×C4×C73—41no—
102C2×C4×C73—41no—
103C2×C4×C73#10012yes—
104C2×C4×C73C4×D412yes—
105C2×C4×C73#12011yescharacteristic
106C2×C4×C73#12112yes—
107C2×C4×C73#12311yescharacteristic
108C2×Dic73—24no—
109C2×Dic73—42no—
110C2×Dic73—42no—
111C2×Dic73—42no—
112C2×Dic73—42no—
113C2×Dic73—42no—
114Dic146—84no—
115C8×C73—82no—
116#10596831—44no—
117C22×C73—21no—
118C22×C73—21no—
119C22×C73#38611yescharacteristic
120C22×C73C2×#10011yescharacteristic
121C22×C73#41311yescharacteristic
122C4×C73—21no—
123C4×C73—22no—
124C4×C73—22no—
125C4×C73—22no—
126C4×C73—41no—
127C4×C73—41no—
128C4×C73—41no—
129C4×C73#45612yes—
130Dic73—44no—
131Dic73—82no—
132#9452—731nomaximal, Sylow
133C2×C73—21no—
134C2×C73—21no—
135C2×C73#188611yescharacteristic
136C2×C73#190011yescharacteristic
137C2×C73#190911yescharacteristic
138#2983—731no—
139#2546—731no—
140#1558—732no—
141#1467D7311yescharacteristic
142#1285—732no—
143C73#945211yescharacteristic, complemented, Sylow
144C2×C4⋊Q8—732no—
145C2×C4⋊Q8—731no—
146C2×C4×Q8C2×D7311yescharacteristic
147#446—1464no—
148#432—732no—
149#432—1461no—
150#432C2×D7312yes—
151#431—1461no—
152#398—1461no—
153#398—1461no—
154#391—732no—
155#389—1461no—
156#389—1461no—
157C4×C4⋊C4—731no—
158#333—1464no—
159#324—21no—
160#324—21no—
161C22×Q8—732no—
162C22×Q8C4×D7311yescharacteristic
163C4⋊Q8—2924no—
164C4⋊Q8—1462no—
165C4⋊Q8—1462no—
166C4×Q8—22no—
167C4×Q8—22no—
168C2×C4⋊C4—1462no—
169C2×C4⋊C4—1462no—
170C2×C4⋊C4—1461no—
171C2×C4⋊C4—1461no—
172C2×C4⋊C4—1461no—
173C2×C4⋊C4C4×D7311yescharacteristic
174C2×C4⋊C4C22⋊D7311yescharacteristic
175C2×C4⋊C4C22⋊D7311yescharacteristic
176C2×C42—732no—
177C2×C42D29211yescharacteristic
178C2×C42D29211yescharacteristic
179C2×C42C22×D7311yescharacteristic
180C4⋊C8—22no—
181C4⋊C8—734no—
182C4⋊C8—1462no—
183C4⋊C8—1462no—
184C22⋊C8—22no—
185C22⋊C8—1462no—
186#97—22no—
187#97—1462no—
188#97—1462no—
189C4×C8—1462no—
190#95—1462no—
191#95—1462no—
192#95—1461no—
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—41no—
196C2×Q8—2922no—
197C2×Q8—2922no—
198C2×Q8—1464no—
199C22×C4—1462no—
200C22×C4—1462no—
201C22×C4#1192400511yescharacteristic
202C22×C4#1192400511yescharacteristic
203C22×C4#1192400511yescharacteristic
204C22×C4#1192400511yescharacteristic
205C22×C4C2×C4×D7311yescharacteristic
206C22×C4C2×C22⋊D7311yescharacteristic
207C22×C4C2×D29211yescharacteristic
208C2×C8—42no—
209C2×C8—1464no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—2924no—
214C4⋊C4—2924no—
215C4⋊C4—2921no—
216C4⋊C4—2922no—
217C4⋊C4—2921no—
218C4⋊C4—1464no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—2922no—
224C42D4×D7312yes—
225C42#1192402712yes—
226C23C2×#1192400511yescharacteristic
227Q8—44no—
228Q8—5844no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—2922no—
243C2×C4—2922no—
244C2×C4—2922no—
245C2×C4—2922no—
246C2×C4—2922no—
247C2×C4—1464no—
248C2×C4#1455650712yes—
249C2×C4#1455655112yes—
250C2×C4#1455656111yescharacteristic
251C2×C4#1455656312yes—
252C2×C4#1455657511yescharacteristic
253C8—82no—
254C8—2924no—
255C22—21no—
256C22—21no—
257C22#1798846411yescharacteristic
258C22C2×#1455650711yescharacteristic
259C22#1798856911yescharacteristic
260C4—22no—
261C4—21no—
262C4—22no—
263C4—22no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—2924no—
268C4—5842no—
269C4#1798877212yes—
270C2—21no—
271C2—21no—
272C2#2261032211yescharacteristic
273C2#2261039211yescharacteristic
274C2#2261045111yescharacteristic
subgroupG/H
centerC22#17988464
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1467C2
socleC22×C73#386
prime radicalC23×C73C2×C22⋊C4
cosocleC2×C42×C73C23
hypercenter#1467D73
hypocenterC73#9452
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
143. C73#9452semidirect

Maximal subgroups

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

subgroupindex
#226190162
#226149162
#226086562
#226077862
C73×#14672
#945273