Finite Group Databasebeta

← #34001460

Subgroups — #34001460

Order 18688.

440 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 110 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#22625858C211yesmaximal, characteristic
2#22625858C211yesmaximal, characteristic
3#22624750C214yesmaximal
4#22612498C211yesmaximal, characteristic
5#17989453—21no—
6#17989453—21no—
7#17989453—21no—
8#17989453—21no—
9#17989453C2212yes—
10#17989453C2212yes—
11C2×#14556591C411yescharacteristic
12C2×#14556556—21no—
13#17988492—21no—
14#17988483—21no—
15#17988483C2212yes—
16C4⋊C4×Dic73—21no—
17C4⋊C4×Dic73C412yes—
18C42×Dic73C2211yescharacteristic
19#384×C73C411yescharacteristic
20C22×#10596833—22no—
21C22×#10596833—22no—
22C22×Dic146—21no—
23#14556591—22no—
24#14556591C814yescomplemented
25#14556556—44no—
26C2×C4⋊Dic73—21no—
27C2×C4⋊Dic73C2×C412yes—
28C2×#11924007—22no—
29C2×C4×Dic73—22no—
30C2×C4×Dic73C2×C411yescharacteristic
31C2×C4×Dic73D411yescharacteristic
32C2×C4×Dic73D411yescharacteristic
33C2×C4×Dic73D411yescharacteristic
34C2×C4×Dic73D411yescharacteristic
35C2×C4×Dic73C2311yescharacteristic
36#14556498—22no—
37#14556498—22no—
38C2×C4⋊C4×C73—21no—
39C2×C4⋊C4×C73—21no—
40C2×C4⋊C4×C73C2×C412yes—
41C2×C42×C73C2×C411yescharacteristic
42C2×#10596833—42no—
43C2×#10596833—42no—
44C2×#10596833—42no—
45C2×#10596833—42no—
46C2×#10596833—42no—
47C2×#10596833—42no—
48C2×Dic146—24no—
49C2×Dic146—42no—
50C2×Dic146—42no—
51C22×Dic73—22no—
52C22×Dic73C22⋊C411yescharacteristic
53C22×Dic73C22⋊C411yescharacteristic
54C22×Dic73C2×D411yescharacteristic
55C22×Dic73C2×D411yescharacteristic
56C4⋊Dic73—24no—
57C4⋊Dic73—22no—
58C4⋊Dic73C2×C814yes—
59#11924007—44no—
60C4×Dic73—22no—
61C4×Dic73—22no—
62C4×Dic73—22no—
63C4×Dic73—41no—
64C4×Dic73—41no—
65C4×Dic73—41no—
66C4×Dic73—44no—
67C22×C4×C73—22no—
68C22×C4×C73C22⋊C411yescharacteristic
69C22×C4×C73C22⋊C411yescharacteristic
70C22×C4×C73C22×C411yescharacteristic
71C4⋊C4×C73—42no—
72C4⋊C4×C73—42no—
73C4⋊C4×C73—42no—
74C42×C73C2×C812yes—
75C42×C73M1612yes—
76C23×C73C2×C22⋊C411yescharacteristic
77C2×C4×C73—21no—
78C2×C4×C73—21no—
79C2×C4×C73—21no—
80C2×C4×C73—21no—
81C2×C4×C73—21no—
82C2×C4×C73—21no—
83C2×C4×C73—42no—
84C2×C4×C73—42no—
85C2×C4×C73—42no—
86C2×C4×C73C22⋊C812yes—
87C2×C4×C73C22⋊C812yes—
88C2×C4×C73C22×C811yescharacteristic
89C2×C4×C73C2×M1611yescharacteristic
90C2×Dic73—21no—
91C2×Dic73—21no—
92C2×Dic73—21no—
93C2×Dic73—21no—
94C2×Dic73—21no—
95C2×Dic73—21no—
96C2×Dic73—24no—
97C2×Dic73—21no—
98C2×Dic73—21no—
99C2×Dic73—21no—
100C2×Dic73—42no—
101C2×Dic73—42no—
102C2×Dic73#10112yes—
103C2×Dic73AGL(1,ℤ/8)12yes—
104C2×Dic73#13712yes—
105Dic146—48no—
106#10596833—82no—
107#10596833—82no—
108C22×C73C2×C22⋊C811yescharacteristic
109C22×C73#41011yescharacteristic
110C22×C73C2×#10111yescharacteristic
111C22×C73#41811yescharacteristic
112C22×C73#41911yescharacteristic
113C22×C73#42111yescharacteristic
114C22×C73#42111yescharacteristic
115C4×C73—21no—
116C4×C73—21no—
117C4×C73—22no—
118C4×C73—22no—
119C4×C73—82no—
120Dic73—22no—
121Dic73—22no—
122Dic73—22no—
123Dic73—41no—
124Dic73—44no—
125#7604—731nomaximal, Sylow
126C2×C73#146111yescharacteristic
127C2×C73#147811yescharacteristic
128C2×C73#147911yescharacteristic
129C2×C73#151411yescharacteristic
130C2×C73#151511yescharacteristic
131C2×C73#153711yescharacteristic
132C2×C73#155611yescharacteristic
133C4×C4⋊Q8—731no—
134#1839—731no—
135#1839—731no—
136#1271—734no—
137C73#760411yescharacteristic, complemented, Sylow
138C2×C4⋊Q8—731no—
139C2×C4×Q8—1461no—
140#391—1461no—
141#389—732no—
142#389—1461no—
143#384#6440811yescharacteristic
144C4×C4⋊C4—732no—
145C4×C4⋊C4—1461no—
146C43—731no—
147#336—732no—
148#336—732no—
149#336—1461no—
150#336—1461no—
151#336—1461no—
152#336—1461no—
153C22×Q8—1461no—
154C22×C8—1462no—
155C22×C8—1462no—
156C4⋊Q8—734no—
157C4⋊Q8—1462no—
158C4×Q8—2924no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—732no—
162C2×C4⋊C4—1462no—
163C2×C4⋊C4—1461no—
164C2×C4⋊C4C2×#6440812yes—
165C2×C42—731no—
166C2×C42—731no—
167C2×C42—731no—
168C2×C42—731no—
169C2×C42—731no—
170C2×C42—731no—
171C2×C42—1462no—
172C2×C42C2×#6440811yescharacteristic
173#95—1462no—
174#95—1462no—
175C2×Q8—2922no—
176C2×Q8—2922no—
177C2×Q8—1464no—
178C22×C4—22no—
179C22×C4—731no—
180C22×C4—731no—
181C22×C4—731no—
182C22×C4—731no—
183C22×C4—1462no—
184C22×C4C22⋊#6440811yescharacteristic
185C22×C4C22⋊#6440811yescharacteristic
186C22×C4C22×#6440811yescharacteristic
187C2×C8—2922no—
188C2×C8—2922no—
189C2×C8—2922no—
190C2×C8—2922no—
191C2×C8—2922no—
192C2×C8—2922no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—2924no—
197C4⋊C4—734no—
198C4⋊C4—1462no—
199C4⋊C4—1464no—
200C42—2921no—
201C42—2921no—
202C42—2921no—
203C42—2924no—
204C42—1462no—
205C42—1462no—
206C42—1462no—
207C42#1192403612yes—
208C42#1192403812yes—
209C23C2×C22⋊#6440811yescharacteristic
210Q8—2928no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—2922no—
221C2×C4—2922no—
222C2×C4—732no—
223C2×C4—732no—
224C2×C4—732no—
225C2×C4—1464no—
226C2×C4—1461no—
227C2×C4—1461no—
228C2×C4—1461no—
229C2×C4—1461no—
230C2×C4—1461no—
231C2×C4—1461no—
232C2×C4—1461no—
233C2×C4—1461no—
234C2×C4—1461no—
235C2×C4#1455664812yes—
236C2×C4#1455664812yes—
237C2×C4C2×#1192403611yescharacteristic
238C2×C4C2×#1192403811yescharacteristic
239C8—5842no—
240C8—5842no—
241C22C2×#1455664811yescharacteristic
242C22#1798956711yescharacteristic
243C22D73⋊#10111yescharacteristic
244C22#1798957911yescharacteristic
245C22#1798958011yescharacteristic
246C22#1798958511yescharacteristic
247C22#1798958611yescharacteristic
248C4—21no—
249C4—21no—
250C4—22no—
251C4—22no—
252C4—82no—
253C4—2921no—
254C4—2924no—
255C4—1462no—
256C4—1462no—
257C4—1462no—
258C2#2262517511yescharacteristic
259C2#2262523211yescharacteristic
260C2#2262523511yescharacteristic
261C2#2262535111yescharacteristic
262C2#2262535511yescharacteristic
263C2#2262542311yescharacteristic
264C2#2262546111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C22×C8
FrattiniC22×C4C22×#64408
Fitting#384×C73C4
socle, prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4×Dic73C23
hypercenter#384#64408
hypocenterC73#7604
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
24. #14556591C8semidirect
137. C73#7604semidirect

Maximal subgroups

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

subgroupindex
#226258582
#226247502
#226124982
#760473