Finite Group Databasebeta

← #34001738

Subgroups — #34001738

Order 18688.

432 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 114 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#22625717C211yesmaximal, characteristic
2#22625646C211yesmaximal, characteristic
3#22624749C214yesmaximal
4#22618292C211yesmaximal, characteristic
5C2×C4⋊#10596833—21no—
6C2×#14556646—21no—
7C2×C4×#10596833—21no—
8#17989453—21no—
9#17989453C2212yes—
10#17989453C2212yes—
11C2×#14556582—21no—
12#17988486—21no—
13#17988486C2212yes—
14#17988483—21no—
15#17988483C412yes—
16#17988457C411yescharacteristic
17#17988452—21no—
18C42×Dic73C2211yescharacteristic
19#384×C73C411yescharacteristic
20C22×#10596833—22no—
21C22×#10596833—22no—
22C4⋊#10596833—24no—
23#14556646—42no—
24C4×#10596833—24no—
25#14556582—44no—
26C2×C4⋊Dic73—22no—
27C2×C4⋊Dic73—21no—
28C2×C4⋊Dic73—21no—
29C2×C4⋊Dic73C2×C412yes—
30C2×#11924007—22no—
31C2×C4×Dic73C2×C411yescharacteristic
32C2×C4×Dic73D411yescharacteristic
33C2×C4×Dic73D411yescharacteristic
34C2×C4×Dic73D411yescharacteristic
35C2×C4×Dic73D411yescharacteristic
36C2×C4×Dic73C2311yescharacteristic
37#14556498—22no—
38#14556498—22no—
39C2×C4⋊C4×C73—21no—
40C2×C4⋊C4×C73—21no—
41C2×C4⋊C4×C73C2×C412yes—
42C2×C42×C73C2×C411yescharacteristic
43C2×#10596833—24no—
44C2×#10596833—24no—
45C2×#10596833—42no—
46C2×#10596833—42no—
47C2×#10596833—42no—
48C2×#10596833—42no—
49C22×Dic73—22no—
50C22×Dic73C22⋊C411yescharacteristic
51C22×Dic73C22⋊C411yescharacteristic
52C22×Dic73C2×D411yescharacteristic
53C22×Dic73C2×D411yescharacteristic
54C4⋊Dic73—42no—
55C4⋊Dic73—42no—
56C4⋊Dic73—44no—
57C4⋊Dic73—42no—
58#11924007—44no—
59C4×Dic73—22no—
60C4×Dic73—22no—
61C4×Dic73—22no—
62C4×Dic73—22no—
63C4×Dic73—41no—
64C4×Dic73SD1612yes—
65C4×Dic73Q1612yes—
66C22×C4×C73—22no—
67C22×C4×C73C22⋊C411yescharacteristic
68C22×C4×C73C22⋊C411yescharacteristic
69C22×C4×C73C22×C411yescharacteristic
70C4⋊C4×C73—24no—
71C4⋊C4×C73—42no—
72C4⋊C4×C73—42no—
73C42×C73—22no—
74C23×C73C2×C22⋊C411yescharacteristic
75C2×C4×C73—21no—
76C2×C4×C73—21no—
77C2×C4×C73—21no—
78C2×C4×C73—21no—
79C2×C4×C73—42no—
80C2×C4×C73—42no—
81C2×C4×C73—42no—
82C2×C4×C73#10112yes—
83C2×C4×C73#10312yes—
84C2×C4×C73#10412yes—
85C2×C4×C73#10412yes—
86C2×C4×C73#13112yes—
87C2×Dic73—21no—
88C2×Dic73—21no—
89C2×Dic73—21no—
90C2×Dic73—21no—
91C2×Dic73—21no—
92C2×Dic73—21no—
93C2×Dic73—21no—
94C2×Dic73—21no—
95C2×Dic73—21no—
96C2×Dic73—42no—
97C2×Dic73—42no—
98C2×Dic73—42no—
99C2×Dic73#10312yes—
100C2×Dic73C2×SD1611yescharacteristic
101C2×Dic73C2×Q1611yescharacteristic
102C2×Dic73AGL(1,ℤ/8)12yes—
103#10596833—44no—
104#10596833—44no—
105C22×C73#40811yescharacteristic
106C22×C73#41011yescharacteristic
107C22×C73C2×#10111yescharacteristic
108C22×C73C2×#10311yescharacteristic
109C22×C73#41811yescharacteristic
110C22×C73C2×#10411yescharacteristic
111C22×C73C2×#10411yescharacteristic
112C4×C73—22no—
113C4×C73—22no—
114C4×C73—82no—
115C4×C73#33014yes—
116Dic73—22no—
117Dic73—21no—
118Dic73—21no—
119Dic73—22no—
120Dic73—41no—
121Dic73—82no—
122#7683—731nomaximal, Sylow
123C2×C73#147011yescharacteristic
124C2×C73#148411yescharacteristic
125C2×C73#149311yescharacteristic
126C2×C73#150311yescharacteristic
127C2×C73#150511yescharacteristic
128C2×C73C2×#33011yescharacteristic
129C2×C73#154911yescharacteristic
130#2859—731no—
131#1767—731no—
132#1744—731no—
133#1271—734no—
134C73#768311yescharacteristic, complemented, Sylow
135C2×#125—1461no—
136C2×C4⋊C8—1461no—
137C2×#97—1461no—
138C2×C4×C8—1461no—
139#389—732no—
140#389—732no—
141#389—1461no—
142#389—1461no—
143#384—731no—
144#384#6440811yescharacteristic
145#382—1461no—
146C43—731no—
147#336—732no—
148#336—732no—
149#336—1461no—
150C22×C8—1462no—
151C22×C8—1462no—
152#125—2924no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—732no—
156C2×C4⋊C4—1462no—
157C2×C4⋊C4—1462no—
158C2×C4⋊C4—1461no—
159C2×C4⋊C4—1461no—
160C2×C4⋊C4C2×#6440812yes—
161C2×C42—731no—
162C2×C42—731no—
163C2×C42—731no—
164C2×C42—731no—
165C2×C42—731no—
166C2×C42—731no—
167C2×C42C2×#6440811yescharacteristic
168C4⋊C8—1464no—
169#97—2922no—
170C4×C8—1464no—
171#95—1462no—
172#95—1462no—
173C22×C4—22no—
174C22×C4—731no—
175C22×C4—731no—
176C22×C4—731no—
177C22×C4—731no—
178C22×C4—1462no—
179C22×C4C22⋊#6440811yescharacteristic
180C22×C4C22⋊#6440811yescharacteristic
181C22×C4C22×#6440811yescharacteristic
182C2×C8—2922no—
183C2×C8—2922no—
184C2×C8—2922no—
185C2×C8—2922no—
186C2×C8—1464no—
187C2×C8—1464no—
188C4⋊C4—24no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—2922no—
192C4⋊C4—2922no—
193C4⋊C4—2924no—
194C4⋊C4—2924no—
195C4⋊C4—2922no—
196C42—22no—
197C42—2921no—
198C42—732no—
199C42—732no—
200C42—1462no—
201C42—1462no—
202C42—1462no—
203C42—1462no—
204C23C2×C22⋊#6440811yescharacteristic
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—2922no—
213C2×C4—2922no—
214C2×C4—2922no—
215C2×C4—731no—
216C2×C4—732no—
217C2×C4—731no—
218C2×C4—732no—
219C2×C4—1461no—
220C2×C4—1461no—
221C2×C4—1461no—
222C2×C4—1461no—
223C2×C4—1461no—
224C2×C4—1461no—
225C2×C4—1461no—
226C2×C4—1461no—
227C2×C4—1461no—
228C2×C4#1455665212yes—
229C2×C4#1455665412yes—
230C2×C4#1455665512yes—
231C2×C4#1455665612yes—
232C2×C4#1455667812yes—
233C8—2924no—
234C8—2924no—
235C22#1798956111yescharacteristic
236C22#1798956811yescharacteristic
237C22C2×#1455665211yescharacteristic
238C22C2×#1455665411yescharacteristic
239C22#1798957911yescharacteristic
240C22C2×#1455665511yescharacteristic
241C22C2×#1455665611yescharacteristic
242C4—22no—
243C4—22no—
244C4—82no—
245C4—2921no—
246C4—5842no—
247C4—1462no—
248C4—1461no—
249C4—1461no—
250C4—1462no—
251C4#1798944414yes—
252C2#2262520411yescharacteristic
253C2#2262525111yescharacteristic
254C2#2262528011yescharacteristic
255C2#2262531411yescharacteristic
256C2#2262532211yescharacteristic
257C2C2×#1798944411yescharacteristic
258C2#2262544611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
Fitting#384×C73C4
socle, prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4×Dic73C23
hypercenter#384#64408
hypocenterC73#7683
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
134. C73#7683semidirect

Maximal subgroups

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

subgroupindex
#226257172
#226256462
#226247492
#226182922
#768373