Finite Group Databasebeta

← #32995653

Subgroups — #32995653

Order 18688.

374 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 95 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#22608275C211yesmaximal, characteristic
2#22608255C211yesmaximal, characteristic
3#22607877C214yesmaximal
4C73×#2567C211yesmaximal, characteristic
5#17988644—21no—
6#17988640—21no—
7#17988313—21no—
8#17988313—21no—
9#17988313C2212yes—
10#17988313C2212yes—
11C2×C4⋊Q8×C73C411yescharacteristic
12C2×C4×Q8×C73C2211yescharacteristic
13#395×C73—21no—
14#395×C73—21no—
15#391×C73C412yes—
16#389×C73—21no—
17#389×C73—21no—
18#384×C73C2212yes—
19C4×C4⋊C4×C73C411yescharacteristic
20C4⋊#10596831—41no—
21C4⋊#10596831—41no—
22C22⋊#10596831—22no—
23C22⋊#10596831—22no—
24#14556502—41no—
25C4×#10596831—41no—
26C22×Q8×C73—21no—
27C22×Q8×C73C2×C411yescharacteristic
28C4⋊Q8×C73—41no—
29C4⋊Q8×C73—41no—
30C4×Q8×C73—41no—
31C4×Q8×C73—41no—
32C2×C4⋊C4×C73—21no—
33C2×C4⋊C4×C73—21no—
34C2×C4⋊C4×C73—22no—
35C2×C4⋊C4×C73—22no—
36C2×C4⋊C4×C73C2×C412yes—
37C2×C4⋊C4×C73D411yescharacteristic
38C2×C4⋊C4×C73D411yescharacteristic
39C2×C4⋊C4×C73C2311yescharacteristic
40C2×C42×C73C2×C412yes—
41C2×C42×C73C2×C411yescharacteristic
42C2×C42×C73D411yescharacteristic
43C2×C42×C73D411yescharacteristic
44#95×C73—21no—
45#95×C73—22no—
46#95×C73—22no—
47C2×#10596831—42no—
48C2×#10596831—42no—
49C2×Q8×C73—22no—
50C2×Q8×C73—22no—
51C2×Q8×C73—41no—
52C2×Q8×C73—42no—
53C2×Q8×C73—82no—
54C22×C4×C73—22no—
55C22×C4×C73—22no—
56C22×C4×C73C22⋊C411yescharacteristic
57C22×C4×C73C22⋊C411yescharacteristic
58C22×C4×C73C22⋊C411yescharacteristic
59C22×C4×C73C22⋊C411yescharacteristic
60C22×C4×C73C22×C411yescharacteristic
61C22×C4×C73C2×D411yescharacteristic
62C22×C4×C73C2×D411yescharacteristic
63C4⋊C4×C73—24no—
64C4⋊C4×C73—41no—
65C4⋊C4×C73—41no—
66C4⋊C4×C73—41no—
67C4⋊C4×C73—42no—
68C4⋊C4×C73—41no—
69C4⋊C4×C73—41no—
70C4⋊C4×C73—82no—
71C4⋊C4×C73—82no—
72C42×C73—21no—
73C42×C73—21no—
74C42×C73—21no—
75C42×C73—21no—
76C42×C73—21no—
77C42×C73—21no—
78C42×C73—24no—
79C23×C73C2×C22⋊C411yescharacteristic
80Q8×C73—44no—
81Q8×C73—84no—
82C2×C4×C73—21no—
83C2×C4×C73—21no—
84C2×C4×C73—21no—
85C2×C4×C73—21no—
86C2×C4×C73—22no—
87C2×C4×C73—24no—
88C2×C4×C73—21no—
89C2×C4×C73—21no—
90C2×C4×C73—21no—
91C2×C4×C73—21no—
92C2×C4×C73—21no—
93C2×C4×C73—21no—
94C2×C4×C73—42no—
95C2×C4×C73—42no—
96C2×C4×C73—41no—
97C2×C4×C73—41no—
98C2×C4×C73—41no—
99C2×C4×C73—42no—
100C2×C4×C73—42no—
101C2×C4×C73—42no—
102C2×C4×C73#9911yescharacteristic
103C2×C4×C73#9911yescharacteristic
104C2×C4×C73#10112yes—
105C2×C4×C73#13112yes—
106#10596831—82no—
107#10596831—82no—
108C22×C73—21no—
109C22×C73—21no—
110C22×C73#40811yescharacteristic
111C22×C73C2×#9911yescharacteristic
112C22×C73C2×#10111yescharacteristic
113C4×C73—21no—
114C4×C73—22no—
115C4×C73—22no—
116C4×C73—44no—
117C4×C73—41no—
118C4×C73—41no—
119C4×C73—41no—
120C4×C73—41no—
121C4×C73—82no—
122C4×C73#35612yes—
123#11574—731nomaximal, Sylow
124C2×C73—21no—
125C2×C73—21no—
126C2×C73#147211yescharacteristic
127C2×C73#212811yescharacteristic
128C2×C73C2×#35611yescharacteristic
129#2567D7311yescharacteristic
130#1467—731no—
131#1461—731no—
132#1325—734no—
133C73#1157411yescharacteristic, complemented, Sylow
134C2×C4⋊Q8Dic7311yescharacteristic
135C2×C4×Q8C2×D7311yescharacteristic
136#432—1461no—
137#431—1461no—
138#395—21no—
139#395—21no—
140#391Dic7312yes—
141#389—21no—
142#389—21no—
143#384C2×D7312yes—
144C4×C4⋊C4Dic7311yescharacteristic
145#324—732no—
146#324—732no—
147#324—1461no—
148#324—1461no—
149C22×Q8—21no—
150C22×Q8C2×Dic7311yescharacteristic
151C4⋊Q8—41no—
152C4⋊Q8—41no—
153C4×Q8—41no—
154C4×Q8—41no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4C2×Dic7312yes—
160C2×C4⋊C4C22⋊D7311yescharacteristic
161C2×C4⋊C4C22⋊D7311yescharacteristic
162C2×C4⋊C4C22×D7311yescharacteristic
163C2×C42C2×Dic7312yes—
164C2×C42C2×Dic7311yescharacteristic
165C2×C42C22⋊D7311yescharacteristic
166C2×C42C22⋊D7311yescharacteristic
167C4⋊C8—2921no—
168C4⋊C8—2921no—
169C22⋊C8—1462no—
170C22⋊C8—1462no—
171#97—2921no—
172C4×C8—2921no—
173#95—21no—
174#95—22no—
175#95—22no—
176C2×Q8—22no—
177C2×Q8—22no—
178C2×Q8—41no—
179C2×Q8—42no—
180C2×Q8—82no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4C22⋊Dic7311yescharacteristic
184C22×C4C22⋊Dic7311yescharacteristic
185C22×C4C22⋊Dic7311yescharacteristic
186C22×C4C22⋊Dic7311yescharacteristic
187C22×C4C22×Dic7311yescharacteristic
188C22×C4C2×C22⋊D7311yescharacteristic
189C22×C4C2×C22⋊D7311yescharacteristic
190C2×C8—2922no—
191C2×C8—2922no—
192C4⋊C4—24no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—42no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—82no—
200C4⋊C4—82no—
201C42—21no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—24no—
208C23C2×C22⋊Dic7311yescharacteristic
209Q8—44no—
210Q8—84no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4#1455650611yescharacteristic
232C2×C4#1455650611yescharacteristic
233C2×C4#1455651012yes—
234C2×C4#1455659812yes—
235C8—5842no—
236C8—5842no—
237C22—21no—
238C22—21no—
239C22#1798855411yescharacteristic
240C22C2×#1455650611yescharacteristic
241C22C2×#1455651011yescharacteristic
242C4—21no—
243C4—22no—
244C4—22no—
245C4—44no—
246C4—41no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—82no—
251C4#1798838612yes—
252C2—21no—
253C2—21no—
254C2#2260829511yescharacteristic
255C2#2261160311yescharacteristic
256C2C2×#1798838611yescharacteristic
subgroupG/H
centerC22C2×#14556506
commutatorC22×C4×C73C22×C4
FrattiniC2×C4⋊C4C22×D73
FittingC73×#2567C2
socleC22×C73C2×#99
prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4⋊C4×C73C23
hypercenter#2567D73
hypocenterC73#11574
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2567

Complements

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

NH ≅ G/Ntype
133. C73#11574semidirect

Maximal subgroups

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

subgroupindex
#226082752
#226082552
#226078772
C73×#25672
#1157473