Finite Group Databasebeta

← #34013091

Subgroups — #34013091

Order 18688.

468 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 90 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
1C2×#17989498C212yesmaximal
2#22625797C212yesmaximal
3#22625028C212yesmaximal
4C4×#14556591C211yesmaximal, characteristic
5#17989590—22no—
6C2×#14556652C2214yes—
7#17989498—24no—
8#17989467—22no—
9C2×#14556591C2211yescharacteristic
10C2×C4×Dic146C411yescharacteristic
11C2×C4×Dic146C2211yescharacteristic
12#17988493C411yescharacteristic
13#17988493C2211yescharacteristic
14#17988485—22no—
15#17988457C411yescharacteristic
16C4×C4⋊Dic73—22no—
17C43×C73C411yescharacteristic
18C2×#11924037—24no—
19#14556658—42no—
20C4⋊#10596833—42no—
21#14556652—24no—
22#14556652—24no—
23C22×Dic146C2×C411yescharacteristic
24C22×Dic146C2311yescharacteristic
25#14556591—22no—
26#14556591D412yes—
27#14556591Q812yes—
28C4×Dic146—41no—
29C4×Dic146—41no—
30C4×Dic146—41no—
31C4×Dic146—41no—
32C2×C4⋊Dic73—22no—
33C2×C4⋊Dic73—22no—
34C2×C4⋊Dic73C2×C411yescharacteristic
35C2×C4⋊Dic73C2×C411yescharacteristic
36C2×#11924007—21no—
37C2×#11924007D412yes—
38C2×C4×Dic73—21no—
39C2×C4×Dic73D412yes—
40#14556498—22no—
41#14556498—22no—
42C2×C42×C73—21no—
43C2×C42×C73—21no—
44C2×C42×C73C2×C411yescharacteristic
45C2×C42×C73C2×C411yescharacteristic
46C2×C42×C73C2×C411yescharacteristic
47#11924037—44no—
48#11924037—44no—
49C2×#10596833—44no—
50C2×Dic146—21no—
51C2×Dic146—41no—
52C2×Dic146—41no—
53C2×Dic146—41no—
54C2×Dic146—41no—
55C2×Dic146C4⋊C412yes—
56C2×Dic146C2×D411yescharacteristic
57C2×Dic146C2×Q811yescharacteristic
58C2×Dic146#4112yes—
59C22×Dic73—21no—
60C22×Dic73—21no—
61C22×Dic73C22⋊C412yes—
62C22×Dic73C2×D412yes—
63C4⋊Dic73—24no—
64C4⋊Dic73—24no—
65C4⋊Dic73—41no—
66C4⋊Dic73—44no—
67C4⋊Dic73—41no—
68#11924007—42no—
69#11924007—42no—
70C4×Dic73—22no—
71C4×Dic73—22no—
72C4×Dic73—41no—
73C4×Dic73—41no—
74C22×C4×C73—21no—
75C22×C4×C73—21no—
76C22×C4×C73C22⋊C411yescharacteristic
77C22×C4×C73C22⋊C411yescharacteristic
78C22×C4×C73C22×C411yescharacteristic
79C42×C73—24no—
80C42×C73—21no—
81C42×C73—21no—
82C42×C73—21no—
83C42×C73—41no—
84C42×C73—42no—
85C42×C73C4⋊C412yes—
86C23×C73C2×C22⋊C411yescharacteristic
87C2×C4×C73—22no—
88C2×C4×C73—22no—
89C2×C4×C73—22no—
90C2×C4×C73—21no—
91C2×C4×C73—21no—
92C2×C4×C73—22no—
93C2×C4×C73—22no—
94C2×C4×C73—21no—
95C2×C4×C73—41no—
96C2×C4×C73—41no—
97C2×C4×C73—41no—
98C2×C4×C73#9911yescharacteristic
99C2×C4×C73#9911yescharacteristic
100C2×C4×C73C2×C4⋊C411yescharacteristic
101C2×C4×C73#11711yescharacteristic
102C2×Dic73—22no—
103C2×Dic73—22no—
104C2×Dic73—22no—
105C2×Dic73—22no—
106C2×Dic73—41no—
107C2×Dic73—41no—
108C2×Dic73—42no—
109C2×Dic73—42no—
110C2×Dic73—41no—
111C2×Dic73#12112yes—
112C2×Dic73C22⋊Q812yes—
113Dic146—41no—
114Dic146—41no—
115Dic146—42no—
116Dic146—42no—
117Dic146—42no—
118#10596833—84no—
119C22×C73—21no—
120C22×C73—21no—
121C22×C73#38011yescharacteristic
122C22×C73C2×#9911yescharacteristic
123C22×C73#41011yescharacteristic
124C4×C73—24no—
125C4×C73—21no—
126C4×C73—21no—
127C4×C73—21no—
128C4×C73—42no—
129C4×C73—41no—
130C4×C73#35612yescomplemented
131Dic73—22no—
132Dic73—22no—
133Dic73—42no—
134Dic73—42no—
135Dic73—81no—
136#12802—731nomaximal, Sylow
137C2×C73—21no—
138C2×C73—21no—
139C2×C73#179911yescharacteristic
140C2×C73C2×#35611yescharacteristic
141C2×C73#213211yescharacteristic
142C4×C4⋊Q8—731no—
143C2×#356—732no—
144#1801—732no—
145#1394—732no—
146C73#1280211yescharacteristic, complemented, Sylow
147C2×C4⋊Q8—731no—
148C2×C4×Q8—731no—
149C2×C4×Q8—731no—
150#423—1462no—
151C2×#101—734no—
152#391—731no—
153#391—731no—
154#389—1462no—
155#384—731no—
156C4×C4⋊C4—1462no—
157C43#6440811yescharacteristic
158#356—1464no—
159#343—1462no—
160C22×Q8—731no—
161C22×Q8—731no—
162C2×M16—1464no—
163C4⋊Q8—732no—
164C4⋊Q8—732no—
165C4⋊Q8—1462no—
166C4×Q8—2921no—
167C4×Q8—2921no—
168C4×Q8—2921no—
169C4×Q8—2921no—
170C2×C4⋊C4—732no—
171C2×C4⋊C4—731no—
172C2×C4⋊C4—731no—
173C2×C4⋊C4—1462no—
174C2×C4⋊C4—1461no—
175C2×C4⋊C4—1462no—
176C2×C42—21no—
177C2×C42—21no—
178C2×C42—732no—
179C2×C42—1461no—
180C2×C42C2×#6440811yescharacteristic
181C2×C42C2×#6440811yescharacteristic
182C2×C42C2×#6440811yescharacteristic
183C4⋊C8—2922no—
184C4⋊C8—2922no—
185#101—1464no—
186#101—1464no—
187#95—1462no—
188#95—1462no—
189C2×Q8—2921no—
190C2×Q8—2921no—
191C2×Q8—2921no—
192C2×Q8—2921no—
193C2×Q8—731no—
194C2×Q8—731no—
195C2×Q8—732no—
196C2×Q8—732no—
197C2×Q8—1461no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—732no—
201C22×C4—732no—
202C22×C4—1461no—
203C22×C4—1461no—
204C22×C4C22⋊#6440811yescharacteristic
205C22×C4C22⋊#6440811yescharacteristic
206C22×C4C22×#6440811yescharacteristic
207M16—2924no—
208M16—2924no—
209C2×C8—2924no—
210C4⋊C4—2921no—
211C4⋊C4—2922no—
212C4⋊C4—2924no—
213C4⋊C4—2922no—
214C4⋊C4—2921no—
215C4⋊C4—1464no—
216C4⋊C4—1464no—
217C42—24no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—41no—
222C42—42no—
223C42—2921no—
224C42—2921no—
225C42—1462no—
226C42—1462no—
227C42C4⋊#6440812yes—
228C23C2×C22⋊#6440811yescharacteristic
229Q8—2922no—
230Q8—2922no—
231Q8—2921no—
232Q8—2921no—
233Q8—2922no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—2921no—
246C2×C4—2921no—
247C2×C4—2922no—
248C2×C4—2922no—
249C2×C4—2921no—
250C2×C4—732no—
251C2×C4—732no—
252C2×C4—1462no—
253C2×C4—1462no—
254C2×C4—1462no—
255C2×C4—1462no—
256C2×C4#1455665011yescharacteristic
257C2×C4#1455665011yescharacteristic
258C2×C4C2×C4⋊#6440811yescharacteristic
259C2×C4#1455667011yescharacteristic
260C8—5844no—
261C22—21no—
262C22—21no—
263C22#1798952911yescharacteristic
264C22C2×#1455665011yescharacteristic
265C22#1798956611yescharacteristic
266C4—24no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—42no—
271C4—41no—
272C4—2922no—
273C4—2922no—
274C4—5841no—
275C4—1462no—
276C4—1462no—
277C4#1798949812yescomplemented
278C2—21no—
279C2—21no—
280C2#2262579211yescharacteristic
281C2C2×#1798949811yescharacteristic
282C2#2262622411yescharacteristic
subgroupG/H
centerC22C2×#14556650
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
FittingC43×C73C4
socleC22×C73C2×#99
prime radicalC23×C73C2×C22⋊C4
cosocleC22×Dic146C23
hypercenterC43#64408
hypocenterC73#12802
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C43

Complements

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

NH ≅ G/Ntype
130. C4×C73#356semidirect
146. C73#12802semidirect
277. C4#17989498semidirect

Maximal subgroups

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

subgroupindex
C2×#179894982
#226257972
#226250282
C4×#145565912
#1280273