Finite Group Databasebeta

← #32995626

Subgroups — #32995626

Order 18688.

394 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 87 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#22614916C211yesmaximal, characteristic
2#22608275C211yesmaximal, characteristic
3#22607864C214yesmaximal
4C73×#1461C211yesmaximal, characteristic
5C2×#14556591C411yescharacteristic
6C2×#14556589C412yes—
7#17988644—21no—
8#17988517—21no—
9#17988517—21no—
10#17988492C2212yes—
11#17988485—21no—
12#17988485—21no—
13C4×C4⋊Dic73C411yescharacteristic
14#17988313—21no—
15#17988313C2212yes—
16C2×C4×Q8×C73C2211yescharacteristic
17#431×C73—21no—
18#324×C73—21no—
19#324×C73C2212yes—
20C22×Dic146C2×C412yes—
21#14556591—41no—
22#14556591—41no—
23#14556589—44no—
24C2×C4⋊Dic73—21no—
25C2×C4⋊Dic73—21no—
26C2×C4⋊Dic73—21no—
27C2×#11924007—22no—
28C2×#11924007—22no—
29C2×C4×Dic73C2×C412yes—
30C4⋊#10596831—41no—
31C22⋊#10596831—22no—
32#14556502—41no—
33#14556498—21no—
34#14556498—22no—
35#14556498—22no—
36C22×Q8×C73C2×C411yescharacteristic
37C4×Q8×C73—41no—
38C4×Q8×C73—41no—
39C2×C4⋊C4×C73D411yescharacteristic
40C2×C4⋊C4×C73D411yescharacteristic
41C2×C4⋊C4×C73C2311yescharacteristic
42C2×C42×C73C2×C411yescharacteristic
43C2×C42×C73D411yescharacteristic
44C2×C42×C73D411yescharacteristic
45C4⋊C8×C73—41no—
46C22⋊C8×C73—22no—
47C4×C8×C73—41no—
48C2×Dic146—24no—
49C2×Dic146—42no—
50C2×Dic146—42no—
51C22×Dic73—22no—
52C22×Dic73—22no—
53C2×#10596831—42no—
54C4⋊Dic73—24no—
55C4⋊Dic73—42no—
56C4⋊Dic73—41no—
57C4⋊Dic73—41no—
58#11924007—44no—
59#11924007—44no—
60C4×Dic73—42no—
61C2×Q8×C73—22no—
62C2×Q8×C73—22no—
63C2×Q8×C73—41no—
64C22×C4×C73C22⋊C411yescharacteristic
65C22×C4×C73C22⋊C411yescharacteristic
66C22×C4×C73C22⋊C411yescharacteristic
67C22×C4×C73C22⋊C411yescharacteristic
68C22×C4×C73C22×C411yescharacteristic
69C22×C4×C73C2×D411yescharacteristic
70C22×C4×C73C2×D411yescharacteristic
71C2×C8×C73—42no—
72C4⋊C4×C73—41no—
73C4⋊C4×C73—41no—
74C4⋊C4×C73—41no—
75C42×C73—21no—
76C42×C73—21no—
77C42×C73—21no—
78C42×C73—21no—
79C42×C73—21no—
80C42×C73—21no—
81C23×C73C2×C22⋊C411yescharacteristic
82Q8×C73—44no—
83C2×C4×C73—21no—
84C2×C4×C73—21no—
85C2×C4×C73—21no—
86C2×C4×C73—21no—
87C2×C4×C73—22no—
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—41no—
95C2×C4×C73—41no—
96C2×C4×C73—41no—
97C2×C4×C73#9911yescharacteristic
98C2×C4×C73#9911yescharacteristic
99C2×C4×C73#10012yes—
100C2×C4×C73#13112yes—
101C2×Dic73—24no—
102C2×Dic73—42no—
103C2×Dic73—42no—
104C2×Dic73—42no—
105C2×Dic73—42no—
106C2×Dic73—42no—
107Dic146—84no—
108C8×C73—82no—
109#10596831—82no—
110C22×C73—21no—
111C22×C73—21no—
112C22×C73#40811yescharacteristic
113C22×C73C2×#9911yescharacteristic
114C22×C73C2×#10011yescharacteristic
115C4×C73—21no—
116C4×C73—22no—
117C4×C73—22no—
118C4×C73—41no—
119C4×C73—41no—
120C4×C73—41no—
121C4×C73—41no—
122C4×C73#35612yes—
123Dic73—44no—
124Dic73—82no—
125#11568—731nomaximal, Sylow
126C2×C73—21no—
127C2×C73—21no—
128C2×C73#147111yescharacteristic
129C2×C73#212911yescharacteristic
130C2×C73C2×#35611yescharacteristic
131#2546—731no—
132#1467—731no—
133#1461D7311yescharacteristic
134#1319—734no—
135C73#1156811yescharacteristic, complemented, Sylow
136C2×C4⋊Q8—732no—
137C2×C4⋊Q8—731no—
138C2×C4×Q8C2×D7311yescharacteristic
139#432—1461no—
140#431—21no—
141#398—1461no—
142#398—1461no—
143#391—732no—
144#389—1461no—
145#389—1461no—
146C4×C4⋊C4—731no—
147#324—21no—
148#324—732no—
149#324—1461no—
150#324C2×D7312yes—
151C22×Q8—732no—
152C22×Q8C4×D7311yescharacteristic
153C4⋊Q8—2921no—
154C4⋊Q8—2921no—
155C4⋊Q8—2924no—
156C4×Q8—41no—
157C4×Q8—41no—
158C2×C4⋊C4—1462no—
159C2×C4⋊C4—1462no—
160C2×C4⋊C4—1461no—
161C2×C4⋊C4—1461no—
162C2×C4⋊C4—1461no—
163C2×C4⋊C4D29211yescharacteristic
164C2×C4⋊C4C22⋊D7311yescharacteristic
165C2×C4⋊C4C22×D7311yescharacteristic
166C2×C42—732no—
167C2×C42C4×D7311yescharacteristic
168C2×C42D29211yescharacteristic
169C2×C42C22⋊D7311yescharacteristic
170C4⋊C8—41no—
171C4⋊C8—2921no—
172C22⋊C8—22no—
173C22⋊C8—1462no—
174#97—2921no—
175C4×C8—41no—
176#95—1461no—
177#95—1462no—
178#95—1462no—
179C2×Q8—22no—
180C2×Q8—22no—
181C2×Q8—41no—
182C2×Q8—2922no—
183C2×Q8—2922no—
184C2×Q8—1464no—
185C22×C4—1462no—
186C22×C4—1462no—
187C22×C4#1192400511yescharacteristic
188C22×C4#1192400511yescharacteristic
189C22×C4#1192400511yescharacteristic
190C22×C4#1192400511yescharacteristic
191C22×C4C2×C4×D7311yescharacteristic
192C22×C4C2×C22⋊D7311yescharacteristic
193C22×C4C2×D29211yescharacteristic
194C2×C8—42no—
195C2×C8—2922no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—2924no—
200C4⋊C4—2922no—
201C4⋊C4—2921no—
202C4⋊C4—2921no—
203C4⋊C4—2924no—
204C4⋊C4—1464no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—2922no—
212C23C2×#1192400511yescharacteristic
213Q8—44no—
214Q8—5844no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—2922no—
230C2×C4—2922no—
231C2×C4—2922no—
232C2×C4—2922no—
233C2×C4—2922no—
234C2×C4—1464no—
235C2×C4#1455650511yescharacteristic
236C2×C4#1455650511yescharacteristic
237C2×C4#1455650712yes—
238C2×C4#1455659712yes—
239C8—82no—
240C8—5842no—
241C22—21no—
242C22—21no—
243C22#1798855311yescharacteristic
244C22C2×#1455650511yescharacteristic
245C22C2×#1455650711yescharacteristic
246C4—21no—
247C4—22no—
248C4—22no—
249C4—41no—
250C4—41no—
251C4—41no—
252C4—41no—
253C4—2924no—
254C4—5842no—
255C4#1798838512yes—
256C2—21no—
257C2—21no—
258C2#2260829011yescharacteristic
259C2#2261160511yescharacteristic
260C2C2×#1798838511yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC2×C4⋊C4C22×D73
FittingC73×#1461C2
socleC22×C73C2×#99
prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4⋊C4×C73C23
hypercenter#1461D73
hypocenterC73#11568
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
135. C73#11568semidirect

Maximal subgroups

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

subgroupindex
#226149162
#226082752
#226078642
C73×#14612
#1156873