Finite Group Databasebeta

← #32981504

Subgroups — #32981504

Order 18688.

474 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 119 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#22612647C211yesmaximal, characteristic
2#22608327C212yesmaximal
3#22608255C211yesmaximal, characteristic
4#22607759C212yesmaximal
5C73×#2983C211yesmaximal, characteristic
6C2×#14556589C411yescharacteristic
7C2×C4×Dic146C2211yescharacteristic
8#17988640C2212yes—
9#17988494C411yescharacteristic
10#17988492C411yescharacteristic
11#17988471—22no—
12#17988468—22no—
13#17988452C411yescharacteristic
14#17988433C2211yescharacteristic
15#17988319—24no—
16#17988313—22no—
17C2×C4×Q8×C73C2211yescharacteristic
18#446×C73—24no—
19#432×C73—22no—
20#431×C73C2212yes—
21C22×Dic146C2×C411yescharacteristic
22#14556589—22no—
23#14556589—22no—
24C4×Dic146—22no—
25C4×Dic146—22no—
26C2×C4⋊Dic73C2×C411yescharacteristic
27C2×#11924007—22no—
28C2×#11924007—21no—
29C2×C4×Dic73—21no—
30C2×C4×Dic73C2×C411yescharacteristic
31C2×C4×Dic73C2×C411yescharacteristic
32C4⋊#10596831—22no—
33C22⋊#10596831—22no—
34C4×#10596831—22no—
35#14556498—22no—
36#14556498—22no—
37#14556498—22no—
38#14556498—21no—
39#14556498—21no—
40C22×Q8×C73C2×C411yescharacteristic
41C4×Q8×C73—22no—
42C4×Q8×C73—22no—
43C2×C4⋊C4×C73C2×C411yescharacteristic
44C2×C4⋊C4×C73D412yes—
45C2×C42×C73D412yes—
46C2×C42×C73C2311yescharacteristic
47C4⋊C8×C73—24no—
48C4⋊C8×C73—22no—
49C22⋊C8×C73—22no—
50#97×C73—24no—
51C4×C8×C73D414yes—
52C2×Dic146—22no—
53C2×Dic146—22no—
54C2×Dic146—21no—
55C2×Dic146M1612yes—
56C22×Dic73—21no—
57C22×Dic73—21no—
58C22×Dic73—21no—
59C22×Dic73—21no—
60C2×#10596831—42no—
61C4⋊Dic73—22no—
62#11924007—28no—
63#11924007—41no—
64#11924007—41no—
65C4×Dic73—21no—
66C4×Dic73—22no—
67C4×Dic73—42no—
68C4×Dic73M1612yes—
69C2×Q8×C73—22no—
70C2×Q8×C73—21no—
71C2×Q8×C73—21no—
72C2×Q8×C73—22no—
73C22×C4×C73C22⋊C412yes—
74C22×C4×C73C22⋊C412yes—
75C22×C4×C73C22×C411yescharacteristic
76C22×C4×C73C2×D411yescharacteristic
77C22×C4×C73C2×D411yescharacteristic
78C2×C8×C73—24no—
79C4⋊C4×C73—22no—
80C4⋊C4×C73—24no—
81C42×C73—22no—
82C42×C73—22no—
83C42×C73C2×D412yes—
84C42×C73#4112yes—
85C23×C73C2×C22⋊C411yescharacteristic
86Q8×C73—42no—
87Q8×C73—42no—
88C2×C4×C73—22no—
89C2×C4×C73—22no—
90C2×C4×C73—22no—
91C2×C4×C73—22no—
92C2×C4×C73—41no—
93C2×C4×C73—41no—
94C2×C4×C73—42no—
95C2×C4×C73C4×D412yes—
96C2×C4×C73#12011yescharacteristic
97C2×C4×C73#12112yes—
98C2×C4×C73#12311yescharacteristic
99C2×C4×C73C2×M1611yescharacteristic
100C2×C4×C73C2×M1611yescharacteristic
101C2×C4×C73#13112yes—
102C2×Dic73—22no—
103C2×Dic73—22no—
104C2×Dic73—41no—
105C2×Dic73—41no—
106C2×Dic73—41no—
107C2×Dic73—41no—
108C2×Dic73—41no—
109C2×Dic73—41no—
110C2×Dic73—42no—
111C2×Dic73—41no—
112C2×Dic73—41no—
113Dic146—24no—
114Dic146—42no—
115C8×C73—44no—
116#10596831—82no—
117C22×C73—21no—
118C22×C73—21no—
119C22×C73#38611yescharacteristic
120C22×C73#40711yescharacteristic
121C22×C73#40811yescharacteristic
122C4×C73—22no—
123C4×C73—21no—
124C4×C73—21no—
125C4×C73—42no—
126C4×C73—42no—
127C4×C73#43512yes—
128C4×C73#43612yes—
129Dic73—42no—
130Dic73—42no—
131Dic73—81no—
132Dic73—81no—
133#9104—731nomaximal, Sylow
134C2×C73—21no—
135C2×C73—21no—
136C2×C73#187011yescharacteristic
137C2×C73#190911yescharacteristic
138C2×C73#191211yescharacteristic
139#2983D7311yescharacteristic
140#2327—731no—
141#1479—732no—
142#1461—731no—
143#1274—732no—
144C73#910411yescharacteristic, complemented, Sylow
145C2×C4⋊Q8—731no—
146C2×C4×Q8—731no—
147C2×C4×Q8C2×D7311yescharacteristic
148#446—24no—
149#432—22no—
150#431—732no—
151#431C2×D7312yes—
152#391—731no—
153#391—731no—
154#387—1462no—
155#387—1462no—
156#382—731no—
157#376—731no—
158Q8⋊C8—1464no—
159#324—1462no—
160C22×Q8—731no—
161C22×Q8C4×D7311yescharacteristic
162C4⋊Q8—1462no—
163C4⋊Q8—1462no—
164C4×Q8—22no—
165C4×Q8—22no—
166C4×Q8—1462no—
167C4×Q8—1462no—
168C2×C4⋊C4—731no—
169C2×C4⋊C4—1461no—
170C2×C4⋊C4—1462no—
171C2×C4⋊C4C4×D7311yescharacteristic
172C2×C4⋊C4D29212yes—
173C2×C42—731no—
174C2×C42—731no—
175C2×C42—1461no—
176C2×C42C22⋊D7312yes—
177C2×C42C22×D7311yescharacteristic
178C4⋊C8—24no—
179C4⋊C8—22no—
180C4⋊C8—1462no—
181C22⋊C8—22no—
182C22⋊C8—1462no—
183#97—24no—
184C4×C8—1462no—
185C4×C8C22⋊D7314yes—
186#95—1462no—
187#95—1462no—
188#95—1462no—
189#95—1461no—
190#95—1461no—
191C2×Q8—22no—
192C2×Q8—21no—
193C2×Q8—21no—
194C2×Q8—22no—
195C2×Q8—732no—
196C2×Q8—1462no—
197C2×Q8—1462no—
198C2×Q8—1461no—
199C22×C4—1461no—
200C22×C4—1461no—
201C22×C4—1461no—
202C22×C4—1461no—
203C22×C4#1192400512yes—
204C22×C4#1192400512yes—
205C22×C4C2×C4×D7311yescharacteristic
206C22×C4C2×C22⋊D7311yescharacteristic
207C22×C4C2×D29211yescharacteristic
208C2×C8—24no—
209C2×C8—2922no—
210C4⋊C4—22no—
211C4⋊C4—24no—
212C4⋊C4—2921no—
213C4⋊C4—2921no—
214C4⋊C4—1468no—
215C4⋊C4—1462no—
216C42—22no—
217C42—22no—
218C42—2922no—
219C42—732no—
220C42—1462no—
221C42—1461no—
222C42C2×C22⋊D7312yes—
223C42#1192402812yes—
224C23C2×#1192400511yescharacteristic
225Q8—42no—
226Q8—42no—
227Q8—2922no—
228Q8—1464no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—2921no—
237C2×C4—2921no—
238C2×C4—2921no—
239C2×C4—2921no—
240C2×C4—2921no—
241C2×C4—2921no—
242C2×C4—2922no—
243C2×C4—2921no—
244C2×C4—2921no—
245C2×C4—1462no—
246C2×C4—1462no—
247C2×C4C4×C22⋊D7312yes—
248C2×C4#1455656011yescharacteristic
249C2×C4#1455656512yes—
250C2×C4#1455657411yescharacteristic
251C2×C4M16×D7311yescharacteristic
252C2×C4M16×D7311yescharacteristic
253C2×C4#1455659912yes—
254C8—44no—
255C8—5842no—
256C22—21no—
257C22—21no—
258C22#1798846611yescharacteristic
259C22#1798855011yescharacteristic
260C22#1798855511yescharacteristic
261C4—22no—
262C4—21no—
263C4—21no—
264C4—42no—
265C4—42no—
266C4—2922no—
267C4—2922no—
268C4—5841no—
269C4—5841no—
270C4#1798865612yes—
271C4#1798866312yes—
272C2—21no—
273C2—21no—
274C2#2261022811yescharacteristic
275C2#2261045311yescharacteristic
276C2#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#9104
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
144. C73#9104semidirect

Maximal subgroups

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

subgroupindex
#226126472
#226083272
#226082552
#226077592
C73×#29832
#910473