Finite Group Databasebeta

← #32983848

Subgroups — #32983848

Order 18688.

454 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 115 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#22615293C211yesmaximal, characteristic
2#22609927C211yesmaximal, characteristic
3#22608361C212yesmaximal
4#22607790C212yesmaximal
5C73×#2983C211yesmaximal, characteristic
6C2×C4×Dic146C2211yescharacteristic
7#17988611C2212yes—
8C2×#14556510—21no—
9#17988526C412yes—
10#17988507C412yes—
11#17988494—21no—
12#17988483—21no—
13#17988471—22no—
14#17988453C2211yescharacteristic
15#17988356—21no—
16#17988319—24no—
17C2×C4×Q8×C73C2211yescharacteristic
18#446×C73—24no—
19#432×C73—22no—
20#431×C73C2212yes—
21C22×Dic146C2×C411yescharacteristic
22C2×#11924012—22no—
23C4×Dic146—22no—
24C4×Dic146—22no—
25C2×C4⋊Dic73—21no—
26C2×C4⋊Dic73C2×C411yescharacteristic
27C2×#11924007—22no—
28C2×#11924007—21no—
29C2×C4×Dic73—21no—
30C4⋊#10596831—22no—
31C4⋊#10596831—22no—
32#14556510—42no—
33#14556498—22no—
34#14556498—22no—
35#14556498—22no—
36#14556498—21no—
37#14556498C2×C412yes—
38C22×Q8×C73D411yescharacteristic
39C4×Q8×C73—22no—
40C4×Q8×C73—22no—
41C2×C4⋊C4×C73C2×C412yes—
42C2×C4⋊C4×C73D411yescharacteristic
43C2×C42×C73D412yes—
44C2×C42×C73C2311yescharacteristic
45C4⋊C8×C73—24no—
46C4⋊C8×C73—22no—
47C22⋊C8×C73—22no—
48#97×C73—24no—
49C4×C8×C73D414yes—
50C2×Dic146—22no—
51C2×Dic146—42no—
52C22×Dic73—21no—
53C22×Dic73—22no—
54C22×Dic73—21no—
55#11924012—42no—
56#11924012—42no—
57C2×#10596831—42no—
58C4⋊Dic73—22no—
59C4⋊Dic73—41no—
60C4⋊Dic73—41no—
61#11924007—44no—
62#11924007—41no—
63#11924007—41no—
64C4×Dic73—42no—
65C2×Q8×C73—22no—
66C2×Q8×C73—21no—
67C2×Q8×C73—21no—
68C2×Q8×C73—22no—
69C22×C4×C73C22⋊C412yes—
70C22×C4×C73C22⋊C412yes—
71C22×C4×C73C22×C411yescharacteristic
72C22×C4×C73C2×D411yescharacteristic
73C22×C4×C73C2×D411yescharacteristic
74C2×C8×C73—24no—
75C4⋊C4×C73—24no—
76C4⋊C4×C73—22no—
77C42×C73—22no—
78C42×C73—22no—
79C42×C73C2×D412yes—
80C42×C73#4112yes—
81C23×C73C2×C22⋊C411yescharacteristic
82Q8×C73—42no—
83Q8×C73—42no—
84C2×C4×C73—22no—
85C2×C4×C73—22no—
86C2×C4×C73—22no—
87C2×C4×C73—22no—
88C2×C4×C73—41no—
89C2×C4×C73—41no—
90C2×C4×C73—42no—
91C2×C4×C73C4×D412yes—
92C2×C4×C73#12011yescharacteristic
93C2×C4×C73#12112yes—
94C2×C4×C73#12311yescharacteristic
95C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
96C2×C4×C73#13712yes—
97C2×C4×C73#13711yescharacteristic
98C2×Dic73—22no—
99C2×Dic73—41no—
100C2×Dic73—41no—
101C2×Dic73—42no—
102C2×Dic73—42no—
103C2×Dic73—42no—
104C2×Dic73—41no—
105C2×Dic73—42no—
106Dic146—24no—
107Dic146—42no—
108C8×C73—44no—
109#10596831—82no—
110C22×C73—21no—
111C22×C73—21no—
112C22×C73#38611yescharacteristic
113C22×C73#41711yescharacteristic
114C22×C73#41911yescharacteristic
115C4×C73—22no—
116C4×C73—21no—
117C4×C73—21no—
118C4×C73—42no—
119C4×C73—42no—
120C4×C73#46812yes—
121C4×C73#47012yes—
122Dic73—42no—
123Dic73—82no—
124Dic73—81no—
125#9488—731nomaximal, Sylow
126C2×C73—21no—
127C2×C73—21no—
128C2×C73#189111yescharacteristic
129C2×C73#189411yescharacteristic
130C2×C73#191211yescharacteristic
131#2983D7311yescharacteristic
132#2581—731no—
133#1801—731no—
134#1487—732no—
135#1286—732no—
136C73#948811yescharacteristic, complemented, Sylow
137C2×C4×Q8—731no—
138C2×C4×Q8C2×D7311yescharacteristic
139#446—24no—
140#432—22no—
141#431C2×D7312yes—
142#423—732no—
143C2×#101—1461no—
144#400—732no—
145#395—732no—
146#391—1461no—
147#389—1461no—
148#387—1462no—
149#382—731no—
150#343—1461no—
151Q8⋊C8—1464no—
152C22×Q8—731no—
153C22×Q8D29211yescharacteristic
154C2×M16—1462no—
155C4×Q8—22no—
156C4×Q8—22no—
157C4×Q8—1462no—
158C4×Q8—1462no—
159C2×C4⋊C4—731no—
160C2×C4⋊C4—1462no—
161C2×C4⋊C4—1461no—
162C2×C4⋊C4—1461no—
163C2×C4⋊C4C4×D7312yes—
164C2×C4⋊C4D29211yescharacteristic
165C2×C42—1461no—
166C2×C42C22⋊D7312yes—
167C2×C42C22×D7311yescharacteristic
168C4⋊C8—24no—
169C4⋊C8—22no—
170C4⋊C8—1462no—
171C4⋊C8—1462no—
172#101—2922no—
173C22⋊C8—22no—
174#97—24no—
175C4×C8C22⋊D7314yes—
176#95—732no—
177#95—1462no—
178#95—1462no—
179#95—1462no—
180#95—1461no—
181C2×Q8—22no—
182C2×Q8—21no—
183C2×Q8—21no—
184C2×Q8—22no—
185C2×Q8—2922no—
186C2×Q8—1462no—
187C22×C4—1462no—
188C22×C4—1461no—
189C22×C4—1461no—
190C22×C4#1192400512yes—
191C22×C4#1192400512yes—
192C22×C4C2×C4×D7311yescharacteristic
193C22×C4C2×C22⋊D7311yescharacteristic
194C22×C4C2×D29211yescharacteristic
195M16—2922no—
196M16—2922no—
197C2×C8—24no—
198C2×C8—2922no—
199C4⋊C4—24no—
200C4⋊C4—22no—
201C4⋊C4—2924no—
202C4⋊C4—2921no—
203C4⋊C4—2921no—
204C4⋊C4—2921no—
205C4⋊C4—2921no—
206C4⋊C4—1462no—
207C42—22no—
208C42—22no—
209C42—2922no—
210C42C2×C22⋊D7312yes—
211C42#1192402812yes—
212C23C2×#1192400511yescharacteristic
213Q8—42no—
214Q8—42no—
215Q8—2922no—
216Q8—1464no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—2921no—
225C2×C4—2921no—
226C2×C4—2922no—
227C2×C4—2922no—
228C2×C4—2922no—
229C2×C4—2921no—
230C2×C4—2922no—
231C2×C4—1462no—
232C2×C4C4×C22⋊D7312yes—
233C2×C4#1455656011yescharacteristic
234C2×C4#1455656512yes—
235C2×C4#1455657411yescharacteristic
236C2×C4#1455661911yescharacteristic
237C2×C4#1455662412yes—
238C2×C4#1455662411yescharacteristic
239C8—44no—
240C8—5842no—
241C22—21no—
242C22—21no—
243C22#1798846611yescharacteristic
244C22#1798858911yescharacteristic
245C22#1798859711yescharacteristic
246C4—21no—
247C4—21no—
248C4—22no—
249C4—42no—
250C4—42no—
251C4—2922no—
252C4—5842no—
253C4—5841no—
254C4#1798883312yes—
255C4#1798884512yes—
256C2—21no—
257C2—21no—
258C2#2261034911yescharacteristic
259C2#2261036411yescharacteristic
260C2#2261046811yescharacteristic
subgroupG/H
centerC22#17988466
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#2983C2
socleC22×C73#386
prime radicalC23×C73C2×C22⋊C4
cosocleC2×C42×C73C23
hypercenter#2983D73
hypocenterC73#9488
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
136. C73#9488semidirect

Maximal subgroups

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

subgroupindex
#226152932
#226099272
#226083612
#226077902
C73×#29832
#948873