Finite Group Databasebeta

← #34004113

Subgroups — #34004113

Order 18688.

810 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 128 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#22625821C212yesmaximal
2C2×#17989433C212yesmaximal
3C2×#17989432C212yesmaximal
4C22×#14556581C211yesmaximal, characteristic
5C2×C22⋊#10596833C2214yes—
6#17989453—24no—
7#17989433—24no—
8#17989432—24no—
9C2×#14556581—24no—
10C2×#14556581—24no—
11C2×#14556581—24no—
12C22×C4⋊Dic73C2211yescharacteristic
13C22×#11924007C411yescharacteristic
14C22×#11924007C411yescharacteristic
15C22×#11924007C411yescharacteristic
16C22×#11924007C2211yescharacteristic
17C22×C4×Dic73C2211yescharacteristic
18C22×C4⋊C4×C73C411yescharacteristic
19C22×#10596833—24no—
20C22⋊#10596833—24no—
21C22⋊#10596833—24no—
22C23×Dic73C2×C411yescharacteristic
23C23×Dic73C2×C411yescharacteristic
24C23×Dic73C2×C411yescharacteristic
25C23×Dic73C2311yescharacteristic
26#14556581—232no—
27C2×C4⋊Dic73—22no—
28C2×C4⋊Dic73—22no—
29C2×C4⋊Dic73D414yes—
30C2×#11924007—22no—
31C2×#11924007—22no—
32C2×#11924007—22no—
33C2×#11924007—22no—
34C2×#11924007—22no—
35C2×#11924007—22no—
36C2×#11924007—22no—
37C2×#11924007—22no—
38C2×#11924007—22no—
39C2×#11924007—22no—
40C2×#11924007—22no—
41C2×#11924007D414yes—
42C2×C4×Dic73—22no—
43C2×C4×Dic73—22no—
44C2×C4×Dic73D414yes—
45C23×C4×C73C2×C411yescharacteristic
46C23×C4×C73C2×C411yescharacteristic
47C23×C4×C73C2×C411yescharacteristic
48C2×C4⋊C4×C73—22no—
49C2×C4⋊C4×C73—22no—
50C2×C4⋊C4×C73—22no—
51C2×#10596833—48no—
52C2×#10596833—44no—
53C22×Dic73—21no—
54C22×Dic73—21no—
55C22×Dic73—24no—
56C22×Dic73—21no—
57C22×Dic73—21no—
58C22×Dic73—21no—
59C22×Dic73—21no—
60C22×Dic73—24no—
61C22×Dic73—42no—
62C22×Dic73—42no—
63C22×Dic73C22⋊C412yes—
64C22×Dic73C22⋊C412yes—
65C22×Dic73C22⋊C412yes—
66C22×Dic73C2×D412yes—
67C22×Dic73C2×D412yes—
68C22×Dic73C2×D412yes—
69C4⋊Dic73—28no—
70#11924007—28no—
71#11924007—28no—
72#11924007—28no—
73#11924007—28no—
74C4×Dic73—28no—
75C24×C73C22×C411yescharacteristic
76C22×C4×C73—21no—
77C22×C4×C73—21no—
78C22×C4×C73—21no—
79C22×C4×C73—21no—
80C22×C4×C73—21no—
81C22×C4×C73—21no—
82C22×C4×C73—24no—
83C22×C4×C73—24no—
84C22×C4×C73—42no—
85C22×C4×C73C22⋊C412yes—
86C22×C4×C73C22⋊C412yes—
87C22×C4×C73C22⋊C412yes—
88C4⋊C4×C73—28no—
89C23×C73—22no—
90C23×C73—22no—
91C23×C73C2×C22⋊C411yescharacteristic
92C23×C73C2×C22⋊C411yescharacteristic
93C23×C73C2×C22⋊C411yescharacteristic
94C23×C73#13114yes—
95C2×C4×C73—22no—
96C2×C4×C73—22no—
97C2×C4×C73—22no—
98C2×C4×C73—24no—
99C2×C4×C73—24no—
100C2×C4×C73—42no—
101C2×C4×C73—42no—
102C2×C4×C73—42no—
103C2×C4×C73—42no—
104C2×C4×C73—42no—
105C2×C4×C73—42no—
106C2×C4×C73—42no—
107C2×Dic73—24no—
108C2×Dic73—24no—
109C2×Dic73—22no—
110C2×Dic73—24no—
111C2×Dic73—22no—
112C2×Dic73—22no—
113C2×Dic73—22no—
114C2×Dic73—24no—
115C2×Dic73—42no—
116C2×Dic73—42no—
117C2×Dic73—42no—
118C2×Dic73—42no—
119C2×Dic73—42no—
120C2×Dic73—42no—
121C2×Dic73—42no—
122C2×Dic73#10114yes—
123C2×Dic73#12014yes—
124#10596833—84no—
125C22×C73—28no—
126C22×C73—21no—
127C22×C73—21no—
128C22×C73—21no—
129C22×C73—21no—
130C22×C73#37911yescharacteristic
131C22×C73#40812yes—
132C22×C73#40812yes—
133C22×C73#40812yes—
134C22×C73#41012yes—
135C22×C73C2×#10112yes—
136C4×C73—42no—
137C4×C73—42no—
138C4×C73—42no—
139Dic73—24no—
140Dic73—24no—
141Dic73—42no—
142Dic73—42no—
143#8306—731nomaximal, Sylow
144C2×C73—22no—
145C2×C73—22no—
146C2×C73#147014yes—
147C2×C73#178011yescharacteristic
148C2×C73#178211yescharacteristic
149C2×C73#178411yescharacteristic
150C22×#125—731no—
151#1817—732no—
152C2×#324—732no—
153C2×#324—732no—
154C73#830611yescharacteristic, complemented, Sylow
155C2×#125—1464no—
156C2×#125—1464no—
157C2×#125—1464no—
158C22×C4⋊C4—731no—
159C22×C4⋊C4—731no—
160C22×C4⋊C4—731no—
161C22×C4⋊C4—731no—
162C22×C4⋊C4—731no—
163C22×C4⋊C4#6440811yescharacteristic
164C22×C42—731no—
165C2×C22⋊C8—734no—
166#336—1464no—
167#324—1464no—
168#324—1464no—
169C23×C4—731no—
170C23×C4—731no—
171C23×C4—731no—
172C23×C4—731no—
173C23×C4C2×#6440811yescharacteristic
174C23×C4C2×#6440811yescharacteristic
175C23×C4C2×#6440811yescharacteristic
176C22×C8—1464no—
177#125—14632no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—734no—
182C2×C4⋊C4—734no—
183C2×C4⋊C4—1462no—
184C2×C4⋊C4—1462no—
185C2×C4⋊C4—1462no—
186C2×C4⋊C4—1462no—
187C2×C4⋊C4—1462no—
188C2×C4⋊C4—1462no—
189C2×C4⋊C4—1462no—
190C2×C4⋊C4—1462no—
191C2×C4⋊C4—1462no—
192C2×C4⋊C4—1462no—
193C2×C4⋊C4—1462no—
194C2×C4⋊C4—1462no—
195C2×C4⋊C4—1462no—
196C2×C42—734no—
197C2×C42—1462no—
198C2×C42—1462no—
199C22⋊C8—1464no—
200C22⋊C8—1464no—
201C24C22×#6440811yescharacteristic
202C22×C4—24no—
203C22×C4—24no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—42no—
211C22×C4—2922no—
212C22×C4—2922no—
213C22×C4—732no—
214C22×C4—732no—
215C22×C4—732no—
216C22×C4—732no—
217C22×C4—732no—
218C22×C4—732no—
219C22×C4—1464no—
220C22×C4—1461no—
221C22×C4—1461no—
222C22×C4—1461no—
223C22×C4—1461no—
224C22×C4—1464no—
225C22×C4—1461no—
226C22×C4—1461no—
227C22×C4C22⋊#6440812yes—
228C22×C4C22⋊#6440812yes—
229C22×C4C22⋊#6440812yes—
230C2×C8—2924no—
231C2×C8—2928no—
232C4⋊C4—28no—
233C4⋊C4—1468no—
234C4⋊C4—1468no—
235C4⋊C4—1468no—
236C4⋊C4—1468no—
237C4⋊C4—1468no—
238C42—1468no—
239C23—22no—
240C23—22no—
241C23C2×C22⋊#6440811yescharacteristic
242C23C2×C22⋊#6440811yescharacteristic
243C23C2×C22⋊#6440811yescharacteristic
244C23#1455667814yes—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—24no—
249C2×C4—24no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—2922no—
258C2×C4—2922no—
259C2×C4—2922no—
260C2×C4—2922no—
261C2×C4—2922no—
262C2×C4—2922no—
263C2×C4—2922no—
264C2×C4—734no—
265C2×C4—734no—
266C2×C4—1462no—
267C2×C4—1462no—
268C2×C4—1464no—
269C2×C4—1464no—
270C2×C4—1464no—
271C2×C4—1462no—
272C2×C4—1464no—
273C2×C4—1462no—
274C8—5844no—
275C22—28no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22#1798952811yescharacteristic
281C22#1798956012yes—
282C22#1798956012yes—
283C22#1798956112yes—
284C22#1798956612yes—
285C22D73⋊#10112yes—
286C4—42no—
287C4—42no—
288C4—42no—
289C4—2922no—
290C4—2922no—
291C4—1464no—
292C4—1464no—
293C2—22no—
294C2—22no—
295C2#2262520314yes—
296C2#2262575511yescharacteristic
297C2#2262576011yescharacteristic
298C2#2262576611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutator, prime radicalC24×C73C22×C4
FrattiniC24C22×#64408
FittingC22×C4⋊C4×C73C4
socleC23×C73C2×C22⋊C4
cosocleC23×Dic73C23
hypercenterC22×C4⋊C4#64408
hypocenterC73#8306
LCSG ▷ C24×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
154. C73#8306semidirect

Maximal subgroups

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

subgroupindex
#226258212
C2×#179894332
C2×#179894322
C22×#145565812
#830673