Finite Group Databasebeta

← #34001405

Subgroups — #34001405

Order 18688.

478 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 132 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#22625846C211yesmaximal, characteristic
2#22625645C211yesmaximal, characteristic
3#22624750C214yesmaximal
4#22612498C211yesmaximal, characteristic
5C2×C4⋊#10596833—21no—
6C2×C4×#10596833—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—
22C4⋊#10596833—42no—
23C4×#10596833—24no—
24C22×Dic146—21no—
25#14556591—22no—
26#14556591C814yescomplemented
27#14556556—42no—
28#14556556—42no—
29C2×C4⋊Dic73—21no—
30C2×C4⋊Dic73C2×C412yes—
31C2×#11924007—22no—
32C2×C4×Dic73—22no—
33C2×C4×Dic73C2×C411yescharacteristic
34C2×C4×Dic73D411yescharacteristic
35C2×C4×Dic73D411yescharacteristic
36C2×C4×Dic73D411yescharacteristic
37C2×C4×Dic73D411yescharacteristic
38C2×C4×Dic73C2311yescharacteristic
39#14556498—22no—
40#14556498—22no—
41C2×C4⋊C4×C73—21no—
42C2×C4⋊C4×C73—21no—
43C2×C4⋊C4×C73C2×C412yes—
44C2×C42×C73C2×C411yescharacteristic
45C2×#10596833—24no—
46C2×#10596833—42no—
47C2×#10596833—42no—
48C2×#10596833—42no—
49C2×#10596833—42no—
50C2×#10596833—42no—
51C2×Dic146—24no—
52C2×Dic146—42no—
53C2×Dic146—42no—
54C22×Dic73—22no—
55C22×Dic73C22⋊C411yescharacteristic
56C22×Dic73C22⋊C411yescharacteristic
57C22×Dic73C2×D411yescharacteristic
58C22×Dic73C2×D411yescharacteristic
59C4⋊Dic73—24no—
60C4⋊Dic73—22no—
61C4⋊Dic73C2×C814yes—
62#11924007—42no—
63#11924007—42no—
64C4×Dic73—22no—
65C4×Dic73—22no—
66C4×Dic73—22no—
67C4×Dic73—41no—
68C4×Dic73—41no—
69C4×Dic73—44no—
70C4×Dic73D812yes—
71C4×Dic73SD1612yes—
72C22×C4×C73—22no—
73C22×C4×C73C22⋊C411yescharacteristic
74C22×C4×C73C22⋊C411yescharacteristic
75C22×C4×C73C22×C411yescharacteristic
76C4⋊C4×C73—42no—
77C4⋊C4×C73—42no—
78C4⋊C4×C73—42no—
79C42×C73C2×C812yes—
80C42×C73M1612yes—
81C23×C73C2×C22⋊C411yescharacteristic
82C2×C4×C73—21no—
83C2×C4×C73—21no—
84C2×C4×C73—21no—
85C2×C4×C73—21no—
86C2×C4×C73—42no—
87C2×C4×C73—42no—
88C2×C4×C73—42no—
89C2×C4×C73C22⋊C812yes—
90C2×C4×C73C22⋊C812yes—
91C2×C4×C73#10212yes—
92C2×C4×C73#10412yes—
93C2×C4×C73C22×C811yescharacteristic
94C2×C4×C73C2×M1611yescharacteristic
95C2×Dic73—21no—
96C2×Dic73—21no—
97C2×Dic73—21no—
98C2×Dic73—21no—
99C2×Dic73—21no—
100C2×Dic73—21no—
101C2×Dic73—21no—
102C2×Dic73—21no—
103C2×Dic73—24no—
104C2×Dic73—42no—
105C2×Dic73—42no—
106C2×Dic73#10112yes—
107C2×Dic73#10212yes—
108C2×Dic73C2×D811yescharacteristic
109C2×Dic73C2×SD1611yescharacteristic
110C2×Dic73#13712yes—
111Dic146—48no—
112#10596833—44no—
113#10596833—82no—
114C22×C73C2×C22⋊C811yescharacteristic
115C22×C73#41011yescharacteristic
116C22×C73C2×#10111yescharacteristic
117C22×C73C2×#10211yescharacteristic
118C22×C73#41911yescharacteristic
119C22×C73C2×#10411yescharacteristic
120C22×C73#42111yescharacteristic
121C4×C73—21no—
122C4×C73—21no—
123C4×C73—22no—
124C4×C73—82no—
125C4×C73D4⋊C814yes—
126Dic73—22no—
127Dic73—22no—
128Dic73—21no—
129Dic73—21no—
130Dic73—22no—
131Dic73—44no—
132#7588—731nomaximal, Sylow
133C2×C73#146111yescharacteristic
134C2×C73C2×D4⋊C811yescharacteristic
135C2×C73#147911yescharacteristic
136C2×C73#150611yescharacteristic
137C2×C73#151711yescharacteristic
138C2×C73#153111yescharacteristic
139C2×C73#154611yescharacteristic
140C4×C4⋊Q8—731no—
141#1831—731no—
142#1744—731no—
143#1271—734no—
144C73#758811yescharacteristic, complemented, Sylow
145C2×C4⋊Q8—731no—
146C2×C4×Q8—1461no—
147C2×C4⋊C8—1461no—
148C2×C4×C8—1461no—
149#391—1461no—
150#389—732no—
151#389—1461no—
152#384#6440811yescharacteristic
153C4×C4⋊C4—732no—
154C4×C4⋊C4—1461no—
155C43—731no—
156#336—732no—
157#336—732no—
158#336—1461no—
159#336—1461no—
160C22×Q8—1461no—
161C22×C8—1462no—
162C22×C8—1462no—
163C4⋊Q8—734no—
164C4⋊Q8—1462no—
165C4×Q8—2922no—
166C4×Q8—2922no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—732no—
170C2×C4⋊C4—1462no—
171C2×C4⋊C4—1461no—
172C2×C4⋊C4C2×#6440812yes—
173C2×C42—731no—
174C2×C42—731no—
175C2×C42—731no—
176C2×C42—731no—
177C2×C42—731no—
178C2×C42—731no—
179C2×C42—1462no—
180C2×C42C2×#6440811yescharacteristic
181C4⋊C8—2922no—
182C4×C8—1464no—
183#95—1462no—
184#95—1462no—
185C2×Q8—2922no—
186C2×Q8—2922no—
187C2×Q8—1464no—
188C22×C4—22no—
189C22×C4—731no—
190C22×C4—731no—
191C22×C4—731no—
192C22×C4—731no—
193C22×C4—1462no—
194C22×C4C22⋊#6440811yescharacteristic
195C22×C4C22⋊#6440811yescharacteristic
196C22×C4C22×#6440811yescharacteristic
197C2×C8—2922no—
198C2×C8—2922no—
199C2×C8—2922no—
200C2×C8—2922no—
201C2×C8—2922no—
202C2×C8—1464no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C4⋊C4—42no—
206C4⋊C4—2922no—
207C4⋊C4—2922no—
208C4⋊C4—734no—
209C4⋊C4—1462no—
210C4⋊C4—1464no—
211C42—2921no—
212C42—2921no—
213C42—2924no—
214C42—732no—
215C42—732no—
216C42—1462no—
217C42—1462no—
218C42—1462no—
219C42#1192403612yes—
220C42#1192403812yes—
221C23C2×C22⋊#6440811yescharacteristic
222Q8—2928no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—2922no—
231C2×C4—2922no—
232C2×C4—732no—
233C2×C4—732no—
234C2×C4—731no—
235C2×C4—731no—
236C2×C4—732no—
237C2×C4—1464no—
238C2×C4—1461no—
239C2×C4—1461no—
240C2×C4—1461no—
241C2×C4—1461no—
242C2×C4—1461no—
243C2×C4—1461no—
244C2×C4—1461no—
245C2×C4—1461no—
246C2×C4#1455664812yes—
247C2×C4#1455664812yes—
248C2×C4#1455665312yes—
249C2×C4#1455665612yes—
250C2×C4C2×#1192403611yescharacteristic
251C2×C4C2×#1192403811yescharacteristic
252C8—2924no—
253C8—5842no—
254C22C2×#1455664811yescharacteristic
255C22#1798956711yescharacteristic
256C22D73⋊#10111yescharacteristic
257C22C2×#1455665311yescharacteristic
258C22#1798958011yescharacteristic
259C22C2×#1455665611yescharacteristic
260C22#1798958511yescharacteristic
261C4—21no—
262C4—21no—
263C4—22no—
264C4—82no—
265C4—2924no—
266C4—1462no—
267C4—1461no—
268C4—1461no—
269C4—1462no—
270C4—1462no—
271C4#1798943514yes—
272C2#2262517511yescharacteristic
273C2C2×#1798943511yescharacteristic
274C2#2262523511yescharacteristic
275C2#2262532511yescharacteristic
276C2#2262536011yescharacteristic
277C2#2262540511yescharacteristic
278C2#2262544111yescharacteristic
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#7588
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
26. #14556591C8semidirect
144. C73#7588semidirect

Maximal subgroups

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

subgroupindex
#226258462
#226256452
#226247502
#226124982
#758873